/* =========================================================================== Doom 3 GPL Source Code Copyright (C) 1999-2011 id Software LLC, a ZeniMax Media company. This file is part of the Doom 3 GPL Source Code ("Doom 3 Source Code"). Doom 3 Source Code is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. Doom 3 Source Code is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with Doom 3 Source Code. If not, see . In addition, the Doom 3 Source Code is also subject to certain additional terms. You should have received a copy of these additional terms immediately following the terms and conditions of the GNU General Public License which accompanied the Doom 3 Source Code. If not, please request a copy in writing from id Software at the address below. If you have questions concerning this license or the applicable additional terms, you may contact in writing id Software LLC, c/o ZeniMax Media Inc., Suite 120, Rockville, Maryland 20850 USA. =========================================================================== */ #ifndef __MATH_MATH_H__ #define __MATH_MATH_H__ #ifdef MACOS_X // for FLT_MIN #include #endif /* =============================================================================== Math =============================================================================== */ #ifdef INFINITY #undef INFINITY #endif #ifdef FLT_EPSILON #undef FLT_EPSILON #endif #define DEG2RAD(a) ( (a) * idMath::M_DEG2RAD ) #define RAD2DEG(a) ( (a) * idMath::M_RAD2DEG ) #define SEC2MS(t) ( idMath::FtoiFast( (t) * idMath::M_SEC2MS ) ) #define MS2SEC(t) ( (t) * idMath::M_MS2SEC ) #define ANGLE2SHORT(x) ( idMath::FtoiFast( (x) * 65536.0f / 360.0f ) & 65535 ) #define SHORT2ANGLE(x) ( (x) * ( 360.0f / 65536.0f ) ) #define ANGLE2BYTE(x) ( idMath::FtoiFast( (x) * 256.0f / 360.0f ) & 255 ) #define BYTE2ANGLE(x) ( (x) * ( 360.0f / 256.0f ) ) #define FLOATSIGNBITSET(f) ((*(const unsigned int *)&(f)) >> 31) #define FLOATSIGNBITNOTSET(f) ((~(*(const unsigned int *)&(f))) >> 31) #define FLOATNOTZERO(f) ((*(const unsigned int *)&(f)) & ~(1<<31) ) #define INTSIGNBITSET(i) (((const unsigned int)(i)) >> 31) #define INTSIGNBITNOTSET(i) ((~((const unsigned int)(i))) >> 31) #define FLOAT_IS_NAN(x) (((*(const unsigned int *)&x) & 0x7f800000) == 0x7f800000) #define FLOAT_IS_INF(x) (((*(const unsigned int *)&x) & 0x7fffffff) == 0x7f800000) #define FLOAT_IS_IND(x) ((*(const unsigned int *)&x) == 0xffc00000) #define FLOAT_IS_DENORMAL(x) (((*(const unsigned int *)&x) & 0x7f800000) == 0x00000000 && \ ((*(const unsigned int *)&x) & 0x007fffff) != 0x00000000 ) #define IEEE_FLT_MANTISSA_BITS 23 #define IEEE_FLT_EXPONENT_BITS 8 #define IEEE_FLT_EXPONENT_BIAS 127 #define IEEE_FLT_SIGN_BIT 31 #define IEEE_DBL_MANTISSA_BITS 52 #define IEEE_DBL_EXPONENT_BITS 11 #define IEEE_DBL_EXPONENT_BIAS 1023 #define IEEE_DBL_SIGN_BIT 63 #define IEEE_DBLE_MANTISSA_BITS 63 #define IEEE_DBLE_EXPONENT_BITS 15 #define IEEE_DBLE_EXPONENT_BIAS 0 #define IEEE_DBLE_SIGN_BIT 79 template ID_INLINE int MaxIndex( T x, T y ) { return ( x > y ) ? 0 : 1; } template ID_INLINE int MinIndex( T x, T y ) { return ( x < y ) ? 0 : 1; } template ID_INLINE T Max3( T x, T y, T z ) { return ( x > y ) ? ( ( x > z ) ? x : z ) : ( ( y > z ) ? y : z ); } template ID_INLINE T Min3( T x, T y, T z ) { return ( x < y ) ? ( ( x < z ) ? x : z ) : ( ( y < z ) ? y : z ); } template ID_INLINE int Max3Index( T x, T y, T z ) { return ( x > y ) ? ( ( x > z ) ? 0 : 2 ) : ( ( y > z ) ? 1 : 2 ); } template ID_INLINE int Min3Index( T x, T y, T z ) { return ( x < y ) ? ( ( x < z ) ? 0 : 2 ) : ( ( y < z ) ? 1 : 2 ); } template ID_INLINE T Sign( T f ) { return ( f > 0 ) ? 1 : ( ( f < 0 ) ? -1 : 0 ); } template ID_INLINE T Square( T x ) { return x * x; } template ID_INLINE T Cube( T x ) { return x * x * x; } class idMath { public: static void Init( void ); static float RSqrt( float x ); // reciprocal square root, returns huge number when x == 0.0 static float InvSqrt( float x ); // inverse square root with 32 bits precision, returns huge number when x == 0.0 static float InvSqrt16( float x ); // inverse square root with 16 bits precision, returns huge number when x == 0.0 static double InvSqrt64( float x ); // inverse square root with 64 bits precision, returns huge number when x == 0.0 static float Sqrt( float x ); // square root with 32 bits precision static float Sqrt16( float x ); // square root with 16 bits precision static double Sqrt64( float x ); // square root with 64 bits precision static float Sin( float a ); // sine with 32 bits precision static float Sin16( float a ); // sine with 16 bits precision, maximum absolute error is 2.3082e-09 static double Sin64( float a ); // sine with 64 bits precision static float Cos( float a ); // cosine with 32 bits precision static float Cos16( float a ); // cosine with 16 bits precision, maximum absolute error is 2.3082e-09 static double Cos64( float a ); // cosine with 64 bits precision static void SinCos( float a, float &s, float &c ); // sine and cosine with 32 bits precision static void SinCos16( float a, float &s, float &c ); // sine and cosine with 16 bits precision static void SinCos64( float a, double &s, double &c ); // sine and cosine with 64 bits precision static float Tan( float a ); // tangent with 32 bits precision static float Tan16( float a ); // tangent with 16 bits precision, maximum absolute error is 1.8897e-08 static double Tan64( float a ); // tangent with 64 bits precision static float ASin( float a ); // arc sine with 32 bits precision, input is clamped to [-1, 1] to avoid a silent NaN static float ASin16( float a ); // arc sine with 16 bits precision, maximum absolute error is 6.7626e-05 static double ASin64( float a ); // arc sine with 64 bits precision static float ACos( float a ); // arc cosine with 32 bits precision, input is clamped to [-1, 1] to avoid a silent NaN static float ACos16( float a ); // arc cosine with 16 bits precision, maximum absolute error is 6.7626e-05 static double ACos64( float a ); // arc cosine with 64 bits precision static float ATan( float a ); // arc tangent with 32 bits precision static float ATan16( float a ); // arc tangent with 16 bits precision, maximum absolute error is 1.3593e-08 static double ATan64( float a ); // arc tangent with 64 bits precision static float ATan( float y, float x ); // arc tangent with 32 bits precision static float ATan16( float y, float x ); // arc tangent with 16 bits precision, maximum absolute error is 1.3593e-08 static double ATan64( float y, float x ); // arc tangent with 64 bits precision static float Pow( float x, float y ); // x raised to the power y with 32 bits precision static float Pow16( float x, float y ); // x raised to the power y with 16 bits precision static double Pow64( float x, float y ); // x raised to the power y with 64 bits precision static float Exp( float f ); // e raised to the power f with 32 bits precision static float Exp16( float f ); // e raised to the power f with 16 bits precision static double Exp64( float f ); // e raised to the power f with 64 bits precision static float Log( float f ); // natural logarithm with 32 bits precision static float Log16( float f ); // natural logarithm with 16 bits precision static double Log64( float f ); // natural logarithm with 64 bits precision static int IPow( int x, int y ); // integral x raised to the power y static int ILog2( float f ); // integral base-2 logarithm of the floating point value static int ILog2( int i ); // integral base-2 logarithm of the integer value static int BitsForFloat( float f ); // minumum number of bits required to represent ceil( f ) static int BitsForInteger( int i ); // minumum number of bits required to represent i static int MaskForFloatSign( float f );// returns 0x00000000 if x >= 0.0f and returns 0xFFFFFFFF if x <= -0.0f static int MaskForIntegerSign( int i );// returns 0x00000000 if x >= 0 and returns 0xFFFFFFFF if x < 0 static int FloorPowerOfTwo( int x ); // round x down to the nearest power of 2 static int CeilPowerOfTwo( int x ); // round x up to the nearest power of 2 static bool IsPowerOfTwo( int x ); // returns true if x is a power of 2 static int BitCount( int x ); // returns the number of 1 bits in x static int BitReverse( int x ); // returns the bit reverse of x static int Abs( int x ); // returns the absolute value of the integer value (for reference only) static float Fabs( float f ); // returns the absolute value of the floating point value static float Floor( float f ); // returns the largest integer that is less than or equal to the given value static float Ceil( float f ); // returns the smallest integer that is greater than or equal to the given value static float Rint( float f ); // returns the nearest integer static int Ftoi( float f ); // float to int conversion static int FtoiFast( float f ); // fast float to int conversion but uses current FPU round mode (default round nearest) static unsigned int Ftol( float f ); // float to int conversion static unsigned int FtolFast( float ); // fast float to int conversion but uses current FPU round mode (default round nearest) static signed char ClampChar( int i ); static signed short ClampShort( int i ); static int ClampInt( int min, int max, int value ); static float ClampFloat( float min, float max, float value ); static float AngleNormalize360( float angle ); static float AngleNormalize180( float angle ); static float AngleDelta( float angle1, float angle2 ); static int FloatToBits( float f, int exponentBits, int mantissaBits ); static float BitsToFloat( int i, int exponentBits, int mantissaBits ); static int FloatHash( const float *array, const int numFloats ); static const float PI; // pi static const float TWO_PI; // pi * 2 static const float HALF_PI; // pi / 2 static const float ONEFOURTH_PI; // pi / 4 static const float E; // e static const float SQRT_TWO; // sqrt( 2 ) static const float SQRT_THREE; // sqrt( 3 ) static const float SQRT_1OVER2; // sqrt( 1 / 2 ) static const float SQRT_1OVER3; // sqrt( 1 / 3 ) static const float M_DEG2RAD; // degrees to radians multiplier static const float M_RAD2DEG; // radians to degrees multiplier static const float M_SEC2MS; // seconds to milliseconds multiplier static const float M_MS2SEC; // milliseconds to seconds multiplier static const float INFINITY; // huge number which should be larger than any valid number used static const float FLT_EPSILON; // smallest positive number such that 1.0+FLT_EPSILON != 1.0 private: enum { LOOKUP_BITS = 8, EXP_POS = 23, EXP_BIAS = 127, LOOKUP_POS = (EXP_POS-LOOKUP_BITS), SEED_POS = (EXP_POS-8), SQRT_TABLE_SIZE = (2<( &x ); i = 0x5f3759df - ( i >> 1 ); r = *reinterpret_cast( &i ); r = r * ( 1.5f - r * r * y ); return r; } ID_INLINE float idMath::InvSqrt16( float x ) { dword a = ((union _flint*)(&x))->i; union _flint seed; assert( initialized ); double y = x * 0.5f; seed.i = (( ( (3*EXP_BIAS-1) - ( (a >> EXP_POS) & 0xFF) ) >> 1)<> (EXP_POS-LOOKUP_BITS)) & LOOKUP_MASK]; double r = seed.f; r = r * ( 1.5f - r * r * y ); return (float) r; } ID_INLINE float idMath::InvSqrt( float x ) { dword a = ((union _flint*)(&x))->i; union _flint seed; assert( initialized ); double y = x * 0.5f; seed.i = (( ( (3*EXP_BIAS-1) - ( (a >> EXP_POS) & 0xFF) ) >> 1)<> (EXP_POS-LOOKUP_BITS)) & LOOKUP_MASK]; double r = seed.f; r = r * ( 1.5f - r * r * y ); r = r * ( 1.5f - r * r * y ); return (float) r; } ID_INLINE double idMath::InvSqrt64( float x ) { dword a = ((union _flint*)(&x))->i; union _flint seed; assert( initialized ); double y = x * 0.5f; seed.i = (( ( (3*EXP_BIAS-1) - ( (a >> EXP_POS) & 0xFF) ) >> 1)<> (EXP_POS-LOOKUP_BITS)) & LOOKUP_MASK]; double r = seed.f; r = r * ( 1.5f - r * r * y ); r = r * ( 1.5f - r * r * y ); r = r * ( 1.5f - r * r * y ); return r; } ID_INLINE float idMath::Sqrt16( float x ) { return x * InvSqrt16( x ); } ID_INLINE float idMath::Sqrt( float x ) { return x * InvSqrt( x ); } ID_INLINE double idMath::Sqrt64( float x ) { return x * InvSqrt64( x ); } ID_INLINE float idMath::Sin( float a ) { return sinf( a ); } ID_INLINE float idMath::Sin16( float a ) { float s; if ( ( a < 0.0f ) || ( a >= TWO_PI ) ) { a -= floorf( a / TWO_PI ) * TWO_PI; } #if 1 if ( a < PI ) { if ( a > HALF_PI ) { a = PI - a; } } else { if ( a > PI + HALF_PI ) { a = a - TWO_PI; } else { a = PI - a; } } #else a = PI - a; if ( fabs( a ) >= HALF_PI ) { a = ( ( a < 0.0f ) ? -PI : PI ) - a; } #endif s = a * a; return a * ( ( ( ( ( -2.39e-08f * s + 2.7526e-06f ) * s - 1.98409e-04f ) * s + 8.3333315e-03f ) * s - 1.666666664e-01f ) * s + 1.0f ); } ID_INLINE double idMath::Sin64( float a ) { return sin( a ); } ID_INLINE float idMath::Cos( float a ) { return cosf( a ); } ID_INLINE float idMath::Cos16( float a ) { float s, d; if ( ( a < 0.0f ) || ( a >= TWO_PI ) ) { a -= floorf( a / TWO_PI ) * TWO_PI; } #if 1 if ( a < PI ) { if ( a > HALF_PI ) { a = PI - a; d = -1.0f; } else { d = 1.0f; } } else { if ( a > PI + HALF_PI ) { a = a - TWO_PI; d = 1.0f; } else { a = PI - a; d = -1.0f; } } #else a = PI - a; if ( fabs( a ) >= HALF_PI ) { a = ( ( a < 0.0f ) ? -PI : PI ) - a; d = 1.0f; } else { d = -1.0f; } #endif s = a * a; return d * ( ( ( ( ( -2.605e-07f * s + 2.47609e-05f ) * s - 1.3888397e-03f ) * s + 4.16666418e-02f ) * s - 4.999999963e-01f ) * s + 1.0f ); } ID_INLINE double idMath::Cos64( float a ) { return cos( a ); } ID_INLINE void idMath::SinCos( float a, float &s, float &c ) { #ifdef _MSC_VER _asm { fld a fsincos mov ecx, c mov edx, s fstp dword ptr [ecx] fstp dword ptr [edx] } #else s = sinf( a ); c = cosf( a ); #endif } ID_INLINE void idMath::SinCos16( float a, float &s, float &c ) { float t, d; if ( ( a < 0.0f ) || ( a >= idMath::TWO_PI ) ) { a -= floorf( a / idMath::TWO_PI ) * idMath::TWO_PI; } #if 1 if ( a < PI ) { if ( a > HALF_PI ) { a = PI - a; d = -1.0f; } else { d = 1.0f; } } else { if ( a > PI + HALF_PI ) { a = a - TWO_PI; d = 1.0f; } else { a = PI - a; d = -1.0f; } } #else a = PI - a; if ( fabs( a ) >= HALF_PI ) { a = ( ( a < 0.0f ) ? -PI : PI ) - a; d = 1.0f; } else { d = -1.0f; } #endif t = a * a; s = a * ( ( ( ( ( -2.39e-08f * t + 2.7526e-06f ) * t - 1.98409e-04f ) * t + 8.3333315e-03f ) * t - 1.666666664e-01f ) * t + 1.0f ); c = d * ( ( ( ( ( -2.605e-07f * t + 2.47609e-05f ) * t - 1.3888397e-03f ) * t + 4.16666418e-02f ) * t - 4.999999963e-01f ) * t + 1.0f ); } ID_INLINE void idMath::SinCos64( float a, double &s, double &c ) { #ifdef _MSC_VER _asm { fld a fsincos mov ecx, c mov edx, s fstp qword ptr [ecx] fstp qword ptr [edx] } #else s = sin( a ); c = cos( a ); #endif } ID_INLINE float idMath::Tan( float a ) { return tanf( a ); } ID_INLINE float idMath::Tan16( float a ) { float s; bool reciprocal; if ( ( a < 0.0f ) || ( a >= PI ) ) { a -= floorf( a / PI ) * PI; } #if 1 if ( a < HALF_PI ) { if ( a > ONEFOURTH_PI ) { a = HALF_PI - a; reciprocal = true; } else { reciprocal = false; } } else { if ( a > HALF_PI + ONEFOURTH_PI ) { a = a - PI; reciprocal = false; } else { a = HALF_PI - a; reciprocal = true; } } #else a = HALF_PI - a; if ( fabs( a ) >= ONEFOURTH_PI ) { a = ( ( a < 0.0f ) ? -HALF_PI : HALF_PI ) - a; reciprocal = false; } else { reciprocal = true; } #endif s = a * a; s = a * ( ( ( ( ( ( 9.5168091e-03f * s + 2.900525e-03f ) * s + 2.45650893e-02f ) * s + 5.33740603e-02f ) * s + 1.333923995e-01f ) * s + 3.333314036e-01f ) * s + 1.0f ); if ( reciprocal ) { return 1.0f / s; } else { return s; } } ID_INLINE double idMath::Tan64( float a ) { return tan( a ); } ID_INLINE float idMath::ASin( float a ) { if ( a <= -1.0f ) { return -HALF_PI; } if ( a >= 1.0f ) { return HALF_PI; } return asinf( a ); } ID_INLINE float idMath::ASin16( float a ) { if ( FLOATSIGNBITSET( a ) ) { if ( a <= -1.0f ) { return -HALF_PI; } a = fabs( a ); return ( ( ( -0.0187293f * a + 0.0742610f ) * a - 0.2121144f ) * a + 1.5707288f ) * sqrt( 1.0f - a ) - HALF_PI; } else { if ( a >= 1.0f ) { return HALF_PI; } return HALF_PI - ( ( ( -0.0187293f * a + 0.0742610f ) * a - 0.2121144f ) * a + 1.5707288f ) * sqrt( 1.0f - a ); } } ID_INLINE double idMath::ASin64( float a ) { if ( a <= -1.0f ) { return -HALF_PI; } if ( a >= 1.0f ) { return HALF_PI; } return asin( a ); } ID_INLINE float idMath::ACos( float a ) { if ( a <= -1.0f ) { return PI; } if ( a >= 1.0f ) { return 0.0f; } return acosf( a ); } ID_INLINE float idMath::ACos16( float a ) { if ( FLOATSIGNBITSET( a ) ) { if ( a <= -1.0f ) { return PI; } a = fabs( a ); return PI - ( ( ( -0.0187293f * a + 0.0742610f ) * a - 0.2121144f ) * a + 1.5707288f ) * sqrt( 1.0f - a ); } else { if ( a >= 1.0f ) { return 0.0f; } return ( ( ( -0.0187293f * a + 0.0742610f ) * a - 0.2121144f ) * a + 1.5707288f ) * sqrt( 1.0f - a ); } } ID_INLINE double idMath::ACos64( float a ) { if ( a <= -1.0f ) { return PI; } if ( a >= 1.0f ) { return 0.0f; } return acos( a ); } ID_INLINE float idMath::ATan( float a ) { return atanf( a ); } ID_INLINE float idMath::ATan16( float a ) { float s; if ( fabs( a ) > 1.0f ) { a = 1.0f / a; s = a * a; s = - ( ( ( ( ( ( ( ( ( 0.0028662257f * s - 0.0161657367f ) * s + 0.0429096138f ) * s - 0.0752896400f ) * s + 0.1065626393f ) * s - 0.1420889944f ) * s + 0.1999355085f ) * s - 0.3333314528f ) * s ) + 1.0f ) * a; if ( FLOATSIGNBITSET( a ) ) { return s - HALF_PI; } else { return s + HALF_PI; } } else { s = a * a; return ( ( ( ( ( ( ( ( ( 0.0028662257f * s - 0.0161657367f ) * s + 0.0429096138f ) * s - 0.0752896400f ) * s + 0.1065626393f ) * s - 0.1420889944f ) * s + 0.1999355085f ) * s - 0.3333314528f ) * s ) + 1.0f ) * a; } } ID_INLINE double idMath::ATan64( float a ) { return atan( a ); } ID_INLINE float idMath::ATan( float y, float x ) { return atan2f( y, x ); } ID_INLINE float idMath::ATan16( float y, float x ) { float a, s; if ( fabs( y ) > fabs( x ) ) { a = x / y; s = a * a; s = - ( ( ( ( ( ( ( ( ( 0.0028662257f * s - 0.0161657367f ) * s + 0.0429096138f ) * s - 0.0752896400f ) * s + 0.1065626393f ) * s - 0.1420889944f ) * s + 0.1999355085f ) * s - 0.3333314528f ) * s ) + 1.0f ) * a; if ( FLOATSIGNBITSET( a ) ) { return s - HALF_PI; } else { return s + HALF_PI; } } else { a = y / x; s = a * a; return ( ( ( ( ( ( ( ( ( 0.0028662257f * s - 0.0161657367f ) * s + 0.0429096138f ) * s - 0.0752896400f ) * s + 0.1065626393f ) * s - 0.1420889944f ) * s + 0.1999355085f ) * s - 0.3333314528f ) * s ) + 1.0f ) * a; } } ID_INLINE double idMath::ATan64( float y, float x ) { return atan2( y, x ); } ID_INLINE float idMath::Pow( float x, float y ) { return powf( x, y ); } ID_INLINE float idMath::Pow16( float x, float y ) { return Exp16( y * Log16( x ) ); } ID_INLINE double idMath::Pow64( float x, float y ) { return pow( x, y ); } ID_INLINE float idMath::Exp( float f ) { return expf( f ); } ID_INLINE float idMath::Exp16( float f ) { int i, s, e, m, exponent; float x, x2, y, p, q; x = f * 1.44269504088896340f; // multiply with ( 1 / log( 2 ) ) #if 1 i = *reinterpret_cast(&x); s = ( i >> IEEE_FLT_SIGN_BIT ); e = ( ( i >> IEEE_FLT_MANTISSA_BITS ) & ( ( 1 << IEEE_FLT_EXPONENT_BITS ) - 1 ) ) - IEEE_FLT_EXPONENT_BIAS; m = ( i & ( ( 1 << IEEE_FLT_MANTISSA_BITS ) - 1 ) ) | ( 1 << IEEE_FLT_MANTISSA_BITS ); i = ( ( m >> ( IEEE_FLT_MANTISSA_BITS - e ) ) & ~( e >> 31 ) ) ^ s; #else i = (int) x; if ( x < 0.0f ) { i--; } #endif exponent = ( i + IEEE_FLT_EXPONENT_BIAS ) << IEEE_FLT_MANTISSA_BITS; y = *reinterpret_cast(&exponent); x -= (float) i; if ( x >= 0.5f ) { x -= 0.5f; y *= 1.4142135623730950488f; // multiply with sqrt( 2 ) } x2 = x * x; p = x * ( 7.2152891511493f + x2 * 0.0576900723731f ); q = 20.8189237930062f + x2; x = y * ( q + p ) / ( q - p ); return x; } ID_INLINE double idMath::Exp64( float f ) { return exp( f ); } ID_INLINE float idMath::Log( float f ) { return logf( f ); } ID_INLINE float idMath::Log16( float f ) { int i, exponent; float y, y2; i = *reinterpret_cast(&f); exponent = ( ( i >> IEEE_FLT_MANTISSA_BITS ) & ( ( 1 << IEEE_FLT_EXPONENT_BITS ) - 1 ) ) - IEEE_FLT_EXPONENT_BIAS; i -= ( exponent + 1 ) << IEEE_FLT_MANTISSA_BITS; // get value in the range [.5, 1> y = *reinterpret_cast(&i); y *= 1.4142135623730950488f; // multiply with sqrt( 2 ) y = ( y - 1.0f ) / ( y + 1.0f ); y2 = y * y; y = y * ( 2.000000000046727f + y2 * ( 0.666666635059382f + y2 * ( 0.4000059794795f + y2 * ( 0.28525381498f + y2 * 0.2376245609f ) ) ) ); y += 0.693147180559945f * ( (float)exponent + 0.5f ); return y; } ID_INLINE double idMath::Log64( float f ) { return log( f ); } ID_INLINE int idMath::IPow( int x, int y ) { int r; for( r = x; y > 1; y-- ) { r *= x; } return r; } ID_INLINE int idMath::ILog2( float f ) { return ( ( (*reinterpret_cast(&f)) >> IEEE_FLT_MANTISSA_BITS ) & ( ( 1 << IEEE_FLT_EXPONENT_BITS ) - 1 ) ) - IEEE_FLT_EXPONENT_BIAS; } ID_INLINE int idMath::ILog2( int i ) { return ILog2( (float)i ); } ID_INLINE int idMath::BitsForFloat( float f ) { return ILog2( f ) + 1; } ID_INLINE int idMath::BitsForInteger( int i ) { return ILog2( (float)i ) + 1; } ID_INLINE int idMath::MaskForFloatSign( float f ) { return ( (*reinterpret_cast(&f)) >> 31 ); } ID_INLINE int idMath::MaskForIntegerSign( int i ) { return ( i >> 31 ); } ID_INLINE int idMath::FloorPowerOfTwo( int x ) { return CeilPowerOfTwo( x ) >> 1; } ID_INLINE int idMath::CeilPowerOfTwo( int x ) { x--; x |= x >> 1; x |= x >> 2; x |= x >> 4; x |= x >> 8; x |= x >> 16; x++; return x; } ID_INLINE bool idMath::IsPowerOfTwo( int x ) { return ( x & ( x - 1 ) ) == 0 && x > 0; } ID_INLINE int idMath::BitCount( int x ) { x -= ( ( x >> 1 ) & 0x55555555 ); x = ( ( ( x >> 2 ) & 0x33333333 ) + ( x & 0x33333333 ) ); x = ( ( ( x >> 4 ) + x ) & 0x0f0f0f0f ); x += ( x >> 8 ); return ( ( x + ( x >> 16 ) ) & 0x0000003f ); } ID_INLINE int idMath::BitReverse( int x ) { x = ( ( ( x >> 1 ) & 0x55555555 ) | ( ( x & 0x55555555 ) << 1 ) ); x = ( ( ( x >> 2 ) & 0x33333333 ) | ( ( x & 0x33333333 ) << 2 ) ); x = ( ( ( x >> 4 ) & 0x0f0f0f0f ) | ( ( x & 0x0f0f0f0f ) << 4 ) ); x = ( ( ( x >> 8 ) & 0x00ff00ff ) | ( ( x & 0x00ff00ff ) << 8 ) ); return ( ( x >> 16 ) | ( x << 16 ) ); } ID_INLINE int idMath::Abs( int x ) { int y = x >> 31; return ( ( x ^ y ) - y ); } ID_INLINE float idMath::Fabs( float f ) { int tmp = *reinterpret_cast( &f ); tmp &= 0x7FFFFFFF; return *reinterpret_cast( &tmp ); } ID_INLINE float idMath::Floor( float f ) { return floorf( f ); } ID_INLINE float idMath::Ceil( float f ) { return ceilf( f ); } ID_INLINE float idMath::Rint( float f ) { return floorf( f + 0.5f ); } ID_INLINE int idMath::Ftoi( float f ) { return (int) f; } ID_INLINE int idMath::FtoiFast( float f ) { #ifdef _MSC_VER int i; __asm fld f __asm fistp i // use default rouding mode (round nearest) return i; #elif 0 // round chop (C/C++ standard) int i, s, e, m, shift; i = *reinterpret_cast(&f); s = i >> IEEE_FLT_SIGN_BIT; e = ( ( i >> IEEE_FLT_MANTISSA_BITS ) & ( ( 1 << IEEE_FLT_EXPONENT_BITS ) - 1 ) ) - IEEE_FLT_EXPONENT_BIAS; m = ( i & ( ( 1 << IEEE_FLT_MANTISSA_BITS ) - 1 ) ) | ( 1 << IEEE_FLT_MANTISSA_BITS ); shift = e - IEEE_FLT_MANTISSA_BITS; return ( ( ( ( m >> -shift ) | ( m << shift ) ) & ~( e >> 31 ) ) ^ s ) - s; //#elif defined( __i386__ ) #elif 0 int i = 0; __asm__ __volatile__ ( "fld %1\n" \ "fistp %0\n" \ : "=m" (i) \ : "m" (f) ); return i; #else return (int) f; #endif } ID_INLINE unsigned int idMath::Ftol( float f ) { return (unsigned int) f; } ID_INLINE unsigned int idMath::FtolFast( float f ) { #ifdef _MSC_VER // FIXME: this overflows on 31bits still .. same as FtoiFast unsigned int i; __asm fld f __asm fistp i // use default rouding mode (round nearest) return i; #elif 0 // round chop (C/C++ standard) int i, s, e, m, shift; i = *reinterpret_cast(&f); s = i >> IEEE_FLT_SIGN_BIT; e = ( ( i >> IEEE_FLT_MANTISSA_BITS ) & ( ( 1 << IEEE_FLT_EXPONENT_BITS ) - 1 ) ) - IEEE_FLT_EXPONENT_BIAS; m = ( i & ( ( 1 << IEEE_FLT_MANTISSA_BITS ) - 1 ) ) | ( 1 << IEEE_FLT_MANTISSA_BITS ); shift = e - IEEE_FLT_MANTISSA_BITS; return ( ( ( ( m >> -shift ) | ( m << shift ) ) & ~( e >> 31 ) ) ^ s ) - s; //#elif defined( __i386__ ) #elif 0 // for some reason, on gcc I need to make sure i == 0 before performing a fistp int i = 0; __asm__ __volatile__ ( "fld %1\n" \ "fistp %0\n" \ : "=m" (i) \ : "m" (f) ); return i; #else return (unsigned int) f; #endif } ID_INLINE signed char idMath::ClampChar( int i ) { if ( i < -128 ) { return -128; } if ( i > 127 ) { return 127; } return i; } ID_INLINE signed short idMath::ClampShort( int i ) { if ( i < -32768 ) { return -32768; } if ( i > 32767 ) { return 32767; } return i; } ID_INLINE int idMath::ClampInt( int min, int max, int value ) { if ( value < min ) { return min; } if ( value > max ) { return max; } return value; } ID_INLINE float idMath::ClampFloat( float min, float max, float value ) { if ( value < min ) { return min; } if ( value > max ) { return max; } return value; } ID_INLINE float idMath::AngleNormalize360( float angle ) { if ( ( angle >= 360.0f ) || ( angle < 0.0f ) ) { angle -= floor( angle / 360.0f ) * 360.0f; } return angle; } ID_INLINE float idMath::AngleNormalize180( float angle ) { angle = AngleNormalize360( angle ); if ( angle > 180.0f ) { angle -= 360.0f; } return angle; } ID_INLINE float idMath::AngleDelta( float angle1, float angle2 ) { return AngleNormalize180( angle1 - angle2 ); } ID_INLINE int idMath::FloatHash( const float *array, const int numFloats ) { int i, hash = 0; const int *ptr; ptr = reinterpret_cast( array ); for ( i = 0; i < numFloats; i++ ) { hash ^= ptr[i]; } return hash; } #endif /* !__MATH_MATH_H__ */