| /************************************************************************** |
| * |
| * 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 |
| |
| |
| #include <math.h> |
| #include <stdarg.h> |
| |
| #ifdef PIPE_OS_UNIX |
| #include <strings.h> /* for ffs */ |
| #endif |
| |
| |
| #ifndef M_SQRT2 |
| #define M_SQRT2 1.41421356237309504880 |
| #endif |
| |
| |
| #if defined(_MSC_VER) |
| |
| #if _MSC_VER < 1400 && !defined(__cplusplus) |
| |
| 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 */ |
| |
| |
| #ifdef PIPE_OS_ANDROID |
| |
| static INLINE |
| double log2(double d) |
| { |
| return log(d) * (1.0 / M_LN2); |
| } |
| |
| /* workaround a conflict with main/imports.h */ |
| #ifdef log2f |
| #undef log2f |
| #endif |
| |
| static INLINE |
| float log2f(float f) |
| { |
| return logf(f) * (float) (1.0 / M_LN2); |
| } |
| |
| #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; |
| }; |
| |
| |
| /** |
| * 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; |
| } |
| |
| |
| /** |
| * 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; |
| } |
| |
| |
| /** |
| * Find first bit set in word. Least significant bit is 1. |
| * Return 0 if no bits set. |
| */ |
| #ifndef FFS_DEFINED |
| #define FFS_DEFINED 1 |
| |
| #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__) || defined(PIPE_OS_ANDROID) |
| #define ffs __builtin_ffs |
| #endif |
| |
| #endif /* FFS_DEFINED */ |
| |
| /** |
| * Find last bit set in a word. The least significant bit is 1. |
| * Return 0 if no bits are set. |
| */ |
| static INLINE unsigned util_last_bit(unsigned u) |
| { |
| unsigned r = 0; |
| while (u) { |
| r++; |
| u >>= 1; |
| } |
| return r; |
| } |
| |
| |
| /* Destructively loop over all of the bits in a mask as in: |
| * |
| * while (mymask) { |
| * int i = u_bit_scan(&mymask); |
| * ... process element i |
| * } |
| * |
| */ |
| static INLINE int u_bit_scan(unsigned *mask) |
| { |
| int i = ffs(*mask) - 1; |
| *mask &= ~(1 << i); |
| return i; |
| } |
| |
| |
| /** |
| * 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) |
| { |
| #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304) |
| 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 |
| } |
| |
| |
| /** |
| * Returns the smallest power of two >= x |
| */ |
| static INLINE unsigned |
| util_next_power_of_two(unsigned x) |
| { |
| #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304) |
| 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(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 |
| } |
| |
| |
| /** |
| * Return number of bits set in n. |
| */ |
| static INLINE unsigned |
| util_bitcount(unsigned n) |
| { |
| #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304) |
| 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 |
| } |
| |
| |
| /** |
| * Convert from little endian to CPU byte order. |
| */ |
| |
| #ifdef PIPE_ARCH_BIG_ENDIAN |
| #define util_le32_to_cpu(x) util_bswap32(x) |
| #define util_le16_to_cpu(x) util_bswap16(x) |
| #else |
| #define util_le32_to_cpu(x) (x) |
| #define util_le16_to_cpu(x) (x) |
| #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 ) ((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); |
| } |
| |
| /** |
| * 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<<frac_bits)); |
| } |
| |
| static INLINE int32_t util_signed_fixed(float value, unsigned frac_bits) |
| { |
| return (int32_t)(value * (1<<frac_bits)); |
| } |
| |
| |
| |
| #ifdef __cplusplus |
| } |
| #endif |
| |
| #endif /* U_MATH_H */ |