LX4Cnh (LodgeX4CorrNoHigh) algorithm of the high-speed multiplication of large numbers.[0]
Copyright (c) 2021 Denis Kuzmin <x-3F@outlook.com> github/3F
| Algorithm | Maximum bits | One multiplication |
|---|---|---|
| LX4Cnh | 128+ × 128+ | less than ~ 4.3 ns == 0.0000000043 sec |
| MLnoCS | 128+ × 16 (*132) | less than ~ 0.31 ns == 0.00000000031 sec |
| LX4Cnh optimized*2 | 128+ × 128+ | *2 less than ~ 0.86 ns == 0.00000000086 sec |
- *1 - theoretically up to 128 x 32 with some correction.
- *2 - The actual calculation using LX4Cnh can be a bit optimized such for FNV1a-128 implementation (find it in my repo):
(1 ns == 0.000000001 sec)
-
Huid - A high-speed FNV-1a-128 hash-based UUID implementation.
-
Fnv1a128 - Non-cryptographic hash function. FNV-1a. 「 128-bit 」 implementation.
✔ Free and Open. MIT License. Fork! Star! Contribute! Share! Enjoy!
LX4Cnh class provides several ways of setting and getting numbers by using uint, ulong, or bytes array. Just play with available Unit-Tests and Speed-Tests.
For example, using ulong (UInt64)
// 0x4BD4823ECC5D03EB19E07DB8FFD5DABE
// × 0x1D05906000069ABC40A30C07A70906D1
ulong high = LX4Cnh.Multiply
(
0x4BD4823ECC5D03EB, 0x19E07DB8FFD5DABE,
0x1D05906000069ABC, 0x40A30C07A70906D1,
out ulong low
);
// high low
// ________________|_______________
// = 0xACBBE8EAB60C77E249B25D708366091ETo reduce the amount of unnecessary stack manipulations (ldloca.s/ldarg.. etc), meet an embeddable version.
// 0xC1F4271980F30FED81EF70CCBC6EF2EF
// × 0xDEF03F0142D0ACD21749BEF1EA30FF94
uint a = 0xC1F42719, b = 0x80F30FED, c = 0x81EF70CC, d = 0xBC6EF2EF;
uint ma = 0xDEF03F01, mb = 0x42D0ACD2, mc = 0x1749BEF1, md = 0xEA30FF94;
//-
ulong high, low;
unchecked{/*LX4Cnh for C# [1.1.0] (c) Denis Kuzmin <[email protected]> github/3F */ulong A=(ulong)b*mb;ulong B=A&0xFFFF_FFFF;ulong C=((A>>32)+B+(a*ma))&0xFFFF_FFFF;ulong D=(a>b)?a-b:b-a;ulong E=(ma>mb)?ma-mb:mb-ma;if(D!=0&&E!=0){ulong F=D*E;if(((a<b)&&(ma>mb))||((a>b)&&(ma<mb))){C+=F&0xFFFF_FFFF;}else{C-=F&0xFFFF_FFFF;}}ulong G=(C<<32)+B;A=(ulong)c*mc;ulong H=(ulong)d*md;B=(H>>32)+(H&0xFFF_FFFF_FFFF_FFFF)+(A&0xFFF_FFFF_FFFF_FFFF)+((A&0xFFF_FFFF)<<32);C=(((A>>28)+(A>>60)+(H>>60))<<28);ulong I=B;D=(c>d)?c-d:d-c;E=(mc>md)?mc-md:md-mc;if(D!=0&&E!=0){ulong F=D*E;if(((c<d)&&(mc>md))||((c>d)&&(mc<md))){I+=F;if(B>I)C+=0x100000000;}else{I-=F;if(B<I)C-=0x100000000;}}ulong J=((I&0xFFFF_FFFF)<<32)+(H&0xFFFF_FFFF);C=G+J+C+(I>>32);G=((ulong)a<<32)+b;I=((ulong)c<<32)+d;A=((ulong)ma<<32)+mb;H=((ulong)mc<<32)+md;D=(G>I)?G-I:I-G;E=(A>H)?A-H:H-A;if(D!=0&&E!=0){ulong F=D*E;if(((G<I)&&(A>H))||((G>I)&&(A<H))){C+=F;}else{C-=F;}}low=J;high=C;}
// high low
// ________________|_______________
// = 0x9633C106748CB7D96650F9EA76F0832C