1047 lines
32 KiB
C++
1047 lines
32 KiB
C++
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#ifndef __MATH_MATH_H__
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#define __MATH_MATH_H__
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/*
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===============================================================================
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Math
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===============================================================================
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*/
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#ifdef INFINITY
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#undef INFINITY
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#endif
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// RAVEN BEGIN
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// jscott: renamed to prevent name clash
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#ifdef FLOAT_EPSILON
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#undef FLOAT_EPSILON
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#endif
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// ddynerman: name clash prevention
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#ifdef INT_MIN
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#undef INT_MIN
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#endif
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#ifdef INT_MAX
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#undef INT_MAX
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#endif
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// jscott: uncomment this to use id's sqrt and trig approximations
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#if defined( __linux__ ) || defined( MACOS_X )
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// TTimo - enabling for OSes I'm covering
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// (14:34:20) mrelusive: in the general case we don't use those functions
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// (14:34:28) mrelusive: they are only for specific cases where they are faster
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#define _FAST_MATH
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#endif
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// RAVEN END
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#define DEG2RAD(a) ( (a) * idMath::M_DEG2RAD )
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#define RAD2DEG(a) ( (a) * idMath::M_RAD2DEG )
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#define SEC2MS(t) ( idMath::FtoiFast( (t) * idMath::M_SEC2MS ) )
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#define MS2SEC(t) ( (t) * idMath::M_MS2SEC )
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#define ANGLE2SHORT(x) ( idMath::FtoiFast( (x) * 65536.0f / 360.0f ) & 65535 )
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#define SHORT2ANGLE(x) ( (x) * ( 360.0f / 65536.0f ) )
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#define ANGLE2BYTE(x) ( idMath::FtoiFast( (x) * 256.0f / 360.0f ) & 255 )
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#define BYTE2ANGLE(x) ( (x) * ( 360.0f / 256.0f ) )
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#define FLOATSIGNBITSET(f) ((*(const unsigned long *)&(f)) >> 31)
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#define FLOATSIGNBITNOTSET(f) ((~(*(const unsigned long *)&(f))) >> 31)
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#define FLOATNOTZERO(f) ((*(const unsigned long *)&(f)) & ~(1<<31) )
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#define INTSIGNBITSET(i) (((const unsigned long)(i)) >> 31)
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#define INTSIGNBITNOTSET(i) ((~((const unsigned long)(i))) >> 31)
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#define FLOAT_IS_NAN(x) (((*(const unsigned long *)&x) & 0x7f800000) == 0x7f800000)
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#define FLOAT_IS_INF(x) (((*(const unsigned long *)&x) & 0x7fffffff) == 0x7f800000)
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#define FLOAT_IS_IND(x) ((*(const unsigned long *)&x) == 0xffc00000)
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#define FLOAT_IS_DENORMAL(x) (((*(const unsigned long *)&x) & 0x7f800000) == 0x00000000 && \
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((*(const unsigned long *)&x) & 0x007fffff) != 0x00000000 )
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#define IEEE_FLT_MANTISSA_BITS 23
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#define IEEE_FLT_EXPONENT_BITS 8
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#define IEEE_FLT_EXPONENT_BIAS 127
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#define IEEE_FLT_SIGN_BIT 31
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#define IEEE_DBL_MANTISSA_BITS 52
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#define IEEE_DBL_EXPONENT_BITS 11
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#define IEEE_DBL_EXPONENT_BIAS 1023
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#define IEEE_DBL_SIGN_BIT 63
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#define IEEE_DBLE_MANTISSA_BITS 63
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#define IEEE_DBLE_EXPONENT_BITS 15
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#define IEEE_DBLE_EXPONENT_BIAS 0
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#define IEEE_DBLE_SIGN_BIT 79
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template<class T> ID_INLINE T Max( T x, T y ) { return ( x > y ) ? x : y; }
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template<class T> ID_INLINE T Min( T x, T y ) { return ( x < y ) ? x : y; }
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template<class T> ID_INLINE int MaxIndex( T x, T y ) { return ( x > y ) ? 0 : 1; }
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template<class T> ID_INLINE int MinIndex( T x, T y ) { return ( x < y ) ? 0 : 1; }
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template<class T> ID_INLINE T Max3( T x, T y, T z ) { return ( x > y ) ? ( ( x > z ) ? x : z ) : ( ( y > z ) ? y : z ); }
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template<class T> ID_INLINE T Min3( T x, T y, T z ) { return ( x < y ) ? ( ( x < z ) ? x : z ) : ( ( y < z ) ? y : z ); }
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template<class T> ID_INLINE int Max3Index( T x, T y, T z ) { return ( x > y ) ? ( ( x > z ) ? 0 : 2 ) : ( ( y > z ) ? 1 : 2 ); }
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template<class T> ID_INLINE int Min3Index( T x, T y, T z ) { return ( x < y ) ? ( ( x < z ) ? 0 : 2 ) : ( ( y < z ) ? 1 : 2 ); }
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template<class T> ID_INLINE T Sign( T f ) { return ( f > 0 ) ? 1 : ( ( f < 0 ) ? -1 : 0 ); }
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// RAVEN BEGIN
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// abahr: I know its not correct but return 1 if zero
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template<class T> ID_INLINE T SignZero( T f ) { return ( f > 0 ) ? 1 : ( ( f < 0 ) ? -1 : 1 ); }
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// RAVEN END
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template<class T> ID_INLINE T Square( T x ) { return x * x; }
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template<class T> ID_INLINE T Cube( T x ) { return x * x * x; }
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class idVec2;
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class idVec3;
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class idMath {
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public:
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static void Init( void );
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static float RSqrt( float x ); // reciprocal square root, returns huge number when x == 0.0
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#ifdef _FAST_MATH
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static float InvSqrt( float x ); // inverse square root with 32 bits precision, returns huge number when x == 0.0
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static float InvSqrt16( float x ); // inverse square root with 16 bits precision, returns huge number when x == 0.0
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static double InvSqrt64( float x ); // inverse square root with 64 bits precision, returns huge number when x == 0.0
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static float Sqrt( float x ); // square root with 32 bits precision
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static float Sqrt16( float x ); // square root with 16 bits precision
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static double Sqrt64( float x ); // square root with 64 bits precision
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static float Sin( float a ); // sine with 32 bits precision
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static float Sin16( float a ); // sine with 16 bits precision, maximum absolute error is 2.3082e-09
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static double Sin64( float a ); // sine with 64 bits precision
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static float Cos( float a ); // cosine with 32 bits precision
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static float Cos16( float a ); // cosine with 16 bits precision, maximum absolute error is 2.3082e-09
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static double Cos64( float a ); // cosine with 64 bits precision
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static float Tan( float a ); // tangent with 32 bits precision
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static float Tan16( float a ); // tangent with 16 bits precision, maximum absolute error is 1.8897e-08
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static double Tan64( float a ); // tangent with 64 bits precision
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static float ATan( float a ); // arc tangent with 32 bits precision
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static float ATan16( float a ); // arc tangent with 16 bits precision, maximum absolute error is 1.3593e-08
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static double ATan64( float a ); // arc tangent with 64 bits precision
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static float ATan( float y, float x ); // arc tangent with 32 bits precision
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static float ATan16( float y, float x ); // arc tangent with 16 bits precision, maximum absolute error is 1.3593e-08
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static double ATan64( float y, float x ); // arc tangent with 64 bits precision
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#else
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static float InvSqrt( float x ) { assert( x > 0.0f ); return( 1.0f / sqrtf( x ) ); } // inverse square root with 32 bits precision, returns huge number when x == 0.0
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static float InvSqrt16( float x ) { assert( x > 0.0f ); return( 1.0f / sqrt( x ) ); } // inverse square root with 16 bits precision, returns huge number when x == 0.0
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static double InvSqrt64( float x ) { assert( x > 0.0f ); return( 1.0f / sqrt( x ) ); } // inverse square root with 64 bits precision, returns huge number when x == 0.0
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static float Sqrt( float x ) { assert( x >= 0.0f ); return( sqrtf( x ) ); } // square root with 32 bits precision
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static float Sqrt16( float x ) { assert( x >= 0.0f ); return( sqrtf( x ) ); } // square root with 16 bits precision
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static double Sqrt64( float x ) { assert( x >= 0.0f ); return( sqrt( x ) ); } // square root with 64 bits precision
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static float Sin( float a ) { return( sinf( a ) ); } // sine with 32 bits precision
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static float Sin16( float a ) { return( sinf( a ) ); } // sine with 16 bits precision, maximum absolute error is 2.3082e-09
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static double Sin64( float a ) { return( sin( a ) ); } // sine with 64 bits precision
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static float Cos( float a ) { return( cosf( a ) ); } // cosine with 32 bits precision
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static float Cos16( float a ) { return( cosf( a ) ); } // cosine with 16 bits precision, maximum absolute error is 2.3082e-09
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static double Cos64( float a ) { return( cos( a ) ); } // cosine with 64 bits precision
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static float Tan( float a ) { return( tanf( a ) ); } // tangent with 32 bits precision
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static float Tan16( float a ) { return( tanf( a ) ); } // tangent with 16 bits precision, maximum absolute error is 1.8897e-08
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static double Tan64( float a ) { return( tan( a ) ); } // tangent with 64 bits precision
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static float ATan( float a ) { return( atanf( a ) ); } // arc tangent with 32 bits precision
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static float ATan16( float a ) { return( atanf( a ) ); } // arc tangent with 16 bits precision, maximum absolute error is 1.3593e-08
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static double ATan64( float a ) { return( atan( a ) ); } // arc tangent with 64 bits precision
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static float ATan( float y, float x ) { return( atan2f( y, x ) ); } // arc tangent with 32 bits precision
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static float ATan16( float y, float x ) { return( atan2f( y, x ) ); } // arc tangent with 16 bits precision, maximum absolute error is 1.3593e-08
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static double ATan64( float y, float x ) { return( atan2( y, x ) ); } // arc tangent with 64 bits precision
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#endif
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static void SinCos( float a, float &s, float &c ); // sine and cosine with 32 bits precision
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static void SinCos16( float a, float &s, float &c ); // sine and cosine with 16 bits precision
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static void SinCos64( float a, double &s, double &c ); // sine and cosine with 64 bits precision
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static float ASin( float a ); // arc sine with 32 bits precision, input is clamped to [-1, 1] to avoid a silent NaN
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static float ASin16( float a ); // arc sine with 16 bits precision, maximum absolute error is 6.7626e-05
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static double ASin64( float a ); // arc sine with 64 bits precision
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static float ACos( float a ); // arc cosine with 32 bits precision, input is clamped to [-1, 1] to avoid a silent NaN
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static float ACos16( float a ); // arc cosine with 16 bits precision, maximum absolute error is 6.7626e-05
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static double ACos64( float a ); // arc cosine with 64 bits precision
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static float Pow( float x, float y ); // x raised to the power y with 32 bits precision
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static float Pow16( float x, float y ); // x raised to the power y with 16 bits precision
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static double Pow64( float x, float y ); // x raised to the power y with 64 bits precision
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static float Exp( float f ); // e raised to the power f with 32 bits precision
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static float Exp16( float f ); // e raised to the power f with 16 bits precision
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static double Exp64( float f ); // e raised to the power f with 64 bits precision
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static float Log( float f ); // natural logarithm with 32 bits precision
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static float Log16( float f ); // natural logarithm with 16 bits precision
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static double Log64( float f ); // natural logarithm with 64 bits precision
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static int IPow( int x, int y ); // integral x raised to the power y
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static int ILog2( float f ); // integral base-2 logarithm of the floating point value
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static int ILog2( int i ); // integral base-2 logarithm of the integer value
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static int BitsForFloat( float f ); // minumum number of bits required to represent ceil( f )
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static int BitsForInteger( int i ); // minumum number of bits required to represent i
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static int MaskForFloatSign( float f );// returns 0x00000000 if x >= 0.0f and returns 0xFFFFFFFF if x <= -0.0f
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static int MaskForIntegerSign( int i );// returns 0x00000000 if x >= 0 and returns 0xFFFFFFFF if x < 0
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static int FloorPowerOfTwo( int x ); // round x down to the nearest power of 2
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static int CeilPowerOfTwo( int x ); // round x up to the nearest power of 2
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static bool IsPowerOfTwo( int x ); // returns true if x is a power of 2
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static int BitCount( int x ); // returns the number of 1 bits in x
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static int BitReverse( int x ); // returns the bit reverse of x
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static int Abs( int x ); // returns the absolute value of the integer value (for reference only)
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static float Fabs( float f ); // returns the absolute value of the floating point value
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static float Floor( float f ); // returns the largest integer that is less than or equal to the given value
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static float Ceil( float f ); // returns the smallest integer that is greater than or equal to the given value
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static float Rint( float f ); // returns the nearest integer
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static int Ftoi( float f ); // float to int conversion
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static int FtoiFast( float f ); // fast float to int conversion but uses current FPU round mode (default round nearest)
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static byte Ftob( float f ); // float to byte conversion, the result is clamped to the range [0-255]
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static signed char ClampChar( int i );
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// RAVEN BEGIN
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static byte ClampByte( int i );
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// RAVEN END
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static signed short ClampShort( int i );
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static int ClampInt( int min, int max, int value );
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static float ClampFloat( float min, float max, float value );
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static float AngleNormalize360( float angle );
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static float AngleNormalize180( float angle );
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static float AngleDelta( float angle1, float angle2 );
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static int FloatToBits( float f, int exponentBits, int mantissaBits );
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static float BitsToFloat( int i, int exponentBits, int mantissaBits );
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static int FloatHash( const float *array, const int numFloats );
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static const float PI; // pi
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static const float TWO_PI; // pi * 2
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static const float HALF_PI; // pi / 2
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static const float ONEFOURTH_PI; // pi / 4
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static const float E; // e
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static const float SQRT_TWO; // sqrt( 2 )
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static const float SQRT_THREE; // sqrt( 3 )
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// RAVEN BEGIN
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static const float THREEFOURTHS_PI; // 3 * pi / 4
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// RAVEN END
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static const float SQRT_1OVER2; // sqrt( 1 / 2 )
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static const float SQRT_1OVER3; // sqrt( 1 / 3 )
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static const float M_DEG2RAD; // degrees to radians multiplier
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static const float M_RAD2DEG; // radians to degrees multiplier
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static const float M_SEC2MS; // seconds to milliseconds multiplier
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static const float M_MS2SEC; // milliseconds to seconds multiplier
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static const float INFINITY; // huge number which should be larger than any valid number used
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// RAVEN BEGIN
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// jscott: renamed to prevent name clash
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static const float FLOAT_EPSILON; // smallest positive number such that 1.0+FLT_EPSILON != 1.0
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// ddynerman: added from limits.h
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static const int INT_MIN;
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static const int INT_MAX;
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// bdube: moved here from modview
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static void ArtesianFromPolar( idVec3 &result, idVec3 view );
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static void PolarFromArtesian( idVec3 &view, idVec3 artesian );
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// jscott: for material type collision
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static float BarycentricTriangleArea( const idVec3 &normal, const idVec3 &a, const idVec3 &b, const idVec3 &c );
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static void BarycentricEvaluate( idVec2 &result, const idVec3 &point, const idVec3 &normal, const float area, const idVec3 t[3], const idVec2 tc[3] );
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// abahr
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static float Lerp( const idVec2& range, float frac );
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static float Lerp( float start, float end, float frac );
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static float MidPointLerp( float start, float mid, float end, float frac );
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// jscott: for sound system
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static float dBToScale( float db );
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static float ScaleToDb( float scale );
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// RAVEN END
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private:
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enum {
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LOOKUP_BITS = 8,
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EXP_POS = 23,
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EXP_BIAS = 127,
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LOOKUP_POS = (EXP_POS-LOOKUP_BITS),
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SEED_POS = (EXP_POS-8),
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SQRT_TABLE_SIZE = (2<<LOOKUP_BITS),
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LOOKUP_MASK = (SQRT_TABLE_SIZE-1)
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};
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union _flint {
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dword i;
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float f;
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};
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static dword iSqrt[SQRT_TABLE_SIZE];
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static bool initialized;
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#ifdef ID_WIN_X86_SSE
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static const float SSE_FLOAT_ZERO;
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static const float SSE_FLOAT_255;
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#endif
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};
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ID_INLINE float idMath::RSqrt( float x ) {
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long i;
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float y, r;
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y = x * 0.5f;
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i = *reinterpret_cast<long *>( &x );
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i = 0x5f3759df - ( i >> 1 );
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r = *reinterpret_cast<float *>( &i );
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r = r * ( 1.5f - r * r * y );
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return r;
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}
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#ifdef _FAST_MATH
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ID_INLINE float idMath::InvSqrt16( float x ) {
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dword a = ((union _flint*)(&x))->i;
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union _flint seed;
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assert( initialized );
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double y = x * 0.5f;
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seed.i = (( ( (3*EXP_BIAS-1) - ( (a >> EXP_POS) & 0xFF) ) >> 1)<<EXP_POS) | iSqrt[(a >> (EXP_POS-LOOKUP_BITS)) & LOOKUP_MASK];
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double r = seed.f;
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r = r * ( 1.5f - r * r * y );
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return (float) r;
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}
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ID_INLINE float idMath::InvSqrt( float x ) {
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dword a = ((union _flint*)(&x))->i;
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union _flint seed;
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assert( initialized );
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double y = x * 0.5f;
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seed.i = (( ( (3*EXP_BIAS-1) - ( (a >> EXP_POS) & 0xFF) ) >> 1)<<EXP_POS) | iSqrt[(a >> (EXP_POS-LOOKUP_BITS)) & LOOKUP_MASK];
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double r = seed.f;
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r = r * ( 1.5f - r * r * y );
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r = r * ( 1.5f - r * r * y );
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return (float) r;
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}
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ID_INLINE double idMath::InvSqrt64( float x ) {
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dword a = ((union _flint*)(&x))->i;
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union _flint seed;
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assert( initialized );
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double y = x * 0.5f;
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seed.i = (( ( (3*EXP_BIAS-1) - ( (a >> EXP_POS) & 0xFF) ) >> 1)<<EXP_POS) | iSqrt[(a >> (EXP_POS-LOOKUP_BITS)) & LOOKUP_MASK];
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double r = seed.f;
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r = r * ( 1.5f - r * r * y );
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r = r * ( 1.5f - r * r * y );
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r = r * ( 1.5f - r * r * y );
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return r;
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}
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ID_INLINE float idMath::Sqrt16( float x ) {
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return x * InvSqrt16( x );
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}
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ID_INLINE float idMath::Sqrt( float x ) {
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return x * InvSqrt( x );
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}
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ID_INLINE double idMath::Sqrt64( float x ) {
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return x * InvSqrt64( x );
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}
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ID_INLINE float idMath::Sin( float a ) {
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return sinf( a );
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}
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ID_INLINE float idMath::Sin16( float a ) {
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float s;
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if ( ( a < 0.0f ) || ( a >= TWO_PI ) ) {
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a -= floorf( a / TWO_PI ) * TWO_PI;
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}
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#if 1
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if ( a < PI ) {
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if ( a > HALF_PI ) {
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a = PI - a;
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}
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} else {
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if ( a > PI + HALF_PI ) {
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a = a - TWO_PI;
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} else {
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a = PI - a;
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}
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}
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#else
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a = PI - a;
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if ( fabs( a ) >= HALF_PI ) {
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a = ( ( a < 0.0f ) ? -PI : PI ) - a;
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}
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#endif
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s = a * a;
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return a * ( ( ( ( ( -2.39e-08f * s + 2.7526e-06f ) * s - 1.98409e-04f ) * s + 8.3333315e-03f ) * s - 1.666666664e-01f ) * s + 1.0f );
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}
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ID_INLINE double idMath::Sin64( float a ) {
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return sin( a );
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}
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|
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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 );
|
|
}
|
|
#endif
|
|
|
|
ID_INLINE void idMath::SinCos( float a, float &s, float &c ) {
|
|
#ifdef ID_WIN_X86_ASM
|
|
_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 ID_WIN_X86_ASM
|
|
_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
|
|
}
|
|
|
|
#ifdef _FAST_MATH
|
|
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 );
|
|
}
|
|
#endif
|
|
|
|
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 );
|
|
}
|
|
|
|
#ifdef _FAST_MATH
|
|
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 );
|
|
}
|
|
#endif
|
|
|
|
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 ) {
|
|
#ifdef ID_WIN_X86_SSE
|
|
// 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.
|
|
int i;
|
|
__asm cvttss2si eax, f
|
|
__asm mov i, eax
|
|
return i;
|
|
#else
|
|
// If a converted result is larger than the maximum signed doubleword integer the result is undefined.
|
|
return (int) f;
|
|
#endif
|
|
}
|
|
|
|
ID_INLINE int idMath::FtoiFast( float f ) {
|
|
#ifdef ID_WIN_X86_ASM
|
|
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( __linux__ )
|
|
#ifdef __i386__
|
|
int i;
|
|
__asm__ __volatile__ (
|
|
"flds %1\n\t"
|
|
"fistpl %0\n\t"
|
|
: "=m"(i) : "m"(f));
|
|
return i;
|
|
#else
|
|
// lrintf is equivalent but only inlines at -O3
|
|
// although that should be more portable
|
|
return lrintf( f );
|
|
#endif
|
|
#elif defined( MACOS_X )
|
|
return lrintf( f );
|
|
#else
|
|
return (int) f;
|
|
#endif
|
|
}
|
|
|
|
ID_INLINE byte idMath::Ftob( float f ) {
|
|
#ifdef ID_WIN_X86_SSE
|
|
// 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.
|
|
byte b;
|
|
__asm movss xmm0, f
|
|
__asm maxss xmm0, SSE_FLOAT_ZERO
|
|
__asm minss xmm0, SSE_FLOAT_255
|
|
__asm cvttss2si eax, xmm0
|
|
__asm mov b, al
|
|
return b;
|
|
#else
|
|
// If a converted result is clamped to the range [0-255].
|
|
int i;
|
|
i = (int) f;
|
|
if ( i < 0 ) {
|
|
return 0;
|
|
} else if ( i > 255 ) {
|
|
return 255;
|
|
}
|
|
return i;
|
|
#endif
|
|
}
|
|
|
|
ID_INLINE signed char idMath::ClampChar( int i ) {
|
|
if ( i < -128 ) {
|
|
return -128;
|
|
}
|
|
if ( i > 127 ) {
|
|
return 127;
|
|
}
|
|
return i;
|
|
}
|
|
|
|
// RAVEN BEGIN
|
|
ID_INLINE byte idMath::ClampByte( int i )
|
|
{
|
|
if( i < 0 )
|
|
{
|
|
return( 0 );
|
|
}
|
|
if( i > 255 )
|
|
{
|
|
return( 255 );
|
|
}
|
|
return( i );
|
|
}
|
|
// RAVEN END
|
|
|
|
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;
|
|
}
|
|
|
|
// RAVEN BEGIN
|
|
// jscott: fast and reliable random routines
|
|
|
|
// This is the VC libc version of rand() without multiple seeds per thread or 12 levels
|
|
// of subroutine calls.
|
|
// Both calls have been designed to minimise the inherent number of float <--> int
|
|
// conversions and the additional math required to get the desired value.
|
|
// eg the typical tint = (rand() * 255) / 32768
|
|
// becomes tint = rvRandom::irand( 0, 255 )
|
|
|
|
class rvRandom {
|
|
private:
|
|
static unsigned long mSeed;
|
|
public:
|
|
rvRandom( void ) { mSeed = 0x89abcdef; }
|
|
|
|
// for a non seed based init
|
|
static int Init( void );
|
|
|
|
// Init the seed to a unique number
|
|
static void Init( unsigned long seed ) { mSeed = seed; }
|
|
|
|
// Returns a float min <= x < max (exclusive; will get max - 0.00001; but never max)
|
|
static float flrand( float min, float max );
|
|
|
|
// Returns a float min <= 0 < 1.0
|
|
static float flrand();
|
|
|
|
static float flrand( const idVec2& v );
|
|
|
|
// Returns an integer min <= x <= max (ie inclusive)
|
|
static int irand( int min, int max );
|
|
};
|
|
|
|
// RAVEN END
|
|
|
|
#endif /* !__MATH_MATH_H__ */
|