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/*************************************************************************/
/* math_funcs.h */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* http://www.godotengine.org */
/*************************************************************************/
/* Copyright (c) 2007-2017 Juan Linietsky, Ariel Manzur. */
/* */
/* Permission is hereby granted, free of charge, to any person obtaining */
/* a copy of this software and associated documentation files (the */
/* "Software"), to deal in the Software without restriction, including */
/* without limitation the rights to use, copy, modify, merge, publish, */
/* distribute, sublicense, and/or sell copies of the Software, and to */
/* permit persons to whom the Software is furnished to do so, subject to */
/* the following conditions: */
/* */
/* The above copyright notice and this permission notice shall be */
/* included in all copies or substantial portions of the Software. */
/* */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
/*************************************************************************/
#ifndef MATH_FUNCS_H
#define MATH_FUNCS_H
#include "typedefs.h"
#include "math_defs.h"
#ifndef NO_MATH_H
#include "math.h"
#endif
class Math {
static uint32_t default_seed;
public:
Math() {}; // useless to instance
enum {
RANDOM_MAX=2147483647L
};
static double sin(double p_x);
static double cos(double p_x);
static double tan(double p_x);
static double sinh(double p_x);
static double cosh(double p_x);
static double tanh(double p_x);
static double asin(double p_x);
static double acos(double p_x);
static double atan(double p_x);
static double atan2(double p_y, double p_x);
static double deg2rad(double p_y);
static double rad2deg(double p_y);
static double sqrt(double p_x);
static double fmod(double p_x,double p_y);
static double fposmod(double p_x,double p_y);
static uint32_t rand_from_seed(uint32_t *seed);
static double floor(double p_x);
static double ceil(double p_x);
static double ease(double p_x, double p_c);
static int step_decimals(double p_step);
static double stepify(double p_value,double p_step);
static void seed(uint32_t x=0);
static void randomize();
static uint32_t larger_prime(uint32_t p_val);
static double dectime(double p_value,double p_amount, double p_step);
static inline double linear2db(double p_linear) {
return Math::log( p_linear ) * 8.6858896380650365530225783783321;
}
static inline double db2linear(double p_db) {
return Math::exp( p_db * 0.11512925464970228420089957273422 );
}
static bool is_nan(double p_val);
static bool is_inf(double p_val);
static uint32_t rand();
static double randf();
static double round(double p_val);
static double random(double from, double to);
static _FORCE_INLINE_ bool isequal_approx(real_t a, real_t b) {
// TODO: Comparing floats for approximate-equality is non-trivial.
// 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.
// A proper implementation in terms of ULPs should eventually replace the contents of this function.
// See https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/ for details.
return abs(a-b) < CMP_EPSILON;
}
static _FORCE_INLINE_ real_t abs(real_t g) {
#ifdef REAL_T_IS_DOUBLE
return absd(g);
#else
return absf(g);
#endif
}
static _FORCE_INLINE_ float absf(float g) {
union {
float f;
uint32_t i;
} u;
u.f=g;
u.i&=2147483647u;
return u.f;
}
static _FORCE_INLINE_ double absd(double g) {
union {
double d;
uint64_t i;
} u;
u.d=g;
u.i&=(uint64_t)9223372036854775807ll;
return u.d;
}
//this function should be as fast as possible and rounding mode should not matter
static _FORCE_INLINE_ int fast_ftoi(float a) {
static int b;
#if (defined(_WIN32_WINNT) && _WIN32_WINNT >= 0x0603) || WINAPI_FAMILY == WINAPI_FAMILY_PHONE_APP // windows 8 phone?
b = (int)((a>0.0f) ? (a + 0.5f):(a -0.5f));
#elif defined(_MSC_VER) && _MSC_VER < 1800
__asm fld a
__asm fistp b
/*#elif defined( __GNUC__ ) && ( defined( __i386__ ) || defined( __x86_64__ ) )
// use AT&T inline assembly style, document that
// we use memory as output (=m) and input (m)
__asm__ __volatile__ (
"flds %1 \n\t"
"fistpl %0 \n\t"
: "=m" (b)
: "m" (a));*/
#else
b=lrintf(a); //assuming everything but msvc 2012 or earlier has lrint
#endif
return b;
}
#if defined(__GNUC__)
static _FORCE_INLINE_ int64_t dtoll(double p_double) { return (int64_t)p_double; } ///@TODO OPTIMIZE
#else
static _FORCE_INLINE_ int64_t dtoll(double p_double) { return (int64_t)p_double; } ///@TODO OPTIMIZE
#endif
static _FORCE_INLINE_ float lerp(float a, float b, float c) {
return a+(b-a)*c;
}
static double pow(double x, double y);
static double log(double x);
static double exp(double x);
static _FORCE_INLINE_ uint32_t halfbits_to_floatbits(uint16_t h)
{
uint16_t h_exp, h_sig;
uint32_t f_sgn, f_exp, f_sig;
h_exp = (h&0x7c00u);
f_sgn = ((uint32_t)h&0x8000u) << 16;
switch (h_exp) {
case 0x0000u: /* 0 or subnormal */
h_sig = (h&0x03ffu);
/* Signed zero */
if (h_sig == 0) {
return f_sgn;
}
/* Subnormal */
h_sig <<= 1;
while ((h_sig&0x0400u) == 0) {
h_sig <<= 1;
h_exp++;
}
f_exp = ((uint32_t)(127 - 15 - h_exp)) << 23;
f_sig = ((uint32_t)(h_sig&0x03ffu)) << 13;
return f_sgn + f_exp + f_sig;
case 0x7c00u: /* inf or NaN */
/* All-ones exponent and a copy of the significand */
return f_sgn + 0x7f800000u + (((uint32_t)(h&0x03ffu)) << 13);
default: /* normalized */
/* Just need to adjust the exponent and shift */
return f_sgn + (((uint32_t)(h&0x7fffu) + 0x1c000u) << 13);
}
}
static _FORCE_INLINE_ float halfptr_to_float(const uint16_t *h) {
union {
uint32_t u32;
float f32;
} u;
u.u32=halfbits_to_floatbits(*h);
return u.f32;
}
static _FORCE_INLINE_ uint16_t make_half_float(float f) {
union {
float fv;
uint32_t ui;
} ci;
ci.fv=f;
uint32_t x = ci.ui;
uint32_t sign = (unsigned short)(x >> 31);
uint32_t mantissa;
uint32_t exp;
uint16_t hf;
// get mantissa
mantissa = x & ((1 << 23) - 1);
// get exponent bits
exp = x & (0xFF << 23);
if (exp >= 0x47800000)
{
// check if the original single precision float number is a NaN
if (mantissa && (exp == (0xFF << 23)))
{
// we have a single precision NaN
mantissa = (1 << 23) - 1;
}
else
{
// 16-bit half-float representation stores number as Inf
mantissa = 0;
}
hf = (((uint16_t)sign) << 15) | (uint16_t)((0x1F << 10)) |
(uint16_t)(mantissa >> 13);
}
// check if exponent is <= -15
else if (exp <= 0x38000000)
{
/*// store a denorm half-float value or zero
exp = (0x38000000 - exp) >> 23;
mantissa >>= (14 + exp);
hf = (((uint16_t)sign) << 15) | (uint16_t)(mantissa);
*/
hf=0; //denormals do not work for 3D, convert to zero
}
else
{
hf = (((uint16_t)sign) << 15) |
(uint16_t)((exp - 0x38000000) >> 13) |
(uint16_t)(mantissa >> 13);
}
return hf;
}
};
#define Math_PI 3.14159265358979323846
#define Math_SQRT12 0.7071067811865475244008443621048490
#endif // MATH_FUNCS_H
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