diff --git a/core/math/math_funcs.cpp b/core/math/math_funcs.cpp index 0d5b0faa9d18..a07d8f70d9d1 100644 --- a/core/math/math_funcs.cpp +++ b/core/math/math_funcs.cpp @@ -31,18 +31,19 @@ #include "math_funcs.h" #include "core/error/error_macros.h" +#include "core/math/random_pcg.h" -RandomPCG Math::default_rand(RandomPCG::DEFAULT_SEED, RandomPCG::DEFAULT_INC); +static RandomPCG default_rand(RandomPCG::DEFAULT_SEED, RandomPCG::DEFAULT_INC); -uint32_t Math::rand_from_seed(uint64_t *seed) { - RandomPCG rng = RandomPCG(*seed, RandomPCG::DEFAULT_INC); +uint32_t Math::rand_from_seed(uint64_t *p_seed) { + RandomPCG rng = RandomPCG(*p_seed, RandomPCG::DEFAULT_INC); uint32_t r = rng.rand(); - *seed = rng.get_seed(); + *p_seed = rng.get_seed(); return r; } -void Math::seed(uint64_t x) { - default_rand.seed(x); +void Math::seed(uint64_t p_value) { + default_rand.seed(p_value); } void Math::randomize() { @@ -53,8 +54,8 @@ uint32_t Math::rand() { return default_rand.rand(); } -double Math::randfn(double mean, double deviation) { - return default_rand.randfn(mean, deviation); +double Math::randfn(double p_mean, double p_deviation) { + return default_rand.randfn(p_mean, p_deviation); } int Math::step_decimals(double p_step) { @@ -168,14 +169,14 @@ uint32_t Math::larger_prime(uint32_t p_val) { } } -double Math::random(double from, double to) { - return default_rand.random(from, to); +double Math::random(double p_from, double p_to) { + return default_rand.random(p_from, p_to); } -float Math::random(float from, float to) { - return default_rand.random(from, to); +float Math::random(float p_from, float p_to) { + return default_rand.random(p_from, p_to); } -int Math::random(int from, int to) { - return default_rand.random(from, to); +int Math::random(int p_from, int p_to) { + return default_rand.random(p_from, p_to); } diff --git a/core/math/math_funcs.h b/core/math/math_funcs.h index 3060f31970c3..d8a89fdd9b7e 100644 --- a/core/math/math_funcs.h +++ b/core/math/math_funcs.h @@ -33,719 +33,704 @@ #include "core/error/error_macros.h" #include "core/math/math_defs.h" -#include "core/math/random_pcg.h" #include "core/typedefs.h" -#include "thirdparty/misc/pcg.h" - #include #include -class Math { - static RandomPCG default_rand; - -public: - Math() {} // useless to instance - - // Not using 'RANDOM_MAX' to avoid conflict with system headers on some OSes (at least NetBSD). - static const uint64_t RANDOM_32BIT_MAX = 0xFFFFFFFF; +namespace Math { - static _ALWAYS_INLINE_ double sin(double p_x) { return ::sin(p_x); } - static _ALWAYS_INLINE_ float sin(float p_x) { return ::sinf(p_x); } +_ALWAYS_INLINE_ double sin(double p_x) { return ::sin(p_x); } +_ALWAYS_INLINE_ float sin(float p_x) { return ::sinf(p_x); } - static _ALWAYS_INLINE_ double cos(double p_x) { return ::cos(p_x); } - static _ALWAYS_INLINE_ float cos(float p_x) { return ::cosf(p_x); } +_ALWAYS_INLINE_ double cos(double p_x) { return ::cos(p_x); } +_ALWAYS_INLINE_ float cos(float p_x) { return ::cosf(p_x); } - static _ALWAYS_INLINE_ double tan(double p_x) { return ::tan(p_x); } - static _ALWAYS_INLINE_ float tan(float p_x) { return ::tanf(p_x); } +_ALWAYS_INLINE_ double tan(double p_x) { return ::tan(p_x); } +_ALWAYS_INLINE_ float tan(float p_x) { return ::tanf(p_x); } - static _ALWAYS_INLINE_ double sinh(double p_x) { return ::sinh(p_x); } - static _ALWAYS_INLINE_ float sinh(float p_x) { return ::sinhf(p_x); } +_ALWAYS_INLINE_ double sinh(double p_x) { return ::sinh(p_x); } +_ALWAYS_INLINE_ float sinh(float p_x) { return ::sinhf(p_x); } - static _ALWAYS_INLINE_ float sinc(float p_x) { return p_x == 0 ? 1 : ::sin(p_x) / p_x; } - static _ALWAYS_INLINE_ double sinc(double p_x) { return p_x == 0 ? 1 : ::sin(p_x) / p_x; } +_ALWAYS_INLINE_ double sinc(double p_x) { return p_x == 0 ? 1 : sin(p_x) / p_x; } +_ALWAYS_INLINE_ float sinc(float p_x) { return p_x == 0 ? 1 : sin(p_x) / p_x; } - static _ALWAYS_INLINE_ float sincn(float p_x) { return sinc((float)Math_PI * p_x); } - static _ALWAYS_INLINE_ double sincn(double p_x) { return sinc(Math_PI * p_x); } +_ALWAYS_INLINE_ double sincn(double p_x) { return sinc(Math_PI * p_x); } +_ALWAYS_INLINE_ float sincn(float p_x) { return sinc((float)Math_PI * p_x); } - static _ALWAYS_INLINE_ double cosh(double p_x) { return ::cosh(p_x); } - static _ALWAYS_INLINE_ float cosh(float p_x) { return ::coshf(p_x); } +_ALWAYS_INLINE_ double cosh(double p_x) { return ::cosh(p_x); } +_ALWAYS_INLINE_ float cosh(float p_x) { return ::coshf(p_x); } - static _ALWAYS_INLINE_ double tanh(double p_x) { return ::tanh(p_x); } - static _ALWAYS_INLINE_ float tanh(float p_x) { return ::tanhf(p_x); } +_ALWAYS_INLINE_ double tanh(double p_x) { return ::tanh(p_x); } +_ALWAYS_INLINE_ float tanh(float p_x) { return ::tanhf(p_x); } - // Always does clamping so always safe to use. - static _ALWAYS_INLINE_ double asin(double p_x) { return p_x < -1 ? (-Math_PI / 2) : (p_x > 1 ? (Math_PI / 2) : ::asin(p_x)); } - static _ALWAYS_INLINE_ float asin(float p_x) { return p_x < -1 ? (-Math_PI / 2) : (p_x > 1 ? (Math_PI / 2) : ::asinf(p_x)); } +// Always does clamping so always safe to use. +_ALWAYS_INLINE_ double asin(double p_x) { return p_x < -1 ? (-Math_PI / 2) : (p_x > 1 ? (Math_PI / 2) : ::asin(p_x)); } +_ALWAYS_INLINE_ float asin(float p_x) { return p_x < -1 ? (-Math_PI / 2) : (p_x > 1 ? (Math_PI / 2) : ::asinf(p_x)); } - // Always does clamping so always safe to use. - static _ALWAYS_INLINE_ double acos(double p_x) { return p_x < -1 ? Math_PI : (p_x > 1 ? 0 : ::acos(p_x)); } - static _ALWAYS_INLINE_ float acos(float p_x) { return p_x < -1 ? Math_PI : (p_x > 1 ? 0 : ::acosf(p_x)); } +// Always does clamping so always safe to use. +_ALWAYS_INLINE_ double acos(double p_x) { return p_x < -1 ? Math_PI : (p_x > 1 ? 0 : ::acos(p_x)); } +_ALWAYS_INLINE_ float acos(float p_x) { return p_x < -1 ? Math_PI : (p_x > 1 ? 0 : ::acosf(p_x)); } - static _ALWAYS_INLINE_ double atan(double p_x) { return ::atan(p_x); } - static _ALWAYS_INLINE_ float atan(float p_x) { return ::atanf(p_x); } +_ALWAYS_INLINE_ double atan(double p_x) { return ::atan(p_x); } +_ALWAYS_INLINE_ float atan(float p_x) { return ::atanf(p_x); } - static _ALWAYS_INLINE_ double atan2(double p_y, double p_x) { return ::atan2(p_y, p_x); } - static _ALWAYS_INLINE_ float atan2(float p_y, float p_x) { return ::atan2f(p_y, p_x); } +_ALWAYS_INLINE_ double atan2(double p_y, double p_x) { return ::atan2(p_y, p_x); } +_ALWAYS_INLINE_ float atan2(float p_y, float p_x) { return ::atan2f(p_y, p_x); } - static _ALWAYS_INLINE_ double asinh(double p_x) { return ::asinh(p_x); } - static _ALWAYS_INLINE_ float asinh(float p_x) { return ::asinhf(p_x); } +_ALWAYS_INLINE_ double asinh(double p_x) { return ::asinh(p_x); } +_ALWAYS_INLINE_ float asinh(float p_x) { return ::asinhf(p_x); } - // Always does clamping so always safe to use. - static _ALWAYS_INLINE_ double acosh(double p_x) { return p_x < 1 ? 0 : ::acosh(p_x); } - static _ALWAYS_INLINE_ float acosh(float p_x) { return p_x < 1 ? 0 : ::acoshf(p_x); } +// Always does clamping so always safe to use. +_ALWAYS_INLINE_ double acosh(double p_x) { return p_x < 1 ? 0 : ::acosh(p_x); } +_ALWAYS_INLINE_ float acosh(float p_x) { return p_x < 1 ? 0 : ::acoshf(p_x); } - // Always does clamping so always safe to use. - static _ALWAYS_INLINE_ double atanh(double p_x) { return p_x <= -1 ? -INFINITY : (p_x >= 1 ? INFINITY : ::atanh(p_x)); } - static _ALWAYS_INLINE_ float atanh(float p_x) { return p_x <= -1 ? -INFINITY : (p_x >= 1 ? INFINITY : ::atanhf(p_x)); } +// Always does clamping so always safe to use. +_ALWAYS_INLINE_ double atanh(double p_x) { return p_x <= -1 ? -INFINITY : (p_x >= 1 ? INFINITY : ::atanh(p_x)); } +_ALWAYS_INLINE_ float atanh(float p_x) { return p_x <= -1 ? -INFINITY : (p_x >= 1 ? INFINITY : ::atanhf(p_x)); } - static _ALWAYS_INLINE_ double sqrt(double p_x) { return ::sqrt(p_x); } - static _ALWAYS_INLINE_ float sqrt(float p_x) { return ::sqrtf(p_x); } +_ALWAYS_INLINE_ double sqrt(double p_x) { return ::sqrt(p_x); } +_ALWAYS_INLINE_ float sqrt(float p_x) { return ::sqrtf(p_x); } - static _ALWAYS_INLINE_ double fmod(double p_x, double p_y) { return ::fmod(p_x, p_y); } - static _ALWAYS_INLINE_ float fmod(float p_x, float p_y) { return ::fmodf(p_x, p_y); } +_ALWAYS_INLINE_ double fmod(double p_x, double p_y) { return ::fmod(p_x, p_y); } +_ALWAYS_INLINE_ float fmod(float p_x, float p_y) { return ::fmodf(p_x, p_y); } - static _ALWAYS_INLINE_ double floor(double p_x) { return ::floor(p_x); } - static _ALWAYS_INLINE_ float floor(float p_x) { return ::floorf(p_x); } +_ALWAYS_INLINE_ double floor(double p_x) { return ::floor(p_x); } +_ALWAYS_INLINE_ float floor(float p_x) { return ::floorf(p_x); } - static _ALWAYS_INLINE_ double ceil(double p_x) { return ::ceil(p_x); } - static _ALWAYS_INLINE_ float ceil(float p_x) { return ::ceilf(p_x); } +_ALWAYS_INLINE_ double ceil(double p_x) { return ::ceil(p_x); } +_ALWAYS_INLINE_ float ceil(float p_x) { return ::ceilf(p_x); } - static _ALWAYS_INLINE_ double pow(double p_x, double p_y) { return ::pow(p_x, p_y); } - static _ALWAYS_INLINE_ float pow(float p_x, float p_y) { return ::powf(p_x, p_y); } +_ALWAYS_INLINE_ double pow(double p_x, double p_y) { return ::pow(p_x, p_y); } +_ALWAYS_INLINE_ float pow(float p_x, float p_y) { return ::powf(p_x, p_y); } - static _ALWAYS_INLINE_ double log(double p_x) { return ::log(p_x); } - static _ALWAYS_INLINE_ float log(float p_x) { return ::logf(p_x); } +_ALWAYS_INLINE_ double log(double p_x) { return ::log(p_x); } +_ALWAYS_INLINE_ float log(float p_x) { return ::logf(p_x); } - static _ALWAYS_INLINE_ double log1p(double p_x) { return ::log1p(p_x); } - static _ALWAYS_INLINE_ float log1p(float p_x) { return ::log1pf(p_x); } +_ALWAYS_INLINE_ double log1p(double p_x) { return ::log1p(p_x); } +_ALWAYS_INLINE_ float log1p(float p_x) { return ::log1pf(p_x); } - static _ALWAYS_INLINE_ double log2(double p_x) { return ::log2(p_x); } - static _ALWAYS_INLINE_ float log2(float p_x) { return ::log2f(p_x); } +_ALWAYS_INLINE_ double log2(double p_x) { return ::log2(p_x); } +_ALWAYS_INLINE_ float log2(float p_x) { return ::log2f(p_x); } - static _ALWAYS_INLINE_ double exp(double p_x) { return ::exp(p_x); } - static _ALWAYS_INLINE_ float exp(float p_x) { return ::expf(p_x); } +_ALWAYS_INLINE_ double exp(double p_x) { return ::exp(p_x); } +_ALWAYS_INLINE_ float exp(float p_x) { return ::expf(p_x); } - static _ALWAYS_INLINE_ bool is_nan(double p_val) { +_ALWAYS_INLINE_ bool is_nan(double p_val) { #ifdef _MSC_VER - return _isnan(p_val); + return _isnan(p_val); #elif defined(__GNUC__) && __GNUC__ < 6 - union { - uint64_t u; - double f; - } ieee754; - ieee754.f = p_val; - // (unsigned)(0x7ff0000000000001 >> 32) : 0x7ff00000 - return ((((unsigned)(ieee754.u >> 32) & 0x7fffffff) + ((unsigned)ieee754.u != 0)) > 0x7ff00000); + union { + uint64_t u; + double f; + } ieee754; + ieee754.f = p_val; + // (unsigned)(0x7ff0000000000001 >> 32) : 0x7ff00000 + return ((((unsigned)(ieee754.u >> 32) & 0x7fffffff) + ((unsigned)ieee754.u != 0)) > 0x7ff00000); #else - return isnan(p_val); + return isnan(p_val); #endif - } +} - static _ALWAYS_INLINE_ bool is_nan(float p_val) { +_ALWAYS_INLINE_ bool is_nan(float p_val) { #ifdef _MSC_VER - return _isnan(p_val); + return _isnan(p_val); #elif defined(__GNUC__) && __GNUC__ < 6 - union { - uint32_t u; - float f; - } ieee754; - ieee754.f = p_val; - // ----------------------------------- - // (single-precision floating-point) - // NaN : s111 1111 1xxx xxxx xxxx xxxx xxxx xxxx - // : (> 0x7f800000) - // where, - // s : sign - // x : non-zero number - // ----------------------------------- - return ((ieee754.u & 0x7fffffff) > 0x7f800000); + union { + uint32_t u; + float f; + } ieee754; + ieee754.f = p_val; + // ----------------------------------- + // (single-precision floating-point) + // NaN : s111 1111 1xxx xxxx xxxx xxxx xxxx xxxx + // : (> 0x7f800000) + // where, + // s : sign + // x : non-zero number + // ----------------------------------- + return ((ieee754.u & 0x7fffffff) > 0x7f800000); #else - return isnan(p_val); + return isnan(p_val); #endif - } +} - static _ALWAYS_INLINE_ bool is_inf(double p_val) { +_ALWAYS_INLINE_ bool is_inf(double p_val) { #ifdef _MSC_VER - return !_finite(p_val); + return !_finite(p_val); // use an inline implementation of isinf as a workaround for problematic libstdc++ versions from gcc 5.x era #elif defined(__GNUC__) && __GNUC__ < 6 - union { - uint64_t u; - double f; - } ieee754; - ieee754.f = p_val; - return ((unsigned)(ieee754.u >> 32) & 0x7fffffff) == 0x7ff00000 && - ((unsigned)ieee754.u == 0); + union { + uint64_t u; + double f; + } ieee754; + ieee754.f = p_val; + return ((unsigned)(ieee754.u >> 32) & 0x7fffffff) == 0x7ff00000 && + ((unsigned)ieee754.u == 0); #else - return isinf(p_val); + return isinf(p_val); #endif - } +} - static _ALWAYS_INLINE_ bool is_inf(float p_val) { +_ALWAYS_INLINE_ bool is_inf(float p_val) { #ifdef _MSC_VER - return !_finite(p_val); + return !_finite(p_val); // use an inline implementation of isinf as a workaround for problematic libstdc++ versions from gcc 5.x era #elif defined(__GNUC__) && __GNUC__ < 6 - union { - uint32_t u; - float f; - } ieee754; - ieee754.f = p_val; - return (ieee754.u & 0x7fffffff) == 0x7f800000; + union { + uint32_t u; + float f; + } ieee754; + ieee754.f = p_val; + return (ieee754.u & 0x7fffffff) == 0x7f800000; #else - return isinf(p_val); + return isinf(p_val); #endif - } - - // These methods assume (p_num + p_den) doesn't overflow. - static _ALWAYS_INLINE_ int32_t division_round_up(int32_t p_num, int32_t p_den) { - int32_t offset = (p_num < 0 && p_den < 0) ? 1 : -1; - return (p_num + p_den + offset) / p_den; - } - static _ALWAYS_INLINE_ uint32_t division_round_up(uint32_t p_num, uint32_t p_den) { - return (p_num + p_den - 1) / p_den; - } - static _ALWAYS_INLINE_ int64_t division_round_up(int64_t p_num, int64_t p_den) { - int32_t offset = (p_num < 0 && p_den < 0) ? 1 : -1; - return (p_num + p_den + offset) / p_den; - } - static _ALWAYS_INLINE_ uint64_t division_round_up(uint64_t p_num, uint64_t p_den) { - return (p_num + p_den - 1) / p_den; - } - - static _ALWAYS_INLINE_ bool is_finite(double p_val) { return isfinite(p_val); } - static _ALWAYS_INLINE_ bool is_finite(float p_val) { return isfinite(p_val); } - - static _ALWAYS_INLINE_ double abs(double g) { return absd(g); } - static _ALWAYS_INLINE_ float abs(float g) { return absf(g); } - static _ALWAYS_INLINE_ int abs(int g) { return g > 0 ? g : -g; } - - static _ALWAYS_INLINE_ double fposmod(double p_x, double p_y) { - double value = Math::fmod(p_x, p_y); - if (((value < 0) && (p_y > 0)) || ((value > 0) && (p_y < 0))) { - value += p_y; - } - value += 0.0; - return value; - } - static _ALWAYS_INLINE_ float fposmod(float p_x, float p_y) { - float value = Math::fmod(p_x, p_y); - if (((value < 0) && (p_y > 0)) || ((value > 0) && (p_y < 0))) { - value += p_y; - } - value += 0.0f; - return value; - } - static _ALWAYS_INLINE_ float fposmodp(float p_x, float p_y) { - float value = Math::fmod(p_x, p_y); - if (value < 0) { - value += p_y; - } - value += 0.0f; - return value; - } - static _ALWAYS_INLINE_ double fposmodp(double p_x, double p_y) { - double value = Math::fmod(p_x, p_y); - if (value < 0) { - value += p_y; - } - value += 0.0; - return value; - } - - static _ALWAYS_INLINE_ int64_t posmod(int64_t p_x, int64_t p_y) { - ERR_FAIL_COND_V_MSG(p_y == 0, 0, "Division by zero in posmod is undefined. Returning 0 as fallback."); - int64_t value = p_x % p_y; - if (((value < 0) && (p_y > 0)) || ((value > 0) && (p_y < 0))) { - value += p_y; - } - return value; - } - - static _ALWAYS_INLINE_ double deg_to_rad(double p_y) { return p_y * (Math_PI / 180.0); } - static _ALWAYS_INLINE_ float deg_to_rad(float p_y) { return p_y * (float)(Math_PI / 180.0); } - - static _ALWAYS_INLINE_ double rad_to_deg(double p_y) { return p_y * (180.0 / Math_PI); } - static _ALWAYS_INLINE_ float rad_to_deg(float p_y) { return p_y * (float)(180.0 / Math_PI); } - - static _ALWAYS_INLINE_ double lerp(double p_from, double p_to, double p_weight) { return p_from + (p_to - p_from) * p_weight; } - static _ALWAYS_INLINE_ float lerp(float p_from, float p_to, float p_weight) { return p_from + (p_to - p_from) * p_weight; } - - static _ALWAYS_INLINE_ double cubic_interpolate(double p_from, double p_to, double p_pre, double p_post, double p_weight) { - return 0.5 * - ((p_from * 2.0) + - (-p_pre + p_to) * p_weight + - (2.0 * p_pre - 5.0 * p_from + 4.0 * p_to - p_post) * (p_weight * p_weight) + - (-p_pre + 3.0 * p_from - 3.0 * p_to + p_post) * (p_weight * p_weight * p_weight)); - } - static _ALWAYS_INLINE_ float cubic_interpolate(float p_from, float p_to, float p_pre, float p_post, float p_weight) { - return 0.5f * - ((p_from * 2.0f) + - (-p_pre + p_to) * p_weight + - (2.0f * p_pre - 5.0f * p_from + 4.0f * p_to - p_post) * (p_weight * p_weight) + - (-p_pre + 3.0f * p_from - 3.0f * p_to + p_post) * (p_weight * p_weight * p_weight)); - } - - static _ALWAYS_INLINE_ double cubic_interpolate_angle(double p_from, double p_to, double p_pre, double p_post, double p_weight) { - double from_rot = fmod(p_from, Math_TAU); - - double pre_diff = fmod(p_pre - from_rot, Math_TAU); - double pre_rot = from_rot + fmod(2.0 * pre_diff, Math_TAU) - pre_diff; - - double to_diff = fmod(p_to - from_rot, Math_TAU); - double to_rot = from_rot + fmod(2.0 * to_diff, Math_TAU) - to_diff; - - double post_diff = fmod(p_post - to_rot, Math_TAU); - double post_rot = to_rot + fmod(2.0 * post_diff, Math_TAU) - post_diff; - - return cubic_interpolate(from_rot, to_rot, pre_rot, post_rot, p_weight); - } - - static _ALWAYS_INLINE_ float cubic_interpolate_angle(float p_from, float p_to, float p_pre, float p_post, float p_weight) { - float from_rot = fmod(p_from, (float)Math_TAU); - - float pre_diff = fmod(p_pre - from_rot, (float)Math_TAU); - float pre_rot = from_rot + fmod(2.0f * pre_diff, (float)Math_TAU) - pre_diff; - - float to_diff = fmod(p_to - from_rot, (float)Math_TAU); - float to_rot = from_rot + fmod(2.0f * to_diff, (float)Math_TAU) - to_diff; - - float post_diff = fmod(p_post - to_rot, (float)Math_TAU); - float post_rot = to_rot + fmod(2.0f * post_diff, (float)Math_TAU) - post_diff; - - return cubic_interpolate(from_rot, to_rot, pre_rot, post_rot, p_weight); - } - - static _ALWAYS_INLINE_ double cubic_interpolate_in_time(double p_from, double p_to, double p_pre, double p_post, double p_weight, - double p_to_t, double p_pre_t, double p_post_t) { - /* Barry-Goldman method */ - double t = Math::lerp(0.0, p_to_t, p_weight); - double a1 = Math::lerp(p_pre, p_from, p_pre_t == 0 ? 0.0 : (t - p_pre_t) / -p_pre_t); - double a2 = Math::lerp(p_from, p_to, p_to_t == 0 ? 0.5 : t / p_to_t); - double a3 = Math::lerp(p_to, p_post, p_post_t - p_to_t == 0 ? 1.0 : (t - p_to_t) / (p_post_t - p_to_t)); - double b1 = Math::lerp(a1, a2, p_to_t - p_pre_t == 0 ? 0.0 : (t - p_pre_t) / (p_to_t - p_pre_t)); - double b2 = Math::lerp(a2, a3, p_post_t == 0 ? 1.0 : t / p_post_t); - return Math::lerp(b1, b2, p_to_t == 0 ? 0.5 : t / p_to_t); - } - - static _ALWAYS_INLINE_ float cubic_interpolate_in_time(float p_from, float p_to, float p_pre, float p_post, float p_weight, - float p_to_t, float p_pre_t, float p_post_t) { - /* Barry-Goldman method */ - float t = Math::lerp(0.0f, p_to_t, p_weight); - float a1 = Math::lerp(p_pre, p_from, p_pre_t == 0 ? 0.0f : (t - p_pre_t) / -p_pre_t); - float a2 = Math::lerp(p_from, p_to, p_to_t == 0 ? 0.5f : t / p_to_t); - float a3 = Math::lerp(p_to, p_post, p_post_t - p_to_t == 0 ? 1.0f : (t - p_to_t) / (p_post_t - p_to_t)); - float b1 = Math::lerp(a1, a2, p_to_t - p_pre_t == 0 ? 0.0f : (t - p_pre_t) / (p_to_t - p_pre_t)); - float b2 = Math::lerp(a2, a3, p_post_t == 0 ? 1.0f : t / p_post_t); - return Math::lerp(b1, b2, p_to_t == 0 ? 0.5f : t / p_to_t); - } - - static _ALWAYS_INLINE_ double cubic_interpolate_angle_in_time(double p_from, double p_to, double p_pre, double p_post, double p_weight, - double p_to_t, double p_pre_t, double p_post_t) { - double from_rot = fmod(p_from, Math_TAU); - - double pre_diff = fmod(p_pre - from_rot, Math_TAU); - double pre_rot = from_rot + fmod(2.0 * pre_diff, Math_TAU) - pre_diff; - - double to_diff = fmod(p_to - from_rot, Math_TAU); - double to_rot = from_rot + fmod(2.0 * to_diff, Math_TAU) - to_diff; - - double post_diff = fmod(p_post - to_rot, Math_TAU); - double post_rot = to_rot + fmod(2.0 * post_diff, Math_TAU) - post_diff; - - return cubic_interpolate_in_time(from_rot, to_rot, pre_rot, post_rot, p_weight, p_to_t, p_pre_t, p_post_t); - } - - static _ALWAYS_INLINE_ float cubic_interpolate_angle_in_time(float p_from, float p_to, float p_pre, float p_post, float p_weight, - float p_to_t, float p_pre_t, float p_post_t) { - float from_rot = fmod(p_from, (float)Math_TAU); - - float pre_diff = fmod(p_pre - from_rot, (float)Math_TAU); - float pre_rot = from_rot + fmod(2.0f * pre_diff, (float)Math_TAU) - pre_diff; - - float to_diff = fmod(p_to - from_rot, (float)Math_TAU); - float to_rot = from_rot + fmod(2.0f * to_diff, (float)Math_TAU) - to_diff; - - float post_diff = fmod(p_post - to_rot, (float)Math_TAU); - float post_rot = to_rot + fmod(2.0f * post_diff, (float)Math_TAU) - post_diff; - - return cubic_interpolate_in_time(from_rot, to_rot, pre_rot, post_rot, p_weight, p_to_t, p_pre_t, p_post_t); - } - - static _ALWAYS_INLINE_ double bezier_interpolate(double p_start, double p_control_1, double p_control_2, double p_end, double p_t) { - /* Formula from Wikipedia article on Bezier curves. */ - double omt = (1.0 - p_t); - double omt2 = omt * omt; - double omt3 = omt2 * omt; - double t2 = p_t * p_t; - double t3 = t2 * p_t; - - return p_start * omt3 + p_control_1 * omt2 * p_t * 3.0 + p_control_2 * omt * t2 * 3.0 + p_end * t3; - } - - static _ALWAYS_INLINE_ float bezier_interpolate(float p_start, float p_control_1, float p_control_2, float p_end, float p_t) { - /* Formula from Wikipedia article on Bezier curves. */ - float omt = (1.0f - p_t); - float omt2 = omt * omt; - float omt3 = omt2 * omt; - float t2 = p_t * p_t; - float t3 = t2 * p_t; - - return p_start * omt3 + p_control_1 * omt2 * p_t * 3.0f + p_control_2 * omt * t2 * 3.0f + p_end * t3; - } - - static _ALWAYS_INLINE_ double bezier_derivative(double p_start, double p_control_1, double p_control_2, double p_end, double p_t) { - /* Formula from Wikipedia article on Bezier curves. */ - double omt = (1.0 - p_t); - double omt2 = omt * omt; - double t2 = p_t * p_t; - - double d = (p_control_1 - p_start) * 3.0 * omt2 + (p_control_2 - p_control_1) * 6.0 * omt * p_t + (p_end - p_control_2) * 3.0 * t2; - return d; - } - - static _ALWAYS_INLINE_ float bezier_derivative(float p_start, float p_control_1, float p_control_2, float p_end, float p_t) { - /* Formula from Wikipedia article on Bezier curves. */ - float omt = (1.0f - p_t); - float omt2 = omt * omt; - float t2 = p_t * p_t; - - float d = (p_control_1 - p_start) * 3.0f * omt2 + (p_control_2 - p_control_1) * 6.0f * omt * p_t + (p_end - p_control_2) * 3.0f * t2; - return d; - } - - static _ALWAYS_INLINE_ double angle_difference(double p_from, double p_to) { - double difference = fmod(p_to - p_from, Math_TAU); - return fmod(2.0 * difference, Math_TAU) - difference; - } - static _ALWAYS_INLINE_ float angle_difference(float p_from, float p_to) { - float difference = fmod(p_to - p_from, (float)Math_TAU); - return fmod(2.0f * difference, (float)Math_TAU) - difference; - } - - static _ALWAYS_INLINE_ double lerp_angle(double p_from, double p_to, double p_weight) { - return p_from + Math::angle_difference(p_from, p_to) * p_weight; - } - static _ALWAYS_INLINE_ float lerp_angle(float p_from, float p_to, float p_weight) { - return p_from + Math::angle_difference(p_from, p_to) * p_weight; - } - - static _ALWAYS_INLINE_ double inverse_lerp(double p_from, double p_to, double p_value) { - return (p_value - p_from) / (p_to - p_from); - } - static _ALWAYS_INLINE_ float inverse_lerp(float p_from, float p_to, float p_value) { - return (p_value - p_from) / (p_to - p_from); - } - - static _ALWAYS_INLINE_ double remap(double p_value, double p_istart, double p_istop, double p_ostart, double p_ostop) { - return Math::lerp(p_ostart, p_ostop, Math::inverse_lerp(p_istart, p_istop, p_value)); - } - static _ALWAYS_INLINE_ float remap(float p_value, float p_istart, float p_istop, float p_ostart, float p_ostop) { - return Math::lerp(p_ostart, p_ostop, Math::inverse_lerp(p_istart, p_istop, p_value)); - } - - static _ALWAYS_INLINE_ double smoothstep(double p_from, double p_to, double p_s) { - if (is_equal_approx(p_from, p_to)) { - return p_from; - } - double s = CLAMP((p_s - p_from) / (p_to - p_from), 0.0, 1.0); - return s * s * (3.0 - 2.0 * s); - } - static _ALWAYS_INLINE_ float smoothstep(float p_from, float p_to, float p_s) { - if (is_equal_approx(p_from, p_to)) { - return p_from; - } - float s = CLAMP((p_s - p_from) / (p_to - p_from), 0.0f, 1.0f); - return s * s * (3.0f - 2.0f * s); - } - - static _ALWAYS_INLINE_ double move_toward(double p_from, double p_to, double p_delta) { - return abs(p_to - p_from) <= p_delta ? p_to : p_from + SIGN(p_to - p_from) * p_delta; - } - static _ALWAYS_INLINE_ float move_toward(float p_from, float p_to, float p_delta) { - return abs(p_to - p_from) <= p_delta ? p_to : p_from + SIGN(p_to - p_from) * p_delta; - } - - static _ALWAYS_INLINE_ double rotate_toward(double p_from, double p_to, double p_delta) { - double difference = Math::angle_difference(p_from, p_to); - double abs_difference = Math::abs(difference); - // When `p_delta < 0` move no further than to PI radians away from `p_to` (as PI is the max possible angle distance). - return p_from + CLAMP(p_delta, abs_difference - Math_PI, abs_difference) * (difference >= 0.0 ? 1.0 : -1.0); - } - static _ALWAYS_INLINE_ float rotate_toward(float p_from, float p_to, float p_delta) { - float difference = Math::angle_difference(p_from, p_to); - float abs_difference = Math::abs(difference); - // When `p_delta < 0` move no further than to PI radians away from `p_to` (as PI is the max possible angle distance). - return p_from + CLAMP(p_delta, abs_difference - (float)Math_PI, abs_difference) * (difference >= 0.0f ? 1.0f : -1.0f); - } - - static _ALWAYS_INLINE_ double linear_to_db(double p_linear) { - return Math::log(p_linear) * 8.6858896380650365530225783783321; - } - static _ALWAYS_INLINE_ float linear_to_db(float p_linear) { - return Math::log(p_linear) * (float)8.6858896380650365530225783783321; - } - - static _ALWAYS_INLINE_ double db_to_linear(double p_db) { - return Math::exp(p_db * 0.11512925464970228420089957273422); - } - static _ALWAYS_INLINE_ float db_to_linear(float p_db) { - return Math::exp(p_db * (float)0.11512925464970228420089957273422); - } - - static _ALWAYS_INLINE_ double round(double p_val) { return ::round(p_val); } - static _ALWAYS_INLINE_ float round(float p_val) { return ::roundf(p_val); } - - static _ALWAYS_INLINE_ int64_t wrapi(int64_t value, int64_t min, int64_t max) { - int64_t range = max - min; - return range == 0 ? min : min + ((((value - min) % range) + range) % range); - } - static _ALWAYS_INLINE_ double wrapf(double value, double min, double max) { - double range = max - min; - if (is_zero_approx(range)) { - return min; - } - double result = value - (range * Math::floor((value - min) / range)); - if (is_equal_approx(result, max)) { - return min; - } - return result; - } - static _ALWAYS_INLINE_ float wrapf(float value, float min, float max) { - float range = max - min; - if (is_zero_approx(range)) { - return min; - } - float result = value - (range * Math::floor((value - min) / range)); - if (is_equal_approx(result, max)) { - return min; - } - return result; - } - - static _ALWAYS_INLINE_ float fract(float value) { - return value - floor(value); - } - static _ALWAYS_INLINE_ double fract(double value) { - return value - floor(value); - } - static _ALWAYS_INLINE_ float pingpong(float value, float length) { - return (length != 0.0f) ? abs(fract((value - length) / (length * 2.0f)) * length * 2.0f - length) : 0.0f; - } - static _ALWAYS_INLINE_ double pingpong(double value, double length) { - return (length != 0.0) ? abs(fract((value - length) / (length * 2.0)) * length * 2.0 - length) : 0.0; - } - - // double only, as these functions are mainly used by the editor and not performance-critical, - static double ease(double p_x, double p_c); - static int step_decimals(double p_step); - static int range_step_decimals(double p_step); // For editor use only. - static double snapped(double p_value, double p_step); - - static uint32_t larger_prime(uint32_t p_val); - - static void seed(uint64_t x); - static void randomize(); - static uint32_t rand_from_seed(uint64_t *seed); - static uint32_t rand(); - static _ALWAYS_INLINE_ double randd() { return (double)rand() / (double)Math::RANDOM_32BIT_MAX; } - static _ALWAYS_INLINE_ float randf() { return (float)rand() / (float)Math::RANDOM_32BIT_MAX; } - static double randfn(double mean, double deviation); - - static double random(double from, double to); - static float random(float from, float to); - static int random(int from, int to); - - static _ALWAYS_INLINE_ bool is_equal_approx(float a, float b) { - // Check for exact equality first, required to handle "infinity" values. - if (a == b) { - return true; - } - // Then check for approximate equality. - float tolerance = (float)CMP_EPSILON * abs(a); - if (tolerance < (float)CMP_EPSILON) { - tolerance = (float)CMP_EPSILON; - } - return abs(a - b) < tolerance; - } - - static _ALWAYS_INLINE_ bool is_equal_approx(float a, float b, float tolerance) { - // Check for exact equality first, required to handle "infinity" values. - if (a == b) { - return true; - } - // Then check for approximate equality. - return abs(a - b) < tolerance; - } - - static _ALWAYS_INLINE_ bool is_zero_approx(float s) { - return abs(s) < (float)CMP_EPSILON; - } - - static _ALWAYS_INLINE_ bool is_equal_approx(double a, double b) { - // Check for exact equality first, required to handle "infinity" values. - if (a == b) { - return true; - } - // Then check for approximate equality. - double tolerance = CMP_EPSILON * abs(a); - if (tolerance < CMP_EPSILON) { - tolerance = CMP_EPSILON; - } - return abs(a - b) < tolerance; - } - - static _ALWAYS_INLINE_ bool is_equal_approx(double a, double b, double tolerance) { - // Check for exact equality first, required to handle "infinity" values. - if (a == b) { - return true; - } - // Then check for approximate equality. - return abs(a - b) < tolerance; - } - - static _ALWAYS_INLINE_ bool is_zero_approx(double s) { - return abs(s) < CMP_EPSILON; - } - - static _ALWAYS_INLINE_ float absf(float g) { - union { - float f; - uint32_t i; - } u; - - u.f = g; - u.i &= 2147483647u; - return u.f; - } - - static _ALWAYS_INLINE_ double absd(double g) { - union { - double d; - uint64_t i; - } u; - u.d = g; - u.i &= (uint64_t)9223372036854775807ll; - return u.d; - } - - // This function should be as fast as possible and rounding mode should not matter. - static _ALWAYS_INLINE_ int fast_ftoi(float a) { - // Assuming every supported compiler has `lrint()`. - return lrintf(a); - } - - static _ALWAYS_INLINE_ uint32_t halfbits_to_floatbits(uint16_t h) { - uint16_t h_exp, h_sig; - uint32_t f_sgn, f_exp, f_sig; - - h_exp = (h & 0x7c00u); - f_sgn = ((uint32_t)h & 0x8000u) << 16; - switch (h_exp) { - case 0x0000u: /* 0 or subnormal */ - h_sig = (h & 0x03ffu); - /* Signed zero */ - if (h_sig == 0) { - return f_sgn; - } - /* Subnormal */ +} + +// These methods assume (p_num + p_den) doesn't overflow. +_ALWAYS_INLINE_ int32_t division_round_up(int32_t p_num, int32_t p_den) { + int32_t offset = (p_num < 0 && p_den < 0) ? 1 : -1; + return (p_num + p_den + offset) / p_den; +} +_ALWAYS_INLINE_ uint32_t division_round_up(uint32_t p_num, uint32_t p_den) { + return (p_num + p_den - 1) / p_den; +} +_ALWAYS_INLINE_ int64_t division_round_up(int64_t p_num, int64_t p_den) { + int32_t offset = (p_num < 0 && p_den < 0) ? 1 : -1; + return (p_num + p_den + offset) / p_den; +} +_ALWAYS_INLINE_ uint64_t division_round_up(uint64_t p_num, uint64_t p_den) { + return (p_num + p_den - 1) / p_den; +} + +_ALWAYS_INLINE_ bool is_finite(double p_val) { return isfinite(p_val); } +_ALWAYS_INLINE_ bool is_finite(float p_val) { return isfinite(p_val); } + +_ALWAYS_INLINE_ double absd(double p_value) { + union { + double d; + uint64_t i; + } u; + u.d = p_value; + u.i &= (uint64_t)9223372036854775807ll; + return u.d; +} +_ALWAYS_INLINE_ float absf(float p_value) { + union { + float f; + uint32_t i; + } u; + u.f = p_value; + u.i &= 2147483647u; + return u.f; +} + +_ALWAYS_INLINE_ double abs(double p_value) { return absd(p_value); } +_ALWAYS_INLINE_ float abs(float p_value) { return absf(p_value); } +_ALWAYS_INLINE_ int abs(int p_value) { return p_value > 0 ? p_value : -p_value; } + +_ALWAYS_INLINE_ double fposmod(double p_x, double p_y) { + double value = fmod(p_x, p_y); + if (((value < 0) && (p_y > 0)) || ((value > 0) && (p_y < 0))) { + value += p_y; + } + value += 0.0; + return value; +} +_ALWAYS_INLINE_ float fposmod(float p_x, float p_y) { + float value = fmod(p_x, p_y); + if (((value < 0) && (p_y > 0)) || ((value > 0) && (p_y < 0))) { + value += p_y; + } + value += 0.0f; + return value; +} + +_ALWAYS_INLINE_ double fposmodp(double p_x, double p_y) { + double value = fmod(p_x, p_y); + if (value < 0) { + value += p_y; + } + value += 0.0; + return value; +} +_ALWAYS_INLINE_ float fposmodp(float p_x, float p_y) { + float value = fmod(p_x, p_y); + if (value < 0) { + value += p_y; + } + value += 0.0f; + return value; +} + +_ALWAYS_INLINE_ int64_t posmod(int64_t p_x, int64_t p_y) { + ERR_FAIL_COND_V_MSG(p_y == 0, 0, "Division by zero in posmod is undefined. Returning 0 as fallback."); + int64_t value = p_x % p_y; + if (((value < 0) && (p_y > 0)) || ((value > 0) && (p_y < 0))) { + value += p_y; + } + return value; +} + +_ALWAYS_INLINE_ double deg_to_rad(double p_y) { return p_y * (Math_PI / 180.0); } +_ALWAYS_INLINE_ float deg_to_rad(float p_y) { return p_y * (float)(Math_PI / 180.0); } + +_ALWAYS_INLINE_ double rad_to_deg(double p_y) { return p_y * (180.0 / Math_PI); } +_ALWAYS_INLINE_ float rad_to_deg(float p_y) { return p_y * (float)(180.0 / Math_PI); } + +_ALWAYS_INLINE_ double lerp(double p_from, double p_to, double p_weight) { return p_from + (p_to - p_from) * p_weight; } +_ALWAYS_INLINE_ float lerp(float p_from, float p_to, float p_weight) { return p_from + (p_to - p_from) * p_weight; } + +_ALWAYS_INLINE_ double cubic_interpolate(double p_from, double p_to, double p_pre, double p_post, double p_weight) { + return 0.5 * + ((p_from * 2.0) + + (-p_pre + p_to) * p_weight + + (2.0 * p_pre - 5.0 * p_from + 4.0 * p_to - p_post) * (p_weight * p_weight) + + (-p_pre + 3.0 * p_from - 3.0 * p_to + p_post) * (p_weight * p_weight * p_weight)); +} +_ALWAYS_INLINE_ float cubic_interpolate(float p_from, float p_to, float p_pre, float p_post, float p_weight) { + return 0.5f * + ((p_from * 2.0f) + + (-p_pre + p_to) * p_weight + + (2.0f * p_pre - 5.0f * p_from + 4.0f * p_to - p_post) * (p_weight * p_weight) + + (-p_pre + 3.0f * p_from - 3.0f * p_to + p_post) * (p_weight * p_weight * p_weight)); +} + +_ALWAYS_INLINE_ double cubic_interpolate_angle(double p_from, double p_to, double p_pre, double p_post, double p_weight) { + double from_rot = fmod(p_from, Math_TAU); + + double pre_diff = fmod(p_pre - from_rot, Math_TAU); + double pre_rot = from_rot + fmod(2.0 * pre_diff, Math_TAU) - pre_diff; + + double to_diff = fmod(p_to - from_rot, Math_TAU); + double to_rot = from_rot + fmod(2.0 * to_diff, Math_TAU) - to_diff; + + double post_diff = fmod(p_post - to_rot, Math_TAU); + double post_rot = to_rot + fmod(2.0 * post_diff, Math_TAU) - post_diff; + + return cubic_interpolate(from_rot, to_rot, pre_rot, post_rot, p_weight); +} + +_ALWAYS_INLINE_ float cubic_interpolate_angle(float p_from, float p_to, float p_pre, float p_post, float p_weight) { + float from_rot = fmod(p_from, (float)Math_TAU); + + float pre_diff = fmod(p_pre - from_rot, (float)Math_TAU); + float pre_rot = from_rot + fmod(2.0f * pre_diff, (float)Math_TAU) - pre_diff; + + float to_diff = fmod(p_to - from_rot, (float)Math_TAU); + float to_rot = from_rot + fmod(2.0f * to_diff, (float)Math_TAU) - to_diff; + + float post_diff = fmod(p_post - to_rot, (float)Math_TAU); + float post_rot = to_rot + fmod(2.0f * post_diff, (float)Math_TAU) - post_diff; + + return cubic_interpolate(from_rot, to_rot, pre_rot, post_rot, p_weight); +} + +_ALWAYS_INLINE_ double cubic_interpolate_in_time(double p_from, double p_to, double p_pre, double p_post, double p_weight, + double p_to_t, double p_pre_t, double p_post_t) { + /* Barry-Goldman method */ + double t = lerp(0.0, p_to_t, p_weight); + double a1 = lerp(p_pre, p_from, p_pre_t == 0 ? 0.0 : (t - p_pre_t) / -p_pre_t); + double a2 = lerp(p_from, p_to, p_to_t == 0 ? 0.5 : t / p_to_t); + double a3 = lerp(p_to, p_post, p_post_t - p_to_t == 0 ? 1.0 : (t - p_to_t) / (p_post_t - p_to_t)); + double b1 = lerp(a1, a2, p_to_t - p_pre_t == 0 ? 0.0 : (t - p_pre_t) / (p_to_t - p_pre_t)); + double b2 = lerp(a2, a3, p_post_t == 0 ? 1.0 : t / p_post_t); + return lerp(b1, b2, p_to_t == 0 ? 0.5 : t / p_to_t); +} +_ALWAYS_INLINE_ float cubic_interpolate_in_time(float p_from, float p_to, float p_pre, float p_post, float p_weight, + float p_to_t, float p_pre_t, float p_post_t) { + /* Barry-Goldman method */ + float t = lerp(0.0f, p_to_t, p_weight); + float a1 = lerp(p_pre, p_from, p_pre_t == 0 ? 0.0f : (t - p_pre_t) / -p_pre_t); + float a2 = lerp(p_from, p_to, p_to_t == 0 ? 0.5f : t / p_to_t); + float a3 = lerp(p_to, p_post, p_post_t - p_to_t == 0 ? 1.0f : (t - p_to_t) / (p_post_t - p_to_t)); + float b1 = lerp(a1, a2, p_to_t - p_pre_t == 0 ? 0.0f : (t - p_pre_t) / (p_to_t - p_pre_t)); + float b2 = lerp(a2, a3, p_post_t == 0 ? 1.0f : t / p_post_t); + return lerp(b1, b2, p_to_t == 0 ? 0.5f : t / p_to_t); +} + +_ALWAYS_INLINE_ double cubic_interpolate_angle_in_time(double p_from, double p_to, double p_pre, double p_post, double p_weight, + double p_to_t, double p_pre_t, double p_post_t) { + double from_rot = fmod(p_from, Math_TAU); + + double pre_diff = fmod(p_pre - from_rot, Math_TAU); + double pre_rot = from_rot + fmod(2.0 * pre_diff, Math_TAU) - pre_diff; + + double to_diff = fmod(p_to - from_rot, Math_TAU); + double to_rot = from_rot + fmod(2.0 * to_diff, Math_TAU) - to_diff; + + double post_diff = fmod(p_post - to_rot, Math_TAU); + double post_rot = to_rot + fmod(2.0 * post_diff, Math_TAU) - post_diff; + + return cubic_interpolate_in_time(from_rot, to_rot, pre_rot, post_rot, p_weight, p_to_t, p_pre_t, p_post_t); +} +_ALWAYS_INLINE_ float cubic_interpolate_angle_in_time(float p_from, float p_to, float p_pre, float p_post, float p_weight, + float p_to_t, float p_pre_t, float p_post_t) { + float from_rot = fmod(p_from, (float)Math_TAU); + + float pre_diff = fmod(p_pre - from_rot, (float)Math_TAU); + float pre_rot = from_rot + fmod(2.0f * pre_diff, (float)Math_TAU) - pre_diff; + + float to_diff = fmod(p_to - from_rot, (float)Math_TAU); + float to_rot = from_rot + fmod(2.0f * to_diff, (float)Math_TAU) - to_diff; + + float post_diff = fmod(p_post - to_rot, (float)Math_TAU); + float post_rot = to_rot + fmod(2.0f * post_diff, (float)Math_TAU) - post_diff; + + return cubic_interpolate_in_time(from_rot, to_rot, pre_rot, post_rot, p_weight, p_to_t, p_pre_t, p_post_t); +} + +_ALWAYS_INLINE_ double bezier_interpolate(double p_start, double p_control_1, double p_control_2, double p_end, double p_t) { + /* Formula from Wikipedia article on Bezier curves. */ + double omt = (1.0 - p_t); + double omt2 = omt * omt; + double omt3 = omt2 * omt; + double t2 = p_t * p_t; + double t3 = t2 * p_t; + + return p_start * omt3 + p_control_1 * omt2 * p_t * 3.0 + p_control_2 * omt * t2 * 3.0 + p_end * t3; +} +_ALWAYS_INLINE_ float bezier_interpolate(float p_start, float p_control_1, float p_control_2, float p_end, float p_t) { + /* Formula from Wikipedia article on Bezier curves. */ + float omt = (1.0f - p_t); + float omt2 = omt * omt; + float omt3 = omt2 * omt; + float t2 = p_t * p_t; + float t3 = t2 * p_t; + + return p_start * omt3 + p_control_1 * omt2 * p_t * 3.0f + p_control_2 * omt * t2 * 3.0f + p_end * t3; +} + +_ALWAYS_INLINE_ double bezier_derivative(double p_start, double p_control_1, double p_control_2, double p_end, double p_t) { + /* Formula from Wikipedia article on Bezier curves. */ + double omt = (1.0 - p_t); + double omt2 = omt * omt; + double t2 = p_t * p_t; + + double d = (p_control_1 - p_start) * 3.0 * omt2 + (p_control_2 - p_control_1) * 6.0 * omt * p_t + (p_end - p_control_2) * 3.0 * t2; + return d; +} +_ALWAYS_INLINE_ float bezier_derivative(float p_start, float p_control_1, float p_control_2, float p_end, float p_t) { + /* Formula from Wikipedia article on Bezier curves. */ + float omt = (1.0f - p_t); + float omt2 = omt * omt; + float t2 = p_t * p_t; + + float d = (p_control_1 - p_start) * 3.0f * omt2 + (p_control_2 - p_control_1) * 6.0f * omt * p_t + (p_end - p_control_2) * 3.0f * t2; + return d; +} + +_ALWAYS_INLINE_ double angle_difference(double p_from, double p_to) { + double difference = fmod(p_to - p_from, Math_TAU); + return fmod(2.0 * difference, Math_TAU) - difference; +} +_ALWAYS_INLINE_ float angle_difference(float p_from, float p_to) { + float difference = fmod(p_to - p_from, (float)Math_TAU); + return fmod(2.0f * difference, (float)Math_TAU) - difference; +} + +_ALWAYS_INLINE_ double lerp_angle(double p_from, double p_to, double p_weight) { + return p_from + angle_difference(p_from, p_to) * p_weight; +} +_ALWAYS_INLINE_ float lerp_angle(float p_from, float p_to, float p_weight) { + return p_from + angle_difference(p_from, p_to) * p_weight; +} + +_ALWAYS_INLINE_ double inverse_lerp(double p_from, double p_to, double p_value) { + return (p_value - p_from) / (p_to - p_from); +} +_ALWAYS_INLINE_ float inverse_lerp(float p_from, float p_to, float p_value) { + return (p_value - p_from) / (p_to - p_from); +} + +_ALWAYS_INLINE_ double remap(double p_value, double p_istart, double p_istop, double p_ostart, double p_ostop) { + return lerp(p_ostart, p_ostop, inverse_lerp(p_istart, p_istop, p_value)); +} +_ALWAYS_INLINE_ float remap(float p_value, float p_istart, float p_istop, float p_ostart, float p_ostop) { + return lerp(p_ostart, p_ostop, inverse_lerp(p_istart, p_istop, p_value)); +} + +_ALWAYS_INLINE_ bool is_equal_approx(double p_left, double p_right, double p_tolerance) { + // Check for exact equality first, required to handle "infinity" values. + if (p_left == p_right) { + return true; + } + // Then check for approximate equality. + return abs(p_left - p_right) < p_tolerance; +} +_ALWAYS_INLINE_ bool is_equal_approx(float p_left, float p_right, float p_tolerance) { + // Check for exact equality first, required to handle "infinity" values. + if (p_left == p_right) { + return true; + } + // Then check for approximate equality. + return abs(p_left - p_right) < p_tolerance; +} + +_ALWAYS_INLINE_ bool is_equal_approx(double p_left, double p_right) { + // Check for exact equality first, required to handle "infinity" values. + if (p_left == p_right) { + return true; + } + // Then check for approximate equality. + double tolerance = CMP_EPSILON * abs(p_left); + if (tolerance < CMP_EPSILON) { + tolerance = CMP_EPSILON; + } + return abs(p_left - p_right) < tolerance; +} +_ALWAYS_INLINE_ bool is_equal_approx(float p_left, float p_right) { + // Check for exact equality first, required to handle "infinity" values. + if (p_left == p_right) { + return true; + } + // Then check for approximate equality. + float tolerance = (float)CMP_EPSILON * abs(p_left); + if (tolerance < (float)CMP_EPSILON) { + tolerance = (float)CMP_EPSILON; + } + return abs(p_left - p_right) < tolerance; +} + +_ALWAYS_INLINE_ bool is_zero_approx(double p_value) { + return abs(p_value) < CMP_EPSILON; +} +_ALWAYS_INLINE_ bool is_zero_approx(float p_value) { + return abs(p_value) < (float)CMP_EPSILON; +} + +_ALWAYS_INLINE_ double smoothstep(double p_from, double p_to, double p_s) { + if (is_equal_approx(p_from, p_to)) { + return p_from; + } + double s = CLAMP((p_s - p_from) / (p_to - p_from), 0.0, 1.0); + return s * s * (3.0 - 2.0 * s); +} +_ALWAYS_INLINE_ float smoothstep(float p_from, float p_to, float p_s) { + if (is_equal_approx(p_from, p_to)) { + return p_from; + } + float s = CLAMP((p_s - p_from) / (p_to - p_from), 0.0f, 1.0f); + return s * s * (3.0f - 2.0f * s); +} + +_ALWAYS_INLINE_ double move_toward(double p_from, double p_to, double p_delta) { + return abs(p_to - p_from) <= p_delta ? p_to : p_from + SIGN(p_to - p_from) * p_delta; +} +_ALWAYS_INLINE_ float move_toward(float p_from, float p_to, float p_delta) { + return abs(p_to - p_from) <= p_delta ? p_to : p_from + SIGN(p_to - p_from) * p_delta; +} + +_ALWAYS_INLINE_ double rotate_toward(double p_from, double p_to, double p_delta) { + double difference = angle_difference(p_from, p_to); + double abs_difference = abs(difference); + // When `p_delta < 0` move no further than to PI radians away from `p_to` (as PI is the max possible angle distance). + return p_from + CLAMP(p_delta, abs_difference - Math_PI, abs_difference) * (difference >= 0.0 ? 1.0 : -1.0); +} +_ALWAYS_INLINE_ float rotate_toward(float p_from, float p_to, float p_delta) { + float difference = angle_difference(p_from, p_to); + float abs_difference = abs(difference); + // When `p_delta < 0` move no further than to PI radians away from `p_to` (as PI is the max possible angle distance). + return p_from + CLAMP(p_delta, abs_difference - (float)Math_PI, abs_difference) * (difference >= 0.0f ? 1.0f : -1.0f); +} + +_ALWAYS_INLINE_ double linear_to_db(double p_linear) { + return log(p_linear) * 8.6858896380650365530225783783321; +} +_ALWAYS_INLINE_ float linear_to_db(float p_linear) { + return log(p_linear) * (float)8.6858896380650365530225783783321; +} + +_ALWAYS_INLINE_ double db_to_linear(double p_db) { + return exp(p_db * 0.11512925464970228420089957273422); +} +_ALWAYS_INLINE_ float db_to_linear(float p_db) { + return exp(p_db * (float)0.11512925464970228420089957273422); +} + +_ALWAYS_INLINE_ double round(double p_val) { return ::round(p_val); } +_ALWAYS_INLINE_ float round(float p_val) { return ::roundf(p_val); } + +_ALWAYS_INLINE_ double wrapf(double p_value, double p_min, double p_max) { + double range = p_max - p_min; + if (is_zero_approx(range)) { + return p_min; + } + double result = p_value - (range * floor((p_value - p_min) / range)); + if (is_equal_approx(result, p_max)) { + return p_min; + } + return result; +} +_ALWAYS_INLINE_ float wrapf(float p_value, float p_min, float p_max) { + float range = p_max - p_min; + if (is_zero_approx(range)) { + return p_min; + } + float result = p_value - (range * floor((p_value - p_min) / range)); + if (is_equal_approx(result, p_max)) { + return p_min; + } + return result; +} + +_ALWAYS_INLINE_ int64_t wrapi(int64_t p_value, int64_t p_min, int64_t p_max) { + int64_t range = p_max - p_min; + return range == 0 ? p_min : p_min + ((((p_value - p_min) % range) + range) % range); +} + +_ALWAYS_INLINE_ double fract(double p_value) { + return p_value - floor(p_value); +} +_ALWAYS_INLINE_ float fract(float p_value) { + return p_value - floor(p_value); +} + +_ALWAYS_INLINE_ double pingpong(double p_value, double p_length) { + return (p_length != 0.0) ? abs(fract((p_value - p_length) / (p_length * 2.0)) * p_length * 2.0 - p_length) : 0.0; +} +_ALWAYS_INLINE_ float pingpong(float p_value, float p_length) { + return (p_length != 0.0f) ? abs(fract((p_value - p_length) / (p_length * 2.0f)) * p_length * 2.0f - p_length) : 0.0f; +} + +// double only, as these functions are mainly used by the editor and not performance-critical, +double ease(double p_x, double p_c); +int step_decimals(double p_step); +int range_step_decimals(double p_step); // For editor use only. +double snapped(double p_value, double p_step); + +uint32_t larger_prime(uint32_t p_val); + +void seed(uint64_t p_seed); +void randomize(); +uint32_t rand_from_seed(uint64_t *p_seed); +uint32_t rand(); +_ALWAYS_INLINE_ double randd() { return (double)rand() / (double)UINT32_MAX; } +_ALWAYS_INLINE_ float randf() { return (float)rand() / (float)UINT32_MAX; } +double randfn(double p_mean, double p_deviation); + +double random(double p_from, double p_to); +float random(float p_from, float p_to); +int random(int p_from, int p_to); + +// This function should be as fast as possible and rounding mode should not matter. +_ALWAYS_INLINE_ int fast_ftoi(float p_value) { + // Assuming every supported compiler has `lrint()`. + return lrintf(p_value); +} + +_ALWAYS_INLINE_ uint32_t halfbits_to_floatbits(uint16_t p_half) { + uint16_t h_exp, h_sig; + uint32_t f_sgn, f_exp, f_sig; + + h_exp = (p_half & 0x7c00u); + f_sgn = ((uint32_t)p_half & 0x8000u) << 16; + switch (h_exp) { + case 0x0000u: /* 0 or subnormal */ + h_sig = (p_half & 0x03ffu); + /* Signed zero */ + if (h_sig == 0) { + return f_sgn; + } + /* Subnormal */ + h_sig <<= 1; + while ((h_sig & 0x0400u) == 0) { h_sig <<= 1; - while ((h_sig & 0x0400u) == 0) { - h_sig <<= 1; - h_exp++; - } - f_exp = ((uint32_t)(127 - 15 - h_exp)) << 23; - f_sig = ((uint32_t)(h_sig & 0x03ffu)) << 13; - return f_sgn + f_exp + f_sig; - case 0x7c00u: /* inf or NaN */ - /* All-ones exponent and a copy of the significand */ - return f_sgn + 0x7f800000u + (((uint32_t)(h & 0x03ffu)) << 13); - default: /* normalized */ - /* Just need to adjust the exponent and shift */ - return f_sgn + (((uint32_t)(h & 0x7fffu) + 0x1c000u) << 13); - } - } - - static _ALWAYS_INLINE_ float halfptr_to_float(const uint16_t *h) { - union { - uint32_t u32; - float f32; - } u; - - u.u32 = halfbits_to_floatbits(*h); - return u.f32; - } - - static _ALWAYS_INLINE_ float half_to_float(const uint16_t h) { - return halfptr_to_float(&h); - } - - static _ALWAYS_INLINE_ uint16_t make_half_float(float f) { - union { - float fv; - uint32_t ui; - } ci; - ci.fv = f; - - uint32_t x = ci.ui; - uint32_t sign = (unsigned short)(x >> 31); - uint32_t mantissa; - uint32_t exponent; - uint16_t hf; - - // get mantissa - mantissa = x & ((1 << 23) - 1); - // get exponent bits - exponent = x & (0xFF << 23); - if (exponent >= 0x47800000) { - // check if the original single precision float number is a NaN - if (mantissa && (exponent == (0xFF << 23))) { - // we have a single precision NaN - mantissa = (1 << 23) - 1; - } else { - // 16-bit half-float representation stores number as Inf - mantissa = 0; + h_exp++; } - hf = (((uint16_t)sign) << 15) | (uint16_t)((0x1F << 10)) | - (uint16_t)(mantissa >> 13); + f_exp = ((uint32_t)(127 - 15 - h_exp)) << 23; + f_sig = ((uint32_t)(h_sig & 0x03ffu)) << 13; + return f_sgn + f_exp + f_sig; + case 0x7c00u: /* inf or NaN */ + /* All-ones exponent and a copy of the significand */ + return f_sgn + 0x7f800000u + (((uint32_t)(p_half & 0x03ffu)) << 13); + default: /* normalized */ + /* Just need to adjust the exponent and shift */ + return f_sgn + (((uint32_t)(p_half & 0x7fffu) + 0x1c000u) << 13); + } +} + +_ALWAYS_INLINE_ float halfptr_to_float(const uint16_t *p_half) { + union { + uint32_t u32; + float f32; + } u; + + u.u32 = halfbits_to_floatbits(*p_half); + return u.f32; +} + +_ALWAYS_INLINE_ float half_to_float(const uint16_t p_half) { + return halfptr_to_float(&p_half); +} + +_ALWAYS_INLINE_ uint16_t make_half_float(float p_value) { + union { + float fv; + uint32_t ui; + } ci; + ci.fv = p_value; + + uint32_t x = ci.ui; + uint32_t sign = (unsigned short)(x >> 31); + uint32_t mantissa; + uint32_t exponent; + uint16_t hf; + + // get mantissa + mantissa = x & ((1 << 23) - 1); + // get exponent bits + exponent = x & (0xFF << 23); + if (exponent >= 0x47800000) { + // check if the original single precision float number is a NaN + if (mantissa && (exponent == (0xFF << 23))) { + // we have a single precision NaN + mantissa = (1 << 23) - 1; + } else { + // 16-bit half-float representation stores number as Inf + mantissa = 0; } - // check if exponent is <= -15 - else if (exponent <= 0x38000000) { - /* - // store a denorm half-float value or zero - exponent = (0x38000000 - exponent) >> 23; - mantissa >>= (14 + exponent); - - hf = (((uint16_t)sign) << 15) | (uint16_t)(mantissa); - */ - hf = 0; //denormals do not work for 3D, convert to zero + hf = (((uint16_t)sign) << 15) | (uint16_t)((0x1F << 10)) | + (uint16_t)(mantissa >> 13); + } + // check if exponent is <= -15 + else if (exponent <= 0x38000000) { + /* + // store a denorm half-float value or zero + exponent = (0x38000000 - exponent) >> 23; + mantissa >>= (14 + exponent); + + hf = (((uint16_t)sign) << 15) | (uint16_t)(mantissa); + */ + hf = 0; //denormals do not work for 3D, convert to zero + } else { + hf = (((uint16_t)sign) << 15) | + (uint16_t)((exponent - 0x38000000) >> 13) | + (uint16_t)(mantissa >> 13); + } + + return hf; +} + +_ALWAYS_INLINE_ float snap_scalar(float p_offset, float p_step, float p_target) { + return p_step != 0 ? snapped(p_target - p_offset, p_step) + p_offset : p_target; +} + +_ALWAYS_INLINE_ float snap_scalar_separation(float p_offset, float p_step, float p_target, float p_separation) { + if (p_step != 0) { + float a = snapped(p_target - p_offset, p_step + p_separation) + p_offset; + float b = a; + if (p_target >= 0) { + b -= p_separation; } else { - hf = (((uint16_t)sign) << 15) | - (uint16_t)((exponent - 0x38000000) >> 13) | - (uint16_t)(mantissa >> 13); + b += p_step; } - - return hf; + return (abs(p_target - a) < abs(p_target - b)) ? a : b; } + return p_target; +} - static _ALWAYS_INLINE_ float snap_scalar(float p_offset, float p_step, float p_target) { - return p_step != 0 ? Math::snapped(p_target - p_offset, p_step) + p_offset : p_target; - } - - static _ALWAYS_INLINE_ float snap_scalar_separation(float p_offset, float p_step, float p_target, float p_separation) { - if (p_step != 0) { - float a = Math::snapped(p_target - p_offset, p_step + p_separation) + p_offset; - float b = a; - if (p_target >= 0) { - b -= p_separation; - } else { - b += p_step; - } - return (Math::abs(p_target - a) < Math::abs(p_target - b)) ? a : b; - } - return p_target; - } -}; +}; //namespace Math #endif // MATH_FUNCS_H diff --git a/editor/plugins/gizmos/navigation_region_3d_gizmo_plugin.cpp b/editor/plugins/gizmos/navigation_region_3d_gizmo_plugin.cpp index 14105f0b3bf6..393e7669f20a 100644 --- a/editor/plugins/gizmos/navigation_region_3d_gizmo_plugin.cpp +++ b/editor/plugins/gizmos/navigation_region_3d_gizmo_plugin.cpp @@ -30,6 +30,7 @@ #include "navigation_region_3d_gizmo_plugin.h" +#include "core/math/random_pcg.h" #include "editor/plugins/node_3d_editor_plugin.h" #include "scene/3d/navigation_region_3d.h" #include "servers/navigation_server_3d.h" diff --git a/editor/plugins/tiles/tile_data_editors.cpp b/editor/plugins/tiles/tile_data_editors.cpp index f985bbc62907..c1d2f5e07d59 100644 --- a/editor/plugins/tiles/tile_data_editors.cpp +++ b/editor/plugins/tiles/tile_data_editors.cpp @@ -33,6 +33,7 @@ #include "tile_set_editor.h" #include "core/math/geometry_2d.h" +#include "core/math/random_pcg.h" #include "core/os/keyboard.h" #include "editor/editor_node.h" diff --git a/editor/plugins/tiles/tile_map_layer_editor.cpp b/editor/plugins/tiles/tile_map_layer_editor.cpp index 4a5953015997..6efc013f1142 100644 --- a/editor/plugins/tiles/tile_map_layer_editor.cpp +++ b/editor/plugins/tiles/tile_map_layer_editor.cpp @@ -46,6 +46,7 @@ #include "core/input/input.h" #include "core/math/geometry_2d.h" +#include "core/math/random_pcg.h" #include "core/os/keyboard.h" TileMapLayer *TileMapLayerSubEditorPlugin::_get_edited_layer() const { diff --git a/scene/2d/navigation_region_2d.cpp b/scene/2d/navigation_region_2d.cpp index 9b3c7bb9ea82..6083e4df005f 100644 --- a/scene/2d/navigation_region_2d.cpp +++ b/scene/2d/navigation_region_2d.cpp @@ -31,6 +31,7 @@ #include "navigation_region_2d.h" #include "core/math/geometry_2d.h" +#include "core/math/random_pcg.h" #include "scene/resources/world_2d.h" #include "servers/navigation_server_2d.h" diff --git a/scene/2d/tile_map_layer.cpp b/scene/2d/tile_map_layer.cpp index 437790bb999c..52aadf338a02 100644 --- a/scene/2d/tile_map_layer.cpp +++ b/scene/2d/tile_map_layer.cpp @@ -31,6 +31,7 @@ #include "tile_map_layer.h" #include "core/io/marshalls.h" +#include "core/math/random_pcg.h" #include "scene/2d/tile_map.h" #include "scene/gui/control.h" #include "scene/resources/world_2d.h" diff --git a/scene/3d/navigation_region_3d.cpp b/scene/3d/navigation_region_3d.cpp index 40e04f0fb458..cc5dd4b32c4c 100644 --- a/scene/3d/navigation_region_3d.cpp +++ b/scene/3d/navigation_region_3d.cpp @@ -30,6 +30,7 @@ #include "navigation_region_3d.h" +#include "core/math/random_pcg.h" #include "scene/resources/3d/navigation_mesh_source_geometry_data_3d.h" #include "servers/navigation_server_3d.h"