390 lines
9.3 KiB
C++
390 lines
9.3 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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/* http://www.godotengine.org */
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/*************************************************************************/
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/* Copyright (c) 2007-2017 Juan Linietsky, Ariel Manzur. */
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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 "typedefs.h"
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#include "math_defs.h"
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#include "pcg.h"
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#include <math.h>
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#include <float.h>
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#define Math_PI 3.14159265358979323846
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#define Math_SQRT12 0.7071067811865475244008443621048490
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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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enum {
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RANDOM_MAX=2147483647L
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};
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static _ALWAYS_INLINE_ double sin(double p_x) {
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return ::sin(p_x);
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}
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static _ALWAYS_INLINE_ double cos(double p_x) {
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return ::cos(p_x);
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}
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static _ALWAYS_INLINE_ double tan(double p_x) {
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return ::tan(p_x);
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}
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static _ALWAYS_INLINE_ double sinh(double p_x) {
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return ::sinh(p_x);
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}
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static _ALWAYS_INLINE_ double cosh(double p_x) {
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return ::cosh(p_x);
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}
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static _ALWAYS_INLINE_ double tanh(double p_x) {
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return ::tanh(p_x);
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}
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static _ALWAYS_INLINE_ double asin(double p_x) {
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return ::asin(p_x);
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}
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static _ALWAYS_INLINE_ double acos(double p_x) {
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return ::acos(p_x);
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}
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static _ALWAYS_INLINE_ double atan(double p_x) {
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return ::atan(p_x);
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}
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static _ALWAYS_INLINE_ double atan2(double p_y, double p_x) {
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return ::atan2(p_y,p_x);
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}
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static _ALWAYS_INLINE_ double deg2rad(double p_y) {
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return p_y*Math_PI/180.0;
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}
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static _ALWAYS_INLINE_ double rad2deg(double p_y) {
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return p_y*180.0/Math_PI;
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}
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static _ALWAYS_INLINE_ double sqrt(double p_x) {
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return ::sqrt(p_x);
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}
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static _ALWAYS_INLINE_ double fmod(double p_x,double p_y) {
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return ::fmod(p_x,p_y);
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}
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static _ALWAYS_INLINE_ double fposmod(double p_x,double p_y) {
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if (p_x>=0) {
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return fmod(p_x,p_y);
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} else {
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return p_y-fmod(-p_x,p_y);
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}
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}
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static _ALWAYS_INLINE_ double floor(double p_x) {
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return ::floor(p_x);
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}
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static _ALWAYS_INLINE_ double ceil(double p_x) {
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return ::ceil(p_x);
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}
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static uint32_t rand_from_seed(uint64_t *seed);
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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 void seed(uint64_t x=0);
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static void randomize();
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static uint32_t larger_prime(uint32_t p_val);
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static double dectime(double p_value,double p_amount, double p_step);
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static inline double linear2db(double p_linear) {
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return Math::log( p_linear ) * 8.6858896380650365530225783783321;
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}
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static inline double db2linear(double p_db) {
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return Math::exp( p_db * 0.11512925464970228420089957273422 );
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}
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static _ALWAYS_INLINE_ bool is_nan(double p_val) {
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return (p_val!=p_val);
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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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#else
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return isinf(p_val);
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#endif
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}
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static uint32_t rand();
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static double randf();
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static double round(double p_val);
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static double random(double from, double to);
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static _FORCE_INLINE_ bool isequal_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 _FORCE_INLINE_ real_t abs(real_t g) {
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#ifdef REAL_T_IS_DOUBLE
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return absd(g);
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#else
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return absf(g);
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#endif
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}
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static _FORCE_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 _FORCE_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 _FORCE_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>0.0f) ? (a + 0.5f):(a -0.5f));
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#elif defined(_MSC_VER) && _MSC_VER < 1800
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__asm fld a
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__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 _FORCE_INLINE_ int64_t dtoll(double p_double) { return (int64_t)p_double; } ///@TODO OPTIMIZE
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#else
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static _FORCE_INLINE_ int64_t dtoll(double p_double) { return (int64_t)p_double; } ///@TODO OPTIMIZE
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#endif
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static _FORCE_INLINE_ float lerp(float a, float b, float c) {
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return a+(b-a)*c;
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}
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static double pow(double x, double y);
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static double log(double x);
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static double exp(double x);
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static _FORCE_INLINE_ uint32_t halfbits_to_floatbits(uint16_t h)
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{
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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 _FORCE_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 _FORCE_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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{
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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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{
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// we have a single precision NaN
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mantissa = (1 << 23) - 1;
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}
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else
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{
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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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{
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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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}
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else
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{
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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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