2014-02-10 02:10:30 +01:00
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/*************************************************************************/
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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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2017-08-27 14:16:55 +02:00
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/* https://godotengine.org */
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2014-02-10 02:10:30 +01:00
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/*************************************************************************/
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2022-01-03 21:27:34 +01:00
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/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur. */
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/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md). */
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2014-02-10 02:10:30 +01:00
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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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2018-01-05 00:50:27 +01:00
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2014-02-10 02:10:30 +01:00
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#ifndef MATH_FUNCS_H
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#define MATH_FUNCS_H
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2018-09-11 18:13:45 +02:00
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#include "core/math/math_defs.h"
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2018-09-21 13:32:17 +02:00
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#include "core/math/random_pcg.h"
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2018-09-11 18:13:45 +02:00
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#include "core/typedefs.h"
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2014-02-10 02:10:30 +01:00
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2017-04-28 18:29:15 +02:00
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#include "thirdparty/misc/pcg.h"
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2017-01-18 11:55:47 +01:00
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#include <float.h>
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2017-03-05 16:44:50 +01:00
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#include <math.h>
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2014-02-10 02:10:30 +01:00
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class Math {
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2018-09-21 13:32:17 +02:00
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static RandomPCG default_rand;
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2014-02-10 02:10:30 +01:00
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public:
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2017-01-12 12:55:19 +01:00
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Math() {} // useless to instance
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2014-02-10 02:10:30 +01:00
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2020-09-18 08:27:02 +02:00
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// Not using 'RANDOM_MAX' to avoid conflict with system headers on some OSes (at least NetBSD).
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static const uint64_t RANDOM_32BIT_MAX = 0xFFFFFFFF;
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2014-02-10 02:10:30 +01:00
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2017-01-14 21:35:39 +01:00
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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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2017-01-12 12:55:19 +01:00
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2017-01-14 21:35:39 +01:00
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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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2017-01-12 12:55:19 +01:00
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2017-01-14 21:35:39 +01:00
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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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2017-01-12 12:55:19 +01:00
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2017-01-14 21:35:39 +01:00
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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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2017-01-12 12:55:19 +01:00
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2019-05-05 14:03:52 +02:00
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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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2022-02-24 08:17:00 +01:00
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static _ALWAYS_INLINE_ float sincn(float p_x) { return sinc((float)Math_PI * p_x); }
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2019-05-05 14:03:52 +02:00
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static _ALWAYS_INLINE_ double sincn(double p_x) { return sinc(Math_PI * p_x); }
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2017-01-14 21:35:39 +01:00
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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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2017-01-12 12:55:19 +01:00
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2017-01-14 21:35:39 +01:00
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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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2017-01-12 12:55:19 +01:00
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2017-01-14 21:35:39 +01:00
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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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2017-01-12 12:55:19 +01:00
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2017-01-14 21:35:39 +01:00
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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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2017-01-12 12:55:19 +01:00
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2017-01-14 21:35:39 +01:00
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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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2017-01-12 12:55:19 +01:00
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2017-03-05 16:44:50 +01:00
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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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2017-01-12 12:55:19 +01:00
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2017-01-14 21:35:39 +01:00
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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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2017-01-12 12:55:19 +01:00
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2017-03-05 16:44:50 +01:00
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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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2017-01-12 12:55:19 +01:00
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2017-01-14 21:35:39 +01:00
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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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2017-01-12 12:55:19 +01:00
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2017-01-14 21:35:39 +01:00
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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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2017-01-12 12:55:19 +01:00
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2017-03-05 16:44:50 +01:00
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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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2017-01-12 12:55:19 +01:00
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2017-01-14 21:35:39 +01:00
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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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2017-01-12 12:55:19 +01:00
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2022-04-07 12:23:40 +02:00
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static _ALWAYS_INLINE_ double log1p(double p_x) { return ::log1p(p_x); }
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static _ALWAYS_INLINE_ float log1p(float p_x) { return ::log1pf(p_x); }
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2021-04-20 18:40:24 +02:00
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static _ALWAYS_INLINE_ double log2(double p_x) { return ::log2(p_x); }
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static _ALWAYS_INLINE_ float log2(float p_x) { return ::log2f(p_x); }
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2017-01-14 21:35:39 +01:00
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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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2017-01-12 12:55:19 +01:00
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2017-09-19 06:09:35 +02:00
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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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2017-01-12 12:55:19 +01:00
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2017-01-14 21:35:39 +01:00
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static _ALWAYS_INLINE_ bool is_inf(double p_val) {
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2017-03-05 16:44:50 +01:00
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#ifdef _MSC_VER
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2017-01-14 21:35:39 +01:00
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return !_finite(p_val);
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2017-06-14 17:11:53 +02:00
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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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2017-04-26 17:49:08 +02:00
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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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2021-10-28 15:19:35 +02:00
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((unsigned)ieee754.u == 0);
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2017-03-05 16:44:50 +01:00
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#else
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2017-01-14 21:35:39 +01:00
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return isinf(p_val);
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2017-03-05 16:44:50 +01:00
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#endif
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2017-01-12 12:55:19 +01:00
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}
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2017-03-05 16:44:50 +01:00
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2017-01-14 21:35:39 +01:00
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static _ALWAYS_INLINE_ bool is_inf(float p_val) {
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2017-03-05 16:44:50 +01:00
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#ifdef _MSC_VER
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2017-01-14 21:35:39 +01:00
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return !_finite(p_val);
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2017-06-14 17:11:53 +02:00
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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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2017-04-26 17:49:08 +02:00
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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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2017-03-05 16:44:50 +01:00
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#else
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2017-01-14 21:35:39 +01:00
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return isinf(p_val);
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2017-03-05 16:44:50 +01:00
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#endif
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2017-01-12 12:55:19 +01:00
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}
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2017-03-05 16:44:50 +01:00
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2022-08-11 10:12:27 +02:00
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static _ALWAYS_INLINE_ bool is_finite(double p_val) { return isfinite(p_val); }
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static _ALWAYS_INLINE_ bool is_finite(float p_val) { return isfinite(p_val); }
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2017-01-14 21:35:39 +01:00
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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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2017-01-12 12:55:19 +01:00
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2018-06-10 22:06:44 +02:00
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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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2022-02-24 08:17:00 +01:00
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if (((value < 0) && (p_y > 0)) || ((value > 0) && (p_y < 0))) {
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2018-06-10 22:06:44 +02:00
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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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2022-02-24 08:17:00 +01:00
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if (((value < 0) && (p_y > 0)) || ((value > 0) && (p_y < 0))) {
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2018-06-10 22:06:44 +02:00
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value += p_y;
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}
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2022-02-06 12:14:58 +01:00
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value += 0.0f;
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2018-06-10 22:06:44 +02:00
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return value;
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}
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2020-12-24 16:18:28 +01:00
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static _ALWAYS_INLINE_ float fposmodp(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) {
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value += p_y;
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}
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2022-02-06 12:14:58 +01:00
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value += 0.0f;
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2020-12-24 16:18:28 +01:00
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return value;
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}
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static _ALWAYS_INLINE_ double fposmodp(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) {
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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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2021-05-04 12:51:03 +02:00
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static _ALWAYS_INLINE_ int64_t posmod(int64_t p_x, int64_t p_y) {
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int64_t value = p_x % p_y;
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2022-02-24 08:17:00 +01:00
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if (((value < 0) && (p_y > 0)) || ((value > 0) && (p_y < 0))) {
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2018-10-27 22:12:27 +02:00
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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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2017-01-12 12:55:19 +01:00
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2022-08-13 17:45:42 +02:00
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static _ALWAYS_INLINE_ double deg_to_rad(double p_y) { return p_y * (Math_PI / 180.0); }
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static _ALWAYS_INLINE_ float deg_to_rad(float p_y) { return p_y * (float)(Math_PI / 180.0); }
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2017-01-12 12:55:19 +01:00
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2022-08-13 17:45:42 +02:00
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static _ALWAYS_INLINE_ double rad_to_deg(double p_y) { return p_y * (180.0 / Math_PI); }
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static _ALWAYS_INLINE_ float rad_to_deg(float p_y) { return p_y * (float)(180.0 / Math_PI); }
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2017-01-12 12:55:19 +01:00
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2017-08-10 16:06:10 +02:00
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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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2022-02-11 04:43:21 +01:00
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static _ALWAYS_INLINE_ double cubic_interpolate(double p_from, double p_to, double p_pre, double p_post, double p_weight) {
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return 0.5 *
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((p_from * 2.0) +
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(-p_pre + p_to) * p_weight +
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|
|
(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));
|
|
|
|
}
|
|
|
|
|
2022-08-26 04:42:00 +02:00
|
|
|
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);
|
|
|
|
}
|
2022-09-19 01:12:34 +02:00
|
|
|
|
2022-08-26 04:42:00 +02:00
|
|
|
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);
|
|
|
|
}
|
|
|
|
|
2022-07-28 21:55:10 +02:00
|
|
|
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);
|
|
|
|
}
|
2022-09-19 01:12:34 +02:00
|
|
|
|
2022-07-28 21:55:10 +02:00
|
|
|
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);
|
|
|
|
}
|
|
|
|
|
2022-08-26 04:42:00 +02:00
|
|
|
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);
|
|
|
|
}
|
2022-09-19 01:12:34 +02:00
|
|
|
|
2022-08-26 04:42:00 +02:00
|
|
|
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);
|
|
|
|
}
|
|
|
|
|
2022-06-27 19:41:32 +02:00
|
|
|
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;
|
|
|
|
}
|
2022-09-19 01:12:34 +02:00
|
|
|
|
2022-06-27 19:41:32 +02:00
|
|
|
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;
|
|
|
|
}
|
|
|
|
|
2019-07-14 06:30:45 +02:00
|
|
|
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;
|
|
|
|
}
|
|
|
|
|
2022-09-19 01:12:34 +02:00
|
|
|
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);
|
|
|
|
}
|
2017-08-10 16:06:10 +02:00
|
|
|
|
2022-09-19 01:12:34 +02:00
|
|
|
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));
|
|
|
|
}
|
2017-01-12 12:55:19 +01:00
|
|
|
|
2020-07-25 16:11:23 +02:00
|
|
|
static _ALWAYS_INLINE_ double smoothstep(double p_from, double p_to, double p_s) {
|
2020-05-14 16:41:43 +02:00
|
|
|
if (is_equal_approx(p_from, p_to)) {
|
2020-05-10 12:56:01 +02:00
|
|
|
return p_from;
|
2020-05-14 16:41:43 +02:00
|
|
|
}
|
2020-07-25 16:11:23 +02:00
|
|
|
double s = CLAMP((p_s - p_from) / (p_to - p_from), 0.0, 1.0);
|
|
|
|
return s * s * (3.0 - 2.0 * s);
|
2019-03-19 12:39:43 +01:00
|
|
|
}
|
2020-07-25 16:11:23 +02:00
|
|
|
static _ALWAYS_INLINE_ float smoothstep(float p_from, float p_to, float p_s) {
|
2020-05-14 16:41:43 +02:00
|
|
|
if (is_equal_approx(p_from, p_to)) {
|
2020-05-10 12:56:01 +02:00
|
|
|
return p_from;
|
2020-05-14 16:41:43 +02:00
|
|
|
}
|
2020-07-25 16:11:23 +02:00
|
|
|
float s = CLAMP((p_s - p_from) / (p_to - p_from), 0.0f, 1.0f);
|
|
|
|
return s * s * (3.0f - 2.0f * s);
|
2019-03-19 12:39:43 +01:00
|
|
|
}
|
2022-09-19 01:12:34 +02:00
|
|
|
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;
|
|
|
|
}
|
2019-03-19 12:39:43 +01:00
|
|
|
|
2022-09-19 01:12:34 +02:00
|
|
|
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;
|
|
|
|
}
|
2017-01-12 12:55:19 +01:00
|
|
|
|
2022-09-19 01:12:34 +02:00
|
|
|
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);
|
|
|
|
}
|
2017-01-12 12:55:19 +01:00
|
|
|
|
2021-05-20 13:18:53 +02:00
|
|
|
static _ALWAYS_INLINE_ double round(double p_val) { return ::round(p_val); }
|
|
|
|
static _ALWAYS_INLINE_ float round(float p_val) { return ::roundf(p_val); }
|
2017-01-12 12:55:19 +01:00
|
|
|
|
2019-02-25 08:51:04 +01:00
|
|
|
static _ALWAYS_INLINE_ int64_t wrapi(int64_t value, int64_t min, int64_t max) {
|
2019-08-05 05:31:26 +02:00
|
|
|
int64_t range = max - min;
|
|
|
|
return range == 0 ? min : min + ((((value - min) % range) + range) % range);
|
2018-03-04 17:16:57 +01:00
|
|
|
}
|
|
|
|
static _ALWAYS_INLINE_ double wrapf(double value, double min, double max) {
|
2019-08-05 05:31:26 +02:00
|
|
|
double range = max - min;
|
2022-06-08 15:55:31 +02:00
|
|
|
double result = is_zero_approx(range) ? min : value - (range * Math::floor((value - min) / range));
|
|
|
|
if (is_equal_approx(result, max)) {
|
|
|
|
return min;
|
|
|
|
}
|
|
|
|
return result;
|
2018-03-04 17:16:57 +01:00
|
|
|
}
|
|
|
|
static _ALWAYS_INLINE_ float wrapf(float value, float min, float max) {
|
2019-08-05 05:31:26 +02:00
|
|
|
float range = max - min;
|
2022-06-08 15:55:31 +02:00
|
|
|
float result = is_zero_approx(range) ? min : value - (range * Math::floor((value - min) / range));
|
|
|
|
if (is_equal_approx(result, max)) {
|
|
|
|
return min;
|
|
|
|
}
|
|
|
|
return result;
|
2018-03-04 17:16:57 +01:00
|
|
|
}
|
2017-10-11 19:38:55 +02:00
|
|
|
|
2021-10-15 15:25:00 +02:00
|
|
|
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;
|
|
|
|
}
|
|
|
|
|
2017-01-14 21:35:39 +01:00
|
|
|
// double only, as these functions are mainly used by the editor and not performance-critical,
|
2014-02-10 02:10:30 +01:00
|
|
|
static double ease(double p_x, double p_c);
|
2016-07-26 22:24:34 +02:00
|
|
|
static int step_decimals(double p_step);
|
2022-03-07 22:12:12 +01:00
|
|
|
static int range_step_decimals(double p_step); // For editor use only.
|
2020-12-21 19:02:57 +01:00
|
|
|
static double snapped(double p_value, double p_step);
|
2014-02-10 02:10:30 +01:00
|
|
|
|
2017-01-14 21:35:39 +01:00
|
|
|
static uint32_t larger_prime(uint32_t p_val);
|
2014-02-10 02:10:30 +01:00
|
|
|
|
2017-04-17 19:50:31 +02:00
|
|
|
static void seed(uint64_t x);
|
2017-01-14 21:35:39 +01:00
|
|
|
static void randomize();
|
|
|
|
static uint32_t rand_from_seed(uint64_t *seed);
|
2014-02-10 02:10:30 +01:00
|
|
|
static uint32_t rand();
|
2020-09-18 08:27:02 +02:00
|
|
|
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; }
|
2021-06-21 11:58:31 +02:00
|
|
|
static double randfn(double mean, double deviation);
|
2014-02-10 02:10:30 +01:00
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static double random(double from, double to);
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2017-01-14 21:35:39 +01:00
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static float random(float from, float to);
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2020-07-26 12:52:24 +02:00
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static int random(int from, int to);
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2016-03-09 00:00:52 +01:00
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2021-05-20 12:04:41 +02:00
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static _ALWAYS_INLINE_ bool is_equal_approx(float a, float b) {
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2019-09-01 19:57:04 +02:00
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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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2022-02-24 08:17:00 +01:00
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float tolerance = (float)CMP_EPSILON * abs(a);
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if (tolerance < (float)CMP_EPSILON) {
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tolerance = (float)CMP_EPSILON;
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2019-04-25 19:19:14 +02:00
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}
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return abs(a - b) < tolerance;
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}
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2021-05-20 12:04:41 +02:00
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static _ALWAYS_INLINE_ bool is_equal_approx(float a, float b, float tolerance) {
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2019-09-01 19:57:04 +02:00
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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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2019-04-25 19:19:14 +02:00
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return abs(a - b) < tolerance;
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}
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2016-10-18 22:50:21 +02:00
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2021-05-20 12:04:41 +02:00
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static _ALWAYS_INLINE_ bool is_zero_approx(float s) {
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2022-02-24 08:17:00 +01:00
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return abs(s) < (float)CMP_EPSILON;
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2021-05-20 12:04:41 +02:00
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}
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static _ALWAYS_INLINE_ bool is_equal_approx(double a, double 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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double 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(double a, double b, double 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(double s) {
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2019-04-25 19:19:14 +02:00
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return abs(s) < CMP_EPSILON;
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2016-10-18 22:50:21 +02:00
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}
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2017-01-14 21:35:39 +01:00
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static _ALWAYS_INLINE_ float absf(float g) {
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2014-02-10 02:10:30 +01:00
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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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2017-03-05 16:44:50 +01:00
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u.f = g;
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u.i &= 2147483647u;
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2014-02-10 02:10:30 +01:00
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return u.f;
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}
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2017-01-14 21:35:39 +01:00
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static _ALWAYS_INLINE_ double absd(double g) {
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2014-02-10 02:10:30 +01:00
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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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2017-03-05 16:44:50 +01:00
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u.d = g;
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u.i &= (uint64_t)9223372036854775807ll;
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2014-02-10 02:10:30 +01:00
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return u.d;
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}
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2021-05-20 22:25:58 +02:00
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// This function should be as fast as possible and rounding mode should not matter.
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2017-01-14 21:35:39 +01:00
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static _ALWAYS_INLINE_ int fast_ftoi(float a) {
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2021-05-20 22:25:58 +02:00
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// Assuming every supported compiler has `lrint()`.
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return lrintf(a);
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2014-02-10 02:10:30 +01:00
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}
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2017-03-05 16:44:50 +01:00
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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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2016-10-19 16:14:41 +02:00
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}
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2017-01-14 21:35:39 +01:00
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static _ALWAYS_INLINE_ float halfptr_to_float(const uint16_t *h) {
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2016-10-19 16:14:41 +02:00
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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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2017-03-05 16:44:50 +01:00
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u.u32 = halfbits_to_floatbits(*h);
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2016-10-19 16:14:41 +02:00
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return u.f32;
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}
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2017-05-27 02:49:49 +02:00
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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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2017-01-14 21:35:39 +01:00
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static _ALWAYS_INLINE_ uint16_t make_half_float(float f) {
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2017-03-05 16:44:50 +01:00
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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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2022-04-05 12:40:26 +02:00
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uint32_t exponent;
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2017-03-05 16:44:50 +01:00
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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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2022-04-05 12:40:26 +02:00
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exponent = x & (0xFF << 23);
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if (exponent >= 0x47800000) {
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2017-03-05 16:44:50 +01:00
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// check if the original single precision float number is a NaN
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2022-04-05 12:40:26 +02:00
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if (mantissa && (exponent == (0xFF << 23))) {
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2017-03-05 16:44:50 +01:00
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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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2021-10-28 15:19:35 +02:00
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(uint16_t)(mantissa >> 13);
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2016-10-19 16:14:41 +02:00
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}
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2017-03-05 16:44:50 +01:00
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// check if exponent is <= -15
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2022-04-05 12:40:26 +02:00
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else if (exponent <= 0x38000000) {
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/*
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// store a denorm half-float value or zero
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exponent = (0x38000000 - exponent) >> 23;
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mantissa >>= (14 + exponent);
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hf = (((uint16_t)sign) << 15) | (uint16_t)(mantissa);
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*/
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2017-03-05 16:44:50 +01:00
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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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2022-04-05 12:40:26 +02:00
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(uint16_t)((exponent - 0x38000000) >> 13) |
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2021-10-28 15:19:35 +02:00
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(uint16_t)(mantissa >> 13);
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2017-03-05 16:44:50 +01:00
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}
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2016-10-19 16:14:41 +02:00
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2017-03-05 16:44:50 +01:00
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return hf;
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}
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2017-09-18 23:44:04 +02:00
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static _ALWAYS_INLINE_ float snap_scalar(float p_offset, float p_step, float p_target) {
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2020-12-21 19:02:57 +01:00
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return p_step != 0 ? Math::snapped(p_target - p_offset, p_step) + p_offset : p_target;
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2017-09-18 23:44:04 +02:00
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}
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2019-10-31 13:40:58 +01:00
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static _ALWAYS_INLINE_ float snap_scalar_separation(float p_offset, float p_step, float p_target, float p_separation) {
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2017-09-18 23:44:04 +02:00
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if (p_step != 0) {
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2020-12-21 19:02:57 +01:00
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float a = Math::snapped(p_target - p_offset, p_step + p_separation) + p_offset;
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2017-09-18 23:44:04 +02:00
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float b = a;
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2020-05-14 16:41:43 +02:00
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if (p_target >= 0) {
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2017-09-18 23:44:04 +02:00
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b -= p_separation;
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2020-05-14 16:41:43 +02:00
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} else {
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2017-09-18 23:44:04 +02:00
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b += p_step;
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2020-05-14 16:41:43 +02:00
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}
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2017-09-18 23:44:04 +02:00
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return (Math::abs(p_target - a) < Math::abs(p_target - b)) ? a : b;
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}
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return p_target;
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}
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2014-02-10 02:10:30 +01:00
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};
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#endif // MATH_FUNCS_H
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