/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// /** * Contains FPU related code. * \file IceFPU.h * \author Pierre Terdiman * \date April, 4, 2000 */ /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// // Include Guard #ifndef __ICEFPU_H__ #define __ICEFPU_H__ #define SIGN_BITMASK 0x80000000 namespace { union float_udword { float f; udword u; }; union float_sdword { float f; sdword s; }; } //! Integer representation of a floating-point value. //#define IR(x) ((udword&)(x)) static inline udword IR(float x) { float_udword fu; fu.f = x; return fu.u; } //! Signed integer representation of a floating-point value. //#define SIR(x) ((sdword&)(x)) static inline sdword SIR(float x) { float_sdword fs; fs.f = x; return fs.s; } //! Absolute integer representation of a floating-point value #define AIR(x) (IR(x)&0x7fffffff) //! Floating-point representation of an integer value. //#define FR(x) ((float&)(x)) static inline float FR(unsigned x) { float_udword fu; fu.u = x; return fu.f; } //! Integer-based comparison of a floating point value. //! Don't use it blindly, it can be faster or slower than the FPU comparison, depends on the context. #define IS_NEGATIVE_FLOAT(x) (IR(x)&0x80000000) //! Fast fabs for floating-point values. It just clears the sign bit. //! Don't use it blindy, it can be faster or slower than the FPU comparison, depends on the context. inline_ float FastFabs(float x) { udword FloatBits = IR(x)&0x7fffffff; return FR(FloatBits); } //! Fast square root for floating-point values. inline_ float FastSqrt(float square) { return sqrtf(square); } //! Saturates positive to zero. inline_ float fsat(float f) { udword y = IR(f) & ~(SIR(f) >>31); return FR(y); } //! Computes 1.0f / sqrtf(x). inline_ float frsqrt(float f) { float x = f * 0.5f; udword y = 0x5f3759df - (IR(f) >> 1); // Iteration... const float fy = FR(y); const float result = fy * ( 1.5f - ( x * fy * fy ) ); // Result return result; } //! Computes 1.0f / sqrtf(x). Comes from NVIDIA. inline_ float InvSqrt(const float& x) { const udword tmp = (udword(IEEE_1_0 << 1) + IEEE_1_0 - IR(x)) >> 1; const float y = FR(tmp); return y * (1.47f - 0.47f * x * y * y); } //! Computes 1.0f / sqrtf(x). Comes from Quake3. Looks like the first one I had above. //! See http://www.magic-software.com/3DGEDInvSqrt.html inline_ float RSqrt(float number) { int i; float x2, y; const float threehalfs = 1.5f; x2 = number * 0.5f; y = number; i = IR(y); i = 0x5f3759df - (i >> 1); y = FR(i); y = y * (threehalfs - (x2 * y * y)); return y; } //! TO BE DOCUMENTED inline_ float fsqrt(float f) { udword y = ( ( SIR(f) - 0x3f800000 ) >> 1 ) + 0x3f800000; // Iteration...? // (float&)y = (3.0f - ((float&)y * (float&)y) / f) * (float&)y * 0.5f; // Result return FR(y); } //! Returns the float ranged espilon value. inline_ float fepsilon(float f) { udword b = IR(f) & 0xff800000; udword a = b | 0x00000001; // Result return FR(a) - FR(b); } //! Is the float valid ? inline_ bool IsNAN(float value) { return (IR(value)&0x7f800000) == 0x7f800000; } inline_ bool IsIndeterminate(float value) { return IR(value) == 0xffc00000; } inline_ bool IsPlusInf(float value) { return IR(value) == 0x7f800000; } inline_ bool IsMinusInf(float value) { return IR(value) == 0xff800000; } inline_ bool IsValidFloat(float value) { if(IsNAN(value)) return false; if(IsIndeterminate(value)) return false; if(IsPlusInf(value)) return false; if(IsMinusInf(value)) return false; return true; } #define CHECK_VALID_FLOAT(x) ASSERT(IsValidFloat(x)); /* //! FPU precision setting function. inline_ void SetFPU() { // This function evaluates whether the floating-point // control word is set to single precision/round to nearest/ // exceptions disabled. If these conditions don't hold, the // function changes the control word to set them and returns // TRUE, putting the old control word value in the passback // location pointed to by pwOldCW. { uword wTemp, wSave; __asm fstcw wSave if (wSave & 0x300 || // Not single mode 0x3f != (wSave & 0x3f) || // Exceptions enabled wSave & 0xC00) // Not round to nearest mode { __asm { mov ax, wSave and ax, not 300h ;; single mode or ax, 3fh ;; disable all exceptions and ax, not 0xC00 ;; round to nearest mode mov wTemp, ax fldcw wTemp } } } } */ //! This function computes the slowest possible floating-point value (you can also directly use FLT_EPSILON) inline_ float ComputeFloatEpsilon() { const float f = FR( IR(1.0f) ^ 1 ); return f - 1.0f; // You can check it's the same as FLT_EPSILON } inline_ bool IsFloatZero(float x, float epsilon=1e-6f) { return x*x < epsilon; } #define FCOMI_ST0 _asm _emit 0xdb _asm _emit 0xf0 #define FCOMIP_ST0 _asm _emit 0xdf _asm _emit 0xf0 #define FCMOVB_ST0 _asm _emit 0xda _asm _emit 0xc0 #define FCMOVNB_ST0 _asm _emit 0xdb _asm _emit 0xc0 #define FCOMI_ST1 _asm _emit 0xdb _asm _emit 0xf1 #define FCOMIP_ST1 _asm _emit 0xdf _asm _emit 0xf1 #define FCMOVB_ST1 _asm _emit 0xda _asm _emit 0xc1 #define FCMOVNB_ST1 _asm _emit 0xdb _asm _emit 0xc1 #define FCOMI_ST2 _asm _emit 0xdb _asm _emit 0xf2 #define FCOMIP_ST2 _asm _emit 0xdf _asm _emit 0xf2 #define FCMOVB_ST2 _asm _emit 0xda _asm _emit 0xc2 #define FCMOVNB_ST2 _asm _emit 0xdb _asm _emit 0xc2 #define FCOMI_ST3 _asm _emit 0xdb _asm _emit 0xf3 #define FCOMIP_ST3 _asm _emit 0xdf _asm _emit 0xf3 #define FCMOVB_ST3 _asm _emit 0xda _asm _emit 0xc3 #define FCMOVNB_ST3 _asm _emit 0xdb _asm _emit 0xc3 #define FCOMI_ST4 _asm _emit 0xdb _asm _emit 0xf4 #define FCOMIP_ST4 _asm _emit 0xdf _asm _emit 0xf4 #define FCMOVB_ST4 _asm _emit 0xda _asm _emit 0xc4 #define FCMOVNB_ST4 _asm _emit 0xdb _asm _emit 0xc4 #define FCOMI_ST5 _asm _emit 0xdb _asm _emit 0xf5 #define FCOMIP_ST5 _asm _emit 0xdf _asm _emit 0xf5 #define FCMOVB_ST5 _asm _emit 0xda _asm _emit 0xc5 #define FCMOVNB_ST5 _asm _emit 0xdb _asm _emit 0xc5 #define FCOMI_ST6 _asm _emit 0xdb _asm _emit 0xf6 #define FCOMIP_ST6 _asm _emit 0xdf _asm _emit 0xf6 #define FCMOVB_ST6 _asm _emit 0xda _asm _emit 0xc6 #define FCMOVNB_ST6 _asm _emit 0xdb _asm _emit 0xc6 #define FCOMI_ST7 _asm _emit 0xdb _asm _emit 0xf7 #define FCOMIP_ST7 _asm _emit 0xdf _asm _emit 0xf7 #define FCMOVB_ST7 _asm _emit 0xda _asm _emit 0xc7 #define FCMOVNB_ST7 _asm _emit 0xdb _asm _emit 0xc7 //! A global function to find MAX(a,b) using FCOMI/FCMOV inline_ float FCMax2(float a, float b) { return (a > b) ? a : b; } //! A global function to find MIN(a,b) using FCOMI/FCMOV inline_ float FCMin2(float a, float b) { return (a < b) ? a : b; } //! A global function to find MAX(a,b,c) using FCOMI/FCMOV inline_ float FCMax3(float a, float b, float c) { return (a > b) ? ((a > c) ? a : c) : ((b > c) ? b : c); } //! A global function to find MIN(a,b,c) using FCOMI/FCMOV inline_ float FCMin3(float a, float b, float c) { return (a < b) ? ((a < c) ? a : c) : ((b < c) ? b : c); } inline_ int ConvertToSortable(float f) { int Fi = SIR(f); int Fmask = (Fi>>31); Fi ^= Fmask; Fmask &= ~(1<<31); Fi -= Fmask; return Fi; } enum FPUMode { FPU_FLOOR = 0, FPU_CEIL = 1, FPU_BEST = 2, FPU_FORCE_DWORD = 0x7fffffff }; FUNCTION ICECORE_API FPUMode GetFPUMode(); FUNCTION ICECORE_API void SaveFPU(); FUNCTION ICECORE_API void RestoreFPU(); FUNCTION ICECORE_API void SetFPUFloorMode(); FUNCTION ICECORE_API void SetFPUCeilMode(); FUNCTION ICECORE_API void SetFPUBestMode(); FUNCTION ICECORE_API void SetFPUPrecision24(); FUNCTION ICECORE_API void SetFPUPrecision53(); FUNCTION ICECORE_API void SetFPUPrecision64(); FUNCTION ICECORE_API void SetFPURoundingChop(); FUNCTION ICECORE_API void SetFPURoundingUp(); FUNCTION ICECORE_API void SetFPURoundingDown(); FUNCTION ICECORE_API void SetFPURoundingNear(); FUNCTION ICECORE_API int intChop(const float& f); FUNCTION ICECORE_API int intFloor(const float& f); FUNCTION ICECORE_API int intCeil(const float& f); #endif // __ICEFPU_H__