/************************************************************************** * * Copyright 2008 Tungsten Graphics, Inc., Cedar Park, Texas. * All Rights Reserved. * * Permission is hereby granted, free of charge, to any person obtaining a * copy of this software and associated documentation files (the * "Software"), to deal in the Software without restriction, including * without limitation the rights to use, copy, modify, merge, publish, * distribute, sub license, and/or sell copies of the Software, and to * permit persons to whom the Software is furnished to do so, subject to * the following conditions: * * The above copyright notice and this permission notice (including the * next paragraph) shall be included in all copies or substantial portions * of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. * IN NO EVENT SHALL TUNGSTEN GRAPHICS AND/OR ITS SUPPLIERS BE LIABLE FOR * ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. * **************************************************************************/ /** * Math utilities and approximations for common math functions. * Reduced precision is usually acceptable in shaders... * * "fast" is used in the names of functions which are low-precision, * or at least lower-precision than the normal C lib functions. */ #ifndef U_MATH_H #define U_MATH_H #include "pipe/p_compiler.h" #include "pipe/p_debug.h" #ifdef __cplusplus extern "C" { #endif #if defined(PIPE_SUBSYSTEM_WINDOWS_MINIPORT) __inline double ceil(double val) { double ceil_val; if((val - (long) val) == 0) { ceil_val = val; } else { if(val > 0) { ceil_val = (long) val + 1; } else { ceil_val = (long) val; } } return ceil_val; } #ifndef PIPE_SUBSYSTEM_WINDOWS_CE __inline double floor(double val) { double floor_val; if((val - (long) val) == 0) { floor_val = val; } else { if(val > 0) { floor_val = (long) val; } else { floor_val = (long) val - 1; } } return floor_val; } #endif #pragma function(pow) __inline double __cdecl pow(double val, double exponent) { /* XXX */ assert(0); return 0; } #pragma function(log) __inline double __cdecl log(double val) { /* XXX */ assert(0); return 0; } #pragma function(atan2) __inline double __cdecl atan2(double val) { /* XXX */ assert(0); return 0; } #else #include #include #endif #if defined(_MSC_VER) #if _MSC_VER < 1400 && !defined(__cplusplus) || defined(PIPE_SUBSYSTEM_WINDOWS_CE) static INLINE float cosf( float f ) { return (float) cos( (double) f ); } static INLINE float sinf( float f ) { return (float) sin( (double) f ); } static INLINE float ceilf( float f ) { return (float) ceil( (double) f ); } static INLINE float floorf( float f ) { return (float) floor( (double) f ); } static INLINE float powf( float f, float g ) { return (float) pow( (double) f, (double) g ); } static INLINE float sqrtf( float f ) { return (float) sqrt( (double) f ); } static INLINE float fabsf( float f ) { return (float) fabs( (double) f ); } static INLINE float logf( float f ) { return (float) log( (double) f ); } #else /* Work-around an extra semi-colon in VS 2005 logf definition */ #ifdef logf #undef logf #define logf(x) ((float)log((double)(x))) #endif /* logf */ #endif #endif /* _MSC_VER */ #define POW2_TABLE_SIZE 256 #define POW2_TABLE_SCALE ((float) (POW2_TABLE_SIZE-1)) extern float pow2_table[POW2_TABLE_SIZE]; extern void util_init_math(void); union fi { float f; int i; unsigned ui; }; /** * Fast approximation to exp(x). * Compute with base 2 exponents: exp(x) = exp2(log2(e) * x) * Note: log2(e) is a constant, k = 1.44269 * So, exp(x) = exp2(k * x); * Identity: exp2(a + b) = exp2(a) * exp2(b) * Let ipart = int(k*x) * Let fpart = k*x - ipart; * So, exp2(k*x) = exp2(ipart) * exp2(fpart) * Compute exp2(ipart) with i << ipart * Compute exp2(fpart) with lookup table. */ static INLINE float util_fast_exp(float x) { if (x >= 0.0f) { float k = 1.44269f; /* = log2(e) */ float kx = k * x; int ipart = (int) kx; float fpart = kx - (float) ipart; float y = (float) (1 << ipart) * pow2_table[(int) (fpart * POW2_TABLE_SCALE)]; return y; } else { /* exp(-x) = 1.0 / exp(x) */ float k = -1.44269f; float kx = k * x; int ipart = (int) kx; float fpart = kx - (float) ipart; float y = (float) (1 << ipart) * pow2_table[(int) (fpart * POW2_TABLE_SCALE)]; return 1.0f / y; } } /** * Fast version of 2^x * XXX the above function could be implemented in terms of this one. */ static INLINE float util_fast_exp2(float x) { if (x >= 0.0f) { int ipart = (int) x; float fpart = x - (float) ipart; float y = (float) (1 << ipart) * pow2_table[(int) (fpart * POW2_TABLE_SCALE)]; return y; } else { /* exp(-x) = 1.0 / exp(x) */ int ipart = (int) -x; float fpart = -x - (float) ipart; float y = (float) (1 << ipart) * pow2_table[(int) (fpart * POW2_TABLE_SCALE)]; return 1.0f / y; } } /** * Based on code from http://www.flipcode.com/archives/Fast_log_Function.shtml */ static INLINE float util_fast_log2(float val) { union fi num; int log_2; num.f = val; log_2 = ((num.i >> 23) & 255) - 128; num.i &= ~(255 << 23); num.i += 127 << 23; num.f = ((-1.0f/3) * num.f + 2) * num.f - 2.0f/3; return num.f + log_2; } static INLINE float util_fast_pow(float x, float y) { /* XXX these tests may need adjustment */ if (y >= 3.0f && (-0.02f <= x && x <= 0.02f)) return 0.0f; if (y >= 50.0f && (-0.9f <= x && x <= 0.9f)) return 0.0f; return util_fast_exp2(util_fast_log2(x) * y); } /** * Floor(x), returned as int. */ static INLINE int util_ifloor(float f) { int ai, bi; double af, bf; union fi u; af = (3 << 22) + 0.5 + (double)f; bf = (3 << 22) + 0.5 - (double)f; u.f = (float) af; ai = u.i; u.f = (float) bf; bi = u.i; return (ai - bi) >> 1; } /** * Round float to nearest int. */ static INLINE int util_iround(float f) { #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86) int r; __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st"); return r; #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86) int r; _asm { fld f fistp r } return r; #else if (f >= 0.0f) return (int) (f + 0.5f); else return (int) (f - 0.5f); #endif } #if defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86) /** * Find first bit set in word. Least significant bit is 1. * Return 0 if no bits set. */ static INLINE unsigned ffs( unsigned u ) { unsigned i; if( u == 0 ) { return 0; } __asm bsf eax, [u] __asm inc eax __asm mov [i], eax return i; } #endif /** * Return float bits. */ static INLINE unsigned fui( float f ) { union fi fi; fi.f = f; return fi.ui; } static INLINE float ubyte_to_float(ubyte ub) { return (float) ub * (1.0f / 255.0f); } /** * Convert float in [0,1] to ubyte in [0,255] with clamping. */ static INLINE ubyte float_to_ubyte(float f) { const int ieee_0996 = 0x3f7f0000; /* 0.996 or so */ union fi tmp; tmp.f = f; if (tmp.i < 0) { return (ubyte) 0; } else if (tmp.i >= ieee_0996) { return (ubyte) 255; } else { tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f; return (ubyte) tmp.i; } } #define CLAMP( X, MIN, MAX ) ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) ) #define MIN2( A, B ) ( (A)<(B) ? (A) : (B) ) #define MAX2( A, B ) ( (A)>(B) ? (A) : (B) ) static INLINE int align(int value, int alignment) { return (value + alignment - 1) & ~(alignment - 1); } #ifndef COPY_4V #define COPY_4V( DST, SRC ) \ do { \ (DST)[0] = (SRC)[0]; \ (DST)[1] = (SRC)[1]; \ (DST)[2] = (SRC)[2]; \ (DST)[3] = (SRC)[3]; \ } while (0) #endif #ifndef COPY_4FV #define COPY_4FV( DST, SRC ) COPY_4V(DST, SRC) #endif #ifndef ASSIGN_4V #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \ do { \ (DST)[0] = (V0); \ (DST)[1] = (V1); \ (DST)[2] = (V2); \ (DST)[3] = (V3); \ } while (0) #endif #ifdef __cplusplus } #endif #endif /* U_MATH_H */