/************************************************************************** * * Copyright 2008 VMware, Inc. * 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 VMWARE 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 "c99_math.h" #include #include #include #include "util/bitscan.h" #ifdef __cplusplus extern "C" { #endif #ifndef M_SQRT2 #define M_SQRT2 1.41421356237309504880 #endif #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; }; union di { double d; int64_t i; uint64_t ui; }; /** * Extract the IEEE float32 exponent. */ static inline signed util_get_float32_exponent(float x) { union fi f; f.f = x; return ((f.ui >> 23) & 0xff) - 127; } /** * 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); } /** * 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 fabsf(b - a) <= tol; } /** * util_is_X_inf_or_nan = test if x is NaN or +/- Inf * util_is_X_nan = test if x is NaN * util_X_inf_sign = return +1 for +Inf, -1 for -Inf, or 0 for not Inf * * NaN can be checked with x != x, however this fails with the fast math flag **/ /** * Single-float */ static inline boolean util_is_inf_or_nan(float x) { union fi tmp; tmp.f = x; return (tmp.ui & 0x7f800000) == 0x7f800000; } static inline boolean util_is_nan(float x) { union fi tmp; tmp.f = x; return (tmp.ui & 0x7fffffff) > 0x7f800000; } static inline int util_inf_sign(float x) { union fi tmp; tmp.f = x; if ((tmp.ui & 0x7fffffff) != 0x7f800000) { return 0; } return (x < 0) ? -1 : 1; } /** * Double-float */ static inline boolean util_is_double_inf_or_nan(double x) { union di tmp; tmp.d = x; return (tmp.ui & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL; } static inline boolean util_is_double_nan(double x) { union di tmp; tmp.d = x; return (tmp.ui & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL; } static inline int util_double_inf_sign(double x) { union di tmp; tmp.d = x; if ((tmp.ui & 0x7fffffffffffffffULL) != 0x7ff0000000000000ULL) { return 0; } return (x < 0) ? -1 : 1; } /** * Half-float */ static inline boolean util_is_half_inf_or_nan(int16_t x) { return (x & 0x7c00) == 0x7c00; } static inline boolean util_is_half_nan(int16_t x) { return (x & 0x7fff) > 0x7c00; } static inline int util_half_inf_sign(int16_t x) { if ((x & 0x7fff) != 0x7c00) { return 0; } return (x < 0) ? -1 : 1; } /** * Return float bits. */ static inline unsigned fui( float f ) { union fi fi; fi.f = f; return fi.ui; } static inline float uif(uint32_t ui) { union fi fi; fi.ui = ui; return fi.f; } /** * 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) { union fi tmp; tmp.f = f; if (tmp.i < 0) { return (ubyte) 0; } else if (tmp.i >= 0x3f800000 /* 1.0f */) { 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) { #if defined(HAVE___BUILTIN_CLZ) return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1)); #else unsigned pos = 0; if (n >= 1<<16) { n >>= 16; pos += 16; } if (n >= 1<< 8) { n >>= 8; pos += 8; } if (n >= 1<< 4) { n >>= 4; pos += 4; } if (n >= 1<< 2) { n >>= 2; pos += 2; } if (n >= 1<< 1) { pos += 1; } return pos; #endif } static inline uint64_t util_logbase2_64(uint64_t n) { #if defined(HAVE___BUILTIN_CLZLL) return ((sizeof(uint64_t) * 8 - 1) - __builtin_clzll(n | 1)); #else uint64_t pos = 0ull; if (n >= 1ull<<32) { n >>= 32; pos += 32; } if (n >= 1ull<<16) { n >>= 16; pos += 16; } if (n >= 1ull<< 8) { n >>= 8; pos += 8; } if (n >= 1ull<< 4) { n >>= 4; pos += 4; } if (n >= 1ull<< 2) { n >>= 2; pos += 2; } if (n >= 1ull<< 1) { pos += 1; } return pos; #endif } /** * Returns the ceiling of log n base 2, and 0 when n == 0. Equivalently, * returns the smallest x such that n <= 2**x. */ static inline unsigned util_logbase2_ceil(unsigned n) { if (n <= 1) return 0; return 1 + util_logbase2(n - 1); } static inline uint64_t util_logbase2_ceil64(uint64_t n) { if (n <= 1) return 0; return 1ull + util_logbase2_64(n - 1); } /** * Returns the smallest power of two >= x */ static inline unsigned util_next_power_of_two(unsigned x) { #if defined(HAVE___BUILTIN_CLZ) if (x <= 1) return 1; return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1))); #else unsigned val = x; if (x <= 1) return 1; if (util_is_power_of_two_or_zero(x)) return x; val--; val = (val >> 1) | val; val = (val >> 2) | val; val = (val >> 4) | val; val = (val >> 8) | val; val = (val >> 16) | val; val++; return val; #endif } static inline uint64_t util_next_power_of_two64(uint64_t x) { #if defined(HAVE___BUILTIN_CLZLL) if (x <= 1) return 1; return (1ull << ((sizeof(uint64_t) * 8) - __builtin_clzll(x - 1))); #else uint64_t val = x; if (x <= 1) return 1; if (util_is_power_of_two_or_zero64(x)) return x; val--; val = (val >> 1) | val; val = (val >> 2) | val; val = (val >> 4) | val; val = (val >> 8) | val; val = (val >> 16) | val; val = (val >> 32) | val; val++; return val; #endif } /** * Return number of bits set in n. */ static inline unsigned util_bitcount(unsigned n) { #if defined(HAVE___BUILTIN_POPCOUNT) 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; for (bits = 0; n; bits++) { n &= n - 1; } return bits; #endif } static inline unsigned util_bitcount64(uint64_t n) { #ifdef HAVE___BUILTIN_POPCOUNTLL return __builtin_popcountll(n); #else return util_bitcount(n) + util_bitcount(n >> 32); #endif } /** * Reverse bits in n * Algorithm taken from: * http://stackoverflow.com/questions/9144800/c-reverse-bits-in-unsigned-integer */ static inline unsigned util_bitreverse(unsigned n) { n = ((n >> 1) & 0x55555555u) | ((n & 0x55555555u) << 1); n = ((n >> 2) & 0x33333333u) | ((n & 0x33333333u) << 2); n = ((n >> 4) & 0x0f0f0f0fu) | ((n & 0x0f0f0f0fu) << 4); n = ((n >> 8) & 0x00ff00ffu) | ((n & 0x00ff00ffu) << 8); n = ((n >> 16) & 0xffffu) | ((n & 0xffffu) << 16); return n; } /** * Convert from little endian to CPU byte order. */ #ifdef PIPE_ARCH_BIG_ENDIAN #define util_le64_to_cpu(x) util_bswap64(x) #define util_le32_to_cpu(x) util_bswap32(x) #define util_le16_to_cpu(x) util_bswap16(x) #else #define util_le64_to_cpu(x) (x) #define util_le32_to_cpu(x) (x) #define util_le16_to_cpu(x) (x) #endif #define util_cpu_to_le64(x) util_le64_to_cpu(x) #define util_cpu_to_le32(x) util_le32_to_cpu(x) #define util_cpu_to_le16(x) util_le16_to_cpu(x) /** * Reverse byte order of a 32 bit word. */ static inline uint32_t util_bswap32(uint32_t n) { #if defined(HAVE___BUILTIN_BSWAP32) return __builtin_bswap32(n); #else return (n >> 24) | ((n >> 8) & 0x0000ff00) | ((n << 8) & 0x00ff0000) | (n << 24); #endif } /** * Reverse byte order of a 64bit word. */ static inline uint64_t util_bswap64(uint64_t n) { #if defined(HAVE___BUILTIN_BSWAP64) return __builtin_bswap64(n); #else return ((uint64_t)util_bswap32((uint32_t)n) << 32) | util_bswap32((n >> 32)); #endif } /** * Reverse byte order of a 16 bit word. */ static inline uint16_t util_bswap16(uint16_t n) { return (n >> 8) | (n << 8); } static inline void* util_memcpy_cpu_to_le32(void * restrict dest, const void * restrict src, size_t n) { #ifdef PIPE_ARCH_BIG_ENDIAN size_t i, e; assert(n % 4 == 0); for (i = 0, e = n / 4; i < e; i++) { uint32_t * restrict d = (uint32_t* restrict)dest; const uint32_t * restrict s = (const uint32_t* restrict)src; d[i] = util_bswap32(s[i]); } return dest; #else return memcpy(dest, src, n); #endif } /** * Clamp X to [MIN, MAX]. * This is a macro to allow float, int, uint, etc. types. * We arbitrarily turn NaN into MIN. */ #define CLAMP( X, MIN, MAX ) ( (X)>(MIN) ? ((X)>(MAX) ? (MAX) : (X)) : (MIN) ) #define MIN2( A, B ) ( (A)<(B) ? (A) : (B) ) #define MAX2( A, B ) ( (A)>(B) ? (A) : (B) ) #define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C)) #define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C)) #define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D)) #define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D)) /** * Align a value, only works pot alignemnts. */ static inline int align(int value, int alignment) { return (value + alignment - 1) & ~(alignment - 1); } static inline uint64_t align64(uint64_t value, unsigned alignment) { return (value + alignment - 1) & ~((uint64_t)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<