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bd7ba0b664
Furthermore, functions which expect a rotation matrix will now give an error simply, rather than trying to orthonormalize such matrices. The documentation for such functions has be updated accordingly. This commit breaks code using 3D rotations, and is a part of the breaking changes in 2.1 -> 3.0 transition. The code affected within Godot code base is fixed in this commit.
296 lines
8.3 KiB
C++
296 lines
8.3 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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#ifndef NO_MATH_H
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#include "math.h"
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#endif
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class Math {
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static uint32_t default_seed;
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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 double sin(double p_x);
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static double cos(double p_x);
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static double tan(double p_x);
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static double sinh(double p_x);
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static double cosh(double p_x);
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static double tanh(double p_x);
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static double asin(double p_x);
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static double acos(double p_x);
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static double atan(double p_x);
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static double atan2(double p_y, double p_x);
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static double deg2rad(double p_y);
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static double rad2deg(double p_y);
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static double sqrt(double p_x);
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static double fmod(double p_x,double p_y);
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static double fposmod(double p_x,double p_y);
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static uint32_t rand_from_seed(uint32_t *seed);
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static double floor(double p_x);
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static double ceil(double p_x);
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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(uint32_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 bool is_nan(double p_val);
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static bool is_inf(double p_val);
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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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#define Math_PI 3.14159265358979323846
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#define Math_SQRT12 0.7071067811865475244008443621048490
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#endif // MATH_FUNCS_H
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