/*************************************************************************/ /* math_funcs.h */ /*************************************************************************/ /* This file is part of: */ /* GODOT ENGINE */ /* https://godotengine.org */ /*************************************************************************/ /* Copyright (c) 2007-2019 Juan Linietsky, Ariel Manzur. */ /* Copyright (c) 2014-2019 Godot Engine contributors (cf. AUTHORS.md) */ /* */ /* Permission is hereby granted, free of charge, to any person obtaining */ /* a copy of this software and associated documentation files (the */ /* "Software"), to deal in the Software without restriction, including */ /* without limitation the rights to use, copy, modify, merge, publish, */ /* distribute, sublicense, and/or sell copies of the Software, and to */ /* permit persons to whom the Software is furnished to do so, subject to */ /* the following conditions: */ /* */ /* The above copyright notice and this permission notice shall be */ /* included in all copies or substantial portions of the Software. */ /* */ /* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */ /* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */ /* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/ /* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */ /* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */ /* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */ /* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ /*************************************************************************/ #ifndef MATH_FUNCS_H #define MATH_FUNCS_H #include "core/math/math_defs.h" #include "core/math/random_pcg.h" #include "core/typedefs.h" #include "thirdparty/misc/pcg.h" #include <float.h> #include <math.h> class Math { static RandomPCG default_rand; public: Math() {} // useless to instance static const uint64_t RANDOM_MAX = 0xFFFFFFFF; static _ALWAYS_INLINE_ double sin(double p_x) { return ::sin(p_x); } static _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); } static _ALWAYS_INLINE_ double tan(double p_x) { return ::tan(p_x); } static _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); } 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; } static _ALWAYS_INLINE_ float sincn(float p_x) { return sinc(Math_PI * p_x); } static _ALWAYS_INLINE_ double sincn(double p_x) { return sinc(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); } static _ALWAYS_INLINE_ double tanh(double p_x) { return ::tanh(p_x); } static _ALWAYS_INLINE_ float tanh(float p_x) { return ::tanhf(p_x); } static _ALWAYS_INLINE_ double asin(double p_x) { return ::asin(p_x); } static _ALWAYS_INLINE_ float asin(float p_x) { return ::asinf(p_x); } static _ALWAYS_INLINE_ double acos(double p_x) { return ::acos(p_x); } static _ALWAYS_INLINE_ float acos(float p_x) { return ::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); } 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); } static _ALWAYS_INLINE_ double sqrt(double p_x) { return ::sqrt(p_x); } static _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); } static _ALWAYS_INLINE_ double floor(double p_x) { return ::floor(p_x); } static _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); } 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); } static _ALWAYS_INLINE_ double log(double p_x) { return ::log(p_x); } static _ALWAYS_INLINE_ float log(float p_x) { return ::logf(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); } static _ALWAYS_INLINE_ bool is_nan(double p_val) { #ifdef _MSC_VER 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); #else return isnan(p_val); #endif } static _ALWAYS_INLINE_ bool is_nan(float p_val) { #ifdef _MSC_VER 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); #else return isnan(p_val); #endif } static _ALWAYS_INLINE_ bool is_inf(double p_val) { #ifdef _MSC_VER 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); #else return isinf(p_val); #endif } static _ALWAYS_INLINE_ bool is_inf(float p_val) { #ifdef _MSC_VER 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; #else return isinf(p_val); #endif } 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 += 0.0; return value; } static _ALWAYS_INLINE_ int posmod(int p_x, int p_y) { int 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 deg2rad(double p_y) { return p_y * Math_PI / 180.0; } static _ALWAYS_INLINE_ float deg2rad(float p_y) { return p_y * Math_PI / 180.0; } static _ALWAYS_INLINE_ double rad2deg(double p_y) { return p_y * 180.0 / Math_PI; } static _ALWAYS_INLINE_ float rad2deg(float p_y) { return p_y * 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 lerp_angle(double p_from, double p_to, double p_weight) { double difference = fmod(p_to - p_from, Math_TAU); double distance = fmod(2.0 * difference, Math_TAU) - difference; return p_from + distance * p_weight; } static _ALWAYS_INLINE_ float lerp_angle(float p_from, float p_to, float p_weight) { float difference = fmod(p_to - p_from, (float)Math_TAU); float distance = fmod(2.0f * difference, (float)Math_TAU) - difference; return p_from + distance * 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 range_lerp(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 range_lerp(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_weight) { if (is_equal_approx(p_from, p_to)) return p_from; double x = CLAMP((p_weight - p_from) / (p_to - p_from), 0.0, 1.0); return x * x * (3.0 - 2.0 * x); } static _ALWAYS_INLINE_ float smoothstep(float p_from, float p_to, float p_weight) { if (is_equal_approx(p_from, p_to)) return p_from; float x = CLAMP((p_weight - p_from) / (p_to - p_from), 0.0f, 1.0f); return x * x * (3.0f - 2.0f * x); } 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 + SGN(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 + SGN(p_to - p_from) * p_delta; } static _ALWAYS_INLINE_ double linear2db(double p_linear) { return Math::log(p_linear) * 8.6858896380650365530225783783321; } static _ALWAYS_INLINE_ float linear2db(float p_linear) { return Math::log(p_linear) * 8.6858896380650365530225783783321; } static _ALWAYS_INLINE_ double db2linear(double p_db) { return Math::exp(p_db * 0.11512925464970228420089957273422); } static _ALWAYS_INLINE_ float db2linear(float p_db) { return Math::exp(p_db * 0.11512925464970228420089957273422); } static _ALWAYS_INLINE_ double round(double p_val) { return (p_val >= 0) ? Math::floor(p_val + 0.5) : -Math::floor(-p_val + 0.5); } static _ALWAYS_INLINE_ float round(float p_val) { return (p_val >= 0) ? Math::floor(p_val + 0.5) : -Math::floor(-p_val + 0.5); } 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; return is_zero_approx(range) ? min : value - (range * Math::floor((value - min) / range)); } static _ALWAYS_INLINE_ float wrapf(float value, float min, float max) { float range = max - min; return is_zero_approx(range) ? min : value - (range * Math::floor((value - min) / range)); } // 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); static double stepify(double p_value, double p_step); static double dectime(double p_value, double p_amount, 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_MAX; } static _ALWAYS_INLINE_ float randf() { return (float)rand() / (float)Math::RANDOM_MAX; } static double random(double from, double to); static float random(float from, float to); static real_t random(int from, int to) { return (real_t)random((real_t)from, (real_t)to); } static _ALWAYS_INLINE_ bool is_equal_approx_ratio(real_t a, real_t b, real_t epsilon = CMP_EPSILON, real_t min_epsilon = CMP_EPSILON) { // this is an approximate way to check that numbers are close, as a ratio of their average size // helps compare approximate numbers that may be very big or very small real_t diff = abs(a - b); if (diff == 0.0 || diff < min_epsilon) { return true; } real_t avg_size = (abs(a) + abs(b)) / 2.0; diff /= avg_size; return diff < epsilon; } static _ALWAYS_INLINE_ bool is_equal_approx(real_t a, real_t b) { // Check for exact equality first, required to handle "infinity" values. if (a == b) { return true; } // Then check for approximate equality. real_t tolerance = CMP_EPSILON * abs(a); if (tolerance < CMP_EPSILON) { tolerance = CMP_EPSILON; } return abs(a - b) < tolerance; } static _ALWAYS_INLINE_ bool is_equal_approx(real_t a, real_t b, real_t 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(real_t 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) { static int b; #if (defined(_WIN32_WINNT) && _WIN32_WINNT >= 0x0603) || WINAPI_FAMILY == WINAPI_FAMILY_PHONE_APP // windows 8 phone? b = (int)((a > 0.0) ? (a + 0.5) : (a - 0.5)); #elif defined(_MSC_VER) && _MSC_VER < 1800 __asm fld a __asm fistp b /*#elif defined( __GNUC__ ) && ( defined( __i386__ ) || defined( __x86_64__ ) ) // use AT&T inline assembly style, document that // we use memory as output (=m) and input (m) __asm__ __volatile__ ( "flds %1 \n\t" "fistpl %0 \n\t" : "=m" (b) : "m" (a));*/ #else b = lrintf(a); //assuming everything but msvc 2012 or earlier has lrint #endif return b; } 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 */ 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 exp; uint16_t hf; // get mantissa mantissa = x & ((1 << 23) - 1); // get exponent bits exp = x & (0xFF << 23); if (exp >= 0x47800000) { // check if the original single precision float number is a NaN if (mantissa && (exp == (0xFF << 23))) { // we have a single precision NaN mantissa = (1 << 23) - 1; } else { // 16-bit half-float representation stores number as Inf mantissa = 0; } hf = (((uint16_t)sign) << 15) | (uint16_t)((0x1F << 10)) | (uint16_t)(mantissa >> 13); } // check if exponent is <= -15 else if (exp <= 0x38000000) { /*// store a denorm half-float value or zero exp = (0x38000000 - exp) >> 23; mantissa >>= (14 + exp); 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)((exp - 0x38000000) >> 13) | (uint16_t)(mantissa >> 13); } return hf; } static _ALWAYS_INLINE_ float snap_scalar(float p_offset, float p_step, float p_target) { return p_step != 0 ? Math::stepify(p_target - p_offset, p_step) + p_offset : p_target; } static _ALWAYS_INLINE_ float snap_scalar_seperation(float p_offset, float p_step, float p_target, float p_separation) { if (p_step != 0) { float a = Math::stepify(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; } }; #endif // MATH_FUNCS_H