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Happy new year to the wonderful Godot community! We're starting a new decade with a well-established, non-profit, free and open source game engine, and tons of further improvements in the pipeline from hundreds of contributors. Godot will keep getting better, and we're looking forward to all the games that the community will keep developing and releasing with it.
490 lines
18 KiB
C++
490 lines
18 KiB
C++
/*************************************************************************/
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/* math_funcs.h */
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/*************************************************************************/
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/* This file is part of: */
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/* GODOT ENGINE */
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/* https://godotengine.org */
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/*************************************************************************/
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/* Copyright (c) 2007-2020 Juan Linietsky, Ariel Manzur. */
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/* Copyright (c) 2014-2020 Godot Engine contributors (cf. AUTHORS.md). */
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/* */
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/* Permission is hereby granted, free of charge, to any person obtaining */
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/* a copy of this software and associated documentation files (the */
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/* "Software"), to deal in the Software without restriction, including */
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/* without limitation the rights to use, copy, modify, merge, publish, */
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/* distribute, sublicense, and/or sell copies of the Software, and to */
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/* permit persons to whom the Software is furnished to do so, subject to */
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/* the following conditions: */
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/* */
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/* The above copyright notice and this permission notice shall be */
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/* included in all copies or substantial portions of the Software. */
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/* */
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/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
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/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
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/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
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/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
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/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
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/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
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/*************************************************************************/
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#ifndef MATH_FUNCS_H
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#define MATH_FUNCS_H
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#include "core/math/math_defs.h"
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#include "core/math/random_pcg.h"
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#include "core/typedefs.h"
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#include "thirdparty/misc/pcg.h"
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#include <float.h>
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#include <math.h>
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class Math {
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static RandomPCG default_rand;
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public:
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Math() {} // useless to instance
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static const uint64_t RANDOM_MAX = 0xFFFFFFFF;
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static _ALWAYS_INLINE_ double sin(double p_x) { return ::sin(p_x); }
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static _ALWAYS_INLINE_ float sin(float p_x) { return ::sinf(p_x); }
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static _ALWAYS_INLINE_ double cos(double p_x) { return ::cos(p_x); }
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static _ALWAYS_INLINE_ float cos(float p_x) { return ::cosf(p_x); }
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static _ALWAYS_INLINE_ double tan(double p_x) { return ::tan(p_x); }
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static _ALWAYS_INLINE_ float tan(float p_x) { return ::tanf(p_x); }
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static _ALWAYS_INLINE_ double sinh(double p_x) { return ::sinh(p_x); }
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static _ALWAYS_INLINE_ float sinh(float p_x) { return ::sinhf(p_x); }
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static _ALWAYS_INLINE_ float sinc(float p_x) { return p_x == 0 ? 1 : ::sin(p_x) / p_x; }
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static _ALWAYS_INLINE_ double sinc(double p_x) { return p_x == 0 ? 1 : ::sin(p_x) / p_x; }
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static _ALWAYS_INLINE_ float sincn(float p_x) { return sinc(Math_PI * p_x); }
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static _ALWAYS_INLINE_ double sincn(double p_x) { return sinc(Math_PI * p_x); }
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static _ALWAYS_INLINE_ double cosh(double p_x) { return ::cosh(p_x); }
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static _ALWAYS_INLINE_ float cosh(float p_x) { return ::coshf(p_x); }
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static _ALWAYS_INLINE_ double tanh(double p_x) { return ::tanh(p_x); }
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static _ALWAYS_INLINE_ float tanh(float p_x) { return ::tanhf(p_x); }
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static _ALWAYS_INLINE_ double asin(double p_x) { return ::asin(p_x); }
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static _ALWAYS_INLINE_ float asin(float p_x) { return ::asinf(p_x); }
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static _ALWAYS_INLINE_ double acos(double p_x) { return ::acos(p_x); }
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static _ALWAYS_INLINE_ float acos(float p_x) { return ::acosf(p_x); }
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static _ALWAYS_INLINE_ double atan(double p_x) { return ::atan(p_x); }
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static _ALWAYS_INLINE_ float atan(float p_x) { return ::atanf(p_x); }
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static _ALWAYS_INLINE_ double atan2(double p_y, double p_x) { return ::atan2(p_y, p_x); }
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static _ALWAYS_INLINE_ float atan2(float p_y, float p_x) { return ::atan2f(p_y, p_x); }
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static _ALWAYS_INLINE_ double sqrt(double p_x) { return ::sqrt(p_x); }
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static _ALWAYS_INLINE_ float sqrt(float p_x) { return ::sqrtf(p_x); }
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static _ALWAYS_INLINE_ double fmod(double p_x, double p_y) { return ::fmod(p_x, p_y); }
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static _ALWAYS_INLINE_ float fmod(float p_x, float p_y) { return ::fmodf(p_x, p_y); }
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static _ALWAYS_INLINE_ double floor(double p_x) { return ::floor(p_x); }
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static _ALWAYS_INLINE_ float floor(float p_x) { return ::floorf(p_x); }
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static _ALWAYS_INLINE_ double ceil(double p_x) { return ::ceil(p_x); }
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static _ALWAYS_INLINE_ float ceil(float p_x) { return ::ceilf(p_x); }
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static _ALWAYS_INLINE_ double pow(double p_x, double p_y) { return ::pow(p_x, p_y); }
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static _ALWAYS_INLINE_ float pow(float p_x, float p_y) { return ::powf(p_x, p_y); }
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static _ALWAYS_INLINE_ double log(double p_x) { return ::log(p_x); }
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static _ALWAYS_INLINE_ float log(float p_x) { return ::logf(p_x); }
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static _ALWAYS_INLINE_ double exp(double p_x) { return ::exp(p_x); }
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static _ALWAYS_INLINE_ float exp(float p_x) { return ::expf(p_x); }
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static _ALWAYS_INLINE_ bool is_nan(double p_val) {
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#ifdef _MSC_VER
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return _isnan(p_val);
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#elif defined(__GNUC__) && __GNUC__ < 6
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union {
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uint64_t u;
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double f;
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} ieee754;
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ieee754.f = p_val;
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// (unsigned)(0x7ff0000000000001 >> 32) : 0x7ff00000
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return ((((unsigned)(ieee754.u >> 32) & 0x7fffffff) + ((unsigned)ieee754.u != 0)) > 0x7ff00000);
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#else
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return isnan(p_val);
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#endif
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}
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static _ALWAYS_INLINE_ bool is_nan(float p_val) {
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#ifdef _MSC_VER
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return _isnan(p_val);
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#elif defined(__GNUC__) && __GNUC__ < 6
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union {
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uint32_t u;
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float f;
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} ieee754;
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ieee754.f = p_val;
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// -----------------------------------
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// (single-precision floating-point)
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// NaN : s111 1111 1xxx xxxx xxxx xxxx xxxx xxxx
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// : (> 0x7f800000)
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// where,
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// s : sign
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// x : non-zero number
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// -----------------------------------
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return ((ieee754.u & 0x7fffffff) > 0x7f800000);
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#else
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return isnan(p_val);
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#endif
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}
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static _ALWAYS_INLINE_ bool is_inf(double p_val) {
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#ifdef _MSC_VER
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return !_finite(p_val);
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// use an inline implementation of isinf as a workaround for problematic libstdc++ versions from gcc 5.x era
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#elif defined(__GNUC__) && __GNUC__ < 6
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union {
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uint64_t u;
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double f;
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} ieee754;
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ieee754.f = p_val;
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return ((unsigned)(ieee754.u >> 32) & 0x7fffffff) == 0x7ff00000 &&
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((unsigned)ieee754.u == 0);
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#else
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return isinf(p_val);
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#endif
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}
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static _ALWAYS_INLINE_ bool is_inf(float p_val) {
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#ifdef _MSC_VER
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return !_finite(p_val);
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// use an inline implementation of isinf as a workaround for problematic libstdc++ versions from gcc 5.x era
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#elif defined(__GNUC__) && __GNUC__ < 6
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union {
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uint32_t u;
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float f;
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} ieee754;
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ieee754.f = p_val;
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return (ieee754.u & 0x7fffffff) == 0x7f800000;
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#else
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return isinf(p_val);
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#endif
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}
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static _ALWAYS_INLINE_ double abs(double g) { return absd(g); }
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static _ALWAYS_INLINE_ float abs(float g) { return absf(g); }
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static _ALWAYS_INLINE_ int abs(int g) { return g > 0 ? g : -g; }
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static _ALWAYS_INLINE_ double fposmod(double p_x, double p_y) {
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double value = Math::fmod(p_x, p_y);
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if ((value < 0 && p_y > 0) || (value > 0 && p_y < 0)) {
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value += p_y;
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}
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value += 0.0;
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return value;
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}
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static _ALWAYS_INLINE_ float fposmod(float p_x, float p_y) {
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float value = Math::fmod(p_x, p_y);
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if ((value < 0 && p_y > 0) || (value > 0 && p_y < 0)) {
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value += p_y;
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}
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value += 0.0;
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return value;
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}
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static _ALWAYS_INLINE_ int posmod(int p_x, int p_y) {
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int value = p_x % p_y;
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if ((value < 0 && p_y > 0) || (value > 0 && p_y < 0)) {
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value += p_y;
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}
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return value;
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}
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static _ALWAYS_INLINE_ double deg2rad(double p_y) { return p_y * Math_PI / 180.0; }
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static _ALWAYS_INLINE_ float deg2rad(float p_y) { return p_y * Math_PI / 180.0; }
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static _ALWAYS_INLINE_ double rad2deg(double p_y) { return p_y * 180.0 / Math_PI; }
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static _ALWAYS_INLINE_ float rad2deg(float p_y) { return p_y * 180.0 / Math_PI; }
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static _ALWAYS_INLINE_ double lerp(double p_from, double p_to, double p_weight) { return p_from + (p_to - p_from) * p_weight; }
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static _ALWAYS_INLINE_ float lerp(float p_from, float p_to, float p_weight) { return p_from + (p_to - p_from) * p_weight; }
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static _ALWAYS_INLINE_ double lerp_angle(double p_from, double p_to, double p_weight) {
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double difference = fmod(p_to - p_from, Math_TAU);
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double distance = fmod(2.0 * difference, Math_TAU) - difference;
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return p_from + distance * p_weight;
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}
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static _ALWAYS_INLINE_ float lerp_angle(float p_from, float p_to, float p_weight) {
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float difference = fmod(p_to - p_from, (float)Math_TAU);
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float distance = fmod(2.0f * difference, (float)Math_TAU) - difference;
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return p_from + distance * p_weight;
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}
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static _ALWAYS_INLINE_ double inverse_lerp(double p_from, double p_to, double p_value) { return (p_value - p_from) / (p_to - p_from); }
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static _ALWAYS_INLINE_ float inverse_lerp(float p_from, float p_to, float p_value) { return (p_value - p_from) / (p_to - p_from); }
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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)); }
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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)); }
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static _ALWAYS_INLINE_ double smoothstep(double p_from, double p_to, double p_weight) {
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if (is_equal_approx(p_from, p_to)) return p_from;
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double x = CLAMP((p_weight - p_from) / (p_to - p_from), 0.0, 1.0);
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return x * x * (3.0 - 2.0 * x);
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}
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static _ALWAYS_INLINE_ float smoothstep(float p_from, float p_to, float p_weight) {
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if (is_equal_approx(p_from, p_to)) return p_from;
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float x = CLAMP((p_weight - p_from) / (p_to - p_from), 0.0f, 1.0f);
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return x * x * (3.0f - 2.0f * x);
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}
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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; }
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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; }
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static _ALWAYS_INLINE_ double linear2db(double p_linear) { return Math::log(p_linear) * 8.6858896380650365530225783783321; }
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static _ALWAYS_INLINE_ float linear2db(float p_linear) { return Math::log(p_linear) * 8.6858896380650365530225783783321; }
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static _ALWAYS_INLINE_ double db2linear(double p_db) { return Math::exp(p_db * 0.11512925464970228420089957273422); }
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static _ALWAYS_INLINE_ float db2linear(float p_db) { return Math::exp(p_db * 0.11512925464970228420089957273422); }
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static _ALWAYS_INLINE_ double round(double p_val) { return (p_val >= 0) ? Math::floor(p_val + 0.5) : -Math::floor(-p_val + 0.5); }
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static _ALWAYS_INLINE_ float round(float p_val) { return (p_val >= 0) ? Math::floor(p_val + 0.5) : -Math::floor(-p_val + 0.5); }
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static _ALWAYS_INLINE_ int64_t wrapi(int64_t value, int64_t min, int64_t max) {
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int64_t range = max - min;
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return range == 0 ? min : min + ((((value - min) % range) + range) % range);
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}
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static _ALWAYS_INLINE_ double wrapf(double value, double min, double max) {
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double range = max - min;
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return is_zero_approx(range) ? min : value - (range * Math::floor((value - min) / range));
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}
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static _ALWAYS_INLINE_ float wrapf(float value, float min, float max) {
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float range = max - min;
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return is_zero_approx(range) ? min : value - (range * Math::floor((value - min) / range));
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}
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// double only, as these functions are mainly used by the editor and not performance-critical,
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static double ease(double p_x, double p_c);
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static int step_decimals(double p_step);
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static int range_step_decimals(double p_step);
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static double stepify(double p_value, double p_step);
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static double dectime(double p_value, double p_amount, double p_step);
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static uint32_t larger_prime(uint32_t p_val);
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static void seed(uint64_t x);
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static void randomize();
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static uint32_t rand_from_seed(uint64_t *seed);
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static uint32_t rand();
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static _ALWAYS_INLINE_ double randd() { return (double)rand() / (double)Math::RANDOM_MAX; }
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static _ALWAYS_INLINE_ float randf() { return (float)rand() / (float)Math::RANDOM_MAX; }
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static double random(double from, double to);
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static float random(float from, float to);
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static real_t random(int from, int to) { return (real_t)random((real_t)from, (real_t)to); }
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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) {
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// this is an approximate way to check that numbers are close, as a ratio of their average size
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// helps compare approximate numbers that may be very big or very small
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real_t diff = abs(a - b);
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if (diff == 0.0 || diff < min_epsilon) {
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return true;
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}
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real_t avg_size = (abs(a) + abs(b)) / 2.0;
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diff /= avg_size;
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return diff < epsilon;
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}
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static _ALWAYS_INLINE_ bool is_equal_approx(real_t a, real_t b) {
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// Check for exact equality first, required to handle "infinity" values.
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if (a == b) {
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return true;
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}
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// Then check for approximate equality.
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real_t tolerance = CMP_EPSILON * abs(a);
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if (tolerance < CMP_EPSILON) {
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tolerance = CMP_EPSILON;
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}
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return abs(a - b) < tolerance;
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}
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static _ALWAYS_INLINE_ bool is_equal_approx(real_t a, real_t b, real_t tolerance) {
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// Check for exact equality first, required to handle "infinity" values.
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if (a == b) {
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return true;
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}
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// Then check for approximate equality.
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return abs(a - b) < tolerance;
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}
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static _ALWAYS_INLINE_ bool is_zero_approx(real_t s) {
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return abs(s) < CMP_EPSILON;
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}
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static _ALWAYS_INLINE_ float absf(float g) {
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union {
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float f;
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uint32_t i;
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} u;
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u.f = g;
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u.i &= 2147483647u;
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return u.f;
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}
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static _ALWAYS_INLINE_ double absd(double g) {
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union {
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double d;
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uint64_t i;
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} u;
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u.d = g;
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u.i &= (uint64_t)9223372036854775807ll;
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return u.d;
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}
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//this function should be as fast as possible and rounding mode should not matter
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static _ALWAYS_INLINE_ int fast_ftoi(float a) {
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static int b;
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#if (defined(_WIN32_WINNT) && _WIN32_WINNT >= 0x0603) || WINAPI_FAMILY == WINAPI_FAMILY_PHONE_APP // windows 8 phone?
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b = (int)((a > 0.0) ? (a + 0.5) : (a - 0.5));
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#elif defined(_MSC_VER) && _MSC_VER < 1800
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__asm fld a __asm fistp b
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/*#elif defined( __GNUC__ ) && ( defined( __i386__ ) || defined( __x86_64__ ) )
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// use AT&T inline assembly style, document that
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// we use memory as output (=m) and input (m)
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__asm__ __volatile__ (
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"flds %1 \n\t"
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"fistpl %0 \n\t"
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: "=m" (b)
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: "m" (a));*/
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#else
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b = lrintf(a); //assuming everything but msvc 2012 or earlier has lrint
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#endif
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return b;
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}
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static _ALWAYS_INLINE_ uint32_t halfbits_to_floatbits(uint16_t h) {
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uint16_t h_exp, h_sig;
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uint32_t f_sgn, f_exp, f_sig;
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h_exp = (h & 0x7c00u);
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f_sgn = ((uint32_t)h & 0x8000u) << 16;
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switch (h_exp) {
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case 0x0000u: /* 0 or subnormal */
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h_sig = (h & 0x03ffu);
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/* Signed zero */
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if (h_sig == 0) {
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return f_sgn;
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}
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/* Subnormal */
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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_separation(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
|