godot/core/math/math_funcs.h

/*************************************************************************/
/*  math_funcs.h                                                         */
/*************************************************************************/
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/* Copyright (c) 2007-2017 Juan Linietsky, Ariel Manzur.                 */
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#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