| #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_EVEN = 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)); } |
| |
| DE_INLINE deInt32 deChopToInt32 (double x) { return (deInt32)x; } |
| DE_INLINE deInt32 deFloorToInt32 (double x) { return (deInt32)(deFloor(x)); } |
| DE_INLINE deInt32 deCeilToInt32 (double x) { return (deInt32)(deCeil(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_INLINE deInt16 deRoundToInt16 (double x) { if(x >= 0.0) return (deInt16)(x + 0.5); else return (deInt16)(x - 0.5); } |
| DE_INLINE deInt32 deRoundToInt32 (double x) { if(x >= 0.0) return (deInt32)(x + 0.5); else return (deInt32)(x - 0.5); } |
| DE_INLINE deInt64 deRoundToInt64 (double x) { if(x >= 0.0) return (deInt64)(x + 0.5); else return (deInt64)(x - 0.5); } |
| |
| DE_END_EXTERN_C |
| |
| #endif /* _DEMATH_H */ |
