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/*
===========================================================================
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 <http://www.gnu.org/licenses/>.
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 <float.h>
#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<class T> ID_INLINE int MaxIndex( T x, T y ) { return ( x > y ) ? 0 : 1; }
template<class T> ID_INLINE int MinIndex( T x, T y ) { return ( x < y ) ? 0 : 1; }
template<class T> ID_INLINE T Max3( T x, T y, T z ) { return ( x > y ) ? ( ( x > z ) ? x : z ) : ( ( y > z ) ? y : z ); }
template<class T> ID_INLINE T Min3( T x, T y, T z ) { return ( x < y ) ? ( ( x < z ) ? x : z ) : ( ( y < z ) ? y : z ); }
template<class T> ID_INLINE int Max3Index( T x, T y, T z ) { return ( x > y ) ? ( ( x > z ) ? 0 : 2 ) : ( ( y > z ) ? 1 : 2 ); }
template<class T> ID_INLINE int Min3Index( T x, T y, T z ) { return ( x < y ) ? ( ( x < z ) ? 0 : 2 ) : ( ( y < z ) ? 1 : 2 ); }
template<class T> ID_INLINE T Sign( T f ) { return ( f > 0 ) ? 1 : ( ( f < 0 ) ? -1 : 0 ); }
template<class T> ID_INLINE T Square( T x ) { return x * x; }
template<class T> 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<<LOOKUP_BITS),
LOOKUP_MASK = (SQRT_TABLE_SIZE-1)
};
union _flint {
dword i;
float f;
};
static dword iSqrt[SQRT_TABLE_SIZE];
static bool initialized;
};
ID_INLINE float idMath::RSqrt( float x ) {
int i;
float y, r;
y = x * 0.5f;
i = *reinterpret_cast<int *>( &x );
i = 0x5f3759df - ( i >> 1 );
r = *reinterpret_cast<float *>( &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) | iSqrt[(a >> (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) | iSqrt[(a >> (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) | iSqrt[(a >> (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 _WIN32
_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 _WIN32
_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<int *>(&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<float *>(&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<int *>(&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<float *>(&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<int *>(&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<int *>(&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<int *>( &f );
tmp &= 0x7FFFFFFF;
return *reinterpret_cast<float *>( &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 _WIN32
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<int *>(&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 _WIN32
// 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<int *>(&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<const int *>( array );
for ( i = 0; i < numFloats; i++ ) {
hash ^= ptr[i];
}
return hash;
}
#endif /* !__MATH_MATH_H__ */
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