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godot/core/math/math_funcs.h
Rémi Verschelde d95794ec8a
One Copyright Update to rule them all 
As many open source projects have started doing it, we're removing the
current year from the copyright notice, so that we don't need to bump
it every year.

It seems like only the first year of publication is technically
relevant for copyright notices, and even that seems to be something
that many companies stopped listing altogether (in a version controlled
codebase, the commits are a much better source of date of publication
than a hardcoded copyright statement).

We also now list Godot Engine contributors first as we're collectively
the current maintainers of the project, and we clarify that the
"exclusive" copyright of the co-founders covers the timespan before
opensourcing (their further contributions are included as part of Godot
Engine contributors).

Also fixed "cf." Frenchism - it's meant as "refer to / see".
2023-01-05 13:25:55 +01:00

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/**************************************************************************/
/* math_funcs.h */
/**************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/**************************************************************************/
/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
/* */
/* 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
// Not using 'RANDOM_MAX' to avoid conflict with system headers on some OSes (at least NetBSD).
static const uint64_t RANDOM_32BIT_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((float)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 log1p(double p_x) { return ::log1p(p_x); }
static _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); }
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_ 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) {
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 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 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 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 */
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;
}
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;
}
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;
}
};
#endif // MATH_FUNCS_H
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