#ifndef _DEMATH_H
#define _DEMATH_H
/*-------------------------------------------------------------------------
* drawElements Base Portability Library
* -------------------------------------
*
* Copyright 2014 The Android Open Source Project
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*//*!
* \file
* \brief Basic mathematical operations.
*//*--------------------------------------------------------------------*/
#include "deDefs.h"
#include <math.h>
#include <float.h>
DE_BEGIN_EXTERN_C
/* Mathematical constants. */
#define DE_PI 3.14159265358979324f /*!< Pi. */
#define DE_LOG_2 0.69314718056f /*!< log_e(2.0) */
#define DE_INV_LOG_2 1.44269504089f /*!< 1.0 / log_e(2.0) */
#define DE_E 2.71828182845904523536f /*!< e. */
#define DE_LOG2_E 1.44269504088896340736f /*!< log_2(e). */
#define DE_INV_LOG2_E 0.69314718055994530942f /*!< 1.0 / log_2(e). */
#define DE_PI_DOUBLE 3.14159265358979323846 /*!< Pi as a double. */
/* Rounding mode control. */
typedef enum deRoundingMode_e
{
DE_ROUNDINGMODE_TO_NEAREST = 0,
DE_ROUNDINGMODE_TO_ZERO,
DE_ROUNDINGMODE_TO_POSITIVE_INF,
DE_ROUNDINGMODE_TO_NEGATIVE_INF,
DE_ROUNDINGMODE_LAST
} deRoundingMode;
deRoundingMode deGetRoundingMode (void);
deBool deSetRoundingMode (deRoundingMode mode);
void deMath_selfTest (void);
/* Float properties */
/* \note The NaN test probably won't work with -ffast-math */
DE_INLINE int deFloatIsInf (float x) { return (x > FLT_MAX) - (x < -FLT_MAX); }
DE_INLINE deBool deFloatIsNaN (float x) { return (x != x); }
DE_INLINE int deIsInf (double x) { return (x > DBL_MAX) - (x < -DBL_MAX); }
DE_INLINE deBool deIsNaN (double x) { return (x != x); }
/* Basic utilities. */
DE_INLINE float deFloatAbs (float x) { return (x >= 0.0f) ? x : -x; }
DE_INLINE float deFloatMin (float a, float b) { return (a <= b) ? a : b; }
DE_INLINE float deFloatMax (float a, float b) { return (a >= b) ? a : b; }
DE_INLINE float deFloatClamp (float x, float mn, float mx) { return (x <= mn) ? mn : ((x >= mx) ? mx : x); }
DE_INLINE double deAbs (double x) { return (x >= 0.0) ? x : -x; }
DE_INLINE double deMin (double a, double b) { return (a <= b) ? a : b; }
DE_INLINE double deMax (double a, double b) { return (a >= b) ? a : b; }
DE_INLINE double deClamp (double x, double mn, double mx) { return (x <= mn) ? mn : ((x >= mx) ? mx : x); }
/* Utility functions. */
DE_INLINE float deFloatSign (float a) { return (a == 0.0f) ? 0.0f : ((a > 0.0f) ? +1.0f : -1.0f); }
DE_INLINE int deFloatIntSign (float a) { return (a == 0.0f) ? 0 : ((a > 0.0f) ? +1 : -1); }
DE_INLINE float deFloatFloor (float a) { return (float)floor(a); }
DE_INLINE float deFloatCeil (float a) { return (float)ceil(a); }
DE_INLINE float deFloatRound (float a) { return deFloatFloor(a + 0.5f); }
DE_INLINE float deFloatFrac (float a) { return a - deFloatFloor(a); }
DE_INLINE float deFloatMod (float a, float b) { return (float)fmod(a, b); }
DE_INLINE float deFloatModf (float x, float* i) { double j = 0; double ret = modf(x, &j); *i = (float)j; return (float)ret; }
DE_INLINE float deFloatMadd (float a, float b, float c) { return (a*b) + c; }
DE_INLINE float deFloatTrunc (float a) { return deFloatSign(a) * deFloatFloor(deFloatAbs(a)); }
DE_INLINE float deFloatLdExp (float a, int exponent) { return (float)ldexp(a, exponent); }
DE_INLINE float deFloatFrExp (float x, int* exponent) { return (float)frexp(x, exponent); }
float deFloatFractExp (float x, int* exponent);
DE_INLINE double deSign (double x) { return deIsNaN(x) ? x : (double)((x > 0.0) - (x < 0.0)); }
DE_INLINE int deIntSign (double x) { return (x > 0.0) - (x < 0.0); }
DE_INLINE double deFloor (double a) { return floor(a); }
DE_INLINE double deCeil (double a) { return ceil(a); }
DE_INLINE double deRound (double a) { return floor(a + 0.5); }
DE_INLINE double deFrac (double a) { return a - deFloor(a); }
DE_INLINE double deMod (double a, double b) { return fmod(a, b); }
DE_INLINE double deModf (double x, double* i) { return modf(x, i); }
DE_INLINE double deMadd (double a, double b, double c) { return (a*b) + c; }
DE_INLINE double deTrunc (double a) { return deSign(a) * floor(fabs(a)); }
DE_INLINE double deLdExp (double a, int exponent) { return ldexp(a, exponent); }
double deRoundEven (double a);
DE_INLINE double deFrExp (double x, int* exponent) { return frexp(x, exponent); }
/* Like frexp, except the returned fraction is in range [1.0, 2.0) */
double deFractExp (double x, int* exponent);
/* Exponential functions. */
DE_INLINE float deFloatPow (float a, float b) { return (float)pow(a, b); }
DE_INLINE float deFloatExp (float a) { return (float)exp(a); }
DE_INLINE float deFloatLog (float a) { return (float)log(a); }
DE_INLINE float deFloatExp2 (float a) { return (float)exp(a * DE_LOG_2); }
DE_INLINE float deFloatLog2 (float a) { return (float)log(a) * DE_INV_LOG_2; }
DE_INLINE float deFloatSqrt (float a) { return (float)sqrt(a); }
DE_INLINE float deFloatRcp (float a) { return (1.0f / a); }
DE_INLINE float deFloatRsq (float a) { float s = (float)sqrt(a); return (s == 0.0f) ? 0.0f : (1.0f / s); }
DE_INLINE double dePow (double a, double b) { return pow(a, b); }
DE_INLINE double deExp (double a) { return exp(a); }
DE_INLINE double deLog (double a) { return log(a); }
DE_INLINE double deExp2 (double a) { return exp(a * log(2.0)); }
DE_INLINE double deLog2 (double a) { return log(a) / log(2.0); }
DE_INLINE double deSqrt (double a) { return sqrt(a); }
DE_INLINE double deCbrt (double a) { return deSign(a) * dePow(deAbs(a), 1.0 / 3.0); }
/* Geometric functions. */
DE_INLINE float deFloatRadians (float a) { return a * (DE_PI / 180.0f); }
DE_INLINE float deFloatDegrees (float a) { return a * (180.0f / DE_PI); }
DE_INLINE float deFloatSin (float a) { return (float)sin(a); }
DE_INLINE float deFloatCos (float a) { return (float)cos(a); }
DE_INLINE float deFloatTan (float a) { return (float)tan(a); }
DE_INLINE float deFloatAsin (float a) { return (float)asin(a); }
DE_INLINE float deFloatAcos (float a) { return (float)acos(a); }
DE_INLINE float deFloatAtan2 (float y, float x) { return (float)atan2(y, x); }
DE_INLINE float deFloatAtanOver (float yOverX) { return (float)atan(yOverX); }
DE_INLINE float deFloatSinh (float a) { return (float)sinh(a); }
DE_INLINE float deFloatCosh (float a) { return (float)cosh(a); }
DE_INLINE float deFloatTanh (float a) { return (float)tanh(a); }
DE_INLINE float deFloatAsinh (float a) { return deFloatLog(a + deFloatSqrt(a*a + 1)); }
DE_INLINE float deFloatAcosh (float a) { return deFloatLog(a + deFloatSqrt(a*a - 1)); }
DE_INLINE float deFloatAtanh (float a) { return 0.5f*deFloatLog((1.0f+a)/(1.0f-a)); }
DE_INLINE double deSin (double a) { return sin(a); }
DE_INLINE double deCos (double a) { return cos(a); }
DE_INLINE double deTan (double a) { return tan(a); }
DE_INLINE double deAsin (double a) { return asin(a); }
DE_INLINE double deAcos (double a) { return acos(a); }
DE_INLINE double deAtan2 (double y, double x) { return atan2(y, x); }
DE_INLINE double deAtanOver (double yOverX) { return atan(yOverX); }
DE_INLINE double deSinh (double a) { return sinh(a); }
DE_INLINE double deCosh (double a) { return cosh(a); }
DE_INLINE double deTanh (double a) { return tanh(a); }
DE_INLINE double deAsinh (double a) { return deLog(a + deSqrt(a*a + 1)); }
DE_INLINE double deAcosh (double a) { return deLog(a + deSqrt(a*a - 1)); }
DE_INLINE double deAtanh (double a) { return 0.5*deLog((1.0+a)/(1.0-a)); }
/* Interpolation. */
DE_INLINE float deFloatMix (float a, float b, float t) { return a*(1.0f-t) + b*t; }
DE_INLINE float deFloatStep (float limit, float val) { return (val < limit) ? 0.0f : 1.0f; }
DE_INLINE float deFloatSmoothStep (float e0, float e1, float v)
{
float t;
if (v <= e0) return 0.0f;
if (v >= e1) return 1.0f;
t = (v - e0) / (e1 - e0);
return t * t * (3.0f - 2.0f * t);
}
DE_INLINE double deMix (double a, double b, double t) { return a*(1.0-t) + b*t; }
DE_INLINE double deStep (double limit, double val) { return (val < limit) ? 0.0 : 1.0; }
/* Comparison functions. */
DE_INLINE deBool deFloatCmpEQ (float a, float b) { return (a == b); }
DE_INLINE deBool deFloatCmpNE (float a, float b) { return (a != b); }
DE_INLINE deBool deFloatCmpLT (float a, float b) { return (a < b); }
DE_INLINE deBool deFloatCmpLE (float a, float b) { return (a <= b); }
DE_INLINE deBool deFloatCmpGT (float a, float b) { return (a > b); }
DE_INLINE deBool deFloatCmpGE (float a, float b) { return (a >= b); }
/* Convert int to float. If the value cannot be represented exactly in native single precision format, return
* either the nearest lower or the nearest higher representable value, chosen in an implementation-defined manner.
*
* \note Choosing either nearest lower or nearest higher means that implementation could for example consistently
* choose the lower value, i.e. this function does not round towards nearest.
* \note Value returned is in native single precision format. For example with x86 extended precision, the value
* returned might not be representable in IEEE single precision float.
*/
DE_INLINE float deInt32ToFloat (deInt32 x) { return (float)x; }
/* Convert to float. If the value cannot be represented exactly in IEEE single precision floating point format,
* return the nearest lower (round towards negative inf). */
float deInt32ToFloatRoundToNegInf (deInt32 x);
/* Convert to float. If the value cannot be represented exactly IEEE single precision floating point format,
* return the nearest higher (round towards positive inf). */
float deInt32ToFloatRoundToPosInf (deInt32 x);
/* Conversion to integer. */
DE_INLINE deInt32 deChopFloatToInt32 (float x) { return (deInt32)x; }
DE_INLINE deInt32 deFloorFloatToInt32 (float x) { return (deInt32)(deFloatFloor(x)); }
DE_INLINE deInt32 deCeilFloatToInt32 (float x) { return (deInt32)(deFloatCeil(x)); }
/* Arithmetic round */
DE_INLINE deInt16 deRoundFloatToInt16 (float x) { if(x >= 0.0f) return (deInt16)(x + 0.5f); else return (deInt16)(x - 0.5f); }
DE_INLINE deInt32 deRoundFloatToInt32 (float x) { if(x >= 0.0f) return (deInt32)(x + 0.5f); else return (deInt32)(x - 0.5f); }
DE_INLINE deInt64 deRoundFloatToInt64 (float x) { if(x >= 0.0f) return (deInt64)(x + 0.5f); else return (deInt64)(x - 0.5f); }
DE_END_EXTERN_C
#endif /* _DEMATH_H */