/************************************************************************** * * 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 "util/u_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_OGL __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 #ifndef M_SQRT2 #define M_SQRT2 1.41421356237309504880 #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 */ #define isfinite(x) _finite((double)(x)) #define isnan(x) _isnan((double)(x)) #endif /* _MSC_VER < 1400 && !defined(__cplusplus) */ static INLINE double log2( double x ) { const double invln2 = 1.442695041; return log( x ) * invln2; } static INLINE double round(double x) { return x >= 0.0 ? floor(x + 0.5) : ceil(x - 0.5); } static INLINE float roundf(float x) { return x >= 0.0f ? floorf(x + 0.5f) : ceilf(x - 0.5f); } #endif /* _MSC_VER */ #define POW2_TABLE_SIZE_LOG2 9 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2) #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2) #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2)) extern float pow2_table[POW2_TABLE_SIZE]; /** * Initialize math module. This should be called before using any * other functions in this module. */ extern void util_init_math(void); union fi { float f; int32_t i; uint32_t ui; }; /** * Fast version of 2^x * Identity: exp2(a + b) = exp2(a) * exp2(b) * Let ipart = int(x) * Let fpart = x - ipart; * So, exp2(x) = exp2(ipart) * exp2(fpart) * Compute exp2(ipart) with i << ipart * Compute exp2(fpart) with lookup table. */ static INLINE float util_fast_exp2(float x) { int32_t ipart; float fpart, mpart; union fi epart; if(x > 129.00000f) return 3.402823466e+38f; if (x < -126.99999f) return 0.0f; ipart = (int32_t) x; fpart = x - (float) ipart; /* same as * epart.f = (float) (1 << ipart) * but faster and without integer overflow for ipart > 31 */ epart.i = (ipart + 127 ) << 23; mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)]; return epart.f * mpart; } /** * Fast approximation to exp(x). */ static INLINE float util_fast_exp(float x) { const float k = 1.44269f; /* = log2(e) */ return util_fast_exp2(k * x); } #define LOG2_TABLE_SIZE_LOG2 16 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2) #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1) extern float log2_table[LOG2_TABLE_SIZE]; /** * Fast approximation to log2(x). */ static INLINE float util_fast_log2(float x) { union fi num; float epart, mpart; num.f = x; epart = (float)(((num.i & 0x7f800000) >> 23) - 127); /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */ mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)]; return epart + mpart; } /** * Fast approximation to x^y. */ static INLINE float util_fast_pow(float x, float y) { return util_fast_exp2(util_fast_log2(x) * y); } /* Note that this counts zero as a power of two. */ static INLINE boolean util_is_power_of_two( unsigned v ) { return (v & (v-1)) == 0; } /** * 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 } /** * Approximate floating point comparison */ static INLINE boolean util_is_approx(float a, float b, float tol) { return fabs(b - a) <= tol; } /** * Test if x is NaN or +/- infinity. */ static INLINE boolean util_is_inf_or_nan(float x) { union fi tmp; tmp.f = x; return !(int)((unsigned int)((tmp.i & 0x7fffffff)-0x7f800000) >> 31); } /** * Find first bit set in word. Least significant bit is 1. * Return 0 if no bits set. */ #if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64) unsigned char _BitScanForward(unsigned long* Index, unsigned long Mask); #pragma intrinsic(_BitScanForward) static INLINE unsigned long ffs( unsigned long u ) { unsigned long i; if (_BitScanForward(&i, u)) return i + 1; else return 0; } #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86) 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; } #elif defined(__MINGW32__) #define ffs __builtin_ffs #endif #ifdef __MINGW32__ #define ffs __builtin_ffs #endif /* Could also binary search for the highest bit. */ static INLINE unsigned util_unsigned_logbase2(unsigned n) { unsigned log2 = 0; while (n >>= 1) ++log2; return log2; } /** * Return float bits. */ static INLINE unsigned fui( float f ) { union fi fi; fi.f = f; return fi.ui; } /** * Convert ubyte to float in [0, 1]. * XXX a 256-entry lookup table would be slightly faster. */ 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; } } static INLINE float byte_to_float_tex(int8_t b) { return (b == -128) ? -1.0F : b * 1.0F / 127.0F; } static INLINE int8_t float_to_byte_tex(float f) { return (int8_t) (127.0F * f); } /** * Calc log base 2 */ static INLINE unsigned util_logbase2(unsigned n) { unsigned log2 = 0; while (n >>= 1) ++log2; return log2; } /** * Returns the smallest power of two >= x */ static INLINE unsigned util_next_power_of_two(unsigned x) { unsigned i; if (x == 0) return 1; --x; for (i = 1; i < sizeof(unsigned) * 8; i <<= 1) x |= x >> i; return x + 1; } /** * Return number of bits set in n. */ static INLINE unsigned util_bitcount(unsigned n) { #if defined(PIPE_CC_GCC) return __builtin_popcount(n); #else /* K&R classic bitcount. * * For each iteration, clear the LSB from the bitfield. * Requires only one iteration per set bit, instead of * one iteration per bit less than highest set bit. */ unsigned bits = 0; for (bits; n; bits++) { n &= n - 1; } return bits; #endif } /** * Reverse byte order of a 32 bit word. */ static INLINE uint32_t util_bswap32(uint32_t n) { #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 403) return __builtin_bswap32(n); #else return (n >> 24) | ((n >> 8) & 0x0000ff00) | ((n << 8) & 0x00ff0000) | (n << 24); #endif } /** * Reverse byte order of a 16 bit word. */ static INLINE uint16_t util_bswap16(uint16_t n) { return (n >> 8) | (n << 8); } /** * Clamp X to [MIN, MAX]. * This is a macro to allow float, int, uint, etc. types. */ #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) ) #define MIN3( A, B, C ) MIN2( MIN2( A, B ), C ) #define MAX3( A, B, C ) MAX2( MAX2( A, B ), C ) #define MIN4( A, B, C, D ) MIN2( MIN2( A, B ), MIN2(C, D) ) #define MAX4( A, B, C, D ) MAX2( MAX2( A, B ), MAX2(C, D) ) /** * Align a value, only works pot alignemnts. */ static INLINE int align(int value, int alignment) { return (value + alignment - 1) & ~(alignment - 1); } /** * Works like align but on npot alignments. */ static INLINE size_t util_align_npot(size_t value, size_t alignment) { if (value % alignment) return value + (alignment - (value % alignment)); return value; } static INLINE unsigned u_minify(unsigned value, unsigned levels) { return MAX2(1, value >> levels); } #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 static INLINE uint32_t util_unsigned_fixed(float value, unsigned frac_bits) { return value < 0 ? 0 : (uint32_t)(value * (1<