id/doom3-bfg
0
0
Fork 0
mirror of https://github.com/id-Software/DOOM-3-BFG.git synced 2024-12-11 21:21:27 +00:00
Code Issues Projects Releases Packages Wiki Activity
doom3-bfg/neo/idlib/math/Math.h

1327 lines
35 KiB
C
Raw Normal View History

Initial commit
2012-11-26 18:58:24 +00:00
/*
===========================================================================
Doom 3 BFG Edition GPL Source Code
Copyright (C) 1993-2012 id Software LLC, a ZeniMax Media company.
This file is part of the Doom 3 BFG Edition GPL Source Code ("Doom 3 BFG Edition Source Code").
Doom 3 BFG Edition 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 BFG Edition 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 BFG Edition Source Code. If not, see <http://www.gnu.org/licenses/>.
In addition, the Doom 3 BFG Edition 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 BFG Edition 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 square root estimate instruction
#include <ppc_intrinsics.h>
// 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::Ftoi( (t) * idMath::M_SEC2MS ) )
#define MS2SEC(t) ( (t) * idMath::M_MS2SEC )
#define ANGLE2SHORT(x) ( idMath::Ftoi( (x) * 65536.0f / 360.0f ) & 65535 )
#define SHORT2ANGLE(x) ( (x) * ( 360.0f / 65536.0f ) )
#define ANGLE2BYTE(x) ( idMath::Ftoi( (x) * 256.0f / 360.0f ) & 255 )
#define BYTE2ANGLE(x) ( (x) * ( 360.0f / 256.0f ) )
#define C_FLOAT_TO_INT( x ) (int)(x)
/*
================================================================================================
two-complements integer bit layouts
================================================================================================
*/
#define INT8_SIGN_BIT 7
#define INT16_SIGN_BIT 15
#define INT32_SIGN_BIT 31
#define INT64_SIGN_BIT 63
#define INT8_SIGN_MASK ( 1 << INT8_SIGN_BIT )
#define INT16_SIGN_MASK ( 1 << INT16_SIGN_BIT )
#define INT32_SIGN_MASK ( 1UL << INT32_SIGN_BIT )
#define INT64_SIGN_MASK ( 1ULL << INT64_SIGN_BIT )
/*
================================================================================================
integer sign bit tests
================================================================================================
*/
// If this was ever compiled on a system that had 64 bit unsigned ints,
// it would fail.
compile_time_assert( sizeof( unsigned int ) == 4 );
#define OLD_INT32_SIGNBITSET(i) (static_cast<const unsigned int>(i) >> INT32_SIGN_BIT)
#define OLD_INT32_SIGNBITNOTSET(i) ((~static_cast<const unsigned int>(i)) >> INT32_SIGN_BIT)
// Unfortunately, /analyze can't figure out that these always return
// either 0 or 1, so this extra wrapper is needed to avoid the static
// alaysis warning.
ID_INLINE_EXTERN int INT32_SIGNBITSET( int i ) {
int r = OLD_INT32_SIGNBITSET( i );
assert( r == 0 || r == 1 );
return r;
}
ID_INLINE_EXTERN int INT32_SIGNBITNOTSET( int i ) {
int r = OLD_INT32_SIGNBITNOTSET( i );
assert( r == 0 || r == 1 );
return r;
}
/*
================================================================================================
floating point bit layouts according to the IEEE 754-1985 and 754-2008 standard
================================================================================================
*/
#define IEEE_FLT16_MANTISSA_BITS 10
#define IEEE_FLT16_EXPONENT_BITS 5
#define IEEE_FLT16_EXPONENT_BIAS 15
#define IEEE_FLT16_SIGN_BIT 15
#define IEEE_FLT16_SIGN_MASK ( 1U << IEEE_FLT16_SIGN_BIT )
#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_FLT_SIGN_MASK ( 1UL << IEEE_FLT_SIGN_BIT )
#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_DBL_SIGN_MASK ( 1ULL << IEEE_DBL_SIGN_BIT )
#define IEEE_DBLE_MANTISSA_BITS 63
#define IEEE_DBLE_EXPONENT_BITS 15
#define IEEE_DBLE_EXPONENT_BIAS 0
#define IEEE_DBLE_SIGN_BIT 79
/*
================================================================================================
floating point sign bit tests
================================================================================================
*/
#define IEEE_FLT_SIGNBITSET( a ) (reinterpret_cast<const unsigned int &>(a) >> IEEE_FLT_SIGN_BIT)
#define IEEE_FLT_SIGNBITNOTSET( a ) ((~reinterpret_cast<const unsigned int &>(a)) >> IEEE_FLT_SIGN_BIT)
#define IEEE_FLT_ISNOTZERO( a ) (reinterpret_cast<const unsigned int &>(a) & ~(1u<<IEEE_FLT_SIGN_BIT))
/*
================================================================================================
floating point special value tests
================================================================================================
*/
/*
========================
IEEE_FLT_IS_NAN
========================
*/
ID_INLINE_EXTERN bool IEEE_FLT_IS_NAN( float x ) {
return x != x;
}
/*
========================
IEEE_FLT_IS_INF
========================
*/
ID_INLINE_EXTERN bool IEEE_FLT_IS_INF( float x ) {
return x == x && x * 0 != x * 0;
}
/*
========================
IEEE_FLT_IS_INF_NAN
========================
*/
ID_INLINE_EXTERN bool IEEE_FLT_IS_INF_NAN( float x ) {
return x * 0 != x * 0;
}
/*
========================
IEEE_FLT_IS_IND
========================
*/
ID_INLINE_EXTERN bool IEEE_FLT_IS_IND( float x ) {
return (reinterpret_cast<const unsigned int &>(x) == 0xffc00000);
}
/*
========================
IEEE_FLT_IS_DENORMAL
========================
*/
ID_INLINE_EXTERN bool IEEE_FLT_IS_DENORMAL( float x ) {
return ((reinterpret_cast<const unsigned int &>(x) & 0x7f800000) == 0x00000000 &&
(reinterpret_cast<const unsigned int &>(x) & 0x007fffff) != 0x00000000 );
}
/*
========================
IsNAN
========================
*/template<class type>
ID_INLINE_EXTERN bool IsNAN( const type &v ) {
for ( int i = 0; i < v.GetDimension(); i++ ) {
const float f = v.ToFloatPtr()[i];
if ( IEEE_FLT_IS_NAN( f ) || IEEE_FLT_IS_INF( f ) || IEEE_FLT_IS_IND( f ) ) {
return true;
}
}
return false;
}
/*
========================
IsValid
========================
*/
template<class type>
ID_INLINE_EXTERN bool IsValid( const type &v ) {
for ( int i = 0; i < v.GetDimension(); i++ ) {
const float f = v.ToFloatPtr()[i];
if ( IEEE_FLT_IS_NAN( f ) || IEEE_FLT_IS_INF( f ) || IEEE_FLT_IS_IND( f ) || IEEE_FLT_IS_DENORMAL( f ) ) {
return false;
}
}
return true;
}
/*
========================
IsValid
========================
*/
template<>
ID_INLINE_EXTERN bool IsValid( const float & f ) { // these parameter must be a reference for the function to be considered a specialization
return !( IEEE_FLT_IS_NAN( f ) || IEEE_FLT_IS_INF( f ) || IEEE_FLT_IS_IND( f ) || IEEE_FLT_IS_DENORMAL( f ) );
}
/*
========================
IsNAN
========================
*/
template<>
ID_INLINE_EXTERN bool IsNAN( const float & f ) { // these parameter must be a reference for the function to be considered a specialization
if ( IEEE_FLT_IS_NAN( f ) || IEEE_FLT_IS_INF( f ) || IEEE_FLT_IS_IND( f ) ) {
return true;
}
return false;
}
/*
========================
IsInRange
Returns true if any scalar is greater than the range or less than the negative range.
========================
*/
template<class type>
ID_INLINE_EXTERN bool IsInRange( const type &v, const float range ) {
for ( int i = 0; i < v.GetDimension(); i++ ) {
const float f = v.ToFloatPtr()[i];
if ( f > range || f < -range ) {
return false;
}
}
return true;
}
/*
================================================================================================
MinIndex/MaxIndex
================================================================================================
*/
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 ); }
/*
================================================================================================
Sign/Square/Cube
================================================================================================
*/
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();
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 float Sqrt( float x ); // square root with 32 bits precision
static float Sqrt16( float x ); // square root with 16 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 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 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 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 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 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 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 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 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 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 float Log( float f ); // natural logarithm with 32 bits precision
static float Log16( float f ); // natural logarithm with 16 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 float Frac( float f ); // f - Floor( f )
static int Ftoi( float f ); // float to int conversion
static char Ftoi8( float f ); // float to char conversion
static short Ftoi16( float f ); // float to short conversion
static unsigned short Ftoui16( float f ); // float to unsigned short conversion
static byte Ftob( float f ); // float to byte conversion, the result is clamped to the range [0-255]
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 float LerpToWithScale( const float cur, const float dest, const float scale );
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 ONEOVER_PI; // 1 / pi
static const float ONEOVER_TWOPI; // 1 / pi * 2
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
static const float FLT_SMALLEST_NON_DENORMAL; // smallest non-denormal 32-bit floating point value
static const __m128 SIMD_SP_zero;
static const __m128 SIMD_SP_255;
static const __m128 SIMD_SP_min_char;
static const __m128 SIMD_SP_max_char;
static const __m128 SIMD_SP_min_short;
static const __m128 SIMD_SP_max_short;
static const __m128 SIMD_SP_smallestNonDenorm;
static const __m128 SIMD_SP_tiny;
static const __m128 SIMD_SP_rsqrt_c0;
static const __m128 SIMD_SP_rsqrt_c1;
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 byte CLAMP_BYTE( int x ) {
return ( (x) < 0 ? (0) : ( (x) > 255 ? 255 : (byte)(x) ) );
}
/*
========================
idMath::InvSqrt
========================
*/
ID_INLINE float idMath::InvSqrt( float x ) {
return ( x > FLT_SMALLEST_NON_DENORMAL ) ? sqrtf( 1.0f / x ) : INFINITY;
}
/*
========================
idMath::InvSqrt16
========================
*/
ID_INLINE float idMath::InvSqrt16( float x ) {
return ( x > FLT_SMALLEST_NON_DENORMAL ) ? sqrtf( 1.0f / x ) : INFINITY;
}
/*
========================
idMath::Sqrt
========================
*/
ID_INLINE float idMath::Sqrt( float x ) {
return ( x >= 0.0f ) ? x * InvSqrt( x ) : 0.0f;
}
/*
========================
idMath::Sqrt16
========================
*/
ID_INLINE float idMath::Sqrt16( float x ) {
return ( x >= 0.0f ) ? x * InvSqrt16( x ) : 0.0f;
}
/*
========================
idMath::Frac
========================
*/
ID_INLINE float idMath::Frac( float f ) {
return f - floorf( f );
}
/*
========================
idMath::Sin
========================
*/
ID_INLINE float idMath::Sin( float a ) {
return sinf( a );
}
/*
========================
idMath::Sin16
========================
*/
ID_INLINE float idMath::Sin16( float a ) {
float s;
if ( ( a < 0.0f ) || ( a >= TWO_PI ) ) {
a -= floorf( a * ONEOVER_TWOPI ) * 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 ( fabsf( 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 );
}
/*
========================
idMath::Cos
========================
*/
ID_INLINE float idMath::Cos( float a ) {
return cosf( a );
}
/*
========================
idMath::Cos16
========================
*/
ID_INLINE float idMath::Cos16( float a ) {
float s, d;
if ( ( a < 0.0f ) || ( a >= TWO_PI ) ) {
a -= floorf( a * ONEOVER_TWOPI ) * 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 ( fabsf( 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 );
}
/*
========================
idMath::SinCos
========================
*/
ID_INLINE void idMath::SinCos( float a, float &s, float &c ) {
_asm {
fld a
fsincos
mov ecx, c
mov edx, s
fstp dword ptr [ecx]
fstp dword ptr [edx]
}
}
/*
========================
idMath::SinCos16
========================
*/
ID_INLINE void idMath::SinCos16( float a, float &s, float &c ) {
float t, d;
if ( ( a < 0.0f ) || ( a >= TWO_PI ) ) {
a -= floorf( a * ONEOVER_TWOPI ) * 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 ( fabsf( 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 );
}
/*
========================
idMath::Tan
========================
*/
ID_INLINE float idMath::Tan( float a ) {
return tanf( a );
}
/*
========================
idMath::Tan16
========================
*/
ID_INLINE float idMath::Tan16( float a ) {
float s;
bool reciprocal;
if ( ( a < 0.0f ) || ( a >= PI ) ) {
a -= floorf( a * ONEOVER_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 ( fabsf( 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;
}
}
/*
========================
idMath::ASin
========================
*/
ID_INLINE float idMath::ASin( float a ) {
if ( a <= -1.0f ) {
return -HALF_PI;
}
if ( a >= 1.0f ) {
return HALF_PI;
}
return asinf( a );
}
/*
========================
idMath::ASin16
========================
*/
ID_INLINE float idMath::ASin16( float a ) {
if ( a < 0.0f ) {
if ( a <= -1.0f ) {
return -HALF_PI;
}
a = fabsf( a );
return ( ( ( -0.0187293f * a + 0.0742610f ) * a - 0.2121144f ) * a + 1.5707288f ) * idMath::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 ) * idMath::Sqrt( 1.0f - a );
}
}
/*
========================
idMath::ACos
========================
*/
ID_INLINE float idMath::ACos( float a ) {
if ( a <= -1.0f ) {
return PI;
}
if ( a >= 1.0f ) {
return 0.0f;
}
return acosf( a );
}
/*
========================
idMath::ACos16
========================
*/
ID_INLINE float idMath::ACos16( float a ) {
if ( a < 0.0f ) {
if ( a <= -1.0f ) {
return PI;
}
a = fabsf( a );
return PI - ( ( ( -0.0187293f * a + 0.0742610f ) * a - 0.2121144f ) * a + 1.5707288f ) * idMath::Sqrt( 1.0f - a );
} else {
if ( a >= 1.0f ) {
return 0.0f;
}
return ( ( ( -0.0187293f * a + 0.0742610f ) * a - 0.2121144f ) * a + 1.5707288f ) * idMath::Sqrt( 1.0f - a );
}
}
/*
========================
idMath::ATan
========================
*/
ID_INLINE float idMath::ATan( float a ) {
return atanf( a );
}
/*
========================
idMath::ATan16
========================
*/
ID_INLINE float idMath::ATan16( float a ) {
float s;
if ( fabsf( 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 ( a < 0.0f ) {
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;
}
}
/*
========================
idMath::ATan
========================
*/
ID_INLINE float idMath::ATan( float y, float x ) {
assert( fabs( y ) > idMath::FLT_SMALLEST_NON_DENORMAL || fabs( x ) > idMath::FLT_SMALLEST_NON_DENORMAL );
return atan2f( y, x );
}
/*
========================
idMath::ATan16
========================
*/
ID_INLINE float idMath::ATan16( float y, float x ) {
assert( fabs( y ) > idMath::FLT_SMALLEST_NON_DENORMAL || fabs( x ) > idMath::FLT_SMALLEST_NON_DENORMAL );
float a, s;
if ( fabsf( y ) > fabsf( 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 ( a < 0.0f ) {
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;
}
}
/*
========================
idMath::Pow
========================
*/
ID_INLINE float idMath::Pow( float x, float y ) {
return powf( x, y );
}
/*
========================
idMath::Pow16
========================
*/
ID_INLINE float idMath::Pow16( float x, float y ) {
return Exp16( y * Log16( x ) );
}
/*
========================
idMath::Exp
========================
*/
ID_INLINE float idMath::Exp( float f ) {
return expf( f );
}
/*
========================
idMath::Exp16
========================
*/
ID_INLINE float idMath::Exp16( float f ) {
float x = f * 1.44269504088896340f; // multiply with ( 1 / log( 2 ) )
#if 1
int i = *reinterpret_cast<int *>(&x);
int s = ( i >> IEEE_FLT_SIGN_BIT );
int e = ( ( i >> IEEE_FLT_MANTISSA_BITS ) & ( ( 1 << IEEE_FLT_EXPONENT_BITS ) - 1 ) ) - IEEE_FLT_EXPONENT_BIAS;
int m = ( i & ( ( 1 << IEEE_FLT_MANTISSA_BITS ) - 1 ) ) | ( 1 << IEEE_FLT_MANTISSA_BITS );
i = ( ( m >> ( IEEE_FLT_MANTISSA_BITS - e ) ) & ~( e >> INT32_SIGN_BIT ) ) ^ s;
#else
int i = (int) x;
if ( x < 0.0f ) {
i--;
}
#endif
int exponent = ( i + IEEE_FLT_EXPONENT_BIAS ) << IEEE_FLT_MANTISSA_BITS;
float y = *reinterpret_cast<float *>(&exponent);
x -= (float) i;
if ( x >= 0.5f ) {
x -= 0.5f;
y *= 1.4142135623730950488f; // multiply with sqrt( 2 )
}
float x2 = x * x;
float p = x * ( 7.2152891511493f + x2 * 0.0576900723731f );
float q = 20.8189237930062f + x2;
x = y * ( q + p ) / ( q - p );
return x;
}
/*
========================
idMath::Log
========================
*/
ID_INLINE float idMath::Log( float f ) {
return logf( f );
}
/*
========================
idMath::Log16
========================
*/
ID_INLINE float idMath::Log16( float f ) {
int i = *reinterpret_cast<int *>(&f);
int 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>
float y = *reinterpret_cast<float *>(&i);
y *= 1.4142135623730950488f; // multiply with sqrt( 2 )
y = ( y - 1.0f ) / ( y + 1.0f );
float 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;
}
/*
========================
idMath::IPow
========================
*/
ID_INLINE int idMath::IPow( int x, int y ) {
int r; for( r = x; y > 1; y-- ) { r *= x; } return r;
}
/*
========================
idMath::ILog2
========================
*/
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;
}
/*
========================
idMath::ILog2
========================
*/
ID_INLINE int idMath::ILog2( int i ) {
return ILog2( (float)i );
}
/*
========================
idMath::BitsForFloat
========================
*/
ID_INLINE int idMath::BitsForFloat( float f ) {
return ILog2( f ) + 1;
}
/*
========================
idMath::BitsForInteger
========================
*/
ID_INLINE int idMath::BitsForInteger( int i ) {
return ILog2( (float)i ) + 1;
}
/*
========================
idMath::MaskForFloatSign
========================
*/
ID_INLINE int idMath::MaskForFloatSign( float f ) {
return ( (*reinterpret_cast<int *>(&f)) >> IEEE_FLT_SIGN_BIT );
}
/*
========================
idMath::MaskForIntegerSign
========================
*/
ID_INLINE int idMath::MaskForIntegerSign( int i ) {
return ( i >> INT32_SIGN_BIT );
}
/*
========================
idMath::FloorPowerOfTwo
========================
*/
ID_INLINE int idMath::FloorPowerOfTwo( int x ) {
x |= x >> 1;
x |= x >> 2;
x |= x >> 4;
x |= x >> 8;
x |= x >> 16;
x++;
return x >> 1;
}
/*
========================
idMath::CeilPowerOfTwo
========================
*/
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;
}
/*
========================
idMath::IsPowerOfTwo
========================
*/
ID_INLINE bool idMath::IsPowerOfTwo( int x ) {
return ( x & ( x - 1 ) ) == 0 && x > 0;
}
/*
========================
idMath::BitCount
========================
*/
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 );
}
/*
========================
idMath::BitReverse
========================
*/
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 ) );
}
/*
========================
idMath::Abs
========================
*/
ID_INLINE int idMath::Abs( int x ) {
#if 1
return abs( x );
#else
int y = x >> INT32_SIGN_BIT;
return ( ( x ^ y ) - y );
#endif
}
/*
========================
idMath::Fabs
========================
*/
ID_INLINE float idMath::Fabs( float f ) {
#if 1
return fabsf( f );
#else
int tmp = *reinterpret_cast<int *>( &f );
tmp &= 0x7FFFFFFF;
return *reinterpret_cast<float *>( &tmp );
#endif
}
/*
========================
idMath::Floor
========================
*/
ID_INLINE float idMath::Floor( float f ) {
return floorf( f );
}
/*
========================
idMath::Ceil
========================
*/
ID_INLINE float idMath::Ceil( float f ) {
return ceilf( f );
}
/*
========================
idMath::Rint
========================
*/
ID_INLINE float idMath::Rint( float f ) {
return floorf( f + 0.5f );
}
/*
========================
idMath::Ftoi
========================
*/
ID_INLINE int idMath::Ftoi( float f ) {
// If a converted result is larger than the maximum signed doubleword integer,
// the floating-point invalid exception is raised, and if this exception is masked,
// the indefinite integer value (80000000H) is returned.
__m128 x = _mm_load_ss( &f );
return _mm_cvttss_si32( x );
}
/*
========================
idMath::Ftoi8
========================
*/
ID_INLINE char idMath::Ftoi8( float f ) {
__m128 x = _mm_load_ss( &f );
x = _mm_max_ss( x, SIMD_SP_min_char );
x = _mm_min_ss( x, SIMD_SP_max_char );
return static_cast<char>( _mm_cvttss_si32( x ) );
}
/*
========================
idMath::Ftoi16
========================
*/
ID_INLINE short idMath::Ftoi16( float f ) {
__m128 x = _mm_load_ss( &f );
x = _mm_max_ss( x, SIMD_SP_min_short );
x = _mm_min_ss( x, SIMD_SP_max_short );
return static_cast<short>( _mm_cvttss_si32( x ) );
}
/*
========================
idMath::Ftoui16
========================
*/
ID_INLINE unsigned short idMath::Ftoui16( float f ) {
// TO DO - SSE ??
// The converted result is clamped to the range [-32768,32767].
int i = C_FLOAT_TO_INT( f );
if ( i < 0 ) {
return 0;
} else if ( i > 65535 ) {
return 65535;
}
return static_cast<unsigned short>( i );
}
/*
========================
idMath::Ftob
========================
*/
ID_INLINE byte idMath::Ftob( float f ) {
// If a converted result is negative the value (0) is returned and if the
// converted result is larger than the maximum byte the value (255) is returned.
__m128 x = _mm_load_ss( &f );
x = _mm_max_ss( x, SIMD_SP_zero );
x = _mm_min_ss( x, SIMD_SP_255 );
return static_cast<byte>( _mm_cvttss_si32( x ) );
}
/*
========================
idMath::ClampChar
========================
*/
ID_INLINE signed char idMath::ClampChar( int i ) {
if ( i < -128 ) {
return -128;
}
if ( i > 127 ) {
return 127;
}
return static_cast<signed char>( i );
}
/*
========================
idMath::ClampShort
========================
*/
ID_INLINE signed short idMath::ClampShort( int i ) {
if ( i < -32768 ) {
return -32768;
}
if ( i > 32767 ) {
return 32767;
}
return static_cast<signed short>( i );
}
/*
========================
idMath::ClampInt
========================
*/
ID_INLINE int idMath::ClampInt( int min, int max, int value ) {
if ( value < min ) {
return min;
}
if ( value > max ) {
return max;
}
return value;
}
/*
========================
idMath::ClampFloat
========================
*/
ID_INLINE float idMath::ClampFloat( float min, float max, float value ) {
return Max( min, Min( max, value ) );
}
/*
========================
idMath::AngleNormalize360
========================
*/
ID_INLINE float idMath::AngleNormalize360( float angle ) {
if ( ( angle >= 360.0f ) || ( angle < 0.0f ) ) {
angle -= floorf( angle * ( 1.0f / 360.0f ) ) * 360.0f;
}
return angle;
}
/*
========================
idMath::AngleNormalize180
========================
*/
ID_INLINE float idMath::AngleNormalize180( float angle ) {
angle = AngleNormalize360( angle );
if ( angle > 180.0f ) {
angle -= 360.0f;
}
return angle;
}
/*
========================
idMath::AngleDelta
========================
*/
ID_INLINE float idMath::AngleDelta( float angle1, float angle2 ) {
return AngleNormalize180( angle1 - angle2 );
}
/*
========================
idMath::FloatHash
========================
*/
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;
}
template< typename T >
ID_INLINE_EXTERN T Lerp( const T from, const T to, float f ) {
return from + ( ( to - from ) * f );
}
template<>
ID_INLINE_EXTERN int Lerp( const int from, const int to, float f ) {
return idMath::Ftoi( (float) from + ( ( (float) to - (float) from ) * f ) );
}
/*
========================
LerpToWithScale
Lerps from "cur" to "dest", scaling the delta to change by "scale"
If the delta between "cur" and "dest" is very small, dest is returned to prevent denormals.
========================
*/
inline float idMath::LerpToWithScale( const float cur, const float dest, const float scale ) {
float delta = dest - cur;
if ( delta > -1.0e-6f && delta < 1.0e-6f ) {
return dest;
}
return cur + ( dest - cur ) * scale;
}
#endif /* !__MATH_MATH_H__ */
Reference in a new issue Copy permalink