+
+// Function definitions for reals
+void VectorNormalize( real *vectorIn, real *vectorOut )
+{
+ real vectorMag;
+ real multiplier;
+
+ // sqrt( v1^2 + v2^2 + v3^2 )
+ vectorMag = VectorMag( vectorIn );
+ multiplier = (real)1.0 / vectorMag;
+
+ vectorOut[0] = multiplier * vectorIn[0];
+ vectorOut[1] = multiplier * vectorIn[1];
+ vectorOut[2] = multiplier * vectorIn[2];
+}
+
+
+// Components must be less than 1239850262 (Q27) ~ 9.23 (dec) in order to use this function without
+// overflow. Else, need to represent the output in another q-format.
+real VectorMag( real *vectorIn )
+{
+ real temp[3];
+
+ //
+ temp[0] = vectorIn[0] * vectorIn[0];
+ temp[1] = vectorIn[1] * vectorIn[1];
+ temp[2] = vectorIn[2] * vectorIn[2];
+
+ // sqrt( v1^2 + v2^2 + v3^2 )
+ return( (real)(sqrtf( temp[0] + temp[1] + temp[2] )) );
+}
+
+
+void VectorCrossProduct( real *vect1, real *vect2, real *vectOut )
+{
+ // | i j k |
+ // | v1[0] v1[1] v1[2] | = i*( v1[1]*v2[2] - v1[2]*v2[1] ) - j*( v1[0]*v2[2] - v1[2]*v2[0] ) + k*( v1[0]*v2[1] - v1[1]*v2[0] )
+ // | v2[0] v2[1] v2[2] |
+
+ vectOut[0] = vect1[1] * vect2[2] - vect1[2] * vect2[1]; // v1[1]*v2[2] - v1[2]*v2[1]
+ vectOut[1] = vect1[2] * vect2[0] - vect1[0] * vect2[2]; // v1[2]*v2[0] - v1[0]*v2[2]
+ vectOut[2] = vect1[0] * vect2[1] - vect1[1] * vect2[0]; // v1[0]*v2[1] - v1[1]*v2[0]
+}
+
+real VectorDotProduct( real *vect1, real *vect2 )
+{
+ real result;
+
+ result = vect1[0] * vect2[0] +
+ vect1[1] * vect2[1] +
+ vect1[2] * vect2[2];
+
+ return( result );
+}
+
+real vecVar(real *a, real am, int n)
+{
+ int i;
+ real sum = 0.0;
+ for (i = 0; i < n; i++)
+ {
+ real d = a[i] - am;
+ sum += d * d;
+ }
+ return sum / n;
+}
+
+void cross(real* a, real* b, real* axb)
+{
+ axb[0] = a[1] * b[2] - a[2] * b[1];
+ axb[1] = a[2] * b[0] - a[0] * b[2];
+ axb[2] = a[0] * b[1] - a[1] * b[0];
+}
diff --git a/examples/OpenIMU300RI/INS/lib/Core/Math/src/arm_common_tables.c b/examples/OpenIMU300RI/INS/lib/Core/Math/src/arm_common_tables.c
new file mode 100644
index 0000000..79fe976
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/lib/Core/Math/src/arm_common_tables.c
@@ -0,0 +1,27251 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
+*
+* $Date: 19. March 2015
+* $Revision: V.1.4.5
+*
+* Project: CMSIS DSP Library
+* Title: arm_common_tables.c
+*
+* Description: This file has common tables like fft twiddle factors, Bitreverse, reciprocal etc which are used across different functions
+*
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+* - Redistributions of source code must retain the above copyright
+* notice, this list of conditions and the following disclaimer.
+* - Redistributions in binary form must reproduce the above copyright
+* notice, this list of conditions and the following disclaimer in
+* the documentation and/or other materials provided with the
+* distribution.
+* - Neither the name of ARM LIMITED nor the names of its contributors
+* may be used to endorse or promote products derived from this
+* software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+* -------------------------------------------------------------------- */
+
+
+#include "arm_math.h"
+#include "arm_common_tables.h"
+
+/**
+ * @ingroup groupTransforms
+ */
+
+/**
+ * @addtogroup CFFT_CIFFT Complex FFT Tables
+ * @{
+ */
+
+/**
+* \par
+* Pseudo code for Generation of Bit reversal Table is
+* \par
+* for(l=1;l <= N/4;l++)
+* {
+* for(i=0;i> 1;
+* }
+* \par
+* where N = 4096 logN2 = 12
+* \par
+* N is the maximum FFT Size supported
+*/
+
+/*
+* @brief Table for bit reversal process
+*/
+const uint16_t armBitRevTable[1024] = {
+ 0x400, 0x200, 0x600, 0x100, 0x500, 0x300, 0x700, 0x80, 0x480, 0x280,
+ 0x680, 0x180, 0x580, 0x380, 0x780, 0x40, 0x440, 0x240, 0x640, 0x140,
+ 0x540, 0x340, 0x740, 0xc0, 0x4c0, 0x2c0, 0x6c0, 0x1c0, 0x5c0, 0x3c0,
+ 0x7c0, 0x20, 0x420, 0x220, 0x620, 0x120, 0x520, 0x320, 0x720, 0xa0,
+ 0x4a0, 0x2a0, 0x6a0, 0x1a0, 0x5a0, 0x3a0, 0x7a0, 0x60, 0x460, 0x260,
+ 0x660, 0x160, 0x560, 0x360, 0x760, 0xe0, 0x4e0, 0x2e0, 0x6e0, 0x1e0,
+ 0x5e0, 0x3e0, 0x7e0, 0x10, 0x410, 0x210, 0x610, 0x110, 0x510, 0x310,
+ 0x710, 0x90, 0x490, 0x290, 0x690, 0x190, 0x590, 0x390, 0x790, 0x50,
+ 0x450, 0x250, 0x650, 0x150, 0x550, 0x350, 0x750, 0xd0, 0x4d0, 0x2d0,
+ 0x6d0, 0x1d0, 0x5d0, 0x3d0, 0x7d0, 0x30, 0x430, 0x230, 0x630, 0x130,
+ 0x530, 0x330, 0x730, 0xb0, 0x4b0, 0x2b0, 0x6b0, 0x1b0, 0x5b0, 0x3b0,
+ 0x7b0, 0x70, 0x470, 0x270, 0x670, 0x170, 0x570, 0x370, 0x770, 0xf0,
+ 0x4f0, 0x2f0, 0x6f0, 0x1f0, 0x5f0, 0x3f0, 0x7f0, 0x8, 0x408, 0x208,
+ 0x608, 0x108, 0x508, 0x308, 0x708, 0x88, 0x488, 0x288, 0x688, 0x188,
+ 0x588, 0x388, 0x788, 0x48, 0x448, 0x248, 0x648, 0x148, 0x548, 0x348,
+ 0x748, 0xc8, 0x4c8, 0x2c8, 0x6c8, 0x1c8, 0x5c8, 0x3c8, 0x7c8, 0x28,
+ 0x428, 0x228, 0x628, 0x128, 0x528, 0x328, 0x728, 0xa8, 0x4a8, 0x2a8,
+ 0x6a8, 0x1a8, 0x5a8, 0x3a8, 0x7a8, 0x68, 0x468, 0x268, 0x668, 0x168,
+ 0x568, 0x368, 0x768, 0xe8, 0x4e8, 0x2e8, 0x6e8, 0x1e8, 0x5e8, 0x3e8,
+ 0x7e8, 0x18, 0x418, 0x218, 0x618, 0x118, 0x518, 0x318, 0x718, 0x98,
+ 0x498, 0x298, 0x698, 0x198, 0x598, 0x398, 0x798, 0x58, 0x458, 0x258,
+ 0x658, 0x158, 0x558, 0x358, 0x758, 0xd8, 0x4d8, 0x2d8, 0x6d8, 0x1d8,
+ 0x5d8, 0x3d8, 0x7d8, 0x38, 0x438, 0x238, 0x638, 0x138, 0x538, 0x338,
+ 0x738, 0xb8, 0x4b8, 0x2b8, 0x6b8, 0x1b8, 0x5b8, 0x3b8, 0x7b8, 0x78,
+ 0x478, 0x278, 0x678, 0x178, 0x578, 0x378, 0x778, 0xf8, 0x4f8, 0x2f8,
+ 0x6f8, 0x1f8, 0x5f8, 0x3f8, 0x7f8, 0x4, 0x404, 0x204, 0x604, 0x104,
+ 0x504, 0x304, 0x704, 0x84, 0x484, 0x284, 0x684, 0x184, 0x584, 0x384,
+ 0x784, 0x44, 0x444, 0x244, 0x644, 0x144, 0x544, 0x344, 0x744, 0xc4,
+ 0x4c4, 0x2c4, 0x6c4, 0x1c4, 0x5c4, 0x3c4, 0x7c4, 0x24, 0x424, 0x224,
+ 0x624, 0x124, 0x524, 0x324, 0x724, 0xa4, 0x4a4, 0x2a4, 0x6a4, 0x1a4,
+ 0x5a4, 0x3a4, 0x7a4, 0x64, 0x464, 0x264, 0x664, 0x164, 0x564, 0x364,
+ 0x764, 0xe4, 0x4e4, 0x2e4, 0x6e4, 0x1e4, 0x5e4, 0x3e4, 0x7e4, 0x14,
+ 0x414, 0x214, 0x614, 0x114, 0x514, 0x314, 0x714, 0x94, 0x494, 0x294,
+ 0x694, 0x194, 0x594, 0x394, 0x794, 0x54, 0x454, 0x254, 0x654, 0x154,
+ 0x554, 0x354, 0x754, 0xd4, 0x4d4, 0x2d4, 0x6d4, 0x1d4, 0x5d4, 0x3d4,
+ 0x7d4, 0x34, 0x434, 0x234, 0x634, 0x134, 0x534, 0x334, 0x734, 0xb4,
+ 0x4b4, 0x2b4, 0x6b4, 0x1b4, 0x5b4, 0x3b4, 0x7b4, 0x74, 0x474, 0x274,
+ 0x674, 0x174, 0x574, 0x374, 0x774, 0xf4, 0x4f4, 0x2f4, 0x6f4, 0x1f4,
+ 0x5f4, 0x3f4, 0x7f4, 0xc, 0x40c, 0x20c, 0x60c, 0x10c, 0x50c, 0x30c,
+ 0x70c, 0x8c, 0x48c, 0x28c, 0x68c, 0x18c, 0x58c, 0x38c, 0x78c, 0x4c,
+ 0x44c, 0x24c, 0x64c, 0x14c, 0x54c, 0x34c, 0x74c, 0xcc, 0x4cc, 0x2cc,
+ 0x6cc, 0x1cc, 0x5cc, 0x3cc, 0x7cc, 0x2c, 0x42c, 0x22c, 0x62c, 0x12c,
+ 0x52c, 0x32c, 0x72c, 0xac, 0x4ac, 0x2ac, 0x6ac, 0x1ac, 0x5ac, 0x3ac,
+ 0x7ac, 0x6c, 0x46c, 0x26c, 0x66c, 0x16c, 0x56c, 0x36c, 0x76c, 0xec,
+ 0x4ec, 0x2ec, 0x6ec, 0x1ec, 0x5ec, 0x3ec, 0x7ec, 0x1c, 0x41c, 0x21c,
+ 0x61c, 0x11c, 0x51c, 0x31c, 0x71c, 0x9c, 0x49c, 0x29c, 0x69c, 0x19c,
+ 0x59c, 0x39c, 0x79c, 0x5c, 0x45c, 0x25c, 0x65c, 0x15c, 0x55c, 0x35c,
+ 0x75c, 0xdc, 0x4dc, 0x2dc, 0x6dc, 0x1dc, 0x5dc, 0x3dc, 0x7dc, 0x3c,
+ 0x43c, 0x23c, 0x63c, 0x13c, 0x53c, 0x33c, 0x73c, 0xbc, 0x4bc, 0x2bc,
+ 0x6bc, 0x1bc, 0x5bc, 0x3bc, 0x7bc, 0x7c, 0x47c, 0x27c, 0x67c, 0x17c,
+ 0x57c, 0x37c, 0x77c, 0xfc, 0x4fc, 0x2fc, 0x6fc, 0x1fc, 0x5fc, 0x3fc,
+ 0x7fc, 0x2, 0x402, 0x202, 0x602, 0x102, 0x502, 0x302, 0x702, 0x82,
+ 0x482, 0x282, 0x682, 0x182, 0x582, 0x382, 0x782, 0x42, 0x442, 0x242,
+ 0x642, 0x142, 0x542, 0x342, 0x742, 0xc2, 0x4c2, 0x2c2, 0x6c2, 0x1c2,
+ 0x5c2, 0x3c2, 0x7c2, 0x22, 0x422, 0x222, 0x622, 0x122, 0x522, 0x322,
+ 0x722, 0xa2, 0x4a2, 0x2a2, 0x6a2, 0x1a2, 0x5a2, 0x3a2, 0x7a2, 0x62,
+ 0x462, 0x262, 0x662, 0x162, 0x562, 0x362, 0x762, 0xe2, 0x4e2, 0x2e2,
+ 0x6e2, 0x1e2, 0x5e2, 0x3e2, 0x7e2, 0x12, 0x412, 0x212, 0x612, 0x112,
+ 0x512, 0x312, 0x712, 0x92, 0x492, 0x292, 0x692, 0x192, 0x592, 0x392,
+ 0x792, 0x52, 0x452, 0x252, 0x652, 0x152, 0x552, 0x352, 0x752, 0xd2,
+ 0x4d2, 0x2d2, 0x6d2, 0x1d2, 0x5d2, 0x3d2, 0x7d2, 0x32, 0x432, 0x232,
+ 0x632, 0x132, 0x532, 0x332, 0x732, 0xb2, 0x4b2, 0x2b2, 0x6b2, 0x1b2,
+ 0x5b2, 0x3b2, 0x7b2, 0x72, 0x472, 0x272, 0x672, 0x172, 0x572, 0x372,
+ 0x772, 0xf2, 0x4f2, 0x2f2, 0x6f2, 0x1f2, 0x5f2, 0x3f2, 0x7f2, 0xa,
+ 0x40a, 0x20a, 0x60a, 0x10a, 0x50a, 0x30a, 0x70a, 0x8a, 0x48a, 0x28a,
+ 0x68a, 0x18a, 0x58a, 0x38a, 0x78a, 0x4a, 0x44a, 0x24a, 0x64a, 0x14a,
+ 0x54a, 0x34a, 0x74a, 0xca, 0x4ca, 0x2ca, 0x6ca, 0x1ca, 0x5ca, 0x3ca,
+ 0x7ca, 0x2a, 0x42a, 0x22a, 0x62a, 0x12a, 0x52a, 0x32a, 0x72a, 0xaa,
+ 0x4aa, 0x2aa, 0x6aa, 0x1aa, 0x5aa, 0x3aa, 0x7aa, 0x6a, 0x46a, 0x26a,
+ 0x66a, 0x16a, 0x56a, 0x36a, 0x76a, 0xea, 0x4ea, 0x2ea, 0x6ea, 0x1ea,
+ 0x5ea, 0x3ea, 0x7ea, 0x1a, 0x41a, 0x21a, 0x61a, 0x11a, 0x51a, 0x31a,
+ 0x71a, 0x9a, 0x49a, 0x29a, 0x69a, 0x19a, 0x59a, 0x39a, 0x79a, 0x5a,
+ 0x45a, 0x25a, 0x65a, 0x15a, 0x55a, 0x35a, 0x75a, 0xda, 0x4da, 0x2da,
+ 0x6da, 0x1da, 0x5da, 0x3da, 0x7da, 0x3a, 0x43a, 0x23a, 0x63a, 0x13a,
+ 0x53a, 0x33a, 0x73a, 0xba, 0x4ba, 0x2ba, 0x6ba, 0x1ba, 0x5ba, 0x3ba,
+ 0x7ba, 0x7a, 0x47a, 0x27a, 0x67a, 0x17a, 0x57a, 0x37a, 0x77a, 0xfa,
+ 0x4fa, 0x2fa, 0x6fa, 0x1fa, 0x5fa, 0x3fa, 0x7fa, 0x6, 0x406, 0x206,
+ 0x606, 0x106, 0x506, 0x306, 0x706, 0x86, 0x486, 0x286, 0x686, 0x186,
+ 0x586, 0x386, 0x786, 0x46, 0x446, 0x246, 0x646, 0x146, 0x546, 0x346,
+ 0x746, 0xc6, 0x4c6, 0x2c6, 0x6c6, 0x1c6, 0x5c6, 0x3c6, 0x7c6, 0x26,
+ 0x426, 0x226, 0x626, 0x126, 0x526, 0x326, 0x726, 0xa6, 0x4a6, 0x2a6,
+ 0x6a6, 0x1a6, 0x5a6, 0x3a6, 0x7a6, 0x66, 0x466, 0x266, 0x666, 0x166,
+ 0x566, 0x366, 0x766, 0xe6, 0x4e6, 0x2e6, 0x6e6, 0x1e6, 0x5e6, 0x3e6,
+ 0x7e6, 0x16, 0x416, 0x216, 0x616, 0x116, 0x516, 0x316, 0x716, 0x96,
+ 0x496, 0x296, 0x696, 0x196, 0x596, 0x396, 0x796, 0x56, 0x456, 0x256,
+ 0x656, 0x156, 0x556, 0x356, 0x756, 0xd6, 0x4d6, 0x2d6, 0x6d6, 0x1d6,
+ 0x5d6, 0x3d6, 0x7d6, 0x36, 0x436, 0x236, 0x636, 0x136, 0x536, 0x336,
+ 0x736, 0xb6, 0x4b6, 0x2b6, 0x6b6, 0x1b6, 0x5b6, 0x3b6, 0x7b6, 0x76,
+ 0x476, 0x276, 0x676, 0x176, 0x576, 0x376, 0x776, 0xf6, 0x4f6, 0x2f6,
+ 0x6f6, 0x1f6, 0x5f6, 0x3f6, 0x7f6, 0xe, 0x40e, 0x20e, 0x60e, 0x10e,
+ 0x50e, 0x30e, 0x70e, 0x8e, 0x48e, 0x28e, 0x68e, 0x18e, 0x58e, 0x38e,
+ 0x78e, 0x4e, 0x44e, 0x24e, 0x64e, 0x14e, 0x54e, 0x34e, 0x74e, 0xce,
+ 0x4ce, 0x2ce, 0x6ce, 0x1ce, 0x5ce, 0x3ce, 0x7ce, 0x2e, 0x42e, 0x22e,
+ 0x62e, 0x12e, 0x52e, 0x32e, 0x72e, 0xae, 0x4ae, 0x2ae, 0x6ae, 0x1ae,
+ 0x5ae, 0x3ae, 0x7ae, 0x6e, 0x46e, 0x26e, 0x66e, 0x16e, 0x56e, 0x36e,
+ 0x76e, 0xee, 0x4ee, 0x2ee, 0x6ee, 0x1ee, 0x5ee, 0x3ee, 0x7ee, 0x1e,
+ 0x41e, 0x21e, 0x61e, 0x11e, 0x51e, 0x31e, 0x71e, 0x9e, 0x49e, 0x29e,
+ 0x69e, 0x19e, 0x59e, 0x39e, 0x79e, 0x5e, 0x45e, 0x25e, 0x65e, 0x15e,
+ 0x55e, 0x35e, 0x75e, 0xde, 0x4de, 0x2de, 0x6de, 0x1de, 0x5de, 0x3de,
+ 0x7de, 0x3e, 0x43e, 0x23e, 0x63e, 0x13e, 0x53e, 0x33e, 0x73e, 0xbe,
+ 0x4be, 0x2be, 0x6be, 0x1be, 0x5be, 0x3be, 0x7be, 0x7e, 0x47e, 0x27e,
+ 0x67e, 0x17e, 0x57e, 0x37e, 0x77e, 0xfe, 0x4fe, 0x2fe, 0x6fe, 0x1fe,
+ 0x5fe, 0x3fe, 0x7fe, 0x1
+};
+
+
+/*
+* @brief Floating-point Twiddle factors Table Generation
+*/
+
+/**
+* \par
+* Example code for Floating-point Twiddle factors Generation:
+* \par
+* for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 16 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are in interleaved fashion
+*
+*/
+const float32_t twiddleCoef_16[32] = {
+ 1.000000000f, 0.000000000f,
+ 0.923879533f, 0.382683432f,
+ 0.707106781f, 0.707106781f,
+ 0.382683432f, 0.923879533f,
+ 0.000000000f, 1.000000000f,
+ -0.382683432f, 0.923879533f,
+ -0.707106781f, 0.707106781f,
+ -0.923879533f, 0.382683432f,
+ -1.000000000f, 0.000000000f,
+ -0.923879533f, -0.382683432f,
+ -0.707106781f, -0.707106781f,
+ -0.382683432f, -0.923879533f,
+ -0.000000000f, -1.000000000f,
+ 0.382683432f, -0.923879533f,
+ 0.707106781f, -0.707106781f,
+ 0.923879533f, -0.382683432f
+};
+
+/**
+* \par
+* Example code for Floating-point Twiddle factors Generation:
+* \par
+* for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 32 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are in interleaved fashion
+*
+*/
+const float32_t twiddleCoef_32[64] = {
+ 1.000000000f, 0.000000000f,
+ 0.980785280f, 0.195090322f,
+ 0.923879533f, 0.382683432f,
+ 0.831469612f, 0.555570233f,
+ 0.707106781f, 0.707106781f,
+ 0.555570233f, 0.831469612f,
+ 0.382683432f, 0.923879533f,
+ 0.195090322f, 0.980785280f,
+ 0.000000000f, 1.000000000f,
+ -0.195090322f, 0.980785280f,
+ -0.382683432f, 0.923879533f,
+ -0.555570233f, 0.831469612f,
+ -0.707106781f, 0.707106781f,
+ -0.831469612f, 0.555570233f,
+ -0.923879533f, 0.382683432f,
+ -0.980785280f, 0.195090322f,
+ -1.000000000f, 0.000000000f,
+ -0.980785280f, -0.195090322f,
+ -0.923879533f, -0.382683432f,
+ -0.831469612f, -0.555570233f,
+ -0.707106781f, -0.707106781f,
+ -0.555570233f, -0.831469612f,
+ -0.382683432f, -0.923879533f,
+ -0.195090322f, -0.980785280f,
+ -0.000000000f, -1.000000000f,
+ 0.195090322f, -0.980785280f,
+ 0.382683432f, -0.923879533f,
+ 0.555570233f, -0.831469612f,
+ 0.707106781f, -0.707106781f,
+ 0.831469612f, -0.555570233f,
+ 0.923879533f, -0.382683432f,
+ 0.980785280f, -0.195090322f
+};
+
+/**
+* \par
+* Example code for Floating-point Twiddle factors Generation:
+* \par
+* for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 64 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are in interleaved fashion
+*
+*/
+const float32_t twiddleCoef_64[128] = {
+ 1.000000000f, 0.000000000f,
+ 0.995184727f, 0.098017140f,
+ 0.980785280f, 0.195090322f,
+ 0.956940336f, 0.290284677f,
+ 0.923879533f, 0.382683432f,
+ 0.881921264f, 0.471396737f,
+ 0.831469612f, 0.555570233f,
+ 0.773010453f, 0.634393284f,
+ 0.707106781f, 0.707106781f,
+ 0.634393284f, 0.773010453f,
+ 0.555570233f, 0.831469612f,
+ 0.471396737f, 0.881921264f,
+ 0.382683432f, 0.923879533f,
+ 0.290284677f, 0.956940336f,
+ 0.195090322f, 0.980785280f,
+ 0.098017140f, 0.995184727f,
+ 0.000000000f, 1.000000000f,
+ -0.098017140f, 0.995184727f,
+ -0.195090322f, 0.980785280f,
+ -0.290284677f, 0.956940336f,
+ -0.382683432f, 0.923879533f,
+ -0.471396737f, 0.881921264f,
+ -0.555570233f, 0.831469612f,
+ -0.634393284f, 0.773010453f,
+ -0.707106781f, 0.707106781f,
+ -0.773010453f, 0.634393284f,
+ -0.831469612f, 0.555570233f,
+ -0.881921264f, 0.471396737f,
+ -0.923879533f, 0.382683432f,
+ -0.956940336f, 0.290284677f,
+ -0.980785280f, 0.195090322f,
+ -0.995184727f, 0.098017140f,
+ -1.000000000f, 0.000000000f,
+ -0.995184727f, -0.098017140f,
+ -0.980785280f, -0.195090322f,
+ -0.956940336f, -0.290284677f,
+ -0.923879533f, -0.382683432f,
+ -0.881921264f, -0.471396737f,
+ -0.831469612f, -0.555570233f,
+ -0.773010453f, -0.634393284f,
+ -0.707106781f, -0.707106781f,
+ -0.634393284f, -0.773010453f,
+ -0.555570233f, -0.831469612f,
+ -0.471396737f, -0.881921264f,
+ -0.382683432f, -0.923879533f,
+ -0.290284677f, -0.956940336f,
+ -0.195090322f, -0.980785280f,
+ -0.098017140f, -0.995184727f,
+ -0.000000000f, -1.000000000f,
+ 0.098017140f, -0.995184727f,
+ 0.195090322f, -0.980785280f,
+ 0.290284677f, -0.956940336f,
+ 0.382683432f, -0.923879533f,
+ 0.471396737f, -0.881921264f,
+ 0.555570233f, -0.831469612f,
+ 0.634393284f, -0.773010453f,
+ 0.707106781f, -0.707106781f,
+ 0.773010453f, -0.634393284f,
+ 0.831469612f, -0.555570233f,
+ 0.881921264f, -0.471396737f,
+ 0.923879533f, -0.382683432f,
+ 0.956940336f, -0.290284677f,
+ 0.980785280f, -0.195090322f,
+ 0.995184727f, -0.098017140f
+};
+
+/**
+* \par
+* Example code for Floating-point Twiddle factors Generation:
+* \par
+* for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 128 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are in interleaved fashion
+*
+*/
+
+const float32_t twiddleCoef_128[256] = {
+ 1.000000000f , 0.000000000f ,
+ 0.998795456f , 0.049067674f ,
+ 0.995184727f , 0.098017140f ,
+ 0.989176510f , 0.146730474f ,
+ 0.980785280f , 0.195090322f ,
+ 0.970031253f , 0.242980180f ,
+ 0.956940336f , 0.290284677f ,
+ 0.941544065f , 0.336889853f ,
+ 0.923879533f , 0.382683432f ,
+ 0.903989293f , 0.427555093f ,
+ 0.881921264f , 0.471396737f ,
+ 0.857728610f , 0.514102744f ,
+ 0.831469612f , 0.555570233f ,
+ 0.803207531f , 0.595699304f ,
+ 0.773010453f , 0.634393284f ,
+ 0.740951125f , 0.671558955f ,
+ 0.707106781f , 0.707106781f ,
+ 0.671558955f , 0.740951125f ,
+ 0.634393284f , 0.773010453f ,
+ 0.595699304f , 0.803207531f ,
+ 0.555570233f , 0.831469612f ,
+ 0.514102744f , 0.857728610f ,
+ 0.471396737f , 0.881921264f ,
+ 0.427555093f , 0.903989293f ,
+ 0.382683432f , 0.923879533f ,
+ 0.336889853f , 0.941544065f ,
+ 0.290284677f , 0.956940336f ,
+ 0.242980180f , 0.970031253f ,
+ 0.195090322f , 0.980785280f ,
+ 0.146730474f , 0.989176510f ,
+ 0.098017140f , 0.995184727f ,
+ 0.049067674f , 0.998795456f ,
+ 0.000000000f , 1.000000000f ,
+ -0.049067674f , 0.998795456f ,
+ -0.098017140f , 0.995184727f ,
+ -0.146730474f , 0.989176510f ,
+ -0.195090322f , 0.980785280f ,
+ -0.242980180f , 0.970031253f ,
+ -0.290284677f , 0.956940336f ,
+ -0.336889853f , 0.941544065f ,
+ -0.382683432f , 0.923879533f ,
+ -0.427555093f , 0.903989293f ,
+ -0.471396737f , 0.881921264f ,
+ -0.514102744f , 0.857728610f ,
+ -0.555570233f , 0.831469612f ,
+ -0.595699304f , 0.803207531f ,
+ -0.634393284f , 0.773010453f ,
+ -0.671558955f , 0.740951125f ,
+ -0.707106781f , 0.707106781f ,
+ -0.740951125f , 0.671558955f ,
+ -0.773010453f , 0.634393284f ,
+ -0.803207531f , 0.595699304f ,
+ -0.831469612f , 0.555570233f ,
+ -0.857728610f , 0.514102744f ,
+ -0.881921264f , 0.471396737f ,
+ -0.903989293f , 0.427555093f ,
+ -0.923879533f , 0.382683432f ,
+ -0.941544065f , 0.336889853f ,
+ -0.956940336f , 0.290284677f ,
+ -0.970031253f , 0.242980180f ,
+ -0.980785280f , 0.195090322f ,
+ -0.989176510f , 0.146730474f ,
+ -0.995184727f , 0.098017140f ,
+ -0.998795456f , 0.049067674f ,
+ -1.000000000f , 0.000000000f ,
+ -0.998795456f , -0.049067674f ,
+ -0.995184727f , -0.098017140f ,
+ -0.989176510f , -0.146730474f ,
+ -0.980785280f , -0.195090322f ,
+ -0.970031253f , -0.242980180f ,
+ -0.956940336f , -0.290284677f ,
+ -0.941544065f , -0.336889853f ,
+ -0.923879533f , -0.382683432f ,
+ -0.903989293f , -0.427555093f ,
+ -0.881921264f , -0.471396737f ,
+ -0.857728610f , -0.514102744f ,
+ -0.831469612f , -0.555570233f ,
+ -0.803207531f , -0.595699304f ,
+ -0.773010453f , -0.634393284f ,
+ -0.740951125f , -0.671558955f ,
+ -0.707106781f , -0.707106781f ,
+ -0.671558955f , -0.740951125f ,
+ -0.634393284f , -0.773010453f ,
+ -0.595699304f , -0.803207531f ,
+ -0.555570233f , -0.831469612f ,
+ -0.514102744f , -0.857728610f ,
+ -0.471396737f , -0.881921264f ,
+ -0.427555093f , -0.903989293f ,
+ -0.382683432f , -0.923879533f ,
+ -0.336889853f , -0.941544065f ,
+ -0.290284677f , -0.956940336f ,
+ -0.242980180f , -0.970031253f ,
+ -0.195090322f , -0.980785280f ,
+ -0.146730474f , -0.989176510f ,
+ -0.098017140f , -0.995184727f ,
+ -0.049067674f , -0.998795456f ,
+ -0.000000000f , -1.000000000f ,
+ 0.049067674f , -0.998795456f ,
+ 0.098017140f , -0.995184727f ,
+ 0.146730474f , -0.989176510f ,
+ 0.195090322f , -0.980785280f ,
+ 0.242980180f , -0.970031253f ,
+ 0.290284677f , -0.956940336f ,
+ 0.336889853f , -0.941544065f ,
+ 0.382683432f , -0.923879533f ,
+ 0.427555093f , -0.903989293f ,
+ 0.471396737f , -0.881921264f ,
+ 0.514102744f , -0.857728610f ,
+ 0.555570233f , -0.831469612f ,
+ 0.595699304f , -0.803207531f ,
+ 0.634393284f , -0.773010453f ,
+ 0.671558955f , -0.740951125f ,
+ 0.707106781f , -0.707106781f ,
+ 0.740951125f , -0.671558955f ,
+ 0.773010453f , -0.634393284f ,
+ 0.803207531f , -0.595699304f ,
+ 0.831469612f , -0.555570233f ,
+ 0.857728610f , -0.514102744f ,
+ 0.881921264f , -0.471396737f ,
+ 0.903989293f , -0.427555093f ,
+ 0.923879533f , -0.382683432f ,
+ 0.941544065f , -0.336889853f ,
+ 0.956940336f , -0.290284677f ,
+ 0.970031253f , -0.242980180f ,
+ 0.980785280f , -0.195090322f ,
+ 0.989176510f , -0.146730474f ,
+ 0.995184727f , -0.098017140f ,
+ 0.998795456f , -0.049067674f
+};
+
+/**
+* \par
+* Example code for Floating-point Twiddle factors Generation:
+* \par
+* for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 256 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are in interleaved fashion
+*
+*/
+const float32_t twiddleCoef_256[512] = {
+ 1.000000000f, 0.000000000f,
+ 0.999698819f, 0.024541229f,
+ 0.998795456f, 0.049067674f,
+ 0.997290457f, 0.073564564f,
+ 0.995184727f, 0.098017140f,
+ 0.992479535f, 0.122410675f,
+ 0.989176510f, 0.146730474f,
+ 0.985277642f, 0.170961889f,
+ 0.980785280f, 0.195090322f,
+ 0.975702130f, 0.219101240f,
+ 0.970031253f, 0.242980180f,
+ 0.963776066f, 0.266712757f,
+ 0.956940336f, 0.290284677f,
+ 0.949528181f, 0.313681740f,
+ 0.941544065f, 0.336889853f,
+ 0.932992799f, 0.359895037f,
+ 0.923879533f, 0.382683432f,
+ 0.914209756f, 0.405241314f,
+ 0.903989293f, 0.427555093f,
+ 0.893224301f, 0.449611330f,
+ 0.881921264f, 0.471396737f,
+ 0.870086991f, 0.492898192f,
+ 0.857728610f, 0.514102744f,
+ 0.844853565f, 0.534997620f,
+ 0.831469612f, 0.555570233f,
+ 0.817584813f, 0.575808191f,
+ 0.803207531f, 0.595699304f,
+ 0.788346428f, 0.615231591f,
+ 0.773010453f, 0.634393284f,
+ 0.757208847f, 0.653172843f,
+ 0.740951125f, 0.671558955f,
+ 0.724247083f, 0.689540545f,
+ 0.707106781f, 0.707106781f,
+ 0.689540545f, 0.724247083f,
+ 0.671558955f, 0.740951125f,
+ 0.653172843f, 0.757208847f,
+ 0.634393284f, 0.773010453f,
+ 0.615231591f, 0.788346428f,
+ 0.595699304f, 0.803207531f,
+ 0.575808191f, 0.817584813f,
+ 0.555570233f, 0.831469612f,
+ 0.534997620f, 0.844853565f,
+ 0.514102744f, 0.857728610f,
+ 0.492898192f, 0.870086991f,
+ 0.471396737f, 0.881921264f,
+ 0.449611330f, 0.893224301f,
+ 0.427555093f, 0.903989293f,
+ 0.405241314f, 0.914209756f,
+ 0.382683432f, 0.923879533f,
+ 0.359895037f, 0.932992799f,
+ 0.336889853f, 0.941544065f,
+ 0.313681740f, 0.949528181f,
+ 0.290284677f, 0.956940336f,
+ 0.266712757f, 0.963776066f,
+ 0.242980180f, 0.970031253f,
+ 0.219101240f, 0.975702130f,
+ 0.195090322f, 0.980785280f,
+ 0.170961889f, 0.985277642f,
+ 0.146730474f, 0.989176510f,
+ 0.122410675f, 0.992479535f,
+ 0.098017140f, 0.995184727f,
+ 0.073564564f, 0.997290457f,
+ 0.049067674f, 0.998795456f,
+ 0.024541229f, 0.999698819f,
+ 0.000000000f, 1.000000000f,
+ -0.024541229f, 0.999698819f,
+ -0.049067674f, 0.998795456f,
+ -0.073564564f, 0.997290457f,
+ -0.098017140f, 0.995184727f,
+ -0.122410675f, 0.992479535f,
+ -0.146730474f, 0.989176510f,
+ -0.170961889f, 0.985277642f,
+ -0.195090322f, 0.980785280f,
+ -0.219101240f, 0.975702130f,
+ -0.242980180f, 0.970031253f,
+ -0.266712757f, 0.963776066f,
+ -0.290284677f, 0.956940336f,
+ -0.313681740f, 0.949528181f,
+ -0.336889853f, 0.941544065f,
+ -0.359895037f, 0.932992799f,
+ -0.382683432f, 0.923879533f,
+ -0.405241314f, 0.914209756f,
+ -0.427555093f, 0.903989293f,
+ -0.449611330f, 0.893224301f,
+ -0.471396737f, 0.881921264f,
+ -0.492898192f, 0.870086991f,
+ -0.514102744f, 0.857728610f,
+ -0.534997620f, 0.844853565f,
+ -0.555570233f, 0.831469612f,
+ -0.575808191f, 0.817584813f,
+ -0.595699304f, 0.803207531f,
+ -0.615231591f, 0.788346428f,
+ -0.634393284f, 0.773010453f,
+ -0.653172843f, 0.757208847f,
+ -0.671558955f, 0.740951125f,
+ -0.689540545f, 0.724247083f,
+ -0.707106781f, 0.707106781f,
+ -0.724247083f, 0.689540545f,
+ -0.740951125f, 0.671558955f,
+ -0.757208847f, 0.653172843f,
+ -0.773010453f, 0.634393284f,
+ -0.788346428f, 0.615231591f,
+ -0.803207531f, 0.595699304f,
+ -0.817584813f, 0.575808191f,
+ -0.831469612f, 0.555570233f,
+ -0.844853565f, 0.534997620f,
+ -0.857728610f, 0.514102744f,
+ -0.870086991f, 0.492898192f,
+ -0.881921264f, 0.471396737f,
+ -0.893224301f, 0.449611330f,
+ -0.903989293f, 0.427555093f,
+ -0.914209756f, 0.405241314f,
+ -0.923879533f, 0.382683432f,
+ -0.932992799f, 0.359895037f,
+ -0.941544065f, 0.336889853f,
+ -0.949528181f, 0.313681740f,
+ -0.956940336f, 0.290284677f,
+ -0.963776066f, 0.266712757f,
+ -0.970031253f, 0.242980180f,
+ -0.975702130f, 0.219101240f,
+ -0.980785280f, 0.195090322f,
+ -0.985277642f, 0.170961889f,
+ -0.989176510f, 0.146730474f,
+ -0.992479535f, 0.122410675f,
+ -0.995184727f, 0.098017140f,
+ -0.997290457f, 0.073564564f,
+ -0.998795456f, 0.049067674f,
+ -0.999698819f, 0.024541229f,
+ -1.000000000f, 0.000000000f,
+ -0.999698819f, -0.024541229f,
+ -0.998795456f, -0.049067674f,
+ -0.997290457f, -0.073564564f,
+ -0.995184727f, -0.098017140f,
+ -0.992479535f, -0.122410675f,
+ -0.989176510f, -0.146730474f,
+ -0.985277642f, -0.170961889f,
+ -0.980785280f, -0.195090322f,
+ -0.975702130f, -0.219101240f,
+ -0.970031253f, -0.242980180f,
+ -0.963776066f, -0.266712757f,
+ -0.956940336f, -0.290284677f,
+ -0.949528181f, -0.313681740f,
+ -0.941544065f, -0.336889853f,
+ -0.932992799f, -0.359895037f,
+ -0.923879533f, -0.382683432f,
+ -0.914209756f, -0.405241314f,
+ -0.903989293f, -0.427555093f,
+ -0.893224301f, -0.449611330f,
+ -0.881921264f, -0.471396737f,
+ -0.870086991f, -0.492898192f,
+ -0.857728610f, -0.514102744f,
+ -0.844853565f, -0.534997620f,
+ -0.831469612f, -0.555570233f,
+ -0.817584813f, -0.575808191f,
+ -0.803207531f, -0.595699304f,
+ -0.788346428f, -0.615231591f,
+ -0.773010453f, -0.634393284f,
+ -0.757208847f, -0.653172843f,
+ -0.740951125f, -0.671558955f,
+ -0.724247083f, -0.689540545f,
+ -0.707106781f, -0.707106781f,
+ -0.689540545f, -0.724247083f,
+ -0.671558955f, -0.740951125f,
+ -0.653172843f, -0.757208847f,
+ -0.634393284f, -0.773010453f,
+ -0.615231591f, -0.788346428f,
+ -0.595699304f, -0.803207531f,
+ -0.575808191f, -0.817584813f,
+ -0.555570233f, -0.831469612f,
+ -0.534997620f, -0.844853565f,
+ -0.514102744f, -0.857728610f,
+ -0.492898192f, -0.870086991f,
+ -0.471396737f, -0.881921264f,
+ -0.449611330f, -0.893224301f,
+ -0.427555093f, -0.903989293f,
+ -0.405241314f, -0.914209756f,
+ -0.382683432f, -0.923879533f,
+ -0.359895037f, -0.932992799f,
+ -0.336889853f, -0.941544065f,
+ -0.313681740f, -0.949528181f,
+ -0.290284677f, -0.956940336f,
+ -0.266712757f, -0.963776066f,
+ -0.242980180f, -0.970031253f,
+ -0.219101240f, -0.975702130f,
+ -0.195090322f, -0.980785280f,
+ -0.170961889f, -0.985277642f,
+ -0.146730474f, -0.989176510f,
+ -0.122410675f, -0.992479535f,
+ -0.098017140f, -0.995184727f,
+ -0.073564564f, -0.997290457f,
+ -0.049067674f, -0.998795456f,
+ -0.024541229f, -0.999698819f,
+ -0.000000000f, -1.000000000f,
+ 0.024541229f, -0.999698819f,
+ 0.049067674f, -0.998795456f,
+ 0.073564564f, -0.997290457f,
+ 0.098017140f, -0.995184727f,
+ 0.122410675f, -0.992479535f,
+ 0.146730474f, -0.989176510f,
+ 0.170961889f, -0.985277642f,
+ 0.195090322f, -0.980785280f,
+ 0.219101240f, -0.975702130f,
+ 0.242980180f, -0.970031253f,
+ 0.266712757f, -0.963776066f,
+ 0.290284677f, -0.956940336f,
+ 0.313681740f, -0.949528181f,
+ 0.336889853f, -0.941544065f,
+ 0.359895037f, -0.932992799f,
+ 0.382683432f, -0.923879533f,
+ 0.405241314f, -0.914209756f,
+ 0.427555093f, -0.903989293f,
+ 0.449611330f, -0.893224301f,
+ 0.471396737f, -0.881921264f,
+ 0.492898192f, -0.870086991f,
+ 0.514102744f, -0.857728610f,
+ 0.534997620f, -0.844853565f,
+ 0.555570233f, -0.831469612f,
+ 0.575808191f, -0.817584813f,
+ 0.595699304f, -0.803207531f,
+ 0.615231591f, -0.788346428f,
+ 0.634393284f, -0.773010453f,
+ 0.653172843f, -0.757208847f,
+ 0.671558955f, -0.740951125f,
+ 0.689540545f, -0.724247083f,
+ 0.707106781f, -0.707106781f,
+ 0.724247083f, -0.689540545f,
+ 0.740951125f, -0.671558955f,
+ 0.757208847f, -0.653172843f,
+ 0.773010453f, -0.634393284f,
+ 0.788346428f, -0.615231591f,
+ 0.803207531f, -0.595699304f,
+ 0.817584813f, -0.575808191f,
+ 0.831469612f, -0.555570233f,
+ 0.844853565f, -0.534997620f,
+ 0.857728610f, -0.514102744f,
+ 0.870086991f, -0.492898192f,
+ 0.881921264f, -0.471396737f,
+ 0.893224301f, -0.449611330f,
+ 0.903989293f, -0.427555093f,
+ 0.914209756f, -0.405241314f,
+ 0.923879533f, -0.382683432f,
+ 0.932992799f, -0.359895037f,
+ 0.941544065f, -0.336889853f,
+ 0.949528181f, -0.313681740f,
+ 0.956940336f, -0.290284677f,
+ 0.963776066f, -0.266712757f,
+ 0.970031253f, -0.242980180f,
+ 0.975702130f, -0.219101240f,
+ 0.980785280f, -0.195090322f,
+ 0.985277642f, -0.170961889f,
+ 0.989176510f, -0.146730474f,
+ 0.992479535f, -0.122410675f,
+ 0.995184727f, -0.098017140f,
+ 0.997290457f, -0.073564564f,
+ 0.998795456f, -0.049067674f,
+ 0.999698819f, -0.024541229f
+};
+
+/**
+* \par
+* Example code for Floating-point Twiddle factors Generation:
+* \par
+* for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 512 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are in interleaved fashion
+*
+*/
+const float32_t twiddleCoef_512[1024] = {
+ 1.000000000f, 0.000000000f,
+ 0.999924702f, 0.012271538f,
+ 0.999698819f, 0.024541229f,
+ 0.999322385f, 0.036807223f,
+ 0.998795456f, 0.049067674f,
+ 0.998118113f, 0.061320736f,
+ 0.997290457f, 0.073564564f,
+ 0.996312612f, 0.085797312f,
+ 0.995184727f, 0.098017140f,
+ 0.993906970f, 0.110222207f,
+ 0.992479535f, 0.122410675f,
+ 0.990902635f, 0.134580709f,
+ 0.989176510f, 0.146730474f,
+ 0.987301418f, 0.158858143f,
+ 0.985277642f, 0.170961889f,
+ 0.983105487f, 0.183039888f,
+ 0.980785280f, 0.195090322f,
+ 0.978317371f, 0.207111376f,
+ 0.975702130f, 0.219101240f,
+ 0.972939952f, 0.231058108f,
+ 0.970031253f, 0.242980180f,
+ 0.966976471f, 0.254865660f,
+ 0.963776066f, 0.266712757f,
+ 0.960430519f, 0.278519689f,
+ 0.956940336f, 0.290284677f,
+ 0.953306040f, 0.302005949f,
+ 0.949528181f, 0.313681740f,
+ 0.945607325f, 0.325310292f,
+ 0.941544065f, 0.336889853f,
+ 0.937339012f, 0.348418680f,
+ 0.932992799f, 0.359895037f,
+ 0.928506080f, 0.371317194f,
+ 0.923879533f, 0.382683432f,
+ 0.919113852f, 0.393992040f,
+ 0.914209756f, 0.405241314f,
+ 0.909167983f, 0.416429560f,
+ 0.903989293f, 0.427555093f,
+ 0.898674466f, 0.438616239f,
+ 0.893224301f, 0.449611330f,
+ 0.887639620f, 0.460538711f,
+ 0.881921264f, 0.471396737f,
+ 0.876070094f, 0.482183772f,
+ 0.870086991f, 0.492898192f,
+ 0.863972856f, 0.503538384f,
+ 0.857728610f, 0.514102744f,
+ 0.851355193f, 0.524589683f,
+ 0.844853565f, 0.534997620f,
+ 0.838224706f, 0.545324988f,
+ 0.831469612f, 0.555570233f,
+ 0.824589303f, 0.565731811f,
+ 0.817584813f, 0.575808191f,
+ 0.810457198f, 0.585797857f,
+ 0.803207531f, 0.595699304f,
+ 0.795836905f, 0.605511041f,
+ 0.788346428f, 0.615231591f,
+ 0.780737229f, 0.624859488f,
+ 0.773010453f, 0.634393284f,
+ 0.765167266f, 0.643831543f,
+ 0.757208847f, 0.653172843f,
+ 0.749136395f, 0.662415778f,
+ 0.740951125f, 0.671558955f,
+ 0.732654272f, 0.680600998f,
+ 0.724247083f, 0.689540545f,
+ 0.715730825f, 0.698376249f,
+ 0.707106781f, 0.707106781f,
+ 0.698376249f, 0.715730825f,
+ 0.689540545f, 0.724247083f,
+ 0.680600998f, 0.732654272f,
+ 0.671558955f, 0.740951125f,
+ 0.662415778f, 0.749136395f,
+ 0.653172843f, 0.757208847f,
+ 0.643831543f, 0.765167266f,
+ 0.634393284f, 0.773010453f,
+ 0.624859488f, 0.780737229f,
+ 0.615231591f, 0.788346428f,
+ 0.605511041f, 0.795836905f,
+ 0.595699304f, 0.803207531f,
+ 0.585797857f, 0.810457198f,
+ 0.575808191f, 0.817584813f,
+ 0.565731811f, 0.824589303f,
+ 0.555570233f, 0.831469612f,
+ 0.545324988f, 0.838224706f,
+ 0.534997620f, 0.844853565f,
+ 0.524589683f, 0.851355193f,
+ 0.514102744f, 0.857728610f,
+ 0.503538384f, 0.863972856f,
+ 0.492898192f, 0.870086991f,
+ 0.482183772f, 0.876070094f,
+ 0.471396737f, 0.881921264f,
+ 0.460538711f, 0.887639620f,
+ 0.449611330f, 0.893224301f,
+ 0.438616239f, 0.898674466f,
+ 0.427555093f, 0.903989293f,
+ 0.416429560f, 0.909167983f,
+ 0.405241314f, 0.914209756f,
+ 0.393992040f, 0.919113852f,
+ 0.382683432f, 0.923879533f,
+ 0.371317194f, 0.928506080f,
+ 0.359895037f, 0.932992799f,
+ 0.348418680f, 0.937339012f,
+ 0.336889853f, 0.941544065f,
+ 0.325310292f, 0.945607325f,
+ 0.313681740f, 0.949528181f,
+ 0.302005949f, 0.953306040f,
+ 0.290284677f, 0.956940336f,
+ 0.278519689f, 0.960430519f,
+ 0.266712757f, 0.963776066f,
+ 0.254865660f, 0.966976471f,
+ 0.242980180f, 0.970031253f,
+ 0.231058108f, 0.972939952f,
+ 0.219101240f, 0.975702130f,
+ 0.207111376f, 0.978317371f,
+ 0.195090322f, 0.980785280f,
+ 0.183039888f, 0.983105487f,
+ 0.170961889f, 0.985277642f,
+ 0.158858143f, 0.987301418f,
+ 0.146730474f, 0.989176510f,
+ 0.134580709f, 0.990902635f,
+ 0.122410675f, 0.992479535f,
+ 0.110222207f, 0.993906970f,
+ 0.098017140f, 0.995184727f,
+ 0.085797312f, 0.996312612f,
+ 0.073564564f, 0.997290457f,
+ 0.061320736f, 0.998118113f,
+ 0.049067674f, 0.998795456f,
+ 0.036807223f, 0.999322385f,
+ 0.024541229f, 0.999698819f,
+ 0.012271538f, 0.999924702f,
+ 0.000000000f, 1.000000000f,
+ -0.012271538f, 0.999924702f,
+ -0.024541229f, 0.999698819f,
+ -0.036807223f, 0.999322385f,
+ -0.049067674f, 0.998795456f,
+ -0.061320736f, 0.998118113f,
+ -0.073564564f, 0.997290457f,
+ -0.085797312f, 0.996312612f,
+ -0.098017140f, 0.995184727f,
+ -0.110222207f, 0.993906970f,
+ -0.122410675f, 0.992479535f,
+ -0.134580709f, 0.990902635f,
+ -0.146730474f, 0.989176510f,
+ -0.158858143f, 0.987301418f,
+ -0.170961889f, 0.985277642f,
+ -0.183039888f, 0.983105487f,
+ -0.195090322f, 0.980785280f,
+ -0.207111376f, 0.978317371f,
+ -0.219101240f, 0.975702130f,
+ -0.231058108f, 0.972939952f,
+ -0.242980180f, 0.970031253f,
+ -0.254865660f, 0.966976471f,
+ -0.266712757f, 0.963776066f,
+ -0.278519689f, 0.960430519f,
+ -0.290284677f, 0.956940336f,
+ -0.302005949f, 0.953306040f,
+ -0.313681740f, 0.949528181f,
+ -0.325310292f, 0.945607325f,
+ -0.336889853f, 0.941544065f,
+ -0.348418680f, 0.937339012f,
+ -0.359895037f, 0.932992799f,
+ -0.371317194f, 0.928506080f,
+ -0.382683432f, 0.923879533f,
+ -0.393992040f, 0.919113852f,
+ -0.405241314f, 0.914209756f,
+ -0.416429560f, 0.909167983f,
+ -0.427555093f, 0.903989293f,
+ -0.438616239f, 0.898674466f,
+ -0.449611330f, 0.893224301f,
+ -0.460538711f, 0.887639620f,
+ -0.471396737f, 0.881921264f,
+ -0.482183772f, 0.876070094f,
+ -0.492898192f, 0.870086991f,
+ -0.503538384f, 0.863972856f,
+ -0.514102744f, 0.857728610f,
+ -0.524589683f, 0.851355193f,
+ -0.534997620f, 0.844853565f,
+ -0.545324988f, 0.838224706f,
+ -0.555570233f, 0.831469612f,
+ -0.565731811f, 0.824589303f,
+ -0.575808191f, 0.817584813f,
+ -0.585797857f, 0.810457198f,
+ -0.595699304f, 0.803207531f,
+ -0.605511041f, 0.795836905f,
+ -0.615231591f, 0.788346428f,
+ -0.624859488f, 0.780737229f,
+ -0.634393284f, 0.773010453f,
+ -0.643831543f, 0.765167266f,
+ -0.653172843f, 0.757208847f,
+ -0.662415778f, 0.749136395f,
+ -0.671558955f, 0.740951125f,
+ -0.680600998f, 0.732654272f,
+ -0.689540545f, 0.724247083f,
+ -0.698376249f, 0.715730825f,
+ -0.707106781f, 0.707106781f,
+ -0.715730825f, 0.698376249f,
+ -0.724247083f, 0.689540545f,
+ -0.732654272f, 0.680600998f,
+ -0.740951125f, 0.671558955f,
+ -0.749136395f, 0.662415778f,
+ -0.757208847f, 0.653172843f,
+ -0.765167266f, 0.643831543f,
+ -0.773010453f, 0.634393284f,
+ -0.780737229f, 0.624859488f,
+ -0.788346428f, 0.615231591f,
+ -0.795836905f, 0.605511041f,
+ -0.803207531f, 0.595699304f,
+ -0.810457198f, 0.585797857f,
+ -0.817584813f, 0.575808191f,
+ -0.824589303f, 0.565731811f,
+ -0.831469612f, 0.555570233f,
+ -0.838224706f, 0.545324988f,
+ -0.844853565f, 0.534997620f,
+ -0.851355193f, 0.524589683f,
+ -0.857728610f, 0.514102744f,
+ -0.863972856f, 0.503538384f,
+ -0.870086991f, 0.492898192f,
+ -0.876070094f, 0.482183772f,
+ -0.881921264f, 0.471396737f,
+ -0.887639620f, 0.460538711f,
+ -0.893224301f, 0.449611330f,
+ -0.898674466f, 0.438616239f,
+ -0.903989293f, 0.427555093f,
+ -0.909167983f, 0.416429560f,
+ -0.914209756f, 0.405241314f,
+ -0.919113852f, 0.393992040f,
+ -0.923879533f, 0.382683432f,
+ -0.928506080f, 0.371317194f,
+ -0.932992799f, 0.359895037f,
+ -0.937339012f, 0.348418680f,
+ -0.941544065f, 0.336889853f,
+ -0.945607325f, 0.325310292f,
+ -0.949528181f, 0.313681740f,
+ -0.953306040f, 0.302005949f,
+ -0.956940336f, 0.290284677f,
+ -0.960430519f, 0.278519689f,
+ -0.963776066f, 0.266712757f,
+ -0.966976471f, 0.254865660f,
+ -0.970031253f, 0.242980180f,
+ -0.972939952f, 0.231058108f,
+ -0.975702130f, 0.219101240f,
+ -0.978317371f, 0.207111376f,
+ -0.980785280f, 0.195090322f,
+ -0.983105487f, 0.183039888f,
+ -0.985277642f, 0.170961889f,
+ -0.987301418f, 0.158858143f,
+ -0.989176510f, 0.146730474f,
+ -0.990902635f, 0.134580709f,
+ -0.992479535f, 0.122410675f,
+ -0.993906970f, 0.110222207f,
+ -0.995184727f, 0.098017140f,
+ -0.996312612f, 0.085797312f,
+ -0.997290457f, 0.073564564f,
+ -0.998118113f, 0.061320736f,
+ -0.998795456f, 0.049067674f,
+ -0.999322385f, 0.036807223f,
+ -0.999698819f, 0.024541229f,
+ -0.999924702f, 0.012271538f,
+ -1.000000000f, 0.000000000f,
+ -0.999924702f, -0.012271538f,
+ -0.999698819f, -0.024541229f,
+ -0.999322385f, -0.036807223f,
+ -0.998795456f, -0.049067674f,
+ -0.998118113f, -0.061320736f,
+ -0.997290457f, -0.073564564f,
+ -0.996312612f, -0.085797312f,
+ -0.995184727f, -0.098017140f,
+ -0.993906970f, -0.110222207f,
+ -0.992479535f, -0.122410675f,
+ -0.990902635f, -0.134580709f,
+ -0.989176510f, -0.146730474f,
+ -0.987301418f, -0.158858143f,
+ -0.985277642f, -0.170961889f,
+ -0.983105487f, -0.183039888f,
+ -0.980785280f, -0.195090322f,
+ -0.978317371f, -0.207111376f,
+ -0.975702130f, -0.219101240f,
+ -0.972939952f, -0.231058108f,
+ -0.970031253f, -0.242980180f,
+ -0.966976471f, -0.254865660f,
+ -0.963776066f, -0.266712757f,
+ -0.960430519f, -0.278519689f,
+ -0.956940336f, -0.290284677f,
+ -0.953306040f, -0.302005949f,
+ -0.949528181f, -0.313681740f,
+ -0.945607325f, -0.325310292f,
+ -0.941544065f, -0.336889853f,
+ -0.937339012f, -0.348418680f,
+ -0.932992799f, -0.359895037f,
+ -0.928506080f, -0.371317194f,
+ -0.923879533f, -0.382683432f,
+ -0.919113852f, -0.393992040f,
+ -0.914209756f, -0.405241314f,
+ -0.909167983f, -0.416429560f,
+ -0.903989293f, -0.427555093f,
+ -0.898674466f, -0.438616239f,
+ -0.893224301f, -0.449611330f,
+ -0.887639620f, -0.460538711f,
+ -0.881921264f, -0.471396737f,
+ -0.876070094f, -0.482183772f,
+ -0.870086991f, -0.492898192f,
+ -0.863972856f, -0.503538384f,
+ -0.857728610f, -0.514102744f,
+ -0.851355193f, -0.524589683f,
+ -0.844853565f, -0.534997620f,
+ -0.838224706f, -0.545324988f,
+ -0.831469612f, -0.555570233f,
+ -0.824589303f, -0.565731811f,
+ -0.817584813f, -0.575808191f,
+ -0.810457198f, -0.585797857f,
+ -0.803207531f, -0.595699304f,
+ -0.795836905f, -0.605511041f,
+ -0.788346428f, -0.615231591f,
+ -0.780737229f, -0.624859488f,
+ -0.773010453f, -0.634393284f,
+ -0.765167266f, -0.643831543f,
+ -0.757208847f, -0.653172843f,
+ -0.749136395f, -0.662415778f,
+ -0.740951125f, -0.671558955f,
+ -0.732654272f, -0.680600998f,
+ -0.724247083f, -0.689540545f,
+ -0.715730825f, -0.698376249f,
+ -0.707106781f, -0.707106781f,
+ -0.698376249f, -0.715730825f,
+ -0.689540545f, -0.724247083f,
+ -0.680600998f, -0.732654272f,
+ -0.671558955f, -0.740951125f,
+ -0.662415778f, -0.749136395f,
+ -0.653172843f, -0.757208847f,
+ -0.643831543f, -0.765167266f,
+ -0.634393284f, -0.773010453f,
+ -0.624859488f, -0.780737229f,
+ -0.615231591f, -0.788346428f,
+ -0.605511041f, -0.795836905f,
+ -0.595699304f, -0.803207531f,
+ -0.585797857f, -0.810457198f,
+ -0.575808191f, -0.817584813f,
+ -0.565731811f, -0.824589303f,
+ -0.555570233f, -0.831469612f,
+ -0.545324988f, -0.838224706f,
+ -0.534997620f, -0.844853565f,
+ -0.524589683f, -0.851355193f,
+ -0.514102744f, -0.857728610f,
+ -0.503538384f, -0.863972856f,
+ -0.492898192f, -0.870086991f,
+ -0.482183772f, -0.876070094f,
+ -0.471396737f, -0.881921264f,
+ -0.460538711f, -0.887639620f,
+ -0.449611330f, -0.893224301f,
+ -0.438616239f, -0.898674466f,
+ -0.427555093f, -0.903989293f,
+ -0.416429560f, -0.909167983f,
+ -0.405241314f, -0.914209756f,
+ -0.393992040f, -0.919113852f,
+ -0.382683432f, -0.923879533f,
+ -0.371317194f, -0.928506080f,
+ -0.359895037f, -0.932992799f,
+ -0.348418680f, -0.937339012f,
+ -0.336889853f, -0.941544065f,
+ -0.325310292f, -0.945607325f,
+ -0.313681740f, -0.949528181f,
+ -0.302005949f, -0.953306040f,
+ -0.290284677f, -0.956940336f,
+ -0.278519689f, -0.960430519f,
+ -0.266712757f, -0.963776066f,
+ -0.254865660f, -0.966976471f,
+ -0.242980180f, -0.970031253f,
+ -0.231058108f, -0.972939952f,
+ -0.219101240f, -0.975702130f,
+ -0.207111376f, -0.978317371f,
+ -0.195090322f, -0.980785280f,
+ -0.183039888f, -0.983105487f,
+ -0.170961889f, -0.985277642f,
+ -0.158858143f, -0.987301418f,
+ -0.146730474f, -0.989176510f,
+ -0.134580709f, -0.990902635f,
+ -0.122410675f, -0.992479535f,
+ -0.110222207f, -0.993906970f,
+ -0.098017140f, -0.995184727f,
+ -0.085797312f, -0.996312612f,
+ -0.073564564f, -0.997290457f,
+ -0.061320736f, -0.998118113f,
+ -0.049067674f, -0.998795456f,
+ -0.036807223f, -0.999322385f,
+ -0.024541229f, -0.999698819f,
+ -0.012271538f, -0.999924702f,
+ -0.000000000f, -1.000000000f,
+ 0.012271538f, -0.999924702f,
+ 0.024541229f, -0.999698819f,
+ 0.036807223f, -0.999322385f,
+ 0.049067674f, -0.998795456f,
+ 0.061320736f, -0.998118113f,
+ 0.073564564f, -0.997290457f,
+ 0.085797312f, -0.996312612f,
+ 0.098017140f, -0.995184727f,
+ 0.110222207f, -0.993906970f,
+ 0.122410675f, -0.992479535f,
+ 0.134580709f, -0.990902635f,
+ 0.146730474f, -0.989176510f,
+ 0.158858143f, -0.987301418f,
+ 0.170961889f, -0.985277642f,
+ 0.183039888f, -0.983105487f,
+ 0.195090322f, -0.980785280f,
+ 0.207111376f, -0.978317371f,
+ 0.219101240f, -0.975702130f,
+ 0.231058108f, -0.972939952f,
+ 0.242980180f, -0.970031253f,
+ 0.254865660f, -0.966976471f,
+ 0.266712757f, -0.963776066f,
+ 0.278519689f, -0.960430519f,
+ 0.290284677f, -0.956940336f,
+ 0.302005949f, -0.953306040f,
+ 0.313681740f, -0.949528181f,
+ 0.325310292f, -0.945607325f,
+ 0.336889853f, -0.941544065f,
+ 0.348418680f, -0.937339012f,
+ 0.359895037f, -0.932992799f,
+ 0.371317194f, -0.928506080f,
+ 0.382683432f, -0.923879533f,
+ 0.393992040f, -0.919113852f,
+ 0.405241314f, -0.914209756f,
+ 0.416429560f, -0.909167983f,
+ 0.427555093f, -0.903989293f,
+ 0.438616239f, -0.898674466f,
+ 0.449611330f, -0.893224301f,
+ 0.460538711f, -0.887639620f,
+ 0.471396737f, -0.881921264f,
+ 0.482183772f, -0.876070094f,
+ 0.492898192f, -0.870086991f,
+ 0.503538384f, -0.863972856f,
+ 0.514102744f, -0.857728610f,
+ 0.524589683f, -0.851355193f,
+ 0.534997620f, -0.844853565f,
+ 0.545324988f, -0.838224706f,
+ 0.555570233f, -0.831469612f,
+ 0.565731811f, -0.824589303f,
+ 0.575808191f, -0.817584813f,
+ 0.585797857f, -0.810457198f,
+ 0.595699304f, -0.803207531f,
+ 0.605511041f, -0.795836905f,
+ 0.615231591f, -0.788346428f,
+ 0.624859488f, -0.780737229f,
+ 0.634393284f, -0.773010453f,
+ 0.643831543f, -0.765167266f,
+ 0.653172843f, -0.757208847f,
+ 0.662415778f, -0.749136395f,
+ 0.671558955f, -0.740951125f,
+ 0.680600998f, -0.732654272f,
+ 0.689540545f, -0.724247083f,
+ 0.698376249f, -0.715730825f,
+ 0.707106781f, -0.707106781f,
+ 0.715730825f, -0.698376249f,
+ 0.724247083f, -0.689540545f,
+ 0.732654272f, -0.680600998f,
+ 0.740951125f, -0.671558955f,
+ 0.749136395f, -0.662415778f,
+ 0.757208847f, -0.653172843f,
+ 0.765167266f, -0.643831543f,
+ 0.773010453f, -0.634393284f,
+ 0.780737229f, -0.624859488f,
+ 0.788346428f, -0.615231591f,
+ 0.795836905f, -0.605511041f,
+ 0.803207531f, -0.595699304f,
+ 0.810457198f, -0.585797857f,
+ 0.817584813f, -0.575808191f,
+ 0.824589303f, -0.565731811f,
+ 0.831469612f, -0.555570233f,
+ 0.838224706f, -0.545324988f,
+ 0.844853565f, -0.534997620f,
+ 0.851355193f, -0.524589683f,
+ 0.857728610f, -0.514102744f,
+ 0.863972856f, -0.503538384f,
+ 0.870086991f, -0.492898192f,
+ 0.876070094f, -0.482183772f,
+ 0.881921264f, -0.471396737f,
+ 0.887639620f, -0.460538711f,
+ 0.893224301f, -0.449611330f,
+ 0.898674466f, -0.438616239f,
+ 0.903989293f, -0.427555093f,
+ 0.909167983f, -0.416429560f,
+ 0.914209756f, -0.405241314f,
+ 0.919113852f, -0.393992040f,
+ 0.923879533f, -0.382683432f,
+ 0.928506080f, -0.371317194f,
+ 0.932992799f, -0.359895037f,
+ 0.937339012f, -0.348418680f,
+ 0.941544065f, -0.336889853f,
+ 0.945607325f, -0.325310292f,
+ 0.949528181f, -0.313681740f,
+ 0.953306040f, -0.302005949f,
+ 0.956940336f, -0.290284677f,
+ 0.960430519f, -0.278519689f,
+ 0.963776066f, -0.266712757f,
+ 0.966976471f, -0.254865660f,
+ 0.970031253f, -0.242980180f,
+ 0.972939952f, -0.231058108f,
+ 0.975702130f, -0.219101240f,
+ 0.978317371f, -0.207111376f,
+ 0.980785280f, -0.195090322f,
+ 0.983105487f, -0.183039888f,
+ 0.985277642f, -0.170961889f,
+ 0.987301418f, -0.158858143f,
+ 0.989176510f, -0.146730474f,
+ 0.990902635f, -0.134580709f,
+ 0.992479535f, -0.122410675f,
+ 0.993906970f, -0.110222207f,
+ 0.995184727f, -0.098017140f,
+ 0.996312612f, -0.085797312f,
+ 0.997290457f, -0.073564564f,
+ 0.998118113f, -0.061320736f,
+ 0.998795456f, -0.049067674f,
+ 0.999322385f, -0.036807223f,
+ 0.999698819f, -0.024541229f,
+ 0.999924702f, -0.012271538f
+};
+/**
+* \par
+* Example code for Floating-point Twiddle factors Generation:
+* \par
+* for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 1024 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are in interleaved fashion
+*
+*/
+const float32_t twiddleCoef_1024[2048] = {
+1.000000000f , 0.000000000f ,
+0.999981175f , 0.006135885f ,
+0.999924702f , 0.012271538f ,
+0.999830582f , 0.018406730f ,
+0.999698819f , 0.024541229f ,
+0.999529418f , 0.030674803f ,
+0.999322385f , 0.036807223f ,
+0.999077728f , 0.042938257f ,
+0.998795456f , 0.049067674f ,
+0.998475581f , 0.055195244f ,
+0.998118113f , 0.061320736f ,
+0.997723067f , 0.067443920f ,
+0.997290457f , 0.073564564f ,
+0.996820299f , 0.079682438f ,
+0.996312612f , 0.085797312f ,
+0.995767414f , 0.091908956f ,
+0.995184727f , 0.098017140f ,
+0.994564571f , 0.104121634f ,
+0.993906970f , 0.110222207f ,
+0.993211949f , 0.116318631f ,
+0.992479535f , 0.122410675f ,
+0.991709754f , 0.128498111f ,
+0.990902635f , 0.134580709f ,
+0.990058210f , 0.140658239f ,
+0.989176510f , 0.146730474f ,
+0.988257568f , 0.152797185f ,
+0.987301418f , 0.158858143f ,
+0.986308097f , 0.164913120f ,
+0.985277642f , 0.170961889f ,
+0.984210092f , 0.177004220f ,
+0.983105487f , 0.183039888f ,
+0.981963869f , 0.189068664f ,
+0.980785280f , 0.195090322f ,
+0.979569766f , 0.201104635f ,
+0.978317371f , 0.207111376f ,
+0.977028143f , 0.213110320f ,
+0.975702130f , 0.219101240f ,
+0.974339383f , 0.225083911f ,
+0.972939952f , 0.231058108f ,
+0.971503891f , 0.237023606f ,
+0.970031253f , 0.242980180f ,
+0.968522094f , 0.248927606f ,
+0.966976471f , 0.254865660f ,
+0.965394442f , 0.260794118f ,
+0.963776066f , 0.266712757f ,
+0.962121404f , 0.272621355f ,
+0.960430519f , 0.278519689f ,
+0.958703475f , 0.284407537f ,
+0.956940336f , 0.290284677f ,
+0.955141168f , 0.296150888f ,
+0.953306040f , 0.302005949f ,
+0.951435021f , 0.307849640f ,
+0.949528181f , 0.313681740f ,
+0.947585591f , 0.319502031f ,
+0.945607325f , 0.325310292f ,
+0.943593458f , 0.331106306f ,
+0.941544065f , 0.336889853f ,
+0.939459224f , 0.342660717f ,
+0.937339012f , 0.348418680f ,
+0.935183510f , 0.354163525f ,
+0.932992799f , 0.359895037f ,
+0.930766961f , 0.365612998f ,
+0.928506080f , 0.371317194f ,
+0.926210242f , 0.377007410f ,
+0.923879533f , 0.382683432f ,
+0.921514039f , 0.388345047f ,
+0.919113852f , 0.393992040f ,
+0.916679060f , 0.399624200f ,
+0.914209756f , 0.405241314f ,
+0.911706032f , 0.410843171f ,
+0.909167983f , 0.416429560f ,
+0.906595705f , 0.422000271f ,
+0.903989293f , 0.427555093f ,
+0.901348847f , 0.433093819f ,
+0.898674466f , 0.438616239f ,
+0.895966250f , 0.444122145f ,
+0.893224301f , 0.449611330f ,
+0.890448723f , 0.455083587f ,
+0.887639620f , 0.460538711f ,
+0.884797098f , 0.465976496f ,
+0.881921264f , 0.471396737f ,
+0.879012226f , 0.476799230f ,
+0.876070094f , 0.482183772f ,
+0.873094978f , 0.487550160f ,
+0.870086991f , 0.492898192f ,
+0.867046246f , 0.498227667f ,
+0.863972856f , 0.503538384f ,
+0.860866939f , 0.508830143f ,
+0.857728610f , 0.514102744f ,
+0.854557988f , 0.519355990f ,
+0.851355193f , 0.524589683f ,
+0.848120345f , 0.529803625f ,
+0.844853565f , 0.534997620f ,
+0.841554977f , 0.540171473f ,
+0.838224706f , 0.545324988f ,
+0.834862875f , 0.550457973f ,
+0.831469612f , 0.555570233f ,
+0.828045045f , 0.560661576f ,
+0.824589303f , 0.565731811f ,
+0.821102515f , 0.570780746f ,
+0.817584813f , 0.575808191f ,
+0.814036330f , 0.580813958f ,
+0.810457198f , 0.585797857f ,
+0.806847554f , 0.590759702f ,
+0.803207531f , 0.595699304f ,
+0.799537269f , 0.600616479f ,
+0.795836905f , 0.605511041f ,
+0.792106577f , 0.610382806f ,
+0.788346428f , 0.615231591f ,
+0.784556597f , 0.620057212f ,
+0.780737229f , 0.624859488f ,
+0.776888466f , 0.629638239f ,
+0.773010453f , 0.634393284f ,
+0.769103338f , 0.639124445f ,
+0.765167266f , 0.643831543f ,
+0.761202385f , 0.648514401f ,
+0.757208847f , 0.653172843f ,
+0.753186799f , 0.657806693f ,
+0.749136395f , 0.662415778f ,
+0.745057785f , 0.666999922f ,
+0.740951125f , 0.671558955f ,
+0.736816569f , 0.676092704f ,
+0.732654272f , 0.680600998f ,
+0.728464390f , 0.685083668f ,
+0.724247083f , 0.689540545f ,
+0.720002508f , 0.693971461f ,
+0.715730825f , 0.698376249f ,
+0.711432196f , 0.702754744f ,
+0.707106781f , 0.707106781f ,
+0.702754744f , 0.711432196f ,
+0.698376249f , 0.715730825f ,
+0.693971461f , 0.720002508f ,
+0.689540545f , 0.724247083f ,
+0.685083668f , 0.728464390f ,
+0.680600998f , 0.732654272f ,
+0.676092704f , 0.736816569f ,
+0.671558955f , 0.740951125f ,
+0.666999922f , 0.745057785f ,
+0.662415778f , 0.749136395f ,
+0.657806693f , 0.753186799f ,
+0.653172843f , 0.757208847f ,
+0.648514401f , 0.761202385f ,
+0.643831543f , 0.765167266f ,
+0.639124445f , 0.769103338f ,
+0.634393284f , 0.773010453f ,
+0.629638239f , 0.776888466f ,
+0.624859488f , 0.780737229f ,
+0.620057212f , 0.784556597f ,
+0.615231591f , 0.788346428f ,
+0.610382806f , 0.792106577f ,
+0.605511041f , 0.795836905f ,
+0.600616479f , 0.799537269f ,
+0.595699304f , 0.803207531f ,
+0.590759702f , 0.806847554f ,
+0.585797857f , 0.810457198f ,
+0.580813958f , 0.814036330f ,
+0.575808191f , 0.817584813f ,
+0.570780746f , 0.821102515f ,
+0.565731811f , 0.824589303f ,
+0.560661576f , 0.828045045f ,
+0.555570233f , 0.831469612f ,
+0.550457973f , 0.834862875f ,
+0.545324988f , 0.838224706f ,
+0.540171473f , 0.841554977f ,
+0.534997620f , 0.844853565f ,
+0.529803625f , 0.848120345f ,
+0.524589683f , 0.851355193f ,
+0.519355990f , 0.854557988f ,
+0.514102744f , 0.857728610f ,
+0.508830143f , 0.860866939f ,
+0.503538384f , 0.863972856f ,
+0.498227667f , 0.867046246f ,
+0.492898192f , 0.870086991f ,
+0.487550160f , 0.873094978f ,
+0.482183772f , 0.876070094f ,
+0.476799230f , 0.879012226f ,
+0.471396737f , 0.881921264f ,
+0.465976496f , 0.884797098f ,
+0.460538711f , 0.887639620f ,
+0.455083587f , 0.890448723f ,
+0.449611330f , 0.893224301f ,
+0.444122145f , 0.895966250f ,
+0.438616239f , 0.898674466f ,
+0.433093819f , 0.901348847f ,
+0.427555093f , 0.903989293f ,
+0.422000271f , 0.906595705f ,
+0.416429560f , 0.909167983f ,
+0.410843171f , 0.911706032f ,
+0.405241314f , 0.914209756f ,
+0.399624200f , 0.916679060f ,
+0.393992040f , 0.919113852f ,
+0.388345047f , 0.921514039f ,
+0.382683432f , 0.923879533f ,
+0.377007410f , 0.926210242f ,
+0.371317194f , 0.928506080f ,
+0.365612998f , 0.930766961f ,
+0.359895037f , 0.932992799f ,
+0.354163525f , 0.935183510f ,
+0.348418680f , 0.937339012f ,
+0.342660717f , 0.939459224f ,
+0.336889853f , 0.941544065f ,
+0.331106306f , 0.943593458f ,
+0.325310292f , 0.945607325f ,
+0.319502031f , 0.947585591f ,
+0.313681740f , 0.949528181f ,
+0.307849640f , 0.951435021f ,
+0.302005949f , 0.953306040f ,
+0.296150888f , 0.955141168f ,
+0.290284677f , 0.956940336f ,
+0.284407537f , 0.958703475f ,
+0.278519689f , 0.960430519f ,
+0.272621355f , 0.962121404f ,
+0.266712757f , 0.963776066f ,
+0.260794118f , 0.965394442f ,
+0.254865660f , 0.966976471f ,
+0.248927606f , 0.968522094f ,
+0.242980180f , 0.970031253f ,
+0.237023606f , 0.971503891f ,
+0.231058108f , 0.972939952f ,
+0.225083911f , 0.974339383f ,
+0.219101240f , 0.975702130f ,
+0.213110320f , 0.977028143f ,
+0.207111376f , 0.978317371f ,
+0.201104635f , 0.979569766f ,
+0.195090322f , 0.980785280f ,
+0.189068664f , 0.981963869f ,
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+0.987301418f , -0.158858143f ,
+0.988257568f , -0.152797185f ,
+0.989176510f , -0.146730474f ,
+0.990058210f , -0.140658239f ,
+0.990902635f , -0.134580709f ,
+0.991709754f , -0.128498111f ,
+0.992479535f , -0.122410675f ,
+0.993211949f , -0.116318631f ,
+0.993906970f , -0.110222207f ,
+0.994564571f , -0.104121634f ,
+0.995184727f , -0.098017140f ,
+0.995767414f , -0.091908956f ,
+0.996312612f , -0.085797312f ,
+0.996820299f , -0.079682438f ,
+0.997290457f , -0.073564564f ,
+0.997723067f , -0.067443920f ,
+0.998118113f , -0.061320736f ,
+0.998475581f , -0.055195244f ,
+0.998795456f , -0.049067674f ,
+0.999077728f , -0.042938257f ,
+0.999322385f , -0.036807223f ,
+0.999529418f , -0.030674803f ,
+0.999698819f , -0.024541229f ,
+0.999830582f , -0.018406730f ,
+0.999924702f , -0.012271538f ,
+0.999981175f , -0.006135885f
+};
+
+/**
+* \par
+* Example code for Floating-point Twiddle factors Generation:
+* \par
+* for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 2048 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are in interleaved fashion
+*
+*/
+const float32_t twiddleCoef_2048[4096] = {
+ 1.000000000f, 0.000000000f,
+ 0.999995294f, 0.003067957f,
+ 0.999981175f, 0.006135885f,
+ 0.999957645f, 0.009203755f,
+ 0.999924702f, 0.012271538f,
+ 0.999882347f, 0.015339206f,
+ 0.999830582f, 0.018406730f,
+ 0.999769405f, 0.021474080f,
+ 0.999698819f, 0.024541229f,
+ 0.999618822f, 0.027608146f,
+ 0.999529418f, 0.030674803f,
+ 0.999430605f, 0.033741172f,
+ 0.999322385f, 0.036807223f,
+ 0.999204759f, 0.039872928f,
+ 0.999077728f, 0.042938257f,
+ 0.998941293f, 0.046003182f,
+ 0.998795456f, 0.049067674f,
+ 0.998640218f, 0.052131705f,
+ 0.998475581f, 0.055195244f,
+ 0.998301545f, 0.058258265f,
+ 0.998118113f, 0.061320736f,
+ 0.997925286f, 0.064382631f,
+ 0.997723067f, 0.067443920f,
+ 0.997511456f, 0.070504573f,
+ 0.997290457f, 0.073564564f,
+ 0.997060070f, 0.076623861f,
+ 0.996820299f, 0.079682438f,
+ 0.996571146f, 0.082740265f,
+ 0.996312612f, 0.085797312f,
+ 0.996044701f, 0.088853553f,
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+ 0.992479535f, -0.122410675f,
+ 0.992850414f, -0.119365215f,
+ 0.993211949f, -0.116318631f,
+ 0.993564136f, -0.113270952f,
+ 0.993906970f, -0.110222207f,
+ 0.994240449f, -0.107172425f,
+ 0.994564571f, -0.104121634f,
+ 0.994879331f, -0.101069863f,
+ 0.995184727f, -0.098017140f,
+ 0.995480755f, -0.094963495f,
+ 0.995767414f, -0.091908956f,
+ 0.996044701f, -0.088853553f,
+ 0.996312612f, -0.085797312f,
+ 0.996571146f, -0.082740265f,
+ 0.996820299f, -0.079682438f,
+ 0.997060070f, -0.076623861f,
+ 0.997290457f, -0.073564564f,
+ 0.997511456f, -0.070504573f,
+ 0.997723067f, -0.067443920f,
+ 0.997925286f, -0.064382631f,
+ 0.998118113f, -0.061320736f,
+ 0.998301545f, -0.058258265f,
+ 0.998475581f, -0.055195244f,
+ 0.998640218f, -0.052131705f,
+ 0.998795456f, -0.049067674f,
+ 0.998941293f, -0.046003182f,
+ 0.999077728f, -0.042938257f,
+ 0.999204759f, -0.039872928f,
+ 0.999322385f, -0.036807223f,
+ 0.999430605f, -0.033741172f,
+ 0.999529418f, -0.030674803f,
+ 0.999618822f, -0.027608146f,
+ 0.999698819f, -0.024541229f,
+ 0.999769405f, -0.021474080f,
+ 0.999830582f, -0.018406730f,
+ 0.999882347f, -0.015339206f,
+ 0.999924702f, -0.012271538f,
+ 0.999957645f, -0.009203755f,
+ 0.999981175f, -0.006135885f,
+ 0.999995294f, -0.003067957f
+};
+
+/**
+* \par
+* Example code for Floating-point Twiddle factors Generation:
+* \par
+* for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 4096 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are in interleaved fashion
+*
+*/
+const float32_t twiddleCoef_4096[8192] = {
+ 1.000000000f, 0.000000000f,
+ 0.999998823f, 0.001533980f,
+ 0.999995294f, 0.003067957f,
+ 0.999989411f, 0.004601926f,
+ 0.999981175f, 0.006135885f,
+ 0.999970586f, 0.007669829f,
+ 0.999957645f, 0.009203755f,
+ 0.999942350f, 0.010737659f,
+ 0.999924702f, 0.012271538f,
+ 0.999904701f, 0.013805389f,
+ 0.999882347f, 0.015339206f,
+ 0.999857641f, 0.016872988f,
+ 0.999830582f, 0.018406730f,
+ 0.999801170f, 0.019940429f,
+ 0.999769405f, 0.021474080f,
+ 0.999735288f, 0.023007681f,
+ 0.999698819f, 0.024541229f,
+ 0.999659997f, 0.026074718f,
+ 0.999618822f, 0.027608146f,
+ 0.999575296f, 0.029141509f,
+ 0.999529418f, 0.030674803f,
+ 0.999481187f, 0.032208025f,
+ 0.999430605f, 0.033741172f,
+ 0.999377670f, 0.035274239f,
+ 0.999322385f, 0.036807223f,
+ 0.999264747f, 0.038340120f,
+ 0.999204759f, 0.039872928f,
+ 0.999142419f, 0.041405641f,
+ 0.999077728f, 0.042938257f,
+ 0.999010686f, 0.044470772f,
+ 0.998941293f, 0.046003182f,
+ 0.998869550f, 0.047535484f,
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+ 0.999481187f, -0.032208025f,
+ 0.999529418f, -0.030674803f,
+ 0.999575296f, -0.029141509f,
+ 0.999618822f, -0.027608146f,
+ 0.999659997f, -0.026074718f,
+ 0.999698819f, -0.024541229f,
+ 0.999735288f, -0.023007681f,
+ 0.999769405f, -0.021474080f,
+ 0.999801170f, -0.019940429f,
+ 0.999830582f, -0.018406730f,
+ 0.999857641f, -0.016872988f,
+ 0.999882347f, -0.015339206f,
+ 0.999904701f, -0.013805389f,
+ 0.999924702f, -0.012271538f,
+ 0.999942350f, -0.010737659f,
+ 0.999957645f, -0.009203755f,
+ 0.999970586f, -0.007669829f,
+ 0.999981175f, -0.006135885f,
+ 0.999989411f, -0.004601926f,
+ 0.999995294f, -0.003067957f,
+ 0.999998823f, -0.001533980f
+};
+
+/*
+* @brief Q31 Twiddle factors Table
+*/
+
+
+/**
+* \par
+* Example code for Q31 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 16 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to Q31(Fixed point 1.31):
+* round(twiddleCoefQ31(i) * pow(2, 31))
+*
+*/
+const q31_t twiddleCoef_16_q31[24] = {
+ 0x7FFFFFFF, 0x00000000,
+ 0x7641AF3C, 0x30FBC54D,
+ 0x5A82799A, 0x5A82799A,
+ 0x30FBC54D, 0x7641AF3C,
+ 0x00000000, 0x7FFFFFFF,
+ 0xCF043AB2, 0x7641AF3C,
+ 0xA57D8666, 0x5A82799A,
+ 0x89BE50C3, 0x30FBC54D,
+ 0x80000000, 0x00000000,
+ 0x89BE50C3, 0xCF043AB2,
+ 0xA57D8666, 0xA57D8666,
+ 0xCF043AB2, 0x89BE50C3
+};
+
+/**
+* \par
+* Example code for Q31 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 32 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to Q31(Fixed point 1.31):
+* round(twiddleCoefQ31(i) * pow(2, 31))
+*
+*/
+const q31_t twiddleCoef_32_q31[48] = {
+ 0x7FFFFFFF, 0x00000000,
+ 0x7D8A5F3F, 0x18F8B83C,
+ 0x7641AF3C, 0x30FBC54D,
+ 0x6A6D98A4, 0x471CECE6,
+ 0x5A82799A, 0x5A82799A,
+ 0x471CECE6, 0x6A6D98A4,
+ 0x30FBC54D, 0x7641AF3C,
+ 0x18F8B83C, 0x7D8A5F3F,
+ 0x00000000, 0x7FFFFFFF,
+ 0xE70747C3, 0x7D8A5F3F,
+ 0xCF043AB2, 0x7641AF3C,
+ 0xB8E31319, 0x6A6D98A4,
+ 0xA57D8666, 0x5A82799A,
+ 0x9592675B, 0x471CECE6,
+ 0x89BE50C3, 0x30FBC54D,
+ 0x8275A0C0, 0x18F8B83C,
+ 0x80000000, 0x00000000,
+ 0x8275A0C0, 0xE70747C3,
+ 0x89BE50C3, 0xCF043AB2,
+ 0x9592675B, 0xB8E31319,
+ 0xA57D8666, 0xA57D8666,
+ 0xB8E31319, 0x9592675B,
+ 0xCF043AB2, 0x89BE50C3,
+ 0xE70747C3, 0x8275A0C0
+};
+
+/**
+* \par
+* Example code for Q31 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 64 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to Q31(Fixed point 1.31):
+* round(twiddleCoefQ31(i) * pow(2, 31))
+*
+*/
+const q31_t twiddleCoef_64_q31[96] = {
+ 0x7FFFFFFF, 0x00000000,
+ 0x7F62368F, 0x0C8BD35E,
+ 0x7D8A5F3F, 0x18F8B83C,
+ 0x7A7D055B, 0x25280C5D,
+ 0x7641AF3C, 0x30FBC54D,
+ 0x70E2CBC6, 0x3C56BA70,
+ 0x6A6D98A4, 0x471CECE6,
+ 0x62F201AC, 0x5133CC94,
+ 0x5A82799A, 0x5A82799A,
+ 0x5133CC94, 0x62F201AC,
+ 0x471CECE6, 0x6A6D98A4,
+ 0x3C56BA70, 0x70E2CBC6,
+ 0x30FBC54D, 0x7641AF3C,
+ 0x25280C5D, 0x7A7D055B,
+ 0x18F8B83C, 0x7D8A5F3F,
+ 0x0C8BD35E, 0x7F62368F,
+ 0x00000000, 0x7FFFFFFF,
+ 0xF3742CA1, 0x7F62368F,
+ 0xE70747C3, 0x7D8A5F3F,
+ 0xDAD7F3A2, 0x7A7D055B,
+ 0xCF043AB2, 0x7641AF3C,
+ 0xC3A9458F, 0x70E2CBC6,
+ 0xB8E31319, 0x6A6D98A4,
+ 0xAECC336B, 0x62F201AC,
+ 0xA57D8666, 0x5A82799A,
+ 0x9D0DFE53, 0x5133CC94,
+ 0x9592675B, 0x471CECE6,
+ 0x8F1D343A, 0x3C56BA70,
+ 0x89BE50C3, 0x30FBC54D,
+ 0x8582FAA4, 0x25280C5D,
+ 0x8275A0C0, 0x18F8B83C,
+ 0x809DC970, 0x0C8BD35E,
+ 0x80000000, 0x00000000,
+ 0x809DC970, 0xF3742CA1,
+ 0x8275A0C0, 0xE70747C3,
+ 0x8582FAA4, 0xDAD7F3A2,
+ 0x89BE50C3, 0xCF043AB2,
+ 0x8F1D343A, 0xC3A9458F,
+ 0x9592675B, 0xB8E31319,
+ 0x9D0DFE53, 0xAECC336B,
+ 0xA57D8666, 0xA57D8666,
+ 0xAECC336B, 0x9D0DFE53,
+ 0xB8E31319, 0x9592675B,
+ 0xC3A9458F, 0x8F1D343A,
+ 0xCF043AB2, 0x89BE50C3,
+ 0xDAD7F3A2, 0x8582FAA4,
+ 0xE70747C3, 0x8275A0C0,
+ 0xF3742CA1, 0x809DC970
+};
+
+/**
+* \par
+* Example code for Q31 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 128 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to Q31(Fixed point 1.31):
+* round(twiddleCoefQ31(i) * pow(2, 31))
+*
+*/
+const q31_t twiddleCoef_128_q31[192] = {
+ 0x7FFFFFFF, 0x00000000,
+ 0x7FD8878D, 0x0647D97C,
+ 0x7F62368F, 0x0C8BD35E,
+ 0x7E9D55FC, 0x12C8106E,
+ 0x7D8A5F3F, 0x18F8B83C,
+ 0x7C29FBEE, 0x1F19F97B,
+ 0x7A7D055B, 0x25280C5D,
+ 0x78848413, 0x2B1F34EB,
+ 0x7641AF3C, 0x30FBC54D,
+ 0x73B5EBD0, 0x36BA2013,
+ 0x70E2CBC6, 0x3C56BA70,
+ 0x6DCA0D14, 0x41CE1E64,
+ 0x6A6D98A4, 0x471CECE6,
+ 0x66CF811F, 0x4C3FDFF3,
+ 0x62F201AC, 0x5133CC94,
+ 0x5ED77C89, 0x55F5A4D2,
+ 0x5A82799A, 0x5A82799A,
+ 0x55F5A4D2, 0x5ED77C89,
+ 0x5133CC94, 0x62F201AC,
+ 0x4C3FDFF3, 0x66CF811F,
+ 0x471CECE6, 0x6A6D98A4,
+ 0x41CE1E64, 0x6DCA0D14,
+ 0x3C56BA70, 0x70E2CBC6,
+ 0x36BA2013, 0x73B5EBD0,
+ 0x30FBC54D, 0x7641AF3C,
+ 0x2B1F34EB, 0x78848413,
+ 0x25280C5D, 0x7A7D055B,
+ 0x1F19F97B, 0x7C29FBEE,
+ 0x18F8B83C, 0x7D8A5F3F,
+ 0x12C8106E, 0x7E9D55FC,
+ 0x0C8BD35E, 0x7F62368F,
+ 0x0647D97C, 0x7FD8878D,
+ 0x00000000, 0x7FFFFFFF,
+ 0xF9B82683, 0x7FD8878D,
+ 0xF3742CA1, 0x7F62368F,
+ 0xED37EF91, 0x7E9D55FC,
+ 0xE70747C3, 0x7D8A5F3F,
+ 0xE0E60684, 0x7C29FBEE,
+ 0xDAD7F3A2, 0x7A7D055B,
+ 0xD4E0CB14, 0x78848413,
+ 0xCF043AB2, 0x7641AF3C,
+ 0xC945DFEC, 0x73B5EBD0,
+ 0xC3A9458F, 0x70E2CBC6,
+ 0xBE31E19B, 0x6DCA0D14,
+ 0xB8E31319, 0x6A6D98A4,
+ 0xB3C0200C, 0x66CF811F,
+ 0xAECC336B, 0x62F201AC,
+ 0xAA0A5B2D, 0x5ED77C89,
+ 0xA57D8666, 0x5A82799A,
+ 0xA1288376, 0x55F5A4D2,
+ 0x9D0DFE53, 0x5133CC94,
+ 0x99307EE0, 0x4C3FDFF3,
+ 0x9592675B, 0x471CECE6,
+ 0x9235F2EB, 0x41CE1E64,
+ 0x8F1D343A, 0x3C56BA70,
+ 0x8C4A142F, 0x36BA2013,
+ 0x89BE50C3, 0x30FBC54D,
+ 0x877B7BEC, 0x2B1F34EB,
+ 0x8582FAA4, 0x25280C5D,
+ 0x83D60411, 0x1F19F97B,
+ 0x8275A0C0, 0x18F8B83C,
+ 0x8162AA03, 0x12C8106E,
+ 0x809DC970, 0x0C8BD35E,
+ 0x80277872, 0x0647D97C,
+ 0x80000000, 0x00000000,
+ 0x80277872, 0xF9B82683,
+ 0x809DC970, 0xF3742CA1,
+ 0x8162AA03, 0xED37EF91,
+ 0x8275A0C0, 0xE70747C3,
+ 0x83D60411, 0xE0E60684,
+ 0x8582FAA4, 0xDAD7F3A2,
+ 0x877B7BEC, 0xD4E0CB14,
+ 0x89BE50C3, 0xCF043AB2,
+ 0x8C4A142F, 0xC945DFEC,
+ 0x8F1D343A, 0xC3A9458F,
+ 0x9235F2EB, 0xBE31E19B,
+ 0x9592675B, 0xB8E31319,
+ 0x99307EE0, 0xB3C0200C,
+ 0x9D0DFE53, 0xAECC336B,
+ 0xA1288376, 0xAA0A5B2D,
+ 0xA57D8666, 0xA57D8666,
+ 0xAA0A5B2D, 0xA1288376,
+ 0xAECC336B, 0x9D0DFE53,
+ 0xB3C0200C, 0x99307EE0,
+ 0xB8E31319, 0x9592675B,
+ 0xBE31E19B, 0x9235F2EB,
+ 0xC3A9458F, 0x8F1D343A,
+ 0xC945DFEC, 0x8C4A142F,
+ 0xCF043AB2, 0x89BE50C3,
+ 0xD4E0CB14, 0x877B7BEC,
+ 0xDAD7F3A2, 0x8582FAA4,
+ 0xE0E60684, 0x83D60411,
+ 0xE70747C3, 0x8275A0C0,
+ 0xED37EF91, 0x8162AA03,
+ 0xF3742CA1, 0x809DC970,
+ 0xF9B82683, 0x80277872
+};
+
+/**
+* \par
+* Example code for Q31 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 256 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to Q31(Fixed point 1.31):
+* round(twiddleCoefQ31(i) * pow(2, 31))
+*
+*/
+const q31_t twiddleCoef_256_q31[384] = {
+ 0x7FFFFFFF, 0x00000000,
+ 0x7FF62182, 0x03242ABF,
+ 0x7FD8878D, 0x0647D97C,
+ 0x7FA736B4, 0x096A9049,
+ 0x7F62368F, 0x0C8BD35E,
+ 0x7F0991C3, 0x0FAB272B,
+ 0x7E9D55FC, 0x12C8106E,
+ 0x7E1D93E9, 0x15E21444,
+ 0x7D8A5F3F, 0x18F8B83C,
+ 0x7CE3CEB1, 0x1C0B826A,
+ 0x7C29FBEE, 0x1F19F97B,
+ 0x7B5D039D, 0x2223A4C5,
+ 0x7A7D055B, 0x25280C5D,
+ 0x798A23B1, 0x2826B928,
+ 0x78848413, 0x2B1F34EB,
+ 0x776C4EDB, 0x2E110A62,
+ 0x7641AF3C, 0x30FBC54D,
+ 0x7504D345, 0x33DEF287,
+ 0x73B5EBD0, 0x36BA2013,
+ 0x72552C84, 0x398CDD32,
+ 0x70E2CBC6, 0x3C56BA70,
+ 0x6F5F02B1, 0x3F1749B7,
+ 0x6DCA0D14, 0x41CE1E64,
+ 0x6C242960, 0x447ACD50,
+ 0x6A6D98A4, 0x471CECE6,
+ 0x68A69E81, 0x49B41533,
+ 0x66CF811F, 0x4C3FDFF3,
+ 0x64E88926, 0x4EBFE8A4,
+ 0x62F201AC, 0x5133CC94,
+ 0x60EC3830, 0x539B2AEF,
+ 0x5ED77C89, 0x55F5A4D2,
+ 0x5CB420DF, 0x5842DD54,
+ 0x5A82799A, 0x5A82799A,
+ 0x5842DD54, 0x5CB420DF,
+ 0x55F5A4D2, 0x5ED77C89,
+ 0x539B2AEF, 0x60EC3830,
+ 0x5133CC94, 0x62F201AC,
+ 0x4EBFE8A4, 0x64E88926,
+ 0x4C3FDFF3, 0x66CF811F,
+ 0x49B41533, 0x68A69E81,
+ 0x471CECE6, 0x6A6D98A4,
+ 0x447ACD50, 0x6C242960,
+ 0x41CE1E64, 0x6DCA0D14,
+ 0x3F1749B7, 0x6F5F02B1,
+ 0x3C56BA70, 0x70E2CBC6,
+ 0x398CDD32, 0x72552C84,
+ 0x36BA2013, 0x73B5EBD0,
+ 0x33DEF287, 0x7504D345,
+ 0x30FBC54D, 0x7641AF3C,
+ 0x2E110A62, 0x776C4EDB,
+ 0x2B1F34EB, 0x78848413,
+ 0x2826B928, 0x798A23B1,
+ 0x25280C5D, 0x7A7D055B,
+ 0x2223A4C5, 0x7B5D039D,
+ 0x1F19F97B, 0x7C29FBEE,
+ 0x1C0B826A, 0x7CE3CEB1,
+ 0x18F8B83C, 0x7D8A5F3F,
+ 0x15E21444, 0x7E1D93E9,
+ 0x12C8106E, 0x7E9D55FC,
+ 0x0FAB272B, 0x7F0991C3,
+ 0x0C8BD35E, 0x7F62368F,
+ 0x096A9049, 0x7FA736B4,
+ 0x0647D97C, 0x7FD8878D,
+ 0x03242ABF, 0x7FF62182,
+ 0x00000000, 0x7FFFFFFF,
+ 0xFCDBD541, 0x7FF62182,
+ 0xF9B82683, 0x7FD8878D,
+ 0xF6956FB6, 0x7FA736B4,
+ 0xF3742CA1, 0x7F62368F,
+ 0xF054D8D4, 0x7F0991C3,
+ 0xED37EF91, 0x7E9D55FC,
+ 0xEA1DEBBB, 0x7E1D93E9,
+ 0xE70747C3, 0x7D8A5F3F,
+ 0xE3F47D95, 0x7CE3CEB1,
+ 0xE0E60684, 0x7C29FBEE,
+ 0xDDDC5B3A, 0x7B5D039D,
+ 0xDAD7F3A2, 0x7A7D055B,
+ 0xD7D946D7, 0x798A23B1,
+ 0xD4E0CB14, 0x78848413,
+ 0xD1EEF59E, 0x776C4EDB,
+ 0xCF043AB2, 0x7641AF3C,
+ 0xCC210D78, 0x7504D345,
+ 0xC945DFEC, 0x73B5EBD0,
+ 0xC67322CD, 0x72552C84,
+ 0xC3A9458F, 0x70E2CBC6,
+ 0xC0E8B648, 0x6F5F02B1,
+ 0xBE31E19B, 0x6DCA0D14,
+ 0xBB8532AF, 0x6C242960,
+ 0xB8E31319, 0x6A6D98A4,
+ 0xB64BEACC, 0x68A69E81,
+ 0xB3C0200C, 0x66CF811F,
+ 0xB140175B, 0x64E88926,
+ 0xAECC336B, 0x62F201AC,
+ 0xAC64D510, 0x60EC3830,
+ 0xAA0A5B2D, 0x5ED77C89,
+ 0xA7BD22AB, 0x5CB420DF,
+ 0xA57D8666, 0x5A82799A,
+ 0xA34BDF20, 0x5842DD54,
+ 0xA1288376, 0x55F5A4D2,
+ 0x9F13C7D0, 0x539B2AEF,
+ 0x9D0DFE53, 0x5133CC94,
+ 0x9B1776D9, 0x4EBFE8A4,
+ 0x99307EE0, 0x4C3FDFF3,
+ 0x9759617E, 0x49B41533,
+ 0x9592675B, 0x471CECE6,
+ 0x93DBD69F, 0x447ACD50,
+ 0x9235F2EB, 0x41CE1E64,
+ 0x90A0FD4E, 0x3F1749B7,
+ 0x8F1D343A, 0x3C56BA70,
+ 0x8DAAD37B, 0x398CDD32,
+ 0x8C4A142F, 0x36BA2013,
+ 0x8AFB2CBA, 0x33DEF287,
+ 0x89BE50C3, 0x30FBC54D,
+ 0x8893B124, 0x2E110A62,
+ 0x877B7BEC, 0x2B1F34EB,
+ 0x8675DC4E, 0x2826B928,
+ 0x8582FAA4, 0x25280C5D,
+ 0x84A2FC62, 0x2223A4C5,
+ 0x83D60411, 0x1F19F97B,
+ 0x831C314E, 0x1C0B826A,
+ 0x8275A0C0, 0x18F8B83C,
+ 0x81E26C16, 0x15E21444,
+ 0x8162AA03, 0x12C8106E,
+ 0x80F66E3C, 0x0FAB272B,
+ 0x809DC970, 0x0C8BD35E,
+ 0x8058C94C, 0x096A9049,
+ 0x80277872, 0x0647D97C,
+ 0x8009DE7D, 0x03242ABF,
+ 0x80000000, 0x00000000,
+ 0x8009DE7D, 0xFCDBD541,
+ 0x80277872, 0xF9B82683,
+ 0x8058C94C, 0xF6956FB6,
+ 0x809DC970, 0xF3742CA1,
+ 0x80F66E3C, 0xF054D8D4,
+ 0x8162AA03, 0xED37EF91,
+ 0x81E26C16, 0xEA1DEBBB,
+ 0x8275A0C0, 0xE70747C3,
+ 0x831C314E, 0xE3F47D95,
+ 0x83D60411, 0xE0E60684,
+ 0x84A2FC62, 0xDDDC5B3A,
+ 0x8582FAA4, 0xDAD7F3A2,
+ 0x8675DC4E, 0xD7D946D7,
+ 0x877B7BEC, 0xD4E0CB14,
+ 0x8893B124, 0xD1EEF59E,
+ 0x89BE50C3, 0xCF043AB2,
+ 0x8AFB2CBA, 0xCC210D78,
+ 0x8C4A142F, 0xC945DFEC,
+ 0x8DAAD37B, 0xC67322CD,
+ 0x8F1D343A, 0xC3A9458F,
+ 0x90A0FD4E, 0xC0E8B648,
+ 0x9235F2EB, 0xBE31E19B,
+ 0x93DBD69F, 0xBB8532AF,
+ 0x9592675B, 0xB8E31319,
+ 0x9759617E, 0xB64BEACC,
+ 0x99307EE0, 0xB3C0200C,
+ 0x9B1776D9, 0xB140175B,
+ 0x9D0DFE53, 0xAECC336B,
+ 0x9F13C7D0, 0xAC64D510,
+ 0xA1288376, 0xAA0A5B2D,
+ 0xA34BDF20, 0xA7BD22AB,
+ 0xA57D8666, 0xA57D8666,
+ 0xA7BD22AB, 0xA34BDF20,
+ 0xAA0A5B2D, 0xA1288376,
+ 0xAC64D510, 0x9F13C7D0,
+ 0xAECC336B, 0x9D0DFE53,
+ 0xB140175B, 0x9B1776D9,
+ 0xB3C0200C, 0x99307EE0,
+ 0xB64BEACC, 0x9759617E,
+ 0xB8E31319, 0x9592675B,
+ 0xBB8532AF, 0x93DBD69F,
+ 0xBE31E19B, 0x9235F2EB,
+ 0xC0E8B648, 0x90A0FD4E,
+ 0xC3A9458F, 0x8F1D343A,
+ 0xC67322CD, 0x8DAAD37B,
+ 0xC945DFEC, 0x8C4A142F,
+ 0xCC210D78, 0x8AFB2CBA,
+ 0xCF043AB2, 0x89BE50C3,
+ 0xD1EEF59E, 0x8893B124,
+ 0xD4E0CB14, 0x877B7BEC,
+ 0xD7D946D7, 0x8675DC4E,
+ 0xDAD7F3A2, 0x8582FAA4,
+ 0xDDDC5B3A, 0x84A2FC62,
+ 0xE0E60684, 0x83D60411,
+ 0xE3F47D95, 0x831C314E,
+ 0xE70747C3, 0x8275A0C0,
+ 0xEA1DEBBB, 0x81E26C16,
+ 0xED37EF91, 0x8162AA03,
+ 0xF054D8D4, 0x80F66E3C,
+ 0xF3742CA1, 0x809DC970,
+ 0xF6956FB6, 0x8058C94C,
+ 0xF9B82683, 0x80277872,
+ 0xFCDBD541, 0x8009DE7D
+};
+
+/**
+* \par
+* Example code for Q31 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 512 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to Q31(Fixed point 1.31):
+* round(twiddleCoefQ31(i) * pow(2, 31))
+*
+*/
+const q31_t twiddleCoef_512_q31[768] = {
+ 0x7FFFFFFF, 0x00000000,
+ 0x7FFD885A, 0x01921D1F,
+ 0x7FF62182, 0x03242ABF,
+ 0x7FE9CBC0, 0x04B6195D,
+ 0x7FD8878D, 0x0647D97C,
+ 0x7FC25596, 0x07D95B9E,
+ 0x7FA736B4, 0x096A9049,
+ 0x7F872BF3, 0x0AFB6805,
+ 0x7F62368F, 0x0C8BD35E,
+ 0x7F3857F5, 0x0E1BC2E3,
+ 0x7F0991C3, 0x0FAB272B,
+ 0x7ED5E5C6, 0x1139F0CE,
+ 0x7E9D55FC, 0x12C8106E,
+ 0x7E5FE493, 0x145576B1,
+ 0x7E1D93E9, 0x15E21444,
+ 0x7DD6668E, 0x176DD9DE,
+ 0x7D8A5F3F, 0x18F8B83C,
+ 0x7D3980EC, 0x1A82A025,
+ 0x7CE3CEB1, 0x1C0B826A,
+ 0x7C894BDD, 0x1D934FE5,
+ 0x7C29FBEE, 0x1F19F97B,
+ 0x7BC5E28F, 0x209F701C,
+ 0x7B5D039D, 0x2223A4C5,
+ 0x7AEF6323, 0x23A6887E,
+ 0x7A7D055B, 0x25280C5D,
+ 0x7A05EEAD, 0x26A82185,
+ 0x798A23B1, 0x2826B928,
+ 0x7909A92C, 0x29A3C484,
+ 0x78848413, 0x2B1F34EB,
+ 0x77FAB988, 0x2C98FBBA,
+ 0x776C4EDB, 0x2E110A62,
+ 0x76D94988, 0x2F875262,
+ 0x7641AF3C, 0x30FBC54D,
+ 0x75A585CF, 0x326E54C7,
+ 0x7504D345, 0x33DEF287,
+ 0x745F9DD1, 0x354D9056,
+ 0x73B5EBD0, 0x36BA2013,
+ 0x7307C3D0, 0x382493B0,
+ 0x72552C84, 0x398CDD32,
+ 0x719E2CD2, 0x3AF2EEB7,
+ 0x70E2CBC6, 0x3C56BA70,
+ 0x70231099, 0x3DB832A5,
+ 0x6F5F02B1, 0x3F1749B7,
+ 0x6E96A99C, 0x4073F21D,
+ 0x6DCA0D14, 0x41CE1E64,
+ 0x6CF934FB, 0x4325C135,
+ 0x6C242960, 0x447ACD50,
+ 0x6B4AF278, 0x45CD358F,
+ 0x6A6D98A4, 0x471CECE6,
+ 0x698C246C, 0x4869E664,
+ 0x68A69E81, 0x49B41533,
+ 0x67BD0FBC, 0x4AFB6C97,
+ 0x66CF811F, 0x4C3FDFF3,
+ 0x65DDFBD3, 0x4D8162C4,
+ 0x64E88926, 0x4EBFE8A4,
+ 0x63EF328F, 0x4FFB654D,
+ 0x62F201AC, 0x5133CC94,
+ 0x61F1003E, 0x5269126E,
+ 0x60EC3830, 0x539B2AEF,
+ 0x5FE3B38D, 0x54CA0A4A,
+ 0x5ED77C89, 0x55F5A4D2,
+ 0x5DC79D7C, 0x571DEEF9,
+ 0x5CB420DF, 0x5842DD54,
+ 0x5B9D1153, 0x59646497,
+ 0x5A82799A, 0x5A82799A,
+ 0x59646497, 0x5B9D1153,
+ 0x5842DD54, 0x5CB420DF,
+ 0x571DEEF9, 0x5DC79D7C,
+ 0x55F5A4D2, 0x5ED77C89,
+ 0x54CA0A4A, 0x5FE3B38D,
+ 0x539B2AEF, 0x60EC3830,
+ 0x5269126E, 0x61F1003E,
+ 0x5133CC94, 0x62F201AC,
+ 0x4FFB654D, 0x63EF328F,
+ 0x4EBFE8A4, 0x64E88926,
+ 0x4D8162C4, 0x65DDFBD3,
+ 0x4C3FDFF3, 0x66CF811F,
+ 0x4AFB6C97, 0x67BD0FBC,
+ 0x49B41533, 0x68A69E81,
+ 0x4869E664, 0x698C246C,
+ 0x471CECE6, 0x6A6D98A4,
+ 0x45CD358F, 0x6B4AF278,
+ 0x447ACD50, 0x6C242960,
+ 0x4325C135, 0x6CF934FB,
+ 0x41CE1E64, 0x6DCA0D14,
+ 0x4073F21D, 0x6E96A99C,
+ 0x3F1749B7, 0x6F5F02B1,
+ 0x3DB832A5, 0x70231099,
+ 0x3C56BA70, 0x70E2CBC6,
+ 0x3AF2EEB7, 0x719E2CD2,
+ 0x398CDD32, 0x72552C84,
+ 0x382493B0, 0x7307C3D0,
+ 0x36BA2013, 0x73B5EBD0,
+ 0x354D9056, 0x745F9DD1,
+ 0x33DEF287, 0x7504D345,
+ 0x326E54C7, 0x75A585CF,
+ 0x30FBC54D, 0x7641AF3C,
+ 0x2F875262, 0x76D94988,
+ 0x2E110A62, 0x776C4EDB,
+ 0x2C98FBBA, 0x77FAB988,
+ 0x2B1F34EB, 0x78848413,
+ 0x29A3C484, 0x7909A92C,
+ 0x2826B928, 0x798A23B1,
+ 0x26A82185, 0x7A05EEAD,
+ 0x25280C5D, 0x7A7D055B,
+ 0x23A6887E, 0x7AEF6323,
+ 0x2223A4C5, 0x7B5D039D,
+ 0x209F701C, 0x7BC5E28F,
+ 0x1F19F97B, 0x7C29FBEE,
+ 0x1D934FE5, 0x7C894BDD,
+ 0x1C0B826A, 0x7CE3CEB1,
+ 0x1A82A025, 0x7D3980EC,
+ 0x18F8B83C, 0x7D8A5F3F,
+ 0x176DD9DE, 0x7DD6668E,
+ 0x15E21444, 0x7E1D93E9,
+ 0x145576B1, 0x7E5FE493,
+ 0x12C8106E, 0x7E9D55FC,
+ 0x1139F0CE, 0x7ED5E5C6,
+ 0x0FAB272B, 0x7F0991C3,
+ 0x0E1BC2E3, 0x7F3857F5,
+ 0x0C8BD35E, 0x7F62368F,
+ 0x0AFB6805, 0x7F872BF3,
+ 0x096A9049, 0x7FA736B4,
+ 0x07D95B9E, 0x7FC25596,
+ 0x0647D97C, 0x7FD8878D,
+ 0x04B6195D, 0x7FE9CBC0,
+ 0x03242ABF, 0x7FF62182,
+ 0x01921D1F, 0x7FFD885A,
+ 0x00000000, 0x7FFFFFFF,
+ 0xFE6DE2E0, 0x7FFD885A,
+ 0xFCDBD541, 0x7FF62182,
+ 0xFB49E6A2, 0x7FE9CBC0,
+ 0xF9B82683, 0x7FD8878D,
+ 0xF826A461, 0x7FC25596,
+ 0xF6956FB6, 0x7FA736B4,
+ 0xF50497FA, 0x7F872BF3,
+ 0xF3742CA1, 0x7F62368F,
+ 0xF1E43D1C, 0x7F3857F5,
+ 0xF054D8D4, 0x7F0991C3,
+ 0xEEC60F31, 0x7ED5E5C6,
+ 0xED37EF91, 0x7E9D55FC,
+ 0xEBAA894E, 0x7E5FE493,
+ 0xEA1DEBBB, 0x7E1D93E9,
+ 0xE8922621, 0x7DD6668E,
+ 0xE70747C3, 0x7D8A5F3F,
+ 0xE57D5FDA, 0x7D3980EC,
+ 0xE3F47D95, 0x7CE3CEB1,
+ 0xE26CB01A, 0x7C894BDD,
+ 0xE0E60684, 0x7C29FBEE,
+ 0xDF608FE3, 0x7BC5E28F,
+ 0xDDDC5B3A, 0x7B5D039D,
+ 0xDC597781, 0x7AEF6323,
+ 0xDAD7F3A2, 0x7A7D055B,
+ 0xD957DE7A, 0x7A05EEAD,
+ 0xD7D946D7, 0x798A23B1,
+ 0xD65C3B7B, 0x7909A92C,
+ 0xD4E0CB14, 0x78848413,
+ 0xD3670445, 0x77FAB988,
+ 0xD1EEF59E, 0x776C4EDB,
+ 0xD078AD9D, 0x76D94988,
+ 0xCF043AB2, 0x7641AF3C,
+ 0xCD91AB38, 0x75A585CF,
+ 0xCC210D78, 0x7504D345,
+ 0xCAB26FA9, 0x745F9DD1,
+ 0xC945DFEC, 0x73B5EBD0,
+ 0xC7DB6C50, 0x7307C3D0,
+ 0xC67322CD, 0x72552C84,
+ 0xC50D1148, 0x719E2CD2,
+ 0xC3A9458F, 0x70E2CBC6,
+ 0xC247CD5A, 0x70231099,
+ 0xC0E8B648, 0x6F5F02B1,
+ 0xBF8C0DE2, 0x6E96A99C,
+ 0xBE31E19B, 0x6DCA0D14,
+ 0xBCDA3ECA, 0x6CF934FB,
+ 0xBB8532AF, 0x6C242960,
+ 0xBA32CA70, 0x6B4AF278,
+ 0xB8E31319, 0x6A6D98A4,
+ 0xB796199B, 0x698C246C,
+ 0xB64BEACC, 0x68A69E81,
+ 0xB5049368, 0x67BD0FBC,
+ 0xB3C0200C, 0x66CF811F,
+ 0xB27E9D3B, 0x65DDFBD3,
+ 0xB140175B, 0x64E88926,
+ 0xB0049AB2, 0x63EF328F,
+ 0xAECC336B, 0x62F201AC,
+ 0xAD96ED91, 0x61F1003E,
+ 0xAC64D510, 0x60EC3830,
+ 0xAB35F5B5, 0x5FE3B38D,
+ 0xAA0A5B2D, 0x5ED77C89,
+ 0xA8E21106, 0x5DC79D7C,
+ 0xA7BD22AB, 0x5CB420DF,
+ 0xA69B9B68, 0x5B9D1153,
+ 0xA57D8666, 0x5A82799A,
+ 0xA462EEAC, 0x59646497,
+ 0xA34BDF20, 0x5842DD54,
+ 0xA2386283, 0x571DEEF9,
+ 0xA1288376, 0x55F5A4D2,
+ 0xA01C4C72, 0x54CA0A4A,
+ 0x9F13C7D0, 0x539B2AEF,
+ 0x9E0EFFC1, 0x5269126E,
+ 0x9D0DFE53, 0x5133CC94,
+ 0x9C10CD70, 0x4FFB654D,
+ 0x9B1776D9, 0x4EBFE8A4,
+ 0x9A22042C, 0x4D8162C4,
+ 0x99307EE0, 0x4C3FDFF3,
+ 0x9842F043, 0x4AFB6C97,
+ 0x9759617E, 0x49B41533,
+ 0x9673DB94, 0x4869E664,
+ 0x9592675B, 0x471CECE6,
+ 0x94B50D87, 0x45CD358F,
+ 0x93DBD69F, 0x447ACD50,
+ 0x9306CB04, 0x4325C135,
+ 0x9235F2EB, 0x41CE1E64,
+ 0x91695663, 0x4073F21D,
+ 0x90A0FD4E, 0x3F1749B7,
+ 0x8FDCEF66, 0x3DB832A5,
+ 0x8F1D343A, 0x3C56BA70,
+ 0x8E61D32D, 0x3AF2EEB7,
+ 0x8DAAD37B, 0x398CDD32,
+ 0x8CF83C30, 0x382493B0,
+ 0x8C4A142F, 0x36BA2013,
+ 0x8BA0622F, 0x354D9056,
+ 0x8AFB2CBA, 0x33DEF287,
+ 0x8A5A7A30, 0x326E54C7,
+ 0x89BE50C3, 0x30FBC54D,
+ 0x8926B677, 0x2F875262,
+ 0x8893B124, 0x2E110A62,
+ 0x88054677, 0x2C98FBBA,
+ 0x877B7BEC, 0x2B1F34EB,
+ 0x86F656D3, 0x29A3C484,
+ 0x8675DC4E, 0x2826B928,
+ 0x85FA1152, 0x26A82185,
+ 0x8582FAA4, 0x25280C5D,
+ 0x85109CDC, 0x23A6887E,
+ 0x84A2FC62, 0x2223A4C5,
+ 0x843A1D70, 0x209F701C,
+ 0x83D60411, 0x1F19F97B,
+ 0x8376B422, 0x1D934FE5,
+ 0x831C314E, 0x1C0B826A,
+ 0x82C67F13, 0x1A82A025,
+ 0x8275A0C0, 0x18F8B83C,
+ 0x82299971, 0x176DD9DE,
+ 0x81E26C16, 0x15E21444,
+ 0x81A01B6C, 0x145576B1,
+ 0x8162AA03, 0x12C8106E,
+ 0x812A1A39, 0x1139F0CE,
+ 0x80F66E3C, 0x0FAB272B,
+ 0x80C7A80A, 0x0E1BC2E3,
+ 0x809DC970, 0x0C8BD35E,
+ 0x8078D40D, 0x0AFB6805,
+ 0x8058C94C, 0x096A9049,
+ 0x803DAA69, 0x07D95B9E,
+ 0x80277872, 0x0647D97C,
+ 0x80163440, 0x04B6195D,
+ 0x8009DE7D, 0x03242ABF,
+ 0x800277A5, 0x01921D1F,
+ 0x80000000, 0x00000000,
+ 0x800277A5, 0xFE6DE2E0,
+ 0x8009DE7D, 0xFCDBD541,
+ 0x80163440, 0xFB49E6A2,
+ 0x80277872, 0xF9B82683,
+ 0x803DAA69, 0xF826A461,
+ 0x8058C94C, 0xF6956FB6,
+ 0x8078D40D, 0xF50497FA,
+ 0x809DC970, 0xF3742CA1,
+ 0x80C7A80A, 0xF1E43D1C,
+ 0x80F66E3C, 0xF054D8D4,
+ 0x812A1A39, 0xEEC60F31,
+ 0x8162AA03, 0xED37EF91,
+ 0x81A01B6C, 0xEBAA894E,
+ 0x81E26C16, 0xEA1DEBBB,
+ 0x82299971, 0xE8922621,
+ 0x8275A0C0, 0xE70747C3,
+ 0x82C67F13, 0xE57D5FDA,
+ 0x831C314E, 0xE3F47D95,
+ 0x8376B422, 0xE26CB01A,
+ 0x83D60411, 0xE0E60684,
+ 0x843A1D70, 0xDF608FE3,
+ 0x84A2FC62, 0xDDDC5B3A,
+ 0x85109CDC, 0xDC597781,
+ 0x8582FAA4, 0xDAD7F3A2,
+ 0x85FA1152, 0xD957DE7A,
+ 0x8675DC4E, 0xD7D946D7,
+ 0x86F656D3, 0xD65C3B7B,
+ 0x877B7BEC, 0xD4E0CB14,
+ 0x88054677, 0xD3670445,
+ 0x8893B124, 0xD1EEF59E,
+ 0x8926B677, 0xD078AD9D,
+ 0x89BE50C3, 0xCF043AB2,
+ 0x8A5A7A30, 0xCD91AB38,
+ 0x8AFB2CBA, 0xCC210D78,
+ 0x8BA0622F, 0xCAB26FA9,
+ 0x8C4A142F, 0xC945DFEC,
+ 0x8CF83C30, 0xC7DB6C50,
+ 0x8DAAD37B, 0xC67322CD,
+ 0x8E61D32D, 0xC50D1148,
+ 0x8F1D343A, 0xC3A9458F,
+ 0x8FDCEF66, 0xC247CD5A,
+ 0x90A0FD4E, 0xC0E8B648,
+ 0x91695663, 0xBF8C0DE2,
+ 0x9235F2EB, 0xBE31E19B,
+ 0x9306CB04, 0xBCDA3ECA,
+ 0x93DBD69F, 0xBB8532AF,
+ 0x94B50D87, 0xBA32CA70,
+ 0x9592675B, 0xB8E31319,
+ 0x9673DB94, 0xB796199B,
+ 0x9759617E, 0xB64BEACC,
+ 0x9842F043, 0xB5049368,
+ 0x99307EE0, 0xB3C0200C,
+ 0x9A22042C, 0xB27E9D3B,
+ 0x9B1776D9, 0xB140175B,
+ 0x9C10CD70, 0xB0049AB2,
+ 0x9D0DFE53, 0xAECC336B,
+ 0x9E0EFFC1, 0xAD96ED91,
+ 0x9F13C7D0, 0xAC64D510,
+ 0xA01C4C72, 0xAB35F5B5,
+ 0xA1288376, 0xAA0A5B2D,
+ 0xA2386283, 0xA8E21106,
+ 0xA34BDF20, 0xA7BD22AB,
+ 0xA462EEAC, 0xA69B9B68,
+ 0xA57D8666, 0xA57D8666,
+ 0xA69B9B68, 0xA462EEAC,
+ 0xA7BD22AB, 0xA34BDF20,
+ 0xA8E21106, 0xA2386283,
+ 0xAA0A5B2D, 0xA1288376,
+ 0xAB35F5B5, 0xA01C4C72,
+ 0xAC64D510, 0x9F13C7D0,
+ 0xAD96ED91, 0x9E0EFFC1,
+ 0xAECC336B, 0x9D0DFE53,
+ 0xB0049AB2, 0x9C10CD70,
+ 0xB140175B, 0x9B1776D9,
+ 0xB27E9D3B, 0x9A22042C,
+ 0xB3C0200C, 0x99307EE0,
+ 0xB5049368, 0x9842F043,
+ 0xB64BEACC, 0x9759617E,
+ 0xB796199B, 0x9673DB94,
+ 0xB8E31319, 0x9592675B,
+ 0xBA32CA70, 0x94B50D87,
+ 0xBB8532AF, 0x93DBD69F,
+ 0xBCDA3ECA, 0x9306CB04,
+ 0xBE31E19B, 0x9235F2EB,
+ 0xBF8C0DE2, 0x91695663,
+ 0xC0E8B648, 0x90A0FD4E,
+ 0xC247CD5A, 0x8FDCEF66,
+ 0xC3A9458F, 0x8F1D343A,
+ 0xC50D1148, 0x8E61D32D,
+ 0xC67322CD, 0x8DAAD37B,
+ 0xC7DB6C50, 0x8CF83C30,
+ 0xC945DFEC, 0x8C4A142F,
+ 0xCAB26FA9, 0x8BA0622F,
+ 0xCC210D78, 0x8AFB2CBA,
+ 0xCD91AB38, 0x8A5A7A30,
+ 0xCF043AB2, 0x89BE50C3,
+ 0xD078AD9D, 0x8926B677,
+ 0xD1EEF59E, 0x8893B124,
+ 0xD3670445, 0x88054677,
+ 0xD4E0CB14, 0x877B7BEC,
+ 0xD65C3B7B, 0x86F656D3,
+ 0xD7D946D7, 0x8675DC4E,
+ 0xD957DE7A, 0x85FA1152,
+ 0xDAD7F3A2, 0x8582FAA4,
+ 0xDC597781, 0x85109CDC,
+ 0xDDDC5B3A, 0x84A2FC62,
+ 0xDF608FE3, 0x843A1D70,
+ 0xE0E60684, 0x83D60411,
+ 0xE26CB01A, 0x8376B422,
+ 0xE3F47D95, 0x831C314E,
+ 0xE57D5FDA, 0x82C67F13,
+ 0xE70747C3, 0x8275A0C0,
+ 0xE8922621, 0x82299971,
+ 0xEA1DEBBB, 0x81E26C16,
+ 0xEBAA894E, 0x81A01B6C,
+ 0xED37EF91, 0x8162AA03,
+ 0xEEC60F31, 0x812A1A39,
+ 0xF054D8D4, 0x80F66E3C,
+ 0xF1E43D1C, 0x80C7A80A,
+ 0xF3742CA1, 0x809DC970,
+ 0xF50497FA, 0x8078D40D,
+ 0xF6956FB6, 0x8058C94C,
+ 0xF826A461, 0x803DAA69,
+ 0xF9B82683, 0x80277872,
+ 0xFB49E6A2, 0x80163440,
+ 0xFCDBD541, 0x8009DE7D,
+ 0xFE6DE2E0, 0x800277A5
+};
+
+/**
+* \par
+* Example code for Q31 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 1024 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to Q31(Fixed point 1.31):
+* round(twiddleCoefQ31(i) * pow(2, 31))
+*
+*/
+const q31_t twiddleCoef_1024_q31[1536] = {
+ 0x7FFFFFFF, 0x00000000,
+ 0x7FFF6216, 0x00C90F88,
+ 0x7FFD885A, 0x01921D1F,
+ 0x7FFA72D1, 0x025B26D7,
+ 0x7FF62182, 0x03242ABF,
+ 0x7FF09477, 0x03ED26E6,
+ 0x7FE9CBC0, 0x04B6195D,
+ 0x7FE1C76B, 0x057F0034,
+ 0x7FD8878D, 0x0647D97C,
+ 0x7FCE0C3E, 0x0710A344,
+ 0x7FC25596, 0x07D95B9E,
+ 0x7FB563B2, 0x08A2009A,
+ 0x7FA736B4, 0x096A9049,
+ 0x7F97CEBC, 0x0A3308BC,
+ 0x7F872BF3, 0x0AFB6805,
+ 0x7F754E7F, 0x0BC3AC35,
+ 0x7F62368F, 0x0C8BD35E,
+ 0x7F4DE450, 0x0D53DB92,
+ 0x7F3857F5, 0x0E1BC2E3,
+ 0x7F2191B4, 0x0EE38765,
+ 0x7F0991C3, 0x0FAB272B,
+ 0x7EF0585F, 0x1072A047,
+ 0x7ED5E5C6, 0x1139F0CE,
+ 0x7EBA3A39, 0x120116D4,
+ 0x7E9D55FC, 0x12C8106E,
+ 0x7E7F3956, 0x138EDBB0,
+ 0x7E5FE493, 0x145576B1,
+ 0x7E3F57FE, 0x151BDF85,
+ 0x7E1D93E9, 0x15E21444,
+ 0x7DFA98A7, 0x16A81305,
+ 0x7DD6668E, 0x176DD9DE,
+ 0x7DB0FDF7, 0x183366E8,
+ 0x7D8A5F3F, 0x18F8B83C,
+ 0x7D628AC5, 0x19BDCBF2,
+ 0x7D3980EC, 0x1A82A025,
+ 0x7D0F4218, 0x1B4732EF,
+ 0x7CE3CEB1, 0x1C0B826A,
+ 0x7CB72724, 0x1CCF8CB3,
+ 0x7C894BDD, 0x1D934FE5,
+ 0x7C5A3D4F, 0x1E56CA1E,
+ 0x7C29FBEE, 0x1F19F97B,
+ 0x7BF88830, 0x1FDCDC1A,
+ 0x7BC5E28F, 0x209F701C,
+ 0x7B920B89, 0x2161B39F,
+ 0x7B5D039D, 0x2223A4C5,
+ 0x7B26CB4F, 0x22E541AE,
+ 0x7AEF6323, 0x23A6887E,
+ 0x7AB6CBA3, 0x24677757,
+ 0x7A7D055B, 0x25280C5D,
+ 0x7A4210D8, 0x25E845B5,
+ 0x7A05EEAD, 0x26A82185,
+ 0x79C89F6D, 0x27679DF4,
+ 0x798A23B1, 0x2826B928,
+ 0x794A7C11, 0x28E5714A,
+ 0x7909A92C, 0x29A3C484,
+ 0x78C7ABA1, 0x2A61B101,
+ 0x78848413, 0x2B1F34EB,
+ 0x78403328, 0x2BDC4E6F,
+ 0x77FAB988, 0x2C98FBBA,
+ 0x77B417DF, 0x2D553AFB,
+ 0x776C4EDB, 0x2E110A62,
+ 0x77235F2D, 0x2ECC681E,
+ 0x76D94988, 0x2F875262,
+ 0x768E0EA5, 0x3041C760,
+ 0x7641AF3C, 0x30FBC54D,
+ 0x75F42C0A, 0x31B54A5D,
+ 0x75A585CF, 0x326E54C7,
+ 0x7555BD4B, 0x3326E2C2,
+ 0x7504D345, 0x33DEF287,
+ 0x74B2C883, 0x3496824F,
+ 0x745F9DD1, 0x354D9056,
+ 0x740B53FA, 0x36041AD9,
+ 0x73B5EBD0, 0x36BA2013,
+ 0x735F6626, 0x376F9E46,
+ 0x7307C3D0, 0x382493B0,
+ 0x72AF05A6, 0x38D8FE93,
+ 0x72552C84, 0x398CDD32,
+ 0x71FA3948, 0x3A402DD1,
+ 0x719E2CD2, 0x3AF2EEB7,
+ 0x71410804, 0x3BA51E29,
+ 0x70E2CBC6, 0x3C56BA70,
+ 0x708378FE, 0x3D07C1D5,
+ 0x70231099, 0x3DB832A5,
+ 0x6FC19385, 0x3E680B2C,
+ 0x6F5F02B1, 0x3F1749B7,
+ 0x6EFB5F12, 0x3FC5EC97,
+ 0x6E96A99C, 0x4073F21D,
+ 0x6E30E349, 0x4121589A,
+ 0x6DCA0D14, 0x41CE1E64,
+ 0x6D6227FA, 0x427A41D0,
+ 0x6CF934FB, 0x4325C135,
+ 0x6C8F351C, 0x43D09AEC,
+ 0x6C242960, 0x447ACD50,
+ 0x6BB812D0, 0x452456BC,
+ 0x6B4AF278, 0x45CD358F,
+ 0x6ADCC964, 0x46756827,
+ 0x6A6D98A4, 0x471CECE6,
+ 0x69FD614A, 0x47C3C22E,
+ 0x698C246C, 0x4869E664,
+ 0x6919E320, 0x490F57EE,
+ 0x68A69E81, 0x49B41533,
+ 0x683257AA, 0x4A581C9D,
+ 0x67BD0FBC, 0x4AFB6C97,
+ 0x6746C7D7, 0x4B9E038F,
+ 0x66CF811F, 0x4C3FDFF3,
+ 0x66573CBB, 0x4CE10034,
+ 0x65DDFBD3, 0x4D8162C4,
+ 0x6563BF92, 0x4E210617,
+ 0x64E88926, 0x4EBFE8A4,
+ 0x646C59BF, 0x4F5E08E3,
+ 0x63EF328F, 0x4FFB654D,
+ 0x637114CC, 0x5097FC5E,
+ 0x62F201AC, 0x5133CC94,
+ 0x6271FA69, 0x51CED46E,
+ 0x61F1003E, 0x5269126E,
+ 0x616F146B, 0x53028517,
+ 0x60EC3830, 0x539B2AEF,
+ 0x60686CCE, 0x5433027D,
+ 0x5FE3B38D, 0x54CA0A4A,
+ 0x5F5E0DB3, 0x556040E2,
+ 0x5ED77C89, 0x55F5A4D2,
+ 0x5E50015D, 0x568A34A9,
+ 0x5DC79D7C, 0x571DEEF9,
+ 0x5D3E5236, 0x57B0D256,
+ 0x5CB420DF, 0x5842DD54,
+ 0x5C290ACC, 0x58D40E8C,
+ 0x5B9D1153, 0x59646497,
+ 0x5B1035CF, 0x59F3DE12,
+ 0x5A82799A, 0x5A82799A,
+ 0x59F3DE12, 0x5B1035CF,
+ 0x59646497, 0x5B9D1153,
+ 0x58D40E8C, 0x5C290ACC,
+ 0x5842DD54, 0x5CB420DF,
+ 0x57B0D256, 0x5D3E5236,
+ 0x571DEEF9, 0x5DC79D7C,
+ 0x568A34A9, 0x5E50015D,
+ 0x55F5A4D2, 0x5ED77C89,
+ 0x556040E2, 0x5F5E0DB3,
+ 0x54CA0A4A, 0x5FE3B38D,
+ 0x5433027D, 0x60686CCE,
+ 0x539B2AEF, 0x60EC3830,
+ 0x53028517, 0x616F146B,
+ 0x5269126E, 0x61F1003E,
+ 0x51CED46E, 0x6271FA69,
+ 0x5133CC94, 0x62F201AC,
+ 0x5097FC5E, 0x637114CC,
+ 0x4FFB654D, 0x63EF328F,
+ 0x4F5E08E3, 0x646C59BF,
+ 0x4EBFE8A4, 0x64E88926,
+ 0x4E210617, 0x6563BF92,
+ 0x4D8162C4, 0x65DDFBD3,
+ 0x4CE10034, 0x66573CBB,
+ 0x4C3FDFF3, 0x66CF811F,
+ 0x4B9E038F, 0x6746C7D7,
+ 0x4AFB6C97, 0x67BD0FBC,
+ 0x4A581C9D, 0x683257AA,
+ 0x49B41533, 0x68A69E81,
+ 0x490F57EE, 0x6919E320,
+ 0x4869E664, 0x698C246C,
+ 0x47C3C22E, 0x69FD614A,
+ 0x471CECE6, 0x6A6D98A4,
+ 0x46756827, 0x6ADCC964,
+ 0x45CD358F, 0x6B4AF278,
+ 0x452456BC, 0x6BB812D0,
+ 0x447ACD50, 0x6C242960,
+ 0x43D09AEC, 0x6C8F351C,
+ 0x4325C135, 0x6CF934FB,
+ 0x427A41D0, 0x6D6227FA,
+ 0x41CE1E64, 0x6DCA0D14,
+ 0x4121589A, 0x6E30E349,
+ 0x4073F21D, 0x6E96A99C,
+ 0x3FC5EC97, 0x6EFB5F12,
+ 0x3F1749B7, 0x6F5F02B1,
+ 0x3E680B2C, 0x6FC19385,
+ 0x3DB832A5, 0x70231099,
+ 0x3D07C1D5, 0x708378FE,
+ 0x3C56BA70, 0x70E2CBC6,
+ 0x3BA51E29, 0x71410804,
+ 0x3AF2EEB7, 0x719E2CD2,
+ 0x3A402DD1, 0x71FA3948,
+ 0x398CDD32, 0x72552C84,
+ 0x38D8FE93, 0x72AF05A6,
+ 0x382493B0, 0x7307C3D0,
+ 0x376F9E46, 0x735F6626,
+ 0x36BA2013, 0x73B5EBD0,
+ 0x36041AD9, 0x740B53FA,
+ 0x354D9056, 0x745F9DD1,
+ 0x3496824F, 0x74B2C883,
+ 0x33DEF287, 0x7504D345,
+ 0x3326E2C2, 0x7555BD4B,
+ 0x326E54C7, 0x75A585CF,
+ 0x31B54A5D, 0x75F42C0A,
+ 0x30FBC54D, 0x7641AF3C,
+ 0x3041C760, 0x768E0EA5,
+ 0x2F875262, 0x76D94988,
+ 0x2ECC681E, 0x77235F2D,
+ 0x2E110A62, 0x776C4EDB,
+ 0x2D553AFB, 0x77B417DF,
+ 0x2C98FBBA, 0x77FAB988,
+ 0x2BDC4E6F, 0x78403328,
+ 0x2B1F34EB, 0x78848413,
+ 0x2A61B101, 0x78C7ABA1,
+ 0x29A3C484, 0x7909A92C,
+ 0x28E5714A, 0x794A7C11,
+ 0x2826B928, 0x798A23B1,
+ 0x27679DF4, 0x79C89F6D,
+ 0x26A82185, 0x7A05EEAD,
+ 0x25E845B5, 0x7A4210D8,
+ 0x25280C5D, 0x7A7D055B,
+ 0x24677757, 0x7AB6CBA3,
+ 0x23A6887E, 0x7AEF6323,
+ 0x22E541AE, 0x7B26CB4F,
+ 0x2223A4C5, 0x7B5D039D,
+ 0x2161B39F, 0x7B920B89,
+ 0x209F701C, 0x7BC5E28F,
+ 0x1FDCDC1A, 0x7BF88830,
+ 0x1F19F97B, 0x7C29FBEE,
+ 0x1E56CA1E, 0x7C5A3D4F,
+ 0x1D934FE5, 0x7C894BDD,
+ 0x1CCF8CB3, 0x7CB72724,
+ 0x1C0B826A, 0x7CE3CEB1,
+ 0x1B4732EF, 0x7D0F4218,
+ 0x1A82A025, 0x7D3980EC,
+ 0x19BDCBF2, 0x7D628AC5,
+ 0x18F8B83C, 0x7D8A5F3F,
+ 0x183366E8, 0x7DB0FDF7,
+ 0x176DD9DE, 0x7DD6668E,
+ 0x16A81305, 0x7DFA98A7,
+ 0x15E21444, 0x7E1D93E9,
+ 0x151BDF85, 0x7E3F57FE,
+ 0x145576B1, 0x7E5FE493,
+ 0x138EDBB0, 0x7E7F3956,
+ 0x12C8106E, 0x7E9D55FC,
+ 0x120116D4, 0x7EBA3A39,
+ 0x1139F0CE, 0x7ED5E5C6,
+ 0x1072A047, 0x7EF0585F,
+ 0x0FAB272B, 0x7F0991C3,
+ 0x0EE38765, 0x7F2191B4,
+ 0x0E1BC2E3, 0x7F3857F5,
+ 0x0D53DB92, 0x7F4DE450,
+ 0x0C8BD35E, 0x7F62368F,
+ 0x0BC3AC35, 0x7F754E7F,
+ 0x0AFB6805, 0x7F872BF3,
+ 0x0A3308BC, 0x7F97CEBC,
+ 0x096A9049, 0x7FA736B4,
+ 0x08A2009A, 0x7FB563B2,
+ 0x07D95B9E, 0x7FC25596,
+ 0x0710A344, 0x7FCE0C3E,
+ 0x0647D97C, 0x7FD8878D,
+ 0x057F0034, 0x7FE1C76B,
+ 0x04B6195D, 0x7FE9CBC0,
+ 0x03ED26E6, 0x7FF09477,
+ 0x03242ABF, 0x7FF62182,
+ 0x025B26D7, 0x7FFA72D1,
+ 0x01921D1F, 0x7FFD885A,
+ 0x00C90F88, 0x7FFF6216,
+ 0x00000000, 0x7FFFFFFF,
+ 0xFF36F078, 0x7FFF6216,
+ 0xFE6DE2E0, 0x7FFD885A,
+ 0xFDA4D928, 0x7FFA72D1,
+ 0xFCDBD541, 0x7FF62182,
+ 0xFC12D919, 0x7FF09477,
+ 0xFB49E6A2, 0x7FE9CBC0,
+ 0xFA80FFCB, 0x7FE1C76B,
+ 0xF9B82683, 0x7FD8878D,
+ 0xF8EF5CBB, 0x7FCE0C3E,
+ 0xF826A461, 0x7FC25596,
+ 0xF75DFF65, 0x7FB563B2,
+ 0xF6956FB6, 0x7FA736B4,
+ 0xF5CCF743, 0x7F97CEBC,
+ 0xF50497FA, 0x7F872BF3,
+ 0xF43C53CA, 0x7F754E7F,
+ 0xF3742CA1, 0x7F62368F,
+ 0xF2AC246D, 0x7F4DE450,
+ 0xF1E43D1C, 0x7F3857F5,
+ 0xF11C789A, 0x7F2191B4,
+ 0xF054D8D4, 0x7F0991C3,
+ 0xEF8D5FB8, 0x7EF0585F,
+ 0xEEC60F31, 0x7ED5E5C6,
+ 0xEDFEE92B, 0x7EBA3A39,
+ 0xED37EF91, 0x7E9D55FC,
+ 0xEC71244F, 0x7E7F3956,
+ 0xEBAA894E, 0x7E5FE493,
+ 0xEAE4207A, 0x7E3F57FE,
+ 0xEA1DEBBB, 0x7E1D93E9,
+ 0xE957ECFB, 0x7DFA98A7,
+ 0xE8922621, 0x7DD6668E,
+ 0xE7CC9917, 0x7DB0FDF7,
+ 0xE70747C3, 0x7D8A5F3F,
+ 0xE642340D, 0x7D628AC5,
+ 0xE57D5FDA, 0x7D3980EC,
+ 0xE4B8CD10, 0x7D0F4218,
+ 0xE3F47D95, 0x7CE3CEB1,
+ 0xE330734C, 0x7CB72724,
+ 0xE26CB01A, 0x7C894BDD,
+ 0xE1A935E1, 0x7C5A3D4F,
+ 0xE0E60684, 0x7C29FBEE,
+ 0xE02323E5, 0x7BF88830,
+ 0xDF608FE3, 0x7BC5E28F,
+ 0xDE9E4C60, 0x7B920B89,
+ 0xDDDC5B3A, 0x7B5D039D,
+ 0xDD1ABE51, 0x7B26CB4F,
+ 0xDC597781, 0x7AEF6323,
+ 0xDB9888A8, 0x7AB6CBA3,
+ 0xDAD7F3A2, 0x7A7D055B,
+ 0xDA17BA4A, 0x7A4210D8,
+ 0xD957DE7A, 0x7A05EEAD,
+ 0xD898620C, 0x79C89F6D,
+ 0xD7D946D7, 0x798A23B1,
+ 0xD71A8EB5, 0x794A7C11,
+ 0xD65C3B7B, 0x7909A92C,
+ 0xD59E4EFE, 0x78C7ABA1,
+ 0xD4E0CB14, 0x78848413,
+ 0xD423B190, 0x78403328,
+ 0xD3670445, 0x77FAB988,
+ 0xD2AAC504, 0x77B417DF,
+ 0xD1EEF59E, 0x776C4EDB,
+ 0xD13397E1, 0x77235F2D,
+ 0xD078AD9D, 0x76D94988,
+ 0xCFBE389F, 0x768E0EA5,
+ 0xCF043AB2, 0x7641AF3C,
+ 0xCE4AB5A2, 0x75F42C0A,
+ 0xCD91AB38, 0x75A585CF,
+ 0xCCD91D3D, 0x7555BD4B,
+ 0xCC210D78, 0x7504D345,
+ 0xCB697DB0, 0x74B2C883,
+ 0xCAB26FA9, 0x745F9DD1,
+ 0xC9FBE527, 0x740B53FA,
+ 0xC945DFEC, 0x73B5EBD0,
+ 0xC89061BA, 0x735F6626,
+ 0xC7DB6C50, 0x7307C3D0,
+ 0xC727016C, 0x72AF05A6,
+ 0xC67322CD, 0x72552C84,
+ 0xC5BFD22E, 0x71FA3948,
+ 0xC50D1148, 0x719E2CD2,
+ 0xC45AE1D7, 0x71410804,
+ 0xC3A9458F, 0x70E2CBC6,
+ 0xC2F83E2A, 0x708378FE,
+ 0xC247CD5A, 0x70231099,
+ 0xC197F4D3, 0x6FC19385,
+ 0xC0E8B648, 0x6F5F02B1,
+ 0xC03A1368, 0x6EFB5F12,
+ 0xBF8C0DE2, 0x6E96A99C,
+ 0xBEDEA765, 0x6E30E349,
+ 0xBE31E19B, 0x6DCA0D14,
+ 0xBD85BE2F, 0x6D6227FA,
+ 0xBCDA3ECA, 0x6CF934FB,
+ 0xBC2F6513, 0x6C8F351C,
+ 0xBB8532AF, 0x6C242960,
+ 0xBADBA943, 0x6BB812D0,
+ 0xBA32CA70, 0x6B4AF278,
+ 0xB98A97D8, 0x6ADCC964,
+ 0xB8E31319, 0x6A6D98A4,
+ 0xB83C3DD1, 0x69FD614A,
+ 0xB796199B, 0x698C246C,
+ 0xB6F0A811, 0x6919E320,
+ 0xB64BEACC, 0x68A69E81,
+ 0xB5A7E362, 0x683257AA,
+ 0xB5049368, 0x67BD0FBC,
+ 0xB461FC70, 0x6746C7D7,
+ 0xB3C0200C, 0x66CF811F,
+ 0xB31EFFCB, 0x66573CBB,
+ 0xB27E9D3B, 0x65DDFBD3,
+ 0xB1DEF9E8, 0x6563BF92,
+ 0xB140175B, 0x64E88926,
+ 0xB0A1F71C, 0x646C59BF,
+ 0xB0049AB2, 0x63EF328F,
+ 0xAF6803A1, 0x637114CC,
+ 0xAECC336B, 0x62F201AC,
+ 0xAE312B91, 0x6271FA69,
+ 0xAD96ED91, 0x61F1003E,
+ 0xACFD7AE8, 0x616F146B,
+ 0xAC64D510, 0x60EC3830,
+ 0xABCCFD82, 0x60686CCE,
+ 0xAB35F5B5, 0x5FE3B38D,
+ 0xAA9FBF1D, 0x5F5E0DB3,
+ 0xAA0A5B2D, 0x5ED77C89,
+ 0xA975CB56, 0x5E50015D,
+ 0xA8E21106, 0x5DC79D7C,
+ 0xA84F2DA9, 0x5D3E5236,
+ 0xA7BD22AB, 0x5CB420DF,
+ 0xA72BF173, 0x5C290ACC,
+ 0xA69B9B68, 0x5B9D1153,
+ 0xA60C21ED, 0x5B1035CF,
+ 0xA57D8666, 0x5A82799A,
+ 0xA4EFCA31, 0x59F3DE12,
+ 0xA462EEAC, 0x59646497,
+ 0xA3D6F533, 0x58D40E8C,
+ 0xA34BDF20, 0x5842DD54,
+ 0xA2C1ADC9, 0x57B0D256,
+ 0xA2386283, 0x571DEEF9,
+ 0xA1AFFEA2, 0x568A34A9,
+ 0xA1288376, 0x55F5A4D2,
+ 0xA0A1F24C, 0x556040E2,
+ 0xA01C4C72, 0x54CA0A4A,
+ 0x9F979331, 0x5433027D,
+ 0x9F13C7D0, 0x539B2AEF,
+ 0x9E90EB94, 0x53028517,
+ 0x9E0EFFC1, 0x5269126E,
+ 0x9D8E0596, 0x51CED46E,
+ 0x9D0DFE53, 0x5133CC94,
+ 0x9C8EEB33, 0x5097FC5E,
+ 0x9C10CD70, 0x4FFB654D,
+ 0x9B93A640, 0x4F5E08E3,
+ 0x9B1776D9, 0x4EBFE8A4,
+ 0x9A9C406D, 0x4E210617,
+ 0x9A22042C, 0x4D8162C4,
+ 0x99A8C344, 0x4CE10034,
+ 0x99307EE0, 0x4C3FDFF3,
+ 0x98B93828, 0x4B9E038F,
+ 0x9842F043, 0x4AFB6C97,
+ 0x97CDA855, 0x4A581C9D,
+ 0x9759617E, 0x49B41533,
+ 0x96E61CDF, 0x490F57EE,
+ 0x9673DB94, 0x4869E664,
+ 0x96029EB5, 0x47C3C22E,
+ 0x9592675B, 0x471CECE6,
+ 0x9523369B, 0x46756827,
+ 0x94B50D87, 0x45CD358F,
+ 0x9447ED2F, 0x452456BC,
+ 0x93DBD69F, 0x447ACD50,
+ 0x9370CAE4, 0x43D09AEC,
+ 0x9306CB04, 0x4325C135,
+ 0x929DD805, 0x427A41D0,
+ 0x9235F2EB, 0x41CE1E64,
+ 0x91CF1CB6, 0x4121589A,
+ 0x91695663, 0x4073F21D,
+ 0x9104A0ED, 0x3FC5EC97,
+ 0x90A0FD4E, 0x3F1749B7,
+ 0x903E6C7A, 0x3E680B2C,
+ 0x8FDCEF66, 0x3DB832A5,
+ 0x8F7C8701, 0x3D07C1D5,
+ 0x8F1D343A, 0x3C56BA70,
+ 0x8EBEF7FB, 0x3BA51E29,
+ 0x8E61D32D, 0x3AF2EEB7,
+ 0x8E05C6B7, 0x3A402DD1,
+ 0x8DAAD37B, 0x398CDD32,
+ 0x8D50FA59, 0x38D8FE93,
+ 0x8CF83C30, 0x382493B0,
+ 0x8CA099D9, 0x376F9E46,
+ 0x8C4A142F, 0x36BA2013,
+ 0x8BF4AC05, 0x36041AD9,
+ 0x8BA0622F, 0x354D9056,
+ 0x8B4D377C, 0x3496824F,
+ 0x8AFB2CBA, 0x33DEF287,
+ 0x8AAA42B4, 0x3326E2C2,
+ 0x8A5A7A30, 0x326E54C7,
+ 0x8A0BD3F5, 0x31B54A5D,
+ 0x89BE50C3, 0x30FBC54D,
+ 0x8971F15A, 0x3041C760,
+ 0x8926B677, 0x2F875262,
+ 0x88DCA0D3, 0x2ECC681E,
+ 0x8893B124, 0x2E110A62,
+ 0x884BE820, 0x2D553AFB,
+ 0x88054677, 0x2C98FBBA,
+ 0x87BFCCD7, 0x2BDC4E6F,
+ 0x877B7BEC, 0x2B1F34EB,
+ 0x8738545E, 0x2A61B101,
+ 0x86F656D3, 0x29A3C484,
+ 0x86B583EE, 0x28E5714A,
+ 0x8675DC4E, 0x2826B928,
+ 0x86376092, 0x27679DF4,
+ 0x85FA1152, 0x26A82185,
+ 0x85BDEF27, 0x25E845B5,
+ 0x8582FAA4, 0x25280C5D,
+ 0x8549345C, 0x24677757,
+ 0x85109CDC, 0x23A6887E,
+ 0x84D934B0, 0x22E541AE,
+ 0x84A2FC62, 0x2223A4C5,
+ 0x846DF476, 0x2161B39F,
+ 0x843A1D70, 0x209F701C,
+ 0x840777CF, 0x1FDCDC1A,
+ 0x83D60411, 0x1F19F97B,
+ 0x83A5C2B0, 0x1E56CA1E,
+ 0x8376B422, 0x1D934FE5,
+ 0x8348D8DB, 0x1CCF8CB3,
+ 0x831C314E, 0x1C0B826A,
+ 0x82F0BDE8, 0x1B4732EF,
+ 0x82C67F13, 0x1A82A025,
+ 0x829D753A, 0x19BDCBF2,
+ 0x8275A0C0, 0x18F8B83C,
+ 0x824F0208, 0x183366E8,
+ 0x82299971, 0x176DD9DE,
+ 0x82056758, 0x16A81305,
+ 0x81E26C16, 0x15E21444,
+ 0x81C0A801, 0x151BDF85,
+ 0x81A01B6C, 0x145576B1,
+ 0x8180C6A9, 0x138EDBB0,
+ 0x8162AA03, 0x12C8106E,
+ 0x8145C5C6, 0x120116D4,
+ 0x812A1A39, 0x1139F0CE,
+ 0x810FA7A0, 0x1072A047,
+ 0x80F66E3C, 0x0FAB272B,
+ 0x80DE6E4C, 0x0EE38765,
+ 0x80C7A80A, 0x0E1BC2E3,
+ 0x80B21BAF, 0x0D53DB92,
+ 0x809DC970, 0x0C8BD35E,
+ 0x808AB180, 0x0BC3AC35,
+ 0x8078D40D, 0x0AFB6805,
+ 0x80683143, 0x0A3308BC,
+ 0x8058C94C, 0x096A9049,
+ 0x804A9C4D, 0x08A2009A,
+ 0x803DAA69, 0x07D95B9E,
+ 0x8031F3C1, 0x0710A344,
+ 0x80277872, 0x0647D97C,
+ 0x801E3894, 0x057F0034,
+ 0x80163440, 0x04B6195D,
+ 0x800F6B88, 0x03ED26E6,
+ 0x8009DE7D, 0x03242ABF,
+ 0x80058D2E, 0x025B26D7,
+ 0x800277A5, 0x01921D1F,
+ 0x80009DE9, 0x00C90F88,
+ 0x80000000, 0x00000000,
+ 0x80009DE9, 0xFF36F078,
+ 0x800277A5, 0xFE6DE2E0,
+ 0x80058D2E, 0xFDA4D928,
+ 0x8009DE7D, 0xFCDBD541,
+ 0x800F6B88, 0xFC12D919,
+ 0x80163440, 0xFB49E6A2,
+ 0x801E3894, 0xFA80FFCB,
+ 0x80277872, 0xF9B82683,
+ 0x8031F3C1, 0xF8EF5CBB,
+ 0x803DAA69, 0xF826A461,
+ 0x804A9C4D, 0xF75DFF65,
+ 0x8058C94C, 0xF6956FB6,
+ 0x80683143, 0xF5CCF743,
+ 0x8078D40D, 0xF50497FA,
+ 0x808AB180, 0xF43C53CA,
+ 0x809DC970, 0xF3742CA1,
+ 0x80B21BAF, 0xF2AC246D,
+ 0x80C7A80A, 0xF1E43D1C,
+ 0x80DE6E4C, 0xF11C789A,
+ 0x80F66E3C, 0xF054D8D4,
+ 0x810FA7A0, 0xEF8D5FB8,
+ 0x812A1A39, 0xEEC60F31,
+ 0x8145C5C6, 0xEDFEE92B,
+ 0x8162AA03, 0xED37EF91,
+ 0x8180C6A9, 0xEC71244F,
+ 0x81A01B6C, 0xEBAA894E,
+ 0x81C0A801, 0xEAE4207A,
+ 0x81E26C16, 0xEA1DEBBB,
+ 0x82056758, 0xE957ECFB,
+ 0x82299971, 0xE8922621,
+ 0x824F0208, 0xE7CC9917,
+ 0x8275A0C0, 0xE70747C3,
+ 0x829D753A, 0xE642340D,
+ 0x82C67F13, 0xE57D5FDA,
+ 0x82F0BDE8, 0xE4B8CD10,
+ 0x831C314E, 0xE3F47D95,
+ 0x8348D8DB, 0xE330734C,
+ 0x8376B422, 0xE26CB01A,
+ 0x83A5C2B0, 0xE1A935E1,
+ 0x83D60411, 0xE0E60684,
+ 0x840777CF, 0xE02323E5,
+ 0x843A1D70, 0xDF608FE3,
+ 0x846DF476, 0xDE9E4C60,
+ 0x84A2FC62, 0xDDDC5B3A,
+ 0x84D934B0, 0xDD1ABE51,
+ 0x85109CDC, 0xDC597781,
+ 0x8549345C, 0xDB9888A8,
+ 0x8582FAA4, 0xDAD7F3A2,
+ 0x85BDEF27, 0xDA17BA4A,
+ 0x85FA1152, 0xD957DE7A,
+ 0x86376092, 0xD898620C,
+ 0x8675DC4E, 0xD7D946D7,
+ 0x86B583EE, 0xD71A8EB5,
+ 0x86F656D3, 0xD65C3B7B,
+ 0x8738545E, 0xD59E4EFE,
+ 0x877B7BEC, 0xD4E0CB14,
+ 0x87BFCCD7, 0xD423B190,
+ 0x88054677, 0xD3670445,
+ 0x884BE820, 0xD2AAC504,
+ 0x8893B124, 0xD1EEF59E,
+ 0x88DCA0D3, 0xD13397E1,
+ 0x8926B677, 0xD078AD9D,
+ 0x8971F15A, 0xCFBE389F,
+ 0x89BE50C3, 0xCF043AB2,
+ 0x8A0BD3F5, 0xCE4AB5A2,
+ 0x8A5A7A30, 0xCD91AB38,
+ 0x8AAA42B4, 0xCCD91D3D,
+ 0x8AFB2CBA, 0xCC210D78,
+ 0x8B4D377C, 0xCB697DB0,
+ 0x8BA0622F, 0xCAB26FA9,
+ 0x8BF4AC05, 0xC9FBE527,
+ 0x8C4A142F, 0xC945DFEC,
+ 0x8CA099D9, 0xC89061BA,
+ 0x8CF83C30, 0xC7DB6C50,
+ 0x8D50FA59, 0xC727016C,
+ 0x8DAAD37B, 0xC67322CD,
+ 0x8E05C6B7, 0xC5BFD22E,
+ 0x8E61D32D, 0xC50D1148,
+ 0x8EBEF7FB, 0xC45AE1D7,
+ 0x8F1D343A, 0xC3A9458F,
+ 0x8F7C8701, 0xC2F83E2A,
+ 0x8FDCEF66, 0xC247CD5A,
+ 0x903E6C7A, 0xC197F4D3,
+ 0x90A0FD4E, 0xC0E8B648,
+ 0x9104A0ED, 0xC03A1368,
+ 0x91695663, 0xBF8C0DE2,
+ 0x91CF1CB6, 0xBEDEA765,
+ 0x9235F2EB, 0xBE31E19B,
+ 0x929DD805, 0xBD85BE2F,
+ 0x9306CB04, 0xBCDA3ECA,
+ 0x9370CAE4, 0xBC2F6513,
+ 0x93DBD69F, 0xBB8532AF,
+ 0x9447ED2F, 0xBADBA943,
+ 0x94B50D87, 0xBA32CA70,
+ 0x9523369B, 0xB98A97D8,
+ 0x9592675B, 0xB8E31319,
+ 0x96029EB5, 0xB83C3DD1,
+ 0x9673DB94, 0xB796199B,
+ 0x96E61CDF, 0xB6F0A811,
+ 0x9759617E, 0xB64BEACC,
+ 0x97CDA855, 0xB5A7E362,
+ 0x9842F043, 0xB5049368,
+ 0x98B93828, 0xB461FC70,
+ 0x99307EE0, 0xB3C0200C,
+ 0x99A8C344, 0xB31EFFCB,
+ 0x9A22042C, 0xB27E9D3B,
+ 0x9A9C406D, 0xB1DEF9E8,
+ 0x9B1776D9, 0xB140175B,
+ 0x9B93A640, 0xB0A1F71C,
+ 0x9C10CD70, 0xB0049AB2,
+ 0x9C8EEB33, 0xAF6803A1,
+ 0x9D0DFE53, 0xAECC336B,
+ 0x9D8E0596, 0xAE312B91,
+ 0x9E0EFFC1, 0xAD96ED91,
+ 0x9E90EB94, 0xACFD7AE8,
+ 0x9F13C7D0, 0xAC64D510,
+ 0x9F979331, 0xABCCFD82,
+ 0xA01C4C72, 0xAB35F5B5,
+ 0xA0A1F24C, 0xAA9FBF1D,
+ 0xA1288376, 0xAA0A5B2D,
+ 0xA1AFFEA2, 0xA975CB56,
+ 0xA2386283, 0xA8E21106,
+ 0xA2C1ADC9, 0xA84F2DA9,
+ 0xA34BDF20, 0xA7BD22AB,
+ 0xA3D6F533, 0xA72BF173,
+ 0xA462EEAC, 0xA69B9B68,
+ 0xA4EFCA31, 0xA60C21ED,
+ 0xA57D8666, 0xA57D8666,
+ 0xA60C21ED, 0xA4EFCA31,
+ 0xA69B9B68, 0xA462EEAC,
+ 0xA72BF173, 0xA3D6F533,
+ 0xA7BD22AB, 0xA34BDF20,
+ 0xA84F2DA9, 0xA2C1ADC9,
+ 0xA8E21106, 0xA2386283,
+ 0xA975CB56, 0xA1AFFEA2,
+ 0xAA0A5B2D, 0xA1288376,
+ 0xAA9FBF1D, 0xA0A1F24C,
+ 0xAB35F5B5, 0xA01C4C72,
+ 0xABCCFD82, 0x9F979331,
+ 0xAC64D510, 0x9F13C7D0,
+ 0xACFD7AE8, 0x9E90EB94,
+ 0xAD96ED91, 0x9E0EFFC1,
+ 0xAE312B91, 0x9D8E0596,
+ 0xAECC336B, 0x9D0DFE53,
+ 0xAF6803A1, 0x9C8EEB33,
+ 0xB0049AB2, 0x9C10CD70,
+ 0xB0A1F71C, 0x9B93A640,
+ 0xB140175B, 0x9B1776D9,
+ 0xB1DEF9E8, 0x9A9C406D,
+ 0xB27E9D3B, 0x9A22042C,
+ 0xB31EFFCB, 0x99A8C344,
+ 0xB3C0200C, 0x99307EE0,
+ 0xB461FC70, 0x98B93828,
+ 0xB5049368, 0x9842F043,
+ 0xB5A7E362, 0x97CDA855,
+ 0xB64BEACC, 0x9759617E,
+ 0xB6F0A811, 0x96E61CDF,
+ 0xB796199B, 0x9673DB94,
+ 0xB83C3DD1, 0x96029EB5,
+ 0xB8E31319, 0x9592675B,
+ 0xB98A97D8, 0x9523369B,
+ 0xBA32CA70, 0x94B50D87,
+ 0xBADBA943, 0x9447ED2F,
+ 0xBB8532AF, 0x93DBD69F,
+ 0xBC2F6513, 0x9370CAE4,
+ 0xBCDA3ECA, 0x9306CB04,
+ 0xBD85BE2F, 0x929DD805,
+ 0xBE31E19B, 0x9235F2EB,
+ 0xBEDEA765, 0x91CF1CB6,
+ 0xBF8C0DE2, 0x91695663,
+ 0xC03A1368, 0x9104A0ED,
+ 0xC0E8B648, 0x90A0FD4E,
+ 0xC197F4D3, 0x903E6C7A,
+ 0xC247CD5A, 0x8FDCEF66,
+ 0xC2F83E2A, 0x8F7C8701,
+ 0xC3A9458F, 0x8F1D343A,
+ 0xC45AE1D7, 0x8EBEF7FB,
+ 0xC50D1148, 0x8E61D32D,
+ 0xC5BFD22E, 0x8E05C6B7,
+ 0xC67322CD, 0x8DAAD37B,
+ 0xC727016C, 0x8D50FA59,
+ 0xC7DB6C50, 0x8CF83C30,
+ 0xC89061BA, 0x8CA099D9,
+ 0xC945DFEC, 0x8C4A142F,
+ 0xC9FBE527, 0x8BF4AC05,
+ 0xCAB26FA9, 0x8BA0622F,
+ 0xCB697DB0, 0x8B4D377C,
+ 0xCC210D78, 0x8AFB2CBA,
+ 0xCCD91D3D, 0x8AAA42B4,
+ 0xCD91AB38, 0x8A5A7A30,
+ 0xCE4AB5A2, 0x8A0BD3F5,
+ 0xCF043AB2, 0x89BE50C3,
+ 0xCFBE389F, 0x8971F15A,
+ 0xD078AD9D, 0x8926B677,
+ 0xD13397E1, 0x88DCA0D3,
+ 0xD1EEF59E, 0x8893B124,
+ 0xD2AAC504, 0x884BE820,
+ 0xD3670445, 0x88054677,
+ 0xD423B190, 0x87BFCCD7,
+ 0xD4E0CB14, 0x877B7BEC,
+ 0xD59E4EFE, 0x8738545E,
+ 0xD65C3B7B, 0x86F656D3,
+ 0xD71A8EB5, 0x86B583EE,
+ 0xD7D946D7, 0x8675DC4E,
+ 0xD898620C, 0x86376092,
+ 0xD957DE7A, 0x85FA1152,
+ 0xDA17BA4A, 0x85BDEF27,
+ 0xDAD7F3A2, 0x8582FAA4,
+ 0xDB9888A8, 0x8549345C,
+ 0xDC597781, 0x85109CDC,
+ 0xDD1ABE51, 0x84D934B0,
+ 0xDDDC5B3A, 0x84A2FC62,
+ 0xDE9E4C60, 0x846DF476,
+ 0xDF608FE3, 0x843A1D70,
+ 0xE02323E5, 0x840777CF,
+ 0xE0E60684, 0x83D60411,
+ 0xE1A935E1, 0x83A5C2B0,
+ 0xE26CB01A, 0x8376B422,
+ 0xE330734C, 0x8348D8DB,
+ 0xE3F47D95, 0x831C314E,
+ 0xE4B8CD10, 0x82F0BDE8,
+ 0xE57D5FDA, 0x82C67F13,
+ 0xE642340D, 0x829D753A,
+ 0xE70747C3, 0x8275A0C0,
+ 0xE7CC9917, 0x824F0208,
+ 0xE8922621, 0x82299971,
+ 0xE957ECFB, 0x82056758,
+ 0xEA1DEBBB, 0x81E26C16,
+ 0xEAE4207A, 0x81C0A801,
+ 0xEBAA894E, 0x81A01B6C,
+ 0xEC71244F, 0x8180C6A9,
+ 0xED37EF91, 0x8162AA03,
+ 0xEDFEE92B, 0x8145C5C6,
+ 0xEEC60F31, 0x812A1A39,
+ 0xEF8D5FB8, 0x810FA7A0,
+ 0xF054D8D4, 0x80F66E3C,
+ 0xF11C789A, 0x80DE6E4C,
+ 0xF1E43D1C, 0x80C7A80A,
+ 0xF2AC246D, 0x80B21BAF,
+ 0xF3742CA1, 0x809DC970,
+ 0xF43C53CA, 0x808AB180,
+ 0xF50497FA, 0x8078D40D,
+ 0xF5CCF743, 0x80683143,
+ 0xF6956FB6, 0x8058C94C,
+ 0xF75DFF65, 0x804A9C4D,
+ 0xF826A461, 0x803DAA69,
+ 0xF8EF5CBB, 0x8031F3C1,
+ 0xF9B82683, 0x80277872,
+ 0xFA80FFCB, 0x801E3894,
+ 0xFB49E6A2, 0x80163440,
+ 0xFC12D919, 0x800F6B88,
+ 0xFCDBD541, 0x8009DE7D,
+ 0xFDA4D928, 0x80058D2E,
+ 0xFE6DE2E0, 0x800277A5,
+ 0xFF36F078, 0x80009DE9
+};
+
+/**
+* \par
+* Example code for Q31 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 2048 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to Q31(Fixed point 1.31):
+* round(twiddleCoefQ31(i) * pow(2, 31))
+*
+*/
+const q31_t twiddleCoef_2048_q31[3072] = {
+ 0x7FFFFFFF, 0x00000000,
+ 0x7FFFD885, 0x006487E3,
+ 0x7FFF6216, 0x00C90F88,
+ 0x7FFE9CB2, 0x012D96B0,
+ 0x7FFD885A, 0x01921D1F,
+ 0x7FFC250F, 0x01F6A296,
+ 0x7FFA72D1, 0x025B26D7,
+ 0x7FF871A1, 0x02BFA9A4,
+ 0x7FF62182, 0x03242ABF,
+ 0x7FF38273, 0x0388A9E9,
+ 0x7FF09477, 0x03ED26E6,
+ 0x7FED5790, 0x0451A176,
+ 0x7FE9CBC0, 0x04B6195D,
+ 0x7FE5F108, 0x051A8E5C,
+ 0x7FE1C76B, 0x057F0034,
+ 0x7FDD4EEC, 0x05E36EA9,
+ 0x7FD8878D, 0x0647D97C,
+ 0x7FD37152, 0x06AC406F,
+ 0x7FCE0C3E, 0x0710A344,
+ 0x7FC85853, 0x077501BE,
+ 0x7FC25596, 0x07D95B9E,
+ 0x7FBC040A, 0x083DB0A7,
+ 0x7FB563B2, 0x08A2009A,
+ 0x7FAE7494, 0x09064B3A,
+ 0x7FA736B4, 0x096A9049,
+ 0x7F9FAA15, 0x09CECF89,
+ 0x7F97CEBC, 0x0A3308BC,
+ 0x7F8FA4AF, 0x0A973BA5,
+ 0x7F872BF3, 0x0AFB6805,
+ 0x7F7E648B, 0x0B5F8D9F,
+ 0x7F754E7F, 0x0BC3AC35,
+ 0x7F6BE9D4, 0x0C27C389,
+ 0x7F62368F, 0x0C8BD35E,
+ 0x7F5834B6, 0x0CEFDB75,
+ 0x7F4DE450, 0x0D53DB92,
+ 0x7F434563, 0x0DB7D376,
+ 0x7F3857F5, 0x0E1BC2E3,
+ 0x7F2D1C0E, 0x0E7FA99D,
+ 0x7F2191B4, 0x0EE38765,
+ 0x7F15B8EE, 0x0F475BFE,
+ 0x7F0991C3, 0x0FAB272B,
+ 0x7EFD1C3C, 0x100EE8AD,
+ 0x7EF0585F, 0x1072A047,
+ 0x7EE34635, 0x10D64DBC,
+ 0x7ED5E5C6, 0x1139F0CE,
+ 0x7EC8371A, 0x119D8940,
+ 0x7EBA3A39, 0x120116D4,
+ 0x7EABEF2C, 0x1264994E,
+ 0x7E9D55FC, 0x12C8106E,
+ 0x7E8E6EB1, 0x132B7BF9,
+ 0x7E7F3956, 0x138EDBB0,
+ 0x7E6FB5F3, 0x13F22F57,
+ 0x7E5FE493, 0x145576B1,
+ 0x7E4FC53E, 0x14B8B17F,
+ 0x7E3F57FE, 0x151BDF85,
+ 0x7E2E9CDF, 0x157F0086,
+ 0x7E1D93E9, 0x15E21444,
+ 0x7E0C3D29, 0x16451A83,
+ 0x7DFA98A7, 0x16A81305,
+ 0x7DE8A670, 0x170AFD8D,
+ 0x7DD6668E, 0x176DD9DE,
+ 0x7DC3D90D, 0x17D0A7BB,
+ 0x7DB0FDF7, 0x183366E8,
+ 0x7D9DD55A, 0x18961727,
+ 0x7D8A5F3F, 0x18F8B83C,
+ 0x7D769BB5, 0x195B49E9,
+ 0x7D628AC5, 0x19BDCBF2,
+ 0x7D4E2C7E, 0x1A203E1B,
+ 0x7D3980EC, 0x1A82A025,
+ 0x7D24881A, 0x1AE4F1D6,
+ 0x7D0F4218, 0x1B4732EF,
+ 0x7CF9AEF0, 0x1BA96334,
+ 0x7CE3CEB1, 0x1C0B826A,
+ 0x7CCDA168, 0x1C6D9053,
+ 0x7CB72724, 0x1CCF8CB3,
+ 0x7CA05FF1, 0x1D31774D,
+ 0x7C894BDD, 0x1D934FE5,
+ 0x7C71EAF8, 0x1DF5163F,
+ 0x7C5A3D4F, 0x1E56CA1E,
+ 0x7C4242F2, 0x1EB86B46,
+ 0x7C29FBEE, 0x1F19F97B,
+ 0x7C116853, 0x1F7B7480,
+ 0x7BF88830, 0x1FDCDC1A,
+ 0x7BDF5B94, 0x203E300D,
+ 0x7BC5E28F, 0x209F701C,
+ 0x7BAC1D31, 0x21009C0B,
+ 0x7B920B89, 0x2161B39F,
+ 0x7B77ADA8, 0x21C2B69C,
+ 0x7B5D039D, 0x2223A4C5,
+ 0x7B420D7A, 0x22847DDF,
+ 0x7B26CB4F, 0x22E541AE,
+ 0x7B0B3D2C, 0x2345EFF7,
+ 0x7AEF6323, 0x23A6887E,
+ 0x7AD33D45, 0x24070B07,
+ 0x7AB6CBA3, 0x24677757,
+ 0x7A9A0E4F, 0x24C7CD32,
+ 0x7A7D055B, 0x25280C5D,
+ 0x7A5FB0D8, 0x2588349D,
+ 0x7A4210D8, 0x25E845B5,
+ 0x7A24256E, 0x26483F6C,
+ 0x7A05EEAD, 0x26A82185,
+ 0x79E76CA6, 0x2707EBC6,
+ 0x79C89F6D, 0x27679DF4,
+ 0x79A98715, 0x27C737D2,
+ 0x798A23B1, 0x2826B928,
+ 0x796A7554, 0x288621B9,
+ 0x794A7C11, 0x28E5714A,
+ 0x792A37FE, 0x2944A7A2,
+ 0x7909A92C, 0x29A3C484,
+ 0x78E8CFB1, 0x2A02C7B8,
+ 0x78C7ABA1, 0x2A61B101,
+ 0x78A63D10, 0x2AC08025,
+ 0x78848413, 0x2B1F34EB,
+ 0x786280BF, 0x2B7DCF17,
+ 0x78403328, 0x2BDC4E6F,
+ 0x781D9B64, 0x2C3AB2B9,
+ 0x77FAB988, 0x2C98FBBA,
+ 0x77D78DAA, 0x2CF72939,
+ 0x77B417DF, 0x2D553AFB,
+ 0x7790583D, 0x2DB330C7,
+ 0x776C4EDB, 0x2E110A62,
+ 0x7747FBCE, 0x2E6EC792,
+ 0x77235F2D, 0x2ECC681E,
+ 0x76FE790E, 0x2F29EBCC,
+ 0x76D94988, 0x2F875262,
+ 0x76B3D0B3, 0x2FE49BA6,
+ 0x768E0EA5, 0x3041C760,
+ 0x76680376, 0x309ED555,
+ 0x7641AF3C, 0x30FBC54D,
+ 0x761B1211, 0x3158970D,
+ 0x75F42C0A, 0x31B54A5D,
+ 0x75CCFD42, 0x3211DF03,
+ 0x75A585CF, 0x326E54C7,
+ 0x757DC5CA, 0x32CAAB6F,
+ 0x7555BD4B, 0x3326E2C2,
+ 0x752D6C6C, 0x3382FA88,
+ 0x7504D345, 0x33DEF287,
+ 0x74DBF1EF, 0x343ACA87,
+ 0x74B2C883, 0x3496824F,
+ 0x7489571B, 0x34F219A7,
+ 0x745F9DD1, 0x354D9056,
+ 0x74359CBD, 0x35A8E624,
+ 0x740B53FA, 0x36041AD9,
+ 0x73E0C3A3, 0x365F2E3B,
+ 0x73B5EBD0, 0x36BA2013,
+ 0x738ACC9E, 0x3714F02A,
+ 0x735F6626, 0x376F9E46,
+ 0x7333B883, 0x37CA2A30,
+ 0x7307C3D0, 0x382493B0,
+ 0x72DB8828, 0x387EDA8E,
+ 0x72AF05A6, 0x38D8FE93,
+ 0x72823C66, 0x3932FF87,
+ 0x72552C84, 0x398CDD32,
+ 0x7227D61C, 0x39E6975D,
+ 0x71FA3948, 0x3A402DD1,
+ 0x71CC5626, 0x3A99A057,
+ 0x719E2CD2, 0x3AF2EEB7,
+ 0x716FBD68, 0x3B4C18BA,
+ 0x71410804, 0x3BA51E29,
+ 0x71120CC5, 0x3BFDFECD,
+ 0x70E2CBC6, 0x3C56BA70,
+ 0x70B34524, 0x3CAF50DA,
+ 0x708378FE, 0x3D07C1D5,
+ 0x70536771, 0x3D600D2B,
+ 0x70231099, 0x3DB832A5,
+ 0x6FF27496, 0x3E10320D,
+ 0x6FC19385, 0x3E680B2C,
+ 0x6F906D84, 0x3EBFBDCC,
+ 0x6F5F02B1, 0x3F1749B7,
+ 0x6F2D532C, 0x3F6EAEB8,
+ 0x6EFB5F12, 0x3FC5EC97,
+ 0x6EC92682, 0x401D0320,
+ 0x6E96A99C, 0x4073F21D,
+ 0x6E63E87F, 0x40CAB957,
+ 0x6E30E349, 0x4121589A,
+ 0x6DFD9A1B, 0x4177CFB0,
+ 0x6DCA0D14, 0x41CE1E64,
+ 0x6D963C54, 0x42244480,
+ 0x6D6227FA, 0x427A41D0,
+ 0x6D2DD027, 0x42D0161E,
+ 0x6CF934FB, 0x4325C135,
+ 0x6CC45697, 0x437B42E1,
+ 0x6C8F351C, 0x43D09AEC,
+ 0x6C59D0A9, 0x4425C923,
+ 0x6C242960, 0x447ACD50,
+ 0x6BEE3F62, 0x44CFA73F,
+ 0x6BB812D0, 0x452456BC,
+ 0x6B81A3CD, 0x4578DB93,
+ 0x6B4AF278, 0x45CD358F,
+ 0x6B13FEF5, 0x4621647C,
+ 0x6ADCC964, 0x46756827,
+ 0x6AA551E8, 0x46C9405C,
+ 0x6A6D98A4, 0x471CECE6,
+ 0x6A359DB9, 0x47706D93,
+ 0x69FD614A, 0x47C3C22E,
+ 0x69C4E37A, 0x4816EA85,
+ 0x698C246C, 0x4869E664,
+ 0x69532442, 0x48BCB598,
+ 0x6919E320, 0x490F57EE,
+ 0x68E06129, 0x4961CD32,
+ 0x68A69E81, 0x49B41533,
+ 0x686C9B4B, 0x4A062FBD,
+ 0x683257AA, 0x4A581C9D,
+ 0x67F7D3C4, 0x4AA9DBA1,
+ 0x67BD0FBC, 0x4AFB6C97,
+ 0x67820BB6, 0x4B4CCF4D,
+ 0x6746C7D7, 0x4B9E038F,
+ 0x670B4443, 0x4BEF092D,
+ 0x66CF811F, 0x4C3FDFF3,
+ 0x66937E90, 0x4C9087B1,
+ 0x66573CBB, 0x4CE10034,
+ 0x661ABBC5, 0x4D31494B,
+ 0x65DDFBD3, 0x4D8162C4,
+ 0x65A0FD0B, 0x4DD14C6E,
+ 0x6563BF92, 0x4E210617,
+ 0x6526438E, 0x4E708F8F,
+ 0x64E88926, 0x4EBFE8A4,
+ 0x64AA907F, 0x4F0F1126,
+ 0x646C59BF, 0x4F5E08E3,
+ 0x642DE50D, 0x4FACCFAB,
+ 0x63EF328F, 0x4FFB654D,
+ 0x63B0426D, 0x5049C999,
+ 0x637114CC, 0x5097FC5E,
+ 0x6331A9D4, 0x50E5FD6C,
+ 0x62F201AC, 0x5133CC94,
+ 0x62B21C7B, 0x518169A4,
+ 0x6271FA69, 0x51CED46E,
+ 0x62319B9D, 0x521C0CC1,
+ 0x61F1003E, 0x5269126E,
+ 0x61B02876, 0x52B5E545,
+ 0x616F146B, 0x53028517,
+ 0x612DC446, 0x534EF1B5,
+ 0x60EC3830, 0x539B2AEF,
+ 0x60AA704F, 0x53E73097,
+ 0x60686CCE, 0x5433027D,
+ 0x60262DD5, 0x547EA073,
+ 0x5FE3B38D, 0x54CA0A4A,
+ 0x5FA0FE1E, 0x55153FD4,
+ 0x5F5E0DB3, 0x556040E2,
+ 0x5F1AE273, 0x55AB0D46,
+ 0x5ED77C89, 0x55F5A4D2,
+ 0x5E93DC1F, 0x56400757,
+ 0x5E50015D, 0x568A34A9,
+ 0x5E0BEC6E, 0x56D42C99,
+ 0x5DC79D7C, 0x571DEEF9,
+ 0x5D8314B0, 0x57677B9D,
+ 0x5D3E5236, 0x57B0D256,
+ 0x5CF95638, 0x57F9F2F7,
+ 0x5CB420DF, 0x5842DD54,
+ 0x5C6EB258, 0x588B913F,
+ 0x5C290ACC, 0x58D40E8C,
+ 0x5BE32A67, 0x591C550E,
+ 0x5B9D1153, 0x59646497,
+ 0x5B56BFBD, 0x59AC3CFD,
+ 0x5B1035CF, 0x59F3DE12,
+ 0x5AC973B4, 0x5A3B47AA,
+ 0x5A82799A, 0x5A82799A,
+ 0x5A3B47AA, 0x5AC973B4,
+ 0x59F3DE12, 0x5B1035CF,
+ 0x59AC3CFD, 0x5B56BFBD,
+ 0x59646497, 0x5B9D1153,
+ 0x591C550E, 0x5BE32A67,
+ 0x58D40E8C, 0x5C290ACC,
+ 0x588B913F, 0x5C6EB258,
+ 0x5842DD54, 0x5CB420DF,
+ 0x57F9F2F7, 0x5CF95638,
+ 0x57B0D256, 0x5D3E5236,
+ 0x57677B9D, 0x5D8314B0,
+ 0x571DEEF9, 0x5DC79D7C,
+ 0x56D42C99, 0x5E0BEC6E,
+ 0x568A34A9, 0x5E50015D,
+ 0x56400757, 0x5E93DC1F,
+ 0x55F5A4D2, 0x5ED77C89,
+ 0x55AB0D46, 0x5F1AE273,
+ 0x556040E2, 0x5F5E0DB3,
+ 0x55153FD4, 0x5FA0FE1E,
+ 0x54CA0A4A, 0x5FE3B38D,
+ 0x547EA073, 0x60262DD5,
+ 0x5433027D, 0x60686CCE,
+ 0x53E73097, 0x60AA704F,
+ 0x539B2AEF, 0x60EC3830,
+ 0x534EF1B5, 0x612DC446,
+ 0x53028517, 0x616F146B,
+ 0x52B5E545, 0x61B02876,
+ 0x5269126E, 0x61F1003E,
+ 0x521C0CC1, 0x62319B9D,
+ 0x51CED46E, 0x6271FA69,
+ 0x518169A4, 0x62B21C7B,
+ 0x5133CC94, 0x62F201AC,
+ 0x50E5FD6C, 0x6331A9D4,
+ 0x5097FC5E, 0x637114CC,
+ 0x5049C999, 0x63B0426D,
+ 0x4FFB654D, 0x63EF328F,
+ 0x4FACCFAB, 0x642DE50D,
+ 0x4F5E08E3, 0x646C59BF,
+ 0x4F0F1126, 0x64AA907F,
+ 0x4EBFE8A4, 0x64E88926,
+ 0x4E708F8F, 0x6526438E,
+ 0x4E210617, 0x6563BF92,
+ 0x4DD14C6E, 0x65A0FD0B,
+ 0x4D8162C4, 0x65DDFBD3,
+ 0x4D31494B, 0x661ABBC5,
+ 0x4CE10034, 0x66573CBB,
+ 0x4C9087B1, 0x66937E90,
+ 0x4C3FDFF3, 0x66CF811F,
+ 0x4BEF092D, 0x670B4443,
+ 0x4B9E038F, 0x6746C7D7,
+ 0x4B4CCF4D, 0x67820BB6,
+ 0x4AFB6C97, 0x67BD0FBC,
+ 0x4AA9DBA1, 0x67F7D3C4,
+ 0x4A581C9D, 0x683257AA,
+ 0x4A062FBD, 0x686C9B4B,
+ 0x49B41533, 0x68A69E81,
+ 0x4961CD32, 0x68E06129,
+ 0x490F57EE, 0x6919E320,
+ 0x48BCB598, 0x69532442,
+ 0x4869E664, 0x698C246C,
+ 0x4816EA85, 0x69C4E37A,
+ 0x47C3C22E, 0x69FD614A,
+ 0x47706D93, 0x6A359DB9,
+ 0x471CECE6, 0x6A6D98A4,
+ 0x46C9405C, 0x6AA551E8,
+ 0x46756827, 0x6ADCC964,
+ 0x4621647C, 0x6B13FEF5,
+ 0x45CD358F, 0x6B4AF278,
+ 0x4578DB93, 0x6B81A3CD,
+ 0x452456BC, 0x6BB812D0,
+ 0x44CFA73F, 0x6BEE3F62,
+ 0x447ACD50, 0x6C242960,
+ 0x4425C923, 0x6C59D0A9,
+ 0x43D09AEC, 0x6C8F351C,
+ 0x437B42E1, 0x6CC45697,
+ 0x4325C135, 0x6CF934FB,
+ 0x42D0161E, 0x6D2DD027,
+ 0x427A41D0, 0x6D6227FA,
+ 0x42244480, 0x6D963C54,
+ 0x41CE1E64, 0x6DCA0D14,
+ 0x4177CFB0, 0x6DFD9A1B,
+ 0x4121589A, 0x6E30E349,
+ 0x40CAB957, 0x6E63E87F,
+ 0x4073F21D, 0x6E96A99C,
+ 0x401D0320, 0x6EC92682,
+ 0x3FC5EC97, 0x6EFB5F12,
+ 0x3F6EAEB8, 0x6F2D532C,
+ 0x3F1749B7, 0x6F5F02B1,
+ 0x3EBFBDCC, 0x6F906D84,
+ 0x3E680B2C, 0x6FC19385,
+ 0x3E10320D, 0x6FF27496,
+ 0x3DB832A5, 0x70231099,
+ 0x3D600D2B, 0x70536771,
+ 0x3D07C1D5, 0x708378FE,
+ 0x3CAF50DA, 0x70B34524,
+ 0x3C56BA70, 0x70E2CBC6,
+ 0x3BFDFECD, 0x71120CC5,
+ 0x3BA51E29, 0x71410804,
+ 0x3B4C18BA, 0x716FBD68,
+ 0x3AF2EEB7, 0x719E2CD2,
+ 0x3A99A057, 0x71CC5626,
+ 0x3A402DD1, 0x71FA3948,
+ 0x39E6975D, 0x7227D61C,
+ 0x398CDD32, 0x72552C84,
+ 0x3932FF87, 0x72823C66,
+ 0x38D8FE93, 0x72AF05A6,
+ 0x387EDA8E, 0x72DB8828,
+ 0x382493B0, 0x7307C3D0,
+ 0x37CA2A30, 0x7333B883,
+ 0x376F9E46, 0x735F6626,
+ 0x3714F02A, 0x738ACC9E,
+ 0x36BA2013, 0x73B5EBD0,
+ 0x365F2E3B, 0x73E0C3A3,
+ 0x36041AD9, 0x740B53FA,
+ 0x35A8E624, 0x74359CBD,
+ 0x354D9056, 0x745F9DD1,
+ 0x34F219A7, 0x7489571B,
+ 0x3496824F, 0x74B2C883,
+ 0x343ACA87, 0x74DBF1EF,
+ 0x33DEF287, 0x7504D345,
+ 0x3382FA88, 0x752D6C6C,
+ 0x3326E2C2, 0x7555BD4B,
+ 0x32CAAB6F, 0x757DC5CA,
+ 0x326E54C7, 0x75A585CF,
+ 0x3211DF03, 0x75CCFD42,
+ 0x31B54A5D, 0x75F42C0A,
+ 0x3158970D, 0x761B1211,
+ 0x30FBC54D, 0x7641AF3C,
+ 0x309ED555, 0x76680376,
+ 0x3041C760, 0x768E0EA5,
+ 0x2FE49BA6, 0x76B3D0B3,
+ 0x2F875262, 0x76D94988,
+ 0x2F29EBCC, 0x76FE790E,
+ 0x2ECC681E, 0x77235F2D,
+ 0x2E6EC792, 0x7747FBCE,
+ 0x2E110A62, 0x776C4EDB,
+ 0x2DB330C7, 0x7790583D,
+ 0x2D553AFB, 0x77B417DF,
+ 0x2CF72939, 0x77D78DAA,
+ 0x2C98FBBA, 0x77FAB988,
+ 0x2C3AB2B9, 0x781D9B64,
+ 0x2BDC4E6F, 0x78403328,
+ 0x2B7DCF17, 0x786280BF,
+ 0x2B1F34EB, 0x78848413,
+ 0x2AC08025, 0x78A63D10,
+ 0x2A61B101, 0x78C7ABA1,
+ 0x2A02C7B8, 0x78E8CFB1,
+ 0x29A3C484, 0x7909A92C,
+ 0x2944A7A2, 0x792A37FE,
+ 0x28E5714A, 0x794A7C11,
+ 0x288621B9, 0x796A7554,
+ 0x2826B928, 0x798A23B1,
+ 0x27C737D2, 0x79A98715,
+ 0x27679DF4, 0x79C89F6D,
+ 0x2707EBC6, 0x79E76CA6,
+ 0x26A82185, 0x7A05EEAD,
+ 0x26483F6C, 0x7A24256E,
+ 0x25E845B5, 0x7A4210D8,
+ 0x2588349D, 0x7A5FB0D8,
+ 0x25280C5D, 0x7A7D055B,
+ 0x24C7CD32, 0x7A9A0E4F,
+ 0x24677757, 0x7AB6CBA3,
+ 0x24070B07, 0x7AD33D45,
+ 0x23A6887E, 0x7AEF6323,
+ 0x2345EFF7, 0x7B0B3D2C,
+ 0x22E541AE, 0x7B26CB4F,
+ 0x22847DDF, 0x7B420D7A,
+ 0x2223A4C5, 0x7B5D039D,
+ 0x21C2B69C, 0x7B77ADA8,
+ 0x2161B39F, 0x7B920B89,
+ 0x21009C0B, 0x7BAC1D31,
+ 0x209F701C, 0x7BC5E28F,
+ 0x203E300D, 0x7BDF5B94,
+ 0x1FDCDC1A, 0x7BF88830,
+ 0x1F7B7480, 0x7C116853,
+ 0x1F19F97B, 0x7C29FBEE,
+ 0x1EB86B46, 0x7C4242F2,
+ 0x1E56CA1E, 0x7C5A3D4F,
+ 0x1DF5163F, 0x7C71EAF8,
+ 0x1D934FE5, 0x7C894BDD,
+ 0x1D31774D, 0x7CA05FF1,
+ 0x1CCF8CB3, 0x7CB72724,
+ 0x1C6D9053, 0x7CCDA168,
+ 0x1C0B826A, 0x7CE3CEB1,
+ 0x1BA96334, 0x7CF9AEF0,
+ 0x1B4732EF, 0x7D0F4218,
+ 0x1AE4F1D6, 0x7D24881A,
+ 0x1A82A025, 0x7D3980EC,
+ 0x1A203E1B, 0x7D4E2C7E,
+ 0x19BDCBF2, 0x7D628AC5,
+ 0x195B49E9, 0x7D769BB5,
+ 0x18F8B83C, 0x7D8A5F3F,
+ 0x18961727, 0x7D9DD55A,
+ 0x183366E8, 0x7DB0FDF7,
+ 0x17D0A7BB, 0x7DC3D90D,
+ 0x176DD9DE, 0x7DD6668E,
+ 0x170AFD8D, 0x7DE8A670,
+ 0x16A81305, 0x7DFA98A7,
+ 0x16451A83, 0x7E0C3D29,
+ 0x15E21444, 0x7E1D93E9,
+ 0x157F0086, 0x7E2E9CDF,
+ 0x151BDF85, 0x7E3F57FE,
+ 0x14B8B17F, 0x7E4FC53E,
+ 0x145576B1, 0x7E5FE493,
+ 0x13F22F57, 0x7E6FB5F3,
+ 0x138EDBB0, 0x7E7F3956,
+ 0x132B7BF9, 0x7E8E6EB1,
+ 0x12C8106E, 0x7E9D55FC,
+ 0x1264994E, 0x7EABEF2C,
+ 0x120116D4, 0x7EBA3A39,
+ 0x119D8940, 0x7EC8371A,
+ 0x1139F0CE, 0x7ED5E5C6,
+ 0x10D64DBC, 0x7EE34635,
+ 0x1072A047, 0x7EF0585F,
+ 0x100EE8AD, 0x7EFD1C3C,
+ 0x0FAB272B, 0x7F0991C3,
+ 0x0F475BFE, 0x7F15B8EE,
+ 0x0EE38765, 0x7F2191B4,
+ 0x0E7FA99D, 0x7F2D1C0E,
+ 0x0E1BC2E3, 0x7F3857F5,
+ 0x0DB7D376, 0x7F434563,
+ 0x0D53DB92, 0x7F4DE450,
+ 0x0CEFDB75, 0x7F5834B6,
+ 0x0C8BD35E, 0x7F62368F,
+ 0x0C27C389, 0x7F6BE9D4,
+ 0x0BC3AC35, 0x7F754E7F,
+ 0x0B5F8D9F, 0x7F7E648B,
+ 0x0AFB6805, 0x7F872BF3,
+ 0x0A973BA5, 0x7F8FA4AF,
+ 0x0A3308BC, 0x7F97CEBC,
+ 0x09CECF89, 0x7F9FAA15,
+ 0x096A9049, 0x7FA736B4,
+ 0x09064B3A, 0x7FAE7494,
+ 0x08A2009A, 0x7FB563B2,
+ 0x083DB0A7, 0x7FBC040A,
+ 0x07D95B9E, 0x7FC25596,
+ 0x077501BE, 0x7FC85853,
+ 0x0710A344, 0x7FCE0C3E,
+ 0x06AC406F, 0x7FD37152,
+ 0x0647D97C, 0x7FD8878D,
+ 0x05E36EA9, 0x7FDD4EEC,
+ 0x057F0034, 0x7FE1C76B,
+ 0x051A8E5C, 0x7FE5F108,
+ 0x04B6195D, 0x7FE9CBC0,
+ 0x0451A176, 0x7FED5790,
+ 0x03ED26E6, 0x7FF09477,
+ 0x0388A9E9, 0x7FF38273,
+ 0x03242ABF, 0x7FF62182,
+ 0x02BFA9A4, 0x7FF871A1,
+ 0x025B26D7, 0x7FFA72D1,
+ 0x01F6A296, 0x7FFC250F,
+ 0x01921D1F, 0x7FFD885A,
+ 0x012D96B0, 0x7FFE9CB2,
+ 0x00C90F88, 0x7FFF6216,
+ 0x006487E3, 0x7FFFD885,
+ 0x00000000, 0x7FFFFFFF,
+ 0xFF9B781D, 0x7FFFD885,
+ 0xFF36F078, 0x7FFF6216,
+ 0xFED2694F, 0x7FFE9CB2,
+ 0xFE6DE2E0, 0x7FFD885A,
+ 0xFE095D69, 0x7FFC250F,
+ 0xFDA4D928, 0x7FFA72D1,
+ 0xFD40565B, 0x7FF871A1,
+ 0xFCDBD541, 0x7FF62182,
+ 0xFC775616, 0x7FF38273,
+ 0xFC12D919, 0x7FF09477,
+ 0xFBAE5E89, 0x7FED5790,
+ 0xFB49E6A2, 0x7FE9CBC0,
+ 0xFAE571A4, 0x7FE5F108,
+ 0xFA80FFCB, 0x7FE1C76B,
+ 0xFA1C9156, 0x7FDD4EEC,
+ 0xF9B82683, 0x7FD8878D,
+ 0xF953BF90, 0x7FD37152,
+ 0xF8EF5CBB, 0x7FCE0C3E,
+ 0xF88AFE41, 0x7FC85853,
+ 0xF826A461, 0x7FC25596,
+ 0xF7C24F58, 0x7FBC040A,
+ 0xF75DFF65, 0x7FB563B2,
+ 0xF6F9B4C5, 0x7FAE7494,
+ 0xF6956FB6, 0x7FA736B4,
+ 0xF6313076, 0x7F9FAA15,
+ 0xF5CCF743, 0x7F97CEBC,
+ 0xF568C45A, 0x7F8FA4AF,
+ 0xF50497FA, 0x7F872BF3,
+ 0xF4A07260, 0x7F7E648B,
+ 0xF43C53CA, 0x7F754E7F,
+ 0xF3D83C76, 0x7F6BE9D4,
+ 0xF3742CA1, 0x7F62368F,
+ 0xF310248A, 0x7F5834B6,
+ 0xF2AC246D, 0x7F4DE450,
+ 0xF2482C89, 0x7F434563,
+ 0xF1E43D1C, 0x7F3857F5,
+ 0xF1805662, 0x7F2D1C0E,
+ 0xF11C789A, 0x7F2191B4,
+ 0xF0B8A401, 0x7F15B8EE,
+ 0xF054D8D4, 0x7F0991C3,
+ 0xEFF11752, 0x7EFD1C3C,
+ 0xEF8D5FB8, 0x7EF0585F,
+ 0xEF29B243, 0x7EE34635,
+ 0xEEC60F31, 0x7ED5E5C6,
+ 0xEE6276BF, 0x7EC8371A,
+ 0xEDFEE92B, 0x7EBA3A39,
+ 0xED9B66B2, 0x7EABEF2C,
+ 0xED37EF91, 0x7E9D55FC,
+ 0xECD48406, 0x7E8E6EB1,
+ 0xEC71244F, 0x7E7F3956,
+ 0xEC0DD0A8, 0x7E6FB5F3,
+ 0xEBAA894E, 0x7E5FE493,
+ 0xEB474E80, 0x7E4FC53E,
+ 0xEAE4207A, 0x7E3F57FE,
+ 0xEA80FF79, 0x7E2E9CDF,
+ 0xEA1DEBBB, 0x7E1D93E9,
+ 0xE9BAE57C, 0x7E0C3D29,
+ 0xE957ECFB, 0x7DFA98A7,
+ 0xE8F50273, 0x7DE8A670,
+ 0xE8922621, 0x7DD6668E,
+ 0xE82F5844, 0x7DC3D90D,
+ 0xE7CC9917, 0x7DB0FDF7,
+ 0xE769E8D8, 0x7D9DD55A,
+ 0xE70747C3, 0x7D8A5F3F,
+ 0xE6A4B616, 0x7D769BB5,
+ 0xE642340D, 0x7D628AC5,
+ 0xE5DFC1E4, 0x7D4E2C7E,
+ 0xE57D5FDA, 0x7D3980EC,
+ 0xE51B0E2A, 0x7D24881A,
+ 0xE4B8CD10, 0x7D0F4218,
+ 0xE4569CCB, 0x7CF9AEF0,
+ 0xE3F47D95, 0x7CE3CEB1,
+ 0xE3926FAC, 0x7CCDA168,
+ 0xE330734C, 0x7CB72724,
+ 0xE2CE88B2, 0x7CA05FF1,
+ 0xE26CB01A, 0x7C894BDD,
+ 0xE20AE9C1, 0x7C71EAF8,
+ 0xE1A935E1, 0x7C5A3D4F,
+ 0xE14794B9, 0x7C4242F2,
+ 0xE0E60684, 0x7C29FBEE,
+ 0xE0848B7F, 0x7C116853,
+ 0xE02323E5, 0x7BF88830,
+ 0xDFC1CFF2, 0x7BDF5B94,
+ 0xDF608FE3, 0x7BC5E28F,
+ 0xDEFF63F4, 0x7BAC1D31,
+ 0xDE9E4C60, 0x7B920B89,
+ 0xDE3D4963, 0x7B77ADA8,
+ 0xDDDC5B3A, 0x7B5D039D,
+ 0xDD7B8220, 0x7B420D7A,
+ 0xDD1ABE51, 0x7B26CB4F,
+ 0xDCBA1008, 0x7B0B3D2C,
+ 0xDC597781, 0x7AEF6323,
+ 0xDBF8F4F8, 0x7AD33D45,
+ 0xDB9888A8, 0x7AB6CBA3,
+ 0xDB3832CD, 0x7A9A0E4F,
+ 0xDAD7F3A2, 0x7A7D055B,
+ 0xDA77CB62, 0x7A5FB0D8,
+ 0xDA17BA4A, 0x7A4210D8,
+ 0xD9B7C093, 0x7A24256E,
+ 0xD957DE7A, 0x7A05EEAD,
+ 0xD8F81439, 0x79E76CA6,
+ 0xD898620C, 0x79C89F6D,
+ 0xD838C82D, 0x79A98715,
+ 0xD7D946D7, 0x798A23B1,
+ 0xD779DE46, 0x796A7554,
+ 0xD71A8EB5, 0x794A7C11,
+ 0xD6BB585D, 0x792A37FE,
+ 0xD65C3B7B, 0x7909A92C,
+ 0xD5FD3847, 0x78E8CFB1,
+ 0xD59E4EFE, 0x78C7ABA1,
+ 0xD53F7FDA, 0x78A63D10,
+ 0xD4E0CB14, 0x78848413,
+ 0xD48230E8, 0x786280BF,
+ 0xD423B190, 0x78403328,
+ 0xD3C54D46, 0x781D9B64,
+ 0xD3670445, 0x77FAB988,
+ 0xD308D6C6, 0x77D78DAA,
+ 0xD2AAC504, 0x77B417DF,
+ 0xD24CCF38, 0x7790583D,
+ 0xD1EEF59E, 0x776C4EDB,
+ 0xD191386D, 0x7747FBCE,
+ 0xD13397E1, 0x77235F2D,
+ 0xD0D61433, 0x76FE790E,
+ 0xD078AD9D, 0x76D94988,
+ 0xD01B6459, 0x76B3D0B3,
+ 0xCFBE389F, 0x768E0EA5,
+ 0xCF612AAA, 0x76680376,
+ 0xCF043AB2, 0x7641AF3C,
+ 0xCEA768F2, 0x761B1211,
+ 0xCE4AB5A2, 0x75F42C0A,
+ 0xCDEE20FC, 0x75CCFD42,
+ 0xCD91AB38, 0x75A585CF,
+ 0xCD355490, 0x757DC5CA,
+ 0xCCD91D3D, 0x7555BD4B,
+ 0xCC7D0577, 0x752D6C6C,
+ 0xCC210D78, 0x7504D345,
+ 0xCBC53578, 0x74DBF1EF,
+ 0xCB697DB0, 0x74B2C883,
+ 0xCB0DE658, 0x7489571B,
+ 0xCAB26FA9, 0x745F9DD1,
+ 0xCA5719DB, 0x74359CBD,
+ 0xC9FBE527, 0x740B53FA,
+ 0xC9A0D1C4, 0x73E0C3A3,
+ 0xC945DFEC, 0x73B5EBD0,
+ 0xC8EB0FD6, 0x738ACC9E,
+ 0xC89061BA, 0x735F6626,
+ 0xC835D5D0, 0x7333B883,
+ 0xC7DB6C50, 0x7307C3D0,
+ 0xC7812571, 0x72DB8828,
+ 0xC727016C, 0x72AF05A6,
+ 0xC6CD0079, 0x72823C66,
+ 0xC67322CD, 0x72552C84,
+ 0xC61968A2, 0x7227D61C,
+ 0xC5BFD22E, 0x71FA3948,
+ 0xC5665FA8, 0x71CC5626,
+ 0xC50D1148, 0x719E2CD2,
+ 0xC4B3E746, 0x716FBD68,
+ 0xC45AE1D7, 0x71410804,
+ 0xC4020132, 0x71120CC5,
+ 0xC3A9458F, 0x70E2CBC6,
+ 0xC350AF25, 0x70B34524,
+ 0xC2F83E2A, 0x708378FE,
+ 0xC29FF2D4, 0x70536771,
+ 0xC247CD5A, 0x70231099,
+ 0xC1EFCDF2, 0x6FF27496,
+ 0xC197F4D3, 0x6FC19385,
+ 0xC1404233, 0x6F906D84,
+ 0xC0E8B648, 0x6F5F02B1,
+ 0xC0915147, 0x6F2D532C,
+ 0xC03A1368, 0x6EFB5F12,
+ 0xBFE2FCDF, 0x6EC92682,
+ 0xBF8C0DE2, 0x6E96A99C,
+ 0xBF3546A8, 0x6E63E87F,
+ 0xBEDEA765, 0x6E30E349,
+ 0xBE88304F, 0x6DFD9A1B,
+ 0xBE31E19B, 0x6DCA0D14,
+ 0xBDDBBB7F, 0x6D963C54,
+ 0xBD85BE2F, 0x6D6227FA,
+ 0xBD2FE9E1, 0x6D2DD027,
+ 0xBCDA3ECA, 0x6CF934FB,
+ 0xBC84BD1E, 0x6CC45697,
+ 0xBC2F6513, 0x6C8F351C,
+ 0xBBDA36DC, 0x6C59D0A9,
+ 0xBB8532AF, 0x6C242960,
+ 0xBB3058C0, 0x6BEE3F62,
+ 0xBADBA943, 0x6BB812D0,
+ 0xBA87246C, 0x6B81A3CD,
+ 0xBA32CA70, 0x6B4AF278,
+ 0xB9DE9B83, 0x6B13FEF5,
+ 0xB98A97D8, 0x6ADCC964,
+ 0xB936BFA3, 0x6AA551E8,
+ 0xB8E31319, 0x6A6D98A4,
+ 0xB88F926C, 0x6A359DB9,
+ 0xB83C3DD1, 0x69FD614A,
+ 0xB7E9157A, 0x69C4E37A,
+ 0xB796199B, 0x698C246C,
+ 0xB7434A67, 0x69532442,
+ 0xB6F0A811, 0x6919E320,
+ 0xB69E32CD, 0x68E06129,
+ 0xB64BEACC, 0x68A69E81,
+ 0xB5F9D042, 0x686C9B4B,
+ 0xB5A7E362, 0x683257AA,
+ 0xB556245E, 0x67F7D3C4,
+ 0xB5049368, 0x67BD0FBC,
+ 0xB4B330B2, 0x67820BB6,
+ 0xB461FC70, 0x6746C7D7,
+ 0xB410F6D2, 0x670B4443,
+ 0xB3C0200C, 0x66CF811F,
+ 0xB36F784E, 0x66937E90,
+ 0xB31EFFCB, 0x66573CBB,
+ 0xB2CEB6B5, 0x661ABBC5,
+ 0xB27E9D3B, 0x65DDFBD3,
+ 0xB22EB392, 0x65A0FD0B,
+ 0xB1DEF9E8, 0x6563BF92,
+ 0xB18F7070, 0x6526438E,
+ 0xB140175B, 0x64E88926,
+ 0xB0F0EEDA, 0x64AA907F,
+ 0xB0A1F71C, 0x646C59BF,
+ 0xB0533055, 0x642DE50D,
+ 0xB0049AB2, 0x63EF328F,
+ 0xAFB63667, 0x63B0426D,
+ 0xAF6803A1, 0x637114CC,
+ 0xAF1A0293, 0x6331A9D4,
+ 0xAECC336B, 0x62F201AC,
+ 0xAE7E965B, 0x62B21C7B,
+ 0xAE312B91, 0x6271FA69,
+ 0xADE3F33E, 0x62319B9D,
+ 0xAD96ED91, 0x61F1003E,
+ 0xAD4A1ABA, 0x61B02876,
+ 0xACFD7AE8, 0x616F146B,
+ 0xACB10E4A, 0x612DC446,
+ 0xAC64D510, 0x60EC3830,
+ 0xAC18CF68, 0x60AA704F,
+ 0xABCCFD82, 0x60686CCE,
+ 0xAB815F8C, 0x60262DD5,
+ 0xAB35F5B5, 0x5FE3B38D,
+ 0xAAEAC02B, 0x5FA0FE1E,
+ 0xAA9FBF1D, 0x5F5E0DB3,
+ 0xAA54F2B9, 0x5F1AE273,
+ 0xAA0A5B2D, 0x5ED77C89,
+ 0xA9BFF8A8, 0x5E93DC1F,
+ 0xA975CB56, 0x5E50015D,
+ 0xA92BD366, 0x5E0BEC6E,
+ 0xA8E21106, 0x5DC79D7C,
+ 0xA8988463, 0x5D8314B0,
+ 0xA84F2DA9, 0x5D3E5236,
+ 0xA8060D08, 0x5CF95638,
+ 0xA7BD22AB, 0x5CB420DF,
+ 0xA7746EC0, 0x5C6EB258,
+ 0xA72BF173, 0x5C290ACC,
+ 0xA6E3AAF2, 0x5BE32A67,
+ 0xA69B9B68, 0x5B9D1153,
+ 0xA653C302, 0x5B56BFBD,
+ 0xA60C21ED, 0x5B1035CF,
+ 0xA5C4B855, 0x5AC973B4,
+ 0xA57D8666, 0x5A82799A,
+ 0xA5368C4B, 0x5A3B47AA,
+ 0xA4EFCA31, 0x59F3DE12,
+ 0xA4A94042, 0x59AC3CFD,
+ 0xA462EEAC, 0x59646497,
+ 0xA41CD598, 0x591C550E,
+ 0xA3D6F533, 0x58D40E8C,
+ 0xA3914DA7, 0x588B913F,
+ 0xA34BDF20, 0x5842DD54,
+ 0xA306A9C7, 0x57F9F2F7,
+ 0xA2C1ADC9, 0x57B0D256,
+ 0xA27CEB4F, 0x57677B9D,
+ 0xA2386283, 0x571DEEF9,
+ 0xA1F41391, 0x56D42C99,
+ 0xA1AFFEA2, 0x568A34A9,
+ 0xA16C23E1, 0x56400757,
+ 0xA1288376, 0x55F5A4D2,
+ 0xA0E51D8C, 0x55AB0D46,
+ 0xA0A1F24C, 0x556040E2,
+ 0xA05F01E1, 0x55153FD4,
+ 0xA01C4C72, 0x54CA0A4A,
+ 0x9FD9D22A, 0x547EA073,
+ 0x9F979331, 0x5433027D,
+ 0x9F558FB0, 0x53E73097,
+ 0x9F13C7D0, 0x539B2AEF,
+ 0x9ED23BB9, 0x534EF1B5,
+ 0x9E90EB94, 0x53028517,
+ 0x9E4FD789, 0x52B5E545,
+ 0x9E0EFFC1, 0x5269126E,
+ 0x9DCE6462, 0x521C0CC1,
+ 0x9D8E0596, 0x51CED46E,
+ 0x9D4DE384, 0x518169A4,
+ 0x9D0DFE53, 0x5133CC94,
+ 0x9CCE562B, 0x50E5FD6C,
+ 0x9C8EEB33, 0x5097FC5E,
+ 0x9C4FBD92, 0x5049C999,
+ 0x9C10CD70, 0x4FFB654D,
+ 0x9BD21AF2, 0x4FACCFAB,
+ 0x9B93A640, 0x4F5E08E3,
+ 0x9B556F80, 0x4F0F1126,
+ 0x9B1776D9, 0x4EBFE8A4,
+ 0x9AD9BC71, 0x4E708F8F,
+ 0x9A9C406D, 0x4E210617,
+ 0x9A5F02F5, 0x4DD14C6E,
+ 0x9A22042C, 0x4D8162C4,
+ 0x99E5443A, 0x4D31494B,
+ 0x99A8C344, 0x4CE10034,
+ 0x996C816F, 0x4C9087B1,
+ 0x99307EE0, 0x4C3FDFF3,
+ 0x98F4BBBC, 0x4BEF092D,
+ 0x98B93828, 0x4B9E038F,
+ 0x987DF449, 0x4B4CCF4D,
+ 0x9842F043, 0x4AFB6C97,
+ 0x98082C3B, 0x4AA9DBA1,
+ 0x97CDA855, 0x4A581C9D,
+ 0x979364B5, 0x4A062FBD,
+ 0x9759617E, 0x49B41533,
+ 0x971F9ED6, 0x4961CD32,
+ 0x96E61CDF, 0x490F57EE,
+ 0x96ACDBBD, 0x48BCB598,
+ 0x9673DB94, 0x4869E664,
+ 0x963B1C85, 0x4816EA85,
+ 0x96029EB5, 0x47C3C22E,
+ 0x95CA6246, 0x47706D93,
+ 0x9592675B, 0x471CECE6,
+ 0x955AAE17, 0x46C9405C,
+ 0x9523369B, 0x46756827,
+ 0x94EC010B, 0x4621647C,
+ 0x94B50D87, 0x45CD358F,
+ 0x947E5C32, 0x4578DB93,
+ 0x9447ED2F, 0x452456BC,
+ 0x9411C09D, 0x44CFA73F,
+ 0x93DBD69F, 0x447ACD50,
+ 0x93A62F56, 0x4425C923,
+ 0x9370CAE4, 0x43D09AEC,
+ 0x933BA968, 0x437B42E1,
+ 0x9306CB04, 0x4325C135,
+ 0x92D22FD8, 0x42D0161E,
+ 0x929DD805, 0x427A41D0,
+ 0x9269C3AC, 0x42244480,
+ 0x9235F2EB, 0x41CE1E64,
+ 0x920265E4, 0x4177CFB0,
+ 0x91CF1CB6, 0x4121589A,
+ 0x919C1780, 0x40CAB957,
+ 0x91695663, 0x4073F21D,
+ 0x9136D97D, 0x401D0320,
+ 0x9104A0ED, 0x3FC5EC97,
+ 0x90D2ACD3, 0x3F6EAEB8,
+ 0x90A0FD4E, 0x3F1749B7,
+ 0x906F927B, 0x3EBFBDCC,
+ 0x903E6C7A, 0x3E680B2C,
+ 0x900D8B69, 0x3E10320D,
+ 0x8FDCEF66, 0x3DB832A5,
+ 0x8FAC988E, 0x3D600D2B,
+ 0x8F7C8701, 0x3D07C1D5,
+ 0x8F4CBADB, 0x3CAF50DA,
+ 0x8F1D343A, 0x3C56BA70,
+ 0x8EEDF33B, 0x3BFDFECD,
+ 0x8EBEF7FB, 0x3BA51E29,
+ 0x8E904298, 0x3B4C18BA,
+ 0x8E61D32D, 0x3AF2EEB7,
+ 0x8E33A9D9, 0x3A99A057,
+ 0x8E05C6B7, 0x3A402DD1,
+ 0x8DD829E4, 0x39E6975D,
+ 0x8DAAD37B, 0x398CDD32,
+ 0x8D7DC399, 0x3932FF87,
+ 0x8D50FA59, 0x38D8FE93,
+ 0x8D2477D8, 0x387EDA8E,
+ 0x8CF83C30, 0x382493B0,
+ 0x8CCC477D, 0x37CA2A30,
+ 0x8CA099D9, 0x376F9E46,
+ 0x8C753361, 0x3714F02A,
+ 0x8C4A142F, 0x36BA2013,
+ 0x8C1F3C5C, 0x365F2E3B,
+ 0x8BF4AC05, 0x36041AD9,
+ 0x8BCA6342, 0x35A8E624,
+ 0x8BA0622F, 0x354D9056,
+ 0x8B76A8E4, 0x34F219A7,
+ 0x8B4D377C, 0x3496824F,
+ 0x8B240E10, 0x343ACA87,
+ 0x8AFB2CBA, 0x33DEF287,
+ 0x8AD29393, 0x3382FA88,
+ 0x8AAA42B4, 0x3326E2C2,
+ 0x8A823A35, 0x32CAAB6F,
+ 0x8A5A7A30, 0x326E54C7,
+ 0x8A3302BD, 0x3211DF03,
+ 0x8A0BD3F5, 0x31B54A5D,
+ 0x89E4EDEE, 0x3158970D,
+ 0x89BE50C3, 0x30FBC54D,
+ 0x8997FC89, 0x309ED555,
+ 0x8971F15A, 0x3041C760,
+ 0x894C2F4C, 0x2FE49BA6,
+ 0x8926B677, 0x2F875262,
+ 0x890186F1, 0x2F29EBCC,
+ 0x88DCA0D3, 0x2ECC681E,
+ 0x88B80431, 0x2E6EC792,
+ 0x8893B124, 0x2E110A62,
+ 0x886FA7C2, 0x2DB330C7,
+ 0x884BE820, 0x2D553AFB,
+ 0x88287255, 0x2CF72939,
+ 0x88054677, 0x2C98FBBA,
+ 0x87E2649B, 0x2C3AB2B9,
+ 0x87BFCCD7, 0x2BDC4E6F,
+ 0x879D7F40, 0x2B7DCF17,
+ 0x877B7BEC, 0x2B1F34EB,
+ 0x8759C2EF, 0x2AC08025,
+ 0x8738545E, 0x2A61B101,
+ 0x8717304E, 0x2A02C7B8,
+ 0x86F656D3, 0x29A3C484,
+ 0x86D5C802, 0x2944A7A2,
+ 0x86B583EE, 0x28E5714A,
+ 0x86958AAB, 0x288621B9,
+ 0x8675DC4E, 0x2826B928,
+ 0x865678EA, 0x27C737D2,
+ 0x86376092, 0x27679DF4,
+ 0x86189359, 0x2707EBC6,
+ 0x85FA1152, 0x26A82185,
+ 0x85DBDA91, 0x26483F6C,
+ 0x85BDEF27, 0x25E845B5,
+ 0x85A04F28, 0x2588349D,
+ 0x8582FAA4, 0x25280C5D,
+ 0x8565F1B0, 0x24C7CD32,
+ 0x8549345C, 0x24677757,
+ 0x852CC2BA, 0x24070B07,
+ 0x85109CDC, 0x23A6887E,
+ 0x84F4C2D3, 0x2345EFF7,
+ 0x84D934B0, 0x22E541AE,
+ 0x84BDF285, 0x22847DDF,
+ 0x84A2FC62, 0x2223A4C5,
+ 0x84885257, 0x21C2B69C,
+ 0x846DF476, 0x2161B39F,
+ 0x8453E2CE, 0x21009C0B,
+ 0x843A1D70, 0x209F701C,
+ 0x8420A46B, 0x203E300D,
+ 0x840777CF, 0x1FDCDC1A,
+ 0x83EE97AC, 0x1F7B7480,
+ 0x83D60411, 0x1F19F97B,
+ 0x83BDBD0D, 0x1EB86B46,
+ 0x83A5C2B0, 0x1E56CA1E,
+ 0x838E1507, 0x1DF5163F,
+ 0x8376B422, 0x1D934FE5,
+ 0x835FA00E, 0x1D31774D,
+ 0x8348D8DB, 0x1CCF8CB3,
+ 0x83325E97, 0x1C6D9053,
+ 0x831C314E, 0x1C0B826A,
+ 0x8306510F, 0x1BA96334,
+ 0x82F0BDE8, 0x1B4732EF,
+ 0x82DB77E5, 0x1AE4F1D6,
+ 0x82C67F13, 0x1A82A025,
+ 0x82B1D381, 0x1A203E1B,
+ 0x829D753A, 0x19BDCBF2,
+ 0x8289644A, 0x195B49E9,
+ 0x8275A0C0, 0x18F8B83C,
+ 0x82622AA5, 0x18961727,
+ 0x824F0208, 0x183366E8,
+ 0x823C26F2, 0x17D0A7BB,
+ 0x82299971, 0x176DD9DE,
+ 0x8217598F, 0x170AFD8D,
+ 0x82056758, 0x16A81305,
+ 0x81F3C2D7, 0x16451A83,
+ 0x81E26C16, 0x15E21444,
+ 0x81D16320, 0x157F0086,
+ 0x81C0A801, 0x151BDF85,
+ 0x81B03AC1, 0x14B8B17F,
+ 0x81A01B6C, 0x145576B1,
+ 0x81904A0C, 0x13F22F57,
+ 0x8180C6A9, 0x138EDBB0,
+ 0x8171914E, 0x132B7BF9,
+ 0x8162AA03, 0x12C8106E,
+ 0x815410D3, 0x1264994E,
+ 0x8145C5C6, 0x120116D4,
+ 0x8137C8E6, 0x119D8940,
+ 0x812A1A39, 0x1139F0CE,
+ 0x811CB9CA, 0x10D64DBC,
+ 0x810FA7A0, 0x1072A047,
+ 0x8102E3C3, 0x100EE8AD,
+ 0x80F66E3C, 0x0FAB272B,
+ 0x80EA4712, 0x0F475BFE,
+ 0x80DE6E4C, 0x0EE38765,
+ 0x80D2E3F1, 0x0E7FA99D,
+ 0x80C7A80A, 0x0E1BC2E3,
+ 0x80BCBA9C, 0x0DB7D376,
+ 0x80B21BAF, 0x0D53DB92,
+ 0x80A7CB49, 0x0CEFDB75,
+ 0x809DC970, 0x0C8BD35E,
+ 0x8094162B, 0x0C27C389,
+ 0x808AB180, 0x0BC3AC35,
+ 0x80819B74, 0x0B5F8D9F,
+ 0x8078D40D, 0x0AFB6805,
+ 0x80705B50, 0x0A973BA5,
+ 0x80683143, 0x0A3308BC,
+ 0x806055EA, 0x09CECF89,
+ 0x8058C94C, 0x096A9049,
+ 0x80518B6B, 0x09064B3A,
+ 0x804A9C4D, 0x08A2009A,
+ 0x8043FBF6, 0x083DB0A7,
+ 0x803DAA69, 0x07D95B9E,
+ 0x8037A7AC, 0x077501BE,
+ 0x8031F3C1, 0x0710A344,
+ 0x802C8EAD, 0x06AC406F,
+ 0x80277872, 0x0647D97C,
+ 0x8022B113, 0x05E36EA9,
+ 0x801E3894, 0x057F0034,
+ 0x801A0EF7, 0x051A8E5C,
+ 0x80163440, 0x04B6195D,
+ 0x8012A86F, 0x0451A176,
+ 0x800F6B88, 0x03ED26E6,
+ 0x800C7D8C, 0x0388A9E9,
+ 0x8009DE7D, 0x03242ABF,
+ 0x80078E5E, 0x02BFA9A4,
+ 0x80058D2E, 0x025B26D7,
+ 0x8003DAF0, 0x01F6A296,
+ 0x800277A5, 0x01921D1F,
+ 0x8001634D, 0x012D96B0,
+ 0x80009DE9, 0x00C90F88,
+ 0x8000277A, 0x006487E3,
+ 0x80000000, 0x00000000,
+ 0x8000277A, 0xFF9B781D,
+ 0x80009DE9, 0xFF36F078,
+ 0x8001634D, 0xFED2694F,
+ 0x800277A5, 0xFE6DE2E0,
+ 0x8003DAF0, 0xFE095D69,
+ 0x80058D2E, 0xFDA4D928,
+ 0x80078E5E, 0xFD40565B,
+ 0x8009DE7D, 0xFCDBD541,
+ 0x800C7D8C, 0xFC775616,
+ 0x800F6B88, 0xFC12D919,
+ 0x8012A86F, 0xFBAE5E89,
+ 0x80163440, 0xFB49E6A2,
+ 0x801A0EF7, 0xFAE571A4,
+ 0x801E3894, 0xFA80FFCB,
+ 0x8022B113, 0xFA1C9156,
+ 0x80277872, 0xF9B82683,
+ 0x802C8EAD, 0xF953BF90,
+ 0x8031F3C1, 0xF8EF5CBB,
+ 0x8037A7AC, 0xF88AFE41,
+ 0x803DAA69, 0xF826A461,
+ 0x8043FBF6, 0xF7C24F58,
+ 0x804A9C4D, 0xF75DFF65,
+ 0x80518B6B, 0xF6F9B4C5,
+ 0x8058C94C, 0xF6956FB6,
+ 0x806055EA, 0xF6313076,
+ 0x80683143, 0xF5CCF743,
+ 0x80705B50, 0xF568C45A,
+ 0x8078D40D, 0xF50497FA,
+ 0x80819B74, 0xF4A07260,
+ 0x808AB180, 0xF43C53CA,
+ 0x8094162B, 0xF3D83C76,
+ 0x809DC970, 0xF3742CA1,
+ 0x80A7CB49, 0xF310248A,
+ 0x80B21BAF, 0xF2AC246D,
+ 0x80BCBA9C, 0xF2482C89,
+ 0x80C7A80A, 0xF1E43D1C,
+ 0x80D2E3F1, 0xF1805662,
+ 0x80DE6E4C, 0xF11C789A,
+ 0x80EA4712, 0xF0B8A401,
+ 0x80F66E3C, 0xF054D8D4,
+ 0x8102E3C3, 0xEFF11752,
+ 0x810FA7A0, 0xEF8D5FB8,
+ 0x811CB9CA, 0xEF29B243,
+ 0x812A1A39, 0xEEC60F31,
+ 0x8137C8E6, 0xEE6276BF,
+ 0x8145C5C6, 0xEDFEE92B,
+ 0x815410D3, 0xED9B66B2,
+ 0x8162AA03, 0xED37EF91,
+ 0x8171914E, 0xECD48406,
+ 0x8180C6A9, 0xEC71244F,
+ 0x81904A0C, 0xEC0DD0A8,
+ 0x81A01B6C, 0xEBAA894E,
+ 0x81B03AC1, 0xEB474E80,
+ 0x81C0A801, 0xEAE4207A,
+ 0x81D16320, 0xEA80FF79,
+ 0x81E26C16, 0xEA1DEBBB,
+ 0x81F3C2D7, 0xE9BAE57C,
+ 0x82056758, 0xE957ECFB,
+ 0x8217598F, 0xE8F50273,
+ 0x82299971, 0xE8922621,
+ 0x823C26F2, 0xE82F5844,
+ 0x824F0208, 0xE7CC9917,
+ 0x82622AA5, 0xE769E8D8,
+ 0x8275A0C0, 0xE70747C3,
+ 0x8289644A, 0xE6A4B616,
+ 0x829D753A, 0xE642340D,
+ 0x82B1D381, 0xE5DFC1E4,
+ 0x82C67F13, 0xE57D5FDA,
+ 0x82DB77E5, 0xE51B0E2A,
+ 0x82F0BDE8, 0xE4B8CD10,
+ 0x8306510F, 0xE4569CCB,
+ 0x831C314E, 0xE3F47D95,
+ 0x83325E97, 0xE3926FAC,
+ 0x8348D8DB, 0xE330734C,
+ 0x835FA00E, 0xE2CE88B2,
+ 0x8376B422, 0xE26CB01A,
+ 0x838E1507, 0xE20AE9C1,
+ 0x83A5C2B0, 0xE1A935E1,
+ 0x83BDBD0D, 0xE14794B9,
+ 0x83D60411, 0xE0E60684,
+ 0x83EE97AC, 0xE0848B7F,
+ 0x840777CF, 0xE02323E5,
+ 0x8420A46B, 0xDFC1CFF2,
+ 0x843A1D70, 0xDF608FE3,
+ 0x8453E2CE, 0xDEFF63F4,
+ 0x846DF476, 0xDE9E4C60,
+ 0x84885257, 0xDE3D4963,
+ 0x84A2FC62, 0xDDDC5B3A,
+ 0x84BDF285, 0xDD7B8220,
+ 0x84D934B0, 0xDD1ABE51,
+ 0x84F4C2D3, 0xDCBA1008,
+ 0x85109CDC, 0xDC597781,
+ 0x852CC2BA, 0xDBF8F4F8,
+ 0x8549345C, 0xDB9888A8,
+ 0x8565F1B0, 0xDB3832CD,
+ 0x8582FAA4, 0xDAD7F3A2,
+ 0x85A04F28, 0xDA77CB62,
+ 0x85BDEF27, 0xDA17BA4A,
+ 0x85DBDA91, 0xD9B7C093,
+ 0x85FA1152, 0xD957DE7A,
+ 0x86189359, 0xD8F81439,
+ 0x86376092, 0xD898620C,
+ 0x865678EA, 0xD838C82D,
+ 0x8675DC4E, 0xD7D946D7,
+ 0x86958AAB, 0xD779DE46,
+ 0x86B583EE, 0xD71A8EB5,
+ 0x86D5C802, 0xD6BB585D,
+ 0x86F656D3, 0xD65C3B7B,
+ 0x8717304E, 0xD5FD3847,
+ 0x8738545E, 0xD59E4EFE,
+ 0x8759C2EF, 0xD53F7FDA,
+ 0x877B7BEC, 0xD4E0CB14,
+ 0x879D7F40, 0xD48230E8,
+ 0x87BFCCD7, 0xD423B190,
+ 0x87E2649B, 0xD3C54D46,
+ 0x88054677, 0xD3670445,
+ 0x88287255, 0xD308D6C6,
+ 0x884BE820, 0xD2AAC504,
+ 0x886FA7C2, 0xD24CCF38,
+ 0x8893B124, 0xD1EEF59E,
+ 0x88B80431, 0xD191386D,
+ 0x88DCA0D3, 0xD13397E1,
+ 0x890186F1, 0xD0D61433,
+ 0x8926B677, 0xD078AD9D,
+ 0x894C2F4C, 0xD01B6459,
+ 0x8971F15A, 0xCFBE389F,
+ 0x8997FC89, 0xCF612AAA,
+ 0x89BE50C3, 0xCF043AB2,
+ 0x89E4EDEE, 0xCEA768F2,
+ 0x8A0BD3F5, 0xCE4AB5A2,
+ 0x8A3302BD, 0xCDEE20FC,
+ 0x8A5A7A30, 0xCD91AB38,
+ 0x8A823A35, 0xCD355490,
+ 0x8AAA42B4, 0xCCD91D3D,
+ 0x8AD29393, 0xCC7D0577,
+ 0x8AFB2CBA, 0xCC210D78,
+ 0x8B240E10, 0xCBC53578,
+ 0x8B4D377C, 0xCB697DB0,
+ 0x8B76A8E4, 0xCB0DE658,
+ 0x8BA0622F, 0xCAB26FA9,
+ 0x8BCA6342, 0xCA5719DB,
+ 0x8BF4AC05, 0xC9FBE527,
+ 0x8C1F3C5C, 0xC9A0D1C4,
+ 0x8C4A142F, 0xC945DFEC,
+ 0x8C753361, 0xC8EB0FD6,
+ 0x8CA099D9, 0xC89061BA,
+ 0x8CCC477D, 0xC835D5D0,
+ 0x8CF83C30, 0xC7DB6C50,
+ 0x8D2477D8, 0xC7812571,
+ 0x8D50FA59, 0xC727016C,
+ 0x8D7DC399, 0xC6CD0079,
+ 0x8DAAD37B, 0xC67322CD,
+ 0x8DD829E4, 0xC61968A2,
+ 0x8E05C6B7, 0xC5BFD22E,
+ 0x8E33A9D9, 0xC5665FA8,
+ 0x8E61D32D, 0xC50D1148,
+ 0x8E904298, 0xC4B3E746,
+ 0x8EBEF7FB, 0xC45AE1D7,
+ 0x8EEDF33B, 0xC4020132,
+ 0x8F1D343A, 0xC3A9458F,
+ 0x8F4CBADB, 0xC350AF25,
+ 0x8F7C8701, 0xC2F83E2A,
+ 0x8FAC988E, 0xC29FF2D4,
+ 0x8FDCEF66, 0xC247CD5A,
+ 0x900D8B69, 0xC1EFCDF2,
+ 0x903E6C7A, 0xC197F4D3,
+ 0x906F927B, 0xC1404233,
+ 0x90A0FD4E, 0xC0E8B648,
+ 0x90D2ACD3, 0xC0915147,
+ 0x9104A0ED, 0xC03A1368,
+ 0x9136D97D, 0xBFE2FCDF,
+ 0x91695663, 0xBF8C0DE2,
+ 0x919C1780, 0xBF3546A8,
+ 0x91CF1CB6, 0xBEDEA765,
+ 0x920265E4, 0xBE88304F,
+ 0x9235F2EB, 0xBE31E19B,
+ 0x9269C3AC, 0xBDDBBB7F,
+ 0x929DD805, 0xBD85BE2F,
+ 0x92D22FD8, 0xBD2FE9E1,
+ 0x9306CB04, 0xBCDA3ECA,
+ 0x933BA968, 0xBC84BD1E,
+ 0x9370CAE4, 0xBC2F6513,
+ 0x93A62F56, 0xBBDA36DC,
+ 0x93DBD69F, 0xBB8532AF,
+ 0x9411C09D, 0xBB3058C0,
+ 0x9447ED2F, 0xBADBA943,
+ 0x947E5C32, 0xBA87246C,
+ 0x94B50D87, 0xBA32CA70,
+ 0x94EC010B, 0xB9DE9B83,
+ 0x9523369B, 0xB98A97D8,
+ 0x955AAE17, 0xB936BFA3,
+ 0x9592675B, 0xB8E31319,
+ 0x95CA6246, 0xB88F926C,
+ 0x96029EB5, 0xB83C3DD1,
+ 0x963B1C85, 0xB7E9157A,
+ 0x9673DB94, 0xB796199B,
+ 0x96ACDBBD, 0xB7434A67,
+ 0x96E61CDF, 0xB6F0A811,
+ 0x971F9ED6, 0xB69E32CD,
+ 0x9759617E, 0xB64BEACC,
+ 0x979364B5, 0xB5F9D042,
+ 0x97CDA855, 0xB5A7E362,
+ 0x98082C3B, 0xB556245E,
+ 0x9842F043, 0xB5049368,
+ 0x987DF449, 0xB4B330B2,
+ 0x98B93828, 0xB461FC70,
+ 0x98F4BBBC, 0xB410F6D2,
+ 0x99307EE0, 0xB3C0200C,
+ 0x996C816F, 0xB36F784E,
+ 0x99A8C344, 0xB31EFFCB,
+ 0x99E5443A, 0xB2CEB6B5,
+ 0x9A22042C, 0xB27E9D3B,
+ 0x9A5F02F5, 0xB22EB392,
+ 0x9A9C406D, 0xB1DEF9E8,
+ 0x9AD9BC71, 0xB18F7070,
+ 0x9B1776D9, 0xB140175B,
+ 0x9B556F80, 0xB0F0EEDA,
+ 0x9B93A640, 0xB0A1F71C,
+ 0x9BD21AF2, 0xB0533055,
+ 0x9C10CD70, 0xB0049AB2,
+ 0x9C4FBD92, 0xAFB63667,
+ 0x9C8EEB33, 0xAF6803A1,
+ 0x9CCE562B, 0xAF1A0293,
+ 0x9D0DFE53, 0xAECC336B,
+ 0x9D4DE384, 0xAE7E965B,
+ 0x9D8E0596, 0xAE312B91,
+ 0x9DCE6462, 0xADE3F33E,
+ 0x9E0EFFC1, 0xAD96ED91,
+ 0x9E4FD789, 0xAD4A1ABA,
+ 0x9E90EB94, 0xACFD7AE8,
+ 0x9ED23BB9, 0xACB10E4A,
+ 0x9F13C7D0, 0xAC64D510,
+ 0x9F558FB0, 0xAC18CF68,
+ 0x9F979331, 0xABCCFD82,
+ 0x9FD9D22A, 0xAB815F8C,
+ 0xA01C4C72, 0xAB35F5B5,
+ 0xA05F01E1, 0xAAEAC02B,
+ 0xA0A1F24C, 0xAA9FBF1D,
+ 0xA0E51D8C, 0xAA54F2B9,
+ 0xA1288376, 0xAA0A5B2D,
+ 0xA16C23E1, 0xA9BFF8A8,
+ 0xA1AFFEA2, 0xA975CB56,
+ 0xA1F41391, 0xA92BD366,
+ 0xA2386283, 0xA8E21106,
+ 0xA27CEB4F, 0xA8988463,
+ 0xA2C1ADC9, 0xA84F2DA9,
+ 0xA306A9C7, 0xA8060D08,
+ 0xA34BDF20, 0xA7BD22AB,
+ 0xA3914DA7, 0xA7746EC0,
+ 0xA3D6F533, 0xA72BF173,
+ 0xA41CD598, 0xA6E3AAF2,
+ 0xA462EEAC, 0xA69B9B68,
+ 0xA4A94042, 0xA653C302,
+ 0xA4EFCA31, 0xA60C21ED,
+ 0xA5368C4B, 0xA5C4B855,
+ 0xA57D8666, 0xA57D8666,
+ 0xA5C4B855, 0xA5368C4B,
+ 0xA60C21ED, 0xA4EFCA31,
+ 0xA653C302, 0xA4A94042,
+ 0xA69B9B68, 0xA462EEAC,
+ 0xA6E3AAF2, 0xA41CD598,
+ 0xA72BF173, 0xA3D6F533,
+ 0xA7746EC0, 0xA3914DA7,
+ 0xA7BD22AB, 0xA34BDF20,
+ 0xA8060D08, 0xA306A9C7,
+ 0xA84F2DA9, 0xA2C1ADC9,
+ 0xA8988463, 0xA27CEB4F,
+ 0xA8E21106, 0xA2386283,
+ 0xA92BD366, 0xA1F41391,
+ 0xA975CB56, 0xA1AFFEA2,
+ 0xA9BFF8A8, 0xA16C23E1,
+ 0xAA0A5B2D, 0xA1288376,
+ 0xAA54F2B9, 0xA0E51D8C,
+ 0xAA9FBF1D, 0xA0A1F24C,
+ 0xAAEAC02B, 0xA05F01E1,
+ 0xAB35F5B5, 0xA01C4C72,
+ 0xAB815F8C, 0x9FD9D22A,
+ 0xABCCFD82, 0x9F979331,
+ 0xAC18CF68, 0x9F558FB0,
+ 0xAC64D510, 0x9F13C7D0,
+ 0xACB10E4A, 0x9ED23BB9,
+ 0xACFD7AE8, 0x9E90EB94,
+ 0xAD4A1ABA, 0x9E4FD789,
+ 0xAD96ED91, 0x9E0EFFC1,
+ 0xADE3F33E, 0x9DCE6462,
+ 0xAE312B91, 0x9D8E0596,
+ 0xAE7E965B, 0x9D4DE384,
+ 0xAECC336B, 0x9D0DFE53,
+ 0xAF1A0293, 0x9CCE562B,
+ 0xAF6803A1, 0x9C8EEB33,
+ 0xAFB63667, 0x9C4FBD92,
+ 0xB0049AB2, 0x9C10CD70,
+ 0xB0533055, 0x9BD21AF2,
+ 0xB0A1F71C, 0x9B93A640,
+ 0xB0F0EEDA, 0x9B556F80,
+ 0xB140175B, 0x9B1776D9,
+ 0xB18F7070, 0x9AD9BC71,
+ 0xB1DEF9E8, 0x9A9C406D,
+ 0xB22EB392, 0x9A5F02F5,
+ 0xB27E9D3B, 0x9A22042C,
+ 0xB2CEB6B5, 0x99E5443A,
+ 0xB31EFFCB, 0x99A8C344,
+ 0xB36F784E, 0x996C816F,
+ 0xB3C0200C, 0x99307EE0,
+ 0xB410F6D2, 0x98F4BBBC,
+ 0xB461FC70, 0x98B93828,
+ 0xB4B330B2, 0x987DF449,
+ 0xB5049368, 0x9842F043,
+ 0xB556245E, 0x98082C3B,
+ 0xB5A7E362, 0x97CDA855,
+ 0xB5F9D042, 0x979364B5,
+ 0xB64BEACC, 0x9759617E,
+ 0xB69E32CD, 0x971F9ED6,
+ 0xB6F0A811, 0x96E61CDF,
+ 0xB7434A67, 0x96ACDBBD,
+ 0xB796199B, 0x9673DB94,
+ 0xB7E9157A, 0x963B1C85,
+ 0xB83C3DD1, 0x96029EB5,
+ 0xB88F926C, 0x95CA6246,
+ 0xB8E31319, 0x9592675B,
+ 0xB936BFA3, 0x955AAE17,
+ 0xB98A97D8, 0x9523369B,
+ 0xB9DE9B83, 0x94EC010B,
+ 0xBA32CA70, 0x94B50D87,
+ 0xBA87246C, 0x947E5C32,
+ 0xBADBA943, 0x9447ED2F,
+ 0xBB3058C0, 0x9411C09D,
+ 0xBB8532AF, 0x93DBD69F,
+ 0xBBDA36DC, 0x93A62F56,
+ 0xBC2F6513, 0x9370CAE4,
+ 0xBC84BD1E, 0x933BA968,
+ 0xBCDA3ECA, 0x9306CB04,
+ 0xBD2FE9E1, 0x92D22FD8,
+ 0xBD85BE2F, 0x929DD805,
+ 0xBDDBBB7F, 0x9269C3AC,
+ 0xBE31E19B, 0x9235F2EB,
+ 0xBE88304F, 0x920265E4,
+ 0xBEDEA765, 0x91CF1CB6,
+ 0xBF3546A8, 0x919C1780,
+ 0xBF8C0DE2, 0x91695663,
+ 0xBFE2FCDF, 0x9136D97D,
+ 0xC03A1368, 0x9104A0ED,
+ 0xC0915147, 0x90D2ACD3,
+ 0xC0E8B648, 0x90A0FD4E,
+ 0xC1404233, 0x906F927B,
+ 0xC197F4D3, 0x903E6C7A,
+ 0xC1EFCDF2, 0x900D8B69,
+ 0xC247CD5A, 0x8FDCEF66,
+ 0xC29FF2D4, 0x8FAC988E,
+ 0xC2F83E2A, 0x8F7C8701,
+ 0xC350AF25, 0x8F4CBADB,
+ 0xC3A9458F, 0x8F1D343A,
+ 0xC4020132, 0x8EEDF33B,
+ 0xC45AE1D7, 0x8EBEF7FB,
+ 0xC4B3E746, 0x8E904298,
+ 0xC50D1148, 0x8E61D32D,
+ 0xC5665FA8, 0x8E33A9D9,
+ 0xC5BFD22E, 0x8E05C6B7,
+ 0xC61968A2, 0x8DD829E4,
+ 0xC67322CD, 0x8DAAD37B,
+ 0xC6CD0079, 0x8D7DC399,
+ 0xC727016C, 0x8D50FA59,
+ 0xC7812571, 0x8D2477D8,
+ 0xC7DB6C50, 0x8CF83C30,
+ 0xC835D5D0, 0x8CCC477D,
+ 0xC89061BA, 0x8CA099D9,
+ 0xC8EB0FD6, 0x8C753361,
+ 0xC945DFEC, 0x8C4A142F,
+ 0xC9A0D1C4, 0x8C1F3C5C,
+ 0xC9FBE527, 0x8BF4AC05,
+ 0xCA5719DB, 0x8BCA6342,
+ 0xCAB26FA9, 0x8BA0622F,
+ 0xCB0DE658, 0x8B76A8E4,
+ 0xCB697DB0, 0x8B4D377C,
+ 0xCBC53578, 0x8B240E10,
+ 0xCC210D78, 0x8AFB2CBA,
+ 0xCC7D0577, 0x8AD29393,
+ 0xCCD91D3D, 0x8AAA42B4,
+ 0xCD355490, 0x8A823A35,
+ 0xCD91AB38, 0x8A5A7A30,
+ 0xCDEE20FC, 0x8A3302BD,
+ 0xCE4AB5A2, 0x8A0BD3F5,
+ 0xCEA768F2, 0x89E4EDEE,
+ 0xCF043AB2, 0x89BE50C3,
+ 0xCF612AAA, 0x8997FC89,
+ 0xCFBE389F, 0x8971F15A,
+ 0xD01B6459, 0x894C2F4C,
+ 0xD078AD9D, 0x8926B677,
+ 0xD0D61433, 0x890186F1,
+ 0xD13397E1, 0x88DCA0D3,
+ 0xD191386D, 0x88B80431,
+ 0xD1EEF59E, 0x8893B124,
+ 0xD24CCF38, 0x886FA7C2,
+ 0xD2AAC504, 0x884BE820,
+ 0xD308D6C6, 0x88287255,
+ 0xD3670445, 0x88054677,
+ 0xD3C54D46, 0x87E2649B,
+ 0xD423B190, 0x87BFCCD7,
+ 0xD48230E8, 0x879D7F40,
+ 0xD4E0CB14, 0x877B7BEC,
+ 0xD53F7FDA, 0x8759C2EF,
+ 0xD59E4EFE, 0x8738545E,
+ 0xD5FD3847, 0x8717304E,
+ 0xD65C3B7B, 0x86F656D3,
+ 0xD6BB585D, 0x86D5C802,
+ 0xD71A8EB5, 0x86B583EE,
+ 0xD779DE46, 0x86958AAB,
+ 0xD7D946D7, 0x8675DC4E,
+ 0xD838C82D, 0x865678EA,
+ 0xD898620C, 0x86376092,
+ 0xD8F81439, 0x86189359,
+ 0xD957DE7A, 0x85FA1152,
+ 0xD9B7C093, 0x85DBDA91,
+ 0xDA17BA4A, 0x85BDEF27,
+ 0xDA77CB62, 0x85A04F28,
+ 0xDAD7F3A2, 0x8582FAA4,
+ 0xDB3832CD, 0x8565F1B0,
+ 0xDB9888A8, 0x8549345C,
+ 0xDBF8F4F8, 0x852CC2BA,
+ 0xDC597781, 0x85109CDC,
+ 0xDCBA1008, 0x84F4C2D3,
+ 0xDD1ABE51, 0x84D934B0,
+ 0xDD7B8220, 0x84BDF285,
+ 0xDDDC5B3A, 0x84A2FC62,
+ 0xDE3D4963, 0x84885257,
+ 0xDE9E4C60, 0x846DF476,
+ 0xDEFF63F4, 0x8453E2CE,
+ 0xDF608FE3, 0x843A1D70,
+ 0xDFC1CFF2, 0x8420A46B,
+ 0xE02323E5, 0x840777CF,
+ 0xE0848B7F, 0x83EE97AC,
+ 0xE0E60684, 0x83D60411,
+ 0xE14794B9, 0x83BDBD0D,
+ 0xE1A935E1, 0x83A5C2B0,
+ 0xE20AE9C1, 0x838E1507,
+ 0xE26CB01A, 0x8376B422,
+ 0xE2CE88B2, 0x835FA00E,
+ 0xE330734C, 0x8348D8DB,
+ 0xE3926FAC, 0x83325E97,
+ 0xE3F47D95, 0x831C314E,
+ 0xE4569CCB, 0x8306510F,
+ 0xE4B8CD10, 0x82F0BDE8,
+ 0xE51B0E2A, 0x82DB77E5,
+ 0xE57D5FDA, 0x82C67F13,
+ 0xE5DFC1E4, 0x82B1D381,
+ 0xE642340D, 0x829D753A,
+ 0xE6A4B616, 0x8289644A,
+ 0xE70747C3, 0x8275A0C0,
+ 0xE769E8D8, 0x82622AA5,
+ 0xE7CC9917, 0x824F0208,
+ 0xE82F5844, 0x823C26F2,
+ 0xE8922621, 0x82299971,
+ 0xE8F50273, 0x8217598F,
+ 0xE957ECFB, 0x82056758,
+ 0xE9BAE57C, 0x81F3C2D7,
+ 0xEA1DEBBB, 0x81E26C16,
+ 0xEA80FF79, 0x81D16320,
+ 0xEAE4207A, 0x81C0A801,
+ 0xEB474E80, 0x81B03AC1,
+ 0xEBAA894E, 0x81A01B6C,
+ 0xEC0DD0A8, 0x81904A0C,
+ 0xEC71244F, 0x8180C6A9,
+ 0xECD48406, 0x8171914E,
+ 0xED37EF91, 0x8162AA03,
+ 0xED9B66B2, 0x815410D3,
+ 0xEDFEE92B, 0x8145C5C6,
+ 0xEE6276BF, 0x8137C8E6,
+ 0xEEC60F31, 0x812A1A39,
+ 0xEF29B243, 0x811CB9CA,
+ 0xEF8D5FB8, 0x810FA7A0,
+ 0xEFF11752, 0x8102E3C3,
+ 0xF054D8D4, 0x80F66E3C,
+ 0xF0B8A401, 0x80EA4712,
+ 0xF11C789A, 0x80DE6E4C,
+ 0xF1805662, 0x80D2E3F1,
+ 0xF1E43D1C, 0x80C7A80A,
+ 0xF2482C89, 0x80BCBA9C,
+ 0xF2AC246D, 0x80B21BAF,
+ 0xF310248A, 0x80A7CB49,
+ 0xF3742CA1, 0x809DC970,
+ 0xF3D83C76, 0x8094162B,
+ 0xF43C53CA, 0x808AB180,
+ 0xF4A07260, 0x80819B74,
+ 0xF50497FA, 0x8078D40D,
+ 0xF568C45A, 0x80705B50,
+ 0xF5CCF743, 0x80683143,
+ 0xF6313076, 0x806055EA,
+ 0xF6956FB6, 0x8058C94C,
+ 0xF6F9B4C5, 0x80518B6B,
+ 0xF75DFF65, 0x804A9C4D,
+ 0xF7C24F58, 0x8043FBF6,
+ 0xF826A461, 0x803DAA69,
+ 0xF88AFE41, 0x8037A7AC,
+ 0xF8EF5CBB, 0x8031F3C1,
+ 0xF953BF90, 0x802C8EAD,
+ 0xF9B82683, 0x80277872,
+ 0xFA1C9156, 0x8022B113,
+ 0xFA80FFCB, 0x801E3894,
+ 0xFAE571A4, 0x801A0EF7,
+ 0xFB49E6A2, 0x80163440,
+ 0xFBAE5E89, 0x8012A86F,
+ 0xFC12D919, 0x800F6B88,
+ 0xFC775616, 0x800C7D8C,
+ 0xFCDBD541, 0x8009DE7D,
+ 0xFD40565B, 0x80078E5E,
+ 0xFDA4D928, 0x80058D2E,
+ 0xFE095D69, 0x8003DAF0,
+ 0xFE6DE2E0, 0x800277A5,
+ 0xFED2694F, 0x8001634D,
+ 0xFF36F078, 0x80009DE9,
+ 0xFF9B781D, 0x8000277A
+};
+
+/**
+* \par
+* Example code for Q31 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 4096 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to Q31(Fixed point 1.31):
+* round(twiddleCoefQ31(i) * pow(2, 31))
+*
+*/
+const q31_t twiddleCoef_4096_q31[6144] =
+{
+ 0x7FFFFFFF, 0x00000000,
+ 0x7FFFF621, 0x003243F5,
+ 0x7FFFD885, 0x006487E3,
+ 0x7FFFA72C, 0x0096CBC1,
+ 0x7FFF6216, 0x00C90F88,
+ 0x7FFF0942, 0x00FB532F,
+ 0x7FFE9CB2, 0x012D96B0,
+ 0x7FFE1C64, 0x015FDA03,
+ 0x7FFD885A, 0x01921D1F,
+ 0x7FFCE093, 0x01C45FFE,
+ 0x7FFC250F, 0x01F6A296,
+ 0x7FFB55CE, 0x0228E4E1,
+ 0x7FFA72D1, 0x025B26D7,
+ 0x7FF97C17, 0x028D6870,
+ 0x7FF871A1, 0x02BFA9A4,
+ 0x7FF7536F, 0x02F1EA6B,
+ 0x7FF62182, 0x03242ABF,
+ 0x7FF4DBD8, 0x03566A96,
+ 0x7FF38273, 0x0388A9E9,
+ 0x7FF21553, 0x03BAE8B1,
+ 0x7FF09477, 0x03ED26E6,
+ 0x7FEEFFE1, 0x041F647F,
+ 0x7FED5790, 0x0451A176,
+ 0x7FEB9B85, 0x0483DDC3,
+ 0x7FE9CBC0, 0x04B6195D,
+ 0x7FE7E840, 0x04E8543D,
+ 0x7FE5F108, 0x051A8E5C,
+ 0x7FE3E616, 0x054CC7B0,
+ 0x7FE1C76B, 0x057F0034,
+ 0x7FDF9508, 0x05B137DF,
+ 0x7FDD4EEC, 0x05E36EA9,
+ 0x7FDAF518, 0x0615A48A,
+ 0x7FD8878D, 0x0647D97C,
+ 0x7FD6064B, 0x067A0D75,
+ 0x7FD37152, 0x06AC406F,
+ 0x7FD0C8A3, 0x06DE7261,
+ 0x7FCE0C3E, 0x0710A344,
+ 0x7FCB3C23, 0x0742D310,
+ 0x7FC85853, 0x077501BE,
+ 0x7FC560CF, 0x07A72F45,
+ 0x7FC25596, 0x07D95B9E,
+ 0x7FBF36A9, 0x080B86C1,
+ 0x7FBC040A, 0x083DB0A7,
+ 0x7FB8BDB7, 0x086FD947,
+ 0x7FB563B2, 0x08A2009A,
+ 0x7FB1F5FC, 0x08D42698,
+ 0x7FAE7494, 0x09064B3A,
+ 0x7FAADF7C, 0x09386E77,
+ 0x7FA736B4, 0x096A9049,
+ 0x7FA37A3C, 0x099CB0A7,
+ 0x7F9FAA15, 0x09CECF89,
+ 0x7F9BC63F, 0x0A00ECE8,
+ 0x7F97CEBC, 0x0A3308BC,
+ 0x7F93C38C, 0x0A6522FE,
+ 0x7F8FA4AF, 0x0A973BA5,
+ 0x7F8B7226, 0x0AC952AA,
+ 0x7F872BF3, 0x0AFB6805,
+ 0x7F82D214, 0x0B2D7BAE,
+ 0x7F7E648B, 0x0B5F8D9F,
+ 0x7F79E35A, 0x0B919DCE,
+ 0x7F754E7F, 0x0BC3AC35,
+ 0x7F70A5FD, 0x0BF5B8CB,
+ 0x7F6BE9D4, 0x0C27C389,
+ 0x7F671A04, 0x0C59CC67,
+ 0x7F62368F, 0x0C8BD35E,
+ 0x7F5D3F75, 0x0CBDD865,
+ 0x7F5834B6, 0x0CEFDB75,
+ 0x7F531654, 0x0D21DC87,
+ 0x7F4DE450, 0x0D53DB92,
+ 0x7F489EAA, 0x0D85D88F,
+ 0x7F434563, 0x0DB7D376,
+ 0x7F3DD87C, 0x0DE9CC3F,
+ 0x7F3857F5, 0x0E1BC2E3,
+ 0x7F32C3D0, 0x0E4DB75B,
+ 0x7F2D1C0E, 0x0E7FA99D,
+ 0x7F2760AF, 0x0EB199A3,
+ 0x7F2191B4, 0x0EE38765,
+ 0x7F1BAF1E, 0x0F1572DC,
+ 0x7F15B8EE, 0x0F475BFE,
+ 0x7F0FAF24, 0x0F7942C6,
+ 0x7F0991C3, 0x0FAB272B,
+ 0x7F0360CB, 0x0FDD0925,
+ 0x7EFD1C3C, 0x100EE8AD,
+ 0x7EF6C418, 0x1040C5BB,
+ 0x7EF0585F, 0x1072A047,
+ 0x7EE9D913, 0x10A4784A,
+ 0x7EE34635, 0x10D64DBC,
+ 0x7EDC9FC6, 0x11082096,
+ 0x7ED5E5C6, 0x1139F0CE,
+ 0x7ECF1837, 0x116BBE5F,
+ 0x7EC8371A, 0x119D8940,
+ 0x7EC1426F, 0x11CF516A,
+ 0x7EBA3A39, 0x120116D4,
+ 0x7EB31E77, 0x1232D978,
+ 0x7EABEF2C, 0x1264994E,
+ 0x7EA4AC58, 0x1296564D,
+ 0x7E9D55FC, 0x12C8106E,
+ 0x7E95EC19, 0x12F9C7AA,
+ 0x7E8E6EB1, 0x132B7BF9,
+ 0x7E86DDC5, 0x135D2D53,
+ 0x7E7F3956, 0x138EDBB0,
+ 0x7E778165, 0x13C0870A,
+ 0x7E6FB5F3, 0x13F22F57,
+ 0x7E67D702, 0x1423D492,
+ 0x7E5FE493, 0x145576B1,
+ 0x7E57DEA6, 0x148715AD,
+ 0x7E4FC53E, 0x14B8B17F,
+ 0x7E47985B, 0x14EA4A1F,
+ 0x7E3F57FE, 0x151BDF85,
+ 0x7E37042A, 0x154D71AA,
+ 0x7E2E9CDF, 0x157F0086,
+ 0x7E26221E, 0x15B08C11,
+ 0x7E1D93E9, 0x15E21444,
+ 0x7E14F242, 0x16139917,
+ 0x7E0C3D29, 0x16451A83,
+ 0x7E03749F, 0x1676987F,
+ 0x7DFA98A7, 0x16A81305,
+ 0x7DF1A942, 0x16D98A0C,
+ 0x7DE8A670, 0x170AFD8D,
+ 0x7DDF9034, 0x173C6D80,
+ 0x7DD6668E, 0x176DD9DE,
+ 0x7DCD2981, 0x179F429F,
+ 0x7DC3D90D, 0x17D0A7BB,
+ 0x7DBA7534, 0x1802092C,
+ 0x7DB0FDF7, 0x183366E8,
+ 0x7DA77359, 0x1864C0E9,
+ 0x7D9DD55A, 0x18961727,
+ 0x7D9423FB, 0x18C7699B,
+ 0x7D8A5F3F, 0x18F8B83C,
+ 0x7D808727, 0x192A0303,
+ 0x7D769BB5, 0x195B49E9,
+ 0x7D6C9CE9, 0x198C8CE6,
+ 0x7D628AC5, 0x19BDCBF2,
+ 0x7D58654C, 0x19EF0706,
+ 0x7D4E2C7E, 0x1A203E1B,
+ 0x7D43E05E, 0x1A517127,
+ 0x7D3980EC, 0x1A82A025,
+ 0x7D2F0E2A, 0x1AB3CB0C,
+ 0x7D24881A, 0x1AE4F1D6,
+ 0x7D19EEBE, 0x1B161479,
+ 0x7D0F4218, 0x1B4732EF,
+ 0x7D048228, 0x1B784D30,
+ 0x7CF9AEF0, 0x1BA96334,
+ 0x7CEEC873, 0x1BDA74F5,
+ 0x7CE3CEB1, 0x1C0B826A,
+ 0x7CD8C1AD, 0x1C3C8B8C,
+ 0x7CCDA168, 0x1C6D9053,
+ 0x7CC26DE5, 0x1C9E90B8,
+ 0x7CB72724, 0x1CCF8CB3,
+ 0x7CABCD27, 0x1D00843C,
+ 0x7CA05FF1, 0x1D31774D,
+ 0x7C94DF82, 0x1D6265DD,
+ 0x7C894BDD, 0x1D934FE5,
+ 0x7C7DA504, 0x1DC4355D,
+ 0x7C71EAF8, 0x1DF5163F,
+ 0x7C661DBB, 0x1E25F281,
+ 0x7C5A3D4F, 0x1E56CA1E,
+ 0x7C4E49B6, 0x1E879D0C,
+ 0x7C4242F2, 0x1EB86B46,
+ 0x7C362904, 0x1EE934C2,
+ 0x7C29FBEE, 0x1F19F97B,
+ 0x7C1DBBB2, 0x1F4AB967,
+ 0x7C116853, 0x1F7B7480,
+ 0x7C0501D1, 0x1FAC2ABF,
+ 0x7BF88830, 0x1FDCDC1A,
+ 0x7BEBFB70, 0x200D888C,
+ 0x7BDF5B94, 0x203E300D,
+ 0x7BD2A89E, 0x206ED295,
+ 0x7BC5E28F, 0x209F701C,
+ 0x7BB9096A, 0x20D0089B,
+ 0x7BAC1D31, 0x21009C0B,
+ 0x7B9F1DE5, 0x21312A65,
+ 0x7B920B89, 0x2161B39F,
+ 0x7B84E61E, 0x219237B4,
+ 0x7B77ADA8, 0x21C2B69C,
+ 0x7B6A6227, 0x21F3304E,
+ 0x7B5D039D, 0x2223A4C5,
+ 0x7B4F920E, 0x225413F8,
+ 0x7B420D7A, 0x22847DDF,
+ 0x7B3475E4, 0x22B4E274,
+ 0x7B26CB4F, 0x22E541AE,
+ 0x7B190DBB, 0x23159B87,
+ 0x7B0B3D2C, 0x2345EFF7,
+ 0x7AFD59A3, 0x23763EF7,
+ 0x7AEF6323, 0x23A6887E,
+ 0x7AE159AE, 0x23D6CC86,
+ 0x7AD33D45, 0x24070B07,
+ 0x7AC50DEB, 0x243743FA,
+ 0x7AB6CBA3, 0x24677757,
+ 0x7AA8766E, 0x2497A517,
+ 0x7A9A0E4F, 0x24C7CD32,
+ 0x7A8B9348, 0x24F7EFA1,
+ 0x7A7D055B, 0x25280C5D,
+ 0x7A6E648A, 0x2558235E,
+ 0x7A5FB0D8, 0x2588349D,
+ 0x7A50EA46, 0x25B84012,
+ 0x7A4210D8, 0x25E845B5,
+ 0x7A33248F, 0x26184581,
+ 0x7A24256E, 0x26483F6C,
+ 0x7A151377, 0x26783370,
+ 0x7A05EEAD, 0x26A82185,
+ 0x79F6B711, 0x26D809A5,
+ 0x79E76CA6, 0x2707EBC6,
+ 0x79D80F6F, 0x2737C7E3,
+ 0x79C89F6D, 0x27679DF4,
+ 0x79B91CA4, 0x27976DF1,
+ 0x79A98715, 0x27C737D2,
+ 0x7999DEC3, 0x27F6FB92,
+ 0x798A23B1, 0x2826B928,
+ 0x797A55E0, 0x2856708C,
+ 0x796A7554, 0x288621B9,
+ 0x795A820E, 0x28B5CCA5,
+ 0x794A7C11, 0x28E5714A,
+ 0x793A6360, 0x29150FA1,
+ 0x792A37FE, 0x2944A7A2,
+ 0x7919F9EB, 0x29743945,
+ 0x7909A92C, 0x29A3C484,
+ 0x78F945C3, 0x29D34958,
+ 0x78E8CFB1, 0x2A02C7B8,
+ 0x78D846FB, 0x2A323F9D,
+ 0x78C7ABA1, 0x2A61B101,
+ 0x78B6FDA8, 0x2A911BDB,
+ 0x78A63D10, 0x2AC08025,
+ 0x789569DE, 0x2AEFDDD8,
+ 0x78848413, 0x2B1F34EB,
+ 0x78738BB3, 0x2B4E8558,
+ 0x786280BF, 0x2B7DCF17,
+ 0x7851633B, 0x2BAD1221,
+ 0x78403328, 0x2BDC4E6F,
+ 0x782EF08B, 0x2C0B83F9,
+ 0x781D9B64, 0x2C3AB2B9,
+ 0x780C33B8, 0x2C69DAA6,
+ 0x77FAB988, 0x2C98FBBA,
+ 0x77E92CD8, 0x2CC815ED,
+ 0x77D78DAA, 0x2CF72939,
+ 0x77C5DC01, 0x2D263595,
+ 0x77B417DF, 0x2D553AFB,
+ 0x77A24148, 0x2D843963,
+ 0x7790583D, 0x2DB330C7,
+ 0x777E5CC3, 0x2DE2211E,
+ 0x776C4EDB, 0x2E110A62,
+ 0x775A2E88, 0x2E3FEC8B,
+ 0x7747FBCE, 0x2E6EC792,
+ 0x7735B6AE, 0x2E9D9B70,
+ 0x77235F2D, 0x2ECC681E,
+ 0x7710F54B, 0x2EFB2D94,
+ 0x76FE790E, 0x2F29EBCC,
+ 0x76EBEA77, 0x2F58A2BD,
+ 0x76D94988, 0x2F875262,
+ 0x76C69646, 0x2FB5FAB2,
+ 0x76B3D0B3, 0x2FE49BA6,
+ 0x76A0F8D2, 0x30133538,
+ 0x768E0EA5, 0x3041C760,
+ 0x767B1230, 0x30705217,
+ 0x76680376, 0x309ED555,
+ 0x7654E279, 0x30CD5114,
+ 0x7641AF3C, 0x30FBC54D,
+ 0x762E69C3, 0x312A31F8,
+ 0x761B1211, 0x3158970D,
+ 0x7607A827, 0x3186F487,
+ 0x75F42C0A, 0x31B54A5D,
+ 0x75E09DBD, 0x31E39889,
+ 0x75CCFD42, 0x3211DF03,
+ 0x75B94A9C, 0x32401DC5,
+ 0x75A585CF, 0x326E54C7,
+ 0x7591AEDD, 0x329C8402,
+ 0x757DC5CA, 0x32CAAB6F,
+ 0x7569CA98, 0x32F8CB07,
+ 0x7555BD4B, 0x3326E2C2,
+ 0x75419DE6, 0x3354F29A,
+ 0x752D6C6C, 0x3382FA88,
+ 0x751928E0, 0x33B0FA84,
+ 0x7504D345, 0x33DEF287,
+ 0x74F06B9E, 0x340CE28A,
+ 0x74DBF1EF, 0x343ACA87,
+ 0x74C7663A, 0x3468AA76,
+ 0x74B2C883, 0x3496824F,
+ 0x749E18CD, 0x34C4520D,
+ 0x7489571B, 0x34F219A7,
+ 0x74748371, 0x351FD917,
+ 0x745F9DD1, 0x354D9056,
+ 0x744AA63E, 0x357B3F5D,
+ 0x74359CBD, 0x35A8E624,
+ 0x74208150, 0x35D684A5,
+ 0x740B53FA, 0x36041AD9,
+ 0x73F614C0, 0x3631A8B7,
+ 0x73E0C3A3, 0x365F2E3B,
+ 0x73CB60A7, 0x368CAB5C,
+ 0x73B5EBD0, 0x36BA2013,
+ 0x73A06522, 0x36E78C5A,
+ 0x738ACC9E, 0x3714F02A,
+ 0x73752249, 0x37424B7A,
+ 0x735F6626, 0x376F9E46,
+ 0x73499838, 0x379CE884,
+ 0x7333B883, 0x37CA2A30,
+ 0x731DC709, 0x37F76340,
+ 0x7307C3D0, 0x382493B0,
+ 0x72F1AED8, 0x3851BB76,
+ 0x72DB8828, 0x387EDA8E,
+ 0x72C54FC0, 0x38ABF0EF,
+ 0x72AF05A6, 0x38D8FE93,
+ 0x7298A9DC, 0x39060372,
+ 0x72823C66, 0x3932FF87,
+ 0x726BBD48, 0x395FF2C9,
+ 0x72552C84, 0x398CDD32,
+ 0x723E8A1F, 0x39B9BEBB,
+ 0x7227D61C, 0x39E6975D,
+ 0x7211107D, 0x3A136712,
+ 0x71FA3948, 0x3A402DD1,
+ 0x71E3507F, 0x3A6CEB95,
+ 0x71CC5626, 0x3A99A057,
+ 0x71B54A40, 0x3AC64C0F,
+ 0x719E2CD2, 0x3AF2EEB7,
+ 0x7186FDDE, 0x3B1F8847,
+ 0x716FBD68, 0x3B4C18BA,
+ 0x71586B73, 0x3B78A007,
+ 0x71410804, 0x3BA51E29,
+ 0x7129931E, 0x3BD19317,
+ 0x71120CC5, 0x3BFDFECD,
+ 0x70FA74FB, 0x3C2A6142,
+ 0x70E2CBC6, 0x3C56BA70,
+ 0x70CB1127, 0x3C830A4F,
+ 0x70B34524, 0x3CAF50DA,
+ 0x709B67C0, 0x3CDB8E09,
+ 0x708378FE, 0x3D07C1D5,
+ 0x706B78E3, 0x3D33EC39,
+ 0x70536771, 0x3D600D2B,
+ 0x703B44AC, 0x3D8C24A7,
+ 0x70231099, 0x3DB832A5,
+ 0x700ACB3B, 0x3DE4371F,
+ 0x6FF27496, 0x3E10320D,
+ 0x6FDA0CAD, 0x3E3C2369,
+ 0x6FC19385, 0x3E680B2C,
+ 0x6FA90920, 0x3E93E94F,
+ 0x6F906D84, 0x3EBFBDCC,
+ 0x6F77C0B3, 0x3EEB889C,
+ 0x6F5F02B1, 0x3F1749B7,
+ 0x6F463383, 0x3F430118,
+ 0x6F2D532C, 0x3F6EAEB8,
+ 0x6F1461AF, 0x3F9A528F,
+ 0x6EFB5F12, 0x3FC5EC97,
+ 0x6EE24B57, 0x3FF17CCA,
+ 0x6EC92682, 0x401D0320,
+ 0x6EAFF098, 0x40487F93,
+ 0x6E96A99C, 0x4073F21D,
+ 0x6E7D5193, 0x409F5AB6,
+ 0x6E63E87F, 0x40CAB957,
+ 0x6E4A6E65, 0x40F60DFB,
+ 0x6E30E349, 0x4121589A,
+ 0x6E17472F, 0x414C992E,
+ 0x6DFD9A1B, 0x4177CFB0,
+ 0x6DE3DC11, 0x41A2FC1A,
+ 0x6DCA0D14, 0x41CE1E64,
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+ 0x2E3FEC8B, 0x775A2E88,
+ 0x2E110A62, 0x776C4EDB,
+ 0x2DE2211E, 0x777E5CC3,
+ 0x2DB330C7, 0x7790583D,
+ 0x2D843963, 0x77A24148,
+ 0x2D553AFB, 0x77B417DF,
+ 0x2D263595, 0x77C5DC01,
+ 0x2CF72939, 0x77D78DAA,
+ 0x2CC815ED, 0x77E92CD8,
+ 0x2C98FBBA, 0x77FAB988,
+ 0x2C69DAA6, 0x780C33B8,
+ 0x2C3AB2B9, 0x781D9B64,
+ 0x2C0B83F9, 0x782EF08B,
+ 0x2BDC4E6F, 0x78403328,
+ 0x2BAD1221, 0x7851633B,
+ 0x2B7DCF17, 0x786280BF,
+ 0x2B4E8558, 0x78738BB3,
+ 0x2B1F34EB, 0x78848413,
+ 0x2AEFDDD8, 0x789569DE,
+ 0x2AC08025, 0x78A63D10,
+ 0x2A911BDB, 0x78B6FDA8,
+ 0x2A61B101, 0x78C7ABA1,
+ 0x2A323F9D, 0x78D846FB,
+ 0x2A02C7B8, 0x78E8CFB1,
+ 0x29D34958, 0x78F945C3,
+ 0x29A3C484, 0x7909A92C,
+ 0x29743945, 0x7919F9EB,
+ 0x2944A7A2, 0x792A37FE,
+ 0x29150FA1, 0x793A6360,
+ 0x28E5714A, 0x794A7C11,
+ 0x28B5CCA5, 0x795A820E,
+ 0x288621B9, 0x796A7554,
+ 0x2856708C, 0x797A55E0,
+ 0x2826B928, 0x798A23B1,
+ 0x27F6FB92, 0x7999DEC3,
+ 0x27C737D2, 0x79A98715,
+ 0x27976DF1, 0x79B91CA4,
+ 0x27679DF4, 0x79C89F6D,
+ 0x2737C7E3, 0x79D80F6F,
+ 0x2707EBC6, 0x79E76CA6,
+ 0x26D809A5, 0x79F6B711,
+ 0x26A82185, 0x7A05EEAD,
+ 0x26783370, 0x7A151377,
+ 0x26483F6C, 0x7A24256E,
+ 0x26184581, 0x7A33248F,
+ 0x25E845B5, 0x7A4210D8,
+ 0x25B84012, 0x7A50EA46,
+ 0x2588349D, 0x7A5FB0D8,
+ 0x2558235E, 0x7A6E648A,
+ 0x25280C5D, 0x7A7D055B,
+ 0x24F7EFA1, 0x7A8B9348,
+ 0x24C7CD32, 0x7A9A0E4F,
+ 0x2497A517, 0x7AA8766E,
+ 0x24677757, 0x7AB6CBA3,
+ 0x243743FA, 0x7AC50DEB,
+ 0x24070B07, 0x7AD33D45,
+ 0x23D6CC86, 0x7AE159AE,
+ 0x23A6887E, 0x7AEF6323,
+ 0x23763EF7, 0x7AFD59A3,
+ 0x2345EFF7, 0x7B0B3D2C,
+ 0x23159B87, 0x7B190DBB,
+ 0x22E541AE, 0x7B26CB4F,
+ 0x22B4E274, 0x7B3475E4,
+ 0x22847DDF, 0x7B420D7A,
+ 0x225413F8, 0x7B4F920E,
+ 0x2223A4C5, 0x7B5D039D,
+ 0x21F3304E, 0x7B6A6227,
+ 0x21C2B69C, 0x7B77ADA8,
+ 0x219237B4, 0x7B84E61E,
+ 0x2161B39F, 0x7B920B89,
+ 0x21312A65, 0x7B9F1DE5,
+ 0x21009C0B, 0x7BAC1D31,
+ 0x20D0089B, 0x7BB9096A,
+ 0x209F701C, 0x7BC5E28F,
+ 0x206ED295, 0x7BD2A89E,
+ 0x203E300D, 0x7BDF5B94,
+ 0x200D888C, 0x7BEBFB70,
+ 0x1FDCDC1A, 0x7BF88830,
+ 0x1FAC2ABF, 0x7C0501D1,
+ 0x1F7B7480, 0x7C116853,
+ 0x1F4AB967, 0x7C1DBBB2,
+ 0x1F19F97B, 0x7C29FBEE,
+ 0x1EE934C2, 0x7C362904,
+ 0x1EB86B46, 0x7C4242F2,
+ 0x1E879D0C, 0x7C4E49B6,
+ 0x1E56CA1E, 0x7C5A3D4F,
+ 0x1E25F281, 0x7C661DBB,
+ 0x1DF5163F, 0x7C71EAF8,
+ 0x1DC4355D, 0x7C7DA504,
+ 0x1D934FE5, 0x7C894BDD,
+ 0x1D6265DD, 0x7C94DF82,
+ 0x1D31774D, 0x7CA05FF1,
+ 0x1D00843C, 0x7CABCD27,
+ 0x1CCF8CB3, 0x7CB72724,
+ 0x1C9E90B8, 0x7CC26DE5,
+ 0x1C6D9053, 0x7CCDA168,
+ 0x1C3C8B8C, 0x7CD8C1AD,
+ 0x1C0B826A, 0x7CE3CEB1,
+ 0x1BDA74F5, 0x7CEEC873,
+ 0x1BA96334, 0x7CF9AEF0,
+ 0x1B784D30, 0x7D048228,
+ 0x1B4732EF, 0x7D0F4218,
+ 0x1B161479, 0x7D19EEBE,
+ 0x1AE4F1D6, 0x7D24881A,
+ 0x1AB3CB0C, 0x7D2F0E2A,
+ 0x1A82A025, 0x7D3980EC,
+ 0x1A517127, 0x7D43E05E,
+ 0x1A203E1B, 0x7D4E2C7E,
+ 0x19EF0706, 0x7D58654C,
+ 0x19BDCBF2, 0x7D628AC5,
+ 0x198C8CE6, 0x7D6C9CE9,
+ 0x195B49E9, 0x7D769BB5,
+ 0x192A0303, 0x7D808727,
+ 0x18F8B83C, 0x7D8A5F3F,
+ 0x18C7699B, 0x7D9423FB,
+ 0x18961727, 0x7D9DD55A,
+ 0x1864C0E9, 0x7DA77359,
+ 0x183366E8, 0x7DB0FDF7,
+ 0x1802092C, 0x7DBA7534,
+ 0x17D0A7BB, 0x7DC3D90D,
+ 0x179F429F, 0x7DCD2981,
+ 0x176DD9DE, 0x7DD6668E,
+ 0x173C6D80, 0x7DDF9034,
+ 0x170AFD8D, 0x7DE8A670,
+ 0x16D98A0C, 0x7DF1A942,
+ 0x16A81305, 0x7DFA98A7,
+ 0x1676987F, 0x7E03749F,
+ 0x16451A83, 0x7E0C3D29,
+ 0x16139917, 0x7E14F242,
+ 0x15E21444, 0x7E1D93E9,
+ 0x15B08C11, 0x7E26221E,
+ 0x157F0086, 0x7E2E9CDF,
+ 0x154D71AA, 0x7E37042A,
+ 0x151BDF85, 0x7E3F57FE,
+ 0x14EA4A1F, 0x7E47985B,
+ 0x14B8B17F, 0x7E4FC53E,
+ 0x148715AD, 0x7E57DEA6,
+ 0x145576B1, 0x7E5FE493,
+ 0x1423D492, 0x7E67D702,
+ 0x13F22F57, 0x7E6FB5F3,
+ 0x13C0870A, 0x7E778165,
+ 0x138EDBB0, 0x7E7F3956,
+ 0x135D2D53, 0x7E86DDC5,
+ 0x132B7BF9, 0x7E8E6EB1,
+ 0x12F9C7AA, 0x7E95EC19,
+ 0x12C8106E, 0x7E9D55FC,
+ 0x1296564D, 0x7EA4AC58,
+ 0x1264994E, 0x7EABEF2C,
+ 0x1232D978, 0x7EB31E77,
+ 0x120116D4, 0x7EBA3A39,
+ 0x11CF516A, 0x7EC1426F,
+ 0x119D8940, 0x7EC8371A,
+ 0x116BBE5F, 0x7ECF1837,
+ 0x1139F0CE, 0x7ED5E5C6,
+ 0x11082096, 0x7EDC9FC6,
+ 0x10D64DBC, 0x7EE34635,
+ 0x10A4784A, 0x7EE9D913,
+ 0x1072A047, 0x7EF0585F,
+ 0x1040C5BB, 0x7EF6C418,
+ 0x100EE8AD, 0x7EFD1C3C,
+ 0x0FDD0925, 0x7F0360CB,
+ 0x0FAB272B, 0x7F0991C3,
+ 0x0F7942C6, 0x7F0FAF24,
+ 0x0F475BFE, 0x7F15B8EE,
+ 0x0F1572DC, 0x7F1BAF1E,
+ 0x0EE38765, 0x7F2191B4,
+ 0x0EB199A3, 0x7F2760AF,
+ 0x0E7FA99D, 0x7F2D1C0E,
+ 0x0E4DB75B, 0x7F32C3D0,
+ 0x0E1BC2E3, 0x7F3857F5,
+ 0x0DE9CC3F, 0x7F3DD87C,
+ 0x0DB7D376, 0x7F434563,
+ 0x0D85D88F, 0x7F489EAA,
+ 0x0D53DB92, 0x7F4DE450,
+ 0x0D21DC87, 0x7F531654,
+ 0x0CEFDB75, 0x7F5834B6,
+ 0x0CBDD865, 0x7F5D3F75,
+ 0x0C8BD35E, 0x7F62368F,
+ 0x0C59CC67, 0x7F671A04,
+ 0x0C27C389, 0x7F6BE9D4,
+ 0x0BF5B8CB, 0x7F70A5FD,
+ 0x0BC3AC35, 0x7F754E7F,
+ 0x0B919DCE, 0x7F79E35A,
+ 0x0B5F8D9F, 0x7F7E648B,
+ 0x0B2D7BAE, 0x7F82D214,
+ 0x0AFB6805, 0x7F872BF3,
+ 0x0AC952AA, 0x7F8B7226,
+ 0x0A973BA5, 0x7F8FA4AF,
+ 0x0A6522FE, 0x7F93C38C,
+ 0x0A3308BC, 0x7F97CEBC,
+ 0x0A00ECE8, 0x7F9BC63F,
+ 0x09CECF89, 0x7F9FAA15,
+ 0x099CB0A7, 0x7FA37A3C,
+ 0x096A9049, 0x7FA736B4,
+ 0x09386E77, 0x7FAADF7C,
+ 0x09064B3A, 0x7FAE7494,
+ 0x08D42698, 0x7FB1F5FC,
+ 0x08A2009A, 0x7FB563B2,
+ 0x086FD947, 0x7FB8BDB7,
+ 0x083DB0A7, 0x7FBC040A,
+ 0x080B86C1, 0x7FBF36A9,
+ 0x07D95B9E, 0x7FC25596,
+ 0x07A72F45, 0x7FC560CF,
+ 0x077501BE, 0x7FC85853,
+ 0x0742D310, 0x7FCB3C23,
+ 0x0710A344, 0x7FCE0C3E,
+ 0x06DE7261, 0x7FD0C8A3,
+ 0x06AC406F, 0x7FD37152,
+ 0x067A0D75, 0x7FD6064B,
+ 0x0647D97C, 0x7FD8878D,
+ 0x0615A48A, 0x7FDAF518,
+ 0x05E36EA9, 0x7FDD4EEC,
+ 0x05B137DF, 0x7FDF9508,
+ 0x057F0034, 0x7FE1C76B,
+ 0x054CC7B0, 0x7FE3E616,
+ 0x051A8E5C, 0x7FE5F108,
+ 0x04E8543D, 0x7FE7E840,
+ 0x04B6195D, 0x7FE9CBC0,
+ 0x0483DDC3, 0x7FEB9B85,
+ 0x0451A176, 0x7FED5790,
+ 0x041F647F, 0x7FEEFFE1,
+ 0x03ED26E6, 0x7FF09477,
+ 0x03BAE8B1, 0x7FF21553,
+ 0x0388A9E9, 0x7FF38273,
+ 0x03566A96, 0x7FF4DBD8,
+ 0x03242ABF, 0x7FF62182,
+ 0x02F1EA6B, 0x7FF7536F,
+ 0x02BFA9A4, 0x7FF871A1,
+ 0x028D6870, 0x7FF97C17,
+ 0x025B26D7, 0x7FFA72D1,
+ 0x0228E4E1, 0x7FFB55CE,
+ 0x01F6A296, 0x7FFC250F,
+ 0x01C45FFE, 0x7FFCE093,
+ 0x01921D1F, 0x7FFD885A,
+ 0x015FDA03, 0x7FFE1C64,
+ 0x012D96B0, 0x7FFE9CB2,
+ 0x00FB532F, 0x7FFF0942,
+ 0x00C90F88, 0x7FFF6216,
+ 0x0096CBC1, 0x7FFFA72C,
+ 0x006487E3, 0x7FFFD885,
+ 0x003243F5, 0x7FFFF621,
+ 0x00000000, 0x7FFFFFFF,
+ 0xFFCDBC0A, 0x7FFFF621,
+ 0xFF9B781D, 0x7FFFD885,
+ 0xFF69343E, 0x7FFFA72C,
+ 0xFF36F078, 0x7FFF6216,
+ 0xFF04ACD0, 0x7FFF0942,
+ 0xFED2694F, 0x7FFE9CB2,
+ 0xFEA025FC, 0x7FFE1C64,
+ 0xFE6DE2E0, 0x7FFD885A,
+ 0xFE3BA001, 0x7FFCE093,
+ 0xFE095D69, 0x7FFC250F,
+ 0xFDD71B1E, 0x7FFB55CE,
+ 0xFDA4D928, 0x7FFA72D1,
+ 0xFD72978F, 0x7FF97C17,
+ 0xFD40565B, 0x7FF871A1,
+ 0xFD0E1594, 0x7FF7536F,
+ 0xFCDBD541, 0x7FF62182,
+ 0xFCA99569, 0x7FF4DBD8,
+ 0xFC775616, 0x7FF38273,
+ 0xFC45174E, 0x7FF21553,
+ 0xFC12D919, 0x7FF09477,
+ 0xFBE09B80, 0x7FEEFFE1,
+ 0xFBAE5E89, 0x7FED5790,
+ 0xFB7C223C, 0x7FEB9B85,
+ 0xFB49E6A2, 0x7FE9CBC0,
+ 0xFB17ABC2, 0x7FE7E840,
+ 0xFAE571A4, 0x7FE5F108,
+ 0xFAB3384F, 0x7FE3E616,
+ 0xFA80FFCB, 0x7FE1C76B,
+ 0xFA4EC820, 0x7FDF9508,
+ 0xFA1C9156, 0x7FDD4EEC,
+ 0xF9EA5B75, 0x7FDAF518,
+ 0xF9B82683, 0x7FD8878D,
+ 0xF985F28A, 0x7FD6064B,
+ 0xF953BF90, 0x7FD37152,
+ 0xF9218D9E, 0x7FD0C8A3,
+ 0xF8EF5CBB, 0x7FCE0C3E,
+ 0xF8BD2CEF, 0x7FCB3C23,
+ 0xF88AFE41, 0x7FC85853,
+ 0xF858D0BA, 0x7FC560CF,
+ 0xF826A461, 0x7FC25596,
+ 0xF7F4793E, 0x7FBF36A9,
+ 0xF7C24F58, 0x7FBC040A,
+ 0xF79026B8, 0x7FB8BDB7,
+ 0xF75DFF65, 0x7FB563B2,
+ 0xF72BD967, 0x7FB1F5FC,
+ 0xF6F9B4C5, 0x7FAE7494,
+ 0xF6C79188, 0x7FAADF7C,
+ 0xF6956FB6, 0x7FA736B4,
+ 0xF6634F58, 0x7FA37A3C,
+ 0xF6313076, 0x7F9FAA15,
+ 0xF5FF1317, 0x7F9BC63F,
+ 0xF5CCF743, 0x7F97CEBC,
+ 0xF59ADD01, 0x7F93C38C,
+ 0xF568C45A, 0x7F8FA4AF,
+ 0xF536AD55, 0x7F8B7226,
+ 0xF50497FA, 0x7F872BF3,
+ 0xF4D28451, 0x7F82D214,
+ 0xF4A07260, 0x7F7E648B,
+ 0xF46E6231, 0x7F79E35A,
+ 0xF43C53CA, 0x7F754E7F,
+ 0xF40A4734, 0x7F70A5FD,
+ 0xF3D83C76, 0x7F6BE9D4,
+ 0xF3A63398, 0x7F671A04,
+ 0xF3742CA1, 0x7F62368F,
+ 0xF342279A, 0x7F5D3F75,
+ 0xF310248A, 0x7F5834B6,
+ 0xF2DE2378, 0x7F531654,
+ 0xF2AC246D, 0x7F4DE450,
+ 0xF27A2770, 0x7F489EAA,
+ 0xF2482C89, 0x7F434563,
+ 0xF21633C0, 0x7F3DD87C,
+ 0xF1E43D1C, 0x7F3857F5,
+ 0xF1B248A5, 0x7F32C3D0,
+ 0xF1805662, 0x7F2D1C0E,
+ 0xF14E665C, 0x7F2760AF,
+ 0xF11C789A, 0x7F2191B4,
+ 0xF0EA8D23, 0x7F1BAF1E,
+ 0xF0B8A401, 0x7F15B8EE,
+ 0xF086BD39, 0x7F0FAF24,
+ 0xF054D8D4, 0x7F0991C3,
+ 0xF022F6DA, 0x7F0360CB,
+ 0xEFF11752, 0x7EFD1C3C,
+ 0xEFBF3A44, 0x7EF6C418,
+ 0xEF8D5FB8, 0x7EF0585F,
+ 0xEF5B87B5, 0x7EE9D913,
+ 0xEF29B243, 0x7EE34635,
+ 0xEEF7DF6A, 0x7EDC9FC6,
+ 0xEEC60F31, 0x7ED5E5C6,
+ 0xEE9441A0, 0x7ECF1837,
+ 0xEE6276BF, 0x7EC8371A,
+ 0xEE30AE95, 0x7EC1426F,
+ 0xEDFEE92B, 0x7EBA3A39,
+ 0xEDCD2687, 0x7EB31E77,
+ 0xED9B66B2, 0x7EABEF2C,
+ 0xED69A9B2, 0x7EA4AC58,
+ 0xED37EF91, 0x7E9D55FC,
+ 0xED063855, 0x7E95EC19,
+ 0xECD48406, 0x7E8E6EB1,
+ 0xECA2D2AC, 0x7E86DDC5,
+ 0xEC71244F, 0x7E7F3956,
+ 0xEC3F78F5, 0x7E778165,
+ 0xEC0DD0A8, 0x7E6FB5F3,
+ 0xEBDC2B6D, 0x7E67D702,
+ 0xEBAA894E, 0x7E5FE493,
+ 0xEB78EA52, 0x7E57DEA6,
+ 0xEB474E80, 0x7E4FC53E,
+ 0xEB15B5E0, 0x7E47985B,
+ 0xEAE4207A, 0x7E3F57FE,
+ 0xEAB28E55, 0x7E37042A,
+ 0xEA80FF79, 0x7E2E9CDF,
+ 0xEA4F73EE, 0x7E26221E,
+ 0xEA1DEBBB, 0x7E1D93E9,
+ 0xE9EC66E8, 0x7E14F242,
+ 0xE9BAE57C, 0x7E0C3D29,
+ 0xE9896780, 0x7E03749F,
+ 0xE957ECFB, 0x7DFA98A7,
+ 0xE92675F4, 0x7DF1A942,
+ 0xE8F50273, 0x7DE8A670,
+ 0xE8C3927F, 0x7DDF9034,
+ 0xE8922621, 0x7DD6668E,
+ 0xE860BD60, 0x7DCD2981,
+ 0xE82F5844, 0x7DC3D90D,
+ 0xE7FDF6D3, 0x7DBA7534,
+ 0xE7CC9917, 0x7DB0FDF7,
+ 0xE79B3F16, 0x7DA77359,
+ 0xE769E8D8, 0x7D9DD55A,
+ 0xE7389664, 0x7D9423FB,
+ 0xE70747C3, 0x7D8A5F3F,
+ 0xE6D5FCFC, 0x7D808727,
+ 0xE6A4B616, 0x7D769BB5,
+ 0xE6737319, 0x7D6C9CE9,
+ 0xE642340D, 0x7D628AC5,
+ 0xE610F8F9, 0x7D58654C,
+ 0xE5DFC1E4, 0x7D4E2C7E,
+ 0xE5AE8ED8, 0x7D43E05E,
+ 0xE57D5FDA, 0x7D3980EC,
+ 0xE54C34F3, 0x7D2F0E2A,
+ 0xE51B0E2A, 0x7D24881A,
+ 0xE4E9EB86, 0x7D19EEBE,
+ 0xE4B8CD10, 0x7D0F4218,
+ 0xE487B2CF, 0x7D048228,
+ 0xE4569CCB, 0x7CF9AEF0,
+ 0xE4258B0A, 0x7CEEC873,
+ 0xE3F47D95, 0x7CE3CEB1,
+ 0xE3C37473, 0x7CD8C1AD,
+ 0xE3926FAC, 0x7CCDA168,
+ 0xE3616F47, 0x7CC26DE5,
+ 0xE330734C, 0x7CB72724,
+ 0xE2FF7BC3, 0x7CABCD27,
+ 0xE2CE88B2, 0x7CA05FF1,
+ 0xE29D9A22, 0x7C94DF82,
+ 0xE26CB01A, 0x7C894BDD,
+ 0xE23BCAA2, 0x7C7DA504,
+ 0xE20AE9C1, 0x7C71EAF8,
+ 0xE1DA0D7E, 0x7C661DBB,
+ 0xE1A935E1, 0x7C5A3D4F,
+ 0xE17862F3, 0x7C4E49B6,
+ 0xE14794B9, 0x7C4242F2,
+ 0xE116CB3D, 0x7C362904,
+ 0xE0E60684, 0x7C29FBEE,
+ 0xE0B54698, 0x7C1DBBB2,
+ 0xE0848B7F, 0x7C116853,
+ 0xE053D541, 0x7C0501D1,
+ 0xE02323E5, 0x7BF88830,
+ 0xDFF27773, 0x7BEBFB70,
+ 0xDFC1CFF2, 0x7BDF5B94,
+ 0xDF912D6A, 0x7BD2A89E,
+ 0xDF608FE3, 0x7BC5E28F,
+ 0xDF2FF764, 0x7BB9096A,
+ 0xDEFF63F4, 0x7BAC1D31,
+ 0xDECED59B, 0x7B9F1DE5,
+ 0xDE9E4C60, 0x7B920B89,
+ 0xDE6DC84B, 0x7B84E61E,
+ 0xDE3D4963, 0x7B77ADA8,
+ 0xDE0CCFB1, 0x7B6A6227,
+ 0xDDDC5B3A, 0x7B5D039D,
+ 0xDDABEC07, 0x7B4F920E,
+ 0xDD7B8220, 0x7B420D7A,
+ 0xDD4B1D8B, 0x7B3475E4,
+ 0xDD1ABE51, 0x7B26CB4F,
+ 0xDCEA6478, 0x7B190DBB,
+ 0xDCBA1008, 0x7B0B3D2C,
+ 0xDC89C108, 0x7AFD59A3,
+ 0xDC597781, 0x7AEF6323,
+ 0xDC293379, 0x7AE159AE,
+ 0xDBF8F4F8, 0x7AD33D45,
+ 0xDBC8BC05, 0x7AC50DEB,
+ 0xDB9888A8, 0x7AB6CBA3,
+ 0xDB685AE8, 0x7AA8766E,
+ 0xDB3832CD, 0x7A9A0E4F,
+ 0xDB08105E, 0x7A8B9348,
+ 0xDAD7F3A2, 0x7A7D055B,
+ 0xDAA7DCA1, 0x7A6E648A,
+ 0xDA77CB62, 0x7A5FB0D8,
+ 0xDA47BFED, 0x7A50EA46,
+ 0xDA17BA4A, 0x7A4210D8,
+ 0xD9E7BA7E, 0x7A33248F,
+ 0xD9B7C093, 0x7A24256E,
+ 0xD987CC8F, 0x7A151377,
+ 0xD957DE7A, 0x7A05EEAD,
+ 0xD927F65B, 0x79F6B711,
+ 0xD8F81439, 0x79E76CA6,
+ 0xD8C8381C, 0x79D80F6F,
+ 0xD898620C, 0x79C89F6D,
+ 0xD868920F, 0x79B91CA4,
+ 0xD838C82D, 0x79A98715,
+ 0xD809046D, 0x7999DEC3,
+ 0xD7D946D7, 0x798A23B1,
+ 0xD7A98F73, 0x797A55E0,
+ 0xD779DE46, 0x796A7554,
+ 0xD74A335A, 0x795A820E,
+ 0xD71A8EB5, 0x794A7C11,
+ 0xD6EAF05E, 0x793A6360,
+ 0xD6BB585D, 0x792A37FE,
+ 0xD68BC6BA, 0x7919F9EB,
+ 0xD65C3B7B, 0x7909A92C,
+ 0xD62CB6A7, 0x78F945C3,
+ 0xD5FD3847, 0x78E8CFB1,
+ 0xD5CDC062, 0x78D846FB,
+ 0xD59E4EFE, 0x78C7ABA1,
+ 0xD56EE424, 0x78B6FDA8,
+ 0xD53F7FDA, 0x78A63D10,
+ 0xD5102227, 0x789569DE,
+ 0xD4E0CB14, 0x78848413,
+ 0xD4B17AA7, 0x78738BB3,
+ 0xD48230E8, 0x786280BF,
+ 0xD452EDDE, 0x7851633B,
+ 0xD423B190, 0x78403328,
+ 0xD3F47C06, 0x782EF08B,
+ 0xD3C54D46, 0x781D9B64,
+ 0xD3962559, 0x780C33B8,
+ 0xD3670445, 0x77FAB988,
+ 0xD337EA12, 0x77E92CD8,
+ 0xD308D6C6, 0x77D78DAA,
+ 0xD2D9CA6A, 0x77C5DC01,
+ 0xD2AAC504, 0x77B417DF,
+ 0xD27BC69C, 0x77A24148,
+ 0xD24CCF38, 0x7790583D,
+ 0xD21DDEE1, 0x777E5CC3,
+ 0xD1EEF59E, 0x776C4EDB,
+ 0xD1C01374, 0x775A2E88,
+ 0xD191386D, 0x7747FBCE,
+ 0xD162648F, 0x7735B6AE,
+ 0xD13397E1, 0x77235F2D,
+ 0xD104D26B, 0x7710F54B,
+ 0xD0D61433, 0x76FE790E,
+ 0xD0A75D42, 0x76EBEA77,
+ 0xD078AD9D, 0x76D94988,
+ 0xD04A054D, 0x76C69646,
+ 0xD01B6459, 0x76B3D0B3,
+ 0xCFECCAC7, 0x76A0F8D2,
+ 0xCFBE389F, 0x768E0EA5,
+ 0xCF8FADE8, 0x767B1230,
+ 0xCF612AAA, 0x76680376,
+ 0xCF32AEEB, 0x7654E279,
+ 0xCF043AB2, 0x7641AF3C,
+ 0xCED5CE08, 0x762E69C3,
+ 0xCEA768F2, 0x761B1211,
+ 0xCE790B78, 0x7607A827,
+ 0xCE4AB5A2, 0x75F42C0A,
+ 0xCE1C6776, 0x75E09DBD,
+ 0xCDEE20FC, 0x75CCFD42,
+ 0xCDBFE23A, 0x75B94A9C,
+ 0xCD91AB38, 0x75A585CF,
+ 0xCD637BFD, 0x7591AEDD,
+ 0xCD355490, 0x757DC5CA,
+ 0xCD0734F8, 0x7569CA98,
+ 0xCCD91D3D, 0x7555BD4B,
+ 0xCCAB0D65, 0x75419DE6,
+ 0xCC7D0577, 0x752D6C6C,
+ 0xCC4F057B, 0x751928E0,
+ 0xCC210D78, 0x7504D345,
+ 0xCBF31D75, 0x74F06B9E,
+ 0xCBC53578, 0x74DBF1EF,
+ 0xCB975589, 0x74C7663A,
+ 0xCB697DB0, 0x74B2C883,
+ 0xCB3BADF2, 0x749E18CD,
+ 0xCB0DE658, 0x7489571B,
+ 0xCAE026E8, 0x74748371,
+ 0xCAB26FA9, 0x745F9DD1,
+ 0xCA84C0A2, 0x744AA63E,
+ 0xCA5719DB, 0x74359CBD,
+ 0xCA297B5A, 0x74208150,
+ 0xC9FBE527, 0x740B53FA,
+ 0xC9CE5748, 0x73F614C0,
+ 0xC9A0D1C4, 0x73E0C3A3,
+ 0xC97354A3, 0x73CB60A7,
+ 0xC945DFEC, 0x73B5EBD0,
+ 0xC91873A5, 0x73A06522,
+ 0xC8EB0FD6, 0x738ACC9E,
+ 0xC8BDB485, 0x73752249,
+ 0xC89061BA, 0x735F6626,
+ 0xC863177B, 0x73499838,
+ 0xC835D5D0, 0x7333B883,
+ 0xC8089CBF, 0x731DC709,
+ 0xC7DB6C50, 0x7307C3D0,
+ 0xC7AE4489, 0x72F1AED8,
+ 0xC7812571, 0x72DB8828,
+ 0xC7540F10, 0x72C54FC0,
+ 0xC727016C, 0x72AF05A6,
+ 0xC6F9FC8D, 0x7298A9DC,
+ 0xC6CD0079, 0x72823C66,
+ 0xC6A00D36, 0x726BBD48,
+ 0xC67322CD, 0x72552C84,
+ 0xC6464144, 0x723E8A1F,
+ 0xC61968A2, 0x7227D61C,
+ 0xC5EC98ED, 0x7211107D,
+ 0xC5BFD22E, 0x71FA3948,
+ 0xC593146A, 0x71E3507F,
+ 0xC5665FA8, 0x71CC5626,
+ 0xC539B3F0, 0x71B54A40,
+ 0xC50D1148, 0x719E2CD2,
+ 0xC4E077B8, 0x7186FDDE,
+ 0xC4B3E746, 0x716FBD68,
+ 0xC4875FF8, 0x71586B73,
+ 0xC45AE1D7, 0x71410804,
+ 0xC42E6CE8, 0x7129931E,
+ 0xC4020132, 0x71120CC5,
+ 0xC3D59EBD, 0x70FA74FB,
+ 0xC3A9458F, 0x70E2CBC6,
+ 0xC37CF5B0, 0x70CB1127,
+ 0xC350AF25, 0x70B34524,
+ 0xC32471F6, 0x709B67C0,
+ 0xC2F83E2A, 0x708378FE,
+ 0xC2CC13C7, 0x706B78E3,
+ 0xC29FF2D4, 0x70536771,
+ 0xC273DB58, 0x703B44AC,
+ 0xC247CD5A, 0x70231099,
+ 0xC21BC8E0, 0x700ACB3B,
+ 0xC1EFCDF2, 0x6FF27496,
+ 0xC1C3DC96, 0x6FDA0CAD,
+ 0xC197F4D3, 0x6FC19385,
+ 0xC16C16B0, 0x6FA90920,
+ 0xC1404233, 0x6F906D84,
+ 0xC1147763, 0x6F77C0B3,
+ 0xC0E8B648, 0x6F5F02B1,
+ 0xC0BCFEE7, 0x6F463383,
+ 0xC0915147, 0x6F2D532C,
+ 0xC065AD70, 0x6F1461AF,
+ 0xC03A1368, 0x6EFB5F12,
+ 0xC00E8335, 0x6EE24B57,
+ 0xBFE2FCDF, 0x6EC92682,
+ 0xBFB7806C, 0x6EAFF098,
+ 0xBF8C0DE2, 0x6E96A99C,
+ 0xBF60A54A, 0x6E7D5193,
+ 0xBF3546A8, 0x6E63E87F,
+ 0xBF09F204, 0x6E4A6E65,
+ 0xBEDEA765, 0x6E30E349,
+ 0xBEB366D1, 0x6E17472F,
+ 0xBE88304F, 0x6DFD9A1B,
+ 0xBE5D03E5, 0x6DE3DC11,
+ 0xBE31E19B, 0x6DCA0D14,
+ 0xBE06C977, 0x6DB02D29,
+ 0xBDDBBB7F, 0x6D963C54,
+ 0xBDB0B7BA, 0x6D7C3A98,
+ 0xBD85BE2F, 0x6D6227FA,
+ 0xBD5ACEE5, 0x6D48047E,
+ 0xBD2FE9E1, 0x6D2DD027,
+ 0xBD050F2C, 0x6D138AFA,
+ 0xBCDA3ECA, 0x6CF934FB,
+ 0xBCAF78C3, 0x6CDECE2E,
+ 0xBC84BD1E, 0x6CC45697,
+ 0xBC5A0BE1, 0x6CA9CE3A,
+ 0xBC2F6513, 0x6C8F351C,
+ 0xBC04C8BA, 0x6C748B3F,
+ 0xBBDA36DC, 0x6C59D0A9,
+ 0xBBAFAF81, 0x6C3F055D,
+ 0xBB8532AF, 0x6C242960,
+ 0xBB5AC06C, 0x6C093CB6,
+ 0xBB3058C0, 0x6BEE3F62,
+ 0xBB05FBB0, 0x6BD3316A,
+ 0xBADBA943, 0x6BB812D0,
+ 0xBAB1617F, 0x6B9CE39B,
+ 0xBA87246C, 0x6B81A3CD,
+ 0xBA5CF210, 0x6B66536A,
+ 0xBA32CA70, 0x6B4AF278,
+ 0xBA08AD94, 0x6B2F80FA,
+ 0xB9DE9B83, 0x6B13FEF5,
+ 0xB9B49442, 0x6AF86C6C,
+ 0xB98A97D8, 0x6ADCC964,
+ 0xB960A64B, 0x6AC115E1,
+ 0xB936BFA3, 0x6AA551E8,
+ 0xB90CE3E6, 0x6A897D7D,
+ 0xB8E31319, 0x6A6D98A4,
+ 0xB8B94D44, 0x6A51A361,
+ 0xB88F926C, 0x6A359DB9,
+ 0xB865E299, 0x6A1987B0,
+ 0xB83C3DD1, 0x69FD614A,
+ 0xB812A419, 0x69E12A8C,
+ 0xB7E9157A, 0x69C4E37A,
+ 0xB7BF91F8, 0x69A88C18,
+ 0xB796199B, 0x698C246C,
+ 0xB76CAC68, 0x696FAC78,
+ 0xB7434A67, 0x69532442,
+ 0xB719F39D, 0x69368BCE,
+ 0xB6F0A811, 0x6919E320,
+ 0xB6C767CA, 0x68FD2A3D,
+ 0xB69E32CD, 0x68E06129,
+ 0xB6750921, 0x68C387E9,
+ 0xB64BEACC, 0x68A69E81,
+ 0xB622D7D5, 0x6889A4F5,
+ 0xB5F9D042, 0x686C9B4B,
+ 0xB5D0D41A, 0x684F8186,
+ 0xB5A7E362, 0x683257AA,
+ 0xB57EFE21, 0x68151DBE,
+ 0xB556245E, 0x67F7D3C4,
+ 0xB52D561E, 0x67DA79C2,
+ 0xB5049368, 0x67BD0FBC,
+ 0xB4DBDC42, 0x679F95B7,
+ 0xB4B330B2, 0x67820BB6,
+ 0xB48A90C0, 0x676471C0,
+ 0xB461FC70, 0x6746C7D7,
+ 0xB43973C9, 0x67290E02,
+ 0xB410F6D2, 0x670B4443,
+ 0xB3E88591, 0x66ED6AA1,
+ 0xB3C0200C, 0x66CF811F,
+ 0xB397C649, 0x66B187C3,
+ 0xB36F784E, 0x66937E90,
+ 0xB3473622, 0x6675658C,
+ 0xB31EFFCB, 0x66573CBB,
+ 0xB2F6D54F, 0x66390422,
+ 0xB2CEB6B5, 0x661ABBC5,
+ 0xB2A6A401, 0x65FC63A9,
+ 0xB27E9D3B, 0x65DDFBD3,
+ 0xB256A26A, 0x65BF8447,
+ 0xB22EB392, 0x65A0FD0B,
+ 0xB206D0BA, 0x65826622,
+ 0xB1DEF9E8, 0x6563BF92,
+ 0xB1B72F23, 0x6545095F,
+ 0xB18F7070, 0x6526438E,
+ 0xB167BDD6, 0x65076E24,
+ 0xB140175B, 0x64E88926,
+ 0xB1187D05, 0x64C99498,
+ 0xB0F0EEDA, 0x64AA907F,
+ 0xB0C96CDF, 0x648B7CDF,
+ 0xB0A1F71C, 0x646C59BF,
+ 0xB07A8D97, 0x644D2722,
+ 0xB0533055, 0x642DE50D,
+ 0xB02BDF5C, 0x640E9385,
+ 0xB0049AB2, 0x63EF328F,
+ 0xAFDD625F, 0x63CFC230,
+ 0xAFB63667, 0x63B0426D,
+ 0xAF8F16D0, 0x6390B34A,
+ 0xAF6803A1, 0x637114CC,
+ 0xAF40FCE0, 0x635166F8,
+ 0xAF1A0293, 0x6331A9D4,
+ 0xAEF314BF, 0x6311DD63,
+ 0xAECC336B, 0x62F201AC,
+ 0xAEA55E9D, 0x62D216B2,
+ 0xAE7E965B, 0x62B21C7B,
+ 0xAE57DAAA, 0x6292130C,
+ 0xAE312B91, 0x6271FA69,
+ 0xAE0A8916, 0x6251D297,
+ 0xADE3F33E, 0x62319B9D,
+ 0xADBD6A10, 0x6211557D,
+ 0xAD96ED91, 0x61F1003E,
+ 0xAD707DC8, 0x61D09BE5,
+ 0xAD4A1ABA, 0x61B02876,
+ 0xAD23C46D, 0x618FA5F6,
+ 0xACFD7AE8, 0x616F146B,
+ 0xACD73E30, 0x614E73D9,
+ 0xACB10E4A, 0x612DC446,
+ 0xAC8AEB3E, 0x610D05B7,
+ 0xAC64D510, 0x60EC3830,
+ 0xAC3ECBC7, 0x60CB5BB6,
+ 0xAC18CF68, 0x60AA704F,
+ 0xABF2DFFA, 0x60897600,
+ 0xABCCFD82, 0x60686CCE,
+ 0xABA72806, 0x604754BE,
+ 0xAB815F8C, 0x60262DD5,
+ 0xAB5BA41A, 0x6004F818,
+ 0xAB35F5B5, 0x5FE3B38D,
+ 0xAB105464, 0x5FC26038,
+ 0xAAEAC02B, 0x5FA0FE1E,
+ 0xAAC53912, 0x5F7F8D46,
+ 0xAA9FBF1D, 0x5F5E0DB3,
+ 0xAA7A5253, 0x5F3C7F6B,
+ 0xAA54F2B9, 0x5F1AE273,
+ 0xAA2FA055, 0x5EF936D1,
+ 0xAA0A5B2D, 0x5ED77C89,
+ 0xA9E52347, 0x5EB5B3A1,
+ 0xA9BFF8A8, 0x5E93DC1F,
+ 0xA99ADB56, 0x5E71F606,
+ 0xA975CB56, 0x5E50015D,
+ 0xA950C8AF, 0x5E2DFE28,
+ 0xA92BD366, 0x5E0BEC6E,
+ 0xA906EB81, 0x5DE9CC32,
+ 0xA8E21106, 0x5DC79D7C,
+ 0xA8BD43FA, 0x5DA5604E,
+ 0xA8988463, 0x5D8314B0,
+ 0xA873D246, 0x5D60BAA6,
+ 0xA84F2DA9, 0x5D3E5236,
+ 0xA82A9693, 0x5D1BDB65,
+ 0xA8060D08, 0x5CF95638,
+ 0xA7E1910E, 0x5CD6C2B4,
+ 0xA7BD22AB, 0x5CB420DF,
+ 0xA798C1E4, 0x5C9170BF,
+ 0xA7746EC0, 0x5C6EB258,
+ 0xA7502943, 0x5C4BE5B0,
+ 0xA72BF173, 0x5C290ACC,
+ 0xA707C756, 0x5C0621B2,
+ 0xA6E3AAF2, 0x5BE32A67,
+ 0xA6BF9C4B, 0x5BC024F0,
+ 0xA69B9B68, 0x5B9D1153,
+ 0xA677A84E, 0x5B79EF96,
+ 0xA653C302, 0x5B56BFBD,
+ 0xA62FEB8B, 0x5B3381CE,
+ 0xA60C21ED, 0x5B1035CF,
+ 0xA5E8662F, 0x5AECDBC4,
+ 0xA5C4B855, 0x5AC973B4,
+ 0xA5A11865, 0x5AA5FDA4,
+ 0xA57D8666, 0x5A82799A,
+ 0xA55A025B, 0x5A5EE79A,
+ 0xA5368C4B, 0x5A3B47AA,
+ 0xA513243B, 0x5A1799D0,
+ 0xA4EFCA31, 0x59F3DE12,
+ 0xA4CC7E31, 0x59D01474,
+ 0xA4A94042, 0x59AC3CFD,
+ 0xA4861069, 0x598857B1,
+ 0xA462EEAC, 0x59646497,
+ 0xA43FDB0F, 0x594063B4,
+ 0xA41CD598, 0x591C550E,
+ 0xA3F9DE4D, 0x58F838A9,
+ 0xA3D6F533, 0x58D40E8C,
+ 0xA3B41A4F, 0x58AFD6BC,
+ 0xA3914DA7, 0x588B913F,
+ 0xA36E8F40, 0x58673E1B,
+ 0xA34BDF20, 0x5842DD54,
+ 0xA3293D4B, 0x581E6EF1,
+ 0xA306A9C7, 0x57F9F2F7,
+ 0xA2E4249A, 0x57D5696C,
+ 0xA2C1ADC9, 0x57B0D256,
+ 0xA29F4559, 0x578C2DB9,
+ 0xA27CEB4F, 0x57677B9D,
+ 0xA25A9FB1, 0x5742BC05,
+ 0xA2386283, 0x571DEEF9,
+ 0xA21633CD, 0x56F9147E,
+ 0xA1F41391, 0x56D42C99,
+ 0xA1D201D7, 0x56AF3750,
+ 0xA1AFFEA2, 0x568A34A9,
+ 0xA18E09F9, 0x566524AA,
+ 0xA16C23E1, 0x56400757,
+ 0xA14A4C5E, 0x561ADCB8,
+ 0xA1288376, 0x55F5A4D2,
+ 0xA106C92E, 0x55D05FAA,
+ 0xA0E51D8C, 0x55AB0D46,
+ 0xA0C38094, 0x5585ADAC,
+ 0xA0A1F24C, 0x556040E2,
+ 0xA08072BA, 0x553AC6ED,
+ 0xA05F01E1, 0x55153FD4,
+ 0xA03D9FC7, 0x54EFAB9C,
+ 0xA01C4C72, 0x54CA0A4A,
+ 0x9FFB07E7, 0x54A45BE5,
+ 0x9FD9D22A, 0x547EA073,
+ 0x9FB8AB41, 0x5458D7F9,
+ 0x9F979331, 0x5433027D,
+ 0x9F7689FF, 0x540D2005,
+ 0x9F558FB0, 0x53E73097,
+ 0x9F34A449, 0x53C13438,
+ 0x9F13C7D0, 0x539B2AEF,
+ 0x9EF2FA48, 0x537514C1,
+ 0x9ED23BB9, 0x534EF1B5,
+ 0x9EB18C26, 0x5328C1D0,
+ 0x9E90EB94, 0x53028517,
+ 0x9E705A09, 0x52DC3B92,
+ 0x9E4FD789, 0x52B5E545,
+ 0x9E2F641A, 0x528F8237,
+ 0x9E0EFFC1, 0x5269126E,
+ 0x9DEEAA82, 0x524295EF,
+ 0x9DCE6462, 0x521C0CC1,
+ 0x9DAE2D68, 0x51F576E9,
+ 0x9D8E0596, 0x51CED46E,
+ 0x9D6DECF4, 0x51A82555,
+ 0x9D4DE384, 0x518169A4,
+ 0x9D2DE94D, 0x515AA162,
+ 0x9D0DFE53, 0x5133CC94,
+ 0x9CEE229C, 0x510CEB40,
+ 0x9CCE562B, 0x50E5FD6C,
+ 0x9CAE9907, 0x50BF031F,
+ 0x9C8EEB33, 0x5097FC5E,
+ 0x9C6F4CB5, 0x5070E92F,
+ 0x9C4FBD92, 0x5049C999,
+ 0x9C303DCF, 0x50229DA0,
+ 0x9C10CD70, 0x4FFB654D,
+ 0x9BF16C7A, 0x4FD420A3,
+ 0x9BD21AF2, 0x4FACCFAB,
+ 0x9BB2D8DD, 0x4F857268,
+ 0x9B93A640, 0x4F5E08E3,
+ 0x9B748320, 0x4F369320,
+ 0x9B556F80, 0x4F0F1126,
+ 0x9B366B67, 0x4EE782FA,
+ 0x9B1776D9, 0x4EBFE8A4,
+ 0x9AF891DB, 0x4E984229,
+ 0x9AD9BC71, 0x4E708F8F,
+ 0x9ABAF6A0, 0x4E48D0DC,
+ 0x9A9C406D, 0x4E210617,
+ 0x9A7D99DD, 0x4DF92F45,
+ 0x9A5F02F5, 0x4DD14C6E,
+ 0x9A407BB8, 0x4DA95D96,
+ 0x9A22042C, 0x4D8162C4,
+ 0x9A039C56, 0x4D595BFE,
+ 0x99E5443A, 0x4D31494B,
+ 0x99C6FBDE, 0x4D092AB0,
+ 0x99A8C344, 0x4CE10034,
+ 0x998A9A73, 0x4CB8C9DD,
+ 0x996C816F, 0x4C9087B1,
+ 0x994E783C, 0x4C6839B6,
+ 0x99307EE0, 0x4C3FDFF3,
+ 0x9912955E, 0x4C177A6E,
+ 0x98F4BBBC, 0x4BEF092D,
+ 0x98D6F1FE, 0x4BC68C36,
+ 0x98B93828, 0x4B9E038F,
+ 0x989B8E3F, 0x4B756F3F,
+ 0x987DF449, 0x4B4CCF4D,
+ 0x98606A48, 0x4B2423BD,
+ 0x9842F043, 0x4AFB6C97,
+ 0x9825863D, 0x4AD2A9E1,
+ 0x98082C3B, 0x4AA9DBA1,
+ 0x97EAE241, 0x4A8101DE,
+ 0x97CDA855, 0x4A581C9D,
+ 0x97B07E7A, 0x4A2F2BE5,
+ 0x979364B5, 0x4A062FBD,
+ 0x97765B0A, 0x49DD282A,
+ 0x9759617E, 0x49B41533,
+ 0x973C7816, 0x498AF6DE,
+ 0x971F9ED6, 0x4961CD32,
+ 0x9702D5C2, 0x49389836,
+ 0x96E61CDF, 0x490F57EE,
+ 0x96C97431, 0x48E60C62,
+ 0x96ACDBBD, 0x48BCB598,
+ 0x96905387, 0x48935397,
+ 0x9673DB94, 0x4869E664,
+ 0x965773E7, 0x48406E07,
+ 0x963B1C85, 0x4816EA85,
+ 0x961ED573, 0x47ED5BE6,
+ 0x96029EB5, 0x47C3C22E,
+ 0x95E6784F, 0x479A1D66,
+ 0x95CA6246, 0x47706D93,
+ 0x95AE5C9E, 0x4746B2BC,
+ 0x9592675B, 0x471CECE6,
+ 0x95768282, 0x46F31C1A,
+ 0x955AAE17, 0x46C9405C,
+ 0x953EEA1E, 0x469F59B4,
+ 0x9523369B, 0x46756827,
+ 0x95079393, 0x464B6BBD,
+ 0x94EC010B, 0x4621647C,
+ 0x94D07F05, 0x45F7526B,
+ 0x94B50D87, 0x45CD358F,
+ 0x9499AC95, 0x45A30DF0,
+ 0x947E5C32, 0x4578DB93,
+ 0x94631C64, 0x454E9E80,
+ 0x9447ED2F, 0x452456BC,
+ 0x942CCE95, 0x44FA044F,
+ 0x9411C09D, 0x44CFA73F,
+ 0x93F6C34A, 0x44A53F93,
+ 0x93DBD69F, 0x447ACD50,
+ 0x93C0FAA2, 0x4450507E,
+ 0x93A62F56, 0x4425C923,
+ 0x938B74C0, 0x43FB3745,
+ 0x9370CAE4, 0x43D09AEC,
+ 0x935631C5, 0x43A5F41E,
+ 0x933BA968, 0x437B42E1,
+ 0x932131D1, 0x4350873C,
+ 0x9306CB04, 0x4325C135,
+ 0x92EC7505, 0x42FAF0D4,
+ 0x92D22FD8, 0x42D0161E,
+ 0x92B7FB82, 0x42A5311A,
+ 0x929DD805, 0x427A41D0,
+ 0x9283C567, 0x424F4845,
+ 0x9269C3AC, 0x42244480,
+ 0x924FD2D6, 0x41F93688,
+ 0x9235F2EB, 0x41CE1E64,
+ 0x921C23EE, 0x41A2FC1A,
+ 0x920265E4, 0x4177CFB0,
+ 0x91E8B8D0, 0x414C992E,
+ 0x91CF1CB6, 0x4121589A,
+ 0x91B5919A, 0x40F60DFB,
+ 0x919C1780, 0x40CAB957,
+ 0x9182AE6C, 0x409F5AB6,
+ 0x91695663, 0x4073F21D,
+ 0x91500F67, 0x40487F93,
+ 0x9136D97D, 0x401D0320,
+ 0x911DB4A8, 0x3FF17CCA,
+ 0x9104A0ED, 0x3FC5EC97,
+ 0x90EB9E50, 0x3F9A528F,
+ 0x90D2ACD3, 0x3F6EAEB8,
+ 0x90B9CC7C, 0x3F430118,
+ 0x90A0FD4E, 0x3F1749B7,
+ 0x90883F4C, 0x3EEB889C,
+ 0x906F927B, 0x3EBFBDCC,
+ 0x9056F6DF, 0x3E93E94F,
+ 0x903E6C7A, 0x3E680B2C,
+ 0x9025F352, 0x3E3C2369,
+ 0x900D8B69, 0x3E10320D,
+ 0x8FF534C4, 0x3DE4371F,
+ 0x8FDCEF66, 0x3DB832A5,
+ 0x8FC4BB53, 0x3D8C24A7,
+ 0x8FAC988E, 0x3D600D2B,
+ 0x8F94871D, 0x3D33EC39,
+ 0x8F7C8701, 0x3D07C1D5,
+ 0x8F64983F, 0x3CDB8E09,
+ 0x8F4CBADB, 0x3CAF50DA,
+ 0x8F34EED8, 0x3C830A4F,
+ 0x8F1D343A, 0x3C56BA70,
+ 0x8F058B04, 0x3C2A6142,
+ 0x8EEDF33B, 0x3BFDFECD,
+ 0x8ED66CE1, 0x3BD19317,
+ 0x8EBEF7FB, 0x3BA51E29,
+ 0x8EA7948C, 0x3B78A007,
+ 0x8E904298, 0x3B4C18BA,
+ 0x8E790222, 0x3B1F8847,
+ 0x8E61D32D, 0x3AF2EEB7,
+ 0x8E4AB5BF, 0x3AC64C0F,
+ 0x8E33A9D9, 0x3A99A057,
+ 0x8E1CAF80, 0x3A6CEB95,
+ 0x8E05C6B7, 0x3A402DD1,
+ 0x8DEEEF82, 0x3A136712,
+ 0x8DD829E4, 0x39E6975D,
+ 0x8DC175E0, 0x39B9BEBB,
+ 0x8DAAD37B, 0x398CDD32,
+ 0x8D9442B7, 0x395FF2C9,
+ 0x8D7DC399, 0x3932FF87,
+ 0x8D675623, 0x39060372,
+ 0x8D50FA59, 0x38D8FE93,
+ 0x8D3AB03F, 0x38ABF0EF,
+ 0x8D2477D8, 0x387EDA8E,
+ 0x8D0E5127, 0x3851BB76,
+ 0x8CF83C30, 0x382493B0,
+ 0x8CE238F6, 0x37F76340,
+ 0x8CCC477D, 0x37CA2A30,
+ 0x8CB667C7, 0x379CE884,
+ 0x8CA099D9, 0x376F9E46,
+ 0x8C8ADDB6, 0x37424B7A,
+ 0x8C753361, 0x3714F02A,
+ 0x8C5F9ADD, 0x36E78C5A,
+ 0x8C4A142F, 0x36BA2013,
+ 0x8C349F58, 0x368CAB5C,
+ 0x8C1F3C5C, 0x365F2E3B,
+ 0x8C09EB40, 0x3631A8B7,
+ 0x8BF4AC05, 0x36041AD9,
+ 0x8BDF7EAF, 0x35D684A5,
+ 0x8BCA6342, 0x35A8E624,
+ 0x8BB559C1, 0x357B3F5D,
+ 0x8BA0622F, 0x354D9056,
+ 0x8B8B7C8F, 0x351FD917,
+ 0x8B76A8E4, 0x34F219A7,
+ 0x8B61E732, 0x34C4520D,
+ 0x8B4D377C, 0x3496824F,
+ 0x8B3899C5, 0x3468AA76,
+ 0x8B240E10, 0x343ACA87,
+ 0x8B0F9461, 0x340CE28A,
+ 0x8AFB2CBA, 0x33DEF287,
+ 0x8AE6D71F, 0x33B0FA84,
+ 0x8AD29393, 0x3382FA88,
+ 0x8ABE6219, 0x3354F29A,
+ 0x8AAA42B4, 0x3326E2C2,
+ 0x8A963567, 0x32F8CB07,
+ 0x8A823A35, 0x32CAAB6F,
+ 0x8A6E5122, 0x329C8402,
+ 0x8A5A7A30, 0x326E54C7,
+ 0x8A46B563, 0x32401DC5,
+ 0x8A3302BD, 0x3211DF03,
+ 0x8A1F6242, 0x31E39889,
+ 0x8A0BD3F5, 0x31B54A5D,
+ 0x89F857D8, 0x3186F487,
+ 0x89E4EDEE, 0x3158970D,
+ 0x89D1963C, 0x312A31F8,
+ 0x89BE50C3, 0x30FBC54D,
+ 0x89AB1D86, 0x30CD5114,
+ 0x8997FC89, 0x309ED555,
+ 0x8984EDCF, 0x30705217,
+ 0x8971F15A, 0x3041C760,
+ 0x895F072D, 0x30133538,
+ 0x894C2F4C, 0x2FE49BA6,
+ 0x893969B9, 0x2FB5FAB2,
+ 0x8926B677, 0x2F875262,
+ 0x89141589, 0x2F58A2BD,
+ 0x890186F1, 0x2F29EBCC,
+ 0x88EF0AB4, 0x2EFB2D94,
+ 0x88DCA0D3, 0x2ECC681E,
+ 0x88CA4951, 0x2E9D9B70,
+ 0x88B80431, 0x2E6EC792,
+ 0x88A5D177, 0x2E3FEC8B,
+ 0x8893B124, 0x2E110A62,
+ 0x8881A33C, 0x2DE2211E,
+ 0x886FA7C2, 0x2DB330C7,
+ 0x885DBEB7, 0x2D843963,
+ 0x884BE820, 0x2D553AFB,
+ 0x883A23FE, 0x2D263595,
+ 0x88287255, 0x2CF72939,
+ 0x8816D327, 0x2CC815ED,
+ 0x88054677, 0x2C98FBBA,
+ 0x87F3CC47, 0x2C69DAA6,
+ 0x87E2649B, 0x2C3AB2B9,
+ 0x87D10F75, 0x2C0B83F9,
+ 0x87BFCCD7, 0x2BDC4E6F,
+ 0x87AE9CC5, 0x2BAD1221,
+ 0x879D7F40, 0x2B7DCF17,
+ 0x878C744C, 0x2B4E8558,
+ 0x877B7BEC, 0x2B1F34EB,
+ 0x876A9621, 0x2AEFDDD8,
+ 0x8759C2EF, 0x2AC08025,
+ 0x87490257, 0x2A911BDB,
+ 0x8738545E, 0x2A61B101,
+ 0x8727B904, 0x2A323F9D,
+ 0x8717304E, 0x2A02C7B8,
+ 0x8706BA3C, 0x29D34958,
+ 0x86F656D3, 0x29A3C484,
+ 0x86E60614, 0x29743945,
+ 0x86D5C802, 0x2944A7A2,
+ 0x86C59C9F, 0x29150FA1,
+ 0x86B583EE, 0x28E5714A,
+ 0x86A57DF1, 0x28B5CCA5,
+ 0x86958AAB, 0x288621B9,
+ 0x8685AA1F, 0x2856708C,
+ 0x8675DC4E, 0x2826B928,
+ 0x8666213C, 0x27F6FB92,
+ 0x865678EA, 0x27C737D2,
+ 0x8646E35B, 0x27976DF1,
+ 0x86376092, 0x27679DF4,
+ 0x8627F090, 0x2737C7E3,
+ 0x86189359, 0x2707EBC6,
+ 0x860948EE, 0x26D809A5,
+ 0x85FA1152, 0x26A82185,
+ 0x85EAEC88, 0x26783370,
+ 0x85DBDA91, 0x26483F6C,
+ 0x85CCDB70, 0x26184581,
+ 0x85BDEF27, 0x25E845B5,
+ 0x85AF15B9, 0x25B84012,
+ 0x85A04F28, 0x2588349D,
+ 0x85919B75, 0x2558235E,
+ 0x8582FAA4, 0x25280C5D,
+ 0x85746CB7, 0x24F7EFA1,
+ 0x8565F1B0, 0x24C7CD32,
+ 0x85578991, 0x2497A517,
+ 0x8549345C, 0x24677757,
+ 0x853AF214, 0x243743FA,
+ 0x852CC2BA, 0x24070B07,
+ 0x851EA652, 0x23D6CC86,
+ 0x85109CDC, 0x23A6887E,
+ 0x8502A65C, 0x23763EF7,
+ 0x84F4C2D3, 0x2345EFF7,
+ 0x84E6F244, 0x23159B87,
+ 0x84D934B0, 0x22E541AE,
+ 0x84CB8A1B, 0x22B4E274,
+ 0x84BDF285, 0x22847DDF,
+ 0x84B06DF1, 0x225413F8,
+ 0x84A2FC62, 0x2223A4C5,
+ 0x84959DD9, 0x21F3304E,
+ 0x84885257, 0x21C2B69C,
+ 0x847B19E1, 0x219237B4,
+ 0x846DF476, 0x2161B39F,
+ 0x8460E21A, 0x21312A65,
+ 0x8453E2CE, 0x21009C0B,
+ 0x8446F695, 0x20D0089B,
+ 0x843A1D70, 0x209F701C,
+ 0x842D5761, 0x206ED295,
+ 0x8420A46B, 0x203E300D,
+ 0x8414048F, 0x200D888C,
+ 0x840777CF, 0x1FDCDC1A,
+ 0x83FAFE2E, 0x1FAC2ABF,
+ 0x83EE97AC, 0x1F7B7480,
+ 0x83E2444D, 0x1F4AB967,
+ 0x83D60411, 0x1F19F97B,
+ 0x83C9D6FB, 0x1EE934C2,
+ 0x83BDBD0D, 0x1EB86B46,
+ 0x83B1B649, 0x1E879D0C,
+ 0x83A5C2B0, 0x1E56CA1E,
+ 0x8399E244, 0x1E25F281,
+ 0x838E1507, 0x1DF5163F,
+ 0x83825AFB, 0x1DC4355D,
+ 0x8376B422, 0x1D934FE5,
+ 0x836B207D, 0x1D6265DD,
+ 0x835FA00E, 0x1D31774D,
+ 0x835432D8, 0x1D00843C,
+ 0x8348D8DB, 0x1CCF8CB3,
+ 0x833D921A, 0x1C9E90B8,
+ 0x83325E97, 0x1C6D9053,
+ 0x83273E52, 0x1C3C8B8C,
+ 0x831C314E, 0x1C0B826A,
+ 0x8311378C, 0x1BDA74F5,
+ 0x8306510F, 0x1BA96334,
+ 0x82FB7DD8, 0x1B784D30,
+ 0x82F0BDE8, 0x1B4732EF,
+ 0x82E61141, 0x1B161479,
+ 0x82DB77E5, 0x1AE4F1D6,
+ 0x82D0F1D5, 0x1AB3CB0C,
+ 0x82C67F13, 0x1A82A025,
+ 0x82BC1FA1, 0x1A517127,
+ 0x82B1D381, 0x1A203E1B,
+ 0x82A79AB3, 0x19EF0706,
+ 0x829D753A, 0x19BDCBF2,
+ 0x82936316, 0x198C8CE6,
+ 0x8289644A, 0x195B49E9,
+ 0x827F78D8, 0x192A0303,
+ 0x8275A0C0, 0x18F8B83C,
+ 0x826BDC04, 0x18C7699B,
+ 0x82622AA5, 0x18961727,
+ 0x82588CA6, 0x1864C0E9,
+ 0x824F0208, 0x183366E8,
+ 0x82458ACB, 0x1802092C,
+ 0x823C26F2, 0x17D0A7BB,
+ 0x8232D67E, 0x179F429F,
+ 0x82299971, 0x176DD9DE,
+ 0x82206FCB, 0x173C6D80,
+ 0x8217598F, 0x170AFD8D,
+ 0x820E56BE, 0x16D98A0C,
+ 0x82056758, 0x16A81305,
+ 0x81FC8B60, 0x1676987F,
+ 0x81F3C2D7, 0x16451A83,
+ 0x81EB0DBD, 0x16139917,
+ 0x81E26C16, 0x15E21444,
+ 0x81D9DDE1, 0x15B08C11,
+ 0x81D16320, 0x157F0086,
+ 0x81C8FBD5, 0x154D71AA,
+ 0x81C0A801, 0x151BDF85,
+ 0x81B867A4, 0x14EA4A1F,
+ 0x81B03AC1, 0x14B8B17F,
+ 0x81A82159, 0x148715AD,
+ 0x81A01B6C, 0x145576B1,
+ 0x819828FD, 0x1423D492,
+ 0x81904A0C, 0x13F22F57,
+ 0x81887E9A, 0x13C0870A,
+ 0x8180C6A9, 0x138EDBB0,
+ 0x8179223A, 0x135D2D53,
+ 0x8171914E, 0x132B7BF9,
+ 0x816A13E6, 0x12F9C7AA,
+ 0x8162AA03, 0x12C8106E,
+ 0x815B53A8, 0x1296564D,
+ 0x815410D3, 0x1264994E,
+ 0x814CE188, 0x1232D978,
+ 0x8145C5C6, 0x120116D4,
+ 0x813EBD90, 0x11CF516A,
+ 0x8137C8E6, 0x119D8940,
+ 0x8130E7C8, 0x116BBE5F,
+ 0x812A1A39, 0x1139F0CE,
+ 0x81236039, 0x11082096,
+ 0x811CB9CA, 0x10D64DBC,
+ 0x811626EC, 0x10A4784A,
+ 0x810FA7A0, 0x1072A047,
+ 0x81093BE8, 0x1040C5BB,
+ 0x8102E3C3, 0x100EE8AD,
+ 0x80FC9F35, 0x0FDD0925,
+ 0x80F66E3C, 0x0FAB272B,
+ 0x80F050DB, 0x0F7942C6,
+ 0x80EA4712, 0x0F475BFE,
+ 0x80E450E2, 0x0F1572DC,
+ 0x80DE6E4C, 0x0EE38765,
+ 0x80D89F51, 0x0EB199A3,
+ 0x80D2E3F1, 0x0E7FA99D,
+ 0x80CD3C2F, 0x0E4DB75B,
+ 0x80C7A80A, 0x0E1BC2E3,
+ 0x80C22783, 0x0DE9CC3F,
+ 0x80BCBA9C, 0x0DB7D376,
+ 0x80B76155, 0x0D85D88F,
+ 0x80B21BAF, 0x0D53DB92,
+ 0x80ACE9AB, 0x0D21DC87,
+ 0x80A7CB49, 0x0CEFDB75,
+ 0x80A2C08B, 0x0CBDD865,
+ 0x809DC970, 0x0C8BD35E,
+ 0x8098E5FB, 0x0C59CC67,
+ 0x8094162B, 0x0C27C389,
+ 0x808F5A02, 0x0BF5B8CB,
+ 0x808AB180, 0x0BC3AC35,
+ 0x80861CA5, 0x0B919DCE,
+ 0x80819B74, 0x0B5F8D9F,
+ 0x807D2DEB, 0x0B2D7BAE,
+ 0x8078D40D, 0x0AFB6805,
+ 0x80748DD9, 0x0AC952AA,
+ 0x80705B50, 0x0A973BA5,
+ 0x806C3C73, 0x0A6522FE,
+ 0x80683143, 0x0A3308BC,
+ 0x806439C0, 0x0A00ECE8,
+ 0x806055EA, 0x09CECF89,
+ 0x805C85C3, 0x099CB0A7,
+ 0x8058C94C, 0x096A9049,
+ 0x80552083, 0x09386E77,
+ 0x80518B6B, 0x09064B3A,
+ 0x804E0A03, 0x08D42698,
+ 0x804A9C4D, 0x08A2009A,
+ 0x80474248, 0x086FD947,
+ 0x8043FBF6, 0x083DB0A7,
+ 0x8040C956, 0x080B86C1,
+ 0x803DAA69, 0x07D95B9E,
+ 0x803A9F31, 0x07A72F45,
+ 0x8037A7AC, 0x077501BE,
+ 0x8034C3DC, 0x0742D310,
+ 0x8031F3C1, 0x0710A344,
+ 0x802F375C, 0x06DE7261,
+ 0x802C8EAD, 0x06AC406F,
+ 0x8029F9B4, 0x067A0D75,
+ 0x80277872, 0x0647D97C,
+ 0x80250AE7, 0x0615A48A,
+ 0x8022B113, 0x05E36EA9,
+ 0x80206AF8, 0x05B137DF,
+ 0x801E3894, 0x057F0034,
+ 0x801C19E9, 0x054CC7B0,
+ 0x801A0EF7, 0x051A8E5C,
+ 0x801817BF, 0x04E8543D,
+ 0x80163440, 0x04B6195D,
+ 0x8014647A, 0x0483DDC3,
+ 0x8012A86F, 0x0451A176,
+ 0x8011001E, 0x041F647F,
+ 0x800F6B88, 0x03ED26E6,
+ 0x800DEAAC, 0x03BAE8B1,
+ 0x800C7D8C, 0x0388A9E9,
+ 0x800B2427, 0x03566A96,
+ 0x8009DE7D, 0x03242ABF,
+ 0x8008AC90, 0x02F1EA6B,
+ 0x80078E5E, 0x02BFA9A4,
+ 0x800683E8, 0x028D6870,
+ 0x80058D2E, 0x025B26D7,
+ 0x8004AA31, 0x0228E4E1,
+ 0x8003DAF0, 0x01F6A296,
+ 0x80031F6C, 0x01C45FFE,
+ 0x800277A5, 0x01921D1F,
+ 0x8001E39B, 0x015FDA03,
+ 0x8001634D, 0x012D96B0,
+ 0x8000F6BD, 0x00FB532F,
+ 0x80009DE9, 0x00C90F88,
+ 0x800058D3, 0x0096CBC1,
+ 0x8000277A, 0x006487E3,
+ 0x800009DE, 0x003243F5,
+ 0x80000000, 0x00000000,
+ 0x800009DE, 0xFFCDBC0A,
+ 0x8000277A, 0xFF9B781D,
+ 0x800058D3, 0xFF69343E,
+ 0x80009DE9, 0xFF36F078,
+ 0x8000F6BD, 0xFF04ACD0,
+ 0x8001634D, 0xFED2694F,
+ 0x8001E39B, 0xFEA025FC,
+ 0x800277A5, 0xFE6DE2E0,
+ 0x80031F6C, 0xFE3BA001,
+ 0x8003DAF0, 0xFE095D69,
+ 0x8004AA31, 0xFDD71B1E,
+ 0x80058D2E, 0xFDA4D928,
+ 0x800683E8, 0xFD72978F,
+ 0x80078E5E, 0xFD40565B,
+ 0x8008AC90, 0xFD0E1594,
+ 0x8009DE7D, 0xFCDBD541,
+ 0x800B2427, 0xFCA99569,
+ 0x800C7D8C, 0xFC775616,
+ 0x800DEAAC, 0xFC45174E,
+ 0x800F6B88, 0xFC12D919,
+ 0x8011001E, 0xFBE09B80,
+ 0x8012A86F, 0xFBAE5E89,
+ 0x8014647A, 0xFB7C223C,
+ 0x80163440, 0xFB49E6A2,
+ 0x801817BF, 0xFB17ABC2,
+ 0x801A0EF7, 0xFAE571A4,
+ 0x801C19E9, 0xFAB3384F,
+ 0x801E3894, 0xFA80FFCB,
+ 0x80206AF8, 0xFA4EC820,
+ 0x8022B113, 0xFA1C9156,
+ 0x80250AE7, 0xF9EA5B75,
+ 0x80277872, 0xF9B82683,
+ 0x8029F9B4, 0xF985F28A,
+ 0x802C8EAD, 0xF953BF90,
+ 0x802F375C, 0xF9218D9E,
+ 0x8031F3C1, 0xF8EF5CBB,
+ 0x8034C3DC, 0xF8BD2CEF,
+ 0x8037A7AC, 0xF88AFE41,
+ 0x803A9F31, 0xF858D0BA,
+ 0x803DAA69, 0xF826A461,
+ 0x8040C956, 0xF7F4793E,
+ 0x8043FBF6, 0xF7C24F58,
+ 0x80474248, 0xF79026B8,
+ 0x804A9C4D, 0xF75DFF65,
+ 0x804E0A03, 0xF72BD967,
+ 0x80518B6B, 0xF6F9B4C5,
+ 0x80552083, 0xF6C79188,
+ 0x8058C94C, 0xF6956FB6,
+ 0x805C85C3, 0xF6634F58,
+ 0x806055EA, 0xF6313076,
+ 0x806439C0, 0xF5FF1317,
+ 0x80683143, 0xF5CCF743,
+ 0x806C3C73, 0xF59ADD01,
+ 0x80705B50, 0xF568C45A,
+ 0x80748DD9, 0xF536AD55,
+ 0x8078D40D, 0xF50497FA,
+ 0x807D2DEB, 0xF4D28451,
+ 0x80819B74, 0xF4A07260,
+ 0x80861CA5, 0xF46E6231,
+ 0x808AB180, 0xF43C53CA,
+ 0x808F5A02, 0xF40A4734,
+ 0x8094162B, 0xF3D83C76,
+ 0x8098E5FB, 0xF3A63398,
+ 0x809DC970, 0xF3742CA1,
+ 0x80A2C08B, 0xF342279A,
+ 0x80A7CB49, 0xF310248A,
+ 0x80ACE9AB, 0xF2DE2378,
+ 0x80B21BAF, 0xF2AC246D,
+ 0x80B76155, 0xF27A2770,
+ 0x80BCBA9C, 0xF2482C89,
+ 0x80C22783, 0xF21633C0,
+ 0x80C7A80A, 0xF1E43D1C,
+ 0x80CD3C2F, 0xF1B248A5,
+ 0x80D2E3F1, 0xF1805662,
+ 0x80D89F51, 0xF14E665C,
+ 0x80DE6E4C, 0xF11C789A,
+ 0x80E450E2, 0xF0EA8D23,
+ 0x80EA4712, 0xF0B8A401,
+ 0x80F050DB, 0xF086BD39,
+ 0x80F66E3C, 0xF054D8D4,
+ 0x80FC9F35, 0xF022F6DA,
+ 0x8102E3C3, 0xEFF11752,
+ 0x81093BE8, 0xEFBF3A44,
+ 0x810FA7A0, 0xEF8D5FB8,
+ 0x811626EC, 0xEF5B87B5,
+ 0x811CB9CA, 0xEF29B243,
+ 0x81236039, 0xEEF7DF6A,
+ 0x812A1A39, 0xEEC60F31,
+ 0x8130E7C8, 0xEE9441A0,
+ 0x8137C8E6, 0xEE6276BF,
+ 0x813EBD90, 0xEE30AE95,
+ 0x8145C5C6, 0xEDFEE92B,
+ 0x814CE188, 0xEDCD2687,
+ 0x815410D3, 0xED9B66B2,
+ 0x815B53A8, 0xED69A9B2,
+ 0x8162AA03, 0xED37EF91,
+ 0x816A13E6, 0xED063855,
+ 0x8171914E, 0xECD48406,
+ 0x8179223A, 0xECA2D2AC,
+ 0x8180C6A9, 0xEC71244F,
+ 0x81887E9A, 0xEC3F78F5,
+ 0x81904A0C, 0xEC0DD0A8,
+ 0x819828FD, 0xEBDC2B6D,
+ 0x81A01B6C, 0xEBAA894E,
+ 0x81A82159, 0xEB78EA52,
+ 0x81B03AC1, 0xEB474E80,
+ 0x81B867A4, 0xEB15B5E0,
+ 0x81C0A801, 0xEAE4207A,
+ 0x81C8FBD5, 0xEAB28E55,
+ 0x81D16320, 0xEA80FF79,
+ 0x81D9DDE1, 0xEA4F73EE,
+ 0x81E26C16, 0xEA1DEBBB,
+ 0x81EB0DBD, 0xE9EC66E8,
+ 0x81F3C2D7, 0xE9BAE57C,
+ 0x81FC8B60, 0xE9896780,
+ 0x82056758, 0xE957ECFB,
+ 0x820E56BE, 0xE92675F4,
+ 0x8217598F, 0xE8F50273,
+ 0x82206FCB, 0xE8C3927F,
+ 0x82299971, 0xE8922621,
+ 0x8232D67E, 0xE860BD60,
+ 0x823C26F2, 0xE82F5844,
+ 0x82458ACB, 0xE7FDF6D3,
+ 0x824F0208, 0xE7CC9917,
+ 0x82588CA6, 0xE79B3F16,
+ 0x82622AA5, 0xE769E8D8,
+ 0x826BDC04, 0xE7389664,
+ 0x8275A0C0, 0xE70747C3,
+ 0x827F78D8, 0xE6D5FCFC,
+ 0x8289644A, 0xE6A4B616,
+ 0x82936316, 0xE6737319,
+ 0x829D753A, 0xE642340D,
+ 0x82A79AB3, 0xE610F8F9,
+ 0x82B1D381, 0xE5DFC1E4,
+ 0x82BC1FA1, 0xE5AE8ED8,
+ 0x82C67F13, 0xE57D5FDA,
+ 0x82D0F1D5, 0xE54C34F3,
+ 0x82DB77E5, 0xE51B0E2A,
+ 0x82E61141, 0xE4E9EB86,
+ 0x82F0BDE8, 0xE4B8CD10,
+ 0x82FB7DD8, 0xE487B2CF,
+ 0x8306510F, 0xE4569CCB,
+ 0x8311378C, 0xE4258B0A,
+ 0x831C314E, 0xE3F47D95,
+ 0x83273E52, 0xE3C37473,
+ 0x83325E97, 0xE3926FAC,
+ 0x833D921A, 0xE3616F47,
+ 0x8348D8DB, 0xE330734C,
+ 0x835432D8, 0xE2FF7BC3,
+ 0x835FA00E, 0xE2CE88B2,
+ 0x836B207D, 0xE29D9A22,
+ 0x8376B422, 0xE26CB01A,
+ 0x83825AFB, 0xE23BCAA2,
+ 0x838E1507, 0xE20AE9C1,
+ 0x8399E244, 0xE1DA0D7E,
+ 0x83A5C2B0, 0xE1A935E1,
+ 0x83B1B649, 0xE17862F3,
+ 0x83BDBD0D, 0xE14794B9,
+ 0x83C9D6FB, 0xE116CB3D,
+ 0x83D60411, 0xE0E60684,
+ 0x83E2444D, 0xE0B54698,
+ 0x83EE97AC, 0xE0848B7F,
+ 0x83FAFE2E, 0xE053D541,
+ 0x840777CF, 0xE02323E5,
+ 0x8414048F, 0xDFF27773,
+ 0x8420A46B, 0xDFC1CFF2,
+ 0x842D5761, 0xDF912D6A,
+ 0x843A1D70, 0xDF608FE3,
+ 0x8446F695, 0xDF2FF764,
+ 0x8453E2CE, 0xDEFF63F4,
+ 0x8460E21A, 0xDECED59B,
+ 0x846DF476, 0xDE9E4C60,
+ 0x847B19E1, 0xDE6DC84B,
+ 0x84885257, 0xDE3D4963,
+ 0x84959DD9, 0xDE0CCFB1,
+ 0x84A2FC62, 0xDDDC5B3A,
+ 0x84B06DF1, 0xDDABEC07,
+ 0x84BDF285, 0xDD7B8220,
+ 0x84CB8A1B, 0xDD4B1D8B,
+ 0x84D934B0, 0xDD1ABE51,
+ 0x84E6F244, 0xDCEA6478,
+ 0x84F4C2D3, 0xDCBA1008,
+ 0x8502A65C, 0xDC89C108,
+ 0x85109CDC, 0xDC597781,
+ 0x851EA652, 0xDC293379,
+ 0x852CC2BA, 0xDBF8F4F8,
+ 0x853AF214, 0xDBC8BC05,
+ 0x8549345C, 0xDB9888A8,
+ 0x85578991, 0xDB685AE8,
+ 0x8565F1B0, 0xDB3832CD,
+ 0x85746CB7, 0xDB08105E,
+ 0x8582FAA4, 0xDAD7F3A2,
+ 0x85919B75, 0xDAA7DCA1,
+ 0x85A04F28, 0xDA77CB62,
+ 0x85AF15B9, 0xDA47BFED,
+ 0x85BDEF27, 0xDA17BA4A,
+ 0x85CCDB70, 0xD9E7BA7E,
+ 0x85DBDA91, 0xD9B7C093,
+ 0x85EAEC88, 0xD987CC8F,
+ 0x85FA1152, 0xD957DE7A,
+ 0x860948EE, 0xD927F65B,
+ 0x86189359, 0xD8F81439,
+ 0x8627F090, 0xD8C8381C,
+ 0x86376092, 0xD898620C,
+ 0x8646E35B, 0xD868920F,
+ 0x865678EA, 0xD838C82D,
+ 0x8666213C, 0xD809046D,
+ 0x8675DC4E, 0xD7D946D7,
+ 0x8685AA1F, 0xD7A98F73,
+ 0x86958AAB, 0xD779DE46,
+ 0x86A57DF1, 0xD74A335A,
+ 0x86B583EE, 0xD71A8EB5,
+ 0x86C59C9F, 0xD6EAF05E,
+ 0x86D5C802, 0xD6BB585D,
+ 0x86E60614, 0xD68BC6BA,
+ 0x86F656D3, 0xD65C3B7B,
+ 0x8706BA3C, 0xD62CB6A7,
+ 0x8717304E, 0xD5FD3847,
+ 0x8727B904, 0xD5CDC062,
+ 0x8738545E, 0xD59E4EFE,
+ 0x87490257, 0xD56EE424,
+ 0x8759C2EF, 0xD53F7FDA,
+ 0x876A9621, 0xD5102227,
+ 0x877B7BEC, 0xD4E0CB14,
+ 0x878C744C, 0xD4B17AA7,
+ 0x879D7F40, 0xD48230E8,
+ 0x87AE9CC5, 0xD452EDDE,
+ 0x87BFCCD7, 0xD423B190,
+ 0x87D10F75, 0xD3F47C06,
+ 0x87E2649B, 0xD3C54D46,
+ 0x87F3CC47, 0xD3962559,
+ 0x88054677, 0xD3670445,
+ 0x8816D327, 0xD337EA12,
+ 0x88287255, 0xD308D6C6,
+ 0x883A23FE, 0xD2D9CA6A,
+ 0x884BE820, 0xD2AAC504,
+ 0x885DBEB7, 0xD27BC69C,
+ 0x886FA7C2, 0xD24CCF38,
+ 0x8881A33C, 0xD21DDEE1,
+ 0x8893B124, 0xD1EEF59E,
+ 0x88A5D177, 0xD1C01374,
+ 0x88B80431, 0xD191386D,
+ 0x88CA4951, 0xD162648F,
+ 0x88DCA0D3, 0xD13397E1,
+ 0x88EF0AB4, 0xD104D26B,
+ 0x890186F1, 0xD0D61433,
+ 0x89141589, 0xD0A75D42,
+ 0x8926B677, 0xD078AD9D,
+ 0x893969B9, 0xD04A054D,
+ 0x894C2F4C, 0xD01B6459,
+ 0x895F072D, 0xCFECCAC7,
+ 0x8971F15A, 0xCFBE389F,
+ 0x8984EDCF, 0xCF8FADE8,
+ 0x8997FC89, 0xCF612AAA,
+ 0x89AB1D86, 0xCF32AEEB,
+ 0x89BE50C3, 0xCF043AB2,
+ 0x89D1963C, 0xCED5CE08,
+ 0x89E4EDEE, 0xCEA768F2,
+ 0x89F857D8, 0xCE790B78,
+ 0x8A0BD3F5, 0xCE4AB5A2,
+ 0x8A1F6242, 0xCE1C6776,
+ 0x8A3302BD, 0xCDEE20FC,
+ 0x8A46B563, 0xCDBFE23A,
+ 0x8A5A7A30, 0xCD91AB38,
+ 0x8A6E5122, 0xCD637BFD,
+ 0x8A823A35, 0xCD355490,
+ 0x8A963567, 0xCD0734F8,
+ 0x8AAA42B4, 0xCCD91D3D,
+ 0x8ABE6219, 0xCCAB0D65,
+ 0x8AD29393, 0xCC7D0577,
+ 0x8AE6D71F, 0xCC4F057B,
+ 0x8AFB2CBA, 0xCC210D78,
+ 0x8B0F9461, 0xCBF31D75,
+ 0x8B240E10, 0xCBC53578,
+ 0x8B3899C5, 0xCB975589,
+ 0x8B4D377C, 0xCB697DB0,
+ 0x8B61E732, 0xCB3BADF2,
+ 0x8B76A8E4, 0xCB0DE658,
+ 0x8B8B7C8F, 0xCAE026E8,
+ 0x8BA0622F, 0xCAB26FA9,
+ 0x8BB559C1, 0xCA84C0A2,
+ 0x8BCA6342, 0xCA5719DB,
+ 0x8BDF7EAF, 0xCA297B5A,
+ 0x8BF4AC05, 0xC9FBE527,
+ 0x8C09EB40, 0xC9CE5748,
+ 0x8C1F3C5C, 0xC9A0D1C4,
+ 0x8C349F58, 0xC97354A3,
+ 0x8C4A142F, 0xC945DFEC,
+ 0x8C5F9ADD, 0xC91873A5,
+ 0x8C753361, 0xC8EB0FD6,
+ 0x8C8ADDB6, 0xC8BDB485,
+ 0x8CA099D9, 0xC89061BA,
+ 0x8CB667C7, 0xC863177B,
+ 0x8CCC477D, 0xC835D5D0,
+ 0x8CE238F6, 0xC8089CBF,
+ 0x8CF83C30, 0xC7DB6C50,
+ 0x8D0E5127, 0xC7AE4489,
+ 0x8D2477D8, 0xC7812571,
+ 0x8D3AB03F, 0xC7540F10,
+ 0x8D50FA59, 0xC727016C,
+ 0x8D675623, 0xC6F9FC8D,
+ 0x8D7DC399, 0xC6CD0079,
+ 0x8D9442B7, 0xC6A00D36,
+ 0x8DAAD37B, 0xC67322CD,
+ 0x8DC175E0, 0xC6464144,
+ 0x8DD829E4, 0xC61968A2,
+ 0x8DEEEF82, 0xC5EC98ED,
+ 0x8E05C6B7, 0xC5BFD22E,
+ 0x8E1CAF80, 0xC593146A,
+ 0x8E33A9D9, 0xC5665FA8,
+ 0x8E4AB5BF, 0xC539B3F0,
+ 0x8E61D32D, 0xC50D1148,
+ 0x8E790222, 0xC4E077B8,
+ 0x8E904298, 0xC4B3E746,
+ 0x8EA7948C, 0xC4875FF8,
+ 0x8EBEF7FB, 0xC45AE1D7,
+ 0x8ED66CE1, 0xC42E6CE8,
+ 0x8EEDF33B, 0xC4020132,
+ 0x8F058B04, 0xC3D59EBD,
+ 0x8F1D343A, 0xC3A9458F,
+ 0x8F34EED8, 0xC37CF5B0,
+ 0x8F4CBADB, 0xC350AF25,
+ 0x8F64983F, 0xC32471F6,
+ 0x8F7C8701, 0xC2F83E2A,
+ 0x8F94871D, 0xC2CC13C7,
+ 0x8FAC988E, 0xC29FF2D4,
+ 0x8FC4BB53, 0xC273DB58,
+ 0x8FDCEF66, 0xC247CD5A,
+ 0x8FF534C4, 0xC21BC8E0,
+ 0x900D8B69, 0xC1EFCDF2,
+ 0x9025F352, 0xC1C3DC96,
+ 0x903E6C7A, 0xC197F4D3,
+ 0x9056F6DF, 0xC16C16B0,
+ 0x906F927B, 0xC1404233,
+ 0x90883F4C, 0xC1147763,
+ 0x90A0FD4E, 0xC0E8B648,
+ 0x90B9CC7C, 0xC0BCFEE7,
+ 0x90D2ACD3, 0xC0915147,
+ 0x90EB9E50, 0xC065AD70,
+ 0x9104A0ED, 0xC03A1368,
+ 0x911DB4A8, 0xC00E8335,
+ 0x9136D97D, 0xBFE2FCDF,
+ 0x91500F67, 0xBFB7806C,
+ 0x91695663, 0xBF8C0DE2,
+ 0x9182AE6C, 0xBF60A54A,
+ 0x919C1780, 0xBF3546A8,
+ 0x91B5919A, 0xBF09F204,
+ 0x91CF1CB6, 0xBEDEA765,
+ 0x91E8B8D0, 0xBEB366D1,
+ 0x920265E4, 0xBE88304F,
+ 0x921C23EE, 0xBE5D03E5,
+ 0x9235F2EB, 0xBE31E19B,
+ 0x924FD2D6, 0xBE06C977,
+ 0x9269C3AC, 0xBDDBBB7F,
+ 0x9283C567, 0xBDB0B7BA,
+ 0x929DD805, 0xBD85BE2F,
+ 0x92B7FB82, 0xBD5ACEE5,
+ 0x92D22FD8, 0xBD2FE9E1,
+ 0x92EC7505, 0xBD050F2C,
+ 0x9306CB04, 0xBCDA3ECA,
+ 0x932131D1, 0xBCAF78C3,
+ 0x933BA968, 0xBC84BD1E,
+ 0x935631C5, 0xBC5A0BE1,
+ 0x9370CAE4, 0xBC2F6513,
+ 0x938B74C0, 0xBC04C8BA,
+ 0x93A62F56, 0xBBDA36DC,
+ 0x93C0FAA2, 0xBBAFAF81,
+ 0x93DBD69F, 0xBB8532AF,
+ 0x93F6C34A, 0xBB5AC06C,
+ 0x9411C09D, 0xBB3058C0,
+ 0x942CCE95, 0xBB05FBB0,
+ 0x9447ED2F, 0xBADBA943,
+ 0x94631C64, 0xBAB1617F,
+ 0x947E5C32, 0xBA87246C,
+ 0x9499AC95, 0xBA5CF210,
+ 0x94B50D87, 0xBA32CA70,
+ 0x94D07F05, 0xBA08AD94,
+ 0x94EC010B, 0xB9DE9B83,
+ 0x95079393, 0xB9B49442,
+ 0x9523369B, 0xB98A97D8,
+ 0x953EEA1E, 0xB960A64B,
+ 0x955AAE17, 0xB936BFA3,
+ 0x95768282, 0xB90CE3E6,
+ 0x9592675B, 0xB8E31319,
+ 0x95AE5C9E, 0xB8B94D44,
+ 0x95CA6246, 0xB88F926C,
+ 0x95E6784F, 0xB865E299,
+ 0x96029EB5, 0xB83C3DD1,
+ 0x961ED573, 0xB812A419,
+ 0x963B1C85, 0xB7E9157A,
+ 0x965773E7, 0xB7BF91F8,
+ 0x9673DB94, 0xB796199B,
+ 0x96905387, 0xB76CAC68,
+ 0x96ACDBBD, 0xB7434A67,
+ 0x96C97431, 0xB719F39D,
+ 0x96E61CDF, 0xB6F0A811,
+ 0x9702D5C2, 0xB6C767CA,
+ 0x971F9ED6, 0xB69E32CD,
+ 0x973C7816, 0xB6750921,
+ 0x9759617E, 0xB64BEACC,
+ 0x97765B0A, 0xB622D7D5,
+ 0x979364B5, 0xB5F9D042,
+ 0x97B07E7A, 0xB5D0D41A,
+ 0x97CDA855, 0xB5A7E362,
+ 0x97EAE241, 0xB57EFE21,
+ 0x98082C3B, 0xB556245E,
+ 0x9825863D, 0xB52D561E,
+ 0x9842F043, 0xB5049368,
+ 0x98606A48, 0xB4DBDC42,
+ 0x987DF449, 0xB4B330B2,
+ 0x989B8E3F, 0xB48A90C0,
+ 0x98B93828, 0xB461FC70,
+ 0x98D6F1FE, 0xB43973C9,
+ 0x98F4BBBC, 0xB410F6D2,
+ 0x9912955E, 0xB3E88591,
+ 0x99307EE0, 0xB3C0200C,
+ 0x994E783C, 0xB397C649,
+ 0x996C816F, 0xB36F784E,
+ 0x998A9A73, 0xB3473622,
+ 0x99A8C344, 0xB31EFFCB,
+ 0x99C6FBDE, 0xB2F6D54F,
+ 0x99E5443A, 0xB2CEB6B5,
+ 0x9A039C56, 0xB2A6A401,
+ 0x9A22042C, 0xB27E9D3B,
+ 0x9A407BB8, 0xB256A26A,
+ 0x9A5F02F5, 0xB22EB392,
+ 0x9A7D99DD, 0xB206D0BA,
+ 0x9A9C406D, 0xB1DEF9E8,
+ 0x9ABAF6A0, 0xB1B72F23,
+ 0x9AD9BC71, 0xB18F7070,
+ 0x9AF891DB, 0xB167BDD6,
+ 0x9B1776D9, 0xB140175B,
+ 0x9B366B67, 0xB1187D05,
+ 0x9B556F80, 0xB0F0EEDA,
+ 0x9B748320, 0xB0C96CDF,
+ 0x9B93A640, 0xB0A1F71C,
+ 0x9BB2D8DD, 0xB07A8D97,
+ 0x9BD21AF2, 0xB0533055,
+ 0x9BF16C7A, 0xB02BDF5C,
+ 0x9C10CD70, 0xB0049AB2,
+ 0x9C303DCF, 0xAFDD625F,
+ 0x9C4FBD92, 0xAFB63667,
+ 0x9C6F4CB5, 0xAF8F16D0,
+ 0x9C8EEB33, 0xAF6803A1,
+ 0x9CAE9907, 0xAF40FCE0,
+ 0x9CCE562B, 0xAF1A0293,
+ 0x9CEE229C, 0xAEF314BF,
+ 0x9D0DFE53, 0xAECC336B,
+ 0x9D2DE94D, 0xAEA55E9D,
+ 0x9D4DE384, 0xAE7E965B,
+ 0x9D6DECF4, 0xAE57DAAA,
+ 0x9D8E0596, 0xAE312B91,
+ 0x9DAE2D68, 0xAE0A8916,
+ 0x9DCE6462, 0xADE3F33E,
+ 0x9DEEAA82, 0xADBD6A10,
+ 0x9E0EFFC1, 0xAD96ED91,
+ 0x9E2F641A, 0xAD707DC8,
+ 0x9E4FD789, 0xAD4A1ABA,
+ 0x9E705A09, 0xAD23C46D,
+ 0x9E90EB94, 0xACFD7AE8,
+ 0x9EB18C26, 0xACD73E30,
+ 0x9ED23BB9, 0xACB10E4A,
+ 0x9EF2FA48, 0xAC8AEB3E,
+ 0x9F13C7D0, 0xAC64D510,
+ 0x9F34A449, 0xAC3ECBC7,
+ 0x9F558FB0, 0xAC18CF68,
+ 0x9F7689FF, 0xABF2DFFA,
+ 0x9F979331, 0xABCCFD82,
+ 0x9FB8AB41, 0xABA72806,
+ 0x9FD9D22A, 0xAB815F8C,
+ 0x9FFB07E7, 0xAB5BA41A,
+ 0xA01C4C72, 0xAB35F5B5,
+ 0xA03D9FC7, 0xAB105464,
+ 0xA05F01E1, 0xAAEAC02B,
+ 0xA08072BA, 0xAAC53912,
+ 0xA0A1F24C, 0xAA9FBF1D,
+ 0xA0C38094, 0xAA7A5253,
+ 0xA0E51D8C, 0xAA54F2B9,
+ 0xA106C92E, 0xAA2FA055,
+ 0xA1288376, 0xAA0A5B2D,
+ 0xA14A4C5E, 0xA9E52347,
+ 0xA16C23E1, 0xA9BFF8A8,
+ 0xA18E09F9, 0xA99ADB56,
+ 0xA1AFFEA2, 0xA975CB56,
+ 0xA1D201D7, 0xA950C8AF,
+ 0xA1F41391, 0xA92BD366,
+ 0xA21633CD, 0xA906EB81,
+ 0xA2386283, 0xA8E21106,
+ 0xA25A9FB1, 0xA8BD43FA,
+ 0xA27CEB4F, 0xA8988463,
+ 0xA29F4559, 0xA873D246,
+ 0xA2C1ADC9, 0xA84F2DA9,
+ 0xA2E4249A, 0xA82A9693,
+ 0xA306A9C7, 0xA8060D08,
+ 0xA3293D4B, 0xA7E1910E,
+ 0xA34BDF20, 0xA7BD22AB,
+ 0xA36E8F40, 0xA798C1E4,
+ 0xA3914DA7, 0xA7746EC0,
+ 0xA3B41A4F, 0xA7502943,
+ 0xA3D6F533, 0xA72BF173,
+ 0xA3F9DE4D, 0xA707C756,
+ 0xA41CD598, 0xA6E3AAF2,
+ 0xA43FDB0F, 0xA6BF9C4B,
+ 0xA462EEAC, 0xA69B9B68,
+ 0xA4861069, 0xA677A84E,
+ 0xA4A94042, 0xA653C302,
+ 0xA4CC7E31, 0xA62FEB8B,
+ 0xA4EFCA31, 0xA60C21ED,
+ 0xA513243B, 0xA5E8662F,
+ 0xA5368C4B, 0xA5C4B855,
+ 0xA55A025B, 0xA5A11865,
+ 0xA57D8666, 0xA57D8666,
+ 0xA5A11865, 0xA55A025B,
+ 0xA5C4B855, 0xA5368C4B,
+ 0xA5E8662F, 0xA513243B,
+ 0xA60C21ED, 0xA4EFCA31,
+ 0xA62FEB8B, 0xA4CC7E31,
+ 0xA653C302, 0xA4A94042,
+ 0xA677A84E, 0xA4861069,
+ 0xA69B9B68, 0xA462EEAC,
+ 0xA6BF9C4B, 0xA43FDB0F,
+ 0xA6E3AAF2, 0xA41CD598,
+ 0xA707C756, 0xA3F9DE4D,
+ 0xA72BF173, 0xA3D6F533,
+ 0xA7502943, 0xA3B41A4F,
+ 0xA7746EC0, 0xA3914DA7,
+ 0xA798C1E4, 0xA36E8F40,
+ 0xA7BD22AB, 0xA34BDF20,
+ 0xA7E1910E, 0xA3293D4B,
+ 0xA8060D08, 0xA306A9C7,
+ 0xA82A9693, 0xA2E4249A,
+ 0xA84F2DA9, 0xA2C1ADC9,
+ 0xA873D246, 0xA29F4559,
+ 0xA8988463, 0xA27CEB4F,
+ 0xA8BD43FA, 0xA25A9FB1,
+ 0xA8E21106, 0xA2386283,
+ 0xA906EB81, 0xA21633CD,
+ 0xA92BD366, 0xA1F41391,
+ 0xA950C8AF, 0xA1D201D7,
+ 0xA975CB56, 0xA1AFFEA2,
+ 0xA99ADB56, 0xA18E09F9,
+ 0xA9BFF8A8, 0xA16C23E1,
+ 0xA9E52347, 0xA14A4C5E,
+ 0xAA0A5B2D, 0xA1288376,
+ 0xAA2FA055, 0xA106C92E,
+ 0xAA54F2B9, 0xA0E51D8C,
+ 0xAA7A5253, 0xA0C38094,
+ 0xAA9FBF1D, 0xA0A1F24C,
+ 0xAAC53912, 0xA08072BA,
+ 0xAAEAC02B, 0xA05F01E1,
+ 0xAB105464, 0xA03D9FC7,
+ 0xAB35F5B5, 0xA01C4C72,
+ 0xAB5BA41A, 0x9FFB07E7,
+ 0xAB815F8C, 0x9FD9D22A,
+ 0xABA72806, 0x9FB8AB41,
+ 0xABCCFD82, 0x9F979331,
+ 0xABF2DFFA, 0x9F7689FF,
+ 0xAC18CF68, 0x9F558FB0,
+ 0xAC3ECBC7, 0x9F34A449,
+ 0xAC64D510, 0x9F13C7D0,
+ 0xAC8AEB3E, 0x9EF2FA48,
+ 0xACB10E4A, 0x9ED23BB9,
+ 0xACD73E30, 0x9EB18C26,
+ 0xACFD7AE8, 0x9E90EB94,
+ 0xAD23C46D, 0x9E705A09,
+ 0xAD4A1ABA, 0x9E4FD789,
+ 0xAD707DC8, 0x9E2F641A,
+ 0xAD96ED91, 0x9E0EFFC1,
+ 0xADBD6A10, 0x9DEEAA82,
+ 0xADE3F33E, 0x9DCE6462,
+ 0xAE0A8916, 0x9DAE2D68,
+ 0xAE312B91, 0x9D8E0596,
+ 0xAE57DAAA, 0x9D6DECF4,
+ 0xAE7E965B, 0x9D4DE384,
+ 0xAEA55E9D, 0x9D2DE94D,
+ 0xAECC336B, 0x9D0DFE53,
+ 0xAEF314BF, 0x9CEE229C,
+ 0xAF1A0293, 0x9CCE562B,
+ 0xAF40FCE0, 0x9CAE9907,
+ 0xAF6803A1, 0x9C8EEB33,
+ 0xAF8F16D0, 0x9C6F4CB5,
+ 0xAFB63667, 0x9C4FBD92,
+ 0xAFDD625F, 0x9C303DCF,
+ 0xB0049AB2, 0x9C10CD70,
+ 0xB02BDF5C, 0x9BF16C7A,
+ 0xB0533055, 0x9BD21AF2,
+ 0xB07A8D97, 0x9BB2D8DD,
+ 0xB0A1F71C, 0x9B93A640,
+ 0xB0C96CDF, 0x9B748320,
+ 0xB0F0EEDA, 0x9B556F80,
+ 0xB1187D05, 0x9B366B67,
+ 0xB140175B, 0x9B1776D9,
+ 0xB167BDD6, 0x9AF891DB,
+ 0xB18F7070, 0x9AD9BC71,
+ 0xB1B72F23, 0x9ABAF6A0,
+ 0xB1DEF9E8, 0x9A9C406D,
+ 0xB206D0BA, 0x9A7D99DD,
+ 0xB22EB392, 0x9A5F02F5,
+ 0xB256A26A, 0x9A407BB8,
+ 0xB27E9D3B, 0x9A22042C,
+ 0xB2A6A401, 0x9A039C56,
+ 0xB2CEB6B5, 0x99E5443A,
+ 0xB2F6D54F, 0x99C6FBDE,
+ 0xB31EFFCB, 0x99A8C344,
+ 0xB3473622, 0x998A9A73,
+ 0xB36F784E, 0x996C816F,
+ 0xB397C649, 0x994E783C,
+ 0xB3C0200C, 0x99307EE0,
+ 0xB3E88591, 0x9912955E,
+ 0xB410F6D2, 0x98F4BBBC,
+ 0xB43973C9, 0x98D6F1FE,
+ 0xB461FC70, 0x98B93828,
+ 0xB48A90C0, 0x989B8E3F,
+ 0xB4B330B2, 0x987DF449,
+ 0xB4DBDC42, 0x98606A48,
+ 0xB5049368, 0x9842F043,
+ 0xB52D561E, 0x9825863D,
+ 0xB556245E, 0x98082C3B,
+ 0xB57EFE21, 0x97EAE241,
+ 0xB5A7E362, 0x97CDA855,
+ 0xB5D0D41A, 0x97B07E7A,
+ 0xB5F9D042, 0x979364B5,
+ 0xB622D7D5, 0x97765B0A,
+ 0xB64BEACC, 0x9759617E,
+ 0xB6750921, 0x973C7816,
+ 0xB69E32CD, 0x971F9ED6,
+ 0xB6C767CA, 0x9702D5C2,
+ 0xB6F0A811, 0x96E61CDF,
+ 0xB719F39D, 0x96C97431,
+ 0xB7434A67, 0x96ACDBBD,
+ 0xB76CAC68, 0x96905387,
+ 0xB796199B, 0x9673DB94,
+ 0xB7BF91F8, 0x965773E7,
+ 0xB7E9157A, 0x963B1C85,
+ 0xB812A419, 0x961ED573,
+ 0xB83C3DD1, 0x96029EB5,
+ 0xB865E299, 0x95E6784F,
+ 0xB88F926C, 0x95CA6246,
+ 0xB8B94D44, 0x95AE5C9E,
+ 0xB8E31319, 0x9592675B,
+ 0xB90CE3E6, 0x95768282,
+ 0xB936BFA3, 0x955AAE17,
+ 0xB960A64B, 0x953EEA1E,
+ 0xB98A97D8, 0x9523369B,
+ 0xB9B49442, 0x95079393,
+ 0xB9DE9B83, 0x94EC010B,
+ 0xBA08AD94, 0x94D07F05,
+ 0xBA32CA70, 0x94B50D87,
+ 0xBA5CF210, 0x9499AC95,
+ 0xBA87246C, 0x947E5C32,
+ 0xBAB1617F, 0x94631C64,
+ 0xBADBA943, 0x9447ED2F,
+ 0xBB05FBB0, 0x942CCE95,
+ 0xBB3058C0, 0x9411C09D,
+ 0xBB5AC06C, 0x93F6C34A,
+ 0xBB8532AF, 0x93DBD69F,
+ 0xBBAFAF81, 0x93C0FAA2,
+ 0xBBDA36DC, 0x93A62F56,
+ 0xBC04C8BA, 0x938B74C0,
+ 0xBC2F6513, 0x9370CAE4,
+ 0xBC5A0BE1, 0x935631C5,
+ 0xBC84BD1E, 0x933BA968,
+ 0xBCAF78C3, 0x932131D1,
+ 0xBCDA3ECA, 0x9306CB04,
+ 0xBD050F2C, 0x92EC7505,
+ 0xBD2FE9E1, 0x92D22FD8,
+ 0xBD5ACEE5, 0x92B7FB82,
+ 0xBD85BE2F, 0x929DD805,
+ 0xBDB0B7BA, 0x9283C567,
+ 0xBDDBBB7F, 0x9269C3AC,
+ 0xBE06C977, 0x924FD2D6,
+ 0xBE31E19B, 0x9235F2EB,
+ 0xBE5D03E5, 0x921C23EE,
+ 0xBE88304F, 0x920265E4,
+ 0xBEB366D1, 0x91E8B8D0,
+ 0xBEDEA765, 0x91CF1CB6,
+ 0xBF09F204, 0x91B5919A,
+ 0xBF3546A8, 0x919C1780,
+ 0xBF60A54A, 0x9182AE6C,
+ 0xBF8C0DE2, 0x91695663,
+ 0xBFB7806C, 0x91500F67,
+ 0xBFE2FCDF, 0x9136D97D,
+ 0xC00E8335, 0x911DB4A8,
+ 0xC03A1368, 0x9104A0ED,
+ 0xC065AD70, 0x90EB9E50,
+ 0xC0915147, 0x90D2ACD3,
+ 0xC0BCFEE7, 0x90B9CC7C,
+ 0xC0E8B648, 0x90A0FD4E,
+ 0xC1147763, 0x90883F4C,
+ 0xC1404233, 0x906F927B,
+ 0xC16C16B0, 0x9056F6DF,
+ 0xC197F4D3, 0x903E6C7A,
+ 0xC1C3DC96, 0x9025F352,
+ 0xC1EFCDF2, 0x900D8B69,
+ 0xC21BC8E0, 0x8FF534C4,
+ 0xC247CD5A, 0x8FDCEF66,
+ 0xC273DB58, 0x8FC4BB53,
+ 0xC29FF2D4, 0x8FAC988E,
+ 0xC2CC13C7, 0x8F94871D,
+ 0xC2F83E2A, 0x8F7C8701,
+ 0xC32471F6, 0x8F64983F,
+ 0xC350AF25, 0x8F4CBADB,
+ 0xC37CF5B0, 0x8F34EED8,
+ 0xC3A9458F, 0x8F1D343A,
+ 0xC3D59EBD, 0x8F058B04,
+ 0xC4020132, 0x8EEDF33B,
+ 0xC42E6CE8, 0x8ED66CE1,
+ 0xC45AE1D7, 0x8EBEF7FB,
+ 0xC4875FF8, 0x8EA7948C,
+ 0xC4B3E746, 0x8E904298,
+ 0xC4E077B8, 0x8E790222,
+ 0xC50D1148, 0x8E61D32D,
+ 0xC539B3F0, 0x8E4AB5BF,
+ 0xC5665FA8, 0x8E33A9D9,
+ 0xC593146A, 0x8E1CAF80,
+ 0xC5BFD22E, 0x8E05C6B7,
+ 0xC5EC98ED, 0x8DEEEF82,
+ 0xC61968A2, 0x8DD829E4,
+ 0xC6464144, 0x8DC175E0,
+ 0xC67322CD, 0x8DAAD37B,
+ 0xC6A00D36, 0x8D9442B7,
+ 0xC6CD0079, 0x8D7DC399,
+ 0xC6F9FC8D, 0x8D675623,
+ 0xC727016C, 0x8D50FA59,
+ 0xC7540F10, 0x8D3AB03F,
+ 0xC7812571, 0x8D2477D8,
+ 0xC7AE4489, 0x8D0E5127,
+ 0xC7DB6C50, 0x8CF83C30,
+ 0xC8089CBF, 0x8CE238F6,
+ 0xC835D5D0, 0x8CCC477D,
+ 0xC863177B, 0x8CB667C7,
+ 0xC89061BA, 0x8CA099D9,
+ 0xC8BDB485, 0x8C8ADDB6,
+ 0xC8EB0FD6, 0x8C753361,
+ 0xC91873A5, 0x8C5F9ADD,
+ 0xC945DFEC, 0x8C4A142F,
+ 0xC97354A3, 0x8C349F58,
+ 0xC9A0D1C4, 0x8C1F3C5C,
+ 0xC9CE5748, 0x8C09EB40,
+ 0xC9FBE527, 0x8BF4AC05,
+ 0xCA297B5A, 0x8BDF7EAF,
+ 0xCA5719DB, 0x8BCA6342,
+ 0xCA84C0A2, 0x8BB559C1,
+ 0xCAB26FA9, 0x8BA0622F,
+ 0xCAE026E8, 0x8B8B7C8F,
+ 0xCB0DE658, 0x8B76A8E4,
+ 0xCB3BADF2, 0x8B61E732,
+ 0xCB697DB0, 0x8B4D377C,
+ 0xCB975589, 0x8B3899C5,
+ 0xCBC53578, 0x8B240E10,
+ 0xCBF31D75, 0x8B0F9461,
+ 0xCC210D78, 0x8AFB2CBA,
+ 0xCC4F057B, 0x8AE6D71F,
+ 0xCC7D0577, 0x8AD29393,
+ 0xCCAB0D65, 0x8ABE6219,
+ 0xCCD91D3D, 0x8AAA42B4,
+ 0xCD0734F8, 0x8A963567,
+ 0xCD355490, 0x8A823A35,
+ 0xCD637BFD, 0x8A6E5122,
+ 0xCD91AB38, 0x8A5A7A30,
+ 0xCDBFE23A, 0x8A46B563,
+ 0xCDEE20FC, 0x8A3302BD,
+ 0xCE1C6776, 0x8A1F6242,
+ 0xCE4AB5A2, 0x8A0BD3F5,
+ 0xCE790B78, 0x89F857D8,
+ 0xCEA768F2, 0x89E4EDEE,
+ 0xCED5CE08, 0x89D1963C,
+ 0xCF043AB2, 0x89BE50C3,
+ 0xCF32AEEB, 0x89AB1D86,
+ 0xCF612AAA, 0x8997FC89,
+ 0xCF8FADE8, 0x8984EDCF,
+ 0xCFBE389F, 0x8971F15A,
+ 0xCFECCAC7, 0x895F072D,
+ 0xD01B6459, 0x894C2F4C,
+ 0xD04A054D, 0x893969B9,
+ 0xD078AD9D, 0x8926B677,
+ 0xD0A75D42, 0x89141589,
+ 0xD0D61433, 0x890186F1,
+ 0xD104D26B, 0x88EF0AB4,
+ 0xD13397E1, 0x88DCA0D3,
+ 0xD162648F, 0x88CA4951,
+ 0xD191386D, 0x88B80431,
+ 0xD1C01374, 0x88A5D177,
+ 0xD1EEF59E, 0x8893B124,
+ 0xD21DDEE1, 0x8881A33C,
+ 0xD24CCF38, 0x886FA7C2,
+ 0xD27BC69C, 0x885DBEB7,
+ 0xD2AAC504, 0x884BE820,
+ 0xD2D9CA6A, 0x883A23FE,
+ 0xD308D6C6, 0x88287255,
+ 0xD337EA12, 0x8816D327,
+ 0xD3670445, 0x88054677,
+ 0xD3962559, 0x87F3CC47,
+ 0xD3C54D46, 0x87E2649B,
+ 0xD3F47C06, 0x87D10F75,
+ 0xD423B190, 0x87BFCCD7,
+ 0xD452EDDE, 0x87AE9CC5,
+ 0xD48230E8, 0x879D7F40,
+ 0xD4B17AA7, 0x878C744C,
+ 0xD4E0CB14, 0x877B7BEC,
+ 0xD5102227, 0x876A9621,
+ 0xD53F7FDA, 0x8759C2EF,
+ 0xD56EE424, 0x87490257,
+ 0xD59E4EFE, 0x8738545E,
+ 0xD5CDC062, 0x8727B904,
+ 0xD5FD3847, 0x8717304E,
+ 0xD62CB6A7, 0x8706BA3C,
+ 0xD65C3B7B, 0x86F656D3,
+ 0xD68BC6BA, 0x86E60614,
+ 0xD6BB585D, 0x86D5C802,
+ 0xD6EAF05E, 0x86C59C9F,
+ 0xD71A8EB5, 0x86B583EE,
+ 0xD74A335A, 0x86A57DF1,
+ 0xD779DE46, 0x86958AAB,
+ 0xD7A98F73, 0x8685AA1F,
+ 0xD7D946D7, 0x8675DC4E,
+ 0xD809046D, 0x8666213C,
+ 0xD838C82D, 0x865678EA,
+ 0xD868920F, 0x8646E35B,
+ 0xD898620C, 0x86376092,
+ 0xD8C8381C, 0x8627F090,
+ 0xD8F81439, 0x86189359,
+ 0xD927F65B, 0x860948EE,
+ 0xD957DE7A, 0x85FA1152,
+ 0xD987CC8F, 0x85EAEC88,
+ 0xD9B7C093, 0x85DBDA91,
+ 0xD9E7BA7E, 0x85CCDB70,
+ 0xDA17BA4A, 0x85BDEF27,
+ 0xDA47BFED, 0x85AF15B9,
+ 0xDA77CB62, 0x85A04F28,
+ 0xDAA7DCA1, 0x85919B75,
+ 0xDAD7F3A2, 0x8582FAA4,
+ 0xDB08105E, 0x85746CB7,
+ 0xDB3832CD, 0x8565F1B0,
+ 0xDB685AE8, 0x85578991,
+ 0xDB9888A8, 0x8549345C,
+ 0xDBC8BC05, 0x853AF214,
+ 0xDBF8F4F8, 0x852CC2BA,
+ 0xDC293379, 0x851EA652,
+ 0xDC597781, 0x85109CDC,
+ 0xDC89C108, 0x8502A65C,
+ 0xDCBA1008, 0x84F4C2D3,
+ 0xDCEA6478, 0x84E6F244,
+ 0xDD1ABE51, 0x84D934B0,
+ 0xDD4B1D8B, 0x84CB8A1B,
+ 0xDD7B8220, 0x84BDF285,
+ 0xDDABEC07, 0x84B06DF1,
+ 0xDDDC5B3A, 0x84A2FC62,
+ 0xDE0CCFB1, 0x84959DD9,
+ 0xDE3D4963, 0x84885257,
+ 0xDE6DC84B, 0x847B19E1,
+ 0xDE9E4C60, 0x846DF476,
+ 0xDECED59B, 0x8460E21A,
+ 0xDEFF63F4, 0x8453E2CE,
+ 0xDF2FF764, 0x8446F695,
+ 0xDF608FE3, 0x843A1D70,
+ 0xDF912D6A, 0x842D5761,
+ 0xDFC1CFF2, 0x8420A46B,
+ 0xDFF27773, 0x8414048F,
+ 0xE02323E5, 0x840777CF,
+ 0xE053D541, 0x83FAFE2E,
+ 0xE0848B7F, 0x83EE97AC,
+ 0xE0B54698, 0x83E2444D,
+ 0xE0E60684, 0x83D60411,
+ 0xE116CB3D, 0x83C9D6FB,
+ 0xE14794B9, 0x83BDBD0D,
+ 0xE17862F3, 0x83B1B649,
+ 0xE1A935E1, 0x83A5C2B0,
+ 0xE1DA0D7E, 0x8399E244,
+ 0xE20AE9C1, 0x838E1507,
+ 0xE23BCAA2, 0x83825AFB,
+ 0xE26CB01A, 0x8376B422,
+ 0xE29D9A22, 0x836B207D,
+ 0xE2CE88B2, 0x835FA00E,
+ 0xE2FF7BC3, 0x835432D8,
+ 0xE330734C, 0x8348D8DB,
+ 0xE3616F47, 0x833D921A,
+ 0xE3926FAC, 0x83325E97,
+ 0xE3C37473, 0x83273E52,
+ 0xE3F47D95, 0x831C314E,
+ 0xE4258B0A, 0x8311378C,
+ 0xE4569CCB, 0x8306510F,
+ 0xE487B2CF, 0x82FB7DD8,
+ 0xE4B8CD10, 0x82F0BDE8,
+ 0xE4E9EB86, 0x82E61141,
+ 0xE51B0E2A, 0x82DB77E5,
+ 0xE54C34F3, 0x82D0F1D5,
+ 0xE57D5FDA, 0x82C67F13,
+ 0xE5AE8ED8, 0x82BC1FA1,
+ 0xE5DFC1E4, 0x82B1D381,
+ 0xE610F8F9, 0x82A79AB3,
+ 0xE642340D, 0x829D753A,
+ 0xE6737319, 0x82936316,
+ 0xE6A4B616, 0x8289644A,
+ 0xE6D5FCFC, 0x827F78D8,
+ 0xE70747C3, 0x8275A0C0,
+ 0xE7389664, 0x826BDC04,
+ 0xE769E8D8, 0x82622AA5,
+ 0xE79B3F16, 0x82588CA6,
+ 0xE7CC9917, 0x824F0208,
+ 0xE7FDF6D3, 0x82458ACB,
+ 0xE82F5844, 0x823C26F2,
+ 0xE860BD60, 0x8232D67E,
+ 0xE8922621, 0x82299971,
+ 0xE8C3927F, 0x82206FCB,
+ 0xE8F50273, 0x8217598F,
+ 0xE92675F4, 0x820E56BE,
+ 0xE957ECFB, 0x82056758,
+ 0xE9896780, 0x81FC8B60,
+ 0xE9BAE57C, 0x81F3C2D7,
+ 0xE9EC66E8, 0x81EB0DBD,
+ 0xEA1DEBBB, 0x81E26C16,
+ 0xEA4F73EE, 0x81D9DDE1,
+ 0xEA80FF79, 0x81D16320,
+ 0xEAB28E55, 0x81C8FBD5,
+ 0xEAE4207A, 0x81C0A801,
+ 0xEB15B5E0, 0x81B867A4,
+ 0xEB474E80, 0x81B03AC1,
+ 0xEB78EA52, 0x81A82159,
+ 0xEBAA894E, 0x81A01B6C,
+ 0xEBDC2B6D, 0x819828FD,
+ 0xEC0DD0A8, 0x81904A0C,
+ 0xEC3F78F5, 0x81887E9A,
+ 0xEC71244F, 0x8180C6A9,
+ 0xECA2D2AC, 0x8179223A,
+ 0xECD48406, 0x8171914E,
+ 0xED063855, 0x816A13E6,
+ 0xED37EF91, 0x8162AA03,
+ 0xED69A9B2, 0x815B53A8,
+ 0xED9B66B2, 0x815410D3,
+ 0xEDCD2687, 0x814CE188,
+ 0xEDFEE92B, 0x8145C5C6,
+ 0xEE30AE95, 0x813EBD90,
+ 0xEE6276BF, 0x8137C8E6,
+ 0xEE9441A0, 0x8130E7C8,
+ 0xEEC60F31, 0x812A1A39,
+ 0xEEF7DF6A, 0x81236039,
+ 0xEF29B243, 0x811CB9CA,
+ 0xEF5B87B5, 0x811626EC,
+ 0xEF8D5FB8, 0x810FA7A0,
+ 0xEFBF3A44, 0x81093BE8,
+ 0xEFF11752, 0x8102E3C3,
+ 0xF022F6DA, 0x80FC9F35,
+ 0xF054D8D4, 0x80F66E3C,
+ 0xF086BD39, 0x80F050DB,
+ 0xF0B8A401, 0x80EA4712,
+ 0xF0EA8D23, 0x80E450E2,
+ 0xF11C789A, 0x80DE6E4C,
+ 0xF14E665C, 0x80D89F51,
+ 0xF1805662, 0x80D2E3F1,
+ 0xF1B248A5, 0x80CD3C2F,
+ 0xF1E43D1C, 0x80C7A80A,
+ 0xF21633C0, 0x80C22783,
+ 0xF2482C89, 0x80BCBA9C,
+ 0xF27A2770, 0x80B76155,
+ 0xF2AC246D, 0x80B21BAF,
+ 0xF2DE2378, 0x80ACE9AB,
+ 0xF310248A, 0x80A7CB49,
+ 0xF342279A, 0x80A2C08B,
+ 0xF3742CA1, 0x809DC970,
+ 0xF3A63398, 0x8098E5FB,
+ 0xF3D83C76, 0x8094162B,
+ 0xF40A4734, 0x808F5A02,
+ 0xF43C53CA, 0x808AB180,
+ 0xF46E6231, 0x80861CA5,
+ 0xF4A07260, 0x80819B74,
+ 0xF4D28451, 0x807D2DEB,
+ 0xF50497FA, 0x8078D40D,
+ 0xF536AD55, 0x80748DD9,
+ 0xF568C45A, 0x80705B50,
+ 0xF59ADD01, 0x806C3C73,
+ 0xF5CCF743, 0x80683143,
+ 0xF5FF1317, 0x806439C0,
+ 0xF6313076, 0x806055EA,
+ 0xF6634F58, 0x805C85C3,
+ 0xF6956FB6, 0x8058C94C,
+ 0xF6C79188, 0x80552083,
+ 0xF6F9B4C5, 0x80518B6B,
+ 0xF72BD967, 0x804E0A03,
+ 0xF75DFF65, 0x804A9C4D,
+ 0xF79026B8, 0x80474248,
+ 0xF7C24F58, 0x8043FBF6,
+ 0xF7F4793E, 0x8040C956,
+ 0xF826A461, 0x803DAA69,
+ 0xF858D0BA, 0x803A9F31,
+ 0xF88AFE41, 0x8037A7AC,
+ 0xF8BD2CEF, 0x8034C3DC,
+ 0xF8EF5CBB, 0x8031F3C1,
+ 0xF9218D9E, 0x802F375C,
+ 0xF953BF90, 0x802C8EAD,
+ 0xF985F28A, 0x8029F9B4,
+ 0xF9B82683, 0x80277872,
+ 0xF9EA5B75, 0x80250AE7,
+ 0xFA1C9156, 0x8022B113,
+ 0xFA4EC820, 0x80206AF8,
+ 0xFA80FFCB, 0x801E3894,
+ 0xFAB3384F, 0x801C19E9,
+ 0xFAE571A4, 0x801A0EF7,
+ 0xFB17ABC2, 0x801817BF,
+ 0xFB49E6A2, 0x80163440,
+ 0xFB7C223C, 0x8014647A,
+ 0xFBAE5E89, 0x8012A86F,
+ 0xFBE09B80, 0x8011001E,
+ 0xFC12D919, 0x800F6B88,
+ 0xFC45174E, 0x800DEAAC,
+ 0xFC775616, 0x800C7D8C,
+ 0xFCA99569, 0x800B2427,
+ 0xFCDBD541, 0x8009DE7D,
+ 0xFD0E1594, 0x8008AC90,
+ 0xFD40565B, 0x80078E5E,
+ 0xFD72978F, 0x800683E8,
+ 0xFDA4D928, 0x80058D2E,
+ 0xFDD71B1E, 0x8004AA31,
+ 0xFE095D69, 0x8003DAF0,
+ 0xFE3BA001, 0x80031F6C,
+ 0xFE6DE2E0, 0x800277A5,
+ 0xFEA025FC, 0x8001E39B,
+ 0xFED2694F, 0x8001634D,
+ 0xFF04ACD0, 0x8000F6BD,
+ 0xFF36F078, 0x80009DE9,
+ 0xFF69343E, 0x800058D3,
+ 0xFF9B781D, 0x8000277A,
+ 0xFFCDBC0A, 0x800009DE
+};
+
+
+
+/*
+* @brief q15 Twiddle factors Table
+*/
+
+
+/**
+* \par
+* Example code for q15 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 16 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to q15(Fixed point 1.15):
+* round(twiddleCoefq15(i) * pow(2, 15))
+*
+*/
+const q15_t twiddleCoef_16_q15[24] = {
+ 0x7FFF, 0x0000,
+ 0x7641, 0x30FB,
+ 0x5A82, 0x5A82,
+ 0x30FB, 0x7641,
+ 0x0000, 0x7FFF,
+ 0xCF04, 0x7641,
+ 0xA57D, 0x5A82,
+ 0x89BE, 0x30FB,
+ 0x8000, 0x0000,
+ 0x89BE, 0xCF04,
+ 0xA57D, 0xA57D,
+ 0xCF04, 0x89BE
+};
+
+/**
+* \par
+* Example code for q15 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 32 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to q15(Fixed point 1.15):
+* round(twiddleCoefq15(i) * pow(2, 15))
+*
+*/
+const q15_t twiddleCoef_32_q15[48] = {
+ 0x7FFF, 0x0000,
+ 0x7D8A, 0x18F8,
+ 0x7641, 0x30FB,
+ 0x6A6D, 0x471C,
+ 0x5A82, 0x5A82,
+ 0x471C, 0x6A6D,
+ 0x30FB, 0x7641,
+ 0x18F8, 0x7D8A,
+ 0x0000, 0x7FFF,
+ 0xE707, 0x7D8A,
+ 0xCF04, 0x7641,
+ 0xB8E3, 0x6A6D,
+ 0xA57D, 0x5A82,
+ 0x9592, 0x471C,
+ 0x89BE, 0x30FB,
+ 0x8275, 0x18F8,
+ 0x8000, 0x0000,
+ 0x8275, 0xE707,
+ 0x89BE, 0xCF04,
+ 0x9592, 0xB8E3,
+ 0xA57D, 0xA57D,
+ 0xB8E3, 0x9592,
+ 0xCF04, 0x89BE,
+ 0xE707, 0x8275
+};
+
+/**
+* \par
+* Example code for q15 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 64 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to q15(Fixed point 1.15):
+* round(twiddleCoefq15(i) * pow(2, 15))
+*
+*/
+const q15_t twiddleCoef_64_q15[96] = {
+ 0x7FFF, 0x0000,
+ 0x7F62, 0x0C8B,
+ 0x7D8A, 0x18F8,
+ 0x7A7D, 0x2528,
+ 0x7641, 0x30FB,
+ 0x70E2, 0x3C56,
+ 0x6A6D, 0x471C,
+ 0x62F2, 0x5133,
+ 0x5A82, 0x5A82,
+ 0x5133, 0x62F2,
+ 0x471C, 0x6A6D,
+ 0x3C56, 0x70E2,
+ 0x30FB, 0x7641,
+ 0x2528, 0x7A7D,
+ 0x18F8, 0x7D8A,
+ 0x0C8B, 0x7F62,
+ 0x0000, 0x7FFF,
+ 0xF374, 0x7F62,
+ 0xE707, 0x7D8A,
+ 0xDAD7, 0x7A7D,
+ 0xCF04, 0x7641,
+ 0xC3A9, 0x70E2,
+ 0xB8E3, 0x6A6D,
+ 0xAECC, 0x62F2,
+ 0xA57D, 0x5A82,
+ 0x9D0D, 0x5133,
+ 0x9592, 0x471C,
+ 0x8F1D, 0x3C56,
+ 0x89BE, 0x30FB,
+ 0x8582, 0x2528,
+ 0x8275, 0x18F8,
+ 0x809D, 0x0C8B,
+ 0x8000, 0x0000,
+ 0x809D, 0xF374,
+ 0x8275, 0xE707,
+ 0x8582, 0xDAD7,
+ 0x89BE, 0xCF04,
+ 0x8F1D, 0xC3A9,
+ 0x9592, 0xB8E3,
+ 0x9D0D, 0xAECC,
+ 0xA57D, 0xA57D,
+ 0xAECC, 0x9D0D,
+ 0xB8E3, 0x9592,
+ 0xC3A9, 0x8F1D,
+ 0xCF04, 0x89BE,
+ 0xDAD7, 0x8582,
+ 0xE707, 0x8275,
+ 0xF374, 0x809D
+};
+
+/**
+* \par
+* Example code for q15 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 128 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to q15(Fixed point 1.15):
+* round(twiddleCoefq15(i) * pow(2, 15))
+*
+*/
+const q15_t twiddleCoef_128_q15[192] = {
+ 0x7FFF, 0x0000,
+ 0x7FD8, 0x0647,
+ 0x7F62, 0x0C8B,
+ 0x7E9D, 0x12C8,
+ 0x7D8A, 0x18F8,
+ 0x7C29, 0x1F19,
+ 0x7A7D, 0x2528,
+ 0x7884, 0x2B1F,
+ 0x7641, 0x30FB,
+ 0x73B5, 0x36BA,
+ 0x70E2, 0x3C56,
+ 0x6DCA, 0x41CE,
+ 0x6A6D, 0x471C,
+ 0x66CF, 0x4C3F,
+ 0x62F2, 0x5133,
+ 0x5ED7, 0x55F5,
+ 0x5A82, 0x5A82,
+ 0x55F5, 0x5ED7,
+ 0x5133, 0x62F2,
+ 0x4C3F, 0x66CF,
+ 0x471C, 0x6A6D,
+ 0x41CE, 0x6DCA,
+ 0x3C56, 0x70E2,
+ 0x36BA, 0x73B5,
+ 0x30FB, 0x7641,
+ 0x2B1F, 0x7884,
+ 0x2528, 0x7A7D,
+ 0x1F19, 0x7C29,
+ 0x18F8, 0x7D8A,
+ 0x12C8, 0x7E9D,
+ 0x0C8B, 0x7F62,
+ 0x0647, 0x7FD8,
+ 0x0000, 0x7FFF,
+ 0xF9B8, 0x7FD8,
+ 0xF374, 0x7F62,
+ 0xED37, 0x7E9D,
+ 0xE707, 0x7D8A,
+ 0xE0E6, 0x7C29,
+ 0xDAD7, 0x7A7D,
+ 0xD4E0, 0x7884,
+ 0xCF04, 0x7641,
+ 0xC945, 0x73B5,
+ 0xC3A9, 0x70E2,
+ 0xBE31, 0x6DCA,
+ 0xB8E3, 0x6A6D,
+ 0xB3C0, 0x66CF,
+ 0xAECC, 0x62F2,
+ 0xAA0A, 0x5ED7,
+ 0xA57D, 0x5A82,
+ 0xA128, 0x55F5,
+ 0x9D0D, 0x5133,
+ 0x9930, 0x4C3F,
+ 0x9592, 0x471C,
+ 0x9235, 0x41CE,
+ 0x8F1D, 0x3C56,
+ 0x8C4A, 0x36BA,
+ 0x89BE, 0x30FB,
+ 0x877B, 0x2B1F,
+ 0x8582, 0x2528,
+ 0x83D6, 0x1F19,
+ 0x8275, 0x18F8,
+ 0x8162, 0x12C8,
+ 0x809D, 0x0C8B,
+ 0x8027, 0x0647,
+ 0x8000, 0x0000,
+ 0x8027, 0xF9B8,
+ 0x809D, 0xF374,
+ 0x8162, 0xED37,
+ 0x8275, 0xE707,
+ 0x83D6, 0xE0E6,
+ 0x8582, 0xDAD7,
+ 0x877B, 0xD4E0,
+ 0x89BE, 0xCF04,
+ 0x8C4A, 0xC945,
+ 0x8F1D, 0xC3A9,
+ 0x9235, 0xBE31,
+ 0x9592, 0xB8E3,
+ 0x9930, 0xB3C0,
+ 0x9D0D, 0xAECC,
+ 0xA128, 0xAA0A,
+ 0xA57D, 0xA57D,
+ 0xAA0A, 0xA128,
+ 0xAECC, 0x9D0D,
+ 0xB3C0, 0x9930,
+ 0xB8E3, 0x9592,
+ 0xBE31, 0x9235,
+ 0xC3A9, 0x8F1D,
+ 0xC945, 0x8C4A,
+ 0xCF04, 0x89BE,
+ 0xD4E0, 0x877B,
+ 0xDAD7, 0x8582,
+ 0xE0E6, 0x83D6,
+ 0xE707, 0x8275,
+ 0xED37, 0x8162,
+ 0xF374, 0x809D,
+ 0xF9B8, 0x8027
+};
+
+/**
+* \par
+* Example code for q15 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 256 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to q15(Fixed point 1.15):
+* round(twiddleCoefq15(i) * pow(2, 15))
+*
+*/
+const q15_t twiddleCoef_256_q15[384] = {
+ 0x7FFF, 0x0000,
+ 0x7FF6, 0x0324,
+ 0x7FD8, 0x0647,
+ 0x7FA7, 0x096A,
+ 0x7F62, 0x0C8B,
+ 0x7F09, 0x0FAB,
+ 0x7E9D, 0x12C8,
+ 0x7E1D, 0x15E2,
+ 0x7D8A, 0x18F8,
+ 0x7CE3, 0x1C0B,
+ 0x7C29, 0x1F19,
+ 0x7B5D, 0x2223,
+ 0x7A7D, 0x2528,
+ 0x798A, 0x2826,
+ 0x7884, 0x2B1F,
+ 0x776C, 0x2E11,
+ 0x7641, 0x30FB,
+ 0x7504, 0x33DE,
+ 0x73B5, 0x36BA,
+ 0x7255, 0x398C,
+ 0x70E2, 0x3C56,
+ 0x6F5F, 0x3F17,
+ 0x6DCA, 0x41CE,
+ 0x6C24, 0x447A,
+ 0x6A6D, 0x471C,
+ 0x68A6, 0x49B4,
+ 0x66CF, 0x4C3F,
+ 0x64E8, 0x4EBF,
+ 0x62F2, 0x5133,
+ 0x60EC, 0x539B,
+ 0x5ED7, 0x55F5,
+ 0x5CB4, 0x5842,
+ 0x5A82, 0x5A82,
+ 0x5842, 0x5CB4,
+ 0x55F5, 0x5ED7,
+ 0x539B, 0x60EC,
+ 0x5133, 0x62F2,
+ 0x4EBF, 0x64E8,
+ 0x4C3F, 0x66CF,
+ 0x49B4, 0x68A6,
+ 0x471C, 0x6A6D,
+ 0x447A, 0x6C24,
+ 0x41CE, 0x6DCA,
+ 0x3F17, 0x6F5F,
+ 0x3C56, 0x70E2,
+ 0x398C, 0x7255,
+ 0x36BA, 0x73B5,
+ 0x33DE, 0x7504,
+ 0x30FB, 0x7641,
+ 0x2E11, 0x776C,
+ 0x2B1F, 0x7884,
+ 0x2826, 0x798A,
+ 0x2528, 0x7A7D,
+ 0x2223, 0x7B5D,
+ 0x1F19, 0x7C29,
+ 0x1C0B, 0x7CE3,
+ 0x18F8, 0x7D8A,
+ 0x15E2, 0x7E1D,
+ 0x12C8, 0x7E9D,
+ 0x0FAB, 0x7F09,
+ 0x0C8B, 0x7F62,
+ 0x096A, 0x7FA7,
+ 0x0647, 0x7FD8,
+ 0x0324, 0x7FF6,
+ 0x0000, 0x7FFF,
+ 0xFCDB, 0x7FF6,
+ 0xF9B8, 0x7FD8,
+ 0xF695, 0x7FA7,
+ 0xF374, 0x7F62,
+ 0xF054, 0x7F09,
+ 0xED37, 0x7E9D,
+ 0xEA1D, 0x7E1D,
+ 0xE707, 0x7D8A,
+ 0xE3F4, 0x7CE3,
+ 0xE0E6, 0x7C29,
+ 0xDDDC, 0x7B5D,
+ 0xDAD7, 0x7A7D,
+ 0xD7D9, 0x798A,
+ 0xD4E0, 0x7884,
+ 0xD1EE, 0x776C,
+ 0xCF04, 0x7641,
+ 0xCC21, 0x7504,
+ 0xC945, 0x73B5,
+ 0xC673, 0x7255,
+ 0xC3A9, 0x70E2,
+ 0xC0E8, 0x6F5F,
+ 0xBE31, 0x6DCA,
+ 0xBB85, 0x6C24,
+ 0xB8E3, 0x6A6D,
+ 0xB64B, 0x68A6,
+ 0xB3C0, 0x66CF,
+ 0xB140, 0x64E8,
+ 0xAECC, 0x62F2,
+ 0xAC64, 0x60EC,
+ 0xAA0A, 0x5ED7,
+ 0xA7BD, 0x5CB4,
+ 0xA57D, 0x5A82,
+ 0xA34B, 0x5842,
+ 0xA128, 0x55F5,
+ 0x9F13, 0x539B,
+ 0x9D0D, 0x5133,
+ 0x9B17, 0x4EBF,
+ 0x9930, 0x4C3F,
+ 0x9759, 0x49B4,
+ 0x9592, 0x471C,
+ 0x93DB, 0x447A,
+ 0x9235, 0x41CE,
+ 0x90A0, 0x3F17,
+ 0x8F1D, 0x3C56,
+ 0x8DAA, 0x398C,
+ 0x8C4A, 0x36BA,
+ 0x8AFB, 0x33DE,
+ 0x89BE, 0x30FB,
+ 0x8893, 0x2E11,
+ 0x877B, 0x2B1F,
+ 0x8675, 0x2826,
+ 0x8582, 0x2528,
+ 0x84A2, 0x2223,
+ 0x83D6, 0x1F19,
+ 0x831C, 0x1C0B,
+ 0x8275, 0x18F8,
+ 0x81E2, 0x15E2,
+ 0x8162, 0x12C8,
+ 0x80F6, 0x0FAB,
+ 0x809D, 0x0C8B,
+ 0x8058, 0x096A,
+ 0x8027, 0x0647,
+ 0x8009, 0x0324,
+ 0x8000, 0x0000,
+ 0x8009, 0xFCDB,
+ 0x8027, 0xF9B8,
+ 0x8058, 0xF695,
+ 0x809D, 0xF374,
+ 0x80F6, 0xF054,
+ 0x8162, 0xED37,
+ 0x81E2, 0xEA1D,
+ 0x8275, 0xE707,
+ 0x831C, 0xE3F4,
+ 0x83D6, 0xE0E6,
+ 0x84A2, 0xDDDC,
+ 0x8582, 0xDAD7,
+ 0x8675, 0xD7D9,
+ 0x877B, 0xD4E0,
+ 0x8893, 0xD1EE,
+ 0x89BE, 0xCF04,
+ 0x8AFB, 0xCC21,
+ 0x8C4A, 0xC945,
+ 0x8DAA, 0xC673,
+ 0x8F1D, 0xC3A9,
+ 0x90A0, 0xC0E8,
+ 0x9235, 0xBE31,
+ 0x93DB, 0xBB85,
+ 0x9592, 0xB8E3,
+ 0x9759, 0xB64B,
+ 0x9930, 0xB3C0,
+ 0x9B17, 0xB140,
+ 0x9D0D, 0xAECC,
+ 0x9F13, 0xAC64,
+ 0xA128, 0xAA0A,
+ 0xA34B, 0xA7BD,
+ 0xA57D, 0xA57D,
+ 0xA7BD, 0xA34B,
+ 0xAA0A, 0xA128,
+ 0xAC64, 0x9F13,
+ 0xAECC, 0x9D0D,
+ 0xB140, 0x9B17,
+ 0xB3C0, 0x9930,
+ 0xB64B, 0x9759,
+ 0xB8E3, 0x9592,
+ 0xBB85, 0x93DB,
+ 0xBE31, 0x9235,
+ 0xC0E8, 0x90A0,
+ 0xC3A9, 0x8F1D,
+ 0xC673, 0x8DAA,
+ 0xC945, 0x8C4A,
+ 0xCC21, 0x8AFB,
+ 0xCF04, 0x89BE,
+ 0xD1EE, 0x8893,
+ 0xD4E0, 0x877B,
+ 0xD7D9, 0x8675,
+ 0xDAD7, 0x8582,
+ 0xDDDC, 0x84A2,
+ 0xE0E6, 0x83D6,
+ 0xE3F4, 0x831C,
+ 0xE707, 0x8275,
+ 0xEA1D, 0x81E2,
+ 0xED37, 0x8162,
+ 0xF054, 0x80F6,
+ 0xF374, 0x809D,
+ 0xF695, 0x8058,
+ 0xF9B8, 0x8027,
+ 0xFCDB, 0x8009
+};
+
+/**
+* \par
+* Example code for q15 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 512 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to q15(Fixed point 1.15):
+* round(twiddleCoefq15(i) * pow(2, 15))
+*
+*/
+const q15_t twiddleCoef_512_q15[768] = {
+ 0x7FFF, 0x0000,
+ 0x7FFD, 0x0192,
+ 0x7FF6, 0x0324,
+ 0x7FE9, 0x04B6,
+ 0x7FD8, 0x0647,
+ 0x7FC2, 0x07D9,
+ 0x7FA7, 0x096A,
+ 0x7F87, 0x0AFB,
+ 0x7F62, 0x0C8B,
+ 0x7F38, 0x0E1B,
+ 0x7F09, 0x0FAB,
+ 0x7ED5, 0x1139,
+ 0x7E9D, 0x12C8,
+ 0x7E5F, 0x1455,
+ 0x7E1D, 0x15E2,
+ 0x7DD6, 0x176D,
+ 0x7D8A, 0x18F8,
+ 0x7D39, 0x1A82,
+ 0x7CE3, 0x1C0B,
+ 0x7C89, 0x1D93,
+ 0x7C29, 0x1F19,
+ 0x7BC5, 0x209F,
+ 0x7B5D, 0x2223,
+ 0x7AEF, 0x23A6,
+ 0x7A7D, 0x2528,
+ 0x7A05, 0x26A8,
+ 0x798A, 0x2826,
+ 0x7909, 0x29A3,
+ 0x7884, 0x2B1F,
+ 0x77FA, 0x2C98,
+ 0x776C, 0x2E11,
+ 0x76D9, 0x2F87,
+ 0x7641, 0x30FB,
+ 0x75A5, 0x326E,
+ 0x7504, 0x33DE,
+ 0x745F, 0x354D,
+ 0x73B5, 0x36BA,
+ 0x7307, 0x3824,
+ 0x7255, 0x398C,
+ 0x719E, 0x3AF2,
+ 0x70E2, 0x3C56,
+ 0x7023, 0x3DB8,
+ 0x6F5F, 0x3F17,
+ 0x6E96, 0x4073,
+ 0x6DCA, 0x41CE,
+ 0x6CF9, 0x4325,
+ 0x6C24, 0x447A,
+ 0x6B4A, 0x45CD,
+ 0x6A6D, 0x471C,
+ 0x698C, 0x4869,
+ 0x68A6, 0x49B4,
+ 0x67BD, 0x4AFB,
+ 0x66CF, 0x4C3F,
+ 0x65DD, 0x4D81,
+ 0x64E8, 0x4EBF,
+ 0x63EF, 0x4FFB,
+ 0x62F2, 0x5133,
+ 0x61F1, 0x5269,
+ 0x60EC, 0x539B,
+ 0x5FE3, 0x54CA,
+ 0x5ED7, 0x55F5,
+ 0x5DC7, 0x571D,
+ 0x5CB4, 0x5842,
+ 0x5B9D, 0x5964,
+ 0x5A82, 0x5A82,
+ 0x5964, 0x5B9D,
+ 0x5842, 0x5CB4,
+ 0x571D, 0x5DC7,
+ 0x55F5, 0x5ED7,
+ 0x54CA, 0x5FE3,
+ 0x539B, 0x60EC,
+ 0x5269, 0x61F1,
+ 0x5133, 0x62F2,
+ 0x4FFB, 0x63EF,
+ 0x4EBF, 0x64E8,
+ 0x4D81, 0x65DD,
+ 0x4C3F, 0x66CF,
+ 0x4AFB, 0x67BD,
+ 0x49B4, 0x68A6,
+ 0x4869, 0x698C,
+ 0x471C, 0x6A6D,
+ 0x45CD, 0x6B4A,
+ 0x447A, 0x6C24,
+ 0x4325, 0x6CF9,
+ 0x41CE, 0x6DCA,
+ 0x4073, 0x6E96,
+ 0x3F17, 0x6F5F,
+ 0x3DB8, 0x7023,
+ 0x3C56, 0x70E2,
+ 0x3AF2, 0x719E,
+ 0x398C, 0x7255,
+ 0x3824, 0x7307,
+ 0x36BA, 0x73B5,
+ 0x354D, 0x745F,
+ 0x33DE, 0x7504,
+ 0x326E, 0x75A5,
+ 0x30FB, 0x7641,
+ 0x2F87, 0x76D9,
+ 0x2E11, 0x776C,
+ 0x2C98, 0x77FA,
+ 0x2B1F, 0x7884,
+ 0x29A3, 0x7909,
+ 0x2826, 0x798A,
+ 0x26A8, 0x7A05,
+ 0x2528, 0x7A7D,
+ 0x23A6, 0x7AEF,
+ 0x2223, 0x7B5D,
+ 0x209F, 0x7BC5,
+ 0x1F19, 0x7C29,
+ 0x1D93, 0x7C89,
+ 0x1C0B, 0x7CE3,
+ 0x1A82, 0x7D39,
+ 0x18F8, 0x7D8A,
+ 0x176D, 0x7DD6,
+ 0x15E2, 0x7E1D,
+ 0x1455, 0x7E5F,
+ 0x12C8, 0x7E9D,
+ 0x1139, 0x7ED5,
+ 0x0FAB, 0x7F09,
+ 0x0E1B, 0x7F38,
+ 0x0C8B, 0x7F62,
+ 0x0AFB, 0x7F87,
+ 0x096A, 0x7FA7,
+ 0x07D9, 0x7FC2,
+ 0x0647, 0x7FD8,
+ 0x04B6, 0x7FE9,
+ 0x0324, 0x7FF6,
+ 0x0192, 0x7FFD,
+ 0x0000, 0x7FFF,
+ 0xFE6D, 0x7FFD,
+ 0xFCDB, 0x7FF6,
+ 0xFB49, 0x7FE9,
+ 0xF9B8, 0x7FD8,
+ 0xF826, 0x7FC2,
+ 0xF695, 0x7FA7,
+ 0xF504, 0x7F87,
+ 0xF374, 0x7F62,
+ 0xF1E4, 0x7F38,
+ 0xF054, 0x7F09,
+ 0xEEC6, 0x7ED5,
+ 0xED37, 0x7E9D,
+ 0xEBAA, 0x7E5F,
+ 0xEA1D, 0x7E1D,
+ 0xE892, 0x7DD6,
+ 0xE707, 0x7D8A,
+ 0xE57D, 0x7D39,
+ 0xE3F4, 0x7CE3,
+ 0xE26C, 0x7C89,
+ 0xE0E6, 0x7C29,
+ 0xDF60, 0x7BC5,
+ 0xDDDC, 0x7B5D,
+ 0xDC59, 0x7AEF,
+ 0xDAD7, 0x7A7D,
+ 0xD957, 0x7A05,
+ 0xD7D9, 0x798A,
+ 0xD65C, 0x7909,
+ 0xD4E0, 0x7884,
+ 0xD367, 0x77FA,
+ 0xD1EE, 0x776C,
+ 0xD078, 0x76D9,
+ 0xCF04, 0x7641,
+ 0xCD91, 0x75A5,
+ 0xCC21, 0x7504,
+ 0xCAB2, 0x745F,
+ 0xC945, 0x73B5,
+ 0xC7DB, 0x7307,
+ 0xC673, 0x7255,
+ 0xC50D, 0x719E,
+ 0xC3A9, 0x70E2,
+ 0xC247, 0x7023,
+ 0xC0E8, 0x6F5F,
+ 0xBF8C, 0x6E96,
+ 0xBE31, 0x6DCA,
+ 0xBCDA, 0x6CF9,
+ 0xBB85, 0x6C24,
+ 0xBA32, 0x6B4A,
+ 0xB8E3, 0x6A6D,
+ 0xB796, 0x698C,
+ 0xB64B, 0x68A6,
+ 0xB504, 0x67BD,
+ 0xB3C0, 0x66CF,
+ 0xB27E, 0x65DD,
+ 0xB140, 0x64E8,
+ 0xB004, 0x63EF,
+ 0xAECC, 0x62F2,
+ 0xAD96, 0x61F1,
+ 0xAC64, 0x60EC,
+ 0xAB35, 0x5FE3,
+ 0xAA0A, 0x5ED7,
+ 0xA8E2, 0x5DC7,
+ 0xA7BD, 0x5CB4,
+ 0xA69B, 0x5B9D,
+ 0xA57D, 0x5A82,
+ 0xA462, 0x5964,
+ 0xA34B, 0x5842,
+ 0xA238, 0x571D,
+ 0xA128, 0x55F5,
+ 0xA01C, 0x54CA,
+ 0x9F13, 0x539B,
+ 0x9E0E, 0x5269,
+ 0x9D0D, 0x5133,
+ 0x9C10, 0x4FFB,
+ 0x9B17, 0x4EBF,
+ 0x9A22, 0x4D81,
+ 0x9930, 0x4C3F,
+ 0x9842, 0x4AFB,
+ 0x9759, 0x49B4,
+ 0x9673, 0x4869,
+ 0x9592, 0x471C,
+ 0x94B5, 0x45CD,
+ 0x93DB, 0x447A,
+ 0x9306, 0x4325,
+ 0x9235, 0x41CE,
+ 0x9169, 0x4073,
+ 0x90A0, 0x3F17,
+ 0x8FDC, 0x3DB8,
+ 0x8F1D, 0x3C56,
+ 0x8E61, 0x3AF2,
+ 0x8DAA, 0x398C,
+ 0x8CF8, 0x3824,
+ 0x8C4A, 0x36BA,
+ 0x8BA0, 0x354D,
+ 0x8AFB, 0x33DE,
+ 0x8A5A, 0x326E,
+ 0x89BE, 0x30FB,
+ 0x8926, 0x2F87,
+ 0x8893, 0x2E11,
+ 0x8805, 0x2C98,
+ 0x877B, 0x2B1F,
+ 0x86F6, 0x29A3,
+ 0x8675, 0x2826,
+ 0x85FA, 0x26A8,
+ 0x8582, 0x2528,
+ 0x8510, 0x23A6,
+ 0x84A2, 0x2223,
+ 0x843A, 0x209F,
+ 0x83D6, 0x1F19,
+ 0x8376, 0x1D93,
+ 0x831C, 0x1C0B,
+ 0x82C6, 0x1A82,
+ 0x8275, 0x18F8,
+ 0x8229, 0x176D,
+ 0x81E2, 0x15E2,
+ 0x81A0, 0x1455,
+ 0x8162, 0x12C8,
+ 0x812A, 0x1139,
+ 0x80F6, 0x0FAB,
+ 0x80C7, 0x0E1B,
+ 0x809D, 0x0C8B,
+ 0x8078, 0x0AFB,
+ 0x8058, 0x096A,
+ 0x803D, 0x07D9,
+ 0x8027, 0x0647,
+ 0x8016, 0x04B6,
+ 0x8009, 0x0324,
+ 0x8002, 0x0192,
+ 0x8000, 0x0000,
+ 0x8002, 0xFE6D,
+ 0x8009, 0xFCDB,
+ 0x8016, 0xFB49,
+ 0x8027, 0xF9B8,
+ 0x803D, 0xF826,
+ 0x8058, 0xF695,
+ 0x8078, 0xF504,
+ 0x809D, 0xF374,
+ 0x80C7, 0xF1E4,
+ 0x80F6, 0xF054,
+ 0x812A, 0xEEC6,
+ 0x8162, 0xED37,
+ 0x81A0, 0xEBAA,
+ 0x81E2, 0xEA1D,
+ 0x8229, 0xE892,
+ 0x8275, 0xE707,
+ 0x82C6, 0xE57D,
+ 0x831C, 0xE3F4,
+ 0x8376, 0xE26C,
+ 0x83D6, 0xE0E6,
+ 0x843A, 0xDF60,
+ 0x84A2, 0xDDDC,
+ 0x8510, 0xDC59,
+ 0x8582, 0xDAD7,
+ 0x85FA, 0xD957,
+ 0x8675, 0xD7D9,
+ 0x86F6, 0xD65C,
+ 0x877B, 0xD4E0,
+ 0x8805, 0xD367,
+ 0x8893, 0xD1EE,
+ 0x8926, 0xD078,
+ 0x89BE, 0xCF04,
+ 0x8A5A, 0xCD91,
+ 0x8AFB, 0xCC21,
+ 0x8BA0, 0xCAB2,
+ 0x8C4A, 0xC945,
+ 0x8CF8, 0xC7DB,
+ 0x8DAA, 0xC673,
+ 0x8E61, 0xC50D,
+ 0x8F1D, 0xC3A9,
+ 0x8FDC, 0xC247,
+ 0x90A0, 0xC0E8,
+ 0x9169, 0xBF8C,
+ 0x9235, 0xBE31,
+ 0x9306, 0xBCDA,
+ 0x93DB, 0xBB85,
+ 0x94B5, 0xBA32,
+ 0x9592, 0xB8E3,
+ 0x9673, 0xB796,
+ 0x9759, 0xB64B,
+ 0x9842, 0xB504,
+ 0x9930, 0xB3C0,
+ 0x9A22, 0xB27E,
+ 0x9B17, 0xB140,
+ 0x9C10, 0xB004,
+ 0x9D0D, 0xAECC,
+ 0x9E0E, 0xAD96,
+ 0x9F13, 0xAC64,
+ 0xA01C, 0xAB35,
+ 0xA128, 0xAA0A,
+ 0xA238, 0xA8E2,
+ 0xA34B, 0xA7BD,
+ 0xA462, 0xA69B,
+ 0xA57D, 0xA57D,
+ 0xA69B, 0xA462,
+ 0xA7BD, 0xA34B,
+ 0xA8E2, 0xA238,
+ 0xAA0A, 0xA128,
+ 0xAB35, 0xA01C,
+ 0xAC64, 0x9F13,
+ 0xAD96, 0x9E0E,
+ 0xAECC, 0x9D0D,
+ 0xB004, 0x9C10,
+ 0xB140, 0x9B17,
+ 0xB27E, 0x9A22,
+ 0xB3C0, 0x9930,
+ 0xB504, 0x9842,
+ 0xB64B, 0x9759,
+ 0xB796, 0x9673,
+ 0xB8E3, 0x9592,
+ 0xBA32, 0x94B5,
+ 0xBB85, 0x93DB,
+ 0xBCDA, 0x9306,
+ 0xBE31, 0x9235,
+ 0xBF8C, 0x9169,
+ 0xC0E8, 0x90A0,
+ 0xC247, 0x8FDC,
+ 0xC3A9, 0x8F1D,
+ 0xC50D, 0x8E61,
+ 0xC673, 0x8DAA,
+ 0xC7DB, 0x8CF8,
+ 0xC945, 0x8C4A,
+ 0xCAB2, 0x8BA0,
+ 0xCC21, 0x8AFB,
+ 0xCD91, 0x8A5A,
+ 0xCF04, 0x89BE,
+ 0xD078, 0x8926,
+ 0xD1EE, 0x8893,
+ 0xD367, 0x8805,
+ 0xD4E0, 0x877B,
+ 0xD65C, 0x86F6,
+ 0xD7D9, 0x8675,
+ 0xD957, 0x85FA,
+ 0xDAD7, 0x8582,
+ 0xDC59, 0x8510,
+ 0xDDDC, 0x84A2,
+ 0xDF60, 0x843A,
+ 0xE0E6, 0x83D6,
+ 0xE26C, 0x8376,
+ 0xE3F4, 0x831C,
+ 0xE57D, 0x82C6,
+ 0xE707, 0x8275,
+ 0xE892, 0x8229,
+ 0xEA1D, 0x81E2,
+ 0xEBAA, 0x81A0,
+ 0xED37, 0x8162,
+ 0xEEC6, 0x812A,
+ 0xF054, 0x80F6,
+ 0xF1E4, 0x80C7,
+ 0xF374, 0x809D,
+ 0xF504, 0x8078,
+ 0xF695, 0x8058,
+ 0xF826, 0x803D,
+ 0xF9B8, 0x8027,
+ 0xFB49, 0x8016,
+ 0xFCDB, 0x8009,
+ 0xFE6D, 0x8002
+};
+
+/**
+* \par
+* Example code for q15 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 1024 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to q15(Fixed point 1.15):
+* round(twiddleCoefq15(i) * pow(2, 15))
+*
+*/
+const q15_t twiddleCoef_1024_q15[1536] = {
+ 0x7FFF, 0x0000,
+ 0x7FFF, 0x00C9,
+ 0x7FFD, 0x0192,
+ 0x7FFA, 0x025B,
+ 0x7FF6, 0x0324,
+ 0x7FF0, 0x03ED,
+ 0x7FE9, 0x04B6,
+ 0x7FE1, 0x057F,
+ 0x7FD8, 0x0647,
+ 0x7FCE, 0x0710,
+ 0x7FC2, 0x07D9,
+ 0x7FB5, 0x08A2,
+ 0x7FA7, 0x096A,
+ 0x7F97, 0x0A33,
+ 0x7F87, 0x0AFB,
+ 0x7F75, 0x0BC3,
+ 0x7F62, 0x0C8B,
+ 0x7F4D, 0x0D53,
+ 0x7F38, 0x0E1B,
+ 0x7F21, 0x0EE3,
+ 0x7F09, 0x0FAB,
+ 0x7EF0, 0x1072,
+ 0x7ED5, 0x1139,
+ 0x7EBA, 0x1201,
+ 0x7E9D, 0x12C8,
+ 0x7E7F, 0x138E,
+ 0x7E5F, 0x1455,
+ 0x7E3F, 0x151B,
+ 0x7E1D, 0x15E2,
+ 0x7DFA, 0x16A8,
+ 0x7DD6, 0x176D,
+ 0x7DB0, 0x1833,
+ 0x7D8A, 0x18F8,
+ 0x7D62, 0x19BD,
+ 0x7D39, 0x1A82,
+ 0x7D0F, 0x1B47,
+ 0x7CE3, 0x1C0B,
+ 0x7CB7, 0x1CCF,
+ 0x7C89, 0x1D93,
+ 0x7C5A, 0x1E56,
+ 0x7C29, 0x1F19,
+ 0x7BF8, 0x1FDC,
+ 0x7BC5, 0x209F,
+ 0x7B92, 0x2161,
+ 0x7B5D, 0x2223,
+ 0x7B26, 0x22E5,
+ 0x7AEF, 0x23A6,
+ 0x7AB6, 0x2467,
+ 0x7A7D, 0x2528,
+ 0x7A42, 0x25E8,
+ 0x7A05, 0x26A8,
+ 0x79C8, 0x2767,
+ 0x798A, 0x2826,
+ 0x794A, 0x28E5,
+ 0x7909, 0x29A3,
+ 0x78C7, 0x2A61,
+ 0x7884, 0x2B1F,
+ 0x7840, 0x2BDC,
+ 0x77FA, 0x2C98,
+ 0x77B4, 0x2D55,
+ 0x776C, 0x2E11,
+ 0x7723, 0x2ECC,
+ 0x76D9, 0x2F87,
+ 0x768E, 0x3041,
+ 0x7641, 0x30FB,
+ 0x75F4, 0x31B5,
+ 0x75A5, 0x326E,
+ 0x7555, 0x3326,
+ 0x7504, 0x33DE,
+ 0x74B2, 0x3496,
+ 0x745F, 0x354D,
+ 0x740B, 0x3604,
+ 0x73B5, 0x36BA,
+ 0x735F, 0x376F,
+ 0x7307, 0x3824,
+ 0x72AF, 0x38D8,
+ 0x7255, 0x398C,
+ 0x71FA, 0x3A40,
+ 0x719E, 0x3AF2,
+ 0x7141, 0x3BA5,
+ 0x70E2, 0x3C56,
+ 0x7083, 0x3D07,
+ 0x7023, 0x3DB8,
+ 0x6FC1, 0x3E68,
+ 0x6F5F, 0x3F17,
+ 0x6EFB, 0x3FC5,
+ 0x6E96, 0x4073,
+ 0x6E30, 0x4121,
+ 0x6DCA, 0x41CE,
+ 0x6D62, 0x427A,
+ 0x6CF9, 0x4325,
+ 0x6C8F, 0x43D0,
+ 0x6C24, 0x447A,
+ 0x6BB8, 0x4524,
+ 0x6B4A, 0x45CD,
+ 0x6ADC, 0x4675,
+ 0x6A6D, 0x471C,
+ 0x69FD, 0x47C3,
+ 0x698C, 0x4869,
+ 0x6919, 0x490F,
+ 0x68A6, 0x49B4,
+ 0x6832, 0x4A58,
+ 0x67BD, 0x4AFB,
+ 0x6746, 0x4B9E,
+ 0x66CF, 0x4C3F,
+ 0x6657, 0x4CE1,
+ 0x65DD, 0x4D81,
+ 0x6563, 0x4E21,
+ 0x64E8, 0x4EBF,
+ 0x646C, 0x4F5E,
+ 0x63EF, 0x4FFB,
+ 0x6371, 0x5097,
+ 0x62F2, 0x5133,
+ 0x6271, 0x51CE,
+ 0x61F1, 0x5269,
+ 0x616F, 0x5302,
+ 0x60EC, 0x539B,
+ 0x6068, 0x5433,
+ 0x5FE3, 0x54CA,
+ 0x5F5E, 0x5560,
+ 0x5ED7, 0x55F5,
+ 0x5E50, 0x568A,
+ 0x5DC7, 0x571D,
+ 0x5D3E, 0x57B0,
+ 0x5CB4, 0x5842,
+ 0x5C29, 0x58D4,
+ 0x5B9D, 0x5964,
+ 0x5B10, 0x59F3,
+ 0x5A82, 0x5A82,
+ 0x59F3, 0x5B10,
+ 0x5964, 0x5B9D,
+ 0x58D4, 0x5C29,
+ 0x5842, 0x5CB4,
+ 0x57B0, 0x5D3E,
+ 0x571D, 0x5DC7,
+ 0x568A, 0x5E50,
+ 0x55F5, 0x5ED7,
+ 0x5560, 0x5F5E,
+ 0x54CA, 0x5FE3,
+ 0x5433, 0x6068,
+ 0x539B, 0x60EC,
+ 0x5302, 0x616F,
+ 0x5269, 0x61F1,
+ 0x51CE, 0x6271,
+ 0x5133, 0x62F2,
+ 0x5097, 0x6371,
+ 0x4FFB, 0x63EF,
+ 0x4F5E, 0x646C,
+ 0x4EBF, 0x64E8,
+ 0x4E21, 0x6563,
+ 0x4D81, 0x65DD,
+ 0x4CE1, 0x6657,
+ 0x4C3F, 0x66CF,
+ 0x4B9E, 0x6746,
+ 0x4AFB, 0x67BD,
+ 0x4A58, 0x6832,
+ 0x49B4, 0x68A6,
+ 0x490F, 0x6919,
+ 0x4869, 0x698C,
+ 0x47C3, 0x69FD,
+ 0x471C, 0x6A6D,
+ 0x4675, 0x6ADC,
+ 0x45CD, 0x6B4A,
+ 0x4524, 0x6BB8,
+ 0x447A, 0x6C24,
+ 0x43D0, 0x6C8F,
+ 0x4325, 0x6CF9,
+ 0x427A, 0x6D62,
+ 0x41CE, 0x6DCA,
+ 0x4121, 0x6E30,
+ 0x4073, 0x6E96,
+ 0x3FC5, 0x6EFB,
+ 0x3F17, 0x6F5F,
+ 0x3E68, 0x6FC1,
+ 0x3DB8, 0x7023,
+ 0x3D07, 0x7083,
+ 0x3C56, 0x70E2,
+ 0x3BA5, 0x7141,
+ 0x3AF2, 0x719E,
+ 0x3A40, 0x71FA,
+ 0x398C, 0x7255,
+ 0x38D8, 0x72AF,
+ 0x3824, 0x7307,
+ 0x376F, 0x735F,
+ 0x36BA, 0x73B5,
+ 0x3604, 0x740B,
+ 0x354D, 0x745F,
+ 0x3496, 0x74B2,
+ 0x33DE, 0x7504,
+ 0x3326, 0x7555,
+ 0x326E, 0x75A5,
+ 0x31B5, 0x75F4,
+ 0x30FB, 0x7641,
+ 0x3041, 0x768E,
+ 0x2F87, 0x76D9,
+ 0x2ECC, 0x7723,
+ 0x2E11, 0x776C,
+ 0x2D55, 0x77B4,
+ 0x2C98, 0x77FA,
+ 0x2BDC, 0x7840,
+ 0x2B1F, 0x7884,
+ 0x2A61, 0x78C7,
+ 0x29A3, 0x7909,
+ 0x28E5, 0x794A,
+ 0x2826, 0x798A,
+ 0x2767, 0x79C8,
+ 0x26A8, 0x7A05,
+ 0x25E8, 0x7A42,
+ 0x2528, 0x7A7D,
+ 0x2467, 0x7AB6,
+ 0x23A6, 0x7AEF,
+ 0x22E5, 0x7B26,
+ 0x2223, 0x7B5D,
+ 0x2161, 0x7B92,
+ 0x209F, 0x7BC5,
+ 0x1FDC, 0x7BF8,
+ 0x1F19, 0x7C29,
+ 0x1E56, 0x7C5A,
+ 0x1D93, 0x7C89,
+ 0x1CCF, 0x7CB7,
+ 0x1C0B, 0x7CE3,
+ 0x1B47, 0x7D0F,
+ 0x1A82, 0x7D39,
+ 0x19BD, 0x7D62,
+ 0x18F8, 0x7D8A,
+ 0x1833, 0x7DB0,
+ 0x176D, 0x7DD6,
+ 0x16A8, 0x7DFA,
+ 0x15E2, 0x7E1D,
+ 0x151B, 0x7E3F,
+ 0x1455, 0x7E5F,
+ 0x138E, 0x7E7F,
+ 0x12C8, 0x7E9D,
+ 0x1201, 0x7EBA,
+ 0x1139, 0x7ED5,
+ 0x1072, 0x7EF0,
+ 0x0FAB, 0x7F09,
+ 0x0EE3, 0x7F21,
+ 0x0E1B, 0x7F38,
+ 0x0D53, 0x7F4D,
+ 0x0C8B, 0x7F62,
+ 0x0BC3, 0x7F75,
+ 0x0AFB, 0x7F87,
+ 0x0A33, 0x7F97,
+ 0x096A, 0x7FA7,
+ 0x08A2, 0x7FB5,
+ 0x07D9, 0x7FC2,
+ 0x0710, 0x7FCE,
+ 0x0647, 0x7FD8,
+ 0x057F, 0x7FE1,
+ 0x04B6, 0x7FE9,
+ 0x03ED, 0x7FF0,
+ 0x0324, 0x7FF6,
+ 0x025B, 0x7FFA,
+ 0x0192, 0x7FFD,
+ 0x00C9, 0x7FFF,
+ 0x0000, 0x7FFF,
+ 0xFF36, 0x7FFF,
+ 0xFE6D, 0x7FFD,
+ 0xFDA4, 0x7FFA,
+ 0xFCDB, 0x7FF6,
+ 0xFC12, 0x7FF0,
+ 0xFB49, 0x7FE9,
+ 0xFA80, 0x7FE1,
+ 0xF9B8, 0x7FD8,
+ 0xF8EF, 0x7FCE,
+ 0xF826, 0x7FC2,
+ 0xF75D, 0x7FB5,
+ 0xF695, 0x7FA7,
+ 0xF5CC, 0x7F97,
+ 0xF504, 0x7F87,
+ 0xF43C, 0x7F75,
+ 0xF374, 0x7F62,
+ 0xF2AC, 0x7F4D,
+ 0xF1E4, 0x7F38,
+ 0xF11C, 0x7F21,
+ 0xF054, 0x7F09,
+ 0xEF8D, 0x7EF0,
+ 0xEEC6, 0x7ED5,
+ 0xEDFE, 0x7EBA,
+ 0xED37, 0x7E9D,
+ 0xEC71, 0x7E7F,
+ 0xEBAA, 0x7E5F,
+ 0xEAE4, 0x7E3F,
+ 0xEA1D, 0x7E1D,
+ 0xE957, 0x7DFA,
+ 0xE892, 0x7DD6,
+ 0xE7CC, 0x7DB0,
+ 0xE707, 0x7D8A,
+ 0xE642, 0x7D62,
+ 0xE57D, 0x7D39,
+ 0xE4B8, 0x7D0F,
+ 0xE3F4, 0x7CE3,
+ 0xE330, 0x7CB7,
+ 0xE26C, 0x7C89,
+ 0xE1A9, 0x7C5A,
+ 0xE0E6, 0x7C29,
+ 0xE023, 0x7BF8,
+ 0xDF60, 0x7BC5,
+ 0xDE9E, 0x7B92,
+ 0xDDDC, 0x7B5D,
+ 0xDD1A, 0x7B26,
+ 0xDC59, 0x7AEF,
+ 0xDB98, 0x7AB6,
+ 0xDAD7, 0x7A7D,
+ 0xDA17, 0x7A42,
+ 0xD957, 0x7A05,
+ 0xD898, 0x79C8,
+ 0xD7D9, 0x798A,
+ 0xD71A, 0x794A,
+ 0xD65C, 0x7909,
+ 0xD59E, 0x78C7,
+ 0xD4E0, 0x7884,
+ 0xD423, 0x7840,
+ 0xD367, 0x77FA,
+ 0xD2AA, 0x77B4,
+ 0xD1EE, 0x776C,
+ 0xD133, 0x7723,
+ 0xD078, 0x76D9,
+ 0xCFBE, 0x768E,
+ 0xCF04, 0x7641,
+ 0xCE4A, 0x75F4,
+ 0xCD91, 0x75A5,
+ 0xCCD9, 0x7555,
+ 0xCC21, 0x7504,
+ 0xCB69, 0x74B2,
+ 0xCAB2, 0x745F,
+ 0xC9FB, 0x740B,
+ 0xC945, 0x73B5,
+ 0xC890, 0x735F,
+ 0xC7DB, 0x7307,
+ 0xC727, 0x72AF,
+ 0xC673, 0x7255,
+ 0xC5BF, 0x71FA,
+ 0xC50D, 0x719E,
+ 0xC45A, 0x7141,
+ 0xC3A9, 0x70E2,
+ 0xC2F8, 0x7083,
+ 0xC247, 0x7023,
+ 0xC197, 0x6FC1,
+ 0xC0E8, 0x6F5F,
+ 0xC03A, 0x6EFB,
+ 0xBF8C, 0x6E96,
+ 0xBEDE, 0x6E30,
+ 0xBE31, 0x6DCA,
+ 0xBD85, 0x6D62,
+ 0xBCDA, 0x6CF9,
+ 0xBC2F, 0x6C8F,
+ 0xBB85, 0x6C24,
+ 0xBADB, 0x6BB8,
+ 0xBA32, 0x6B4A,
+ 0xB98A, 0x6ADC,
+ 0xB8E3, 0x6A6D,
+ 0xB83C, 0x69FD,
+ 0xB796, 0x698C,
+ 0xB6F0, 0x6919,
+ 0xB64B, 0x68A6,
+ 0xB5A7, 0x6832,
+ 0xB504, 0x67BD,
+ 0xB461, 0x6746,
+ 0xB3C0, 0x66CF,
+ 0xB31E, 0x6657,
+ 0xB27E, 0x65DD,
+ 0xB1DE, 0x6563,
+ 0xB140, 0x64E8,
+ 0xB0A1, 0x646C,
+ 0xB004, 0x63EF,
+ 0xAF68, 0x6371,
+ 0xAECC, 0x62F2,
+ 0xAE31, 0x6271,
+ 0xAD96, 0x61F1,
+ 0xACFD, 0x616F,
+ 0xAC64, 0x60EC,
+ 0xABCC, 0x6068,
+ 0xAB35, 0x5FE3,
+ 0xAA9F, 0x5F5E,
+ 0xAA0A, 0x5ED7,
+ 0xA975, 0x5E50,
+ 0xA8E2, 0x5DC7,
+ 0xA84F, 0x5D3E,
+ 0xA7BD, 0x5CB4,
+ 0xA72B, 0x5C29,
+ 0xA69B, 0x5B9D,
+ 0xA60C, 0x5B10,
+ 0xA57D, 0x5A82,
+ 0xA4EF, 0x59F3,
+ 0xA462, 0x5964,
+ 0xA3D6, 0x58D4,
+ 0xA34B, 0x5842,
+ 0xA2C1, 0x57B0,
+ 0xA238, 0x571D,
+ 0xA1AF, 0x568A,
+ 0xA128, 0x55F5,
+ 0xA0A1, 0x5560,
+ 0xA01C, 0x54CA,
+ 0x9F97, 0x5433,
+ 0x9F13, 0x539B,
+ 0x9E90, 0x5302,
+ 0x9E0E, 0x5269,
+ 0x9D8E, 0x51CE,
+ 0x9D0D, 0x5133,
+ 0x9C8E, 0x5097,
+ 0x9C10, 0x4FFB,
+ 0x9B93, 0x4F5E,
+ 0x9B17, 0x4EBF,
+ 0x9A9C, 0x4E21,
+ 0x9A22, 0x4D81,
+ 0x99A8, 0x4CE1,
+ 0x9930, 0x4C3F,
+ 0x98B9, 0x4B9E,
+ 0x9842, 0x4AFB,
+ 0x97CD, 0x4A58,
+ 0x9759, 0x49B4,
+ 0x96E6, 0x490F,
+ 0x9673, 0x4869,
+ 0x9602, 0x47C3,
+ 0x9592, 0x471C,
+ 0x9523, 0x4675,
+ 0x94B5, 0x45CD,
+ 0x9447, 0x4524,
+ 0x93DB, 0x447A,
+ 0x9370, 0x43D0,
+ 0x9306, 0x4325,
+ 0x929D, 0x427A,
+ 0x9235, 0x41CE,
+ 0x91CF, 0x4121,
+ 0x9169, 0x4073,
+ 0x9104, 0x3FC5,
+ 0x90A0, 0x3F17,
+ 0x903E, 0x3E68,
+ 0x8FDC, 0x3DB8,
+ 0x8F7C, 0x3D07,
+ 0x8F1D, 0x3C56,
+ 0x8EBE, 0x3BA5,
+ 0x8E61, 0x3AF2,
+ 0x8E05, 0x3A40,
+ 0x8DAA, 0x398C,
+ 0x8D50, 0x38D8,
+ 0x8CF8, 0x3824,
+ 0x8CA0, 0x376F,
+ 0x8C4A, 0x36BA,
+ 0x8BF4, 0x3604,
+ 0x8BA0, 0x354D,
+ 0x8B4D, 0x3496,
+ 0x8AFB, 0x33DE,
+ 0x8AAA, 0x3326,
+ 0x8A5A, 0x326E,
+ 0x8A0B, 0x31B5,
+ 0x89BE, 0x30FB,
+ 0x8971, 0x3041,
+ 0x8926, 0x2F87,
+ 0x88DC, 0x2ECC,
+ 0x8893, 0x2E11,
+ 0x884B, 0x2D55,
+ 0x8805, 0x2C98,
+ 0x87BF, 0x2BDC,
+ 0x877B, 0x2B1F,
+ 0x8738, 0x2A61,
+ 0x86F6, 0x29A3,
+ 0x86B5, 0x28E5,
+ 0x8675, 0x2826,
+ 0x8637, 0x2767,
+ 0x85FA, 0x26A8,
+ 0x85BD, 0x25E8,
+ 0x8582, 0x2528,
+ 0x8549, 0x2467,
+ 0x8510, 0x23A6,
+ 0x84D9, 0x22E5,
+ 0x84A2, 0x2223,
+ 0x846D, 0x2161,
+ 0x843A, 0x209F,
+ 0x8407, 0x1FDC,
+ 0x83D6, 0x1F19,
+ 0x83A5, 0x1E56,
+ 0x8376, 0x1D93,
+ 0x8348, 0x1CCF,
+ 0x831C, 0x1C0B,
+ 0x82F0, 0x1B47,
+ 0x82C6, 0x1A82,
+ 0x829D, 0x19BD,
+ 0x8275, 0x18F8,
+ 0x824F, 0x1833,
+ 0x8229, 0x176D,
+ 0x8205, 0x16A8,
+ 0x81E2, 0x15E2,
+ 0x81C0, 0x151B,
+ 0x81A0, 0x1455,
+ 0x8180, 0x138E,
+ 0x8162, 0x12C8,
+ 0x8145, 0x1201,
+ 0x812A, 0x1139,
+ 0x810F, 0x1072,
+ 0x80F6, 0x0FAB,
+ 0x80DE, 0x0EE3,
+ 0x80C7, 0x0E1B,
+ 0x80B2, 0x0D53,
+ 0x809D, 0x0C8B,
+ 0x808A, 0x0BC3,
+ 0x8078, 0x0AFB,
+ 0x8068, 0x0A33,
+ 0x8058, 0x096A,
+ 0x804A, 0x08A2,
+ 0x803D, 0x07D9,
+ 0x8031, 0x0710,
+ 0x8027, 0x0647,
+ 0x801E, 0x057F,
+ 0x8016, 0x04B6,
+ 0x800F, 0x03ED,
+ 0x8009, 0x0324,
+ 0x8005, 0x025B,
+ 0x8002, 0x0192,
+ 0x8000, 0x00C9,
+ 0x8000, 0x0000,
+ 0x8000, 0xFF36,
+ 0x8002, 0xFE6D,
+ 0x8005, 0xFDA4,
+ 0x8009, 0xFCDB,
+ 0x800F, 0xFC12,
+ 0x8016, 0xFB49,
+ 0x801E, 0xFA80,
+ 0x8027, 0xF9B8,
+ 0x8031, 0xF8EF,
+ 0x803D, 0xF826,
+ 0x804A, 0xF75D,
+ 0x8058, 0xF695,
+ 0x8068, 0xF5CC,
+ 0x8078, 0xF504,
+ 0x808A, 0xF43C,
+ 0x809D, 0xF374,
+ 0x80B2, 0xF2AC,
+ 0x80C7, 0xF1E4,
+ 0x80DE, 0xF11C,
+ 0x80F6, 0xF054,
+ 0x810F, 0xEF8D,
+ 0x812A, 0xEEC6,
+ 0x8145, 0xEDFE,
+ 0x8162, 0xED37,
+ 0x8180, 0xEC71,
+ 0x81A0, 0xEBAA,
+ 0x81C0, 0xEAE4,
+ 0x81E2, 0xEA1D,
+ 0x8205, 0xE957,
+ 0x8229, 0xE892,
+ 0x824F, 0xE7CC,
+ 0x8275, 0xE707,
+ 0x829D, 0xE642,
+ 0x82C6, 0xE57D,
+ 0x82F0, 0xE4B8,
+ 0x831C, 0xE3F4,
+ 0x8348, 0xE330,
+ 0x8376, 0xE26C,
+ 0x83A5, 0xE1A9,
+ 0x83D6, 0xE0E6,
+ 0x8407, 0xE023,
+ 0x843A, 0xDF60,
+ 0x846D, 0xDE9E,
+ 0x84A2, 0xDDDC,
+ 0x84D9, 0xDD1A,
+ 0x8510, 0xDC59,
+ 0x8549, 0xDB98,
+ 0x8582, 0xDAD7,
+ 0x85BD, 0xDA17,
+ 0x85FA, 0xD957,
+ 0x8637, 0xD898,
+ 0x8675, 0xD7D9,
+ 0x86B5, 0xD71A,
+ 0x86F6, 0xD65C,
+ 0x8738, 0xD59E,
+ 0x877B, 0xD4E0,
+ 0x87BF, 0xD423,
+ 0x8805, 0xD367,
+ 0x884B, 0xD2AA,
+ 0x8893, 0xD1EE,
+ 0x88DC, 0xD133,
+ 0x8926, 0xD078,
+ 0x8971, 0xCFBE,
+ 0x89BE, 0xCF04,
+ 0x8A0B, 0xCE4A,
+ 0x8A5A, 0xCD91,
+ 0x8AAA, 0xCCD9,
+ 0x8AFB, 0xCC21,
+ 0x8B4D, 0xCB69,
+ 0x8BA0, 0xCAB2,
+ 0x8BF4, 0xC9FB,
+ 0x8C4A, 0xC945,
+ 0x8CA0, 0xC890,
+ 0x8CF8, 0xC7DB,
+ 0x8D50, 0xC727,
+ 0x8DAA, 0xC673,
+ 0x8E05, 0xC5BF,
+ 0x8E61, 0xC50D,
+ 0x8EBE, 0xC45A,
+ 0x8F1D, 0xC3A9,
+ 0x8F7C, 0xC2F8,
+ 0x8FDC, 0xC247,
+ 0x903E, 0xC197,
+ 0x90A0, 0xC0E8,
+ 0x9104, 0xC03A,
+ 0x9169, 0xBF8C,
+ 0x91CF, 0xBEDE,
+ 0x9235, 0xBE31,
+ 0x929D, 0xBD85,
+ 0x9306, 0xBCDA,
+ 0x9370, 0xBC2F,
+ 0x93DB, 0xBB85,
+ 0x9447, 0xBADB,
+ 0x94B5, 0xBA32,
+ 0x9523, 0xB98A,
+ 0x9592, 0xB8E3,
+ 0x9602, 0xB83C,
+ 0x9673, 0xB796,
+ 0x96E6, 0xB6F0,
+ 0x9759, 0xB64B,
+ 0x97CD, 0xB5A7,
+ 0x9842, 0xB504,
+ 0x98B9, 0xB461,
+ 0x9930, 0xB3C0,
+ 0x99A8, 0xB31E,
+ 0x9A22, 0xB27E,
+ 0x9A9C, 0xB1DE,
+ 0x9B17, 0xB140,
+ 0x9B93, 0xB0A1,
+ 0x9C10, 0xB004,
+ 0x9C8E, 0xAF68,
+ 0x9D0D, 0xAECC,
+ 0x9D8E, 0xAE31,
+ 0x9E0E, 0xAD96,
+ 0x9E90, 0xACFD,
+ 0x9F13, 0xAC64,
+ 0x9F97, 0xABCC,
+ 0xA01C, 0xAB35,
+ 0xA0A1, 0xAA9F,
+ 0xA128, 0xAA0A,
+ 0xA1AF, 0xA975,
+ 0xA238, 0xA8E2,
+ 0xA2C1, 0xA84F,
+ 0xA34B, 0xA7BD,
+ 0xA3D6, 0xA72B,
+ 0xA462, 0xA69B,
+ 0xA4EF, 0xA60C,
+ 0xA57D, 0xA57D,
+ 0xA60C, 0xA4EF,
+ 0xA69B, 0xA462,
+ 0xA72B, 0xA3D6,
+ 0xA7BD, 0xA34B,
+ 0xA84F, 0xA2C1,
+ 0xA8E2, 0xA238,
+ 0xA975, 0xA1AF,
+ 0xAA0A, 0xA128,
+ 0xAA9F, 0xA0A1,
+ 0xAB35, 0xA01C,
+ 0xABCC, 0x9F97,
+ 0xAC64, 0x9F13,
+ 0xACFD, 0x9E90,
+ 0xAD96, 0x9E0E,
+ 0xAE31, 0x9D8E,
+ 0xAECC, 0x9D0D,
+ 0xAF68, 0x9C8E,
+ 0xB004, 0x9C10,
+ 0xB0A1, 0x9B93,
+ 0xB140, 0x9B17,
+ 0xB1DE, 0x9A9C,
+ 0xB27E, 0x9A22,
+ 0xB31E, 0x99A8,
+ 0xB3C0, 0x9930,
+ 0xB461, 0x98B9,
+ 0xB504, 0x9842,
+ 0xB5A7, 0x97CD,
+ 0xB64B, 0x9759,
+ 0xB6F0, 0x96E6,
+ 0xB796, 0x9673,
+ 0xB83C, 0x9602,
+ 0xB8E3, 0x9592,
+ 0xB98A, 0x9523,
+ 0xBA32, 0x94B5,
+ 0xBADB, 0x9447,
+ 0xBB85, 0x93DB,
+ 0xBC2F, 0x9370,
+ 0xBCDA, 0x9306,
+ 0xBD85, 0x929D,
+ 0xBE31, 0x9235,
+ 0xBEDE, 0x91CF,
+ 0xBF8C, 0x9169,
+ 0xC03A, 0x9104,
+ 0xC0E8, 0x90A0,
+ 0xC197, 0x903E,
+ 0xC247, 0x8FDC,
+ 0xC2F8, 0x8F7C,
+ 0xC3A9, 0x8F1D,
+ 0xC45A, 0x8EBE,
+ 0xC50D, 0x8E61,
+ 0xC5BF, 0x8E05,
+ 0xC673, 0x8DAA,
+ 0xC727, 0x8D50,
+ 0xC7DB, 0x8CF8,
+ 0xC890, 0x8CA0,
+ 0xC945, 0x8C4A,
+ 0xC9FB, 0x8BF4,
+ 0xCAB2, 0x8BA0,
+ 0xCB69, 0x8B4D,
+ 0xCC21, 0x8AFB,
+ 0xCCD9, 0x8AAA,
+ 0xCD91, 0x8A5A,
+ 0xCE4A, 0x8A0B,
+ 0xCF04, 0x89BE,
+ 0xCFBE, 0x8971,
+ 0xD078, 0x8926,
+ 0xD133, 0x88DC,
+ 0xD1EE, 0x8893,
+ 0xD2AA, 0x884B,
+ 0xD367, 0x8805,
+ 0xD423, 0x87BF,
+ 0xD4E0, 0x877B,
+ 0xD59E, 0x8738,
+ 0xD65C, 0x86F6,
+ 0xD71A, 0x86B5,
+ 0xD7D9, 0x8675,
+ 0xD898, 0x8637,
+ 0xD957, 0x85FA,
+ 0xDA17, 0x85BD,
+ 0xDAD7, 0x8582,
+ 0xDB98, 0x8549,
+ 0xDC59, 0x8510,
+ 0xDD1A, 0x84D9,
+ 0xDDDC, 0x84A2,
+ 0xDE9E, 0x846D,
+ 0xDF60, 0x843A,
+ 0xE023, 0x8407,
+ 0xE0E6, 0x83D6,
+ 0xE1A9, 0x83A5,
+ 0xE26C, 0x8376,
+ 0xE330, 0x8348,
+ 0xE3F4, 0x831C,
+ 0xE4B8, 0x82F0,
+ 0xE57D, 0x82C6,
+ 0xE642, 0x829D,
+ 0xE707, 0x8275,
+ 0xE7CC, 0x824F,
+ 0xE892, 0x8229,
+ 0xE957, 0x8205,
+ 0xEA1D, 0x81E2,
+ 0xEAE4, 0x81C0,
+ 0xEBAA, 0x81A0,
+ 0xEC71, 0x8180,
+ 0xED37, 0x8162,
+ 0xEDFE, 0x8145,
+ 0xEEC6, 0x812A,
+ 0xEF8D, 0x810F,
+ 0xF054, 0x80F6,
+ 0xF11C, 0x80DE,
+ 0xF1E4, 0x80C7,
+ 0xF2AC, 0x80B2,
+ 0xF374, 0x809D,
+ 0xF43C, 0x808A,
+ 0xF504, 0x8078,
+ 0xF5CC, 0x8068,
+ 0xF695, 0x8058,
+ 0xF75D, 0x804A,
+ 0xF826, 0x803D,
+ 0xF8EF, 0x8031,
+ 0xF9B8, 0x8027,
+ 0xFA80, 0x801E,
+ 0xFB49, 0x8016,
+ 0xFC12, 0x800F,
+ 0xFCDB, 0x8009,
+ 0xFDA4, 0x8005,
+ 0xFE6D, 0x8002,
+ 0xFF36, 0x8000
+};
+
+/**
+* \par
+* Example code for q15 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 2048 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to q15(Fixed point 1.15):
+* round(twiddleCoefq15(i) * pow(2, 15))
+*
+*/
+const q15_t twiddleCoef_2048_q15[3072] = {
+ 0x7FFF, 0x0000,
+ 0x7FFF, 0x0064,
+ 0x7FFF, 0x00C9,
+ 0x7FFE, 0x012D,
+ 0x7FFD, 0x0192,
+ 0x7FFC, 0x01F6,
+ 0x7FFA, 0x025B,
+ 0x7FF8, 0x02BF,
+ 0x7FF6, 0x0324,
+ 0x7FF3, 0x0388,
+ 0x7FF0, 0x03ED,
+ 0x7FED, 0x0451,
+ 0x7FE9, 0x04B6,
+ 0x7FE5, 0x051A,
+ 0x7FE1, 0x057F,
+ 0x7FDD, 0x05E3,
+ 0x7FD8, 0x0647,
+ 0x7FD3, 0x06AC,
+ 0x7FCE, 0x0710,
+ 0x7FC8, 0x0775,
+ 0x7FC2, 0x07D9,
+ 0x7FBC, 0x083D,
+ 0x7FB5, 0x08A2,
+ 0x7FAE, 0x0906,
+ 0x7FA7, 0x096A,
+ 0x7F9F, 0x09CE,
+ 0x7F97, 0x0A33,
+ 0x7F8F, 0x0A97,
+ 0x7F87, 0x0AFB,
+ 0x7F7E, 0x0B5F,
+ 0x7F75, 0x0BC3,
+ 0x7F6B, 0x0C27,
+ 0x7F62, 0x0C8B,
+ 0x7F58, 0x0CEF,
+ 0x7F4D, 0x0D53,
+ 0x7F43, 0x0DB7,
+ 0x7F38, 0x0E1B,
+ 0x7F2D, 0x0E7F,
+ 0x7F21, 0x0EE3,
+ 0x7F15, 0x0F47,
+ 0x7F09, 0x0FAB,
+ 0x7EFD, 0x100E,
+ 0x7EF0, 0x1072,
+ 0x7EE3, 0x10D6,
+ 0x7ED5, 0x1139,
+ 0x7EC8, 0x119D,
+ 0x7EBA, 0x1201,
+ 0x7EAB, 0x1264,
+ 0x7E9D, 0x12C8,
+ 0x7E8E, 0x132B,
+ 0x7E7F, 0x138E,
+ 0x7E6F, 0x13F2,
+ 0x7E5F, 0x1455,
+ 0x7E4F, 0x14B8,
+ 0x7E3F, 0x151B,
+ 0x7E2E, 0x157F,
+ 0x7E1D, 0x15E2,
+ 0x7E0C, 0x1645,
+ 0x7DFA, 0x16A8,
+ 0x7DE8, 0x170A,
+ 0x7DD6, 0x176D,
+ 0x7DC3, 0x17D0,
+ 0x7DB0, 0x1833,
+ 0x7D9D, 0x1896,
+ 0x7D8A, 0x18F8,
+ 0x7D76, 0x195B,
+ 0x7D62, 0x19BD,
+ 0x7D4E, 0x1A20,
+ 0x7D39, 0x1A82,
+ 0x7D24, 0x1AE4,
+ 0x7D0F, 0x1B47,
+ 0x7CF9, 0x1BA9,
+ 0x7CE3, 0x1C0B,
+ 0x7CCD, 0x1C6D,
+ 0x7CB7, 0x1CCF,
+ 0x7CA0, 0x1D31,
+ 0x7C89, 0x1D93,
+ 0x7C71, 0x1DF5,
+ 0x7C5A, 0x1E56,
+ 0x7C42, 0x1EB8,
+ 0x7C29, 0x1F19,
+ 0x7C11, 0x1F7B,
+ 0x7BF8, 0x1FDC,
+ 0x7BDF, 0x203E,
+ 0x7BC5, 0x209F,
+ 0x7BAC, 0x2100,
+ 0x7B92, 0x2161,
+ 0x7B77, 0x21C2,
+ 0x7B5D, 0x2223,
+ 0x7B42, 0x2284,
+ 0x7B26, 0x22E5,
+ 0x7B0B, 0x2345,
+ 0x7AEF, 0x23A6,
+ 0x7AD3, 0x2407,
+ 0x7AB6, 0x2467,
+ 0x7A9A, 0x24C7,
+ 0x7A7D, 0x2528,
+ 0x7A5F, 0x2588,
+ 0x7A42, 0x25E8,
+ 0x7A24, 0x2648,
+ 0x7A05, 0x26A8,
+ 0x79E7, 0x2707,
+ 0x79C8, 0x2767,
+ 0x79A9, 0x27C7,
+ 0x798A, 0x2826,
+ 0x796A, 0x2886,
+ 0x794A, 0x28E5,
+ 0x792A, 0x2944,
+ 0x7909, 0x29A3,
+ 0x78E8, 0x2A02,
+ 0x78C7, 0x2A61,
+ 0x78A6, 0x2AC0,
+ 0x7884, 0x2B1F,
+ 0x7862, 0x2B7D,
+ 0x7840, 0x2BDC,
+ 0x781D, 0x2C3A,
+ 0x77FA, 0x2C98,
+ 0x77D7, 0x2CF7,
+ 0x77B4, 0x2D55,
+ 0x7790, 0x2DB3,
+ 0x776C, 0x2E11,
+ 0x7747, 0x2E6E,
+ 0x7723, 0x2ECC,
+ 0x76FE, 0x2F29,
+ 0x76D9, 0x2F87,
+ 0x76B3, 0x2FE4,
+ 0x768E, 0x3041,
+ 0x7668, 0x309E,
+ 0x7641, 0x30FB,
+ 0x761B, 0x3158,
+ 0x75F4, 0x31B5,
+ 0x75CC, 0x3211,
+ 0x75A5, 0x326E,
+ 0x757D, 0x32CA,
+ 0x7555, 0x3326,
+ 0x752D, 0x3382,
+ 0x7504, 0x33DE,
+ 0x74DB, 0x343A,
+ 0x74B2, 0x3496,
+ 0x7489, 0x34F2,
+ 0x745F, 0x354D,
+ 0x7435, 0x35A8,
+ 0x740B, 0x3604,
+ 0x73E0, 0x365F,
+ 0x73B5, 0x36BA,
+ 0x738A, 0x3714,
+ 0x735F, 0x376F,
+ 0x7333, 0x37CA,
+ 0x7307, 0x3824,
+ 0x72DB, 0x387E,
+ 0x72AF, 0x38D8,
+ 0x7282, 0x3932,
+ 0x7255, 0x398C,
+ 0x7227, 0x39E6,
+ 0x71FA, 0x3A40,
+ 0x71CC, 0x3A99,
+ 0x719E, 0x3AF2,
+ 0x716F, 0x3B4C,
+ 0x7141, 0x3BA5,
+ 0x7112, 0x3BFD,
+ 0x70E2, 0x3C56,
+ 0x70B3, 0x3CAF,
+ 0x7083, 0x3D07,
+ 0x7053, 0x3D60,
+ 0x7023, 0x3DB8,
+ 0x6FF2, 0x3E10,
+ 0x6FC1, 0x3E68,
+ 0x6F90, 0x3EBF,
+ 0x6F5F, 0x3F17,
+ 0x6F2D, 0x3F6E,
+ 0x6EFB, 0x3FC5,
+ 0x6EC9, 0x401D,
+ 0x6E96, 0x4073,
+ 0x6E63, 0x40CA,
+ 0x6E30, 0x4121,
+ 0x6DFD, 0x4177,
+ 0x6DCA, 0x41CE,
+ 0x6D96, 0x4224,
+ 0x6D62, 0x427A,
+ 0x6D2D, 0x42D0,
+ 0x6CF9, 0x4325,
+ 0x6CC4, 0x437B,
+ 0x6C8F, 0x43D0,
+ 0x6C59, 0x4425,
+ 0x6C24, 0x447A,
+ 0x6BEE, 0x44CF,
+ 0x6BB8, 0x4524,
+ 0x6B81, 0x4578,
+ 0x6B4A, 0x45CD,
+ 0x6B13, 0x4621,
+ 0x6ADC, 0x4675,
+ 0x6AA5, 0x46C9,
+ 0x6A6D, 0x471C,
+ 0x6A35, 0x4770,
+ 0x69FD, 0x47C3,
+ 0x69C4, 0x4816,
+ 0x698C, 0x4869,
+ 0x6953, 0x48BC,
+ 0x6919, 0x490F,
+ 0x68E0, 0x4961,
+ 0x68A6, 0x49B4,
+ 0x686C, 0x4A06,
+ 0x6832, 0x4A58,
+ 0x67F7, 0x4AA9,
+ 0x67BD, 0x4AFB,
+ 0x6782, 0x4B4C,
+ 0x6746, 0x4B9E,
+ 0x670B, 0x4BEF,
+ 0x66CF, 0x4C3F,
+ 0x6693, 0x4C90,
+ 0x6657, 0x4CE1,
+ 0x661A, 0x4D31,
+ 0x65DD, 0x4D81,
+ 0x65A0, 0x4DD1,
+ 0x6563, 0x4E21,
+ 0x6526, 0x4E70,
+ 0x64E8, 0x4EBF,
+ 0x64AA, 0x4F0F,
+ 0x646C, 0x4F5E,
+ 0x642D, 0x4FAC,
+ 0x63EF, 0x4FFB,
+ 0x63B0, 0x5049,
+ 0x6371, 0x5097,
+ 0x6331, 0x50E5,
+ 0x62F2, 0x5133,
+ 0x62B2, 0x5181,
+ 0x6271, 0x51CE,
+ 0x6231, 0x521C,
+ 0x61F1, 0x5269,
+ 0x61B0, 0x52B5,
+ 0x616F, 0x5302,
+ 0x612D, 0x534E,
+ 0x60EC, 0x539B,
+ 0x60AA, 0x53E7,
+ 0x6068, 0x5433,
+ 0x6026, 0x547E,
+ 0x5FE3, 0x54CA,
+ 0x5FA0, 0x5515,
+ 0x5F5E, 0x5560,
+ 0x5F1A, 0x55AB,
+ 0x5ED7, 0x55F5,
+ 0x5E93, 0x5640,
+ 0x5E50, 0x568A,
+ 0x5E0B, 0x56D4,
+ 0x5DC7, 0x571D,
+ 0x5D83, 0x5767,
+ 0x5D3E, 0x57B0,
+ 0x5CF9, 0x57F9,
+ 0x5CB4, 0x5842,
+ 0x5C6E, 0x588B,
+ 0x5C29, 0x58D4,
+ 0x5BE3, 0x591C,
+ 0x5B9D, 0x5964,
+ 0x5B56, 0x59AC,
+ 0x5B10, 0x59F3,
+ 0x5AC9, 0x5A3B,
+ 0x5A82, 0x5A82,
+ 0x5A3B, 0x5AC9,
+ 0x59F3, 0x5B10,
+ 0x59AC, 0x5B56,
+ 0x5964, 0x5B9D,
+ 0x591C, 0x5BE3,
+ 0x58D4, 0x5C29,
+ 0x588B, 0x5C6E,
+ 0x5842, 0x5CB4,
+ 0x57F9, 0x5CF9,
+ 0x57B0, 0x5D3E,
+ 0x5767, 0x5D83,
+ 0x571D, 0x5DC7,
+ 0x56D4, 0x5E0B,
+ 0x568A, 0x5E50,
+ 0x5640, 0x5E93,
+ 0x55F5, 0x5ED7,
+ 0x55AB, 0x5F1A,
+ 0x5560, 0x5F5E,
+ 0x5515, 0x5FA0,
+ 0x54CA, 0x5FE3,
+ 0x547E, 0x6026,
+ 0x5433, 0x6068,
+ 0x53E7, 0x60AA,
+ 0x539B, 0x60EC,
+ 0x534E, 0x612D,
+ 0x5302, 0x616F,
+ 0x52B5, 0x61B0,
+ 0x5269, 0x61F1,
+ 0x521C, 0x6231,
+ 0x51CE, 0x6271,
+ 0x5181, 0x62B2,
+ 0x5133, 0x62F2,
+ 0x50E5, 0x6331,
+ 0x5097, 0x6371,
+ 0x5049, 0x63B0,
+ 0x4FFB, 0x63EF,
+ 0x4FAC, 0x642D,
+ 0x4F5E, 0x646C,
+ 0x4F0F, 0x64AA,
+ 0x4EBF, 0x64E8,
+ 0x4E70, 0x6526,
+ 0x4E21, 0x6563,
+ 0x4DD1, 0x65A0,
+ 0x4D81, 0x65DD,
+ 0x4D31, 0x661A,
+ 0x4CE1, 0x6657,
+ 0x4C90, 0x6693,
+ 0x4C3F, 0x66CF,
+ 0x4BEF, 0x670B,
+ 0x4B9E, 0x6746,
+ 0x4B4C, 0x6782,
+ 0x4AFB, 0x67BD,
+ 0x4AA9, 0x67F7,
+ 0x4A58, 0x6832,
+ 0x4A06, 0x686C,
+ 0x49B4, 0x68A6,
+ 0x4961, 0x68E0,
+ 0x490F, 0x6919,
+ 0x48BC, 0x6953,
+ 0x4869, 0x698C,
+ 0x4816, 0x69C4,
+ 0x47C3, 0x69FD,
+ 0x4770, 0x6A35,
+ 0x471C, 0x6A6D,
+ 0x46C9, 0x6AA5,
+ 0x4675, 0x6ADC,
+ 0x4621, 0x6B13,
+ 0x45CD, 0x6B4A,
+ 0x4578, 0x6B81,
+ 0x4524, 0x6BB8,
+ 0x44CF, 0x6BEE,
+ 0x447A, 0x6C24,
+ 0x4425, 0x6C59,
+ 0x43D0, 0x6C8F,
+ 0x437B, 0x6CC4,
+ 0x4325, 0x6CF9,
+ 0x42D0, 0x6D2D,
+ 0x427A, 0x6D62,
+ 0x4224, 0x6D96,
+ 0x41CE, 0x6DCA,
+ 0x4177, 0x6DFD,
+ 0x4121, 0x6E30,
+ 0x40CA, 0x6E63,
+ 0x4073, 0x6E96,
+ 0x401D, 0x6EC9,
+ 0x3FC5, 0x6EFB,
+ 0x3F6E, 0x6F2D,
+ 0x3F17, 0x6F5F,
+ 0x3EBF, 0x6F90,
+ 0x3E68, 0x6FC1,
+ 0x3E10, 0x6FF2,
+ 0x3DB8, 0x7023,
+ 0x3D60, 0x7053,
+ 0x3D07, 0x7083,
+ 0x3CAF, 0x70B3,
+ 0x3C56, 0x70E2,
+ 0x3BFD, 0x7112,
+ 0x3BA5, 0x7141,
+ 0x3B4C, 0x716F,
+ 0x3AF2, 0x719E,
+ 0x3A99, 0x71CC,
+ 0x3A40, 0x71FA,
+ 0x39E6, 0x7227,
+ 0x398C, 0x7255,
+ 0x3932, 0x7282,
+ 0x38D8, 0x72AF,
+ 0x387E, 0x72DB,
+ 0x3824, 0x7307,
+ 0x37CA, 0x7333,
+ 0x376F, 0x735F,
+ 0x3714, 0x738A,
+ 0x36BA, 0x73B5,
+ 0x365F, 0x73E0,
+ 0x3604, 0x740B,
+ 0x35A8, 0x7435,
+ 0x354D, 0x745F,
+ 0x34F2, 0x7489,
+ 0x3496, 0x74B2,
+ 0x343A, 0x74DB,
+ 0x33DE, 0x7504,
+ 0x3382, 0x752D,
+ 0x3326, 0x7555,
+ 0x32CA, 0x757D,
+ 0x326E, 0x75A5,
+ 0x3211, 0x75CC,
+ 0x31B5, 0x75F4,
+ 0x3158, 0x761B,
+ 0x30FB, 0x7641,
+ 0x309E, 0x7668,
+ 0x3041, 0x768E,
+ 0x2FE4, 0x76B3,
+ 0x2F87, 0x76D9,
+ 0x2F29, 0x76FE,
+ 0x2ECC, 0x7723,
+ 0x2E6E, 0x7747,
+ 0x2E11, 0x776C,
+ 0x2DB3, 0x7790,
+ 0x2D55, 0x77B4,
+ 0x2CF7, 0x77D7,
+ 0x2C98, 0x77FA,
+ 0x2C3A, 0x781D,
+ 0x2BDC, 0x7840,
+ 0x2B7D, 0x7862,
+ 0x2B1F, 0x7884,
+ 0x2AC0, 0x78A6,
+ 0x2A61, 0x78C7,
+ 0x2A02, 0x78E8,
+ 0x29A3, 0x7909,
+ 0x2944, 0x792A,
+ 0x28E5, 0x794A,
+ 0x2886, 0x796A,
+ 0x2826, 0x798A,
+ 0x27C7, 0x79A9,
+ 0x2767, 0x79C8,
+ 0x2707, 0x79E7,
+ 0x26A8, 0x7A05,
+ 0x2648, 0x7A24,
+ 0x25E8, 0x7A42,
+ 0x2588, 0x7A5F,
+ 0x2528, 0x7A7D,
+ 0x24C7, 0x7A9A,
+ 0x2467, 0x7AB6,
+ 0x2407, 0x7AD3,
+ 0x23A6, 0x7AEF,
+ 0x2345, 0x7B0B,
+ 0x22E5, 0x7B26,
+ 0x2284, 0x7B42,
+ 0x2223, 0x7B5D,
+ 0x21C2, 0x7B77,
+ 0x2161, 0x7B92,
+ 0x2100, 0x7BAC,
+ 0x209F, 0x7BC5,
+ 0x203E, 0x7BDF,
+ 0x1FDC, 0x7BF8,
+ 0x1F7B, 0x7C11,
+ 0x1F19, 0x7C29,
+ 0x1EB8, 0x7C42,
+ 0x1E56, 0x7C5A,
+ 0x1DF5, 0x7C71,
+ 0x1D93, 0x7C89,
+ 0x1D31, 0x7CA0,
+ 0x1CCF, 0x7CB7,
+ 0x1C6D, 0x7CCD,
+ 0x1C0B, 0x7CE3,
+ 0x1BA9, 0x7CF9,
+ 0x1B47, 0x7D0F,
+ 0x1AE4, 0x7D24,
+ 0x1A82, 0x7D39,
+ 0x1A20, 0x7D4E,
+ 0x19BD, 0x7D62,
+ 0x195B, 0x7D76,
+ 0x18F8, 0x7D8A,
+ 0x1896, 0x7D9D,
+ 0x1833, 0x7DB0,
+ 0x17D0, 0x7DC3,
+ 0x176D, 0x7DD6,
+ 0x170A, 0x7DE8,
+ 0x16A8, 0x7DFA,
+ 0x1645, 0x7E0C,
+ 0x15E2, 0x7E1D,
+ 0x157F, 0x7E2E,
+ 0x151B, 0x7E3F,
+ 0x14B8, 0x7E4F,
+ 0x1455, 0x7E5F,
+ 0x13F2, 0x7E6F,
+ 0x138E, 0x7E7F,
+ 0x132B, 0x7E8E,
+ 0x12C8, 0x7E9D,
+ 0x1264, 0x7EAB,
+ 0x1201, 0x7EBA,
+ 0x119D, 0x7EC8,
+ 0x1139, 0x7ED5,
+ 0x10D6, 0x7EE3,
+ 0x1072, 0x7EF0,
+ 0x100E, 0x7EFD,
+ 0x0FAB, 0x7F09,
+ 0x0F47, 0x7F15,
+ 0x0EE3, 0x7F21,
+ 0x0E7F, 0x7F2D,
+ 0x0E1B, 0x7F38,
+ 0x0DB7, 0x7F43,
+ 0x0D53, 0x7F4D,
+ 0x0CEF, 0x7F58,
+ 0x0C8B, 0x7F62,
+ 0x0C27, 0x7F6B,
+ 0x0BC3, 0x7F75,
+ 0x0B5F, 0x7F7E,
+ 0x0AFB, 0x7F87,
+ 0x0A97, 0x7F8F,
+ 0x0A33, 0x7F97,
+ 0x09CE, 0x7F9F,
+ 0x096A, 0x7FA7,
+ 0x0906, 0x7FAE,
+ 0x08A2, 0x7FB5,
+ 0x083D, 0x7FBC,
+ 0x07D9, 0x7FC2,
+ 0x0775, 0x7FC8,
+ 0x0710, 0x7FCE,
+ 0x06AC, 0x7FD3,
+ 0x0647, 0x7FD8,
+ 0x05E3, 0x7FDD,
+ 0x057F, 0x7FE1,
+ 0x051A, 0x7FE5,
+ 0x04B6, 0x7FE9,
+ 0x0451, 0x7FED,
+ 0x03ED, 0x7FF0,
+ 0x0388, 0x7FF3,
+ 0x0324, 0x7FF6,
+ 0x02BF, 0x7FF8,
+ 0x025B, 0x7FFA,
+ 0x01F6, 0x7FFC,
+ 0x0192, 0x7FFD,
+ 0x012D, 0x7FFE,
+ 0x00C9, 0x7FFF,
+ 0x0064, 0x7FFF,
+ 0x0000, 0x7FFF,
+ 0xFF9B, 0x7FFF,
+ 0xFF36, 0x7FFF,
+ 0xFED2, 0x7FFE,
+ 0xFE6D, 0x7FFD,
+ 0xFE09, 0x7FFC,
+ 0xFDA4, 0x7FFA,
+ 0xFD40, 0x7FF8,
+ 0xFCDB, 0x7FF6,
+ 0xFC77, 0x7FF3,
+ 0xFC12, 0x7FF0,
+ 0xFBAE, 0x7FED,
+ 0xFB49, 0x7FE9,
+ 0xFAE5, 0x7FE5,
+ 0xFA80, 0x7FE1,
+ 0xFA1C, 0x7FDD,
+ 0xF9B8, 0x7FD8,
+ 0xF953, 0x7FD3,
+ 0xF8EF, 0x7FCE,
+ 0xF88A, 0x7FC8,
+ 0xF826, 0x7FC2,
+ 0xF7C2, 0x7FBC,
+ 0xF75D, 0x7FB5,
+ 0xF6F9, 0x7FAE,
+ 0xF695, 0x7FA7,
+ 0xF631, 0x7F9F,
+ 0xF5CC, 0x7F97,
+ 0xF568, 0x7F8F,
+ 0xF504, 0x7F87,
+ 0xF4A0, 0x7F7E,
+ 0xF43C, 0x7F75,
+ 0xF3D8, 0x7F6B,
+ 0xF374, 0x7F62,
+ 0xF310, 0x7F58,
+ 0xF2AC, 0x7F4D,
+ 0xF248, 0x7F43,
+ 0xF1E4, 0x7F38,
+ 0xF180, 0x7F2D,
+ 0xF11C, 0x7F21,
+ 0xF0B8, 0x7F15,
+ 0xF054, 0x7F09,
+ 0xEFF1, 0x7EFD,
+ 0xEF8D, 0x7EF0,
+ 0xEF29, 0x7EE3,
+ 0xEEC6, 0x7ED5,
+ 0xEE62, 0x7EC8,
+ 0xEDFE, 0x7EBA,
+ 0xED9B, 0x7EAB,
+ 0xED37, 0x7E9D,
+ 0xECD4, 0x7E8E,
+ 0xEC71, 0x7E7F,
+ 0xEC0D, 0x7E6F,
+ 0xEBAA, 0x7E5F,
+ 0xEB47, 0x7E4F,
+ 0xEAE4, 0x7E3F,
+ 0xEA80, 0x7E2E,
+ 0xEA1D, 0x7E1D,
+ 0xE9BA, 0x7E0C,
+ 0xE957, 0x7DFA,
+ 0xE8F5, 0x7DE8,
+ 0xE892, 0x7DD6,
+ 0xE82F, 0x7DC3,
+ 0xE7CC, 0x7DB0,
+ 0xE769, 0x7D9D,
+ 0xE707, 0x7D8A,
+ 0xE6A4, 0x7D76,
+ 0xE642, 0x7D62,
+ 0xE5DF, 0x7D4E,
+ 0xE57D, 0x7D39,
+ 0xE51B, 0x7D24,
+ 0xE4B8, 0x7D0F,
+ 0xE456, 0x7CF9,
+ 0xE3F4, 0x7CE3,
+ 0xE392, 0x7CCD,
+ 0xE330, 0x7CB7,
+ 0xE2CE, 0x7CA0,
+ 0xE26C, 0x7C89,
+ 0xE20A, 0x7C71,
+ 0xE1A9, 0x7C5A,
+ 0xE147, 0x7C42,
+ 0xE0E6, 0x7C29,
+ 0xE084, 0x7C11,
+ 0xE023, 0x7BF8,
+ 0xDFC1, 0x7BDF,
+ 0xDF60, 0x7BC5,
+ 0xDEFF, 0x7BAC,
+ 0xDE9E, 0x7B92,
+ 0xDE3D, 0x7B77,
+ 0xDDDC, 0x7B5D,
+ 0xDD7B, 0x7B42,
+ 0xDD1A, 0x7B26,
+ 0xDCBA, 0x7B0B,
+ 0xDC59, 0x7AEF,
+ 0xDBF8, 0x7AD3,
+ 0xDB98, 0x7AB6,
+ 0xDB38, 0x7A9A,
+ 0xDAD7, 0x7A7D,
+ 0xDA77, 0x7A5F,
+ 0xDA17, 0x7A42,
+ 0xD9B7, 0x7A24,
+ 0xD957, 0x7A05,
+ 0xD8F8, 0x79E7,
+ 0xD898, 0x79C8,
+ 0xD838, 0x79A9,
+ 0xD7D9, 0x798A,
+ 0xD779, 0x796A,
+ 0xD71A, 0x794A,
+ 0xD6BB, 0x792A,
+ 0xD65C, 0x7909,
+ 0xD5FD, 0x78E8,
+ 0xD59E, 0x78C7,
+ 0xD53F, 0x78A6,
+ 0xD4E0, 0x7884,
+ 0xD482, 0x7862,
+ 0xD423, 0x7840,
+ 0xD3C5, 0x781D,
+ 0xD367, 0x77FA,
+ 0xD308, 0x77D7,
+ 0xD2AA, 0x77B4,
+ 0xD24C, 0x7790,
+ 0xD1EE, 0x776C,
+ 0xD191, 0x7747,
+ 0xD133, 0x7723,
+ 0xD0D6, 0x76FE,
+ 0xD078, 0x76D9,
+ 0xD01B, 0x76B3,
+ 0xCFBE, 0x768E,
+ 0xCF61, 0x7668,
+ 0xCF04, 0x7641,
+ 0xCEA7, 0x761B,
+ 0xCE4A, 0x75F4,
+ 0xCDEE, 0x75CC,
+ 0xCD91, 0x75A5,
+ 0xCD35, 0x757D,
+ 0xCCD9, 0x7555,
+ 0xCC7D, 0x752D,
+ 0xCC21, 0x7504,
+ 0xCBC5, 0x74DB,
+ 0xCB69, 0x74B2,
+ 0xCB0D, 0x7489,
+ 0xCAB2, 0x745F,
+ 0xCA57, 0x7435,
+ 0xC9FB, 0x740B,
+ 0xC9A0, 0x73E0,
+ 0xC945, 0x73B5,
+ 0xC8EB, 0x738A,
+ 0xC890, 0x735F,
+ 0xC835, 0x7333,
+ 0xC7DB, 0x7307,
+ 0xC781, 0x72DB,
+ 0xC727, 0x72AF,
+ 0xC6CD, 0x7282,
+ 0xC673, 0x7255,
+ 0xC619, 0x7227,
+ 0xC5BF, 0x71FA,
+ 0xC566, 0x71CC,
+ 0xC50D, 0x719E,
+ 0xC4B3, 0x716F,
+ 0xC45A, 0x7141,
+ 0xC402, 0x7112,
+ 0xC3A9, 0x70E2,
+ 0xC350, 0x70B3,
+ 0xC2F8, 0x7083,
+ 0xC29F, 0x7053,
+ 0xC247, 0x7023,
+ 0xC1EF, 0x6FF2,
+ 0xC197, 0x6FC1,
+ 0xC140, 0x6F90,
+ 0xC0E8, 0x6F5F,
+ 0xC091, 0x6F2D,
+ 0xC03A, 0x6EFB,
+ 0xBFE2, 0x6EC9,
+ 0xBF8C, 0x6E96,
+ 0xBF35, 0x6E63,
+ 0xBEDE, 0x6E30,
+ 0xBE88, 0x6DFD,
+ 0xBE31, 0x6DCA,
+ 0xBDDB, 0x6D96,
+ 0xBD85, 0x6D62,
+ 0xBD2F, 0x6D2D,
+ 0xBCDA, 0x6CF9,
+ 0xBC84, 0x6CC4,
+ 0xBC2F, 0x6C8F,
+ 0xBBDA, 0x6C59,
+ 0xBB85, 0x6C24,
+ 0xBB30, 0x6BEE,
+ 0xBADB, 0x6BB8,
+ 0xBA87, 0x6B81,
+ 0xBA32, 0x6B4A,
+ 0xB9DE, 0x6B13,
+ 0xB98A, 0x6ADC,
+ 0xB936, 0x6AA5,
+ 0xB8E3, 0x6A6D,
+ 0xB88F, 0x6A35,
+ 0xB83C, 0x69FD,
+ 0xB7E9, 0x69C4,
+ 0xB796, 0x698C,
+ 0xB743, 0x6953,
+ 0xB6F0, 0x6919,
+ 0xB69E, 0x68E0,
+ 0xB64B, 0x68A6,
+ 0xB5F9, 0x686C,
+ 0xB5A7, 0x6832,
+ 0xB556, 0x67F7,
+ 0xB504, 0x67BD,
+ 0xB4B3, 0x6782,
+ 0xB461, 0x6746,
+ 0xB410, 0x670B,
+ 0xB3C0, 0x66CF,
+ 0xB36F, 0x6693,
+ 0xB31E, 0x6657,
+ 0xB2CE, 0x661A,
+ 0xB27E, 0x65DD,
+ 0xB22E, 0x65A0,
+ 0xB1DE, 0x6563,
+ 0xB18F, 0x6526,
+ 0xB140, 0x64E8,
+ 0xB0F0, 0x64AA,
+ 0xB0A1, 0x646C,
+ 0xB053, 0x642D,
+ 0xB004, 0x63EF,
+ 0xAFB6, 0x63B0,
+ 0xAF68, 0x6371,
+ 0xAF1A, 0x6331,
+ 0xAECC, 0x62F2,
+ 0xAE7E, 0x62B2,
+ 0xAE31, 0x6271,
+ 0xADE3, 0x6231,
+ 0xAD96, 0x61F1,
+ 0xAD4A, 0x61B0,
+ 0xACFD, 0x616F,
+ 0xACB1, 0x612D,
+ 0xAC64, 0x60EC,
+ 0xAC18, 0x60AA,
+ 0xABCC, 0x6068,
+ 0xAB81, 0x6026,
+ 0xAB35, 0x5FE3,
+ 0xAAEA, 0x5FA0,
+ 0xAA9F, 0x5F5E,
+ 0xAA54, 0x5F1A,
+ 0xAA0A, 0x5ED7,
+ 0xA9BF, 0x5E93,
+ 0xA975, 0x5E50,
+ 0xA92B, 0x5E0B,
+ 0xA8E2, 0x5DC7,
+ 0xA898, 0x5D83,
+ 0xA84F, 0x5D3E,
+ 0xA806, 0x5CF9,
+ 0xA7BD, 0x5CB4,
+ 0xA774, 0x5C6E,
+ 0xA72B, 0x5C29,
+ 0xA6E3, 0x5BE3,
+ 0xA69B, 0x5B9D,
+ 0xA653, 0x5B56,
+ 0xA60C, 0x5B10,
+ 0xA5C4, 0x5AC9,
+ 0xA57D, 0x5A82,
+ 0xA536, 0x5A3B,
+ 0xA4EF, 0x59F3,
+ 0xA4A9, 0x59AC,
+ 0xA462, 0x5964,
+ 0xA41C, 0x591C,
+ 0xA3D6, 0x58D4,
+ 0xA391, 0x588B,
+ 0xA34B, 0x5842,
+ 0xA306, 0x57F9,
+ 0xA2C1, 0x57B0,
+ 0xA27C, 0x5767,
+ 0xA238, 0x571D,
+ 0xA1F4, 0x56D4,
+ 0xA1AF, 0x568A,
+ 0xA16C, 0x5640,
+ 0xA128, 0x55F5,
+ 0xA0E5, 0x55AB,
+ 0xA0A1, 0x5560,
+ 0xA05F, 0x5515,
+ 0xA01C, 0x54CA,
+ 0x9FD9, 0x547E,
+ 0x9F97, 0x5433,
+ 0x9F55, 0x53E7,
+ 0x9F13, 0x539B,
+ 0x9ED2, 0x534E,
+ 0x9E90, 0x5302,
+ 0x9E4F, 0x52B5,
+ 0x9E0E, 0x5269,
+ 0x9DCE, 0x521C,
+ 0x9D8E, 0x51CE,
+ 0x9D4D, 0x5181,
+ 0x9D0D, 0x5133,
+ 0x9CCE, 0x50E5,
+ 0x9C8E, 0x5097,
+ 0x9C4F, 0x5049,
+ 0x9C10, 0x4FFB,
+ 0x9BD2, 0x4FAC,
+ 0x9B93, 0x4F5E,
+ 0x9B55, 0x4F0F,
+ 0x9B17, 0x4EBF,
+ 0x9AD9, 0x4E70,
+ 0x9A9C, 0x4E21,
+ 0x9A5F, 0x4DD1,
+ 0x9A22, 0x4D81,
+ 0x99E5, 0x4D31,
+ 0x99A8, 0x4CE1,
+ 0x996C, 0x4C90,
+ 0x9930, 0x4C3F,
+ 0x98F4, 0x4BEF,
+ 0x98B9, 0x4B9E,
+ 0x987D, 0x4B4C,
+ 0x9842, 0x4AFB,
+ 0x9808, 0x4AA9,
+ 0x97CD, 0x4A58,
+ 0x9793, 0x4A06,
+ 0x9759, 0x49B4,
+ 0x971F, 0x4961,
+ 0x96E6, 0x490F,
+ 0x96AC, 0x48BC,
+ 0x9673, 0x4869,
+ 0x963B, 0x4816,
+ 0x9602, 0x47C3,
+ 0x95CA, 0x4770,
+ 0x9592, 0x471C,
+ 0x955A, 0x46C9,
+ 0x9523, 0x4675,
+ 0x94EC, 0x4621,
+ 0x94B5, 0x45CD,
+ 0x947E, 0x4578,
+ 0x9447, 0x4524,
+ 0x9411, 0x44CF,
+ 0x93DB, 0x447A,
+ 0x93A6, 0x4425,
+ 0x9370, 0x43D0,
+ 0x933B, 0x437B,
+ 0x9306, 0x4325,
+ 0x92D2, 0x42D0,
+ 0x929D, 0x427A,
+ 0x9269, 0x4224,
+ 0x9235, 0x41CE,
+ 0x9202, 0x4177,
+ 0x91CF, 0x4121,
+ 0x919C, 0x40CA,
+ 0x9169, 0x4073,
+ 0x9136, 0x401D,
+ 0x9104, 0x3FC5,
+ 0x90D2, 0x3F6E,
+ 0x90A0, 0x3F17,
+ 0x906F, 0x3EBF,
+ 0x903E, 0x3E68,
+ 0x900D, 0x3E10,
+ 0x8FDC, 0x3DB8,
+ 0x8FAC, 0x3D60,
+ 0x8F7C, 0x3D07,
+ 0x8F4C, 0x3CAF,
+ 0x8F1D, 0x3C56,
+ 0x8EED, 0x3BFD,
+ 0x8EBE, 0x3BA5,
+ 0x8E90, 0x3B4C,
+ 0x8E61, 0x3AF2,
+ 0x8E33, 0x3A99,
+ 0x8E05, 0x3A40,
+ 0x8DD8, 0x39E6,
+ 0x8DAA, 0x398C,
+ 0x8D7D, 0x3932,
+ 0x8D50, 0x38D8,
+ 0x8D24, 0x387E,
+ 0x8CF8, 0x3824,
+ 0x8CCC, 0x37CA,
+ 0x8CA0, 0x376F,
+ 0x8C75, 0x3714,
+ 0x8C4A, 0x36BA,
+ 0x8C1F, 0x365F,
+ 0x8BF4, 0x3604,
+ 0x8BCA, 0x35A8,
+ 0x8BA0, 0x354D,
+ 0x8B76, 0x34F2,
+ 0x8B4D, 0x3496,
+ 0x8B24, 0x343A,
+ 0x8AFB, 0x33DE,
+ 0x8AD2, 0x3382,
+ 0x8AAA, 0x3326,
+ 0x8A82, 0x32CA,
+ 0x8A5A, 0x326E,
+ 0x8A33, 0x3211,
+ 0x8A0B, 0x31B5,
+ 0x89E4, 0x3158,
+ 0x89BE, 0x30FB,
+ 0x8997, 0x309E,
+ 0x8971, 0x3041,
+ 0x894C, 0x2FE4,
+ 0x8926, 0x2F87,
+ 0x8901, 0x2F29,
+ 0x88DC, 0x2ECC,
+ 0x88B8, 0x2E6E,
+ 0x8893, 0x2E11,
+ 0x886F, 0x2DB3,
+ 0x884B, 0x2D55,
+ 0x8828, 0x2CF7,
+ 0x8805, 0x2C98,
+ 0x87E2, 0x2C3A,
+ 0x87BF, 0x2BDC,
+ 0x879D, 0x2B7D,
+ 0x877B, 0x2B1F,
+ 0x8759, 0x2AC0,
+ 0x8738, 0x2A61,
+ 0x8717, 0x2A02,
+ 0x86F6, 0x29A3,
+ 0x86D5, 0x2944,
+ 0x86B5, 0x28E5,
+ 0x8695, 0x2886,
+ 0x8675, 0x2826,
+ 0x8656, 0x27C7,
+ 0x8637, 0x2767,
+ 0x8618, 0x2707,
+ 0x85FA, 0x26A8,
+ 0x85DB, 0x2648,
+ 0x85BD, 0x25E8,
+ 0x85A0, 0x2588,
+ 0x8582, 0x2528,
+ 0x8565, 0x24C7,
+ 0x8549, 0x2467,
+ 0x852C, 0x2407,
+ 0x8510, 0x23A6,
+ 0x84F4, 0x2345,
+ 0x84D9, 0x22E5,
+ 0x84BD, 0x2284,
+ 0x84A2, 0x2223,
+ 0x8488, 0x21C2,
+ 0x846D, 0x2161,
+ 0x8453, 0x2100,
+ 0x843A, 0x209F,
+ 0x8420, 0x203E,
+ 0x8407, 0x1FDC,
+ 0x83EE, 0x1F7B,
+ 0x83D6, 0x1F19,
+ 0x83BD, 0x1EB8,
+ 0x83A5, 0x1E56,
+ 0x838E, 0x1DF5,
+ 0x8376, 0x1D93,
+ 0x835F, 0x1D31,
+ 0x8348, 0x1CCF,
+ 0x8332, 0x1C6D,
+ 0x831C, 0x1C0B,
+ 0x8306, 0x1BA9,
+ 0x82F0, 0x1B47,
+ 0x82DB, 0x1AE4,
+ 0x82C6, 0x1A82,
+ 0x82B1, 0x1A20,
+ 0x829D, 0x19BD,
+ 0x8289, 0x195B,
+ 0x8275, 0x18F8,
+ 0x8262, 0x1896,
+ 0x824F, 0x1833,
+ 0x823C, 0x17D0,
+ 0x8229, 0x176D,
+ 0x8217, 0x170A,
+ 0x8205, 0x16A8,
+ 0x81F3, 0x1645,
+ 0x81E2, 0x15E2,
+ 0x81D1, 0x157F,
+ 0x81C0, 0x151B,
+ 0x81B0, 0x14B8,
+ 0x81A0, 0x1455,
+ 0x8190, 0x13F2,
+ 0x8180, 0x138E,
+ 0x8171, 0x132B,
+ 0x8162, 0x12C8,
+ 0x8154, 0x1264,
+ 0x8145, 0x1201,
+ 0x8137, 0x119D,
+ 0x812A, 0x1139,
+ 0x811C, 0x10D6,
+ 0x810F, 0x1072,
+ 0x8102, 0x100E,
+ 0x80F6, 0x0FAB,
+ 0x80EA, 0x0F47,
+ 0x80DE, 0x0EE3,
+ 0x80D2, 0x0E7F,
+ 0x80C7, 0x0E1B,
+ 0x80BC, 0x0DB7,
+ 0x80B2, 0x0D53,
+ 0x80A7, 0x0CEF,
+ 0x809D, 0x0C8B,
+ 0x8094, 0x0C27,
+ 0x808A, 0x0BC3,
+ 0x8081, 0x0B5F,
+ 0x8078, 0x0AFB,
+ 0x8070, 0x0A97,
+ 0x8068, 0x0A33,
+ 0x8060, 0x09CE,
+ 0x8058, 0x096A,
+ 0x8051, 0x0906,
+ 0x804A, 0x08A2,
+ 0x8043, 0x083D,
+ 0x803D, 0x07D9,
+ 0x8037, 0x0775,
+ 0x8031, 0x0710,
+ 0x802C, 0x06AC,
+ 0x8027, 0x0647,
+ 0x8022, 0x05E3,
+ 0x801E, 0x057F,
+ 0x801A, 0x051A,
+ 0x8016, 0x04B6,
+ 0x8012, 0x0451,
+ 0x800F, 0x03ED,
+ 0x800C, 0x0388,
+ 0x8009, 0x0324,
+ 0x8007, 0x02BF,
+ 0x8005, 0x025B,
+ 0x8003, 0x01F6,
+ 0x8002, 0x0192,
+ 0x8001, 0x012D,
+ 0x8000, 0x00C9,
+ 0x8000, 0x0064,
+ 0x8000, 0x0000,
+ 0x8000, 0xFF9B,
+ 0x8000, 0xFF36,
+ 0x8001, 0xFED2,
+ 0x8002, 0xFE6D,
+ 0x8003, 0xFE09,
+ 0x8005, 0xFDA4,
+ 0x8007, 0xFD40,
+ 0x8009, 0xFCDB,
+ 0x800C, 0xFC77,
+ 0x800F, 0xFC12,
+ 0x8012, 0xFBAE,
+ 0x8016, 0xFB49,
+ 0x801A, 0xFAE5,
+ 0x801E, 0xFA80,
+ 0x8022, 0xFA1C,
+ 0x8027, 0xF9B8,
+ 0x802C, 0xF953,
+ 0x8031, 0xF8EF,
+ 0x8037, 0xF88A,
+ 0x803D, 0xF826,
+ 0x8043, 0xF7C2,
+ 0x804A, 0xF75D,
+ 0x8051, 0xF6F9,
+ 0x8058, 0xF695,
+ 0x8060, 0xF631,
+ 0x8068, 0xF5CC,
+ 0x8070, 0xF568,
+ 0x8078, 0xF504,
+ 0x8081, 0xF4A0,
+ 0x808A, 0xF43C,
+ 0x8094, 0xF3D8,
+ 0x809D, 0xF374,
+ 0x80A7, 0xF310,
+ 0x80B2, 0xF2AC,
+ 0x80BC, 0xF248,
+ 0x80C7, 0xF1E4,
+ 0x80D2, 0xF180,
+ 0x80DE, 0xF11C,
+ 0x80EA, 0xF0B8,
+ 0x80F6, 0xF054,
+ 0x8102, 0xEFF1,
+ 0x810F, 0xEF8D,
+ 0x811C, 0xEF29,
+ 0x812A, 0xEEC6,
+ 0x8137, 0xEE62,
+ 0x8145, 0xEDFE,
+ 0x8154, 0xED9B,
+ 0x8162, 0xED37,
+ 0x8171, 0xECD4,
+ 0x8180, 0xEC71,
+ 0x8190, 0xEC0D,
+ 0x81A0, 0xEBAA,
+ 0x81B0, 0xEB47,
+ 0x81C0, 0xEAE4,
+ 0x81D1, 0xEA80,
+ 0x81E2, 0xEA1D,
+ 0x81F3, 0xE9BA,
+ 0x8205, 0xE957,
+ 0x8217, 0xE8F5,
+ 0x8229, 0xE892,
+ 0x823C, 0xE82F,
+ 0x824F, 0xE7CC,
+ 0x8262, 0xE769,
+ 0x8275, 0xE707,
+ 0x8289, 0xE6A4,
+ 0x829D, 0xE642,
+ 0x82B1, 0xE5DF,
+ 0x82C6, 0xE57D,
+ 0x82DB, 0xE51B,
+ 0x82F0, 0xE4B8,
+ 0x8306, 0xE456,
+ 0x831C, 0xE3F4,
+ 0x8332, 0xE392,
+ 0x8348, 0xE330,
+ 0x835F, 0xE2CE,
+ 0x8376, 0xE26C,
+ 0x838E, 0xE20A,
+ 0x83A5, 0xE1A9,
+ 0x83BD, 0xE147,
+ 0x83D6, 0xE0E6,
+ 0x83EE, 0xE084,
+ 0x8407, 0xE023,
+ 0x8420, 0xDFC1,
+ 0x843A, 0xDF60,
+ 0x8453, 0xDEFF,
+ 0x846D, 0xDE9E,
+ 0x8488, 0xDE3D,
+ 0x84A2, 0xDDDC,
+ 0x84BD, 0xDD7B,
+ 0x84D9, 0xDD1A,
+ 0x84F4, 0xDCBA,
+ 0x8510, 0xDC59,
+ 0x852C, 0xDBF8,
+ 0x8549, 0xDB98,
+ 0x8565, 0xDB38,
+ 0x8582, 0xDAD7,
+ 0x85A0, 0xDA77,
+ 0x85BD, 0xDA17,
+ 0x85DB, 0xD9B7,
+ 0x85FA, 0xD957,
+ 0x8618, 0xD8F8,
+ 0x8637, 0xD898,
+ 0x8656, 0xD838,
+ 0x8675, 0xD7D9,
+ 0x8695, 0xD779,
+ 0x86B5, 0xD71A,
+ 0x86D5, 0xD6BB,
+ 0x86F6, 0xD65C,
+ 0x8717, 0xD5FD,
+ 0x8738, 0xD59E,
+ 0x8759, 0xD53F,
+ 0x877B, 0xD4E0,
+ 0x879D, 0xD482,
+ 0x87BF, 0xD423,
+ 0x87E2, 0xD3C5,
+ 0x8805, 0xD367,
+ 0x8828, 0xD308,
+ 0x884B, 0xD2AA,
+ 0x886F, 0xD24C,
+ 0x8893, 0xD1EE,
+ 0x88B8, 0xD191,
+ 0x88DC, 0xD133,
+ 0x8901, 0xD0D6,
+ 0x8926, 0xD078,
+ 0x894C, 0xD01B,
+ 0x8971, 0xCFBE,
+ 0x8997, 0xCF61,
+ 0x89BE, 0xCF04,
+ 0x89E4, 0xCEA7,
+ 0x8A0B, 0xCE4A,
+ 0x8A33, 0xCDEE,
+ 0x8A5A, 0xCD91,
+ 0x8A82, 0xCD35,
+ 0x8AAA, 0xCCD9,
+ 0x8AD2, 0xCC7D,
+ 0x8AFB, 0xCC21,
+ 0x8B24, 0xCBC5,
+ 0x8B4D, 0xCB69,
+ 0x8B76, 0xCB0D,
+ 0x8BA0, 0xCAB2,
+ 0x8BCA, 0xCA57,
+ 0x8BF4, 0xC9FB,
+ 0x8C1F, 0xC9A0,
+ 0x8C4A, 0xC945,
+ 0x8C75, 0xC8EB,
+ 0x8CA0, 0xC890,
+ 0x8CCC, 0xC835,
+ 0x8CF8, 0xC7DB,
+ 0x8D24, 0xC781,
+ 0x8D50, 0xC727,
+ 0x8D7D, 0xC6CD,
+ 0x8DAA, 0xC673,
+ 0x8DD8, 0xC619,
+ 0x8E05, 0xC5BF,
+ 0x8E33, 0xC566,
+ 0x8E61, 0xC50D,
+ 0x8E90, 0xC4B3,
+ 0x8EBE, 0xC45A,
+ 0x8EED, 0xC402,
+ 0x8F1D, 0xC3A9,
+ 0x8F4C, 0xC350,
+ 0x8F7C, 0xC2F8,
+ 0x8FAC, 0xC29F,
+ 0x8FDC, 0xC247,
+ 0x900D, 0xC1EF,
+ 0x903E, 0xC197,
+ 0x906F, 0xC140,
+ 0x90A0, 0xC0E8,
+ 0x90D2, 0xC091,
+ 0x9104, 0xC03A,
+ 0x9136, 0xBFE2,
+ 0x9169, 0xBF8C,
+ 0x919C, 0xBF35,
+ 0x91CF, 0xBEDE,
+ 0x9202, 0xBE88,
+ 0x9235, 0xBE31,
+ 0x9269, 0xBDDB,
+ 0x929D, 0xBD85,
+ 0x92D2, 0xBD2F,
+ 0x9306, 0xBCDA,
+ 0x933B, 0xBC84,
+ 0x9370, 0xBC2F,
+ 0x93A6, 0xBBDA,
+ 0x93DB, 0xBB85,
+ 0x9411, 0xBB30,
+ 0x9447, 0xBADB,
+ 0x947E, 0xBA87,
+ 0x94B5, 0xBA32,
+ 0x94EC, 0xB9DE,
+ 0x9523, 0xB98A,
+ 0x955A, 0xB936,
+ 0x9592, 0xB8E3,
+ 0x95CA, 0xB88F,
+ 0x9602, 0xB83C,
+ 0x963B, 0xB7E9,
+ 0x9673, 0xB796,
+ 0x96AC, 0xB743,
+ 0x96E6, 0xB6F0,
+ 0x971F, 0xB69E,
+ 0x9759, 0xB64B,
+ 0x9793, 0xB5F9,
+ 0x97CD, 0xB5A7,
+ 0x9808, 0xB556,
+ 0x9842, 0xB504,
+ 0x987D, 0xB4B3,
+ 0x98B9, 0xB461,
+ 0x98F4, 0xB410,
+ 0x9930, 0xB3C0,
+ 0x996C, 0xB36F,
+ 0x99A8, 0xB31E,
+ 0x99E5, 0xB2CE,
+ 0x9A22, 0xB27E,
+ 0x9A5F, 0xB22E,
+ 0x9A9C, 0xB1DE,
+ 0x9AD9, 0xB18F,
+ 0x9B17, 0xB140,
+ 0x9B55, 0xB0F0,
+ 0x9B93, 0xB0A1,
+ 0x9BD2, 0xB053,
+ 0x9C10, 0xB004,
+ 0x9C4F, 0xAFB6,
+ 0x9C8E, 0xAF68,
+ 0x9CCE, 0xAF1A,
+ 0x9D0D, 0xAECC,
+ 0x9D4D, 0xAE7E,
+ 0x9D8E, 0xAE31,
+ 0x9DCE, 0xADE3,
+ 0x9E0E, 0xAD96,
+ 0x9E4F, 0xAD4A,
+ 0x9E90, 0xACFD,
+ 0x9ED2, 0xACB1,
+ 0x9F13, 0xAC64,
+ 0x9F55, 0xAC18,
+ 0x9F97, 0xABCC,
+ 0x9FD9, 0xAB81,
+ 0xA01C, 0xAB35,
+ 0xA05F, 0xAAEA,
+ 0xA0A1, 0xAA9F,
+ 0xA0E5, 0xAA54,
+ 0xA128, 0xAA0A,
+ 0xA16C, 0xA9BF,
+ 0xA1AF, 0xA975,
+ 0xA1F4, 0xA92B,
+ 0xA238, 0xA8E2,
+ 0xA27C, 0xA898,
+ 0xA2C1, 0xA84F,
+ 0xA306, 0xA806,
+ 0xA34B, 0xA7BD,
+ 0xA391, 0xA774,
+ 0xA3D6, 0xA72B,
+ 0xA41C, 0xA6E3,
+ 0xA462, 0xA69B,
+ 0xA4A9, 0xA653,
+ 0xA4EF, 0xA60C,
+ 0xA536, 0xA5C4,
+ 0xA57D, 0xA57D,
+ 0xA5C4, 0xA536,
+ 0xA60C, 0xA4EF,
+ 0xA653, 0xA4A9,
+ 0xA69B, 0xA462,
+ 0xA6E3, 0xA41C,
+ 0xA72B, 0xA3D6,
+ 0xA774, 0xA391,
+ 0xA7BD, 0xA34B,
+ 0xA806, 0xA306,
+ 0xA84F, 0xA2C1,
+ 0xA898, 0xA27C,
+ 0xA8E2, 0xA238,
+ 0xA92B, 0xA1F4,
+ 0xA975, 0xA1AF,
+ 0xA9BF, 0xA16C,
+ 0xAA0A, 0xA128,
+ 0xAA54, 0xA0E5,
+ 0xAA9F, 0xA0A1,
+ 0xAAEA, 0xA05F,
+ 0xAB35, 0xA01C,
+ 0xAB81, 0x9FD9,
+ 0xABCC, 0x9F97,
+ 0xAC18, 0x9F55,
+ 0xAC64, 0x9F13,
+ 0xACB1, 0x9ED2,
+ 0xACFD, 0x9E90,
+ 0xAD4A, 0x9E4F,
+ 0xAD96, 0x9E0E,
+ 0xADE3, 0x9DCE,
+ 0xAE31, 0x9D8E,
+ 0xAE7E, 0x9D4D,
+ 0xAECC, 0x9D0D,
+ 0xAF1A, 0x9CCE,
+ 0xAF68, 0x9C8E,
+ 0xAFB6, 0x9C4F,
+ 0xB004, 0x9C10,
+ 0xB053, 0x9BD2,
+ 0xB0A1, 0x9B93,
+ 0xB0F0, 0x9B55,
+ 0xB140, 0x9B17,
+ 0xB18F, 0x9AD9,
+ 0xB1DE, 0x9A9C,
+ 0xB22E, 0x9A5F,
+ 0xB27E, 0x9A22,
+ 0xB2CE, 0x99E5,
+ 0xB31E, 0x99A8,
+ 0xB36F, 0x996C,
+ 0xB3C0, 0x9930,
+ 0xB410, 0x98F4,
+ 0xB461, 0x98B9,
+ 0xB4B3, 0x987D,
+ 0xB504, 0x9842,
+ 0xB556, 0x9808,
+ 0xB5A7, 0x97CD,
+ 0xB5F9, 0x9793,
+ 0xB64B, 0x9759,
+ 0xB69E, 0x971F,
+ 0xB6F0, 0x96E6,
+ 0xB743, 0x96AC,
+ 0xB796, 0x9673,
+ 0xB7E9, 0x963B,
+ 0xB83C, 0x9602,
+ 0xB88F, 0x95CA,
+ 0xB8E3, 0x9592,
+ 0xB936, 0x955A,
+ 0xB98A, 0x9523,
+ 0xB9DE, 0x94EC,
+ 0xBA32, 0x94B5,
+ 0xBA87, 0x947E,
+ 0xBADB, 0x9447,
+ 0xBB30, 0x9411,
+ 0xBB85, 0x93DB,
+ 0xBBDA, 0x93A6,
+ 0xBC2F, 0x9370,
+ 0xBC84, 0x933B,
+ 0xBCDA, 0x9306,
+ 0xBD2F, 0x92D2,
+ 0xBD85, 0x929D,
+ 0xBDDB, 0x9269,
+ 0xBE31, 0x9235,
+ 0xBE88, 0x9202,
+ 0xBEDE, 0x91CF,
+ 0xBF35, 0x919C,
+ 0xBF8C, 0x9169,
+ 0xBFE2, 0x9136,
+ 0xC03A, 0x9104,
+ 0xC091, 0x90D2,
+ 0xC0E8, 0x90A0,
+ 0xC140, 0x906F,
+ 0xC197, 0x903E,
+ 0xC1EF, 0x900D,
+ 0xC247, 0x8FDC,
+ 0xC29F, 0x8FAC,
+ 0xC2F8, 0x8F7C,
+ 0xC350, 0x8F4C,
+ 0xC3A9, 0x8F1D,
+ 0xC402, 0x8EED,
+ 0xC45A, 0x8EBE,
+ 0xC4B3, 0x8E90,
+ 0xC50D, 0x8E61,
+ 0xC566, 0x8E33,
+ 0xC5BF, 0x8E05,
+ 0xC619, 0x8DD8,
+ 0xC673, 0x8DAA,
+ 0xC6CD, 0x8D7D,
+ 0xC727, 0x8D50,
+ 0xC781, 0x8D24,
+ 0xC7DB, 0x8CF8,
+ 0xC835, 0x8CCC,
+ 0xC890, 0x8CA0,
+ 0xC8EB, 0x8C75,
+ 0xC945, 0x8C4A,
+ 0xC9A0, 0x8C1F,
+ 0xC9FB, 0x8BF4,
+ 0xCA57, 0x8BCA,
+ 0xCAB2, 0x8BA0,
+ 0xCB0D, 0x8B76,
+ 0xCB69, 0x8B4D,
+ 0xCBC5, 0x8B24,
+ 0xCC21, 0x8AFB,
+ 0xCC7D, 0x8AD2,
+ 0xCCD9, 0x8AAA,
+ 0xCD35, 0x8A82,
+ 0xCD91, 0x8A5A,
+ 0xCDEE, 0x8A33,
+ 0xCE4A, 0x8A0B,
+ 0xCEA7, 0x89E4,
+ 0xCF04, 0x89BE,
+ 0xCF61, 0x8997,
+ 0xCFBE, 0x8971,
+ 0xD01B, 0x894C,
+ 0xD078, 0x8926,
+ 0xD0D6, 0x8901,
+ 0xD133, 0x88DC,
+ 0xD191, 0x88B8,
+ 0xD1EE, 0x8893,
+ 0xD24C, 0x886F,
+ 0xD2AA, 0x884B,
+ 0xD308, 0x8828,
+ 0xD367, 0x8805,
+ 0xD3C5, 0x87E2,
+ 0xD423, 0x87BF,
+ 0xD482, 0x879D,
+ 0xD4E0, 0x877B,
+ 0xD53F, 0x8759,
+ 0xD59E, 0x8738,
+ 0xD5FD, 0x8717,
+ 0xD65C, 0x86F6,
+ 0xD6BB, 0x86D5,
+ 0xD71A, 0x86B5,
+ 0xD779, 0x8695,
+ 0xD7D9, 0x8675,
+ 0xD838, 0x8656,
+ 0xD898, 0x8637,
+ 0xD8F8, 0x8618,
+ 0xD957, 0x85FA,
+ 0xD9B7, 0x85DB,
+ 0xDA17, 0x85BD,
+ 0xDA77, 0x85A0,
+ 0xDAD7, 0x8582,
+ 0xDB38, 0x8565,
+ 0xDB98, 0x8549,
+ 0xDBF8, 0x852C,
+ 0xDC59, 0x8510,
+ 0xDCBA, 0x84F4,
+ 0xDD1A, 0x84D9,
+ 0xDD7B, 0x84BD,
+ 0xDDDC, 0x84A2,
+ 0xDE3D, 0x8488,
+ 0xDE9E, 0x846D,
+ 0xDEFF, 0x8453,
+ 0xDF60, 0x843A,
+ 0xDFC1, 0x8420,
+ 0xE023, 0x8407,
+ 0xE084, 0x83EE,
+ 0xE0E6, 0x83D6,
+ 0xE147, 0x83BD,
+ 0xE1A9, 0x83A5,
+ 0xE20A, 0x838E,
+ 0xE26C, 0x8376,
+ 0xE2CE, 0x835F,
+ 0xE330, 0x8348,
+ 0xE392, 0x8332,
+ 0xE3F4, 0x831C,
+ 0xE456, 0x8306,
+ 0xE4B8, 0x82F0,
+ 0xE51B, 0x82DB,
+ 0xE57D, 0x82C6,
+ 0xE5DF, 0x82B1,
+ 0xE642, 0x829D,
+ 0xE6A4, 0x8289,
+ 0xE707, 0x8275,
+ 0xE769, 0x8262,
+ 0xE7CC, 0x824F,
+ 0xE82F, 0x823C,
+ 0xE892, 0x8229,
+ 0xE8F5, 0x8217,
+ 0xE957, 0x8205,
+ 0xE9BA, 0x81F3,
+ 0xEA1D, 0x81E2,
+ 0xEA80, 0x81D1,
+ 0xEAE4, 0x81C0,
+ 0xEB47, 0x81B0,
+ 0xEBAA, 0x81A0,
+ 0xEC0D, 0x8190,
+ 0xEC71, 0x8180,
+ 0xECD4, 0x8171,
+ 0xED37, 0x8162,
+ 0xED9B, 0x8154,
+ 0xEDFE, 0x8145,
+ 0xEE62, 0x8137,
+ 0xEEC6, 0x812A,
+ 0xEF29, 0x811C,
+ 0xEF8D, 0x810F,
+ 0xEFF1, 0x8102,
+ 0xF054, 0x80F6,
+ 0xF0B8, 0x80EA,
+ 0xF11C, 0x80DE,
+ 0xF180, 0x80D2,
+ 0xF1E4, 0x80C7,
+ 0xF248, 0x80BC,
+ 0xF2AC, 0x80B2,
+ 0xF310, 0x80A7,
+ 0xF374, 0x809D,
+ 0xF3D8, 0x8094,
+ 0xF43C, 0x808A,
+ 0xF4A0, 0x8081,
+ 0xF504, 0x8078,
+ 0xF568, 0x8070,
+ 0xF5CC, 0x8068,
+ 0xF631, 0x8060,
+ 0xF695, 0x8058,
+ 0xF6F9, 0x8051,
+ 0xF75D, 0x804A,
+ 0xF7C2, 0x8043,
+ 0xF826, 0x803D,
+ 0xF88A, 0x8037,
+ 0xF8EF, 0x8031,
+ 0xF953, 0x802C,
+ 0xF9B8, 0x8027,
+ 0xFA1C, 0x8022,
+ 0xFA80, 0x801E,
+ 0xFAE5, 0x801A,
+ 0xFB49, 0x8016,
+ 0xFBAE, 0x8012,
+ 0xFC12, 0x800F,
+ 0xFC77, 0x800C,
+ 0xFCDB, 0x8009,
+ 0xFD40, 0x8007,
+ 0xFDA4, 0x8005,
+ 0xFE09, 0x8003,
+ 0xFE6D, 0x8002,
+ 0xFED2, 0x8001,
+ 0xFF36, 0x8000,
+ 0xFF9B, 0x8000
+};
+
+/**
+* \par
+* Example code for q15 Twiddle factors Generation::
+* \par
+* for(i = 0; i< 3N/4; i++)
+* {
+* twiddleCoefq15[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoefq15[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par
+* where N = 4096 and PI = 3.14159265358979
+* \par
+* Cos and Sin values are interleaved fashion
+* \par
+* Convert Floating point to q15(Fixed point 1.15):
+* round(twiddleCoefq15(i) * pow(2, 15))
+*
+*/
+const q15_t twiddleCoef_4096_q15[6144] =
+{
+ 0x7FFF, 0x0000,
+ 0x7FFF, 0x0032,
+ 0x7FFF, 0x0064,
+ 0x7FFF, 0x0096,
+ 0x7FFF, 0x00C9,
+ 0x7FFF, 0x00FB,
+ 0x7FFE, 0x012D,
+ 0x7FFE, 0x015F,
+ 0x7FFD, 0x0192,
+ 0x7FFC, 0x01C4,
+ 0x7FFC, 0x01F6,
+ 0x7FFB, 0x0228,
+ 0x7FFA, 0x025B,
+ 0x7FF9, 0x028D,
+ 0x7FF8, 0x02BF,
+ 0x7FF7, 0x02F1,
+ 0x7FF6, 0x0324,
+ 0x7FF4, 0x0356,
+ 0x7FF3, 0x0388,
+ 0x7FF2, 0x03BA,
+ 0x7FF0, 0x03ED,
+ 0x7FEE, 0x041F,
+ 0x7FED, 0x0451,
+ 0x7FEB, 0x0483,
+ 0x7FE9, 0x04B6,
+ 0x7FE7, 0x04E8,
+ 0x7FE5, 0x051A,
+ 0x7FE3, 0x054C,
+ 0x7FE1, 0x057F,
+ 0x7FDF, 0x05B1,
+ 0x7FDD, 0x05E3,
+ 0x7FDA, 0x0615,
+ 0x7FD8, 0x0647,
+ 0x7FD6, 0x067A,
+ 0x7FD3, 0x06AC,
+ 0x7FD0, 0x06DE,
+ 0x7FCE, 0x0710,
+ 0x7FCB, 0x0742,
+ 0x7FC8, 0x0775,
+ 0x7FC5, 0x07A7,
+ 0x7FC2, 0x07D9,
+ 0x7FBF, 0x080B,
+ 0x7FBC, 0x083D,
+ 0x7FB8, 0x086F,
+ 0x7FB5, 0x08A2,
+ 0x7FB1, 0x08D4,
+ 0x7FAE, 0x0906,
+ 0x7FAA, 0x0938,
+ 0x7FA7, 0x096A,
+ 0x7FA3, 0x099C,
+ 0x7F9F, 0x09CE,
+ 0x7F9B, 0x0A00,
+ 0x7F97, 0x0A33,
+ 0x7F93, 0x0A65,
+ 0x7F8F, 0x0A97,
+ 0x7F8B, 0x0AC9,
+ 0x7F87, 0x0AFB,
+ 0x7F82, 0x0B2D,
+ 0x7F7E, 0x0B5F,
+ 0x7F79, 0x0B91,
+ 0x7F75, 0x0BC3,
+ 0x7F70, 0x0BF5,
+ 0x7F6B, 0x0C27,
+ 0x7F67, 0x0C59,
+ 0x7F62, 0x0C8B,
+ 0x7F5D, 0x0CBD,
+ 0x7F58, 0x0CEF,
+ 0x7F53, 0x0D21,
+ 0x7F4D, 0x0D53,
+ 0x7F48, 0x0D85,
+ 0x7F43, 0x0DB7,
+ 0x7F3D, 0x0DE9,
+ 0x7F38, 0x0E1B,
+ 0x7F32, 0x0E4D,
+ 0x7F2D, 0x0E7F,
+ 0x7F27, 0x0EB1,
+ 0x7F21, 0x0EE3,
+ 0x7F1B, 0x0F15,
+ 0x7F15, 0x0F47,
+ 0x7F0F, 0x0F79,
+ 0x7F09, 0x0FAB,
+ 0x7F03, 0x0FDD,
+ 0x7EFD, 0x100E,
+ 0x7EF6, 0x1040,
+ 0x7EF0, 0x1072,
+ 0x7EE9, 0x10A4,
+ 0x7EE3, 0x10D6,
+ 0x7EDC, 0x1108,
+ 0x7ED5, 0x1139,
+ 0x7ECF, 0x116B,
+ 0x7EC8, 0x119D,
+ 0x7EC1, 0x11CF,
+ 0x7EBA, 0x1201,
+ 0x7EB3, 0x1232,
+ 0x7EAB, 0x1264,
+ 0x7EA4, 0x1296,
+ 0x7E9D, 0x12C8,
+ 0x7E95, 0x12F9,
+ 0x7E8E, 0x132B,
+ 0x7E86, 0x135D,
+ 0x7E7F, 0x138E,
+ 0x7E77, 0x13C0,
+ 0x7E6F, 0x13F2,
+ 0x7E67, 0x1423,
+ 0x7E5F, 0x1455,
+ 0x7E57, 0x1487,
+ 0x7E4F, 0x14B8,
+ 0x7E47, 0x14EA,
+ 0x7E3F, 0x151B,
+ 0x7E37, 0x154D,
+ 0x7E2E, 0x157F,
+ 0x7E26, 0x15B0,
+ 0x7E1D, 0x15E2,
+ 0x7E14, 0x1613,
+ 0x7E0C, 0x1645,
+ 0x7E03, 0x1676,
+ 0x7DFA, 0x16A8,
+ 0x7DF1, 0x16D9,
+ 0x7DE8, 0x170A,
+ 0x7DDF, 0x173C,
+ 0x7DD6, 0x176D,
+ 0x7DCD, 0x179F,
+ 0x7DC3, 0x17D0,
+ 0x7DBA, 0x1802,
+ 0x7DB0, 0x1833,
+ 0x7DA7, 0x1864,
+ 0x7D9D, 0x1896,
+ 0x7D94, 0x18C7,
+ 0x7D8A, 0x18F8,
+ 0x7D80, 0x192A,
+ 0x7D76, 0x195B,
+ 0x7D6C, 0x198C,
+ 0x7D62, 0x19BD,
+ 0x7D58, 0x19EF,
+ 0x7D4E, 0x1A20,
+ 0x7D43, 0x1A51,
+ 0x7D39, 0x1A82,
+ 0x7D2F, 0x1AB3,
+ 0x7D24, 0x1AE4,
+ 0x7D19, 0x1B16,
+ 0x7D0F, 0x1B47,
+ 0x7D04, 0x1B78,
+ 0x7CF9, 0x1BA9,
+ 0x7CEE, 0x1BDA,
+ 0x7CE3, 0x1C0B,
+ 0x7CD8, 0x1C3C,
+ 0x7CCD, 0x1C6D,
+ 0x7CC2, 0x1C9E,
+ 0x7CB7, 0x1CCF,
+ 0x7CAB, 0x1D00,
+ 0x7CA0, 0x1D31,
+ 0x7C94, 0x1D62,
+ 0x7C89, 0x1D93,
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+ 0x843A, 0x209F,
+ 0x842D, 0x206E,
+ 0x8420, 0x203E,
+ 0x8414, 0x200D,
+ 0x8407, 0x1FDC,
+ 0x83FA, 0x1FAC,
+ 0x83EE, 0x1F7B,
+ 0x83E2, 0x1F4A,
+ 0x83D6, 0x1F19,
+ 0x83C9, 0x1EE9,
+ 0x83BD, 0x1EB8,
+ 0x83B1, 0x1E87,
+ 0x83A5, 0x1E56,
+ 0x8399, 0x1E25,
+ 0x838E, 0x1DF5,
+ 0x8382, 0x1DC4,
+ 0x8376, 0x1D93,
+ 0x836B, 0x1D62,
+ 0x835F, 0x1D31,
+ 0x8354, 0x1D00,
+ 0x8348, 0x1CCF,
+ 0x833D, 0x1C9E,
+ 0x8332, 0x1C6D,
+ 0x8327, 0x1C3C,
+ 0x831C, 0x1C0B,
+ 0x8311, 0x1BDA,
+ 0x8306, 0x1BA9,
+ 0x82FB, 0x1B78,
+ 0x82F0, 0x1B47,
+ 0x82E6, 0x1B16,
+ 0x82DB, 0x1AE4,
+ 0x82D0, 0x1AB3,
+ 0x82C6, 0x1A82,
+ 0x82BC, 0x1A51,
+ 0x82B1, 0x1A20,
+ 0x82A7, 0x19EF,
+ 0x829D, 0x19BD,
+ 0x8293, 0x198C,
+ 0x8289, 0x195B,
+ 0x827F, 0x192A,
+ 0x8275, 0x18F8,
+ 0x826B, 0x18C7,
+ 0x8262, 0x1896,
+ 0x8258, 0x1864,
+ 0x824F, 0x1833,
+ 0x8245, 0x1802,
+ 0x823C, 0x17D0,
+ 0x8232, 0x179F,
+ 0x8229, 0x176D,
+ 0x8220, 0x173C,
+ 0x8217, 0x170A,
+ 0x820E, 0x16D9,
+ 0x8205, 0x16A8,
+ 0x81FC, 0x1676,
+ 0x81F3, 0x1645,
+ 0x81EB, 0x1613,
+ 0x81E2, 0x15E2,
+ 0x81D9, 0x15B0,
+ 0x81D1, 0x157F,
+ 0x81C8, 0x154D,
+ 0x81C0, 0x151B,
+ 0x81B8, 0x14EA,
+ 0x81B0, 0x14B8,
+ 0x81A8, 0x1487,
+ 0x81A0, 0x1455,
+ 0x8198, 0x1423,
+ 0x8190, 0x13F2,
+ 0x8188, 0x13C0,
+ 0x8180, 0x138E,
+ 0x8179, 0x135D,
+ 0x8171, 0x132B,
+ 0x816A, 0x12F9,
+ 0x8162, 0x12C8,
+ 0x815B, 0x1296,
+ 0x8154, 0x1264,
+ 0x814C, 0x1232,
+ 0x8145, 0x1201,
+ 0x813E, 0x11CF,
+ 0x8137, 0x119D,
+ 0x8130, 0x116B,
+ 0x812A, 0x1139,
+ 0x8123, 0x1108,
+ 0x811C, 0x10D6,
+ 0x8116, 0x10A4,
+ 0x810F, 0x1072,
+ 0x8109, 0x1040,
+ 0x8102, 0x100E,
+ 0x80FC, 0x0FDD,
+ 0x80F6, 0x0FAB,
+ 0x80F0, 0x0F79,
+ 0x80EA, 0x0F47,
+ 0x80E4, 0x0F15,
+ 0x80DE, 0x0EE3,
+ 0x80D8, 0x0EB1,
+ 0x80D2, 0x0E7F,
+ 0x80CD, 0x0E4D,
+ 0x80C7, 0x0E1B,
+ 0x80C2, 0x0DE9,
+ 0x80BC, 0x0DB7,
+ 0x80B7, 0x0D85,
+ 0x80B2, 0x0D53,
+ 0x80AC, 0x0D21,
+ 0x80A7, 0x0CEF,
+ 0x80A2, 0x0CBD,
+ 0x809D, 0x0C8B,
+ 0x8098, 0x0C59,
+ 0x8094, 0x0C27,
+ 0x808F, 0x0BF5,
+ 0x808A, 0x0BC3,
+ 0x8086, 0x0B91,
+ 0x8081, 0x0B5F,
+ 0x807D, 0x0B2D,
+ 0x8078, 0x0AFB,
+ 0x8074, 0x0AC9,
+ 0x8070, 0x0A97,
+ 0x806C, 0x0A65,
+ 0x8068, 0x0A33,
+ 0x8064, 0x0A00,
+ 0x8060, 0x09CE,
+ 0x805C, 0x099C,
+ 0x8058, 0x096A,
+ 0x8055, 0x0938,
+ 0x8051, 0x0906,
+ 0x804E, 0x08D4,
+ 0x804A, 0x08A2,
+ 0x8047, 0x086F,
+ 0x8043, 0x083D,
+ 0x8040, 0x080B,
+ 0x803D, 0x07D9,
+ 0x803A, 0x07A7,
+ 0x8037, 0x0775,
+ 0x8034, 0x0742,
+ 0x8031, 0x0710,
+ 0x802F, 0x06DE,
+ 0x802C, 0x06AC,
+ 0x8029, 0x067A,
+ 0x8027, 0x0647,
+ 0x8025, 0x0615,
+ 0x8022, 0x05E3,
+ 0x8020, 0x05B1,
+ 0x801E, 0x057F,
+ 0x801C, 0x054C,
+ 0x801A, 0x051A,
+ 0x8018, 0x04E8,
+ 0x8016, 0x04B6,
+ 0x8014, 0x0483,
+ 0x8012, 0x0451,
+ 0x8011, 0x041F,
+ 0x800F, 0x03ED,
+ 0x800D, 0x03BA,
+ 0x800C, 0x0388,
+ 0x800B, 0x0356,
+ 0x8009, 0x0324,
+ 0x8008, 0x02F1,
+ 0x8007, 0x02BF,
+ 0x8006, 0x028D,
+ 0x8005, 0x025B,
+ 0x8004, 0x0228,
+ 0x8003, 0x01F6,
+ 0x8003, 0x01C4,
+ 0x8002, 0x0192,
+ 0x8001, 0x015F,
+ 0x8001, 0x012D,
+ 0x8000, 0x00FB,
+ 0x8000, 0x00C9,
+ 0x8000, 0x0096,
+ 0x8000, 0x0064,
+ 0x8000, 0x0032,
+ 0x8000, 0x0000,
+ 0x8000, 0xFFCD,
+ 0x8000, 0xFF9B,
+ 0x8000, 0xFF69,
+ 0x8000, 0xFF36,
+ 0x8000, 0xFF04,
+ 0x8001, 0xFED2,
+ 0x8001, 0xFEA0,
+ 0x8002, 0xFE6D,
+ 0x8003, 0xFE3B,
+ 0x8003, 0xFE09,
+ 0x8004, 0xFDD7,
+ 0x8005, 0xFDA4,
+ 0x8006, 0xFD72,
+ 0x8007, 0xFD40,
+ 0x8008, 0xFD0E,
+ 0x8009, 0xFCDB,
+ 0x800B, 0xFCA9,
+ 0x800C, 0xFC77,
+ 0x800D, 0xFC45,
+ 0x800F, 0xFC12,
+ 0x8011, 0xFBE0,
+ 0x8012, 0xFBAE,
+ 0x8014, 0xFB7C,
+ 0x8016, 0xFB49,
+ 0x8018, 0xFB17,
+ 0x801A, 0xFAE5,
+ 0x801C, 0xFAB3,
+ 0x801E, 0xFA80,
+ 0x8020, 0xFA4E,
+ 0x8022, 0xFA1C,
+ 0x8025, 0xF9EA,
+ 0x8027, 0xF9B8,
+ 0x8029, 0xF985,
+ 0x802C, 0xF953,
+ 0x802F, 0xF921,
+ 0x8031, 0xF8EF,
+ 0x8034, 0xF8BD,
+ 0x8037, 0xF88A,
+ 0x803A, 0xF858,
+ 0x803D, 0xF826,
+ 0x8040, 0xF7F4,
+ 0x8043, 0xF7C2,
+ 0x8047, 0xF790,
+ 0x804A, 0xF75D,
+ 0x804E, 0xF72B,
+ 0x8051, 0xF6F9,
+ 0x8055, 0xF6C7,
+ 0x8058, 0xF695,
+ 0x805C, 0xF663,
+ 0x8060, 0xF631,
+ 0x8064, 0xF5FF,
+ 0x8068, 0xF5CC,
+ 0x806C, 0xF59A,
+ 0x8070, 0xF568,
+ 0x8074, 0xF536,
+ 0x8078, 0xF504,
+ 0x807D, 0xF4D2,
+ 0x8081, 0xF4A0,
+ 0x8086, 0xF46E,
+ 0x808A, 0xF43C,
+ 0x808F, 0xF40A,
+ 0x8094, 0xF3D8,
+ 0x8098, 0xF3A6,
+ 0x809D, 0xF374,
+ 0x80A2, 0xF342,
+ 0x80A7, 0xF310,
+ 0x80AC, 0xF2DE,
+ 0x80B2, 0xF2AC,
+ 0x80B7, 0xF27A,
+ 0x80BC, 0xF248,
+ 0x80C2, 0xF216,
+ 0x80C7, 0xF1E4,
+ 0x80CD, 0xF1B2,
+ 0x80D2, 0xF180,
+ 0x80D8, 0xF14E,
+ 0x80DE, 0xF11C,
+ 0x80E4, 0xF0EA,
+ 0x80EA, 0xF0B8,
+ 0x80F0, 0xF086,
+ 0x80F6, 0xF054,
+ 0x80FC, 0xF022,
+ 0x8102, 0xEFF1,
+ 0x8109, 0xEFBF,
+ 0x810F, 0xEF8D,
+ 0x8116, 0xEF5B,
+ 0x811C, 0xEF29,
+ 0x8123, 0xEEF7,
+ 0x812A, 0xEEC6,
+ 0x8130, 0xEE94,
+ 0x8137, 0xEE62,
+ 0x813E, 0xEE30,
+ 0x8145, 0xEDFE,
+ 0x814C, 0xEDCD,
+ 0x8154, 0xED9B,
+ 0x815B, 0xED69,
+ 0x8162, 0xED37,
+ 0x816A, 0xED06,
+ 0x8171, 0xECD4,
+ 0x8179, 0xECA2,
+ 0x8180, 0xEC71,
+ 0x8188, 0xEC3F,
+ 0x8190, 0xEC0D,
+ 0x8198, 0xEBDC,
+ 0x81A0, 0xEBAA,
+ 0x81A8, 0xEB78,
+ 0x81B0, 0xEB47,
+ 0x81B8, 0xEB15,
+ 0x81C0, 0xEAE4,
+ 0x81C8, 0xEAB2,
+ 0x81D1, 0xEA80,
+ 0x81D9, 0xEA4F,
+ 0x81E2, 0xEA1D,
+ 0x81EB, 0xE9EC,
+ 0x81F3, 0xE9BA,
+ 0x81FC, 0xE989,
+ 0x8205, 0xE957,
+ 0x820E, 0xE926,
+ 0x8217, 0xE8F5,
+ 0x8220, 0xE8C3,
+ 0x8229, 0xE892,
+ 0x8232, 0xE860,
+ 0x823C, 0xE82F,
+ 0x8245, 0xE7FD,
+ 0x824F, 0xE7CC,
+ 0x8258, 0xE79B,
+ 0x8262, 0xE769,
+ 0x826B, 0xE738,
+ 0x8275, 0xE707,
+ 0x827F, 0xE6D5,
+ 0x8289, 0xE6A4,
+ 0x8293, 0xE673,
+ 0x829D, 0xE642,
+ 0x82A7, 0xE610,
+ 0x82B1, 0xE5DF,
+ 0x82BC, 0xE5AE,
+ 0x82C6, 0xE57D,
+ 0x82D0, 0xE54C,
+ 0x82DB, 0xE51B,
+ 0x82E6, 0xE4E9,
+ 0x82F0, 0xE4B8,
+ 0x82FB, 0xE487,
+ 0x8306, 0xE456,
+ 0x8311, 0xE425,
+ 0x831C, 0xE3F4,
+ 0x8327, 0xE3C3,
+ 0x8332, 0xE392,
+ 0x833D, 0xE361,
+ 0x8348, 0xE330,
+ 0x8354, 0xE2FF,
+ 0x835F, 0xE2CE,
+ 0x836B, 0xE29D,
+ 0x8376, 0xE26C,
+ 0x8382, 0xE23B,
+ 0x838E, 0xE20A,
+ 0x8399, 0xE1DA,
+ 0x83A5, 0xE1A9,
+ 0x83B1, 0xE178,
+ 0x83BD, 0xE147,
+ 0x83C9, 0xE116,
+ 0x83D6, 0xE0E6,
+ 0x83E2, 0xE0B5,
+ 0x83EE, 0xE084,
+ 0x83FA, 0xE053,
+ 0x8407, 0xE023,
+ 0x8414, 0xDFF2,
+ 0x8420, 0xDFC1,
+ 0x842D, 0xDF91,
+ 0x843A, 0xDF60,
+ 0x8446, 0xDF2F,
+ 0x8453, 0xDEFF,
+ 0x8460, 0xDECE,
+ 0x846D, 0xDE9E,
+ 0x847B, 0xDE6D,
+ 0x8488, 0xDE3D,
+ 0x8495, 0xDE0C,
+ 0x84A2, 0xDDDC,
+ 0x84B0, 0xDDAB,
+ 0x84BD, 0xDD7B,
+ 0x84CB, 0xDD4B,
+ 0x84D9, 0xDD1A,
+ 0x84E6, 0xDCEA,
+ 0x84F4, 0xDCBA,
+ 0x8502, 0xDC89,
+ 0x8510, 0xDC59,
+ 0x851E, 0xDC29,
+ 0x852C, 0xDBF8,
+ 0x853A, 0xDBC8,
+ 0x8549, 0xDB98,
+ 0x8557, 0xDB68,
+ 0x8565, 0xDB38,
+ 0x8574, 0xDB08,
+ 0x8582, 0xDAD7,
+ 0x8591, 0xDAA7,
+ 0x85A0, 0xDA77,
+ 0x85AF, 0xDA47,
+ 0x85BD, 0xDA17,
+ 0x85CC, 0xD9E7,
+ 0x85DB, 0xD9B7,
+ 0x85EA, 0xD987,
+ 0x85FA, 0xD957,
+ 0x8609, 0xD927,
+ 0x8618, 0xD8F8,
+ 0x8627, 0xD8C8,
+ 0x8637, 0xD898,
+ 0x8646, 0xD868,
+ 0x8656, 0xD838,
+ 0x8666, 0xD809,
+ 0x8675, 0xD7D9,
+ 0x8685, 0xD7A9,
+ 0x8695, 0xD779,
+ 0x86A5, 0xD74A,
+ 0x86B5, 0xD71A,
+ 0x86C5, 0xD6EA,
+ 0x86D5, 0xD6BB,
+ 0x86E6, 0xD68B,
+ 0x86F6, 0xD65C,
+ 0x8706, 0xD62C,
+ 0x8717, 0xD5FD,
+ 0x8727, 0xD5CD,
+ 0x8738, 0xD59E,
+ 0x8749, 0xD56E,
+ 0x8759, 0xD53F,
+ 0x876A, 0xD510,
+ 0x877B, 0xD4E0,
+ 0x878C, 0xD4B1,
+ 0x879D, 0xD482,
+ 0x87AE, 0xD452,
+ 0x87BF, 0xD423,
+ 0x87D1, 0xD3F4,
+ 0x87E2, 0xD3C5,
+ 0x87F3, 0xD396,
+ 0x8805, 0xD367,
+ 0x8816, 0xD337,
+ 0x8828, 0xD308,
+ 0x883A, 0xD2D9,
+ 0x884B, 0xD2AA,
+ 0x885D, 0xD27B,
+ 0x886F, 0xD24C,
+ 0x8881, 0xD21D,
+ 0x8893, 0xD1EE,
+ 0x88A5, 0xD1C0,
+ 0x88B8, 0xD191,
+ 0x88CA, 0xD162,
+ 0x88DC, 0xD133,
+ 0x88EF, 0xD104,
+ 0x8901, 0xD0D6,
+ 0x8914, 0xD0A7,
+ 0x8926, 0xD078,
+ 0x8939, 0xD04A,
+ 0x894C, 0xD01B,
+ 0x895F, 0xCFEC,
+ 0x8971, 0xCFBE,
+ 0x8984, 0xCF8F,
+ 0x8997, 0xCF61,
+ 0x89AB, 0xCF32,
+ 0x89BE, 0xCF04,
+ 0x89D1, 0xCED5,
+ 0x89E4, 0xCEA7,
+ 0x89F8, 0xCE79,
+ 0x8A0B, 0xCE4A,
+ 0x8A1F, 0xCE1C,
+ 0x8A33, 0xCDEE,
+ 0x8A46, 0xCDBF,
+ 0x8A5A, 0xCD91,
+ 0x8A6E, 0xCD63,
+ 0x8A82, 0xCD35,
+ 0x8A96, 0xCD07,
+ 0x8AAA, 0xCCD9,
+ 0x8ABE, 0xCCAB,
+ 0x8AD2, 0xCC7D,
+ 0x8AE6, 0xCC4F,
+ 0x8AFB, 0xCC21,
+ 0x8B0F, 0xCBF3,
+ 0x8B24, 0xCBC5,
+ 0x8B38, 0xCB97,
+ 0x8B4D, 0xCB69,
+ 0x8B61, 0xCB3B,
+ 0x8B76, 0xCB0D,
+ 0x8B8B, 0xCAE0,
+ 0x8BA0, 0xCAB2,
+ 0x8BB5, 0xCA84,
+ 0x8BCA, 0xCA57,
+ 0x8BDF, 0xCA29,
+ 0x8BF4, 0xC9FB,
+ 0x8C09, 0xC9CE,
+ 0x8C1F, 0xC9A0,
+ 0x8C34, 0xC973,
+ 0x8C4A, 0xC945,
+ 0x8C5F, 0xC918,
+ 0x8C75, 0xC8EB,
+ 0x8C8A, 0xC8BD,
+ 0x8CA0, 0xC890,
+ 0x8CB6, 0xC863,
+ 0x8CCC, 0xC835,
+ 0x8CE2, 0xC808,
+ 0x8CF8, 0xC7DB,
+ 0x8D0E, 0xC7AE,
+ 0x8D24, 0xC781,
+ 0x8D3A, 0xC754,
+ 0x8D50, 0xC727,
+ 0x8D67, 0xC6F9,
+ 0x8D7D, 0xC6CD,
+ 0x8D94, 0xC6A0,
+ 0x8DAA, 0xC673,
+ 0x8DC1, 0xC646,
+ 0x8DD8, 0xC619,
+ 0x8DEE, 0xC5EC,
+ 0x8E05, 0xC5BF,
+ 0x8E1C, 0xC593,
+ 0x8E33, 0xC566,
+ 0x8E4A, 0xC539,
+ 0x8E61, 0xC50D,
+ 0x8E79, 0xC4E0,
+ 0x8E90, 0xC4B3,
+ 0x8EA7, 0xC487,
+ 0x8EBE, 0xC45A,
+ 0x8ED6, 0xC42E,
+ 0x8EED, 0xC402,
+ 0x8F05, 0xC3D5,
+ 0x8F1D, 0xC3A9,
+ 0x8F34, 0xC37C,
+ 0x8F4C, 0xC350,
+ 0x8F64, 0xC324,
+ 0x8F7C, 0xC2F8,
+ 0x8F94, 0xC2CC,
+ 0x8FAC, 0xC29F,
+ 0x8FC4, 0xC273,
+ 0x8FDC, 0xC247,
+ 0x8FF5, 0xC21B,
+ 0x900D, 0xC1EF,
+ 0x9025, 0xC1C3,
+ 0x903E, 0xC197,
+ 0x9056, 0xC16C,
+ 0x906F, 0xC140,
+ 0x9088, 0xC114,
+ 0x90A0, 0xC0E8,
+ 0x90B9, 0xC0BC,
+ 0x90D2, 0xC091,
+ 0x90EB, 0xC065,
+ 0x9104, 0xC03A,
+ 0x911D, 0xC00E,
+ 0x9136, 0xBFE2,
+ 0x9150, 0xBFB7,
+ 0x9169, 0xBF8C,
+ 0x9182, 0xBF60,
+ 0x919C, 0xBF35,
+ 0x91B5, 0xBF09,
+ 0x91CF, 0xBEDE,
+ 0x91E8, 0xBEB3,
+ 0x9202, 0xBE88,
+ 0x921C, 0xBE5D,
+ 0x9235, 0xBE31,
+ 0x924F, 0xBE06,
+ 0x9269, 0xBDDB,
+ 0x9283, 0xBDB0,
+ 0x929D, 0xBD85,
+ 0x92B7, 0xBD5A,
+ 0x92D2, 0xBD2F,
+ 0x92EC, 0xBD05,
+ 0x9306, 0xBCDA,
+ 0x9321, 0xBCAF,
+ 0x933B, 0xBC84,
+ 0x9356, 0xBC5A,
+ 0x9370, 0xBC2F,
+ 0x938B, 0xBC04,
+ 0x93A6, 0xBBDA,
+ 0x93C0, 0xBBAF,
+ 0x93DB, 0xBB85,
+ 0x93F6, 0xBB5A,
+ 0x9411, 0xBB30,
+ 0x942C, 0xBB05,
+ 0x9447, 0xBADB,
+ 0x9463, 0xBAB1,
+ 0x947E, 0xBA87,
+ 0x9499, 0xBA5C,
+ 0x94B5, 0xBA32,
+ 0x94D0, 0xBA08,
+ 0x94EC, 0xB9DE,
+ 0x9507, 0xB9B4,
+ 0x9523, 0xB98A,
+ 0x953E, 0xB960,
+ 0x955A, 0xB936,
+ 0x9576, 0xB90C,
+ 0x9592, 0xB8E3,
+ 0x95AE, 0xB8B9,
+ 0x95CA, 0xB88F,
+ 0x95E6, 0xB865,
+ 0x9602, 0xB83C,
+ 0x961E, 0xB812,
+ 0x963B, 0xB7E9,
+ 0x9657, 0xB7BF,
+ 0x9673, 0xB796,
+ 0x9690, 0xB76C,
+ 0x96AC, 0xB743,
+ 0x96C9, 0xB719,
+ 0x96E6, 0xB6F0,
+ 0x9702, 0xB6C7,
+ 0x971F, 0xB69E,
+ 0x973C, 0xB675,
+ 0x9759, 0xB64B,
+ 0x9776, 0xB622,
+ 0x9793, 0xB5F9,
+ 0x97B0, 0xB5D0,
+ 0x97CD, 0xB5A7,
+ 0x97EA, 0xB57E,
+ 0x9808, 0xB556,
+ 0x9825, 0xB52D,
+ 0x9842, 0xB504,
+ 0x9860, 0xB4DB,
+ 0x987D, 0xB4B3,
+ 0x989B, 0xB48A,
+ 0x98B9, 0xB461,
+ 0x98D6, 0xB439,
+ 0x98F4, 0xB410,
+ 0x9912, 0xB3E8,
+ 0x9930, 0xB3C0,
+ 0x994E, 0xB397,
+ 0x996C, 0xB36F,
+ 0x998A, 0xB347,
+ 0x99A8, 0xB31E,
+ 0x99C6, 0xB2F6,
+ 0x99E5, 0xB2CE,
+ 0x9A03, 0xB2A6,
+ 0x9A22, 0xB27E,
+ 0x9A40, 0xB256,
+ 0x9A5F, 0xB22E,
+ 0x9A7D, 0xB206,
+ 0x9A9C, 0xB1DE,
+ 0x9ABA, 0xB1B7,
+ 0x9AD9, 0xB18F,
+ 0x9AF8, 0xB167,
+ 0x9B17, 0xB140,
+ 0x9B36, 0xB118,
+ 0x9B55, 0xB0F0,
+ 0x9B74, 0xB0C9,
+ 0x9B93, 0xB0A1,
+ 0x9BB2, 0xB07A,
+ 0x9BD2, 0xB053,
+ 0x9BF1, 0xB02B,
+ 0x9C10, 0xB004,
+ 0x9C30, 0xAFDD,
+ 0x9C4F, 0xAFB6,
+ 0x9C6F, 0xAF8F,
+ 0x9C8E, 0xAF68,
+ 0x9CAE, 0xAF40,
+ 0x9CCE, 0xAF1A,
+ 0x9CEE, 0xAEF3,
+ 0x9D0D, 0xAECC,
+ 0x9D2D, 0xAEA5,
+ 0x9D4D, 0xAE7E,
+ 0x9D6D, 0xAE57,
+ 0x9D8E, 0xAE31,
+ 0x9DAE, 0xAE0A,
+ 0x9DCE, 0xADE3,
+ 0x9DEE, 0xADBD,
+ 0x9E0E, 0xAD96,
+ 0x9E2F, 0xAD70,
+ 0x9E4F, 0xAD4A,
+ 0x9E70, 0xAD23,
+ 0x9E90, 0xACFD,
+ 0x9EB1, 0xACD7,
+ 0x9ED2, 0xACB1,
+ 0x9EF2, 0xAC8A,
+ 0x9F13, 0xAC64,
+ 0x9F34, 0xAC3E,
+ 0x9F55, 0xAC18,
+ 0x9F76, 0xABF2,
+ 0x9F97, 0xABCC,
+ 0x9FB8, 0xABA7,
+ 0x9FD9, 0xAB81,
+ 0x9FFB, 0xAB5B,
+ 0xA01C, 0xAB35,
+ 0xA03D, 0xAB10,
+ 0xA05F, 0xAAEA,
+ 0xA080, 0xAAC5,
+ 0xA0A1, 0xAA9F,
+ 0xA0C3, 0xAA7A,
+ 0xA0E5, 0xAA54,
+ 0xA106, 0xAA2F,
+ 0xA128, 0xAA0A,
+ 0xA14A, 0xA9E5,
+ 0xA16C, 0xA9BF,
+ 0xA18E, 0xA99A,
+ 0xA1AF, 0xA975,
+ 0xA1D2, 0xA950,
+ 0xA1F4, 0xA92B,
+ 0xA216, 0xA906,
+ 0xA238, 0xA8E2,
+ 0xA25A, 0xA8BD,
+ 0xA27C, 0xA898,
+ 0xA29F, 0xA873,
+ 0xA2C1, 0xA84F,
+ 0xA2E4, 0xA82A,
+ 0xA306, 0xA806,
+ 0xA329, 0xA7E1,
+ 0xA34B, 0xA7BD,
+ 0xA36E, 0xA798,
+ 0xA391, 0xA774,
+ 0xA3B4, 0xA750,
+ 0xA3D6, 0xA72B,
+ 0xA3F9, 0xA707,
+ 0xA41C, 0xA6E3,
+ 0xA43F, 0xA6BF,
+ 0xA462, 0xA69B,
+ 0xA486, 0xA677,
+ 0xA4A9, 0xA653,
+ 0xA4CC, 0xA62F,
+ 0xA4EF, 0xA60C,
+ 0xA513, 0xA5E8,
+ 0xA536, 0xA5C4,
+ 0xA55A, 0xA5A1,
+ 0xA57D, 0xA57D,
+ 0xA5A1, 0xA55A,
+ 0xA5C4, 0xA536,
+ 0xA5E8, 0xA513,
+ 0xA60C, 0xA4EF,
+ 0xA62F, 0xA4CC,
+ 0xA653, 0xA4A9,
+ 0xA677, 0xA486,
+ 0xA69B, 0xA462,
+ 0xA6BF, 0xA43F,
+ 0xA6E3, 0xA41C,
+ 0xA707, 0xA3F9,
+ 0xA72B, 0xA3D6,
+ 0xA750, 0xA3B4,
+ 0xA774, 0xA391,
+ 0xA798, 0xA36E,
+ 0xA7BD, 0xA34B,
+ 0xA7E1, 0xA329,
+ 0xA806, 0xA306,
+ 0xA82A, 0xA2E4,
+ 0xA84F, 0xA2C1,
+ 0xA873, 0xA29F,
+ 0xA898, 0xA27C,
+ 0xA8BD, 0xA25A,
+ 0xA8E2, 0xA238,
+ 0xA906, 0xA216,
+ 0xA92B, 0xA1F4,
+ 0xA950, 0xA1D2,
+ 0xA975, 0xA1AF,
+ 0xA99A, 0xA18E,
+ 0xA9BF, 0xA16C,
+ 0xA9E5, 0xA14A,
+ 0xAA0A, 0xA128,
+ 0xAA2F, 0xA106,
+ 0xAA54, 0xA0E5,
+ 0xAA7A, 0xA0C3,
+ 0xAA9F, 0xA0A1,
+ 0xAAC5, 0xA080,
+ 0xAAEA, 0xA05F,
+ 0xAB10, 0xA03D,
+ 0xAB35, 0xA01C,
+ 0xAB5B, 0x9FFB,
+ 0xAB81, 0x9FD9,
+ 0xABA7, 0x9FB8,
+ 0xABCC, 0x9F97,
+ 0xABF2, 0x9F76,
+ 0xAC18, 0x9F55,
+ 0xAC3E, 0x9F34,
+ 0xAC64, 0x9F13,
+ 0xAC8A, 0x9EF2,
+ 0xACB1, 0x9ED2,
+ 0xACD7, 0x9EB1,
+ 0xACFD, 0x9E90,
+ 0xAD23, 0x9E70,
+ 0xAD4A, 0x9E4F,
+ 0xAD70, 0x9E2F,
+ 0xAD96, 0x9E0E,
+ 0xADBD, 0x9DEE,
+ 0xADE3, 0x9DCE,
+ 0xAE0A, 0x9DAE,
+ 0xAE31, 0x9D8E,
+ 0xAE57, 0x9D6D,
+ 0xAE7E, 0x9D4D,
+ 0xAEA5, 0x9D2D,
+ 0xAECC, 0x9D0D,
+ 0xAEF3, 0x9CEE,
+ 0xAF1A, 0x9CCE,
+ 0xAF40, 0x9CAE,
+ 0xAF68, 0x9C8E,
+ 0xAF8F, 0x9C6F,
+ 0xAFB6, 0x9C4F,
+ 0xAFDD, 0x9C30,
+ 0xB004, 0x9C10,
+ 0xB02B, 0x9BF1,
+ 0xB053, 0x9BD2,
+ 0xB07A, 0x9BB2,
+ 0xB0A1, 0x9B93,
+ 0xB0C9, 0x9B74,
+ 0xB0F0, 0x9B55,
+ 0xB118, 0x9B36,
+ 0xB140, 0x9B17,
+ 0xB167, 0x9AF8,
+ 0xB18F, 0x9AD9,
+ 0xB1B7, 0x9ABA,
+ 0xB1DE, 0x9A9C,
+ 0xB206, 0x9A7D,
+ 0xB22E, 0x9A5F,
+ 0xB256, 0x9A40,
+ 0xB27E, 0x9A22,
+ 0xB2A6, 0x9A03,
+ 0xB2CE, 0x99E5,
+ 0xB2F6, 0x99C6,
+ 0xB31E, 0x99A8,
+ 0xB347, 0x998A,
+ 0xB36F, 0x996C,
+ 0xB397, 0x994E,
+ 0xB3C0, 0x9930,
+ 0xB3E8, 0x9912,
+ 0xB410, 0x98F4,
+ 0xB439, 0x98D6,
+ 0xB461, 0x98B9,
+ 0xB48A, 0x989B,
+ 0xB4B3, 0x987D,
+ 0xB4DB, 0x9860,
+ 0xB504, 0x9842,
+ 0xB52D, 0x9825,
+ 0xB556, 0x9808,
+ 0xB57E, 0x97EA,
+ 0xB5A7, 0x97CD,
+ 0xB5D0, 0x97B0,
+ 0xB5F9, 0x9793,
+ 0xB622, 0x9776,
+ 0xB64B, 0x9759,
+ 0xB675, 0x973C,
+ 0xB69E, 0x971F,
+ 0xB6C7, 0x9702,
+ 0xB6F0, 0x96E6,
+ 0xB719, 0x96C9,
+ 0xB743, 0x96AC,
+ 0xB76C, 0x9690,
+ 0xB796, 0x9673,
+ 0xB7BF, 0x9657,
+ 0xB7E9, 0x963B,
+ 0xB812, 0x961E,
+ 0xB83C, 0x9602,
+ 0xB865, 0x95E6,
+ 0xB88F, 0x95CA,
+ 0xB8B9, 0x95AE,
+ 0xB8E3, 0x9592,
+ 0xB90C, 0x9576,
+ 0xB936, 0x955A,
+ 0xB960, 0x953E,
+ 0xB98A, 0x9523,
+ 0xB9B4, 0x9507,
+ 0xB9DE, 0x94EC,
+ 0xBA08, 0x94D0,
+ 0xBA32, 0x94B5,
+ 0xBA5C, 0x9499,
+ 0xBA87, 0x947E,
+ 0xBAB1, 0x9463,
+ 0xBADB, 0x9447,
+ 0xBB05, 0x942C,
+ 0xBB30, 0x9411,
+ 0xBB5A, 0x93F6,
+ 0xBB85, 0x93DB,
+ 0xBBAF, 0x93C0,
+ 0xBBDA, 0x93A6,
+ 0xBC04, 0x938B,
+ 0xBC2F, 0x9370,
+ 0xBC5A, 0x9356,
+ 0xBC84, 0x933B,
+ 0xBCAF, 0x9321,
+ 0xBCDA, 0x9306,
+ 0xBD05, 0x92EC,
+ 0xBD2F, 0x92D2,
+ 0xBD5A, 0x92B7,
+ 0xBD85, 0x929D,
+ 0xBDB0, 0x9283,
+ 0xBDDB, 0x9269,
+ 0xBE06, 0x924F,
+ 0xBE31, 0x9235,
+ 0xBE5D, 0x921C,
+ 0xBE88, 0x9202,
+ 0xBEB3, 0x91E8,
+ 0xBEDE, 0x91CF,
+ 0xBF09, 0x91B5,
+ 0xBF35, 0x919C,
+ 0xBF60, 0x9182,
+ 0xBF8C, 0x9169,
+ 0xBFB7, 0x9150,
+ 0xBFE2, 0x9136,
+ 0xC00E, 0x911D,
+ 0xC03A, 0x9104,
+ 0xC065, 0x90EB,
+ 0xC091, 0x90D2,
+ 0xC0BC, 0x90B9,
+ 0xC0E8, 0x90A0,
+ 0xC114, 0x9088,
+ 0xC140, 0x906F,
+ 0xC16C, 0x9056,
+ 0xC197, 0x903E,
+ 0xC1C3, 0x9025,
+ 0xC1EF, 0x900D,
+ 0xC21B, 0x8FF5,
+ 0xC247, 0x8FDC,
+ 0xC273, 0x8FC4,
+ 0xC29F, 0x8FAC,
+ 0xC2CC, 0x8F94,
+ 0xC2F8, 0x8F7C,
+ 0xC324, 0x8F64,
+ 0xC350, 0x8F4C,
+ 0xC37C, 0x8F34,
+ 0xC3A9, 0x8F1D,
+ 0xC3D5, 0x8F05,
+ 0xC402, 0x8EED,
+ 0xC42E, 0x8ED6,
+ 0xC45A, 0x8EBE,
+ 0xC487, 0x8EA7,
+ 0xC4B3, 0x8E90,
+ 0xC4E0, 0x8E79,
+ 0xC50D, 0x8E61,
+ 0xC539, 0x8E4A,
+ 0xC566, 0x8E33,
+ 0xC593, 0x8E1C,
+ 0xC5BF, 0x8E05,
+ 0xC5EC, 0x8DEE,
+ 0xC619, 0x8DD8,
+ 0xC646, 0x8DC1,
+ 0xC673, 0x8DAA,
+ 0xC6A0, 0x8D94,
+ 0xC6CD, 0x8D7D,
+ 0xC6F9, 0x8D67,
+ 0xC727, 0x8D50,
+ 0xC754, 0x8D3A,
+ 0xC781, 0x8D24,
+ 0xC7AE, 0x8D0E,
+ 0xC7DB, 0x8CF8,
+ 0xC808, 0x8CE2,
+ 0xC835, 0x8CCC,
+ 0xC863, 0x8CB6,
+ 0xC890, 0x8CA0,
+ 0xC8BD, 0x8C8A,
+ 0xC8EB, 0x8C75,
+ 0xC918, 0x8C5F,
+ 0xC945, 0x8C4A,
+ 0xC973, 0x8C34,
+ 0xC9A0, 0x8C1F,
+ 0xC9CE, 0x8C09,
+ 0xC9FB, 0x8BF4,
+ 0xCA29, 0x8BDF,
+ 0xCA57, 0x8BCA,
+ 0xCA84, 0x8BB5,
+ 0xCAB2, 0x8BA0,
+ 0xCAE0, 0x8B8B,
+ 0xCB0D, 0x8B76,
+ 0xCB3B, 0x8B61,
+ 0xCB69, 0x8B4D,
+ 0xCB97, 0x8B38,
+ 0xCBC5, 0x8B24,
+ 0xCBF3, 0x8B0F,
+ 0xCC21, 0x8AFB,
+ 0xCC4F, 0x8AE6,
+ 0xCC7D, 0x8AD2,
+ 0xCCAB, 0x8ABE,
+ 0xCCD9, 0x8AAA,
+ 0xCD07, 0x8A96,
+ 0xCD35, 0x8A82,
+ 0xCD63, 0x8A6E,
+ 0xCD91, 0x8A5A,
+ 0xCDBF, 0x8A46,
+ 0xCDEE, 0x8A33,
+ 0xCE1C, 0x8A1F,
+ 0xCE4A, 0x8A0B,
+ 0xCE79, 0x89F8,
+ 0xCEA7, 0x89E4,
+ 0xCED5, 0x89D1,
+ 0xCF04, 0x89BE,
+ 0xCF32, 0x89AB,
+ 0xCF61, 0x8997,
+ 0xCF8F, 0x8984,
+ 0xCFBE, 0x8971,
+ 0xCFEC, 0x895F,
+ 0xD01B, 0x894C,
+ 0xD04A, 0x8939,
+ 0xD078, 0x8926,
+ 0xD0A7, 0x8914,
+ 0xD0D6, 0x8901,
+ 0xD104, 0x88EF,
+ 0xD133, 0x88DC,
+ 0xD162, 0x88CA,
+ 0xD191, 0x88B8,
+ 0xD1C0, 0x88A5,
+ 0xD1EE, 0x8893,
+ 0xD21D, 0x8881,
+ 0xD24C, 0x886F,
+ 0xD27B, 0x885D,
+ 0xD2AA, 0x884B,
+ 0xD2D9, 0x883A,
+ 0xD308, 0x8828,
+ 0xD337, 0x8816,
+ 0xD367, 0x8805,
+ 0xD396, 0x87F3,
+ 0xD3C5, 0x87E2,
+ 0xD3F4, 0x87D1,
+ 0xD423, 0x87BF,
+ 0xD452, 0x87AE,
+ 0xD482, 0x879D,
+ 0xD4B1, 0x878C,
+ 0xD4E0, 0x877B,
+ 0xD510, 0x876A,
+ 0xD53F, 0x8759,
+ 0xD56E, 0x8749,
+ 0xD59E, 0x8738,
+ 0xD5CD, 0x8727,
+ 0xD5FD, 0x8717,
+ 0xD62C, 0x8706,
+ 0xD65C, 0x86F6,
+ 0xD68B, 0x86E6,
+ 0xD6BB, 0x86D5,
+ 0xD6EA, 0x86C5,
+ 0xD71A, 0x86B5,
+ 0xD74A, 0x86A5,
+ 0xD779, 0x8695,
+ 0xD7A9, 0x8685,
+ 0xD7D9, 0x8675,
+ 0xD809, 0x8666,
+ 0xD838, 0x8656,
+ 0xD868, 0x8646,
+ 0xD898, 0x8637,
+ 0xD8C8, 0x8627,
+ 0xD8F8, 0x8618,
+ 0xD927, 0x8609,
+ 0xD957, 0x85FA,
+ 0xD987, 0x85EA,
+ 0xD9B7, 0x85DB,
+ 0xD9E7, 0x85CC,
+ 0xDA17, 0x85BD,
+ 0xDA47, 0x85AF,
+ 0xDA77, 0x85A0,
+ 0xDAA7, 0x8591,
+ 0xDAD7, 0x8582,
+ 0xDB08, 0x8574,
+ 0xDB38, 0x8565,
+ 0xDB68, 0x8557,
+ 0xDB98, 0x8549,
+ 0xDBC8, 0x853A,
+ 0xDBF8, 0x852C,
+ 0xDC29, 0x851E,
+ 0xDC59, 0x8510,
+ 0xDC89, 0x8502,
+ 0xDCBA, 0x84F4,
+ 0xDCEA, 0x84E6,
+ 0xDD1A, 0x84D9,
+ 0xDD4B, 0x84CB,
+ 0xDD7B, 0x84BD,
+ 0xDDAB, 0x84B0,
+ 0xDDDC, 0x84A2,
+ 0xDE0C, 0x8495,
+ 0xDE3D, 0x8488,
+ 0xDE6D, 0x847B,
+ 0xDE9E, 0x846D,
+ 0xDECE, 0x8460,
+ 0xDEFF, 0x8453,
+ 0xDF2F, 0x8446,
+ 0xDF60, 0x843A,
+ 0xDF91, 0x842D,
+ 0xDFC1, 0x8420,
+ 0xDFF2, 0x8414,
+ 0xE023, 0x8407,
+ 0xE053, 0x83FA,
+ 0xE084, 0x83EE,
+ 0xE0B5, 0x83E2,
+ 0xE0E6, 0x83D6,
+ 0xE116, 0x83C9,
+ 0xE147, 0x83BD,
+ 0xE178, 0x83B1,
+ 0xE1A9, 0x83A5,
+ 0xE1DA, 0x8399,
+ 0xE20A, 0x838E,
+ 0xE23B, 0x8382,
+ 0xE26C, 0x8376,
+ 0xE29D, 0x836B,
+ 0xE2CE, 0x835F,
+ 0xE2FF, 0x8354,
+ 0xE330, 0x8348,
+ 0xE361, 0x833D,
+ 0xE392, 0x8332,
+ 0xE3C3, 0x8327,
+ 0xE3F4, 0x831C,
+ 0xE425, 0x8311,
+ 0xE456, 0x8306,
+ 0xE487, 0x82FB,
+ 0xE4B8, 0x82F0,
+ 0xE4E9, 0x82E6,
+ 0xE51B, 0x82DB,
+ 0xE54C, 0x82D0,
+ 0xE57D, 0x82C6,
+ 0xE5AE, 0x82BC,
+ 0xE5DF, 0x82B1,
+ 0xE610, 0x82A7,
+ 0xE642, 0x829D,
+ 0xE673, 0x8293,
+ 0xE6A4, 0x8289,
+ 0xE6D5, 0x827F,
+ 0xE707, 0x8275,
+ 0xE738, 0x826B,
+ 0xE769, 0x8262,
+ 0xE79B, 0x8258,
+ 0xE7CC, 0x824F,
+ 0xE7FD, 0x8245,
+ 0xE82F, 0x823C,
+ 0xE860, 0x8232,
+ 0xE892, 0x8229,
+ 0xE8C3, 0x8220,
+ 0xE8F5, 0x8217,
+ 0xE926, 0x820E,
+ 0xE957, 0x8205,
+ 0xE989, 0x81FC,
+ 0xE9BA, 0x81F3,
+ 0xE9EC, 0x81EB,
+ 0xEA1D, 0x81E2,
+ 0xEA4F, 0x81D9,
+ 0xEA80, 0x81D1,
+ 0xEAB2, 0x81C8,
+ 0xEAE4, 0x81C0,
+ 0xEB15, 0x81B8,
+ 0xEB47, 0x81B0,
+ 0xEB78, 0x81A8,
+ 0xEBAA, 0x81A0,
+ 0xEBDC, 0x8198,
+ 0xEC0D, 0x8190,
+ 0xEC3F, 0x8188,
+ 0xEC71, 0x8180,
+ 0xECA2, 0x8179,
+ 0xECD4, 0x8171,
+ 0xED06, 0x816A,
+ 0xED37, 0x8162,
+ 0xED69, 0x815B,
+ 0xED9B, 0x8154,
+ 0xEDCD, 0x814C,
+ 0xEDFE, 0x8145,
+ 0xEE30, 0x813E,
+ 0xEE62, 0x8137,
+ 0xEE94, 0x8130,
+ 0xEEC6, 0x812A,
+ 0xEEF7, 0x8123,
+ 0xEF29, 0x811C,
+ 0xEF5B, 0x8116,
+ 0xEF8D, 0x810F,
+ 0xEFBF, 0x8109,
+ 0xEFF1, 0x8102,
+ 0xF022, 0x80FC,
+ 0xF054, 0x80F6,
+ 0xF086, 0x80F0,
+ 0xF0B8, 0x80EA,
+ 0xF0EA, 0x80E4,
+ 0xF11C, 0x80DE,
+ 0xF14E, 0x80D8,
+ 0xF180, 0x80D2,
+ 0xF1B2, 0x80CD,
+ 0xF1E4, 0x80C7,
+ 0xF216, 0x80C2,
+ 0xF248, 0x80BC,
+ 0xF27A, 0x80B7,
+ 0xF2AC, 0x80B2,
+ 0xF2DE, 0x80AC,
+ 0xF310, 0x80A7,
+ 0xF342, 0x80A2,
+ 0xF374, 0x809D,
+ 0xF3A6, 0x8098,
+ 0xF3D8, 0x8094,
+ 0xF40A, 0x808F,
+ 0xF43C, 0x808A,
+ 0xF46E, 0x8086,
+ 0xF4A0, 0x8081,
+ 0xF4D2, 0x807D,
+ 0xF504, 0x8078,
+ 0xF536, 0x8074,
+ 0xF568, 0x8070,
+ 0xF59A, 0x806C,
+ 0xF5CC, 0x8068,
+ 0xF5FF, 0x8064,
+ 0xF631, 0x8060,
+ 0xF663, 0x805C,
+ 0xF695, 0x8058,
+ 0xF6C7, 0x8055,
+ 0xF6F9, 0x8051,
+ 0xF72B, 0x804E,
+ 0xF75D, 0x804A,
+ 0xF790, 0x8047,
+ 0xF7C2, 0x8043,
+ 0xF7F4, 0x8040,
+ 0xF826, 0x803D,
+ 0xF858, 0x803A,
+ 0xF88A, 0x8037,
+ 0xF8BD, 0x8034,
+ 0xF8EF, 0x8031,
+ 0xF921, 0x802F,
+ 0xF953, 0x802C,
+ 0xF985, 0x8029,
+ 0xF9B8, 0x8027,
+ 0xF9EA, 0x8025,
+ 0xFA1C, 0x8022,
+ 0xFA4E, 0x8020,
+ 0xFA80, 0x801E,
+ 0xFAB3, 0x801C,
+ 0xFAE5, 0x801A,
+ 0xFB17, 0x8018,
+ 0xFB49, 0x8016,
+ 0xFB7C, 0x8014,
+ 0xFBAE, 0x8012,
+ 0xFBE0, 0x8011,
+ 0xFC12, 0x800F,
+ 0xFC45, 0x800D,
+ 0xFC77, 0x800C,
+ 0xFCA9, 0x800B,
+ 0xFCDB, 0x8009,
+ 0xFD0E, 0x8008,
+ 0xFD40, 0x8007,
+ 0xFD72, 0x8006,
+ 0xFDA4, 0x8005,
+ 0xFDD7, 0x8004,
+ 0xFE09, 0x8003,
+ 0xFE3B, 0x8003,
+ 0xFE6D, 0x8002,
+ 0xFEA0, 0x8001,
+ 0xFED2, 0x8001,
+ 0xFF04, 0x8000,
+ 0xFF36, 0x8000,
+ 0xFF69, 0x8000,
+ 0xFF9B, 0x8000,
+ 0xFFCD, 0x8000
+};
+
+
+/**
+* @} end of CFFT_CIFFT group
+*/
+
+/*
+* @brief Q15 table for reciprocal
+*/
+const q15_t ALIGN4 armRecipTableQ15[64] = {
+ 0x7F03, 0x7D13, 0x7B31, 0x795E, 0x7798, 0x75E0,
+ 0x7434, 0x7294, 0x70FF, 0x6F76, 0x6DF6, 0x6C82,
+ 0x6B16, 0x69B5, 0x685C, 0x670C, 0x65C4, 0x6484,
+ 0x634C, 0x621C, 0x60F3, 0x5FD0, 0x5EB5, 0x5DA0,
+ 0x5C91, 0x5B88, 0x5A85, 0x5988, 0x5890, 0x579E,
+ 0x56B0, 0x55C8, 0x54E4, 0x5405, 0x532B, 0x5255,
+ 0x5183, 0x50B6, 0x4FEC, 0x4F26, 0x4E64, 0x4DA6,
+ 0x4CEC, 0x4C34, 0x4B81, 0x4AD0, 0x4A23, 0x4978,
+ 0x48D1, 0x482D, 0x478C, 0x46ED, 0x4651, 0x45B8,
+ 0x4521, 0x448D, 0x43FC, 0x436C, 0x42DF, 0x4255,
+ 0x41CC, 0x4146, 0x40C2, 0x4040
+};
+
+/*
+* @brief Q31 table for reciprocal
+*/
+const q31_t armRecipTableQ31[64] = {
+ 0x7F03F03F, 0x7D137420, 0x7B31E739, 0x795E9F94, 0x7798FD29, 0x75E06928,
+ 0x7434554D, 0x72943B4B, 0x70FF9C40, 0x6F760031, 0x6DF6F593, 0x6C8210E3,
+ 0x6B16EC3A, 0x69B526F6, 0x685C655F, 0x670C505D, 0x65C4952D, 0x6484E519,
+ 0x634CF53E, 0x621C7E4F, 0x60F33C61, 0x5FD0EEB3, 0x5EB55785, 0x5DA03BEB,
+ 0x5C9163A1, 0x5B8898E6, 0x5A85A85A, 0x598860DF, 0x58909373, 0x579E1318,
+ 0x56B0B4B8, 0x55C84F0B, 0x54E4BA80, 0x5405D124, 0x532B6E8F, 0x52556FD0,
+ 0x5183B35A, 0x50B618F3, 0x4FEC81A2, 0x4F26CFA2, 0x4E64E64E, 0x4DA6AA1D,
+ 0x4CEC008B, 0x4C34D010, 0x4B810016, 0x4AD078EF, 0x4A2323C4, 0x4978EA96,
+ 0x48D1B827, 0x482D77FE, 0x478C1657, 0x46ED801D, 0x4651A2E5, 0x45B86CE2,
+ 0x4521CCE1, 0x448DB244, 0x43FC0CFA, 0x436CCD78, 0x42DFE4B4, 0x42554426,
+ 0x41CCDDB6, 0x4146A3C6, 0x40C28923, 0x40408102
+};
+
+const uint16_t armBitRevIndexTable16[ARMBITREVINDEXTABLE__16_TABLE_LENGTH] =
+{
+ //8x2, size 20
+ 8,64, 24,72, 16,64, 40,80, 32,64, 56,88, 48,72, 88,104, 72,96, 104,112
+};
+
+const uint16_t armBitRevIndexTable32[ARMBITREVINDEXTABLE__32_TABLE_LENGTH] =
+{
+ //8x4, size 48
+ 8,64, 16,128, 24,192, 32,64, 40,72, 48,136, 56,200, 64,128, 72,80, 88,208,
+ 80,144, 96,192, 104,208, 112,152, 120,216, 136,192, 144,160, 168,208,
+ 152,224, 176,208, 184,232, 216,240, 200,224, 232,240
+};
+
+const uint16_t armBitRevIndexTable64[ARMBITREVINDEXTABLE__64_TABLE_LENGTH] =
+{
+ //radix 8, size 56
+ 8,64, 16,128, 24,192, 32,256, 40,320, 48,384, 56,448, 80,136, 88,200,
+ 96,264, 104,328, 112,392, 120,456, 152,208, 160,272, 168,336, 176,400,
+ 184,464, 224,280, 232,344, 240,408, 248,472, 296,352, 304,416, 312,480,
+ 368,424, 376,488, 440,496
+};
+
+const uint16_t armBitRevIndexTable128[ARMBITREVINDEXTABLE_128_TABLE_LENGTH] =
+{
+ //8x2, size 208
+ 8,512, 16,64, 24,576, 32,128, 40,640, 48,192, 56,704, 64,256, 72,768,
+ 80,320, 88,832, 96,384, 104,896, 112,448, 120,960, 128,512, 136,520,
+ 144,768, 152,584, 160,520, 168,648, 176,200, 184,712, 192,264, 200,776,
+ 208,328, 216,840, 224,392, 232,904, 240,456, 248,968, 264,528, 272,320,
+ 280,592, 288,768, 296,656, 304,328, 312,720, 328,784, 344,848, 352,400,
+ 360,912, 368,464, 376,976, 384,576, 392,536, 400,832, 408,600, 416,584,
+ 424,664, 432,840, 440,728, 448,592, 456,792, 464,848, 472,856, 480,600,
+ 488,920, 496,856, 504,984, 520,544, 528,576, 536,608, 552,672, 560,608,
+ 568,736, 576,768, 584,800, 592,832, 600,864, 608,800, 616,928, 624,864,
+ 632,992, 648,672, 656,896, 664,928, 688,904, 696,744, 704,896, 712,808,
+ 720,912, 728,872, 736,928, 744,936, 752,920, 760,1000, 776,800, 784,832,
+ 792,864, 808,904, 816,864, 824,920, 840,864, 856,880, 872,944, 888,1008,
+ 904,928, 912,960, 920,992, 944,968, 952,1000, 968,992, 984,1008
+};
+
+const uint16_t armBitRevIndexTable256[ARMBITREVINDEXTABLE_256_TABLE_LENGTH] =
+{
+ //8x4, size 440
+ 8,512, 16,1024, 24,1536, 32,64, 40,576, 48,1088, 56,1600, 64,128, 72,640,
+ 80,1152, 88,1664, 96,192, 104,704, 112,1216, 120,1728, 128,256, 136,768,
+ 144,1280, 152,1792, 160,320, 168,832, 176,1344, 184,1856, 192,384,
+ 200,896, 208,1408, 216,1920, 224,448, 232,960, 240,1472, 248,1984,
+ 256,512, 264,520, 272,1032, 280,1544, 288,640, 296,584, 304,1096, 312,1608,
+ 320,768, 328,648, 336,1160, 344,1672, 352,896, 360,712, 368,1224, 376,1736,
+ 384,520, 392,776, 400,1288, 408,1800, 416,648, 424,840, 432,1352, 440,1864,
+ 448,776, 456,904, 464,1416, 472,1928, 480,904, 488,968, 496,1480, 504,1992,
+ 520,528, 512,1024, 528,1040, 536,1552, 544,1152, 552,592, 560,1104,
+ 568,1616, 576,1280, 584,656, 592,1168, 600,1680, 608,1408, 616,720,
+ 624,1232, 632,1744, 640,1032, 648,784, 656,1296, 664,1808, 672,1160,
+ 680,848, 688,1360, 696,1872, 704,1288, 712,912, 720,1424, 728,1936,
+ 736,1416, 744,976, 752,1488, 760,2000, 768,1536, 776,1552, 784,1048,
+ 792,1560, 800,1664, 808,1680, 816,1112, 824,1624, 832,1792, 840,1808,
+ 848,1176, 856,1688, 864,1920, 872,1936, 880,1240, 888,1752, 896,1544,
+ 904,1560, 912,1304, 920,1816, 928,1672, 936,1688, 944,1368, 952,1880,
+ 960,1800, 968,1816, 976,1432, 984,1944, 992,1928, 1000,1944, 1008,1496,
+ 1016,2008, 1032,1152, 1040,1056, 1048,1568, 1064,1408, 1072,1120,
+ 1080,1632, 1088,1536, 1096,1160, 1104,1184, 1112,1696, 1120,1552,
+ 1128,1416, 1136,1248, 1144,1760, 1160,1664, 1168,1312, 1176,1824,
+ 1184,1544, 1192,1920, 1200,1376, 1208,1888, 1216,1568, 1224,1672,
+ 1232,1440, 1240,1952, 1248,1560, 1256,1928, 1264,1504, 1272,2016,
+ 1288,1312, 1296,1408, 1304,1576, 1320,1424, 1328,1416, 1336,1640,
+ 1344,1792, 1352,1824, 1360,1920, 1368,1704, 1376,1800, 1384,1432,
+ 1392,1928, 1400,1768, 1416,1680, 1432,1832, 1440,1576, 1448,1936,
+ 1456,1832, 1464,1896, 1472,1808, 1480,1688, 1488,1936, 1496,1960,
+ 1504,1816, 1512,1944, 1520,1944, 1528,2024, 1560,1584, 1592,1648,
+ 1600,1792, 1608,1920, 1616,1800, 1624,1712, 1632,1808, 1640,1936,
+ 1648,1816, 1656,1776, 1672,1696, 1688,1840, 1704,1952, 1712,1928,
+ 1720,1904, 1728,1824, 1736,1952, 1744,1832, 1752,1968, 1760,1840,
+ 1768,1960, 1776,1944, 1784,2032, 1864,1872, 1848,1944, 1872,1888,
+ 1880,1904, 1888,1984, 1896,2000, 1912,2032, 1904,2016, 1976,2032,
+ 1960,1968, 2008,2032, 1992,2016, 2024,2032
+};
+
+const uint16_t armBitRevIndexTable512[ARMBITREVINDEXTABLE_512_TABLE_LENGTH] =
+{
+ //radix 8, size 448
+ 8,512, 16,1024, 24,1536, 32,2048, 40,2560, 48,3072, 56,3584, 72,576,
+ 80,1088, 88,1600, 96,2112, 104,2624, 112,3136, 120,3648, 136,640, 144,1152,
+ 152,1664, 160,2176, 168,2688, 176,3200, 184,3712, 200,704, 208,1216,
+ 216,1728, 224,2240, 232,2752, 240,3264, 248,3776, 264,768, 272,1280,
+ 280,1792, 288,2304, 296,2816, 304,3328, 312,3840, 328,832, 336,1344,
+ 344,1856, 352,2368, 360,2880, 368,3392, 376,3904, 392,896, 400,1408,
+ 408,1920, 416,2432, 424,2944, 432,3456, 440,3968, 456,960, 464,1472,
+ 472,1984, 480,2496, 488,3008, 496,3520, 504,4032, 528,1032, 536,1544,
+ 544,2056, 552,2568, 560,3080, 568,3592, 592,1096, 600,1608, 608,2120,
+ 616,2632, 624,3144, 632,3656, 656,1160, 664,1672, 672,2184, 680,2696,
+ 688,3208, 696,3720, 720,1224, 728,1736, 736,2248, 744,2760, 752,3272,
+ 760,3784, 784,1288, 792,1800, 800,2312, 808,2824, 816,3336, 824,3848,
+ 848,1352, 856,1864, 864,2376, 872,2888, 880,3400, 888,3912, 912,1416,
+ 920,1928, 928,2440, 936,2952, 944,3464, 952,3976, 976,1480, 984,1992,
+ 992,2504, 1000,3016, 1008,3528, 1016,4040, 1048,1552, 1056,2064, 1064,2576,
+ 1072,3088, 1080,3600, 1112,1616, 1120,2128, 1128,2640, 1136,3152,
+ 1144,3664, 1176,1680, 1184,2192, 1192,2704, 1200,3216, 1208,3728,
+ 1240,1744, 1248,2256, 1256,2768, 1264,3280, 1272,3792, 1304,1808,
+ 1312,2320, 1320,2832, 1328,3344, 1336,3856, 1368,1872, 1376,2384,
+ 1384,2896, 1392,3408, 1400,3920, 1432,1936, 1440,2448, 1448,2960,
+ 1456,3472, 1464,3984, 1496,2000, 1504,2512, 1512,3024, 1520,3536,
+ 1528,4048, 1568,2072, 1576,2584, 1584,3096, 1592,3608, 1632,2136,
+ 1640,2648, 1648,3160, 1656,3672, 1696,2200, 1704,2712, 1712,3224,
+ 1720,3736, 1760,2264, 1768,2776, 1776,3288, 1784,3800, 1824,2328,
+ 1832,2840, 1840,3352, 1848,3864, 1888,2392, 1896,2904, 1904,3416,
+ 1912,3928, 1952,2456, 1960,2968, 1968,3480, 1976,3992, 2016,2520,
+ 2024,3032, 2032,3544, 2040,4056, 2088,2592, 2096,3104, 2104,3616,
+ 2152,2656, 2160,3168, 2168,3680, 2216,2720, 2224,3232, 2232,3744,
+ 2280,2784, 2288,3296, 2296,3808, 2344,2848, 2352,3360, 2360,3872,
+ 2408,2912, 2416,3424, 2424,3936, 2472,2976, 2480,3488, 2488,4000,
+ 2536,3040, 2544,3552, 2552,4064, 2608,3112, 2616,3624, 2672,3176,
+ 2680,3688, 2736,3240, 2744,3752, 2800,3304, 2808,3816, 2864,3368,
+ 2872,3880, 2928,3432, 2936,3944, 2992,3496, 3000,4008, 3056,3560,
+ 3064,4072, 3128,3632, 3192,3696, 3256,3760, 3320,3824, 3384,3888,
+ 3448,3952, 3512,4016, 3576,4080
+};
+
+const uint16_t armBitRevIndexTable1024[ARMBITREVINDEXTABLE1024_TABLE_LENGTH] =
+{
+ //8x2, size 1800
+ 8,4096, 16,512, 24,4608, 32,1024, 40,5120, 48,1536, 56,5632, 64,2048,
+ 72,6144, 80,2560, 88,6656, 96,3072, 104,7168, 112,3584, 120,7680, 128,2048,
+ 136,4160, 144,576, 152,4672, 160,1088, 168,5184, 176,1600, 184,5696,
+ 192,2112, 200,6208, 208,2624, 216,6720, 224,3136, 232,7232, 240,3648,
+ 248,7744, 256,2048, 264,4224, 272,640, 280,4736, 288,1152, 296,5248,
+ 304,1664, 312,5760, 320,2176, 328,6272, 336,2688, 344,6784, 352,3200,
+ 360,7296, 368,3712, 376,7808, 384,2112, 392,4288, 400,704, 408,4800,
+ 416,1216, 424,5312, 432,1728, 440,5824, 448,2240, 456,6336, 464,2752,
+ 472,6848, 480,3264, 488,7360, 496,3776, 504,7872, 512,2048, 520,4352,
+ 528,768, 536,4864, 544,1280, 552,5376, 560,1792, 568,5888, 576,2304,
+ 584,6400, 592,2816, 600,6912, 608,3328, 616,7424, 624,3840, 632,7936,
+ 640,2176, 648,4416, 656,832, 664,4928, 672,1344, 680,5440, 688,1856,
+ 696,5952, 704,2368, 712,6464, 720,2880, 728,6976, 736,3392, 744,7488,
+ 752,3904, 760,8000, 768,2112, 776,4480, 784,896, 792,4992, 800,1408,
+ 808,5504, 816,1920, 824,6016, 832,2432, 840,6528, 848,2944, 856,7040,
+ 864,3456, 872,7552, 880,3968, 888,8064, 896,2240, 904,4544, 912,960,
+ 920,5056, 928,1472, 936,5568, 944,1984, 952,6080, 960,2496, 968,6592,
+ 976,3008, 984,7104, 992,3520, 1000,7616, 1008,4032, 1016,8128, 1024,4096,
+ 1032,4104, 1040,4352, 1048,4616, 1056,4104, 1064,5128, 1072,1544,
+ 1080,5640, 1088,2056, 1096,6152, 1104,2568, 1112,6664, 1120,3080,
+ 1128,7176, 1136,3592, 1144,7688, 1152,6144, 1160,4168, 1168,6400,
+ 1176,4680, 1184,6152, 1192,5192, 1200,1608, 1208,5704, 1216,2120,
+ 1224,6216, 1232,2632, 1240,6728, 1248,3144, 1256,7240, 1264,3656,
+ 1272,7752, 1280,4160, 1288,4232, 1296,4416, 1304,4744, 1312,4168,
+ 1320,5256, 1328,1672, 1336,5768, 1344,2184, 1352,6280, 1360,2696,
+ 1368,6792, 1376,3208, 1384,7304, 1392,3720, 1400,7816, 1408,6208,
+ 1416,4296, 1424,6464, 1432,4808, 1440,6216, 1448,5320, 1456,1736,
+ 1464,5832, 1472,2248, 1480,6344, 1488,2760, 1496,6856, 1504,3272,
+ 1512,7368, 1520,3784, 1528,7880, 1536,4224, 1544,4360, 1552,4480,
+ 1560,4872, 1568,4232, 1576,5384, 1584,1800, 1592,5896, 1600,2312,
+ 1608,6408, 1616,2824, 1624,6920, 1632,3336, 1640,7432, 1648,3848,
+ 1656,7944, 1664,6272, 1672,4424, 1680,6528, 1688,4936, 1696,6280,
+ 1704,5448, 1712,1864, 1720,5960, 1728,2376, 1736,6472, 1744,2888,
+ 1752,6984, 1760,3400, 1768,7496, 1776,3912, 1784,8008, 1792,4288,
+ 1800,4488, 1808,4544, 1816,5000, 1824,4296, 1832,5512, 1840,1928,
+ 1848,6024, 1856,2440, 1864,6536, 1872,2952, 1880,7048, 1888,3464,
+ 1896,7560, 1904,3976, 1912,8072, 1920,6336, 1928,4552, 1936,6592,
+ 1944,5064, 1952,6344, 1960,5576, 1968,1992, 1976,6088, 1984,2504,
+ 1992,6600, 2000,3016, 2008,7112, 2016,3528, 2024,7624, 2032,4040,
+ 2040,8136, 2056,4112, 2064,2112, 2072,4624, 2080,4352, 2088,5136,
+ 2096,4480, 2104,5648, 2120,6160, 2128,2576, 2136,6672, 2144,3088,
+ 2152,7184, 2160,3600, 2168,7696, 2176,2560, 2184,4176, 2192,2816,
+ 2200,4688, 2208,2568, 2216,5200, 2224,2824, 2232,5712, 2240,2576,
+ 2248,6224, 2256,2640, 2264,6736, 2272,3152, 2280,7248, 2288,3664,
+ 2296,7760, 2312,4240, 2320,2432, 2328,4752, 2336,6400, 2344,5264,
+ 2352,6528, 2360,5776, 2368,2816, 2376,6288, 2384,2704, 2392,6800,
+ 2400,3216, 2408,7312, 2416,3728, 2424,7824, 2432,2624, 2440,4304,
+ 2448,2880, 2456,4816, 2464,2632, 2472,5328, 2480,2888, 2488,5840,
+ 2496,2640, 2504,6352, 2512,2768, 2520,6864, 2528,3280, 2536,7376,
+ 2544,3792, 2552,7888, 2568,4368, 2584,4880, 2592,4416, 2600,5392,
+ 2608,4544, 2616,5904, 2632,6416, 2640,2832, 2648,6928, 2656,3344,
+ 2664,7440, 2672,3856, 2680,7952, 2696,4432, 2704,2944, 2712,4944,
+ 2720,4432, 2728,5456, 2736,2952, 2744,5968, 2752,2944, 2760,6480,
+ 2768,2896, 2776,6992, 2784,3408, 2792,7504, 2800,3920, 2808,8016,
+ 2824,4496, 2840,5008, 2848,6464, 2856,5520, 2864,6592, 2872,6032,
+ 2888,6544, 2896,2960, 2904,7056, 2912,3472, 2920,7568, 2928,3984,
+ 2936,8080, 2952,4560, 2960,3008, 2968,5072, 2976,6480, 2984,5584,
+ 2992,3016, 3000,6096, 3016,6608, 3032,7120, 3040,3536, 3048,7632,
+ 3056,4048, 3064,8144, 3072,4608, 3080,4120, 3088,4864, 3096,4632,
+ 3104,4616, 3112,5144, 3120,4872, 3128,5656, 3136,4624, 3144,6168,
+ 3152,4880, 3160,6680, 3168,4632, 3176,7192, 3184,3608, 3192,7704,
+ 3200,6656, 3208,4184, 3216,6912, 3224,4696, 3232,6664, 3240,5208,
+ 3248,6920, 3256,5720, 3264,6672, 3272,6232, 3280,6928, 3288,6744,
+ 3296,6680, 3304,7256, 3312,3672, 3320,7768, 3328,4672, 3336,4248,
+ 3344,4928, 3352,4760, 3360,4680, 3368,5272, 3376,4936, 3384,5784,
+ 3392,4688, 3400,6296, 3408,4944, 3416,6808, 3424,4696, 3432,7320,
+ 3440,3736, 3448,7832, 3456,6720, 3464,4312, 3472,6976, 3480,4824,
+ 3488,6728, 3496,5336, 3504,6984, 3512,5848, 3520,6736, 3528,6360,
+ 3536,6992, 3544,6872, 3552,6744, 3560,7384, 3568,3800, 3576,7896,
+ 3584,4736, 3592,4376, 3600,4992, 3608,4888, 3616,4744, 3624,5400,
+ 3632,5000, 3640,5912, 3648,4752, 3656,6424, 3664,5008, 3672,6936,
+ 3680,4760, 3688,7448, 3696,3864, 3704,7960, 3712,6784, 3720,4440,
+ 3728,7040, 3736,4952, 3744,6792, 3752,5464, 3760,7048, 3768,5976,
+ 3776,6800, 3784,6488, 3792,7056, 3800,7000, 3808,6808, 3816,7512,
+ 3824,3928, 3832,8024, 3840,4800, 3848,4504, 3856,5056, 3864,5016,
+ 3872,4808, 3880,5528, 3888,5064, 3896,6040, 3904,4816, 3912,6552,
+ 3920,5072, 3928,7064, 3936,4824, 3944,7576, 3952,3992, 3960,8088,
+ 3968,6848, 3976,4568, 3984,7104, 3992,5080, 4000,6856, 4008,5592,
+ 4016,7112, 4024,6104, 4032,6864, 4040,6616, 4048,7120, 4056,7128,
+ 4064,6872, 4072,7640, 4080,7128, 4088,8152, 4104,4128, 4112,4160,
+ 4120,4640, 4136,5152, 4144,4232, 4152,5664, 4160,4352, 4168,6176,
+ 4176,4416, 4184,6688, 4192,4616, 4200,7200, 4208,4744, 4216,7712,
+ 4224,4608, 4232,4616, 4240,4672, 4248,4704, 4256,4640, 4264,5216,
+ 4272,4704, 4280,5728, 4288,4864, 4296,6240, 4304,4928, 4312,6752,
+ 4320,4632, 4328,7264, 4336,4760, 4344,7776, 4360,4640, 4368,4416,
+ 4376,4768, 4384,6152, 4392,5280, 4400,6280, 4408,5792, 4424,6304,
+ 4440,6816, 4448,6664, 4456,7328, 4464,6792, 4472,7840, 4480,4624,
+ 4488,4632, 4496,4688, 4504,4832, 4512,6168, 4520,5344, 4528,6296,
+ 4536,5856, 4544,4880, 4552,6368, 4560,4944, 4568,6880, 4576,6680,
+ 4584,7392, 4592,6808, 4600,7904, 4608,6144, 4616,6152, 4624,6208,
+ 4632,4896, 4640,6176, 4648,5408, 4656,6240, 4664,5920, 4672,6400,
+ 4680,6432, 4688,6464, 4696,6944, 4704,6432, 4712,7456, 4720,4808,
+ 4728,7968, 4736,6656, 4744,6664, 4752,6720, 4760,4960, 4768,6688,
+ 4776,5472, 4784,6752, 4792,5984, 4800,6912, 4808,6496, 4816,6976,
+ 4824,7008, 4832,6944, 4840,7520, 4848,7008, 4856,8032, 4864,6160,
+ 4872,6168, 4880,6224, 4888,5024, 4896,6216, 4904,5536, 4912,6344,
+ 4920,6048, 4928,6416, 4936,6560, 4944,6480, 4952,7072, 4960,6728,
+ 4968,7584, 4976,6856, 4984,8096, 4992,6672, 5000,6680, 5008,6736,
+ 5016,5088, 5024,6232, 5032,5600, 5040,6360, 5048,6112, 5056,6928,
+ 5064,6624, 5072,6992, 5080,7136, 5088,6744, 5096,7648, 5104,6872,
+ 5112,8160, 5128,5152, 5136,5376, 5144,5408, 5168,5384, 5176,5672,
+ 5184,5376, 5192,6184, 5200,5392, 5208,6696, 5216,5408, 5224,7208,
+ 5232,5400, 5240,7720, 5248,7168, 5256,7200, 5264,7424, 5272,7456,
+ 5280,7176, 5288,7208, 5296,7432, 5304,5736, 5312,7184, 5320,6248,
+ 5328,7440, 5336,6760, 5344,7192, 5352,7272, 5360,7448, 5368,7784,
+ 5384,5408, 5392,5440, 5400,5472, 5408,6184, 5416,7208, 5424,5448,
+ 5432,5800, 5448,6312, 5464,6824, 5472,6696, 5480,7336, 5488,6824,
+ 5496,7848, 5504,7232, 5512,7264, 5520,7488, 5528,7520, 5536,7240,
+ 5544,7272, 5552,7496, 5560,5864, 5568,7248, 5576,6376, 5584,7504,
+ 5592,6888, 5600,7256, 5608,7400, 5616,7512, 5624,7912, 5632,7168,
+ 5640,7176, 5648,7232, 5656,7240, 5664,7200, 5672,7208, 5680,7264,
+ 5688,5928, 5696,7424, 5704,6440, 5712,7488, 5720,6952, 5728,7456,
+ 5736,7464, 5744,7520, 5752,7976, 5760,7296, 5768,7328, 5776,7552,
+ 5784,7584, 5792,7304, 5800,7336, 5808,7560, 5816,5992, 5824,7312,
+ 5832,6504, 5840,7568, 5848,7016, 5856,7320, 5864,7528, 5872,7576,
+ 5880,8040, 5888,7184, 5896,7192, 5904,7248, 5912,7256, 5920,6248,
+ 5928,7272, 5936,6376, 5944,6056, 5952,7440, 5960,6568, 5968,7504,
+ 5976,7080, 5984,6760, 5992,7592, 6000,6888, 6008,8104, 6016,7360,
+ 6024,7392, 6032,7616, 6040,7648, 6048,7368, 6056,7400, 6064,7624,
+ 6072,6120, 6080,7376, 6088,6632, 6096,7632, 6104,7144, 6112,7384,
+ 6120,7656, 6128,7640, 6136,8168, 6168,6240, 6192,6216, 6200,7264,
+ 6232,6704, 6248,7216, 6256,6680, 6264,7728, 6272,6656, 6280,6664,
+ 6288,6912, 6296,6496, 6304,6688, 6312,6696, 6320,6944, 6328,7520,
+ 6336,6672, 6344,6680, 6352,6928, 6360,6768, 6368,6704, 6376,7280,
+ 6384,6744, 6392,7792, 6408,6432, 6424,6752, 6440,7432, 6448,6536,
+ 6456,7560, 6472,6944, 6488,6832, 6496,6920, 6504,7344, 6512,7048,
+ 6520,7856, 6528,6720, 6536,6728, 6544,6976, 6552,7008, 6560,6752,
+ 6568,7448, 6576,7008, 6584,7576, 6592,6736, 6600,6744, 6608,6992,
+ 6616,6896, 6624,6936, 6632,7408, 6640,7064, 6648,7920, 6712,7280,
+ 6744,6960, 6760,7472, 6768,6936, 6776,7984, 6800,6848, 6808,6856,
+ 6832,6880, 6840,6888, 6848,7040, 6856,7048, 6864,7104, 6872,7024,
+ 6880,7072, 6888,7536, 6896,7136, 6904,8048, 6952,7496, 6968,7624,
+ 6984,7008, 7000,7088, 7016,7600, 7024,7112, 7032,8112, 7056,7104,
+ 7064,7112, 7080,7512, 7088,7136, 7096,7640, 7128,7152, 7144,7664,
+ 7160,8176, 7176,7200, 7192,7216, 7224,7272, 7240,7264, 7256,7280,
+ 7288,7736, 7296,7680, 7304,7712, 7312,7936, 7320,7968, 7328,7688,
+ 7336,7720, 7344,7944, 7352,7976, 7360,7696, 7368,7728, 7376,7952,
+ 7384,7984, 7392,7704, 7400,7736, 7408,7960, 7416,7800, 7432,7456,
+ 7448,7472, 7480,7592, 7496,7520, 7512,7536, 7528,7976, 7544,7864,
+ 7552,7744, 7560,7776, 7568,8000, 7576,8032, 7584,7752, 7592,7784,
+ 7600,8008, 7608,8040, 7616,7760, 7624,7792, 7632,8016, 7640,8048,
+ 7648,7768, 7656,7800, 7664,8024, 7672,7928, 7688,7712, 7704,7728,
+ 7752,7776, 7768,7792, 7800,7992, 7816,7840, 7824,8064, 7832,8096,
+ 7856,8072, 7864,8104, 7872,8064, 7880,8072, 7888,8080, 7896,8112,
+ 7904,8096, 7912,8104, 7920,8088, 7928,8056, 7944,7968, 7960,7984,
+ 8008,8032, 8024,8048, 8056,8120, 8072,8096, 8080,8128, 8088,8160,
+ 8112,8136, 8120,8168, 8136,8160, 8152,8176
+};
+
+const uint16_t armBitRevIndexTable2048[ARMBITREVINDEXTABLE2048_TABLE_LENGTH] =
+{
+ //8x2, size 3808
+ 8,4096, 16,8192, 24,12288, 32,512, 40,4608, 48,8704, 56,12800, 64,1024,
+ 72,5120, 80,9216, 88,13312, 96,1536, 104,5632, 112,9728, 120,13824,
+ 128,2048, 136,6144, 144,10240, 152,14336, 160,2560, 168,6656, 176,10752,
+ 184,14848, 192,3072, 200,7168, 208,11264, 216,15360, 224,3584, 232,7680,
+ 240,11776, 248,15872, 256,1024, 264,4160, 272,8256, 280,12352, 288,576,
+ 296,4672, 304,8768, 312,12864, 320,1088, 328,5184, 336,9280, 344,13376,
+ 352,1600, 360,5696, 368,9792, 376,13888, 384,2112, 392,6208, 400,10304,
+ 408,14400, 416,2624, 424,6720, 432,10816, 440,14912, 448,3136, 456,7232,
+ 464,11328, 472,15424, 480,3648, 488,7744, 496,11840, 504,15936, 512,2048,
+ 520,4224, 528,8320, 536,12416, 544,640, 552,4736, 560,8832, 568,12928,
+ 576,1152, 584,5248, 592,9344, 600,13440, 608,1664, 616,5760, 624,9856,
+ 632,13952, 640,2176, 648,6272, 656,10368, 664,14464, 672,2688, 680,6784,
+ 688,10880, 696,14976, 704,3200, 712,7296, 720,11392, 728,15488, 736,3712,
+ 744,7808, 752,11904, 760,16000, 768,3072, 776,4288, 784,8384, 792,12480,
+ 800,3200, 808,4800, 816,8896, 824,12992, 832,1216, 840,5312, 848,9408,
+ 856,13504, 864,1728, 872,5824, 880,9920, 888,14016, 896,2240, 904,6336,
+ 912,10432, 920,14528, 928,2752, 936,6848, 944,10944, 952,15040, 960,3264,
+ 968,7360, 976,11456, 984,15552, 992,3776, 1000,7872, 1008,11968, 1016,16064,
+ 1032,4352, 1040,8448, 1048,12544, 1056,3072, 1064,4864, 1072,8960,
+ 1080,13056, 1088,1280, 1096,5376, 1104,9472, 1112,13568, 1120,1792,
+ 1128,5888, 1136,9984, 1144,14080, 1152,2304, 1160,6400, 1168,10496,
+ 1176,14592, 1184,2816, 1192,6912, 1200,11008, 1208,15104, 1216,3328,
+ 1224,7424, 1232,11520, 1240,15616, 1248,3840, 1256,7936, 1264,12032,
+ 1272,16128, 1288,4416, 1296,8512, 1304,12608, 1312,3328, 1320,4928,
+ 1328,9024, 1336,13120, 1352,5440, 1360,9536, 1368,13632, 1376,1856,
+ 1384,5952, 1392,10048, 1400,14144, 1408,2368, 1416,6464, 1424,10560,
+ 1432,14656, 1440,2880, 1448,6976, 1456,11072, 1464,15168, 1472,3392,
+ 1480,7488, 1488,11584, 1496,15680, 1504,3904, 1512,8000, 1520,12096,
+ 1528,16192, 1536,2112, 1544,4480, 1552,8576, 1560,12672, 1568,2240,
+ 1576,4992, 1584,9088, 1592,13184, 1600,2368, 1608,5504, 1616,9600,
+ 1624,13696, 1632,1920, 1640,6016, 1648,10112, 1656,14208, 1664,2432,
+ 1672,6528, 1680,10624, 1688,14720, 1696,2944, 1704,7040, 1712,11136,
+ 1720,15232, 1728,3456, 1736,7552, 1744,11648, 1752,15744, 1760,3968,
+ 1768,8064, 1776,12160, 1784,16256, 1792,3136, 1800,4544, 1808,8640,
+ 1816,12736, 1824,3264, 1832,5056, 1840,9152, 1848,13248, 1856,3392,
+ 1864,5568, 1872,9664, 1880,13760, 1888,1984, 1896,6080, 1904,10176,
+ 1912,14272, 1920,2496, 1928,6592, 1936,10688, 1944,14784, 1952,3008,
+ 1960,7104, 1968,11200, 1976,15296, 1984,3520, 1992,7616, 2000,11712,
+ 2008,15808, 2016,4032, 2024,8128, 2032,12224, 2040,16320, 2048,4096,
+ 2056,4104, 2064,8200, 2072,12296, 2080,4224, 2088,4616, 2096,8712,
+ 2104,12808, 2112,4352, 2120,5128, 2128,9224, 2136,13320, 2144,4480,
+ 2152,5640, 2160,9736, 2168,13832, 2176,4104, 2184,6152, 2192,10248,
+ 2200,14344, 2208,2568, 2216,6664, 2224,10760, 2232,14856, 2240,3080,
+ 2248,7176, 2256,11272, 2264,15368, 2272,3592, 2280,7688, 2288,11784,
+ 2296,15880, 2304,5120, 2312,4168, 2320,8264, 2328,12360, 2336,5248,
+ 2344,4680, 2352,8776, 2360,12872, 2368,5376, 2376,5192, 2384,9288,
+ 2392,13384, 2400,5504, 2408,5704, 2416,9800, 2424,13896, 2432,5128,
+ 2440,6216, 2448,10312, 2456,14408, 2464,2632, 2472,6728, 2480,10824,
+ 2488,14920, 2496,3144, 2504,7240, 2512,11336, 2520,15432, 2528,3656,
+ 2536,7752, 2544,11848, 2552,15944, 2560,6144, 2568,4232, 2576,8328,
+ 2584,12424, 2592,6272, 2600,4744, 2608,8840, 2616,12936, 2624,6400,
+ 2632,5256, 2640,9352, 2648,13448, 2656,6528, 2664,5768, 2672,9864,
+ 2680,13960, 2688,6152, 2696,6280, 2704,10376, 2712,14472, 2720,6280,
+ 2728,6792, 2736,10888, 2744,14984, 2752,3208, 2760,7304, 2768,11400,
+ 2776,15496, 2784,3720, 2792,7816, 2800,11912, 2808,16008, 2816,7168,
+ 2824,4296, 2832,8392, 2840,12488, 2848,7296, 2856,4808, 2864,8904,
+ 2872,13000, 2880,7424, 2888,5320, 2896,9416, 2904,13512, 2912,7552,
+ 2920,5832, 2928,9928, 2936,14024, 2944,7176, 2952,6344, 2960,10440,
+ 2968,14536, 2976,7304, 2984,6856, 2992,10952, 3000,15048, 3008,3272,
+ 3016,7368, 3024,11464, 3032,15560, 3040,3784, 3048,7880, 3056,11976,
+ 3064,16072, 3072,4160, 3080,4360, 3088,8456, 3096,12552, 3104,4288,
+ 3112,4872, 3120,8968, 3128,13064, 3136,4416, 3144,5384, 3152,9480,
+ 3160,13576, 3168,4544, 3176,5896, 3184,9992, 3192,14088, 3200,4168,
+ 3208,6408, 3216,10504, 3224,14600, 3232,4296, 3240,6920, 3248,11016,
+ 3256,15112, 3264,3336, 3272,7432, 3280,11528, 3288,15624, 3296,3848,
+ 3304,7944, 3312,12040, 3320,16136, 3328,5184, 3336,4424, 3344,8520,
+ 3352,12616, 3360,5312, 3368,4936, 3376,9032, 3384,13128, 3392,5440,
+ 3400,5448, 3408,9544, 3416,13640, 3424,5568, 3432,5960, 3440,10056,
+ 3448,14152, 3456,5192, 3464,6472, 3472,10568, 3480,14664, 3488,5320,
+ 3496,6984, 3504,11080, 3512,15176, 3520,5448, 3528,7496, 3536,11592,
+ 3544,15688, 3552,3912, 3560,8008, 3568,12104, 3576,16200, 3584,6208,
+ 3592,4488, 3600,8584, 3608,12680, 3616,6336, 3624,5000, 3632,9096,
+ 3640,13192, 3648,6464, 3656,5512, 3664,9608, 3672,13704, 3680,6592,
+ 3688,6024, 3696,10120, 3704,14216, 3712,6216, 3720,6536, 3728,10632,
+ 3736,14728, 3744,6344, 3752,7048, 3760,11144, 3768,15240, 3776,6472,
+ 3784,7560, 3792,11656, 3800,15752, 3808,3976, 3816,8072, 3824,12168,
+ 3832,16264, 3840,7232, 3848,4552, 3856,8648, 3864,12744, 3872,7360,
+ 3880,5064, 3888,9160, 3896,13256, 3904,7488, 3912,5576, 3920,9672,
+ 3928,13768, 3936,7616, 3944,6088, 3952,10184, 3960,14280, 3968,7240,
+ 3976,6600, 3984,10696, 3992,14792, 4000,7368, 4008,7112, 4016,11208,
+ 4024,15304, 4032,7496, 4040,7624, 4048,11720, 4056,15816, 4064,7624,
+ 4072,8136, 4080,12232, 4088,16328, 4096,8192, 4104,4112, 4112,8208,
+ 4120,12304, 4128,8320, 4136,4624, 4144,8720, 4152,12816, 4160,8448,
+ 4168,5136, 4176,9232, 4184,13328, 4192,8576, 4200,5648, 4208,9744,
+ 4216,13840, 4224,8200, 4232,6160, 4240,10256, 4248,14352, 4256,8328,
+ 4264,6672, 4272,10768, 4280,14864, 4288,8456, 4296,7184, 4304,11280,
+ 4312,15376, 4320,8584, 4328,7696, 4336,11792, 4344,15888, 4352,9216,
+ 4360,9232, 4368,8272, 4376,12368, 4384,9344, 4392,4688, 4400,8784,
+ 4408,12880, 4416,9472, 4424,5200, 4432,9296, 4440,13392, 4448,9600,
+ 4456,5712, 4464,9808, 4472,13904, 4480,9224, 4488,6224, 4496,10320,
+ 4504,14416, 4512,9352, 4520,6736, 4528,10832, 4536,14928, 4544,9480,
+ 4552,7248, 4560,11344, 4568,15440, 4576,9608, 4584,7760, 4592,11856,
+ 4600,15952, 4608,10240, 4616,10256, 4624,8336, 4632,12432, 4640,10368,
+ 4648,4752, 4656,8848, 4664,12944, 4672,10496, 4680,5264, 4688,9360,
+ 4696,13456, 4704,10624, 4712,5776, 4720,9872, 4728,13968, 4736,10248,
+ 4744,6288, 4752,10384, 4760,14480, 4768,10376, 4776,6800, 4784,10896,
+ 4792,14992, 4800,10504, 4808,7312, 4816,11408, 4824,15504, 4832,10632,
+ 4840,7824, 4848,11920, 4856,16016, 4864,11264, 4872,11280, 4880,8400,
+ 4888,12496, 4896,11392, 4904,11408, 4912,8912, 4920,13008, 4928,11520,
+ 4936,5328, 4944,9424, 4952,13520, 4960,11648, 4968,5840, 4976,9936,
+ 4984,14032, 4992,11272, 5000,6352, 5008,10448, 5016,14544, 5024,11400,
+ 5032,6864, 5040,10960, 5048,15056, 5056,11528, 5064,7376, 5072,11472,
+ 5080,15568, 5088,11656, 5096,7888, 5104,11984, 5112,16080, 5120,8256,
+ 5128,8272, 5136,8464, 5144,12560, 5152,8384, 5160,8400, 5168,8976,
+ 5176,13072, 5184,8512, 5192,5392, 5200,9488, 5208,13584, 5216,8640,
+ 5224,5904, 5232,10000, 5240,14096, 5248,8264, 5256,6416, 5264,10512,
+ 5272,14608, 5280,8392, 5288,6928, 5296,11024, 5304,15120, 5312,8520,
+ 5320,7440, 5328,11536, 5336,15632, 5344,8648, 5352,7952, 5360,12048,
+ 5368,16144, 5376,9280, 5384,9296, 5392,8528, 5400,12624, 5408,9408,
+ 5416,9424, 5424,9040, 5432,13136, 5440,9536, 5448,5456, 5456,9552,
+ 5464,13648, 5472,9664, 5480,5968, 5488,10064, 5496,14160, 5504,9288,
+ 5512,6480, 5520,10576, 5528,14672, 5536,9416, 5544,6992, 5552,11088,
+ 5560,15184, 5568,9544, 5576,7504, 5584,11600, 5592,15696, 5600,9672,
+ 5608,8016, 5616,12112, 5624,16208, 5632,10304, 5640,10320, 5648,8592,
+ 5656,12688, 5664,10432, 5672,10448, 5680,9104, 5688,13200, 5696,10560,
+ 5704,10576, 5712,9616, 5720,13712, 5728,10688, 5736,6032, 5744,10128,
+ 5752,14224, 5760,10312, 5768,6544, 5776,10640, 5784,14736, 5792,10440,
+ 5800,7056, 5808,11152, 5816,15248, 5824,10568, 5832,7568, 5840,11664,
+ 5848,15760, 5856,10696, 5864,8080, 5872,12176, 5880,16272, 5888,11328,
+ 5896,11344, 5904,8656, 5912,12752, 5920,11456, 5928,11472, 5936,9168,
+ 5944,13264, 5952,11584, 5960,11600, 5968,9680, 5976,13776, 5984,11712,
+ 5992,6096, 6000,10192, 6008,14288, 6016,11336, 6024,6608, 6032,10704,
+ 6040,14800, 6048,11464, 6056,7120, 6064,11216, 6072,15312, 6080,11592,
+ 6088,7632, 6096,11728, 6104,15824, 6112,11720, 6120,8144, 6128,12240,
+ 6136,16336, 6144,12288, 6152,12304, 6160,8216, 6168,12312, 6176,12416,
+ 6184,12432, 6192,8728, 6200,12824, 6208,12544, 6216,12560, 6224,9240,
+ 6232,13336, 6240,12672, 6248,12688, 6256,9752, 6264,13848, 6272,12296,
+ 6280,12312, 6288,10264, 6296,14360, 6304,12424, 6312,6680, 6320,10776,
+ 6328,14872, 6336,12552, 6344,7192, 6352,11288, 6360,15384, 6368,12680,
+ 6376,7704, 6384,11800, 6392,15896, 6400,13312, 6408,13328, 6416,8280,
+ 6424,12376, 6432,13440, 6440,13456, 6448,8792, 6456,12888, 6464,13568,
+ 6472,13584, 6480,9304, 6488,13400, 6496,13696, 6504,13712, 6512,9816,
+ 6520,13912, 6528,13320, 6536,13336, 6544,10328, 6552,14424, 6560,13448,
+ 6568,6744, 6576,10840, 6584,14936, 6592,13576, 6600,7256, 6608,11352,
+ 6616,15448, 6624,13704, 6632,7768, 6640,11864, 6648,15960, 6656,14336,
+ 6664,14352, 6672,8344, 6680,12440, 6688,14464, 6696,14480, 6704,8856,
+ 6712,12952, 6720,14592, 6728,14608, 6736,9368, 6744,13464, 6752,14720,
+ 6760,14736, 6768,9880, 6776,13976, 6784,14344, 6792,14360, 6800,10392,
+ 6808,14488, 6816,14472, 6824,14488, 6832,10904, 6840,15000, 6848,14600,
+ 6856,7320, 6864,11416, 6872,15512, 6880,14728, 6888,7832, 6896,11928,
+ 6904,16024, 6912,15360, 6920,15376, 6928,8408, 6936,12504, 6944,15488,
+ 6952,15504, 6960,8920, 6968,13016, 6976,15616, 6984,15632, 6992,9432,
+ 7000,13528, 7008,15744, 7016,15760, 7024,9944, 7032,14040, 7040,15368,
+ 7048,15384, 7056,10456, 7064,14552, 7072,15496, 7080,15512, 7088,10968,
+ 7096,15064, 7104,15624, 7112,7384, 7120,11480, 7128,15576, 7136,15752,
+ 7144,7896, 7152,11992, 7160,16088, 7168,12352, 7176,12368, 7184,8472,
+ 7192,12568, 7200,12480, 7208,12496, 7216,8984, 7224,13080, 7232,12608,
+ 7240,12624, 7248,9496, 7256,13592, 7264,12736, 7272,12752, 7280,10008,
+ 7288,14104, 7296,12360, 7304,12376, 7312,10520, 7320,14616, 7328,12488,
+ 7336,12504, 7344,11032, 7352,15128, 7360,12616, 7368,7448, 7376,11544,
+ 7384,15640, 7392,12744, 7400,7960, 7408,12056, 7416,16152, 7424,13376,
+ 7432,13392, 7440,8536, 7448,12632, 7456,13504, 7464,13520, 7472,9048,
+ 7480,13144, 7488,13632, 7496,13648, 7504,9560, 7512,13656, 7520,13760,
+ 7528,13776, 7536,10072, 7544,14168, 7552,13384, 7560,13400, 7568,10584,
+ 7576,14680, 7584,13512, 7592,13528, 7600,11096, 7608,15192, 7616,13640,
+ 7624,13656, 7632,11608, 7640,15704, 7648,13768, 7656,8024, 7664,12120,
+ 7672,16216, 7680,14400, 7688,14416, 7696,8600, 7704,12696, 7712,14528,
+ 7720,14544, 7728,9112, 7736,13208, 7744,14656, 7752,14672, 7760,9624,
+ 7768,13720, 7776,14784, 7784,14800, 7792,10136, 7800,14232, 7808,14408,
+ 7816,14424, 7824,10648, 7832,14744, 7840,14536, 7848,14552, 7856,11160,
+ 7864,15256, 7872,14664, 7880,14680, 7888,11672, 7896,15768, 7904,14792,
+ 7912,8088, 7920,12184, 7928,16280, 7936,15424, 7944,15440, 7952,8664,
+ 7960,12760, 7968,15552, 7976,15568, 7984,9176, 7992,13272, 8000,15680,
+ 8008,15696, 8016,9688, 8024,13784, 8032,15808, 8040,15824, 8048,10200,
+ 8056,14296, 8064,15432, 8072,15448, 8080,10712, 8088,14808, 8096,15560,
+ 8104,15576, 8112,11224, 8120,15320, 8128,15688, 8136,15704, 8144,11736,
+ 8152,15832, 8160,15816, 8168,15832, 8176,12248, 8184,16344, 8200,8320,
+ 8208,8224, 8216,12320, 8232,10368, 8240,8736, 8248,12832, 8256,8448,
+ 8264,8384, 8272,9248, 8280,13344, 8288,9232, 8296,10432, 8304,9760,
+ 8312,13856, 8328,12416, 8336,10272, 8344,14368, 8352,12296, 8360,14464,
+ 8368,10784, 8376,14880, 8384,8456, 8392,12480, 8400,11296, 8408,15392,
+ 8416,12552, 8424,14528, 8432,11808, 8440,15904, 8448,9216, 8456,8576,
+ 8464,9232, 8472,12384, 8480,9248, 8488,10624, 8496,8800, 8504,12896,
+ 8512,9472, 8520,8640, 8528,9312, 8536,13408, 8544,9296, 8552,10688,
+ 8560,9824, 8568,13920, 8576,9224, 8584,12672, 8592,10336, 8600,14432,
+ 8608,13320, 8616,14720, 8624,10848, 8632,14944, 8640,9480, 8648,12736,
+ 8656,11360, 8664,15456, 8672,13576, 8680,14784, 8688,11872, 8696,15968,
+ 8704,12288, 8712,12416, 8720,12296, 8728,12448, 8736,12304, 8744,10376,
+ 8752,8864, 8760,12960, 8768,12352, 8776,12480, 8784,9376, 8792,13472,
+ 8800,12368, 8808,10440, 8816,9888, 8824,13984, 8832,12320, 8840,12424,
+ 8848,10400, 8856,14496, 8864,12312, 8872,14472, 8880,10912, 8888,15008,
+ 8896,12384, 8904,12488, 8912,11424, 8920,15520, 8928,12568, 8936,14536,
+ 8944,11936, 8952,16032, 8960,12544, 8968,12672, 8976,12552, 8984,12512,
+ 8992,12560, 9000,10632, 9008,12568, 9016,13024, 9024,12608, 9032,12736,
+ 9040,9440, 9048,13536, 9056,12624, 9064,10696, 9072,9952, 9080,14048,
+ 9088,9240, 9096,12680, 9104,10464, 9112,14560, 9120,13336, 9128,14728,
+ 9136,10976, 9144,15072, 9152,9496, 9160,12744, 9168,11488, 9176,15584,
+ 9184,13592, 9192,14792, 9200,12000, 9208,16096, 9224,9344, 9232,9248,
+ 9240,12576, 9256,11392, 9264,12560, 9272,13088, 9280,9472, 9288,9408,
+ 9296,9504, 9304,13600, 9312,9488, 9320,11456, 9328,10016, 9336,14112,
+ 9352,13440, 9360,10528, 9368,14624, 9376,12360, 9384,15488, 9392,11040,
+ 9400,15136, 9408,9480, 9416,13504, 9424,11552, 9432,15648, 9440,12616,
+ 9448,15552, 9456,12064, 9464,16160, 9480,9600, 9488,9504, 9496,12640,
+ 9512,11648, 9520,12624, 9528,13152, 9544,9664, 9552,9568, 9560,13664,
+ 9576,11712, 9584,10080, 9592,14176, 9608,13696, 9616,10592, 9624,14688,
+ 9632,13384, 9640,15744, 9648,11104, 9656,15200, 9672,13760, 9680,11616,
+ 9688,15712, 9696,13640, 9704,15808, 9712,12128, 9720,16224, 9728,13312,
+ 9736,13440, 9744,13320, 9752,12704, 9760,13328, 9768,11400, 9776,13336,
+ 9784,13216, 9792,13376, 9800,13504, 9808,13384, 9816,13728, 9824,13392,
+ 9832,11464, 9840,10144, 9848,14240, 9856,13344, 9864,13448, 9872,10656,
+ 9880,14752, 9888,12376, 9896,15496, 9904,11168, 9912,15264, 9920,13408,
+ 9928,13512, 9936,11680, 9944,15776, 9952,12632, 9960,15560, 9968,12192,
+ 9976,16288, 9984,13568, 9992,13696, 10000,13576, 10008,12768, 10016,13584,
+ 10024,11656, 10032,13592, 10040,13280, 10048,13632, 10056,13760,
+ 10064,13640, 10072,13792, 10080,13648, 10088,11720, 10096,10208,
+ 10104,14304, 10112,13600, 10120,13704, 10128,10720, 10136,14816,
+ 10144,13400, 10152,15752, 10160,11232, 10168,15328, 10176,13664,
+ 10184,13768, 10192,11744, 10200,15840, 10208,13656, 10216,15816,
+ 10224,12256, 10232,16352, 10248,10272, 10256,10368, 10264,12328,
+ 10280,10384, 10288,10376, 10296,12840, 10304,11264, 10312,11296,
+ 10320,11392, 10328,13352, 10336,11272, 10344,10448, 10352,11400,
+ 10360,13864, 10376,12432, 10392,14376, 10400,12328, 10408,14480,
+ 10416,10792, 10424,14888, 10432,11280, 10440,12496, 10448,11304,
+ 10456,15400, 10464,11288, 10472,14544, 10480,11816, 10488,15912,
+ 10496,11264, 10504,11272, 10512,11280, 10520,12392, 10528,11296,
+ 10536,10640, 10544,12496, 10552,12904, 10560,11328, 10568,11360,
+ 10576,11456, 10584,13416, 10592,11336, 10600,10704, 10608,11464,
+ 10616,13928, 10624,11392, 10632,12688, 10640,11304, 10648,14440,
+ 10656,13352, 10664,14736, 10672,10856, 10680,14952, 10688,11344,
+ 10696,12752, 10704,11368, 10712,15464, 10720,11352, 10728,14800,
+ 10736,11880, 10744,15976, 10752,14336, 10760,14368, 10768,14464,
+ 10776,12456, 10784,14344, 10792,14376, 10800,14472, 10808,12968,
+ 10816,15360, 10824,15392, 10832,15488, 10840,13480, 10848,15368,
+ 10856,15400, 10864,15496, 10872,13992, 10880,14352, 10888,12440,
+ 10896,14480, 10904,14504, 10912,14360, 10920,14488, 10928,14488,
+ 10936,15016, 10944,15376, 10952,12504, 10960,11432, 10968,15528,
+ 10976,15384, 10984,14552, 10992,11944, 11000,16040, 11008,14400,
+ 11016,14432, 11024,14528, 11032,12520, 11040,14408, 11048,14440,
+ 11056,14536, 11064,13032, 11072,15424, 11080,15456, 11088,15552,
+ 11096,13544, 11104,15432, 11112,15464, 11120,15560, 11128,14056,
+ 11136,14416, 11144,12696, 11152,14544, 11160,14568, 11168,14424,
+ 11176,14744, 11184,14552, 11192,15080, 11200,15440, 11208,12760,
+ 11216,11496, 11224,15592, 11232,15448, 11240,14808, 11248,12008,
+ 11256,16104, 11272,11296, 11280,11392, 11288,12584, 11304,11408,
+ 11312,12688, 11320,13096, 11328,11520, 11336,11552, 11344,11648,
+ 11352,13608, 11360,11528, 11368,11472, 11376,11656, 11384,14120,
+ 11400,13456, 11416,14632, 11424,12392, 11432,15504, 11440,14440,
+ 11448,15144, 11456,11536, 11464,13520, 11472,11560, 11480,15656,
+ 11488,11544, 11496,15568, 11504,12072, 11512,16168, 11528,11552,
+ 11536,11648, 11544,12648, 11560,11664, 11568,12752, 11576,13160,
+ 11592,11616, 11600,11712, 11608,13672, 11624,11728, 11632,11720,
+ 11640,14184, 11656,13712, 11672,14696, 11680,13416, 11688,15760,
+ 11696,15464, 11704,15208, 11720,13776, 11736,15720, 11744,13672,
+ 11752,15824, 11760,12136, 11768,16232, 11776,14592, 11784,14624,
+ 11792,14720, 11800,12712, 11808,14600, 11816,14632, 11824,14728,
+ 11832,13224, 11840,15616, 11848,15648, 11856,15744, 11864,13736,
+ 11872,15624, 11880,15656, 11888,15752, 11896,14248, 11904,14608,
+ 11912,13464, 11920,14736, 11928,14760, 11936,14616, 11944,15512,
+ 11952,14744, 11960,15272, 11968,15632, 11976,13528, 11984,15760,
+ 11992,15784, 12000,15640, 12008,15576, 12016,12200, 12024,16296,
+ 12032,14656, 12040,14688, 12048,14784, 12056,12776, 12064,14664,
+ 12072,14696, 12080,14792, 12088,13288, 12096,15680, 12104,15712,
+ 12112,15808, 12120,13800, 12128,15688, 12136,15720, 12144,15816,
+ 12152,14312, 12160,14672, 12168,13720, 12176,14800, 12184,14824,
+ 12192,14680, 12200,15768, 12208,14808, 12216,15336, 12224,15696,
+ 12232,13784, 12240,15824, 12248,15848, 12256,15704, 12264,15832,
+ 12272,15832, 12280,16360, 12312,12336, 12344,12848, 12352,12544,
+ 12360,12552, 12368,12560, 12376,13360, 12384,12576, 12392,12584,
+ 12400,13336, 12408,13872, 12424,12448, 12440,14384, 12456,14496,
+ 12464,14472, 12472,14896, 12480,12672, 12488,12512, 12496,12688,
+ 12504,15408, 12512,12680, 12520,14560, 12528,14728, 12536,15920,
+ 12544,13312, 12552,13320, 12560,13328, 12568,13336, 12576,13344,
+ 12584,13352, 12592,13360, 12600,12912, 12608,13568, 12616,13576,
+ 12624,13584, 12632,13424, 12640,13600, 12648,13608, 12656,13400,
+ 12664,13936, 12672,13440, 12680,12704, 12688,13456, 12696,14448,
+ 12704,13448, 12712,14752, 12720,15496, 12728,14960, 12736,13696,
+ 12744,12768, 12752,13712, 12760,15472, 12768,13704, 12776,14816,
+ 12784,15752, 12792,15984, 12800,14336, 12808,14464, 12816,14344,
+ 12824,14472, 12832,14352, 12840,14480, 12848,14360, 12856,12976,
+ 12864,14400, 12872,14528, 12880,14408, 12888,13488, 12896,14416,
+ 12904,14544, 12912,14424, 12920,14000, 12928,14368, 12936,14496,
+ 12944,14376, 12952,14512, 12960,14384, 12968,14504, 12976,14488,
+ 12984,15024, 12992,14432, 13000,14560, 13008,14440, 13016,15536,
+ 13024,14448, 13032,14568, 13040,14744, 13048,16048, 13056,14592,
+ 13064,14720, 13072,14600, 13080,14728, 13088,14608, 13096,14736,
+ 13104,14616, 13112,14744, 13120,14656, 13128,14784, 13136,14664,
+ 13144,13552, 13152,14672, 13160,14800, 13168,14680, 13176,14064,
+ 13184,14624, 13192,14752, 13200,14632, 13208,14576, 13216,13464,
+ 13224,14760, 13232,15512, 13240,15088, 13248,14688, 13256,14816,
+ 13264,14696, 13272,15600, 13280,13720, 13288,14824, 13296,15768,
+ 13304,16112, 13336,13360, 13368,14616, 13376,13568, 13384,13576,
+ 13392,13584, 13400,13616, 13408,13600, 13416,13608, 13424,13592,
+ 13432,14128, 13448,13472, 13464,14640, 13480,15520, 13488,14536,
+ 13496,15152, 13504,13696, 13512,13536, 13520,13712, 13528,15664,
+ 13536,13704, 13544,15584, 13552,14792, 13560,16176, 13592,13616,
+ 13624,14680, 13656,13680, 13688,14192, 13704,13728, 13720,14704,
+ 13736,15776, 13744,15560, 13752,15216, 13768,13792, 13784,15728,
+ 13800,15840, 13808,15816, 13816,16240, 13824,15360, 13832,15488,
+ 13840,15368, 13848,15496, 13856,15376, 13864,15504, 13872,15384,
+ 13880,15512, 13888,15424, 13896,15552, 13904,15432, 13912,15560,
+ 13920,15440, 13928,15568, 13936,15448, 13944,14256, 13952,15392,
+ 13960,15520, 13968,15400, 13976,14768, 13984,15408, 13992,15528,
+ 14000,14552, 14008,15280, 14016,15456, 14024,15584, 14032,15464,
+ 14040,15792, 14048,15472, 14056,15592, 14064,14808, 14072,16304,
+ 14080,15616, 14088,15744, 14096,15624, 14104,15752, 14112,15632,
+ 14120,15760, 14128,15640, 14136,15768, 14144,15680, 14152,15808,
+ 14160,15688, 14168,15816, 14176,15696, 14184,15824, 14192,15704,
+ 14200,14320, 14208,15648, 14216,15776, 14224,15656, 14232,14832,
+ 14240,15664, 14248,15784, 14256,15576, 14264,15344, 14272,15712,
+ 14280,15840, 14288,15720, 14296,15856, 14304,15728, 14312,15848,
+ 14320,15832, 14328,16368, 14392,14488, 14400,14592, 14408,14600,
+ 14416,14608, 14424,14616, 14432,14624, 14440,14632, 14448,14640,
+ 14456,15512, 14504,14512, 14520,14904, 14528,14720, 14536,14728,
+ 14544,14736, 14552,15416, 14560,14752, 14568,14576, 14584,15928,
+ 14576,14760, 14592,15360, 14600,15368, 14608,15376, 14616,15384,
+ 14624,15392, 14632,15400, 14640,15408, 14648,15416, 14656,15616,
+ 14664,15624, 14672,15632, 14680,15640, 14688,15648, 14696,15656,
+ 14704,15664, 14712,15576, 14720,15488, 14728,15496, 14736,15504,
+ 14744,15512, 14752,15520, 14760,14768, 14776,14968, 14768,15528,
+ 14784,15744, 14792,15752, 14800,15760, 14808,15480, 14816,15776,
+ 14824,14832, 14840,15992, 14832,15784, 14856,14864, 14864,14880,
+ 14872,14896, 14880,14976, 14888,14992, 14896,15008, 14904,15024,
+ 14912,15104, 14920,15120, 14928,15136, 14936,15152, 14944,15232,
+ 14952,15248, 14960,15264, 14968,15280, 14984,15008, 15000,15024,
+ 15016,15024, 15040,15112, 15048,15128, 15056,15144, 15064,15544,
+ 15072,15240, 15080,15256, 15088,15272, 15096,16056, 15104,15872,
+ 15112,15888, 15120,15904, 15128,15920, 15136,16000, 15144,16016,
+ 15152,16032, 15160,16048, 15168,16128, 15176,16144, 15184,16160,
+ 15192,16176, 15200,16256, 15208,16272, 15216,16288, 15224,16304,
+ 15232,15880, 15240,15896, 15248,15912, 15256,15928, 15264,16008,
+ 15272,16024, 15280,16040, 15288,16056, 15296,16136, 15304,16152,
+ 15312,16168, 15320,15608, 15328,16264, 15336,16280, 15344,16296,
+ 15352,16120, 15416,15512, 15424,15616, 15432,15624, 15440,15632,
+ 15448,15640, 15456,15648, 15464,15656, 15472,15664, 15480,15768,
+ 15528,15536, 15544,16048, 15552,15744, 15560,15752, 15568,15760,
+ 15576,15672, 15584,15776, 15592,15600, 15600,15784, 15608,16184,
+ 15672,15768, 15736,15832, 15784,15792, 15800,16304, 15848,15856,
+ 15880,16000, 15864,16248, 15888,16000, 15896,16008, 15904,16000,
+ 15912,16016, 15920,16008, 15928,16024, 15936,16128, 15944,16160,
+ 15952,16256, 15960,16288, 15968,16136, 15976,16168, 15984,16264,
+ 15992,16296, 16008,16032, 16024,16040, 16064,16144, 16040,16048,
+ 16072,16176, 16080,16272, 16088,16304, 16096,16152, 16104,16184,
+ 16112,16280, 16136,16256, 16120,16312, 16144,16256, 16152,16264,
+ 16160,16256, 16168,16272, 16176,16264, 16184,16280, 16200,16208,
+ 16208,16224, 16216,16240, 16224,16320, 16232,16336, 16240,16352,
+ 16248,16368, 16264,16288, 16280,16296, 16296,16304, 16344,16368,
+ 16328,16352, 16360,16368
+};
+
+const uint16_t armBitRevIndexTable4096[ARMBITREVINDEXTABLE4096_TABLE_LENGTH] =
+{
+ //radix 8, size 4032
+ 8,4096, 16,8192, 24,12288, 32,16384, 40,20480, 48,24576, 56,28672, 64,512,
+ 72,4608, 80,8704, 88,12800, 96,16896, 104,20992, 112,25088, 120,29184,
+ 128,1024, 136,5120, 144,9216, 152,13312, 160,17408, 168,21504, 176,25600,
+ 184,29696, 192,1536, 200,5632, 208,9728, 216,13824, 224,17920, 232,22016,
+ 240,26112, 248,30208, 256,2048, 264,6144, 272,10240, 280,14336, 288,18432,
+ 296,22528, 304,26624, 312,30720, 320,2560, 328,6656, 336,10752, 344,14848,
+ 352,18944, 360,23040, 368,27136, 376,31232, 384,3072, 392,7168, 400,11264,
+ 408,15360, 416,19456, 424,23552, 432,27648, 440,31744, 448,3584, 456,7680,
+ 464,11776, 472,15872, 480,19968, 488,24064, 496,28160, 504,32256, 520,4160,
+ 528,8256, 536,12352, 544,16448, 552,20544, 560,24640, 568,28736, 584,4672,
+ 592,8768, 600,12864, 608,16960, 616,21056, 624,25152, 632,29248, 640,1088,
+ 648,5184, 656,9280, 664,13376, 672,17472, 680,21568, 688,25664, 696,29760,
+ 704,1600, 712,5696, 720,9792, 728,13888, 736,17984, 744,22080, 752,26176,
+ 760,30272, 768,2112, 776,6208, 784,10304, 792,14400, 800,18496, 808,22592,
+ 816,26688, 824,30784, 832,2624, 840,6720, 848,10816, 856,14912, 864,19008,
+ 872,23104, 880,27200, 888,31296, 896,3136, 904,7232, 912,11328, 920,15424,
+ 928,19520, 936,23616, 944,27712, 952,31808, 960,3648, 968,7744, 976,11840,
+ 984,15936, 992,20032, 1000,24128, 1008,28224, 1016,32320, 1032,4224,
+ 1040,8320, 1048,12416, 1056,16512, 1064,20608, 1072,24704, 1080,28800,
+ 1096,4736, 1104,8832, 1112,12928, 1120,17024, 1128,21120, 1136,25216,
+ 1144,29312, 1160,5248, 1168,9344, 1176,13440, 1184,17536, 1192,21632,
+ 1200,25728, 1208,29824, 1216,1664, 1224,5760, 1232,9856, 1240,13952,
+ 1248,18048, 1256,22144, 1264,26240, 1272,30336, 1280,2176, 1288,6272,
+ 1296,10368, 1304,14464, 1312,18560, 1320,22656, 1328,26752, 1336,30848,
+ 1344,2688, 1352,6784, 1360,10880, 1368,14976, 1376,19072, 1384,23168,
+ 1392,27264, 1400,31360, 1408,3200, 1416,7296, 1424,11392, 1432,15488,
+ 1440,19584, 1448,23680, 1456,27776, 1464,31872, 1472,3712, 1480,7808,
+ 1488,11904, 1496,16000, 1504,20096, 1512,24192, 1520,28288, 1528,32384,
+ 1544,4288, 1552,8384, 1560,12480, 1568,16576, 1576,20672, 1584,24768,
+ 1592,28864, 1608,4800, 1616,8896, 1624,12992, 1632,17088, 1640,21184,
+ 1648,25280, 1656,29376, 1672,5312, 1680,9408, 1688,13504, 1696,17600,
+ 1704,21696, 1712,25792, 1720,29888, 1736,5824, 1744,9920, 1752,14016,
+ 1760,18112, 1768,22208, 1776,26304, 1784,30400, 1792,2240, 1800,6336,
+ 1808,10432, 1816,14528, 1824,18624, 1832,22720, 1840,26816, 1848,30912,
+ 1856,2752, 1864,6848, 1872,10944, 1880,15040, 1888,19136, 1896,23232,
+ 1904,27328, 1912,31424, 1920,3264, 1928,7360, 1936,11456, 1944,15552,
+ 1952,19648, 1960,23744, 1968,27840, 1976,31936, 1984,3776, 1992,7872,
+ 2000,11968, 2008,16064, 2016,20160, 2024,24256, 2032,28352, 2040,32448,
+ 2056,4352, 2064,8448, 2072,12544, 2080,16640, 2088,20736, 2096,24832,
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+ 15784,23960, 15792,28056, 15800,32152, 15832,16280, 15840,20376,
+ 15848,24472, 15856,28568, 15864,32664, 15904,16856, 15912,20952,
+ 15920,25048, 15928,29144, 15968,17368, 15976,21464, 15984,25560,
+ 15992,29656, 16032,17880, 16040,21976, 16048,26072, 16056,30168,
+ 16096,18392, 16104,22488, 16112,26584, 16120,30680, 16160,18904,
+ 16168,23000, 16176,27096, 16184,31192, 16224,19416, 16232,23512,
+ 16240,27608, 16248,31704, 16288,19928, 16296,24024, 16304,28120,
+ 16312,32216, 16352,20440, 16360,24536, 16368,28632, 16376,32728,
+ 16424,20512, 16432,24608, 16440,28704, 16480,16928, 16488,21024,
+ 16496,25120, 16504,29216, 16544,17440, 16552,21536, 16560,25632,
+ 16568,29728, 16608,17952, 16616,22048, 16624,26144, 16632,30240,
+ 16672,18464, 16680,22560, 16688,26656, 16696,30752, 16736,18976,
+ 16744,23072, 16752,27168, 16760,31264, 16800,19488, 16808,23584,
+ 16816,27680, 16824,31776, 16864,20000, 16872,24096, 16880,28192,
+ 16888,32288, 16936,20576, 16944,24672, 16952,28768, 17000,21088,
+ 17008,25184, 17016,29280, 17056,17504, 17064,21600, 17072,25696,
+ 17080,29792, 17120,18016, 17128,22112, 17136,26208, 17144,30304,
+ 17184,18528, 17192,22624, 17200,26720, 17208,30816, 17248,19040,
+ 17256,23136, 17264,27232, 17272,31328, 17312,19552, 17320,23648,
+ 17328,27744, 17336,31840, 17376,20064, 17384,24160, 17392,28256,
+ 17400,32352, 17448,20640, 17456,24736, 17464,28832, 17512,21152,
+ 17520,25248, 17528,29344, 17576,21664, 17584,25760, 17592,29856,
+ 17632,18080, 17640,22176, 17648,26272, 17656,30368, 17696,18592,
+ 17704,22688, 17712,26784, 17720,30880, 17760,19104, 17768,23200,
+ 17776,27296, 17784,31392, 17824,19616, 17832,23712, 17840,27808,
+ 17848,31904, 17888,20128, 17896,24224, 17904,28320, 17912,32416,
+ 17960,20704, 17968,24800, 17976,28896, 18024,21216, 18032,25312,
+ 18040,29408, 18088,21728, 18096,25824, 18104,29920, 18152,22240,
+ 18160,26336, 18168,30432, 18208,18656, 18216,22752, 18224,26848,
+ 18232,30944, 18272,19168, 18280,23264, 18288,27360, 18296,31456,
+ 18336,19680, 18344,23776, 18352,27872, 18360,31968, 18400,20192,
+ 18408,24288, 18416,28384, 18424,32480, 18472,20768, 18480,24864,
+ 18488,28960, 18536,21280, 18544,25376, 18552,29472, 18600,21792,
+ 18608,25888, 18616,29984, 18664,22304, 18672,26400, 18680,30496,
+ 18728,22816, 18736,26912, 18744,31008, 18784,19232, 18792,23328,
+ 18800,27424, 18808,31520, 18848,19744, 18856,23840, 18864,27936,
+ 18872,32032, 18912,20256, 18920,24352, 18928,28448, 18936,32544,
+ 18984,20832, 18992,24928, 19000,29024, 19048,21344, 19056,25440,
+ 19064,29536, 19112,21856, 19120,25952, 19128,30048, 19176,22368,
+ 19184,26464, 19192,30560, 19240,22880, 19248,26976, 19256,31072,
+ 19304,23392, 19312,27488, 19320,31584, 19360,19808, 19368,23904,
+ 19376,28000, 19384,32096, 19424,20320, 19432,24416, 19440,28512,
+ 19448,32608, 19496,20896, 19504,24992, 19512,29088, 19560,21408,
+ 19568,25504, 19576,29600, 19624,21920, 19632,26016, 19640,30112,
+ 19688,22432, 19696,26528, 19704,30624, 19752,22944, 19760,27040,
+ 19768,31136, 19816,23456, 19824,27552, 19832,31648, 19880,23968,
+ 19888,28064, 19896,32160, 19936,20384, 19944,24480, 19952,28576,
+ 19960,32672, 20008,20960, 20016,25056, 20024,29152, 20072,21472,
+ 20080,25568, 20088,29664, 20136,21984, 20144,26080, 20152,30176,
+ 20200,22496, 20208,26592, 20216,30688, 20264,23008, 20272,27104,
+ 20280,31200, 20328,23520, 20336,27616, 20344,31712, 20392,24032,
+ 20400,28128, 20408,32224, 20456,24544, 20464,28640, 20472,32736,
+ 20528,24616, 20536,28712, 20584,21032, 20592,25128, 20600,29224,
+ 20648,21544, 20656,25640, 20664,29736, 20712,22056, 20720,26152,
+ 20728,30248, 20776,22568, 20784,26664, 20792,30760, 20840,23080,
+ 20848,27176, 20856,31272, 20904,23592, 20912,27688, 20920,31784,
+ 20968,24104, 20976,28200, 20984,32296, 21040,24680, 21048,28776,
+ 21104,25192, 21112,29288, 21160,21608, 21168,25704, 21176,29800,
+ 21224,22120, 21232,26216, 21240,30312, 21288,22632, 21296,26728,
+ 21304,30824, 21352,23144, 21360,27240, 21368,31336, 21416,23656,
+ 21424,27752, 21432,31848, 21480,24168, 21488,28264, 21496,32360,
+ 21552,24744, 21560,28840, 21616,25256, 21624,29352, 21680,25768,
+ 21688,29864, 21736,22184, 21744,26280, 21752,30376, 21800,22696,
+ 21808,26792, 21816,30888, 21864,23208, 21872,27304, 21880,31400,
+ 21928,23720, 21936,27816, 21944,31912, 21992,24232, 22000,28328,
+ 22008,32424, 22064,24808, 22072,28904, 22128,25320, 22136,29416,
+ 22192,25832, 22200,29928, 22256,26344, 22264,30440, 22312,22760,
+ 22320,26856, 22328,30952, 22376,23272, 22384,27368, 22392,31464,
+ 22440,23784, 22448,27880, 22456,31976, 22504,24296, 22512,28392,
+ 22520,32488, 22576,24872, 22584,28968, 22640,25384, 22648,29480,
+ 22704,25896, 22712,29992, 22768,26408, 22776,30504, 22832,26920,
+ 22840,31016, 22888,23336, 22896,27432, 22904,31528, 22952,23848,
+ 22960,27944, 22968,32040, 23016,24360, 23024,28456, 23032,32552,
+ 23088,24936, 23096,29032, 23152,25448, 23160,29544, 23216,25960,
+ 23224,30056, 23280,26472, 23288,30568, 23344,26984, 23352,31080,
+ 23408,27496, 23416,31592, 23464,23912, 23472,28008, 23480,32104,
+ 23528,24424, 23536,28520, 23544,32616, 23600,25000, 23608,29096,
+ 23664,25512, 23672,29608, 23728,26024, 23736,30120, 23792,26536,
+ 23800,30632, 23856,27048, 23864,31144, 23920,27560, 23928,31656,
+ 23984,28072, 23992,32168, 24040,24488, 24048,28584, 24056,32680,
+ 24112,25064, 24120,29160, 24176,25576, 24184,29672, 24240,26088,
+ 24248,30184, 24304,26600, 24312,30696, 24368,27112, 24376,31208,
+ 24432,27624, 24440,31720, 24496,28136, 24504,32232, 24560,28648,
+ 24568,32744, 24632,28720, 24688,25136, 24696,29232, 24752,25648,
+ 24760,29744, 24816,26160, 24824,30256, 24880,26672, 24888,30768,
+ 24944,27184, 24952,31280, 25008,27696, 25016,31792, 25072,28208,
+ 25080,32304, 25144,28784, 25208,29296, 25264,25712, 25272,29808,
+ 25328,26224, 25336,30320, 25392,26736, 25400,30832, 25456,27248,
+ 25464,31344, 25520,27760, 25528,31856, 25584,28272, 25592,32368,
+ 25656,28848, 25720,29360, 25784,29872, 25840,26288, 25848,30384,
+ 25904,26800, 25912,30896, 25968,27312, 25976,31408, 26032,27824,
+ 26040,31920, 26096,28336, 26104,32432, 26168,28912, 26232,29424,
+ 26296,29936, 26360,30448, 26416,26864, 26424,30960, 26480,27376,
+ 26488,31472, 26544,27888, 26552,31984, 26608,28400, 26616,32496,
+ 26680,28976, 26744,29488, 26808,30000, 26872,30512, 26936,31024,
+ 26992,27440, 27000,31536, 27056,27952, 27064,32048, 27120,28464,
+ 27128,32560, 27192,29040, 27256,29552, 27320,30064, 27384,30576,
+ 27448,31088, 27512,31600, 27568,28016, 27576,32112, 27632,28528,
+ 27640,32624, 27704,29104, 27768,29616, 27832,30128, 27896,30640,
+ 27960,31152, 28024,31664, 28088,32176, 28144,28592, 28152,32688,
+ 28216,29168, 28280,29680, 28344,30192, 28408,30704, 28472,31216,
+ 28536,31728, 28600,32240, 28664,32752, 28792,29240, 28856,29752,
+ 28920,30264, 28984,30776, 29048,31288, 29112,31800, 29176,32312,
+ 29368,29816, 29432,30328, 29496,30840, 29560,31352, 29624,31864,
+ 29688,32376, 29944,30392, 30008,30904, 30072,31416, 30136,31928,
+ 30200,32440, 30520,30968, 30584,31480, 30648,31992, 30712,32504,
+ 31096,31544, 31160,32056, 31224,32568, 31672,32120, 31736,32632,
+ 32248,32696
+};
+
+
+const uint16_t armBitRevIndexTable_fixed_16[ARMBITREVINDEXTABLE_FIXED___16_TABLE_LENGTH] =
+{
+ //radix 4, size 12
+ 8,64, 16,32, 24,96, 40,80, 56,112, 88,104
+};
+
+const uint16_t armBitRevIndexTable_fixed_32[ARMBITREVINDEXTABLE_FIXED___32_TABLE_LENGTH] =
+{
+ //4x2, size 24
+ 8,128, 16,64, 24,192, 40,160, 48,96, 56,224, 72,144,
+ 88,208, 104,176, 120,240, 152,200, 184,232
+};
+
+const uint16_t armBitRevIndexTable_fixed_64[ARMBITREVINDEXTABLE_FIXED___64_TABLE_LENGTH] =
+{
+ //radix 4, size 56
+ 8,256, 16,128, 24,384, 32,64, 40,320, 48,192, 56,448, 72,288, 80,160, 88,416, 104,352,
+ 112,224, 120,480, 136,272, 152,400, 168,336, 176,208, 184,464, 200,304, 216,432,
+ 232,368, 248,496, 280,392, 296,328, 312,456, 344,424, 376,488, 440,472
+};
+
+const uint16_t armBitRevIndexTable_fixed_128[ARMBITREVINDEXTABLE_FIXED__128_TABLE_LENGTH] =
+{
+ //4x2, size 112
+ 8,512, 16,256, 24,768, 32,128, 40,640, 48,384, 56,896, 72,576, 80,320, 88,832, 96,192,
+ 104,704, 112,448, 120,960, 136,544, 144,288, 152,800, 168,672, 176,416, 184,928, 200,608,
+ 208,352, 216,864, 232,736, 240,480, 248,992, 264,528, 280,784, 296,656, 304,400, 312,912,
+ 328,592, 344,848, 360,720, 368,464, 376,976, 392,560, 408,816, 424,688, 440,944, 456,624,
+ 472,880, 488,752, 504,1008, 536,776, 552,648, 568,904, 600,840, 616,712, 632,968,
+ 664,808, 696,936, 728,872, 760,1000, 824,920, 888,984
+};
+
+const uint16_t armBitRevIndexTable_fixed_256[ARMBITREVINDEXTABLE_FIXED__256_TABLE_LENGTH] =
+{
+ //radix 4, size 240
+ 8,1024, 16,512, 24,1536, 32,256, 40,1280, 48,768, 56,1792, 64,128, 72,1152, 80,640,
+ 88,1664, 96,384, 104,1408, 112,896, 120,1920, 136,1088, 144,576, 152,1600, 160,320,
+ 168,1344, 176,832, 184,1856, 200,1216, 208,704, 216,1728, 224,448, 232,1472, 240,960,
+ 248,1984, 264,1056, 272,544, 280,1568, 296,1312, 304,800, 312,1824, 328,1184, 336,672,
+ 344,1696, 352,416, 360,1440, 368,928, 376,1952, 392,1120, 400,608, 408,1632, 424,1376,
+ 432,864, 440,1888, 456,1248, 464,736, 472,1760, 488,1504, 496,992, 504,2016, 520,1040,
+ 536,1552, 552,1296, 560,784, 568,1808, 584,1168, 592,656, 600,1680, 616,1424, 624,912,
+ 632,1936, 648,1104, 664,1616, 680,1360, 688,848, 696,1872, 712,1232, 728,1744, 744,1488,
+ 752,976, 760,2000, 776,1072, 792,1584, 808,1328, 824,1840, 840,1200, 856,1712, 872,1456,
+ 880,944, 888,1968, 904,1136, 920,1648, 936,1392, 952,1904, 968,1264, 984,1776, 1000,1520,
+ 1016,2032, 1048,1544, 1064,1288, 1080,1800, 1096,1160, 1112,1672, 1128,1416, 1144,1928,
+ 1176,1608, 1192,1352, 1208,1864, 1240,1736, 1256,1480, 1272,1992, 1304,1576, 1336,1832,
+ 1368,1704, 1384,1448, 1400,1960, 1432,1640, 1464,1896, 1496,1768, 1528,2024, 1592,1816,
+ 1624,1688, 1656,1944, 1720,1880, 1784,2008, 1912,1976
+};
+
+const uint16_t armBitRevIndexTable_fixed_512[ARMBITREVINDEXTABLE_FIXED__512_TABLE_LENGTH] =
+{
+ //4x2, size 480
+ 8,2048, 16,1024, 24,3072, 32,512, 40,2560, 48,1536, 56,3584, 64,256, 72,2304, 80,1280,
+ 88,3328, 96,768, 104,2816, 112,1792, 120,3840, 136,2176, 144,1152, 152,3200, 160,640,
+ 168,2688, 176,1664, 184,3712, 192,384, 200,2432, 208,1408, 216,3456, 224,896, 232,2944,
+ 240,1920, 248,3968, 264,2112, 272,1088, 280,3136, 288,576, 296,2624, 304,1600, 312,3648,
+ 328,2368, 336,1344, 344,3392, 352,832, 360,2880, 368,1856, 376,3904, 392,2240, 400,1216,
+ 408,3264, 416,704, 424,2752, 432,1728, 440,3776, 456,2496, 464,1472, 472,3520, 480,960,
+ 488,3008, 496,1984, 504,4032, 520,2080, 528,1056, 536,3104, 552,2592, 560,1568, 568,3616,
+ 584,2336, 592,1312, 600,3360, 608,800, 616,2848, 624,1824, 632,3872, 648,2208, 656,1184,
+ 664,3232, 680,2720, 688,1696, 696,3744, 712,2464, 720,1440, 728,3488, 736,928, 744,2976,
+ 752,1952, 760,4000, 776,2144, 784,1120, 792,3168, 808,2656, 816,1632, 824,3680, 840,2400,
+ 848,1376, 856,3424, 872,2912, 880,1888, 888,3936, 904,2272, 912,1248, 920,3296, 936,2784,
+ 944,1760, 952,3808, 968,2528, 976,1504, 984,3552, 1000,3040, 1008,2016, 1016,4064,
+ 1032,2064, 1048,3088, 1064,2576, 1072,1552, 1080,3600, 1096,2320, 1104,1296, 1112,3344,
+ 1128,2832, 1136,1808, 1144,3856, 1160,2192, 1176,3216, 1192,2704, 1200,1680, 1208,3728,
+ 1224,2448, 1232,1424, 1240,3472, 1256,2960, 1264,1936, 1272,3984, 1288,2128, 1304,3152,
+ 1320,2640, 1328,1616, 1336,3664, 1352,2384, 1368,3408, 1384,2896, 1392,1872, 1400,3920,
+ 1416,2256, 1432,3280, 1448,2768, 1456,1744, 1464,3792, 1480,2512, 1496,3536, 1512,3024,
+ 1520,2000, 1528,4048, 1544,2096, 1560,3120, 1576,2608, 1592,3632, 1608,2352, 1624,3376,
+ 1640,2864, 1648,1840, 1656,3888, 1672,2224, 1688,3248, 1704,2736, 1720,3760, 1736,2480,
+ 1752,3504, 1768,2992, 1776,1968, 1784,4016, 1800,2160, 1816,3184, 1832,2672, 1848,3696,
+ 1864,2416, 1880,3440, 1896,2928, 1912,3952, 1928,2288, 1944,3312, 1960,2800, 1976,3824,
+ 1992,2544, 2008,3568, 2024,3056, 2040,4080, 2072,3080, 2088,2568, 2104,3592, 2120,2312,
+ 2136,3336, 2152,2824, 2168,3848, 2200,3208, 2216,2696, 2232,3720, 2248,2440, 2264,3464,
+ 2280,2952, 2296,3976, 2328,3144, 2344,2632, 2360,3656, 2392,3400, 2408,2888, 2424,3912,
+ 2456,3272, 2472,2760, 2488,3784, 2520,3528, 2536,3016, 2552,4040, 2584,3112, 2616,3624,
+ 2648,3368, 2664,2856, 2680,3880, 2712,3240, 2744,3752, 2776,3496, 2792,2984, 2808,4008,
+ 2840,3176, 2872,3688, 2904,3432, 2936,3944, 2968,3304, 3000,3816, 3032,3560, 3064,4072,
+ 3128,3608, 3160,3352, 3192,3864, 3256,3736, 3288,3480, 3320,3992, 3384,3672, 3448,3928,
+ 3512,3800, 3576,4056, 3704,3896, 3832,4024
+};
+
+const uint16_t armBitRevIndexTable_fixed_1024[ARMBITREVINDEXTABLE_FIXED_1024_TABLE_LENGTH] =
+{
+ //radix 4, size 992
+ 8,4096, 16,2048, 24,6144, 32,1024, 40,5120, 48,3072, 56,7168, 64,512, 72,4608,
+ 80,2560, 88,6656, 96,1536, 104,5632, 112,3584, 120,7680, 128,256, 136,4352,
+ 144,2304, 152,6400, 160,1280, 168,5376, 176,3328, 184,7424, 192,768, 200,4864,
+ 208,2816, 216,6912, 224,1792, 232,5888, 240,3840, 248,7936, 264,4224, 272,2176,
+ 280,6272, 288,1152, 296,5248, 304,3200, 312,7296, 320,640, 328,4736, 336,2688,
+ 344,6784, 352,1664, 360,5760, 368,3712, 376,7808, 392,4480, 400,2432, 408,6528,
+ 416,1408, 424,5504, 432,3456, 440,7552, 448,896, 456,4992, 464,2944, 472,7040,
+ 480,1920, 488,6016, 496,3968, 504,8064, 520,4160, 528,2112, 536,6208, 544,1088,
+ 552,5184, 560,3136, 568,7232, 584,4672, 592,2624, 600,6720, 608,1600, 616,5696,
+ 624,3648, 632,7744, 648,4416, 656,2368, 664,6464, 672,1344, 680,5440, 688,3392,
+ 696,7488, 704,832, 712,4928, 720,2880, 728,6976, 736,1856, 744,5952, 752,3904,
+ 760,8000, 776,4288, 784,2240, 792,6336, 800,1216, 808,5312, 816,3264, 824,7360,
+ 840,4800, 848,2752, 856,6848, 864,1728, 872,5824, 880,3776, 888,7872, 904,4544,
+ 912,2496, 920,6592, 928,1472, 936,5568, 944,3520, 952,7616, 968,5056, 976,3008,
+ 984,7104, 992,1984, 1000,6080, 1008,4032, 1016,8128, 1032,4128, 1040,2080,
+ 1048,6176, 1064,5152, 1072,3104, 1080,7200, 1096,4640, 1104,2592, 1112,6688,
+ 1120,1568, 1128,5664, 1136,3616, 1144,7712, 1160,4384, 1168,2336, 1176,6432,
+ 1184,1312, 1192,5408, 1200,3360, 1208,7456, 1224,4896, 1232,2848, 1240,6944,
+ 1248,1824, 1256,5920, 1264,3872, 1272,7968, 1288,4256, 1296,2208, 1304,6304,
+ 1320,5280, 1328,3232, 1336,7328, 1352,4768, 1360,2720, 1368,6816, 1376,1696,
+ 1384,5792, 1392,3744, 1400,7840, 1416,4512, 1424,2464, 1432,6560, 1448,5536,
+ 1456,3488, 1464,7584, 1480,5024, 1488,2976, 1496,7072, 1504,1952, 1512,6048,
+ 1520,4000, 1528,8096, 1544,4192, 1552,2144, 1560,6240, 1576,5216, 1584,3168,
+ 1592,7264, 1608,4704, 1616,2656, 1624,6752, 1640,5728, 1648,3680, 1656,7776,
+ 1672,4448, 1680,2400, 1688,6496, 1704,5472, 1712,3424, 1720,7520, 1736,4960,
+ 1744,2912, 1752,7008, 1760,1888, 1768,5984, 1776,3936, 1784,8032, 1800,4320,
+ 1808,2272, 1816,6368, 1832,5344, 1840,3296, 1848,7392, 1864,4832, 1872,2784,
+ 1880,6880, 1896,5856, 1904,3808, 1912,7904, 1928,4576, 1936,2528, 1944,6624,
+ 1960,5600, 1968,3552, 1976,7648, 1992,5088, 2000,3040, 2008,7136, 2024,6112,
+ 2032,4064, 2040,8160, 2056,4112, 2072,6160, 2088,5136, 2096,3088, 2104,7184,
+ 2120,4624, 2128,2576, 2136,6672, 2152,5648, 2160,3600, 2168,7696, 2184,4368,
+ 2192,2320, 2200,6416, 2216,5392, 2224,3344, 2232,7440, 2248,4880, 2256,2832,
+ 2264,6928, 2280,5904, 2288,3856, 2296,7952, 2312,4240, 2328,6288, 2344,5264,
+ 2352,3216, 2360,7312, 2376,4752, 2384,2704, 2392,6800, 2408,5776, 2416,3728,
+ 2424,7824, 2440,4496, 2456,6544, 2472,5520, 2480,3472, 2488,7568, 2504,5008,
+ 2512,2960, 2520,7056, 2536,6032, 2544,3984, 2552,8080, 2568,4176, 2584,6224,
+ 2600,5200, 2608,3152, 2616,7248, 2632,4688, 2648,6736, 2664,5712, 2672,3664,
+ 2680,7760, 2696,4432, 2712,6480, 2728,5456, 2736,3408, 2744,7504, 2760,4944,
+ 2768,2896, 2776,6992, 2792,5968, 2800,3920, 2808,8016, 2824,4304, 2840,6352,
+ 2856,5328, 2864,3280, 2872,7376, 2888,4816, 2904,6864, 2920,5840, 2928,3792,
+ 2936,7888, 2952,4560, 2968,6608, 2984,5584, 2992,3536, 3000,7632, 3016,5072,
+ 3032,7120, 3048,6096, 3056,4048, 3064,8144, 3080,4144, 3096,6192, 3112,5168,
+ 3128,7216, 3144,4656, 3160,6704, 3176,5680, 3184,3632, 3192,7728, 3208,4400,
+ 3224,6448, 3240,5424, 3248,3376, 3256,7472, 3272,4912, 3288,6960, 3304,5936,
+ 3312,3888, 3320,7984, 3336,4272, 3352,6320, 3368,5296, 3384,7344, 3400,4784,
+ 3416,6832, 3432,5808, 3440,3760, 3448,7856, 3464,4528, 3480,6576, 3496,5552,
+ 3512,7600, 3528,5040, 3544,7088, 3560,6064, 3568,4016, 3576,8112, 3592,4208,
+ 3608,6256, 3624,5232, 3640,7280, 3656,4720, 3672,6768, 3688,5744, 3704,7792,
+ 3720,4464, 3736,6512, 3752,5488, 3768,7536, 3784,4976, 3800,7024, 3816,6000,
+ 3824,3952, 3832,8048, 3848,4336, 3864,6384, 3880,5360, 3896,7408, 3912,4848,
+ 3928,6896, 3944,5872, 3960,7920, 3976,4592, 3992,6640, 4008,5616, 4024,7664,
+ 4040,5104, 4056,7152, 4072,6128, 4088,8176, 4120,6152, 4136,5128, 4152,7176,
+ 4168,4616, 4184,6664, 4200,5640, 4216,7688, 4232,4360, 4248,6408, 4264,5384,
+ 4280,7432, 4296,4872, 4312,6920, 4328,5896, 4344,7944, 4376,6280, 4392,5256,
+ 4408,7304, 4424,4744, 4440,6792, 4456,5768, 4472,7816, 4504,6536, 4520,5512,
+ 4536,7560, 4552,5000, 4568,7048, 4584,6024, 4600,8072, 4632,6216, 4648,5192,
+ 4664,7240, 4696,6728, 4712,5704, 4728,7752, 4760,6472, 4776,5448, 4792,7496,
+ 4808,4936, 4824,6984, 4840,5960, 4856,8008, 4888,6344, 4904,5320, 4920,7368,
+ 4952,6856, 4968,5832, 4984,7880, 5016,6600, 5032,5576, 5048,7624, 5080,7112,
+ 5096,6088, 5112,8136, 5144,6184, 5176,7208, 5208,6696, 5224,5672, 5240,7720,
+ 5272,6440, 5288,5416, 5304,7464, 5336,6952, 5352,5928, 5368,7976, 5400,6312,
+ 5432,7336, 5464,6824, 5480,5800, 5496,7848, 5528,6568, 5560,7592, 5592,7080,
+ 5608,6056, 5624,8104, 5656,6248, 5688,7272, 5720,6760, 5752,7784, 5784,6504,
+ 5816,7528, 5848,7016, 5864,5992, 5880,8040, 5912,6376, 5944,7400, 5976,6888,
+ 6008,7912, 6040,6632, 6072,7656, 6104,7144, 6136,8168, 6200,7192, 6232,6680,
+ 6264,7704, 6296,6424, 6328,7448, 6360,6936, 6392,7960, 6456,7320, 6488,6808,
+ 6520,7832, 6584,7576, 6616,7064, 6648,8088, 6712,7256, 6776,7768, 6840,7512,
+ 6872,7000, 6904,8024, 6968,7384, 7032,7896, 7096,7640, 7160,8152, 7288,7736,
+ 7352,7480, 7416,7992, 7544,7864, 7672,8120, 7928,8056
+};
+
+const uint16_t armBitRevIndexTable_fixed_2048[ARMBITREVINDEXTABLE_FIXED_2048_TABLE_LENGTH] =
+{
+ //4x2, size 1984
+ 8,8192, 16,4096, 24,12288, 32,2048, 40,10240, 48,6144, 56,14336, 64,1024,
+ 72,9216, 80,5120, 88,13312, 96,3072, 104,11264, 112,7168, 120,15360, 128,512,
+ 136,8704, 144,4608, 152,12800, 160,2560, 168,10752, 176,6656, 184,14848,
+ 192,1536, 200,9728, 208,5632, 216,13824, 224,3584, 232,11776, 240,7680,
+ 248,15872, 264,8448, 272,4352, 280,12544, 288,2304, 296,10496, 304,6400,
+ 312,14592, 320,1280, 328,9472, 336,5376, 344,13568, 352,3328, 360,11520,
+ 368,7424, 376,15616, 384,768, 392,8960, 400,4864, 408,13056, 416,2816,
+ 424,11008, 432,6912, 440,15104, 448,1792, 456,9984, 464,5888, 472,14080,
+ 480,3840, 488,12032, 496,7936, 504,16128, 520,8320, 528,4224, 536,12416,
+ 544,2176, 552,10368, 560,6272, 568,14464, 576,1152, 584,9344, 592,5248,
+ 600,13440, 608,3200, 616,11392, 624,7296, 632,15488, 648,8832, 656,4736,
+ 664,12928, 672,2688, 680,10880, 688,6784, 696,14976, 704,1664, 712,9856,
+ 720,5760, 728,13952, 736,3712, 744,11904, 752,7808, 760,16000, 776,8576,
+ 784,4480, 792,12672, 800,2432, 808,10624, 816,6528, 824,14720, 832,1408,
+ 840,9600, 848,5504, 856,13696, 864,3456, 872,11648, 880,7552, 888,15744,
+ 904,9088, 912,4992, 920,13184, 928,2944, 936,11136, 944,7040, 952,15232,
+ 960,1920, 968,10112, 976,6016, 984,14208, 992,3968, 1000,12160, 1008,8064,
+ 1016,16256, 1032,8256, 1040,4160, 1048,12352, 1056,2112, 1064,10304, 1072,6208,
+ 1080,14400, 1096,9280, 1104,5184, 1112,13376, 1120,3136, 1128,11328, 1136,7232,
+ 1144,15424, 1160,8768, 1168,4672, 1176,12864, 1184,2624, 1192,10816, 1200,6720,
+ 1208,14912, 1216,1600, 1224,9792, 1232,5696, 1240,13888, 1248,3648, 1256,11840,
+ 1264,7744, 1272,15936, 1288,8512, 1296,4416, 1304,12608, 1312,2368, 1320,10560,
+ 1328,6464, 1336,14656, 1352,9536, 1360,5440, 1368,13632, 1376,3392, 1384,11584,
+ 1392,7488, 1400,15680, 1416,9024, 1424,4928, 1432,13120, 1440,2880, 1448,11072,
+ 1456,6976, 1464,15168, 1472,1856, 1480,10048, 1488,5952, 1496,14144, 1504,3904,
+ 1512,12096, 1520,8000, 1528,16192, 1544,8384, 1552,4288, 1560,12480, 1568,2240,
+ 1576,10432, 1584,6336, 1592,14528, 1608,9408, 1616,5312, 1624,13504, 1632,3264,
+ 1640,11456, 1648,7360, 1656,15552, 1672,8896, 1680,4800, 1688,12992, 1696,2752,
+ 1704,10944, 1712,6848, 1720,15040, 1736,9920, 1744,5824, 1752,14016, 1760,3776,
+ 1768,11968, 1776,7872, 1784,16064, 1800,8640, 1808,4544, 1816,12736, 1824,2496,
+ 1832,10688, 1840,6592, 1848,14784, 1864,9664, 1872,5568, 1880,13760, 1888,3520,
+ 1896,11712, 1904,7616, 1912,15808, 1928,9152, 1936,5056, 1944,13248, 1952,3008,
+ 1960,11200, 1968,7104, 1976,15296, 1992,10176, 2000,6080, 2008,14272, 2016,4032,
+ 2024,12224, 2032,8128, 2040,16320, 2056,8224, 2064,4128, 2072,12320, 2088,10272,
+ 2096,6176, 2104,14368, 2120,9248, 2128,5152, 2136,13344, 2144,3104, 2152,11296,
+ 2160,7200, 2168,15392, 2184,8736, 2192,4640, 2200,12832, 2208,2592, 2216,10784,
+ 2224,6688, 2232,14880, 2248,9760, 2256,5664, 2264,13856, 2272,3616, 2280,11808,
+ 2288,7712, 2296,15904, 2312,8480, 2320,4384, 2328,12576, 2344,10528, 2352,6432,
+ 2360,14624, 2376,9504, 2384,5408, 2392,13600, 2400,3360, 2408,11552, 2416,7456,
+ 2424,15648, 2440,8992, 2448,4896, 2456,13088, 2464,2848, 2472,11040, 2480,6944,
+ 2488,15136, 2504,10016, 2512,5920, 2520,14112, 2528,3872, 2536,12064, 2544,7968,
+ 2552,16160, 2568,8352, 2576,4256, 2584,12448, 2600,10400, 2608,6304, 2616,14496,
+ 2632,9376, 2640,5280, 2648,13472, 2656,3232, 2664,11424, 2672,7328, 2680,15520,
+ 2696,8864, 2704,4768, 2712,12960, 2728,10912, 2736,6816, 2744,15008, 2760,9888,
+ 2768,5792, 2776,13984, 2784,3744, 2792,11936, 2800,7840, 2808,16032, 2824,8608,
+ 2832,4512, 2840,12704, 2856,10656, 2864,6560, 2872,14752, 2888,9632, 2896,5536,
+ 2904,13728, 2912,3488, 2920,11680, 2928,7584, 2936,15776, 2952,9120, 2960,5024,
+ 2968,13216, 2984,11168, 2992,7072, 3000,15264, 3016,10144, 3024,6048,
+ 3032,14240, 3040,4000, 3048,12192, 3056,8096, 3064,16288, 3080,8288, 3088,4192,
+ 3096,12384, 3112,10336, 3120,6240, 3128,14432, 3144,9312, 3152,5216, 3160,13408,
+ 3176,11360, 3184,7264, 3192,15456, 3208,8800, 3216,4704, 3224,12896, 3240,10848,
+ 3248,6752, 3256,14944, 3272,9824, 3280,5728, 3288,13920, 3296,3680, 3304,11872,
+ 3312,7776, 3320,15968, 3336,8544, 3344,4448, 3352,12640, 3368,10592, 3376,6496,
+ 3384,14688, 3400,9568, 3408,5472, 3416,13664, 3432,11616, 3440,7520, 3448,15712,
+ 3464,9056, 3472,4960, 3480,13152, 3496,11104, 3504,7008, 3512,15200, 3528,10080,
+ 3536,5984, 3544,14176, 3552,3936, 3560,12128, 3568,8032, 3576,16224, 3592,8416,
+ 3600,4320, 3608,12512, 3624,10464, 3632,6368, 3640,14560, 3656,9440, 3664,5344,
+ 3672,13536, 3688,11488, 3696,7392, 3704,15584, 3720,8928, 3728,4832, 3736,13024,
+ 3752,10976, 3760,6880, 3768,15072, 3784,9952, 3792,5856, 3800,14048, 3816,12000,
+ 3824,7904, 3832,16096, 3848,8672, 3856,4576, 3864,12768, 3880,10720, 3888,6624,
+ 3896,14816, 3912,9696, 3920,5600, 3928,13792, 3944,11744, 3952,7648, 3960,15840,
+ 3976,9184, 3984,5088, 3992,13280, 4008,11232, 4016,7136, 4024,15328, 4040,10208,
+ 4048,6112, 4056,14304, 4072,12256, 4080,8160, 4088,16352, 4104,8208, 4120,12304,
+ 4136,10256, 4144,6160, 4152,14352, 4168,9232, 4176,5136, 4184,13328, 4200,11280,
+ 4208,7184, 4216,15376, 4232,8720, 4240,4624, 4248,12816, 4264,10768, 4272,6672,
+ 4280,14864, 4296,9744, 4304,5648, 4312,13840, 4328,11792, 4336,7696, 4344,15888,
+ 4360,8464, 4376,12560, 4392,10512, 4400,6416, 4408,14608, 4424,9488, 4432,5392,
+ 4440,13584, 4456,11536, 4464,7440, 4472,15632, 4488,8976, 4496,4880, 4504,13072,
+ 4520,11024, 4528,6928, 4536,15120, 4552,10000, 4560,5904, 4568,14096,
+ 4584,12048, 4592,7952, 4600,16144, 4616,8336, 4632,12432, 4648,10384, 4656,6288,
+ 4664,14480, 4680,9360, 4688,5264, 4696,13456, 4712,11408, 4720,7312, 4728,15504,
+ 4744,8848, 4760,12944, 4776,10896, 4784,6800, 4792,14992, 4808,9872, 4816,5776,
+ 4824,13968, 4840,11920, 4848,7824, 4856,16016, 4872,8592, 4888,12688,
+ 4904,10640, 4912,6544, 4920,14736, 4936,9616, 4944,5520, 4952,13712, 4968,11664,
+ 4976,7568, 4984,15760, 5000,9104, 5016,13200, 5032,11152, 5040,7056, 5048,15248,
+ 5064,10128, 5072,6032, 5080,14224, 5096,12176, 5104,8080, 5112,16272, 5128,8272,
+ 5144,12368, 5160,10320, 5168,6224, 5176,14416, 5192,9296, 5208,13392,
+ 5224,11344, 5232,7248, 5240,15440, 5256,8784, 5272,12880, 5288,10832, 5296,6736,
+ 5304,14928, 5320,9808, 5328,5712, 5336,13904, 5352,11856, 5360,7760, 5368,15952,
+ 5384,8528, 5400,12624, 5416,10576, 5424,6480, 5432,14672, 5448,9552, 5464,13648,
+ 5480,11600, 5488,7504, 5496,15696, 5512,9040, 5528,13136, 5544,11088, 5552,6992,
+ 5560,15184, 5576,10064, 5584,5968, 5592,14160, 5608,12112, 5616,8016,
+ 5624,16208, 5640,8400, 5656,12496, 5672,10448, 5680,6352, 5688,14544, 5704,9424,
+ 5720,13520, 5736,11472, 5744,7376, 5752,15568, 5768,8912, 5784,13008,
+ 5800,10960, 5808,6864, 5816,15056, 5832,9936, 5848,14032, 5864,11984, 5872,7888,
+ 5880,16080, 5896,8656, 5912,12752, 5928,10704, 5936,6608, 5944,14800, 5960,9680,
+ 5976,13776, 5992,11728, 6000,7632, 6008,15824, 6024,9168, 6040,13264,
+ 6056,11216, 6064,7120, 6072,15312, 6088,10192, 6104,14288, 6120,12240,
+ 6128,8144, 6136,16336, 6152,8240, 6168,12336, 6184,10288, 6200,14384, 6216,9264,
+ 6232,13360, 6248,11312, 6256,7216, 6264,15408, 6280,8752, 6296,12848,
+ 6312,10800, 6320,6704, 6328,14896, 6344,9776, 6360,13872, 6376,11824, 6384,7728,
+ 6392,15920, 6408,8496, 6424,12592, 6440,10544, 6456,14640, 6472,9520,
+ 6488,13616, 6504,11568, 6512,7472, 6520,15664, 6536,9008, 6552,13104,
+ 6568,11056, 6576,6960, 6584,15152, 6600,10032, 6616,14128, 6632,12080,
+ 6640,7984, 6648,16176, 6664,8368, 6680,12464, 6696,10416, 6712,14512, 6728,9392,
+ 6744,13488, 6760,11440, 6768,7344, 6776,15536, 6792,8880, 6808,12976,
+ 6824,10928, 6840,15024, 6856,9904, 6872,14000, 6888,11952, 6896,7856,
+ 6904,16048, 6920,8624, 6936,12720, 6952,10672, 6968,14768, 6984,9648,
+ 7000,13744, 7016,11696, 7024,7600, 7032,15792, 7048,9136, 7064,13232,
+ 7080,11184, 7096,15280, 7112,10160, 7128,14256, 7144,12208, 7152,8112,
+ 7160,16304, 7176,8304, 7192,12400, 7208,10352, 7224,14448, 7240,9328,
+ 7256,13424, 7272,11376, 7288,15472, 7304,8816, 7320,12912, 7336,10864,
+ 7352,14960, 7368,9840, 7384,13936, 7400,11888, 7408,7792, 7416,15984, 7432,8560,
+ 7448,12656, 7464,10608, 7480,14704, 7496,9584, 7512,13680, 7528,11632,
+ 7544,15728, 7560,9072, 7576,13168, 7592,11120, 7608,15216, 7624,10096,
+ 7640,14192, 7656,12144, 7664,8048, 7672,16240, 7688,8432, 7704,12528,
+ 7720,10480, 7736,14576, 7752,9456, 7768,13552, 7784,11504, 7800,15600,
+ 7816,8944, 7832,13040, 7848,10992, 7864,15088, 7880,9968, 7896,14064,
+ 7912,12016, 7928,16112, 7944,8688, 7960,12784, 7976,10736, 7992,14832,
+ 8008,9712, 8024,13808, 8040,11760, 8056,15856, 8072,9200, 8088,13296,
+ 8104,11248, 8120,15344, 8136,10224, 8152,14320, 8168,12272, 8184,16368,
+ 8216,12296, 8232,10248, 8248,14344, 8264,9224, 8280,13320, 8296,11272,
+ 8312,15368, 8328,8712, 8344,12808, 8360,10760, 8376,14856, 8392,9736,
+ 8408,13832, 8424,11784, 8440,15880, 8472,12552, 8488,10504, 8504,14600,
+ 8520,9480, 8536,13576, 8552,11528, 8568,15624, 8584,8968, 8600,13064,
+ 8616,11016, 8632,15112, 8648,9992, 8664,14088, 8680,12040, 8696,16136,
+ 8728,12424, 8744,10376, 8760,14472, 8776,9352, 8792,13448, 8808,11400,
+ 8824,15496, 8856,12936, 8872,10888, 8888,14984, 8904,9864, 8920,13960,
+ 8936,11912, 8952,16008, 8984,12680, 9000,10632, 9016,14728, 9032,9608,
+ 9048,13704, 9064,11656, 9080,15752, 9112,13192, 9128,11144, 9144,15240,
+ 9160,10120, 9176,14216, 9192,12168, 9208,16264, 9240,12360, 9256,10312,
+ 9272,14408, 9304,13384, 9320,11336, 9336,15432, 9368,12872, 9384,10824,
+ 9400,14920, 9416,9800, 9432,13896, 9448,11848, 9464,15944, 9496,12616,
+ 9512,10568, 9528,14664, 9560,13640, 9576,11592, 9592,15688, 9624,13128,
+ 9640,11080, 9656,15176, 9672,10056, 9688,14152, 9704,12104, 9720,16200,
+ 9752,12488, 9768,10440, 9784,14536, 9816,13512, 9832,11464, 9848,15560,
+ 9880,13000, 9896,10952, 9912,15048, 9944,14024, 9960,11976, 9976,16072,
+ 10008,12744, 10024,10696, 10040,14792, 10072,13768, 10088,11720, 10104,15816,
+ 10136,13256, 10152,11208, 10168,15304, 10200,14280, 10216,12232, 10232,16328,
+ 10264,12328, 10296,14376, 10328,13352, 10344,11304, 10360,15400, 10392,12840,
+ 10408,10792, 10424,14888, 10456,13864, 10472,11816, 10488,15912, 10520,12584,
+ 10552,14632, 10584,13608, 10600,11560, 10616,15656, 10648,13096, 10664,11048,
+ 10680,15144, 10712,14120, 10728,12072, 10744,16168, 10776,12456, 10808,14504,
+ 10840,13480, 10856,11432, 10872,15528, 10904,12968, 10936,15016, 10968,13992,
+ 10984,11944, 11000,16040, 11032,12712, 11064,14760, 11096,13736, 11112,11688,
+ 11128,15784, 11160,13224, 11192,15272, 11224,14248, 11240,12200, 11256,16296,
+ 11288,12392, 11320,14440, 11352,13416, 11384,15464, 11416,12904, 11448,14952,
+ 11480,13928, 11496,11880, 11512,15976, 11544,12648, 11576,14696, 11608,13672,
+ 11640,15720, 11672,13160, 11704,15208, 11736,14184, 11752,12136, 11768,16232,
+ 11800,12520, 11832,14568, 11864,13544, 11896,15592, 11928,13032, 11960,15080,
+ 11992,14056, 12024,16104, 12056,12776, 12088,14824, 12120,13800, 12152,15848,
+ 12184,13288, 12216,15336, 12248,14312, 12280,16360, 12344,14360, 12376,13336,
+ 12408,15384, 12440,12824, 12472,14872, 12504,13848, 12536,15896, 12600,14616,
+ 12632,13592, 12664,15640, 12696,13080, 12728,15128, 12760,14104, 12792,16152,
+ 12856,14488, 12888,13464, 12920,15512, 12984,15000, 13016,13976, 13048,16024,
+ 13112,14744, 13144,13720, 13176,15768, 13240,15256, 13272,14232, 13304,16280,
+ 13368,14424, 13432,15448, 13496,14936, 13528,13912, 13560,15960, 13624,14680,
+ 13688,15704, 13752,15192, 13784,14168, 13816,16216, 13880,14552, 13944,15576,
+ 14008,15064, 14072,16088, 14136,14808, 14200,15832, 14264,15320, 14328,16344,
+ 14456,15416, 14520,14904, 14584,15928, 14712,15672, 14776,15160, 14840,16184,
+ 14968,15544, 15096,16056, 15224,15800, 15352,16312, 15608,15992, 15864,16248
+};
+
+const uint16_t armBitRevIndexTable_fixed_4096[ARMBITREVINDEXTABLE_FIXED_4096_TABLE_LENGTH] =
+{
+ //radix 4, size 4032
+ 8,16384, 16,8192, 24,24576, 32,4096, 40,20480, 48,12288, 56,28672, 64,2048,
+ 72,18432, 80,10240, 88,26624, 96,6144, 104,22528, 112,14336, 120,30720,
+ 128,1024, 136,17408, 144,9216, 152,25600, 160,5120, 168,21504, 176,13312,
+ 184,29696, 192,3072, 200,19456, 208,11264, 216,27648, 224,7168, 232,23552,
+ 240,15360, 248,31744, 256,512, 264,16896, 272,8704, 280,25088, 288,4608,
+ 296,20992, 304,12800, 312,29184, 320,2560, 328,18944, 336,10752, 344,27136,
+ 352,6656, 360,23040, 368,14848, 376,31232, 384,1536, 392,17920, 400,9728,
+ 408,26112, 416,5632, 424,22016, 432,13824, 440,30208, 448,3584, 456,19968,
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+ 13296,16176, 13304,32560, 13320,16560, 13336,24752, 13352,20656, 13368,28848,
+ 13384,18608, 13400,26800, 13416,22704, 13424,14512, 13432,30896, 13448,17584,
+ 13464,25776, 13480,21680, 13496,29872, 13512,19632, 13528,27824, 13544,23728,
+ 13552,15536, 13560,31920, 13576,17072, 13592,25264, 13608,21168, 13624,29360,
+ 13640,19120, 13656,27312, 13672,23216, 13680,15024, 13688,31408, 13704,18096,
+ 13720,26288, 13736,22192, 13744,14000, 13752,30384, 13768,20144, 13784,28336,
+ 13800,24240, 13808,16048, 13816,32432, 13832,16816, 13848,25008, 13864,20912,
+ 13880,29104, 13896,18864, 13912,27056, 13928,22960, 13936,14768, 13944,31152,
+ 13960,17840, 13976,26032, 13992,21936, 14008,30128, 14024,19888, 14040,28080,
+ 14056,23984, 14064,15792, 14072,32176, 14088,17328, 14104,25520, 14120,21424,
+ 14136,29616, 14152,19376, 14168,27568, 14184,23472, 14192,15280, 14200,31664,
+ 14216,18352, 14232,26544, 14248,22448, 14264,30640, 14280,20400, 14296,28592,
+ 14312,24496, 14320,16304, 14328,32688, 14344,16496, 14360,24688, 14376,20592,
+ 14392,28784, 14408,18544, 14424,26736, 14440,22640, 14456,30832, 14472,17520,
+ 14488,25712, 14504,21616, 14520,29808, 14536,19568, 14552,27760, 14568,23664,
+ 14576,15472, 14584,31856, 14600,17008, 14616,25200, 14632,21104, 14648,29296,
+ 14664,19056, 14680,27248, 14696,23152, 14704,14960, 14712,31344, 14728,18032,
+ 14744,26224, 14760,22128, 14776,30320, 14792,20080, 14808,28272, 14824,24176,
+ 14832,15984, 14840,32368, 14856,16752, 14872,24944, 14888,20848, 14904,29040,
+ 14920,18800, 14936,26992, 14952,22896, 14968,31088, 14984,17776, 15000,25968,
+ 15016,21872, 15032,30064, 15048,19824, 15064,28016, 15080,23920, 15088,15728,
+ 15096,32112, 15112,17264, 15128,25456, 15144,21360, 15160,29552, 15176,19312,
+ 15192,27504, 15208,23408, 15224,31600, 15240,18288, 15256,26480, 15272,22384,
+ 15288,30576, 15304,20336, 15320,28528, 15336,24432, 15344,16240, 15352,32624,
+ 15368,16624, 15384,24816, 15400,20720, 15416,28912, 15432,18672, 15448,26864,
+ 15464,22768, 15480,30960, 15496,17648, 15512,25840, 15528,21744, 15544,29936,
+ 15560,19696, 15576,27888, 15592,23792, 15608,31984, 15624,17136, 15640,25328,
+ 15656,21232, 15672,29424, 15688,19184, 15704,27376, 15720,23280, 15736,31472,
+ 15752,18160, 15768,26352, 15784,22256, 15800,30448, 15816,20208, 15832,28400,
+ 15848,24304, 15856,16112, 15864,32496, 15880,16880, 15896,25072, 15912,20976,
+ 15928,29168, 15944,18928, 15960,27120, 15976,23024, 15992,31216, 16008,17904,
+ 16024,26096, 16040,22000, 16056,30192, 16072,19952, 16088,28144, 16104,24048,
+ 16120,32240, 16136,17392, 16152,25584, 16168,21488, 16184,29680, 16200,19440,
+ 16216,27632, 16232,23536, 16248,31728, 16264,18416, 16280,26608, 16296,22512,
+ 16312,30704, 16328,20464, 16344,28656, 16360,24560, 16376,32752, 16408,24584,
+ 16424,20488, 16440,28680, 16456,18440, 16472,26632, 16488,22536, 16504,30728,
+ 16520,17416, 16536,25608, 16552,21512, 16568,29704, 16584,19464, 16600,27656,
+ 16616,23560, 16632,31752, 16648,16904, 16664,25096, 16680,21000, 16696,29192,
+ 16712,18952, 16728,27144, 16744,23048, 16760,31240, 16776,17928, 16792,26120,
+ 16808,22024, 16824,30216, 16840,19976, 16856,28168, 16872,24072, 16888,32264,
+ 16920,24840, 16936,20744, 16952,28936, 16968,18696, 16984,26888, 17000,22792,
+ 17016,30984, 17032,17672, 17048,25864, 17064,21768, 17080,29960, 17096,19720,
+ 17112,27912, 17128,23816, 17144,32008, 17176,25352, 17192,21256, 17208,29448,
+ 17224,19208, 17240,27400, 17256,23304, 17272,31496, 17288,18184, 17304,26376,
+ 17320,22280, 17336,30472, 17352,20232, 17368,28424, 17384,24328, 17400,32520,
+ 17432,24712, 17448,20616, 17464,28808, 17480,18568, 17496,26760, 17512,22664,
+ 17528,30856, 17560,25736, 17576,21640, 17592,29832, 17608,19592, 17624,27784,
+ 17640,23688, 17656,31880, 17688,25224, 17704,21128, 17720,29320, 17736,19080,
+ 17752,27272, 17768,23176, 17784,31368, 17800,18056, 17816,26248, 17832,22152,
+ 17848,30344, 17864,20104, 17880,28296, 17896,24200, 17912,32392, 17944,24968,
+ 17960,20872, 17976,29064, 17992,18824, 18008,27016, 18024,22920, 18040,31112,
+ 18072,25992, 18088,21896, 18104,30088, 18120,19848, 18136,28040, 18152,23944,
+ 18168,32136, 18200,25480, 18216,21384, 18232,29576, 18248,19336, 18264,27528,
+ 18280,23432, 18296,31624, 18328,26504, 18344,22408, 18360,30600, 18376,20360,
+ 18392,28552, 18408,24456, 18424,32648, 18456,24648, 18472,20552, 18488,28744,
+ 18520,26696, 18536,22600, 18552,30792, 18584,25672, 18600,21576, 18616,29768,
+ 18632,19528, 18648,27720, 18664,23624, 18680,31816, 18712,25160, 18728,21064,
+ 18744,29256, 18760,19016, 18776,27208, 18792,23112, 18808,31304, 18840,26184,
+ 18856,22088, 18872,30280, 18888,20040, 18904,28232, 18920,24136, 18936,32328,
+ 18968,24904, 18984,20808, 19000,29000, 19032,26952, 19048,22856, 19064,31048,
+ 19096,25928, 19112,21832, 19128,30024, 19144,19784, 19160,27976, 19176,23880,
+ 19192,32072, 19224,25416, 19240,21320, 19256,29512, 19288,27464, 19304,23368,
+ 19320,31560, 19352,26440, 19368,22344, 19384,30536, 19400,20296, 19416,28488,
+ 19432,24392, 19448,32584, 19480,24776, 19496,20680, 19512,28872, 19544,26824,
+ 19560,22728, 19576,30920, 19608,25800, 19624,21704, 19640,29896, 19672,27848,
+ 19688,23752, 19704,31944, 19736,25288, 19752,21192, 19768,29384, 19800,27336,
+ 19816,23240, 19832,31432, 19864,26312, 19880,22216, 19896,30408, 19912,20168,
+ 19928,28360, 19944,24264, 19960,32456, 19992,25032, 20008,20936, 20024,29128,
+ 20056,27080, 20072,22984, 20088,31176, 20120,26056, 20136,21960, 20152,30152,
+ 20184,28104, 20200,24008, 20216,32200, 20248,25544, 20264,21448, 20280,29640,
+ 20312,27592, 20328,23496, 20344,31688, 20376,26568, 20392,22472, 20408,30664,
+ 20440,28616, 20456,24520, 20472,32712, 20504,24616, 20536,28712, 20568,26664,
+ 20584,22568, 20600,30760, 20632,25640, 20648,21544, 20664,29736, 20696,27688,
+ 20712,23592, 20728,31784, 20760,25128, 20776,21032, 20792,29224, 20824,27176,
+ 20840,23080, 20856,31272, 20888,26152, 20904,22056, 20920,30248, 20952,28200,
+ 20968,24104, 20984,32296, 21016,24872, 21048,28968, 21080,26920, 21096,22824,
+ 21112,31016, 21144,25896, 21160,21800, 21176,29992, 21208,27944, 21224,23848,
+ 21240,32040, 21272,25384, 21304,29480, 21336,27432, 21352,23336, 21368,31528,
+ 21400,26408, 21416,22312, 21432,30504, 21464,28456, 21480,24360, 21496,32552,
+ 21528,24744, 21560,28840, 21592,26792, 21608,22696, 21624,30888, 21656,25768,
+ 21688,29864, 21720,27816, 21736,23720, 21752,31912, 21784,25256, 21816,29352,
+ 21848,27304, 21864,23208, 21880,31400, 21912,26280, 21928,22184, 21944,30376,
+ 21976,28328, 21992,24232, 22008,32424, 22040,25000, 22072,29096, 22104,27048,
+ 22120,22952, 22136,31144, 22168,26024, 22200,30120, 22232,28072, 22248,23976,
+ 22264,32168, 22296,25512, 22328,29608, 22360,27560, 22376,23464, 22392,31656,
+ 22424,26536, 22456,30632, 22488,28584, 22504,24488, 22520,32680, 22552,24680,
+ 22584,28776, 22616,26728, 22648,30824, 22680,25704, 22712,29800, 22744,27752,
+ 22760,23656, 22776,31848, 22808,25192, 22840,29288, 22872,27240, 22888,23144,
+ 22904,31336, 22936,26216, 22968,30312, 23000,28264, 23016,24168, 23032,32360,
+ 23064,24936, 23096,29032, 23128,26984, 23160,31080, 23192,25960, 23224,30056,
+ 23256,28008, 23272,23912, 23288,32104, 23320,25448, 23352,29544, 23384,27496,
+ 23416,31592, 23448,26472, 23480,30568, 23512,28520, 23528,24424, 23544,32616,
+ 23576,24808, 23608,28904, 23640,26856, 23672,30952, 23704,25832, 23736,29928,
+ 23768,27880, 23800,31976, 23832,25320, 23864,29416, 23896,27368, 23928,31464,
+ 23960,26344, 23992,30440, 24024,28392, 24040,24296, 24056,32488, 24088,25064,
+ 24120,29160, 24152,27112, 24184,31208, 24216,26088, 24248,30184, 24280,28136,
+ 24312,32232, 24344,25576, 24376,29672, 24408,27624, 24440,31720, 24472,26600,
+ 24504,30696, 24536,28648, 24568,32744, 24632,28696, 24664,26648, 24696,30744,
+ 24728,25624, 24760,29720, 24792,27672, 24824,31768, 24856,25112, 24888,29208,
+ 24920,27160, 24952,31256, 24984,26136, 25016,30232, 25048,28184, 25080,32280,
+ 25144,28952, 25176,26904, 25208,31000, 25240,25880, 25272,29976, 25304,27928,
+ 25336,32024, 25400,29464, 25432,27416, 25464,31512, 25496,26392, 25528,30488,
+ 25560,28440, 25592,32536, 25656,28824, 25688,26776, 25720,30872, 25784,29848,
+ 25816,27800, 25848,31896, 25912,29336, 25944,27288, 25976,31384, 26008,26264,
+ 26040,30360, 26072,28312, 26104,32408, 26168,29080, 26200,27032, 26232,31128,
+ 26296,30104, 26328,28056, 26360,32152, 26424,29592, 26456,27544, 26488,31640,
+ 26552,30616, 26584,28568, 26616,32664, 26680,28760, 26744,30808, 26808,29784,
+ 26840,27736, 26872,31832, 26936,29272, 26968,27224, 27000,31320, 27064,30296,
+ 27096,28248, 27128,32344, 27192,29016, 27256,31064, 27320,30040, 27352,27992,
+ 27384,32088, 27448,29528, 27512,31576, 27576,30552, 27608,28504, 27640,32600,
+ 27704,28888, 27768,30936, 27832,29912, 27896,31960, 27960,29400, 28024,31448,
+ 28088,30424, 28120,28376, 28152,32472, 28216,29144, 28280,31192, 28344,30168,
+ 28408,32216, 28472,29656, 28536,31704, 28600,30680, 28664,32728, 28792,30776,
+ 28856,29752, 28920,31800, 28984,29240, 29048,31288, 29112,30264, 29176,32312,
+ 29304,31032, 29368,30008, 29432,32056, 29560,31544, 29624,30520, 29688,32568,
+ 29816,30904, 29944,31928, 30072,31416, 30136,30392, 30200,32440, 30328,31160,
+ 30456,32184, 30584,31672, 30712,32696, 30968,31864, 31096,31352, 31224,32376,
+ 31480,32120, 31736,32632, 32248,32504
+};
+
+/**
+* \par
+* Example code for Floating-point RFFT Twiddle factors Generation:
+* \par
+* TW = exp(2*pi*i*[0:L/2-1]/L - pi/2*i).'
+* \par
+* Real and Imag values are in interleaved fashion
+*/
+const float32_t twiddleCoef_rfft_32[32] = {
+0.0f , 1.0f ,
+0.195090322f , 0.98078528f ,
+0.382683432f , 0.923879533f ,
+0.555570233f , 0.831469612f ,
+0.707106781f , 0.707106781f ,
+0.831469612f , 0.555570233f ,
+0.923879533f , 0.382683432f ,
+0.98078528f , 0.195090322f ,
+1.0f , 0.0f ,
+0.98078528f , -0.195090322f ,
+0.923879533f , -0.382683432f ,
+0.831469612f , -0.555570233f ,
+0.707106781f , -0.707106781f ,
+0.555570233f , -0.831469612f ,
+0.382683432f , -0.923879533f ,
+0.195090322f , -0.98078528f
+};
+
+const float32_t twiddleCoef_rfft_64[64] = {
+0.0f, 1.0f,
+0.098017140329561f, 0.995184726672197f,
+0.195090322016128f, 0.98078528040323f,
+0.290284677254462f, 0.956940335732209f,
+0.38268343236509f, 0.923879532511287f,
+0.471396736825998f, 0.881921264348355f,
+0.555570233019602f, 0.831469612302545f,
+0.634393284163645f, 0.773010453362737f,
+0.707106781186547f, 0.707106781186548f,
+0.773010453362737f, 0.634393284163645f,
+0.831469612302545f, 0.555570233019602f,
+0.881921264348355f, 0.471396736825998f,
+0.923879532511287f, 0.38268343236509f,
+0.956940335732209f, 0.290284677254462f,
+0.98078528040323f, 0.195090322016128f,
+0.995184726672197f, 0.098017140329561f,
+1.0f, 0.0f,
+0.995184726672197f, -0.098017140329561f,
+0.98078528040323f, -0.195090322016128f,
+0.956940335732209f, -0.290284677254462f,
+0.923879532511287f, -0.38268343236509f,
+0.881921264348355f, -0.471396736825998f,
+0.831469612302545f, -0.555570233019602f,
+0.773010453362737f, -0.634393284163645f,
+0.707106781186548f, -0.707106781186547f,
+0.634393284163645f, -0.773010453362737f,
+0.555570233019602f, -0.831469612302545f,
+0.471396736825998f, -0.881921264348355f,
+0.38268343236509f, -0.923879532511287f,
+0.290284677254462f, -0.956940335732209f,
+0.195090322016129f, -0.98078528040323f,
+0.098017140329561f, -0.995184726672197f
+};
+
+const float32_t twiddleCoef_rfft_128[128] = {
+ 0.000000000f, 1.000000000f,
+ 0.049067674f, 0.998795456f,
+ 0.098017140f, 0.995184727f,
+ 0.146730474f, 0.989176510f,
+ 0.195090322f, 0.980785280f,
+ 0.242980180f, 0.970031253f,
+ 0.290284677f, 0.956940336f,
+ 0.336889853f, 0.941544065f,
+ 0.382683432f, 0.923879533f,
+ 0.427555093f, 0.903989293f,
+ 0.471396737f, 0.881921264f,
+ 0.514102744f, 0.857728610f,
+ 0.555570233f, 0.831469612f,
+ 0.595699304f, 0.803207531f,
+ 0.634393284f, 0.773010453f,
+ 0.671558955f, 0.740951125f,
+ 0.707106781f, 0.707106781f,
+ 0.740951125f, 0.671558955f,
+ 0.773010453f, 0.634393284f,
+ 0.803207531f, 0.595699304f,
+ 0.831469612f, 0.555570233f,
+ 0.857728610f, 0.514102744f,
+ 0.881921264f, 0.471396737f,
+ 0.903989293f, 0.427555093f,
+ 0.923879533f, 0.382683432f,
+ 0.941544065f, 0.336889853f,
+ 0.956940336f, 0.290284677f,
+ 0.970031253f, 0.242980180f,
+ 0.980785280f, 0.195090322f,
+ 0.989176510f, 0.146730474f,
+ 0.995184727f, 0.098017140f,
+ 0.998795456f, 0.049067674f,
+ 1.000000000f, 0.000000000f,
+ 0.998795456f, -0.049067674f,
+ 0.995184727f, -0.098017140f,
+ 0.989176510f, -0.146730474f,
+ 0.980785280f, -0.195090322f,
+ 0.970031253f, -0.242980180f,
+ 0.956940336f, -0.290284677f,
+ 0.941544065f, -0.336889853f,
+ 0.923879533f, -0.382683432f,
+ 0.903989293f, -0.427555093f,
+ 0.881921264f, -0.471396737f,
+ 0.857728610f, -0.514102744f,
+ 0.831469612f, -0.555570233f,
+ 0.803207531f, -0.595699304f,
+ 0.773010453f, -0.634393284f,
+ 0.740951125f, -0.671558955f,
+ 0.707106781f, -0.707106781f,
+ 0.671558955f, -0.740951125f,
+ 0.634393284f, -0.773010453f,
+ 0.595699304f, -0.803207531f,
+ 0.555570233f, -0.831469612f,
+ 0.514102744f, -0.857728610f,
+ 0.471396737f, -0.881921264f,
+ 0.427555093f, -0.903989293f,
+ 0.382683432f, -0.923879533f,
+ 0.336889853f, -0.941544065f,
+ 0.290284677f, -0.956940336f,
+ 0.242980180f, -0.970031253f,
+ 0.195090322f, -0.980785280f,
+ 0.146730474f, -0.989176510f,
+ 0.098017140f, -0.995184727f,
+ 0.049067674f, -0.998795456f
+};
+
+const float32_t twiddleCoef_rfft_256[256] = {
+ 0.000000000f, 1.000000000f,
+ 0.024541229f, 0.999698819f,
+ 0.049067674f, 0.998795456f,
+ 0.073564564f, 0.997290457f,
+ 0.098017140f, 0.995184727f,
+ 0.122410675f, 0.992479535f,
+ 0.146730474f, 0.989176510f,
+ 0.170961889f, 0.985277642f,
+ 0.195090322f, 0.980785280f,
+ 0.219101240f, 0.975702130f,
+ 0.242980180f, 0.970031253f,
+ 0.266712757f, 0.963776066f,
+ 0.290284677f, 0.956940336f,
+ 0.313681740f, 0.949528181f,
+ 0.336889853f, 0.941544065f,
+ 0.359895037f, 0.932992799f,
+ 0.382683432f, 0.923879533f,
+ 0.405241314f, 0.914209756f,
+ 0.427555093f, 0.903989293f,
+ 0.449611330f, 0.893224301f,
+ 0.471396737f, 0.881921264f,
+ 0.492898192f, 0.870086991f,
+ 0.514102744f, 0.857728610f,
+ 0.534997620f, 0.844853565f,
+ 0.555570233f, 0.831469612f,
+ 0.575808191f, 0.817584813f,
+ 0.595699304f, 0.803207531f,
+ 0.615231591f, 0.788346428f,
+ 0.634393284f, 0.773010453f,
+ 0.653172843f, 0.757208847f,
+ 0.671558955f, 0.740951125f,
+ 0.689540545f, 0.724247083f,
+ 0.707106781f, 0.707106781f,
+ 0.724247083f, 0.689540545f,
+ 0.740951125f, 0.671558955f,
+ 0.757208847f, 0.653172843f,
+ 0.773010453f, 0.634393284f,
+ 0.788346428f, 0.615231591f,
+ 0.803207531f, 0.595699304f,
+ 0.817584813f, 0.575808191f,
+ 0.831469612f, 0.555570233f,
+ 0.844853565f, 0.534997620f,
+ 0.857728610f, 0.514102744f,
+ 0.870086991f, 0.492898192f,
+ 0.881921264f, 0.471396737f,
+ 0.893224301f, 0.449611330f,
+ 0.903989293f, 0.427555093f,
+ 0.914209756f, 0.405241314f,
+ 0.923879533f, 0.382683432f,
+ 0.932992799f, 0.359895037f,
+ 0.941544065f, 0.336889853f,
+ 0.949528181f, 0.313681740f,
+ 0.956940336f, 0.290284677f,
+ 0.963776066f, 0.266712757f,
+ 0.970031253f, 0.242980180f,
+ 0.975702130f, 0.219101240f,
+ 0.980785280f, 0.195090322f,
+ 0.985277642f, 0.170961889f,
+ 0.989176510f, 0.146730474f,
+ 0.992479535f, 0.122410675f,
+ 0.995184727f, 0.098017140f,
+ 0.997290457f, 0.073564564f,
+ 0.998795456f, 0.049067674f,
+ 0.999698819f, 0.024541229f,
+ 1.000000000f, 0.000000000f,
+ 0.999698819f, -0.024541229f,
+ 0.998795456f, -0.049067674f,
+ 0.997290457f, -0.073564564f,
+ 0.995184727f, -0.098017140f,
+ 0.992479535f, -0.122410675f,
+ 0.989176510f, -0.146730474f,
+ 0.985277642f, -0.170961889f,
+ 0.980785280f, -0.195090322f,
+ 0.975702130f, -0.219101240f,
+ 0.970031253f, -0.242980180f,
+ 0.963776066f, -0.266712757f,
+ 0.956940336f, -0.290284677f,
+ 0.949528181f, -0.313681740f,
+ 0.941544065f, -0.336889853f,
+ 0.932992799f, -0.359895037f,
+ 0.923879533f, -0.382683432f,
+ 0.914209756f, -0.405241314f,
+ 0.903989293f, -0.427555093f,
+ 0.893224301f, -0.449611330f,
+ 0.881921264f, -0.471396737f,
+ 0.870086991f, -0.492898192f,
+ 0.857728610f, -0.514102744f,
+ 0.844853565f, -0.534997620f,
+ 0.831469612f, -0.555570233f,
+ 0.817584813f, -0.575808191f,
+ 0.803207531f, -0.595699304f,
+ 0.788346428f, -0.615231591f,
+ 0.773010453f, -0.634393284f,
+ 0.757208847f, -0.653172843f,
+ 0.740951125f, -0.671558955f,
+ 0.724247083f, -0.689540545f,
+ 0.707106781f, -0.707106781f,
+ 0.689540545f, -0.724247083f,
+ 0.671558955f, -0.740951125f,
+ 0.653172843f, -0.757208847f,
+ 0.634393284f, -0.773010453f,
+ 0.615231591f, -0.788346428f,
+ 0.595699304f, -0.803207531f,
+ 0.575808191f, -0.817584813f,
+ 0.555570233f, -0.831469612f,
+ 0.534997620f, -0.844853565f,
+ 0.514102744f, -0.857728610f,
+ 0.492898192f, -0.870086991f,
+ 0.471396737f, -0.881921264f,
+ 0.449611330f, -0.893224301f,
+ 0.427555093f, -0.903989293f,
+ 0.405241314f, -0.914209756f,
+ 0.382683432f, -0.923879533f,
+ 0.359895037f, -0.932992799f,
+ 0.336889853f, -0.941544065f,
+ 0.313681740f, -0.949528181f,
+ 0.290284677f, -0.956940336f,
+ 0.266712757f, -0.963776066f,
+ 0.242980180f, -0.970031253f,
+ 0.219101240f, -0.975702130f,
+ 0.195090322f, -0.980785280f,
+ 0.170961889f, -0.985277642f,
+ 0.146730474f, -0.989176510f,
+ 0.122410675f, -0.992479535f,
+ 0.098017140f, -0.995184727f,
+ 0.073564564f, -0.997290457f,
+ 0.049067674f, -0.998795456f,
+ 0.024541229f, -0.999698819f
+};
+
+const float32_t twiddleCoef_rfft_512[512] = {
+ 0.000000000f, 1.000000000f,
+ 0.012271538f, 0.999924702f,
+ 0.024541229f, 0.999698819f,
+ 0.036807223f, 0.999322385f,
+ 0.049067674f, 0.998795456f,
+ 0.061320736f, 0.998118113f,
+ 0.073564564f, 0.997290457f,
+ 0.085797312f, 0.996312612f,
+ 0.098017140f, 0.995184727f,
+ 0.110222207f, 0.993906970f,
+ 0.122410675f, 0.992479535f,
+ 0.134580709f, 0.990902635f,
+ 0.146730474f, 0.989176510f,
+ 0.158858143f, 0.987301418f,
+ 0.170961889f, 0.985277642f,
+ 0.183039888f, 0.983105487f,
+ 0.195090322f, 0.980785280f,
+ 0.207111376f, 0.978317371f,
+ 0.219101240f, 0.975702130f,
+ 0.231058108f, 0.972939952f,
+ 0.242980180f, 0.970031253f,
+ 0.254865660f, 0.966976471f,
+ 0.266712757f, 0.963776066f,
+ 0.278519689f, 0.960430519f,
+ 0.290284677f, 0.956940336f,
+ 0.302005949f, 0.953306040f,
+ 0.313681740f, 0.949528181f,
+ 0.325310292f, 0.945607325f,
+ 0.336889853f, 0.941544065f,
+ 0.348418680f, 0.937339012f,
+ 0.359895037f, 0.932992799f,
+ 0.371317194f, 0.928506080f,
+ 0.382683432f, 0.923879533f,
+ 0.393992040f, 0.919113852f,
+ 0.405241314f, 0.914209756f,
+ 0.416429560f, 0.909167983f,
+ 0.427555093f, 0.903989293f,
+ 0.438616239f, 0.898674466f,
+ 0.449611330f, 0.893224301f,
+ 0.460538711f, 0.887639620f,
+ 0.471396737f, 0.881921264f,
+ 0.482183772f, 0.876070094f,
+ 0.492898192f, 0.870086991f,
+ 0.503538384f, 0.863972856f,
+ 0.514102744f, 0.857728610f,
+ 0.524589683f, 0.851355193f,
+ 0.534997620f, 0.844853565f,
+ 0.545324988f, 0.838224706f,
+ 0.555570233f, 0.831469612f,
+ 0.565731811f, 0.824589303f,
+ 0.575808191f, 0.817584813f,
+ 0.585797857f, 0.810457198f,
+ 0.595699304f, 0.803207531f,
+ 0.605511041f, 0.795836905f,
+ 0.615231591f, 0.788346428f,
+ 0.624859488f, 0.780737229f,
+ 0.634393284f, 0.773010453f,
+ 0.643831543f, 0.765167266f,
+ 0.653172843f, 0.757208847f,
+ 0.662415778f, 0.749136395f,
+ 0.671558955f, 0.740951125f,
+ 0.680600998f, 0.732654272f,
+ 0.689540545f, 0.724247083f,
+ 0.698376249f, 0.715730825f,
+ 0.707106781f, 0.707106781f,
+ 0.715730825f, 0.698376249f,
+ 0.724247083f, 0.689540545f,
+ 0.732654272f, 0.680600998f,
+ 0.740951125f, 0.671558955f,
+ 0.749136395f, 0.662415778f,
+ 0.757208847f, 0.653172843f,
+ 0.765167266f, 0.643831543f,
+ 0.773010453f, 0.634393284f,
+ 0.780737229f, 0.624859488f,
+ 0.788346428f, 0.615231591f,
+ 0.795836905f, 0.605511041f,
+ 0.803207531f, 0.595699304f,
+ 0.810457198f, 0.585797857f,
+ 0.817584813f, 0.575808191f,
+ 0.824589303f, 0.565731811f,
+ 0.831469612f, 0.555570233f,
+ 0.838224706f, 0.545324988f,
+ 0.844853565f, 0.534997620f,
+ 0.851355193f, 0.524589683f,
+ 0.857728610f, 0.514102744f,
+ 0.863972856f, 0.503538384f,
+ 0.870086991f, 0.492898192f,
+ 0.876070094f, 0.482183772f,
+ 0.881921264f, 0.471396737f,
+ 0.887639620f, 0.460538711f,
+ 0.893224301f, 0.449611330f,
+ 0.898674466f, 0.438616239f,
+ 0.903989293f, 0.427555093f,
+ 0.909167983f, 0.416429560f,
+ 0.914209756f, 0.405241314f,
+ 0.919113852f, 0.393992040f,
+ 0.923879533f, 0.382683432f,
+ 0.928506080f, 0.371317194f,
+ 0.932992799f, 0.359895037f,
+ 0.937339012f, 0.348418680f,
+ 0.941544065f, 0.336889853f,
+ 0.945607325f, 0.325310292f,
+ 0.949528181f, 0.313681740f,
+ 0.953306040f, 0.302005949f,
+ 0.956940336f, 0.290284677f,
+ 0.960430519f, 0.278519689f,
+ 0.963776066f, 0.266712757f,
+ 0.966976471f, 0.254865660f,
+ 0.970031253f, 0.242980180f,
+ 0.972939952f, 0.231058108f,
+ 0.975702130f, 0.219101240f,
+ 0.978317371f, 0.207111376f,
+ 0.980785280f, 0.195090322f,
+ 0.983105487f, 0.183039888f,
+ 0.985277642f, 0.170961889f,
+ 0.987301418f, 0.158858143f,
+ 0.989176510f, 0.146730474f,
+ 0.990902635f, 0.134580709f,
+ 0.992479535f, 0.122410675f,
+ 0.993906970f, 0.110222207f,
+ 0.995184727f, 0.098017140f,
+ 0.996312612f, 0.085797312f,
+ 0.997290457f, 0.073564564f,
+ 0.998118113f, 0.061320736f,
+ 0.998795456f, 0.049067674f,
+ 0.999322385f, 0.036807223f,
+ 0.999698819f, 0.024541229f,
+ 0.999924702f, 0.012271538f,
+ 1.000000000f, 0.000000000f,
+ 0.999924702f, -0.012271538f,
+ 0.999698819f, -0.024541229f,
+ 0.999322385f, -0.036807223f,
+ 0.998795456f, -0.049067674f,
+ 0.998118113f, -0.061320736f,
+ 0.997290457f, -0.073564564f,
+ 0.996312612f, -0.085797312f,
+ 0.995184727f, -0.098017140f,
+ 0.993906970f, -0.110222207f,
+ 0.992479535f, -0.122410675f,
+ 0.990902635f, -0.134580709f,
+ 0.989176510f, -0.146730474f,
+ 0.987301418f, -0.158858143f,
+ 0.985277642f, -0.170961889f,
+ 0.983105487f, -0.183039888f,
+ 0.980785280f, -0.195090322f,
+ 0.978317371f, -0.207111376f,
+ 0.975702130f, -0.219101240f,
+ 0.972939952f, -0.231058108f,
+ 0.970031253f, -0.242980180f,
+ 0.966976471f, -0.254865660f,
+ 0.963776066f, -0.266712757f,
+ 0.960430519f, -0.278519689f,
+ 0.956940336f, -0.290284677f,
+ 0.953306040f, -0.302005949f,
+ 0.949528181f, -0.313681740f,
+ 0.945607325f, -0.325310292f,
+ 0.941544065f, -0.336889853f,
+ 0.937339012f, -0.348418680f,
+ 0.932992799f, -0.359895037f,
+ 0.928506080f, -0.371317194f,
+ 0.923879533f, -0.382683432f,
+ 0.919113852f, -0.393992040f,
+ 0.914209756f, -0.405241314f,
+ 0.909167983f, -0.416429560f,
+ 0.903989293f, -0.427555093f,
+ 0.898674466f, -0.438616239f,
+ 0.893224301f, -0.449611330f,
+ 0.887639620f, -0.460538711f,
+ 0.881921264f, -0.471396737f,
+ 0.876070094f, -0.482183772f,
+ 0.870086991f, -0.492898192f,
+ 0.863972856f, -0.503538384f,
+ 0.857728610f, -0.514102744f,
+ 0.851355193f, -0.524589683f,
+ 0.844853565f, -0.534997620f,
+ 0.838224706f, -0.545324988f,
+ 0.831469612f, -0.555570233f,
+ 0.824589303f, -0.565731811f,
+ 0.817584813f, -0.575808191f,
+ 0.810457198f, -0.585797857f,
+ 0.803207531f, -0.595699304f,
+ 0.795836905f, -0.605511041f,
+ 0.788346428f, -0.615231591f,
+ 0.780737229f, -0.624859488f,
+ 0.773010453f, -0.634393284f,
+ 0.765167266f, -0.643831543f,
+ 0.757208847f, -0.653172843f,
+ 0.749136395f, -0.662415778f,
+ 0.740951125f, -0.671558955f,
+ 0.732654272f, -0.680600998f,
+ 0.724247083f, -0.689540545f,
+ 0.715730825f, -0.698376249f,
+ 0.707106781f, -0.707106781f,
+ 0.698376249f, -0.715730825f,
+ 0.689540545f, -0.724247083f,
+ 0.680600998f, -0.732654272f,
+ 0.671558955f, -0.740951125f,
+ 0.662415778f, -0.749136395f,
+ 0.653172843f, -0.757208847f,
+ 0.643831543f, -0.765167266f,
+ 0.634393284f, -0.773010453f,
+ 0.624859488f, -0.780737229f,
+ 0.615231591f, -0.788346428f,
+ 0.605511041f, -0.795836905f,
+ 0.595699304f, -0.803207531f,
+ 0.585797857f, -0.810457198f,
+ 0.575808191f, -0.817584813f,
+ 0.565731811f, -0.824589303f,
+ 0.555570233f, -0.831469612f,
+ 0.545324988f, -0.838224706f,
+ 0.534997620f, -0.844853565f,
+ 0.524589683f, -0.851355193f,
+ 0.514102744f, -0.857728610f,
+ 0.503538384f, -0.863972856f,
+ 0.492898192f, -0.870086991f,
+ 0.482183772f, -0.876070094f,
+ 0.471396737f, -0.881921264f,
+ 0.460538711f, -0.887639620f,
+ 0.449611330f, -0.893224301f,
+ 0.438616239f, -0.898674466f,
+ 0.427555093f, -0.903989293f,
+ 0.416429560f, -0.909167983f,
+ 0.405241314f, -0.914209756f,
+ 0.393992040f, -0.919113852f,
+ 0.382683432f, -0.923879533f,
+ 0.371317194f, -0.928506080f,
+ 0.359895037f, -0.932992799f,
+ 0.348418680f, -0.937339012f,
+ 0.336889853f, -0.941544065f,
+ 0.325310292f, -0.945607325f,
+ 0.313681740f, -0.949528181f,
+ 0.302005949f, -0.953306040f,
+ 0.290284677f, -0.956940336f,
+ 0.278519689f, -0.960430519f,
+ 0.266712757f, -0.963776066f,
+ 0.254865660f, -0.966976471f,
+ 0.242980180f, -0.970031253f,
+ 0.231058108f, -0.972939952f,
+ 0.219101240f, -0.975702130f,
+ 0.207111376f, -0.978317371f,
+ 0.195090322f, -0.980785280f,
+ 0.183039888f, -0.983105487f,
+ 0.170961889f, -0.985277642f,
+ 0.158858143f, -0.987301418f,
+ 0.146730474f, -0.989176510f,
+ 0.134580709f, -0.990902635f,
+ 0.122410675f, -0.992479535f,
+ 0.110222207f, -0.993906970f,
+ 0.098017140f, -0.995184727f,
+ 0.085797312f, -0.996312612f,
+ 0.073564564f, -0.997290457f,
+ 0.061320736f, -0.998118113f,
+ 0.049067674f, -0.998795456f,
+ 0.036807223f, -0.999322385f,
+ 0.024541229f, -0.999698819f,
+ 0.012271538f, -0.999924702f
+};
+
+const float32_t twiddleCoef_rfft_1024[1024] = {
+ 0.000000000f, 1.000000000f,
+ 0.006135885f, 0.999981175f,
+ 0.012271538f, 0.999924702f,
+ 0.018406730f, 0.999830582f,
+ 0.024541229f, 0.999698819f,
+ 0.030674803f, 0.999529418f,
+ 0.036807223f, 0.999322385f,
+ 0.042938257f, 0.999077728f,
+ 0.049067674f, 0.998795456f,
+ 0.055195244f, 0.998475581f,
+ 0.061320736f, 0.998118113f,
+ 0.067443920f, 0.997723067f,
+ 0.073564564f, 0.997290457f,
+ 0.079682438f, 0.996820299f,
+ 0.085797312f, 0.996312612f,
+ 0.091908956f, 0.995767414f,
+ 0.098017140f, 0.995184727f,
+ 0.104121634f, 0.994564571f,
+ 0.110222207f, 0.993906970f,
+ 0.116318631f, 0.993211949f,
+ 0.122410675f, 0.992479535f,
+ 0.128498111f, 0.991709754f,
+ 0.134580709f, 0.990902635f,
+ 0.140658239f, 0.990058210f,
+ 0.146730474f, 0.989176510f,
+ 0.152797185f, 0.988257568f,
+ 0.158858143f, 0.987301418f,
+ 0.164913120f, 0.986308097f,
+ 0.170961889f, 0.985277642f,
+ 0.177004220f, 0.984210092f,
+ 0.183039888f, 0.983105487f,
+ 0.189068664f, 0.981963869f,
+ 0.195090322f, 0.980785280f,
+ 0.201104635f, 0.979569766f,
+ 0.207111376f, 0.978317371f,
+ 0.213110320f, 0.977028143f,
+ 0.219101240f, 0.975702130f,
+ 0.225083911f, 0.974339383f,
+ 0.231058108f, 0.972939952f,
+ 0.237023606f, 0.971503891f,
+ 0.242980180f, 0.970031253f,
+ 0.248927606f, 0.968522094f,
+ 0.254865660f, 0.966976471f,
+ 0.260794118f, 0.965394442f,
+ 0.266712757f, 0.963776066f,
+ 0.272621355f, 0.962121404f,
+ 0.278519689f, 0.960430519f,
+ 0.284407537f, 0.958703475f,
+ 0.290284677f, 0.956940336f,
+ 0.296150888f, 0.955141168f,
+ 0.302005949f, 0.953306040f,
+ 0.307849640f, 0.951435021f,
+ 0.313681740f, 0.949528181f,
+ 0.319502031f, 0.947585591f,
+ 0.325310292f, 0.945607325f,
+ 0.331106306f, 0.943593458f,
+ 0.336889853f, 0.941544065f,
+ 0.342660717f, 0.939459224f,
+ 0.348418680f, 0.937339012f,
+ 0.354163525f, 0.935183510f,
+ 0.359895037f, 0.932992799f,
+ 0.365612998f, 0.930766961f,
+ 0.371317194f, 0.928506080f,
+ 0.377007410f, 0.926210242f,
+ 0.382683432f, 0.923879533f,
+ 0.388345047f, 0.921514039f,
+ 0.393992040f, 0.919113852f,
+ 0.399624200f, 0.916679060f,
+ 0.405241314f, 0.914209756f,
+ 0.410843171f, 0.911706032f,
+ 0.416429560f, 0.909167983f,
+ 0.422000271f, 0.906595705f,
+ 0.427555093f, 0.903989293f,
+ 0.433093819f, 0.901348847f,
+ 0.438616239f, 0.898674466f,
+ 0.444122145f, 0.895966250f,
+ 0.449611330f, 0.893224301f,
+ 0.455083587f, 0.890448723f,
+ 0.460538711f, 0.887639620f,
+ 0.465976496f, 0.884797098f,
+ 0.471396737f, 0.881921264f,
+ 0.476799230f, 0.879012226f,
+ 0.482183772f, 0.876070094f,
+ 0.487550160f, 0.873094978f,
+ 0.492898192f, 0.870086991f,
+ 0.498227667f, 0.867046246f,
+ 0.503538384f, 0.863972856f,
+ 0.508830143f, 0.860866939f,
+ 0.514102744f, 0.857728610f,
+ 0.519355990f, 0.854557988f,
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+ 0.006135885f, -0.999981175f
+};
+
+const float32_t twiddleCoef_rfft_2048[2048] = {
+ 0.000000000f, 1.000000000f,
+ 0.003067957f, 0.999995294f,
+ 0.006135885f, 0.999981175f,
+ 0.009203755f, 0.999957645f,
+ 0.012271538f, 0.999924702f,
+ 0.015339206f, 0.999882347f,
+ 0.018406730f, 0.999830582f,
+ 0.021474080f, 0.999769405f,
+ 0.024541229f, 0.999698819f,
+ 0.027608146f, 0.999618822f,
+ 0.030674803f, 0.999529418f,
+ 0.033741172f, 0.999430605f,
+ 0.036807223f, 0.999322385f,
+ 0.039872928f, 0.999204759f,
+ 0.042938257f, 0.999077728f,
+ 0.046003182f, 0.998941293f,
+ 0.049067674f, 0.998795456f,
+ 0.052131705f, 0.998640218f,
+ 0.055195244f, 0.998475581f,
+ 0.058258265f, 0.998301545f,
+ 0.061320736f, 0.998118113f,
+ 0.064382631f, 0.997925286f,
+ 0.067443920f, 0.997723067f,
+ 0.070504573f, 0.997511456f,
+ 0.073564564f, 0.997290457f,
+ 0.076623861f, 0.997060070f,
+ 0.079682438f, 0.996820299f,
+ 0.082740265f, 0.996571146f,
+ 0.085797312f, 0.996312612f,
+ 0.088853553f, 0.996044701f,
+ 0.091908956f, 0.995767414f,
+ 0.094963495f, 0.995480755f,
+ 0.098017140f, 0.995184727f,
+ 0.101069863f, 0.994879331f,
+ 0.104121634f, 0.994564571f,
+ 0.107172425f, 0.994240449f,
+ 0.110222207f, 0.993906970f,
+ 0.113270952f, 0.993564136f,
+ 0.116318631f, 0.993211949f,
+ 0.119365215f, 0.992850414f,
+ 0.122410675f, 0.992479535f,
+ 0.125454983f, 0.992099313f,
+ 0.128498111f, 0.991709754f,
+ 0.131540029f, 0.991310860f,
+ 0.134580709f, 0.990902635f,
+ 0.137620122f, 0.990485084f,
+ 0.140658239f, 0.990058210f,
+ 0.143695033f, 0.989622017f,
+ 0.146730474f, 0.989176510f,
+ 0.149764535f, 0.988721692f,
+ 0.152797185f, 0.988257568f,
+ 0.155828398f, 0.987784142f,
+ 0.158858143f, 0.987301418f,
+ 0.161886394f, 0.986809402f,
+ 0.164913120f, 0.986308097f,
+ 0.167938295f, 0.985797509f,
+ 0.170961889f, 0.985277642f,
+ 0.173983873f, 0.984748502f,
+ 0.177004220f, 0.984210092f,
+ 0.180022901f, 0.983662419f,
+ 0.183039888f, 0.983105487f,
+ 0.186055152f, 0.982539302f,
+ 0.189068664f, 0.981963869f,
+ 0.192080397f, 0.981379193f,
+ 0.195090322f, 0.980785280f,
+ 0.198098411f, 0.980182136f,
+ 0.201104635f, 0.979569766f,
+ 0.204108966f, 0.978948175f,
+ 0.207111376f, 0.978317371f,
+ 0.210111837f, 0.977677358f,
+ 0.213110320f, 0.977028143f,
+ 0.216106797f, 0.976369731f,
+ 0.219101240f, 0.975702130f,
+ 0.222093621f, 0.975025345f,
+ 0.225083911f, 0.974339383f,
+ 0.228072083f, 0.973644250f,
+ 0.231058108f, 0.972939952f,
+ 0.234041959f, 0.972226497f,
+ 0.237023606f, 0.971503891f,
+ 0.240003022f, 0.970772141f,
+ 0.242980180f, 0.970031253f,
+ 0.245955050f, 0.969281235f,
+ 0.248927606f, 0.968522094f,
+ 0.251897818f, 0.967753837f,
+ 0.254865660f, 0.966976471f,
+ 0.257831102f, 0.966190003f,
+ 0.260794118f, 0.965394442f,
+ 0.263754679f, 0.964589793f,
+ 0.266712757f, 0.963776066f,
+ 0.269668326f, 0.962953267f,
+ 0.272621355f, 0.962121404f,
+ 0.275571819f, 0.961280486f,
+ 0.278519689f, 0.960430519f,
+ 0.281464938f, 0.959571513f,
+ 0.284407537f, 0.958703475f,
+ 0.287347460f, 0.957826413f,
+ 0.290284677f, 0.956940336f,
+ 0.293219163f, 0.956045251f,
+ 0.296150888f, 0.955141168f,
+ 0.299079826f, 0.954228095f,
+ 0.302005949f, 0.953306040f,
+ 0.304929230f, 0.952375013f,
+ 0.307849640f, 0.951435021f,
+ 0.310767153f, 0.950486074f,
+ 0.313681740f, 0.949528181f,
+ 0.316593376f, 0.948561350f,
+ 0.319502031f, 0.947585591f,
+ 0.322407679f, 0.946600913f,
+ 0.325310292f, 0.945607325f,
+ 0.328209844f, 0.944604837f,
+ 0.331106306f, 0.943593458f,
+ 0.333999651f, 0.942573198f,
+ 0.336889853f, 0.941544065f,
+ 0.339776884f, 0.940506071f,
+ 0.342660717f, 0.939459224f,
+ 0.345541325f, 0.938403534f,
+ 0.348418680f, 0.937339012f,
+ 0.351292756f, 0.936265667f,
+ 0.354163525f, 0.935183510f,
+ 0.357030961f, 0.934092550f,
+ 0.359895037f, 0.932992799f,
+ 0.362755724f, 0.931884266f,
+ 0.365612998f, 0.930766961f,
+ 0.368466830f, 0.929640896f,
+ 0.371317194f, 0.928506080f,
+ 0.374164063f, 0.927362526f,
+ 0.377007410f, 0.926210242f,
+ 0.379847209f, 0.925049241f,
+ 0.382683432f, 0.923879533f,
+ 0.385516054f, 0.922701128f,
+ 0.388345047f, 0.921514039f,
+ 0.391170384f, 0.920318277f,
+ 0.393992040f, 0.919113852f,
+ 0.396809987f, 0.917900776f,
+ 0.399624200f, 0.916679060f,
+ 0.402434651f, 0.915448716f,
+ 0.405241314f, 0.914209756f,
+ 0.408044163f, 0.912962190f,
+ 0.410843171f, 0.911706032f,
+ 0.413638312f, 0.910441292f,
+ 0.416429560f, 0.909167983f,
+ 0.419216888f, 0.907886116f,
+ 0.422000271f, 0.906595705f,
+ 0.424779681f, 0.905296759f,
+ 0.427555093f, 0.903989293f,
+ 0.430326481f, 0.902673318f,
+ 0.433093819f, 0.901348847f,
+ 0.435857080f, 0.900015892f,
+ 0.438616239f, 0.898674466f,
+ 0.441371269f, 0.897324581f,
+ 0.444122145f, 0.895966250f,
+ 0.446868840f, 0.894599486f,
+ 0.449611330f, 0.893224301f,
+ 0.452349587f, 0.891840709f,
+ 0.455083587f, 0.890448723f,
+ 0.457813304f, 0.889048356f,
+ 0.460538711f, 0.887639620f,
+ 0.463259784f, 0.886222530f,
+ 0.465976496f, 0.884797098f,
+ 0.468688822f, 0.883363339f,
+ 0.471396737f, 0.881921264f,
+ 0.474100215f, 0.880470889f,
+ 0.476799230f, 0.879012226f,
+ 0.479493758f, 0.877545290f,
+ 0.482183772f, 0.876070094f,
+ 0.484869248f, 0.874586652f,
+ 0.487550160f, 0.873094978f,
+ 0.490226483f, 0.871595087f,
+ 0.492898192f, 0.870086991f,
+ 0.495565262f, 0.868570706f,
+ 0.498227667f, 0.867046246f,
+ 0.500885383f, 0.865513624f,
+ 0.503538384f, 0.863972856f,
+ 0.506186645f, 0.862423956f,
+ 0.508830143f, 0.860866939f,
+ 0.511468850f, 0.859301818f,
+ 0.514102744f, 0.857728610f,
+ 0.516731799f, 0.856147328f,
+ 0.519355990f, 0.854557988f,
+ 0.521975293f, 0.852960605f,
+ 0.524589683f, 0.851355193f,
+ 0.527199135f, 0.849741768f,
+ 0.529803625f, 0.848120345f,
+ 0.532403128f, 0.846490939f,
+ 0.534997620f, 0.844853565f,
+ 0.537587076f, 0.843208240f,
+ 0.540171473f, 0.841554977f,
+ 0.542750785f, 0.839893794f,
+ 0.545324988f, 0.838224706f,
+ 0.547894059f, 0.836547727f,
+ 0.550457973f, 0.834862875f,
+ 0.553016706f, 0.833170165f,
+ 0.555570233f, 0.831469612f,
+ 0.558118531f, 0.829761234f,
+ 0.560661576f, 0.828045045f,
+ 0.563199344f, 0.826321063f,
+ 0.565731811f, 0.824589303f,
+ 0.568258953f, 0.822849781f,
+ 0.570780746f, 0.821102515f,
+ 0.573297167f, 0.819347520f,
+ 0.575808191f, 0.817584813f,
+ 0.578313796f, 0.815814411f,
+ 0.580813958f, 0.814036330f,
+ 0.583308653f, 0.812250587f,
+ 0.585797857f, 0.810457198f,
+ 0.588281548f, 0.808656182f,
+ 0.590759702f, 0.806847554f,
+ 0.593232295f, 0.805031331f,
+ 0.595699304f, 0.803207531f,
+ 0.598160707f, 0.801376172f,
+ 0.600616479f, 0.799537269f,
+ 0.603066599f, 0.797690841f,
+ 0.605511041f, 0.795836905f,
+ 0.607949785f, 0.793975478f,
+ 0.610382806f, 0.792106577f,
+ 0.612810082f, 0.790230221f,
+ 0.615231591f, 0.788346428f,
+ 0.617647308f, 0.786455214f,
+ 0.620057212f, 0.784556597f,
+ 0.622461279f, 0.782650596f,
+ 0.624859488f, 0.780737229f,
+ 0.627251815f, 0.778816512f,
+ 0.629638239f, 0.776888466f,
+ 0.632018736f, 0.774953107f,
+ 0.634393284f, 0.773010453f,
+ 0.636761861f, 0.771060524f,
+ 0.639124445f, 0.769103338f,
+ 0.641481013f, 0.767138912f,
+ 0.643831543f, 0.765167266f,
+ 0.646176013f, 0.763188417f,
+ 0.648514401f, 0.761202385f,
+ 0.650846685f, 0.759209189f,
+ 0.653172843f, 0.757208847f,
+ 0.655492853f, 0.755201377f,
+ 0.657806693f, 0.753186799f,
+ 0.660114342f, 0.751165132f,
+ 0.662415778f, 0.749136395f,
+ 0.664710978f, 0.747100606f,
+ 0.666999922f, 0.745057785f,
+ 0.669282588f, 0.743007952f,
+ 0.671558955f, 0.740951125f,
+ 0.673829000f, 0.738887324f,
+ 0.676092704f, 0.736816569f,
+ 0.678350043f, 0.734738878f,
+ 0.680600998f, 0.732654272f,
+ 0.682845546f, 0.730562769f,
+ 0.685083668f, 0.728464390f,
+ 0.687315341f, 0.726359155f,
+ 0.689540545f, 0.724247083f,
+ 0.691759258f, 0.722128194f,
+ 0.693971461f, 0.720002508f,
+ 0.696177131f, 0.717870045f,
+ 0.698376249f, 0.715730825f,
+ 0.700568794f, 0.713584869f,
+ 0.702754744f, 0.711432196f,
+ 0.704934080f, 0.709272826f,
+ 0.707106781f, 0.707106781f,
+ 0.709272826f, 0.704934080f,
+ 0.711432196f, 0.702754744f,
+ 0.713584869f, 0.700568794f,
+ 0.715730825f, 0.698376249f,
+ 0.717870045f, 0.696177131f,
+ 0.720002508f, 0.693971461f,
+ 0.722128194f, 0.691759258f,
+ 0.724247083f, 0.689540545f,
+ 0.726359155f, 0.687315341f,
+ 0.728464390f, 0.685083668f,
+ 0.730562769f, 0.682845546f,
+ 0.732654272f, 0.680600998f,
+ 0.734738878f, 0.678350043f,
+ 0.736816569f, 0.676092704f,
+ 0.738887324f, 0.673829000f,
+ 0.740951125f, 0.671558955f,
+ 0.743007952f, 0.669282588f,
+ 0.745057785f, 0.666999922f,
+ 0.747100606f, 0.664710978f,
+ 0.749136395f, 0.662415778f,
+ 0.751165132f, 0.660114342f,
+ 0.753186799f, 0.657806693f,
+ 0.755201377f, 0.655492853f,
+ 0.757208847f, 0.653172843f,
+ 0.759209189f, 0.650846685f,
+ 0.761202385f, 0.648514401f,
+ 0.763188417f, 0.646176013f,
+ 0.765167266f, 0.643831543f,
+ 0.767138912f, 0.641481013f,
+ 0.769103338f, 0.639124445f,
+ 0.771060524f, 0.636761861f,
+ 0.773010453f, 0.634393284f,
+ 0.774953107f, 0.632018736f,
+ 0.776888466f, 0.629638239f,
+ 0.778816512f, 0.627251815f,
+ 0.780737229f, 0.624859488f,
+ 0.782650596f, 0.622461279f,
+ 0.784556597f, 0.620057212f,
+ 0.786455214f, 0.617647308f,
+ 0.788346428f, 0.615231591f,
+ 0.790230221f, 0.612810082f,
+ 0.792106577f, 0.610382806f,
+ 0.793975478f, 0.607949785f,
+ 0.795836905f, 0.605511041f,
+ 0.797690841f, 0.603066599f,
+ 0.799537269f, 0.600616479f,
+ 0.801376172f, 0.598160707f,
+ 0.803207531f, 0.595699304f,
+ 0.805031331f, 0.593232295f,
+ 0.806847554f, 0.590759702f,
+ 0.808656182f, 0.588281548f,
+ 0.810457198f, 0.585797857f,
+ 0.812250587f, 0.583308653f,
+ 0.814036330f, 0.580813958f,
+ 0.815814411f, 0.578313796f,
+ 0.817584813f, 0.575808191f,
+ 0.819347520f, 0.573297167f,
+ 0.821102515f, 0.570780746f,
+ 0.822849781f, 0.568258953f,
+ 0.824589303f, 0.565731811f,
+ 0.826321063f, 0.563199344f,
+ 0.828045045f, 0.560661576f,
+ 0.829761234f, 0.558118531f,
+ 0.831469612f, 0.555570233f,
+ 0.833170165f, 0.553016706f,
+ 0.834862875f, 0.550457973f,
+ 0.836547727f, 0.547894059f,
+ 0.838224706f, 0.545324988f,
+ 0.839893794f, 0.542750785f,
+ 0.841554977f, 0.540171473f,
+ 0.843208240f, 0.537587076f,
+ 0.844853565f, 0.534997620f,
+ 0.846490939f, 0.532403128f,
+ 0.848120345f, 0.529803625f,
+ 0.849741768f, 0.527199135f,
+ 0.851355193f, 0.524589683f,
+ 0.852960605f, 0.521975293f,
+ 0.854557988f, 0.519355990f,
+ 0.856147328f, 0.516731799f,
+ 0.857728610f, 0.514102744f,
+ 0.859301818f, 0.511468850f,
+ 0.860866939f, 0.508830143f,
+ 0.862423956f, 0.506186645f,
+ 0.863972856f, 0.503538384f,
+ 0.865513624f, 0.500885383f,
+ 0.867046246f, 0.498227667f,
+ 0.868570706f, 0.495565262f,
+ 0.870086991f, 0.492898192f,
+ 0.871595087f, 0.490226483f,
+ 0.873094978f, 0.487550160f,
+ 0.874586652f, 0.484869248f,
+ 0.876070094f, 0.482183772f,
+ 0.877545290f, 0.479493758f,
+ 0.879012226f, 0.476799230f,
+ 0.880470889f, 0.474100215f,
+ 0.881921264f, 0.471396737f,
+ 0.883363339f, 0.468688822f,
+ 0.884797098f, 0.465976496f,
+ 0.886222530f, 0.463259784f,
+ 0.887639620f, 0.460538711f,
+ 0.889048356f, 0.457813304f,
+ 0.890448723f, 0.455083587f,
+ 0.891840709f, 0.452349587f,
+ 0.893224301f, 0.449611330f,
+ 0.894599486f, 0.446868840f,
+ 0.895966250f, 0.444122145f,
+ 0.897324581f, 0.441371269f,
+ 0.898674466f, 0.438616239f,
+ 0.900015892f, 0.435857080f,
+ 0.901348847f, 0.433093819f,
+ 0.902673318f, 0.430326481f,
+ 0.903989293f, 0.427555093f,
+ 0.905296759f, 0.424779681f,
+ 0.906595705f, 0.422000271f,
+ 0.907886116f, 0.419216888f,
+ 0.909167983f, 0.416429560f,
+ 0.910441292f, 0.413638312f,
+ 0.911706032f, 0.410843171f,
+ 0.912962190f, 0.408044163f,
+ 0.914209756f, 0.405241314f,
+ 0.915448716f, 0.402434651f,
+ 0.916679060f, 0.399624200f,
+ 0.917900776f, 0.396809987f,
+ 0.919113852f, 0.393992040f,
+ 0.920318277f, 0.391170384f,
+ 0.921514039f, 0.388345047f,
+ 0.922701128f, 0.385516054f,
+ 0.923879533f, 0.382683432f,
+ 0.925049241f, 0.379847209f,
+ 0.926210242f, 0.377007410f,
+ 0.927362526f, 0.374164063f,
+ 0.928506080f, 0.371317194f,
+ 0.929640896f, 0.368466830f,
+ 0.930766961f, 0.365612998f,
+ 0.931884266f, 0.362755724f,
+ 0.932992799f, 0.359895037f,
+ 0.934092550f, 0.357030961f,
+ 0.935183510f, 0.354163525f,
+ 0.936265667f, 0.351292756f,
+ 0.937339012f, 0.348418680f,
+ 0.938403534f, 0.345541325f,
+ 0.939459224f, 0.342660717f,
+ 0.940506071f, 0.339776884f,
+ 0.941544065f, 0.336889853f,
+ 0.942573198f, 0.333999651f,
+ 0.943593458f, 0.331106306f,
+ 0.944604837f, 0.328209844f,
+ 0.945607325f, 0.325310292f,
+ 0.946600913f, 0.322407679f,
+ 0.947585591f, 0.319502031f,
+ 0.948561350f, 0.316593376f,
+ 0.949528181f, 0.313681740f,
+ 0.950486074f, 0.310767153f,
+ 0.951435021f, 0.307849640f,
+ 0.952375013f, 0.304929230f,
+ 0.953306040f, 0.302005949f,
+ 0.954228095f, 0.299079826f,
+ 0.955141168f, 0.296150888f,
+ 0.956045251f, 0.293219163f,
+ 0.956940336f, 0.290284677f,
+ 0.957826413f, 0.287347460f,
+ 0.958703475f, 0.284407537f,
+ 0.959571513f, 0.281464938f,
+ 0.960430519f, 0.278519689f,
+ 0.961280486f, 0.275571819f,
+ 0.962121404f, 0.272621355f,
+ 0.962953267f, 0.269668326f,
+ 0.963776066f, 0.266712757f,
+ 0.964589793f, 0.263754679f,
+ 0.965394442f, 0.260794118f,
+ 0.966190003f, 0.257831102f,
+ 0.966976471f, 0.254865660f,
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+ 0.514102744f, -0.857728610f,
+ 0.511468850f, -0.859301818f,
+ 0.508830143f, -0.860866939f,
+ 0.506186645f, -0.862423956f,
+ 0.503538384f, -0.863972856f,
+ 0.500885383f, -0.865513624f,
+ 0.498227667f, -0.867046246f,
+ 0.495565262f, -0.868570706f,
+ 0.492898192f, -0.870086991f,
+ 0.490226483f, -0.871595087f,
+ 0.487550160f, -0.873094978f,
+ 0.484869248f, -0.874586652f,
+ 0.482183772f, -0.876070094f,
+ 0.479493758f, -0.877545290f,
+ 0.476799230f, -0.879012226f,
+ 0.474100215f, -0.880470889f,
+ 0.471396737f, -0.881921264f,
+ 0.468688822f, -0.883363339f,
+ 0.465976496f, -0.884797098f,
+ 0.463259784f, -0.886222530f,
+ 0.460538711f, -0.887639620f,
+ 0.457813304f, -0.889048356f,
+ 0.455083587f, -0.890448723f,
+ 0.452349587f, -0.891840709f,
+ 0.449611330f, -0.893224301f,
+ 0.446868840f, -0.894599486f,
+ 0.444122145f, -0.895966250f,
+ 0.441371269f, -0.897324581f,
+ 0.438616239f, -0.898674466f,
+ 0.435857080f, -0.900015892f,
+ 0.433093819f, -0.901348847f,
+ 0.430326481f, -0.902673318f,
+ 0.427555093f, -0.903989293f,
+ 0.424779681f, -0.905296759f,
+ 0.422000271f, -0.906595705f,
+ 0.419216888f, -0.907886116f,
+ 0.416429560f, -0.909167983f,
+ 0.413638312f, -0.910441292f,
+ 0.410843171f, -0.911706032f,
+ 0.408044163f, -0.912962190f,
+ 0.405241314f, -0.914209756f,
+ 0.402434651f, -0.915448716f,
+ 0.399624200f, -0.916679060f,
+ 0.396809987f, -0.917900776f,
+ 0.393992040f, -0.919113852f,
+ 0.391170384f, -0.920318277f,
+ 0.388345047f, -0.921514039f,
+ 0.385516054f, -0.922701128f,
+ 0.382683432f, -0.923879533f,
+ 0.379847209f, -0.925049241f,
+ 0.377007410f, -0.926210242f,
+ 0.374164063f, -0.927362526f,
+ 0.371317194f, -0.928506080f,
+ 0.368466830f, -0.929640896f,
+ 0.365612998f, -0.930766961f,
+ 0.362755724f, -0.931884266f,
+ 0.359895037f, -0.932992799f,
+ 0.357030961f, -0.934092550f,
+ 0.354163525f, -0.935183510f,
+ 0.351292756f, -0.936265667f,
+ 0.348418680f, -0.937339012f,
+ 0.345541325f, -0.938403534f,
+ 0.342660717f, -0.939459224f,
+ 0.339776884f, -0.940506071f,
+ 0.336889853f, -0.941544065f,
+ 0.333999651f, -0.942573198f,
+ 0.331106306f, -0.943593458f,
+ 0.328209844f, -0.944604837f,
+ 0.325310292f, -0.945607325f,
+ 0.322407679f, -0.946600913f,
+ 0.319502031f, -0.947585591f,
+ 0.316593376f, -0.948561350f,
+ 0.313681740f, -0.949528181f,
+ 0.310767153f, -0.950486074f,
+ 0.307849640f, -0.951435021f,
+ 0.304929230f, -0.952375013f,
+ 0.302005949f, -0.953306040f,
+ 0.299079826f, -0.954228095f,
+ 0.296150888f, -0.955141168f,
+ 0.293219163f, -0.956045251f,
+ 0.290284677f, -0.956940336f,
+ 0.287347460f, -0.957826413f,
+ 0.284407537f, -0.958703475f,
+ 0.281464938f, -0.959571513f,
+ 0.278519689f, -0.960430519f,
+ 0.275571819f, -0.961280486f,
+ 0.272621355f, -0.962121404f,
+ 0.269668326f, -0.962953267f,
+ 0.266712757f, -0.963776066f,
+ 0.263754679f, -0.964589793f,
+ 0.260794118f, -0.965394442f,
+ 0.257831102f, -0.966190003f,
+ 0.254865660f, -0.966976471f,
+ 0.251897818f, -0.967753837f,
+ 0.248927606f, -0.968522094f,
+ 0.245955050f, -0.969281235f,
+ 0.242980180f, -0.970031253f,
+ 0.240003022f, -0.970772141f,
+ 0.237023606f, -0.971503891f,
+ 0.234041959f, -0.972226497f,
+ 0.231058108f, -0.972939952f,
+ 0.228072083f, -0.973644250f,
+ 0.225083911f, -0.974339383f,
+ 0.222093621f, -0.975025345f,
+ 0.219101240f, -0.975702130f,
+ 0.216106797f, -0.976369731f,
+ 0.213110320f, -0.977028143f,
+ 0.210111837f, -0.977677358f,
+ 0.207111376f, -0.978317371f,
+ 0.204108966f, -0.978948175f,
+ 0.201104635f, -0.979569766f,
+ 0.198098411f, -0.980182136f,
+ 0.195090322f, -0.980785280f,
+ 0.192080397f, -0.981379193f,
+ 0.189068664f, -0.981963869f,
+ 0.186055152f, -0.982539302f,
+ 0.183039888f, -0.983105487f,
+ 0.180022901f, -0.983662419f,
+ 0.177004220f, -0.984210092f,
+ 0.173983873f, -0.984748502f,
+ 0.170961889f, -0.985277642f,
+ 0.167938295f, -0.985797509f,
+ 0.164913120f, -0.986308097f,
+ 0.161886394f, -0.986809402f,
+ 0.158858143f, -0.987301418f,
+ 0.155828398f, -0.987784142f,
+ 0.152797185f, -0.988257568f,
+ 0.149764535f, -0.988721692f,
+ 0.146730474f, -0.989176510f,
+ 0.143695033f, -0.989622017f,
+ 0.140658239f, -0.990058210f,
+ 0.137620122f, -0.990485084f,
+ 0.134580709f, -0.990902635f,
+ 0.131540029f, -0.991310860f,
+ 0.128498111f, -0.991709754f,
+ 0.125454983f, -0.992099313f,
+ 0.122410675f, -0.992479535f,
+ 0.119365215f, -0.992850414f,
+ 0.116318631f, -0.993211949f,
+ 0.113270952f, -0.993564136f,
+ 0.110222207f, -0.993906970f,
+ 0.107172425f, -0.994240449f,
+ 0.104121634f, -0.994564571f,
+ 0.101069863f, -0.994879331f,
+ 0.098017140f, -0.995184727f,
+ 0.094963495f, -0.995480755f,
+ 0.091908956f, -0.995767414f,
+ 0.088853553f, -0.996044701f,
+ 0.085797312f, -0.996312612f,
+ 0.082740265f, -0.996571146f,
+ 0.079682438f, -0.996820299f,
+ 0.076623861f, -0.997060070f,
+ 0.073564564f, -0.997290457f,
+ 0.070504573f, -0.997511456f,
+ 0.067443920f, -0.997723067f,
+ 0.064382631f, -0.997925286f,
+ 0.061320736f, -0.998118113f,
+ 0.058258265f, -0.998301545f,
+ 0.055195244f, -0.998475581f,
+ 0.052131705f, -0.998640218f,
+ 0.049067674f, -0.998795456f,
+ 0.046003182f, -0.998941293f,
+ 0.042938257f, -0.999077728f,
+ 0.039872928f, -0.999204759f,
+ 0.036807223f, -0.999322385f,
+ 0.033741172f, -0.999430605f,
+ 0.030674803f, -0.999529418f,
+ 0.027608146f, -0.999618822f,
+ 0.024541229f, -0.999698819f,
+ 0.021474080f, -0.999769405f,
+ 0.018406730f, -0.999830582f,
+ 0.015339206f, -0.999882347f,
+ 0.012271538f, -0.999924702f,
+ 0.009203755f, -0.999957645f,
+ 0.006135885f, -0.999981175f,
+ 0.003067957f, -0.999995294f
+};
+
+const float32_t twiddleCoef_rfft_4096[4096] = {
+ 0.000000000f, 1.000000000f,
+ 0.001533980f, 0.999998823f,
+ 0.003067957f, 0.999995294f,
+ 0.004601926f, 0.999989411f,
+ 0.006135885f, 0.999981175f,
+ 0.007669829f, 0.999970586f,
+ 0.009203755f, 0.999957645f,
+ 0.010737659f, 0.999942350f,
+ 0.012271538f, 0.999924702f,
+ 0.013805389f, 0.999904701f,
+ 0.015339206f, 0.999882347f,
+ 0.016872988f, 0.999857641f,
+ 0.018406730f, 0.999830582f,
+ 0.019940429f, 0.999801170f,
+ 0.021474080f, 0.999769405f,
+ 0.023007681f, 0.999735288f,
+ 0.024541229f, 0.999698819f,
+ 0.026074718f, 0.999659997f,
+ 0.027608146f, 0.999618822f,
+ 0.029141509f, 0.999575296f,
+ 0.030674803f, 0.999529418f,
+ 0.032208025f, 0.999481187f,
+ 0.033741172f, 0.999430605f,
+ 0.035274239f, 0.999377670f,
+ 0.036807223f, 0.999322385f,
+ 0.038340120f, 0.999264747f,
+ 0.039872928f, 0.999204759f,
+ 0.041405641f, 0.999142419f,
+ 0.042938257f, 0.999077728f,
+ 0.044470772f, 0.999010686f,
+ 0.046003182f, 0.998941293f,
+ 0.047535484f, 0.998869550f,
+ 0.049067674f, 0.998795456f,
+ 0.050599749f, 0.998719012f,
+ 0.052131705f, 0.998640218f,
+ 0.053663538f, 0.998559074f,
+ 0.055195244f, 0.998475581f,
+ 0.056726821f, 0.998389737f,
+ 0.058258265f, 0.998301545f,
+ 0.059789571f, 0.998211003f,
+ 0.061320736f, 0.998118113f,
+ 0.062851758f, 0.998022874f,
+ 0.064382631f, 0.997925286f,
+ 0.065913353f, 0.997825350f,
+ 0.067443920f, 0.997723067f,
+ 0.068974328f, 0.997618435f,
+ 0.070504573f, 0.997511456f,
+ 0.072034653f, 0.997402130f,
+ 0.073564564f, 0.997290457f,
+ 0.075094301f, 0.997176437f,
+ 0.076623861f, 0.997060070f,
+ 0.078153242f, 0.996941358f,
+ 0.079682438f, 0.996820299f,
+ 0.081211447f, 0.996696895f,
+ 0.082740265f, 0.996571146f,
+ 0.084268888f, 0.996443051f,
+ 0.085797312f, 0.996312612f,
+ 0.087325535f, 0.996179829f,
+ 0.088853553f, 0.996044701f,
+ 0.090381361f, 0.995907229f,
+ 0.091908956f, 0.995767414f,
+ 0.093436336f, 0.995625256f,
+ 0.094963495f, 0.995480755f,
+ 0.096490431f, 0.995333912f,
+ 0.098017140f, 0.995184727f,
+ 0.099543619f, 0.995033199f,
+ 0.101069863f, 0.994879331f,
+ 0.102595869f, 0.994723121f,
+ 0.104121634f, 0.994564571f,
+ 0.105647154f, 0.994403680f,
+ 0.107172425f, 0.994240449f,
+ 0.108697444f, 0.994074879f,
+ 0.110222207f, 0.993906970f,
+ 0.111746711f, 0.993736722f,
+ 0.113270952f, 0.993564136f,
+ 0.114794927f, 0.993389211f,
+ 0.116318631f, 0.993211949f,
+ 0.117842062f, 0.993032350f,
+ 0.119365215f, 0.992850414f,
+ 0.120888087f, 0.992666142f,
+ 0.122410675f, 0.992479535f,
+ 0.123932975f, 0.992290591f,
+ 0.125454983f, 0.992099313f,
+ 0.126976696f, 0.991905700f,
+ 0.128498111f, 0.991709754f,
+ 0.130019223f, 0.991511473f,
+ 0.131540029f, 0.991310860f,
+ 0.133060525f, 0.991107914f,
+ 0.134580709f, 0.990902635f,
+ 0.136100575f, 0.990695025f,
+ 0.137620122f, 0.990485084f,
+ 0.139139344f, 0.990272812f,
+ 0.140658239f, 0.990058210f,
+ 0.142176804f, 0.989841278f,
+ 0.143695033f, 0.989622017f,
+ 0.145212925f, 0.989400428f,
+ 0.146730474f, 0.989176510f,
+ 0.148247679f, 0.988950265f,
+ 0.149764535f, 0.988721692f,
+ 0.151281038f, 0.988490793f,
+ 0.152797185f, 0.988257568f,
+ 0.154312973f, 0.988022017f,
+ 0.155828398f, 0.987784142f,
+ 0.157343456f, 0.987543942f,
+ 0.158858143f, 0.987301418f,
+ 0.160372457f, 0.987056571f,
+ 0.161886394f, 0.986809402f,
+ 0.163399949f, 0.986559910f,
+ 0.164913120f, 0.986308097f,
+ 0.166425904f, 0.986053963f,
+ 0.167938295f, 0.985797509f,
+ 0.169450291f, 0.985538735f,
+ 0.170961889f, 0.985277642f,
+ 0.172473084f, 0.985014231f,
+ 0.173983873f, 0.984748502f,
+ 0.175494253f, 0.984480455f,
+ 0.177004220f, 0.984210092f,
+ 0.178513771f, 0.983937413f,
+ 0.180022901f, 0.983662419f,
+ 0.181531608f, 0.983385110f,
+ 0.183039888f, 0.983105487f,
+ 0.184547737f, 0.982823551f,
+ 0.186055152f, 0.982539302f,
+ 0.187562129f, 0.982252741f,
+ 0.189068664f, 0.981963869f,
+ 0.190574755f, 0.981672686f,
+ 0.192080397f, 0.981379193f,
+ 0.193585587f, 0.981083391f,
+ 0.195090322f, 0.980785280f,
+ 0.196594598f, 0.980484862f,
+ 0.198098411f, 0.980182136f,
+ 0.199601758f, 0.979877104f,
+ 0.201104635f, 0.979569766f,
+ 0.202607039f, 0.979260123f,
+ 0.204108966f, 0.978948175f,
+ 0.205610413f, 0.978633924f,
+ 0.207111376f, 0.978317371f,
+ 0.208611852f, 0.977998515f,
+ 0.210111837f, 0.977677358f,
+ 0.211611327f, 0.977353900f,
+ 0.213110320f, 0.977028143f,
+ 0.214608811f, 0.976700086f,
+ 0.216106797f, 0.976369731f,
+ 0.217604275f, 0.976037079f,
+ 0.219101240f, 0.975702130f,
+ 0.220597690f, 0.975364885f,
+ 0.222093621f, 0.975025345f,
+ 0.223589029f, 0.974683511f,
+ 0.225083911f, 0.974339383f,
+ 0.226578264f, 0.973992962f,
+ 0.228072083f, 0.973644250f,
+ 0.229565366f, 0.973293246f,
+ 0.231058108f, 0.972939952f,
+ 0.232550307f, 0.972584369f,
+ 0.234041959f, 0.972226497f,
+ 0.235533059f, 0.971866337f,
+ 0.237023606f, 0.971503891f,
+ 0.238513595f, 0.971139158f,
+ 0.240003022f, 0.970772141f,
+ 0.241491885f, 0.970402839f,
+ 0.242980180f, 0.970031253f,
+ 0.244467903f, 0.969657385f,
+ 0.245955050f, 0.969281235f,
+ 0.247441619f, 0.968902805f,
+ 0.248927606f, 0.968522094f,
+ 0.250413007f, 0.968139105f,
+ 0.251897818f, 0.967753837f,
+ 0.253382037f, 0.967366292f,
+ 0.254865660f, 0.966976471f,
+ 0.256348682f, 0.966584374f,
+ 0.257831102f, 0.966190003f,
+ 0.259312915f, 0.965793359f,
+ 0.260794118f, 0.965394442f,
+ 0.262274707f, 0.964993253f,
+ 0.263754679f, 0.964589793f,
+ 0.265234030f, 0.964184064f,
+ 0.266712757f, 0.963776066f,
+ 0.268190857f, 0.963365800f,
+ 0.269668326f, 0.962953267f,
+ 0.271145160f, 0.962538468f,
+ 0.272621355f, 0.962121404f,
+ 0.274096910f, 0.961702077f,
+ 0.275571819f, 0.961280486f,
+ 0.277046080f, 0.960856633f,
+ 0.278519689f, 0.960430519f,
+ 0.279992643f, 0.960002146f,
+ 0.281464938f, 0.959571513f,
+ 0.282936570f, 0.959138622f,
+ 0.284407537f, 0.958703475f,
+ 0.285877835f, 0.958266071f,
+ 0.287347460f, 0.957826413f,
+ 0.288816408f, 0.957384501f,
+ 0.290284677f, 0.956940336f,
+ 0.291752263f, 0.956493919f,
+ 0.293219163f, 0.956045251f,
+ 0.294685372f, 0.955594334f,
+ 0.296150888f, 0.955141168f,
+ 0.297615707f, 0.954685755f,
+ 0.299079826f, 0.954228095f,
+ 0.300543241f, 0.953768190f,
+ 0.302005949f, 0.953306040f,
+ 0.303467947f, 0.952841648f,
+ 0.304929230f, 0.952375013f,
+ 0.306389795f, 0.951906137f,
+ 0.307849640f, 0.951435021f,
+ 0.309308760f, 0.950961666f,
+ 0.310767153f, 0.950486074f,
+ 0.312224814f, 0.950008245f,
+ 0.313681740f, 0.949528181f,
+ 0.315137929f, 0.949045882f,
+ 0.316593376f, 0.948561350f,
+ 0.318048077f, 0.948074586f,
+ 0.319502031f, 0.947585591f,
+ 0.320955232f, 0.947094366f,
+ 0.322407679f, 0.946600913f,
+ 0.323859367f, 0.946105232f,
+ 0.325310292f, 0.945607325f,
+ 0.326760452f, 0.945107193f,
+ 0.328209844f, 0.944604837f,
+ 0.329658463f, 0.944100258f,
+ 0.331106306f, 0.943593458f,
+ 0.332553370f, 0.943084437f,
+ 0.333999651f, 0.942573198f,
+ 0.335445147f, 0.942059740f,
+ 0.336889853f, 0.941544065f,
+ 0.338333767f, 0.941026175f,
+ 0.339776884f, 0.940506071f,
+ 0.341219202f, 0.939983753f,
+ 0.342660717f, 0.939459224f,
+ 0.344101426f, 0.938932484f,
+ 0.345541325f, 0.938403534f,
+ 0.346980411f, 0.937872376f,
+ 0.348418680f, 0.937339012f,
+ 0.349856130f, 0.936803442f,
+ 0.351292756f, 0.936265667f,
+ 0.352728556f, 0.935725689f,
+ 0.354163525f, 0.935183510f,
+ 0.355597662f, 0.934639130f,
+ 0.357030961f, 0.934092550f,
+ 0.358463421f, 0.933543773f,
+ 0.359895037f, 0.932992799f,
+ 0.361325806f, 0.932439629f,
+ 0.362755724f, 0.931884266f,
+ 0.364184790f, 0.931326709f,
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+ 0.178513771f, -0.983937413f,
+ 0.177004220f, -0.984210092f,
+ 0.175494253f, -0.984480455f,
+ 0.173983873f, -0.984748502f,
+ 0.172473084f, -0.985014231f,
+ 0.170961889f, -0.985277642f,
+ 0.169450291f, -0.985538735f,
+ 0.167938295f, -0.985797509f,
+ 0.166425904f, -0.986053963f,
+ 0.164913120f, -0.986308097f,
+ 0.163399949f, -0.986559910f,
+ 0.161886394f, -0.986809402f,
+ 0.160372457f, -0.987056571f,
+ 0.158858143f, -0.987301418f,
+ 0.157343456f, -0.987543942f,
+ 0.155828398f, -0.987784142f,
+ 0.154312973f, -0.988022017f,
+ 0.152797185f, -0.988257568f,
+ 0.151281038f, -0.988490793f,
+ 0.149764535f, -0.988721692f,
+ 0.148247679f, -0.988950265f,
+ 0.146730474f, -0.989176510f,
+ 0.145212925f, -0.989400428f,
+ 0.143695033f, -0.989622017f,
+ 0.142176804f, -0.989841278f,
+ 0.140658239f, -0.990058210f,
+ 0.139139344f, -0.990272812f,
+ 0.137620122f, -0.990485084f,
+ 0.136100575f, -0.990695025f,
+ 0.134580709f, -0.990902635f,
+ 0.133060525f, -0.991107914f,
+ 0.131540029f, -0.991310860f,
+ 0.130019223f, -0.991511473f,
+ 0.128498111f, -0.991709754f,
+ 0.126976696f, -0.991905700f,
+ 0.125454983f, -0.992099313f,
+ 0.123932975f, -0.992290591f,
+ 0.122410675f, -0.992479535f,
+ 0.120888087f, -0.992666142f,
+ 0.119365215f, -0.992850414f,
+ 0.117842062f, -0.993032350f,
+ 0.116318631f, -0.993211949f,
+ 0.114794927f, -0.993389211f,
+ 0.113270952f, -0.993564136f,
+ 0.111746711f, -0.993736722f,
+ 0.110222207f, -0.993906970f,
+ 0.108697444f, -0.994074879f,
+ 0.107172425f, -0.994240449f,
+ 0.105647154f, -0.994403680f,
+ 0.104121634f, -0.994564571f,
+ 0.102595869f, -0.994723121f,
+ 0.101069863f, -0.994879331f,
+ 0.099543619f, -0.995033199f,
+ 0.098017140f, -0.995184727f,
+ 0.096490431f, -0.995333912f,
+ 0.094963495f, -0.995480755f,
+ 0.093436336f, -0.995625256f,
+ 0.091908956f, -0.995767414f,
+ 0.090381361f, -0.995907229f,
+ 0.088853553f, -0.996044701f,
+ 0.087325535f, -0.996179829f,
+ 0.085797312f, -0.996312612f,
+ 0.084268888f, -0.996443051f,
+ 0.082740265f, -0.996571146f,
+ 0.081211447f, -0.996696895f,
+ 0.079682438f, -0.996820299f,
+ 0.078153242f, -0.996941358f,
+ 0.076623861f, -0.997060070f,
+ 0.075094301f, -0.997176437f,
+ 0.073564564f, -0.997290457f,
+ 0.072034653f, -0.997402130f,
+ 0.070504573f, -0.997511456f,
+ 0.068974328f, -0.997618435f,
+ 0.067443920f, -0.997723067f,
+ 0.065913353f, -0.997825350f,
+ 0.064382631f, -0.997925286f,
+ 0.062851758f, -0.998022874f,
+ 0.061320736f, -0.998118113f,
+ 0.059789571f, -0.998211003f,
+ 0.058258265f, -0.998301545f,
+ 0.056726821f, -0.998389737f,
+ 0.055195244f, -0.998475581f,
+ 0.053663538f, -0.998559074f,
+ 0.052131705f, -0.998640218f,
+ 0.050599749f, -0.998719012f,
+ 0.049067674f, -0.998795456f,
+ 0.047535484f, -0.998869550f,
+ 0.046003182f, -0.998941293f,
+ 0.044470772f, -0.999010686f,
+ 0.042938257f, -0.999077728f,
+ 0.041405641f, -0.999142419f,
+ 0.039872928f, -0.999204759f,
+ 0.038340120f, -0.999264747f,
+ 0.036807223f, -0.999322385f,
+ 0.035274239f, -0.999377670f,
+ 0.033741172f, -0.999430605f,
+ 0.032208025f, -0.999481187f,
+ 0.030674803f, -0.999529418f,
+ 0.029141509f, -0.999575296f,
+ 0.027608146f, -0.999618822f,
+ 0.026074718f, -0.999659997f,
+ 0.024541229f, -0.999698819f,
+ 0.023007681f, -0.999735288f,
+ 0.021474080f, -0.999769405f,
+ 0.019940429f, -0.999801170f,
+ 0.018406730f, -0.999830582f,
+ 0.016872988f, -0.999857641f,
+ 0.015339206f, -0.999882347f,
+ 0.013805389f, -0.999904701f,
+ 0.012271538f, -0.999924702f,
+ 0.010737659f, -0.999942350f,
+ 0.009203755f, -0.999957645f,
+ 0.007669829f, -0.999970586f,
+ 0.006135885f, -0.999981175f,
+ 0.004601926f, -0.999989411f,
+ 0.003067957f, -0.999995294f,
+ 0.001533980f, -0.999998823f
+};
+
+
+/**
+ * \par
+ * Example code for the generation of the floating-point sine table:
+ *
+ * tableSize = 512;
+ * for(n = 0; n < (tableSize + 1); n++)
+ * {
+ * sinTable[n]=sin(2*pi*n/tableSize);
+ * }
+ * \par
+ * where pi value is 3.14159265358979
+ */
+
+const float32_t sinTable_f32[FAST_MATH_TABLE_SIZE + 1] = {
+ 0.00000000f, 0.01227154f, 0.02454123f, 0.03680722f, 0.04906767f, 0.06132074f,
+ 0.07356456f, 0.08579731f, 0.09801714f, 0.11022221f, 0.12241068f, 0.13458071f,
+ 0.14673047f, 0.15885814f, 0.17096189f, 0.18303989f, 0.19509032f, 0.20711138f,
+ 0.21910124f, 0.23105811f, 0.24298018f, 0.25486566f, 0.26671276f, 0.27851969f,
+ 0.29028468f, 0.30200595f, 0.31368174f, 0.32531029f, 0.33688985f, 0.34841868f,
+ 0.35989504f, 0.37131719f, 0.38268343f, 0.39399204f, 0.40524131f, 0.41642956f,
+ 0.42755509f, 0.43861624f, 0.44961133f, 0.46053871f, 0.47139674f, 0.48218377f,
+ 0.49289819f, 0.50353838f, 0.51410274f, 0.52458968f, 0.53499762f, 0.54532499f,
+ 0.55557023f, 0.56573181f, 0.57580819f, 0.58579786f, 0.59569930f, 0.60551104f,
+ 0.61523159f, 0.62485949f, 0.63439328f, 0.64383154f, 0.65317284f, 0.66241578f,
+ 0.67155895f, 0.68060100f, 0.68954054f, 0.69837625f, 0.70710678f, 0.71573083f,
+ 0.72424708f, 0.73265427f, 0.74095113f, 0.74913639f, 0.75720885f, 0.76516727f,
+ 0.77301045f, 0.78073723f, 0.78834643f, 0.79583690f, 0.80320753f, 0.81045720f,
+ 0.81758481f, 0.82458930f, 0.83146961f, 0.83822471f, 0.84485357f, 0.85135519f,
+ 0.85772861f, 0.86397286f, 0.87008699f, 0.87607009f, 0.88192126f, 0.88763962f,
+ 0.89322430f, 0.89867447f, 0.90398929f, 0.90916798f, 0.91420976f, 0.91911385f,
+ 0.92387953f, 0.92850608f, 0.93299280f, 0.93733901f, 0.94154407f, 0.94560733f,
+ 0.94952818f, 0.95330604f, 0.95694034f, 0.96043052f, 0.96377607f, 0.96697647f,
+ 0.97003125f, 0.97293995f, 0.97570213f, 0.97831737f, 0.98078528f, 0.98310549f,
+ 0.98527764f, 0.98730142f, 0.98917651f, 0.99090264f, 0.99247953f, 0.99390697f,
+ 0.99518473f, 0.99631261f, 0.99729046f, 0.99811811f, 0.99879546f, 0.99932238f,
+ 0.99969882f, 0.99992470f, 1.00000000f, 0.99992470f, 0.99969882f, 0.99932238f,
+ 0.99879546f, 0.99811811f, 0.99729046f, 0.99631261f, 0.99518473f, 0.99390697f,
+ 0.99247953f, 0.99090264f, 0.98917651f, 0.98730142f, 0.98527764f, 0.98310549f,
+ 0.98078528f, 0.97831737f, 0.97570213f, 0.97293995f, 0.97003125f, 0.96697647f,
+ 0.96377607f, 0.96043052f, 0.95694034f, 0.95330604f, 0.94952818f, 0.94560733f,
+ 0.94154407f, 0.93733901f, 0.93299280f, 0.92850608f, 0.92387953f, 0.91911385f,
+ 0.91420976f, 0.90916798f, 0.90398929f, 0.89867447f, 0.89322430f, 0.88763962f,
+ 0.88192126f, 0.87607009f, 0.87008699f, 0.86397286f, 0.85772861f, 0.85135519f,
+ 0.84485357f, 0.83822471f, 0.83146961f, 0.82458930f, 0.81758481f, 0.81045720f,
+ 0.80320753f, 0.79583690f, 0.78834643f, 0.78073723f, 0.77301045f, 0.76516727f,
+ 0.75720885f, 0.74913639f, 0.74095113f, 0.73265427f, 0.72424708f, 0.71573083f,
+ 0.70710678f, 0.69837625f, 0.68954054f, 0.68060100f, 0.67155895f, 0.66241578f,
+ 0.65317284f, 0.64383154f, 0.63439328f, 0.62485949f, 0.61523159f, 0.60551104f,
+ 0.59569930f, 0.58579786f, 0.57580819f, 0.56573181f, 0.55557023f, 0.54532499f,
+ 0.53499762f, 0.52458968f, 0.51410274f, 0.50353838f, 0.49289819f, 0.48218377f,
+ 0.47139674f, 0.46053871f, 0.44961133f, 0.43861624f, 0.42755509f, 0.41642956f,
+ 0.40524131f, 0.39399204f, 0.38268343f, 0.37131719f, 0.35989504f, 0.34841868f,
+ 0.33688985f, 0.32531029f, 0.31368174f, 0.30200595f, 0.29028468f, 0.27851969f,
+ 0.26671276f, 0.25486566f, 0.24298018f, 0.23105811f, 0.21910124f, 0.20711138f,
+ 0.19509032f, 0.18303989f, 0.17096189f, 0.15885814f, 0.14673047f, 0.13458071f,
+ 0.12241068f, 0.11022221f, 0.09801714f, 0.08579731f, 0.07356456f, 0.06132074f,
+ 0.04906767f, 0.03680722f, 0.02454123f, 0.01227154f, 0.00000000f, -0.01227154f,
+ -0.02454123f, -0.03680722f, -0.04906767f, -0.06132074f, -0.07356456f,
+ -0.08579731f, -0.09801714f, -0.11022221f, -0.12241068f, -0.13458071f,
+ -0.14673047f, -0.15885814f, -0.17096189f, -0.18303989f, -0.19509032f,
+ -0.20711138f, -0.21910124f, -0.23105811f, -0.24298018f, -0.25486566f,
+ -0.26671276f, -0.27851969f, -0.29028468f, -0.30200595f, -0.31368174f,
+ -0.32531029f, -0.33688985f, -0.34841868f, -0.35989504f, -0.37131719f,
+ -0.38268343f, -0.39399204f, -0.40524131f, -0.41642956f, -0.42755509f,
+ -0.43861624f, -0.44961133f, -0.46053871f, -0.47139674f, -0.48218377f,
+ -0.49289819f, -0.50353838f, -0.51410274f, -0.52458968f, -0.53499762f,
+ -0.54532499f, -0.55557023f, -0.56573181f, -0.57580819f, -0.58579786f,
+ -0.59569930f, -0.60551104f, -0.61523159f, -0.62485949f, -0.63439328f,
+ -0.64383154f, -0.65317284f, -0.66241578f, -0.67155895f, -0.68060100f,
+ -0.68954054f, -0.69837625f, -0.70710678f, -0.71573083f, -0.72424708f,
+ -0.73265427f, -0.74095113f, -0.74913639f, -0.75720885f, -0.76516727f,
+ -0.77301045f, -0.78073723f, -0.78834643f, -0.79583690f, -0.80320753f,
+ -0.81045720f, -0.81758481f, -0.82458930f, -0.83146961f, -0.83822471f,
+ -0.84485357f, -0.85135519f, -0.85772861f, -0.86397286f, -0.87008699f,
+ -0.87607009f, -0.88192126f, -0.88763962f, -0.89322430f, -0.89867447f,
+ -0.90398929f, -0.90916798f, -0.91420976f, -0.91911385f, -0.92387953f,
+ -0.92850608f, -0.93299280f, -0.93733901f, -0.94154407f, -0.94560733f,
+ -0.94952818f, -0.95330604f, -0.95694034f, -0.96043052f, -0.96377607f,
+ -0.96697647f, -0.97003125f, -0.97293995f, -0.97570213f, -0.97831737f,
+ -0.98078528f, -0.98310549f, -0.98527764f, -0.98730142f, -0.98917651f,
+ -0.99090264f, -0.99247953f, -0.99390697f, -0.99518473f, -0.99631261f,
+ -0.99729046f, -0.99811811f, -0.99879546f, -0.99932238f, -0.99969882f,
+ -0.99992470f, -1.00000000f, -0.99992470f, -0.99969882f, -0.99932238f,
+ -0.99879546f, -0.99811811f, -0.99729046f, -0.99631261f, -0.99518473f,
+ -0.99390697f, -0.99247953f, -0.99090264f, -0.98917651f, -0.98730142f,
+ -0.98527764f, -0.98310549f, -0.98078528f, -0.97831737f, -0.97570213f,
+ -0.97293995f, -0.97003125f, -0.96697647f, -0.96377607f, -0.96043052f,
+ -0.95694034f, -0.95330604f, -0.94952818f, -0.94560733f, -0.94154407f,
+ -0.93733901f, -0.93299280f, -0.92850608f, -0.92387953f, -0.91911385f,
+ -0.91420976f, -0.90916798f, -0.90398929f, -0.89867447f, -0.89322430f,
+ -0.88763962f, -0.88192126f, -0.87607009f, -0.87008699f, -0.86397286f,
+ -0.85772861f, -0.85135519f, -0.84485357f, -0.83822471f, -0.83146961f,
+ -0.82458930f, -0.81758481f, -0.81045720f, -0.80320753f, -0.79583690f,
+ -0.78834643f, -0.78073723f, -0.77301045f, -0.76516727f, -0.75720885f,
+ -0.74913639f, -0.74095113f, -0.73265427f, -0.72424708f, -0.71573083f,
+ -0.70710678f, -0.69837625f, -0.68954054f, -0.68060100f, -0.67155895f,
+ -0.66241578f, -0.65317284f, -0.64383154f, -0.63439328f, -0.62485949f,
+ -0.61523159f, -0.60551104f, -0.59569930f, -0.58579786f, -0.57580819f,
+ -0.56573181f, -0.55557023f, -0.54532499f, -0.53499762f, -0.52458968f,
+ -0.51410274f, -0.50353838f, -0.49289819f, -0.48218377f, -0.47139674f,
+ -0.46053871f, -0.44961133f, -0.43861624f, -0.42755509f, -0.41642956f,
+ -0.40524131f, -0.39399204f, -0.38268343f, -0.37131719f, -0.35989504f,
+ -0.34841868f, -0.33688985f, -0.32531029f, -0.31368174f, -0.30200595f,
+ -0.29028468f, -0.27851969f, -0.26671276f, -0.25486566f, -0.24298018f,
+ -0.23105811f, -0.21910124f, -0.20711138f, -0.19509032f, -0.18303989f,
+ -0.17096189f, -0.15885814f, -0.14673047f, -0.13458071f, -0.12241068f,
+ -0.11022221f, -0.09801714f, -0.08579731f, -0.07356456f, -0.06132074f,
+ -0.04906767f, -0.03680722f, -0.02454123f, -0.01227154f, -0.00000000f
+};
+
+/**
+ * \par
+ * Table values are in Q31 (1.31 fixed-point format) and generation is done in
+ * three steps. First, generate sin values in floating point:
+ *
+ * tableSize = 512;
+ * for(n = 0; n < (tableSize + 1); n++)
+ * {
+ * sinTable[n]= sin(2*pi*n/tableSize);
+ * }
+ * where pi value is 3.14159265358979
+ * \par
+ * Second, convert floating-point to Q31 (Fixed point):
+ * (sinTable[i] * pow(2, 31))
+ * \par
+ * Finally, round to the nearest integer value:
+ * sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);
+ */
+const q31_t sinTable_q31[FAST_MATH_TABLE_SIZE + 1] = {
+ 0x00000000, 0x01921D20, 0x03242ABF, 0x04B6195D, 0x0647D97C, 0x07D95B9E,
+ 0x096A9049, 0x0AFB6805, 0x0C8BD35E, 0x0E1BC2E4, 0x0FAB272B, 0x1139F0CF,
+ 0x12C8106F, 0x145576B1, 0x15E21445, 0x176DD9DE, 0x18F8B83C, 0x1A82A026,
+ 0x1C0B826A, 0x1D934FE5, 0x1F19F97B, 0x209F701C, 0x2223A4C5, 0x23A6887F,
+ 0x25280C5E, 0x26A82186, 0x2826B928, 0x29A3C485, 0x2B1F34EB, 0x2C98FBBA,
+ 0x2E110A62, 0x2F875262, 0x30FBC54D, 0x326E54C7, 0x33DEF287, 0x354D9057,
+ 0x36BA2014, 0x382493B0, 0x398CDD32, 0x3AF2EEB7, 0x3C56BA70, 0x3DB832A6,
+ 0x3F1749B8, 0x4073F21D, 0x41CE1E65, 0x4325C135, 0x447ACD50, 0x45CD358F,
+ 0x471CECE7, 0x4869E665, 0x49B41533, 0x4AFB6C98, 0x4C3FDFF4, 0x4D8162C4,
+ 0x4EBFE8A5, 0x4FFB654D, 0x5133CC94, 0x5269126E, 0x539B2AF0, 0x54CA0A4B,
+ 0x55F5A4D2, 0x571DEEFA, 0x5842DD54, 0x59646498, 0x5A82799A, 0x5B9D1154,
+ 0x5CB420E0, 0x5DC79D7C, 0x5ED77C8A, 0x5FE3B38D, 0x60EC3830, 0x61F1003F,
+ 0x62F201AC, 0x63EF3290, 0x64E88926, 0x65DDFBD3, 0x66CF8120, 0x67BD0FBD,
+ 0x68A69E81, 0x698C246C, 0x6A6D98A4, 0x6B4AF279, 0x6C242960, 0x6CF934FC,
+ 0x6DCA0D14, 0x6E96A99D, 0x6F5F02B2, 0x7023109A, 0x70E2CBC6, 0x719E2CD2,
+ 0x72552C85, 0x7307C3D0, 0x73B5EBD1, 0x745F9DD1, 0x7504D345, 0x75A585CF,
+ 0x7641AF3D, 0x76D94989, 0x776C4EDB, 0x77FAB989, 0x78848414, 0x7909A92D,
+ 0x798A23B1, 0x7A05EEAD, 0x7A7D055B, 0x7AEF6323, 0x7B5D039E, 0x7BC5E290,
+ 0x7C29FBEE, 0x7C894BDE, 0x7CE3CEB2, 0x7D3980EC, 0x7D8A5F40, 0x7DD6668F,
+ 0x7E1D93EA, 0x7E5FE493, 0x7E9D55FC, 0x7ED5E5C6, 0x7F0991C4, 0x7F3857F6,
+ 0x7F62368F, 0x7F872BF3, 0x7FA736B4, 0x7FC25596, 0x7FD8878E, 0x7FE9CBC0,
+ 0x7FF62182, 0x7FFD885A, 0x7FFFFFFF, 0x7FFD885A, 0x7FF62182, 0x7FE9CBC0,
+ 0x7FD8878E, 0x7FC25596, 0x7FA736B4, 0x7F872BF3, 0x7F62368F, 0x7F3857F6,
+ 0x7F0991C4, 0x7ED5E5C6, 0x7E9D55FC, 0x7E5FE493, 0x7E1D93EA, 0x7DD6668F,
+ 0x7D8A5F40, 0x7D3980EC, 0x7CE3CEB2, 0x7C894BDE, 0x7C29FBEE, 0x7BC5E290,
+ 0x7B5D039E, 0x7AEF6323, 0x7A7D055B, 0x7A05EEAD, 0x798A23B1, 0x7909A92D,
+ 0x78848414, 0x77FAB989, 0x776C4EDB, 0x76D94989, 0x7641AF3D, 0x75A585CF,
+ 0x7504D345, 0x745F9DD1, 0x73B5EBD1, 0x7307C3D0, 0x72552C85, 0x719E2CD2,
+ 0x70E2CBC6, 0x7023109A, 0x6F5F02B2, 0x6E96A99D, 0x6DCA0D14, 0x6CF934FC,
+ 0x6C242960, 0x6B4AF279, 0x6A6D98A4, 0x698C246C, 0x68A69E81, 0x67BD0FBD,
+ 0x66CF8120, 0x65DDFBD3, 0x64E88926, 0x63EF3290, 0x62F201AC, 0x61F1003F,
+ 0x60EC3830, 0x5FE3B38D, 0x5ED77C8A, 0x5DC79D7C, 0x5CB420E0, 0x5B9D1154,
+ 0x5A82799A, 0x59646498, 0x5842DD54, 0x571DEEFA, 0x55F5A4D2, 0x54CA0A4B,
+ 0x539B2AF0, 0x5269126E, 0x5133CC94, 0x4FFB654D, 0x4EBFE8A5, 0x4D8162C4,
+ 0x4C3FDFF4, 0x4AFB6C98, 0x49B41533, 0x4869E665, 0x471CECE7, 0x45CD358F,
+ 0x447ACD50, 0x4325C135, 0x41CE1E65, 0x4073F21D, 0x3F1749B8, 0x3DB832A6,
+ 0x3C56BA70, 0x3AF2EEB7, 0x398CDD32, 0x382493B0, 0x36BA2014, 0x354D9057,
+ 0x33DEF287, 0x326E54C7, 0x30FBC54D, 0x2F875262, 0x2E110A62, 0x2C98FBBA,
+ 0x2B1F34EB, 0x29A3C485, 0x2826B928, 0x26A82186, 0x25280C5E, 0x23A6887F,
+ 0x2223A4C5, 0x209F701C, 0x1F19F97B, 0x1D934FE5, 0x1C0B826A, 0x1A82A026,
+ 0x18F8B83C, 0x176DD9DE, 0x15E21445, 0x145576B1, 0x12C8106F, 0x1139F0CF,
+ 0x0FAB272B, 0x0E1BC2E4, 0x0C8BD35E, 0x0AFB6805, 0x096A9049, 0x07D95B9E,
+ 0x0647D97C, 0x04B6195D, 0x03242ABF, 0x01921D20, 0x00000000, 0xFE6DE2E0,
+ 0xFCDBD541, 0xFB49E6A3, 0xF9B82684, 0xF826A462, 0xF6956FB7, 0xF50497FB,
+ 0xF3742CA2, 0xF1E43D1C, 0xF054D8D5, 0xEEC60F31, 0xED37EF91, 0xEBAA894F,
+ 0xEA1DEBBB, 0xE8922622, 0xE70747C4, 0xE57D5FDA, 0xE3F47D96, 0xE26CB01B,
+ 0xE0E60685, 0xDF608FE4, 0xDDDC5B3B, 0xDC597781, 0xDAD7F3A2, 0xD957DE7A,
+ 0xD7D946D8, 0xD65C3B7B, 0xD4E0CB15, 0xD3670446, 0xD1EEF59E, 0xD078AD9E,
+ 0xCF043AB3, 0xCD91AB39, 0xCC210D79, 0xCAB26FA9, 0xC945DFEC, 0xC7DB6C50,
+ 0xC67322CE, 0xC50D1149, 0xC3A94590, 0xC247CD5A, 0xC0E8B648, 0xBF8C0DE3,
+ 0xBE31E19B, 0xBCDA3ECB, 0xBB8532B0, 0xBA32CA71, 0xB8E31319, 0xB796199B,
+ 0xB64BEACD, 0xB5049368, 0xB3C0200C, 0xB27E9D3C, 0xB140175B, 0xB0049AB3,
+ 0xAECC336C, 0xAD96ED92, 0xAC64D510, 0xAB35F5B5, 0xAA0A5B2E, 0xA8E21106,
+ 0xA7BD22AC, 0xA69B9B68, 0xA57D8666, 0xA462EEAC, 0xA34BDF20, 0xA2386284,
+ 0xA1288376, 0xA01C4C73, 0x9F13C7D0, 0x9E0EFFC1, 0x9D0DFE54, 0x9C10CD70,
+ 0x9B1776DA, 0x9A22042D, 0x99307EE0, 0x9842F043, 0x9759617F, 0x9673DB94,
+ 0x9592675C, 0x94B50D87, 0x93DBD6A0, 0x9306CB04, 0x9235F2EC, 0x91695663,
+ 0x90A0FD4E, 0x8FDCEF66, 0x8F1D343A, 0x8E61D32E, 0x8DAAD37B, 0x8CF83C30,
+ 0x8C4A142F, 0x8BA0622F, 0x8AFB2CBB, 0x8A5A7A31, 0x89BE50C3, 0x8926B677,
+ 0x8893B125, 0x88054677, 0x877B7BEC, 0x86F656D3, 0x8675DC4F, 0x85FA1153,
+ 0x8582FAA5, 0x85109CDD, 0x84A2FC62, 0x843A1D70, 0x83D60412, 0x8376B422,
+ 0x831C314E, 0x82C67F14, 0x8275A0C0, 0x82299971, 0x81E26C16, 0x81A01B6D,
+ 0x8162AA04, 0x812A1A3A, 0x80F66E3C, 0x80C7A80A, 0x809DC971, 0x8078D40D,
+ 0x8058C94C, 0x803DAA6A, 0x80277872, 0x80163440, 0x8009DE7E, 0x800277A6,
+ 0x80000000, 0x800277A6, 0x8009DE7E, 0x80163440, 0x80277872, 0x803DAA6A,
+ 0x8058C94C, 0x8078D40D, 0x809DC971, 0x80C7A80A, 0x80F66E3C, 0x812A1A3A,
+ 0x8162AA04, 0x81A01B6D, 0x81E26C16, 0x82299971, 0x8275A0C0, 0x82C67F14,
+ 0x831C314E, 0x8376B422, 0x83D60412, 0x843A1D70, 0x84A2FC62, 0x85109CDD,
+ 0x8582FAA5, 0x85FA1153, 0x8675DC4F, 0x86F656D3, 0x877B7BEC, 0x88054677,
+ 0x8893B125, 0x8926B677, 0x89BE50C3, 0x8A5A7A31, 0x8AFB2CBB, 0x8BA0622F,
+ 0x8C4A142F, 0x8CF83C30, 0x8DAAD37B, 0x8E61D32E, 0x8F1D343A, 0x8FDCEF66,
+ 0x90A0FD4E, 0x91695663, 0x9235F2EC, 0x9306CB04, 0x93DBD6A0, 0x94B50D87,
+ 0x9592675C, 0x9673DB94, 0x9759617F, 0x9842F043, 0x99307EE0, 0x9A22042D,
+ 0x9B1776DA, 0x9C10CD70, 0x9D0DFE54, 0x9E0EFFC1, 0x9F13C7D0, 0xA01C4C73,
+ 0xA1288376, 0xA2386284, 0xA34BDF20, 0xA462EEAC, 0xA57D8666, 0xA69B9B68,
+ 0xA7BD22AC, 0xA8E21106, 0xAA0A5B2E, 0xAB35F5B5, 0xAC64D510, 0xAD96ED92,
+ 0xAECC336C, 0xB0049AB3, 0xB140175B, 0xB27E9D3C, 0xB3C0200C, 0xB5049368,
+ 0xB64BEACD, 0xB796199B, 0xB8E31319, 0xBA32CA71, 0xBB8532B0, 0xBCDA3ECB,
+ 0xBE31E19B, 0xBF8C0DE3, 0xC0E8B648, 0xC247CD5A, 0xC3A94590, 0xC50D1149,
+ 0xC67322CE, 0xC7DB6C50, 0xC945DFEC, 0xCAB26FA9, 0xCC210D79, 0xCD91AB39,
+ 0xCF043AB3, 0xD078AD9E, 0xD1EEF59E, 0xD3670446, 0xD4E0CB15, 0xD65C3B7B,
+ 0xD7D946D8, 0xD957DE7A, 0xDAD7F3A2, 0xDC597781, 0xDDDC5B3B, 0xDF608FE4,
+ 0xE0E60685, 0xE26CB01B, 0xE3F47D96, 0xE57D5FDA, 0xE70747C4, 0xE8922622,
+ 0xEA1DEBBB, 0xEBAA894F, 0xED37EF91, 0xEEC60F31, 0xF054D8D5, 0xF1E43D1C,
+ 0xF3742CA2, 0xF50497FB, 0xF6956FB7, 0xF826A462, 0xF9B82684, 0xFB49E6A3,
+ 0xFCDBD541, 0xFE6DE2E0, 0x00000000
+};
+
+/**
+ * \par
+ * Table values are in Q15 (1.15 fixed-point format) and generation is done in
+ * three steps. First, generate sin values in floating point:
+ *
+ * tableSize = 512;
+ * for(n = 0; n < (tableSize + 1); n++)
+ * {
+ * sinTable[n]= sin(2*pi*n/tableSize);
+ * }
+ * where pi value is 3.14159265358979
+ * \par
+ * Second, convert floating-point to Q15 (Fixed point):
+ * (sinTable[i] * pow(2, 15))
+ * \par
+ * Finally, round to the nearest integer value:
+ * sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);
+ */
+const q15_t sinTable_q15[FAST_MATH_TABLE_SIZE + 1] = {
+ 0x0000, 0x0192, 0x0324, 0x04B6, 0x0648, 0x07D9, 0x096B, 0x0AFB, 0x0C8C, 0x0E1C, 0x0FAB, 0x113A, 0x12C8,
+ 0x1455, 0x15E2, 0x176E, 0x18F9, 0x1A83, 0x1C0C, 0x1D93, 0x1F1A, 0x209F, 0x2224, 0x23A7, 0x2528, 0x26A8,
+ 0x2827, 0x29A4, 0x2B1F, 0x2C99, 0x2E11, 0x2F87, 0x30FC, 0x326E, 0x33DF, 0x354E, 0x36BA, 0x3825, 0x398D,
+ 0x3AF3, 0x3C57, 0x3DB8, 0x3F17, 0x4074, 0x41CE, 0x4326, 0x447B, 0x45CD, 0x471D, 0x486A, 0x49B4, 0x4AFB,
+ 0x4C40, 0x4D81, 0x4EC0, 0x4FFB, 0x5134, 0x5269, 0x539B, 0x54CA, 0x55F6, 0x571E, 0x5843, 0x5964, 0x5A82,
+ 0x5B9D, 0x5CB4, 0x5DC8, 0x5ED7, 0x5FE4, 0x60EC, 0x61F1, 0x62F2, 0x63EF, 0x64E9, 0x65DE, 0x66D0, 0x67BD,
+ 0x68A7, 0x698C, 0x6A6E, 0x6B4B, 0x6C24, 0x6CF9, 0x6DCA, 0x6E97, 0x6F5F, 0x7023, 0x70E3, 0x719E, 0x7255,
+ 0x7308, 0x73B6, 0x7460, 0x7505, 0x75A6, 0x7642, 0x76D9, 0x776C, 0x77FB, 0x7885, 0x790A, 0x798A, 0x7A06,
+ 0x7A7D, 0x7AEF, 0x7B5D, 0x7BC6, 0x7C2A, 0x7C89, 0x7CE4, 0x7D3A, 0x7D8A, 0x7DD6, 0x7E1E, 0x7E60, 0x7E9D,
+ 0x7ED6, 0x7F0A, 0x7F38, 0x7F62, 0x7F87, 0x7FA7, 0x7FC2, 0x7FD9, 0x7FEA, 0x7FF6, 0x7FFE, 0x7FFF, 0x7FFE,
+ 0x7FF6, 0x7FEA, 0x7FD9, 0x7FC2, 0x7FA7, 0x7F87, 0x7F62, 0x7F38, 0x7F0A, 0x7ED6, 0x7E9D, 0x7E60, 0x7E1E,
+ 0x7DD6, 0x7D8A, 0x7D3A, 0x7CE4, 0x7C89, 0x7C2A, 0x7BC6, 0x7B5D, 0x7AEF, 0x7A7D, 0x7A06, 0x798A, 0x790A,
+ 0x7885, 0x77FB, 0x776C, 0x76D9, 0x7642, 0x75A6, 0x7505, 0x7460, 0x73B6, 0x7308, 0x7255, 0x719E, 0x70E3,
+ 0x7023, 0x6F5F, 0x6E97, 0x6DCA, 0x6CF9, 0x6C24, 0x6B4B, 0x6A6E, 0x698C, 0x68A7, 0x67BD, 0x66D0, 0x65DE,
+ 0x64E9, 0x63EF, 0x62F2, 0x61F1, 0x60EC, 0x5FE4, 0x5ED7, 0x5DC8, 0x5CB4, 0x5B9D, 0x5A82, 0x5964, 0x5843,
+ 0x571E, 0x55F6, 0x54CA, 0x539B, 0x5269, 0x5134, 0x4FFB, 0x4EC0, 0x4D81, 0x4C40, 0x4AFB, 0x49B4, 0x486A,
+ 0x471D, 0x45CD, 0x447B, 0x4326, 0x41CE, 0x4074, 0x3F17, 0x3DB8, 0x3C57, 0x3AF3, 0x398D, 0x3825, 0x36BA,
+ 0x354E, 0x33DF, 0x326E, 0x30FC, 0x2F87, 0x2E11, 0x2C99, 0x2B1F, 0x29A4, 0x2827, 0x26A8, 0x2528, 0x23A7,
+ 0x2224, 0x209F, 0x1F1A, 0x1D93, 0x1C0C, 0x1A83, 0x18F9, 0x176E, 0x15E2, 0x1455, 0x12C8, 0x113A, 0x0FAB,
+ 0x0E1C, 0x0C8C, 0x0AFB, 0x096B, 0x07D9, 0x0648, 0x04B6, 0x0324, 0x0192, 0x0000, 0xFE6E, 0xFCDC, 0xFB4A,
+ 0xF9B8, 0xF827, 0xF695, 0xF505, 0xF374, 0xF1E4, 0xF055, 0xEEC6, 0xED38, 0xEBAB, 0xEA1E, 0xE892, 0xE707,
+ 0xE57D, 0xE3F4, 0xE26D, 0xE0E6, 0xDF61, 0xDDDC, 0xDC59, 0xDAD8, 0xD958, 0xD7D9, 0xD65C, 0xD4E1, 0xD367,
+ 0xD1EF, 0xD079, 0xCF04, 0xCD92, 0xCC21, 0xCAB2, 0xC946, 0xC7DB, 0xC673, 0xC50D, 0xC3A9, 0xC248, 0xC0E9,
+ 0xBF8C, 0xBE32, 0xBCDA, 0xBB85, 0xBA33, 0xB8E3, 0xB796, 0xB64C, 0xB505, 0xB3C0, 0xB27F, 0xB140, 0xB005,
+ 0xAECC, 0xAD97, 0xAC65, 0xAB36, 0xAA0A, 0xA8E2, 0xA7BD, 0xA69C, 0xA57E, 0xA463, 0xA34C, 0xA238, 0xA129,
+ 0xA01C, 0x9F14, 0x9E0F, 0x9D0E, 0x9C11, 0x9B17, 0x9A22, 0x9930, 0x9843, 0x9759, 0x9674, 0x9592, 0x94B5,
+ 0x93DC, 0x9307, 0x9236, 0x9169, 0x90A1, 0x8FDD, 0x8F1D, 0x8E62, 0x8DAB, 0x8CF8, 0x8C4A, 0x8BA0, 0x8AFB,
+ 0x8A5A, 0x89BE, 0x8927, 0x8894, 0x8805, 0x877B, 0x86F6, 0x8676, 0x85FA, 0x8583, 0x8511, 0x84A3, 0x843A,
+ 0x83D6, 0x8377, 0x831C, 0x82C6, 0x8276, 0x822A, 0x81E2, 0x81A0, 0x8163, 0x812A, 0x80F6, 0x80C8, 0x809E,
+ 0x8079, 0x8059, 0x803E, 0x8027, 0x8016, 0x800A, 0x8002, 0x8000, 0x8002, 0x800A, 0x8016, 0x8027, 0x803E,
+ 0x8059, 0x8079, 0x809E, 0x80C8, 0x80F6, 0x812A, 0x8163, 0x81A0, 0x81E2, 0x822A, 0x8276, 0x82C6, 0x831C,
+ 0x8377, 0x83D6, 0x843A, 0x84A3, 0x8511, 0x8583, 0x85FA, 0x8676, 0x86F6, 0x877B, 0x8805, 0x8894, 0x8927,
+ 0x89BE, 0x8A5A, 0x8AFB, 0x8BA0, 0x8C4A, 0x8CF8, 0x8DAB, 0x8E62, 0x8F1D, 0x8FDD, 0x90A1, 0x9169, 0x9236,
+ 0x9307, 0x93DC, 0x94B5, 0x9592, 0x9674, 0x9759, 0x9843, 0x9930, 0x9A22, 0x9B17, 0x9C11, 0x9D0E, 0x9E0F,
+ 0x9F14, 0xA01C, 0xA129, 0xA238, 0xA34C, 0xA463, 0xA57E, 0xA69C, 0xA7BD, 0xA8E2, 0xAA0A, 0xAB36, 0xAC65,
+ 0xAD97, 0xAECC, 0xB005, 0xB140, 0xB27F, 0xB3C0, 0xB505, 0xB64C, 0xB796, 0xB8E3, 0xBA33, 0xBB85, 0xBCDA,
+ 0xBE32, 0xBF8C, 0xC0E9, 0xC248, 0xC3A9, 0xC50D, 0xC673, 0xC7DB, 0xC946, 0xCAB2, 0xCC21, 0xCD92, 0xCF04,
+ 0xD079, 0xD1EF, 0xD367, 0xD4E1, 0xD65C, 0xD7D9, 0xD958, 0xDAD8, 0xDC59, 0xDDDC, 0xDF61, 0xE0E6, 0xE26D,
+ 0xE3F4, 0xE57D, 0xE707, 0xE892, 0xEA1E, 0xEBAB, 0xED38, 0xEEC6, 0xF055, 0xF1E4, 0xF374, 0xF505, 0xF695,
+ 0xF827, 0xF9B8, 0xFB4A, 0xFCDC, 0xFE6E, 0x0000
+};
diff --git a/examples/OpenIMU300RI/INS/lib/Core/Math/src/arm_const_structs.c b/examples/OpenIMU300RI/INS/lib/Core/Math/src/arm_const_structs.c
new file mode 100644
index 0000000..f05c1c2
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/lib/Core/Math/src/arm_const_structs.c
@@ -0,0 +1,156 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
+*
+* $Date: 19. March 2015
+* $Revision: V.1.4.5
+*
+* Project: CMSIS DSP Library
+* Title: arm_const_structs.c
+*
+* Description: This file has constant structs that are initialized for
+* user convenience. For example, some can be given as
+* arguments to the arm_cfft_f32() function.
+*
+* Target Processor: Cortex-M4/Cortex-M3
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+* - Redistributions of source code must retain the above copyright
+* notice, this list of conditions and the following disclaimer.
+* - Redistributions in binary form must reproduce the above copyright
+* notice, this list of conditions and the following disclaimer in
+* the documentation and/or other materials provided with the
+* distribution.
+* - Neither the name of ARM LIMITED nor the names of its contributors
+* may be used to endorse or promote products derived from this
+* software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+* -------------------------------------------------------------------- */
+
+#include "arm_const_structs.h"
+
+//Floating-point structs
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len16 = {
+ 16, twiddleCoef_16, armBitRevIndexTable16, ARMBITREVINDEXTABLE__16_TABLE_LENGTH
+};
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len32 = {
+ 32, twiddleCoef_32, armBitRevIndexTable32, ARMBITREVINDEXTABLE__32_TABLE_LENGTH
+};
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len64 = {
+ 64, twiddleCoef_64, armBitRevIndexTable64, ARMBITREVINDEXTABLE__64_TABLE_LENGTH
+};
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len128 = {
+ 128, twiddleCoef_128, armBitRevIndexTable128, ARMBITREVINDEXTABLE_128_TABLE_LENGTH
+};
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len256 = {
+ 256, twiddleCoef_256, armBitRevIndexTable256, ARMBITREVINDEXTABLE_256_TABLE_LENGTH
+};
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len512 = {
+ 512, twiddleCoef_512, armBitRevIndexTable512, ARMBITREVINDEXTABLE_512_TABLE_LENGTH
+};
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len1024 = {
+ 1024, twiddleCoef_1024, armBitRevIndexTable1024, ARMBITREVINDEXTABLE1024_TABLE_LENGTH
+};
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len2048 = {
+ 2048, twiddleCoef_2048, armBitRevIndexTable2048, ARMBITREVINDEXTABLE2048_TABLE_LENGTH
+};
+
+const arm_cfft_instance_f32 arm_cfft_sR_f32_len4096 = {
+ 4096, twiddleCoef_4096, armBitRevIndexTable4096, ARMBITREVINDEXTABLE4096_TABLE_LENGTH
+};
+
+//Fixed-point structs
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len16 = {
+ 16, twiddleCoef_16_q31, armBitRevIndexTable_fixed_16, ARMBITREVINDEXTABLE_FIXED___16_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len32 = {
+ 32, twiddleCoef_32_q31, armBitRevIndexTable_fixed_32, ARMBITREVINDEXTABLE_FIXED___32_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len64 = {
+ 64, twiddleCoef_64_q31, armBitRevIndexTable_fixed_64, ARMBITREVINDEXTABLE_FIXED___64_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len128 = {
+ 128, twiddleCoef_128_q31, armBitRevIndexTable_fixed_128, ARMBITREVINDEXTABLE_FIXED__128_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len256 = {
+ 256, twiddleCoef_256_q31, armBitRevIndexTable_fixed_256, ARMBITREVINDEXTABLE_FIXED__256_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len512 = {
+ 512, twiddleCoef_512_q31, armBitRevIndexTable_fixed_512, ARMBITREVINDEXTABLE_FIXED__512_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len1024 = {
+ 1024, twiddleCoef_1024_q31, armBitRevIndexTable_fixed_1024, ARMBITREVINDEXTABLE_FIXED_1024_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len2048 = {
+ 2048, twiddleCoef_2048_q31, armBitRevIndexTable_fixed_2048, ARMBITREVINDEXTABLE_FIXED_2048_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q31 arm_cfft_sR_q31_len4096 = {
+ 4096, twiddleCoef_4096_q31, armBitRevIndexTable_fixed_4096, ARMBITREVINDEXTABLE_FIXED_4096_TABLE_LENGTH
+};
+
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len16 = {
+ 16, twiddleCoef_16_q15, armBitRevIndexTable_fixed_16, ARMBITREVINDEXTABLE_FIXED___16_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len32 = {
+ 32, twiddleCoef_32_q15, armBitRevIndexTable_fixed_32, ARMBITREVINDEXTABLE_FIXED___32_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len64 = {
+ 64, twiddleCoef_64_q15, armBitRevIndexTable_fixed_64, ARMBITREVINDEXTABLE_FIXED___64_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len128 = {
+ 128, twiddleCoef_128_q15, armBitRevIndexTable_fixed_128, ARMBITREVINDEXTABLE_FIXED__128_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len256 = {
+ 256, twiddleCoef_256_q15, armBitRevIndexTable_fixed_256, ARMBITREVINDEXTABLE_FIXED__256_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len512 = {
+ 512, twiddleCoef_512_q15, armBitRevIndexTable_fixed_512, ARMBITREVINDEXTABLE_FIXED__512_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len1024 = {
+ 1024, twiddleCoef_1024_q15, armBitRevIndexTable_fixed_1024, ARMBITREVINDEXTABLE_FIXED_1024_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len2048 = {
+ 2048, twiddleCoef_2048_q15, armBitRevIndexTable_fixed_2048, ARMBITREVINDEXTABLE_FIXED_2048_TABLE_LENGTH
+};
+
+const arm_cfft_instance_q15 arm_cfft_sR_q15_len4096 = {
+ 4096, twiddleCoef_4096_q15, armBitRevIndexTable_fixed_4096, ARMBITREVINDEXTABLE_FIXED_4096_TABLE_LENGTH
+};
diff --git a/examples/OpenIMU300RI/INS/lib/Core/Math/src/arm_cos_f32.c b/examples/OpenIMU300RI/INS/lib/Core/Math/src/arm_cos_f32.c
new file mode 100644
index 0000000..29e82e7
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/lib/Core/Math/src/arm_cos_f32.c
@@ -0,0 +1,128 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
+*
+* $Date: 21. September 2015
+* $Revision: V.1.4.5 a
+*
+* Project: CMSIS DSP Library
+* Title: arm_cos_f32.c
+*
+* Description: Fast cosine calculation for floating-point values.
+*
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+* - Redistributions of source code must retain the above copyright
+* notice, this list of conditions and the following disclaimer.
+* - Redistributions in binary form must reproduce the above copyright
+* notice, this list of conditions and the following disclaimer in
+* the documentation and/or other materials provided with the
+* distribution.
+* - Neither the name of ARM LIMITED nor the names of its contributors
+* may be used to endorse or promote products derived from this
+* software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+#include "arm_common_tables.h"
+
+/**
+ * @ingroup groupFastMath
+ */
+
+/**
+ * @defgroup cos Cosine
+ *
+ * Computes the trigonometric cosine function using a combination of table lookup
+ * and linear interpolation. There are separate functions for
+ * Q15, Q31, and floating-point data types.
+ * The input to the floating-point version is in radians while the
+ * fixed-point Q15 and Q31 have a scaled input with the range
+ * [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a
+ * value of 2*pi wraps around to 0.
+ *
+ * The implementation is based on table lookup using 256 values together with linear interpolation.
+ * The steps used are:
+ * -# Calculation of the nearest integer table index
+ * -# Compute the fractional portion (fract) of the table index.
+ * -# The final result equals (1.0f-fract)*a + fract*b;
+ *
+ * where
+ *
+ * b=Table[index+0];
+ * c=Table[index+1];
+ *
+ */
+
+ /**
+ * @addtogroup cos
+ * @{
+ */
+
+/**
+ * @brief Fast approximation to the trigonometric cosine function for floating-point data.
+ * @param[in] x input value in radians.
+ * @return cos(x).
+ */
+
+float32_t arm_cos_f32(
+ float32_t x)
+{
+ float32_t cosVal, fract, in; /* Temporary variables for input, output */
+ uint16_t index; /* Index variable */
+ float32_t a, b; /* Two nearest output values */
+ int32_t n;
+ float32_t findex;
+
+ /* input x is in radians */
+ /* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi, add 0.25 (pi/2) to read sine table */
+ in = x * 0.159154943092f + 0.25f;
+
+ /* Calculation of floor value of input */
+ n = (int32_t) in;
+
+ /* Make negative values towards -infinity */
+ if(in < 0.0f)
+ {
+ n--;
+ }
+
+ /* Map input value to [0 1] */
+ in = in - (float32_t) n;
+
+ /* Calculation of index of the table */
+ findex = (float32_t) FAST_MATH_TABLE_SIZE * in;
+ index = ((uint16_t)findex) & 0x1ff;
+
+ /* fractional value calculation */
+ fract = findex - (float32_t) index;
+
+ /* Read two nearest values of input value from the cos table */
+ a = sinTable_f32[index];
+ b = sinTable_f32[index+1];
+
+ /* Linear interpolation process */
+ cosVal = (1.0f-fract)*a + fract*b;
+
+ /* Return the output value */
+ return (cosVal);
+}
+
+/**
+ * @} end of cos group
+ */
diff --git a/examples/OpenIMU300RI/INS/lib/Core/Math/src/arm_sin_f32.c b/examples/OpenIMU300RI/INS/lib/Core/Math/src/arm_sin_f32.c
new file mode 100644
index 0000000..8655cf9
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/lib/Core/Math/src/arm_sin_f32.c
@@ -0,0 +1,133 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
+*
+* $Date: 21. September 2015
+* $Revision: V.1.4.5 a
+*
+* Project: CMSIS DSP Library
+* Title: arm_sin_f32.c
+*
+* Description: Fast sine calculation for floating-point values.
+*
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+* - Redistributions of source code must retain the above copyright
+* notice, this list of conditions and the following disclaimer.
+* - Redistributions in binary form must reproduce the above copyright
+* notice, this list of conditions and the following disclaimer in
+* the documentation and/or other materials provided with the
+* distribution.
+* - Neither the name of ARM LIMITED nor the names of its contributors
+* may be used to endorse or promote products derived from this
+* software without specific prior written permission.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+#include "arm_common_tables.h"
+#include
+
+/**
+ * @ingroup groupFastMath
+ */
+
+/**
+ * @defgroup sin Sine
+ *
+ * Computes the trigonometric sine function using a combination of table lookup
+ * and linear interpolation. There are separate functions for
+ * Q15, Q31, and floating-point data types.
+ * The input to the floating-point version is in radians while the
+ * fixed-point Q15 and Q31 have a scaled input with the range
+ * [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a
+ * value of 2*pi wraps around to 0.
+ *
+ * The implementation is based on table lookup using 256 values together with linear interpolation.
+ * The steps used are:
+ * -# Calculation of the nearest integer table index
+ * -# Compute the fractional portion (fract) of the table index.
+ * -# The final result equals (1.0f-fract)*a + fract*b;
+ *
+ * where
+ *
+ * b=Table[index+0];
+ * c=Table[index+1];
+ *
+ */
+
+/**
+ * @addtogroup sin
+ * @{
+ */
+
+/**
+ * @brief Fast approximation to the trigonometric sine function for floating-point data.
+ * @param[in] x input value in radians.
+ * @return sin(x).
+ */
+
+float32_t arm_sin_f32(
+ float32_t x)
+{
+ float32_t sinVal, fract, in; /* Temporary variables for input, output */
+ uint16_t index; /* Index variable */
+ float32_t a, b; /* Two nearest output values */
+ int32_t n;
+ float32_t findex;
+
+ /* input x is in radians */
+ /* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */
+ in = x * 0.159154943092f;
+
+ /* Calculation of floor value of input */
+ n = (int32_t) in;
+
+ /* Make negative values towards -infinity */
+ if(x < 0.0f)
+ {
+ n--;
+ }
+
+ /* Map input value to [0 1] */
+ in = in - (float32_t) n;
+
+ /* Calculation of index of the table */
+ findex = (float32_t) FAST_MATH_TABLE_SIZE * in;
+ if (findex >= 512.0f) {
+ findex -= 512.0f;
+ }
+
+ index = ((uint16_t)findex) & 0x1ff;
+
+ /* fractional value calculation */
+ fract = findex - (float32_t) index;
+
+ /* Read two nearest values of input value from the sin table */
+ a = sinTable_f32[index];
+ b = sinTable_f32[index+1];
+
+ /* Linear interpolation process */
+ sinVal = (1.0f-fract)*a + fract*b;
+
+ /* Return the output value */
+ return (sinVal);
+}
+
+/**
+ * @} end of sin group
+ */
diff --git a/examples/OpenIMU300RI/INS/lib/Core/Math/src/qmath.c b/examples/OpenIMU300RI/INS/lib/Core/Math/src/qmath.c
new file mode 100644
index 0000000..c483256
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/lib/Core/Math/src/qmath.c
@@ -0,0 +1,1322 @@
+/** ***************************************************************************
+ * @file qmath.c Fixed Point Math Library
+ * @Author Alex Forencich alex@alexelectronics.com
+ * Jordan Rhee rhee.jordan@gmail.com
+ * @date September, 2008
+ * @brief Copyright (c) 2013, 2014 All Rights Reserved.
+ *
+ * THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
+ * KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
+ * PARTICULAR PURPOSE.
+ * @brief IEEE UCSD
+ * http://ieee.ucsd.edu
+ *****************************************************************************/
+#include "qmath.h"
+#include "math.h"
+
+
+#ifdef DISPLAY_DIAGNOSTIC_MSG
+#include "debug.h"
+#endif
+
+#include "Indices.h"
+
+#define Q27 134217728
+#define Q54 18014398509481984
+
+/**
+ * square root
+ */
+fixedp qsqrt( fixedp p_Square )
+{
+ // fixedp = long
+ fixedp res;
+ fixedp delta;
+ fixedp maxError;
+
+ if ( p_Square <= 0 )
+ return 0;
+
+ /* start at half */
+ res = (p_Square >> 1);
+
+ /* determine allowable error */
+ maxError = qmul( p_Square, FIXED_SQRT_ERR );
+
+//#define qmul(x, y) _qmul(x, y, FIXED_FRACBITS, FIXED_FRACBITS, FIXED_FRACBITS)
+
+ do {
+ delta = ( qmul( res, res ) - p_Square );
+ res -= qdiv( delta, ( res << 1 ) );
+ } while ( delta > maxError || delta < -maxError );
+
+ return res;
+}
+
+
+// Range of input: +/- 16
+int32_t qsqrt_q27( int32_t pSquare_q27 )
+{
+ // fixedp = long
+ int32_t res;
+ int32_t delta;
+ int32_t maxError;
+
+ // Check for negative number and return 0 (error checking: return -1???)
+ if( pSquare_q27 <= 0 ) {
+ return 0;
+ }
+
+ /* start at half */
+ res = ( pSquare_q27 >> 1 );
+
+ /* determine allowable error */
+ // this limits the error to be less than 1e-6
+ maxError = 135;
+
+ uint8_t loopCntr = 0;
+ do {
+ loopCntr++;
+ delta = ( _qmul( res, res, 27, 27, 27 ) - pSquare_q27 );
+ res = res - _qdiv( delta, ( res << 1 ), 27, 27, 27 );
+ if( loopCntr >= 250 ) {
+// DEBUG_STRING( " SQRT27 Err " );
+ break;
+ }
+ } while ( delta > maxError || delta < -maxError );
+
+ // Do one more iteration for the heck of it
+ delta = ( _qmul( res, res, 27, 27, 27 ) - pSquare_q27 );
+ res = res - _qdiv( delta, ( res << 1 ), 27, 27, 27 );
+ return res;
+}
+
+
+// Range of input: +/- 2
+int32_t qsqrt_q30( int32_t pSquare_q30 )
+{
+ // fixedp = long
+ int32_t res;
+ int32_t delta;
+ int32_t maxError;
+
+ // Check for negative number and return 0 (error checking: return -1???)
+ if( pSquare_q30 <= 0 ) {
+ return 0;
+ }
+
+ /* start at one (2^30) */
+ res = 536870912; //pSquare_q30 >> 1;
+
+ /* determine allowable error */
+ // this limits the error to be less than 1e-6
+ //maxError = 135;
+ maxError = 1080;
+
+ uint8_t loopCntr = 0;
+ do {
+ loopCntr++;
+
+ delta = ( _qmul( res, res, 30, 30, 30 ) - pSquare_q30 );
+ res = res - _qdiv( delta, ( res << 1 ), 30, 30, 30 );
+
+ if( loopCntr == 250 ) {
+ // DEBUG_ENDLINE();
+ // DEBUG_INT( " QSQRT_Q30 stopped at iteration ", loopCntr );
+ // DEBUG_LONGINT( " (function argument: ", pSquare_q30 );
+ // DEBUG_STRING( ")" );
+ // DEBUG_ENDLINE();
+ break;
+ }
+ } while ( ( delta > maxError ) || ( delta < -maxError ) );
+
+// for( int loopCntr = 0; loopCntr < 8; loopCntr++ ) {
+// delta = ( _qmul( res, res, 30, 30, 30 ) - pSquare_q30 );
+// res = res - _qdiv( delta, ( res << 1 ), 30, 30, 30 );
+// }
+
+ // Do one more iteration for the heck of it
+ delta = ( _qmul( res, res, 30, 30, 30 ) - pSquare_q30 );
+ res = res - _qdiv( delta, ( res << 1 ), 30, 30, 30 );
+ return res;
+}
+
+
+// Range of input: +/- 2
+int32_t qsqrt_q29( int32_t pSquare_q29 )
+{
+ // fixedp = long
+ int32_t res;
+ int32_t delta;
+ int32_t maxError;
+
+ // Check for negative number and return 0 (error checking: return -1???)
+ if( pSquare_q29 <= 0 ) {
+ return 0;
+ }
+
+ /* start at one (2^30) */
+ res = pSquare_q29 >> 1;
+
+ /* determine allowable error */
+ // this limits the error to be less than 1e-6
+ //maxError = 135;
+ maxError = 1080;
+
+ uint8_t loopCntr = 0;
+ do {
+ loopCntr++;
+
+ delta = ( _qmul( res, res, 29, 29, 29 ) - pSquare_q29 );
+ res = res - _qdiv( delta, ( res << 1 ), 29, 29, 29 );
+
+ if( loopCntr == 250 ) {
+// DEBUG_ENDLINE();
+// DEBUG_INT( " QSQRT_Q29 stopped at iteration ", loopCntr );
+// DEBUG_LONGINT( " (function argument: ", pSquare_q29 );
+// DEBUG_STRING( ")" );
+// DEBUG_ENDLINE();
+ break;
+ }
+ } while ( ( delta > maxError ) || ( delta < -maxError ) );
+
+// for( int loopCntr = 0; loopCntr < 8; loopCntr++ ) {
+// delta = ( _qmul( res, res, 30, 30, 30 ) - pSquare_q30 );
+// res = res - _qdiv( delta, ( res << 1 ), 30, 30, 30 );
+// }
+
+ // Do one more iteration for the heck of it
+ delta = ( _qmul( res, res, 29, 29, 29 ) - pSquare_q29 );
+ res = res - _qdiv( delta, ( res << 1 ), 29, 29, 29 );
+ return res;
+}
+
+
+//
+int32_t qsqrt_q23( int32_t pSquare_q23 )
+{
+ // fixedp = long
+ int32_t res;
+ int32_t delta;
+ int32_t maxError;
+
+ if( pSquare_q23 <= 0 )
+ return 0;
+
+ /* start at half */
+ res = ( pSquare_q23 >> 1 );
+
+ /* determine allowable error */
+ // this limits the error to be less than 1e-6
+ maxError = 10;
+
+ do {
+ delta = ( _qmul( res, res, 23, 23, 23 ) - pSquare_q23 );
+ res = res - _qdiv( delta, ( res << 1 ), 23, 23, 23 );
+ } while ( delta > maxError || delta < -maxError );
+
+ // Do one more iteration for the heck of it
+ delta = ( _qmul( res, res, 23, 23, 23 ) - pSquare_q23 );
+ res = res - _qdiv( delta, ( res << 1 ), 23, 23, 23 );
+ return res;
+}
+
+
+
+/**
+ * log (base e)
+ */
+fixedp qlog( fixedp p_Base )
+{
+ fixedp w = 0;
+ fixedp y = 0;
+ fixedp z = 0;
+ fixedp num = int2q(1);
+ fixedp dec = 0;
+
+ if ( p_Base == int2q(1) )
+ return 0;
+
+ if ( p_Base == 0 )
+ return 0xffffffff;
+
+ for ( dec=0 ; qabs( p_Base ) >= int2q(2) ; dec += int2q(1) )
+ p_Base = qdiv(p_Base, QLN_E);
+
+ p_Base -= int2q(1);
+ z = p_Base;
+ y = p_Base;
+ w = int2q(1);
+
+ while ( y != y + w )
+ {
+ z = 0 - qmul( z , p_Base );
+ num += int2q(1);
+ w = qdiv( z , num );
+ y += w;
+ }
+
+ return y + dec;
+}
+
+/**
+ * log base 10
+ */
+fixedp qlog10( fixedp p_Base )
+{
+ // ln(p_Base)/ln(10)
+ // more accurately, ln(p_Base) * (1/ln(10))
+ return qmul(qlog(p_Base), Q1OLN_10);
+}
+
+/**
+ * exp (e to the x)
+ */
+fixedp qexp(fixedp p_Base)
+{
+ fixedp w;
+ fixedp y;
+ fixedp num;
+
+ for ( w=int2q(1), y=int2q(1), num=int2q(1) ; y != y+w ; num += int2q(1) )
+ {
+ w = qmul(w, qdiv(p_Base, num));
+ y += w;
+ }
+
+ return y;
+}
+
+/**
+ * pow
+ */
+fixedp qpow( fixedp p_Base,
+ fixedp p_Power )
+{
+ if ( p_Base < 0 && qmod(p_Power, int2q(2)) != 0 )
+ return - qexp( qmul(p_Power, qlog( -p_Base )) );
+ else
+ return qexp( qmul(p_Power, qlog(qabs( p_Base ))) );
+}
+
+/**
+ * sinx, internal sine function
+ */
+static fixedp sinx(fixedp x)
+{
+ fixedp xpwr;
+ long xftl;
+ fixedp xresult;
+ short positive;
+ int i;
+
+ xresult = 0;
+ xpwr = x;
+ xftl = 1;
+ positive = -1;
+
+ // Note: 12! largest for long
+ for (i = 1; i < 7; i+=2)
+ {
+ if ( positive )
+ xresult += qdiv(xpwr, long2q(xftl));
+ else
+ xresult -= qdiv(xpwr, long2q(xftl));
+
+ xpwr = qmul(x, xpwr);
+ xpwr = qmul(x, xpwr);
+ xftl *= i+1;
+ xftl *= i+2;
+ positive = !positive;
+ }
+
+ return xresult;
+}
+
+/**
+ * sine
+ */
+fixedp qsin(fixedp theta)
+{
+ fixedp xresult;
+ short bBottom = 0;
+ //static fixed xPI = XPI;
+ //static fixed x2PI = X2PI;
+ //static fixed xPIO2 = XPIO2;
+
+ fixedp x = qmod(theta, Q2PI);
+ if ( x < 0 )
+ x += Q2PI;
+
+ if ( x > QPI )
+ {
+ bBottom = -1;
+ x -= QPI;
+ }
+
+ if ( x <= QPIO2 )
+ xresult = sinx(x);
+ else
+ xresult = sinx(QPIO2-(x-QPIO2));
+
+ if ( bBottom )
+ return -xresult;
+
+ return xresult;
+}
+
+/**
+ * cosine
+ */
+fixedp qcos(fixedp theta)
+{
+ return qsin(theta + QPIO2);
+}
+
+/**
+ * tangent
+ */
+fixedp qtan(fixedp theta)
+{
+ return qdiv(qsin(theta), qcos(theta));
+}
+
+/**
+ * q2a - converts a fixed point number to a string
+ */
+char *q2a(char *buf,
+ fixedp n)
+{
+ long ipart = qipart(n);
+ long fpart = qfpart(n);
+ long intdigits = 0;
+
+ int i = 0;
+ int j = 0;
+ int d = 0;
+
+ int offset = 0;
+
+ long v;
+ long t;
+ long st = 0;
+
+ if (n != 0)
+ {
+ intdigits = qipart(qceil(qlog10(qabs(n))));
+ }
+
+ if (intdigits < 1) intdigits = 1;
+
+ offset = intdigits - 1;
+
+ if (n < 0)
+ {
+ buf[0] = '-';
+ offset++;
+ n = -n;
+ ipart = -ipart;
+ fpart = -fpart;
+ }
+
+ // integer portion
+ for (i = 0; i < intdigits; i++)
+ {
+ j = offset - i;
+ d = ipart % 10;
+ ipart = ipart / 10;
+ buf[j] = '0' + d;
+ }
+
+ // decimal point
+ buf[offset + 1] = '.';
+
+ // fractional portion
+ v = 5;
+ t = FIXED_RESOLUTION >> 1;
+
+ for (i = 0; i < FIXED_DECIMALDIGITS - 1; i++)
+ {
+ v = (v << 1) + (v << 3);
+ }
+
+ for (i = 0; i < FIXED_FRACBITS; i++)
+ {
+ if (fpart & t)
+ {
+ st += v;
+ }
+ v = v >> 1;
+ t = t >> 1;
+ }
+
+ offset += FIXED_DECIMALDIGITS + 1;
+
+ for (i = 0; i < FIXED_DECIMALDIGITS; i++)
+ {
+ j = offset - i;
+ d = st % 10;
+ st = st / 10;
+ buf[j] = '0' + d;
+ }
+
+ buf[offset + 1] = '\0'; // ending zero
+
+ return buf;
+}
+
+
+//
+int32_t nabs( int32_t signedInteger )
+{
+ if( signedInteger >= 0 ) {
+ return signedInteger;
+ } else {
+ return -signedInteger;
+ }
+}
+
+
+//
+int32_t nabs_32( int32_t signedInteger )
+{
+ if( signedInteger >= 0 ) {
+ return signedInteger;
+ } else {
+ return -signedInteger;
+ }
+}
+
+//
+int64_t nabs_64( int64_t signedInteger )
+{
+ if( signedInteger >= 0 ) {
+ return signedInteger;
+ } else {
+ return -signedInteger;
+ }
+}
+
+//
+int32_t sign( int32_t signedInteger )
+{
+ if( signedInteger >= 0 ) {
+ return 1;
+ } else {
+ return -1;
+ }
+}
+
+
+// asin function based on sqrt and atan2
+// asin( x ) returns an angle (between -pi and +pi) for an input between -1 and +1
+// however, x is represented as a q number (i.e. q27). Tested. Result is within ~0.2 degrees
+// (the precision of the atan2 function). FIXME: change atan2 to increase precision.
+int32_t asin_q27( int32_t x_q27 )
+{
+ int32_t tmp1_q27;
+
+ tmp1_q27 = _qmul( x_q27, x_q27, 27, 27, 27 );
+ tmp1_q27 = Q27 - tmp1_q27; // 1 - x^2 (x < 1)
+ tmp1_q27 = qsqrt_q27( tmp1_q27 );
+
+ return atan2_q27( x_q27, tmp1_q27 );
+}
+
+
+// asin function based on sqrt and atan2
+// asin( x ) returns an angle (between -pi and +pi) for an input between -1 and +1
+// however, x is represented as a q number (i.e. q27). Tested. Result is within ~0.2 degrees
+// (the precision of the atan2 function). FIXME: change atan2 to increase precision.
+int32_t asin_q29( int32_t x_q30 )
+{
+ int32_t tmp1_q30;
+
+ tmp1_q30 = _qmul( x_q30, x_q30, 30, 30, 30 );
+ tmp1_q30 = ONE_Q30 - tmp1_q30; // 1 - x^2 (x <= 1)
+//DEBUG_STRING( " A" );
+// tmp1_q30 = qsqrt_q30( tmp1_q30 );
+ tmp1_q30 = qsqrt_q27( tmp1_q30 >> 3) << 3;
+
+ return atan2_q29( x_q30, tmp1_q30, 30 );
+}
+
+//asin(x) = atan2 (x, sqrt ((1.0 + x) * (1.0 - x)))
+//acos(x) = atan2 (sqrt ((1.0 + x) * (1.0 - x)), x)
+
+//[ 1072959488, 345219611, 157684912, 42200635 ]
+
+typedef struct atan2_coeff {
+ int32_t a0_q27;
+ int32_t a1_q27;
+ int32_t a2_q27;
+ int32_t a3_q27;
+
+ int32_t a0_q29;
+ int32_t a1_q29;
+ int32_t a2_q29;
+ int32_t a3_q29;
+
+ int32_t a0_q30;
+ int32_t a1_q30;
+ int32_t a2_q30;
+ int32_t a3_q30;
+} atan2_coeff;
+
+
+//
+// 32-bit fixed point (Q27) four-quadrant arctangent. Given a Cartesian vector (x, y), return the
+// angle subtended by the vector and the positive x-axis. Both function input and output are in
+// q27 format. Accuracy is greater than 5 mdeg (18 arcsec).
+//
+// The value returned falls in the follwing range: [ -pi, pi ) and is converted to a q27 data-type
+// (floating-point value is multiplied by 2^27).
+//
+// * Because the magnitude of the input vector does not change the angle it
+// * represents, the inputs can be in any signed 16-bit fixed-point format.
+// *
+// * @param y y-coordinate is int32_t, q27 format
+// * @param x x-coordinate is int32_t, q27 format
+// * @return angle in int32_t, q27 format between -( pi*2^27 ) and +( pi*2^27 )
+//
+// atan( y, x ) returns an angle in the range [ -pi, +pi ). A Q29 representation will encompass
+// the range of output values. The input must support a wider range of values
+int32_t atan2_q27( int32_t y_q27, int32_t x_q27 )
+{
+ static atan2_coeff coeff;
+ coeff.a0_q27 = 134119936;
+ coeff.a1_q27 = 43152451;
+ coeff.a2_q27 = 19710614;
+ coeff.a3_q27 = 5275079;
+
+ coeff.a0_q29 = 536479744;
+ coeff.a1_q29 = 172609805;
+ coeff.a2_q29 = 78842456;
+ coeff.a3_q29 = 21100318;
+
+ int32_t nabs_y = nabs( y_q27 );
+ int32_t nabs_x = nabs( x_q27 );
+
+ int32_t angle;
+
+ int32_t tmp1_q27, tmp2_q27, tmp3_q27;
+ int32_t xOverY_q27, yOverX_q27;
+ int32_t xOverYSquared_q27, yOverXSquared_q27;
+
+ // If the absolute values of x and y are the same, then the angle is 45 degrees off the x-axis.
+ // Only need to determine the quadrant to find the angle. Additionally, check if both are
+ // zero. FIXME: Return zero but should also set a bit indicating this.
+ if( nabs_y == nabs_x ) {
+ if( y_q27 > 0 ) {
+ if( x_q27 > 0 ) {
+ // angle = round( ( 45* pi/180 ) * 2^27 );
+ return 105414357;
+ } else {
+ // angle = round( ( 3*45* pi/180 ) * 2^27 )
+ return 316243071;
+ }
+ } else if( y_q27 < 0 ) {
+ if( x_q27 > 0 ) {
+ // angle = round( ( -45* pi/180 ) * 2^27 );
+ return -105414357;
+ } else {
+ // angle = round( ( -3*45* pi/180 ) * 2^27 );
+ return -316243071;
+ }
+ } else {
+ // Both x and y are zero. Indeterminate angle (return 0 but set an error flag)
+ return 0;
+ }
+ }
+
+ // The point is on the y-axis. Angle = +/-90 deg
+ if( nabs_x == 0 ) {
+ if( y_q27 > 0 ) {
+ //angle = round( ( 90 * pi/180 ) * 2^27 );
+ return 210828714;
+ } else {
+ // angle = round( ( -90 * pi/180 ) * 2^27 );
+ return -210828714;
+ }
+ }
+
+ // The point is on the x-axis; angle = 0, 180 deg (but return -180 degrees to be consistent with
+ // range definition: [ -pi, +pi )
+ if( nabs_y == 0 ) {
+ if( x_q27 > 0 ) {
+ // angle = round( ( 0 * pi/180 ) * 2^27 );
+ return 0;
+ } else {
+ // angle = round( ( -180 * pi/180 ) * 2^27 );
+ return -421657428;
+ }
+ }
+
+ // Point is not on the x or y-axes nor is it on a +/-45 degree line. Calculate the angle
+ if( nabs_x < nabs_y ) {
+ // The point is above a line that is 45 degree above the x-axis (octants II, III, Vi, and VII)
+ xOverY_q27 = _qdiv( x_q27, y_q27, 27, 27, 27 ); // ( x >> 27 ) / y;
+ xOverYSquared_q27 = _qmul( xOverY_q27, xOverY_q27, 27, 27, 27 );
+
+ tmp1_q27 = coeff.a2_q27 - _qmul( coeff.a3_q27, xOverYSquared_q27, 27, 27, 27 );
+ tmp2_q27 = coeff.a1_q27 - _qmul( tmp1_q27, xOverYSquared_q27, 27, 27, 27 );
+ tmp3_q27 = coeff.a0_q27 - _qmul( tmp2_q27, xOverYSquared_q27, 27, 27, 27 );
+ angle = _qmul( xOverY_q27, tmp3_q27, 27, 27, 27 );
+
+ // Adjust the angle depending upon the octant in which the point falls
+ if( y_q27 > 0 ) {
+ // angle = 90 - result
+ angle = 210828714 - angle;
+ } else {
+ angle = -210828714 - angle;
+ }
+ } else {
+ // The point is below a line that is 45 degree above the x-axis (octants I, IV, V, and VIII)
+ yOverX_q27 = _qdiv( y_q27, x_q27, 27, 27, 27 );
+ yOverXSquared_q27 = _qmul( yOverX_q27, yOverX_q27, 27, 27, 27 );
+
+ tmp1_q27 = coeff.a2_q27 - _qmul( coeff.a3_q27, yOverXSquared_q27, 27, 27, 27 );
+ tmp2_q27 = coeff.a1_q27 - _qmul( tmp1_q27, yOverXSquared_q27, 27, 27, 27 );
+ tmp3_q27 = coeff.a0_q27 - _qmul( tmp2_q27, yOverXSquared_q27, 27, 27, 27 );
+ angle = _qmul( yOverX_q27, tmp3_q27, 27, 27, 27 );
+
+ // Near theta = 180 degrees, the program needs to check the quadrant when computing the
+ // angle as the output must fall between -pi (-180 deg) and +pi (180 deg)
+ if( x_q27 < 0 ) {
+ if( y_q27 > 0 ) {
+ // In octant IV
+ angle = 421657428 + angle;
+ } else {
+ // In octant V
+ angle = -421657429 + angle;
+ }
+ }
+ }
+
+ // Must be less than 2,147,483,648 = 2^15-1
+ return (int32_t)angle;
+}
+
+// atan( y, x ) returns an angle in the range [ -pi, +pi ). A Q29 representation will encompass
+// the range of output values. The input must support a wider range of values
+int32_t atan2_q29Out_q27In( int32_t y_q27, int32_t x_q27 )
+{
+ static atan2_coeff coeff;
+
+ // fixed-point floating-point
+ // value value
+ coeff.a0_q29 = 536479744; // a0 = 0.999271392822266
+ coeff.a1_q29 = 172609805; // a1 = 0.321510815992951
+ coeff.a2_q29 = 78842456; // a2 = 0.146855518221855
+ coeff.a3_q29 = 21100318; // a3 = 0.039302404969931
+
+ coeff.a0_q30 = 1072959488;
+ coeff.a1_q30 = 345219611;
+ coeff.a2_q30 = 157684912;
+ coeff.a3_q30 = 42200635;
+
+ int32_t nabs_y = nabs( y_q27 );
+ int32_t nabs_x = nabs( x_q27 );
+
+ int32_t angle_q29;
+
+ int32_t tmp1_q30, tmp2_q30, tmp3_q30;
+ int32_t xOverY_q30, yOverX_q30;
+ int32_t xOverYSquared_q30, yOverXSquared_q30;
+
+ // If the absolute values of x and y are the same, then the angle is 45 degrees off the x-axis.
+ // Only need to determine the quadrant to find the angle. Additionally, check if both are
+ // zero. FIXME: Return zero but should also set a bit indicating this.
+ if( nabs_y == nabs_x ) {
+ if( y_q27 > 0 ) {
+ if( x_q27 > 0 ) {
+ return FORTY_FIVE_DEGREES_Q29;
+ } else {
+ return ONE_HUNDRED_THIRTY_FIVE_DEGREES_Q29;
+ }
+ } else if( y_q27 < 0 ) {
+ if( x_q27 > 0 ) {
+ return -FORTY_FIVE_DEGREES_Q29;
+ } else {
+ return -ONE_HUNDRED_THIRTY_FIVE_DEGREES_Q29;
+ }
+ } else {
+ // Both x and y are zero. Indeterminate angle (return 0 but set an error flag)
+ return 0;
+ }
+ }
+
+ // The point is on the y-axis. Angle = +/-90 deg
+ if( nabs_x == 0 ) {
+ if( y_q27 > 0 ) {
+ return NINETY_DEGREES_Q29;
+ } else {
+ return -NINETY_DEGREES_Q29;
+ }
+ }
+
+ // The point is on the x-axis; angle = 0, 180 deg (but return -180 degrees to be consistent with
+ // range definition: [ -pi, +pi )
+ if( nabs_y == 0 ) {
+ if( x_q27 > 0 ) {
+ return 0;
+ } else {
+ return -ONE_HUNDRED_EIGHTY_DEGS_Q29;
+ }
+ }
+
+ // Point is not on the x or y-axes nor is it on a +/-45 degree line. Calculate the angle.
+ if( nabs_x < nabs_y ) {
+ // The point is above a line that is 45 degree above the x-axis (octants II, III, VI, and VII)
+ // The slope is always less than one as, in this case, it is computed from the y-axis
+ xOverY_q30 = _qdiv( x_q27, y_q27, 27, 27, 30 );
+ xOverYSquared_q30 = _qmul( xOverY_q30, xOverY_q30, 30, 30, 30 );
+
+ // Can use Q30 since the angle will be less than 45 degrees (pi/4) but convert it at the end
+ // so it can be combined with the offset in q_29 format.
+ tmp1_q30 = coeff.a2_q30 - _qmul( coeff.a3_q30, xOverYSquared_q30, 30, 30, 30 );
+ tmp2_q30 = coeff.a1_q30 - _qmul( tmp1_q30, xOverYSquared_q30, 30, 30, 30 );
+ tmp3_q30 = coeff.a0_q30 - _qmul( tmp2_q30, xOverYSquared_q30, 30, 30, 30 );
+ angle_q29 = _qmul( xOverY_q30, tmp3_q30, 30, 30, 29 );
+
+ // Adjust the angle depending upon the octant in which the point falls
+ if( y_q27 > 0 ) {
+ // angle = 90 - result
+ angle_q29 = NINETY_DEGREES_Q29 - angle_q29;
+ } else {
+ angle_q29 = -NINETY_DEGREES_Q29 - angle_q29;
+ }
+ } else {
+ // The point is below a line that is 45 degree above the x-axis (octants I, IV, V, and VIII)
+ yOverX_q30 = _qdiv( y_q27, x_q27, 27, 27, 30 );
+ yOverXSquared_q30 = _qmul( yOverX_q30, yOverX_q30, 30, 30, 30 );
+
+ // Can use Q30 since the angle will be less than 45 degrees (pi/4) but convert it at the end
+ // so it can be combined with the offset in q_29 format.
+ tmp1_q30 = coeff.a2_q30 - _qmul( coeff.a3_q30, yOverXSquared_q30, 30, 30, 30 );
+ tmp2_q30 = coeff.a1_q30 - _qmul( tmp1_q30, yOverXSquared_q30, 30, 30, 30 );
+ tmp3_q30 = coeff.a0_q30 - _qmul( tmp2_q30, yOverXSquared_q30, 30, 30, 30 );
+ angle_q29 = _qmul( yOverX_q30, tmp3_q30, 30, 30, 29 );
+
+ // Near theta = 180 degrees, the program needs to check the quadrant when computing the
+ // angle as the output must fall between -pi (-180 deg) and +pi (180 deg)
+ if( x_q27 < 0 ) {
+ if( y_q27 > 0 ) {
+ // In octant IV
+ angle_q29 = ONE_HUNDRED_EIGHTY_DEGS_Q29 + angle_q29;
+ } else {
+ // In octant V
+ angle_q29 = -ONE_HUNDRED_EIGHTY_DEGS_Q29 + angle_q29;
+ }
+ }
+ }
+
+ // Must be less than 2,147,483,648 = 2^15-1
+ return (int32_t)angle_q29;
+}
+
+// atan( y, x ) returns an angle in the range [ -pi, +pi ). A Q29 representation will encompass
+// the range of output values. The input must support a wider range of values
+int32_t atan2_q29Out_q30In( int32_t y_q30,
+ int32_t x_q30 )
+{
+ static atan2_coeff coeff;
+
+ // fixed-point floating-point
+ // value value
+ coeff.a0_q29 = 536479744; // a0 = 0.999271392822266
+ coeff.a1_q29 = 172609805; // a1 = 0.321510815992951
+ coeff.a2_q29 = 78842456; // a2 = 0.146855518221855
+ coeff.a3_q29 = 21100318; // a3 = 0.039302404969931
+
+ coeff.a0_q30 = 1072959488;
+ coeff.a1_q30 = 345219611;
+ coeff.a2_q30 = 157684912;
+ coeff.a3_q30 = 42200635;
+
+ int32_t nabs_y = nabs( y_q30 );
+ int32_t nabs_x = nabs( x_q30 );
+
+ int32_t angle_q29;
+
+ int32_t tmp1_q30, tmp2_q30, tmp3_q30;
+ int32_t xOverY_q30, yOverX_q30;
+ int32_t xOverYSquared_q30, yOverXSquared_q30;
+
+ // If the absolute values of x and y are the same, then the angle is 45 degrees off the x-axis.
+ // Only need to determine the quadrant to find the angle. Additionally, check if both are
+ // zero. FIXME: Return zero but should also set a bit indicating this.
+ if( nabs_y == nabs_x ) {
+ if( y_q30 > 0 ) {
+ if( x_q30 > 0 ) {
+ return FORTY_FIVE_DEGREES_Q29;
+ } else {
+ return ONE_HUNDRED_THIRTY_FIVE_DEGREES_Q29;
+ }
+ } else if( y_q30 < 0 ) {
+ if( x_q30 > 0 ) {
+ return -FORTY_FIVE_DEGREES_Q29;
+ } else {
+ return -ONE_HUNDRED_THIRTY_FIVE_DEGREES_Q29;
+ }
+ } else {
+ // Both x and y are zero. Indeterminate angle (return 0 but set an error flag)
+ return 0;
+ }
+ }
+
+ // The point is on the y-axis. Angle = +/-90 deg
+ if( nabs_x == 0 ) {
+ if( y_q30 > 0 ) {
+ return NINETY_DEGREES_Q29;
+ } else {
+ return -NINETY_DEGREES_Q29;
+ }
+ }
+
+ // The point is on the x-axis; angle = 0, 180 deg (but return -180 degrees to be consistent with
+ // range definition: [ -pi, +pi )
+ if( nabs_y == 0 ) {
+ if( x_q30 > 0 ) {
+ return 0;
+ } else {
+ return -ONE_HUNDRED_EIGHTY_DEGS_Q29;
+ }
+ }
+
+ // Point is not on the x or y-axes nor is it on a +/-45 degree line. Calculate the angle.
+ if( nabs_x < nabs_y ) {
+ // The point is above a line that is 45 degree above the x-axis (octants II, III, VI, and VII)
+ // The slope is always less than one as, in this case, it is computed from the y-axis
+ xOverY_q30 = _qdiv( x_q30, y_q30, 30, 30, 30 );
+ xOverYSquared_q30 = _qmul( xOverY_q30, xOverY_q30, 30, 30, 30 );
+
+ // Can use Q30 since the angle will be less than 45 degrees (pi/4) but convert it at the end
+ // so it can be combined with the offset in q_29 format.
+ tmp1_q30 = coeff.a2_q30 - _qmul( coeff.a3_q30, xOverYSquared_q30, 30, 30, 30 );
+ tmp2_q30 = coeff.a1_q30 - _qmul( tmp1_q30, xOverYSquared_q30, 30, 30, 30 );
+ tmp3_q30 = coeff.a0_q30 - _qmul( tmp2_q30, xOverYSquared_q30, 30, 30, 30 );
+ angle_q29 = _qmul( xOverY_q30, tmp3_q30, 30, 30, 29 );
+
+ // Adjust the angle depending upon the octant in which the point falls
+ if( y_q30 > 0 ) {
+ // angle = 90 - result
+ angle_q29 = NINETY_DEGREES_Q29 - angle_q29;
+ } else {
+ angle_q29 = -NINETY_DEGREES_Q29 - angle_q29;
+ }
+ } else {
+ // The point is below a line that is 45 degree above the x-axis (octants I, IV, V, and VIII)
+ yOverX_q30 = _qdiv( y_q30, x_q30, 30, 30, 30 );
+ yOverXSquared_q30 = _qmul( yOverX_q30, yOverX_q30, 30, 30, 30 );
+
+ // Can use Q30 since the angle will be less than 45 degrees (pi/4) but convert it at the end
+ // so it can be combined with the offset in q_29 format.
+ tmp1_q30 = coeff.a2_q30 - _qmul( coeff.a3_q30, yOverXSquared_q30, 30, 30, 30 );
+ tmp2_q30 = coeff.a1_q30 - _qmul( tmp1_q30, yOverXSquared_q30, 30, 30, 30 );
+ tmp3_q30 = coeff.a0_q30 - _qmul( tmp2_q30, yOverXSquared_q30, 30, 30, 30 );
+ angle_q29 = _qmul( yOverX_q30, tmp3_q30, 30, 30, 29 );
+
+ // Near theta = 180 degrees, the program needs to check the quadrant when computing the
+ // angle as the output must fall between -pi (-180 deg) and +pi (180 deg)
+ if( x_q30 < 0 ) {
+ if( y_q30 > 0 ) {
+ // In octant IV
+ angle_q29 = ONE_HUNDRED_EIGHTY_DEGS_Q29 + angle_q29;
+ } else {
+ // In octant V
+ angle_q29 = -ONE_HUNDRED_EIGHTY_DEGS_Q29 + angle_q29;
+ }
+ }
+ }
+ return (int32_t)angle_q29; // Must be less than 2,147,483,648 = 2^15-1
+}
+
+// atan( y, x ) returns an angle in the range [ -pi, +pi ). A Q29 representation will encompass
+// the range of output values. The input must support a wider range of values
+int32_t atan2_q29( int32_t y_qX,
+ int32_t x_qX,
+ uint8_t qVal )
+{
+ static atan2_coeff coeff;
+
+ // Note: while the result of the calculation below is an angle represented in Q29 format, the
+ // intermediate calculation generates an angle between -45 and +45 degrees (pi/4 = 0.7854)
+ // radians. Therefore, all calulations prior to the final one can be performed using Q30
+ // math.
+ // fixed-point floating-point
+ // value value
+ coeff.a0_q30 = 1072959488;
+ coeff.a1_q30 = 345219611;
+ coeff.a2_q30 = 157684912;
+ coeff.a3_q30 = 42200635;
+
+ int32_t nabs_y = nabs( y_qX );
+ int32_t nabs_x = nabs( x_qX );
+
+ int32_t angle_q29;
+
+ int32_t tmp1_q30, tmp2_q30, tmp3_q30;
+ int32_t xOverY_q30, yOverX_q30;
+ int32_t xOverYSquared_q30, yOverXSquared_q30;
+
+ // If the absolute values of x and y are the same, then the angle is 45 degrees off the x-axis.
+ // Only need to determine the quadrant to find the angle. Additionally, check if both are
+ // zero. FIXME: Return zero but should also set a bit indicating this.
+ if( nabs_y == nabs_x ) {
+ if( y_qX > 0 ) {
+ if( x_qX > 0 ) {
+ return FORTY_FIVE_DEGREES_Q29;
+ } else {
+ return ONE_HUNDRED_THIRTY_FIVE_DEGREES_Q29;
+ }
+ } else if( y_qX < 0 ) {
+ if( x_qX > 0 ) {
+ return -FORTY_FIVE_DEGREES_Q29;
+ } else {
+ return -ONE_HUNDRED_THIRTY_FIVE_DEGREES_Q29;
+ }
+ } else {
+ // Both x and y are zero. Indeterminate angle (return 0 but set an error flag)
+ return 0;
+ }
+ }
+
+ // The point is on the y-axis. Angle = +/-90 deg
+ if( nabs_x == 0 ) {
+ if( y_qX > 0 ) {
+ return NINETY_DEGREES_Q29;
+ } else {
+ return -NINETY_DEGREES_Q29;
+ }
+ }
+
+ // The point is on the x-axis; angle = 0, 180 deg (but return -180 degrees to be consistent with
+ // range definition: [ -pi, +pi )
+ if( nabs_y == 0 ) {
+ if( x_qX > 0 ) {
+ return 0;
+ } else {
+ return -ONE_HUNDRED_EIGHTY_DEGS_Q29;
+ }
+ }
+
+ // Point is not on the x or y-axes nor is it on a +/-45 degree line. Calculate the angle.
+ if( nabs_x < nabs_y ) {
+ // The point is above a line that is 45 degree above the x-axis (octants II, III, VI, and VII)
+ // The slope is always less than one as, in this case, it is computed from the y-axis
+ xOverY_q30 = _qdiv( x_qX, y_qX, qVal, qVal, 30 ); // slope < 1 (Q30)
+ xOverYSquared_q30 = _qmul( xOverY_q30, xOverY_q30, 30, 30, 30 ); // slope^2 < 1 (Q30)
+
+ // Can use Q30 since the angle will be less than 45 degrees (pi/4) but convert it at the end
+ // so it can be combined with the offset in q_29 format.
+ tmp1_q30 = coeff.a2_q30 - _qmul( coeff.a3_q30, xOverYSquared_q30, 30, 30, 30 );
+ tmp2_q30 = coeff.a1_q30 - _qmul( tmp1_q30, xOverYSquared_q30, 30, 30, 30 );
+ tmp3_q30 = coeff.a0_q30 - _qmul( tmp2_q30, xOverYSquared_q30, 30, 30, 30 );
+ angle_q29 = _qmul( xOverY_q30, tmp3_q30, 30, 30, 29 );
+
+ // Adjust the angle depending upon the octant in which the point falls
+ if( y_qX > 0 ) {
+ // angle = 90 - result
+ angle_q29 = NINETY_DEGREES_Q29 - angle_q29;
+ } else {
+ angle_q29 = -NINETY_DEGREES_Q29 - angle_q29;
+ }
+ } else {
+ // The point is below a line that is 45 degree above the x-axis (octants I, IV, V, and VIII)
+ yOverX_q30 = _qdiv( y_qX, x_qX, qVal, qVal, 30 );
+ yOverXSquared_q30 = _qmul( yOverX_q30, yOverX_q30, 30, 30, 30 );
+
+ // Can use Q30 since the angle will be less than 45 degrees (pi/4) but convert it at the end
+ // so it can be combined with the offset in q_29 format.
+ tmp1_q30 = coeff.a2_q30 - _qmul( coeff.a3_q30, yOverXSquared_q30, 30, 30, 30 );
+ tmp2_q30 = coeff.a1_q30 - _qmul( tmp1_q30, yOverXSquared_q30, 30, 30, 30 );
+ tmp3_q30 = coeff.a0_q30 - _qmul( tmp2_q30, yOverXSquared_q30, 30, 30, 30 );
+ angle_q29 = _qmul( yOverX_q30, tmp3_q30, 30, 30, 29 );
+
+ // Near theta = 180 degrees check the quadrant
+ // the output must fall between -pi (-180 deg) and +pi (180 deg)
+ if( x_qX < 0 ) {
+ if( y_qX > 0 ) {
+ // In octant IV
+ angle_q29 = ONE_HUNDRED_EIGHTY_DEGS_Q29 + angle_q29;
+ } else {
+ // In octant V
+ angle_q29 = -ONE_HUNDRED_EIGHTY_DEGS_Q29 + angle_q29;
+ }
+ }
+ }
+
+ // Must be less than 2,147,483,648 = 2^15-1
+ return (int32_t)angle_q29;
+}
+
+
+// Create an atan function
+typedef struct sin_coeff {
+ int32_t a0_q29;
+ int32_t a1_q29;
+ int32_t a2_q29;
+ int32_t a3_q29;
+ int32_t a4_q29;
+ int32_t a5_q29;
+} sin_coeff;
+
+
+#define PI_OVER_TWO_Q29 843314857
+#define PI_Q29 1686629713
+
+//#define ONE_Q30 1073741824
+
+// Input can range from -pi to +pi. Must not be larger than 4.0, so angles larger than 229 degrees
+// can't be used.
+// Input: angle in radians
+// Checked and verified on May 15, 2014
+int32_t sin_q30( int32_t angleRad_q29 )
+{
+ static sin_coeff coeff;
+ coeff.a0_q29 = 536870912;
+ coeff.a1_q29 = 89478485;
+ coeff.a2_q29 = 4473924;
+ coeff.a3_q29 = 106522;
+ coeff.a4_q29 = 1479;
+ coeff.a5_q29 = 13;
+
+ // find the absolute value of the angle and, if greater than pi/2 (843314857), reduce the value
+ int32_t ang_q29 = nabs( angleRad_q29 );
+ if( ang_q29 > PI_OVER_TWO_Q29 ) {
+ // constrain the value to be less than 90 degrees
+ ang_q29 = PI_Q29 - ang_q29;
+ }
+
+ // check for zero or pi
+ if( angleRad_q29 == 0 || ang_q29 == PI_Q29 ) {
+ return 0;
+ }
+
+ int32_t angleSign = sign( angleRad_q29 );
+
+ // Check for +/- 90 degrees = pi/2 radians = 1073741824 rad_q30
+ if( ang_q29 == PI_OVER_TWO_Q29 ) {
+ return( angleSign*ONE_Q30 );
+ }
+
+ int32_t tmp1_q29, tmp2_q29, tmp3_q29, tmp4_q29, tmp5_q29, tmp6_q30;
+ int32_t angleSquared_q29 = _qmul( ang_q29, ang_q29, 29, 29, 29 );
+
+ // Maclaurin series for sine
+ // sin( x ) = x*( 1 - x^2*( 1/3! - x^2*( 1/5! - x^2*( 1/7! - x^2*( 1/9! - x^2*( 1/11! - � ) ) ) ) )
+ tmp1_q29 = coeff.a4_q29 - _qmul( angleSquared_q29, coeff.a5_q29, 29, 29, 29 );
+ tmp2_q29 = coeff.a3_q29 - _qmul( angleSquared_q29, tmp1_q29, 29, 29, 29 );
+ tmp3_q29 = coeff.a2_q29 - _qmul( angleSquared_q29, tmp2_q29, 29, 29, 29 );
+ tmp4_q29 = coeff.a1_q29 - _qmul( angleSquared_q29, tmp3_q29, 29, 29, 29 );
+ tmp5_q29 = coeff.a0_q29 - _qmul( angleSquared_q29, tmp4_q29, 29, 29, 29 );
+ tmp6_q30 = _qmul( ang_q29, tmp5_q29, 29, 29, 30 );
+
+ return( angleSign * tmp6_q30 );
+}
+
+
+// Input can range from -pi to +pi. Input value cannot be larger than 4.0, so
+// angles larger than 229 degrees won't produce correct results.
+// Input: angle in radians
+// Checked and verified on May 15, 2014
+int32_t cos_q30( int32_t angleRad_q29 )
+{
+ // Use the identity to calc cosine from sin:
+ // cos( x ) = sin( x + 90 ), where x is in degrees.
+ if( angleRad_q29 >= PI_OVER_TWO_Q29 ) {
+ // Note: the angle (x+90) cannot be larger than 229 degrees and remain in q29 format (the
+ // value is represented in radians). Therefore, if the angle is greater than 90
+ // degrees, subtract 270 (+90-360) from the angle to prevent the intermediate value
+ // from going beyond 229 degrees.
+ angleRad_q29 = angleRad_q29 - PI_OVER_TWO_Q29; // -90
+ angleRad_q29 = angleRad_q29 - PI_OVER_TWO_Q29; // -180
+ angleRad_q29 = angleRad_q29 - PI_OVER_TWO_Q29; // -270
+ // Equivalent to (int32_t)( (int64_t)angleRad_q29 - 2529944570 );
+ } else {
+ // x is less than 90 degrees: cos( x ) = sin( x + 90 )
+ angleRad_q29 = angleRad_q29 + PI_OVER_TWO_Q29;
+ }
+ return sin_q30( angleRad_q29 );
+}
+
+
+void VectorNormalize_q30( int32_t *vectorIn_q27,
+ int32_t *vectorOut_q30 )
+{
+ int32_t vectorMag_q27;
+
+ // sqrt( v1^2 + v2^2 + v3^2 )
+ vectorMag_q27 = VectorMag_q27( vectorIn_q27 );
+
+ vectorOut_q30[0] = _qdiv( vectorIn_q27[0], vectorMag_q27, 27, 27, 30 );
+ vectorOut_q30[1] = _qdiv( vectorIn_q27[1], vectorMag_q27, 27, 27, 30 );
+ vectorOut_q30[2] = _qdiv( vectorIn_q27[2], vectorMag_q27, 27, 27, 30 );
+}
+
+
+// Components must be less than 1239850262 (Q27) ~ 9.23 (dec) in order to use this function without
+// overflow. Else, need to represent the output in another q-format.
+int32_t VectorMag_q27( int32_t *vectorIn_q27 )
+{
+ int32_t temp_q27[3];
+
+ //
+ temp_q27[0] = _qmul( vectorIn_q27[0], vectorIn_q27[0], 27, 27, 27 );
+ temp_q27[1] = _qmul( vectorIn_q27[1], vectorIn_q27[1], 27, 27, 27 );
+ temp_q27[2] = _qmul( vectorIn_q27[2], vectorIn_q27[2], 27, 27, 27 );
+
+ // sqrt( v1^2 + v2^2 + v3^2 )
+ return( qsqrt_q27( temp_q27[0] + temp_q27[1] + temp_q27[2] ) );
+}
+
+
+void VectorCrossProduct_q27( int32_t *vect1_q27,
+ int32_t *vect2_q27,
+ int32_t *vectOut_q27 )
+{
+ // | i j k |
+ // | v1[0] v1[1] v1[2] | = i*( v1[1]*v2[2] - v1[2]*v2[1] ) - j*( v1[0]*v2[2] - v1[2]*v2[0] ) + k*( v1[0]*v2[1] - v1[1]*v2[0] )
+ // | v2[0] v2[1] v2[2] |
+
+ vectOut_q27[0] = _qmul( vect1_q27[1], vect2_q27[2], 27, 27, 27 ) -
+ _qmul( vect1_q27[2], vect2_q27[1], 27, 27, 27 ); // v1[1]*v2[2] - v1[2]*v2[1]
+ vectOut_q27[1] = _qmul( vect1_q27[2], vect2_q27[0], 27, 27, 27 ) -
+ _qmul( vect1_q27[0], vect2_q27[2], 27, 27, 27 ); // v1[2]*v2[0] - v1[0]*v2[2]
+ vectOut_q27[2] = _qmul( vect1_q27[0], vect2_q27[1], 27, 27, 27 ) -
+ _qmul( vect1_q27[1], vect2_q27[0], 27, 27, 27 ); // v1[0]*v2[1] - v1[1]*v2[0]
+}
+
+int32_t VectorDotProduct_q27( int32_t *vect1_q27, int32_t *vect2_q27 )
+{
+ int32_t result_q27;
+
+ result_q27 = _qmul( vect1_q27[0], vect2_q27[0], 27, 27, 27 ) +
+ _qmul( vect1_q27[1], vect2_q27[1], 27, 27, 27 ) +
+ _qmul( vect1_q27[2], vect2_q27[2], 27, 27, 27 );
+
+ return result_q27;
+}
+
+
+//
+// 32-bit fixed point (Q27) four-quadrant arctangent. Given a Cartesian vector (x, y), return the
+// angle subtended by the vector and the positive x-axis. Both function input and output are in
+// q27 format.
+//
+// The value returned falls in the follwing range: [ -pi, pi ) and is converted to a q27 data-type
+// (floating-point value is multiplied by 2^27).
+//
+// * Because the magnitude of the input vector does not change the angle it
+// * represents, the inputs can be in any signed 16-bit fixed-point format.
+// *
+// * @param y y-coordinate is int32_t, q27 format
+// * @param x x-coordinate is int32_t, q27 format
+// * @return angle in int32_t, q27 format between -( pi*2^27 ) and +( pi*2^27 )
+//
+int32_t atan2Old_q27( int32_t y,
+ int32_t x )
+{
+ int32_t nabs_y = nabs( y );
+ int32_t nabs_x = nabs( x );
+
+ int32_t angle;
+ int32_t innerTerm_q27;
+
+ // If the absolute values of x and y are the same, then the angle is 45 degrees off the x-axis.
+ // Only need to determine the quadrant to find the angle.
+ if( nabs_y == nabs_x ) {
+ if( y > 0 ) {
+ if( x > 0 ) {
+ return 105414357; // angle = round( ( 45* pi/180 ) * 2^27 );
+ } else {
+ return 316243071; // angle = round( ( 3*45* pi/180 ) * 2^27 )
+ }
+ } else if( y < 0 ) {
+ if( x > 0 )
+ {
+ return -105414357; // angle = round( ( -45* pi/180 ) * 2^27 );
+ } else {
+ return -316243071; // angle = round( ( -3*45* pi/180 ) * 2^27 );
+ }
+ } else {
+ // Both x and y are zero. Indeterminate angle (return 0 but set error flag)
+ return 0;
+ }
+ }
+
+ // The point is on the y-axis. Angle = +/-90 deg
+ if( nabs_x == 0 ) {
+ if( y > 0 ) {
+ return 210828714; // angle = round( ( 90 * pi/180 ) * 2^27 );
+ } else {
+ return -210828714; // angle = round( ( -90 * pi/180 ) * 2^27 );
+ }
+ }
+
+ // The point is on the x-axis; angle = 0, 180 deg
+ if( nabs_y == 0 ) {
+ if( x > 0 ) {
+ return 0; // angle = round( ( 0 * pi/180 ) * 2^27 );
+ } else {
+ return -421657428; // angle = round( ( -180 * pi/180 ) * 2^27 );
+ }
+ }
+
+ // Point is not on the x or y-axis nor is it on a +/-45 degree line. Calculate the angle
+ if( nabs_x < nabs_y ) {
+ // The point is above a line that is 45 degree above the x-axis (octants II and III)
+ int32_t xOverY_q27 = _qdiv( x, y, 27, 27, 27 ); // ( x >> 27 ) / y;
+ int32_t absXOverY_q27 = nabs( xOverY_q27 );
+
+ // ( pi/4 + 0.273 ) = round( ( pi/4 + 0.273 ) * 2^27 ) = 142055797
+ // 0.273 = round( 0.273 * 2^27 ) = 36641440
+ innerTerm_q27 = 142055797 - _qmul( 36641440, absXOverY_q27, 27, 27, 27 );
+ if( y > 0 ) {
+ // angle = 90 - result
+ angle = 210828714 - _qmul( xOverY_q27, innerTerm_q27, 27, 27, 27 );
+ } else {
+ angle = -210828714 - _qmul( xOverY_q27, innerTerm_q27, 27, 27, 27 );
+ }
+ } else {
+ // The point is below a line that is 45 degree above the x-axis (octants I and IV)
+ int32_t yOverX_q27 = _qdiv( y, x, 27, 27, 27 ); //fix( y * 2^27 / x );
+ int32_t absYOverX_q27 = nabs( yOverX_q27 );
+
+ // ( pi/4 + 0.273 ) = round( ( pi/4 + 0.273 ) * 2^27 ) = 142055797
+ // 0.273 = round( 0.273 * 2^27 ) = 36641440
+ innerTerm_q27 = 142055797 - _qmul( 36641440, absYOverX_q27, 27, 27, 27 );
+ if( x > 0 ) {
+ // In octant I or VIII
+ angle = _qmul( yOverX_q27, innerTerm_q27, 27, 27, 27 );
+ } else {
+ // Near theta = 180 degrees, the program needs to check the quadrant when computing the
+ // angle as the output must fall between -pi (-180 deg) and +pi (180 deg)
+ if( y > 0 ) {
+ // In octant IV or V
+ angle = 421657428 + _qmul( yOverX_q27, innerTerm_q27, 27, 27, 27 );
+ } else {
+ angle = -421657429 + _qmul( yOverX_q27, innerTerm_q27, 27, 27, 27 );
+ }
+ }
+ }
+ return (int32_t)angle; // Must be less than 2,147,483,648 = 2^15-1
+}
+
+
+// This is a replacement for 'lowPass2Pole' found in the 440 code. Note, the implementation in the
+// 440 SW is not a second-order filter but is an implementation of a first-order filter.
+void firstOrderLowPass_q27( int32_t *output_q27,
+ int32_t *input_q27,
+ int32_t *inputPast_q27,
+ uint8_t shiftCoeff )
+{
+ *output_q27 = *output_q27 +
+ _qmul( ( *input_q27 - *output_q27 ), ONE_Q30 >> shiftCoeff, 27, 30, 27 ) +
+ _qmul( ( *inputPast_q27 - *output_q27 ), ONE_Q30 >> shiftCoeff, 27, 30, 27 );
+
+ *inputPast_q27 = *input_q27;
+}
+
diff --git a/examples/OpenIMU300RI/INS/lib/Core/Odo/odoAPI.h b/examples/OpenIMU300RI/INS/lib/Core/Odo/odoAPI.h
new file mode 100644
index 0000000..458560b
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/lib/Core/Odo/odoAPI.h
@@ -0,0 +1,40 @@
+/** ***************************************************************************
+ * @file odoApi.h Odometer interface.
+ *
+ * THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
+ * KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
+ * PARTICULAR PURPOSE.
+ *
+ * @brief This is a generalized odometer interface.
+ *****************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+
+#ifndef ODO_API_H
+#define ODO_API_H
+
+#include
+#include "GlobalConstants.h"
+
+typedef struct {
+ uint8_t update; // 1 if contains new data
+ real v; // velocity measured by odometer, [m/s]
+} odoDataStruct_t;
+
+extern odoDataStruct_t gOdo;
+
+#endif /* ODO_API_H */
diff --git a/examples/OpenIMU300RI/INS/lib/Core/UARTComm/CommonMessages.c b/examples/OpenIMU300RI/INS/lib/Core/UARTComm/CommonMessages.c
new file mode 100644
index 0000000..09cbf0b
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/lib/Core/UARTComm/CommonMessages.c
@@ -0,0 +1,362 @@
+/** ***************************************************************************
+ * @file UARTMessages.c
+ *
+ * THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
+ * KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
+ * PARTICULAR PURPOSE.
+ *
+ ******************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+
+#include
+#include
+#include
+
+#include "algorithmAPI.h"
+#include "platformAPI.h"
+#include "sensorsAPI.h"
+#include "appVersion.h"
+
+#include "CommonMessages.h"
+#include "algorithm.h"
+
+#include "EKF_Algorithm.h"
+
+
+/******************************************************************************
+ * @name FillPingPacketPayload - API call ro prepare user output packet
+ * @brief general handler
+ * @param [in] payload pointer to put user data to
+ * @param [in/out] number of bytes in user payload
+ * @retval N/A
+ ******************************************************************************/
+BOOL Fill_PingPacketPayload(uint8_t *payload, uint8_t *payloadLen)
+{
+ int len;
+ uint8_t *model = (uint8_t*)unitVersionString();
+ uint8_t *rev = (uint8_t*)platformBuildInfo();
+ unsigned int serialNum = unitSerialNumber();
+ len = snprintf((char*)payload, 250, "%s %s SN:%u", model, rev, serialNum );
+ *payloadLen = len;
+ return TRUE;
+}
+
+/******************************************************************************
+ * @name FillVersionPacketPayload - API call ro prepare user output packet
+ * @brief general handler
+ * @param [in] payload pointer to put user data to
+ * @param [in/out] number of bytes in user payload
+ * @retval N/A
+ ******************************************************************************/
+BOOL Fill_VersionPacketPayload(uint8_t *payload, uint8_t *payloadLen)
+{
+ int len = snprintf((char*)payload, 250, "%s", APP_VERSION_STRING );
+ *payloadLen = len;
+ return TRUE;
+}
+
+/******************************************************************************
+ * @name FillTestPacketPayload - API call ro prepare user output packet
+ * @brief general handler
+ * @param [in] payload pointer to put user data to
+ * @param [in/out] number of bytes in user payload
+ * @retval N/A
+ ******************************************************************************/
+BOOL Fill_zTPacketPayload(uint8_t *payload, uint8_t *payloadLen)
+{
+ static uint32_t _testVal = 0;
+ test_payload_t* pld = (test_payload_t*)payload;
+ pld->counter = _testVal++;
+ *payloadLen = sizeof(test_payload_t);
+ return TRUE;
+}
+
+/******************************************************************************
+ * @name FillTestPacketPayloadt - API call ro prepare user output packet
+ * @brief general handler
+ * @param [in] payload pointer to put user data to
+ * @param [in/out] number of bytes in user payload
+ * @retval N/A
+ ******************************************************************************/
+BOOL Fill_z1PacketPayload(uint8_t *payload, uint8_t *payloadLen)
+{
+ uint64_t tstamp;
+ double accels[NUM_AXIS];
+ double mags[NUM_AXIS];
+ double rates[NUM_AXIS];
+
+ data1_payload_t *pld = (data1_payload_t *)payload;
+
+// tstamp = platformGetDacqTimeStamp(); // time stamp of last sensor sample in microseconds from system start
+ tstamp = platformGetCurrTimeStamp(); // current time stamp in microseconds from system start
+// tstamp /= 1000; // convert to miliseconds
+// timer = getSystemTime(); // OS timer value (tick defined in FreeRTOSConfig.h)
+ pld->timer = tstamp;
+ GetAccelData_mPerSecSq(accels);
+ GetRateData_degPerSec(rates);
+ GetMagData_G(mags);
+
+ for (int i = 0; i < NUM_AXIS; i++){
+ pld->accel_mpss[i] = (float)accels[i];
+ pld->rate_dps[i] = (float)rates[i];
+ pld->mag_G[i] = (float)mags[i];
+ }
+
+ *payloadLen = sizeof(data1_payload_t);
+ return TRUE;
+}
+
+
+/******************************************************************************
+ * @name FillTestPacketPayloadt - API call ro prepare user output packet
+ * @brief general handler
+ * @param [in] payload pointer to put user data to
+ * @param [in/out] number of bytes in user payload
+ * @retval N/A
+ ******************************************************************************/
+BOOL Fill_a1PacketPayload(uint8_t *payload, uint8_t *payloadLen)
+{
+ angle1_payload_t* pld = (angle1_payload_t*)payload;
+
+ // Variables used to hold the EKF values
+ real EulerAngles[NUM_AXIS];
+ real CorrRates_B[NUM_AXIS];
+ double accels[NUM_AXIS];
+ // Diagnostic flags
+ uint8_t OperMode, LinAccelSwitch, TurnSwitch;
+
+ EKF_GetAttitude_EA(EulerAngles);
+ EKF_GetCorrectedAngRates(CorrRates_B);
+ GetAccelData_mPerSecSq(accels);
+ EKF_GetOperationalMode(&OperMode);
+ EKF_GetOperationalSwitches(&LinAccelSwitch, &TurnSwitch);
+
+ pld->itow = getAlgorithmITOW();
+ pld->dblItow = 1.0e-3 * pld->itow;
+ pld->roll = (float)EulerAngles[ROLL];
+ pld->pitch = (float)EulerAngles[PITCH];
+ pld->ekfOpMode = OperMode;
+ pld->accelLinSwitch = LinAccelSwitch;
+ pld->turnSwitch = TurnSwitch;
+
+ for(int i = 0; i < NUM_AXIS; i++){
+ pld->corrRates[i] = (float)CorrRates_B[i];
+ pld->accels[i] = (float)accels[i];
+ }
+
+ *payloadLen = sizeof(angle1_payload_t);
+
+ return TRUE;
+}
+
+/******************************************************************************
+ * @name FillTestPacketPayloadt - API call ro prepare user output packet
+ * @brief general handler
+ * @param [in] payload pointer to put user data to
+ * @param [in/out] number of bytes in user payload
+ * @retval N/A
+ ******************************************************************************/
+BOOL Fill_a2PacketPayload(uint8_t *payload, uint8_t *payloadLen)
+{
+ angle2_payload_t* pld = (angle2_payload_t*)payload;
+
+ // Variables used to hold the EKF values
+ real EulerAngles[NUM_AXIS];
+ real CorrRates_B[NUM_AXIS];
+ double accels[NUM_AXIS];
+
+ EKF_GetAttitude_EA(EulerAngles);
+ EKF_GetCorrectedAngRates(CorrRates_B);
+ GetAccelData_mPerSecSq(accels);
+
+ pld->itow = getAlgorithmITOW();
+ pld->dblItow = 1.0e-3 * pld->itow;
+ pld->roll = (float)EulerAngles[ROLL];
+ pld->pitch = (float)EulerAngles[PITCH];
+ pld->yaw = (float)EulerAngles[YAW];
+
+ for(int i = 0; i < NUM_AXIS; i++){
+ pld->corrRates[i] = (float)CorrRates_B[i];
+ pld->accels[i] = (float)accels[i];
+ }
+
+ *payloadLen = sizeof(angle2_payload_t);
+
+ return TRUE;
+}
+
+/******************************************************************************
+ * @name Fills1PacketPayloadt - API call ro prepare user output packet
+ * @brief general handler
+ * @param [in] payload pointer to put user data to
+ * @param [in/out] number of bytes in user payload
+ * @retval N/A
+ ******************************************************************************/
+BOOL Fill_s1PacketPayload(uint8_t *payload, uint8_t *payloadLen)
+{
+ double accels[NUM_AXIS];
+ double mags[NUM_AXIS];
+ double rates[NUM_AXIS];
+ double temp;
+ scaled1_payload_t *pld = (scaled1_payload_t *)payload;
+ *payloadLen = sizeof(scaled1_payload_t);
+
+ GetAccelData_mPerSecSq(accels);
+ GetRateData_degPerSec(rates);
+ GetMagData_G(mags);
+ GetBoardTempData(&temp);
+
+ pld->tstmp = platformGetIMUCounter();
+ pld->dbTstmp = (double)pld->tstmp * 1.0e-3; // seconds
+
+ for (int i = 0; i < NUM_AXIS; i++){
+ pld->accel_g[i] = (float)accels[i];
+ pld->rate_dps[i] = (float)rates[i];
+ pld->mag_G[i] = (float)mags[i];
+ }
+
+ pld->temp_C = (float)temp;
+
+ return TRUE;
+}
+
+/******************************************************************************
+ * @name Fille1PacketPayloadt - API call ro prepare user output packet - EKF data 1
+ * @brief general handler
+ * @param [in] payload pointer to put user data to
+ * @param [in/out] number of bytes in user payload
+ * @retval N/A
+ ******************************************************************************/
+BOOL Fill_e1PacketPayload(uint8_t *payload, uint8_t *payloadLen)
+{
+ // Variables used to hold the EKF values
+ uint8_t opMode, linAccelSw, turnSw;
+ double data[NUM_AXIS];
+ real EulerAngles[NUM_AXIS];
+
+ ekf1_payload_t *pld = (ekf1_payload_t *)payload;
+
+ *payloadLen = sizeof(ekf1_payload_t);
+ pld->tstmp = platformGetIMUCounter();
+ pld->dbTstmp = platformGetSolutionTstampAsDouble() * 0.000001; // seconds
+
+ EKF_GetAttitude_EA(EulerAngles);
+ pld->roll = (float)EulerAngles[ROLL];
+ pld->pitch = (float)EulerAngles[PITCH];
+ pld->yaw = (float)EulerAngles[YAW];
+
+ GetAccelData_g(data);
+ for(int i = 0; i < NUM_AXIS; i++){
+ pld->accels_g[i] = (float)data[i];
+ }
+
+ GetRateData_degPerSec(data);
+ for(int i = 0; i < NUM_AXIS; i++){
+ pld->rates_dps[i] = data[i];
+ }
+
+ GetMagData_G(data);
+ for(int i = 0; i < NUM_AXIS; i++){
+ pld->mags[i] = data[i];
+ }
+
+ float rateBias[NUM_AXIS];
+ EKF_GetEstimatedAngRateBias(rateBias);
+ for(int i = 0; i < NUM_AXIS; i++){
+ pld->rateBias[i] = (float)rateBias[i];
+ }
+
+ EKF_GetOperationalMode(&opMode);
+ EKF_GetOperationalSwitches(&linAccelSw, &turnSw);
+ pld->opMode = opMode;
+ pld->accelLinSwitch = linAccelSw;
+ pld->turnSwitch = turnSw;
+ return TRUE;
+}
+
+/******************************************************************************
+ * @name Fille2PacketPayloadt - API call ro prepare user output packet
+ * @brief general handler
+ * @param [in] payload pointer to put user data to
+ * @param [in/out] number of bytes in user payload
+ * @retval N/A
+ ******************************************************************************/
+BOOL Fill_e2PacketPayload(uint8_t *payload, uint8_t *payloadLen)
+{
+ float fData[3];
+ real rData[3];
+ double dData[3];
+
+ ekf2_payload_t *pld = (ekf2_payload_t *)payload;
+
+ *payloadLen = sizeof(ekf2_payload_t);
+ pld->tstmp = platformGetIMUCounter();
+ pld->dbTstmp = platformGetSolutionTstampAsDouble() * 0.000001; // seconds
+
+ EKF_GetAttitude_EA(rData);
+ pld->roll = (float)rData[ROLL];
+ pld->pitch = (float)rData[PITCH];
+ pld->yaw = (float)rData[YAW];
+
+ GetAccelData_g(dData);
+ for(int i = 0; i < NUM_AXIS; i++){
+ pld->accels_g[i] = (float)dData[i];
+ }
+
+ EKF_GetEstimatedAccelBias(fData);
+ for(int i = 0; i < NUM_AXIS; i++){
+ pld->accelBias[i] = fData[i];
+ }
+
+ GetRateData_degPerSec(dData);
+ for(int i = 0; i < NUM_AXIS; i++){
+ pld->rates_dps[i] = (float)dData[i];
+ }
+
+ EKF_GetEstimatedAngRateBias(fData);
+ for(int i = 0; i < NUM_AXIS; i++){
+ pld->rateBias[i] = fData[i];
+ }
+
+
+ EKF_GetEstimatedVelocity(fData);
+ for(int i = 0; i < NUM_AXIS; i++){
+ pld->velocity[i] = fData[i];
+ }
+
+ GetMagData_G(dData);
+ for(int i = 0; i < NUM_AXIS; i++){
+ pld->mags[i] = (float)dData[i];
+ }
+
+ EKF_GetEstimatedLLA(dData);
+ for(int i = 0; i < NUM_AXIS; i++){
+ pld->pos[i] = dData[i];
+ }
+
+ uint8_t opMode, linAccelSw, turnSw;
+ EKF_GetOperationalMode(&opMode);
+ EKF_GetOperationalSwitches(&linAccelSw, &turnSw);
+
+ pld->opMode = opMode;
+ pld->accelLinSwitch = linAccelSw;
+ pld->turnSwitch = turnSw;
+
+ return TRUE;
+}
+
diff --git a/examples/OpenIMU300RI/INS/lib/Core/UARTComm/CommonMessages.h b/examples/OpenIMU300RI/INS/lib/Core/UARTComm/CommonMessages.h
new file mode 100644
index 0000000..0f373f0
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/lib/Core/UARTComm/CommonMessages.h
@@ -0,0 +1,126 @@
+/** ***************************************************************************
+ * @file UARTMessages.h
+ *
+ * THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
+ * KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
+ * PARTICULAR PURPOSE.
+ *
+ ******************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+#ifndef _UART_MESSAGES_H
+#define _UART_MESSAGES_H
+#include
+
+#pragma pack(1)
+
+// payload structure of standard IMU data message
+typedef struct {
+ uint32_t timer;
+ float accel_mpss[3];
+ float rate_dps[3];
+ float mag_G[3];
+}data1_payload_t;
+
+// payload structure of standard test message
+typedef struct {
+ uint32_t counter;
+}test_payload_t;
+
+// payload structure of standard unit attitude message
+typedef struct {
+ uint32_t itow;
+ double dblItow;
+ float roll;
+ float pitch;
+ float corrRates[3];
+ float accels[3];
+ uint8_t ekfOpMode;
+ uint8_t accelLinSwitch;
+ uint8_t turnSwitch;
+}angle1_payload_t;
+
+// payload structure of alternative IMU data message
+typedef struct {
+ uint32_t tstmp;
+ double dbTstmp;
+ float accel_g[3];
+ float rate_dps[3];
+ float mag_G[3];
+ float temp_C;
+}scaled1_payload_t;
+
+// payload structure of standard EKF message
+typedef struct {
+ uint32_t tstmp;
+ double dbTstmp;
+ float roll;
+ float pitch;
+ float yaw;
+ float accels_g[3];
+ float rates_dps[3];
+ float rateBias[3];
+ float mags[3];
+ uint8_t opMode;
+ uint8_t accelLinSwitch;
+ uint8_t turnSwitch;
+}ekf1_payload_t;
+
+// payload structure of enchanced EKF message
+typedef struct {
+ uint32_t tstmp;
+ double dbTstmp;
+ float roll;
+ float pitch;
+ float yaw;
+ float accels_g[3];
+ float accelBias[3];
+ float rates_dps[3];
+ float rateBias[3];
+ float velocity[3];
+ float mags[3];
+ double pos[3];
+ uint8_t opMode;
+ uint8_t accelLinSwitch;
+ uint8_t turnSwitch;
+}ekf2_payload_t;
+
+// payload structure of standard unit attitude message
+typedef struct {
+ uint32_t itow;
+ double dblItow;
+ float roll;
+ float pitch;
+ float yaw;
+ float corrRates[3];
+ float accels[3];
+}angle2_payload_t;
+
+
+#pragma pack()
+
+BOOL Fill_PingPacketPayload(uint8_t *payload, uint8_t *payloadLen);
+BOOL Fill_VersionPacketPayload(uint8_t *payload, uint8_t *payloadLen);
+BOOL Fill_zTPacketPayload(uint8_t *payload, uint8_t *payloadLen);
+BOOL Fill_z1PacketPayload(uint8_t *payload, uint8_t *payloadLen);
+BOOL Fill_a1PacketPayload(uint8_t *payload, uint8_t *payloadLen);
+BOOL Fill_a2PacketPayload(uint8_t *payload, uint8_t *payloadLen);
+BOOL Fill_s1PacketPayload(uint8_t *payload, uint8_t *payloadLen);
+BOOL Fill_e1PacketPayload(uint8_t *payload, uint8_t *payloadLen);
+BOOL Fill_e2PacketPayload(uint8_t *payload, uint8_t *payloadLen);
+
+#endif
diff --git a/examples/OpenIMU300RI/INS/lib/Core/library.json b/examples/OpenIMU300RI/INS/lib/Core/library.json
new file mode 100644
index 0000000..f5babce
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/lib/Core/library.json
@@ -0,0 +1,24 @@
+{
+ "name": "Core",
+ "version": "1.0.4",
+ "description": "Algorithm and GPS libraries",
+ "build": {
+ "flags": [
+ "-I Algorithm",
+ "-I Algorithm/include",
+ "-I Buffer",
+ "-I Buffer/include",
+ "-I Common",
+ "-I Common/include",
+ "-I GPS",
+ "-I GPS/include",
+ "-I Odo",
+ "-I Odo/include",
+ "-I Math",
+ "-I Math/include",
+ "-I SPIComm",
+ "-I UARTComm",
+ "-I ."
+ ]
+ }
+ }
diff --git a/examples/OpenIMU300RI/IMU/lib/readme.txt b/examples/OpenIMU300RI/INS/lib/readme.txt
similarity index 100%
rename from examples/OpenIMU300RI/IMU/lib/readme.txt
rename to examples/OpenIMU300RI/INS/lib/readme.txt
diff --git a/examples/OpenIMU300RI/INS/openimu.json b/examples/OpenIMU300RI/INS/openimu.json
new file mode 100644
index 0000000..109c95b
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/openimu.json
@@ -0,0 +1,730 @@
+{
+ "appVersion": "OpenIMU300ZI INS 1.1.0",
+ "description": "9-axis OpenIMU with triaxial rate, acceleration, and magnetic measurement",
+ "userConfiguration": [
+ { "paramId": 0,"category": "General", "paramType": "disabled", "type": "uint64", "name": "Data CRC" },
+ { "paramId": 1,"category": "General", "paramType": "disabled", "type": "uint64", "name": "Data Size" },
+ { "paramId": 2, "category": "General","paramType": "select", "type": "int64", "name": "Baud Rate", "argument": "baud_rate","value_range":[-1,1], "value_accuracy":6, "options": [115200, 57600, 230400, 38400,0] },
+ { "paramId": 3, "category": "General","paramType": "select", "type": "char8", "name": "Packet Type", "argument": "type", "value_range":[-1,1],"value_accuracy":6, "options": ["z1", "zT", "s1", "e1", "e2"] },
+ { "paramId": 4, "category": "General","paramType": "select", "type": "int64", "name": "Packet Rate", "argument": "rate", "value_range":[-1,1],"value_accuracy":6, "options": [200, 100, 50, 20, 10, 5, 2, 0] },
+ { "paramId": 5, "category": "General","paramType": "select", "type": "int64", "name": "Accel LPF", "argument": "xl_lpf", "value_range":[-1,1],"value_accuracy":6,"options": [50, 40, 25, 20, 10, 5, 2] },
+ { "paramId": 6, "category": "General","paramType": "select", "type": "int64", "name": "Rate LPF", "argument": "rate_lpf", "value_range":[-1,1],"value_accuracy":6,"options": [50, 40, 25, 20, 10, 5, 2] },
+ { "paramId": 7, "category": "General","paramType": "select", "type": "char8", "name": "Orientation", "argument": "orien", "value_range":[-1,1],"value_accuracy":6,"options": ["+X+Y+Z"] }
+ ],
+ "userMessages": {
+ "inputPackets": [{
+ "name": "pG",
+ "description": "Get device serial number & factory ID",
+ "inputPayload": {},
+ "responsePayload": {
+ "type": "string",
+ "name": "Device ID and SN"
+ }
+ },
+ {
+ "name": "gV",
+ "description": "Get user app version",
+ "inputPayload": {},
+ "responsePayload": {
+ "type": "string",
+ "name": "User Version"
+ }
+ },
+ {
+ "name": "gA",
+ "description": "Get All Configuration Parameters",
+ "inputPayload": {},
+ "responsePayload": {
+ "type": "userConfiguration",
+ "name": "Full Current Configuration"
+ }
+ },
+ {
+ "name": "gP",
+ "description": "Get a Configuration Parameter",
+ "inputPayload": {
+ "type": "paramId",
+ "name": "Request Parameter Id"
+ },
+ "responsePayload": {
+ "type": "userParameter",
+ "name": "User Parameter"
+ }
+ },
+ {
+ "name": "uP",
+ "description": "Update Configuration Parameter",
+ "inputPayload": {
+ "type": "userParameter",
+ "name": "Parameter to be Updated"
+ },
+ "responsePayload": {
+ "type": "paramId",
+ "name": "ID of the Updated Parameter"
+ }
+ }
+ ],
+ "outputPackets": [{
+ "name": "z1",
+ "description": "Scaled 9-Axis IMU",
+ "payload": [{
+ "type": "uint32",
+ "name": "time",
+ "unit": "s"
+ },
+ {
+ "type": "float",
+ "name": "xAccel",
+ "unit": "m/s/sG"
+ },
+ {
+ "type": "float",
+ "name": "yAccel",
+ "unit": "m/s/sG"
+ },
+ {
+ "type": "float",
+ "name": "zAccel",
+ "unit": "m/s/sG"
+ },
+ {
+ "type": "float",
+ "name": "xRate",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "yRate",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "zRate",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "xMag",
+ "unit": "Gauss"
+ },
+ {
+ "type": "float",
+ "name": "yMag",
+ "unit": "Gauss"
+ },
+ {
+ "type": "float",
+ "name": "zMag",
+ "unit": "Gauss"
+ }
+ ],
+ "graphs": [{
+ "name": "Acceleration",
+ "units": "m/s/s",
+ "xAxis": "Time (s)",
+ "yAxes": ["xAccel", "yAccel", "zAccel"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 80
+ },
+ {
+ "name": "Angular Rate",
+ "units": "deg/s",
+ "xAxis": "Time (s)",
+ "yAxes": ["xRate", "yRate", "zRate"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 400
+ }
+ ]
+ },
+ {
+ "name": "e1",
+ "description": "VG/AHRS Output Message",
+ "payload": [{
+ "type": "uint32",
+ "name": "timeCntr",
+ "unit": "msec"
+ },
+ {
+ "type": "double",
+ "name": "time",
+ "unit": "s"
+ },
+ {
+ "type": "float",
+ "name": "roll",
+ "unit": "rad"
+ },
+ {
+ "type": "float",
+ "name": "pitch",
+ "unit": "rad"
+ },
+ {
+ "type": "float",
+ "name": "heading",
+ "unit": "rad"
+ },
+ {
+ "type": "float",
+ "name": "xAccel",
+ "unit": "g"
+ },
+ {
+ "type": "float",
+ "name": "yAccel",
+ "unit": "g"
+ },
+ {
+ "type": "float",
+ "name": "zAccel",
+ "unit": "g"
+ },
+ {
+ "type": "float",
+ "name": "xRate",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "yRate",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "zRate",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "xRateBias",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "yRateBias",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "zRateBias",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "xMag",
+ "unit": "G"
+ },
+ {
+ "type": "float",
+ "name": "yMag",
+ "unit": "G"
+ },
+ {
+ "type": "float",
+ "name": "zMag",
+ "unit": "G"
+ },
+ {
+ "type": "uint8",
+ "name": "opMode",
+ "unit": "unitless"
+ },
+ {
+ "type": "uint8",
+ "name": "linAccSw",
+ "unit": "unitless"
+ },
+ {
+ "type": "uint8",
+ "name": "turnSw",
+ "unit": "unitless"
+ }
+ ],
+ "graphs": [
+ {
+ "name": "Euler Angles (Roll and Pitch)",
+ "units": "deg",
+ "xAxis": "Time (s)",
+ "yAxes": ["roll", "pitch"],
+ "colors": ["#FF0000", "#00FF00"],
+ "yMax": 90
+ },
+ {
+ "name": "Euler Angles (Heading)",
+ "units": "deg",
+ "xAxis": "Time (s)",
+ "yAxes": ["heading"],
+ "colors": ["#FF0000"],
+ "yMax": 190
+ },
+ {
+ "name": "Acceleration",
+ "units": "g",
+ "xAxis": "Time (s)",
+ "yAxes": ["xAccel", "yAccel", "zAccel"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 5
+ },
+ {
+ "name": "Angular-Rate",
+ "units": "deg/s",
+ "xAxis": "Time (s)",
+ "yAxes": ["xRate", "yRate", "zRate"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 200
+ },
+ {
+ "name": "Angular-Rate Bias",
+ "units": "deg/s",
+ "xAxis": "Time (s)",
+ "yAxes": ["xRateBias", "yRateBias", "zRateBias"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 200
+ },
+ {
+ "name": "Magnetic-Field",
+ "units": "G",
+ "xAxis": "Time (s)",
+ "yAxes": ["xMag", "yMag", "zMag"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 20
+ },
+ {
+ "name": "Operational Flags",
+ "units": "unitless",
+ "xAxis": "Time (s)",
+ "yAxes": ["opMode", "linAccSw", "turnSw"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 5
+ }
+ ]
+ },
+ {
+ "name": "e2",
+ "description": "INS Output Message",
+ "payload": [{
+ "type": "uint32",
+ "name": "timeCntr",
+ "unit": "msec"
+ },
+ {
+ "type": "double",
+ "name": "time",
+ "unit": "s"
+ },
+ {
+ "type": "float",
+ "name": "roll",
+ "unit": "rad"
+ },
+ {
+ "type": "float",
+ "name": "pitch",
+ "unit": "rad"
+ },
+ {
+ "type": "float",
+ "name": "heading",
+ "unit": "rad"
+ },
+ {
+ "type": "float",
+ "name": "xAccel",
+ "unit": "g"
+ },
+ {
+ "type": "float",
+ "name": "yAccel",
+ "unit": "g"
+ },
+ {
+ "type": "float",
+ "name": "zAccel",
+ "unit": "g"
+ },
+ {
+ "type": "float",
+ "name": "xAccelBias",
+ "unit": "g"
+ },
+ {
+ "type": "float",
+ "name": "yAccelBias",
+ "unit": "g"
+ },
+ {
+ "type": "float",
+ "name": "zAccelBias",
+ "unit": "g"
+ },
+ {
+ "type": "float",
+ "name": "xRate",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "yRate",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "zRate",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "xRateBias",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "yRateBias",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "zRateBias",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "velNorth",
+ "unit": "m/s"
+ },
+ {
+ "type": "float",
+ "name": "velEast",
+ "unit": "m/s"
+ },
+ {
+ "type": "float",
+ "name": "velDown",
+ "unit": "m/s"
+ },
+ {
+ "type": "float",
+ "name": "xMag",
+ "unit": "G"
+ },
+ {
+ "type": "float",
+ "name": "yMag",
+ "unit": "G"
+ },
+ {
+ "type": "float",
+ "name": "zMag",
+ "unit": "G"
+ },
+ {
+ "type": "double",
+ "name": "lat",
+ "unit": "deg"
+ },
+ {
+ "type": "double",
+ "name": "lon",
+ "unit": "deg"
+ },
+ {
+ "type": "double",
+ "name": "alt",
+ "unit": "m"
+ },
+ {
+ "type": "uint8",
+ "name": "opMode",
+ "unit": "unitless"
+ },
+ {
+ "type": "uint8",
+ "name": "linAccSw",
+ "unit": "unitless"
+ },
+ {
+ "type": "uint8",
+ "name": "turnSw",
+ "unit": "unitless"
+ }
+ ],
+ "graphs": [
+ {
+ "name": "Euler Angles (Roll and Pitch)",
+ "units": "deg",
+ "xAxis": "Time (s)",
+ "yAxes": ["roll", "pitch"],
+ "colors": ["#FF0000", "#00FF00"],
+ "yMax": 90
+ },
+ {
+ "name": "Euler Angles (Heading)",
+ "units": "deg",
+ "xAxis": "Time (s)",
+ "yAxes": ["heading"],
+ "colors": ["#FF0000"],
+ "yMax": 190
+ },
+ {
+ "name": "Acceleration",
+ "units": "g",
+ "xAxis": "Time (s)",
+ "yAxes": ["xAccel", "yAccel", "zAccel"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 8
+ },
+ {
+ "name": "Angular-Rate",
+ "units": "deg/s",
+ "xAxis": "Time (s)",
+ "yAxes": ["xRate", "yRate", "zRate"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 400
+ },
+ {
+ "name": "Angular-Rate Bias",
+ "units": "deg/s",
+ "xAxis": "Time (s)",
+ "yAxes": ["xRateBias", "yRateBias", "zRateBias"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 400
+ },
+ {
+ "name": "Acceleration Bias",
+ "units": "g",
+ "xAxis": "Time (s)",
+ "yAxes": ["xAccelBias", "yAccelBias", "zAccelBias"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 8
+ },
+ {
+ "name": "Magnetic-Field",
+ "units": "G",
+ "xAxis": "Time (s)",
+ "yAxes": ["xMag", "yMag", "zMag"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 8
+ },
+ {
+ "name": "Latitude/Longitude",
+ "units": "deg",
+ "xAxis": "Time (s)",
+ "yAxes": ["lat", "lon"],
+ "colors": ["#FF0000", "#00FF00"],
+ "yMax": 200
+ },
+ {
+ "name": "Altitude",
+ "units": "m",
+ "xAxis": "Time (s)",
+ "yAxes": ["alt"],
+ "colors": ["#FF0000"],
+ "yMax": 100
+ },
+ {
+ "name": "NED Velocity",
+ "units": "m/s",
+ "xAxis": "Time (s)",
+ "yAxes": ["velNorth", "velEast", "velDown"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 100
+ },
+ {
+ "name": "Operational Flags",
+ "units": "unitless",
+ "xAxis": "Time (s)",
+ "yAxes": ["opMode", "linAccSw", "turnSw"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 5
+ }
+ ]
+ },
+ {
+ "name": "s1",
+ "description": "IMU Scaled-Sensor Output Message",
+ "payload": [{
+ "type": "uint32",
+ "name": "timeCntr",
+ "unit": "msec"
+ },
+ {
+ "type": "double",
+ "name": "time",
+ "unit": "s"
+ },
+ {
+ "type": "float",
+ "name": "xAccel",
+ "unit": "m/s/sg"
+ },
+ {
+ "type": "float",
+ "name": "yAccel",
+ "unit": "m/s/s"
+ },
+ {
+ "type": "float",
+ "name": "zAccel",
+ "unit": "m/s/s"
+ },
+ {
+ "type": "float",
+ "name": "xRate",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "yRate",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "zRate",
+ "unit": "deg/s"
+ },
+ {
+ "type": "float",
+ "name": "xMag",
+ "unit": "G"
+ },
+ {
+ "type": "float",
+ "name": "yMag",
+ "unit": "G"
+ },
+ {
+ "type": "float",
+ "name": "zMag",
+ "unit": "G"
+ },
+ {
+ "type": "float",
+ "name": "temp",
+ "unit": "degC"
+ }
+ ],
+ "graphs": [{
+ "name": "Acceleration",
+ "units": "m/s/s",
+ "xAxis": "Time (s)",
+ "yAxes": ["xAccel", "yAccel", "zAccel"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 5
+ },
+ {
+ "name": "Angular-Rate",
+ "units": "deg/s",
+ "xAxis": "Time (s)",
+ "yAxes": ["xRate", "yRate", "zRate"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 200
+ },
+ {
+ "name": "Magnetic-Field",
+ "units": "G",
+ "xAxis": "Time (s)",
+ "yAxes": ["xMag", "yMag", "zMag"],
+ "colors": ["#FF0000", "#00FF00", "#0000FF"],
+ "yMax": 5
+ },
+ {
+ "name": "Board-Temperature",
+ "units": "degC",
+ "xAxis": "Time (s)",
+ "yAxes": ["temp"],
+ "colors": ["#FF0000"],
+ "yMax": 100
+ }
+ ]
+ }
+ ]
+ },
+ "bootloaderMessages": [{
+ "name": "JI",
+ "description": "Jump to Bootloader",
+ "inputPayload": {},
+ "responsePayload": {
+ "type": "ack",
+ "response": "Acknowledgement"
+ }
+ },
+ {
+ "name": "JA",
+ "description": "Jump to App",
+ "inputPayload": {},
+ "responsePayload": {
+ "type": "none",
+ "response": "Empty"
+ }
+ },
+ {
+ "name": "WA",
+ "description": "Write App Block",
+ "inputPayload": {
+ "type": "block",
+ "name": "4 byte block address followed by up to 240 bytes data"
+ },
+ "responsePayload": {
+ "type": "ack",
+ "response": "Acknowledgement"
+ }
+ }
+ ],
+ "CLICommands": [{
+ "name": "help",
+ "description": "CLI help menu",
+ "function": "help_handler"
+ },
+ {
+ "name": "exit",
+ "description": "exit CLI",
+ "function": ""
+ },
+ {
+ "name": "run",
+ "description": "Operations defined by users",
+ "function": "run_handler"
+ },
+ {
+ "name": "save",
+ "description": "Save the configuration into EEPROM",
+ "function": "save_handler"
+ },
+ {
+ "name": "connect",
+ "description": "Find OpenIMU device",
+ "function": "connect_handler"
+ },
+ {
+ "name": "upgrade",
+ "description": "Upgrade firmware",
+ "function": "upgrade_handler"
+ },
+ {
+ "name": "record",
+ "description": "Record output data of OpenIMU on local machine",
+ "function": "record_handler"
+ },
+ {
+ "name": "stop",
+ "description": "stop recording outputs on local machine",
+ "function": "stop_handler"
+ },
+ {
+ "name": "server_start",
+ "description": "start server thread and must use exit command to quit",
+ "function": "server_start_handler"
+ },
+ {
+ "name": "get",
+ "description": "Read the current configuration and output data",
+ "function": "get_handler"
+ },
+ {
+ "name": "set",
+ "description": "Write parameters to OpenIMU",
+ "function": "set_handler"
+ }
+ ]
+}
+
diff --git a/examples/OpenIMU300RI/INS/platformio.ini b/examples/OpenIMU300RI/INS/platformio.ini
new file mode 100644
index 0000000..9e3284a
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/platformio.ini
@@ -0,0 +1,45 @@
+; PlatformIO Project Configuration File
+;
+; Build options: build flags, source filter
+; Upload options: custom upload port, speed and extra flags
+; Library options: dependencies, extra library storages
+; Advanced options: extra scripting
+;
+; Please visit documentation for the other options and examples
+; http://docs.platformio.org/page/projectconf.html
+[platformio]
+description = A Kalman filter based algorithm that uses rate-sensors to propagate attitude (roll, pitch, and heading angles) forward in time and accelerometers and magnetometers as references, to correct for bias in the rate-sensor signal. Sensors data messages sent over CAN using J1939 protocol.
+
+[env:OpenIMU300RI]
+platform = aceinna_imu
+lib_archive = false
+board = OpenIMU300
+;lib_deps = ../../openIMU300-lib\openIMU300-lib
+lib_deps = OpenIMU300-base-library@1.1.6
+build_flags =
+ -D GPS
+ -D GPS_OVER_CAN
+ -D SAE_J1939
+ -D CAN_BUS_COMM
+ -D DETECT_USER_SERIAL_CMD
+ -D __FPU_PRESENT
+ -D ARM_MATH_CM4
+ -I include
+ -I src/user
+ -I src
+ -I lib/CAN/include
+ -I lib/CAN
+; -L ldscripts
+ -Og
+; -Wno-comment
+; -Wl,-Map,imu380.map
+; -Wl,-Tstm32f40x.ld
+ -mthumb -mcpu=cortex-m4 -mfloat-abi=softfp -mfpu=fpv4-sp-d16
+
+;upload_protocol = jlink
+;debug_tool = jlink
+
+
+;debug_tool = custom
+;debug_port = :4242
+;debug_server = $PLATFORMIO_HOME_DIR/packages/tool-stlink/bin/st-util
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Common/src/dummy.c b/examples/OpenIMU300RI/INS/src/appVersion.h
similarity index 77%
rename from examples/OpenIMU300RI/VG_AHRS/lib/Core/Common/src/dummy.c
rename to examples/OpenIMU300RI/INS/src/appVersion.h
index 395b50f..94fac93 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Common/src/dummy.c
+++ b/examples/OpenIMU300RI/INS/src/appVersion.h
@@ -1,11 +1,12 @@
-/** ***************************************************************************
- * @file spi_dummy.c
+/*****************************************************************************
+ * @file appVersion.h
*
* THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
* KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
* PARTICULAR PURPOSE.
*
+ * @brief Version definition based on UCB serial protocol.
******************************************************************************/
/*******************************************************************************
Copyright 2018 ACEINNA, INC
@@ -22,21 +23,10 @@ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*******************************************************************************/
-#ifndef SPI_BUS_COMM
+#ifndef _IMU_APP_VERSION_H
+#define _IMU_APP_VERSION_H
-#include
-#include
+#define APP_VERSION_STRING "INS_J1939 1.0.3"
-// Dummy placeholder function
-void SPI_ProcessCommand(uint8_t cmd)
-{
-
-}
-
-// Dummy placeholder function
-void SPI_ProcessData(uint8_t* in)
-{
-
-}
#endif
diff --git a/examples/OpenIMU300RI/INS/src/main.c b/examples/OpenIMU300RI/INS/src/main.c
new file mode 100644
index 0000000..f1a5a8f
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/src/main.c
@@ -0,0 +1,201 @@
+/** ***************************************************************************
+ * @file main.c
+ *
+ * THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
+ * KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
+ * PARTICULAR PURPOSE.
+ *
+ * main is the center of the system universe, it all starts here. And never ends.
+ * entry point for system (pins, clocks, interrupts), data and task initialization.
+ * contains the main processing loop. - this is a standard implementation
+ * which has mainly os functionality in the main loop
+ ******************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+#define __MAIN
+
+#include
+
+#include "boardAPI.h"
+#include "magAPI.h"
+#include "platformAPI.h"
+#include "userAPI.h"
+#include "debug.h"
+
+#include "taskDataAcquisition.h"
+#include "taskCanCommunicationJ1939.h"
+
+#include "osapi.h"
+#include "osresources.h"
+#include "canAPI.h"
+
+char buildInfo[] = {__DATE__"," __TIME__};
+
+/** ***************************************************************************
+ * @name getBuildInfo - provides the pointer to the build date and time string
+ * @brief
+ *
+ * @param [in] N/A
+ * @param [out] pointer to build info string
+ * @retval N/A
+ ******************************************************************************/
+char *getBuildInfo()
+{
+ return buildInfo;
+}
+
+/** ***************************************************************************
+ * @name initDebugInterface Debug serial interface initialization
+ * @brief Initializes debug serial console messaging support
+ *
+ * @param [in] N/A
+ * @param [out] "#> " out serial to console
+ * @retval N/A
+ ******************************************************************************/
+void DebugInterfaceInit(void)
+{
+ char status[100];
+
+ BOOL res = platformAssignPortTypeToSerialChannel(DEBUG_SERIAL_PORT, UART_CHANNEL_0); // assign debug output to user serial channel
+
+ if(!res){
+ // some error
+ return;
+ }
+#ifdef GPS_OVER_CAN
+ res = platformAssignPortTypeToSerialChannel(USER_SERIAL_PORT, UART_CHANNEL_0); // assign debug output to user serial channel
+ if(!res){
+ // some error
+ return;
+ }
+#endif
+
+ // Initialize the debug serial port
+ InitDebugSerialCommunication(38400);
+
+ BoardGetResetStatus(status, sizeof(status));
+
+}
+
+void CreateTasks(void)
+{
+ osThreadId iD;
+
+ /// Create RTOS tasks:
+ // dacq task
+ osThreadDef(DACQ_TASK, TaskDataAcquisition, osPriorityAboveNormal, 0, 2048);
+ iD = osThreadCreate(osThread(DACQ_TASK), NULL);
+ if(iD == NULL){
+ while(1);
+ }
+
+ //user communication task
+ osThreadDef(CAN_COMM_TASK, TaskCANCommunicationJ1939, osPriorityNormal, 0, 2048);
+ iD = osThreadCreate(osThread(CAN_COMM_TASK), NULL);
+ if(iD == NULL){
+ while(1);
+ }
+
+#ifdef GPS
+ // GPS task
+ osThreadDef(GPS_TASK, TaskGps, osPriorityBelowNormal, 0, 1024);
+ iD = osThreadCreate(osThread(GPS_TASK), NULL);
+ if(iD == NULL){
+ while(1);
+ }
+
+ // WMM task
+ osThreadDef(WMM_TASK, TaskWorldMagneticModel, osPriorityLow, 0, 512);
+ iD = osThreadCreate(osThread(WMM_TASK), NULL);
+ if(iD == NULL){
+ while(1);
+ }
+
+#endif
+
+
+ gyroReadySem = osSemaphoreCreate(osSemaphore(GYRO_READY_SEM), 1);
+ accelReadySem = osSemaphoreCreate(osSemaphore(ACCEL_READY_SEM), 1);
+ magReadySem = osSemaphoreCreate(osSemaphore(MAG_READY_SEM), 1);
+ tempReadySem = osSemaphoreCreate(osSemaphore(TEMP_READY_SEM), 1);
+ canDataSem = osSemaphoreCreate(osSemaphore(CAN_DATA_SEM), 1);
+ dataAcqSem = osSemaphoreCreate(osSemaphore(DATA_ACQ_SEM), 1);
+
+}
+
+/** ***************************************************************************
+ * @name main() The DMU380 firmware initialization and entry point
+ * @brief creates tasks for data collection SPI1 and user communications SPI3
+ * or USART serial stream (Nav-View) debug serial console messaging
+ *
+ * @param [in] N/A
+ * @param [out] "#> " out serial to console
+ * @retval N/A
+ ******************************************************************************/
+int main(void)
+{
+#ifdef GPS
+ BOOL res;
+#endif
+
+ // Initialize processor and board-related signals
+ BoardInit();
+
+ platformSetUnitCommunicationType(CAN_BUS);
+
+ #ifdef GPS
+ platformUnassignSerialChannels();
+
+ #ifndef GPS_OVER_CAN
+ // user serial port will be used for GPS
+ res = platformAssignPortTypeToSerialChannel(GPS_SERIAL_PORT, UART_CHANNEL_0);
+ while(!res){}; // check if valid
+ #else
+ DebugInterfaceInit();
+ #endif
+#else
+ DebugInterfaceInit();
+#endif
+
+ // Apply factory configuration
+ platformInitConfigureUnit();
+
+ // Apply user-chosen configuration
+ userInitConfigureUnit();
+
+ // Initialize OS and create required tasks
+ CreateTasks();
+
+ // Start Running the tasks...
+ // Start scheduler
+ osKernelStart();
+
+ // We should never get here as control is now taken by the scheduler
+ for (;;);
+
+}
+
+
+void vApplicationStackOverflowHook()
+{
+ while(1);
+}
+void vApplicationMallocFailedHook()
+{
+ while(1);
+}
+
diff --git a/examples/OpenIMU300RI/INS/src/taskDataAcquisition.c b/examples/OpenIMU300RI/INS/src/taskDataAcquisition.c
new file mode 100644
index 0000000..5db5a57
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/src/taskDataAcquisition.c
@@ -0,0 +1,155 @@
+/*****************************************************************************
+ * @file taskDataAcquisition.c
+ *
+ * THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
+ * KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
+ * PARTICULAR PURPOSE.
+ *
+ * sensor data acquisition task runs at 100Hz, gets the data for each sensor
+ * and applies available calibration
+ ******************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+
+#include "algorithmAPI.h"
+#include "bitAPI.h"
+#include "boardAPI.h"
+#include "magAPI.h"
+#include "platformAPI.h"
+#include "userAPI.h"
+
+#include "taskDataAcquisition.h"
+
+#include "osapi.h"
+#include "osresources.h"
+
+/** ***************************************************************************
+ * @name TaskDataAcquisition() CALLBACK main loop
+ * @brief Get the sensor data at the specified frequency (based on the
+ * configuration of the accelerometer rate-sensor). Process and provide
+ * information to the user via the UART or SPI.
+ * @param N/A
+ * @retval N/A
+ ******************************************************************************/
+void TaskDataAcquisition(void const *argument)
+{
+ //
+ int res;
+ uint16_t dacqRate;
+
+#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
+ BOOL overRange = FALSE; //uncomment this line if overrange processing required
+#pragma GCC diagnostic warning "-Wunused-but-set-variable"
+
+ // This routine sets up the timer. Can use the structure below this point.
+ TaskDataAcquisition_Init();
+ // Initialize user algorithm parameters, if needed
+ initUserDataProcessingEngine();
+ // set the mag align scale factors
+ InitMagAlignParams();
+ // Start sensors data acquisition
+ DataAquisitionStart();
+
+ // Set the sampling frequency of data acquisition task
+ dacqRate = DACQ_200_HZ;
+
+ //************** Add user initialization here, if needed ****************
+
+ // Data is provided by the primary sensors (accelerometer and rate-sensor)
+ // as fast as possible. Data is obtained from secondary sensors at a
+ // lower rate. The rate-sensor data read is synced to TIM5 or an
+ // external signal. When the read is commanded and in the data buffer,
+ // The data-event flag is set and the wait is bypassed. Data is obtained
+ // from the buffer, calibrated, filtered and provided to the user for
+ // subsequent processing.
+
+ while( 1 )
+ {
+ // *****************************************************************
+ // NOTE: This task loop runs at 200 Hz
+ // *****************************************************************
+ // Handle Timing vard, watchdog and BIT
+ PrepareToNewDacqTickAndProcessUartMessages();
+ // Wait for next tick
+ // Upon timeout of TIM5(orTIM2 or user sync), let the process continue
+
+ res = osSemaphoreWait(dataAcqSem, 1000);
+ if(res != osOK){
+ // Wait timeout expired. Something wrong wit the dacq system
+ // Process timeout here
+ }
+
+ // Get calibrated sensor data:
+ // Inside next function the sensor data is filtered by a second-order low-pass
+ // Butterworth filter, with a cutoff frequency selected by the user (or zero to
+ // disable). The cutoff is selected using the following:
+ //
+ // Select_LP_filter(rawSensor_e sensorType, eFilterType filterType)
+ //
+ // Refer to UserConfiguration.c for implementation and to the enumerator structure
+ // 'eFilterType' in file filter.h for available selections.
+ //
+ // Low pass filtering is followed by application of the unit calibration parameters
+ // - scaling, temperature compensation, bias removal, and misalignment.
+ //
+ // Results are placed in the structure of type double. The pointer to this
+ // structure is 'pScaledSensors'. Ordering of sensors data in this structure
+ // defined by 'rawSensor_e' enumerator in the file indices.h
+ GetSensorsData();
+
+ // Check if sensors data over range
+ // If overRange is TRUE - limit values are put into sensors data based
+ // on chosen sensors sensitivity
+ overRange = handleOverRange();
+
+ // *****************************************************************
+ // At this point sensors data is in next units
+ // Acceleration - g's
+ // Rates - rad/s
+ // Magnetometer - Gauss
+ // Temperature - degrees C
+ //******************************************************************
+
+ // BIT status. May have inadvertently changed this during an update.
+ updateBITandStatus();
+
+ // ********************** Algorithm ************************
+ // Due to CPU performance related to algorithm math operations, GPS related
+ // algorithms are run at 100 Hz or less (large number of calculations
+ // involved). Incorporate timing logic inside algorithm function, if
+ // desired.
+ //
+ // For the initial simplicity use pScaledSensors array as algorithm input
+ // and output. Use 'is100Hz' variable to determine the rate of this task
+ // loop.
+ inertialAndPositionDataProcessing(dacqRate);
+
+ // Uncomment next line if there is intention of using S0 or S1 xbow
+ // packets for continuous data output
+ //*****************************************************************
+ // applyNewScaledSensorsData();
+ //*****************************************************************
+
+ if (platformHasMag() ) {
+ // Mag Alignment (follows Kalman filter or user algorithm as the
+ // innovation routine calculates the euler angles and the magnetic
+ // vector in the NED-frame)
+ MagAlign(); // only does this on align
+ }
+
+ }
+}
diff --git a/examples/OpenIMU300RI/INS/src/taskDataAcquisition.h b/examples/OpenIMU300RI/INS/src/taskDataAcquisition.h
new file mode 100644
index 0000000..dd8dfd8
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/src/taskDataAcquisition.h
@@ -0,0 +1,42 @@
+/** ***************************************************************************
+ * @file taskDataAcquisition.h
+ *
+ * THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
+ * KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
+ * PARTICULAR PURPOSE.
+ *
+ * sensor data acquisition task runs at 100Hz, gets the data for each sensor
+ * and applies available calibration
+ ******************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+
+#ifndef _TASK_DATA_ACQUISITION_H_
+#define _TASK_DATA_ACQUISITION_H_
+
+#include "stdint.h"
+#include "GlobalConstants.h"
+extern void TaskDataAcquisition(void const *argument);
+extern void PrepareToNewDacqTick();
+extern void PrepareToNewDacqTickAndProcessUartMessages();
+extern void TaskDataAcquisition_Init(void);
+extern void GetSensorsData(void);
+extern void EnterMainAlgLoop(void);
+extern void DataAquisitionStart(void);
+extern BOOL isOneHundredHertzFlag(void);
+
+#endif
diff --git a/examples/OpenIMU300RI/INS/src/user/UserAlgorithm.c b/examples/OpenIMU300RI/INS/src/user/UserAlgorithm.c
new file mode 100644
index 0000000..7dc6ec0
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/src/user/UserAlgorithm.c
@@ -0,0 +1,278 @@
+/** ***************************************************************************
+ * @file UserAlgorithm.c
+ *
+ * THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
+ * KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
+ * PARTICULAR PURPOSE.
+ *
+ ******************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+
+#include
+
+#include "algorithmAPI.h"
+#include "gpsAPI.h"
+#include "platformAPI.h"
+#include "userAPI.h"
+#include "osapi.h"
+
+#include "Indices.h"
+#include "GlobalConstants.h"
+
+#include "algorithm.h"
+#include "EKF_Algorithm.h"
+#include "BitStatus.h"
+#include "UserConfiguration.h"
+#include "bsp.h"
+#include "debug.h"
+
+#include "MagAlign.h"
+#include "sae_j1939.h"
+
+#define DEBUG_FREQ_0HZ 0
+#define DEBUG_FREQ_1HZ 1
+#define DEBUG_FREQ_2HZ 2
+#define DEBUG_FREQ_5HZ 5
+
+//
+static void _Algorithm(uint16_t dacqRate, uint8_t algoType);
+static void _InitAlgo(uint8_t algoType);
+
+#ifndef INS_OFFLINE
+static void _GenerateDebugMessage(uint16_t dacqRate, uint16_t debugOutputFreq);
+#endif // !INS_OFFLINE
+
+// Initialize GPS algorithm variables
+void InitUserAlgorithm()
+{
+ // Initialize built-in algorithm structure
+ InitializeAlgorithmStruct(FREQ_100_HZ);
+
+ setLeverArm( (real)gUserConfiguration.leverArmBx,
+ (real)gUserConfiguration.leverArmBy,
+ (real)gUserConfiguration.leverArmBz );
+ setPointOfInterest( (real)gUserConfiguration.pointOfInterestBx,
+ (real)gUserConfiguration.pointOfInterestBy,
+ (real)gUserConfiguration.pointOfInterestBz );
+
+}
+
+// Initialization variable
+int initAlgo = 1;
+odoDataStruct_t gOdo;
+
+void *RunUserNavAlgorithm(double *accels, double *rates, double *mags, gpsDataStruct_t *gps, uint16_t dacqRate)
+{
+
+ // This can be set at startup based on the packet type selected
+ static uint8_t algoType = INS;
+
+ // Initialize variable related to the UserNavAlgorithm
+ _InitAlgo(algoType);
+
+ // Populate the EKF input data structure
+ EKF_SetInputStruct(accels, rates, mags, gps, &gOdo, FALSE);
+
+ // Call the desired algorithm based on the EKF with different
+ // calling rates and different settings.
+ _Algorithm(dacqRate, algoType);
+
+ // Fill the output data structure with the EKF states and other
+ // desired information
+ OSDisableHook();
+ EKF_SetOutputStruct();
+ OSEnableHook();
+
+#ifndef INS_OFFLINE
+ // Generate a debug message that provides algorithm output to verify the
+ // algorithm is generating the proper output.
+ _GenerateDebugMessage(dacqRate, ZERO_HZ);
+#endif // !INS_OFFLINE
+
+ // The returned value from this function is unused by external functions. The
+ // NULL pointer is returned instead of a data structure.
+ return NULL;
+}
+
+//
+static void _InitAlgo(uint8_t algoType)
+{
+ // Initialize the timer variables
+ static uint8_t initAlgo = 1;
+ if(initAlgo) {
+ // Reset 'initAlgo' so this is not executed more than once. This
+ // prevents the algorithm from being switched during run-time.
+ initAlgo = 0;
+
+ // Set the configuration variables for a VG-type solution
+ // (useMags = 0 forces the VG solution)
+ gAlgorithm.Behavior.bit.freeIntegrate = 0;
+ gAlgorithm.Behavior.bit.useMag = 0;
+ gAlgorithm.Behavior.bit.useGPS = 0;
+ gAlgorithm.Behavior.bit.useOdo = 0;
+ gAlgorithm.Behavior.bit.restartOnOverRange = 0;
+ gAlgorithm.Behavior.bit.dynamicMotion = 1;
+
+ // Set the system configuration based on system type
+ switch( algoType ) {
+ case VG:
+ // Nothing additional to do (already configured for a VG
+ // solution)
+ break;
+ case AHRS:
+ // Set the configuration variables for AHRS solution
+ // (useMags = 1 and enable mags)
+ enableMagInAlgorithm(TRUE);
+ break;
+ case INS:
+ /* Set the configuration variables for INS solution.
+ * (Enable GPS and set algorithm calling frequency to 100Hz)
+ */
+ enableMagInAlgorithm(FALSE);
+ enableGpsInAlgorithm(TRUE);
+ gAlgorithm.callingFreq = FREQ_100_HZ; // redundant; set above
+ break;
+ default:
+ // Nothing to do
+ break;
+ }
+ }
+}
+
+
+
+//
+static void _Algorithm(uint16_t dacqRate, uint8_t algoType)
+{
+ // Aceinna VG/AHRS/INS algorithm
+ EKF_Algorithm();
+}
+
+#ifndef INS_OFFLINE
+//
+static void _GenerateDebugMessage(uint16_t dacqRate, uint16_t debugOutputFreq)
+{
+ // Variables that control the output frequency of the debug statement
+ static uint8_t debugOutputCntr, debugOutputCntrLimit;
+
+ // Check debug flag. If set then generate the debug message to verify
+ // the output of the EKF algorithm
+ if( debugOutputFreq > ZERO_HZ ) {
+ // Initialize variables used to control the output of the debug messages
+ static int initFlag = 1;
+ if(initFlag) {
+ // Reset 'initFlag' so this section is not executed more than once.
+ initFlag = 0;
+
+ // Set the variables that control the debug-message output-rate (based on
+ // the desired calling frequency of the debug output)
+ debugOutputCntrLimit = (uint8_t)( (float)dacqRate / (float)debugOutputFreq + 0.5 );
+ debugOutputCntr = debugOutputCntrLimit;
+ }
+
+ debugOutputCntr++;
+ if(debugOutputCntr >= debugOutputCntrLimit) {
+ debugOutputCntr = 0;
+#if 1
+ // For testing, the output packet should contain:
+ // 1) ITOW
+ // 2) Euler Angles
+ // 3) Ang-rate (meas)
+ // 4) Est ang-rate bias
+ // 5) Accel (meas)
+ // 6) Est accel bias
+ // 7) LLA (est)
+ // 8) NED-Vel (est)
+ // 9) Oper mode
+
+ DebugPrintLongInt("", gGPS.itow );
+
+ DebugPrintFloat(", ", gEKFOutput.eulerAngs_BinN[ROLL], 4);
+ DebugPrintFloat(", ", gEKFOutput.eulerAngs_BinN[PITCH], 4);
+ DebugPrintFloat(", ", gEKFOutput.eulerAngs_BinN[YAW], 4);
+
+ DebugPrintFloat(", ", gEKFInput.angRate_B[X_AXIS], 5);
+ DebugPrintFloat(", ", gEKFInput.angRate_B[Y_AXIS], 5);
+ DebugPrintFloat(", ", gEKFInput.angRate_B[Z_AXIS], 5);
+
+ DebugPrintFloat(", ", gEKFOutput.angRateBias_B[X_AXIS], 5);
+ DebugPrintFloat(", ", gEKFOutput.angRateBias_B[Y_AXIS], 5);
+ DebugPrintFloat(", ", gEKFOutput.angRateBias_B[Z_AXIS], 5);
+
+ DebugPrintFloat(", ", gEKFInput.accel_B[X_AXIS], 5);
+ DebugPrintFloat(", ", gEKFInput.accel_B[Y_AXIS], 5);
+ DebugPrintFloat(", ", gEKFInput.accel_B[Z_AXIS], 5);
+
+ DebugPrintFloat(", ", gEKFOutput.accelBias_B[X_AXIS], 5);
+ DebugPrintFloat(", ", gEKFOutput.accelBias_B[Y_AXIS], 5);
+ DebugPrintFloat(", ", gEKFOutput.accelBias_B[Z_AXIS], 5);
+
+ DebugPrintFloat(", ", gEKFOutput.llaDeg[LAT], 8);
+ DebugPrintFloat(", ", gEKFOutput.llaDeg[LON], 8);
+ DebugPrintFloat(", ", gEKFOutput.llaDeg[ALT], 5);
+
+ DebugPrintFloat(", ", gEKFOutput.velocity_N[X_AXIS], 5);
+ DebugPrintFloat(", ", gEKFOutput.velocity_N[Y_AXIS], 5);
+ DebugPrintFloat(", ", gEKFOutput.velocity_N[Z_AXIS], 5);
+#if 1
+ DebugPrintInt(", ", gEKFOutput.opMode);
+#else
+ switch(gEKFOutputData.opMode) {
+ case 0:
+ DebugPrintString(", Stab");
+ break;
+ case 1:
+ DebugPrintString(", Init");
+ break;
+ case 2:
+ DebugPrintString(", HG");
+ break;
+ case 3:
+ DebugPrintString(", LG");
+ break;
+ case 4:
+ DebugPrintString(", INS");
+ break;
+ }
+#endif
+ DebugPrintEndline();
+#else
+ //
+ DebugPrintLongInt("ITOW: ", gGPS.itow );
+ // LLA
+ DebugPrintFloat(", valid: ", (float)gGPS.gpsValid, 1);
+ // LLA
+ DebugPrintFloat(", Lat: ", (float)gGPS.latitude, 8);
+ DebugPrintFloat(", Lon: ", (float)gGPS.longitude, 8);
+ DebugPrintFloat(", Alt: ", (float)gGPS.altitude, 5);
+ // Velocity
+ //DebugPrintFloat(", vN: ", (float)gGPS.vNed[X_AXIS], 5);
+ //DebugPrintFloat(", vE: ", (float)gGPS.vNed[Y_AXIS], 5);
+ //DebugPrintFloat(", vD: ", (float)gGPS.vNed[Z_AXIS], 5);
+ // v^2
+ //double vSquared = gGPS.vNed[X_AXIS] * gGPS.vNed[X_AXIS] +
+ // gGPS.vNed[Y_AXIS] * gGPS.vNed[Y_AXIS];
+ //DebugPrintFloat(", vSq: ", (float)vSquared, 5);
+ //DebugPrintFloat(", vSq: ", (float)gGPS.rawGroundSpeed * (float)gGPS.rawGroundSpeed, 5);
+ // Newline
+ DebugPrintEndline();
+#endif
+ }
+ }
+}
+#endif // !INS_OFFLINE
diff --git a/examples/OpenIMU300RI/INS/src/user/UserAlgorithm.h b/examples/OpenIMU300RI/INS/src/user/UserAlgorithm.h
new file mode 100644
index 0000000..1c8c3d6
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/src/user/UserAlgorithm.h
@@ -0,0 +1,13 @@
+/*
+ * File: UserAlgorithm.h
+ * Author: joemotyka
+ *
+ * Created on June 28, 2018, 12:23 AM
+ */
+
+#ifndef _USER_ALGORITHM_H_
+#define _USER_ALGORITHM_H_
+
+
+#endif /* _USER_ALGORITHM_H_ */
+
diff --git a/examples/OpenIMU300RI/INS/src/user/UserConfiguration.c b/examples/OpenIMU300RI/INS/src/user/UserConfiguration.c
new file mode 100644
index 0000000..613a67f
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/src/user/UserConfiguration.c
@@ -0,0 +1,401 @@
+/** ***************************************************************************
+ * @file UserConfiguration.c
+ *
+ * THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
+ * KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
+ * PARTICULAR PURPOSE.
+ *
+ ******************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+
+#include "string.h"
+
+#include "algorithmAPI.h"
+#include "gpsAPI.h"
+#include "magAPI.h"
+#include "platformAPI.h"
+#include "userAPI.h"
+
+#include "UserConfiguration.h"
+#include "eepromAPI.h"
+#include "Indices.h"
+#include "sae_j1939.h"
+
+EcuConfigurationStruct *gEcuConfigPtr;
+
+
+// Default user configuration structure
+// Applied to unit upon reception of "zR" command
+// Do Not remove - just add extra parameters if needed
+// Change default settings if desired
+const UserConfigurationStruct gDefaultUserConfig = {
+ .dataCRC = 0,
+ .dataSize = sizeof(UserConfigurationStruct),
+ .ecuAddress = 128,
+ .ecuBaudRate = _ECU_250K,
+ .ecuPacketRate = 10, // 10Hz
+ .ecuFilterFreqAccel = 25,
+ .ecuFilterFreqRate = 25,
+
+ .ecuPacketType = ( ACEINNA_SAE_J1939_PACKET_SLOPE_SENSOR |
+ ACEINNA_SAE_J1939_PACKET_ANGULAR_RATE |
+ ACEINNA_SAE_J1939_PACKET_ACCELERATION |
+ ACEINNA_SAE_J1939_PACKET_RAPID_COURSE_UPDATE |
+ ACEINNA_SAE_J1939_PACKET_ATTITUDE |
+ ACEINNA_SAE_J1939_PACKET_RAPID_POSITION_UPDATE
+ ),
+
+// .ecuPacketType = 0,
+ .ecuOrientation = 0, // +X +Y +Z
+ .canTermResistorEnabled = 0,
+ .canBaudRateDetectEnabled = 0,
+ .userBehavior =
+ USER_BEHAVIOR_RUN_ALGORITHM_MASK | // algorithm enabled
+ USER_BEHAVIOR_USE_GNSS_OVER_CAN | // gnss input data coming over CAN bus
+ USER_BEHAVIOR_USE_MAGS_MASK | // if usage of mags desired
+ USER_BEHAVIOR_DUMMY_MASK,
+ .algResetPs = 0,
+ .saveCfgPs = 0,
+ .packetTypePs = 0,
+ .packetRatePs = 0,
+ .filterPs = 0,
+ .orientationPs = 0,
+ .userBehvPs = 0,
+ .statusPs = 0,
+//***********************************************
+// INS - related parameters
+//***********************************************
+ .gpsBaudRate = 9600,
+ .gpsProtocol = UBLOX_BINARY,
+ .hardIron_X = 0.0,
+ .hardIron_Y = 0.0,
+ .softIron_Ratio = 1.0,
+ .softIron_Angle = 0.0,
+ .leverArmBx = 0.0,
+ .leverArmBy = 0.0,
+ .leverArmBz = 0.0,
+ .pointOfInterestBx = 0.0,
+ .pointOfInterestBy = 0.0,
+ .pointOfInterestBz = 0.0,
+ // add default parameter values here, if desired
+};
+
+UserConfigurationStruct gUserConfiguration;
+UserConfigurationStruct gTmpUserConfiguration;
+
+uint8_t UserDataBuffer[4096];
+volatile char *info;
+BOOL configValid = FALSE;
+
+void setUserMagAlignParams(magAlignUserParams_t *params)
+{
+ gUserConfiguration.hardIron_X = params->hardIron_X;
+ gUserConfiguration.hardIron_Y = params->hardIron_Y;
+ gUserConfiguration.softIron_Ratio = params->softIron_Ratio;
+ gUserConfiguration.softIron_Angle = params->softIron_Angle;
+}
+
+void getUserMagAlignParams(magAlignUserParams_t *params)
+{
+ params->hardIron_X = gUserConfiguration.hardIron_X;
+ params->hardIron_Y = gUserConfiguration.hardIron_Y;
+ params->softIron_Ratio = gUserConfiguration.softIron_Ratio;
+ params->softIron_Angle = gUserConfiguration.softIron_Angle;
+}
+
+
+void userInitConfigureUnit()
+{
+ int size = sizeof(gUserConfiguration); // total size in bytes
+
+ // sanity check for maximum size of user config structure;
+ if(size >= 0x4000){
+ while(1);
+ }
+
+ if(EEPROM_IsAppStartedFirstTime()) {
+ // comment next line if want to keep previously stored in EEPROM parameters
+ // after rebuilding and/or reloading new application
+ LoadDefaultUserConfig(TRUE);
+ }
+
+ // Validate checksum of user configuration structure
+ configValid = EEPROM_ValidateUserConfig(&size);
+
+ if(configValid == TRUE){
+ // Here we have validated User configuration image.
+ // Load it from eeprom into ram on top of the default configuration
+ EEPROM_LoadUserConfig((void*)&gUserConfiguration, &size);
+ }else{
+ LoadDefaultUserConfig(FALSE);
+ }
+
+ // assign new actual size
+ gUserConfiguration.dataSize = sizeof(UserConfigurationStruct);
+ memset(&gEcuConfig, 0, sizeof(gEcuConfig));
+
+ ApplyEcuSettings(&gEcuConfig);
+
+ if(EEPROM_IsUserApplicationActive())
+ {
+ ApplySystemParameters(&gEcuConfig);
+ }
+
+#ifndef GPS_OVER_CAN
+ SetGpsBaudRate((int) gUserConfiguration.gpsBaudRate, TRUE);
+ SetGpsProtocol((int) gUserConfiguration.gpsProtocol, TRUE);
+#endif
+
+
+ info = getBuildInfo();
+}
+
+
+/** ***************************************************************************
+ * @name SaveUserConfig - saving of user configuration structure un the
+ * predefined flash sector
+ * @brief
+ *
+ * @param [in] N/A
+ * @retval error (0), no error (1)
+ ******************************************************************************/
+BOOL SaveUserConfig(void)
+{
+ int size;
+ BOOL status;
+
+ size = sizeof(UserConfigurationStruct);
+ status = EEPROM_SaveUserConfig((uint8_t *)&gUserConfiguration, size);
+
+ if(status){
+ return TRUE;
+ }
+
+ return FALSE;
+
+}
+
+
+BOOL LoadDefaultUserConfig(BOOL fSave)
+{
+ BOOL valid = TRUE;
+ // Load default user configuration
+ memcpy((void*)&gUserConfiguration, (void*)&gDefaultUserConfig, sizeof(UserConfigurationStruct));
+
+ if(!fSave){
+ return TRUE;
+ }
+
+ if(!SaveUserConfig()){
+ valid = FALSE;
+ }
+ return valid;
+}
+
+
+/** ***************************************************************************
+ * @name user_config_save() save current configuration to EEPROM while getting
+ * config save request
+* @brief write global parameters of configuration in RAM to EEPROM
+ *
+ * @param [in]
+ * @retval 1 successfuk or 0 failure
+ ******************************************************************************/
+BOOL UpdateEcuConfig(EcuConfigurationStruct *gEcuConfigPtr, BOOL fSave)
+{
+ // address, baud rate, new PS, orientation and lpf
+ gUserConfiguration.ecuAddress = (uint16_t)gEcuConfigPtr->address;
+ gUserConfiguration.ecuBaudRate = (uint16_t)gEcuConfigPtr->baudRate;
+
+ gUserConfiguration.algResetPs = gEcuConfigPtr->alg_reset_ps;
+ gUserConfiguration.saveCfgPs = gEcuConfigPtr->save_cfg_ps;
+ gUserConfiguration.statusPs = gEcuConfigPtr->status_ps;
+ gUserConfiguration.packetRatePs = gEcuConfigPtr->packet_rate_ps;
+ gUserConfiguration.packetTypePs = gEcuConfigPtr->packet_type_ps;
+ gUserConfiguration.filterPs = gEcuConfigPtr->digital_filter_ps;
+ gUserConfiguration.orientationPs = gEcuConfigPtr->orientation_ps;
+ gUserConfiguration.userBehvPs = gEcuConfigPtr->user_behavior_ps;
+ gUserConfiguration.magAlignPs = gEcuConfigPtr->mag_align_ps;
+
+ if(fSave){
+ return SaveUserConfig();
+ }
+
+ return TRUE;
+}
+
+BOOL SaveEcuConfig(EcuConfigurationStruct *gEcuConfigPtr)
+{
+ return UpdateEcuConfig(gEcuConfigPtr, TRUE);
+}
+
+void SaveEcuAddress(uint16_t address)
+{
+ gUserConfiguration.ecuAddress = address;
+ SaveUserConfig();
+}
+
+
+/** ***************************************************************************
+ * @name is_valid_config_command() check incoming SET packets are valid or invalid
+ * @brief a general API of checking supported SET commands
+ *
+ * @param [in] ident, identifier message
+ *
+ * @retval ACEINNA_J1939_INVALID_IDENTIFIER, ACEINNA_J1939_CONFIG or ACEINNA_J1939_IGNORE
+ ******************************************************************************/
+ACEINNA_J1939_PACKET_TYPE is_valid_config_command(SAE_J1939_IDENTIFIER_FIELD *ident)
+{
+ uint8_t pf_val, ps_val;
+
+ if (ident == NULL)
+ return ACEINNA_J1939_INVALID_IDENTIFIER;
+
+ pf_val = ident->pdu_format;
+ ps_val = ident->pdu_specific;
+
+ if (
+ (pf_val == SAE_J1939_PDU_FORMAT_GLOBAL) &&
+ (
+ ((ps_val >= SAE_J1939_GROUP_EXTENSION_ALGORITHM_RESET) && (ps_val <= SAE_J1939_GROUP_EXTENSION_ACCELERATION_PARAM)) ||
+ (ps_val == SAE_J1939_GROUP_EXTENSION_BANK0) ||
+ (ps_val == SAE_J1939_GROUP_EXTENSION_BANK1) ||
+ (ps_val == gEcuConfig.alg_reset_ps) ||
+ (ps_val == gEcuConfig.status_ps) ||
+ (ps_val == gEcuConfig.packet_rate_ps) ||
+ (ps_val == gEcuConfig.packet_type_ps) ||
+ (ps_val == gEcuConfig.digital_filter_ps) ||
+ (ps_val == gEcuConfig.mag_align_ps) ||
+ (ps_val == gEcuConfig.orientation_ps))
+ ) {
+ return ACEINNA_J1939_CONFIG;
+ }
+
+ return ACEINNA_J1939_IGNORE;
+}
+
+uint8_t GetEcuAddress()
+{
+ return gUserConfiguration.ecuAddress;
+}
+
+int GetEcuBaudRate()
+{
+ return gUserConfiguration.ecuBaudRate;
+}
+
+void SetEcuBaudRate(_ECU_BAUD_RATE rate )
+{
+ gUserConfiguration.ecuBaudRate = rate;
+}
+
+void SetEcuPacketType(uint16_t type)
+{
+ gUserConfiguration.ecuPacketType = type;
+}
+
+void SetEcuPacketRate(uint16_t rate)
+{
+ gUserConfiguration.ecuPacketRate = rate;
+}
+
+void SetEcuFilterFreq(EcuConfigurationStruct *pEcuConfig)
+{
+ platformSelectLPFilter(RATE_SENSOR, pEcuConfig->rate_cut_off, TRUE);
+ platformSelectLPFilter(ACCEL_SENSOR, pEcuConfig->accel_cut_off, TRUE);
+ gUserConfiguration.ecuFilterFreqAccel = pEcuConfig->accel_cut_off;
+ gUserConfiguration.ecuFilterFreqRate = pEcuConfig->rate_cut_off;
+}
+
+void SetEcuOrientation(uint16_t orien_bits)
+{
+ if(platformApplyOrientation(orien_bits)){
+ gUserConfiguration.ecuOrientation = orien_bits;
+ }
+}
+
+
+void ApplyEcuSettings(void *pConfig)
+{
+ EcuConfigurationStruct *pEcuConfig = (EcuConfigurationStruct *)pConfig;
+
+ // Add/Remove/Verify ECU-specific parameters here
+ pEcuConfig->address = gUserConfiguration.ecuAddress;
+ pEcuConfig->baudRate = gUserConfiguration.ecuBaudRate;
+ pEcuConfig->packet_rate = gUserConfiguration.ecuPacketRate;
+ pEcuConfig->accel_cut_off = gUserConfiguration.ecuFilterFreqAccel;
+ pEcuConfig->rate_cut_off = gUserConfiguration.ecuFilterFreqRate;
+ pEcuConfig->packet_type = gUserConfiguration.ecuPacketType;
+ pEcuConfig->orien_bits = gUserConfiguration.ecuOrientation;
+
+ // Add/Remove/Verify payload specific codes here
+ // If Payload-specific code here is zero - it will be substituted by predefined code
+ // in function initialize_j1939_config(uint16_t baudRate, uint8_t address)
+
+ pEcuConfig->alg_reset_ps = gUserConfiguration.algResetPs;
+ pEcuConfig->save_cfg_ps = gUserConfiguration.saveCfgPs;
+ pEcuConfig->packet_type_ps = gUserConfiguration.packetTypePs;
+ pEcuConfig->packet_rate_ps = gUserConfiguration.packetRatePs;
+ pEcuConfig->digital_filter_ps = gUserConfiguration.filterPs;
+ pEcuConfig->orientation_ps = gUserConfiguration.orientationPs;
+ pEcuConfig->user_behavior_ps = gUserConfiguration.userBehvPs;
+ pEcuConfig->status_ps = gUserConfiguration.statusPs;
+ pEcuConfig->mag_align_ps = gUserConfiguration.magAlignPs;
+
+}
+
+
+BOOL CanTermResistorEnabled()
+{
+ return gUserConfiguration.canTermResistorEnabled != 0;
+}
+
+BOOL CanBaudRateDetectionEnabled()
+{
+ return gUserConfiguration.canBaudRateDetectEnabled != 0;
+}
+
+BOOL UseAlgorithm()
+{
+ return (gUserConfiguration.userBehavior & USER_BEHAVIOR_RUN_ALGORITHM_MASK) != 0? TRUE : FALSE;
+}
+
+BOOL UseMags()
+{
+ return (gUserConfiguration.userBehavior & USER_BEHAVIOR_USE_MAGS_MASK) != 0? TRUE : FALSE;
+}
+
+BOOL GnssInputDataOverCan()
+{
+ return (gUserConfiguration.userBehavior & USER_BEHAVIOR_USE_GNSS_OVER_CAN) != 0? TRUE : FALSE;
+}
+
+
+void ApplySystemParameters(void *pConfig)
+{
+ EcuConfigurationStruct *pEcuConfig = (EcuConfigurationStruct *)pConfig;
+
+ platformSelectLPFilter(RATE_SENSOR, pEcuConfig->rate_cut_off, TRUE);
+ platformSelectLPFilter(ACCEL_SENSOR, pEcuConfig->accel_cut_off, TRUE);
+ platformApplyOrientation(pEcuConfig->orien_bits);
+ if(UseMags()){
+ platformForceMagUsage();
+ }
+ userInitConfigureUart();
+}
+
diff --git a/examples/OpenIMU300RI/INS/src/user/UserConfiguration.h b/examples/OpenIMU300RI/INS/src/user/UserConfiguration.h
new file mode 100644
index 0000000..56506fb
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/src/user/UserConfiguration.h
@@ -0,0 +1,209 @@
+/*******************************************************************************
+ * File: UserConfiguration.h
+ * Created on JAn 25, 2017
+ ******************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+
+#ifndef USER_CONFIGURATION_H
+#define USER_CONFIGURATION_H
+
+#include
+
+#include "GlobalConstants.h"
+#include "filter.h"
+
+/// User defined configuration strucrture
+///Please notice, that parameters are 64 bit to accomodate double types as well as longer string types
+
+typedef struct {
+ uint64_t dataCRC; // CRC of user configuration structure CRC-16
+ uint64_t dataSize; // Size of the user configuration structure
+
+ uint16_t ecuAddress; // ecu address
+ uint16_t ecuBaudRate; // ecu baudrate - 250, 500, 1000
+ uint16_t ecuPacketRate; // divider for 200Hz tick
+ uint16_t ecuFilterFreqAccel; // accels cutoff frequency for digital filter
+ uint16_t ecuFilterFreqRate; // rates cutoff frequency for digital filter
+ uint16_t ecuPacketType; // packet types being transmitted
+ uint16_t canTermResistorEnabled; // enable/disable CAN termination resistor
+ uint16_t canBaudRateDetectEnabled; // enable/disable CAN baud rate auto detection
+ uint16_t ecuOrientation; // unit orientation
+ //0 +Z +Y +X
+ //9 +Z -Y -X
+ // 35 +Z +X +Y
+ // 42 +Z -X +Y
+ // 65 -Z +Y -X
+ // 72 -Z -Y +X
+ // 98 -Z +X +Y
+ // 107 -Z -X -Y
+ // 133 +X +Y -Z
+ // 140 +X -Y +Z
+ // 146 +X +Z +Y
+ // 155 +X -Z -Y
+ // 196 -X +Y +Z
+ // 205 -X -Y -Z
+ // 211 -X +Z -Y
+ // 218 -X -Z +Y
+ // 273 +Y +Z -X
+ // 280 +Y -Z +X
+ // 292 +Y +X +Z
+ // 301 +Y -X -Z
+ // 336 -Y +Z +X
+ // 345 -Y -Z -X
+ // 357 -Y +X -Z
+ // 364 -Y -X +Z
+ uint16_t userBehavior; // user algorithm behaviour
+
+ uint16_t statusPs; // ps value of status message
+ uint16_t algResetPs; // ps value of alg reset
+ uint16_t saveCfgPs; // ps value of config save
+ uint16_t packetRatePs; // ps value of packet type
+ uint16_t packetTypePs; // ps value of packet type
+ uint16_t filterPs; // ps value of lpf
+ uint16_t orientationPs; // ps value of orientation
+ uint16_t userBehvPs; // ps value of user behavior
+ uint16_t magAlignPs; // ps value of mag align command
+ int64_t gpsBaudRate; /// baudrate of GPS UART, bps.
+ /// valid options are:
+ /// 4800
+ /// 9600
+ /// 19200
+ /// 38400
+ /// 57600
+ /// 115200
+ /// 230400
+ int64_t gpsProtocol; /// protocol of GPS receicer.
+ /// so far valid options are:
+ /// NMEA_TEXT
+ /// NOVATEL_BINARY
+ double hardIron_X;
+ double hardIron_Y;
+ double softIron_Ratio;
+ double softIron_Angle;
+ double leverArmBx;
+ double leverArmBy;
+ double leverArmBz;
+ double pointOfInterestBx;
+ double pointOfInterestBy;
+ double pointOfInterestBz;
+
+} UserConfigurationStruct;
+
+/// User defined configuration strucrture
+///Please notice, that parameters are 64 bit to accomodate double types as well as longer string types
+
+typedef struct {
+ uint64_t dataCRC; /// CRC of user configuration structure CRC-16
+ uint64_t dataSize; /// Size of the user configuration structure
+
+ int64_t userUartBaudRate; /// baudrate of user UART, bps.
+ /// valid options are:
+ /// 4800
+ /// 9600
+ /// 19200
+ /// 38400
+ /// 57600
+ /// 115200
+ /// 230400
+ /// 460800
+ uint8_t userPacketType[8]; /// User packet to be continiously sent by unit
+ /// Packet types defined in structure UserOutPacketType
+ /// in file UserMessaging.h
+
+ int64_t userPacketRate; /// Packet rate for continiously output packet, Hz.
+ /// Valid settings are: 0 ,2, 5, 10, 20, 25, 50, 100, 200
+
+ int64_t lpfAccelFilterFreq; /// built-in lpf filter cutoff frequency selection for accelerometers
+ int64_t lpfRateFilterFreq; /// built-in lpf filter cutoff frequency selection for rate sensors
+ /// Options are:
+ /// 0 - Filter turned off
+ /// 50 - Butterworth LPF 50HZ
+ /// 20 - Butterworth LPF 20HZ
+ /// 10 - Butterworth LPF 10HZ
+ /// 05 - Butterworth LPF 5HZ
+ /// 02 - Butterworth LPF 2HZ
+ /// 25 - Butterworth LPF 25HZ
+ /// 40 - Butterworth LPF 40HZ
+
+ uint8_t orientation[8]; /// unit orientation in format 0x0000000000ddrrff
+ /// where dd - down axis, rr - right axis, ff - forward axis
+ /// next axis values a valid :
+ /// 'X' (0x58) -> plus X, 'Y' (0x59) -> plus Y, 'Z' (0x5a) -> plus Z
+ /// 'x' (0x78) -> minus X, 'y' (0x79) -> minus Y, 'z' (0x7a) ->minusZ
+
+ //***************************************************************************************
+ // here is the border between arbitrary parameters and platform configuration parameters
+ //***************************************************************************************
+
+ // place new arbitrary configuration parameters here
+ // parameter size should even to 8 bytes
+ // Add parameter offset in UserConfigParamOffset structure if validation or
+ // special processing required
+
+} UserConfigurationUartStruct;
+
+enum{
+//*****************************************************************************************
+// These parateters are not saved into eeprom as of yet
+ USER_UART_CRC = 0,
+ USER_UART_CONFIG_SIZE , // 1
+ USER_UART_BAUD_RATE , // 2
+ USER_UART_PACKET_TYPE , // 3
+ USER_UART_PACKET_RATE , // 4
+ USER_UART_LPF_ACCEL_TYPE , // 5 prefered LPF filter type for accelerometer
+ USER_UART_LPF_RATE_TYPE , // 6 prefered LPF filter type for rate sensor
+ USER_UART_ORIENTATION , // 7 unit orientation
+ USER_UART_MAX_PARAM // 8
+};
+
+
+#define MAX_SYSTEM_PARAM USER_ORIENTATION
+
+extern int userPacketOut;
+
+#define USER_OK 0x00
+#define USER_NAK 0x80
+#define USER_INVALID 0x81
+
+#define INVALID_PARAM -1
+#define INVALID_VALUE -2
+#define INVALID_PAYLOAD_SIZE -3
+
+#define USER_BEHAVIOR_DUMMY_MASK 0x0000 // to conveniently select default behavior
+#define USER_BEHAVIOR_RUN_ALGORITHM_MASK 0x0001
+#define USER_BEHAVIOR_USE_MAGS_MASK 0x0002
+#define USER_BEHAVIOR_USE_GNSS_OVER_CAN 0x0004
+// define additional algorithm flavours here
+
+extern UserConfigurationStruct gUserConfiguration;
+
+extern void InitializeUserAlgorithmParams(void);
+extern BOOL validateUserConfigInEeprom(int *numParams);
+extern uint32_t getUserParamFromEeprom(uint32_t offset);
+extern BOOL saveUserConfigInEeprom(uint8_t *ptrToUserConfigStruct, int userConfigStructLen);
+extern BOOL checkIfUserEEPROMErased(void);
+extern BOOL loadUserConfigFromEeprom(uint8_t *ptrToUserConfigInRam, int *userConfigSize);
+extern BOOL SaveUserConfig(void);
+extern BOOL LoadDefaultUserConfig(BOOL fSave);
+extern void ApplyEcuSettings(void* pEcuConfig);
+extern void ApplySystemParameters(void* pEcuConfig);
+
+
+
+#endif /* USER_CONFIGURATION_H */
+
+
diff --git a/examples/OpenIMU300RI/INS/src/user/UserConfigurationUart.c b/examples/OpenIMU300RI/INS/src/user/UserConfigurationUart.c
new file mode 100644
index 0000000..b564b3f
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/src/user/UserConfigurationUart.c
@@ -0,0 +1,364 @@
+/** ***************************************************************************
+ * @file UserConfiguration.c
+ *
+ * THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
+ * KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
+ * PARTICULAR PURPOSE.
+ *
+ ******************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+
+#include "string.h"
+#include "magAPI.h"
+#include "platformAPI.h"
+#include "UserConfiguration.h"
+#include "UserMessagingUART.h"
+#include "Indices.h"
+#include "eepromAPI.h"
+
+// Default user configuration structure
+// Not save4d to EEPROM so far
+// Do Not remove - just add extra parameters if needed
+// Change default settings if desired
+UserConfigurationUartStruct gUserUartConfig = {
+ .dataCRC = 0,
+ .dataSize = sizeof(UserConfigurationUartStruct),
+ .userUartBaudRate = 115200, // needs to be changed to 230400 for e1 and e2 packets at 100 Hz
+ .userPacketType = "z1",
+ .userPacketRate = 0,
+ .lpfAccelFilterFreq = 25,
+ .lpfRateFilterFreq = 25,
+ .orientation = "+X+Y+Z",
+ // add default parameter values here, if desired
+};
+
+uint8_t UserDataBuffer[4096];
+static volatile char *info;
+
+
+
+/** ***************************************************************************
+ * @name UpdateSystemParameter - updating of system configuration parameter based of user preferences
+ * @brief
+ *
+ * @param [in] number - parameter number in user configuration structure
+ * @param [in] data - value of the parameter in little endian format
+ * @retval error (1), no error (0)
+ ******************************************************************************/
+// NEEDS TO BE CHECKED
+BOOL UpdateSystemParameter(uint32_t number, uint64_t data, BOOL fApply)
+{
+ BOOL result = TRUE;
+ uint64_t *ptr = (uint64_t *)&gUserUartConfig;
+
+ if(number < USER_UART_CRC || number >= USER_UART_MAX_PARAM ){
+ return FALSE;
+ }
+
+ switch (number) {
+ case USER_UART_BAUD_RATE:
+ result = platformSetBaudRate((int)data, fApply);
+ break;
+ case USER_UART_PACKET_TYPE:
+ result = setUserPacketType((uint8_t*)&data, fApply);
+ break;
+ case USER_UART_PACKET_RATE:
+ result = platformSetPacketRate((int)data, fApply);
+ break;
+ case USER_UART_CRC:
+ case USER_UART_CONFIG_SIZE:
+ return TRUE;
+
+ // case USER_XXX: add function calls here if parameter XXXX
+ // required be updated on the fly
+ // break;
+ default:
+ // by default result should be FALSE for system parameter
+ result = FALSE;
+ break;
+ }
+
+ if(result == TRUE){
+ ptr[number] = data;
+ }
+
+ return result;
+}
+
+
+void userInitConfigureUart()
+{
+
+ uint64_t *ptr = (uint64_t*)&gUserUartConfig;
+
+ // apply parameters to the platform
+ for(int i = USER_UART_BAUD_RATE; i < USER_UART_MAX_PARAM; i++){
+ UpdateSystemParameter(i, ptr[i], TRUE);
+ }
+
+ info = getBuildInfo();
+}
+
+
+
+/** ****************************************************************************
+ * @name UpdateUserConfig
+ * @brief writes user data into user configuration structure, validates data if
+ * required, updates system parameters
+ *
+ * @param [in] pointer to userData payload in the packet
+ * @retval N/A
+ ******************************************************************************/
+BOOL UpdateUserConfig(userConfigPayload* pld, uint8_t *payloadLen)
+{
+ uint32_t offset, i;
+ BOOL offsetValid = TRUE;
+ BOOL lenValid = TRUE;
+ BOOL numValid = TRUE;
+ BOOL ret = TRUE;
+ int32_t result = 0;
+
+ // Validate parameters numbers and quantity
+ if(pld->numParams >= USER_UART_MAX_PARAM){
+ lenValid = FALSE;
+ result = INVALID_PAYLOAD_SIZE;
+ }
+
+
+ if((pld->numParams + pld->paramOffset) >= USER_UART_MAX_PARAM){
+ numValid = FALSE;
+ result = INVALID_PARAM;
+ }
+
+ if(offsetValid && numValid && lenValid){
+ // Validate parameters values first
+ offset = pld->paramOffset;
+ for (i = 0; i < pld->numParams && ret; i++){
+ ret = UpdateSystemParameter(offset, pld->parameters[i], FALSE);
+ offset++;
+ }
+ if(ret == TRUE){
+ // Apply parameters values here
+ offset = pld->paramOffset;
+ for (i = 0; i < pld->numParams; i++){
+ ret = UpdateSystemParameter(offset, pld->parameters[i], TRUE);
+ offset++;
+ }
+ }
+ }
+
+ if(ret == FALSE){
+ result = INVALID_VALUE;
+ }
+
+ pld->numParams = result;
+ *payloadLen = 4;
+
+ return TRUE;
+}
+
+
+/** ****************************************************************************
+ * @name UpdateUserParam
+ * @brief writes user data into user configuration structure, validates data if
+ * required, updates system parameters
+ *
+ * @param [in] pointer to userData payload in the packet
+ * @retval N/A
+ ******************************************************************************/
+BOOL UpdateUserParam(userParamPayload* pld, uint8_t *payloadLen)
+{
+ BOOL offsetValid;
+ BOOL ret = TRUE;
+ int32_t result = 0;
+
+ offsetValid = pld->paramNum <= USER_UART_MAX_PARAM;
+
+ if(offsetValid){
+ // Validate parameter first
+ ret = UpdateSystemParameter(pld->paramNum, pld->parameter, FALSE);
+ if(ret == TRUE){
+ // Apply parameter if valid
+ ret = UpdateSystemParameter(pld->paramNum, pld->parameter, TRUE);
+ }else{
+ result = INVALID_VALUE;
+ }
+ } else {
+ result = INVALID_PARAM;
+ }
+
+ pld->paramNum = result;
+ *payloadLen = 4;
+
+ return TRUE;
+}
+
+
+/** ****************************************************************************
+ * @name UpdateAllUserParams
+ * @brief writes user data into user configuration structure, validates data if
+ * required, updates system parameters
+ *
+ * @param [in] pointer to userData payload in the packet
+ * @retval N/A
+ ******************************************************************************/
+/** ****************************************************************************
+ * @name UpdateUserConfig
+ * @brief writes user data into user configuration structure, validates data if
+ * required, updates system parameters
+ *
+ * @param [in] pointer to userData payload in the packet
+ * @retval N/A
+ ******************************************************************************/
+BOOL UpdateAllUserParams(allUserParamsPayload* pld, uint8_t *payloadLen)
+{
+ uint32_t offset, i;
+ BOOL numValid = TRUE;
+ BOOL ret = TRUE;
+ int32_t result = 0;
+
+ int numParams = (*payloadLen)/8;
+
+ if(numParams > USER_UART_MAX_PARAM){
+ numValid = FALSE;
+ result = INVALID_PAYLOAD_SIZE;
+ }
+
+
+ if(numValid){
+ // Validate parameters here
+ offset = 0;
+ for (i = 0; i < numParams && ret; i++){
+ ret = UpdateSystemParameter(offset, pld->parameters[i], FALSE);
+ offset++;
+ }
+ if(ret == TRUE){
+ // Apply parameters here
+ offset = 0;
+ for (i = 0; i < numParams; i++){
+ UpdateSystemParameter(offset, pld->parameters[i], TRUE);
+ offset++;
+ }
+ }
+ }
+
+ if(ret == FALSE){
+ result = INVALID_VALUE;
+ }
+
+ pld->parameters[0] = result;
+ *payloadLen = 4; // return error code
+
+ return TRUE;
+
+}
+
+
+/** ****************************************************************************
+ * @name GetUserConfig
+ * @brief Retrieves specified number of user configuration parameters data for
+ * sending to the external host starting from specified offset in user
+ * configuration structure (refer to UserConfigParamOffset structure for
+ * specific value of offsets)
+ * @param [in] pointer to userData payload in the packet
+ * @retval N/A
+ ******************************************************************************/
+BOOL GetUserConfig(userConfigPayload* pld, uint8_t *payloadLen)
+{
+ uint32_t offset, i;
+ BOOL lenValid = TRUE;
+ uint64_t *ptr = (uint64_t *)&gUserUartConfig;
+
+ lenValid = (pld->numParams + pld->paramOffset) <= USER_UART_MAX_PARAM;
+
+ if(lenValid){
+ offset = pld->paramOffset;
+ for (i = 0; i < pld->numParams; i++, offset++)
+ {
+ pld->parameters[i] = ptr[offset];
+ }
+ *payloadLen = (pld->numParams + 1) * 8;
+ } else {
+ *payloadLen = 4;
+ pld->numParams = INVALID_PARAM;
+ }
+
+ return TRUE;
+
+}
+
+
+/** ****************************************************************************
+ * @name GetUserParam
+ * @brief Retrieves specified number of user configuration parameters data for
+ * sending to the external host starting from specified offset in user
+ * configuration structure (refer to UserConfigParamOffset structure for
+ * specific value of offsets)
+ * @param [in] pointer to userData payload in the packet
+ * @retval N/A
+ ******************************************************************************/
+BOOL GetUserParam(userParamPayload* pld, uint8_t *payloadLen)
+{
+ uint32_t offset;
+ BOOL offsetValid;
+ uint64_t *ptr = (uint64_t *)&gUserUartConfig;
+
+ offsetValid = pld->paramNum < USER_UART_MAX_PARAM;
+
+ if(offsetValid){
+ offset = pld->paramNum;
+ pld->parameter = ptr[offset];
+ *payloadLen = 8 + 4; // parameter + number
+ } else {
+ *payloadLen = 4; // number
+ pld->paramNum = INVALID_PARAM; // invalid
+ }
+
+ return TRUE;
+
+}
+
+
+/** ****************************************************************************
+ * @name GetAllUserParams
+ * @brief Retrieves specified number of user configuration parameters data for
+ * sending to the external host starting from specified offset in user
+ * configuration structure (refer to UserConfigParamOffset structure for
+ * specific value of offsets)
+ * @param [in] pointer to userData payload in the packet
+ * @retval N/A
+ ******************************************************************************/
+BOOL GetAllUserParams(allUserParamsPayload* pld, uint8_t *payloadLen)
+{
+ uint32_t offset, i, numParams;
+ uint64_t *ptr = (uint64_t *)&gUserUartConfig;
+
+ numParams = USER_UART_MAX_PARAM;
+
+ offset = 0;
+
+ for (i = 0; i < numParams; i++, offset++){
+ pld->parameters[i] = ptr[offset];
+ }
+
+ *payloadLen = numParams* 8;
+
+ return TRUE;
+}
+
+
diff --git a/examples/OpenIMU300RI/INS/src/user/UserMessagingCAN.c b/examples/OpenIMU300RI/INS/src/user/UserMessagingCAN.c
new file mode 100644
index 0000000..82183dd
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/src/user/UserMessagingCAN.c
@@ -0,0 +1,659 @@
+/** ***************************************************************************
+ * @file UserConfiguration.c
+ *
+ * THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
+ * KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
+ * PARTICULAR PURPOSE.
+ *
+ ******************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+
+#include
+#include
+#include
+
+#include "algorithmAPI.h"
+#include "magAPI.h"
+#include "platformAPI.h"
+#include "sensorsAPI.h"
+#include "userAPI.h"
+#include "UserMessagingCAN.h"
+#include "UserConfiguration.h"
+#include "canAPI.h"
+#include "MagAlign.h"
+#include "algorithm.h"
+#include "BITStatus.h"
+#include "sensorsAPI.h"
+#include "sae_j1939.h"
+#include "math.h"
+#include "osapi.h"
+#include "ins_params_j1939.h"
+#include "driverGPS.h"
+
+// for EKFOutputDataStruct
+#include "EKF_Algorithm.h"
+EKF_OutputDataStruct *algo_res;
+extern int initAlgo;
+uint32_t forced_packets = 0, gpsFixTypeTmp;
+j1939_input_nav_params_t canInputNavParams;
+
+/** ***************************************************************************
+ * @name process_request() an API of processing request message
+ * @brief decode identifier of incoming request message
+ *
+ * @param [in] desc, rx descriptor
+ * @retval N/A
+ ******************************************************************************/
+void ProcessRequest(void *dsc)
+{
+ struct sae_j1939_rx_desc *desc = (struct sae_j1939_rx_desc*)dsc;
+ SAE_J1939_IDENTIFIER_FIELD *ident;
+ uint8_t pf_val, req_pf_val, req_ps_val;
+ uint8_t *command;
+
+ // check desc
+ if (desc == NULL)
+ return;
+
+
+ // check identifier
+ ident = &(desc->rx_identifier);
+ if (ident == NULL)
+ return;
+
+ // check receiving buffer
+ if (desc->rx_buffer.RTR || !desc->rx_buffer.IDE || (desc->rx_buffer.DLC != 3))
+ return;
+
+ // check commands
+ command = desc->rx_buffer.Data;
+ if (command == NULL)
+ return;
+
+ pf_val = ident->pdu_format;
+ req_pf_val = command[1];
+ req_ps_val = command[2];
+
+ if (pf_val != SAE_J1939_PDU_FORMAT_REQUEST)
+ return;
+
+ // dispatch the requests to the corresponding handlers
+ switch(req_pf_val) {
+ // software version request
+ case SAE_J1939_PDU_FORMAT_254:
+ {
+ if(req_ps_val == SAE_J1939_GROUP_EXTENSION_SOFTWARE_VERSION){
+ aceinna_j1939_send_software_version();
+ }
+ }
+ break;
+ // ecu id request
+ case SAE_J1939_PDU_FORMAT_ECU:
+ {
+ aceinna_j1939_send_ecu_id();
+ }
+ break;
+ // data packet request
+ case SAE_J1939_PDU_FORMAT_DATA:
+ forced_packets = 0;
+ if(req_ps_val == SAE_J1939_GROUP_EXTENSION_SLOPE_SENSOR)
+ {
+ forced_packets |= ACEINNA_SAE_J1939_PACKET_SLOPE_SENSOR;
+ }
+ if(req_ps_val == SAE_J1939_GROUP_EXTENSION_ANGULAR_RATE)
+ {
+ forced_packets |= ACEINNA_SAE_J1939_PACKET_ANGULAR_RATE;
+ }
+ if(req_ps_val == SAE_J1939_GROUP_EXTENSION_ACCELERATION)
+ {
+ forced_packets |= ACEINNA_SAE_J1939_PACKET_ACCELERATION;
+ }
+ if(req_ps_val == SAE_J1939_GROUP_EXTENSION_MAG)
+ {
+ forced_packets |= ACEINNA_SAE_J1939_PACKET_MAG;
+ }
+ break;
+
+ case SAE_J1939_PDU_FORMAT_GLOBAL:
+ // status request
+ if ((req_ps_val == gEcuConfigPtr->status_ps)) {
+ STATUS_TEST_PAYLOAD status_bits;
+ status_bits.masterStatus = (gBitStatus.BITStatus.all & 0x1E00) ? 1:0;
+ status_bits.hardwareStatus = gBitStatus.hwStatus.all? 1 : 0;
+ status_bits.softwareStatus = gBitStatus.swStatus.all? 1 : 0;
+ status_bits.sensorStatus = gBitStatus.sensorStatus.all? 1 : 0;
+ status_bits.unlocked1PPS = gBitStatus.hwStatus.bit.unlocked1PPS;
+ status_bits.unlockedInternalGPS = gBitStatus.hwStatus.bit.unlockedInternalGPS;
+ status_bits.noDGPS = gBitStatus.hwStatus.bit.unlockedInternalGPS;
+ status_bits.unlockedEEPROM = gBitStatus.hwStatus.bit.unlockedEEPROM;
+ status_bits.algorithmInit = gBitStatus.swStatus.bit.algorithmInit;
+ status_bits.highGain = gBitStatus.swStatus.bit.highGain;
+ status_bits.attitudeOnlyAlgorithm = gBitStatus.swStatus.bit.attitudeOnlyAlgorithm;
+ status_bits.turnSwitch = gBitStatus.swStatus.bit.turnSwitch;
+ status_bits.sensorOverRange = gBitStatus.sensorStatus.bit.overRange;
+ aceinna_j1939_send_status_packet(ACEINNA_SAE_J1939_BUILTIN_STATUS, (void *)&status_bits);
+ }
+ // packet rate request
+ else if ((req_ps_val == gEcuConfigPtr->packet_rate_ps)) {
+ aceinna_j1939_send_packet_rate(gEcuConfigPtr->packet_rate);
+ }
+ // packet type request
+ else if ((req_ps_val == gEcuConfigPtr->packet_type_ps)) {
+ aceinna_j1939_send_packet_type(gEcuConfigPtr->packet_type);
+ }
+ // filter settings request
+ else if ((req_ps_val == gEcuConfigPtr->digital_filter_ps)) {
+ aceinna_j1939_send_digital_filter(gEcuConfigPtr->accel_cut_off, gEcuConfigPtr->rate_cut_off);
+ }
+ // orientation settings request
+ else if ((req_ps_val == gEcuConfigPtr->orien_bits)) {
+ uint8_t bytes[2];
+ bytes[0] = (gEcuConfigPtr->orien_bits >> 8) & 0xff;
+ bytes[1] = (gEcuConfigPtr->orien_bits) & 0xff;
+ aceinna_j1939_send_orientation(bytes);
+ }
+
+ break;
+ // address claim request
+ case SAE_J1939_PDU_FORMAT_ADDRESS_CLAIM:
+ process_request_pg(desc);
+ break;
+ default:
+ break;
+ }
+
+ return;
+}
+
+void ProcessVehiclePosition(struct sae_j1939_rx_desc *desc)
+{
+ GPS_DATA *posData = (GPS_DATA*)desc->rx_buffer.Data;
+ canInputNavParams.latitude = (double)posData->latitude*0.000001 - 210; // degrees
+ canInputNavParams.longitude = (double)posData->longitude*0.000001 - 210; // degrees
+ canInputNavParams.status |= J1939_GPS_POSITION_DATA_UPDATED;
+ gCanGps.latitude = (double)posData->latitude*0.000001 - 210; // degrees
+ gCanGps.longitude = (double)posData->longitude*0.000001 - 210; // degrees
+}
+
+void ProcessWheelSpeed(struct sae_j1939_rx_desc *desc)
+{
+ WHEEL_SPEED_DATA *speedData = (WHEEL_SPEED_DATA*)desc->rx_buffer.Data;
+
+ canInputNavParams.frontAxleSpeed = (float)speedData->frontAxleSpeed * 0.00390625;
+ canInputNavParams.relSpeedFrontAxleLeftWheel = (float)speedData->relSpeedFrontAxleLeftWheel * 0.0625;
+ canInputNavParams.relSpeedFrontAxleRightWheel = (float)speedData->relSpeedFrontAxleRightWheel * 0.0625;
+ canInputNavParams.relSpeedRearAxle1LeftWheel = (float)speedData->relSpeedRearAxle1LeftWheel * 0.0625;
+ canInputNavParams.relSpeedRearAxle1RigthWheel = (float)speedData->relSpeedRearAxle1RigthWheel * 0.0625;
+ canInputNavParams.relSpeedRearAxle2LeftWheel = (float)speedData->relSpeedRearAxle2LeftWheel * 0.0625;
+ canInputNavParams.relSpeedRearAxle2RigthWheel = (float)speedData->relSpeedRearAxle2RigthWheel * 0.0625;
+ canInputNavParams.status |= J1939_VEH_SPEED_DATA_UPDATED;
+}
+
+void ProcesVehicleDirection(struct sae_j1939_rx_desc *desc)
+{
+ DIR_SPEED_DATA* dirData = (DIR_SPEED_DATA*)desc->rx_buffer.Data;
+
+ canInputNavParams.gpsBearing = (float)dirData->compassBearing * 0.0078125; //
+ canInputNavParams.navSpeed = (float)dirData->navSpeed * 0.00390625; // kph
+ canInputNavParams.pitch = (float)dirData->pitch * 0.0078125 - 200; //
+ canInputNavParams.altitude = (float)dirData->altitude * 0.125 - 2500; //
+ canInputNavParams.status |= J1939_GPS_ALTITUDE_DATA_UPDATED;
+}
+
+void ProcessCustomGnssDopPacket(struct sae_j1939_rx_desc *desc)
+{
+ CUSTOM_GNSS_DOP_DATA* dopData = (CUSTOM_GNSS_DOP_DATA*)desc->rx_buffer.Data;
+
+ gCanGps.GPSHorizAcc = (float)dopData->hAcc; // in meters
+ gCanGps.GPSVertAcc = (float)dopData->vAcc; // in meters
+ gCanGps.HDOP = ((float)dopData->pDOP * 0.01)*0.7;
+ gCanGps.trueCourse = (float)dopData->headMot * 0.01;
+}
+
+void ProcessCustomGnssFixPacket(struct sae_j1939_rx_desc *desc)
+{
+ CUSTOM_GNSS_FIX_DATA* fixData = (CUSTOM_GNSS_FIX_DATA*)desc->rx_buffer.Data;
+
+ gpsFixTypeTmp = (fixData->fixType == 3) || (fixData->fixType == 4) ;
+ gCanGps.altitude = (float)fixData->height * 1.0e-3; // in m
+ gCanGps.numSatellites = fixData->numSV;
+}
+
+void ProcessCustomGnssTimePacket(struct sae_j1939_rx_desc *desc)
+{
+ CUSTOM_GNSS_TIME_DATA* dopData = (CUSTOM_GNSS_TIME_DATA*)desc->rx_buffer.Data;
+
+ gCanGps.itow = dopData->iTOW; // in m
+
+ if(gCanGps.itow%1000 != 0){
+ gCanGps.itow+=1; // correction of numerical issue
+ }
+ gCanGps.rawGroundSpeed = (double)dopData->gSpeed * 1.0e-3; // m/s
+ gCanGps.vNed[0] = gCanGps.rawGroundSpeed * cos(D2R * gCanGps.trueCourse);
+ gCanGps.vNed[1] = gCanGps.rawGroundSpeed * sin(D2R * gCanGps.trueCourse);
+
+ gCanGps.gpsFixType = gpsFixTypeTmp;
+ gpsFixTypeTmp = 0;
+ // update flag
+ gCanGps.gpsUpdate = 1;
+}
+
+
+/** ***************************************************************************
+ * @name ProcessDataPackets() an API of processing network data messages
+ * @brief decode identifier of incoming request message
+ *
+ * @param [in] desc, rx descriptor
+ * @retval N/A
+ ******************************************************************************/
+void ProcessDataPackets(void *dsc)
+{
+ struct sae_j1939_rx_desc *desc = (struct sae_j1939_rx_desc*)dsc;
+ SAE_J1939_IDENTIFIER_FIELD *ident;
+ uint8_t pf_val, ps_val;
+
+ // check desc
+ if (desc == NULL)
+ return;
+
+
+ // check identifier
+ ident = (SAE_J1939_IDENTIFIER_FIELD*)&(desc->rx_identifier);
+ if (ident == NULL)
+ return;
+
+
+ pf_val = ident->pdu_format;
+ ps_val = ident->pdu_specific;
+
+ if (pf_val == SAE_J1939_PDU_FORMAT_254){
+
+ // dispatch the requests to the corresponding handlers
+ switch(ps_val) {
+ // software version request
+ case SAE_J1939_PDU_SPECIFIC_243: // 65267 Vehicle Position 1 FEF3
+ ProcessVehiclePosition(desc);
+ break;
+ case SAE_J1939_PDU_SPECIFIC_191: // 65215 Wheel Speed Information FEBF
+ ProcessWheelSpeed(desc);
+ break;
+ case SAE_J1939_PDU_SPECIFIC_232: // 65256 Vehicle Direction/Speed FEE8
+ ProcesVehicleDirection(desc);
+ break;
+ default:
+ break;
+ }
+ } else if(pf_val == SAE_J1939_PDU_FORMAT_GLOBAL){
+ switch(ps_val) {
+ // software version request
+ case SAE_J1939_PDU_SPECIFIC_110: // 65390 Vehicle Position 1 FEF3
+ ProcessCustomGnssTimePacket(desc);
+ break;
+ case SAE_J1939_PDU_SPECIFIC_111: // 65391 Wheel Speed Information FEBF
+ ProcessCustomGnssFixPacket(desc);
+ break;
+ case SAE_J1939_PDU_SPECIFIC_112: // 65392 Vehicle Direction/Speed FEE8
+ ProcessCustomGnssDopPacket(desc);
+ break;
+ }
+ }
+
+ return;
+}
+
+
+/** ***************************************************************************
+ * @name send_tilt_sensor_data() an API of data packet generation
+ * @brief build up MTLT's data packets and send out
+ *
+ * @param [in]
+ * @retval N/A
+ ******************************************************************************/
+static int outputCounter = 0;
+
+void EnqeuePeriodicDataPackets(int latency, int sendPeriodicPackets)
+{
+ SLOPE_SENSOR_2 slope_data;
+ AUGULAR_RATE angle_data;
+ ACCELERATION_SENSOR accel_data;
+ MAGNETIC_SENSOR mag_data;
+ int packets_to_send = 0;
+ float rate[3];
+ int i;
+ static uint8_t SID = 0;
+
+ outputCounter++;
+ SID++;
+
+ if (sendPeriodicPackets && gEcuConfig.packet_rate != 0){
+ packets_to_send = gEcuConfigPtr->packet_type;
+ }
+
+ packets_to_send |= forced_packets;
+
+ // ss2 packets supported by 9DOF
+ if (packets_to_send & ACEINNA_SAE_J1939_PACKET_SLOPE_SENSOR) {
+ slope_data.pitch = (uint32_t)((gKalmanFilter.eulerAngles[PITCH] * 57.296 + 250.00) * 32768);
+ slope_data.roll = (uint32_t)((gKalmanFilter.eulerAngles[ROLL] * 57.296 + 250.00) * 32768);
+ slope_data.pitch_compensation = 0;
+ slope_data.pitch_merit = 3;
+ slope_data.roll_compensation = 0;
+ slope_data.roll_merit = 3;
+ slope_data.measure_latency = latency/5;
+
+ aceinna_j1939_send_slope_sensor(&slope_data);
+ }
+
+ // ss2 packets supported by 9DOF
+ if (packets_to_send & ACEINNA_SAE_J1939_PACKET_LATLONG) {
+ GPS_DATA gpsData;
+
+#ifdef GPS
+ GetGPSData(&gGPS);
+#endif
+
+ double lat = gGPS.latitude; // +- 90 degrees
+ double lon = gGPS.longitude; // +- 180 degrees
+
+ gpsData.latitude = (int32_t)((lat + 210.0) * 10000000);
+ gpsData.longitude = (int32_t)((lon + 210.0) * 10000000);
+
+ aceinna_j1939_send_GPS(&gpsData);
+ }
+
+
+ // acceleration packets
+ if (packets_to_send & ACEINNA_SAE_J1939_PACKET_ACCELERATION) {
+ double accelData[3];
+ GetAccelData_mPerSecSq(accelData);
+ accel_data.acceleration_x = (uint16_t)(((accelData[0]) + 320.00) * 100);
+ accel_data.acceleration_y = (uint16_t)(((accelData[1]) + 320.00) * 100);
+ accel_data.acceleration_z = (uint16_t)(((accelData[2]) + 320.00) * 100);
+
+ accel_data.lateral_merit = 3;
+ accel_data.longitudinal_merit = 3;
+ accel_data.vertical_merit = 3;
+ accel_data.transmit_rate = 2;
+ accel_data.rsvd = 0;
+
+ aceinna_j1939_send_acceleration(&accel_data);
+ }
+
+ if (packets_to_send & ACEINNA_SAE_J1939_PACKET_MAG) {
+ double magData[3];
+ GetMagData_G(magData);
+ mag_data.mag_x = (uint16_t)(((magData[0]) + 8.00)/0.00025);
+ mag_data.mag_y = (uint16_t)(((magData[1]) + 8.00)/0.00025);
+ mag_data.mag_z = (uint16_t)(((magData[2]) + 8.00)/0.00025);
+ mag_data.unuzed = 0;
+ aceinna_j1939_send_mags(&mag_data);
+ }
+
+ if (packets_to_send & ACEINNA_SAE_J1939_PACKET_ANGULAR_RATE) {
+ if(UseAlgorithm()) {
+ rate[0] = (float)(gKalmanFilter.correctedRate_B[0] * 57.296);
+ rate[1] = (float)(gKalmanFilter.correctedRate_B[1] * 57.296);
+ rate[2] = (float)(gKalmanFilter.correctedRate_B[2] * 57.296);
+ }
+ else {
+ double rateData[3];
+ GetRateData_degPerSec(rateData);
+ rate[0] = (float)(rateData[0]);
+ rate[1] = (float)(rateData[1]);
+ rate[2] = (float)(rateData[2]);
+ }
+
+ for (i = 0; i < 3; i++)
+ {
+ if (rate[i] < -250.00)
+ rate[i] = -250.00;
+
+ if (rate[i] > 250.00)
+ rate[i] = 250.00;
+ }
+ angle_data.pitch_rate = (uint16_t)((rate[0] + 250.00) * 128);
+ angle_data.roll_rate = (uint16_t)((rate[1] + 250.00) * 128);
+ angle_data.yaw_rate = (uint16_t)((rate[2] + 250.00) * 128);
+ angle_data.pitch_merit = 3;
+ angle_data.roll_merit = 3;
+ angle_data.yaw_merit = 3;
+ angle_data.rsvd = 0;
+ angle_data.measurement_latency = latency/5;
+
+ aceinna_j1939_send_angular_rate(&angle_data);
+ }
+
+ if (packets_to_send & ACEINNA_SAE_J1939_PACKET_RAPID_POSITION_UPDATE) {
+ GPS_DATA data;
+ double lla[3];
+ OSDisableHook();
+ EKF_GetEstimatedLLA(lla);
+ OSEnableHook();
+ data.latitude = (uint32_t)((lla[LAT] + 210) * 10000000.0);
+ data.longitude = (uint32_t)((lla[LON] + 210) * 10000000.0);
+ aceinna_j1939_send_position_rapid_update(&data);
+ }
+
+ if (packets_to_send & ACEINNA_SAE_J1939_PACKET_RAPID_COURSE_UPDATE) {
+ COURSE_RAPID_UPDATE_DATA data;
+ real EstVelocity[3];
+ real EulerAngles[3];
+
+ OSDisableHook();
+ EKF_GetEstimatedVelocity(EstVelocity);
+ EKF_GetAttitude_EA_RAD(EulerAngles);
+ OSEnableHook();
+
+ real SOG = sqrt(pow(EstVelocity[X_AXIS],2) + pow(EstVelocity[Y_AXIS],2)) * 100; ;
+
+ data.COG = (int16_t)((EulerAngles[YAW] + 3.141592653589) * 10000);
+ data.SOG = (int16_t)SOG;
+ data.SID = SID;
+ data.Rsvd = 0xffff;
+ data.Reserved = 0x3f;
+
+ aceinna_j1939_send_course_rapid_update(&data);
+ }
+
+ if (packets_to_send & ACEINNA_SAE_J1939_PACKET_ATTITUDE) {
+ ATTITUDE_DATA data;
+ real EulerAngles[3];
+
+ OSDisableHook();
+ EKF_GetAttitude_EA_RAD(EulerAngles);
+ OSEnableHook();
+
+ data.SID = SID;
+ data.Pitch = (int16_t)((EulerAngles[PITCH] + 3.141592653589) * 10000);
+ data.Roll = (int16_t)((EulerAngles[ROLL] + 3.141592653589) * 10000);
+ data.Yaw = (int16_t)((EulerAngles[YAW] + 3.141592653589) * 10000);
+ data.Rsvd = 0xff;
+ aceinna_j1939_send_attitude(&data);
+ }
+
+
+ forced_packets = 0;
+
+ return;
+}
+
+/** ***************************************************************************
+ * @name ProcessEcuCommands
+* @brief decode incoming SET packets and put the request into the corresponding
+ * handlers
+ * @param [in] command, SET request
+ * ps, pdu specific value
+ * addr, host address
+ * @retval 1 successfuk or 0 failure
+ ******************************************************************************/
+void ProcessEcuCommands(void * command, uint8_t ps, uint8_t addr)
+{
+ // SET request is NULL
+ if (command == NULL)
+ return;
+
+ // Go to the correponding handlers
+ if (ps == gEcuConfigPtr->alg_reset_ps)
+ {
+ // Algotithm restart command
+ COMMAND_SET_PAYLOAD * pld = (COMMAND_SET_PAYLOAD *)command;
+ if (pld->request == ACEINNA_SAE_J1939_REQUEST && pld->dest_address == *(uint8_t *)gEcu->addr)
+ {
+ ECU_ADDRESS_ENTRY target;
+ initAlgo = 1;
+ target.address = addr;
+ target.category = _ECU_MASTER;
+ aceinna_j1939_send_algrst_cfgsave(&target, 1, 1);
+ }
+ }
+ else if ((ps == SAE_J1939_GROUP_EXTENSION_SAVE_CONFIGURATION) ||
+ (ps == gEcuConfigPtr->save_cfg_ps))
+ {
+ // Save configuration command
+ COMMAND_SET_PAYLOAD * pld = (COMMAND_SET_PAYLOAD *)command;
+ if (pld->request == ACEINNA_SAE_J1939_REQUEST && pld->dest_address == *(uint8_t *)gEcu->addr){
+ ECU_ADDRESS_ENTRY target;
+ SaveEcuConfig(gEcuConfigPtr);
+ target.address = addr;
+ target.category = _ECU_MASTER;
+ aceinna_j1939_send_algrst_cfgsave(&target, 0, 1);
+ }
+ }
+ else if (ps == gEcuConfigPtr->packet_rate_ps)
+ {
+ // Update packet rate command
+ RATE_CONFIG_PAYLOAD * pld = (RATE_CONFIG_PAYLOAD *)command;
+ if (pld->dest_address == *(uint8_t *)gEcu->addr) {
+ gEcuConfigPtr->packet_rate = pld->odr;
+ gUserConfiguration.ecuPacketRate = pld->odr;
+ }
+ }
+ else if (ps == gEcuConfigPtr->packet_type_ps)
+ {
+ // Update set of transmitted packets
+ PACKET_TYPE_PAYLOAD * pld = (PACKET_TYPE_PAYLOAD *)command;
+ if(pld->dest_address == *(uint8_t *)gEcu->addr) {
+ gEcuConfigPtr->packet_type = pld->type1_bits.r | (pld->type2_bits.r << 8);
+ gUserConfiguration.ecuPacketType = gEcuConfigPtr->packet_type;
+ }
+ }
+ else if (ps == gEcuConfigPtr->digital_filter_ps)
+ {
+ // Update cutoff frequencies for digital filters
+ DIGITAL_FILTER_PAYLOAD * pld = (DIGITAL_FILTER_PAYLOAD *)command;
+ if (pld->dest_address == *(uint8_t *)gEcu->addr) {
+ gEcuConfigPtr->rate_cut_off = pld->rate_cutoff;
+ gEcuConfigPtr->accel_cut_off = pld->accel_cutoff;
+ gUserConfiguration.ecuFilterFreqAccel = pld->accel_cutoff;
+ gUserConfiguration.ecuFilterFreqRate = pld->rate_cutoff;
+ platformSelectLPFilter(RATE_SENSOR, gEcuConfigPtr->rate_cut_off, TRUE);
+ platformSelectLPFilter(ACCEL_SENSOR, gEcuConfigPtr->accel_cut_off, TRUE);
+ }
+ }
+ else if (ps == gEcuConfigPtr->orientation_ps)
+ {
+ // Update unit orientation
+ ORIENTATION_SETTING * pld = (ORIENTATION_SETTING *)command;
+ if (pld->dest_address == *(uint8_t *)gEcu->addr) {
+ gEcuConfigPtr->orien_bits = pld->orien_bits[0] << 8 | pld->orien_bits[1];
+ if(platformApplyOrientation(gEcuConfigPtr->orien_bits)){
+ gUserConfiguration.ecuOrientation = gEcuConfigPtr->orien_bits;
+ }
+ }
+ }
+ else if (ps == gEcuConfigPtr->mag_align_ps)
+ {
+ // Update unit orientation
+ MAG_ALIGN_PAYLOAD *pld = (MAG_ALIGN_PAYLOAD *)command;
+ if (pld->dest_address == *(uint8_t *)gEcu->addr) {
+ uint8_t len = 1;
+ uint8_t cmd = pld->cmd[0];
+ uint8_t state;
+ real params[4];
+ ProcessMagAlignCmds((magAlignCmdPayload*)&pld->cmd[0], &len);
+ state = GetMagAlignEstimatedParams(params);
+ aceinna_j1939_send_mag_align(cmd, state, params);
+ }
+ }
+ else if (ps == gEcuConfigPtr->user_behavior_ps)
+ {
+ // Update algotirtm behaviour
+ USER_BEHAVIOR_PAYLOAD * pld = (USER_BEHAVIOR_PAYLOAD *)command;
+ if (pld->dest_address == *(uint8_t *)gEcu->addr) {
+ gEcuConfigPtr->restart_on_overrange = pld->restart_on_overrange;
+ gEcuConfigPtr->dynamic_motion = pld->dynamic_motion;
+ }
+ }
+ else if (ps == SAE_J1939_GROUP_EXTENSION_BANK0)
+ {
+ // Reassign pdu-specific codes
+ BANK0_PS_PAYLOAD * pld = (BANK0_PS_PAYLOAD *)command;
+ if (pld->dest_address == *(uint8_t *)gEcu->addr) {
+ gEcuConfigPtr->alg_reset_ps = pld->alg_reset_ps;
+ gEcuConfigPtr->status_ps = pld->status_ps;
+ gEcuConfigPtr->mag_align_ps = pld->mag_align_ps;
+ UpdateEcuConfig(gEcuConfigPtr, FALSE);
+ }
+ }
+ else if (ps == SAE_J1939_GROUP_EXTENSION_BANK1)
+ {
+ // Reassign pdu-specific codes
+ BANK1_PS_PAYLOAD * pld = (BANK1_PS_PAYLOAD *)command;
+ if (pld->dest_address == *(uint8_t *)gEcu->addr) {
+ gEcuConfigPtr->packet_rate_ps = pld->packet_rate_ps;
+ gEcuConfigPtr->packet_type_ps = pld->packet_type_ps;
+ gEcuConfigPtr->digital_filter_ps = pld->digital_filter_ps;
+ gEcuConfigPtr->orientation_ps = pld->orientation_ps;
+ gEcuConfigPtr->user_behavior_ps = pld->user_behavior_ps;
+ UpdateEcuConfig(gEcuConfigPtr, FALSE);
+ }
+ }
+
+ return;
+}
+
+
+// configure CAN controller for selective reception of CAN messages
+/** ***************************************************************************
+ * @name ConfigureCANMessageFilters
+* @brief configure CAN controller for selective reception of CAN messages
+******************************************************************************/
+void ConfigureCANMessageFilters()
+{
+ // initialize filter for ECU ID
+ ConfigureCANMessageFilter(SAE_J1939_ECU_ID_BASE, SAE_J1939_ECU_FILTER_BASE_MASK);
+ // initialize filter for control messages
+ ConfigureCANMessageFilter(SAE_J1939_CONTROL1_ID_BASE, SAE_J1939_CONTROL1_FILTER_BASE_MASK);
+ // initialize filter for requests
+ ConfigureCANMessageFilter(SAE_J1939_REQUEST_ID_BASE, SAE_J1939_REQUEST_FILTER_BASE_MASK);
+ // initialize filter for address claim
+ ConfigureCANMessageFilter(SAE_J1939_ADDRESS_CLAIM_ID_BASE, SAE_J1939_ADDRESS_CLAIM_FILTER_BASE_MASK);
+ // initialize filter for Bank 1 and Bank 0 commands
+ ConfigureCANMessageFilter(ACEINNA_BANK_ID_BASE, ACEINNA_BANK_FILTER_BASE_MASK);
+ // initialize Filter for incoming data messages
+ ConfigureCANMessageFilter(VEHICLE_DATA_ID_BASE, VEHICLE_DATA_FILTER_BASE_MASK);
+ // initialize Filter for incoming data1 messages
+ ConfigureCANMessageFilter(VEHICLE_DATA2_ID_BASE, VEHICLE_DATA2_FILTER_BASE_MASK);
+}
+
+
+void GetGPSFromCAN(gpsDataStruct_t *data)
+{
+
+}
+
diff --git a/examples/OpenIMU300RI/INS/src/user/UserMessagingCAN.h b/examples/OpenIMU300RI/INS/src/user/UserMessagingCAN.h
new file mode 100644
index 0000000..a4e6f40
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/src/user/UserMessagingCAN.h
@@ -0,0 +1,175 @@
+/*******************************************************************************
+ * File: UserConfiguration.h
+ * Created on Jan 25, 2017
+ ******************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+
+#ifndef USER_MESSAGING_H
+#define USER_MESSAGING_H
+
+#include
+
+#include "GlobalConstants.h"
+
+
+extern int userPacketOut;
+
+
+
+typedef struct {
+ uint16_t masterFail : 1; // 0 = normal, 1 = fatal error has occurred
+ uint16_t hardwareError : 1; // 0 = normal, 1 = internal hardware error
+ uint16_t reserved : 1;
+ uint16_t softwareError : 1; // 0 = normal, 1 = internal software error
+ uint16_t inpPower : 1; // 0 = normal, 1 = out of bounds
+ uint16_t inpCurrent : 1; // 0 = normal, 1 = out of bounds
+ uint16_t inpVoltage : 1; // 0 = normal, 1 = out of bounds
+ uint16_t fiveVolt : 1; // 0 = normal, 1 = out of bounds
+ uint16_t threeVolt : 1; // 0 = normal, 1 = out of bounds
+ uint16_t twoVolt : 1; // 0 = normal, 1 = out of bounds
+ uint16_t twoFiveref : 1; // 0 = normal, 1 = out of bounds
+ uint16_t sixVolt : 1; // 0 = normal, 1 = out of bounds
+ uint16_t grdRef : 1; // 0 = normal, 1 = out of bounds
+ uint16_t pcbTemp : 1; // 0 = normal, 1 = out of bounds
+ uint16_t reserved1 : 2;
+} HARDWARE_TEST_PAYLOAD;
+
+typedef struct {
+ uint16_t softwareError : 1; // 0 = normal, 1 = internal software error
+ uint16_t algorithmerror : 1; // 0 = normal, 1 = error
+ uint16_t dataError : 1; // 0 = normal, 1 = error
+ uint16_t initialization : 1; // 0 = normal, 1 = error during algorithm initialization
+ uint16_t overRange : 1; // 0 = normal, 1 = fatal sensor over range
+ uint16_t missedNavigationStep : 1; // 0 = normal, 1 = deadline missed for navigation
+ uint16_t calibrationCRCError : 1; // 0 = normal, 1 = incorrect CRC on calibration EEPROM data
+ uint16_t reserved : 9;
+} SOFTWARE_TEST_PAYLOAD;
+
+typedef struct {
+ uint16_t masterStatus : 1; // 0 = normal, 1 = hardware, sensor, CAN, or software alert
+ uint16_t hardwareStatus : 1; // 0 = normal, 1 = programmable alert
+ uint16_t softwareStatus : 1; // 0 = normal, 1 = programmable alert
+ uint16_t sensorStatus : 1; // 0 = normal, 1 = programmable alert
+ uint16_t unlocked1PPS : 1; // 0 = not asserted, 1 = asserted
+ uint16_t unlockedInternalGPS : 1; // 0 = not asserted, 1 = asserted
+ uint16_t noDGPS : 1; // 0 = DGPS lock, 1 = no DGPS
+ uint16_t unlockedEEPROM : 1; // 0 = locked, 1 = unlocked
+ uint16_t algorithmInit : 1; // 0 = normal, 1 = in initialization mode
+ uint16_t highGain : 1; // 0 = low gain mode, 1 = high gain mode
+ uint16_t attitudeOnlyAlgorithm : 1; // 0 = navigation state tracking, 1 = attitude only state tracking
+ uint16_t turnSwitch : 1; // 0 = off, 1 = yaw rate greater than turnSwitch threshold
+ uint16_t sensorOverRange : 1; // 0 = not asserted, 1 = asserted
+ uint16_t reserved : 3;
+} STATUS_TEST_PAYLOAD;
+
+
+// ODR set packet type
+typedef struct {
+ uint8_t dest_address; // target's address
+ uint8_t odr; // odr values
+} RATE_CONFIG_PAYLOAD;
+
+// data packet payload
+typedef struct {
+ uint8_t dest_address; // targer address
+ union {
+ struct {
+ uint8_t slope_sensor : 1; // ss2 packet
+ uint8_t angular_rate : 1; // angular rate packet
+ uint8_t accelerator : 1; // acceleration packet
+ uint8_t reserved : 5;
+ } b;
+
+ uint8_t r;
+ } type1_bits;
+ union {
+ struct {
+ uint8_t reserved : 8;
+ } b;
+
+ uint8_t r;
+ } type2_bits;
+} PACKET_TYPE_PAYLOAD;
+
+
+// LPF set payload format
+typedef struct {
+ uint8_t dest_address; // target's address
+ uint8_t rate_cutoff; // LPF of rate sensor
+ uint8_t accel_cutoff; // LPF of XL sensor
+} DIGITAL_FILTER_PAYLOAD;
+
+
+// orientation set payload format
+typedef struct {
+ uint8_t dest_address; // target's address
+ uint8_t orien_bits[2]; // orientation setting
+} ORIENTATION_SETTING;
+
+// orientation set payload format
+typedef struct {
+ uint8_t dest_address; // target's address
+ uint8_t cmd[7]; // command
+} MAG_ALIGN_PAYLOAD;
+
+
+// user behavior set payload format
+typedef struct {
+ uint8_t dest_address; // target's address
+ uint8_t restart_on_overrange; // restart or not while over range
+ uint8_t dynamic_motion; // dynamic motion
+} USER_BEHAVIOR_PAYLOAD;
+
+
+// Angle alarm set payload format
+typedef struct {
+ uint8_t dest_address; // targert's address
+ uint8_t roll_upper; // upper limitation of roll
+ uint8_t roll_lower; // lower limitation of roll
+ uint8_t pitch_upper; // upper limitation of pitch
+ uint8_t pitch_lower; // lower limitation of pitch
+ uint8_t roll_hysteresis; // hysteresis of roll
+ uint8_t pitch_hyseresis; // hysteresis of pitch
+} ANGLE_ALARM_PAYLOAD;
+
+
+// Cone alarm set payload format
+typedef struct {
+ uint8_t dest_address; // target's address
+ uint16_t alarm_selector; // alarm selector
+ uint16_t angle_limit; // angular limitation
+ uint16_t angle_hysteresis; // angular hysteresis
+} CONE_ALARM_PAYLOAD;
+
+
+// acceleration set payload format
+typedef struct {
+ uint8_t dest_address; // target's address
+ uint16_t x_acceleration; // x-axis acceleration
+ uint16_t y_acceleration; // y-axis acceleration
+ uint16_t z_acceleration; // z-axis acceleration
+} ACCELERATION_PARAM_PAYLOAD;
+
+extern void ProcessRequest(void *dsc);
+extern void ProcessEcuCommands(void * command, uint8_t ps, uint8_t addr);
+extern void PrepareJ1939DataPackets(void);
+extern void EnqeuePeriodicDataPackets(int latency, int sendPeriodicPackets);
+extern void ProcessDataPackets(void *dsc);
+
+
+
+#endif /* USER_CONFIGURATION_H */
diff --git a/examples/OpenIMU300RI/INS/src/user/UserMessagingUART.c b/examples/OpenIMU300RI/INS/src/user/UserMessagingUART.c
new file mode 100644
index 0000000..ad7debd
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/src/user/UserMessagingUART.c
@@ -0,0 +1,391 @@
+/** ***************************************************************************
+ * @file UserConfiguration.c
+ *
+ * THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
+ * KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
+ * PARTICULAR PURPOSE.
+ *
+ ******************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+
+#include
+#include
+#include
+
+#include "algorithmAPI.h"
+#include "platformAPI.h"
+#include "sensorsAPI.h"
+#include "userAPI.h"
+#include "appVersion.h"
+
+#include "UserMessagingUART.h"
+#include "UserConfiguration.h"
+
+#include "Indices.h" // For X_AXIS, etc
+#include "CommonMessages.h"
+
+// Declare the IMU data structure
+IMUDataStruct gIMU;
+
+// Version string
+//char userVersionString[] = "IMU 1.0.0";
+
+
+
+
+
+/// List of allowed packet codes
+usr_packet_t userInputPackets[] = {
+ {USR_IN_NONE, {0,0}},
+ {USR_IN_PING, "pG"},
+ {USR_IN_UPDATE_CONFIG, "uC"},
+ {USR_IN_UPDATE_PARAM, "uP"},
+ {USR_IN_UPDATE_ALL, "uA"},
+ {USR_IN_SAVE_CONFIG, "sC"},
+ {USR_IN_GET_CONFIG, "gC"},
+ {USR_IN_GET_PARAM, "gP"},
+ {USR_IN_GET_ALL, "gA"},
+ {USR_IN_GET_VERSION, "gV"},
+ {USR_IN_RESET, "rS"},
+// place new input packet code here, before USR_IN_MAX
+ {USR_IN_MAX, {0xff, 0xff}}, // ""
+};
+
+
+// packet codes here should be unique -
+// should not overlap codes for input packets and system packets
+// First byte of Packet code should have value >= 0x61
+usr_packet_t userOutputPackets[] = {
+// Packet Type Packet Code
+ {USR_OUT_NONE, {0x00, 0x00}},
+ {USR_OUT_TEST, "zT"},
+ {USR_OUT_DATA1, "z1"},
+ {USR_OUT_DATA2, "z2"},
+// place new type and code here
+ {USR_OUT_SCALED1, "s1"},
+ {USR_OUT_EKF1, "e1"},
+ {USR_OUT_EKF2, "e2"},
+ {USR_OUT_MAX, {0xff, 0xff}}, // ""
+};
+
+volatile char *info;
+static int _userPayloadLen = 0;
+static int _outputPacketType = USR_OUT_MAX;
+static int _inputPacketType = USR_IN_MAX;
+
+
+int checkUserPacketType(uint16_t receivedCode)
+{
+ int res = UCB_ERROR_INVALID_TYPE;
+ usr_packet_t *packet = &userInputPackets[1];
+ uint16_t code;
+
+ // validate packet code here and memorise for further processing
+ while(packet->packetType != USR_IN_MAX){
+ code = (packet->packetCode[0] << 8) | packet->packetCode[1];
+ if(code == receivedCode){
+ _inputPacketType = packet->packetType;
+ return UCB_USER_IN;
+ }
+ packet++;
+ }
+
+ packet = &userOutputPackets[1];
+
+ // validate packet code here and memorize for further processing
+ while(packet->packetType != USR_OUT_MAX){
+ code = (packet->packetCode[0] << 8) | packet->packetCode[1];
+ if(code == receivedCode){
+ _outputPacketType = packet->packetType;
+ return UCB_USER_OUT;
+ }
+ packet++;
+ }
+
+ return res;
+}
+
+
+void userPacketTypeToBytes(uint8_t bytes[])
+{
+ if(_inputPacketType && _inputPacketType < USR_IN_MAX){
+ // response to request. Return same packet code
+ bytes[0] = userInputPackets[_inputPacketType].packetCode[0];
+ bytes[1] = userInputPackets[_inputPacketType].packetCode[1];
+ _inputPacketType = USR_IN_MAX; // wait for next input packet
+ return;
+ }
+
+ if(_outputPacketType && _outputPacketType < USR_OUT_MAX){
+ // continuous packet
+ bytes[0] = userOutputPackets[_outputPacketType].packetCode[0];
+ bytes[1] = userOutputPackets[_outputPacketType].packetCode[1];
+ }else {
+ bytes[0] = 0;
+ bytes[1] = 0;
+ }
+
+}
+
+
+/** ***************************************************************************
+ * @name setUserPacketType - set user output packet type
+ * @brief
+ * @param [in] packet type
+ * @retval - TRUE if success, FALSE otherwise
+ ******************************************************************************/
+BOOL setUserPacketType(uint8_t *data, BOOL fApply)
+{
+ int type = -1;
+ uint16_t *code = (uint16_t*)data;
+ uint16_t tmp;
+ BOOL result = TRUE;
+
+ usr_packet_t *packet = &userOutputPackets[1];
+ for(int i = 0; i < USR_OUT_MAX; i++, packet++){
+ if(*code == *((uint16_t*)packet->packetCode)){
+ type = packet->packetType;
+ break;
+ }
+ }
+
+ switch(type){
+ case USR_OUT_TEST: // simple test packet to check communication
+ _outputPacketType = type;
+ _userPayloadLen = USR_OUT_TEST_PAYLOAD_LEN;
+ break;
+ case USR_OUT_DATA1: // packet with sensors data. Change at will
+ _outputPacketType = type;
+ _userPayloadLen = USR_OUT_DATA1_PAYLOAD_LEN;
+ break;
+ case USR_OUT_DATA2: // packet with arbitrary data
+ _outputPacketType = type;
+ _userPayloadLen = sizeof(data2_payload_t);
+ break;
+ case USR_OUT_SCALED1: // packet with arbitrary data
+ _outputPacketType = type;
+ _userPayloadLen = USR_OUT_SCALED1_PAYLOAD_LEN;
+ break;
+ case USR_OUT_EKF1: // packet with EKF algorithm data
+ _outputPacketType = type;
+ _userPayloadLen = USR_OUT_EKF1_PAYLOAD_LEN;
+ break;
+ case USR_OUT_EKF2: // packet with EKF algorithm data
+ _outputPacketType = type;
+ _userPayloadLen = USR_OUT_EKF2_PAYLOAD_LEN;
+ break;
+ default:
+ result = FALSE;
+ break;
+ }
+
+ if(result == FALSE){
+ return FALSE;
+ }
+
+ tmp = (data[0] << 8) | data[1];
+
+ result = platformSetOutputPacketCode(tmp, fApply);
+
+ return result;
+}
+
+
+/** ***************************************************************************
+ * @name getUserPayloadLength - get user payload length for sanity check
+ * @brief
+ *
+ * @retval - user payload length
+ ******************************************************************************/
+int getUserPayloadLength(void)
+{
+ // ATTENTION: return actual user payload length, if user packet used
+ return _userPayloadLen;
+}
+
+/******************************************************************************
+ * @name HandleUserInputPacket - API
+ * @brief general handler
+ * @param [out] packetPtr - filled in packet from the mapped physical port
+ * @retval N/A
+ ******************************************************************************/
+int HandleUserInputPacket(UcbPacketStruct *ptrUcbPacket)
+{
+ BOOL valid = TRUE;
+ int ret = USER_PACKET_OK;
+// userPacket *pkt = (userPacket *)ptrUcbPacket->payload;
+
+ /// call appropriate function based on packet type
+ switch (_inputPacketType) {
+ case USR_IN_RESET:
+ Reset();
+ break;
+ case USR_IN_PING:
+ {
+ uint8_t len;
+ Fill_PingPacketPayload(ptrUcbPacket->payload, &len);
+ ptrUcbPacket->payloadLength = len;
+ }
+ // leave all the same - it will be bounced back unchanged
+ break;
+ case USR_IN_GET_VERSION:
+ {
+ uint8_t len;
+ Fill_VersionPacketPayload(ptrUcbPacket->payload, &len);
+ ptrUcbPacket->payloadLength = len;
+ }
+ break;
+ case USR_IN_SAVE_CONFIG:
+ // payload length does not change
+ if(!SaveUserConfig()){
+ valid = FALSE;
+ }
+ break;
+ case USR_IN_UPDATE_CONFIG:
+ UpdateUserConfig((userConfigPayload*)ptrUcbPacket->payload, &ptrUcbPacket->payloadLength);
+ break;
+ case USR_IN_UPDATE_PARAM:
+ UpdateUserParam((userParamPayload*)ptrUcbPacket->payload, &ptrUcbPacket->payloadLength);
+ break;
+ case USR_IN_UPDATE_ALL:
+ UpdateAllUserParams((allUserParamsPayload*)ptrUcbPacket->payload, &ptrUcbPacket->payloadLength);
+ break;
+ case USR_IN_GET_CONFIG:
+ if(!GetUserConfig((userConfigPayload*)ptrUcbPacket->payload, &ptrUcbPacket->payloadLength)){
+ valid = FALSE;
+ }
+ break;
+ case USR_IN_GET_PARAM:
+ if(!GetUserParam((userParamPayload*)ptrUcbPacket->payload, &ptrUcbPacket->payloadLength)){
+ valid = FALSE;
+ }
+ break;
+ case USR_IN_GET_ALL:
+ if(!GetAllUserParams((allUserParamsPayload*)ptrUcbPacket->payload, &ptrUcbPacket->payloadLength)){
+ valid = FALSE;
+ }
+ break;
+ default:
+ /// default handler - unknown packet
+ valid = FALSE;
+ break;
+ }
+
+ if(!valid){
+ ptrUcbPacket->payloadLength = 0;
+ ret = USER_PACKET_ERROR;
+ }
+
+ ptrUcbPacket->packetType = UCB_USER_OUT; // do not remove - done for proper packet routing
+
+ return ret;
+}
+
+
+/******************************************************************************
+ * @name HandleUserOutputPacket - API call ro prepare continuous user output packet
+ * @brief general handler
+ * @param [in] payload pointer to put user data to
+ * @param [in/out] number of bytes in user payload
+ * @retval N/A
+ ******************************************************************************/
+BOOL HandleUserOutputPacket(uint8_t *payload, uint8_t *payloadLen)
+{
+ static uint32_t _testVal = 0;
+ static uint64_t ppsTstamp = 0;
+ BOOL ret = TRUE;
+
+ switch (_outputPacketType) {
+ case USR_OUT_TEST:
+ {
+ uint32_t *testParam = (uint32_t*)(payload);
+ *payloadLen = USR_OUT_TEST_PAYLOAD_LEN;
+ *testParam = _testVal++;
+ }
+ break;
+
+ case USR_OUT_DATA1:
+ {
+ uint8_t len;
+ Fill_z1PacketPayload(payload, &len);
+ *payloadLen = len;
+ }
+ break;
+ case USR_OUT_DATA2:
+ {
+ data2_payload_t *pld = (data2_payload_t *)payload;
+ pld->timer = platformGetCurrTimeStamp()/1000; // in miliseconds
+ pld->c = 'A';
+ pld->s = 1234;
+ pld->i = -5;
+ if(platformGetPpsFlag(TRUE)){
+ ppsTstamp = platformGetPpsTimeStamp();
+ }
+// pld->ll = platformGetDacqTimeStamp(); // in microseconds;
+ pld->ll = ppsTstamp; // time stamp of last PPS edge in microseconds from system start
+ pld->d = 1.23456789;
+ *payloadLen = sizeof(data2_payload_t);
+ }
+ break;
+ case USR_OUT_SCALED1:
+ {
+ uint8_t len;
+ Fill_s1PacketPayload(payload, &len);
+ *payloadLen = len;
+ }
+ break;
+ case USR_OUT_EKF1:
+ {
+ // Variables used to hold the EKF values
+ uint8_t len;
+ Fill_e1PacketPayload(payload, &len);
+ *payloadLen = len;
+ }
+ break;
+
+ case USR_OUT_EKF2:
+ {
+ // Variables used to hold the EKF values
+ uint8_t len;
+ Fill_e2PacketPayload(payload, &len);
+ *payloadLen = len;
+ }
+ break;
+ // place additional user packet preparing calls here
+ // case USR_OUT_XXXX:
+ // *payloadLen = YYYY; // total user payload length, including user packet type
+ // payload[0] = ZZZZ; // user packet type
+ // prepare dada here
+ // break;
+ default:
+ {
+ *payloadLen = 0;
+ ret = FALSE;
+ }
+ break; /// unknown user packet, will send error in response
+ }
+
+ return ret;
+}
+
+
+void WriteResultsIntoOutputStream(void *results)
+{
+// implement specific data processing/saving here
+
+}
diff --git a/examples/OpenIMU300RI/INS/src/user/UserMessagingUART.h b/examples/OpenIMU300RI/INS/src/user/UserMessagingUART.h
new file mode 100644
index 0000000..e8615ef
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/src/user/UserMessagingUART.h
@@ -0,0 +1,155 @@
+/*******************************************************************************
+ * File: UserConfiguration.h
+ * Created on Jan 25, 2017
+ ******************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+
+#ifndef _USER_MESSAGING_UART_H
+#define _USER_MESSAGING_UART_H
+
+#include
+
+#include "GlobalConstants.h"
+#include "ucb_packet_struct.h"
+
+#define USER_PACKET_OK 0
+#define UNKNOWN_USER_PACKET 1
+#define USER_PACKET_ERROR 2
+
+// here is definition for packet rate divider
+// considering that data acquisition task runs at 200 Hz
+typedef enum {
+ PACKET_RATE_INVALID = -1,
+ PACKET_RATE_QUIET = 0, // quiet mode
+ PACKET_RATE_200HZ = 200, // packet rate 200 Hz
+ PACKET_RATE_100HZ = 100, // packet rate 100 Hz
+ PACKET_RATE_50HZ = 50, // packet rate 50 Hz
+ PACKET_RATE_25HZ = 25, // packet rate 25 Hz
+ PACKET_RATE_20HZ = 20, // packet rate 20 Hz
+ PACKET_RATE_10HZ = 10, // packet rate 10 Hz
+ PACKET_RATE_5HZ = 5, // packet rate 5 Hz
+ PACKET_RATE_2HZ = 2, // packet rate 2 Hz
+ PACKET_RATE_1HZ = 1, // packet rate 1 Hz
+} packet_rate_t;
+
+
+// User Input packet payload has next structure:
+// number offset
+// of of first
+// parameters parameter
+// U2 U2 U4/I4/F
+// XXXX YYYY [parameters]
+// User input packet codes, change at will
+typedef enum {
+ USR_IN_NONE = 0 ,
+ USR_IN_PING ,
+ USR_IN_UPDATE_CONFIG ,
+ USR_IN_UPDATE_PARAM ,
+ USR_IN_UPDATE_ALL ,
+ USR_IN_SAVE_CONFIG ,
+ USR_IN_GET_CONFIG ,
+ USR_IN_GET_PARAM ,
+ USR_IN_GET_ALL ,
+ USR_IN_GET_VERSION ,
+ USR_IN_RESET ,
+ // add new packet type here, before USR_IN_MAX
+ USR_IN_MAX ,
+}UserInPacketType;
+
+// User output packet codes, change at will
+typedef enum {
+ USR_OUT_NONE = 0, // 0
+ USR_OUT_TEST, // 1
+ USR_OUT_DATA1, // 2
+ USR_OUT_DATA2, // 3
+// add new output packet type here, before USR_OUT_MAX
+ USR_OUT_SCALED1, // 4
+ USR_OUT_EKF1,
+ USR_OUT_EKF2,
+ USR_OUT_MAX
+} UserOutPacketType;
+
+
+// total size of user packet structure should not exceed 255 bytes
+#pragma pack(1)
+typedef struct {
+ uint8_t packetPayload[252]; // maximum 252 bytes
+} userPacket;
+#define MAX_NUMBER_OF_USER_PARAMS_IN_THE_PACKET 30
+#define FIRST_30_PARAMS 0xFFFFFFFF
+
+// example of user payload structure
+typedef struct {
+ uint32_t numParams; // number of consecutive parameters to update (little endian)
+ uint32_t paramOffset; // parameter number in parameters structure (little endian)
+ uint64_t parameters[MAX_NUMBER_OF_USER_PARAMS_IN_THE_PACKET]; // up to 30 64-bit parameters (little endian)
+}userConfigPayload;
+
+#pragma pack(1)
+// example of user payload structure
+typedef struct {
+ uint32_t paramNum; // parameter number in parameters structure (little endian)
+ uint64_t parameter; // up to 30 64-bit parameters (little endian)
+}userParamPayload;
+#pragma pack()
+
+// example of user payload structure
+typedef struct {
+ uint64_t parameters[MAX_NUMBER_OF_USER_PARAMS_IN_THE_PACKET]; // up to 30 64-bit parameters (little endian)
+}allUserParamsPayload;
+
+#pragma pack(1)
+typedef struct {
+ uint32_t timer;
+ uint8_t c;
+ short s;
+ int i;
+ long long ll;
+ double d;
+}data2_payload_t;
+
+#pragma pack()
+
+
+#define USR_OUT_TEST_PAYLOAD_LEN (4) // test parameter (uint32_t)
+#define USR_OUT_DATA1_PAYLOAD_LEN (4*10) // 1 integer +3accels (float LE) + 3gyros (float LE) + 3 mags (floatLE)
+#define USR_OUT_SCALED1_PAYLOAD_LEN (52) // See UserMessaging.c for make-up of Scaled1 message
+#define USR_OUT_EKF1_PAYLOAD_LEN (75)
+#define USR_OUT_EKF2_PAYLOAD_LEN (123)
+
+
+#define USER_OK 0x00
+#define USER_NAK 0x80
+#define USER_INVALID 0x81
+
+extern int userPacketOut;
+
+extern int getUserPayloadLength(void);
+extern int checkUserPacketType(uint16_t receivedCode);
+extern void userPacketTypeToBytes(uint8_t bytes[]);
+extern void WriteResultsIntoOutputStream(void *results);
+BOOL setUserPacketType(uint8_t* type, BOOL fApply);
+
+
+extern BOOL UpdateUserConfig(userConfigPayload* pld, uint8_t *payloadLen);
+extern BOOL UpdateUserParam(userParamPayload* pld, uint8_t *payloadLen);
+extern BOOL UpdateAllUserParams(allUserParamsPayload* pld, uint8_t *payloadLen);
+extern BOOL GetUserConfig(userConfigPayload* pld, uint8_t *payloadLen);
+extern BOOL GetUserParam(userParamPayload* pld, uint8_t *payloadLen);
+extern BOOL GetAllUserParams(allUserParamsPayload* pld, uint8_t *payloadLen);
+
+#endif /* USER_CONFIGURATION_H */
diff --git a/examples/OpenIMU300RI/INS/src/user/dataProcessingAndPresentation.c b/examples/OpenIMU300RI/INS/src/user/dataProcessingAndPresentation.c
new file mode 100644
index 0000000..d66f256
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/src/user/dataProcessingAndPresentation.c
@@ -0,0 +1,283 @@
+/*****************************************************************************
+ * @file dataProcessingAndPresentation.c
+ *
+ * THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
+ * KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
+ * PARTICULAR PURPOSE.
+ *
+ * contains of data post-processing framework
+ ******************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+
+#include "string.h"
+#include "userAPI.h"
+#include "sensorsAPI.h"
+#include "gpsAPI.h"
+#include "algorithmAPI.h"
+#include "UserMessagingCAN.h"
+#include "BITStatus.h"
+
+#include "Indices.h" // For X_AXIS and Z_AXIS
+#include "debug.h" // For debug commands
+
+IMUDataStruct gIMU;
+gpsDataStruct_t gGPS, gCanGps, *gpsDataPtr;
+BOOL GNSS_From_Serial = 1;
+
+// Local-function prototypes
+static void _IncrementIMUTimer(uint16_t dacqRate);
+static void _GenerateDebugMessage(uint16_t dacqRate, uint16_t debugOutputFreq);
+static void _IMUDebugMessage(void);
+static void _GPSDebugMessage(void);
+
+/* *
+ ******************
+ *
+ Sensors data processing flow (from left to right)
+
+Raw *************** Filtered * ************ Calibrated **************** ********************* Data
+Data * Built-in * Raw Data * * Data * User Filter s* * Algorithm * Output
+****** LP Filter ************* Calibration ************* (if desired) ***** (Kalman Filter ********
+ * * * * * * * or user Algorithm)*
+ ************* * ************** **************** *********************
+ ^^^^^^^
+ Can be selected during
+ initialization or turned
+ OFF
+*///<--------------------- Cyclical processing at 100 or 200 Hz in Data Acquisition Task -------------->
+
+
+// Next function is common for all platforms, but implementation of the methods inside is platform-dependent
+// Call to this function made from DataAcquisitionTask during initialization phase
+// All user algorithm and data structures should be initialized here, if used
+void initUserDataProcessingEngine()
+{
+ InitUserAlgorithm(); // default implementation located in file user_algorithm.c
+}
+
+
+// Notes:
+// 1) 'inertialAndPositionDataProcessing' is common for all platforms, but implementation
+// of the methods inside is platform and user-dependent.
+// 2) 'DataAcquisitionTask' calls this function after retrieving samples of current
+// sensors data and applying corresponding calibration
+// 3) 'dacqRate' is rate with which new set of sensors data arrives
+void inertialAndPositionDataProcessing(uint16_t dacqRate)
+{
+ // Increment the IMU timer by the calling rate of the data-acquisition task
+ _IncrementIMUTimer(dacqRate);
+
+ static uint8_t initAlgo = 1;
+ static uint8_t algoCntr = 0, algoCntrLimit = 0;
+ if(initAlgo)
+ {
+ if(GnssInputDataOverCan()){
+ gpsDataPtr = &gCanGps;
+ }else{
+ gpsDataPtr = &gGPS;
+ }
+ gpsDataPtr->gpsUpdate = FALSE;
+
+ // Reset 'initAlgo' so this is not executed more than once. This
+ // prevents the algorithm from being switched during run-time.
+ initAlgo = 0;
+
+ // Set the variables that control the algorithm execution rate
+ algoCntrLimit = (uint8_t)( (float)dacqRate / (float)gAlgorithm.callingFreq + 0.5 );
+ if( algoCntrLimit < 1 )
+ {
+ // If this logic is reached, also need to adjust the algorithm
+ // parameters to match the modified calling freq (or stop the
+ // program to indicate that the user must adjust the program)
+ algoCntrLimit = 1;
+ }
+ algoCntr = algoCntrLimit;
+ }
+ algoCntr++;
+ if(algoCntr >= algoCntrLimit)
+ {
+ // Reset counter
+ algoCntr = 0;
+
+ // Obtain accelerometer data [g]
+ GetAccelData_g(gIMU.accel_g);
+
+ // Obtain rate-sensor data [rad/sec]
+ GetRateData_radPerSec(gIMU.rate_radPerSec);
+ GetRateData_degPerSec(gIMU.rate_degPerSec);
+
+ // Obtain magnetometer data [G]
+ GetMagData_G(gIMU.mag_G);
+
+ // Obtain board temperature data [degC]
+ GetBoardTempData(&gIMU.temp_C);
+
+ // Obtain GPS data (lat/lon: deg, alt: meters, vel: m/s, ITOW: msec, )
+#ifdef GPS
+ if(!GnssInputDataOverCan()){
+ GetGPSData(gpsDataPtr);
+ }else{
+ // data should be in gCanGps if any
+ }
+#endif
+ // Execute user algorithm (default implementation located in file user_algorithm.c)
+ RunUserNavAlgorithm(gIMU.accel_g, gIMU.rate_radPerSec, gIMU.mag_G, gpsDataPtr, dacqRate);
+
+ if(gpsDataPtr->gpsUpdate){
+ gpsDataPtr->gpsUpdate = 0;
+ }
+
+ // Get algorithm status, and set the state in system status
+ AlgoStatus algoStatus;
+ GetAlgoStatus(&algoStatus);
+ gBitStatus.swStatus.all = algoStatus.all;
+ gBitStatus.swAlgBIT.bit.initialization = algoStatus.bit.algorithmInit;
+ }
+
+ // Generate a debug message that provide sensor data in order to verify the
+ // Algorithm input data is as expected.
+ _GenerateDebugMessage(dacqRate, ZERO_HZ);
+
+
+}
+
+
+//
+static void _IncrementIMUTimer(uint16_t dacqRate)
+{
+ // Initialize timer variables (used to control the output of the debug
+ // messages and the IMU timer value)
+ static int initFlag = 1;
+ if(initFlag) {
+ // Reset 'initFlag' so this section is not executed more than once.
+ initFlag = 0;
+
+ // Set the IMU output delta-counter value
+ gIMU.dTimerCntr = (uint32_t)( 1000.0 / (float)(dacqRate) + 0.5 );
+ }
+
+ // Increment the timer-counter by the sampling period equivalent to the
+ // rate at which inertialAndPositionDataProcessing is called
+ gIMU.timerCntr = gIMU.timerCntr + gIMU.dTimerCntr;
+}
+
+
+//
+static void _GenerateDebugMessage(uint16_t dacqRate, uint16_t debugOutputFreq)
+{
+ // Variables that control the output frequency of the debug statement
+ static uint8_t debugOutputCntr, debugOutputCntrLimit;
+
+ // Check debug flag. If set then generate the debug message to verify
+ // the loading of the GPS data into the GPS data structure
+ if( debugOutputFreq > ZERO_HZ ) {
+ // Initialize variables used to control the output of the debug messages
+ static int initFlag = 1;
+ if(initFlag) {
+ // Reset 'initFlag' so this section is not executed more than once.
+ initFlag = 0;
+
+ // Set the variables that control the debug-message output-rate (based on
+ // the desired calling frequency of the debug output)
+ debugOutputCntrLimit = (uint8_t)( (float)dacqRate / (float)debugOutputFreq + 0.5 );
+ debugOutputCntr = debugOutputCntrLimit;
+ }
+
+ debugOutputCntr++;
+ if(debugOutputCntr >= debugOutputCntrLimit) {
+ debugOutputCntr = 0;
+
+ // Reset 'new GPS data' flag (this should be done in UpdateFunctions
+ // to ensure the EKF can use the data)
+ //gGPS.updateFlag = 0; <-- This would make a difference as the input
+ // to the algorithm isn't set yet.
+
+ // Create message here
+ static uint8_t msgType = 1;
+ switch( msgType )
+ {
+ case 0:
+ // None
+ break;
+
+ case 1:
+ // IMU data
+ _IMUDebugMessage();
+ break;
+
+ case 2:
+ // GPS data
+ _GPSDebugMessage();
+ break;
+ }
+ }
+ }
+}
+
+
+static void _IMUDebugMessage(void)
+{
+ // IMU Data
+ DebugPrintFloat("Time: ", 0.001 * (real)gIMU.timerCntr, 3);
+ DebugPrintFloat(", a: [ ", (float)gIMU.accel_g[X_AXIS], 3);
+ DebugPrintFloat(" ", (float)gIMU.accel_g[Y_AXIS], 3);
+ DebugPrintFloat(" ", (float)gIMU.accel_g[Z_AXIS], 3);
+ DebugPrintFloat(" ], w: [ ", (float)gIMU.rate_radPerSec[X_AXIS] * RAD_TO_DEG, 3);
+ DebugPrintFloat(" ", (float)gIMU.rate_radPerSec[Y_AXIS] * RAD_TO_DEG, 3);
+ DebugPrintFloat(" ", (float)gIMU.rate_radPerSec[Z_AXIS] * RAD_TO_DEG, 3);
+ DebugPrintFloat(" ], m: [ ", (float)gIMU.mag_G[X_AXIS], 3);
+ DebugPrintFloat(" ", (float)gIMU.mag_G[Y_AXIS], 3);
+ DebugPrintFloat(" ", (float)gIMU.mag_G[Z_AXIS], 3);
+ DebugPrintString(" ]");
+ DebugPrintEndline();
+}
+
+
+static void _GPSDebugMessage(void)
+{
+#if 1
+ // GPS Data
+ DebugPrintFloat("Time: ", 0.001 * (real)gIMU.timerCntr, 3);
+ DebugPrintFloat(", Lat: ", (float)gGPS.latitude, 8);
+ DebugPrintFloat(", Lon: ", (float)gGPS.longitude, 8);
+ DebugPrintFloat(", Alt: ", (float)gGPS.altitude, 5);
+ DebugPrintLongInt(", ITOW: ", gGPS.itow );
+#else
+ //
+ DebugPrintFloat("Time: ", 0.001 * (real)gIMU.timerCntr, 3);
+ DebugPrintLongInt(", ITOW: ", gGPS.itow );
+
+ // LLA
+ DebugPrintFloat(", valid: ", (float)gGPS.gpsValid, 1);
+ // LLA
+ DebugPrintFloat(", Lat: ", (float)gGPS.latitude, 8);
+ DebugPrintFloat(", Lon: ", (float)gGPS.longitude, 8);
+ DebugPrintFloat(", Alt: ", (float)gGPS.altitude, 5);
+ // Velocity
+ //DebugPrintFloat(", vN: ", (float)gGPS.vNed[X_AXIS], 5);
+ //DebugPrintFloat(", vE: ", (float)gGPS.vNed[Y_AXIS], 5);
+ //DebugPrintFloat(", vD: ", (float)gGPS.vNed[Z_AXIS], 5);
+ // v^2
+ //double vSquared = gGPS.vNed[X_AXIS] * gGPS.vNed[X_AXIS] +
+ // gGPS.vNed[Y_AXIS] * gGPS.vNed[Y_AXIS];
+ //DebugPrintFloat(", vSq: ", (float)vSquared, 5);
+ //DebugPrintFloat(", vSq: ", (float)gGPS.rawGroundSpeed * (float)gGPS.rawGroundSpeed, 5);
+ // Newline
+#endif
+ DebugPrintEndline();
+}
diff --git a/examples/OpenIMU300RI/INS/src/user/userAPI.h b/examples/OpenIMU300RI/INS/src/user/userAPI.h
new file mode 100644
index 0000000..7bd9004
--- /dev/null
+++ b/examples/OpenIMU300RI/INS/src/user/userAPI.h
@@ -0,0 +1,72 @@
+/** ******************************************************************************
+ * @file userAPI.h API functions for Interfacing with user algorithm
+ *
+ * THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
+ * KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
+ * PARTICULAR PURPOSE.
+ *
+ *****************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+
+#ifndef _USER_API_H
+#define _USER_API_H
+
+// Some common constants used in the user algorithm logic
+#define ZERO_HZ 0
+#define ONE_HZ 1
+#define TWO_HZ 2
+#define FOUR_HZ 4
+#define FIVE_HZ 5
+#define TEN_HZ 10
+#define TWENTY_HZ 20
+#define TWENTY_FIVE_HZ 25
+#define FIFTY_HZ 50
+
+#define NUM_AXIS 3
+
+#include
+#include "gpsAPI.h"
+
+void inertialAndPositionDataProcessing(uint16_t dacqRate);
+
+void *RunUserNavAlgorithm(double *accels, double *rates, double* mags, gpsDataStruct_t *gps, uint16_t dacqRate);
+void WriteResultsIntoOutputStream(void *results) ;
+void InitUserDataStructures();
+void InitUserFilters();
+void InitUserAlgorithm();
+void initUserDataProcessingEngine();
+void userInitConfigureUnit();
+void userInitConfigureUart();
+BOOL GnssInputDataOverCan();
+
+// IMU data structure
+typedef struct {
+ // Timer output counter
+ uint32_t timerCntr, dTimerCntr;
+
+ // Algorithm states
+ double accel_g[3];
+ double rate_radPerSec[3];
+ double rate_degPerSec[3];
+ double mag_G[3];
+ double temp_C;
+} IMUDataStruct;
+
+extern IMUDataStruct gIMU;
+
+#endif
diff --git a/examples/OpenIMU300RI/VG_AHRS/board/OpenIMU300.json b/examples/OpenIMU300RI/VG_AHRS/board/OpenIMU300.json
deleted file mode 100644
index cacb4ca..0000000
--- a/examples/OpenIMU300RI/VG_AHRS/board/OpenIMU300.json
+++ /dev/null
@@ -1,38 +0,0 @@
-{
- "build": {
- "core": "stm32",
- "cpu": "cortex-m4",
- "extra_flags": [
- "-mcpu=cortex-m4",
- "-mfloat-abi=softfp",
- "-mfpu=fpv4-sp-d16",
- "-DSTM32F4",
- "-DSTM32F405RG",
- "-DSTM32F405xx"
- ],
- "ldscript": "stm32f40x.ld",
- "f_cpu": "120000000L",
- "mcu": "stm32f405rg"
- },
- "debug": {
- "default_tools": ["stlink"],
- "openocd_target": "stm32f4x",
- "jlink_device": "STM32F405RG",
- "svd_path": "STM32F40x.svd"
- },
- "frameworks": [],
- "name": "Aceinna OpenIMU 300",
- "upload": {
- "offset_address": "0x08010000",
- "maximum_ram_size": 131072,
- "maximum_size": 1048576,
- "protocols": [
- "blackmagic",
- "stlink",
- "jlink"
- ],
- "protocol": "stlink"
- },
- "url": "https://www.aceinna.com/inertial-systems/",
- "vendor": "Aceinna"
-}
diff --git a/examples/OpenIMU300RI/VG_AHRS/include/FreeRTOSConfig.h b/examples/OpenIMU300RI/VG_AHRS/include/FreeRTOSConfig.h
new file mode 100644
index 0000000..80ca6b9
--- /dev/null
+++ b/examples/OpenIMU300RI/VG_AHRS/include/FreeRTOSConfig.h
@@ -0,0 +1,180 @@
+/*
+ FreeRTOS V9.0.0 - Copyright (C) 2016 Real Time Engineers Ltd.
+ All rights reserved
+
+ VISIT http://www.FreeRTOS.org TO ENSURE YOU ARE USING THE LATEST VERSION.
+
+ This file is part of the FreeRTOS distribution.
+
+ FreeRTOS is free software; you can redistribute it and/or modify it under
+ the terms of the GNU General Public License (version 2) as published by the
+ Free Software Foundation >>>> AND MODIFIED BY <<<< the FreeRTOS exception.
+
+ ***************************************************************************
+ >>! NOTE: The modification to the GPL is included to allow you to !<<
+ >>! distribute a combined work that includes FreeRTOS without being !<<
+ >>! obliged to provide the source code for proprietary components !<<
+ >>! outside of the FreeRTOS kernel. !<<
+ ***************************************************************************
+
+ FreeRTOS is distributed in the hope that it will be useful, but WITHOUT ANY
+ WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+ FOR A PARTICULAR PURPOSE. Full license text is available on the following
+ link: http://www.freertos.org/a00114.html
+
+ ***************************************************************************
+ * *
+ * FreeRTOS provides completely free yet professionally developed, *
+ * robust, strictly quality controlled, supported, and cross *
+ * platform software that is more than just the market leader, it *
+ * is the industry's de facto standard. *
+ * *
+ * Help yourself get started quickly while simultaneously helping *
+ * to support the FreeRTOS project by purchasing a FreeRTOS *
+ * tutorial book, reference manual, or both: *
+ * http://www.FreeRTOS.org/Documentation *
+ * *
+ ***************************************************************************
+
+ http://www.FreeRTOS.org/FAQHelp.html - Having a problem? Start by reading
+ the FAQ page "My application does not run, what could be wrong?". Have you
+ defined configASSERT()?
+
+ http://www.FreeRTOS.org/support - In return for receiving this top quality
+ embedded software for free we request you assist our global community by
+ participating in the support forum.
+
+ http://www.FreeRTOS.org/training - Investing in training allows your team to
+ be as productive as possible as early as possible. Now you can receive
+ FreeRTOS training directly from Richard Barry, CEO of Real Time Engineers
+ Ltd, and the world's leading authority on the world's leading RTOS.
+
+ http://www.FreeRTOS.org/plus - A selection of FreeRTOS ecosystem products,
+ including FreeRTOS+Trace - an indispensable productivity tool, a DOS
+ compatible FAT file system, and our tiny thread aware UDP/IP stack.
+
+ http://www.FreeRTOS.org/labs - Where new FreeRTOS products go to incubate.
+ Come and try FreeRTOS+TCP, our new open source TCP/IP stack for FreeRTOS.
+
+ http://www.OpenRTOS.com - Real Time Engineers ltd. license FreeRTOS to High
+ Integrity Systems ltd. to sell under the OpenRTOS brand. Low cost OpenRTOS
+ licenses offer ticketed support, indemnification and commercial middleware.
+
+ http://www.SafeRTOS.com - High Integrity Systems also provide a safety
+ engineered and independently SIL3 certified version for use in safety and
+ mission critical applications that require provable dependability.
+
+ 1 tab == 4 spaces!
+*/
+
+
+#ifndef FREERTOS_CONFIG_H
+#define FREERTOS_CONFIG_H
+
+/*-----------------------------------------------------------
+ * Application specific definitions.
+ *
+ * These definitions should be adjusted for your particular hardware and
+ * application requirements.
+ *
+ * THESE PARAMETERS ARE DESCRIBED WITHIN THE 'CONFIGURATION' SECTION OF THE
+ * FreeRTOS API DOCUMENTATION AVAILABLE ON THE FreeRTOS.org WEB SITE.
+ *
+ * See http://www.freertos.org/a00110.html.
+ *----------------------------------------------------------*/
+
+/* Ensure stdint is only used by the compiler, and not the assembler. */
+#if defined(__ICCARM__) || defined(__CC_ARM) || defined(__GNUC__)
+ #include
+ extern uint32_t SystemCoreClock;
+#endif
+
+#define configUSE_PREEMPTION 1
+#define configUSE_IDLE_HOOK 0
+#define configUSE_TICK_HOOK 0
+#define configCPU_CLOCK_HZ (SystemCoreClock)
+#define configTICK_RATE_HZ ((TickType_t)1000)
+#define configMAX_PRIORITIES (7)
+#define configMINIMAL_STACK_SIZE ((uint16_t)2048)
+#define configTOTAL_HEAP_SIZE ((size_t)(38000))
+#define configMAX_TASK_NAME_LEN (30)
+#define configUSE_TRACE_FACILITY 1
+#define configUSE_16_BIT_TICKS 0
+#define configIDLE_SHOULD_YIELD 1
+#define configUSE_MUTEXES 1
+#define configQUEUE_REGISTRY_SIZE 8
+#define configCHECK_FOR_STACK_OVERFLOW 1
+#define configUSE_RECURSIVE_MUTEXES 1
+#define configUSE_MALLOC_FAILED_HOOK 1
+#define configUSE_APPLICATION_TASK_TAG 0
+#define configUSE_COUNTING_SEMAPHORES 1
+#define configGENERATE_RUN_TIME_STATS 0
+#define configAPPLICATION_ALLOCATED_HEAP 0
+
+/* Co-routine definitions. */
+#define configUSE_CO_ROUTINES 0
+#define configMAX_CO_ROUTINE_PRIORITIES (2)
+
+/* Software timer definitions. */
+#define configUSE_TIMERS 0
+#define configTIMER_TASK_PRIORITY (2)
+#define configTIMER_QUEUE_LENGTH 10
+#define configTIMER_TASK_STACK_DEPTH (configMINIMAL_STACK_SIZE * 2)
+
+/* Set the following definitions to 1 to include the API function, or zero
+to exclude the API function. */
+#define INCLUDE_vTaskPrioritySet 1
+#define INCLUDE_uxTaskPriorityGet 1
+#define INCLUDE_vTaskDelete 1
+#define INCLUDE_vTaskCleanUpResources 0
+#define INCLUDE_vTaskSuspend 1
+#define INCLUDE_vTaskDelayUntil 0
+#define INCLUDE_vTaskDelay 1
+#define INCLUDE_xTaskGetSchedulerState 1
+
+/* Cortex-M specific definitions. */
+#ifdef __NVIC_PRIO_BITS
+ /* __BVIC_PRIO_BITS will be specified when CMSIS is being used. */
+ #define configPRIO_BITS __NVIC_PRIO_BITS
+#else
+ #define configPRIO_BITS 4 /* 15 priority levels */
+#endif
+
+/* The lowest interrupt priority that can be used in a call to a "set priority"
+function. */
+#define configLIBRARY_LOWEST_INTERRUPT_PRIORITY 0xf
+
+/* The highest interrupt priority that can be used by any interrupt service
+routine that makes calls to interrupt safe FreeRTOS API functions. DO NOT CALL
+INTERRUPT SAFE FREERTOS API FUNCTIONS FROM ANY INTERRUPT THAT HAS A HIGHER
+PRIORITY THAN THIS! (higher priorities are lower numeric values. */
+#define configLIBRARY_MAX_SYSCALL_INTERRUPT_PRIORITY 1
+
+
+//#define configKERNEL_INTERRUPT_PRIORITY ( 0x01 << 4 ) /* Priority 15, or 255 as only the top four bits are implemented. This is the lowest priority. */
+//#define configMAX_SYSCALL_INTERRUPT_PRIORITY ( 0x01 << 4 ) /* Priority 5, or 80 as only the top four bits are implemented. */
+
+
+/* Interrupt priorities used by the kernel port layer itself. These are generic
+to all Cortex-M ports, and do not rely on any particular library functions. */
+#define configKERNEL_INTERRUPT_PRIORITY ( configLIBRARY_LOWEST_INTERRUPT_PRIORITY << (8 - configPRIO_BITS) )
+/* !!!! configMAX_SYSCALL_INTERRUPT_PRIORITY must not be set to zero !!!!
+See http://www.FreeRTOS.org/RTOS-Cortex-M3-M4.html. */
+#define configMAX_SYSCALL_INTERRUPT_PRIORITY ( configLIBRARY_MAX_SYSCALL_INTERRUPT_PRIORITY << (8 - configPRIO_BITS) )
+
+/* Normal assert() semantics without relying on the provision of an assert.h
+header file. */
+#define configASSERT( x ) if( ( x ) == 0 ) { taskDISABLE_INTERRUPTS(); for( ;; ); }
+
+/* Definitions that map the FreeRTOS port interrupt handlers to their CMSIS
+ standard names. */
+#define vPortSVCHandler SVC_Handler
+#define xPortPendSVHandler PendSV_Handler
+
+/* IMPORTANT: This define MUST be commented when used with STM32Cube firmware,
+ to prevent overwriting SysTick_Handler defined within STM32Cube HAL */
+//#define xPortSysTickHandler SysTick_Handler
+#define osSystickHandler SysTick_Handler
+
+#endif /* FREERTOS_CONFIG_H */
+
diff --git a/examples/OpenIMU300RI/VG_AHRS/include/osresources.h b/examples/OpenIMU300RI/VG_AHRS/include/osresources.h
new file mode 100644
index 0000000..47ac800
--- /dev/null
+++ b/examples/OpenIMU300RI/VG_AHRS/include/osresources.h
@@ -0,0 +1,42 @@
+#ifndef _OS_RES_H
+#define _OS_RES_H
+#include "cmsis_os.h"
+#include "portmacro.h"
+
+
+#ifdef __MAIN
+
+osSemaphoreDef(GYRO_READY_SEM);
+osSemaphoreDef(ACCEL_READY_SEM);
+osSemaphoreDef(MAG_READY_SEM);
+osSemaphoreDef(TEMP_READY_SEM);
+osSemaphoreDef(NAV_DATA_READY_SEM);
+osSemaphoreDef(CLI_READY_SEM);
+osSemaphoreDef(DATA_ACQ_SEM);
+osSemaphoreDef(CAN_DATA_SEM);
+osSemaphoreDef(CLI_SEM);
+osSemaphoreId gyroReadySem;
+osSemaphoreId accelReadySem;
+osSemaphoreId magReadySem;
+osSemaphoreId tempReadySem;
+osSemaphoreId navDataReadySem;
+osSemaphoreId cliReadySem;
+osSemaphoreId dataAcqSem;
+osSemaphoreId canDataSem;
+osSemaphoreId cliSem;
+
+#else
+
+extern osSemaphoreId gyroReadySem;
+extern osSemaphoreId accelReadySem;
+extern osSemaphoreId magReadySem;
+extern osSemaphoreId tempReadySem;
+extern osSemaphoreId navDataReadySem;
+extern osSemaphoreId dataAcqSem;
+extern osSemaphoreId canDataSem;
+extern osSemaphoreId cliSem;
+
+#endif
+
+
+#endif
diff --git a/examples/OpenIMU300RI/VG_AHRS/ldscripts/stm32f40x.ld b/examples/OpenIMU300RI/VG_AHRS/ldscripts/stm32f40x.ld
deleted file mode 100644
index 1c0c9f6..0000000
--- a/examples/OpenIMU300RI/VG_AHRS/ldscripts/stm32f40x.ld
+++ /dev/null
@@ -1,202 +0,0 @@
-/*
-*****************************************************************************
-**
-
-** File : LinkerScript.ld
-**
-** Abstract : Linker script for STM32F405RGx Device with
-** 1024KByte FLASH, 128KByte RAM
-**
-** Set heap size, stack size and stack location according
-** to application requirements.
-**
-** Set memory bank area and size if external memory is used.
-**
-** Target : STMicroelectronics STM32
-**
-**
-** Distribution: The file is distributed as is, without any warranty
-** of any kind.
-**
-*****************************************************************************
-** @attention
-**
-** © COPYRIGHT(c) 2014 Ac6
-**
-** Redistribution and use in source and binary forms, with or without modification,
-** are permitted provided that the following conditions are met:
-** 1. Redistributions of source code must retain the above copyright notice,
-** this list of conditions and the following disclaimer.
-** 2. Redistributions in binary form must reproduce the above copyright notice,
-** this list of conditions and the following disclaimer in the documentation
-** and/or other materials provided with the distribution.
-** 3. Neither the name of Ac6 nor the names of its contributors
-** may be used to endorse or promote products derived from this software
-** without specific prior written permission.
-**
-** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
-** AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
-** IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
-** DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
-** FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
-** DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
-** SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
-** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
-** OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
-** OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-**
-*****************************************************************************
-*/
-
-/* Entry Point */
-ENTRY(Reset_Handler)
-
-/* Highest address of the user mode stack */
-_estack = 0x2001ff00; /* end of RAM */
-/* Generate a link error if heap and stack don't fit into RAM */
-_Min_Heap_Size = 0x2000; /* required amount of heap */
-_Min_Stack_Size = 0x2000; /* required amount of stack */
-
-/* Specify the memory areas */
-MEMORY
-{
-FLASH (rx) : ORIGIN = 0x08010000, LENGTH = 448K
-EEPROM (rw) : ORIGIN = 0x08008000, LENGTH = 16K
-USER_EEPROM(rw) : ORIGIN = 0x0800C000, LENGTH = 16K
-RAM (xrw) : ORIGIN = 0x20000000, LENGTH = 128K
-}
-
-/* Define output sections */
-SECTIONS
-{
- /* The startup code goes first into FLASH */
- .isr_vector :
- {
- . = ALIGN(4);
- KEEP(*(.isr_vector)) /* Startup code */
- . = ALIGN(4);
- } >FLASH
-
- /* The program code and other data goes into FLASH */
- .text :
- {
- . = ALIGN(4);
- *(.text) /* .text sections (code) */
- *(.text*) /* .text* sections (code) */
- *(.glue_7) /* glue arm to thumb code */
- *(.glue_7t) /* glue thumb to arm code */
- *(.eh_frame)
-
- KEEP (*(.init))
- KEEP (*(.fini))
-
- . = ALIGN(4);
- _etext = .; /* define a global symbols at end of code */
- } >FLASH
-
- /* Constant data goes into FLASH */
- .rodata :
- {
- . = ALIGN(4);
- *(.rodata) /* .rodata sections (constants, strings, etc.) */
- *(.rodata*) /* .rodata* sections (constants, strings, etc.) */
- . = ALIGN(4);
- } >FLASH
-
- .ARM.extab : { *(.ARM.extab* .gnu.linkonce.armextab.*) } >FLASH
- .ARM : {
- __exidx_start = .;
- *(.ARM.exidx*)
- __exidx_end = .;
- } >FLASH
-
- .preinit_array :
- {
- PROVIDE_HIDDEN (__preinit_array_start = .);
- KEEP (*(.preinit_array*))
- PROVIDE_HIDDEN (__preinit_array_end = .);
- } >FLASH
- .init_array :
- {
- PROVIDE_HIDDEN (__init_array_start = .);
- KEEP (*(SORT(.init_array.*)))
- KEEP (*(.init_array*))
- PROVIDE_HIDDEN (__init_array_end = .);
- } >FLASH
- .fini_array :
- {
- PROVIDE_HIDDEN (__fini_array_start = .);
- KEEP (*(SORT(.fini_array.*)))
- KEEP (*(.fini_array*))
- PROVIDE_HIDDEN (__fini_array_end = .);
- } >FLASH
-
- /* used by the startup to initialize data */
- _sidata = LOADADDR(.data);
-
- /* Initialized data sections goes into RAM, load LMA copy after code */
- .data :
- {
- . = ALIGN(4);
- _sdata = .; /* create a global symbol at data start */
- *(.data) /* .data sections */
- *(.data*) /* .data* sections */
-
- . = ALIGN(4);
- _edata = .; /* define a global symbol at data end */
- } >RAM AT> FLASH
-
-
- /* Uninitialized data section */
- . = ALIGN(4);
- .bss :
- {
- /* This is used by the startup in order to initialize the .bss secion */
- _sbss = .; /* define a global symbol at bss start */
- __bss_start__ = _sbss;
- *(.bss)
- *(.bss*)
- *(COMMON)
-
- . = ALIGN(4);
- _ebss = .; /* define a global symbol at bss end */
- __bss_end__ = _ebss;
- } >RAM
-
- /* User_heap_stack section, used to check that there is enough RAM left */
- ._user_heap_stack :
- {
- . = ALIGN(8);
- PROVIDE ( end = . );
- PROVIDE ( _end = . );
- . = . + _Min_Heap_Size;
- . = . + _Min_Stack_Size;
- . = ALIGN(8);
- } >RAM
-
- .eeprom 0x08008000:
- {
- . = ALIGN(4);
- KEEP(*(.xbowEeprom)) /* keep my variable even if not referenced */
- . = ALIGN(4);
- _eeeprom = .; /* define a global symbols at end of code */
- } >EEPROM
-
- .usereeprom 0x0800C000:
- {
- . = ALIGN(4);
- KEEP(*(.userEeprom)) /* keep my variable even if not referenced */
- . = ALIGN(4);
- _eusereeprom = .; /* define a global symbols at end of code */
- } >USER_EEPROM
-
- /* Remove information from the standard libraries */
- /DISCARD/ :
- {
- libc.a ( * )
- libm.a ( * )
- libgcc.a ( * )
- }
-
- .ARM.attributes 0 : { *(.ARM.attributes) }
-}
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/algorithmAPI.h b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/algorithmAPI.h
index 80b664b..95f0185 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/algorithmAPI.h
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/algorithmAPI.h
@@ -36,7 +36,7 @@ limitations under the License.
*
* @retval N/A
*****************************************************************************/
-void InitializeAlgorithmStruct(uint16_t callingFreq);
+void InitializeAlgorithmStruct(uint8_t callingFreq);
/******************************************************************************
* @brief Get algorithm status.
@@ -68,7 +68,23 @@ void enableGpsInAlgorithm(BOOL enable);
BOOL gpsUsedInAlgorithm();
-void SetAlgorithmUseDgps(BOOL d);
+void enableOdoInAlgorithm(BOOL enable);
+
+BOOL odoUsedInAlgorithm();
+
+void enableFreeIntegration(BOOL enable);
+
+BOOL freeIntegrationEnabled();
+
+void enableStationaryLockYaw(BOOL enable);
+
+BOOL stationaryLockYawEnabled();
+
+void enableImuStaticDetect(BOOL enable);
+
+BOOL imuStaticDetectEnabled();
+
+void SetAlgorithmUseDgps(BOOL d);
void updateAlgorithmTimings(int corr, uint32_t tmrVal );
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/AlgorithmLimits.h b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/AlgorithmLimits.h
index 0aa7590..6a1262c 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/AlgorithmLimits.h
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/AlgorithmLimits.h
@@ -39,12 +39,13 @@ limitations under the License.
#define LIMIT_BIAS_RATE_UPDATE_INS 5.0e-4
#define LIMIT_MIN_GPS_VELOCITY_HEADING 0.45 //0.45 m/s ~= 1.0 mph
+#define RELIABLE_GPS_VELOCITY_HEADING 1.0 // velocity of 1.0m/s should provide reliable GNSS heading
#define LIMIT_OBS_JACOBIAN_DENOM 1e-3;
// The following times are compared against ITOW (units in [msec])
-//#define LIMIT_MAX_GPS_DROP_TIME 3 // 3 [sec]
-#define LIMIT_MAX_GPS_DROP_TIME 30 // [sec]
+#define LIMIT_MAX_GPS_DROP_TIME 300 // [sec]
+#define LIMIT_RELIABLE_DR_TIME 10 // [sec]
#define LIMIT_MAX_REST_TIME_BEFORE_DROP_TO_AHRS 60000 // 60000 [ msec ] = 60 [ sec ]
#define LIMIT_MAX_REST_TIME_BEFORE_HEADING_INVALID 120000 // 120sec, heading drifts much slower than pos
#define LIMIT_DECL_EXPIRATION_TIME 60000 // 60,000 [ counts ] = 10 [ min ]
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/EKF_Algorithm.h b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/EKF_Algorithm.h
index f6bc5b0..6c0e946 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/EKF_Algorithm.h
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/EKF_Algorithm.h
@@ -14,6 +14,7 @@
#include "StateIndices.h"
#include "gpsAPI.h" // For gpsDataStruct_t in EKF setter
+#include "odoAPI.h"
#include "Indices.h"
@@ -30,8 +31,6 @@ typedef struct {
real rateBias_B[NUM_AXIS];
real accelBias_B[NUM_AXIS];
- real stateUpdate[NUMBER_OF_EKF_STATES];
-
// Prediction variables: P = FxPxFTranspose + Q
real F[NUMBER_OF_EKF_STATES][NUMBER_OF_EKF_STATES];
real P[NUMBER_OF_EKF_STATES][NUMBER_OF_EKF_STATES];
@@ -42,27 +41,47 @@ typedef struct {
* is symmetric, only 6 off-diagonal terms need stored.
*/
- real correctedRate_B[NUM_AXIS];
- real correctedAccel_B[NUM_AXIS];
- real aCorr_N[NUM_AXIS];
+ real correctedRate_B[NUM_AXIS]; // [rad/s]
+ real correctedAccel_B[NUM_AXIS]; // [m/s/s]
+ real linearAccel_B[NUM_AXIS]; // [m/s/s], linear acceleration in body frame, used to detect drive position
+
+ /* Algorithm results. Velocity states are directly used as results for output.
+ * The following two are calculated from state
+ */
+ real eulerAngles[NUM_AXIS];
+ double llaDeg[NUM_AXIS];
- real R_BinN[NUM_AXIS][NUM_AXIS]; // convert body to NED
- real eulerAngles[NUM_AXIS], measuredEulerAngles[NUM_AXIS];
+ // measurements
+ real R_BinN[3][3]; // convert body to NED
+ real Rn2e[3][3]; // Coordinate tranformation matrix from NED to ECEF
+ real measuredEulerAngles[3]; // Euler angles measurements
+ real rGPS_N[3]; // current IMU position w.r.t rGPS0_E in NED.
+ double rGPS0_E[3]; // Initial IMU ECEF position when first entering INS state.
+ double rGPS_E[3]; // current IMU ECEF position
// Update variables: S = HxPxHTranspose + R
- // DEBUG H is 3x16 or 9x16 (AHRS vs INS)
real nu[9];
-
real H[3][NUMBER_OF_EKF_STATES];
real R[9];
real K[NUMBER_OF_EKF_STATES][3];
+ real stateUpdate[NUMBER_OF_EKF_STATES];
+ real deltaP_tmp[NUMBER_OF_EKF_STATES][NUMBER_OF_EKF_STATES];
- double llaDeg[NUM_AXIS];
-// double Position_E[NUM_AXIS];
-
+ // The following two are used in more than one functions, so they are pre-computed.
real wTrueTimesDtOverTwo[NUM_AXIS];
-
real turnSwitchMultiplier;
+
+ // saved states when pps comes in
+ real ppsP[NUMBER_OF_EKF_STATES][NUMBER_OF_EKF_STATES];
+ real phi[NUMBER_OF_EKF_STATES][NUMBER_OF_EKF_STATES];
+ real dQ[NUMBER_OF_EKF_STATES][NUMBER_OF_EKF_STATES];
+ real ppsPosition_N[NUM_AXIS];
+ real ppsVelocity_N[NUM_AXIS];
+ //real ppsQuaternion[4];
+ real ppsEulerAngles[NUM_AXIS];
+ //real ppsRateBias_B[NUM_AXIS];
+ //real ppsAccelBias_B[NUM_AXIS];
+ uint32_t ppsITow;
} KalmanFilterStruct;
extern KalmanFilterStruct gKalmanFilter;
@@ -70,27 +89,37 @@ extern KalmanFilterStruct gKalmanFilter;
/* Global Algorithm structure */
typedef struct {
// Sensor readings in the body-frame (B)
- real accel_B[NUM_AXIS]; // [g]
- real angRate_B[NUM_AXIS]; // [rad/s]
- real magField_B[NUM_AXIS]; // [G]
+ real accel_B[NUM_AXIS]; // [m/s/s]
+ real angRate_B[NUM_AXIS]; // [rad/s]
+ real magField_B[NUM_AXIS]; // [G]
// GPS information
- BOOL gpsValid;
- BOOL gpsUpdate;
-
- double llaRad[3];
- double vNed[NUM_AXIS];
-
- double trueCourse;
- double rawGroundSpeed;
-
uint32_t itow;
-
- float GPSHorizAcc, GPSVertAcc;
+ double llaAnt[3]; // Antenna Lat, Lon, ellipsoid Altitude, [rad, rad, meter]
+ double vNedAnt[NUM_AXIS]; // Antenna NED velocity, [m/s, m/s, m/s]
+ double lla[3]; // IMU Lat, Lon, ellipsoid Altitude, [rad, rad, meter]
+ double vNed[3]; // IMU NED velocity, [m/s, m/s, m/s]
+ float geoidAboveEllipsoid; // [m]
+ real trueCourse; // Antenna heading, [deg]
+ real rawGroundSpeed; // IMU ground speed, calculated from vNed, [m/s]
+ float GPSHorizAcc; // [m]
+ float GPSVertAcc; // [m]
float HDOP;
+ uint8_t gpsFixType; // Indicate if this GNSS measurement is valid
+ uint8_t numSatellites; /* Num of satellites in this GNSS measurement.
+ * This is valid only when there is gps udpate.
+ */
+ BOOL gpsUpdate; // Indicate if GNSS measurement is updated.
+
+ // odometer
+ BOOL odoUpdate; // indicate if odo measurement is updated
+ real odoVelocity; // velocity from odo, [m/s]
+
+ // 1PPS from GNSS receiver
+ BOOL ppsDetected;
} EKF_InputDataStruct;
-extern EKF_InputDataStruct gEKFInputData;
+extern EKF_InputDataStruct gEKFInput;
/* Global Algorithm structure */
@@ -113,21 +142,13 @@ typedef struct {
uint8_t opMode;
uint8_t turnSwitchFlag;
uint8_t linAccelSwitch;
- uint8_t gpsMeasurementUpdate;
} EKF_OutputDataStruct;
-extern EKF_OutputDataStruct gEKFOutputData;
+extern EKF_OutputDataStruct gEKFOutput;
+
-typedef struct
-{
- BOOL bValid; // tell if stats are valid
- BOOL accelErrLimit; // accelErr is set to max/min limit
- real lpfAccel[3]; // low-pass filtered accel
- real accelNorm; // magnitude of current accel
- real accelMean[3]; // average of past n accel
- real accelVar[3]; // variance of past n accel
- real accelErr[3]; // estimated accel error
-} AccelStatsStruct;
+// Initialize Kalman filter parameters of the INS app
+uint8_t InitINSFilter(void);
void EKF_Algorithm(void);
void enableFreeIntegration(BOOL enable);
@@ -148,7 +169,9 @@ void EKF_GetOperationalMode(uint8_t *EKF_OperMode);
void EKF_GetOperationalSwitches(uint8_t *EKF_LinAccelSwitch, uint8_t *EKF_TurnSwitch);
// Setter functions
-void EKF_SetInputStruct(double *accels, double *rates, double *mags, gpsDataStruct_t *gps);
+void EKF_SetInputStruct(double *accels, double *rates, double *mags,
+ gpsDataStruct_t *gps, odoDataStruct_t *odo,
+ BOOL ppsDetected);
void EKF_SetOutputStruct(void);
#endif /* _EKF_ALGORITHM_H_ */
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/MotionStatus.h b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/MotionStatus.h
new file mode 100644
index 0000000..785ac68
--- /dev/null
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/MotionStatus.h
@@ -0,0 +1,90 @@
+/*****************************************************************************
+ * @file MotionStatus.h
+ * @brief Calculate sensor stats, and detect motion status using IMU/ODO/GNSS
+ * @author Dong Xiaoguang
+ * @version 1.0
+ * @date 20190801
+ *****************************************************************************/
+
+#ifndef MOTION_STATUS_H_INCLUDED
+#define MOTION_STATUS_H_INCLUDED
+
+#include
+#include "GlobalConstants.h"
+#include "algorithm.h"
+
+
+typedef struct
+{
+ BOOL bValid; // tell if stats are valid
+ BOOL bStaticIMU; // Static period detected by IMU
+ BOOL accelErrLimit; // accelErr is set to max/min limit
+ real lpfAccel[3]; // [m/s/s], low-pass filtered accel
+ real accelNorm; // [m/s/s], magnitude of current accel
+ real accelMean[3]; // [m/s/s], average of past n accel samples
+ real accelVar[3]; // [m/s/s]^2, variance of past n accel samples
+ real accelErr[3]; // [m/s/s], estimated accel error
+ real lpfGyro[3]; // [rad/s], low-pass filtered gyro
+ real gyroMean[3]; // [rad/s], average of past n gyro samples
+ real gyroVar[3]; // [rad/s]^2, variance of past n gyro samples
+} ImuStatsStruct;
+
+/******************************************************************************
+ * @brief Calculate IMU data stats, and detect zero velocity.
+ * TRACE:
+ * @param [in] gyro [rad/s]
+ * @param [in] accel [m/s/s]
+ * @param [in] reset TRUE to reset this process
+ * @param [Out] imuStats results
+ * @retval None.
+******************************************************************************/
+void MotionStatusImu(real *gyro, real *accel, ImuStatsStruct *imuStats, BOOL reset);
+
+/******************************************************************************
+ * @brief Using gyro propagation to estimate accel error.
+ * g_dot = -cross(w, g), g is gravity and w is angular rate.
+ * TRACE:
+ * @param [in] accel Input accel, m/s/s.
+ * @param [in] w Input angular rate, rad/s.
+ * @param [in] dt Sampling interval, sec.
+ * @param [in] staticDelay A Counter. When static period detected, delay [staticDelay] samples before
+ * lowering accel error. [staticDelay] is also used to reset initial accel that
+ * is propagated using gyro to estimate future accel.
+ * @param [out] gAccelStats A struct for results storage.
+ * @retval None.
+******************************************************************************/
+void EstimateAccelError(real *accel, real *w, real dt, uint32_t staticDelay, ImuStatsStruct *gAccelStats);
+
+/******************************************************************************
+ * @brief Detect motion according to the difference between measured accel magnitude and 1g.
+ * Set gAlgorithm.linAccelSwitch to be True if being static for a while.
+ * This result is no longer used in current algorithm.
+ * TRACE:
+ * @param [in] accelNorm Input accel magnitude, g.
+ * @param [in] iReset Reset the procedure.
+ * @retval Always true.
+******************************************************************************/
+BOOL DetectMotionFromAccel(real accelNorm, int iReset);
+
+/******************************************************************************
+ * @brief Detect zero velocity using GNSS speed.
+ * TRACE:
+ * @param [in] vNED NED velocity measured by GNSS [m/s]
+ * @param [in] gnssValid Indicate if GNSS measurement is valid.
+ * If valid, vNED will be used to detect zero velocity.
+ * If not, detection will be reset and FALSE is always
+ * returned.
+ * @retval TRUE if static, otherwise FALSE.
+******************************************************************************/
+BOOL DetectStaticGnssVelocity(double *vNED, real threshold, BOOL gnssValid);
+
+/******************************************************************************
+ * @brief Detect zero velocity using odometer data.
+ * TRACE:
+ * @param [in] odo velocity measured by odometer [m/s]
+ * @retval TRUE if static, otherwise FALSE.
+******************************************************************************/
+BOOL DetectStaticOdo(real odo);
+
+#endif // MOTION_STATUS_H_INCLUDED
+
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/SensorNoiseParameters.h b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/SensorNoiseParameters.h
index 462161a..5b509d2 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/SensorNoiseParameters.h
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/SensorNoiseParameters.h
@@ -10,13 +10,30 @@
#include "GlobalConstants.h"
- // Add 25% uncertainty to the noise parameter
-#define SENSOR_NOISE_RATE_STD_DEV (1.25 * 1e-1 * D2R)
-#define SENSOR_NOISE_ACCEL_STD_DEV 1.25 * 7.0e-4 * GRAVITY
-#define SENSOR_NOISE_MAG_STD_DEV 0.00 // todo tm20160603 - ?check this value ?
-
-#define R_VALS_GPS_TRACK 0.1
-
+// IMU spec
+#define RW_ODR 100.0 /* [Hz], The data sampling rate when calculate ARW and VRW.
+ * ARW = sigma * sqrt(dt) = sigma * sqrt(1/ODR)
+ */
+#define ARW_300ZA 8.73e-5 /* [rad/sqrt(s)], gyro angular random walk, sampled at 100Hz
+ * 0.3deg/sqrt(Hr) = 0.3 / 60 * D2R = 8.72664625997165e-05rad/sqrt(s)
+ */
+#define BIW_300ZA 2.91e-5 /* [rad/s], gyro bias instability
+ * 6.0deg/Hr = 6.0 / 3600 * D2R = 2.90888208665722e-05rad/s
+ */
+#define MAX_BW 8.73e-3 /* [rad/s], max possible gyro bias
+ * 0.5deg/s = 0.5 * D2R = 0.00872664625997165rad/s
+ */
+#define VRW_300ZA 1.0e-3 /* [m/s/sqrt(s)], accel velocity random walk, sampled at 100Hz
+ * 0.06m/s/sqrt(Hr) = 0.06 / 60 = 0.001m/s/sqrt(s)
+ */
+#define BIA_300ZA 10.0e-6 * GRAVITY /* [m/s/s], accel bias instability
+ * 10ug = 10.0e-6g * GRAVITY
+ */
+#define MAX_BA 3.0e-3 * GRAVITY /* [m/s/s], max possible accel bias
+ * 3mg = 3.0e-3g * GRAVITY
+ */
+
+// GNSS spec
#define R_VALS_GPS_POS_X 5.0
#define R_VALS_GPS_POS_Y 5.0
#define R_VALS_GPS_POS_Z 7.5
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/TimingVars.h b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/TimingVars.h
index 1799cbc..5f545f0 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/TimingVars.h
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/TimingVars.h
@@ -33,6 +33,7 @@ float TimingVars_GetTime(void);
void TimingVars_SetTMin(float tMin);
float TimingVars_GetTMin(void);
+void TimingVars_dacqFrequency(int freq);
void TimingVars_DisplayTimerVars(signed long timeStep);
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/algorithm.h b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/algorithm.h
index 47e11f3..8b92c36 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/algorithm.h
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/include/algorithm.h
@@ -47,6 +47,12 @@ limitations under the License.
#define HIGH_GAIN_AHRS_DURATION 30.0 // 60.0 * SAMPLING_RATE
#define LOW_GAIN_AHRS_DURATION 30.0 // 30.0 * SAMPLING_RATE
+// Define heading initialization reliability
+#define HEADING_UNINITIALIZED 0
+#define HEADING_MAG 1
+#define HEADING_GNSS_LOW 2
+#define HEADING_GNSS_HIGH 3
+
typedef struct {
uint32_t Stabilize_System; // SAMPLING_RATE * 0.36
uint32_t Initialize_Attitude; // SAMPLING_RATE * ( 1.0 - 0.36 )
@@ -61,13 +67,16 @@ typedef struct {
} InnovationStruct;
typedef struct {
- int32_t Max_GPS_Drop_Time; // [msec]
+ int32_t maxGpsDropTime; // [msec]
+ int32_t maxReliableDRTime; /* [msec] When GPS outage duration exceeds this limit,
+ * the position and velocity will be reinitialized when GPS
+ * is available again. Otherwise, the fusion algorithm will
+ * gradually correct the position and velocity to the GPS.
+ */
int32_t Max_Rest_Time_Before_Drop_To_AHRS; // [msec]
int32_t Declination_Expiration_Time; // [msec]
uint16_t Free_Integration_Cntr; // [count]
-//#define LIMIT_MAX_REST_TIME_BEFORE_DROP_TO_AHRS 60000 // 60000 [ msec ] = 60 [ sec ]
-//#define LIMIT_DECL_EXPIRATION_TIME 60000 // 60,000 [ counts ] = 10 [ min ]
real accelSwitch;
uint32_t linAccelSwitchDelay;
@@ -76,14 +85,16 @@ typedef struct {
} LimitStruct;
/// specifying how the user sets up the device algorithm
-struct algoBehavior_BITS { /// bits description
- uint16_t freeIntegrate : 1; /// 0
- uint16_t useMag : 1; /// 1
- uint16_t useGPS : 1; /// 2 - Not used yet
- uint16_t stationaryLockYaw : 1; /// 3 - Not used yet
- uint16_t restartOnOverRange : 1; /// 4
- uint16_t dynamicMotion : 1; /// 5 - Not used
- uint16_t rsvd : 10; /// 6:15
+struct algoBehavior_BITS { // bits description
+ uint16_t freeIntegrate : 1; // 0
+ uint16_t useMag : 1; // 1
+ uint16_t useGPS : 1; // 2
+ uint16_t useOdo : 1; // 3
+ uint16_t enableStationaryLockYaw : 1; // 4
+ uint16_t restartOnOverRange : 1; // 5
+ uint16_t dynamicMotion : 1; // 6
+ uint16_t enableImuStaticDetect : 1; // 7
+ uint16_t rsvd : 8; // 8:15
};
union AlgoBehavior
@@ -95,15 +106,25 @@ union AlgoBehavior
// Algorithm states
struct ALGO_STATUS_BITS
{
- uint16_t algorithmInit : 1; // 0 algorithm initialization
- uint16_t highGain : 1; // 1 high gain mode
+ uint16_t algorithmInit : 1; // 0 algorithm initialization
+ uint16_t highGain : 1; // 1 high gain mode
uint16_t attitudeOnlyAlgorithm : 1; // 2 attitude only algorithm
- uint16_t turnSwitch : 1; // 3 turn switch
- uint16_t noAirdataAiding : 1; // 4 airdata aiding
- uint16_t noMagnetometerheading : 1; // 5 magnetometer heading
- uint16_t noGPSTrackReference : 1; // 6 GPS track
- uint16_t gpsUpdate : 1; // 7 GPS measurement update
- uint16_t rsvd : 8; // 8:15
+ uint16_t turnSwitch : 1; // 3 turn switch
+ uint16_t linearAccel : 1; // 4 Linear acceleration detected by difference from gravity
+ uint16_t staticImu : 1; // 5 zero velocity detected by IMU
+ uint16_t gpsHeadingValid : 1; /* 6 When GPS velocity is above a certain threshold,
+ * this is set to TRUE, and GPS heading measurement
+ * is used, otherwise, this is set to FALSE and magnetic
+ * heading (if available) is used.
+ */
+ uint16_t stationaryYawLock : 1; // 7 Yaw is locked when unit is static
+ uint16_t ppsAvailable : 1; /* 8.
+ * This will be initialized as FALSE.
+ * This will become TRUE when PPS is detected for the first time.
+ * This will become FALSE when PPS has not been detected for more than 2sec.
+ * This will become FALSE when GNSS measurement is refrshed and used.
+ */
+ uint16_t rsvd : 7; // 9:15
};
typedef union ALGO_STATUS
@@ -114,57 +135,92 @@ typedef union ALGO_STATUS
extern AlgoStatus gAlgoStatus;
+typedef struct
+{
+ real arw; // [rad/sqrt(s)], gyro angle random walk
+ real sigmaW; // [rad/s], gyro noise std
+ real biW; // [rad/s], gyro bias instability
+ real maxBiasW; // [rad/s], max possible gyro bias
+ real vrw; // [m/s/sqrt(s)], accel velocity random walk
+ real sigmaA; // [m/s/s], accel noise std
+ real biA; // [m/s/s], accel bias instability
+ real maxBiasA; // [m/s/s], max possible accel bias
+} IMU_SPEC;
+
+typedef struct
+{
+ real staticVarGyro; // [rad/s]^2
+ real staticVarAccel; // [m/s/s]^2
+ real maxGyroBias; // [rad/s]
+ real staticGnssVel; // [m/s]
+ real staticNoiseMultiplier[3]; /* Use IMU noise level and gyro output to detect static period.
+ * The nominal noise level and max gyro bias of an IMU is defined in
+ * SensorNoiseParameters.h. These parameters are determined by IMU
+ * output when static and are hightly related to ARW and VRW.
+ * When IMU is installed on a vehicle, its noise level when
+ * vehicle is static could be higher than the nominal noise
+ * level due to vibration. This setting is used to scale
+ * the nominal noise level and gyro bias for static detection.
+ * [scale_gyro_var, scale_accel_var, scale_gyro_bias]
+ */
+} STATIC_DETECT_SETTING;
+
+
/* Global Algorithm structure */
typedef struct {
- uint32_t itow;
- uint32_t dITOW;
+ uint32_t itow;
+ uint32_t dITOW;
+
+ // control the stage of operation for the algorithms
+ uint32_t stateTimer;
+ uint8_t state; // takes values from HARDWARE_STABILIZE to INIT_ATTITUDE to HG_AHRS
- // control the stage of operation for the algorithms
- uint32_t stateTimer;
- uint8_t state; // takes values from HARDWARE_STABILIZE to INIT_ATTITUDE to HG_AHRS
+ uint8_t insFirstTime;
+ uint8_t headingIni;
+ uint8_t applyDeclFlag;
- uint8_t insFirstTime;
- uint8_t gnssHeadingFirstTime;
- uint8_t applyDeclFlag;
+ int32_t timeOfLastSufficientGPSVelocity;
+ int32_t timeOfLastGoodGPSReading;
- int32_t timeOfLastSufficientGPSVelocity;
- int32_t timeOfLastGoodGPSReading;
+ real filteredYawRate; // Yaw-Rate (Turn-Switch) filter
- real rGPS_N[3]; // current IMU position (lever-arm) w.r.t rGPS0_E in NED.
- real R_NinE[3][3]; // convert NED to ECEF
- double rGPS0_E[3]; // Initial antenna ECEF position when first entering INS state
- double rGPS_E[3]; // current antenna ECEF position
+ /* The following variables are used to increase the Kalman filter gain when the
+ * acceleration is very close to one (i.e. the system is at rest)
+ */
+ uint32_t linAccelSwitchCntr;
+ uint8_t linAccelSwitch;
- real filteredYawRate; // Yaw-Rate (Turn-Switch) filter
+ uint8_t linAccelLPFType;
+ uint8_t useRawAccToDetectLinAccel;
- /* The following variables are used to increase the Kalman filter gain when the
- * acceleration is very close to one (i.e. the system is at rest)
- */
- uint32_t linAccelSwitchCntr;
- uint8_t linAccelSwitch;
+ uint8_t callingFreq;
+ real dt;
+ real dtOverTwo;
+ real dtSquared;
+ real sqrtDt;
- uint8_t linAccelLPFType;
- uint8_t useRawAccToDetectLinAccel;
+ volatile uint32_t timer; // timer since power up (ms)
+ volatile uint16_t counter; // inc. with every continuous mode output packet
- uint8_t callingFreq;
- real dt;
- real dtOverTwo;
- real dtSquared;
- real sqrtDt;
+ union AlgoBehavior Behavior;
+ float turnSwitchThreshold; // 0, 0.4, 10 driving, 1 flying [deg/sec] 0x000d
- volatile uint32_t timer; // timer since power up (ms)
- volatile uint16_t counter; // inc. with every continuous mode output packet
+ real leverArmB[3]; // Antenna position w.r.t IMU in vehicle body frame
+ real pointOfInterestB[3]; // Point of interest position w.r.t IMU in vehicle body frame
- union AlgoBehavior Behavior;
- float turnSwitchThreshold; // 0, 0.4, 10 driving, 1 flying [deg/sec] 0x000d
+ BOOL velocityAlwaysAlongBodyX; // enable zero velocity update
- real leverArmB[3]; // Antenna position w.r.t IMU in vehicle body frame
- real pointOfInterestB[3]; // Point of interest position w.r.t IMU in vehicle body frame
+ IMU_SPEC imuSpec; // IMU specifications
+ STATIC_DETECT_SETTING staticDetectParam; // params used for static detection
- DurationStruct Duration;
- LimitStruct Limit;
+ DurationStruct Duration;
+ LimitStruct Limit;
} AlgorithmStruct;
extern AlgorithmStruct gAlgorithm;
+// Update IMU specs.
+void UpdateImuSpec(real rwOdr, real arw, real biw, real maxBiasW,
+ real vrw, real bia, real maxBiasA);
+
#endif
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/EKF_Algorithm.c b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/EKF_Algorithm.c
index c3faadf..8e79f6b 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/EKF_Algorithm.c
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/EKF_Algorithm.c
@@ -7,17 +7,19 @@
#include // std::abs
#include // EXIT_FAILURE
#include
+#include // memset
#include "GlobalConstants.h" // TRUE, FALSE, etc
#include "platformAPI.h"
#include "Indices.h" // IND
#include "MagAlign.h"
+#include "QuaternionMath.h"
#include "algorithm.h" // gAlgorithm
#include "AlgorithmLimits.h"
#include "TransformationMath.h"
#include "VectorMath.h"
-#include "buffer.h"
+#include "MotionStatus.h"
#include "SelectState.h"
#include "EKF_Algorithm.h"
#include "PredictFunctions.h"
@@ -31,88 +33,36 @@
#endif
#endif
-KalmanFilterStruct gKalmanFilter;
-EKF_InputDataStruct gEKFInputData;
-EKF_OutputDataStruct gEKFOutputData;
-AccelStatsStruct gAccelStats;
-
-//=============================================================================
-// Filter variables (Third-Order BWF w/ default 5 Hz Cutoff)
-#define FILTER_ORDER 3
-
-#define CURRENT 0
-#define PASTx1 1
-#define PASTx2 2
-#define PASTx3 3
-/* Replace this with a fuction that will compute the coefficients so the
- * input is the cutoff frequency in Hertz
- */
-#define NO_LPF 0
-#define TWO_HZ_LPF 1
-#define FIVE_HZ_LPF 2
-#define TEN_HZ_LPF 3
-#define TWENTY_HZ_LPF 4
-#define TWENTY_FIVE_HZ_LPF 5
-#define N_LPF 6
-
-/******************************************************************************
- * @brief Get filter coefficients of a 3rd Butterworth low-pass filter.
- * For now only a few specific cut-off frequencies are supported.
- * TRACE:
- * @param [in] lpfType Low-pass filter cut-off frequency.
- * @param [in] callingFreq Sampling frequency, only 100Hz and 200Hz are supported.
- * @param [out] b coefficients of the numerator of the filter.
- * @param [out] a coefficients of the denominator of the filter.
- * @retval None.
-******************************************************************************/
-static void _PopulateFilterCoefficients( uint8_t lpfType, uint8_t callingFreq, real *b, real *a );
-
-/******************************************************************************
- * @brief Process input data through a low-pass Butterworth filter.
- * TRACE:
- * @param [in] accel Input accel
- * @param [in] lpfType Low-pass filter cut-off frequency.
- * @param [in] callingFreq Sampling frequency, only 100Hz and 200Hz are supported.
- * @param [out] filteredAccel Filter accel.
- * @retval None.
-******************************************************************************/
-static void _AccelLPF( real *accel, uint8_t lpfType, uint8_t callingFreq, real *filteredAccel );
-
-#define DATA_NUM_FOR_STATS 20 // 20 samples can give a relative good estimate of var
-/******************************************************************************
- * @brief Compute mean and var of the input data.
- * A recursive mean calculation and a naive var calculation are implemented. A recursive var
- * calculation was also tested but abandoned due to its inherent numerical stability.
- * TRACE:
- * @param [in] accel Input accel, g.
- * @param [in] iReset Reset the procedure.
- * @param [out] gAccelStats A struct for results storage.
- * @retval None.
-******************************************************************************/
-static void ComputeAccelStats( real *accel, AccelStatsStruct *gAccelStats, int iReset );
+KalmanFilterStruct gKalmanFilter;
+EKF_InputDataStruct gEKFInput;
+EKF_OutputDataStruct gEKFOutput;
+ImuStatsStruct gImuStats;
/******************************************************************************
- * @brief Using gyro propagation to estimate accel error.
- * g_dot = -cross(w, g), g is gravity and w is angular rate.
+ * @brief Remove lever arm in position and velocity.
+ * GNSS measured position is the position of the antenna. For GNSS/INS integration,
+ * the position of IMU is needed. Before using the GNSS position and velocity,
+ * those shold be first converted to the IMU position and velocity by removing
+ * lever arm effects. Lever arm introduces an offset in position. This offset
+ * can be directly canceled by substracting lever arm. Combined with angular
+ * velocity, lever arm further introduces relative velocity.
* TRACE:
- * @param [in] accel Input accel, g.
- * @param [in] w Input angular rate, rad/s.
- * @param [in] dt Sampling interval, sec.
- * @param [out] gAccelStats A struct for results storage.
- * @retval None.
+ * @param [in/out] LLA [rad, rad, m], Lat, lon and alt of the antenna, and
+ * will be converted to LLA of the IMU.
+ * @param [in/out] vNed [m/s], NED velocity of the antenna, and will be
+ * converted to NED velocity of the IMU.
+ * @param [in] w [rad/s], angular velocity of the vehicle relative to
+ * ECEF in the body frame.
+ * @param [in] leverArmB [m], lever arm in the body frame.
+ * @param [out] rn2e Transformation matrix from NED to ECEF.
+ * @param [out] ecef [m], ECEF position without lever arm.
+ * @retval TRUE if heading initialized, FALSE if not.
******************************************************************************/
-static void EstimateAccelError( real *accel, real *w, real dt, AccelStatsStruct *gAccelStats);
+static void RemoveLeverArm(double *lla, double *vNed, real *w, real *leverArmB,
+ real *rn2e, double *ecef);
-/******************************************************************************
- * @brief Detect motion according to the difference between measured accel magnitude and 1g.
- * Set gAlgorithm.linAccelSwitch to be True if being static for a while.
- * This result is no longer used in current algorithm.
- * TRACE:
- * @param [in] accelNorm Input accel magnitude, g.
- * @param [in] iReset Reset the procedure.
- * @retval Always true.
-******************************************************************************/
-static BOOL DetectMotionFromAccel(real accelNorm, int iReset);
+static void HandlePps();
+static void SaveKfStateAtPps();
//=============================================================================
@@ -131,39 +81,40 @@ void EKF_Algorithm(void)
*/
if ( gAlgorithm.state > STABILIZE_SYSTEM )
{
- // Low-pass filter
- _AccelLPF( gEKFInputData.accel_B,
- gAlgorithm.linAccelLPFType,
- gAlgorithm.callingFreq,
- gAccelStats.lpfAccel );
- // Compute accel norm using raw accel data. The norm will be used to detect static periods.
- gAccelStats.accelNorm = sqrtf(gEKFInputData.accel_B[X_AXIS] * gEKFInputData.accel_B[X_AXIS] +
- gEKFInputData.accel_B[Y_AXIS] * gEKFInputData.accel_B[Y_AXIS] +
- gEKFInputData.accel_B[Z_AXIS] * gEKFInputData.accel_B[Z_AXIS] );
- /* Compute accel mean/var.
- * Compute this after STABILIZE_SYSTEM so there is enough data to fill the buffer
- * Before buffer is full, results are not accurate and not used indeed.
+ /* Compute IMU mean/var, filter IMU data (optional), detect static.
+ * After STABILIZE_SYSTEM, each IMU sample is pushed into a buffer.
+ * Before the buffer is full, results are not accurate should not be used.
*/
- ComputeAccelStats(gAccelStats.lpfAccel, &gAccelStats, 0);
+ MotionStatusImu(gEKFInput.angRate_B, gEKFInput.accel_B, &gImuStats, FALSE);
// estimate accel error
if (gAlgorithm.useRawAccToDetectLinAccel)
{
- EstimateAccelError( gEKFInputData.accel_B,
- gEKFInputData.angRate_B,
+ EstimateAccelError( gEKFInput.accel_B,
+ gEKFInput.angRate_B,
gAlgorithm.dt,
- &gAccelStats);
+ gAlgorithm.Limit.linAccelSwitchDelay,
+ &gImuStats);
}
else
{
- EstimateAccelError( gAccelStats.lpfAccel,
- gEKFInputData.angRate_B,
+ EstimateAccelError( gImuStats.lpfAccel,
+ gEKFInput.angRate_B,
gAlgorithm.dt,
- &gAccelStats);
+ gAlgorithm.Limit.linAccelSwitchDelay,
+ &gImuStats);
}
// Detect if the unit is static or dynamic
- DetectMotionFromAccel(gAccelStats.accelNorm, 0);
+ DetectMotionFromAccel(gImuStats.accelNorm, 0);
+ gAlgoStatus.bit.linearAccel = !gAlgorithm.linAccelSwitch;
+
+ // if zero velocity detection by IMU is not enabled, detection result is always false.
+ if (!gAlgorithm.Behavior.bit.enableImuStaticDetect)
+ {
+ gImuStats.bStaticIMU = FALSE;
+ }
+ gAlgoStatus.bit.staticImu = gImuStats.bStaticIMU;
}
// Compute the EKF solution if past the stabilization and initialization stages
@@ -173,7 +124,12 @@ void EKF_Algorithm(void)
gAlgorithm.itow = gAlgorithm.itow + gAlgorithm.dITOW;
// Perform EKF Prediction
- EKF_PredictionStage(gAccelStats.lpfAccel);
+ EKF_PredictionStage(gImuStats.lpfAccel);
+
+ if (gAlgorithm.state == INS_SOLUTION)
+ {
+ HandlePps();
+ }
/* Update the predicted states if not freely integrating
* NOTE: free- integration is not applicable in HG AHRS mode.
@@ -207,6 +163,7 @@ void EKF_Algorithm(void)
// Perform EKF Update
EKF_UpdateStage();
}
+
/* Save the past attitude quaternion before updating (for use in the
* covariance estimation calculations).
*/
@@ -214,6 +171,41 @@ void EKF_Algorithm(void)
gKalmanFilter.quaternion_Past[Q1] = gKalmanFilter.quaternion[Q1];
gKalmanFilter.quaternion_Past[Q2] = gKalmanFilter.quaternion[Q2];
gKalmanFilter.quaternion_Past[Q3] = gKalmanFilter.quaternion[Q3];
+
+ /* Generate the transformation matrix (R_BinN) based on the past value of
+ * the attitude quaternion (prior to prediction at the new time-step)
+ */
+ QuaternionToR321(gKalmanFilter.quaternion, &gKalmanFilter.R_BinN[0][0]);
+
+ /* Euler angels are not calcualted here because it is used as a propagation resutls
+ * to calculate system innovation. So, Euler angles are updated in the prediction
+ * stage. In theory, Euler angles should be updated after each measurement update.
+ * However, after EKF converges, it does not matter.
+ */
+
+ // Update LLA
+ if ((gAlgorithm.insFirstTime == FALSE))
+ {
+ double r_E[NUM_AXIS];
+ float pointOfInterestN[3];
+ pointOfInterestN[0] = gKalmanFilter.R_BinN[0][0] * gAlgorithm.pointOfInterestB[0] +
+ gKalmanFilter.R_BinN[0][1] * gAlgorithm.pointOfInterestB[1] +
+ gKalmanFilter.R_BinN[0][2] * gAlgorithm.pointOfInterestB[2];
+ pointOfInterestN[1] = gKalmanFilter.R_BinN[1][0] * gAlgorithm.pointOfInterestB[0] +
+ gKalmanFilter.R_BinN[1][1] * gAlgorithm.pointOfInterestB[1] +
+ gKalmanFilter.R_BinN[1][2] * gAlgorithm.pointOfInterestB[2];
+ pointOfInterestN[2] = gKalmanFilter.R_BinN[2][0] * gAlgorithm.pointOfInterestB[0] +
+ gKalmanFilter.R_BinN[2][1] * gAlgorithm.pointOfInterestB[1] +
+ gKalmanFilter.R_BinN[2][2] * gAlgorithm.pointOfInterestB[2];
+ pointOfInterestN[0] += gKalmanFilter.Position_N[0];
+ pointOfInterestN[1] += gKalmanFilter.Position_N[1];
+ pointOfInterestN[2] += gKalmanFilter.Position_N[2];
+ PosNED_To_PosECEF(pointOfInterestN, &gKalmanFilter.rGPS0_E[0], &gKalmanFilter.Rn2e[0][0], &r_E[0]);
+ // 100 Hz generated once 1 Hz 100 Hz
+ // output variable (ned used for anything else); this is in [ deg, deg, m ]
+ ECEF_To_LLA(&gKalmanFilter.llaDeg[LAT], &r_E[X_AXIS]);
+ // 100 Hz 100 Hz
+ }
}
/* Select the algorithm state based upon the present state as well as
@@ -239,14 +231,6 @@ void EKF_Algorithm(void)
INS_To_AHRS_Transition_Test();
break;
default:
-#ifdef DISPLAY_DIAGNOSTIC_MSG
-#ifdef INS_OFFLINE
- // Shouldn't be able to make it here
- TimingVars_DiagnosticMsg("Uh-oh! Invalid algorithm state in EKF_Algorithm.cpp");
- std::cout << "Press enter to finish ...";
- std::cin.get();
-#endif
-#endif
return;
}
@@ -254,46 +238,67 @@ void EKF_Algorithm(void)
DynamicMotion();
}
-void enableFreeIntegration(BOOL enable)
-{
- gAlgorithm.Behavior.bit.freeIntegrate = enable;
-}
-
-
-BOOL freeIntegrationEnabled()
+static void HandlePps()
{
- return gAlgorithm.Behavior.bit.freeIntegrate;
-}
-
-void enableMagInAlgorithm(BOOL enable)
-{
- if(1)
+ // PPS not detected for a long time?
+ int32_t timeSinceLastPps = (int32_t)(gAlgorithm.itow - gKalmanFilter.ppsITow);
+ if (timeSinceLastPps < 0)
{
- gAlgorithm.Behavior.bit.useMag = enable;
+ timeSinceLastPps = timeSinceLastPps + MAX_ITOW;
}
- else
+ if (timeSinceLastPps > 2000)
{
- gAlgorithm.Behavior.bit.useMag = FALSE;
+ gAlgoStatus.bit.ppsAvailable = FALSE;
+ }
+ // PPS detected
+ if (gEKFInput.ppsDetected)
+ {
+ // PPS is available from now.
+ gAlgoStatus.bit.ppsAvailable = TRUE;
+ // save states when pps detected
+ SaveKfStateAtPps();
}
}
-BOOL magUsedInAlgorithm()
-{
- return gAlgorithm.Behavior.bit.useMag != 0;
-}
-
-BOOL gpsUsedInAlgorithm(void)
-{
- return gAlgorithm.Behavior.bit.useGPS;
-}
-
-void enableGpsInAlgorithm(BOOL enable)
+static void SaveKfStateAtPps()
{
- gAlgorithm.Behavior.bit.useGPS = enable;
+ // save time
+ gKalmanFilter.ppsITow = gAlgorithm.itow;
+
+ // save states
+ gKalmanFilter.ppsPosition_N[0] = gKalmanFilter.Position_N[0];
+ gKalmanFilter.ppsPosition_N[1] = gKalmanFilter.Position_N[1];
+ gKalmanFilter.ppsPosition_N[2] = gKalmanFilter.Position_N[2];
+ gKalmanFilter.ppsVelocity_N[0] = gKalmanFilter.Velocity_N[0];
+ gKalmanFilter.ppsVelocity_N[1] = gKalmanFilter.Velocity_N[1];
+ gKalmanFilter.ppsVelocity_N[2] = gKalmanFilter.Velocity_N[2];
+ //gKalmanFilter.ppsQuaternion[0] = gKalmanFilter.quaternion[0];
+ //gKalmanFilter.ppsQuaternion[1] = gKalmanFilter.quaternion[1];
+ //gKalmanFilter.ppsQuaternion[2] = gKalmanFilter.quaternion[2];
+ //gKalmanFilter.ppsQuaternion[3] = gKalmanFilter.quaternion[3];
+ gKalmanFilter.ppsEulerAngles[0] = gKalmanFilter.eulerAngles[0];
+ gKalmanFilter.ppsEulerAngles[1] = gKalmanFilter.eulerAngles[1];
+ gKalmanFilter.ppsEulerAngles[2] = gKalmanFilter.eulerAngles[2];
+ //gKalmanFilter.ppsRateBias_B[0] = gKalmanFilter.rateBias_B[0];
+ //gKalmanFilter.ppsRateBias_B[1] = gKalmanFilter.rateBias_B[1];
+ //gKalmanFilter.ppsRateBias_B[2] = gKalmanFilter.rateBias_B[2];
+ //gKalmanFilter.ppsAccelBias_B[0] = gKalmanFilter.accelBias_B[0];
+ //gKalmanFilter.ppsAccelBias_B[1] = gKalmanFilter.accelBias_B[1];
+ //gKalmanFilter.ppsAccelBias_B[2] = gKalmanFilter.accelBias_B[2];
+ // save state covariance matrix
+ memcpy(&gKalmanFilter.ppsP[0][0], &gKalmanFilter.P[0][0], sizeof(gKalmanFilter.P));
+
+ /* reset state transition matrix and state covariance matrix increment between pps and update
+ * phi is reset to an identity matrix, and dQ is reset to a zero matrix.
+ */
+ memset(&gKalmanFilter.phi[0][0], 0, sizeof(gKalmanFilter.phi));
+ memset(&gKalmanFilter.dQ[0][0], 0, sizeof(gKalmanFilter.dQ));
+ for (int i = 0; i < NUMBER_OF_EKF_STATES; i++)
+ {
+ gKalmanFilter.phi[i][i] = 1.0;
+ }
}
-
-
// Getters based on results structure passed to WriteResultsIntoOutputStream()
/* Extract the attitude (expressed as Euler-angles) of the body-frame (B)
@@ -302,9 +307,9 @@ void enableGpsInAlgorithm(BOOL enable)
void EKF_GetAttitude_EA(real *EulerAngles)
{
// Euler-angles in [deg]
- EulerAngles[ROLL] = (real)gEKFOutputData.eulerAngs_BinN[ROLL];
- EulerAngles[PITCH] = (real)gEKFOutputData.eulerAngs_BinN[PITCH];
- EulerAngles[YAW] = (real)gEKFOutputData.eulerAngs_BinN[YAW];
+ EulerAngles[ROLL] = (real)gEKFOutput.eulerAngs_BinN[ROLL];
+ EulerAngles[PITCH] = (real)gEKFOutput.eulerAngs_BinN[PITCH];
+ EulerAngles[YAW] = (real)gEKFOutput.eulerAngs_BinN[YAW];
}
@@ -322,10 +327,10 @@ void EKF_GetAttitude_EA_RAD(real *EulerAngles)
*/
void EKF_GetAttitude_Q(real *Quaternions)
{
- Quaternions[Q0] = (real)gEKFOutputData.quaternion_BinN[Q0];
- Quaternions[Q1] = (real)gEKFOutputData.quaternion_BinN[Q1];
- Quaternions[Q2] = (real)gEKFOutputData.quaternion_BinN[Q2];
- Quaternions[Q3] = (real)gEKFOutputData.quaternion_BinN[Q3];
+ Quaternions[Q0] = (real)gEKFOutput.quaternion_BinN[Q0];
+ Quaternions[Q1] = (real)gEKFOutput.quaternion_BinN[Q1];
+ Quaternions[Q2] = (real)gEKFOutput.quaternion_BinN[Q2];
+ Quaternions[Q3] = (real)gEKFOutput.quaternion_BinN[Q3];
}
@@ -335,9 +340,9 @@ void EKF_GetAttitude_Q(real *Quaternions)
void EKF_GetCorrectedAngRates(real *CorrAngRates_B)
{
// Angular-rate in [deg/s]
- CorrAngRates_B[X_AXIS] = (real)gEKFOutputData.corrAngRates_B[X_AXIS];
- CorrAngRates_B[Y_AXIS] = (real)gEKFOutputData.corrAngRates_B[Y_AXIS];
- CorrAngRates_B[Z_AXIS] = (real)gEKFOutputData.corrAngRates_B[Z_AXIS];
+ CorrAngRates_B[X_AXIS] = (real)gEKFOutput.corrAngRates_B[X_AXIS];
+ CorrAngRates_B[Y_AXIS] = (real)gEKFOutput.corrAngRates_B[Y_AXIS];
+ CorrAngRates_B[Z_AXIS] = (real)gEKFOutput.corrAngRates_B[Z_AXIS];
}
@@ -347,9 +352,9 @@ void EKF_GetCorrectedAngRates(real *CorrAngRates_B)
void EKF_GetCorrectedAccels(real *CorrAccels_B)
{
// Acceleration in [m/s^2]
- CorrAccels_B[X_AXIS] = (real)gEKFOutputData.corrAccel_B[X_AXIS];
- CorrAccels_B[Y_AXIS] = (real)gEKFOutputData.corrAccel_B[Y_AXIS];
- CorrAccels_B[Z_AXIS] = (real)gEKFOutputData.corrAccel_B[Z_AXIS];
+ CorrAccels_B[X_AXIS] = (real)gEKFOutput.corrAccel_B[X_AXIS];
+ CorrAccels_B[Y_AXIS] = (real)gEKFOutput.corrAccel_B[Y_AXIS];
+ CorrAccels_B[Z_AXIS] = (real)gEKFOutput.corrAccel_B[Z_AXIS];
}
@@ -359,9 +364,9 @@ void EKF_GetCorrectedAccels(real *CorrAccels_B)
void EKF_GetEstimatedAngRateBias(real *AngRateBias_B)
{
// Angular-rate bias in [deg/sec]
- AngRateBias_B[X_AXIS] = (real)gEKFOutputData.angRateBias_B[X_AXIS];
- AngRateBias_B[Y_AXIS] = (real)gEKFOutputData.angRateBias_B[Y_AXIS];
- AngRateBias_B[Z_AXIS] = (real)gEKFOutputData.angRateBias_B[Z_AXIS];
+ AngRateBias_B[X_AXIS] = (real)gEKFOutput.angRateBias_B[X_AXIS];
+ AngRateBias_B[Y_AXIS] = (real)gEKFOutput.angRateBias_B[Y_AXIS];
+ AngRateBias_B[Z_AXIS] = (real)gEKFOutput.angRateBias_B[Z_AXIS];
}
@@ -371,9 +376,9 @@ void EKF_GetEstimatedAngRateBias(real *AngRateBias_B)
void EKF_GetEstimatedAccelBias(real *AccelBias_B)
{
// Acceleration-bias in [m/s^2]
- AccelBias_B[X_AXIS] = (real)gEKFOutputData.accelBias_B[X_AXIS];
- AccelBias_B[Y_AXIS] = (real)gEKFOutputData.accelBias_B[Y_AXIS];
- AccelBias_B[Z_AXIS] = (real)gEKFOutputData.accelBias_B[Z_AXIS];
+ AccelBias_B[X_AXIS] = (real)gEKFOutput.accelBias_B[X_AXIS];
+ AccelBias_B[Y_AXIS] = (real)gEKFOutput.accelBias_B[Y_AXIS];
+ AccelBias_B[Z_AXIS] = (real)gEKFOutput.accelBias_B[Z_AXIS];
}
@@ -381,9 +386,9 @@ void EKF_GetEstimatedAccelBias(real *AccelBias_B)
void EKF_GetEstimatedPosition(real *Position_N)
{
// Position in [m]
- Position_N[X_AXIS] = (real)gEKFOutputData.position_N[X_AXIS];
- Position_N[Y_AXIS] = (real)gEKFOutputData.position_N[Y_AXIS];
- Position_N[Z_AXIS] = (real)gEKFOutputData.position_N[Z_AXIS];
+ Position_N[X_AXIS] = (real)gEKFOutput.position_N[X_AXIS];
+ Position_N[Y_AXIS] = (real)gEKFOutput.position_N[Y_AXIS];
+ Position_N[Z_AXIS] = (real)gEKFOutput.position_N[Z_AXIS];
}
@@ -391,9 +396,9 @@ void EKF_GetEstimatedPosition(real *Position_N)
void EKF_GetEstimatedVelocity(real *Velocity_N)
{
// Velocity in [m/s]
- Velocity_N[X_AXIS] = (real)gEKFOutputData.velocity_N[X_AXIS];
- Velocity_N[Y_AXIS] = (real)gEKFOutputData.velocity_N[Y_AXIS];
- Velocity_N[Z_AXIS] = (real)gEKFOutputData.velocity_N[Z_AXIS];
+ Velocity_N[X_AXIS] = (real)gEKFOutput.velocity_N[X_AXIS];
+ Velocity_N[Y_AXIS] = (real)gEKFOutput.velocity_N[Y_AXIS];
+ Velocity_N[Z_AXIS] = (real)gEKFOutput.velocity_N[Z_AXIS];
}
@@ -401,9 +406,9 @@ void EKF_GetEstimatedVelocity(real *Velocity_N)
void EKF_GetEstimatedLLA(double *LLA)
{
// Velocity in [m/s]
- LLA[X_AXIS] = (double)gEKFOutputData.llaDeg[X_AXIS];
- LLA[Y_AXIS] = (double)gEKFOutputData.llaDeg[Y_AXIS];
- LLA[Z_AXIS] = (double)gEKFOutputData.llaDeg[Z_AXIS];
+ LLA[X_AXIS] = (double)gEKFOutput.llaDeg[X_AXIS];
+ LLA[Y_AXIS] = (double)gEKFOutput.llaDeg[Y_AXIS];
+ LLA[Z_AXIS] = (double)gEKFOutput.llaDeg[Z_AXIS];
}
@@ -416,69 +421,123 @@ void EKF_GetEstimatedLLA(double *LLA)
*/
void EKF_GetOperationalMode(uint8_t *EKF_OperMode)
{
- *EKF_OperMode = gEKFOutputData.opMode;
+ *EKF_OperMode = gEKFOutput.opMode;
}
// Extract the linear-acceleration and turn-switch flags
void EKF_GetOperationalSwitches(uint8_t *EKF_LinAccelSwitch, uint8_t *EKF_TurnSwitch)
{
- *EKF_LinAccelSwitch = gEKFOutputData.linAccelSwitch;
- *EKF_TurnSwitch = gEKFOutputData.turnSwitchFlag;
+ *EKF_LinAccelSwitch = gEKFOutput.linAccelSwitch;
+ *EKF_TurnSwitch = gEKFOutput.turnSwitchFlag;
}
// SETTERS: for EKF input and output structures
// Populate the EKF input structure with sensor and GPS data (if used)
-void EKF_SetInputStruct(double *accels, double *rates, double *mags, gpsDataStruct_t *gps)
+void EKF_SetInputStruct(double *accels, double *rates, double *mags,
+ gpsDataStruct_t *gps, odoDataStruct_t *odo,
+ BOOL ppsDetected)
{
- // Accelerometer signal is in [g]
- gEKFInputData.accel_B[X_AXIS] = (real)accels[X_AXIS];
- gEKFInputData.accel_B[Y_AXIS] = (real)accels[Y_AXIS];
- gEKFInputData.accel_B[Z_AXIS] = (real)accels[Z_AXIS];
+ // Accelerometer signal is in [m/s/s]
+ gEKFInput.accel_B[X_AXIS] = (real)accels[X_AXIS] * GRAVITY;
+ gEKFInput.accel_B[Y_AXIS] = (real)accels[Y_AXIS] * GRAVITY;
+ gEKFInput.accel_B[Z_AXIS] = (real)accels[Z_AXIS] * GRAVITY;
// Angular-rate signal is in [rad/s]
- gEKFInputData.angRate_B[X_AXIS] = (real)rates[X_AXIS];
- gEKFInputData.angRate_B[Y_AXIS] = (real)rates[Y_AXIS];
- gEKFInputData.angRate_B[Z_AXIS] = (real)rates[Z_AXIS];
+ gEKFInput.angRate_B[X_AXIS] = (real)rates[X_AXIS];
+ gEKFInput.angRate_B[Y_AXIS] = (real)rates[Y_AXIS];
+ gEKFInput.angRate_B[Z_AXIS] = (real)rates[Z_AXIS];
// Magnetometer signal is in [G]
- gEKFInputData.magField_B[X_AXIS] = (real)mags[X_AXIS];
- gEKFInputData.magField_B[Y_AXIS] = (real)mags[Y_AXIS];
- gEKFInputData.magField_B[Z_AXIS] = (real)mags[Z_AXIS];
+ gEKFInput.magField_B[X_AXIS] = (real)mags[X_AXIS];
+ gEKFInput.magField_B[Y_AXIS] = (real)mags[Y_AXIS];
+ gEKFInput.magField_B[Z_AXIS] = (real)mags[Z_AXIS];
real tmp[2];
- tmp[X_AXIS] = gEKFInputData.magField_B[X_AXIS] - gMagAlign.hardIronBias[X_AXIS];
- tmp[Y_AXIS] = gEKFInputData.magField_B[Y_AXIS] - gMagAlign.hardIronBias[Y_AXIS];
- gEKFInputData.magField_B[X_AXIS] = gMagAlign.SF[0] * tmp[X_AXIS] + gMagAlign.SF[1] * tmp[Y_AXIS];
- gEKFInputData.magField_B[Y_AXIS] = gMagAlign.SF[2] * tmp[X_AXIS] + gMagAlign.SF[3] * tmp[Y_AXIS];
+ tmp[X_AXIS] = gEKFInput.magField_B[X_AXIS] - gMagAlign.hardIronBias[X_AXIS];
+ tmp[Y_AXIS] = gEKFInput.magField_B[Y_AXIS] - gMagAlign.hardIronBias[Y_AXIS];
+ gEKFInput.magField_B[X_AXIS] = gMagAlign.SF[0] * tmp[X_AXIS] + gMagAlign.SF[1] * tmp[Y_AXIS];
+ gEKFInput.magField_B[Y_AXIS] = gMagAlign.SF[2] * tmp[X_AXIS] + gMagAlign.SF[3] * tmp[Y_AXIS];
// ----- Input from the GPS goes here -----
- // Validity data
- gEKFInputData.gpsValid = (BOOL)gps->gpsValid;
- gEKFInputData.gpsUpdate = gps->gpsUpdate;
-
- // Lat/Lon/Alt data
- gEKFInputData.llaRad[LAT] = gps->latitude * D2R;
- gEKFInputData.llaRad[LON] = gps->longitude * D2R;
- gEKFInputData.llaRad[ALT] = gps->altitude;
-
- // Velocity data
- gEKFInputData.vNed[X_AXIS] = gps->vNed[X_AXIS];
- gEKFInputData.vNed[Y_AXIS] = gps->vNed[Y_AXIS];
- gEKFInputData.vNed[Z_AXIS] = gps->vNed[Z_AXIS];
-
- // Course and velocity data
- gEKFInputData.rawGroundSpeed = gps->rawGroundSpeed;
- gEKFInputData.trueCourse = gps->trueCourse;
-
- // ITOW data
- gEKFInputData.itow = gps->itow;
-
- // Data quality measures
- gEKFInputData.GPSHorizAcc = gps->GPSHorizAcc;
- gEKFInputData.GPSVertAcc = gps->GPSVertAcc;
- gEKFInputData.HDOP = gps->HDOP;
+ gEKFInput.gpsUpdate = gps->gpsUpdate;
+
+ if (gEKFInput.gpsUpdate)
+ {
+ // Validity data
+ gEKFInput.gpsFixType = gps->gpsFixType;
+
+ // num of satellites
+ gEKFInput.numSatellites = gps->numSatellites;
+
+ // ITOW data
+ gEKFInput.itow = gps->itow;
+
+ // Data quality measures
+ gEKFInput.GPSHorizAcc = gps->GPSHorizAcc;
+ gEKFInput.GPSVertAcc = gps->GPSVertAcc;
+ gEKFInput.HDOP = gps->HDOP;
+
+ // Lat/Lon/Alt data
+ gEKFInput.llaAnt[LAT] = gps->latitude * D2R;
+ gEKFInput.llaAnt[LON] = gps->longitude * D2R;
+ gEKFInput.llaAnt[ALT] = gps->altitude;
+ gEKFInput.geoidAboveEllipsoid = gps->geoidAboveEllipsoid;
+
+ // Velocity data
+ gEKFInput.vNedAnt[X_AXIS] = gps->vNed[X_AXIS];
+ gEKFInput.vNedAnt[Y_AXIS] = gps->vNed[Y_AXIS];
+ gEKFInput.vNedAnt[Z_AXIS] = gps->vNed[Z_AXIS];
+
+ // Course and velocity data
+ gEKFInput.rawGroundSpeed = (real)sqrt(SQUARE(gps->vNed[0]) +
+ SQUARE(gps->vNed[1]));// gps->rawGroundSpeed;
+ gEKFInput.trueCourse = (real)gps->trueCourse;
+
+ /* Remove lever arm effects in LLA/Velocity. To do this requires transformation matrix
+ * from the body frame to the NED frame. Before heading initialized, lever arm cannot
+ * be correctly removed. After heading initialized, there would be position jump if
+ * initial heading is different from uninitlized one and the lever arm is large.
+ * After heading intialized, the position/velocity could also be reinitialized, and
+ * lever arm effects on the position/velocity are not corrected removed.
+ * LLA without lever arm is used to update Rn2e/ECEF postion, and calculate relative
+ * position in NED
+ */
+ if (gEKFInput.gpsFixType)
+ {
+ gEKFInput.lla[LAT] = gEKFInput.llaAnt[LAT];
+ gEKFInput.lla[LON] = gEKFInput.llaAnt[LON];
+ gEKFInput.lla[ALT] = gEKFInput.llaAnt[ALT];
+ gEKFInput.vNed[0] = gEKFInput.vNedAnt[0];
+ gEKFInput.vNed[1] = gEKFInput.vNedAnt[1];
+ gEKFInput.vNed[2] = gEKFInput.vNedAnt[2];
+ /* remove lever arm. Indeed, corrected angular rate should be used. Considering angular
+ * bias is small, raw angular rate is used.
+ */
+ RemoveLeverArm( gEKFInput.lla,
+ gEKFInput.vNed,
+ gEKFInput.angRate_B,
+ gAlgorithm.leverArmB,
+ &gKalmanFilter.Rn2e[0][0],
+ gKalmanFilter.rGPS_E);
+
+ /* Calculate relative position in the NED frame. The initial position is rGPS0_E which.
+ * is determined when the algorithm first enters the INS mode (InitINSFilter).
+ */
+ ECEF_To_Base( &gKalmanFilter.rGPS0_E[0],
+ &gKalmanFilter.rGPS_E[0],
+ &gKalmanFilter.Rn2e[0][0],
+ &gKalmanFilter.rGPS_N[0]);
+ }
+ }
+
+ // odometer
+ gEKFInput.odoUpdate = odo->update;
+ gEKFInput.odoVelocity = odo->v;
+
+ // 1PPS signal from GNSS receiver
+ gEKFInput.ppsDetected = ppsDetected;
}
@@ -488,563 +547,236 @@ void EKF_SetOutputStruct(void)
// ------------------ States ------------------
// Position in [m]
- gEKFOutputData.position_N[X_AXIS] = gKalmanFilter.Position_N[X_AXIS];
- gEKFOutputData.position_N[Y_AXIS] = gKalmanFilter.Position_N[Y_AXIS];
- gEKFOutputData.position_N[Z_AXIS] = gKalmanFilter.Position_N[Z_AXIS];
+ gEKFOutput.position_N[X_AXIS] = gKalmanFilter.Position_N[X_AXIS];
+ gEKFOutput.position_N[Y_AXIS] = gKalmanFilter.Position_N[Y_AXIS];
+ gEKFOutput.position_N[Z_AXIS] = gKalmanFilter.Position_N[Z_AXIS];
// Velocity in [m/s]
- gEKFOutputData.velocity_N[X_AXIS] = gKalmanFilter.Velocity_N[X_AXIS];
- gEKFOutputData.velocity_N[Y_AXIS] = gKalmanFilter.Velocity_N[Y_AXIS];
- gEKFOutputData.velocity_N[Z_AXIS] = gKalmanFilter.Velocity_N[Z_AXIS];
+ gEKFOutput.velocity_N[X_AXIS] = gKalmanFilter.Velocity_N[X_AXIS];
+ gEKFOutput.velocity_N[Y_AXIS] = gKalmanFilter.Velocity_N[Y_AXIS];
+ gEKFOutput.velocity_N[Z_AXIS] = gKalmanFilter.Velocity_N[Z_AXIS];
// Position in [N/A]
- gEKFOutputData.quaternion_BinN[Q0] = gKalmanFilter.quaternion[Q0];
- gEKFOutputData.quaternion_BinN[Q1] = gKalmanFilter.quaternion[Q1];
- gEKFOutputData.quaternion_BinN[Q2] = gKalmanFilter.quaternion[Q2];
- gEKFOutputData.quaternion_BinN[Q3] = gKalmanFilter.quaternion[Q3];
+ gEKFOutput.quaternion_BinN[Q0] = gKalmanFilter.quaternion[Q0];
+ gEKFOutput.quaternion_BinN[Q1] = gKalmanFilter.quaternion[Q1];
+ gEKFOutput.quaternion_BinN[Q2] = gKalmanFilter.quaternion[Q2];
+ gEKFOutput.quaternion_BinN[Q3] = gKalmanFilter.quaternion[Q3];
// Angular-rate bias in [deg/sec]
- gEKFOutputData.angRateBias_B[X_AXIS] = gKalmanFilter.rateBias_B[X_AXIS] * RAD_TO_DEG;
- gEKFOutputData.angRateBias_B[Y_AXIS] = gKalmanFilter.rateBias_B[Y_AXIS] * RAD_TO_DEG;
- gEKFOutputData.angRateBias_B[Z_AXIS] = gKalmanFilter.rateBias_B[Z_AXIS] * RAD_TO_DEG;
+ gEKFOutput.angRateBias_B[X_AXIS] = gKalmanFilter.rateBias_B[X_AXIS] * RAD_TO_DEG;
+ gEKFOutput.angRateBias_B[Y_AXIS] = gKalmanFilter.rateBias_B[Y_AXIS] * RAD_TO_DEG;
+ gEKFOutput.angRateBias_B[Z_AXIS] = gKalmanFilter.rateBias_B[Z_AXIS] * RAD_TO_DEG;
// Acceleration-bias in [m/s^2]
- gEKFOutputData.accelBias_B[X_AXIS] = gKalmanFilter.accelBias_B[X_AXIS];
- gEKFOutputData.accelBias_B[Y_AXIS] = gKalmanFilter.accelBias_B[Y_AXIS];
- gEKFOutputData.accelBias_B[Z_AXIS] = gKalmanFilter.accelBias_B[Z_AXIS];
+ gEKFOutput.accelBias_B[X_AXIS] = gKalmanFilter.accelBias_B[X_AXIS];
+ gEKFOutput.accelBias_B[Y_AXIS] = gKalmanFilter.accelBias_B[Y_AXIS];
+ gEKFOutput.accelBias_B[Z_AXIS] = gKalmanFilter.accelBias_B[Z_AXIS];
// ------------------ Derived variables ------------------
// Euler-angles in [deg]
- gEKFOutputData.eulerAngs_BinN[ROLL] = gKalmanFilter.eulerAngles[ROLL] * RAD_TO_DEG;
- gEKFOutputData.eulerAngs_BinN[PITCH] = gKalmanFilter.eulerAngles[PITCH] * RAD_TO_DEG;
- gEKFOutputData.eulerAngs_BinN[YAW] = gKalmanFilter.eulerAngles[YAW] * RAD_TO_DEG;
+ gEKFOutput.eulerAngs_BinN[ROLL] = gKalmanFilter.eulerAngles[ROLL] * RAD_TO_DEG;
+ gEKFOutput.eulerAngs_BinN[PITCH] = gKalmanFilter.eulerAngles[PITCH] * RAD_TO_DEG;
+ gEKFOutput.eulerAngs_BinN[YAW] = gKalmanFilter.eulerAngles[YAW] * RAD_TO_DEG;
// Angular-rate in [deg/s]
- gEKFOutputData.corrAngRates_B[X_AXIS] = ( gEKFInputData.angRate_B[X_AXIS] -
+ gEKFOutput.corrAngRates_B[X_AXIS] = ( gEKFInput.angRate_B[X_AXIS] -
gKalmanFilter.rateBias_B[X_AXIS] ) * RAD_TO_DEG;
- gEKFOutputData.corrAngRates_B[Y_AXIS] = ( gEKFInputData.angRate_B[Y_AXIS] -
+ gEKFOutput.corrAngRates_B[Y_AXIS] = ( gEKFInput.angRate_B[Y_AXIS] -
gKalmanFilter.rateBias_B[Y_AXIS] ) * RAD_TO_DEG;
- gEKFOutputData.corrAngRates_B[Z_AXIS] = ( gEKFInputData.angRate_B[Z_AXIS] -
+ gEKFOutput.corrAngRates_B[Z_AXIS] = ( gEKFInput.angRate_B[Z_AXIS] -
gKalmanFilter.rateBias_B[Z_AXIS] ) * RAD_TO_DEG;
// Acceleration in [m/s^2]
- gEKFOutputData.corrAccel_B[X_AXIS] = gEKFInputData.accel_B[X_AXIS] * GRAVITY -
- gKalmanFilter.accelBias_B[X_AXIS];
- gEKFOutputData.corrAccel_B[Y_AXIS] = gEKFInputData.accel_B[Y_AXIS] * GRAVITY -
- gKalmanFilter.accelBias_B[Y_AXIS];
- gEKFOutputData.corrAccel_B[Z_AXIS] = gEKFInputData.accel_B[Z_AXIS] * GRAVITY -
- gKalmanFilter.accelBias_B[Z_AXIS];
+ gEKFOutput.corrAccel_B[X_AXIS] = gEKFInput.accel_B[X_AXIS] - gKalmanFilter.accelBias_B[X_AXIS];
+ gEKFOutput.corrAccel_B[Y_AXIS] = gEKFInput.accel_B[Y_AXIS] - gKalmanFilter.accelBias_B[Y_AXIS];
+ gEKFOutput.corrAccel_B[Z_AXIS] = gEKFInput.accel_B[Z_AXIS] - gKalmanFilter.accelBias_B[Z_AXIS];
// ------------------ Algorithm flags ------------------
- gEKFOutputData.opMode = gAlgorithm.state;
- gEKFOutputData.linAccelSwitch = gAlgorithm.linAccelSwitch;
- gEKFOutputData.turnSwitchFlag = gAlgoStatus.bit.turnSwitch;
- gEKFOutputData.gpsMeasurementUpdate = gAlgoStatus.bit.gpsUpdate;
+ gEKFOutput.opMode = gAlgorithm.state;
+ gEKFOutput.linAccelSwitch = gAlgorithm.linAccelSwitch;
+ gEKFOutput.turnSwitchFlag = gAlgoStatus.bit.turnSwitch;
// ------------------ Latitude and Longitude Data ------------------
- gEKFOutputData.llaDeg[LAT] = gKalmanFilter.llaDeg[LAT];
- gEKFOutputData.llaDeg[LON] = gKalmanFilter.llaDeg[LON];
- gEKFOutputData.llaDeg[ALT] = gKalmanFilter.llaDeg[ALT];
+ gEKFOutput.llaDeg[LAT] = gKalmanFilter.llaDeg[LAT];
+ gEKFOutput.llaDeg[LON] = gKalmanFilter.llaDeg[LON];
+ gEKFOutput.llaDeg[ALT] = gKalmanFilter.llaDeg[ALT];
}
-static void EstimateAccelError( real *accel, real *w, real dt, AccelStatsStruct *gAccelStats)
+
+//
+uint8_t InitINSFilter(void)
{
- static BOOL bIni = false; // indicate if the procedure is initialized
- static real lastAccel[3]; // accel input of last step
- static real lastGyro[3]; // gyro input of last step
- static float lastEstimatedAccel[3]; // propagated accel of last step
- static uint32_t counter = 0; // propagation counter
- static uint32_t t[3];
- // initialize
- if ( !bIni )
- {
- bIni = true;
- lastAccel[0] = accel[0];
- lastAccel[1] = accel[1];
- lastAccel[2] = accel[2];
- lastGyro[0] = w[0];
- lastGyro[1] = w[1];
- lastGyro[2] = w[2];
- t[0] = 0;
- t[1] = 0;
- t[2] = 0;
- gAccelStats->accelErr[0] = 0.0;
- gAccelStats->accelErr[1] = 0.0;
- gAccelStats->accelErr[2] = 0.0;
- return;
- }
+ real tmp[7][7];
+ int rowNum, colNum;
+
+#ifdef INS_OFFLINE
+ printf("reset INS filter.\n");
+#endif // INS_OFFLINE
+
+ gAlgorithm.insFirstTime = FALSE;
+
+ // Sync the algorithm and GPS ITOW
+ gAlgorithm.itow = gEKFInput.itow;
- /* Using gyro to propagate accel and then to detect accel error can give valid result for a
- * short period of time because the inhere long-term drift of integrating gyro data.
- * So, after this period of time, a new accel input will be selected.
- * Beside, this method cannot detect long-time smooth linear acceleration. In this case, we
- * can only hope the linear acceleration is large enough to make an obvious diffeerence from
- * the Earth gravity 1g.
+ /* We have a good GPS reading now - set this variable so we
+ * don't drop into INS right away
*/
- if ( counter==0 )
- {
- lastEstimatedAccel[0] = lastAccel[0];
- lastEstimatedAccel[1] = lastAccel[1];
- lastEstimatedAccel[2] = lastAccel[2];
- }
- counter++;
- if ( counter == gAlgorithm.Limit.linAccelSwitchDelay )
- {
- counter = 0;
- }
-
- // propagate accel using gyro
- // a(k) = a(k-1) -w x a(k-1)*dt
- real ae[3];
- lastGyro[0] *= -dt;
- lastGyro[1] *= -dt;
- lastGyro[2] *= -dt;
- cross(lastGyro, lastEstimatedAccel, ae);
- ae[0] += lastEstimatedAccel[0];
- ae[1] += lastEstimatedAccel[1];
- ae[2] += lastEstimatedAccel[2];
-
- // save this estimated accel
- lastEstimatedAccel[0] = ae[0];
- lastEstimatedAccel[1] = ae[1];
- lastEstimatedAccel[2] = ae[2];
-
- // err = a(k) - am
- ae[0] -= accel[0];
- ae[1] -= accel[1];
- ae[2] -= accel[2];
-
- /* If the difference between the propagted accel and the input accel exceeds some threshold,
- * we assume there is linear acceleration and set .accelErr to be a large value (0.1g).
- * If the difference has been within the threshold for a period of time, we start to decrease
- * estimated accel error .accelErr.
+ gAlgorithm.timeOfLastGoodGPSReading = gEKFInput.itow;
+
+ /* Upon the first entry into INS, save off the base position and reset the
+ * Kalman filter variables.
*/
- int j;
- gAccelStats->accelErrLimit = false;
- for(j=0; j<3; j++)
- {
- if ( fabs(ae[j]) > 1.0e-2 ) // linear accel detected
- {
- t[j] = 0;
- gAccelStats->accelErr[j] = 0.1f;
- }
- else // no linear accel detected, start to decrease estimated accel error
- {
- if ( t[j] > gAlgorithm.Limit.linAccelSwitchDelay ) // decrase error
- {
- gAccelStats->accelErr[j] *= 0.9f;
- gAccelStats->accelErr[j] += 0.1f * ae[j];
- }
- else // keep previous error value
- {
- t[j]++;
- // gAccelStats->accelErr[j];
- }
- }
- // limit error, not taking effect here since the max accelErr should be 0.1
- if ( gAccelStats->accelErr[j] > 0.5 )
- {
- gAccelStats->accelErr[j] = 0.5;
- gAccelStats->accelErrLimit = true;
- }
- if ( gAccelStats->accelErr[j] < -0.5 )
- {
- gAccelStats->accelErr[j] = -0.5;
- gAccelStats->accelErrLimit = true;
- }
- }
- // record accel for next step
- lastAccel[0] = accel[0];
- lastAccel[1] = accel[1];
- lastAccel[2] = accel[2];
- lastGyro[0] = w[0];
- lastGyro[1] = w[1];
- lastGyro[2] = w[2];
-}
+ // Save off the base ECEF location
+ gKalmanFilter.rGPS0_E[X_AXIS] = gKalmanFilter.rGPS_E[X_AXIS];
+ gKalmanFilter.rGPS0_E[Y_AXIS] = gKalmanFilter.rGPS_E[Y_AXIS];
+ gKalmanFilter.rGPS0_E[Z_AXIS] = gKalmanFilter.rGPS_E[Z_AXIS];
-static void ComputeAccelStats( real *accel, AccelStatsStruct *gAccelStats, int iReset )
-{
- static BOOL bIni = false; // indicate the routine is initialized or not
- static real data[3][DATA_NUM_FOR_STATS]; // a section in memoty to store buffer data
- static Buffer bf; // a ring buffer using the above memory section
-
- // reset the calculation of motion stats
- if ( iReset )
- {
- bIni = false;
- }
+ // Reset the gps position (as position is relative to starting location)
+ gKalmanFilter.rGPS_N[X_AXIS] = 0.0;
+ gKalmanFilter.rGPS_N[Y_AXIS] = 0.0;
+ gKalmanFilter.rGPS_N[Z_AXIS] = 0.0;
- // initialization
- if ( !bIni )
- {
- bIni = true;
- // reset stats
- gAccelStats->bValid = false;
- gAccelStats->accelMean[0] = 0.0;
- gAccelStats->accelMean[1] = 0.0;
- gAccelStats->accelMean[2] = 0.0;
- gAccelStats->accelVar[0] = 0.0;
- gAccelStats->accelVar[1] = 0.0;
- gAccelStats->accelVar[2] = 0.0;
- // create/reset buffer
- bfNew(&bf, &data[0][0], 3, DATA_NUM_FOR_STATS);
- }
+ // Reset prediction values. Position_N is also IMU position.
+ gKalmanFilter.Position_N[X_AXIS] = (real)0.0;
+ gKalmanFilter.Position_N[Y_AXIS] = (real)0.0;
+ gKalmanFilter.Position_N[Z_AXIS] = (real)0.0;
+
+ gKalmanFilter.Velocity_N[X_AXIS] = (real)gEKFInput.vNed[X_AXIS];
+ gKalmanFilter.Velocity_N[Y_AXIS] = (real)gEKFInput.vNed[Y_AXIS];
+ gKalmanFilter.Velocity_N[Z_AXIS] = (real)gEKFInput.vNed[Z_AXIS];
+
+ gKalmanFilter.accelBias_B[X_AXIS] = (real)0.0;
+ gKalmanFilter.accelBias_B[Y_AXIS] = (real)0.0;
+ gKalmanFilter.accelBias_B[Z_AXIS] = (real)0.0;
- /* Compute mean/variance from input data.
- * When the input data buffer is full, the stats can be assumed valid.
+ gKalmanFilter.linearAccel_B[X_AXIS] = (real)0.0;
+
+ /* Extract the Quaternion and rate-bias values from the matrix before
+ * resetting
*/
- // save last stats for recursive calculation
- real lastMean[3];
- real lastVar[3];
- lastMean[0] = gAccelStats->accelMean[0];
- lastMean[1] = gAccelStats->accelMean[1];
- lastMean[2] = gAccelStats->accelMean[2];
- lastVar[0] = gAccelStats->accelVar[0];
- lastVar[1] = gAccelStats->accelVar[1];
- lastVar[2] = gAccelStats->accelVar[2];
- if ( bf.full )
+ // Save off the quaternion and rate-bias covariance values
+ for (rowNum = Q0; rowNum <= Q3 + Z_AXIS + 1; rowNum++)
{
- // Enough data collected, stats can be assumed valid
- gAccelStats->bValid = true;
- /* when buffer is full, the var and mean are computed from
- * all data in the buffer. From now on, the var and mean
- * should be computed by removing the oldest data and including
- * the latest data.
- */
- // Get the oldest data which will be removed by following bfPut
- real oldest[3];
- bfGet(&bf, oldest, bf.num-1);
- // put this accel into buffer
- bfPut(&bf, accel);
- // mean(n+1) = ( mean(n) * n - x(1) + x(n+1) ) / n
- gAccelStats->accelMean[0] = lastMean[0] + ( accel[0] - oldest[0] ) / (real)(bf.num);
- gAccelStats->accelMean[1] = lastMean[1] + ( accel[1] - oldest[1] ) / (real)(bf.num);
- gAccelStats->accelMean[2] = lastMean[2] + ( accel[2] - oldest[2] ) / (real)(bf.num);
-
- // naive var calculation is adopted because recursive method is numerically instable
- real tmpVar[3];
- tmpVar[0] = vecVar(&bf.d[0], gAccelStats->accelMean[0], bf.num);
- tmpVar[1] = vecVar(&bf.d[bf.n], gAccelStats->accelMean[1], bf.num);
- tmpVar[2] = vecVar(&bf.d[2*bf.n], gAccelStats->accelMean[2], bf.num);
- // make var estimation smooth
- real k = 0.99f;
- int i;
- for ( i=0; i<3; i++ )
+ for (colNum = Q0; colNum <= Q3 + Z_AXIS + 1; colNum++)
{
- if ( tmpVar[i] >= gAccelStats->accelVar[i] )
- {
- gAccelStats->accelVar[i] = tmpVar[i];
- }
- else
- {
- gAccelStats->accelVar[i] = k*gAccelStats->accelVar[i] + (1.0f-k)*tmpVar[i];
- }
+ tmp[rowNum][colNum] = gKalmanFilter.P[rowNum + STATE_Q0][colNum + STATE_Q0];
}
}
- else
- {
- // put this accel into buffer
- bfPut(&bf, accel);
- /* Recursivly include new accel. The data num used to compute mean and
- * var are increasing.
- */
- // mean(n+1) = mean(n) *n / (n+1) + x(n+1) / (n+1)
- gAccelStats->accelMean[0] = lastMean[0] + ( accel[0] - lastMean[0] ) / (real)(bf.num);
- gAccelStats->accelMean[1] = lastMean[1] + ( accel[1] - lastMean[1] ) / (real)(bf.num);
- gAccelStats->accelMean[2] = lastMean[2] + ( accel[2] - lastMean[2] ) / (real)(bf.num);
- gAccelStats->accelVar[0] = lastVar[0] + lastMean[0]*lastMean[0] -
- gAccelStats->accelMean[0] * gAccelStats->accelMean[0] +
- ( accel[0]*accel[0] - lastVar[0] -lastMean[0]*lastMean[0] ) / (real)(bf.num);
- gAccelStats->accelVar[1] = lastVar[1] + lastMean[1]*lastMean[1] -
- gAccelStats->accelMean[1] * gAccelStats->accelMean[1] +
- ( accel[1]*accel[1] - lastVar[1] -lastMean[1]*lastMean[1] ) / (real)(bf.num);
- gAccelStats->accelVar[2] = lastVar[2] + lastMean[2]*lastMean[2] -
- gAccelStats->accelMean[2] * gAccelStats->accelMean[2] +
- ( accel[2]*accel[2] - lastVar[2] -lastMean[2]*lastMean[2] ) / (real)(bf.num);
- }
-}
-
-static BOOL DetectMotionFromAccel(real accelNorm, int iReset)
-{
- if( iReset )
+ // Reset P
+ memset(gKalmanFilter.P, 0, sizeof(gKalmanFilter.P));
+ for (rowNum = 0; rowNum < NUMBER_OF_EKF_STATES; rowNum++)
{
- gAlgorithm.linAccelSwitch = false;
- gAlgorithm.linAccelSwitchCntr = 0;
+ gKalmanFilter.P[rowNum][rowNum] = (real)INIT_P_INS;
}
- /* Check for times when the acceleration is 'close' to 1 [g]. When thisoccurs,
- * increment a counter. When it exceeds a threshold (indicating that the system
- * has been at rest for a given period) then decrease the R-values (in the
- * update stage of the EKF), effectively increasing the Kalman gain.
- */
- if (fabs( 1.0 - accelNorm ) < gAlgorithm.Limit.accelSwitch )
+
+ // Repopulate the P matrix with the quaternion and rate-bias values
+ for (rowNum = Q0; rowNum <= Q3 + Z_AXIS + 1; rowNum++)
{
- gAlgorithm.linAccelSwitchCntr++;
- if ( gAlgorithm.linAccelSwitchCntr >= gAlgorithm.Limit.linAccelSwitchDelay )
+ for (colNum = Q0; colNum <= Q3 + Z_AXIS + 1; colNum++)
{
- gAlgorithm.linAccelSwitch = TRUE;
+ gKalmanFilter.P[rowNum + STATE_Q0][colNum + STATE_Q0] = tmp[rowNum][colNum];
}
- else
- {
- gAlgorithm.linAccelSwitch = FALSE;
- }
- }
- else
- {
- gAlgorithm.linAccelSwitchCntr = 0;
- gAlgorithm.linAccelSwitch = FALSE;
}
- return true;
-}
+ /* Use the GPS-provided horizontal and vertical accuracy values to populate
+ * the covariance values.
+ */
+ gKalmanFilter.P[STATE_RX][STATE_RX] = gEKFInput.GPSHorizAcc * gEKFInput.GPSHorizAcc;
+ gKalmanFilter.P[STATE_RY][STATE_RY] = gKalmanFilter.P[STATE_RX][STATE_RX];
+ gKalmanFilter.P[STATE_RZ][STATE_RZ] = gEKFInput.GPSVertAcc * gEKFInput.GPSVertAcc;
-/* Set the accelerometer filter coefficients, which are used to filter the
- * accelerometer readings prior to determining the setting of the linear-
- * acceleration switch and computing the roll and pitch from accelerometer
- * readings.
- */
-static void _PopulateFilterCoefficients( uint8_t lpfType, uint8_t callingFreq, real *b, real *a )
-{
- switch( lpfType )
+ /* Scale the best velocity error by HDOP then multiply by the z-axis angular
+ * rate PLUS one (to prevent the number from being zero) so the velocity
+ * update during high-rate turns is reduced.
+ */
+ float temp = (real)0.0625 * gEKFInput.HDOP; // 0.0625 = 0.05 / 0.8
+ real absFilteredYawRate = (real)fabs(gAlgorithm.filteredYawRate);
+ if (absFilteredYawRate > TEN_DEGREES_IN_RAD)
{
- case NO_LPF:
- b[0] = (real)(1.0);
- b[1] = (real)(0.0);
- b[2] = (real)(0.0);
- b[3] = (real)(0.0);
-
- a[0] = (real)(0.0);
- a[1] = (real)(0.0);
- a[2] = (real)(0.0);
- a[3] = (real)(0.0);
- break;
- case TWO_HZ_LPF:
- if( callingFreq == FREQ_100_HZ)
- {
- b[0] = (real)(2.19606211225382e-4);
- b[1] = (real)(6.58818633676145e-4);
- b[2] = (real)(6.58818633676145e-4);
- b[3] = (real)(2.19606211225382e-4);
-
- a[0] = (real)( 1.000000000000000);
- a[1] = (real)(-2.748835809214676);
- a[2] = (real)( 2.528231219142559);
- a[3] = (real)(-0.777638560238080);
- }
- else
- {
- b[0] = (real)(2.91464944656705e-5);
- b[1] = (real)(8.74394833970116e-5);
- b[2] = (real)(8.74394833970116e-5);
- b[3] = (real)(2.91464944656705e-5);
-
- a[0] = (real)( 1.000000000000000);
- a[1] = (real)(-2.874356892677485);
- a[2] = (real)( 2.756483195225695);
- a[3] = (real)(-0.881893130592486);
- }
- break;
- case FIVE_HZ_LPF:
- if( callingFreq == FREQ_100_HZ)
- {
- b[0] = (real)( 0.002898194633721);
- b[1] = (real)( 0.008694583901164);
- b[2] = (real)( 0.008694583901164);
- b[3] = (real)( 0.002898194633721);
-
- a[0] = (real)( 1.000000000000000);
- a[1] = (real)(-2.374094743709352);
- a[2] = (real)( 1.929355669091215);
- a[3] = (real)(-0.532075368312092);
- }
- else
- {
- b[0] = (real)( 0.000416546139076);
- b[1] = (real)( 0.001249638417227);
- b[2] = (real)( 0.001249638417227);
- b[3] = (real)( 0.000416546139076);
-
- a[0] = (real)( 1.000000000000000);
- a[1] = (real)(-2.686157396548143);
- a[2] = (real)( 2.419655110966473);
- a[3] = (real)(-0.730165345305723);
- }
- break;
- case TWENTY_HZ_LPF:
- if (callingFreq == FREQ_100_HZ)
- {
- // [B,A] = butter(3,20/(100/2))
- b[0] = (real)( 0.098531160923927);
- b[1] = (real)( 0.295593482771781);
- b[2] = (real)( 0.295593482771781);
- b[3] = (real)( 0.098531160923927);
-
- a[0] = (real)( 1.000000000000000);
- a[1] = (real)(-0.577240524806303);
- a[2] = (real)( 0.421787048689562);
- a[3] = (real)(-0.056297236491843);
- }
- else
- {
- // [B,A] = butter(3,20/(200/2))
- b[0] = (real)( 0.018098933007514);
- b[1] = (real)( 0.054296799022543);
- b[2] = (real)( 0.054296799022543);
- b[3] = (real)( 0.018098933007514);
-
- a[0] = (real)( 1.000000000000000);
- a[1] = (real)(-1.760041880343169);
- a[2] = (real)( 1.182893262037831);
- a[3] = (real)(-0.278059917634546);
- }
- break;
- case TWENTY_FIVE_HZ_LPF:
- if (callingFreq == FREQ_100_HZ)
- {
- b[0] = (real)( 0.166666666666667);
- b[1] = (real)( 0.500000000000000);
- b[2] = (real)( 0.500000000000000);
- b[3] = (real)( 0.166666666666667);
-
- a[0] = (real)( 1.000000000000000);
- a[1] = (real)(-0.000000000000000);
- a[2] = (real)( 0.333333333333333);
- a[3] = (real)(-0.000000000000000);
- }
- else
- {
- b[0] = (real)( 0.031689343849711);
- b[1] = (real)( 0.095068031549133);
- b[2] = (real)( 0.095068031549133);
- b[3] = (real)( 0.031689343849711);
-
- a[0] = (real)( 1.000000000000000);
- a[1] = (real)(-1.459029062228061);
- a[2] = (real)( 0.910369000290069);
- a[3] = (real)(-0.197825187264319);
- }
- break;
- case TEN_HZ_LPF:
- default:
- if( callingFreq == FREQ_100_HZ)
- {
- b[0] = (real)( 0.0180989330075144);
- b[1] = (real)( 0.0542967990225433);
- b[2] = (real)( 0.0542967990225433);
- b[3] = (real)( 0.0180989330075144);
-
- a[0] = (real)( 1.0000000000000000);
- a[1] = (real)(-1.7600418803431690);
- a[2] = (real)( 1.1828932620378310);
- a[3] = (real)(-0.2780599176345460);
- }
- else
- {
- b[0] = (real)( 0.002898194633721);
- b[1] = (real)( 0.008694583901164);
- b[2] = (real)( 0.008694583901164);
- b[3] = (real)( 0.002898194633721);
-
- a[0] = (real)( 1.000000000000000);
- a[1] = (real)(-2.374094743709352);
- a[2] = (real)( 1.929355669091215);
- a[3] = (real)(-0.532075368312092);
- }
- break;
+ temp *= (1.0f + absFilteredYawRate);
}
-}
-
-static void _AccelLPF( real *accel, uint8_t lpfType, uint8_t callingFreq, real *filteredAccel )
-{
- // Floating-point filter variables
- static real accelFilt[FILTER_ORDER+1][NUM_AXIS];
- static real accelReading[FILTER_ORDER+1][NUM_AXIS];
+ gKalmanFilter.P[STATE_VX][STATE_VX] = temp;// *((real)1.0 + fabs(gAlgorithm.filteredYawRate) * (real)RAD_TO_DEG);
+ gKalmanFilter.P[STATE_VX][STATE_VX] = gKalmanFilter.P[STATE_VX][STATE_VX] * gKalmanFilter.P[STATE_VX][STATE_VX];
+ gKalmanFilter.P[STATE_VY][STATE_VY] = gKalmanFilter.P[STATE_VX][STATE_VX];
- // filter coefficients. y/x = b/a
- static real b_AccelFilt[FILTER_ORDER+1];
- static real a_AccelFilt[FILTER_ORDER+1];
+ // z-axis velocity isn't really a function of yaw-rate and hdop
+ //gKalmanFilter.R[STATE_VZ][STATE_VZ] = gKalmanFilter.R[STATE_VX][STATE_VX];
+ gKalmanFilter.P[STATE_VZ][STATE_VZ] = (float)(0.1 * 0.1);
- // Compute filter coefficients and initialize data buffer
- static BOOL initAccelFilt = true;
- if (initAccelFilt)
- {
- initAccelFilt = false;
-
- // Set the filter coefficients based on selected cutoff frequency and sampling rate
- _PopulateFilterCoefficients( lpfType, callingFreq, b_AccelFilt, a_AccelFilt);
-
- // Initialize the filter variables (do not need to populate the 0th element
- // as it is never used)
- for( int i = PASTx1; i <= PASTx3; i++ )
- {
- accelReading[i][X_AXIS] = accel[X_AXIS];
- accelReading[i][Y_AXIS] = accel[Y_AXIS];
- accelReading[i][Z_AXIS] = accel[Z_AXIS];
-
- accelFilt[i][X_AXIS] = accel[X_AXIS];
- accelFilt[i][Y_AXIS] = accel[Y_AXIS];
- accelFilt[i][Z_AXIS] = accel[Z_AXIS];
- }
- }
+ return 1;
+}
- /* Filter accelerometer readings (Note: a[0] = 1.0 and the filter coefficients are symmetric)
- * y = filtered output; x = raw input;
- */
- /* a[0]*y(k) + a[1]*y(k-1) + a[2]*y(k-2) + a[3]*y(k-3) =
- * b[0]*x(k) + b[1]*x(k-1) + b[2]*x(k-2) + b[3]*x(k-3) =
- * b[0]*( x(k) + x(k-3) ) + b[1]*( x(k-1) + x(k-2) )
+static void RemoveLeverArm(double *lla, double *vNed, real *w, real *leverArmB, real *rn2e, double *ecef)
+{
+ // Using position with lever arm to calculate rm and rn
+ double sinLat = sin(lla[LAT]);
+ double cosLat = cos(lla[LAT]);
+ double tmp = 1.0 - (E_ECC_SQ * sinLat * sinLat);
+ double sqrtTmp = sqrt(tmp);
+ double rn = E_MAJOR / sqrtTmp; // radius of Curvature [meters]
+ double rm = rn * (1.0 - E_ECC_SQ) / tmp;
+ // Remove lever arm from position
+ real leverArmN[3]; // lever arm in the NED frame
+ leverArmN[0] = gKalmanFilter.R_BinN[0][0] * leverArmB[0] +
+ gKalmanFilter.R_BinN[0][1] * leverArmB[1] +
+ gKalmanFilter.R_BinN[0][2] * leverArmB[2];
+ leverArmN[1] = gKalmanFilter.R_BinN[1][0] * leverArmB[0] +
+ gKalmanFilter.R_BinN[1][1] * leverArmB[1] +
+ gKalmanFilter.R_BinN[1][2] * leverArmB[2];
+ leverArmN[2] = gKalmanFilter.R_BinN[2][0] * leverArmB[0] +
+ gKalmanFilter.R_BinN[2][1] * leverArmB[1] +
+ gKalmanFilter.R_BinN[2][2] * leverArmB[2];
+ lla[0] -= leverArmN[0] / rm;
+ lla[1] -= leverArmN[1] / rn / cosLat;
+ lla[2] += leverArmN[2]; /* Notice: lever arm is now in NED frame while altitude is
+ * in the opposite direction of the z axis of NED frame.
+ */
+
+ /* Remove lever arm effects from velocity
+ * v_gnss = v_imu + C_b2n * cross(wB, leverArmB)
*/
- accelFilt[CURRENT][X_AXIS] = b_AccelFilt[CURRENT] * accel[X_AXIS] +
- b_AccelFilt[PASTx1] * ( accelReading[PASTx1][X_AXIS] +
- accelReading[PASTx2][X_AXIS] ) +
- b_AccelFilt[PASTx3] * accelReading[PASTx3][X_AXIS] -
- a_AccelFilt[PASTx1] * accelFilt[PASTx1][X_AXIS] -
- a_AccelFilt[PASTx2] * accelFilt[PASTx2][X_AXIS] -
- a_AccelFilt[PASTx3] * accelFilt[PASTx3][X_AXIS];
- accelFilt[CURRENT][Y_AXIS] = b_AccelFilt[CURRENT] * accel[Y_AXIS] +
- b_AccelFilt[PASTx1] * ( accelReading[PASTx1][Y_AXIS] +
- accelReading[PASTx2][Y_AXIS] ) +
- b_AccelFilt[PASTx3] * accelReading[PASTx3][Y_AXIS] -
- a_AccelFilt[PASTx1] * accelFilt[PASTx1][Y_AXIS] -
- a_AccelFilt[PASTx2] * accelFilt[PASTx2][Y_AXIS] -
- a_AccelFilt[PASTx3] * accelFilt[PASTx3][Y_AXIS];
- accelFilt[CURRENT][Z_AXIS] = b_AccelFilt[CURRENT] * accel[Z_AXIS] +
- b_AccelFilt[PASTx1] * ( accelReading[PASTx1][Z_AXIS] +
- accelReading[PASTx2][Z_AXIS] ) +
- b_AccelFilt[PASTx3] * accelReading[PASTx3][Z_AXIS] -
- a_AccelFilt[PASTx1] * accelFilt[PASTx1][Z_AXIS] -
- a_AccelFilt[PASTx2] * accelFilt[PASTx2][Z_AXIS] -
- a_AccelFilt[PASTx3] * accelFilt[PASTx3][Z_AXIS];
-
- // Update past readings
- accelReading[PASTx3][X_AXIS] = accelReading[PASTx2][X_AXIS];
- accelReading[PASTx2][X_AXIS] = accelReading[PASTx1][X_AXIS];
- accelReading[PASTx1][X_AXIS] = accel[X_AXIS];
-
- accelReading[PASTx3][Y_AXIS] = accelReading[PASTx2][Y_AXIS];
- accelReading[PASTx2][Y_AXIS] = accelReading[PASTx1][Y_AXIS];
- accelReading[PASTx1][Y_AXIS] = accel[Y_AXIS];
-
- accelReading[PASTx3][Z_AXIS] = accelReading[PASTx2][Z_AXIS];
- accelReading[PASTx2][Z_AXIS] = accelReading[PASTx1][Z_AXIS];
- accelReading[PASTx1][Z_AXIS] = accel[Z_AXIS];
-
- accelFilt[PASTx3][X_AXIS] = accelFilt[PASTx2][X_AXIS];
- accelFilt[PASTx2][X_AXIS] = accelFilt[PASTx1][X_AXIS];
- accelFilt[PASTx1][X_AXIS] = accelFilt[CURRENT][X_AXIS];
-
- accelFilt[PASTx3][Y_AXIS] = accelFilt[PASTx2][Y_AXIS];
- accelFilt[PASTx2][Y_AXIS] = accelFilt[PASTx1][Y_AXIS];
- accelFilt[PASTx1][Y_AXIS] = accelFilt[CURRENT][Y_AXIS];
-
- accelFilt[PASTx3][Z_AXIS] = accelFilt[PASTx2][Z_AXIS];
- accelFilt[PASTx2][Z_AXIS] = accelFilt[PASTx1][Z_AXIS];
- accelFilt[PASTx1][Z_AXIS] = accelFilt[CURRENT][Z_AXIS];
-
- // Output filtered accel
- filteredAccel[X_AXIS] = accelFilt[CURRENT][X_AXIS];
- filteredAccel[Y_AXIS] = accelFilt[CURRENT][Y_AXIS];
- filteredAccel[Z_AXIS] = accelFilt[CURRENT][Z_AXIS];
+ cross(w, leverArmB, leverArmN); // use leverArmN to temporatily hold w x leverArmB in body frame
+ vNed[0] -= gKalmanFilter.R_BinN[0][0] * leverArmN[0] +
+ gKalmanFilter.R_BinN[0][1] * leverArmN[1] +
+ gKalmanFilter.R_BinN[0][2] * leverArmN[2];
+ vNed[1] -= gKalmanFilter.R_BinN[1][0] * leverArmN[0] +
+ gKalmanFilter.R_BinN[1][1] * leverArmN[1] +
+ gKalmanFilter.R_BinN[1][2] * leverArmN[2];
+ vNed[2] -= gKalmanFilter.R_BinN[2][0] * leverArmN[0] +
+ gKalmanFilter.R_BinN[2][1] * leverArmN[1] +
+ gKalmanFilter.R_BinN[2][2] * leverArmN[2];
+
+ // calcualte transfromation matrix from NED to ECEF
+ sinLat = sin(lla[LAT]); // recalculate with LLA without lever arm
+ cosLat = cos(lla[LAT]);
+ double sinLon = sin(lla[LON]);
+ double cosLon = cos(lla[LON]);
+
+ real sinLat_r = (real)sinLat;
+ real cosLat_r = (real)cosLat;
+ real sinLon_r = (real)sinLon;
+ real cosLon_r = (real)cosLon;
+
+ // Form the transformation matrix from NED to ECEF
+ // First row
+ *(rn2e + 0 * 3 + 0) = -sinLat_r * cosLon_r;
+ *(rn2e + 0 * 3 + 1) = -sinLon_r;
+ *(rn2e + 0 * 3 + 2) = -cosLat_r * cosLon_r;
+ // Second row
+ *(rn2e + 1 * 3 + 0) = -sinLat_r * sinLon_r;
+ *(rn2e + 1 * 3 + 1) = cosLon_r;
+ *(rn2e + 1 * 3 + 2) = -cosLat_r * sinLon_r;
+ // Third row
+ *(rn2e + 2 * 3 + 0) = cosLat_r;
+ *(rn2e + 2 * 3 + 1) = 0.0;
+ *(rn2e + 2 * 3 + 2) = -sinLat_r;
+
+ // calculate ECEF position
+ tmp = (rn + lla[ALT]) * cosLat;
+ ecef[X_AXIS] = tmp * cosLon;
+ ecef[Y_AXIS] = tmp * sinLon;
+ ecef[Z_AXIS] = ((E_MINOR_OVER_MAJOR_SQ * (rn)) + lla[ALT]) * sinLat;
}
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/MotionStatus.c b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/MotionStatus.c
new file mode 100644
index 0000000..220f0cd
--- /dev/null
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/MotionStatus.c
@@ -0,0 +1,642 @@
+/*****************************************************************************
+ * @file MotionStatus.c
+ * @brief Calculate sensor stats, and detect motion status using IMU/ODO/GNSS
+ * @author Dong Xiaoguang
+ * @version 1.0
+ * @date 20190801
+ *****************************************************************************/
+#include
+#include "MotionStatus.h"
+#include "buffer.h"
+#include "VectorMath.h"
+
+
+//=============================================================================
+// Filter variables (Third-Order BWF w/ default 5 Hz Cutoff)
+#define FILTER_ORDER 3
+
+#define CURRENT 0
+#define PASTx1 1
+#define PASTx2 2
+#define PASTx3 3
+/* Replace this with a fuction that will compute the coefficients so the
+ * input is the cutoff frequency in Hertz
+ */
+#define NO_LPF 0
+#define TWO_HZ_LPF 1
+#define FIVE_HZ_LPF 2
+#define TEN_HZ_LPF 3
+#define TWENTY_HZ_LPF 4
+#define TWENTY_FIVE_HZ_LPF 5
+#define N_LPF 6
+
+#define SAMPLES_FOR_STATS 20 /* 20 samples can give a relative good estimate of var
+ * This value should not be below FILTER_ORDER.
+ */
+
+ /******************************************************************************
+ * @brief Get filter coefficients of a 3rd Butterworth low-pass filter.
+ * For now only a few specific cut-off frequencies are supported.
+ * TRACE:
+ * @param [in] lpfType Low-pass filter cut-off frequency.
+ * @param [in] callingFreq Sampling frequency, only 100Hz and 200Hz are supported.
+ * @param [out] b coefficients of the numerator of the filter.
+ * @param [out] a coefficients of the denominator of the filter.
+ * @retval None.
+ ******************************************************************************/
+static void _PopulateFilterCoefficients(uint8_t lpfType, uint8_t callingFreq, real *b, real *a);
+
+/******************************************************************************
+ * @brief Process input data through a low-pass Butterworth filter.
+ * TRACE:
+ * @param [in] in Input data
+ * @param [in] bfIn Input data buffer
+ * @param [in] bfOut Output data buffer
+ * @param [in] b Numerator coef of the filter
+ * @param [in] a Denominator coef of the filter
+ *
+ * @param [out] filtered Filtered IMU data.
+ * @retval None.
+******************************************************************************/
+static void LowPassFilter(real *in, Buffer *bfIn, Buffer *bfOut, real *b, real *a, real *filtered);
+
+/******************************************************************************
+ * @brief Compute mean and var of the input data.
+ * Calculate mena and var of the latest n samples.
+ * TRACE:
+ * @param [in] bf The buffer to hold the latest n samples.
+ * @param [in] latest The latest sample.
+ * @param [in/out] mean Mean of samples already in buffer is used as input, and
+ * mean of latest samples (remove oldest and include latest)
+ * is returned as output.
+ * @param [in/out] var Var of samples already in buffer is used as input, and
+ * var of latest samples (remove oldest and include latest)
+ * is returned as output.
+ * @retval None.
+******************************************************************************/
+static void ComputeStats(Buffer *bf, real *latest, real *mean, real *var);
+
+/******************************************************************************
+ * @brief Detect zero velocity using IMU data.
+ * TRACE:
+ * @param [in] gyroVar variance of gyro [rad/s]^2
+ * @param [in] gyroMean mean of gyro [rad/s]
+ * @param [in] accelVar variance of accel [m/s/s]^2
+ * @param [in] threshold threshold to detect zero velocity
+ * @retval TRUE if static, otherwise FALSE.
+******************************************************************************/
+BOOL DetectStaticIMU(real *gyroVar, real *gyroMean, real *accelVar, STATIC_DETECT_SETTING *threshold);
+
+
+void MotionStatusImu(real *gyro, real *accel, ImuStatsStruct *imuStats, BOOL reset)
+{
+ static BOOL bIni = false; // indicate the routine is initialized or not
+ // Buffer to store input IMU data. Data in buffer is ued to calcualte filtered IMU dat.
+ static real dAccel[3][FILTER_ORDER]; // a section in memory as buffer to store accel data
+ static real dGyro[3][FILTER_ORDER]; // a section in memory as buffer to store gyro data
+ static Buffer bfAccel; // a ring buffer of accel
+ static Buffer bfGyro; // a ring buffer of gyro
+ // Buffer to store filtered IMU data. Data in buffer is used to calculate IMU stats.
+ static real dLpfAccel[3][SAMPLES_FOR_STATS]; // a section in memory as buffer to store accel data
+ static real dLpfGyro[3][SAMPLES_FOR_STATS]; // a section in memory as buffer to store gyro data
+ static Buffer bfLpfAccel; // a ring buffer of accel
+ static Buffer bfLpfGyro; // a ring buffer of gyro
+ // filter coefficients. y/x = b/a
+ static real b_AccelFilt[FILTER_ORDER + 1];
+ static real a_AccelFilt[FILTER_ORDER + 1];
+
+ // reset the calculation of motion stats
+ if (reset)
+ {
+ bIni = false;
+ }
+
+ // initialization
+ if (!bIni)
+ {
+ bIni = true;
+ // reset stats
+ imuStats->bValid = false;
+ imuStats->accelMean[0] = 0.0;
+ imuStats->accelMean[1] = 0.0;
+ imuStats->accelMean[2] = 0.0;
+ imuStats->accelVar[0] = 0.0;
+ imuStats->accelVar[1] = 0.0;
+ imuStats->accelVar[2] = 0.0;
+ imuStats->gyroMean[0] = 0.0;
+ imuStats->gyroMean[1] = 0.0;
+ imuStats->gyroMean[2] = 0.0;
+ imuStats->gyroVar[0] = 0.0;
+ imuStats->gyroVar[1] = 0.0;
+ imuStats->gyroVar[2] = 0.0;
+ // create/reset buffer
+ bfNew(&bfGyro, &dGyro[0][0], 3, FILTER_ORDER);
+ bfNew(&bfAccel, &dAccel[0][0], 3, FILTER_ORDER);
+ bfNew(&bfLpfGyro, &dLpfGyro[0][0], 3, SAMPLES_FOR_STATS);
+ bfNew(&bfLpfAccel, &dLpfAccel[0][0], 3, SAMPLES_FOR_STATS);
+ // Set the filter coefficients based on selected cutoff frequency and sampling rate
+ _PopulateFilterCoefficients(gAlgorithm.linAccelLPFType, gAlgorithm.callingFreq, b_AccelFilt, a_AccelFilt);
+ }
+
+ /* Low-pass filter.
+ * The input IMU data is put into the buffer, and then filtered.
+ */
+ LowPassFilter(gyro, &bfGyro, &bfLpfGyro, b_AccelFilt, a_AccelFilt, imuStats->lpfGyro);
+ LowPassFilter(accel, &bfAccel, &bfLpfAccel, b_AccelFilt, a_AccelFilt, imuStats->lpfAccel);
+
+ /* Compute accel norm using raw accel data.
+ * The norm will be used to detect static periods via magnitude.
+ */
+ imuStats->accelNorm = sqrtf(accel[0] * accel[0] + accel[1] * accel[1] + accel[2] * accel[2]);
+
+ /* Compute mean/variance from input data.
+ * The latest will be put into the buffer, and stats of data in buffer is then calculated.
+ * When the input data buffer is full, the stats can be assumed valid.
+ */
+ ComputeStats(&bfLpfGyro, imuStats->lpfGyro, imuStats->gyroMean, imuStats->gyroVar);
+ ComputeStats(&bfLpfAccel, imuStats->lpfAccel, imuStats->accelMean, imuStats->accelVar);
+ imuStats->bValid = bfLpfGyro.full && bfLpfAccel.full;
+
+ // Detect static period using var calculated above.
+ imuStats->bStaticIMU = DetectStaticIMU( imuStats->gyroVar,
+ imuStats->gyroMean,
+ imuStats->accelVar,
+ &gAlgorithm.staticDetectParam);
+}
+
+static void ComputeStats(Buffer *bf, real *latest, real *mean, real *var)
+{
+ real lastMean[3];
+ real lastVar[3];
+ lastMean[0] = mean[0];
+ lastMean[1] = mean[1];
+ lastMean[2] = mean[2];
+ lastVar[0] = var[0];
+ lastVar[1] = var[1];
+ lastVar[2] = var[2];
+ if (bf->full)
+ {
+ /* when buffer is full, the var and mean are computed from
+ * all data in the buffer. From now on, the var and mean
+ * should be computed by removing the oldest data and including
+ * the latest data.
+ */
+ // Get the oldest data which will be removed by following bfPut
+ real oldest[3];
+ bfGet(bf, oldest, bf->num - 1);
+ // put this accel into buffer
+ bfPut(bf, latest);
+ // mean(n+1) = ( mean(n) * n - x(1) + x(n+1) ) / n
+ mean[0] += (latest[0] - oldest[0]) / (real)(bf->num);
+ mean[1] += (latest[1] - oldest[1]) / (real)(bf->num);
+ mean[2] += (latest[2] - oldest[2]) / (real)(bf->num);
+
+ // naive var calculation is adopted because recursive method is numerically instable
+ real tmpVar[3];
+ tmpVar[0] = vecVar(&(bf->d[0]), mean[0], bf->num);
+ tmpVar[1] = vecVar(&(bf->d[bf->n]), mean[1], bf->num);
+ tmpVar[2] = vecVar(&(bf->d[2 * bf->n]), mean[2], bf->num);
+ // make var estimation smooth
+ real k = 0.96f;
+ int i;
+ for (i = 0; i < 3; i++)
+ {
+ if (tmpVar[i] >= var[i])
+ {
+ var[i] = tmpVar[i];
+ }
+ else
+ {
+ var[i] = k * var[i] + (1.0f - k)*tmpVar[i];
+ }
+ }
+ }
+ else
+ {
+ // put this accel into buffer
+ bfPut(bf, latest);
+ /* Recursivly include new accel. The data num used to compute mean and
+ * var are increasing.
+ */
+ // mean(n+1) = mean(n) *n / (n+1) + x(n+1) / (n+1)
+ mean[0] = lastMean[0] + (latest[0] - lastMean[0]) / (real)(bf->num);
+ mean[1] = lastMean[1] + (latest[1] - lastMean[1]) / (real)(bf->num);
+ mean[2] = lastMean[2] + (latest[2] - lastMean[2]) / (real)(bf->num);
+ var[0] = lastVar[0] + lastMean[0] * lastMean[0] - mean[0] * mean[0] +
+ (latest[0] * latest[0] - lastVar[0] - lastMean[0] * lastMean[0]) / (real)(bf->num);
+ var[1] = lastVar[1] + lastMean[1] * lastMean[1] - mean[1] * mean[1] +
+ (latest[1] * latest[1] - lastVar[1] - lastMean[1] * lastMean[1]) / (real)(bf->num);
+ var[2] = lastVar[2] + lastMean[2] * lastMean[2] - mean[2] * mean[2] +
+ (latest[2] * latest[2] - lastVar[2] - lastMean[2] * lastMean[2]) / (real)(bf->num);
+ }
+}
+
+BOOL DetectStaticIMU(real *gyroVar, real *gyroMean, real *accelVar, STATIC_DETECT_SETTING *threshold)
+{
+ BOOL bStatic = TRUE;
+ int i;
+ static float multiplier[3] = { 0.0, 0.0, 0.0 };
+ static float gyroVarThreshold = 0.0;
+ static float accelVarThreshold = 0.0;
+ static float gyroBiasThreshold = 0.0;
+ // Update threshold
+ if (multiplier[0] != threshold->staticNoiseMultiplier[0])
+ {
+ multiplier[0] = threshold->staticNoiseMultiplier[0];
+ gyroVarThreshold = multiplier[0] * threshold->staticVarGyro;
+ }
+ if (multiplier[1] != threshold->staticNoiseMultiplier[1])
+ {
+ multiplier[1] = threshold->staticNoiseMultiplier[1];
+ accelVarThreshold = multiplier[1] * threshold->staticVarAccel;
+ }
+ if (multiplier[2] != threshold->staticNoiseMultiplier[2])
+ {
+ multiplier[2] = threshold->staticNoiseMultiplier[2];
+ gyroBiasThreshold = multiplier[2] * threshold->maxGyroBias;
+ }
+
+ for (i = 0; i < 3; i++)
+ {
+ if (gyroVar[i] > gyroVarThreshold ||
+ accelVar[i] > accelVarThreshold ||
+ fabs(gyroMean[i]) > gyroBiasThreshold)
+ {
+ bStatic = FALSE;
+ break;
+ }
+ }
+
+ return bStatic;
+}
+
+/* Set the accelerometer filter coefficients, which are used to filter the
+ * accelerometer readings prior to determining the setting of the linear-
+ * acceleration switch and computing the roll and pitch from accelerometer
+ * readings.
+ */
+static void _PopulateFilterCoefficients(uint8_t lpfType, uint8_t callingFreq, real *b, real *a)
+{
+ switch (lpfType)
+ {
+ case NO_LPF:
+ b[0] = (real)(1.0);
+ b[1] = (real)(0.0);
+ b[2] = (real)(0.0);
+ b[3] = (real)(0.0);
+
+ a[0] = (real)(0.0);
+ a[1] = (real)(0.0);
+ a[2] = (real)(0.0);
+ a[3] = (real)(0.0);
+ break;
+ case TWO_HZ_LPF:
+ if (callingFreq == FREQ_100_HZ)
+ {
+ b[0] = (real)(2.19606211225382e-4);
+ b[1] = (real)(6.58818633676145e-4);
+ b[2] = (real)(6.58818633676145e-4);
+ b[3] = (real)(2.19606211225382e-4);
+
+ a[0] = (real)(1.000000000000000);
+ a[1] = (real)(-2.748835809214676);
+ a[2] = (real)(2.528231219142559);
+ a[3] = (real)(-0.777638560238080);
+ }
+ else
+ {
+ b[0] = (real)(2.91464944656705e-5);
+ b[1] = (real)(8.74394833970116e-5);
+ b[2] = (real)(8.74394833970116e-5);
+ b[3] = (real)(2.91464944656705e-5);
+
+ a[0] = (real)(1.000000000000000);
+ a[1] = (real)(-2.874356892677485);
+ a[2] = (real)(2.756483195225695);
+ a[3] = (real)(-0.881893130592486);
+ }
+ break;
+ case FIVE_HZ_LPF:
+ if (callingFreq == FREQ_100_HZ)
+ {
+ b[0] = (real)(0.002898194633721);
+ b[1] = (real)(0.008694583901164);
+ b[2] = (real)(0.008694583901164);
+ b[3] = (real)(0.002898194633721);
+
+ a[0] = (real)(1.000000000000000);
+ a[1] = (real)(-2.374094743709352);
+ a[2] = (real)(1.929355669091215);
+ a[3] = (real)(-0.532075368312092);
+ }
+ else
+ {
+ b[0] = (real)(0.000416546139076);
+ b[1] = (real)(0.001249638417227);
+ b[2] = (real)(0.001249638417227);
+ b[3] = (real)(0.000416546139076);
+
+ a[0] = (real)(1.000000000000000);
+ a[1] = (real)(-2.686157396548143);
+ a[2] = (real)(2.419655110966473);
+ a[3] = (real)(-0.730165345305723);
+ }
+ break;
+ case TWENTY_HZ_LPF:
+ if (callingFreq == FREQ_100_HZ)
+ {
+ // [B,A] = butter(3,20/(100/2))
+ b[0] = (real)(0.098531160923927);
+ b[1] = (real)(0.295593482771781);
+ b[2] = (real)(0.295593482771781);
+ b[3] = (real)(0.098531160923927);
+
+ a[0] = (real)(1.000000000000000);
+ a[1] = (real)(-0.577240524806303);
+ a[2] = (real)(0.421787048689562);
+ a[3] = (real)(-0.056297236491843);
+ }
+ else
+ {
+ // [B,A] = butter(3,20/(200/2))
+ b[0] = (real)(0.018098933007514);
+ b[1] = (real)(0.054296799022543);
+ b[2] = (real)(0.054296799022543);
+ b[3] = (real)(0.018098933007514);
+
+ a[0] = (real)(1.000000000000000);
+ a[1] = (real)(-1.760041880343169);
+ a[2] = (real)(1.182893262037831);
+ a[3] = (real)(-0.278059917634546);
+ }
+ break;
+ case TWENTY_FIVE_HZ_LPF:
+ if (callingFreq == FREQ_100_HZ)
+ {
+ b[0] = (real)(0.166666666666667);
+ b[1] = (real)(0.500000000000000);
+ b[2] = (real)(0.500000000000000);
+ b[3] = (real)(0.166666666666667);
+
+ a[0] = (real)(1.000000000000000);
+ a[1] = (real)(-0.000000000000000);
+ a[2] = (real)(0.333333333333333);
+ a[3] = (real)(-0.000000000000000);
+ }
+ else
+ {
+ b[0] = (real)(0.031689343849711);
+ b[1] = (real)(0.095068031549133);
+ b[2] = (real)(0.095068031549133);
+ b[3] = (real)(0.031689343849711);
+
+ a[0] = (real)(1.000000000000000);
+ a[1] = (real)(-1.459029062228061);
+ a[2] = (real)(0.910369000290069);
+ a[3] = (real)(-0.197825187264319);
+ }
+ break;
+ case TEN_HZ_LPF:
+ default:
+ if (callingFreq == FREQ_100_HZ)
+ {
+ b[0] = (real)(0.0180989330075144);
+ b[1] = (real)(0.0542967990225433);
+ b[2] = (real)(0.0542967990225433);
+ b[3] = (real)(0.0180989330075144);
+
+ a[0] = (real)(1.0000000000000000);
+ a[1] = (real)(-1.7600418803431690);
+ a[2] = (real)(1.1828932620378310);
+ a[3] = (real)(-0.2780599176345460);
+ }
+ else
+ {
+ b[0] = (real)(0.002898194633721);
+ b[1] = (real)(0.008694583901164);
+ b[2] = (real)(0.008694583901164);
+ b[3] = (real)(0.002898194633721);
+
+ a[0] = (real)(1.000000000000000);
+ a[1] = (real)(-2.374094743709352);
+ a[2] = (real)(1.929355669091215);
+ a[3] = (real)(-0.532075368312092);
+ }
+ break;
+ }
+}
+
+static void LowPassFilter(real *in, Buffer *bfIn, Buffer *bfOut, real *b, real *a, real *filtered)
+{
+ // Fill the buffer with the first input.
+ if (!bfIn->full)
+ {
+ bfPut(bfIn, in);
+ filtered[0] = in[0];
+ filtered[1] = in[1];
+ filtered[2] = in[2];
+ return;
+ }
+
+ /* Filter accelerometer readings (Note: a[0] = 1.0 and the filter coefficients are symmetric)
+ * y = filtered output; x = raw input;
+ * a[0]*y(k) + a[1]*y(k-1) + a[2]*y(k-2) + a[3]*y(k-3) =
+ * b[0]*x(k) + b[1]*x(k-1) + b[2]*x(k-2) + b[3]*x(k-3) =
+ * b[0]*( x(k) + x(k-3) ) + b[1]*( x(k-1) + x(k-2) )
+ */
+ int i;
+ real tmpIn[3];
+ real tmpOut[3];
+ filtered[0] = b[CURRENT] * in[0];
+ filtered[1] = b[CURRENT] * in[1];
+ filtered[2] = b[CURRENT] * in[2];
+ for (i = PASTx1; i <= PASTx3; i++)
+ {
+ bfGet(bfIn, tmpIn, i-1);
+ bfGet(bfOut, tmpOut, i-1);
+ filtered[0] += b[i] * tmpIn[0] - a[i] * tmpOut[0];
+ filtered[1] += b[i] * tmpIn[1] - a[i] * tmpOut[1];
+ filtered[2] += b[i] * tmpIn[2] - a[i] * tmpOut[2];
+ }
+
+ // New data into buffer
+ bfPut(bfIn, in);
+}
+
+void EstimateAccelError(real *accel, real *w, real dt, uint32_t staticDelay, ImuStatsStruct *imuStats)
+{
+ static BOOL bIni = false; // indicate if the procedure is initialized
+ static real lastAccel[3]; // accel input of last step
+ static real lastGyro[3]; // gyro input of last step
+ static float lastEstimatedAccel[3]; // propagated accel of last step
+ static uint32_t counter = 0; // propagation counter
+ static uint32_t t[3];
+ // initialize
+ if (!bIni)
+ {
+ bIni = true;
+ lastAccel[0] = accel[0];
+ lastAccel[1] = accel[1];
+ lastAccel[2] = accel[2];
+ lastGyro[0] = w[0];
+ lastGyro[1] = w[1];
+ lastGyro[2] = w[2];
+ t[0] = 0;
+ t[1] = 0;
+ t[2] = 0;
+ imuStats->accelErr[0] = 0.0;
+ imuStats->accelErr[1] = 0.0;
+ imuStats->accelErr[2] = 0.0;
+ return;
+ }
+
+ /* Using gyro to propagate accel and then to detect accel error can give valid result for a
+ * short period of time because the inhere long-term drift of integrating gyro data.
+ * So, after this period of time, a new accel input will be selected.
+ * Beside, this method cannot detect long-time smooth linear acceleration. In this case, we
+ * can only hope the linear acceleration is large enough to make an obvious diffeerence from
+ * the Earth gravity 1g.
+ */
+ if (counter == 0)
+ {
+ lastEstimatedAccel[0] = lastAccel[0];
+ lastEstimatedAccel[1] = lastAccel[1];
+ lastEstimatedAccel[2] = lastAccel[2];
+ }
+ counter++;
+ if (counter == staticDelay)
+ {
+ counter = 0;
+ }
+
+ // propagate accel using gyro
+ // a(k) = a(k-1) -w x a(k-1)*dt
+ real ae[3];
+ lastGyro[0] *= -dt;
+ lastGyro[1] *= -dt;
+ lastGyro[2] *= -dt;
+ cross(lastGyro, lastEstimatedAccel, ae);
+ ae[0] += lastEstimatedAccel[0];
+ ae[1] += lastEstimatedAccel[1];
+ ae[2] += lastEstimatedAccel[2];
+
+ // save this estimated accel
+ lastEstimatedAccel[0] = ae[0];
+ lastEstimatedAccel[1] = ae[1];
+ lastEstimatedAccel[2] = ae[2];
+
+ // err = a(k) - am
+ ae[0] -= accel[0];
+ ae[1] -= accel[1];
+ ae[2] -= accel[2];
+
+ /* If the difference between the propagted accel and the input accel exceeds some threshold,
+ * we assume there is linear acceleration and set .accelErr to be a large value (0.1g).
+ * If the difference has been within the threshold for a period of time, we start to decrease
+ * estimated accel error .accelErr.
+ */
+ int j;
+ imuStats->accelErrLimit = false;
+ for (j = 0; j < 3; j++)
+ {
+ if (fabs(ae[j]) > 0.0980665) // linear accel detected, 0.01g
+ {
+ t[j] = 0;
+ imuStats->accelErr[j] = (real)0.980665; // 0.1g
+ }
+ else // no linear accel detected, start to decrease estimated accel error
+ {
+ if (t[j] > staticDelay) // decrease error
+ {
+ imuStats->accelErr[j] *= 0.9f;
+ imuStats->accelErr[j] += 0.1f * ae[j];
+ }
+ else // keep previous error value
+ {
+ t[j]++;
+ // imuStats->accelErr[j];
+ }
+ }
+ // limit error, not taking effect here since the max accelErr should be 0.1g
+ if (imuStats->accelErr[j] > 5.0) // 0.5g
+ {
+ imuStats->accelErr[j] = 5.0;
+ imuStats->accelErrLimit = true;
+ }
+ if (imuStats->accelErr[j] < -5.0)
+ {
+ imuStats->accelErr[j] = -5.0;
+ imuStats->accelErrLimit = true;
+ }
+ }
+ // record accel for next step
+ lastAccel[0] = accel[0];
+ lastAccel[1] = accel[1];
+ lastAccel[2] = accel[2];
+ lastGyro[0] = w[0];
+ lastGyro[1] = w[1];
+ lastGyro[2] = w[2];
+}
+
+BOOL DetectMotionFromAccel(real accelNorm, int iReset)
+{
+ if (iReset)
+ {
+ gAlgorithm.linAccelSwitch = false;
+ gAlgorithm.linAccelSwitchCntr = 0;
+ }
+ /* Check for times when the acceleration is 'close' to 1 [g]. When this occurs,
+ * increment a counter. When it exceeds a threshold (indicating that the system
+ * has been at rest for a given period) then decrease the R-values (in the
+ * update stage of the EKF), effectively increasing the Kalman gain.
+ */
+ if (fabs(1.0 - accelNorm/GRAVITY) < gAlgorithm.Limit.accelSwitch)
+ {
+ gAlgorithm.linAccelSwitchCntr++;
+ if (gAlgorithm.linAccelSwitchCntr >= gAlgorithm.Limit.linAccelSwitchDelay)
+ {
+ gAlgorithm.linAccelSwitch = TRUE;
+ }
+ else
+ {
+ gAlgorithm.linAccelSwitch = FALSE;
+ }
+ }
+ else
+ {
+ gAlgorithm.linAccelSwitchCntr = 0;
+ gAlgorithm.linAccelSwitch = FALSE;
+ }
+
+ return TRUE;
+}
+
+BOOL DetectStaticGnssVelocity(double *vNED, real threshold, BOOL gnssValid)
+{
+ static uint8_t cntr = 0;
+ if (gnssValid)
+ {
+ if (fabs(vNED[0]) < threshold && fabs(vNED[1]) < threshold && fabs(vNED[2]) < threshold)
+ {
+ if (cntr < 3)
+ {
+ cntr++;
+ }
+ }
+ else
+ {
+ cntr = 0;
+ }
+ }
+ else
+ {
+ cntr = 0;
+ }
+
+ return cntr >= 3;
+}
+
+BOOL DetectStaticOdo(real odo)
+{
+ return FALSE;
+}
\ No newline at end of file
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/PredictFunctions.c b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/PredictFunctions.c
index 3ac9131..e728dca 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/PredictFunctions.c
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/PredictFunctions.c
@@ -22,19 +22,20 @@
#include "algorithm.h"
#include "algorithmAPI.h"
#include "SensorNoiseParameters.h"
+#include "MotionStatus.h"
#include "EKF_Algorithm.h"
#include "PredictFunctions.h"
#include "AlgorithmLimits.h"
#include "WorldMagneticModel.h"
-#ifdef INS_OFFLINE
-#include "SimulationParameters.h"
-#else
+#ifndef INS_OFFLINE
#ifdef DISPLAY_DIAGNOSTIC_MSG
#include "debug.h"
#endif
#endif
+extern ImuStatsStruct gImuStats;
+
/* F is sparse and has elements in the following locations...
* There may be some more efficient ways of implementing this as this method
* still performs multiplication with zero values. (Ask Andrey)
@@ -77,7 +78,7 @@ uint8_t RLE_Q[ROWS_IN_F][2] = { { STATE_RX, STATE_RX },
// Local functions
static void _PredictStateEstimate(void);
static void _PredictCovarianceEstimate(void);
-
+static void StateCovarianceChange();
static void _UpdateProcessJacobian(void);
static void _UpdateProcessCovariance(void);
@@ -100,6 +101,19 @@ void EKF_PredictionStage(real *filteredAccel)
_PredictStateEstimate(); // x(k+1) = x(k) + f(x(k), u(k))
_PredictCovarianceEstimate(); // P = F*P*FTrans + Q
+ /* calculate state transition matrix and state covarariance increment
+ *P(k) = F(k)*( F(k-1) * P(k-1) * F(k-1)' )*F(k)' + Q(k)
+ * = F(k)...F(1)*P(1)*F(1)'...F(k)' + F(k)...F(2)*Q1*F(2)'...F(k)' + ... + F(k)*Q(k-1)*F(k)' + Q(k)
+ * = phi(k)*P(1)*phi(k)' + dQ(k)
+ * phi(k) = F(k)*phi(k-1), phi(1) = eye(N)
+ * dQ(k) = F(k)*dQ(k-1)*F(k)' + Q(k), dQ(1) = zeros(N)
+ */
+ if (gAlgoStatus.bit.ppsAvailable)
+ {
+ // This is done only when pps is detected.
+ StateCovarianceChange();
+ }
+
// Extract the predicted Euler angles from the predicted quaternion
QuaternionToEulerAngles( gKalmanFilter.eulerAngles,
gKalmanFilter.quaternion );
@@ -117,9 +131,9 @@ void EKF_PredictionStage(real *filteredAccel)
*/
if(magUsedInAlgorithm())
{
- magFieldVector[X_AXIS] = (real)gEKFInputData.magField_B[X_AXIS];
- magFieldVector[Y_AXIS] = (real)gEKFInputData.magField_B[Y_AXIS];
- magFieldVector[Z_AXIS] = (real)gEKFInputData.magField_B[Z_AXIS];
+ magFieldVector[X_AXIS] = (real)gEKFInput.magField_B[X_AXIS];
+ magFieldVector[Y_AXIS] = (real)gEKFInput.magField_B[Y_AXIS];
+ magFieldVector[Z_AXIS] = (real)gEKFInput.magField_B[Z_AXIS];
}
else
{
@@ -184,10 +198,6 @@ static void _PredictStateEstimate(void)
{
real aCorr_N[3];
real deltaQuaternion[4];
- /* Generate the transformation matrix (R_BinN) based on the past value of
- * the attitude quaternion (prior to prediction at the new time-step)
- */
- QuaternionToR321(gKalmanFilter.quaternion, &gKalmanFilter.R_BinN[0][0]);
if( gAlgorithm.state > LOW_GAIN_AHRS )
{
@@ -202,34 +212,45 @@ static void _PredictStateEstimate(void)
// ================= NED Velocity (v_N) =================
// aCorr_B = aMeas_B - aBias_B
- // gEKFInputData.accel_B in g's, convert to m/s^2 for integration
- gKalmanFilter.correctedAccel_B[X_AXIS] = (real)(gEKFInputData.accel_B[X_AXIS] * GRAVITY) -
+ // gEKFInput.accel_B in g's, convert to m/s^2 for integration
+ gKalmanFilter.correctedAccel_B[X_AXIS] = gEKFInput.accel_B[X_AXIS] -
gKalmanFilter.accelBias_B[X_AXIS];
- gKalmanFilter.correctedAccel_B[Y_AXIS] = (real)(gEKFInputData.accel_B[Y_AXIS] * GRAVITY) -
+ gKalmanFilter.correctedAccel_B[Y_AXIS] = gEKFInput.accel_B[Y_AXIS] -
gKalmanFilter.accelBias_B[Y_AXIS];
- gKalmanFilter.correctedAccel_B[Z_AXIS] = (real)(gEKFInputData.accel_B[Z_AXIS] * GRAVITY) -
+ gKalmanFilter.correctedAccel_B[Z_AXIS] = gEKFInput.accel_B[Z_AXIS] -
gKalmanFilter.accelBias_B[Z_AXIS];
- // Transform the corrected acceleration vector from the body to the NED-frame
- // a_N = R_BinN * a_B
- aCorr_N[X_AXIS] = gKalmanFilter.R_BinN[X_AXIS][X_AXIS] * gKalmanFilter.correctedAccel_B[X_AXIS] +
- gKalmanFilter.R_BinN[X_AXIS][Y_AXIS] * gKalmanFilter.correctedAccel_B[Y_AXIS] +
- gKalmanFilter.R_BinN[X_AXIS][Z_AXIS] * gKalmanFilter.correctedAccel_B[Z_AXIS];
- aCorr_N[Y_AXIS] = gKalmanFilter.R_BinN[Y_AXIS][X_AXIS] * gKalmanFilter.correctedAccel_B[X_AXIS] +
- gKalmanFilter.R_BinN[Y_AXIS][Y_AXIS] * gKalmanFilter.correctedAccel_B[Y_AXIS] +
- gKalmanFilter.R_BinN[Y_AXIS][Z_AXIS] * gKalmanFilter.correctedAccel_B[Z_AXIS];
- aCorr_N[Z_AXIS] = gKalmanFilter.R_BinN[Z_AXIS][X_AXIS] * gKalmanFilter.correctedAccel_B[X_AXIS] +
- gKalmanFilter.R_BinN[Z_AXIS][Y_AXIS] * gKalmanFilter.correctedAccel_B[Y_AXIS] +
- gKalmanFilter.R_BinN[Z_AXIS][Z_AXIS] * gKalmanFilter.correctedAccel_B[Z_AXIS];
-
- // Determine the acceleration of the system by removing the gravity vector
- // v_N(k+1) = v_N(k) + dV = v_N(k) + aMotion_N*DT = v_N(k) + ( a_N - g_N )*DT
- gKalmanFilter.Velocity_N[X_AXIS] = gKalmanFilter.Velocity_N[X_AXIS] +
- ( aCorr_N[X_AXIS] ) * gAlgorithm.dt;
- gKalmanFilter.Velocity_N[Y_AXIS] = gKalmanFilter.Velocity_N[Y_AXIS] +
- ( aCorr_N[Y_AXIS] ) * gAlgorithm.dt;
- gKalmanFilter.Velocity_N[Z_AXIS] = gKalmanFilter.Velocity_N[Z_AXIS] +
- ( aCorr_N[Z_AXIS] + (real)GRAVITY ) * gAlgorithm.dt;
+ /* Transform the corrected acceleration vector from the body to the NED-frame and remove gravity
+ * a_N = R_BinN * a_B
+ */
+ aCorr_N[X_AXIS] =
+ gKalmanFilter.R_BinN[X_AXIS][X_AXIS] * gKalmanFilter.correctedAccel_B[X_AXIS] +
+ gKalmanFilter.R_BinN[X_AXIS][Y_AXIS] * gKalmanFilter.correctedAccel_B[Y_AXIS] +
+ gKalmanFilter.R_BinN[X_AXIS][Z_AXIS] * gKalmanFilter.correctedAccel_B[Z_AXIS];
+ aCorr_N[Y_AXIS] =
+ gKalmanFilter.R_BinN[Y_AXIS][X_AXIS] * gKalmanFilter.correctedAccel_B[X_AXIS] +
+ gKalmanFilter.R_BinN[Y_AXIS][Y_AXIS] * gKalmanFilter.correctedAccel_B[Y_AXIS] +
+ gKalmanFilter.R_BinN[Y_AXIS][Z_AXIS] * gKalmanFilter.correctedAccel_B[Z_AXIS];
+ aCorr_N[Z_AXIS] =
+ gKalmanFilter.R_BinN[Z_AXIS][X_AXIS] * gKalmanFilter.correctedAccel_B[X_AXIS] +
+ gKalmanFilter.R_BinN[Z_AXIS][Y_AXIS] * gKalmanFilter.correctedAccel_B[Y_AXIS] +
+ gKalmanFilter.R_BinN[Z_AXIS][Z_AXIS] * gKalmanFilter.correctedAccel_B[Z_AXIS] +
+ (real)GRAVITY;
+
+ /* Determine the acceleration of the system by removing the gravity vector
+ * v_N(k+1) = v_N(k) + dV = v_N(k) + aMotion_N*DT = v_N(k) + ( a_N - g_N )*DT
+ */
+ gKalmanFilter.Velocity_N[X_AXIS] = gKalmanFilter.Velocity_N[X_AXIS] + aCorr_N[X_AXIS] * gAlgorithm.dt;
+ gKalmanFilter.Velocity_N[Y_AXIS] = gKalmanFilter.Velocity_N[Y_AXIS] + aCorr_N[Y_AXIS] * gAlgorithm.dt;
+ gKalmanFilter.Velocity_N[Z_AXIS] = gKalmanFilter.Velocity_N[Z_AXIS] + aCorr_N[Z_AXIS] * gAlgorithm.dt;
+
+ // Calculate linear acceleration in the body frame.
+ gKalmanFilter.linearAccel_B[X_AXIS] += (gKalmanFilter.correctedAccel_B[X_AXIS] +
+ gKalmanFilter.R_BinN[Z_AXIS][X_AXIS] * (real)GRAVITY)*gAlgorithm.dt;
+ gKalmanFilter.linearAccel_B[Y_AXIS] = gKalmanFilter.correctedAccel_B[Y_AXIS] +
+ gKalmanFilter.R_BinN[Z_AXIS][Y_AXIS] * (real)GRAVITY;
+ gKalmanFilter.linearAccel_B[Z_AXIS] = gKalmanFilter.correctedAccel_B[Z_AXIS] +
+ gKalmanFilter.R_BinN[Z_AXIS][Z_AXIS] * (real)GRAVITY;
}
else
{
@@ -243,18 +264,18 @@ static void _PredictStateEstimate(void)
gKalmanFilter.Velocity_N[Z_AXIS] = (real)0.0;
// what should this be???
- gKalmanFilter.correctedAccel_B[XACCEL] = (real)gEKFInputData.accel_B[X_AXIS] * (real)GRAVITY;
- gKalmanFilter.correctedAccel_B[YACCEL] = (real)gEKFInputData.accel_B[Y_AXIS] * (real)GRAVITY;
- gKalmanFilter.correctedAccel_B[ZACCEL] = (real)gEKFInputData.accel_B[Z_AXIS] * (real)GRAVITY;
+ gKalmanFilter.correctedAccel_B[XACCEL] = gEKFInput.accel_B[X_AXIS];
+ gKalmanFilter.correctedAccel_B[YACCEL] = gEKFInput.accel_B[Y_AXIS];
+ gKalmanFilter.correctedAccel_B[ZACCEL] = gEKFInput.accel_B[Z_AXIS];
}
// ================= Attitude quaternion =================
// Find the 'true' angular rate (wTrue_B = wCorr_B = wMeas_B - wBias_B)
- gKalmanFilter.correctedRate_B[X_AXIS] = gEKFInputData.angRate_B[X_AXIS] -
+ gKalmanFilter.correctedRate_B[X_AXIS] = gEKFInput.angRate_B[X_AXIS] -
gKalmanFilter.rateBias_B[X_AXIS];
- gKalmanFilter.correctedRate_B[Y_AXIS] = gEKFInputData.angRate_B[Y_AXIS] -
+ gKalmanFilter.correctedRate_B[Y_AXIS] = gEKFInput.angRate_B[Y_AXIS] -
gKalmanFilter.rateBias_B[Y_AXIS];
- gKalmanFilter.correctedRate_B[Z_AXIS] = gEKFInputData.angRate_B[Z_AXIS] -
+ gKalmanFilter.correctedRate_B[Z_AXIS] = gEKFInput.angRate_B[Z_AXIS] -
gKalmanFilter.rateBias_B[Z_AXIS];
// Placed in gKalmanFilter as wTrueTimesDtOverTwo is used to compute the Jacobian (F)
@@ -637,7 +658,7 @@ static void _UpdateProcessJacobian(void)
static void _UpdateProcessCovariance(void)
{
// Variables used to initially populate the Q-matrix
- real arw, biSq[3] = {(real)1.0e-10, (real)1.0e-10, (real)1.0e-10};
+ real biSq[3] = {(real)1.0e-10, (real)1.0e-10, (real)1.0e-10};
real sigDriftDot;
// Variables used to populate the Q-matrix each time-step
@@ -651,83 +672,16 @@ static void _UpdateProcessCovariance(void)
{
initQ_HG = FALSE;
-#ifdef INS_OFFLINE
- /* This value is set based on the version string specified in the
- * simulation configuration file, ekfSim.cfg
- */
- uint8_t sysRange = gSimulation.sysRange;
- uint8_t rsType = gSimulation.rsType;
-#else
- // This value is set based on the version string loaded into the unit
- // via the system configuration load
- uint8_t sysRange = platformGetSysRange(); // from system config
- uint8_t rsType = BMI_RS;
-#endif
-
- /* Set the matrix, Q, based on whether the system is a -200 or -400
- * Q-values are based on the rate-sensor's ARW (noise) and BI values
- * passed through the process model.
- */
- switch (sysRange)
- {
- case _200_DPS_RANGE: // same as default
- // Bias-stability value for the rate-sensors
- if (rsType == BMI_RS)
- {
- // BMI: 1.508e-3 [deg/sec] = 2.63e-5 [rad/sec]
- biSq[X_AXIS] = (real)(6.92e-10); // (2.63e-5)^2
- biSq[Y_AXIS] = biSq[X_AXIS];
- biSq[Z_AXIS] = biSq[X_AXIS];
- }
- else
- {
- // Maxim x/y: 1.85e-3 [deg/sec] = 3.24E-05 [rad/sec]
- // Maxim z: 7.25e-4 [deg/sec] = 1.27E-05 [rad/sec]
- biSq[X_AXIS] = (real)(1.05e-9); // (3.25e-5)^2
- biSq[Y_AXIS] = biSq[X_AXIS];
- biSq[Z_AXIS] = (real)(1.61e-10); // (1.27e-5)^2
- }
- break;
-
- // -400 values
- case _400_DPS_RANGE:
- // bi in [rad]
- if (rsType == BMI_RS)
- {
- // BMI: 6 [deg/hr] = 1.7e-3 [deg/sec] = 2.91e-5 [rad/sec]
- biSq[X_AXIS] = (real)(8.46e-10); // (2.91e-5)^2
- biSq[Y_AXIS] = biSq[X_AXIS];
- biSq[Z_AXIS] = biSq[X_AXIS];
- }
- else
- {
- // Maxim x/y: 2.16e-3 [deg/sec] = 3.24E-05 [rad/sec]
- // Maxim z: 1.07e-3 [deg/sec] = 1.86E-05 [rad/sec]
- biSq[X_AXIS] = (real)(1.41e-09); // (3.24e-5)^2
- biSq[Y_AXIS] = biSq[X_AXIS];
- biSq[Z_AXIS] = (real)(3.46e-10); // (1.86e-5)^2
- }
- break;
- }
-
- // ARW is unaffected by range setting, 200/400 (or it seems). Value is in
- // units of [rad/rt-sec]
- if (rsType == BMI_RS)
- {
- // BMI: 4.39e-3 [deg/rt-sec] = 7.66e-5 [rad/rt-sec]
- arw = (real)7.66e-5;
- }
- else
- {
- // Maxim: 5.63e-3 [deg/rt-sec] = 9.82E-05 [rad/rt-sec]
- arw = (real)9.82e-5;
- }
+ // squated gyro bias instability
+ biSq[X_AXIS] = gAlgorithm.imuSpec.biW * gAlgorithm.imuSpec.biW;
+ biSq[Y_AXIS] = biSq[X_AXIS];
+ biSq[Z_AXIS] = biSq[X_AXIS];
/* Rate-bias terms (computed once as it does not change with attitude).
* sigDriftDot = (2*pi/ln(2)) * BI^2 / ARW
* 2*pi/ln(2) = 9.064720283654388
*/
- sigDriftDot = (real)9.064720283654388 / arw;
+ sigDriftDot = (real)9.064720283654388 / gAlgorithm.imuSpec.arw;
// Rate-bias terms (Q is ultimately the squared value, which is done in the second line of the assignment)
gKalmanFilter.Q[STATE_WBX] = sigDriftDot * biSq[X_AXIS] * gAlgorithm.dt;
@@ -738,9 +692,16 @@ static void _UpdateProcessCovariance(void)
gKalmanFilter.Q[STATE_WBZ] = sigDriftDot * biSq[Z_AXIS] * gAlgorithm.dt;
gKalmanFilter.Q[STATE_WBZ] = gKalmanFilter.Q[STATE_WBZ] * gKalmanFilter.Q[STATE_WBZ];
- gKalmanFilter.Q[STATE_ABX] = (real)6.839373353251920e-10;
- gKalmanFilter.Q[STATE_ABY] = (real)6.839373353251920e-10;
- gKalmanFilter.Q[STATE_ABZ] = (real)6.839373353251920e-10;
+ // Accel bias
+ biSq[X_AXIS] = gAlgorithm.imuSpec.biA * gAlgorithm.imuSpec.biA;
+ biSq[Y_AXIS] = biSq[X_AXIS];
+ biSq[Z_AXIS] = biSq[X_AXIS];
+ sigDriftDot = (real)9.064720283654388 / gAlgorithm.imuSpec.vrw;
+ gKalmanFilter.Q[STATE_ABX] = sigDriftDot * biSq[X_AXIS] * gAlgorithm.dt;
+ gKalmanFilter.Q[STATE_ABX] = gKalmanFilter.Q[STATE_ABX] * gKalmanFilter.Q[STATE_ABX];
+ //gKalmanFilter.Q[STATE_ABX] = (real)1.0e-12;
+ gKalmanFilter.Q[STATE_ABY] = gKalmanFilter.Q[STATE_ABX];
+ gKalmanFilter.Q[STATE_ABZ] = gKalmanFilter.Q[STATE_ABX];
/* Precalculate the multiplier applied to the Q terms associated with
* attitude. sigRate = ARW / sqrt( dt )
@@ -748,7 +709,7 @@ static void _UpdateProcessCovariance(void)
* = 0.5 * sqrt(dt) * sqrt(dt) * ( ARW / sqrt(dt) )
* = 0.5 * sqrt(dt) * ARW
*/
- multiplier_Q = (real)(0.5) * gAlgorithm.sqrtDt * arw;
+ multiplier_Q = (real)(0.5) * gAlgorithm.sqrtDt * gAlgorithm.imuSpec.arw;
multiplier_Q_Sq = multiplier_Q * multiplier_Q;
}
@@ -771,9 +732,9 @@ static void _UpdateProcessCovariance(void)
* drive-test). Note: this is only called upon the first-entry
* into low-gain mode.
*/
- gKalmanFilter.Q[STATE_WBX] = (real)1.0e-3 * gKalmanFilter.Q[STATE_WBX];
+ /*gKalmanFilter.Q[STATE_WBX] = (real)1.0e-3 * gKalmanFilter.Q[STATE_WBX];
gKalmanFilter.Q[STATE_WBY] = (real)1.0e-3 * gKalmanFilter.Q[STATE_WBY];
- gKalmanFilter.Q[STATE_WBZ] = (real)1.0e-3 * gKalmanFilter.Q[STATE_WBZ];
+ gKalmanFilter.Q[STATE_WBZ] = (real)1.0e-3 * gKalmanFilter.Q[STATE_WBZ];*/
}
}
@@ -782,6 +743,17 @@ static void _UpdateProcessCovariance(void)
* block of the Q-matrix). The rest of the elements in the matrix are set
* during the transition into and between EKF states (high-gain, low-gain,
* etc) or above (upon first entry into this function).
+ * The process cov matrix of quaternion is
+ * [1-q0*q0 -q0*q1 -q0*q2 -q0*q3;
+ * -q0*q1 1-q1*q1 -q1*q2 -q1*q3;
+ * -q0*q2 -q1*q2 1-q2*q2 -q2*q3;
+ * -q0*q3 -q1*q3 -q2*q3 1-q3*q3] * (0.5*dt*sigma_gyro)^2
+ * The eigenvalue of the matrix is [1 1 1 1-q0^2-q1^2-q2^2-q3^2], which means it
+ * is not positive defintie when quaternion norm is above or equal to 1. Quaternion
+ * norm can be above 1 due to numerical accuray. A scale factor 0.99 is added here to
+ * make sure the positive definiteness of the covariance matrix. The eigenvalues now
+ * are [1 1 1 1-0.99*(q0^2+q1^2+q2^2+q3^2)]. Even if there is numerical accuracy issue,
+ * the cov matrix is still positive definite.
*/
real q0q0 = gKalmanFilter.quaternion_Past[Q0] * gKalmanFilter.quaternion_Past[Q0] * 0.99f;
real q0q1 = gKalmanFilter.quaternion_Past[Q0] * gKalmanFilter.quaternion_Past[Q1] * 0.99f;
@@ -799,9 +771,13 @@ static void _UpdateProcessCovariance(void)
// Note: this block of the covariance matrix is symmetric
real tmpQMultiplier = multiplier_Q_Sq;
- if ( gAlgorithm.state == INS_SOLUTION )
+ /* Only considering gyro noise can underestimate the cov of the quaternion.
+ * A scale factor 100 is added here. This is mainly for faster convergence
+ * of the heading angle in the INS solution.
+ */
+ if (gAlgorithm.state == INS_SOLUTION)
{
- tmpQMultiplier = 100.0 * multiplier_Q_Sq;
+ tmpQMultiplier = 1.0f * multiplier_Q_Sq;
}
gKalmanFilter.Q[STATE_Q0] = ((real)1.0 - q0q0) * tmpQMultiplier;
gKalmanFilter.Qq[0] = (-q0q1) * tmpQMultiplier;
@@ -831,7 +807,7 @@ void GenerateProcessCovariance(void)
*/
// Acceleration based values
- real dtSigAccelSq = (real)(gAlgorithm.dt * SENSOR_NOISE_ACCEL_STD_DEV);
+ real dtSigAccelSq = (real)(gAlgorithm.dt * gAlgorithm.imuSpec.sigmaA);
dtSigAccelSq = dtSigAccelSq * dtSigAccelSq;
// Position
@@ -839,17 +815,99 @@ void GenerateProcessCovariance(void)
gKalmanFilter.Q[STATE_RY] = gAlgorithm.dtSquared * dtSigAccelSq;
gKalmanFilter.Q[STATE_RZ] = gAlgorithm.dtSquared * dtSigAccelSq;
- // Velocity
+ /* Velocity, todo. 100 is to take under-estimated accel bias, gyro bias and
+ * attitude error since none of them is Gaussian. Non-Gaussian error produces
+ * velocity drift. High-freq vibration can also be handled by this.
+ */
gKalmanFilter.Q[STATE_VX] = 100 * dtSigAccelSq;//(real)1e-10;
gKalmanFilter.Q[STATE_VY] = 100 * dtSigAccelSq;
gKalmanFilter.Q[STATE_VZ] = 100 * dtSigAccelSq;
-
- // Acceleration - bias
- gKalmanFilter.Q[STATE_ABX] = (real)5e-11; //(real)1e-10; // dtSigAccelSq; //%1e-8 %sigmaAccelBiasSq;
- gKalmanFilter.Q[STATE_ABY] = (real)5e-11; //(real)1e-10; //dtSigAccelSq; //%sigmaAccelBiasSq;
- gKalmanFilter.Q[STATE_ABZ] = (real)5e-11; //(real)1e-10; //dtSigAccelSq; //%sigmaAccelBiasSq;
}
+static void StateCovarianceChange()
+{
+ uint8_t rowNum, colNum, multIndex;
+ // 1) phi(k) = F(k)*phi(k-1)
+ // deltaP_tmp is used to hold F(k)*phi(k-1)
+ memset(&gKalmanFilter.deltaP_tmp[0][0], 0, sizeof(gKalmanFilter.deltaP_tmp));
+ for (rowNum = 0; rowNum < 16; rowNum++)
+ {
+ for (colNum = 0; colNum < 16; colNum++)
+ {
+ for (multIndex = RLE_F[rowNum][0]; multIndex <= RLE_F[rowNum][1]; multIndex++)
+ {
+ gKalmanFilter.deltaP_tmp[rowNum][colNum] +=
+ gKalmanFilter.F[rowNum][multIndex] * gKalmanFilter.phi[multIndex][colNum];
+ }
+ }
+ }
+ memcpy(&gKalmanFilter.phi[0][0], &gKalmanFilter.deltaP_tmp[0][0], sizeof(gKalmanFilter.phi));
+
+ // 2) dQ(k) = F(k)*dQ(k-1)*F(k)' + Q(k)
+ // 2.1) deltaP_tmp is used to hold F(k)*dQ(k-1)
+ memset(&gKalmanFilter.deltaP_tmp[0][0], 0, sizeof(gKalmanFilter.deltaP_tmp));
+ for (rowNum = 0; rowNum < 16; rowNum++)
+ {
+ for (colNum = 0; colNum < 16; colNum++)
+ {
+ for (multIndex = RLE_F[rowNum][0]; multIndex <= RLE_F[rowNum][1]; multIndex++)
+ {
+ gKalmanFilter.deltaP_tmp[rowNum][colNum] +=
+ gKalmanFilter.F[rowNum][multIndex] * gKalmanFilter.dQ[multIndex][colNum];
+ }
+ }
+ }
+ // 2.2) Calculate F(k)*dQ(k-1)*F(k)' = deltaP_tmp*F(k)'
+ memset(&gKalmanFilter.dQ[0][0], 0, sizeof(gKalmanFilter.dQ));
+ for (rowNum = 0; rowNum < ROWS_IN_F; rowNum++)
+ {
+ for (colNum = rowNum; colNum < ROWS_IN_F; colNum++)
+ {
+ for (multIndex = RLE_F[colNum][0]; multIndex <= RLE_F[colNum][1]; multIndex++)
+ {
+ gKalmanFilter.dQ[rowNum][colNum] = gKalmanFilter.dQ[rowNum][colNum] +
+ gKalmanFilter.deltaP_tmp[rowNum][multIndex] * gKalmanFilter.F[colNum][multIndex];
+ }
+ gKalmanFilter.dQ[colNum][rowNum] = gKalmanFilter.dQ[rowNum][colNum];
+ }
+ }
+ // 2.3) Calculate F(k)*dQ(k-1)*F(k)' + Q(k)
+ gKalmanFilter.dQ[STATE_RX][STATE_RX] += gKalmanFilter.Q[STATE_RX];
+ gKalmanFilter.dQ[STATE_RY][STATE_RY] += gKalmanFilter.Q[STATE_RY];
+ gKalmanFilter.dQ[STATE_RZ][STATE_RZ] += gKalmanFilter.Q[STATE_RZ];
+
+ gKalmanFilter.dQ[STATE_VX][STATE_VX] += gKalmanFilter.Q[STATE_VX];
+ gKalmanFilter.dQ[STATE_VY][STATE_VY] += gKalmanFilter.Q[STATE_VY];
+ gKalmanFilter.dQ[STATE_VZ][STATE_VZ] += gKalmanFilter.Q[STATE_VZ];
+
+ gKalmanFilter.dQ[STATE_Q0][STATE_Q0] += gKalmanFilter.Q[STATE_Q0];
+ gKalmanFilter.dQ[STATE_Q0][STATE_Q1] += gKalmanFilter.Qq[0];
+ gKalmanFilter.dQ[STATE_Q0][STATE_Q2] += gKalmanFilter.Qq[1];
+ gKalmanFilter.dQ[STATE_Q0][STATE_Q3] += gKalmanFilter.Qq[2];
+
+ gKalmanFilter.dQ[STATE_Q1][STATE_Q0] = gKalmanFilter.dQ[STATE_Q0][STATE_Q1];
+ gKalmanFilter.dQ[STATE_Q1][STATE_Q1] += gKalmanFilter.Q[STATE_Q1];
+ gKalmanFilter.dQ[STATE_Q1][STATE_Q2] += gKalmanFilter.Qq[3];
+ gKalmanFilter.dQ[STATE_Q1][STATE_Q3] += gKalmanFilter.Qq[4];
+
+ gKalmanFilter.dQ[STATE_Q2][STATE_Q0] = gKalmanFilter.dQ[STATE_Q0][STATE_Q2];
+ gKalmanFilter.dQ[STATE_Q2][STATE_Q1] = gKalmanFilter.dQ[STATE_Q1][STATE_Q2];
+ gKalmanFilter.dQ[STATE_Q2][STATE_Q2] += gKalmanFilter.Q[STATE_Q2];
+ gKalmanFilter.dQ[STATE_Q2][STATE_Q3] += gKalmanFilter.Qq[5];
+
+ gKalmanFilter.dQ[STATE_Q3][STATE_Q0] = gKalmanFilter.dQ[STATE_Q0][STATE_Q3];
+ gKalmanFilter.dQ[STATE_Q3][STATE_Q1] = gKalmanFilter.dQ[STATE_Q1][STATE_Q3];
+ gKalmanFilter.dQ[STATE_Q3][STATE_Q2] = gKalmanFilter.dQ[STATE_Q2][STATE_Q3];
+ gKalmanFilter.dQ[STATE_Q3][STATE_Q3] += gKalmanFilter.Q[STATE_Q3];
+
+ gKalmanFilter.dQ[STATE_WBX][STATE_WBX] += gKalmanFilter.Q[STATE_WBX];
+ gKalmanFilter.dQ[STATE_WBY][STATE_WBY] += gKalmanFilter.Q[STATE_WBY];
+ gKalmanFilter.dQ[STATE_WBZ][STATE_WBZ] += gKalmanFilter.Q[STATE_WBZ];
+
+ gKalmanFilter.dQ[STATE_ABX][STATE_ABX] += gKalmanFilter.Q[STATE_ABX];
+ gKalmanFilter.dQ[STATE_ABY][STATE_ABY] += gKalmanFilter.Q[STATE_ABY];
+ gKalmanFilter.dQ[STATE_ABZ][STATE_ABZ] += gKalmanFilter.Q[STATE_ABZ];
+}
/** ****************************************************************************
* @name: firstOrderLowPass_float implements a low pass yaw axis filter
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/SelectState.c b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/SelectState.c
index 3513336..0fe20ee 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/SelectState.c
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/SelectState.c
@@ -11,6 +11,7 @@
#include "GlobalConstants.h"
#include "platformAPI.h"
+#include "TimingVars.h"
#include "algorithm.h" // gAlgorithm
#include "algorithmAPI.h"
@@ -22,7 +23,6 @@
#include "TransformationMath.h" // FieldVectorsToEulerAngles
#include "EKF_Algorithm.h"
#include "PredictFunctions.h"
-#include "TimingVars.h"
#ifndef INS_OFFLINE
#ifdef DISPLAY_DIAGNOSTIC_MSG
@@ -45,8 +45,6 @@ static BOOL _AverageFieldVectors(uint16_t pointsToAverage);
static void _DropToHighGainAHRS(void);
static void _ResetAlgorithm(void);
-static uint8_t _InitINSFilter(real* leverArmN);
-
// StabilizeSystem: Run for a prescribed period to let the sensors settle.
void StabilizeSystem(void)
{
@@ -60,11 +58,11 @@ void StabilizeSystem(void)
*/
if (gAlgorithm.stateTimer == 0) {
#ifdef INS_OFFLINE
- printf("To ini att. %u\n", gEKFInputData.itow);
+ printf("To ini att. %u\n", gEKFInput.itow);
#else
#ifdef DISPLAY_DIAGNOSTIC_MSG
DebugPrintString("To ini att. ");
- DebugPrintInt("", gEKFInputData.itow);
+ DebugPrintInt("", gEKFInput.itow);
DebugPrintEndline();
#endif
#endif
@@ -111,9 +109,9 @@ void InitializeAttitude(void)
/* Quasi-static check: check for motion over threshold. If detected, reset
* the accumulation variables and restart initialization phase.
*/
- if ((fabs(gEKFInputData.angRate_B[X_AXIS]) > LIMIT_QUASI_STATIC_STARTUP_RATE) ||
- (fabs(gEKFInputData.angRate_B[Y_AXIS]) > LIMIT_QUASI_STATIC_STARTUP_RATE) ||
- (fabs(gEKFInputData.angRate_B[Z_AXIS]) > LIMIT_QUASI_STATIC_STARTUP_RATE))
+ if ((fabs(gEKFInput.angRate_B[X_AXIS]) > LIMIT_QUASI_STATIC_STARTUP_RATE) ||
+ (fabs(gEKFInput.angRate_B[Y_AXIS]) > LIMIT_QUASI_STATIC_STARTUP_RATE) ||
+ (fabs(gEKFInput.angRate_B[Z_AXIS]) > LIMIT_QUASI_STATIC_STARTUP_RATE))
{
accumulatedAccelVector[X_AXIS] = (real)0.0;
accumulatedAccelVector[Y_AXIS] = (real)0.0;
@@ -136,11 +134,11 @@ void InitializeAttitude(void)
*/
if (gAlgorithm.stateTimer == 0) {
#ifdef INS_OFFLINE
- printf("To HG. %u\n", gEKFInputData.itow);
+ printf("To HG. %u\n", gEKFInput.itow);
#else
#ifdef DISPLAY_DIAGNOSTIC_MSG
DebugPrintString("To HG. ");
- DebugPrintInt("", gEKFInputData.itow);
+ DebugPrintInt("", gEKFInput.itow);
DebugPrintEndline();
#endif
#endif
@@ -187,6 +185,10 @@ void InitializeAttitude(void)
*/
EulerAnglesToQuaternion( gKalmanFilter.measuredEulerAngles,
gKalmanFilter.quaternion );
+ gKalmanFilter.quaternion_Past[0] = gKalmanFilter.quaternion[0];
+ gKalmanFilter.quaternion_Past[1] = gKalmanFilter.quaternion[1];
+ gKalmanFilter.quaternion_Past[2] = gKalmanFilter.quaternion[2];
+ gKalmanFilter.quaternion_Past[3] = gKalmanFilter.quaternion[3];
// Euler angles from the initial measurement (DEBUG: initial output of the system)
gKalmanFilter.eulerAngles[ROLL] = gKalmanFilter.measuredEulerAngles[ROLL];
gKalmanFilter.eulerAngles[PITCH] = gKalmanFilter.measuredEulerAngles[PITCH];
@@ -242,11 +244,11 @@ void HG_To_LG_Transition_Test(void)
*/
if (gAlgorithm.stateTimer == 0) {
#ifdef INS_OFFLINE
- printf("To LG. %u\n", gEKFInputData.itow);
+ printf("To LG. %u\n", gEKFInput.itow);
#else
#ifdef DISPLAY_DIAGNOSTIC_MSG
DebugPrintString("To LG. ");
- DebugPrintInt("", gEKFInputData.itow);
+ DebugPrintInt("", gEKFInput.itow);
DebugPrintEndline();
#endif
#endif
@@ -292,14 +294,14 @@ void LG_To_INS_Transition_Test(void)
/* If GPS output is valid (GPS providing data with a good signal lock)
* then transit to INS mode.
*/
- if ( gpsUsedInAlgorithm() && gEKFInputData.gpsUpdate )
+ if ( gpsUsedInAlgorithm() && gEKFInput.gpsUpdate && gEKFInput.gpsFixType )
{
#ifdef INS_OFFLINE
- printf("To INS. %u\n", gEKFInputData.itow);
+ printf("To INS. %u\n", gEKFInput.itow);
#else
#ifdef DISPLAY_DIAGNOSTIC_MSG
DebugPrintString("To INS. ");
- DebugPrintInt("", gEKFInputData.itow);
+ DebugPrintInt("", gEKFInput.itow);
DebugPrintEndline();
#endif
#endif
@@ -310,43 +312,10 @@ void LG_To_INS_Transition_Test(void)
// Transit to INS solution
gAlgorithm.state = INS_SOLUTION;
- // Sync the algorithm and GPS ITOW
- gAlgorithm.itow = gEKFInputData.itow;
-
- /* We have a good GPS reading now - set this variable so we
- * don't drop into INS right away
- */
- gAlgorithm.timeOfLastGoodGPSReading = gEKFInputData.itow;
-
- /* Prepare for INS.
- * R_NinE and rGPS_E are used later. rGPS_E is used in _InitINSFilter to initialize rGPS0_E.
- * R_NinE is in UpdateFunctions.c to convert position to ECEF. R_NinE is also calculated in
- * UpdateFunctions.c. But it is necessary here because it is needed to calculate position
- * after switching to INS and before the next GNSS measurement to trigger a Kalman update.
- */
- LLA_To_Base(&gEKFInputData.llaRad[0],
- &gAlgorithm.rGPS0_E[0],
- &gAlgorithm.rGPS_N[0],
- &gAlgorithm.R_NinE[0][0],
- &gAlgorithm.rGPS_E[0]);
-
- /* Lever-arm is antenna position w.r.t to IMU in body. rGPS_N is antenna positive
- * w.r.t to initial point in NED. IMU positive w.r.t initial point is
- * rGPS_N - R_b_to_N * lever-arm
- */
- float leverArmN[3];
- leverArmN[0] = gKalmanFilter.R_BinN[0][0] * gAlgorithm.leverArmB[0] +
- gKalmanFilter.R_BinN[0][1] * gAlgorithm.leverArmB[1] +
- gKalmanFilter.R_BinN[0][2] * gAlgorithm.leverArmB[2];
- leverArmN[1] = gKalmanFilter.R_BinN[1][0] * gAlgorithm.leverArmB[0] +
- gKalmanFilter.R_BinN[1][1] * gAlgorithm.leverArmB[1] +
- gKalmanFilter.R_BinN[1][2] * gAlgorithm.leverArmB[2];
- leverArmN[2] = gKalmanFilter.R_BinN[2][0] * gAlgorithm.leverArmB[0] +
- gKalmanFilter.R_BinN[2][1] * gAlgorithm.leverArmB[1] +
- gKalmanFilter.R_BinN[2][2] * gAlgorithm.leverArmB[2];
+ gAlgoStatus.bit.attitudeOnlyAlgorithm = FALSE;
// Initialize the algorithm with GNSS position and lever arm
- _InitINSFilter(leverArmN);
+ InitINSFilter();
// Set linear-acceleration switch variables
gAlgorithm.linAccelSwitchCntr = 0;
@@ -354,103 +323,6 @@ void LG_To_INS_Transition_Test(void)
}
}
-
-
-
-//
-static uint8_t _InitINSFilter(real* leverArmN)
-{
- real tmp[7][7];
- int rowNum, colNum;
-
- gAlgorithm.insFirstTime = FALSE;
-
- /* Upon the first entry into INS, save off the base position and reset the
- * Kalman filter variables.
- */
- // Save off the base ECEF location
- gAlgorithm.rGPS0_E[X_AXIS] = gAlgorithm.rGPS_E[X_AXIS];
- gAlgorithm.rGPS0_E[Y_AXIS] = gAlgorithm.rGPS_E[Y_AXIS];
- gAlgorithm.rGPS0_E[Z_AXIS] = gAlgorithm.rGPS_E[Z_AXIS];
-
- /* Reset the gps position (as position is relative to starting location)
- * rGPS_N is the IMU position, while starting location is the antenna position.
- * rGPS_N is reset to lever-arm.
- */
- gAlgorithm.rGPS_N[X_AXIS] = -leverArmN[0];
- gAlgorithm.rGPS_N[Y_AXIS] = -leverArmN[1];
- gAlgorithm.rGPS_N[Z_AXIS] = -leverArmN[2];
-
- // Reset prediction values. Position_N is also IMU position.
- gKalmanFilter.Position_N[X_AXIS] = (real)-leverArmN[0];
- gKalmanFilter.Position_N[Y_AXIS] = (real)-leverArmN[1];
- gKalmanFilter.Position_N[Z_AXIS] = (real)-leverArmN[2];
-
- gKalmanFilter.Velocity_N[X_AXIS] = (real)gEKFInputData.vNed[X_AXIS];
- gKalmanFilter.Velocity_N[Y_AXIS] = (real)gEKFInputData.vNed[Y_AXIS];
- gKalmanFilter.Velocity_N[Z_AXIS] = (real)gEKFInputData.vNed[Z_AXIS];
-
- gKalmanFilter.accelBias_B[X_AXIS] = (real)0.0;
- gKalmanFilter.accelBias_B[Y_AXIS] = (real)0.0;
- gKalmanFilter.accelBias_B[Z_AXIS] = (real)0.0;
-
- /* Extract the Quaternion and rate-bias values from the matrix before
- * resetting
- */
- // Save off the quaternion and rate-bias covariance values
- for (rowNum = Q0; rowNum <= Q3 + Z_AXIS + 1; rowNum++)
- {
- for (colNum = Q0; colNum <= Q3 + Z_AXIS + 1; colNum++)
- {
- tmp[rowNum][colNum] = gKalmanFilter.P[rowNum + STATE_Q0][colNum + STATE_Q0];
- }
- }
-
- // Reset P
- memset(gKalmanFilter.P, 0, sizeof(gKalmanFilter.P));
- for (rowNum = 0; rowNum < NUMBER_OF_EKF_STATES; rowNum++)
- {
- gKalmanFilter.P[rowNum][rowNum] = (real)INIT_P_INS;
- }
-
- // Repopulate the P matrix with the quaternion and rate-bias values
- for (rowNum = Q0; rowNum <= Q3 + Z_AXIS + 1; rowNum++)
- {
- for (colNum = Q0; colNum <= Q3 + Z_AXIS + 1; colNum++)
- {
- gKalmanFilter.P[rowNum + STATE_Q0][colNum + STATE_Q0] = tmp[rowNum][colNum];
- }
- }
-
- /* Use the GPS-provided horizontal and vertical accuracy values to populate
- * the covariance values.
- */
- gKalmanFilter.P[STATE_RX][STATE_RX] = gEKFInputData.GPSHorizAcc * gEKFInputData.GPSHorizAcc;
- gKalmanFilter.P[STATE_RY][STATE_RY] = gKalmanFilter.P[STATE_RX][STATE_RX];
- gKalmanFilter.P[STATE_RZ][STATE_RZ] = gEKFInputData.GPSVertAcc * gEKFInputData.GPSVertAcc;
-
- /* Scale the best velocity error by HDOP then multiply by the z-axis angular
- * rate PLUS one (to prevent the number from being zero) so the velocity
- * update during high-rate turns is reduced.
- */
- float temp = (real)0.0625 * gEKFInputData.HDOP; // 0.0625 = 0.05 / 0.8
- real absFilteredYawRate = (real)fabs(gAlgorithm.filteredYawRate);
- if (absFilteredYawRate > TEN_DEGREES_IN_RAD)
- {
- temp *= (1.0f + absFilteredYawRate);
- }
- gKalmanFilter.P[STATE_VX][STATE_VX] = temp;// *((real)1.0 + fabs(gAlgorithm.filteredYawRate) * (real)RAD_TO_DEG);
- gKalmanFilter.P[STATE_VX][STATE_VX] = gKalmanFilter.P[STATE_VX][STATE_VX] * gKalmanFilter.P[STATE_VX][STATE_VX];
- gKalmanFilter.P[STATE_VY][STATE_VY] = gKalmanFilter.P[STATE_VX][STATE_VX];
-
- // z-axis velocity isn't really a function of yaw-rate and hdop
- //gKalmanFilter.R[STATE_VZ][STATE_VZ] = gKalmanFilter.R[STATE_VX][STATE_VX];
- gKalmanFilter.P[STATE_VZ][STATE_VZ] = (float)(0.1 * 0.1);
-
- return 1;
-}
-
-
/* INS_To_AHRS_Transition_Test: Drop back to LG AHRS operation if...
* 1) GPS drops out for more than 3 seconds
* 2) magnetometer data not available AND at rest too long
@@ -459,21 +331,25 @@ static uint8_t _InitINSFilter(real* leverArmN)
void INS_To_AHRS_Transition_Test(void)
{
// Record last GPS velocity large enough to give a good heading measurement
- if (gEKFInputData.rawGroundSpeed >= LIMIT_MIN_GPS_VELOCITY_HEADING)
+ if (gEKFInput.rawGroundSpeed >= LIMIT_MIN_GPS_VELOCITY_HEADING)
{
- gAlgorithm.timeOfLastSufficientGPSVelocity = (int32_t)gEKFInputData.itow;
+ gAlgorithm.timeOfLastSufficientGPSVelocity = (int32_t)gEKFInput.itow;
}
/* Determine the length of time it has been since the system 'moved' --
* only linear motion considered (rotations ignored).
*/
- int32_t timeSinceRestBegan = (int32_t)gEKFInputData.itow - gAlgorithm.timeOfLastSufficientGPSVelocity;
+ int32_t timeSinceRestBegan = (int32_t)gEKFInput.itow - gAlgorithm.timeOfLastSufficientGPSVelocity;
if (timeSinceRestBegan < 0)
{
timeSinceRestBegan = timeSinceRestBegan + MAX_ITOW;
}
- if (timeSinceRestBegan > LIMIT_MAX_REST_TIME_BEFORE_HEADING_INVALID)
+ if (timeSinceRestBegan > LIMIT_MAX_REST_TIME_BEFORE_HEADING_INVALID && gAlgorithm.headingIni != HEADING_UNINITIALIZED)
{
- gAlgorithm.gnssHeadingFirstTime = TRUE;
+ gAlgorithm.headingIni = HEADING_GNSS_LOW;
+#ifdef DISPLAY_DIAGNOSTIC_MSG
+ DebugPrintString("Rest for too long.");
+ DebugPrintEndline();
+#endif
}
// compute time since the last good GPS reading
@@ -482,11 +358,15 @@ void INS_To_AHRS_Transition_Test(void)
timeSinceLastGoodGPSReading = timeSinceLastGoodGPSReading + MAX_ITOW;
}
- if ( timeSinceLastGoodGPSReading > gAlgorithm.Limit.Max_GPS_Drop_Time )
+ if ( timeSinceLastGoodGPSReading > gAlgorithm.Limit.maxGpsDropTime )
{
+#ifdef INS_OFFLINE
+ printf("GPS outage too long\n");
+#endif // INS_OFFLINE
+
// Currently in INS mode but requiring a transition to AHRS / VG
gAlgorithm.insFirstTime = TRUE;
- gAlgorithm.gnssHeadingFirstTime = TRUE;
+ gAlgorithm.headingIni = HEADING_UNINITIALIZED;
/* The transition from INS to AHRS and back to INS does not seem to
* generate a stable solution if we transition to LG AHRS for only 30
@@ -511,7 +391,6 @@ void INS_To_AHRS_Transition_Test(void)
gAlgoStatus.bit.highGain = ( gAlgorithm.state == HIGH_GAIN_AHRS );
gAlgoStatus.bit.attitudeOnlyAlgorithm = TRUE;
}
-
}
@@ -581,22 +460,22 @@ static void _DropToHighGainAHRS(void)
static BOOL _AccumulateFieldVectors(void)
{
// Accumulate the acceleration vector readings (accels in g's)
- accumulatedAccelVector[X_AXIS] += (real)gEKFInputData.accel_B[X_AXIS];
- accumulatedAccelVector[Y_AXIS] += (real)gEKFInputData.accel_B[Y_AXIS];
- accumulatedAccelVector[Z_AXIS] += (real)gEKFInputData.accel_B[Z_AXIS];
+ accumulatedAccelVector[X_AXIS] += (real)gEKFInput.accel_B[X_AXIS];
+ accumulatedAccelVector[Y_AXIS] += (real)gEKFInput.accel_B[Y_AXIS];
+ accumulatedAccelVector[Z_AXIS] += (real)gEKFInput.accel_B[Z_AXIS];
// Accumulate the gyroscope vector readings (accels in rad/s)
- accumulatedGyroVector[X_AXIS] += gEKFInputData.angRate_B[X_AXIS];
- accumulatedGyroVector[Y_AXIS] += gEKFInputData.angRate_B[Y_AXIS];
- accumulatedGyroVector[Z_AXIS] += gEKFInputData.angRate_B[Z_AXIS];
+ accumulatedGyroVector[X_AXIS] += gEKFInput.angRate_B[X_AXIS];
+ accumulatedGyroVector[Y_AXIS] += gEKFInput.angRate_B[Y_AXIS];
+ accumulatedGyroVector[Z_AXIS] += gEKFInput.angRate_B[Z_AXIS];
// Accumulate the magnetic-field vector readings (or set to zero if the
// product does not have magnetometers)
if (magUsedInAlgorithm() )
{
- accumulatedMagVector[X_AXIS] += (real)gEKFInputData.magField_B[X_AXIS];
- accumulatedMagVector[Y_AXIS] += (real)gEKFInputData.magField_B[Y_AXIS];
- accumulatedMagVector[Z_AXIS] += (real)gEKFInputData.magField_B[Z_AXIS];
+ accumulatedMagVector[X_AXIS] += (real)gEKFInput.magField_B[X_AXIS];
+ accumulatedMagVector[Y_AXIS] += (real)gEKFInput.magField_B[Y_AXIS];
+ accumulatedMagVector[Z_AXIS] += (real)gEKFInput.magField_B[Z_AXIS];
} else {
accumulatedMagVector[X_AXIS] = (real)0.0;
accumulatedMagVector[Y_AXIS] = (real)0.0;
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/TimingVars.c b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/TimingVars.c
index 00ba3dc..f4de8d9 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/TimingVars.c
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/TimingVars.c
@@ -19,9 +19,6 @@ limitations under the License.
#include "TimingVars.h"
-#ifdef INS_OFFLINE
-#include "SimulationParameters.h"
-#endif
TimingVars timer; // for InitTimingVars
@@ -161,14 +158,11 @@ void Initialize_Timing(void)
// toggles between 0 and 1 at 200 Hz (currently used in firmware)
timer.oneHundredHertzFlag = 0;
-#ifdef INS_OFFLINE
- // This value is set based on the version string specified in the
- // simulation configuration file, ekfSim.cfg
- // IMU: 0/1, VG: 2, AHRS: 3, Aided-VG: 4, Aided-AHRS: 5, INS: 6
- uint8_t sysType = gSimulation.sysType;
-#endif
-
// Override execution rate of taskDataAcquisition() based on the configuration
timer.dacqFrequency = DACQ_200_HZ; // default
}
+void TimingVars_dacqFrequency(int freq)
+{
+ timer.dacqFrequency = freq;
+}
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/UpdateFunctions.c b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/UpdateFunctions.c
index ab4beb1..2759483 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/UpdateFunctions.c
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/UpdateFunctions.c
@@ -24,20 +24,19 @@
#include "algorithm.h"
#include "algorithmAPI.h"
#include "AlgorithmLimits.h"
+#include "MotionStatus.h"
#include "EKF_Algorithm.h"
#include "UpdateFunctions.h"
#include "SensorNoiseParameters.h"
-extern AccelStatsStruct gAccelStats;
+extern ImuStatsStruct gImuStats;
#if FAST_MATH
#include "arm_math.h"
#endif // FAST_MATH
-#ifdef INS_OFFLINE
-#include "SimulationParameters.h"
-#else
+#ifndef INS_OFFLINE
#ifdef DISPLAY_DIAGNOSTIC_MSG
#include "debug.h"
#endif
@@ -63,20 +62,36 @@ static real _UnwrapAttitudeError( real attitudeError );
static real _LimitValue( real value, real limit );
static BOOL _CheckForUpdateTrigger(uint8_t updateRate);
+static void ApplyGpsDealyCorrForStateCov();
+
+/******************************************************************************
+ * @brief Initializa heading using GNSS heading.
+ * If the GNSS heading is valid and the vehicle is drving forward, the GNSS
+ * heading is considered valid, and the eading will be initialized to be
+ * gEKFInput.trueCourse, and velocity will also be initiazlied as the
+ * corresponding NED speed. After this, the quaternion (q0 and q3) and velocity
+ * terms in the state covariance matrix P will be reset. Non-diagonal terms will be
+ * set as 0s, and diagonal terms will be set according to estimated variance. The
+ * cov(quaternion, velocity) should also be updated. But the positive-definiteness
+ * is not guaranteed this way.
+ * TRACE:
+ * @retval TRUE if heading initialized/reinitialized, FALSE if not.
+******************************************************************************/
+static int InitializeHeadingFromGnss();
+
/******************************************************************************
- * @brief Initializa heading when GPS velocity is above a certain threshhold.
- * If the GPS velocity is above a certain threshold, a global variable useGpsHeading
- * will be set to 1. And in this function, the heading will be initialized to be
- * gEKFInputData.trueCourse, and velocity will also be initiazlied as the
+ * @brief When heading is ready for initialization, the heading angle (yaw, and
+ * indeed quaternion in the Kalman filter) is initialized to match the value of
+ * gEKFInput.trueCourse, and velocity will also be initiazlied as the
* corresponding NED speed. After this, the quaternion (q0 and q3) and velocity
* terms in the state covariance matrix P will be reset. Non-diagonal terms will be
* set as 0s, and diagonal terms will be set according to estimated variance. The
* cov(quaternion, velocity) should also be updated. But the positive-definiteness
* is not guaranteed this way.
* TRACE:
- * @retval TRUE if heading initialized, FALSE if not.
+ * @retval None.
******************************************************************************/
-static int InitializeGnssHeading();
+static void InitializeEkfHeading();
// Update rates
#define TEN_HERTZ_UPDATE 10
@@ -85,25 +100,28 @@ static int InitializeGnssHeading();
#define FIFTY_HERTZ_UPDATE 50
#define ONE_HUNDRED_HERTZ_UPDATE 100
-static uint32_t updateCntr[2] = { 0, 0 };
static BOOL useGpsHeading = 0; /* When GPS velocity is above a certain threshold,
* this is set to 1, and GPS heading measurement
* is used, otherwise, this is set to 0 and magnetic
- * heading is used. */
+ * heading is used.
+ */
static int runInsUpdate = 0; /* To enable the update to be broken up into
* two sequential calculations in two sucessive
- * 100 Hz periods. */
+ * 100 Hz periods.
+ */
// Uncomment to run only AHRS-type updates
//#define ATT_UPDATE_ONLY
static void Update_GPS(void);
+static void Update_PseudoMeasurement(void);
+static void GenPseudoMeasCov(real *r);
// EKF_UpdateStage.m
void EKF_UpdateStage(void)
{
/* Perform a VG/AHRS update, regardless of GPS availability or health,
- * when the state is HG AHRS or LG AHRS. Once GPS becomes healthy
+ * when the state is HG AHRS or LG AHRS. Once GPS becomes healthy
* (and the right conditions are met) perform an INS or reduced-order GPS update.
*/
if( gAlgorithm.state <= LOW_GAIN_AHRS )
@@ -131,12 +149,76 @@ void EKF_UpdateStage(void)
* Check for 'new GPS data'. If new, and GPS is valid, perform a
* GPS-Based update and reset timer values to resync the attitude updates.
*/
- if( gEKFInputData.gpsUpdate )
- {
- if (gEKFInputData.gpsValid)
+ if( gEKFInput.gpsUpdate )
+ {
+ /* Sync the algorithm itow to the GPS value. GPS time is the time of pps.
+ * It is delayed by (gAlgorithm.itow-gEKFInput.itow). If there is loss of
+ * PPS detection or GPS measuremetn, gEKFInput.itow equals gKalmanFilter.ppsITow.
+ */
+ if (gAlgoStatus.bit.ppsAvailable)
+ {
+ /* If GPS itow is above algorithm itow, something is wrong.
+ * If algorithm itow is more than 1sec ahead of GPS itow, GPS delay is
+ * too large and measurement is not used.
+ */
+ int32_t gnssDelay = gAlgorithm.itow - gEKFInput.itow;
+ if (gnssDelay < 0 || gnssDelay > 1000)
+ {
+ gAlgoStatus.bit.ppsAvailable = FALSE;
+ }
+ // sync with GPS time
+ gAlgorithm.itow = gEKFInput.itow + gAlgorithm.itow - gKalmanFilter.ppsITow;
+ }
+ else
+ {
+ gAlgorithm.itow = gEKFInput.itow;
+ }
+ // update pps detection time
+ gKalmanFilter.ppsITow = gEKFInput.itow;
+
+ // Resync timer
+ timer.tenHertzCntr = 0;
+ timer.subFrameCntr = 0;
+
+ // GNSS update
+ if (gEKFInput.gpsFixType)
+ {
+ // GPS heading valid?
+ gAlgoStatus.bit.gpsHeadingValid = (gEKFInput.rawGroundSpeed >= LIMIT_MIN_GPS_VELOCITY_HEADING);
+ useGpsHeading = gAlgoStatus.bit.gpsHeadingValid;
+
+ /* If GNSS outage is longer than a threshold (maxReliableDRTime), DR results get unreliable
+ * So, when GNSS comes back, the EKF is reinitialized. Otherwise, the DR results are still
+ * good, just correct the filter states with input GNSS measurement.
+ */
+ int32_t timeSinceLastGoodGPSReading = (int32_t)gAlgorithm.itow - gAlgorithm.timeOfLastGoodGPSReading;
+ if (timeSinceLastGoodGPSReading < 0)
+ {
+ timeSinceLastGoodGPSReading = timeSinceLastGoodGPSReading + MAX_ITOW;
+ }
+ if (timeSinceLastGoodGPSReading > gAlgorithm.Limit.maxReliableDRTime)
+ {
+#ifdef INS_OFFLINE
+ printf("GPS relocked.\n");
+#endif // INS_OFFLINE
+ // Since a relative long time has passed since DR begins, INS states need reinitialized.
+ InitINSFilter();
+ }
+ else
+ {
+ // DR for a relative short time, no need to reinitialize the filter.
+ Update_GPS();
+ }
+ // reset the "last good reading" time
+ gAlgorithm.timeOfLastGoodGPSReading = gEKFInput.itow;
+ }
+
+ // apply motion constraints
+ if (gAlgorithm.velocityAlwaysAlongBodyX && gAlgorithm.headingIni>HEADING_UNINITIALIZED)
{
- Update_GPS();
+ Update_PseudoMeasurement();
}
+
// At 1 Hz mark, update when GPS data is valid, else do an AHRS-update
runInsUpdate = 1;
}
@@ -144,33 +226,12 @@ void EKF_UpdateStage(void)
{
Update_Att();
runInsUpdate = 0; // set up for next pass
- useGpsHeading = 0;
- }
-
- // Update LLA at 100/200 Hz
- if ( gEKFInputData.gpsValid && ( gAlgorithm.insFirstTime == FALSE ) )
- {
- //r_E = Base_To_ECEF( &gKalmanFilter.Position_N[0], &gAlgorithm.rGPS0_E[0], &R_NinE[0][0] ); //
- double r_E[NUM_AXIS];
- float pointOfInterestN[3];
- pointOfInterestN[0] = gKalmanFilter.R_BinN[0][0] * gAlgorithm.pointOfInterestB[0] +
- gKalmanFilter.R_BinN[0][1] * gAlgorithm.pointOfInterestB[1] +
- gKalmanFilter.R_BinN[0][2] * gAlgorithm.pointOfInterestB[2];
- pointOfInterestN[1] = gKalmanFilter.R_BinN[1][0] * gAlgorithm.pointOfInterestB[0] +
- gKalmanFilter.R_BinN[1][1] * gAlgorithm.pointOfInterestB[1] +
- gKalmanFilter.R_BinN[1][2] * gAlgorithm.pointOfInterestB[2];
- pointOfInterestN[2] = gKalmanFilter.R_BinN[2][0] * gAlgorithm.pointOfInterestB[0] +
- gKalmanFilter.R_BinN[2][1] * gAlgorithm.pointOfInterestB[1] +
- gKalmanFilter.R_BinN[2][2] * gAlgorithm.pointOfInterestB[2];
- pointOfInterestN[0] += gKalmanFilter.Position_N[0];
- pointOfInterestN[1] += gKalmanFilter.Position_N[1];
- pointOfInterestN[2] += gKalmanFilter.Position_N[2];
- PosNED_To_PosECEF(pointOfInterestN, &gAlgorithm.rGPS0_E[0], &gAlgorithm.R_NinE[0][0], &r_E[0] );
- // 100 Hz generated once 1 Hz 100 Hz
-
- //gKalmanFilter.llaDeg[LAT_IDX] = ECEF2LLA( r_E ); // output variable (ned used for anything else); this is in [ deg, deg, m ]
- ECEF_To_LLA(&gKalmanFilter.llaDeg[LAT], &r_E[X_AXIS]);
- // 100 Hz 100 Hz
+ // handle P when PPS is available
+ if (gAlgoStatus.bit.ppsAvailable)
+ {
+ ApplyGpsDealyCorrForStateCov();
+ gAlgoStatus.bit.ppsAvailable = FALSE;
+ }
}
}
}
@@ -179,9 +240,18 @@ void EKF_UpdateStage(void)
void ComputeSystemInnovation_Pos(void)
{
// Position error
- gKalmanFilter.nu[STATE_RX] = gAlgorithm.rGPS_N[X_AXIS] - gKalmanFilter.Position_N[X_AXIS];
- gKalmanFilter.nu[STATE_RY] = gAlgorithm.rGPS_N[Y_AXIS] - gKalmanFilter.Position_N[Y_AXIS];
- gKalmanFilter.nu[STATE_RZ] = gAlgorithm.rGPS_N[Z_AXIS] - gKalmanFilter.Position_N[Z_AXIS];
+ if (gAlgoStatus.bit.ppsAvailable)
+ {
+ gKalmanFilter.nu[STATE_RX] = gKalmanFilter.rGPS_N[X_AXIS] - gKalmanFilter.ppsPosition_N[X_AXIS];
+ gKalmanFilter.nu[STATE_RY] = gKalmanFilter.rGPS_N[Y_AXIS] - gKalmanFilter.ppsPosition_N[Y_AXIS];
+ gKalmanFilter.nu[STATE_RZ] = gKalmanFilter.rGPS_N[Z_AXIS] - gKalmanFilter.ppsPosition_N[Z_AXIS];
+ }
+ else
+ {
+ gKalmanFilter.nu[STATE_RX] = gKalmanFilter.rGPS_N[X_AXIS] - gKalmanFilter.Position_N[X_AXIS];
+ gKalmanFilter.nu[STATE_RY] = gKalmanFilter.rGPS_N[Y_AXIS] - gKalmanFilter.Position_N[Y_AXIS];
+ gKalmanFilter.nu[STATE_RZ] = gKalmanFilter.rGPS_N[Z_AXIS] - gKalmanFilter.Position_N[Z_AXIS];
+ }
gKalmanFilter.nu[STATE_RX] = _LimitValue(gKalmanFilter.nu[STATE_RX], gAlgorithm.Limit.Innov.positionError);
gKalmanFilter.nu[STATE_RY] = _LimitValue(gKalmanFilter.nu[STATE_RY], gAlgorithm.Limit.Innov.positionError);
@@ -193,9 +263,18 @@ void ComputeSystemInnovation_Pos(void)
void ComputeSystemInnovation_Vel(void)
{
// Velocity error
- gKalmanFilter.nu[STATE_VX] = (real)gEKFInputData.vNed[X_AXIS] - gKalmanFilter.Velocity_N[X_AXIS];
- gKalmanFilter.nu[STATE_VY] = (real)gEKFInputData.vNed[Y_AXIS] - gKalmanFilter.Velocity_N[Y_AXIS];
- gKalmanFilter.nu[STATE_VZ] = (real)gEKFInputData.vNed[Z_AXIS] - gKalmanFilter.Velocity_N[Z_AXIS];
+ if (gAlgoStatus.bit.ppsAvailable)
+ {
+ gKalmanFilter.nu[STATE_VX] = (real)gEKFInput.vNed[X_AXIS] - gKalmanFilter.ppsVelocity_N[X_AXIS];
+ gKalmanFilter.nu[STATE_VY] = (real)gEKFInput.vNed[Y_AXIS] - gKalmanFilter.ppsVelocity_N[Y_AXIS];
+ gKalmanFilter.nu[STATE_VZ] = (real)gEKFInput.vNed[Z_AXIS] - gKalmanFilter.ppsVelocity_N[Z_AXIS];
+ }
+ else
+ {
+ gKalmanFilter.nu[STATE_VX] = (real)gEKFInput.vNed[X_AXIS] - gKalmanFilter.Velocity_N[X_AXIS];
+ gKalmanFilter.nu[STATE_VY] = (real)gEKFInput.vNed[Y_AXIS] - gKalmanFilter.Velocity_N[Y_AXIS];
+ gKalmanFilter.nu[STATE_VZ] = (real)gEKFInput.vNed[Z_AXIS] - gKalmanFilter.Velocity_N[Z_AXIS];
+ }
gKalmanFilter.nu[STATE_VX] = _LimitValue(gKalmanFilter.nu[STATE_VX], gAlgorithm.Limit.Innov.velocityError);
gKalmanFilter.nu[STATE_VY] = _LimitValue(gKalmanFilter.nu[STATE_VY], gAlgorithm.Limit.Innov.velocityError);
@@ -224,8 +303,24 @@ void ComputeSystemInnovation_Att(void)
// CHANGED TO SWITCH BETWEEN GPS AND MAG UPDATES
if ( useGpsHeading )
{
- gKalmanFilter.nu[STATE_YAW] = (real)gEKFInputData.trueCourse * (real)DEG_TO_RAD -
- gKalmanFilter.eulerAngles[YAW];
+ if (gAlgorithm.headingIni >= HEADING_GNSS_LOW) // heading already initialized with GNSS heading
+ {
+ if (gAlgoStatus.bit.ppsAvailable)
+ {
+ gKalmanFilter.nu[STATE_YAW] = gEKFInput.trueCourse * (real)DEG_TO_RAD -
+ gKalmanFilter.ppsEulerAngles[YAW];
+ }
+ else
+ {
+ gKalmanFilter.nu[STATE_YAW] = gEKFInput.trueCourse * (real)DEG_TO_RAD -
+ gKalmanFilter.eulerAngles[YAW];
+ }
+ }
+ else
+ {
+ gKalmanFilter.nu[STATE_YAW] = 0.0;
+ }
+
}
else if ( magUsedInAlgorithm() && gAlgorithm.state <= LOW_GAIN_AHRS )
{
@@ -368,7 +463,6 @@ uint8_t _GenerateObservationJacobian_AHRS(void)
//
void _GenerateObservationCovariance_AHRS(void)
{
- //
static real Rnom;
// Only need to compute certain elements of R once
@@ -382,48 +476,12 @@ void _GenerateObservationCovariance_AHRS(void)
*/
memset(gKalmanFilter.R, 0, sizeof(gKalmanFilter.R));
-#ifdef INS_OFFLINE
- /* This value is set based on the version string specified in the
- * simulation configuration file, ekfSim.cfg
- */
- uint8_t sysRange = gSimulation.sysRange;
-#else
- /* This value is set based on the version string loaded into the unit
- * via the system configuration load
- */
- uint8_t sysRange = platformGetSysRange(); // from system config
-#endif
-
- /* Set the matrix, R, based on whether the system is operating in high
- * or low-gain (is the acceleration above or below the acceleration threshold)
- *
- * R-values are based on the variance of the roll and pitch angles
- * generated from the sensor noise passed through the measurement
- * model. The values are multiplied by dt^2 as well as vary with the
- * angle. The value can be made large enough to work with all angles
- * but it may slow the response.
- *
- * These values are found by passing the accelerometer VRW values
- * (determined from a very limited data set) through a Matlab
- * script which generates the roll and pitch noise based on the
- * sensor noise. The value below is the 1-sigma value at 0
- * degrees. The quadratic correction below is meant to increase
- * R as the angle increases (due to the geometry and
- * mathematical function used to compute the angle).
- *
- * Matlab script: R_Versus_Theta.m
+ /* Calculate accel var when static from IMU specs.
+ * This accel var is the min accel var. If real-time accel var is below this value,
+ * the min accel var is used.
+ * Accel var is further converted to Euler angels measurement var.
*/
- switch (sysRange)
- {
- case _200_DPS_RANGE:
- // -200 VRW value (average x/y/z): 7.2e-4 [(m/sec)/rt-sec]
- Rnom = (real)9.82e-07; // (9.91e-4)^2
- break;
- case _400_DPS_RANGE:
- // -400 VRW value (average x/y/z): 8.8e-4 [(m/sec)/rt-sec]
- Rnom = (real)1.54e-06; // (1.24e-3)^2
- break;
- }
+ Rnom = gAlgorithm.imuSpec.sigmaA * gAlgorithm.imuSpec.sigmaA;
}
/* Dynamically tune measurement covariance matrix R to get proper Kalman filter
@@ -433,13 +491,13 @@ void _GenerateObservationCovariance_AHRS(void)
*/
// Rnom, accel var and accel error
- real totalAccelVar[3];
+ real totalAccelVar[3]; // [m/s/s]^2
for (int i = 0; i < 3; i++)
{
// replace sensor noise var with vibration var
- if (gAccelStats.accelVar[i] > Rnom)
+ if (gImuStats.accelVar[i] > Rnom)
{
- totalAccelVar[i] = gAccelStats.accelVar[i];
+ totalAccelVar[i] = gImuStats.accelVar[i];
}
else
{
@@ -447,7 +505,7 @@ void _GenerateObservationCovariance_AHRS(void)
}
// linear accel? (including noise and vibration)
real errSqr;
- errSqr = gAccelStats.accelErr[i] * gAccelStats.accelErr[i];
+ errSqr = gImuStats.accelErr[i] * gImuStats.accelErr[i];
if (errSqr > totalAccelVar[i])
{
totalAccelVar[i] = errSqr;
@@ -458,13 +516,13 @@ void _GenerateObservationCovariance_AHRS(void)
* Notice: totalAccelVarSum just approximates accel norm var
*/
real totalAccelVarSum = totalAccelVar[X_AXIS] + totalAccelVar[Y_AXIS] + totalAccelVar[Z_AXIS];
- real diff = gAccelStats.accelNorm - 1.0f;
+ real diff = gImuStats.accelNorm - GRAVITY;
diff *= diff;
real additionalR = 0.0;
/* if diff is larger than estimated accel err and the estimated accel err does
* not reach limit, diff will be used as additional measurement noise var.
*/
- if (diff > 4.0*totalAccelVarSum && gAccelStats.accelErrLimit == false)
+ if (diff > 4.0*totalAccelVarSum && gImuStats.accelErrLimit == false)
{
// the magnitude of diff is too big, there is linear acceleration
additionalR = diff;
@@ -481,9 +539,9 @@ void _GenerateObservationCovariance_AHRS(void)
* Notice: var(kx) = k*k*var(x)
*/
// Get ax^2, ay^2 and az^2 of normalized accel
- real axSqr = gAccelStats.lpfAccel[0] * gAccelStats.lpfAccel[0];
- real aySqr = gAccelStats.lpfAccel[1] * gAccelStats.lpfAccel[1];
- real azSqr = gAccelStats.lpfAccel[2] * gAccelStats.lpfAccel[2];
+ real axSqr = gImuStats.lpfAccel[0] * gImuStats.lpfAccel[0];
+ real aySqr = gImuStats.lpfAccel[1] * gImuStats.lpfAccel[1];
+ real azSqr = gImuStats.lpfAccel[2] * gImuStats.lpfAccel[2];
real sumSqr = axSqr + aySqr + azSqr;
axSqr /= sumSqr;
aySqr /= sumSqr;
@@ -505,7 +563,20 @@ void _GenerateObservationCovariance_AHRS(void)
gKalmanFilter.R[STATE_ROLL] += additionalR;
gKalmanFilter.R[STATE_PITCH] += additionalR;
- // limit R
+ /* We are indeed using var of multiple accel samples to estimate the var of Euler
+ * angles. From the formula above, accel var should be var of normalized accel.
+ * However, we choose GRAVITY instead of real accel norm to normalize the accel.
+ * Besides, accel var is only an estimate of Euler angles var, and Euler angels
+ * var is indeed not Gaussian.
+ */
+ gKalmanFilter.R[STATE_ROLL] /= GRAVITY * GRAVITY;
+ gKalmanFilter.R[STATE_PITCH] /= GRAVITY * GRAVITY;
+
+ /* limit R
+ * In previous version, Rnom is in untis of [g]^2, and maxR = 40000.0f*Rnom.
+ * After accel in the algorithm is changed to [m/s/s],
+ * 40000*Rnom(g^2) = 40000*Rnom([m/s/s]^2)/gravity/gravity = 400*Rnom([m/s/s]^2)
+ */
real maxR = 400.0f * Rnom;
if (gKalmanFilter.R[STATE_ROLL] > maxR)
{
@@ -550,7 +621,7 @@ void _GenerateObservationCovariance_AHRS(void)
*/
if ( useGpsHeading )
{
- float temp = (float)atan( 0.05 / gEKFInputData.rawGroundSpeed );
+ float temp = (float)atan( 0.05 / gEKFInput.rawGroundSpeed );
gKalmanFilter.R[STATE_YAW] = temp * temp;
if (gAlgoStatus.bit.turnSwitch)
{
@@ -583,7 +654,7 @@ void _GenerateObservationCovariance_AHRS(void)
}
else
{
- gKalmanFilter.R[STATE_YAW] = (real)0.1;
+ gKalmanFilter.R[STATE_YAW] = (real)1.0;
}
}
@@ -608,15 +679,15 @@ void _GenerateObservationCovariance_INS(void)
/* Use the GPS-provided horizontal and vertical accuracy values to populate
* the covariance values.
*/
- gKalmanFilter.R[STATE_RX] = gEKFInputData.GPSHorizAcc * gEKFInputData.GPSHorizAcc;
+ gKalmanFilter.R[STATE_RX] = gEKFInput.GPSHorizAcc * gEKFInput.GPSHorizAcc;
gKalmanFilter.R[STATE_RY] = gKalmanFilter.R[STATE_RX];
- gKalmanFilter.R[STATE_RZ] = gEKFInputData.GPSVertAcc * gEKFInputData.GPSVertAcc;
+ gKalmanFilter.R[STATE_RZ] = gEKFInput.GPSVertAcc * gEKFInput.GPSVertAcc;
/* Scale the best velocity error by HDOP then multiply by the z-axis angular
* rate PLUS one (to prevent the number from being zero) so the velocity
* update during high-rate turns is reduced.
*/
- float temp = (real)0.0625 * gEKFInputData.HDOP; // 0.0625 = 0.05 / 0.8
+ float temp = (real)0.0625 * gEKFInput.HDOP; // 0.0625 = 0.05 / 0.8
real absFilteredYawRate = (real)fabs(gAlgorithm.filteredYawRate);
if (absFilteredYawRate > TEN_DEGREES_IN_RAD)
{
@@ -625,6 +696,14 @@ void _GenerateObservationCovariance_INS(void)
gKalmanFilter.R[STATE_VX] = temp;// *((real)1.0 + fabs(gAlgorithm.filteredYawRate) * (real)RAD_TO_DEG);
gKalmanFilter.R[STATE_VX] = gKalmanFilter.R[STATE_VX] * gKalmanFilter.R[STATE_VX];
gKalmanFilter.R[STATE_VY] = gKalmanFilter.R[STATE_VX];
+ if (gAlgorithm.headingIni == HEADING_UNINITIALIZED)
+ {
+ /* When heading is not initialized, velocity measurement is not able to correct
+ * attitude/rate bias/accel bias, the larger the velocity, the more uncertain it is.
+ */
+ gKalmanFilter.R[STATE_VX] += SQUARE(gEKFInput.vNed[0]) + SQUARE(gEKFInput.vNed[1]);
+ gKalmanFilter.R[STATE_VY] += gKalmanFilter.R[STATE_VX];
+ }
// z-axis velocity isn't really a function of yaw-rate and hdop
gKalmanFilter.R[STATE_VZ] = (float)(0.1 * 0.1);
@@ -637,10 +716,10 @@ uint8_t rowNum, colNum, multIndex;
real S_3x3[3][3], SInverse_3x3[3][3];
real PxHTranspose[ROWS_IN_P][ROWS_IN_H];
real KxH[NUMBER_OF_EKF_STATES][COLS_IN_H] = {{ 0.0 }};
-real deltaP_tmp[ROWS_IN_P][COLS_IN_P];
void Update_Att(void)
{
+ static real lastYaw = 7.0; // a values larger than 2pi means this yaw is invalid
// which state is updated in Update_Att()
uint8_t updatedStatesAtt[16] = { 1, 1, 1, // Positions are not updated
1, 1, 1, // Velocities are not updated
@@ -653,14 +732,67 @@ void Update_Att(void)
*/
_GenerateObservationJacobian_AHRS(); // gKF.H: 3x16
_GenerateObservationCovariance_AHRS(); // gKF.R: 3x3
- // If neither mag or GPS headig is available, update measuremnt matrix H to 2x16
- if (gKalmanFilter.R[STATE_YAW] > 0.9)
+
+ // In INS mode, do not do pitch and roll update while heading update is kept.
+ if (gAlgorithm.state == INS_SOLUTION)
{
+ // reset this state.
+ gAlgoStatus.bit.stationaryYawLock = FALSE;
+
+ /* Heading measurement is invalid, check if static yaw lock should take effect.
+ * Even if IMU static detection fails and the vehicle runs at a certain speed,
+ * static yaw lock should not take effect. This is guaranteed by R[STATE_YAW], which
+ * is set to 1.0 when vehicle speed is below a certian threshold.
+ * The risk is that the mechnism fails when the vehicle is below the threshold but not
+ * static.
+ */
+ if (gKalmanFilter.R[STATE_YAW] > 0.9)
+ {
+ if (!gImuStats.bStaticIMU)
+ {
+ /* Heading measurement is invaid and IMU is not static, yaw lock should not
+ * take effect. That is, there is no heading update
+ */
+ for (colNum = 0; colNum < COLS_IN_H; colNum++)
+ {
+ gKalmanFilter.H[2][colNum] = 0.0;
+ }
+ lastYaw = 7.0;
+ }
+ else if (gAlgorithm.Behavior.bit.enableStationaryLockYaw)
+ {
+ /* IMU is static and static yaw lock is enabled. The first time when the algo runs here,
+ * the staic yaw is acquired. And yaw will be locked to this value.
+ */
+ if (lastYaw > TWO_PI)
+ {
+ lastYaw = gKalmanFilter.eulerAngles[YAW];
+ }
+ else
+ {
+ real diff = lastYaw - gKalmanFilter.eulerAngles[YAW];
+ // if angle change exceeds max bias, it is not static
+ if (fabs(diff) > gAlgorithm.imuSpec.maxBiasW)
+ {
+ lastYaw = 7.0;
+ }
+ else
+ {
+ gKalmanFilter.nu[STATE_YAW] = diff;
+ gKalmanFilter.R[STATE_YAW] = 1e-8;
+ gAlgoStatus.bit.stationaryYawLock = TRUE;
+ }
+ }
+ }
+ }
+ // Do not perform roll and pitch update
for (colNum = 0; colNum < COLS_IN_H; colNum++)
{
- gKalmanFilter.H[2][colNum] = 0.0;
+ gKalmanFilter.H[0][colNum] = 0.0;
+ gKalmanFilter.H[1][colNum] = 0.0;
}
}
+
/* This solution consists of an integrated roll/pitch/yaw solution
* S = H*P*HTrans + R (However the matrix math can be simplified since
* H is very sparse! P is fully populated)
@@ -751,9 +883,6 @@ void Update_Att(void)
/* Update covariance: P = P + DP = P - K*H*P
* KxH = gKF.K * gKF.H;
*/
- /* 2) Use gKalmanFilter.P as a temporary variable to hold FxPxFTranspose
- * to reduce the number of "large" variables on the heap
- */
memset(KxH, 0, sizeof(KxH));
for (rowNum = 0; rowNum < ROWS_IN_K; rowNum++)
{
@@ -768,7 +897,7 @@ void Update_Att(void)
}
// deltaP = KxH * gKF.P;
- memset(deltaP_tmp, 0, sizeof(deltaP_tmp));
+ memset(&gKalmanFilter.deltaP_tmp[0][0], 0, sizeof(gKalmanFilter.deltaP_tmp));
/* deltaP is symmetric so only need to multiply one half and reflect the values
* across the diagonal
*/
@@ -779,10 +908,10 @@ void Update_Att(void)
{
for (multIndex = RLE_KxH[rowNum][0]; multIndex <= RLE_KxH[rowNum][1]; multIndex++)
{
- deltaP_tmp[rowNum][colNum] = deltaP_tmp[rowNum][colNum] +
+ gKalmanFilter.deltaP_tmp[rowNum][colNum] = gKalmanFilter.deltaP_tmp[rowNum][colNum] +
KxH[rowNum][multIndex] * gKalmanFilter.P[multIndex][colNum];
}
- deltaP_tmp[colNum][rowNum] = deltaP_tmp[rowNum][colNum];
+ gKalmanFilter.deltaP_tmp[colNum][rowNum] = gKalmanFilter.deltaP_tmp[rowNum][colNum];
}
}
#else
@@ -804,10 +933,10 @@ void Update_Att(void)
{
continue;
}
- deltaP_tmp[rowNum][colNum] = deltaP_tmp[rowNum][colNum] +
+ gKalmanFilter.deltaP_tmp[rowNum][colNum] = gKalmanFilter.deltaP_tmp[rowNum][colNum] +
KxH[rowNum][multIndex] * gKalmanFilter.P[multIndex][colNum];
}
- deltaP_tmp[colNum][rowNum] = deltaP_tmp[rowNum][colNum];
+ gKalmanFilter.deltaP_tmp[colNum][rowNum] = gKalmanFilter.deltaP_tmp[rowNum][colNum];
}
}
#endif
@@ -819,7 +948,7 @@ void Update_Att(void)
for (colNum = rowNum; colNum < COLS_IN_P; colNum++)
{
gKalmanFilter.P[rowNum][colNum] = gKalmanFilter.P[rowNum][colNum] -
- deltaP_tmp[rowNum][colNum];
+ gKalmanFilter.deltaP_tmp[rowNum][colNum];
gKalmanFilter.P[colNum][rowNum] = gKalmanFilter.P[rowNum][colNum];
}
}
@@ -831,7 +960,7 @@ void Update_Att(void)
*/
void Update_Pos(void)
{
- // which state is updated in Update_Att()
+ // which state is updated in Update_Pos()
uint8_t updatedStatesPos[16] = { 1, 1, 1, // Positions are updated
1, 1, 1, // Velocities are updated
1, 1, 1, 1, // Quaternions are NOT updated
@@ -891,7 +1020,7 @@ void Update_Pos(void)
// Compute the intermediate state update, stateUpdate
AxB(&gKalmanFilter.K[0][0], &gKalmanFilter.nu[STATE_RX], NUMBER_OF_EKF_STATES, 3, 1, &gKalmanFilter.stateUpdate[0]);
- memset(deltaP_tmp, 0, sizeof(deltaP_tmp));
+ memset(&gKalmanFilter.deltaP_tmp[0][0], 0, sizeof(gKalmanFilter.deltaP_tmp));
// Update the intermediate covariance estimate
for (rowNum = 0; rowNum < NUMBER_OF_EKF_STATES; rowNum++)
{
@@ -914,14 +1043,15 @@ void Update_Pos(void)
{
continue;
}
- deltaP_tmp[rowNum][colNum] = deltaP_tmp[rowNum][colNum] +
+ gKalmanFilter.deltaP_tmp[rowNum][colNum] = gKalmanFilter.deltaP_tmp[rowNum][colNum] +
gKalmanFilter.K[rowNum][multIndex] * gKalmanFilter.P[multIndex][colNum];
}
- deltaP_tmp[colNum][rowNum] = deltaP_tmp[rowNum][colNum];
+ gKalmanFilter.deltaP_tmp[colNum][rowNum] = gKalmanFilter.deltaP_tmp[rowNum][colNum];
}
}
- AMinusB(&gKalmanFilter.P[0][0], &deltaP_tmp[0][0], NUMBER_OF_EKF_STATES, NUMBER_OF_EKF_STATES, &gKalmanFilter.P[0][0]);
+ AMinusB(&gKalmanFilter.P[0][0], &gKalmanFilter.deltaP_tmp[0][0],
+ NUMBER_OF_EKF_STATES, NUMBER_OF_EKF_STATES, &gKalmanFilter.P[0][0]);
// Update states
gKalmanFilter.Position_N[X_AXIS] = gKalmanFilter.Position_N[X_AXIS] + gKalmanFilter.stateUpdate[STATE_RX];
@@ -932,21 +1062,21 @@ void Update_Pos(void)
gKalmanFilter.Velocity_N[Y_AXIS] = gKalmanFilter.Velocity_N[Y_AXIS] + gKalmanFilter.stateUpdate[STATE_VY];
gKalmanFilter.Velocity_N[Z_AXIS] = gKalmanFilter.Velocity_N[Z_AXIS] + gKalmanFilter.stateUpdate[STATE_VZ];
- //gKalmanFilter.quaternion[Q0] = gKalmanFilter.quaternion[Q0] + gKalmanFilter.stateUpdate[STATE_Q0];
- //gKalmanFilter.quaternion[Q1] = gKalmanFilter.quaternion[Q1] + gKalmanFilter.stateUpdate[STATE_Q1];
- //gKalmanFilter.quaternion[Q2] = gKalmanFilter.quaternion[Q2] + gKalmanFilter.stateUpdate[STATE_Q2];
- //gKalmanFilter.quaternion[Q3] = gKalmanFilter.quaternion[Q3] + gKalmanFilter.stateUpdate[STATE_Q3];
- //
- //// Normalize quaternion and force q0 to be positive
- //QuatNormalize(gKalmanFilter.quaternion);
- //
- //gKalmanFilter.rateBias_B[X_AXIS] = gKalmanFilter.rateBias_B[X_AXIS] + gKalmanFilter.stateUpdate[STATE_WBX];
- //gKalmanFilter.rateBias_B[Y_AXIS] = gKalmanFilter.rateBias_B[Y_AXIS] + gKalmanFilter.stateUpdate[STATE_WBY];
- //gKalmanFilter.rateBias_B[Z_AXIS] = gKalmanFilter.rateBias_B[Z_AXIS] + gKalmanFilter.stateUpdate[STATE_WBZ];
- //
- //gKalmanFilter.accelBias_B[X_AXIS] = gKalmanFilter.accelBias_B[X_AXIS] + gKalmanFilter.stateUpdate[STATE_ABX];
- //gKalmanFilter.accelBias_B[Y_AXIS] = gKalmanFilter.accelBias_B[Y_AXIS] + gKalmanFilter.stateUpdate[STATE_ABY];
- //gKalmanFilter.accelBias_B[Z_AXIS] = gKalmanFilter.accelBias_B[Z_AXIS] + gKalmanFilter.stateUpdate[STATE_ABZ];
+ gKalmanFilter.quaternion[Q0] = gKalmanFilter.quaternion[Q0] + gKalmanFilter.stateUpdate[STATE_Q0];
+ gKalmanFilter.quaternion[Q1] = gKalmanFilter.quaternion[Q1] + gKalmanFilter.stateUpdate[STATE_Q1];
+ gKalmanFilter.quaternion[Q2] = gKalmanFilter.quaternion[Q2] + gKalmanFilter.stateUpdate[STATE_Q2];
+ gKalmanFilter.quaternion[Q3] = gKalmanFilter.quaternion[Q3] + gKalmanFilter.stateUpdate[STATE_Q3];
+
+ // Normalize quaternion and force q0 to be positive
+ QuatNormalize(gKalmanFilter.quaternion);
+
+ gKalmanFilter.rateBias_B[X_AXIS] = gKalmanFilter.rateBias_B[X_AXIS] + gKalmanFilter.stateUpdate[STATE_WBX];
+ gKalmanFilter.rateBias_B[Y_AXIS] = gKalmanFilter.rateBias_B[Y_AXIS] + gKalmanFilter.stateUpdate[STATE_WBY];
+ gKalmanFilter.rateBias_B[Z_AXIS] = gKalmanFilter.rateBias_B[Z_AXIS] + gKalmanFilter.stateUpdate[STATE_WBZ];
+
+ gKalmanFilter.accelBias_B[X_AXIS] = gKalmanFilter.accelBias_B[X_AXIS] + gKalmanFilter.stateUpdate[STATE_ABX];
+ gKalmanFilter.accelBias_B[Y_AXIS] = gKalmanFilter.accelBias_B[Y_AXIS] + gKalmanFilter.stateUpdate[STATE_ABY];
+ gKalmanFilter.accelBias_B[Z_AXIS] = gKalmanFilter.accelBias_B[Z_AXIS] + gKalmanFilter.stateUpdate[STATE_ABZ];
}
@@ -955,7 +1085,7 @@ void Update_Pos(void)
*/
void Update_Vel(void)
{
- // which state is updated in Update_Att()
+ // which state is updated in Update_Vel()
uint8_t updatedStatesVel[16] = { 1, 1, 1, // Positions are NOT updated
1, 1, 1, // Velocities are updated
1, 1, 1, 1, // Quaternions are updated
@@ -1015,7 +1145,7 @@ void Update_Vel(void)
// Compute the intermediate state update
AxB(&gKalmanFilter.K[0][0], &gKalmanFilter.nu[STATE_VX], NUMBER_OF_EKF_STATES, 3, 1, &gKalmanFilter.stateUpdate[0]);
- memset(deltaP_tmp, 0, sizeof(deltaP_tmp));
+ memset(&gKalmanFilter.deltaP_tmp[0][0], 0, sizeof(gKalmanFilter.deltaP_tmp));
// Update the intermediate covariance estimate
for (rowNum = 0; rowNum < NUMBER_OF_EKF_STATES; rowNum++)
{
@@ -1034,21 +1164,21 @@ void Update_Vel(void)
*/
for (multIndex = STATE_VX; multIndex <= STATE_VZ; multIndex++)
{
- deltaP_tmp[rowNum][colNum] = deltaP_tmp[rowNum][colNum] +
+ gKalmanFilter.deltaP_tmp[rowNum][colNum] = gKalmanFilter.deltaP_tmp[rowNum][colNum] +
gKalmanFilter.K[rowNum][multIndex - STATE_VX] * gKalmanFilter.P[multIndex][colNum];
}
- deltaP_tmp[colNum][rowNum] = deltaP_tmp[rowNum][colNum];
+ gKalmanFilter.deltaP_tmp[colNum][rowNum] = gKalmanFilter.deltaP_tmp[rowNum][colNum];
}
}
// P2 = P2 - KxHxP2
- AMinusB(&gKalmanFilter.P[0][0], &deltaP_tmp[0][0], NUMBER_OF_EKF_STATES, NUMBER_OF_EKF_STATES, &gKalmanFilter.P[0][0]);
+ AMinusB(&gKalmanFilter.P[0][0], &gKalmanFilter.deltaP_tmp[0][0], NUMBER_OF_EKF_STATES, NUMBER_OF_EKF_STATES, &gKalmanFilter.P[0][0]);
// ++++++++++++++++++++++ END OF VELOCITY ++++++++++++++++++++++
// Update states
- //gKalmanFilter.Position_N[X_AXIS] = gKalmanFilter.Position_N[X_AXIS] + gKalmanFilter.stateUpdate[STATE_RX];
- //gKalmanFilter.Position_N[Y_AXIS] = gKalmanFilter.Position_N[Y_AXIS] + gKalmanFilter.stateUpdate[STATE_RY];
- //gKalmanFilter.Position_N[Z_AXIS] = gKalmanFilter.Position_N[Z_AXIS] + gKalmanFilter.stateUpdate[STATE_RZ];
+ gKalmanFilter.Position_N[X_AXIS] = gKalmanFilter.Position_N[X_AXIS] + gKalmanFilter.stateUpdate[STATE_RX];
+ gKalmanFilter.Position_N[Y_AXIS] = gKalmanFilter.Position_N[Y_AXIS] + gKalmanFilter.stateUpdate[STATE_RY];
+ gKalmanFilter.Position_N[Z_AXIS] = gKalmanFilter.Position_N[Z_AXIS] + gKalmanFilter.stateUpdate[STATE_RZ];
gKalmanFilter.Velocity_N[X_AXIS] = gKalmanFilter.Velocity_N[X_AXIS] + gKalmanFilter.stateUpdate[STATE_VX];
gKalmanFilter.Velocity_N[Y_AXIS] = gKalmanFilter.Velocity_N[Y_AXIS] + gKalmanFilter.stateUpdate[STATE_VY];
@@ -1062,59 +1192,20 @@ void Update_Vel(void)
// Normalize quaternion and force q0 to be positive
QuatNormalize(gKalmanFilter.quaternion);
- //gKalmanFilter.rateBias_B[X_AXIS] = gKalmanFilter.rateBias_B[X_AXIS] + gKalmanFilter.stateUpdate[STATE_WBX];
- //gKalmanFilter.rateBias_B[Y_AXIS] = gKalmanFilter.rateBias_B[Y_AXIS] + gKalmanFilter.stateUpdate[STATE_WBY];
- //gKalmanFilter.rateBias_B[Z_AXIS] = gKalmanFilter.rateBias_B[Z_AXIS] + gKalmanFilter.stateUpdate[STATE_WBZ];
-
- gKalmanFilter.accelBias_B[X_AXIS] = gKalmanFilter.accelBias_B[X_AXIS] + gKalmanFilter.stateUpdate[STATE_ABX];
- gKalmanFilter.accelBias_B[Y_AXIS] = gKalmanFilter.accelBias_B[Y_AXIS] + gKalmanFilter.stateUpdate[STATE_ABY];
- gKalmanFilter.accelBias_B[Z_AXIS] = gKalmanFilter.accelBias_B[Z_AXIS] + gKalmanFilter.stateUpdate[STATE_ABZ];
+ gKalmanFilter.rateBias_B[X_AXIS] = gKalmanFilter.rateBias_B[X_AXIS] + gKalmanFilter.stateUpdate[STATE_WBX];
+ gKalmanFilter.rateBias_B[Y_AXIS] = gKalmanFilter.rateBias_B[Y_AXIS] + gKalmanFilter.stateUpdate[STATE_WBY];
+ gKalmanFilter.rateBias_B[Z_AXIS] = gKalmanFilter.rateBias_B[Z_AXIS] + gKalmanFilter.stateUpdate[STATE_WBZ];
+
+ gKalmanFilter.accelBias_B[X_AXIS] += gKalmanFilter.stateUpdate[STATE_ABX];
+ gKalmanFilter.accelBias_B[Y_AXIS] += gKalmanFilter.stateUpdate[STATE_ABY];
+ gKalmanFilter.accelBias_B[Z_AXIS] += gKalmanFilter.stateUpdate[STATE_ABZ];
}
static void Update_GPS(void)
-{
- // Sync the algorithm itow to the GPS value
- gAlgorithm.itow = gEKFInputData.itow;
-
- // Resync timer
- timer.tenHertzCntr = 0;
- timer.subFrameCntr = 0;
-
- // Debugging counter: updateCntr[0] should be about 9x less than updateCntr[1]
- updateCntr[0] = updateCntr[0] + 1;
-
- // reset the "last good reading" time
- gAlgorithm.timeOfLastGoodGPSReading = gEKFInputData.itow;
-
- // GPS heading valid?
- useGpsHeading = (gEKFInputData.rawGroundSpeed >= LIMIT_MIN_GPS_VELOCITY_HEADING);
+{
+ // Calculate the R-values for the INS measurements
+ _GenerateObservationCovariance_INS();
- /* Extract what's common between the following function and the
- * routines below so we aren't repeating calculations
- */
- LLA_To_Base(&gEKFInputData.llaRad[0],
- &gAlgorithm.rGPS0_E[0],
- &gAlgorithm.rGPS_N[0],
- &gAlgorithm.R_NinE[0][0],
- &gAlgorithm.rGPS_E[0]);
-
- /* Lever-arm is antenna position w.r.t to IMU in body. rGPS_N is antenna positive
- * w.r.t to initial point in NED. IMU positive w.r.t initial point is
- * rGPS_N - R_b_to_N * lever-arm
- */
- float leverArmN[3];
- leverArmN[0] = gKalmanFilter.R_BinN[0][0] * gAlgorithm.leverArmB[0] +
- gKalmanFilter.R_BinN[0][1] * gAlgorithm.leverArmB[1] +
- gKalmanFilter.R_BinN[0][2] * gAlgorithm.leverArmB[2];
- leverArmN[1] = gKalmanFilter.R_BinN[1][0] * gAlgorithm.leverArmB[0] +
- gKalmanFilter.R_BinN[1][1] * gAlgorithm.leverArmB[1] +
- gKalmanFilter.R_BinN[1][2] * gAlgorithm.leverArmB[2];
- leverArmN[2] = gKalmanFilter.R_BinN[2][0] * gAlgorithm.leverArmB[0] +
- gKalmanFilter.R_BinN[2][1] * gAlgorithm.leverArmB[1] +
- gKalmanFilter.R_BinN[2][2] * gAlgorithm.leverArmB[2];
- gAlgorithm.rGPS_N[0] -= leverArmN[0];
- gAlgorithm.rGPS_N[1] -= leverArmN[1];
- gAlgorithm.rGPS_N[2] -= leverArmN[2];
/* This Sequential-Filter (three-stage approach) is nearly as
* good as the full implementation -- we also can split it
* across multiple iterations to not exceed 10 ms execution on
@@ -1123,22 +1214,25 @@ static void Update_GPS(void)
/* Compute the system error: z = meas, h = pred = q, nu - z - h
* Do this at the same time even if the update is spread across time-steps
*/
+ if (gAlgoStatus.bit.ppsAvailable)
+ {
+ // use P saved when PPS is detected if PPS is available.
+ memcpy(&gKalmanFilter.P[0][0], &gKalmanFilter.ppsP[0][0], sizeof(gKalmanFilter.P));
+ }
ComputeSystemInnovation_Pos();
- ComputeSystemInnovation_Vel();
- ComputeSystemInnovation_Att();
-
- // Calculate the R-values for the INS measurements
- _GenerateObservationCovariance_INS();
-
Update_Pos();
-
+ ComputeSystemInnovation_Vel();
Update_Vel();
+ ComputeSystemInnovation_Att();
// Initialize heading. If getting initial heading at this step, do not update att
- if (gAlgorithm.gnssHeadingFirstTime)
+ if (gAlgorithm.headingIni < HEADING_GNSS_HIGH)
{
- if (InitializeGnssHeading())
+ if (InitializeHeadingFromGnss())
{
+ // Heading is initialized. Related elements in the EKF also need intializing.
+ InitializeEkfHeading();
+
/* This heading measurement is used to initialize heading, and should not be
* used to update heading.
*/
@@ -1147,6 +1241,268 @@ static void Update_GPS(void)
}
}
+static void Update_PseudoMeasurement(void)
+{
+ // which state is updated in Update_Vel()
+ uint8_t updatedStatesPseudo[16] = { 1, 1, 1, // Positions are NOT updated
+ 1, 1, 1, // Velocities are updated
+ 1, 1, 1, 1, // Quaternions are updated
+ 1, 1, 1, // Gyro biases are updated
+ 1, 1, 1 }; // Accel biases are upated
+
+ /* Get current rb2n.
+ * gKalmanFilter.R_BinN is updated every time the algo enters _PredictStateEstimate
+ * After prediction and GPS update, this matrix needs updated.
+ */
+ real rb2n[3][3];
+ QuaternionToR321(gKalmanFilter.quaternion, &rb2n[0][0]);
+
+ // detect zero velocity using GNSS vNED
+ BOOL staticGnss = DetectStaticGnssVelocity(gEKFInput.vNed,
+ gAlgorithm.staticDetectParam.staticGnssVel,
+ gEKFInput.gpsFixType);
+
+ // measurement cov
+ real r[3] = { 1.0e-4f, 1.0e-4f, 1.0e-4f };
+ if (!gImuStats.bStaticIMU)
+ {
+ /* If zero velocity is not detected by IMU, the covariance for the lateral and
+ * vertical velocity measurement should be increased.
+ */
+ GenPseudoMeasCov(r);
+ r[1] = 1.0e-1;
+ r[2] = 1.0e-1;
+ }
+
+ /* Compute innovation (measured - estimated) of velocity expressed in the body frame:
+ * innovation = [odo/0.0, 0.0, 0.0] - Rn2b * v_ned
+ * When odometer is available, front velocity measurement is given by odometer.
+ * When zero velocity detected, front velocity measurement is 0.
+ * Zero velocity detection result has a higher priority to determine the front velocity because
+ * odometer is also used for zero velocity detection when odometer is available.
+ */
+ BOOL frontVelMeaValid = FALSE;
+ real frontVelMea = 0.0;
+ /* Front velocity is first determined by odometer. If odometer is not available, zero velocity
+ * detection results are used to determine if front velocity is zero. If neither odometer is
+ * available nor zero velocity detected, front velocity measurement is not valid.
+ */
+ if (odoUsedInAlgorithm())
+ {
+ frontVelMeaValid = TRUE;
+ frontVelMea = gEKFInput.odoVelocity;
+ r[0] = 1.0e-4; // variance of front velocity measurement should be from odo spec
+ }
+ else if (gImuStats.bStaticIMU)
+ {
+ /* Only when GNSS is invalid or zero velocity is also detected by GNSS, zero velocity
+ * detected by IMU (and GNSS) can be used to determine the along-track velocity.
+ * When front velocity measurement is not available, it is not necessary to readjust
+ * its variance since it will not be used.
+ */
+ if ((!gEKFInput.gpsFixType) || staticGnss)
+ {
+ frontVelMeaValid = TRUE;
+ frontVelMea = 0.0;
+ }
+ }
+ // front vel error
+ gKalmanFilter.nu[STATE_VX] = frontVelMea
+ -rb2n[0][0] * gKalmanFilter.Velocity_N[0]
+ -rb2n[1][0] * gKalmanFilter.Velocity_N[1]
+ -rb2n[2][0] * gKalmanFilter.Velocity_N[2];
+ // lateral (right) vel error
+ gKalmanFilter.nu[STATE_VY] =
+ -rb2n[0][1] * gKalmanFilter.Velocity_N[0]
+ -rb2n[1][1] * gKalmanFilter.Velocity_N[1]
+ -rb2n[2][1] * gKalmanFilter.Velocity_N[2];
+ // vertical (downwards) vel erro
+ gKalmanFilter.nu[STATE_VZ] =
+ -rb2n[0][2] * gKalmanFilter.Velocity_N[0]
+ -rb2n[1][2] * gKalmanFilter.Velocity_N[1]
+ -rb2n[2][2] * gKalmanFilter.Velocity_N[2];
+ gKalmanFilter.nu[STATE_VY] = _LimitValue(gKalmanFilter.nu[STATE_VY], gAlgorithm.Limit.Innov.velocityError);
+ gKalmanFilter.nu[STATE_VZ] = _LimitValue(gKalmanFilter.nu[STATE_VZ], gAlgorithm.Limit.Innov.velocityError);
+
+ // p*H'. PxHTranspose is 16x3, only the last two columns are used when only lateral and vertical measurements
+ memset(PxHTranspose, 0, sizeof(PxHTranspose));
+ for (rowNum = 0; rowNum < NUMBER_OF_EKF_STATES; rowNum++)
+ {
+ for (colNum = 0; colNum < 3; colNum++)
+ {
+ PxHTranspose[rowNum][colNum] =
+ gKalmanFilter.P[rowNum][3] * rb2n[0][colNum] +
+ gKalmanFilter.P[rowNum][4] * rb2n[1][colNum] +
+ gKalmanFilter.P[rowNum][5] * rb2n[2][colNum];
+ }
+ }
+
+ // s = H*P*H' + R
+ for (rowNum = 0; rowNum < 3; rowNum++)
+ {
+ for (colNum = rowNum; colNum < 3; colNum++)
+ {
+ S_3x3[rowNum][colNum] = rb2n[0][rowNum] * PxHTranspose[3][colNum] +
+ rb2n[1][rowNum] * PxHTranspose[4][colNum] +
+ rb2n[2][rowNum] * PxHTranspose[5][colNum];
+ S_3x3[colNum][rowNum] = S_3x3[rowNum][colNum];
+ }
+ S_3x3[rowNum][rowNum] += r[rowNum];
+ }
+
+ // Calculate inv(H*P*H'+R) according to if front velocity measurement is available
+ if (frontVelMeaValid)
+ {
+ matrixInverse_3x3(&S_3x3[0][0], &SInverse_3x3[0][0]);
+ }
+ else
+ {
+ S_3x3[0][0] = 1.0;
+ S_3x3[0][1] = 0.0;
+ S_3x3[0][2] = 0.0;
+ S_3x3[1][0] = 0.0;
+ S_3x3[2][0] = 0.0;
+ matrixInverse_3x3(&S_3x3[0][0], &SInverse_3x3[0][0]);
+ SInverse_3x3[0][0] = 0.0;
+ }
+
+ // K = P*H' * inv(H*P*H' + R). gKalmanFilter.K is 16x3, only the last two columns are used.
+ for (rowNum = 0; rowNum < NUMBER_OF_EKF_STATES; rowNum++)
+ {
+ for (colNum = 0; colNum < 3; colNum++)
+ {
+ gKalmanFilter.K[rowNum][colNum] =
+ PxHTranspose[rowNum][0] * SInverse_3x3[0][colNum] +
+ PxHTranspose[rowNum][1] * SInverse_3x3[1][colNum] +
+ PxHTranspose[rowNum][2] * SInverse_3x3[2][colNum];
+ }
+ }
+ // force uncorrected terms in K to be 0
+ for (rowNum = STATE_RX; rowNum <= STATE_ABZ; rowNum++)
+ {
+ if (!updatedStatesPseudo[rowNum])
+ {
+ for (colNum = 0; colNum < 3; colNum++)
+ {
+ gKalmanFilter.K[rowNum][colNum] = 0.0;
+ }
+ }
+ }
+
+ // dx = k * nu
+ for (rowNum = 0; rowNum < NUMBER_OF_EKF_STATES; rowNum++)
+ {
+ gKalmanFilter.stateUpdate[rowNum] =
+ gKalmanFilter.K[rowNum][0] * gKalmanFilter.nu[STATE_VX] +
+ gKalmanFilter.K[rowNum][1] * gKalmanFilter.nu[STATE_VY] +
+ gKalmanFilter.K[rowNum][2] * gKalmanFilter.nu[STATE_VZ];
+ }
+
+ // update state
+ //gKalmanFilter.Position_N[X_AXIS] = gKalmanFilter.Position_N[X_AXIS] + gKalmanFilter.stateUpdate[STATE_RX];
+ //gKalmanFilter.Position_N[Y_AXIS] = gKalmanFilter.Position_N[Y_AXIS] + gKalmanFilter.stateUpdate[STATE_RY];
+ //gKalmanFilter.Position_N[Z_AXIS] = gKalmanFilter.Position_N[Z_AXIS] + gKalmanFilter.stateUpdate[STATE_RZ];
+
+ gKalmanFilter.Velocity_N[X_AXIS] = gKalmanFilter.Velocity_N[X_AXIS] + gKalmanFilter.stateUpdate[STATE_VX];
+ gKalmanFilter.Velocity_N[Y_AXIS] = gKalmanFilter.Velocity_N[Y_AXIS] + gKalmanFilter.stateUpdate[STATE_VY];
+ gKalmanFilter.Velocity_N[Z_AXIS] = gKalmanFilter.Velocity_N[Z_AXIS] + gKalmanFilter.stateUpdate[STATE_VZ];
+
+ gKalmanFilter.quaternion[Q0] = gKalmanFilter.quaternion[Q0] + gKalmanFilter.stateUpdate[STATE_Q0];
+ gKalmanFilter.quaternion[Q1] = gKalmanFilter.quaternion[Q1] + gKalmanFilter.stateUpdate[STATE_Q1];
+ gKalmanFilter.quaternion[Q2] = gKalmanFilter.quaternion[Q2] + gKalmanFilter.stateUpdate[STATE_Q2];
+ gKalmanFilter.quaternion[Q3] = gKalmanFilter.quaternion[Q3] + gKalmanFilter.stateUpdate[STATE_Q3];
+
+ // Normalize quaternion and force q0 to be positive
+ QuatNormalize(gKalmanFilter.quaternion);
+
+ gKalmanFilter.rateBias_B[X_AXIS] = gKalmanFilter.rateBias_B[X_AXIS] + gKalmanFilter.stateUpdate[STATE_WBX];
+ gKalmanFilter.rateBias_B[Y_AXIS] = gKalmanFilter.rateBias_B[Y_AXIS] + gKalmanFilter.stateUpdate[STATE_WBY];
+ gKalmanFilter.rateBias_B[Z_AXIS] = gKalmanFilter.rateBias_B[Z_AXIS] + gKalmanFilter.stateUpdate[STATE_WBZ];
+
+ gKalmanFilter.accelBias_B[X_AXIS] += gKalmanFilter.stateUpdate[STATE_ABX];
+ gKalmanFilter.accelBias_B[Y_AXIS] += gKalmanFilter.stateUpdate[STATE_ABY];
+ gKalmanFilter.accelBias_B[Z_AXIS] += gKalmanFilter.stateUpdate[STATE_ABZ];
+
+ // Update covariance: P = P + DP = P - K*H*P
+ // Use transpose(PxHTranspose) to hold H*P (3x16).
+ // Only the last two columns are used when only lateral and vertical measurements
+ for (colNum = 0; colNum < NUMBER_OF_EKF_STATES; colNum++)
+ {
+ for (rowNum = 0; rowNum < 3; rowNum++)
+ {
+ PxHTranspose[colNum][rowNum] = rb2n[0][rowNum] * gKalmanFilter.P[3][colNum] +
+ rb2n[1][rowNum] * gKalmanFilter.P[4][colNum] +
+ rb2n[2][rowNum] * gKalmanFilter.P[5][colNum];
+ }
+ }
+
+ // deltaP = KxH * gKF.P;
+ memset(&gKalmanFilter.deltaP_tmp[0][0], 0, sizeof(gKalmanFilter.deltaP_tmp));
+ /* deltaP is symmetric so only need to multiply one half and reflect the values
+ * across the diagonal
+ */
+ for (rowNum = 0; rowNum <= STATE_ABZ; rowNum++)
+ {
+ if (!updatedStatesPseudo[rowNum])
+ {
+ continue;
+ }
+ for (colNum = rowNum; colNum <= STATE_ABZ; colNum++)
+ {
+ if (!updatedStatesPseudo[colNum])
+ {
+ continue;
+ }
+ gKalmanFilter.deltaP_tmp[rowNum][colNum] = gKalmanFilter.K[rowNum][0] * PxHTranspose[colNum][0] +
+ gKalmanFilter.K[rowNum][1] * PxHTranspose[colNum][1] +
+ gKalmanFilter.K[rowNum][2] * PxHTranspose[colNum][2];
+ gKalmanFilter.deltaP_tmp[colNum][rowNum] = gKalmanFilter.deltaP_tmp[rowNum][colNum];
+ }
+ }
+
+ /* P is symmetric so only need to multiply one half and reflect the values
+ * across the diagonal
+ */
+ for (rowNum = 0; rowNum < ROWS_IN_P; rowNum++)
+ {
+ for (colNum = rowNum; colNum < COLS_IN_P; colNum++)
+ {
+ gKalmanFilter.P[rowNum][colNum] = gKalmanFilter.P[rowNum][colNum] -
+ gKalmanFilter.deltaP_tmp[rowNum][colNum];
+ gKalmanFilter.P[colNum][rowNum] = gKalmanFilter.P[rowNum][colNum];
+ }
+ }
+}
+
+static void GenPseudoMeasCov(real *r)
+{
+ real absYawRate = (real)fabs(gEKFInput.angRate_B[2]);
+ r[1] = absYawRate;
+ r[2] = absYawRate;
+
+ real minVar = 1e-4;
+ real maxVar = 1e-2;
+ if (r[1] < minVar)
+ {
+ r[1] = minVar;
+ }
+ if (r[1] > maxVar)
+ {
+ r[1] = maxVar;
+ }
+
+ if (r[2] < minVar)
+ {
+ r[2] = minVar;
+ }
+ if (r[2] > maxVar)
+ {
+ r[2] = maxVar;
+ }
+ //printf("rr: %f,%f\n", r[1], r[2]);
+}
+
+
/* Conversion from turn-rate threshold (values loaded into gConfiguration) to
* decimal value in [rad/sec]:
*
@@ -1185,7 +1541,6 @@ static void _TurnSwitch(void)
if ((gAlgorithm.state > HIGH_GAIN_AHRS) && (absYawRate > minSwitch))
{
gAlgoStatus.bit.turnSwitch = TRUE;
- // std::cout << "TurnSwitch (INS): Activated\n";
/* When the rate is below the maximum rate defined by turnSwitchThreshold,
* then generate a scale-factor that is between ( 1.0 - G ) and 0.0 (based on absYawRate).
@@ -1252,7 +1607,7 @@ static BOOL _CheckForUpdateTrigger(uint8_t updateRate)
{
//
uint8_t oneHundredHzCntr;
- uint8_t gpsUpdate = 0;
+ uint8_t updateFlag = 0;
//
switch( updateRate )
@@ -1261,7 +1616,7 @@ static BOOL _CheckForUpdateTrigger(uint8_t updateRate)
case 10:
if( timer.subFrameCntr == 0 )
{
- gpsUpdate = 1;
+ updateFlag = 1;
}
break;
@@ -1269,7 +1624,7 @@ static BOOL _CheckForUpdateTrigger(uint8_t updateRate)
case 20:
if( timer.subFrameCntr == 0 || timer.subFrameCntr == 5 )
{
- gpsUpdate = 1;
+ updateFlag = 1;
}
break;
@@ -1304,7 +1659,7 @@ static BOOL _CheckForUpdateTrigger(uint8_t updateRate)
oneHundredHzCntr == 92 ||
oneHundredHzCntr == 96 )
{
- gpsUpdate = 1;
+ updateFlag = 1;
}
break;
@@ -1316,142 +1671,323 @@ static BOOL _CheckForUpdateTrigger(uint8_t updateRate)
timer.subFrameCntr == 6 ||
timer.subFrameCntr == 8 )
{
- gpsUpdate = 1;
+ updateFlag = 1;
}
break;
// fifty-hertz update
case 100:
- gpsUpdate = 1;
+ updateFlag = 1;
break;
}
- return gpsUpdate;
+ return updateFlag;
}
-
-static int InitializeGnssHeading()
+static int InitializeHeadingFromGnss()
{
/* enable declination correction, but the corrected magnetic yaw will not
* be used if GPS is available.
*/
gAlgorithm.applyDeclFlag = TRUE;
- if (useGpsHeading)// && gEKFInputData.rawGroundSpeed>1.0)
+ /* backward drive detection for heading initialization using GNSS heading.
+ * Detection happends every second. Velocity increment is relatively reliable
+ * if it is accumulated for 1sec.
+ */
+ static real lastVelBxGnss = 0;
+ static uint8_t forwardDriveConfidence = 0;
+ static uint32_t lastTOW = 0;
+ uint32_t timeSinceLastDetection = gAlgorithm.itow - lastTOW;
+ if (timeSinceLastDetection < 0)
{
- // Heading is initialized with GNSS
- gAlgorithm.gnssHeadingFirstTime = FALSE;
+ timeSinceLastDetection = timeSinceLastDetection + MAX_ITOW;
+ }
+ if (timeSinceLastDetection > 950) // 950ms is set as the threshold for 1sec
+ {
+ lastTOW = gAlgorithm.itow;
+ /* assume velocity is always along the body x axis. otherwise, GNSS heading
+ * cannot be used to initialize fusion heading
+ */
+ real velBx = sqrtf(SQUARE(gEKFInput.vNed[0]) + SQUARE(gEKFInput.vNed[1]) + SQUARE(gEKFInput.vNed[2]));
+ velBx = fabs(velBx);
+ real dv = velBx - lastVelBxGnss;
+ if ((dv * gKalmanFilter.linearAccel_B[X_AXIS]) > 0.0 && fabs(gKalmanFilter.linearAccel_B[X_AXIS]) > 0.2)
+ {
+ if (forwardDriveConfidence < 255)
+ {
+ forwardDriveConfidence++;
+ }
+ }
+ else
+ {
+ forwardDriveConfidence = 0;
+ }
+ // record this velocity along body x axis for next run
+ lastVelBxGnss = velBx;
+ // reset accumulated x body axis velocity change.
+ gKalmanFilter.linearAccel_B[X_AXIS] = 0.0;
+ }
+
+ // detect if GNSS heading is reliable
+ static uint8_t gnssHeadingGoodCntr = 0;
+ static float lastGnssHeading = 0.0;
+ static float lastFusionHeading = 0.0;
+ BOOL gnssHeadingGood = 0;
+ float angleDiff = 0.0;
+ if (useGpsHeading)
+ {
+ float calculatedGnssHeading = (float)(atan2(gEKFInput.vNed[1], gEKFInput.vNed[0]) * R2D);
+ float diffHeading = AngleErrDeg(gEKFInput.trueCourse - calculatedGnssHeading);
+ // input GNSS heading matches heading calculated from vNED
+ if (fabs(diffHeading) < 5.0)
+ {
+ // GNSS heading change matches fusion yaw angle
+ float gnssHeadingChange = gEKFInput.trueCourse - lastGnssHeading;
+ float fusionHeadingChange = gKalmanFilter.eulerAngles[2] * (float)R2D - lastFusionHeading;
+ angleDiff = (float)fabs( AngleErrDeg(gnssHeadingChange - fusionHeadingChange) );
+ if (angleDiff < 5.0)
+ {
+ gnssHeadingGood = TRUE;
+ }
+ }
+ lastGnssHeading = gEKFInput.trueCourse;
+ lastFusionHeading = gKalmanFilter.eulerAngles[2] * (float)R2D;
+ }
+ if (gnssHeadingGood)
+ {
+ gnssHeadingGoodCntr++;
+ }
+ else
+ {
+ gnssHeadingGoodCntr = 0;
+ }
+
+ // Heading initialization when drive forward and GNSS heading is reliable
+ BOOL thisHeadingUsedForIni = FALSE;
+ if (gAlgorithm.headingIni < HEADING_GNSS_LOW) // heading is immediately but maybe unreliably initialized
+ {
+ if (gnssHeadingGoodCntr >= 1 && forwardDriveConfidence >= 1) // Only one sample is checked, so heading may be unreliable
+ {
+ gnssHeadingGoodCntr = 0;
+ // Heading is initialized with GNSS
+ gAlgorithm.headingIni = HEADING_GNSS_LOW;
#ifdef INS_OFFLINE
- printf("gps heading: %f\n", gEKFInputData.trueCourse);
+ printf("quick gps heading: %f\n", gEKFInput.trueCourse);
#else
#ifdef DISPLAY_DIAGNOSTIC_MSG
- DebugPrintString("gps heading");
- DebugPrintFloat(": ", gEKFInputData.trueCourse, 9);
- DebugPrintEndline();
+ DebugPrintString("quick gps heading");
+ DebugPrintFloat(": ", gEKFInput.trueCourse, 9);
+ DebugPrintEndline();
#endif
#endif
- // initialize yaw angle with GPS heading
- gKalmanFilter.eulerAngles[YAW] = (real)(gEKFInputData.trueCourse * D2R);
- if (gKalmanFilter.eulerAngles[YAW] > PI)
+ thisHeadingUsedForIni = TRUE;
+ }
+ }
+ else
+ {
+ /* Three points are checked, and the latest ground speed is above a certian threshold.
+ * The latest GNSS heading should be reliable.
+ */
+ if (gnssHeadingGoodCntr >= 3 &&
+ forwardDriveConfidence >= 5 &&
+ gEKFInput.rawGroundSpeed > RELIABLE_GPS_VELOCITY_HEADING)
{
- gKalmanFilter.eulerAngles[YAW] -= (real)TWO_PI;
+ gnssHeadingGoodCntr = 0;
+ forwardDriveConfidence = 0;
+ gAlgorithm.headingIni = HEADING_GNSS_HIGH;
+#ifdef INS_OFFLINE
+ printf("reliable gps heading: %f\n", gEKFInput.trueCourse);
+#else
+#ifdef DISPLAY_DIAGNOSTIC_MSG
+ DebugPrintString("reliable gps heading");
+ DebugPrintFloat(": ", gEKFInput.trueCourse, 9);
+ DebugPrintEndline();
+#endif
+#endif
+ thisHeadingUsedForIni = TRUE;
}
- EulerAnglesToQuaternion(gKalmanFilter.eulerAngles, gKalmanFilter.quaternion);
-
- // reinitialize NED velocity
- gKalmanFilter.Velocity_N[X_AXIS] = (real)gEKFInputData.vNed[X_AXIS];
- gKalmanFilter.Velocity_N[Y_AXIS] = (real)gEKFInputData.vNed[Y_AXIS];
- gKalmanFilter.Velocity_N[Z_AXIS] = (real)gEKFInputData.vNed[Z_AXIS];
-
+ }
+
+ return thisHeadingUsedForIni;
+}
+
+static void InitializeEkfHeading()
+{
+ /* Compare the reliable heading with Kalamn filter heading. If the difference exceeds
+ * a certain threshold, this means the immediate heading initialization is unreliable,
+ * and the Kalman filter needs reinitialized with the reliable one.
+ */
+ float angleDiff = (float)fabs(AngleErrDeg(gEKFInput.trueCourse -
+ gKalmanFilter.eulerAngles[2] * (float)R2D));
+ if (angleDiff <= 2.0)
+ {
+ return;
+ }
+
+#ifdef INS_OFFLINE
+ printf("Reinitialize KF: %f\n", angleDiff);
+#else
+#ifdef DISPLAY_DIAGNOSTIC_MSG
+ DebugPrintString("Reinitialize KF: ");
+ DebugPrintFloat("", angleDiff, 9);
+ DebugPrintEndline();
+#endif
+#endif
+
+ // initialize yaw angle with GPS heading
+ gKalmanFilter.eulerAngles[YAW] = (gEKFInput.trueCourse * D2R);
+ if (gKalmanFilter.eulerAngles[YAW] > PI)
+ {
+ gKalmanFilter.eulerAngles[YAW] -= (real)TWO_PI;
+ }
+ EulerAnglesToQuaternion(gKalmanFilter.eulerAngles, gKalmanFilter.quaternion);
+
+ // reinitialize NED position
+ gKalmanFilter.Position_N[0] = (real)gKalmanFilter.rGPS_N[0];
+ gKalmanFilter.Position_N[1] = (real)gKalmanFilter.rGPS_N[1];
+ gKalmanFilter.Position_N[2] = (real)gKalmanFilter.rGPS_N[2];
+
+ // reinitialize NED velocity
+ gKalmanFilter.Velocity_N[X_AXIS] = (real)gEKFInput.vNed[X_AXIS];
+ gKalmanFilter.Velocity_N[Y_AXIS] = (real)gEKFInput.vNed[Y_AXIS];
+ gKalmanFilter.Velocity_N[Z_AXIS] = (real)gEKFInput.vNed[Z_AXIS];
+
#if 1 // mod, DXG
- // reset quaternion and velocity terms in the P matrix
- int i, j;
- // vel row
- for (i = STATE_VX; i < STATE_VZ; i++)
+ // reset quaternion and velocity terms in the P matrix
+ int i, j;
+ // pos row
+ gKalmanFilter.P[STATE_RX][STATE_RX] = gKalmanFilter.R[STATE_RX];
+ gKalmanFilter.P[STATE_RY][STATE_RY] = gKalmanFilter.R[STATE_RY];
+ gKalmanFilter.P[STATE_RZ][STATE_RZ] = gKalmanFilter.R[STATE_RZ];
+ for (i = STATE_RX; i < STATE_RZ; i++)
+ {
+ for (j = 0; j < NUMBER_OF_EKF_STATES; j++)
{
- for (j = 0; j < NUMBER_OF_EKF_STATES; j++)
+ if (i != j)
{
- if (i != j)
- {
- gKalmanFilter.P[i][j] = 0;
- gKalmanFilter.P[j][i] = 0;
- }
+ gKalmanFilter.P[i][j] = 0;
+ gKalmanFilter.P[j][i] = 0;
}
}
- // q0 row
- for (i = 0; i < NUMBER_OF_EKF_STATES; i++)
+ }
+ // vel row
+ gKalmanFilter.P[STATE_VX][STATE_VX] = gKalmanFilter.R[STATE_VX];
+ gKalmanFilter.P[STATE_VY][STATE_VY] = gKalmanFilter.R[STATE_VY];
+ gKalmanFilter.P[STATE_VZ][STATE_VZ] = gKalmanFilter.R[STATE_VZ];
+ for (i = STATE_VX; i < STATE_VZ; i++)
+ {
+ for (j = 0; j < NUMBER_OF_EKF_STATES; j++)
{
- if (i != STATE_Q0)
+ if (i != j)
{
- gKalmanFilter.P[STATE_Q0][i] = 0;
- gKalmanFilter.P[i][STATE_Q0] = 0;
+ gKalmanFilter.P[i][j] = 0;
+ gKalmanFilter.P[j][i] = 0;
}
}
- // q3 row
- for (i = 0; i < NUMBER_OF_EKF_STATES; i++)
+ }
+ // q0 row
+ for (i = 0; i < NUMBER_OF_EKF_STATES; i++)
+ {
+ if (i != STATE_Q0)
{
- if (i != STATE_Q3)
- {
- gKalmanFilter.P[STATE_Q3][i] = 0;
- gKalmanFilter.P[i][STATE_Q3] = 0;
- }
+ gKalmanFilter.P[STATE_Q0][i] = 0;
+ gKalmanFilter.P[i][STATE_Q0] = 0;
}
-
- // the initial covariance of the quaternion is estimated from ground speed.
- float temp = (float)atan(0.05 / gEKFInputData.rawGroundSpeed);
- temp *= temp; // heading var
- if (gAlgoStatus.bit.turnSwitch)
+ }
+ // q3 row
+ for (i = 0; i < NUMBER_OF_EKF_STATES; i++)
+ {
+ if (i != STATE_Q3)
{
- temp *= 10.0; // when rotating, heading var increases
+ gKalmanFilter.P[STATE_Q3][i] = 0;
+ gKalmanFilter.P[i][STATE_Q3] = 0;
}
- temp /= 4.0; // sin(heading/2) or cos(heading/2)
- float sinYawSqr = (real)sin(gKalmanFilter.eulerAngles[YAW] / 2.0f);
- sinYawSqr *= sinYawSqr;
- // Assume roll and pitch are close to 0deg
- gKalmanFilter.P[STATE_Q0][STATE_Q0] = temp * sinYawSqr;
- gKalmanFilter.P[STATE_Q3][STATE_Q3] = temp * (1.0f - sinYawSqr);
+ }
+
+ // the initial covariance of the quaternion is estimated from ground speed.
+ float temp = (float)atan(0.05 / gEKFInput.rawGroundSpeed);
+ temp *= temp; // heading var
+ if (gAlgoStatus.bit.turnSwitch)
+ {
+ temp *= 10.0; // when rotating, heading var increases
+ }
+ temp /= 4.0; // sin(heading/2) or cos(heading/2)
+ float sinYawSqr = (real)sin(gKalmanFilter.eulerAngles[YAW] / 2.0f);
+ sinYawSqr *= sinYawSqr;
+ // Assume roll and pitch are close to 0deg
+ gKalmanFilter.P[STATE_Q0][STATE_Q0] = temp * sinYawSqr;
+ gKalmanFilter.P[STATE_Q3][STATE_Q3] = temp * (1.0f - sinYawSqr);
- gKalmanFilter.P[STATE_VX][STATE_VX] = gKalmanFilter.R[STATE_VX];
- gKalmanFilter.P[STATE_VY][STATE_VY] = gKalmanFilter.R[STATE_VY];
- gKalmanFilter.P[STATE_VZ][STATE_VZ] = gKalmanFilter.R[STATE_VZ];
+ gKalmanFilter.P[STATE_VX][STATE_VX] = gKalmanFilter.R[STATE_VX];
+ gKalmanFilter.P[STATE_VY][STATE_VY] = gKalmanFilter.R[STATE_VY];
+ gKalmanFilter.P[STATE_VZ][STATE_VZ] = gKalmanFilter.R[STATE_VZ];
#if 0
- // reset velocity and quaternion terms in the P matrix
- real v2 = gEKFInputData.rawGroundSpeed * gEKFInputData.rawGroundSpeed;
- real v3by4 = 4.0 * v2 * gEKFInputData.rawGroundSpeed;
- real vn2 = gEKFInputData.vNed[0] * gEKFInputData.vNed[0];
- real q0q0 = gKalmanFilter.quaternion[0] * gKalmanFilter.quaternion[0];
- real q3q3 = gKalmanFilter.quaternion[3] * gKalmanFilter.quaternion[3];
- if (q0q0 < 1.0e-3)
- {
- q0q0 = 1.0e-3;
- }
- if (q3q3 < 1.0e-3)
- {
- q3q3 = 1.0e-3;
- }
- real multiplerQVn = (v2 - vn2) / v3by4;
- multiplerQVn *= multiplerQVn;
- real multiplerQVe = (gEKFInputData.vNed[0] * gEKFInputData.vNed[1]) / v3by4;
- multiplerQVe *= multiplerQVe;
- gKalmanFilter.P[STATE_VX][STATE_Q0] = multiplerQVn / q0q0 * gKalmanFilter.R[STATE_VX][STATE_VX];
- gKalmanFilter.P[STATE_VX][STATE_Q3] = multiplerQVn / q3q3 * gKalmanFilter.R[STATE_VX][STATE_VX];
- gKalmanFilter.P[STATE_VY][STATE_Q0] = multiplerQVe / q0q0 * gKalmanFilter.R[STATE_VY][STATE_VY];
- gKalmanFilter.P[STATE_VY][STATE_Q3] = multiplerQVe / q3q3 * gKalmanFilter.R[STATE_VY][STATE_VY];
-
-
- gKalmanFilter.P[STATE_Q0][STATE_VX] = gKalmanFilter.P[STATE_VX][STATE_Q0];
- gKalmanFilter.P[STATE_Q3][STATE_VX] = gKalmanFilter.P[STATE_VX][STATE_Q3];
- gKalmanFilter.P[STATE_Q0][STATE_VY] = gKalmanFilter.P[STATE_VY][STATE_Q0];
- gKalmanFilter.P[STATE_Q3][STATE_VY] = gKalmanFilter.P[STATE_VY][STATE_Q3];
+ // reset velocity and quaternion terms in the P matrix
+ real v2 = gEKFInput.rawGroundSpeed * gEKFInput.rawGroundSpeed;
+ real v3by4 = 4.0 * v2 * gEKFInput.rawGroundSpeed;
+ real vn2 = gEKFInput.vNed[0] * gEKFInput.vNed[0];
+ real q0q0 = gKalmanFilter.quaternion[0] * gKalmanFilter.quaternion[0];
+ real q3q3 = gKalmanFilter.quaternion[3] * gKalmanFilter.quaternion[3];
+ if (q0q0 < 1.0e-3)
+ {
+ q0q0 = 1.0e-3;
+ }
+ if (q3q3 < 1.0e-3)
+ {
+ q3q3 = 1.0e-3;
+ }
+ real multiplerQVn = (v2 - vn2) / v3by4;
+ multiplerQVn *= multiplerQVn;
+ real multiplerQVe = (gEKFInput.vNed[0] * gEKFInput.vNed[1]) / v3by4;
+ multiplerQVe *= multiplerQVe;
+ gKalmanFilter.P[STATE_VX][STATE_Q0] = multiplerQVn / q0q0 * gKalmanFilter.R[STATE_VX][STATE_VX];
+ gKalmanFilter.P[STATE_VX][STATE_Q3] = multiplerQVn / q3q3 * gKalmanFilter.R[STATE_VX][STATE_VX];
+ gKalmanFilter.P[STATE_VY][STATE_Q0] = multiplerQVe / q0q0 * gKalmanFilter.R[STATE_VY][STATE_VY];
+ gKalmanFilter.P[STATE_VY][STATE_Q3] = multiplerQVe / q3q3 * gKalmanFilter.R[STATE_VY][STATE_VY];
+
+
+ gKalmanFilter.P[STATE_Q0][STATE_VX] = gKalmanFilter.P[STATE_VX][STATE_Q0];
+ gKalmanFilter.P[STATE_Q3][STATE_VX] = gKalmanFilter.P[STATE_VX][STATE_Q3];
+ gKalmanFilter.P[STATE_Q0][STATE_VY] = gKalmanFilter.P[STATE_VY][STATE_Q0];
+ gKalmanFilter.P[STATE_Q3][STATE_VY] = gKalmanFilter.P[STATE_VY][STATE_Q3];
#endif
#endif
- return 1;
+}
+
+static void ApplyGpsDealyCorrForStateCov()
+{
+ uint8_t i, j, k;
+
+ // P = phi * P * phi' + dQ
+ // 1) use deltaP_tmp to hold phi * p
+ AxB(&gKalmanFilter.phi[0][0], &gKalmanFilter.P[0][0], NUMBER_OF_EKF_STATES, NUMBER_OF_EKF_STATES,
+ NUMBER_OF_EKF_STATES, &gKalmanFilter.deltaP_tmp[0][0]);
+
+ // 2) phi * p * phi' = deltaP_tmp * phi'
+ for (i = 0; i < NUMBER_OF_EKF_STATES; i++)
+ {
+ for (j = i; j < NUMBER_OF_EKF_STATES; j++)
+ {
+ gKalmanFilter.P[i][j] = 0;
+ for (k = 0; k < NUMBER_OF_EKF_STATES; k++)
+ {
+ gKalmanFilter.P[i][j] += gKalmanFilter.deltaP_tmp[i][k] * gKalmanFilter.phi[j][k];
+ }
+ gKalmanFilter.P[j][i] = gKalmanFilter.P[i][j];
+ }
}
- else
+
+ // 3) add dQ
+ for (i = 0; i < NUMBER_OF_EKF_STATES; i++)
{
- return 0;
+ for (j = i; j < NUMBER_OF_EKF_STATES; j++)
+ {
+ gKalmanFilter.P[i][j] += gKalmanFilter.dQ[i][j];
+ gKalmanFilter.P[j][i] = gKalmanFilter.P[i][j];
+ }
}
-}
\ No newline at end of file
+}
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/WorldMagneticModel.c b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/WorldMagneticModel.c
index e9b20dc..c3f9403 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/WorldMagneticModel.c
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/WorldMagneticModel.c
@@ -157,7 +157,7 @@ void TaskWorldMagneticModel(void const *argument)
while(1) {
OS_Delay( 5000 );
#ifdef GPS
- if( gGpsDataPtr->gpsValid )
+ if( gGpsDataPtr->gpsFixType )
{
// caution - safety checks on the dates are fine, but we don't want
// to rely on these hard-coded dates in operation
@@ -204,7 +204,7 @@ void TaskWorldMagneticModel(void const *argument)
// /*
// % WorldMagneticModel.m
//
-// if( gGpsDataPtr.GPSValid ),
+// if( gGpsDataPtr.gpsFixType ),
// % WMM here
// declinationAngle_rad = ( 13 + 36 / 60 + 43/3600 ) * CONV.DEG_TO_RAD;
//
@@ -216,7 +216,7 @@ void TaskWorldMagneticModel(void const *argument)
// */
//
// // VERY SIMPLE WMM (declination near San Jose only)
-//// if (gGpsDataPtr->gpsValid) {
+//// if (gGpsDataPtr->gpsFixType) {
//// gWorldMagModel.decl_rad = (real)( (13.0 + 40.0 / 60.0 + 29.0 / 3600.0) * D2R );
//// } else {
//// gWorldMagModel.decl_rad = (real)0.0;
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/algorithm.c b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/algorithm.c
index 13fb6c5..c5a2087 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/algorithm.c
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Algorithm/src/algorithm.c
@@ -15,6 +15,9 @@
******************************************************************************/
#include
+#include
+
+#include "SensorNoiseParameters.h"
#include "platformAPI.h"
#include "algorithm.h"
#include "AlgorithmLimits.h"
@@ -24,11 +27,17 @@ AlgorithmStruct gAlgorithm;
AlgoStatus gAlgoStatus;
-void InitializeAlgorithmStruct(uint16_t callingFreq)
+void InitializeAlgorithmStruct(uint8_t callingFreq)
{
- gAlgorithm.Behavior.bit.freeIntegrate = FALSE;
+ memset(&gAlgorithm, 0, sizeof(AlgorithmStruct));
+
+ //----------------------------algortihm config-----------------------------
// The calling frequency drives the execution rate of the EKF and dictates
// the algorithm constants
+ if(callingFreq == 0){
+ // IMU case
+ callingFreq = FREQ_200_HZ;
+ }
gAlgorithm.callingFreq = callingFreq;
// Set dt based on the calling frequency of the EKF
@@ -50,7 +59,7 @@ void InitializeAlgorithmStruct(uint16_t callingFreq)
// Set up other timing variables
gAlgorithm.dtOverTwo = (real)(0.5) * gAlgorithm.dt;
gAlgorithm.dtSquared = gAlgorithm.dt * gAlgorithm.dt;
- gAlgorithm.sqrtDt = sqrt(gAlgorithm.dt);
+ gAlgorithm.sqrtDt = sqrtf(gAlgorithm.dt);
// Set the algorithm duration periods
gAlgorithm.Duration.Stabilize_System = (uint32_t)(gAlgorithm.callingFreq * STABILIZE_SYSTEM_DURATION);
@@ -72,6 +81,7 @@ void InitializeAlgorithmStruct(uint16_t callingFreq)
gAlgorithm.applyDeclFlag = FALSE;
gAlgorithm.insFirstTime = TRUE;
+ gAlgorithm.headingIni = HEADING_UNINITIALIZED;
//gAlgorithm.magAlignUnderway = FALSE; // Set and reset in mag-align code
@@ -79,7 +89,8 @@ void InitializeAlgorithmStruct(uint16_t callingFreq)
gAlgorithm.itow = 0;
// Limit is compared to ITOW. Time must be in [msec].
- gAlgorithm.Limit.Max_GPS_Drop_Time = LIMIT_MAX_GPS_DROP_TIME * 1000;
+ gAlgorithm.Limit.maxGpsDropTime = LIMIT_MAX_GPS_DROP_TIME * 1000;
+ gAlgorithm.Limit.maxReliableDRTime = LIMIT_RELIABLE_DR_TIME * 1000;
// Limit is compared to count (incremented upon loop through
// taskDataAcquisition). Time must be in [count] based on ODR.
@@ -105,15 +116,42 @@ void InitializeAlgorithmStruct(uint16_t callingFreq)
gAlgorithm.useRawAccToDetectLinAccel = TRUE;
// Set the turn-switch threshold to a default value in [deg/sec]
- gAlgorithm.turnSwitchThreshold = 2.0;
+ gAlgorithm.turnSwitchThreshold = 6.0;
// default lever arm and point of interest
- gAlgorithm.leverArmB[X_AXIS] = 0.0;
- gAlgorithm.leverArmB[Y_AXIS] = 0.0;
- gAlgorithm.leverArmB[Z_AXIS] = 0.0;
- gAlgorithm.pointOfInterestB[X_AXIS] = 0.0;
- gAlgorithm.pointOfInterestB[Y_AXIS] = 0.0;
- gAlgorithm.pointOfInterestB[Z_AXIS] = 0.0;
+ gAlgorithm.leverArmB[X_AXIS] = 0.0;
+ gAlgorithm.leverArmB[Y_AXIS] = 0.0;
+ gAlgorithm.leverArmB[Z_AXIS] = 0.0;
+ gAlgorithm.pointOfInterestB[X_AXIS] = 0.0;
+ gAlgorithm.pointOfInterestB[Y_AXIS] = 0.0;
+ gAlgorithm.pointOfInterestB[Z_AXIS] = 0.0;
+
+ // For most vehicles, the velocity is always along the body x axis
+ gAlgorithm.velocityAlwaysAlongBodyX = TRUE;
+
+ // get IMU specifications
+ gAlgorithm.imuSpec.arw = (real)ARW_300ZA;
+ gAlgorithm.imuSpec.sigmaW = (real)(1.25 * ARW_300ZA / sqrt(1.0/RW_ODR));
+ gAlgorithm.imuSpec.biW = (real)BIW_300ZA;
+ gAlgorithm.imuSpec.maxBiasW = (real)MAX_BW;
+ gAlgorithm.imuSpec.vrw = (real)VRW_300ZA;
+ gAlgorithm.imuSpec.sigmaA = (real)(1.25 * VRW_300ZA / sqrt(1.0/RW_ODR));
+ gAlgorithm.imuSpec.biA = (real)BIA_300ZA;
+ gAlgorithm.imuSpec.maxBiasA = (real)MAX_BA;
+
+ // default noise level multiplier for static detection
+ gAlgorithm.staticDetectParam.staticVarGyro = (real)(gAlgorithm.imuSpec.sigmaW * gAlgorithm.imuSpec.sigmaW);
+ gAlgorithm.staticDetectParam.staticVarAccel = (real)(gAlgorithm.imuSpec.sigmaA * gAlgorithm.imuSpec.sigmaA);
+ gAlgorithm.staticDetectParam.maxGyroBias = gAlgorithm.imuSpec.maxBiasW;
+ gAlgorithm.staticDetectParam.staticGnssVel = 0.2;
+ gAlgorithm.staticDetectParam.staticNoiseMultiplier[0] = 4.0;
+ gAlgorithm.staticDetectParam.staticNoiseMultiplier[1] = 4.0;
+ gAlgorithm.staticDetectParam.staticNoiseMultiplier[2] = 1.0;
+
+ gAlgorithm.Behavior.bit.dynamicMotion = 1;
+
+ //----------------------------algorithm states-----------------------------
+ memset(&gAlgoStatus, 0, sizeof(gAlgoStatus));
}
void GetAlgoStatus(AlgoStatus *algoStatus)
@@ -170,4 +208,90 @@ void setPointOfInterest( real poiBx, real poiBy, real poiBz )
gAlgorithm.pointOfInterestB[0] = poiBx;
gAlgorithm.pointOfInterestB[1] = poiBy;
gAlgorithm.pointOfInterestB[2] = poiBz;
+}
+
+void UpdateImuSpec(real rwOdr, real arw, real biw, real maxBiasW,
+ real vrw, real bia, real maxBiasA)
+{
+ // Update IMU specifications
+ gAlgorithm.imuSpec.arw = arw;
+ gAlgorithm.imuSpec.sigmaW = (real)(1.25 * arw / sqrt(1.0 / rwOdr));
+ gAlgorithm.imuSpec.biW = biw;
+ gAlgorithm.imuSpec.maxBiasW = maxBiasW;
+ gAlgorithm.imuSpec.vrw = vrw;
+ gAlgorithm.imuSpec.sigmaA = (real)(1.25 * vrw / sqrt(1.0 / rwOdr));
+ gAlgorithm.imuSpec.biA = bia;
+ gAlgorithm.imuSpec.maxBiasA = maxBiasA;
+
+ // Update affected params related to zero velocity detection
+ gAlgorithm.staticDetectParam.staticVarGyro = (real)(gAlgorithm.imuSpec.sigmaW * gAlgorithm.imuSpec.sigmaW);
+ gAlgorithm.staticDetectParam.staticVarAccel = (real)(gAlgorithm.imuSpec.sigmaA * gAlgorithm.imuSpec.sigmaA);
+ gAlgorithm.staticDetectParam.maxGyroBias = gAlgorithm.imuSpec.maxBiasW;
+}
+
+void enableMagInAlgorithm(BOOL enable)
+{
+ if (1)
+ {
+ gAlgorithm.Behavior.bit.useMag = enable;
+ }
+ else
+ {
+ gAlgorithm.Behavior.bit.useMag = FALSE;
+ }
+}
+
+void enableGpsInAlgorithm(BOOL enable)
+{
+ gAlgorithm.Behavior.bit.useGPS = enable;
+}
+
+void enableOdoInAlgorithm(BOOL enable)
+{
+ gAlgorithm.Behavior.bit.useOdo = enable;
+}
+
+BOOL magUsedInAlgorithm()
+{
+ return gAlgorithm.Behavior.bit.useMag != 0;
+}
+
+BOOL gpsUsedInAlgorithm(void)
+{
+ return (BOOL)gAlgorithm.Behavior.bit.useGPS;
+}
+
+BOOL odoUsedInAlgorithm(void)
+{
+ return (BOOL)gAlgorithm.Behavior.bit.useOdo;
+}
+
+void enableFreeIntegration(BOOL enable)
+{
+ gAlgorithm.Behavior.bit.freeIntegrate = enable;
+}
+
+BOOL freeIntegrationEnabled()
+{
+ return (BOOL)gAlgorithm.Behavior.bit.freeIntegrate;
+}
+
+void enableStationaryLockYaw(BOOL enable)
+{
+ gAlgorithm.Behavior.bit.enableStationaryLockYaw = enable;
+}
+
+BOOL stationaryLockYawEnabled()
+{
+ return (BOOL)gAlgorithm.Behavior.bit.enableStationaryLockYaw;
+}
+
+void enableImuStaticDetect(BOOL enable)
+{
+ gAlgorithm.Behavior.bit.enableImuStaticDetect = enable;
+}
+
+BOOL imuStaticDetectEnabled()
+{
+ return (BOOL)gAlgorithm.Behavior.bit.enableImuStaticDetect;
}
\ No newline at end of file
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/gpsAPI.h b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/gpsAPI.h
index aef45ab..3a24ea4 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/gpsAPI.h
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/gpsAPI.h
@@ -43,33 +43,45 @@ void TaskGps(void const *argument);
}
#endif
+// Fix type
+#define INVALID 0 // GNSS not fixed yet
+#define SPP 1 // Single Point Positioning
+#define DGPS 2 // Pseudorange Differential
+#define PPP 3 // Precise Point Positioning
+#define RTK_FIX 4 // RTK Fixed
+#define RTK_FLOAT 5 // RTK Float
+#define DEAD_REC 6 // Dead Reckoning (will be considered as INVALID)
+#define MANUAL 7 // Manual Input Mode (will be considered as INVALID)
+#define SIMULATION 8 // Simulation Mode (will be considered as INVALID)
+
typedef struct {
- int gpsValid; // 1 if data is valid
- uint8_t gpsUpdate; // 1 if contains new data
-
- double latitude; // latitude , degrees
- double longitude; // longitude, degrees
- double vNed[3]; // velocities, m/s NED (North East Down) x, y, z
- double trueCourse; // [deg]
- double rawGroundSpeed; // NMEA kph, SiRf m/s - change to m/s
- double altitude; // above ellipsoid [m]
- double GPSSecondFraction;
- float altEllipsoid; // [km] altitude above ellipsoid for WMM
-
- uint32_t itow; // gps Time Of Week, miliseconds
+ uint8_t gpsFixType; // 1 if data is valid
+ uint8_t gpsUpdate; // 1 if contains new data
+ uint8_t numSatellites; // num of satellites in the solution
+ uint32_t itow; // gps Time Of Week, miliseconds
+
+ double latitude; // latitude , degrees
+ double longitude; // longitude, degrees
+ double vNed[3]; // velocities, m/s NED (North East Down) x, y, z
+ double trueCourse; // [deg]
+ double rawGroundSpeed; // [m/s]
+ double altitude; // above WGS84 ellipsoid [m]
+ double GPSSecondFraction;
+
- uint8_t GPSmonth; // mm
- uint8_t GPSday; // dd
- uint8_t GPSyear; // yy last two digits of year
- char GPSHour; // hh
- char GPSMinute; // mm
- char GPSSecond; // ss
-
- float GPSHorizAcc, GPSVertAcc;
- float HDOP;
+ uint8_t GPSmonth; // mm
+ uint8_t GPSday; // dd
+ uint8_t GPSyear; // yy last two digits of year
+ char GPSHour; // hh
+ char GPSMinute; // mm
+ char GPSSecond; // ss
+
+ float GPSHorizAcc, GPSVertAcc;
+ float HDOP;
+ float geoidAboveEllipsoid; // [m] Height of geoid (mean sea level) above WGS84 ellipsoid
} gpsDataStruct_t;
-extern gpsDataStruct_t gGPS;
+extern gpsDataStruct_t gGPS, gCanGps;
/** ****************************************************************************
* @name GetGPSData
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/include/GpsData.h b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/include/GpsData.h
index 10a514b..cb21530 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/include/GpsData.h
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/include/GpsData.h
@@ -43,35 +43,36 @@ This Data structure is not only used for all GPS interface and process
but also used to be accessed by other modules rather than GPS files.
*/
typedef struct {
- BOOL gpsValid;
- long double lat; // concatinated from int components [deg.dec]
- long double lon;
- double vNed[3]; // NED North East Down [m/s] x, y, z
- uint32_t itow; ///< gps milisecond Interval Time Of Week
-
- int updateFlagForEachCall; /// changed to 16 bits
- int totalGGA;
- int totalVTG;
-
- double trueCourse; // [deg]
- double rawGroundSpeed; // NMEA kph, SiRf m/s
-
- double alt; // above mean sea level [m]
- double filteredAlt; // FIXME should this be local?
- float altEllipsoid; // [km] altitude above ellipsoid for WMM
- uint8_t GPSmonth; // mm
- uint8_t GPSday; // dd
- uint8_t GPSyear; // yy last two digits of year
- char GPSHour; // hh
- char GPSMinute; // mm
- char GPSSecond; // ss
- double GPSSecondFraction; // FIXME used?
+ uint8_t gpsFixType; // GPS solution type: invalid, spp, dgps, spp, rtk_float, rtk_fix
+ uint8_t numSatellites;
+
+ uint8_t GPSmonth; // mm
+ uint8_t GPSday; // dd
+ uint8_t GPSyear; // yy last two digits of year
+ char GPSHour; // hh
+ char GPSMinute; // mm
+ char GPSSecond; // ss
+ double GPSSecondFraction; // FIXME used?
+
+ uint32_t itow; ///< gps milisecond Interval Time Of Week
+ int updateFlagForEachCall; /// changed to 16 bits
+
+ int totalGGA;
+ int totalVTG;
+
+ double lat; // [deg], latitude
+ double lon; // [lon], longitude
+ double alt; // [m] above WGS84 ellipsoid
+ double vNed[3]; // NED North East Down [m/s] x, y, z
+ double trueCourse; // [deg]
+ double rawGroundSpeed; // [m/s]
+
+ float geoidAboveEllipsoid; // [m] Height of geoid (mean sea level) above WGS84 ellipsoid
/// compatible with Ublox driver FIXME should these be seperate data structure?
unsigned char ubloxClassID;
unsigned char ubloxMsgID;
signed long LonLatH[3]; // SiRF Lat Lon[deg] * 10^7 Alt ellipse [m]*100 <-- UNUSED
- char GPSFix;
float HDOP; // Horizontal Dilution Of Precision x.x
double GPSVelAcc;
unsigned short GPSStatusWord; /// will replace GPSfix
@@ -114,9 +115,6 @@ typedef struct {
float GPSHorizAcc;
float GPSVertAcc;
-
- int numSatelites;
-
} GpsData_t;
extern GpsData_t *gGpsDataPtr; // definition in driverGPSAllentrance.c
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/include/driverGPS.h b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/include/driverGPS.h
index f114857..c7681a8 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/include/driverGPS.h
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/include/driverGPS.h
@@ -159,23 +159,33 @@ typedef struct
uint8_t hour;
uint8_t min;
uint8_t sec;
- uint8_t valid;
+ uint8_t valid; // Validity flags
uint32_t tAcc; // time accuracy estimate (UTC), ns
int32_t nano; // fraction of second, range -1e9..1e9 (UTC), ns
- uint8_t fixType; // GNSS fix type
- // 0: no fix
- // 1: dead reckoning only
- // 2: 2D-fix
- // 3: 3D-fix
- // 4: GNSS + dead reckoning combined
- // 5: time only fix
- uint8_t flags;
+ uint8_t fixType; /* GNSS fix type
+ * 0: no fix
+ * 1: dead reckoning only
+ * 2: 2D-fix
+ * 3: 3D-fix
+ * 4: GNSS + dead reckoning combined
+ * 5: time only fix
+ */
+ uint8_t flags; /* Fix status flags
+ * bit0: gnssFixOK, 1 = valid fix (i.e within DOP & accuracy masks)
+ * bit1: diffSoln, 1 = differential corrections were applied
+ * bit2-4: psmState, Power Save Mode state
+ * bit5: headVehValid, 1 = heading of vehicle is valid
+ * bit6-7: carrSoln, Carrier phase range solution status:
+ * 0: no carrier phase range solution
+ * 1: float solution
+ * 2: fixed solution
+ */
uint8_t flags2;
uint8_t numSV; // number of satellites in Nav solution;
int32_t lon; // deg, scaling is 1e-7
int32_t lat; // deg, scaling is 1e-7
int32_t height; // mm, height above ellipsoid;
- int32_t hMSL;
+ int32_t hMSL; // mm, hegiht above mean seal level
uint32_t hAcc; // mm, horizontal accuracy estimate
uint32_t vAcc; // mm, vertical accuracy estimate
int32_t velN; // mm/s, north velocity
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/driverGPS.c b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/driverGPS.c
index 2cf7a92..89416a6 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/driverGPS.c
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/driverGPS.c
@@ -273,7 +273,6 @@ int writeGps(char *data, uint16_t len)
void GetGPSData(gpsDataStruct_t *data)
{
- data->gpsValid = gGpsDataPtr->gpsValid;
data->gpsUpdate = ( gGpsDataPtr->updateFlagForEachCall >> GOT_VTG_MSG ) & 0x00000001 &&
( gGpsDataPtr->updateFlagForEachCall >> GOT_GGA_MSG ) & 0x00000001;
// gGpsDataPtr->updateFlagForEachCall &= 0xFFFFFFFD;
@@ -281,33 +280,36 @@ void GetGPSData(gpsDataStruct_t *data)
{
// Reset GPS update flag only when pos and vel are both available
gGpsDataPtr->updateFlagForEachCall &= 0xFFFFFFFC;
- }
- data->latitude = gGpsDataPtr->lat;
- data->longitude = gGpsDataPtr->lon;
- data->altitude = gGpsDataPtr->alt;
+ data->gpsFixType = gGpsDataPtr->gpsFixType;
+ data->numSatellites = gGpsDataPtr->numSatellites;
+
+ data->latitude = gGpsDataPtr->lat;
+ data->longitude = gGpsDataPtr->lon;
+ data->altitude = gGpsDataPtr->alt;
- data->vNed[0] = gGpsDataPtr->vNed[0];
- data->vNed[1] = gGpsDataPtr->vNed[1];
- data->vNed[2] = gGpsDataPtr->vNed[2];
+ data->vNed[0] = gGpsDataPtr->vNed[0];
+ data->vNed[1] = gGpsDataPtr->vNed[1];
+ data->vNed[2] = gGpsDataPtr->vNed[2];
- data->trueCourse = gGpsDataPtr->trueCourse;
- data->rawGroundSpeed = gGpsDataPtr->rawGroundSpeed;
+ data->trueCourse = gGpsDataPtr->trueCourse;
+ data->rawGroundSpeed = gGpsDataPtr->rawGroundSpeed;
- data->GPSSecondFraction = gGpsDataPtr->GPSSecondFraction;
- data->altEllipsoid = gGpsDataPtr->altEllipsoid;
+ data->GPSSecondFraction = gGpsDataPtr->GPSSecondFraction;
- data->itow = gGpsDataPtr->itow;
- data->GPSmonth = gGpsDataPtr->GPSmonth;
- data->GPSday = gGpsDataPtr->GPSday;
- data->GPSyear = gGpsDataPtr->GPSyear;
- data->GPSHour = gGpsDataPtr->GPSHour;
- data->GPSMinute = gGpsDataPtr->GPSMinute;
- data->GPSSecond = gGpsDataPtr->GPSSecond;
+ data->itow = gGpsDataPtr->itow;
+ data->GPSmonth = gGpsDataPtr->GPSmonth;
+ data->GPSday = gGpsDataPtr->GPSday;
+ data->GPSyear = gGpsDataPtr->GPSyear;
+ data->GPSHour = gGpsDataPtr->GPSHour;
+ data->GPSMinute = gGpsDataPtr->GPSMinute;
+ data->GPSSecond = gGpsDataPtr->GPSSecond;
- data->HDOP = gGpsDataPtr->HDOP;
- data->GPSHorizAcc = gGpsDataPtr->GPSHorizAcc;
- data->GPSVertAcc = gGpsDataPtr->GPSVertAcc;
+ data->HDOP = gGpsDataPtr->HDOP;
+ data->GPSHorizAcc = gGpsDataPtr->GPSHorizAcc;
+ data->GPSVertAcc = gGpsDataPtr->GPSVertAcc;
+ data->geoidAboveEllipsoid = gGpsDataPtr->geoidAboveEllipsoid;
+ }
}
@@ -439,9 +441,6 @@ BOOL _handleGpsMessages(GpsData_t *GPSData)
}
tmp = gpsUartBuf[pos++];
bytesInBuffer--;
-#ifdef DETECT_USER_SERIAL_CMD
- platformDetectUserSerialCmd(tmp);
-#endif
switch(GPSData->GPSProtocol){
case NMEA_TEXT:
parseNMEAMessage(tmp, gpsMsg, GPSData);
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/processNMEAGPS.c b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/processNMEAGPS.c
index 00e31d0..f51ada5 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/processNMEAGPS.c
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/processNMEAGPS.c
@@ -33,6 +33,7 @@ limitations under the License.
#include
#include
+#include "gpsAPI.h"
#include "driverGPS.h"
#include "BITStatus.h"
@@ -42,6 +43,9 @@ char _parseRMC(char *msgBody, GpsData_t* GPSData);
void _handleNMEAmsg(char *msgID, char *msgBody,GpsData_t* GPSData);
void _NMEA2UbloxAndLLA(NmeaLatLonSTRUCT* NmeaData, GpsData_t* GPSData);
void _smoothVerticalData(GpsData_t* GPSData);
+
+int dayofweek(int day, int month, int year);
+
int crcError = 0;
int starError = 0;
/** ****************************************************************************
@@ -181,6 +185,9 @@ void _handleNMEAmsg(char *msgID,
GPSData->totalVTG++;
_parseVTG(msgBody, GPSData);
}
+ if( strncmp(ptr, "RMC", 3) == 0 ) {
+ _parseRMC(msgBody, GPSData);
+ }
}
/** ****************************************************************************
@@ -244,6 +251,8 @@ char extractNMEAfield(char *msgBody,
break;
}
}
+ outField[outIndex] = '\x0';
+
// Leave the currentField as the one returned so the next search passes
// the currrent doesn't match requested test
// Back up one so the next search picks up the end ','
@@ -252,7 +261,7 @@ char extractNMEAfield(char *msgBody,
}
/** ****************************************************************************
- * @name: _parseGPGGA LOCAL parse GPGGA message. Tiem, position, fix data
+ * @name: _parseGPGGA LOCAL parse GPGGA message. Time, position, fix data
* @author Dong An
* @param [in] msgBody - data to parse
* @param [in] GPSData - data structure to parst he data into
@@ -285,6 +294,7 @@ char extractNMEAfield(char *msgBody,
* decimal
* 02/16/15 dkh move convert to after check for flag
******************************************************************************/
+#include "debug.h"
char _parseGPGGA(char *msgBody,
GpsData_t *GPSData)
{
@@ -292,8 +302,6 @@ char _parseGPGGA(char *msgBody,
char status = 0;
int parseReset = true;
NmeaLatLonSTRUCT nmeaLatLon;
- // this is the local using the NMEA convention
- char GPSFix = 0; // no fix
memset(&nmeaLatLon, 0, sizeof(nmeaLatLon) );
/// Time - convert from ascii digits to decimal '0' = 48d
@@ -344,7 +352,17 @@ char _parseGPGGA(char *msgBody,
/// GPS quality
if( extractNMEAfield(msgBody, field, 5, parseReset) ) {
- GPSFix = field[0] - '0'; // convert ascii digit to decimal
+ GPSData->gpsFixType = field[0] - '0'; // convert ascii digit to decimal
+ if (GPSData->gpsFixType >= DEAD_REC) // DR, manual and simulation is considered invalid
+ {
+ GPSData->gpsFixType = INVALID;
+ }
+ } else
+ status = 1;
+
+ // Number of satellites
+ if( extractNMEAfield(msgBody, field, 6, parseReset) ) {
+ GPSData->numSatellites = atoi((char *)field);
} else
status = 1;
@@ -354,32 +372,37 @@ char _parseGPGGA(char *msgBody,
} else
status = 1;
- if(GPSFix >= 1) {
- convertItow(GPSData); // create pseudo ITOW
- gBitStatus.hwStatus.bit.unlockedInternalGPS = 0; // locked
- gBitStatus.swStatus.bit.noGPSTrackReference = 0; // GPS track
- } else {
- gBitStatus.hwStatus.bit.unlockedInternalGPS = 1; // no signal lock
- gBitStatus.swStatus.bit.noGPSTrackReference = 1; // no GPS track
- }
-
-
/// Altitude
if( extractNMEAfield(msgBody, field, 8, parseReset) ) {
- GPSData->alt = atof((char *)field);
+ GPSData->alt = atof((char *)field); // altitude above MSL
+ } else{
+ status = 1;
+ }
+ if( extractNMEAfield(msgBody, field, 10, parseReset) ) {
+ GPSData->geoidAboveEllipsoid = atof((char *)field);
} else{
status = 1;
}
- if(GPSFix >= 1) {
+ // if fixed, convert data
+ if(GPSData->gpsFixType > INVALID)
+ {
+ // Convert deg/min/sec to xxx.xxx deg
_NMEA2UbloxAndLLA(&nmeaLatLon, GPSData);
+ // convert geiod height to ellipsoid height
+ GPSData->alt += GPSData->geoidAboveEllipsoid;
+ // create pseudo ITOW
+ convertItow(GPSData);
+
+ gBitStatus.hwStatus.bit.unlockedInternalGPS = 0; // locked
+ gBitStatus.swStatus.bit.noGPSTrackReference = 0; // GPS track
}
- // flip the sense from the NMEA convention to match the propiatery binary messages
- if (GPSData->HDOP < 20) { // the threshold may get set lower in algorithm.c
- GPSData->GPSFix = 0; // fix
- } else {
- GPSData->GPSFix = 1; // no fix
+ else
+ {
+ gBitStatus.hwStatus.bit.unlockedInternalGPS = 1; // no signal lock
+ gBitStatus.swStatus.bit.noGPSTrackReference = 1; // no GPS track
}
+
if( status == 0) {
GPSData->updateFlagForEachCall |= 1 << GOT_GGA_MSG;
GPSData->LLHCounter++;
@@ -422,6 +445,7 @@ char _parseVTG(char *msgBody,
/// speed over ground [km/hr]
if( extractNMEAfield(msgBody, field, 6, parseReset) ) {
GPSData->rawGroundSpeed = atof((char *)field); // double [kph]
+ GPSData->rawGroundSpeed *= 0.2777777777778; // convert km/hr to m/s
// the heading of the VTG of some receiver is empty when velocity is low.
// a default zero will be set to the heading value.
if ( status == 1 ) {
@@ -474,7 +498,6 @@ char _parseRMC(char *msgBody,
GPSData->GPSyear = ( (field[4] - '0') * 10) + field[5] - '0'; /// year
} else
status = 1;
-
return status;
}
@@ -553,10 +576,8 @@ void _NMEA2UbloxAndLLA(NmeaLatLonSTRUCT *NmeaData,
******************************************************************************/
void convertNorhEastVelocity(GpsData_t* GPSData)
{
- GPSData->vNed[0] = (GPSData->rawGroundSpeed * 0.2777777777778) *
- cos(D2R * GPSData->trueCourse); // 0.277 = 1000/3600 kph -> m/s
- GPSData->vNed[1] = (GPSData->rawGroundSpeed * 0.2777777777778) *
- sin(D2R * GPSData->trueCourse);
+ GPSData->vNed[0] = GPSData->rawGroundSpeed * cos(D2R * GPSData->trueCourse);
+ GPSData->vNed[1] = GPSData->rawGroundSpeed * sin(D2R * GPSData->trueCourse);
_smoothVerticalData(GPSData); // synthesize and filter down velocity
}
@@ -603,7 +624,6 @@ void _smoothVerticalData(GpsData_t* GPSData)
}
if ( OutAltCounter >= 5 ) {
firstFlag = 0; // reset
- GPSData->filteredAlt = filteredAlt ;
GPSData->vNed[2] = filteredVd ;
return;
}
@@ -623,7 +643,6 @@ void _smoothVerticalData(GpsData_t* GPSData)
CurrentVd = -(tmpDouble / delta_T); ///down is positive
} else { /// may be NMEA is lost
firstFlag = 0; /// reset
- GPSData->filteredAlt = filteredAlt ;
GPSData->vNed[2] = filteredVd ;
return;
}
@@ -643,7 +662,6 @@ void _smoothVerticalData(GpsData_t* GPSData)
if (OutVelCounter >= 5) {
firstFlag = 0; /// reset
- GPSData->filteredAlt = filteredAlt ;
GPSData->vNed[2] = filteredVd ;
return;
}
@@ -655,8 +673,7 @@ void _smoothVerticalData(GpsData_t* GPSData)
// save the current time local to calc delta T next time
LastTotalTime = TotalTime;
- /// output the filtered alt and vel values
- GPSData->filteredAlt = filteredAlt;
+ /// output the vel
GPSData->vNed[2] = filteredVd;
}
@@ -668,14 +685,30 @@ void _smoothVerticalData(GpsData_t* GPSData)
******************************************************************************/
void convertItow(GpsData_t* GPSData)
{
- long double tmp;
-
- tmp = ((long double)GPSData->GPSHour) * 3600.0 + ((long double)GPSData->GPSMinute) * 60.0;
- tmp += (long double)GPSData->GPSSecond + (long double)GPSData->GPSSecondFraction;
+ double tmp;
+ // calculate day of week
+ int tow = dayofweek(GPSData->GPSday, GPSData->GPSmonth, GPSData->GPSyear+2000);
+ // calculate second of week
+ tmp = (double)tow * 86400.0;
+ tmp += ((double)GPSData->GPSHour) * 3600.0 + ((double)GPSData->GPSMinute) * 60.0;
+ tmp += (double)GPSData->GPSSecond + (double)GPSData->GPSSecondFraction;
/// converting UTC to GPS time is impossible without GPS satellite
/// Navigation message. using UTC time directly by scaling to ms.
GPSData->itow = (unsigned long) (tmp * 1000);
}
+int dayofweek(int day, int month, int year)
+{
+
+ int adjustment, mm, yy;
+
+ adjustment = (14 - month) / 12;
+ mm = month + 12 * adjustment - 2;
+ yy = year - adjustment;
+
+ return (day + (13 * mm - 1) / 5 +
+ yy + yy / 4 - yy / 100 + yy / 400) % 7;
+}
+
#endif // GPS
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/processNovAtelGPS.c b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/processNovAtelGPS.c
index a385ac9..6722855 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/processNovAtelGPS.c
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/processNovAtelGPS.c
@@ -221,16 +221,17 @@ void _parseBestPosB_Fast(logBestPosB *bestPosB,
{
GPSData->lat = bestPosB->Lat;
GPSData->lon = bestPosB->Lon;
- GPSData->alt = bestPosB->hgt; ///alt
+ GPSData->alt = bestPosB->hgt + bestPosB->undulation; // altitude above ellipsoid
+ GPSData->geoidAboveEllipsoid = bestPosB->undulation; // geoid above ellipsoid
if (bestPosB->sol_status != 0) // zero is good fix anything else is
{ // enumeration for bad fix
- GPSData->GPSFix = 0;// PosVelType
+ GPSData->gpsFixType = 0;// PosVelType
gBitStatus.hwStatus.bit.unlockedInternalGPS = 1; // locked
gBitStatus.swStatus.bit.noGPSTrackReference = 1; // no GPS track
gGpsDataPtr->HDOP = 21.0f; // force to above threshold
} else {
- GPSData->GPSFix = bestPosB->pos_type;
+ GPSData->gpsFixType = bestPosB->pos_type;
gBitStatus.hwStatus.bit.unlockedInternalGPS = 0; // locked
gBitStatus.swStatus.bit.noGPSTrackReference = 0; // GPS track
gGpsDataPtr->HDOP = 1.0f; // force to below threshold
@@ -269,7 +270,7 @@ void _parseBestPosB_Fast(logBestPosB *bestPosB,
GPSData->GPSHorizAcc = sqrtf( bestPosB->lat_sigma * bestPosB->lat_sigma + bestPosB->lon_sigma * bestPosB->lon_sigma ); // [m]
GPSData->GPSVertAcc = bestPosB->hgt_sigma; // [m]
- GPSData->numSatelites = bestPosB->num_obs;
+ GPSData->numSatellites = bestPosB->num_obs;
}
/** ****************************************************************************
@@ -329,7 +330,7 @@ void _parseBestPosB(char *completeMessage,
gBitStatus.hwStatus.bit.unlockedInternalGPS = 0; // locked
gBitStatus.swStatus.bit.noGPSTrackReference = 0; // GPS track
}
- GPSData->GPSFix = SolStatus[0];
+ GPSData->gpsFixType = SolStatus[0];
memcpy(&GPSData->itow, &completeMessage[16], 4); ///Itow
@@ -371,12 +372,12 @@ void _parseBestVelB_Fast(logBestVelB *bestVelB,
if (bestVelB->sol_status != 0) // zero is good fix anything else is
{ // enumeration for bad fix
- GPSData->GPSFix = bestVelB->vel_type;
+ GPSData->gpsFixType = bestVelB->vel_type;
gBitStatus.hwStatus.bit.unlockedInternalGPS = 1; // not locked
gBitStatus.swStatus.bit.noGPSTrackReference = 1; // no GPS track
gGpsDataPtr->HDOP = 21.0f; //
} else {
- GPSData->GPSFix = 0;
+ GPSData->gpsFixType = 0;
gBitStatus.hwStatus.bit.unlockedInternalGPS = 0; // not locked
gBitStatus.swStatus.bit.noGPSTrackReference = 0; // GPS track
gGpsDataPtr->HDOP = 1.0f; //
@@ -437,7 +438,7 @@ void _parseBestVelB(char *completeMessage,
gBitStatus.hwStatus.bit.unlockedInternalGPS = 0; // not locked
gBitStatus.swStatus.bit.noGPSTrackReference = 0; // GPS track
}
- GPSData->GPSFix = SolStatus[0];
+ GPSData->gpsFixType = SolStatus[0];
memcpy(&GPSData->itow, &completeMessage[16], 4); ///Itow
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/processSiRFGPS.c b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/processSiRFGPS.c
index 681af14..56c579d 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/processSiRFGPS.c
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/processSiRFGPS.c
@@ -398,12 +398,12 @@ static void _parseSiRFGeodeticNavMsg(char *msg,
// Switched at the sazme time as PPS 5 satellites
if ( geo->navValid > 0) {
GPSData->HDOP = 50.0;
- GPSData->GPSFix = 1; // zero is valid anything else is degraded
+ GPSData->gpsFixType = 1; // zero is valid anything else is degraded
gBitStatus.hwStatus.bit.unlockedInternalGPS = 1; // no signal lock
gBitStatus.swStatus.bit.noGPSTrackReference = 1; // no GPS track
} else {
GPSData->HDOP = geo->hdop;
- GPSData->GPSFix = 0;
+ GPSData->gpsFixType = 0;
gBitStatus.hwStatus.bit.unlockedInternalGPS = 0; // locked
gBitStatus.swStatus.bit.noGPSTrackReference = 0; // GPS track
}
@@ -422,7 +422,7 @@ static void _parseSiRFGeodeticNavMsg(char *msg,
GPSData->GPSday = geo->utcDay; // dd
GPSData->GPSyear = byteSwap16(geo->utcYear) - 2000; // last two digits of year
- GPSData->altEllipsoid = (float)byteSwap32(geo->altitudeEllipsoid) / 100.; // 0x2221201f in m * 10^2
+ GPSData->geoidAboveEllipsoid = (float)byteSwap32(geo->altitudeEllipsoid - geo->altitudeMSL) / 100.; // 0x2221201f in m * 10^2
GPSData->GPSHour = geo->utcHour;
GPSData->GPSMinute = geo->utcMinute;
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/processUbloxGPS.c b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/processUbloxGPS.c
index 2e75a53..9354476 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/processUbloxGPS.c
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/processUbloxGPS.c
@@ -32,6 +32,7 @@ limitations under the License.
#include "driverGPS.h"
#include "platformAPI.h"
+#include "gpsAPI.h"
#ifdef DISPLAY_DIAGNOSTIC_MSG
#include "debug.h"
@@ -312,7 +313,7 @@ void processUbloxBinaryMessage(char *msg,
GPSData->VELCounter++;
break;
case UBLOX_NAV_STATUS: ///NAV_STATUS
- GPSData->GPSFix = msg[10]; ///fix indicator
+ GPSData->gpsFixType = msg[10]; ///fix indicator
if((msg[11]&0x02) == 0x02) ///6+5
GPSData->GPSStatusWord |=1 << DGPS_ON; ///on
else
@@ -422,10 +423,34 @@ void processUbloxBinaryMessage(char *msg,
void decodeNavPvt(char *msg, GpsData_t *GPSData)
{
+ // Decode
ubloxNavPvtSTRUCT *navPvt;
navPvt = (ubloxNavPvtSTRUCT*)(&msg[UBLOX_BINAERY_HEADER_LEN]);
+
+ // Get decoded results
// fix type
- GPSData->gpsValid = navPvt->fixType == 3;
+ GPSData->gpsFixType = INVALID;
+ if (navPvt->flags & 0x01)
+ {
+ GPSData->gpsFixType = SPP;
+ if (navPvt->flags & 0x02)
+ {
+ GPSData->gpsFixType = DGPS;
+ }
+ uint8_t carrSoln = navPvt->flags >> 6;
+ if (carrSoln == 1)
+ {
+ GPSData->gpsFixType = RTK_FLOAT;
+ }
+ else if(carrSoln == 2)
+ {
+ GPSData->gpsFixType = RTK_FIX;
+ }
+ }
+
+ // num of satellites
+ GPSData->numSatellites = navPvt->numSV;
+
// lat
GPSData->lat = navPvt->lat * 1.0e-7;
@@ -444,9 +469,12 @@ void decodeNavPvt(char *msg, GpsData_t *GPSData)
// fractional second
GPSData->GPSSecondFraction = navPvt->nano * 1.0e-9;
// ellipsoid height
- GPSData->altEllipsoid = navPvt->height * 1.0e-3;
+ GPSData->geoidAboveEllipsoid = (navPvt->height - navPvt->hMSL) * 1.0e-3;
// itow
GPSData->itow = navPvt->iTOW;
+ if(GPSData->itow%1000 != 0){
+ GPSData->itow+=1; // correction of numerical issue
+ }
platformUpdateITOW(GPSData->itow);
// year month day hour min sec
GPSData->GPSmonth = navPvt->month;
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/taskGps.c b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/taskGps.c
index 3854b95..56a62a1 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/taskGps.c
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/GPS/src/taskGps.c
@@ -89,16 +89,6 @@ void TaskGps(void const *argument)
pollSirfCnt++;
}
}
-
- // Set the GPS validity, based on the Horizontal Dilution of Precision
- if (gGpsDataPtr->gpsValid && gGpsDataPtr->HDOP > 15.0)
- {
- gGpsDataPtr->gpsValid = false;
- }
- else if (gGpsDataPtr->HDOP < 10.0)
- {
- gGpsDataPtr->gpsValid = true;
- }
}
}
}
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Math/include/TransformationMath.h b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Math/include/TransformationMath.h
index 910b5fc..2a01980 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Math/include/TransformationMath.h
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Math/include/TransformationMath.h
@@ -73,12 +73,28 @@ real UnitGravityAndMagToYaw(real *unitGravityVector, real *magFieldVector);
******************************************************************************/
real RollPitchAndMagToYaw(real roll, real pitch, real *magFieldVector);
+/******************************************************************************
+* @brief Limit angle error to be [-180, 180].
+* TRACE:
+* @param [in] aErr in [deg].
+* @retval aErr within [-180, 180]deg.
+******************************************************************************/
+real AngleErrDeg(real aErr);
+
+/******************************************************************************
+* @brief Limit angle error to be [-PI, PI].
+* TRACE:
+* @param [in] aErr in [rad].
+* @retval aErr within [-2*PI, 2*PI].
+******************************************************************************/
+real AngleErrRad(real aErr);
//
BOOL LLA_To_R_EinN( double* llaRad, real* R_EinN);
BOOL LLA_To_R_NinE( double* llaRad, real* R_NinE);
-BOOL LLA_To_Base( double* llaRad, double* rECEF_Init,
- real* dr_N,
- real* R_NinE, double* rECEF );
+BOOL ECEF_To_Base( double* rECEF_Init,
+ double* rECEF ,
+ real* R_NinE,
+ real* dr_N);
BOOL LLA_To_ECEF( double* lla_Rad, double* ecef_m);
BOOL PosNED_To_PosECEF( real* r_N, double* rECEF_Init,
real* R_NinE, double* rECEF );
@@ -86,10 +102,9 @@ BOOL ECEF_To_LLA( double* llaDeg, double* ecef_m );
BOOL VelECEF_To_VelNED( double* LLA, real* VelECEF, real* VelNED );
+
void printMtx(float *a, int m, int n);
void printVec(float *v, int n);
-int realSymmetricMtxEig(float *a, int n, float *v, float eps, int jt);
-
#endif /* TRANSFORMATIONMATH_H */
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Math/src/TransformationMath.c b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Math/src/TransformationMath.c
index 9fc4b2c..9158f9b 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Math/src/TransformationMath.c
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Math/src/TransformationMath.c
@@ -204,68 +204,32 @@ BOOL LLA_To_R_NinE( double* llaRad,
///** ***************************************************************************
-//* @name LLA2Base Express LLA in a local NED Base Frame
+//* @name Calculate NED relative position of two ECEF positions.
//* @details Pre calculated all non-changing constants and unfolded the matrices
-//* @param [in] LLA - array with the current Latitude, Longitude and Altitude [rad]
-//* @param [in] BaseECEF - start of frame position
-//* @param [in] Rne - rotation matrix from ECEF to NED
-//* @param [out] NED - output of the position in North East and Down coords
-//* @param [out] newECEF - current position in ECEF from LLA
+//* @param [in] rECEF_Init - start of frame position
+//* @param [in] rECEF - current position in ECEF from LLA
+//* @param [in] R_NinE - rotation matrix from NED to ECEF
+//* @param [out] dr_N - output of the position in North East and Down coords
//* @retval always 1
//******************************************************************************/
-BOOL LLA_To_Base( double* llaRad, // in
- double* rECEF_Init, // in
- real* dr_N, //NED,
+BOOL ECEF_To_Base( double* rECEF_Init,
+ double* rECEF,
real* R_NinE,
- double* rECEF) // out
+ real* dr_N)
{
real dr_E[NUM_AXIS];
- double N;
- double sinLat = sin(llaRad[LAT]);
- double cosLat = cos(llaRad[LAT]);
- double sinLon = sin(llaRad[LON]);
- double cosLon = cos(llaRad[LON]);
-
- real sinLat_r = (real)sinLat;
- real cosLat_r = (real)cosLat;
- real sinLon_r = (real)sinLon;
- real cosLon_r = (real)cosLon;
-
- N = E_MAJOR / sqrt(1.0 - (E_ECC_SQ * sinLat * sinLat)); // radius of Curvature [meters]
-
- //LLA_To_ECEF(llaRad, rECEF);
- double temp_d = (N + llaRad[ALT]) * cosLat;
- rECEF[X_AXIS] = temp_d * cosLon;
- rECEF[Y_AXIS] = temp_d * sinLon;
- rECEF[Z_AXIS] = ((E_MINOR_OVER_MAJOR_SQ * N) + llaRad[ALT]) * sinLat;
-
dr_E[X_AXIS] = (real)( rECEF[X_AXIS] - *(rECEF_Init + X_AXIS) );
dr_E[Y_AXIS] = (real)( rECEF[Y_AXIS] - *(rECEF_Init + Y_AXIS) );
dr_E[Z_AXIS] = (real)( rECEF[Z_AXIS] - *(rECEF_Init + Z_AXIS) );
- // Form R_NinE
- // First row
- *(R_NinE + 0 * 3 + 0) = -sinLat_r * cosLon_r;
- *(R_NinE + 0 * 3 + 1) = -sinLon_r;
- *(R_NinE + 0 * 3 + 2) = -cosLat_r * cosLon_r;
-
- // Second row
- *(R_NinE + 1 * 3 + 0) = -sinLat_r * sinLon_r;
- *(R_NinE + 1 * 3 + 1) = cosLon_r;
- *(R_NinE + 1 * 3 + 2) = -cosLat_r * sinLon_r;
-
- // Third row
- *(R_NinE + 2 * 3 + 0) = cosLat_r;
- *(R_NinE + 2 * 3 + 1) = 0.0;
- *(R_NinE + 2 * 3 + 2) = -sinLat_r;
-
- // Convert from delta-position in the ECEF-frame to the NED-frame (the transpose
- // in the equations that followed is handled in the formulation)
- //
- // N E ( E N )T
- // dr_N = R * dr_E = ( R ) * dr_E
- // ( )
+ /* Convert from delta-position in the ECEF-frame to the NED-frame (the transpose
+ * in the equations that followed is handled in the formulation)
+ *
+ * N E ( E N )T
+ * dr_N = R * dr_E = ( R ) * dr_E
+ * ( )
+ */
dr_N[X_AXIS] = *(R_NinE + X_AXIS * 3 + X_AXIS) * dr_E[X_AXIS] +
*(R_NinE + Y_AXIS * 3 + X_AXIS) * dr_E[Y_AXIS] +
*(R_NinE + Z_AXIS * 3 + X_AXIS) * dr_E[Z_AXIS];
@@ -438,97 +402,36 @@ void printVec(float *v, int n)
printf("%.9g\n", v[i]);
}
-int realSymmetricMtxEig(float *a, int n, float *v, float eps, int jt)
+real AngleErrDeg(real aErr)
{
- int i, j, p, q, u, w, t, s, l;
- double fm, cn, sn, omega, x, y, d;
- l = 1;
- p = 0; q = 0; // initialized AB
- for (i = 0; i <= n - 1; i++)
- {
- v[i*n + i] = 1.0;
- for (j = 0; j <= n - 1; j++)
- {
- if (i != j)
- {
- v[i*n + j] = 0.0;
- }
- }
- }
- while (1)
+ while (fabs(aErr) > 180.0)
{
- fm = 0.0;
- for (i = 0; i <= n - 1; i++)
+ if (aErr > 180.0)
{
- for (j = 0; j <= n - 1; j++)
- {
- d = fabs(a[i*n + j]);
- if ((i != j) && (d > fm))
- {
- fm = d;
- p = i;
- q = j;
- }
- }
+ aErr -= (real)360.0;
}
- if (fm < eps)
+ else if (aErr < -180.0)
{
- return(1);
+ aErr += (real)360.0;
}
- if (l > jt)
- {
- return(-1);
- }
- l = l + 1;
- u = p * n + q;
- w = p * n + p;
- t = q * n + p;
- s = q * n + q;
- x = -a[u];
- y = (a[s] - a[w]) / 2.0;
- omega = x / sqrt(x*x + y * y);
- if (y < 0.0)
- {
- omega = -omega;
- }
- sn = 1.0 + sqrt(1.0 - omega * omega);
- sn = omega / sqrt(2.0*sn);
- cn = sqrt(1.0 - sn * sn);
- fm = a[w];
- a[w] = fm * cn*cn + a[s] * sn*sn + a[u] * omega;
- a[s] = fm * sn*sn + a[s] * cn*cn - a[u] * omega;
- a[u] = 0.0;
- a[t] = 0.0;
- for (j = 0; j <= n - 1; j++)
- {
- if ((j != p) && (j != q))
- {
- u = p * n + j;
- w = q * n + j;
- fm = a[u];
- a[u] = fm * cn + a[w] * sn;
- a[w] = -fm * sn + a[w] * cn;
- }
- }
- for (i = 0; i <= n - 1; i++)
+ }
+
+ return aErr;
+}
+
+real AngleErrRad(real aErr)
+{
+ while (fabs(aErr) > PI)
+ {
+ if (aErr > PI)
{
- if ((i != p) && (i != q))
- {
- u = i * n + p;
- w = i * n + q;
- fm = a[u];
- a[u] = fm * cn + a[w] * sn;
- a[w] = -fm * sn + a[w] * cn;
- }
+ aErr -= (real)TWO_PI;
}
- for (i = 0; i <= n - 1; i++)
+ else if (aErr < -PI)
{
- u = i * n + p;
- w = i * n + q;
- fm = v[u];
- v[u] = fm * cn + v[w] * sn;
- v[w] = -fm * sn + v[w] * cn;
+ aErr += (real)TWO_PI;
}
}
- return(1);
-}
\ No newline at end of file
+
+ return aErr;
+}
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/Odo/odoAPI.h b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Odo/odoAPI.h
new file mode 100644
index 0000000..458560b
--- /dev/null
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/Odo/odoAPI.h
@@ -0,0 +1,40 @@
+/** ***************************************************************************
+ * @file odoApi.h Odometer interface.
+ *
+ * THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
+ * KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
+ * PARTICULAR PURPOSE.
+ *
+ * @brief This is a generalized odometer interface.
+ *****************************************************************************/
+/*******************************************************************************
+Copyright 2018 ACEINNA, INC
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*******************************************************************************/
+
+#ifndef ODO_API_H
+#define ODO_API_H
+
+#include
+#include "GlobalConstants.h"
+
+typedef struct {
+ uint8_t update; // 1 if contains new data
+ real v; // velocity measured by odometer, [m/s]
+} odoDataStruct_t;
+
+extern odoDataStruct_t gOdo;
+
+#endif /* ODO_API_H */
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/UARTComm/CommonMessages.c b/examples/OpenIMU300RI/VG_AHRS/lib/Core/UARTComm/CommonMessages.c
index 4812cfb..09cbf0b 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/UARTComm/CommonMessages.c
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/UARTComm/CommonMessages.c
@@ -253,7 +253,7 @@ BOOL Fill_e1PacketPayload(uint8_t *payload, uint8_t *payloadLen)
*payloadLen = sizeof(ekf1_payload_t);
pld->tstmp = platformGetIMUCounter();
- pld->dbTstmp = (double)platformGetSolutionTstamp() * 0.000001; // seconds
+ pld->dbTstmp = platformGetSolutionTstampAsDouble() * 0.000001; // seconds
EKF_GetAttitude_EA(EulerAngles);
pld->roll = (float)EulerAngles[ROLL];
@@ -306,8 +306,7 @@ BOOL Fill_e2PacketPayload(uint8_t *payload, uint8_t *payloadLen)
*payloadLen = sizeof(ekf2_payload_t);
pld->tstmp = platformGetIMUCounter();
- pld->dbTstmp = (double)platformGetSolutionTstamp() * 0.000001; // seconds
-
+ pld->dbTstmp = platformGetSolutionTstampAsDouble() * 0.000001; // seconds
EKF_GetAttitude_EA(rData);
pld->roll = (float)rData[ROLL];
@@ -347,7 +346,7 @@ BOOL Fill_e2PacketPayload(uint8_t *payload, uint8_t *payloadLen)
EKF_GetEstimatedLLA(dData);
for(int i = 0; i < NUM_AXIS; i++){
- pld->pos[i] = (float)dData[i];
+ pld->pos[i] = dData[i];
}
uint8_t opMode, linAccelSw, turnSw;
diff --git a/examples/OpenIMU300RI/VG_AHRS/lib/Core/library.json b/examples/OpenIMU300RI/VG_AHRS/lib/Core/library.json
index 497943a..f5babce 100644
--- a/examples/OpenIMU300RI/VG_AHRS/lib/Core/library.json
+++ b/examples/OpenIMU300RI/VG_AHRS/lib/Core/library.json
@@ -1,22 +1,24 @@
{
- "name": "Core",
- "version": "1.0.4",
- "description": "Algorithm and GPS libraries",
- "build": {
- "flags": [
- "-I Algorithm",
- "-I Algorithm/include",
- "-I Buffer",
- "-I Buffer/include",
- "-I Common",
- "-I Common/include",
- "-I GPS",
- "-I GPS/include",
- "-I Math",
- "-I Math/include",
- "-I SPIComm",
- "-I UARTComm",
- "-I ."
+ "name": "Core",
+ "version": "1.0.4",
+ "description": "Algorithm and GPS libraries",
+ "build": {
+ "flags": [
+ "-I Algorithm",
+ "-I Algorithm/include",
+ "-I Buffer",
+ "-I Buffer/include",
+ "-I Common",
+ "-I Common/include",
+ "-I GPS",
+ "-I GPS/include",
+ "-I Odo",
+ "-I Odo/include",
+ "-I Math",
+ "-I Math/include",
+ "-I SPIComm",
+ "-I UARTComm",
+ "-I ."
]
}
}
diff --git a/examples/OpenIMU300RI/VG_AHRS/platformio.ini b/examples/OpenIMU300RI/VG_AHRS/platformio.ini
index 48475ca..cceb861 100644
--- a/examples/OpenIMU300RI/VG_AHRS/platformio.ini
+++ b/examples/OpenIMU300RI/VG_AHRS/platformio.ini
@@ -14,16 +14,17 @@ description = VG_AHRS application example. A Kalman filter based algorithm that
platform = aceinna_imu
lib_archive = false
board = OpenIMU300
-;lib_deps= ../../openIMU300-lib
-lib_deps = OpenIMU300-base-library@1.0.8
+;lib_deps = ../../openIMU300-lib/openIMU300-lib
+lib_deps = OpenIMU300-base-library@1.1.6
build_flags =
; -D CLI
+; Comment next line for VG algorithm
+ -D AHRS_ALGORITHM
-D SAE_J1939
-D CAN_BUS_COMM
-D __FPU_PRESENT
-D ARM_MATH_CM4
-I include
- -I include/API
-I src/user
-I src
-I lib/CAN/include
diff --git a/examples/OpenIMU300RI/VG_AHRS/src/appVersion.h b/examples/OpenIMU300RI/VG_AHRS/src/appVersion.h
index 26d4d90..69dcb01 100644
--- a/examples/OpenIMU300RI/VG_AHRS/src/appVersion.h
+++ b/examples/OpenIMU300RI/VG_AHRS/src/appVersion.h
@@ -26,7 +26,7 @@ limitations under the License.
#ifndef _IMU_APP_VERSION_H
#define _IMU_APP_VERSION_H
-#define APP_VERSION_STRING "VG_AHRS_J1939 1.0.1"
+#define APP_VERSION_STRING "VG_AHRS_J1939 1.0.3"
#endif
diff --git a/examples/OpenIMU300RI/VG_AHRS/src/user/UserAlgorithm.c b/examples/OpenIMU300RI/VG_AHRS/src/user/UserAlgorithm.c
index ae49480..7479a3d 100644
--- a/examples/OpenIMU300RI/VG_AHRS/src/user/UserAlgorithm.c
+++ b/examples/OpenIMU300RI/VG_AHRS/src/user/UserAlgorithm.c
@@ -24,166 +24,77 @@ limitations under the License.
*******************************************************************************/
#include
+#include
-#include "algorithmAPI.h"
-#include "gpsAPI.h"
#include "platformAPI.h"
#include "userAPI.h"
#include "Indices.h"
#include "GlobalConstants.h"
+#if FAST_MATH
+#include "arm_math.h"
+#endif
+
+#include "UserConfiguration.h"
+#include "algorithmAPI.h"
#include "algorithm.h"
+#include "UserAlgorithm.h"
#include "EKF_Algorithm.h"
-#include "BitStatus.h"
-#include "UserConfiguration.h"
-#include "bsp.h"
-#include "debug.h"
-#include "MagAlign.h"
-#include "sae_j1939.h"
+#ifndef INS_OFFLINE
+#include "debug.h"
+#endif // !INS_OFFLINE
-#define DEBUG_FREQ_0HZ 0
-#define DEBUG_FREQ_1HZ 1
-#define DEBUG_FREQ_2HZ 2
-#define DEBUG_FREQ_5HZ 5
+// Declare the IMU data structure
+IMUDataStruct gIMU;
+gpsDataStruct_t gGPS;
+odoDataStruct_t gOdo;
+int initAlgo = 0;;
//
-void _Algorithm(int dacqRate, uint8_t algoType);
+static void _Algorithm();
-// Initialize GPS algorithm variables
+// Initialize algorithm variables
void InitUserAlgorithm()
{
// Initialize built-in algorithm structure
InitializeAlgorithmStruct(FREQ_200_HZ);
// place additional required initialization here
+ /* Set the configuration variables for AHRS solution
+ * Enable mag
+ */
+#ifdef AHRS_ALGORITHM
+ enableMagInAlgorithm(TRUE);
+#endif
}
-// Initialization variable
-int initAlgo = 1;
-void *RunUserNavAlgorithm(double *accels, double *rates, double *mags, gpsDataStruct_t *gps, uint16_t dacqRate)
+void *RunUserNavAlgorithm(double *accels, double *rates, double *mags,
+ gpsDataStruct_t *gps, odoDataStruct_t *odo, BOOL ppsDetected)
{
- static int debugOutputCntr = 0, debugOutputCntrLimit = 0, debugOutputFreq = DEBUG_FREQ_0HZ;
-
- if(!UseAlgorithm()){
- return NULL;
- }
-
-
- // Initialize the timer variables
- if(initAlgo) {
- // Reset 'initAlgo' so this is not executed more than once.
- initAlgo = 0;
- // Set the variables that control the debug-message output-rate (based on
- // the desired calling frequency of the debug output)
- debugOutputCntr = 0;
-
- if(debugOutputFreq != DEBUG_FREQ_0HZ){
- debugOutputCntrLimit = (int)( (float)dacqRate / (float)debugOutputFreq + 0.5 );
- }else{
- debugOutputCntrLimit = 0;
- }
- }
-
- // Populate the EKF input data structure. Load the GPS data
- // structure as NULL.
- EKF_SetInputStruct(accels, rates, mags, NULL);
+ // Populate the EKF input data structure
+ EKF_SetInputStruct(accels, rates, mags, gps, odo, ppsDetected);
// Call the desired algorithm based on the EKF with different
// calling rates and different settings.
- //******************************************************************
- // NOTE: Provide algorithm type as a parameter here (VG or AHRS)
- //******************************************************************
- _Algorithm(dacqRate, VG);
+ _Algorithm();
// Fill the output data structure with the EKF states and other
// desired information
EKF_SetOutputStruct();
- // Generate the debug output
- if(debugOutputCntrLimit) {
- debugOutputCntr++;
- if(debugOutputCntr >= debugOutputCntrLimit) {
- debugOutputCntr = 0;
- DebugPrintFloat("Roll: ", gEKFOutputData.eulerAngs_BinN[ROLL], 5);
- DebugPrintFloat(", Pitch: ", gEKFOutputData.eulerAngs_BinN[PITCH], 5);
- DebugPrintFloat(", aX: ", gEKFInputData.accel_B[X_AXIS], 5);
- DebugPrintFloat(", aY: ", gEKFInputData.accel_B[Y_AXIS], 5);
- DebugPrintFloat(", aZ: ", gEKFInputData.accel_B[Z_AXIS], 5);
- DebugPrintInt(", Mode: ", gEKFOutputData.opMode);
- DebugPrintEndline();
- }
- }
-
// The returned value from this function is unused by external functions. The
// NULL pointer is returned instead of a data structure.
return NULL;
}
-
//
-void _Algorithm(int dacqRate, uint8_t algoType)
+static void _Algorithm()
{
- //
- static int initAlgo = 1;
- static uint8_t algoCntr = 0, algoCntrLimit = 0;
-
- // Initialize the configuration variables needed to make the system
- // generate a VG-type solution.
- if(initAlgo) {
- // Reset 'initAlgo' so this is not executed more than once. This
- // prevents the algorithm from being switched during run-time.
- initAlgo = 0;
-
- // Set the configuration variables for a VG-type solution
- // (useMags = 0 forces the VG solution)
- gAlgorithm.Behavior.bit.freeIntegrate = 0;
- gAlgorithm.Behavior.bit.useMag = 0;
- gAlgorithm.Behavior.bit.useGPS = 0;
- gAlgorithm.Behavior.bit.stationaryLockYaw = 0;
- gAlgorithm.Behavior.bit.restartOnOverRange = 0;
- gAlgorithm.Behavior.bit.dynamicMotion = 1;
-
- // While not needed, set hasMags to false
- enableMagInAlgorithm(FALSE);
-
- if(algoType == VG) {
- // Configuration already set for a VG solution
- } else if(algoType == AHRS) {
- // Set the configuration variables for AHRS solution
- // (useMags = 1 and enable mags)
- enableMagInAlgorithm(TRUE);
- gAlgorithm.Behavior.bit.useMag = 1;
- } else if(algoType == INS) {
- while(1);
- } else {
- while(1);
- }
-
- algoCntr = 0;
- algoCntrLimit = (int)( dacqRate / (int)gAlgorithm.callingFreq );
- if( algoCntrLimit < 1 ) {
- // If this logic is reached, also need to adjust the algorithm
- // parameters to match the modified calling freq (or stop the
- // program to indicate that the user must adjust the program)
- algoCntrLimit = 1;
- }
- }
-
// Aceinna VG/AHRS/INS algorithm
- if(algoCntr == 0) {
EKF_Algorithm();
- }
-
- // Increment the counter. If greater than or equal to the limit, reset
- // the counter to cause the algorithm to run on the next pass through.
- algoCntr++;
- if(algoCntr >= algoCntrLimit) {
- algoCntr = 0;
- }
}
-
diff --git a/examples/OpenIMU300RI/VG_AHRS/src/user/UserAlgorithm.h b/examples/OpenIMU300RI/VG_AHRS/src/user/UserAlgorithm.h
index 1c8c3d6..2dd0719 100644
--- a/examples/OpenIMU300RI/VG_AHRS/src/user/UserAlgorithm.h
+++ b/examples/OpenIMU300RI/VG_AHRS/src/user/UserAlgorithm.h
@@ -8,6 +8,23 @@
#ifndef _USER_ALGORITHM_H_
#define _USER_ALGORITHM_H_
+#include
+#include "GlobalConstants.h"
+
+ // IMU data structure
+typedef struct {
+ // Timer output counter
+ uint32_t timerCntr, dTimerCntr;
+
+ // Algorithm states
+ double accel_g[3];
+ double rate_radPerSec[3];
+ double rate_degPerSec[3];
+ double mag_G[3];
+ double temp_C;
+} IMUDataStruct;
+
+extern IMUDataStruct gIMU;
#endif /* _USER_ALGORITHM_H_ */
diff --git a/examples/OpenIMU300RI/VG_AHRS/src/user/UserConfiguration.c b/examples/OpenIMU300RI/VG_AHRS/src/user/UserConfiguration.c
index 630d38a..c4de528 100644
--- a/examples/OpenIMU300RI/VG_AHRS/src/user/UserConfiguration.c
+++ b/examples/OpenIMU300RI/VG_AHRS/src/user/UserConfiguration.c
@@ -32,6 +32,7 @@ limitations under the License.
#include "userAPI.h"
#include "UserConfiguration.h"
+#include "UserMessagingUart.h"
#include "eepromAPI.h"
#include "Indices.h"
#include "sae_j1939.h"
@@ -365,10 +366,12 @@ void ApplySystemParameters(void *pConfig)
platformSelectLPFilter(RATE_SENSOR, pEcuConfig->rate_cut_off, TRUE);
platformSelectLPFilter(ACCEL_SENSOR, pEcuConfig->accel_cut_off, TRUE);
platformApplyOrientation(pEcuConfig->orien_bits);
+
if(UseMags()){
platformForceMagUsage();
}
- userInitConfigureUart();
+
+ UserInitConfigureUart();
}
diff --git a/examples/OpenIMU300RI/VG_AHRS/src/user/UserConfigurationUart.c b/examples/OpenIMU300RI/VG_AHRS/src/user/UserConfigurationUart.c
index 6e20226..7b79f6b 100644
--- a/examples/OpenIMU300RI/VG_AHRS/src/user/UserConfigurationUart.c
+++ b/examples/OpenIMU300RI/VG_AHRS/src/user/UserConfigurationUart.c
@@ -101,7 +101,7 @@ BOOL UpdateSystemParameter(uint32_t number, uint64_t data, BOOL fApply)
}
-void userInitConfigureUart()
+void UserInitConfigureUart()
{
uint64_t *ptr = (uint64_t*)&gUserUartConfig;
diff --git a/examples/OpenIMU300RI/VG_AHRS/src/user/UserMessagingCAN.c b/examples/OpenIMU300RI/VG_AHRS/src/user/UserMessagingCAN.c
index 65f109c..4a33a00 100644
--- a/examples/OpenIMU300RI/VG_AHRS/src/user/UserMessagingCAN.c
+++ b/examples/OpenIMU300RI/VG_AHRS/src/user/UserMessagingCAN.c
@@ -40,6 +40,7 @@ limitations under the License.
#include "BITStatus.h"
#include "sensorsAPI.h"
#include "sae_j1939.h"
+#include "math.h"
// for EKFOutputDataStruct
#include "EKF_Algorithm.h"
@@ -276,6 +277,25 @@ void EnqeuePeriodicDataPackets(int latency, int sendPeriodicPackets)
aceinna_j1939_send_angular_rate(&angle_data);
}
+ if (packets_to_send & ACEINNA_SAE_J1939_PACKET_HEADING) {
+ VEHICLE_DIR_SPEED ds_data;
+ real velocity[3];
+ double tmp;
+ EKF_GetEstimatedVelocity(velocity); // m/s
+ ds_data.altitude = 2500 * 8; // 0 m
+ tmp = gKalmanFilter.eulerAngles[YAW] * 57.296;
+ tmp = tmp < 0 ? 360.0 + tmp : tmp;
+ tmp = tmp * 128 + 0.5;
+ ds_data.bearing = (uint16_t)(tmp);
+ ds_data.pitch = (uint16_t)((gKalmanFilter.eulerAngles[PITCH] * 57.296 + 200.00) * 128 + 0.5);
+ tmp = sqrtf(powf(velocity[0],2) + powf(velocity[1],2));
+ tmp = (tmp*3.6); // km/h
+ ds_data.speed = (uint16_t)tmp*256;
+
+ aceinna_j1939_send_veh_dir_speed(&ds_data);
+ }
+
+
forced_packets = 0;
return;
diff --git a/examples/OpenIMU300RI/VG_AHRS/src/user/UserMessagingUART.c b/examples/OpenIMU300RI/VG_AHRS/src/user/UserMessagingUART.c
index 33ad77a..c7060a4 100644
--- a/examples/OpenIMU300RI/VG_AHRS/src/user/UserMessagingUART.c
+++ b/examples/OpenIMU300RI/VG_AHRS/src/user/UserMessagingUART.c
@@ -39,13 +39,6 @@ limitations under the License.
#include "Indices.h" // For X_AXIS, etc
#include "CommonMessages.h"
-// Declare the IMU data structure
-IMUDataStruct gIMU;
-
-// Version string
-//char userVersionString[] = "IMU 1.0.0";
-
-
@@ -332,9 +325,8 @@ BOOL HandleUserOutputPacket(uint8_t *payload, uint8_t *payloadLen)
pld->c = 'A';
pld->s = 1234;
pld->i = -5;
- if(platformGetPpsFlag()){
+ if(platformGetPpsFlag(FALSE)){
ppsTstamp = platformGetPpsTimeStamp();
- platformSetPpsFlag(FALSE);
}
// pld->ll = platformGetDacqTimeStamp(); // in microseconds;
pld->ll = ppsTstamp; // time stamp of last PPS edge in microseconds from system start
diff --git a/examples/OpenIMU300RI/VG_AHRS/src/user/UserMessagingUART.h b/examples/OpenIMU300RI/VG_AHRS/src/user/UserMessagingUART.h
index 7d96e1c..61a0c19 100644
--- a/examples/OpenIMU300RI/VG_AHRS/src/user/UserMessagingUART.h
+++ b/examples/OpenIMU300RI/VG_AHRS/src/user/UserMessagingUART.h
@@ -151,5 +151,6 @@ extern BOOL UpdateAllUserParams(allUserParamsPayload* pld, uint8_t *payloa
extern BOOL GetUserConfig(userConfigPayload* pld, uint8_t *payloadLen);
extern BOOL GetUserParam(userParamPayload* pld, uint8_t *payloadLen);
extern BOOL GetAllUserParams(allUserParamsPayload* pld, uint8_t *payloadLen);
+extern void UserInitConfigureUart();
#endif /* USER_CONFIGURATION_H */
diff --git a/examples/OpenIMU300RI/VG_AHRS/src/user/dataProcessingAndPresentation.c b/examples/OpenIMU300RI/VG_AHRS/src/user/dataProcessingAndPresentation.c
index 1e97a1e..a467230 100644
--- a/examples/OpenIMU300RI/VG_AHRS/src/user/dataProcessingAndPresentation.c
+++ b/examples/OpenIMU300RI/VG_AHRS/src/user/dataProcessingAndPresentation.c
@@ -24,16 +24,26 @@ See the License for the specific language governing permissions and
limitations under the License.
*******************************************************************************/
+#include "BITStatus.h"
+
#include "userAPI.h"
#include "sensorsAPI.h"
#include "gpsAPI.h"
-#include "UserMessagingCAN.h"
+#include "UserAlgorithm.h"
+#include "algorithm.h"
+#include "algorithmAPI.h"
+#include "platformAPI.h"
#include "Indices.h" // For X_AXIS and Z_AXIS
#include "debug.h" // For debug commands
-// Declare the IMU data structure
-IMUDataStruct gIMU;
+BOOL fAlgorithmSynced;
+
+// Local-function prototypes
+static void _IncrementIMUTimer(uint16_t dacqRate);
+static void _GenerateDebugMessage(uint16_t dacqRate, uint16_t debugOutputFreq);
+static void _IMUDebugMessage(void);
+//static void _GPSDebugMessage(void);
/* *
******************
@@ -58,6 +68,8 @@ Data * Built-in * Raw Data * * Data * User Filter s* * Al
void initUserDataProcessingEngine()
{
InitUserAlgorithm(); // default implementation located in file user_algorithm.c
+// init PPS sync engine
+ platformEnableGpsPps(TRUE);
}
@@ -67,71 +79,219 @@ void initUserDataProcessingEngine()
// 2) 'DataAcquisitionTask' calls this function after retrieving samples of current
// sensors data and applying corresponding calibration
// 3) 'dacqRate' is rate with which new set of sensors data arrives
-int algorithmInitFlag = 0;
-
void inertialAndPositionDataProcessing(uint16_t dacqRate)
{
+ //
+ void *results;
- // Initialization variable
- static int initFlag = 1;
+ // Increment the IMU timer by the calling rate of the data-acquisition task
+ _IncrementIMUTimer(dacqRate);
- // Variables that control the output frequency of the debug statement
- static int debugFlag = 0;
- static uint8_t debugOutputCntr, debugOutputCntrLimit;
+ static uint8_t initAlgo = 1;
+ static uint8_t algoCntr = 0, algoCntrLimit = 0;
+ static BOOL firstTimeSync = TRUE;
+
+ if (initAlgo)
+ {
+ // Reset 'initAlgo' so this is not executed more than once. This
+ // prevents the algorithm from being switched during run-time.
+ initAlgo = 0;
+
+ // Set the variables that control the algorithm execution rate
+ algoCntrLimit = (uint8_t)((float)dacqRate / (float)gAlgorithm.callingFreq + 0.5);
+ if (algoCntrLimit < 1)
+ {
+ // If this logic is reached, also need to adjust the algorithm
+ // parameters to match the modified calling freq (or stop the
+ // program to indicate that the user must adjust the program)
+ algoCntrLimit = 1;
+ }
+ algoCntr = algoCntrLimit;
+ }
+
+ // call the algorithm
+ algoCntr++;
+ // syn the calling of the algorithm with PPS. This is done only once.
+ if(firstTimeSync)
+ {
+ if (platformGetPpsFlag(FALSE)) // do not reset pps detection state
+ {
+ firstTimeSync = FALSE;
+ fAlgorithmSynced = TRUE;
+ algoCntr = algoCntrLimit;
+ }
+ }
+ if (algoCntr >= algoCntrLimit)
+ {
+ // Reset counter
+ algoCntr = 0;
- if(algorithmInitFlag){
- InitUserAlgorithm(); // default implementation located in file user_algorithm.c
+ // Obtain accelerometer data [g]
+ GetAccelData_g(gIMU.accel_g);
+
+ // Obtain rate-sensor data [rad/sec]
+ GetRateData_radPerSec(gIMU.rate_radPerSec);
+ GetRateData_degPerSec(gIMU.rate_degPerSec);
+
+ // Obtain magnetometer data [G]
+ GetMagData_G(gIMU.mag_G);
+
+ // Obtain board temperature data [degC]
+ GetBoardTempData(&gIMU.temp_C);
+
+ // Obtain GPS data (lat/lon: deg, alt: meters, vel: m/s, ITOW: msec, )
+#ifdef GPS
+ GetGPSData(&gGPS);
+#endif
+
+ // check if pps is detected right before this excution of the task.
+ BOOL ppsDetected = platformGetPpsFlag(TRUE);
+
+ // Execute user algorithm (default implementation located in file user_algorithm.c)
+ results = RunUserNavAlgorithm(gIMU.accel_g, gIMU.rate_radPerSec, gIMU.mag_G, &gGPS, &gOdo, ppsDetected);
+
+ // Get algorithm status, and set the state in system status
+ AlgoStatus algoStatus;
+ GetAlgoStatus(&algoStatus);
+ gBitStatus.swStatus.all = algoStatus.all;
+ gBitStatus.swAlgBIT.bit.initialization = algoStatus.bit.algorithmInit;
+
+ // add current result to output queue for subsequent sending out as continuous packet // returns pointer to user-defined results structure
+ WriteResultsIntoOutputStream(results); // default implementation located in file file UserMessaging.c
}
+ // Generate a debug message that provide sensor data in order to verify the
+ // algorithm input data is as expected.
+ _GenerateDebugMessage(dacqRate, ZERO_HZ);
+}
+
+
+//
+static void _IncrementIMUTimer(uint16_t dacqRate)
+{
// Initialize timer variables (used to control the output of the debug
// messages and the IMU timer value)
+ static int initFlag = 1;
if(initFlag) {
// Reset 'initFlag' so this section is not executed more than once.
initFlag = 0;
- // Set the variables that control the debug-message output-rate (based on
- // the desired calling frequency of the debug output)
- debugOutputCntr = 0;
-
- uint16_t debugOutputFreq = 4; // [Hz]
- debugOutputCntrLimit = dacqRate / debugOutputFreq;
-
// Set the IMU output delta-counter value
gIMU.dTimerCntr = (uint32_t)( 1000.0 / (float)(dacqRate) + 0.5 );
}
- // Increment the timer-counter by the sampling period equivalent to the rate at which
- // inertialAndPositionDataProcessing is called
+ // Increment the timer-counter by the sampling period equivalent to the
+ // rate at which inertialAndPositionDataProcessing is called
gIMU.timerCntr = gIMU.timerCntr + gIMU.dTimerCntr;
+}
- // Obtain accelerometer data [g]
- GetAccelData_g(gIMU.accel_g);
-
- // Obtain rate-sensor data [rad/sec]
- GetRateData_radPerSec(gIMU.rate_radPerSec);
+//
+static void _GenerateDebugMessage(uint16_t dacqRate, uint16_t debugOutputFreq)
+{
+ // Variables that control the output frequency of the debug statement
+ static uint8_t debugOutputCntr, debugOutputCntrLimit;
- // Obtain magnetometer data [G]
- GetMagData_G(gIMU.mag_G);
+ // Check debug flag. If set then generate the debug message to verify
+ // the loading of the GPS data into the GPS data structure
+ if( debugOutputFreq > ZERO_HZ ) {
+ // Initialize variables used to control the output of the debug messages
+ static int initFlag = 1;
+ if(initFlag) {
+ // Reset 'initFlag' so this section is not executed more than once.
+ initFlag = 0;
- // Obtain board temperature data [degC]
- GetBoardTempData(&gIMU.temp_C);
+ // Set the variables that control the debug-message output-rate (based on
+ // the desired calling frequency of the debug output)
+ debugOutputCntrLimit = (uint8_t)( (float)dacqRate / (float)debugOutputFreq + 0.5 );
+ debugOutputCntr = debugOutputCntrLimit;
+ }
- // Generate the debug output to test the loading of the sensor data
- // into the IMU data structure
- if( debugFlag ) {
debugOutputCntr++;
if(debugOutputCntr >= debugOutputCntrLimit) {
debugOutputCntr = 0;
- DebugPrintFloat("Time: ", 0.001 * (real)gIMU.timerCntr, 3);
- DebugPrintFloat(", AccelZ: ", gIMU.accel_g[Z_AXIS], 3);
- DebugPrintFloat(", RateZ: ", gIMU.rate_radPerSec[Z_AXIS] * RAD_TO_DEG, 3);
- DebugPrintFloat(", MagX: ", gIMU.mag_G[X_AXIS], 3);
- DebugPrintFloat(", Temp: ", gIMU.temp_C,2);
- DebugPrintEndline();
+
+ // Reset 'new GPS data' flag (this should be done in UpdateFunctions
+ // to ensure the EKF can use the data)
+ //gGPS.updateFlag = 0; <-- This would make a difference as the input
+ // to the algorithm isn't set yet.
+
+ // Create message here
+ static uint8_t msgType = 1;
+ switch( msgType )
+ {
+ case 0:
+ // None
+ break;
+
+ case 1:
+ // IMU data
+ _IMUDebugMessage();
+ break;
+
+#ifdef GPS
+ case 2:
+ // GPS data
+ _GPSDebugMessage();
+ break;
+#endif
}
}
+ }
+}
+
+
+static void _IMUDebugMessage(void)
+{
+ // IMU Data
+ DebugPrintFloat("Time: ", 0.001 * (real)gIMU.timerCntr, 3);
+ DebugPrintFloat(", a: [ ", (float)gIMU.accel_g[X_AXIS], 3);
+ DebugPrintFloat(" ", (float)gIMU.accel_g[Y_AXIS], 3);
+ DebugPrintFloat(" ", (float)gIMU.accel_g[Z_AXIS], 3);
+ DebugPrintFloat(" ], w: [ ", (float)gIMU.rate_radPerSec[X_AXIS] * RAD_TO_DEG, 3);
+ DebugPrintFloat(" ", (float)gIMU.rate_radPerSec[Y_AXIS] * RAD_TO_DEG, 3);
+ DebugPrintFloat(" ", (float)gIMU.rate_radPerSec[Z_AXIS] * RAD_TO_DEG, 3);
+ DebugPrintFloat(" ], m: [ ", (float)gIMU.mag_G[X_AXIS], 3);
+ DebugPrintFloat(" ", (float)gIMU.mag_G[Y_AXIS], 3);
+ DebugPrintFloat(" ", (float)gIMU.mag_G[Z_AXIS], 3);
+ DebugPrintString(" ]");
+ DebugPrintEndline();
+}
- // Execute user algorithm (default implementation located in file user_algorithm.c)
- RunUserNavAlgorithm(gIMU.accel_g, gIMU.rate_radPerSec, gIMU.mag_G, NULL, dacqRate);
+#ifdef GPS
+static void _GPSDebugMessage(void)
+{
+#if 1
+ // GPS Data
+ DebugPrintFloat("Time: ", 0.001 * (real)gIMU.timerCntr, 3);
+ DebugPrintFloat(", Lat: ", (float)gGPS.latitude, 8);
+ DebugPrintFloat(", Lon: ", (float)gGPS.longitude, 8);
+ DebugPrintFloat(", Alt: ", (float)gGPS.altitude, 5);
+ DebugPrintLongInt(", ITOW: ", gGPS.itow );
+ DebugPrintLongInt(", EstITOW: ", platformGetEstimatedITOW() );
+ DebugPrintLongInt(", SolutionTstamp: ", (uint64_t)platformGetSolutionTstampAsDouble());
+#else
+ //
+ DebugPrintFloat("Time: ", 0.001 * (real)gIMU.timerCntr, 3);
+ DebugPrintLongInt(", ITOW: ", gGPS.itow );
+
+ // LLA
+ DebugPrintFloat(", valid: ", (float)gGPS.gpsValid, 1);
+ // LLA
+ DebugPrintFloat(", Lat: ", (float)gGPS.latitude, 8);
+ DebugPrintFloat(", Lon: ", (float)gGPS.longitude, 8);
+ DebugPrintFloat(", Alt: ", (float)gGPS.altitude, 5);
+ // Velocity
+ //DebugPrintFloat(", vN: ", (float)gGPS.vNed[X_AXIS], 5);
+ //DebugPrintFloat(", vE: ", (float)gGPS.vNed[Y_AXIS], 5);
+ //DebugPrintFloat(", vD: ", (float)gGPS.vNed[Z_AXIS], 5);
+ // v^2
+ //double vSquared = gGPS.vNed[X_AXIS] * gGPS.vNed[X_AXIS] +
+ // gGPS.vNed[Y_AXIS] * gGPS.vNed[Y_AXIS];
+ //DebugPrintFloat(", vSq: ", (float)vSquared, 5);
+ //DebugPrintFloat(", vSq: ", (float)gGPS.rawGroundSpeed * (float)gGPS.rawGroundSpeed, 5);
+ // Newline
+#endif
+ DebugPrintEndline();
}
+#endif
diff --git a/examples/OpenIMU300RI/VG_AHRS/src/user/userAPI.h b/examples/OpenIMU300RI/VG_AHRS/src/user/userAPI.h
index 9ca2ff2..86ca868 100644
--- a/examples/OpenIMU300RI/VG_AHRS/src/user/userAPI.h
+++ b/examples/OpenIMU300RI/VG_AHRS/src/user/userAPI.h
@@ -41,30 +41,17 @@ limitations under the License.
#include
#include "gpsAPI.h"
+#include "odoAPI.h"
void inertialAndPositionDataProcessing(uint16_t dacqRate);
-void *RunUserNavAlgorithm(double *accels, double *rates, double* mags, gpsDataStruct_t *gps, uint16_t dacqRate);
+void *RunUserNavAlgorithm(double *accels, double *rates, double *mags,
+ gpsDataStruct_t *gps, odoDataStruct_t *odo, BOOL ppsDetected);
void WriteResultsIntoOutputStream(void *results) ;
void InitUserDataStructures();
void InitUserFilters();
void InitUserAlgorithm();
void initUserDataProcessingEngine();
void userInitConfigureUnit();
-void userInitConfigureUart();
-// IMU data structure
-typedef struct {
- // Timer output counter
- uint32_t timerCntr, dTimerCntr;
-
- // Algorithm states
- double accel_g[3];
- double rate_radPerSec[3];
- double rate_degPerSec[3];
- double mag_G[3];
- double temp_C;
-} IMUDataStruct;
-
-extern IMUDataStruct gIMU;
#endif
diff --git a/examples/OpenIMU300ZI/INS/platformio.ini b/examples/OpenIMU300ZI/INS/platformio.ini
index bf18776..4271e75 100644
--- a/examples/OpenIMU300ZI/INS/platformio.ini
+++ b/examples/OpenIMU300ZI/INS/platformio.ini
@@ -19,7 +19,7 @@ description =
[env:OpenIMU300ZI]
platform = aceinna_imu
lib_archive = false
-board = openIMU300
+board = OpenIMU300
;lib_deps= ../../OpenIMU300-lib
lib_deps = OpenIMU300-base-library@1.0.9
build_flags =
diff --git a/platform.json b/platform.json
index d6b89e8..92d1e75 100644
--- a/platform.json
+++ b/platform.json
@@ -13,7 +13,7 @@
"type": "git",
"url": "https://github.com/aceinna/platform-aceinna_imu.git"
},
- "version": "1.2.6",
+ "version": "1.2.7",
"packageRepositories": [
"https://dl.bintray.com/platformio/dl-packages/manifest.json",
"http://dl.platformio.org/packages/manifest.json"