u_math.h revision f62e1f41b4d6047e72222aebbb0b55a508269b0c
1/************************************************************************** 2 * 3 * Copyright 2008 Tungsten Graphics, Inc., Cedar Park, Texas. 4 * All Rights Reserved. 5 * 6 * Permission is hereby granted, free of charge, to any person obtaining a 7 * copy of this software and associated documentation files (the 8 * "Software"), to deal in the Software without restriction, including 9 * without limitation the rights to use, copy, modify, merge, publish, 10 * distribute, sub license, and/or sell copies of the Software, and to 11 * permit persons to whom the Software is furnished to do so, subject to 12 * the following conditions: 13 * 14 * The above copyright notice and this permission notice (including the 15 * next paragraph) shall be included in all copies or substantial portions 16 * of the Software. 17 * 18 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 19 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF 20 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. 21 * IN NO EVENT SHALL TUNGSTEN GRAPHICS AND/OR ITS SUPPLIERS BE LIABLE FOR 22 * ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, 23 * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE 24 * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 25 * 26 **************************************************************************/ 27 28 29/** 30 * Math utilities and approximations for common math functions. 31 * Reduced precision is usually acceptable in shaders... 32 * 33 * "fast" is used in the names of functions which are low-precision, 34 * or at least lower-precision than the normal C lib functions. 35 */ 36 37 38#ifndef U_MATH_H 39#define U_MATH_H 40 41 42#include "pipe/p_compiler.h" 43#include "util/u_debug.h" 44 45 46#ifdef __cplusplus 47extern "C" { 48#endif 49 50 51#if defined(PIPE_SUBSYSTEM_WINDOWS_MINIPORT) 52__inline double ceil(double val) 53{ 54 double ceil_val; 55 56 if ((val - (long) val) == 0) { 57 ceil_val = val; 58 } 59 else { 60 if (val > 0) { 61 ceil_val = (long) val + 1; 62 } 63 else { 64 ceil_val = (long) val; 65 } 66 } 67 68 return ceil_val; 69} 70 71#ifndef PIPE_SUBSYSTEM_WINDOWS_CE_OGL 72__inline double floor(double val) 73{ 74 double floor_val; 75 76 if ((val - (long) val) == 0) { 77 floor_val = val; 78 } 79 else { 80 if (val > 0) { 81 floor_val = (long) val; 82 } 83 else { 84 floor_val = (long) val - 1; 85 } 86 } 87 88 return floor_val; 89} 90#endif 91 92#pragma function(pow) 93__inline double __cdecl pow(double val, double exponent) 94{ 95 /* XXX */ 96 assert(0); 97 return 0; 98} 99 100#pragma function(log) 101__inline double __cdecl log(double val) 102{ 103 /* XXX */ 104 assert(0); 105 return 0; 106} 107 108#pragma function(atan2) 109__inline double __cdecl atan2(double val) 110{ 111 /* XXX */ 112 assert(0); 113 return 0; 114} 115#else 116#include <math.h> 117#include <stdarg.h> 118#endif 119 120 121#ifndef M_SQRT2 122#define M_SQRT2 1.41421356237309504880 123#endif 124 125 126#if defined(_MSC_VER) 127 128#if _MSC_VER < 1400 && !defined(__cplusplus) || defined(PIPE_SUBSYSTEM_WINDOWS_CE) 129 130static INLINE float cosf( float f ) 131{ 132 return (float) cos( (double) f ); 133} 134 135static INLINE float sinf( float f ) 136{ 137 return (float) sin( (double) f ); 138} 139 140static INLINE float ceilf( float f ) 141{ 142 return (float) ceil( (double) f ); 143} 144 145static INLINE float floorf( float f ) 146{ 147 return (float) floor( (double) f ); 148} 149 150static INLINE float powf( float f, float g ) 151{ 152 return (float) pow( (double) f, (double) g ); 153} 154 155static INLINE float sqrtf( float f ) 156{ 157 return (float) sqrt( (double) f ); 158} 159 160static INLINE float fabsf( float f ) 161{ 162 return (float) fabs( (double) f ); 163} 164 165static INLINE float logf( float f ) 166{ 167 return (float) log( (double) f ); 168} 169 170#else 171/* Work-around an extra semi-colon in VS 2005 logf definition */ 172#ifdef logf 173#undef logf 174#define logf(x) ((float)log((double)(x))) 175#endif /* logf */ 176 177#define isfinite(x) _finite((double)(x)) 178#define isnan(x) _isnan((double)(x)) 179#endif /* _MSC_VER < 1400 && !defined(__cplusplus) */ 180 181static INLINE double log2( double x ) 182{ 183 const double invln2 = 1.442695041; 184 return log( x ) * invln2; 185} 186 187static INLINE double 188round(double x) 189{ 190 return x >= 0.0 ? floor(x + 0.5) : ceil(x - 0.5); 191} 192 193static INLINE float 194roundf(float x) 195{ 196 return x >= 0.0f ? floorf(x + 0.5f) : ceilf(x - 0.5f); 197} 198 199#endif /* _MSC_VER */ 200 201 202 203 204 205#define POW2_TABLE_SIZE_LOG2 9 206#define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2) 207#define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2) 208#define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2)) 209extern float pow2_table[POW2_TABLE_SIZE]; 210 211 212/** 213 * Initialize math module. This should be called before using any 214 * other functions in this module. 215 */ 216extern void 217util_init_math(void); 218 219 220union fi { 221 float f; 222 int32_t i; 223 uint32_t ui; 224}; 225 226 227/** 228 * Fast version of 2^x 229 * Identity: exp2(a + b) = exp2(a) * exp2(b) 230 * Let ipart = int(x) 231 * Let fpart = x - ipart; 232 * So, exp2(x) = exp2(ipart) * exp2(fpart) 233 * Compute exp2(ipart) with i << ipart 234 * Compute exp2(fpart) with lookup table. 235 */ 236static INLINE float 237util_fast_exp2(float x) 238{ 239 int32_t ipart; 240 float fpart, mpart; 241 union fi epart; 242 243 if(x > 129.00000f) 244 return 3.402823466e+38f; 245 246 if (x < -126.99999f) 247 return 0.0f; 248 249 ipart = (int32_t) x; 250 fpart = x - (float) ipart; 251 252 /* same as 253 * epart.f = (float) (1 << ipart) 254 * but faster and without integer overflow for ipart > 31 255 */ 256 epart.i = (ipart + 127 ) << 23; 257 258 mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)]; 259 260 return epart.f * mpart; 261} 262 263 264/** 265 * Fast approximation to exp(x). 266 */ 267static INLINE float 268util_fast_exp(float x) 269{ 270 const float k = 1.44269f; /* = log2(e) */ 271 return util_fast_exp2(k * x); 272} 273 274 275#define LOG2_TABLE_SIZE_LOG2 16 276#define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2) 277#define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1) 278extern float log2_table[LOG2_TABLE_SIZE]; 279 280 281/** 282 * Fast approximation to log2(x). 283 */ 284static INLINE float 285util_fast_log2(float x) 286{ 287 union fi num; 288 float epart, mpart; 289 num.f = x; 290 epart = (float)(((num.i & 0x7f800000) >> 23) - 127); 291 /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */ 292 mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)]; 293 return epart + mpart; 294} 295 296 297/** 298 * Fast approximation to x^y. 299 */ 300static INLINE float 301util_fast_pow(float x, float y) 302{ 303 return util_fast_exp2(util_fast_log2(x) * y); 304} 305 306/* Note that this counts zero as a power of two. 307 */ 308static INLINE boolean 309util_is_power_of_two( unsigned v ) 310{ 311 return (v & (v-1)) == 0; 312} 313 314 315/** 316 * Floor(x), returned as int. 317 */ 318static INLINE int 319util_ifloor(float f) 320{ 321 int ai, bi; 322 double af, bf; 323 union fi u; 324 af = (3 << 22) + 0.5 + (double) f; 325 bf = (3 << 22) + 0.5 - (double) f; 326 u.f = (float) af; ai = u.i; 327 u.f = (float) bf; bi = u.i; 328 return (ai - bi) >> 1; 329} 330 331 332/** 333 * Round float to nearest int. 334 */ 335static INLINE int 336util_iround(float f) 337{ 338#if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86) 339 int r; 340 __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st"); 341 return r; 342#elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86) 343 int r; 344 _asm { 345 fld f 346 fistp r 347 } 348 return r; 349#else 350 if (f >= 0.0f) 351 return (int) (f + 0.5f); 352 else 353 return (int) (f - 0.5f); 354#endif 355} 356 357 358/** 359 * Approximate floating point comparison 360 */ 361static INLINE boolean 362util_is_approx(float a, float b, float tol) 363{ 364 return fabs(b - a) <= tol; 365} 366 367 368/** 369 * Test if x is NaN or +/- infinity. 370 */ 371static INLINE boolean 372util_is_inf_or_nan(float x) 373{ 374 union fi tmp; 375 tmp.f = x; 376 return !(int)((unsigned int)((tmp.i & 0x7fffffff)-0x7f800000) >> 31); 377} 378 379 380/** 381 * Find first bit set in word. Least significant bit is 1. 382 * Return 0 if no bits set. 383 */ 384#if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64) 385unsigned char _BitScanForward(unsigned long* Index, unsigned long Mask); 386#pragma intrinsic(_BitScanForward) 387static INLINE 388unsigned long ffs( unsigned long u ) 389{ 390 unsigned long i; 391 if (_BitScanForward(&i, u)) 392 return i + 1; 393 else 394 return 0; 395} 396#elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86) 397static INLINE 398unsigned ffs( unsigned u ) 399{ 400 unsigned i; 401 402 if (u == 0) { 403 return 0; 404 } 405 406 __asm bsf eax, [u] 407 __asm inc eax 408 __asm mov [i], eax 409 410 return i; 411} 412#elif defined(__MINGW32__) 413#define ffs __builtin_ffs 414#endif 415 416 417/** 418 * Return float bits. 419 */ 420static INLINE unsigned 421fui( float f ) 422{ 423 union fi fi; 424 fi.f = f; 425 return fi.ui; 426} 427 428 429/** 430 * Convert ubyte to float in [0, 1]. 431 * XXX a 256-entry lookup table would be slightly faster. 432 */ 433static INLINE float 434ubyte_to_float(ubyte ub) 435{ 436 return (float) ub * (1.0f / 255.0f); 437} 438 439 440/** 441 * Convert float in [0,1] to ubyte in [0,255] with clamping. 442 */ 443static INLINE ubyte 444float_to_ubyte(float f) 445{ 446 const int ieee_0996 = 0x3f7f0000; /* 0.996 or so */ 447 union fi tmp; 448 449 tmp.f = f; 450 if (tmp.i < 0) { 451 return (ubyte) 0; 452 } 453 else if (tmp.i >= ieee_0996) { 454 return (ubyte) 255; 455 } 456 else { 457 tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f; 458 return (ubyte) tmp.i; 459 } 460} 461 462static INLINE float 463byte_to_float_tex(int8_t b) 464{ 465 return (b == -128) ? -1.0F : b * 1.0F / 127.0F; 466} 467 468static INLINE int8_t 469float_to_byte_tex(float f) 470{ 471 return (int8_t) (127.0F * f); 472} 473 474/** 475 * Calc log base 2 476 */ 477static INLINE unsigned 478util_logbase2(unsigned n) 479{ 480 unsigned pos = 0; 481 if (n >= 1<<16) { n >>= 16; pos += 16; } 482 if (n >= 1<< 8) { n >>= 8; pos += 8; } 483 if (n >= 1<< 4) { n >>= 4; pos += 4; } 484 if (n >= 1<< 2) { n >>= 2; pos += 2; } 485 if (n >= 1<< 1) { pos += 1; } 486 return pos; 487} 488 489 490/** 491 * Returns the smallest power of two >= x 492 */ 493static INLINE unsigned 494util_next_power_of_two(unsigned x) 495{ 496 unsigned i; 497 498 if (x == 0) 499 return 1; 500 501 --x; 502 503 for (i = 1; i < sizeof(unsigned) * 8; i <<= 1) 504 x |= x >> i; 505 506 return x + 1; 507} 508 509 510/** 511 * Return number of bits set in n. 512 */ 513static INLINE unsigned 514util_bitcount(unsigned n) 515{ 516#if defined(PIPE_CC_GCC) 517 return __builtin_popcount(n); 518#else 519 /* K&R classic bitcount. 520 * 521 * For each iteration, clear the LSB from the bitfield. 522 * Requires only one iteration per set bit, instead of 523 * one iteration per bit less than highest set bit. 524 */ 525 unsigned bits = 0; 526 for (bits; n; bits++) { 527 n &= n - 1; 528 } 529 return bits; 530#endif 531} 532 533 534/** 535 * Reverse byte order of a 32 bit word. 536 */ 537static INLINE uint32_t 538util_bswap32(uint32_t n) 539{ 540#if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 403) 541 return __builtin_bswap32(n); 542#else 543 return (n >> 24) | 544 ((n >> 8) & 0x0000ff00) | 545 ((n << 8) & 0x00ff0000) | 546 (n << 24); 547#endif 548} 549 550 551/** 552 * Reverse byte order of a 16 bit word. 553 */ 554static INLINE uint16_t 555util_bswap16(uint16_t n) 556{ 557 return (n >> 8) | 558 (n << 8); 559} 560 561 562/** 563 * Clamp X to [MIN, MAX]. 564 * This is a macro to allow float, int, uint, etc. types. 565 */ 566#define CLAMP( X, MIN, MAX ) ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) ) 567 568#define MIN2( A, B ) ( (A)<(B) ? (A) : (B) ) 569#define MAX2( A, B ) ( (A)>(B) ? (A) : (B) ) 570 571#define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C)) 572#define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C)) 573 574#define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D)) 575#define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D)) 576 577 578/** 579 * Align a value, only works pot alignemnts. 580 */ 581static INLINE int 582align(int value, int alignment) 583{ 584 return (value + alignment - 1) & ~(alignment - 1); 585} 586 587/** 588 * Works like align but on npot alignments. 589 */ 590static INLINE size_t 591util_align_npot(size_t value, size_t alignment) 592{ 593 if (value % alignment) 594 return value + (alignment - (value % alignment)); 595 return value; 596} 597 598static INLINE unsigned 599u_minify(unsigned value, unsigned levels) 600{ 601 return MAX2(1, value >> levels); 602} 603 604#ifndef COPY_4V 605#define COPY_4V( DST, SRC ) \ 606do { \ 607 (DST)[0] = (SRC)[0]; \ 608 (DST)[1] = (SRC)[1]; \ 609 (DST)[2] = (SRC)[2]; \ 610 (DST)[3] = (SRC)[3]; \ 611} while (0) 612#endif 613 614 615#ifndef COPY_4FV 616#define COPY_4FV( DST, SRC ) COPY_4V(DST, SRC) 617#endif 618 619 620#ifndef ASSIGN_4V 621#define ASSIGN_4V( DST, V0, V1, V2, V3 ) \ 622do { \ 623 (DST)[0] = (V0); \ 624 (DST)[1] = (V1); \ 625 (DST)[2] = (V2); \ 626 (DST)[3] = (V3); \ 627} while (0) 628#endif 629 630 631static INLINE uint32_t util_unsigned_fixed(float value, unsigned frac_bits) 632{ 633 return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits)); 634} 635 636static INLINE int32_t util_signed_fixed(float value, unsigned frac_bits) 637{ 638 return (int32_t)(value * (1<<frac_bits)); 639} 640 641 642 643#ifdef __cplusplus 644} 645#endif 646 647#endif /* U_MATH_H */ 648