text: #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 "deMemory.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.		*/
  #define DE_PI_16BIT		0x4248					/*!< Pi. as a float16b		*/
  
  /* 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); }
  
  DE_INLINE deUint32 deFloatBitsToUint32(float x)
  {
  	deUint32 bits;
  	deMemcpy((void *)&bits, (void *)&x, 4);
  	return bits;
  }
  
  DE_INLINE deUint64 deDoubleBitsToUint64(double x)
  {
  	deUint64 bits;
  	deMemcpy((void *)&bits, (void *)&x, 8);
  	return bits;
  }
  
  DE_INLINE deBool deFloatIsPositiveZero(float x)
  {
  	return x == 0 && (deFloatBitsToUint32(x) >> 31) == 0;
  }
  
  DE_INLINE deBool deDoubleIsPositiveZero(double x)
  {
  	return x == 0 && (deDoubleBitsToUint64(x) >> 63) == 0;
  }
  
  DE_INLINE deBool deFloatIsNegativeZero(float x)
  {
  	return x == 0 && (deFloatBitsToUint32(x) >> 31) != 0;
  }
  
  DE_INLINE deBool deDoubleIsNegativeZero(double x)
  {
  	return x == 0 && (deDoubleBitsToUint64(x) >> 63) != 0;
  }
  
  DE_INLINE deBool deFloatIsIEEENaN(float x)
  {
  	deUint32 e = (deFloatBitsToUint32(x) & 0x7f800000u) >> 23;
  	deUint32 m = (deFloatBitsToUint32(x) & 0x007fffffu);
  	return e == 0xff && m != 0;
  }
  
  DE_INLINE deBool deDoubleIsIEEENaN(double x)
  {
  	deUint64 e = (deDoubleBitsToUint64(x) & 0x7ff0000000000000ull) >> 52;
  	deUint64 m = (deDoubleBitsToUint64(x) & 0x000fffffffffffffull);
  	return e == 0x7ff && m != 0;
  }
  
  /* \note The definition used for signaling NaN here is valid for ARM and
   * x86 but possibly not for other platforms.
   *
   * These are defined as overloads so that they can be used in templated
   * code without risking a type conversion which would triggern an exception
   * on a signaling NaN.  We don't use deIsNan in these helpers because they
   * do a comparison operation which may also trigger exceptions.
   */
  DE_INLINE deBool deFloatIsSignalingNaN(float x)
  {
  	return deFloatIsIEEENaN(x) && (deFloatBitsToUint32(x) & (1u << 22)) == 0;
  }
  
  DE_INLINE deBool deDoubleIsSignalingNaN(double x)
  {
  	return deDoubleIsIEEENaN(x) && (deDoubleBitsToUint64(x) & (1ull << 51)) == 0;
  }
  
  DE_INLINE deBool deFloatIsQuietNaN(float x)
  {
  	return deFloatIsIEEENaN(x) && (deFloatBitsToUint32(x) & (1u << 22)) != 0;
  }
  
  DE_INLINE deBool deDoubleIsQuietNaN(double x)
  {
  	return deDoubleIsIEEENaN(x) && (deDoubleBitsToUint64(x) & (1ull << 51)) != 0;
  }
  
  /* 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 */
  