393 lines
14 KiB
C++
393 lines
14 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) 2007-2017 Juan Linietsky, Ariel Manzur. */
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/* Copyright (c) 2014-2017 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 "math_defs.h"
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#include "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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#define Math_PI 3.14159265358979323846
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#define Math_SQRT12 0.7071067811865475244008443621048490
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#define Math_LN2 0.693147180559945309417
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#define Math_INF INFINITY
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#define Math_NAN NAN
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class Math {
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static pcg32_random_t default_pcg;
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public:
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Math() {} // useless to instance
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static const uint64_t RANDOM_MAX = 4294967295;
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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_ 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) { return (p_x >= 0) ? Math::fmod(p_x, p_y) : p_y - Math::fmod(-p_x, p_y); }
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static _ALWAYS_INLINE_ float fposmod(float p_x, float p_y) { return (p_x >= 0) ? Math::fmod(p_x, p_y) : p_y - Math::fmod(-p_x, p_y); }
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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 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 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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// 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 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 randf() { return (double)rand() / (double)Math::RANDOM_MAX; }
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static _ALWAYS_INLINE_ float randd() { 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(real_t a, real_t b) {
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// TODO: Comparing floats for approximate-equality is non-trivial.
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// Using epsilon should cover the typical cases in Godot (where a == b is used to compare two reals), such as matrix and vector comparison operators.
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// A proper implementation in terms of ULPs should eventually replace the contents of this function.
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// See https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/ for details.
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return abs(a - b) < 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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#if defined(__GNUC__)
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static _ALWAYS_INLINE_ int64_t dtoll(double p_double) { return (int64_t)p_double; } ///@TODO OPTIMIZE
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static _ALWAYS_INLINE_ int64_t dtoll(float p_float) { return (int64_t)p_float; } ///@TODO OPTIMIZE and rename
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#else
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static _ALWAYS_INLINE_ int64_t dtoll(double p_double) { return (int64_t)p_double; } ///@TODO OPTIMIZE
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static _ALWAYS_INLINE_ int64_t dtoll(float p_float) { return (int64_t)p_float; } ///@TODO OPTIMIZE and rename
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#endif
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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;
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while ((h_sig & 0x0400u) == 0) {
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h_sig <<= 1;
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h_exp++;
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}
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f_exp = ((uint32_t)(127 - 15 - h_exp)) << 23;
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f_sig = ((uint32_t)(h_sig & 0x03ffu)) << 13;
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return f_sgn + f_exp + f_sig;
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case 0x7c00u: /* inf or NaN */
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/* All-ones exponent and a copy of the significand */
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return f_sgn + 0x7f800000u + (((uint32_t)(h & 0x03ffu)) << 13);
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default: /* normalized */
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/* Just need to adjust the exponent and shift */
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return f_sgn + (((uint32_t)(h & 0x7fffu) + 0x1c000u) << 13);
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}
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}
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static _ALWAYS_INLINE_ float halfptr_to_float(const uint16_t *h) {
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union {
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uint32_t u32;
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float f32;
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} u;
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u.u32 = halfbits_to_floatbits(*h);
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return u.f32;
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}
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static _ALWAYS_INLINE_ float half_to_float(const uint16_t h) {
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return halfptr_to_float(&h);
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}
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static _ALWAYS_INLINE_ uint16_t make_half_float(float f) {
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union {
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float fv;
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uint32_t ui;
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} ci;
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ci.fv = f;
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uint32_t x = ci.ui;
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uint32_t sign = (unsigned short)(x >> 31);
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uint32_t mantissa;
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uint32_t exp;
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uint16_t hf;
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// get mantissa
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mantissa = x & ((1 << 23) - 1);
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// get exponent bits
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exp = x & (0xFF << 23);
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if (exp >= 0x47800000) {
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// check if the original single precision float number is a NaN
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if (mantissa && (exp == (0xFF << 23))) {
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// we have a single precision NaN
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mantissa = (1 << 23) - 1;
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} else {
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// 16-bit half-float representation stores number as Inf
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mantissa = 0;
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}
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hf = (((uint16_t)sign) << 15) | (uint16_t)((0x1F << 10)) |
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(uint16_t)(mantissa >> 13);
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}
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// check if exponent is <= -15
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else if (exp <= 0x38000000) {
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/*// store a denorm half-float value or zero
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exp = (0x38000000 - exp) >> 23;
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mantissa >>= (14 + exp);
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hf = (((uint16_t)sign) << 15) | (uint16_t)(mantissa);
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*/
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hf = 0; //denormals do not work for 3D, convert to zero
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} else {
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hf = (((uint16_t)sign) << 15) |
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(uint16_t)((exp - 0x38000000) >> 13) |
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(uint16_t)(mantissa >> 13);
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}
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return hf;
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}
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};
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#endif // MATH_FUNCS_H
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