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 47 extern "C" { 48 #endif 49 50 51 #include <math.h> 52 #include <stdarg.h> 53 54 #ifdef PIPE_OS_UNIX 55 #include <strings.h> /* for ffs */ 56 #endif 57 58 59 #ifndef M_SQRT2 60 #define M_SQRT2 1.41421356237309504880 61 #endif 62 63 64 #if defined(_MSC_VER) 65 66 #if _MSC_VER < 1400 && !defined(__cplusplus) 67 68 static INLINE float cosf( float f ) 69 { 70 return (float) cos( (double) f ); 71 } 72 73 static INLINE float sinf( float f ) 74 { 75 return (float) sin( (double) f ); 76 } 77 78 static INLINE float ceilf( float f ) 79 { 80 return (float) ceil( (double) f ); 81 } 82 83 static INLINE float floorf( float f ) 84 { 85 return (float) floor( (double) f ); 86 } 87 88 static INLINE float powf( float f, float g ) 89 { 90 return (float) pow( (double) f, (double) g ); 91 } 92 93 static INLINE float sqrtf( float f ) 94 { 95 return (float) sqrt( (double) f ); 96 } 97 98 static INLINE float fabsf( float f ) 99 { 100 return (float) fabs( (double) f ); 101 } 102 103 static INLINE float logf( float f ) 104 { 105 return (float) log( (double) f ); 106 } 107 108 #else 109 /* Work-around an extra semi-colon in VS 2005 logf definition */ 110 #ifdef logf 111 #undef logf 112 #define logf(x) ((float)log((double)(x))) 113 #endif /* logf */ 114 115 #define isfinite(x) _finite((double)(x)) 116 #define isnan(x) _isnan((double)(x)) 117 #endif /* _MSC_VER < 1400 && !defined(__cplusplus) */ 118 119 static INLINE double log2( double x ) 120 { 121 const double invln2 = 1.442695041; 122 return log( x ) * invln2; 123 } 124 125 static INLINE double 126 round(double x) 127 { 128 return x >= 0.0 ? floor(x + 0.5) : ceil(x - 0.5); 129 } 130 131 static INLINE float 132 roundf(float x) 133 { 134 return x >= 0.0f ? floorf(x + 0.5f) : ceilf(x - 0.5f); 135 } 136 137 #endif /* _MSC_VER */ 138 139 140 #ifdef PIPE_OS_ANDROID 141 142 static INLINE 143 double log2(double d) 144 { 145 return log(d) * (1.0 / M_LN2); 146 } 147 148 /* workaround a conflict with main/imports.h */ 149 #ifdef log2f 150 #undef log2f 151 #endif 152 153 static INLINE 154 float log2f(float f) 155 { 156 return logf(f) * (float) (1.0 / M_LN2); 157 } 158 159 #endif 160 161 162 163 164 #define POW2_TABLE_SIZE_LOG2 9 165 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2) 166 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2) 167 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2)) 168 extern float pow2_table[POW2_TABLE_SIZE]; 169 170 171 /** 172 * Initialize math module. This should be called before using any 173 * other functions in this module. 174 */ 175 extern void 176 util_init_math(void); 177 178 179 union fi { 180 float f; 181 int32_t i; 182 uint32_t ui; 183 }; 184 185 186 union di { 187 double d; 188 int64_t i; 189 uint64_t ui; 190 }; 191 192 193 /** 194 * Fast version of 2^x 195 * Identity: exp2(a + b) = exp2(a) * exp2(b) 196 * Let ipart = int(x) 197 * Let fpart = x - ipart; 198 * So, exp2(x) = exp2(ipart) * exp2(fpart) 199 * Compute exp2(ipart) with i << ipart 200 * Compute exp2(fpart) with lookup table. 201 */ 202 static INLINE float 203 util_fast_exp2(float x) 204 { 205 int32_t ipart; 206 float fpart, mpart; 207 union fi epart; 208 209 if(x > 129.00000f) 210 return 3.402823466e+38f; 211 212 if (x < -126.99999f) 213 return 0.0f; 214 215 ipart = (int32_t) x; 216 fpart = x - (float) ipart; 217 218 /* same as 219 * epart.f = (float) (1 << ipart) 220 * but faster and without integer overflow for ipart > 31 221 */ 222 epart.i = (ipart + 127 ) << 23; 223 224 mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)]; 225 226 return epart.f * mpart; 227 } 228 229 230 /** 231 * Fast approximation to exp(x). 232 */ 233 static INLINE float 234 util_fast_exp(float x) 235 { 236 const float k = 1.44269f; /* = log2(e) */ 237 return util_fast_exp2(k * x); 238 } 239 240 241 #define LOG2_TABLE_SIZE_LOG2 16 242 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2) 243 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1) 244 extern float log2_table[LOG2_TABLE_SIZE]; 245 246 247 /** 248 * Fast approximation to log2(x). 249 */ 250 static INLINE float 251 util_fast_log2(float x) 252 { 253 union fi num; 254 float epart, mpart; 255 num.f = x; 256 epart = (float)(((num.i & 0x7f800000) >> 23) - 127); 257 /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */ 258 mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)]; 259 return epart + mpart; 260 } 261 262 263 /** 264 * Fast approximation to x^y. 265 */ 266 static INLINE float 267 util_fast_pow(float x, float y) 268 { 269 return util_fast_exp2(util_fast_log2(x) * y); 270 } 271 272 /* Note that this counts zero as a power of two. 273 */ 274 static INLINE boolean 275 util_is_power_of_two( unsigned v ) 276 { 277 return (v & (v-1)) == 0; 278 } 279 280 281 /** 282 * Floor(x), returned as int. 283 */ 284 static INLINE int 285 util_ifloor(float f) 286 { 287 int ai, bi; 288 double af, bf; 289 union fi u; 290 af = (3 << 22) + 0.5 + (double) f; 291 bf = (3 << 22) + 0.5 - (double) f; 292 u.f = (float) af; ai = u.i; 293 u.f = (float) bf; bi = u.i; 294 return (ai - bi) >> 1; 295 } 296 297 298 /** 299 * Round float to nearest int. 300 */ 301 static INLINE int 302 util_iround(float f) 303 { 304 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86) 305 int r; 306 __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st"); 307 return r; 308 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86) 309 int r; 310 _asm { 311 fld f 312 fistp r 313 } 314 return r; 315 #else 316 if (f >= 0.0f) 317 return (int) (f + 0.5f); 318 else 319 return (int) (f - 0.5f); 320 #endif 321 } 322 323 324 /** 325 * Approximate floating point comparison 326 */ 327 static INLINE boolean 328 util_is_approx(float a, float b, float tol) 329 { 330 return fabs(b - a) <= tol; 331 } 332 333 334 /** 335 * util_is_X_inf_or_nan = test if x is NaN or +/- Inf 336 * util_is_X_nan = test if x is NaN 337 * util_X_inf_sign = return +1 for +Inf, -1 for -Inf, or 0 for not Inf 338 * 339 * NaN can be checked with x != x, however this fails with the fast math flag 340 **/ 341 342 343 /** 344 * Single-float 345 */ 346 static INLINE boolean 347 util_is_inf_or_nan(float x) 348 { 349 union fi tmp; 350 tmp.f = x; 351 return (tmp.ui & 0x7f800000) == 0x7f800000; 352 } 353 354 355 static INLINE boolean 356 util_is_nan(float x) 357 { 358 union fi tmp; 359 tmp.f = x; 360 return (tmp.ui & 0x7fffffff) > 0x7f800000; 361 } 362 363 364 static INLINE int 365 util_inf_sign(float x) 366 { 367 union fi tmp; 368 tmp.f = x; 369 if ((tmp.ui & 0x7fffffff) != 0x7f800000) { 370 return 0; 371 } 372 373 return (x < 0) ? -1 : 1; 374 } 375 376 377 /** 378 * Double-float 379 */ 380 static INLINE boolean 381 util_is_double_inf_or_nan(double x) 382 { 383 union di tmp; 384 tmp.d = x; 385 return (tmp.ui & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL; 386 } 387 388 389 static INLINE boolean 390 util_is_double_nan(double x) 391 { 392 union di tmp; 393 tmp.d = x; 394 return (tmp.ui & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL; 395 } 396 397 398 static INLINE int 399 util_double_inf_sign(double x) 400 { 401 union di tmp; 402 tmp.d = x; 403 if ((tmp.ui & 0x7fffffffffffffffULL) != 0x7ff0000000000000ULL) { 404 return 0; 405 } 406 407 return (x < 0) ? -1 : 1; 408 } 409 410 411 /** 412 * Half-float 413 */ 414 static INLINE boolean 415 util_is_half_inf_or_nan(int16_t x) 416 { 417 return (x & 0x7c00) == 0x7c00; 418 } 419 420 421 static INLINE boolean 422 util_is_half_nan(int16_t x) 423 { 424 return (x & 0x7fff) > 0x7c00; 425 } 426 427 428 static INLINE int 429 util_half_inf_sign(int16_t x) 430 { 431 if ((x & 0x7fff) != 0x7c00) { 432 return 0; 433 } 434 435 return (x < 0) ? -1 : 1; 436 } 437 438 439 /** 440 * Find first bit set in word. Least significant bit is 1. 441 * Return 0 if no bits set. 442 */ 443 #ifndef FFS_DEFINED 444 #define FFS_DEFINED 1 445 446 #if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64) 447 unsigned char _BitScanForward(unsigned long* Index, unsigned long Mask); 448 #pragma intrinsic(_BitScanForward) 449 static INLINE 450 unsigned long ffs( unsigned long u ) 451 { 452 unsigned long i; 453 if (_BitScanForward(&i, u)) 454 return i + 1; 455 else 456 return 0; 457 } 458 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86) 459 static INLINE 460 unsigned ffs( unsigned u ) 461 { 462 unsigned i; 463 464 if (u == 0) { 465 return 0; 466 } 467 468 __asm bsf eax, [u] 469 __asm inc eax 470 __asm mov [i], eax 471 472 return i; 473 } 474 #elif defined(__MINGW32__) || defined(PIPE_OS_ANDROID) 475 #define ffs __builtin_ffs 476 #endif 477 478 #endif /* FFS_DEFINED */ 479 480 /** 481 * Find last bit set in a word. The least significant bit is 1. 482 * Return 0 if no bits are set. 483 */ 484 static INLINE unsigned util_last_bit(unsigned u) 485 { 486 unsigned r = 0; 487 while (u) { 488 r++; 489 u >>= 1; 490 } 491 return r; 492 } 493 494 495 /* Destructively loop over all of the bits in a mask as in: 496 * 497 * while (mymask) { 498 * int i = u_bit_scan(&mymask); 499 * ... process element i 500 * } 501 * 502 */ 503 static INLINE int u_bit_scan(unsigned *mask) 504 { 505 int i = ffs(*mask) - 1; 506 *mask &= ~(1 << i); 507 return i; 508 } 509 510 511 /** 512 * Return float bits. 513 */ 514 static INLINE unsigned 515 fui( float f ) 516 { 517 union fi fi; 518 fi.f = f; 519 return fi.ui; 520 } 521 522 523 /** 524 * Convert ubyte to float in [0, 1]. 525 * XXX a 256-entry lookup table would be slightly faster. 526 */ 527 static INLINE float 528 ubyte_to_float(ubyte ub) 529 { 530 return (float) ub * (1.0f / 255.0f); 531 } 532 533 534 /** 535 * Convert float in [0,1] to ubyte in [0,255] with clamping. 536 */ 537 static INLINE ubyte 538 float_to_ubyte(float f) 539 { 540 const int ieee_0996 = 0x3f7f0000; /* 0.996 or so */ 541 union fi tmp; 542 543 tmp.f = f; 544 if (tmp.i < 0) { 545 return (ubyte) 0; 546 } 547 else if (tmp.i >= ieee_0996) { 548 return (ubyte) 255; 549 } 550 else { 551 tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f; 552 return (ubyte) tmp.i; 553 } 554 } 555 556 static INLINE float 557 byte_to_float_tex(int8_t b) 558 { 559 return (b == -128) ? -1.0F : b * 1.0F / 127.0F; 560 } 561 562 static INLINE int8_t 563 float_to_byte_tex(float f) 564 { 565 return (int8_t) (127.0F * f); 566 } 567 568 /** 569 * Calc log base 2 570 */ 571 static INLINE unsigned 572 util_logbase2(unsigned n) 573 { 574 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304) 575 return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1)); 576 #else 577 unsigned pos = 0; 578 if (n >= 1<<16) { n >>= 16; pos += 16; } 579 if (n >= 1<< 8) { n >>= 8; pos += 8; } 580 if (n >= 1<< 4) { n >>= 4; pos += 4; } 581 if (n >= 1<< 2) { n >>= 2; pos += 2; } 582 if (n >= 1<< 1) { pos += 1; } 583 return pos; 584 #endif 585 } 586 587 588 /** 589 * Returns the smallest power of two >= x 590 */ 591 static INLINE unsigned 592 util_next_power_of_two(unsigned x) 593 { 594 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304) 595 if (x <= 1) 596 return 1; 597 598 return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1))); 599 #else 600 unsigned val = x; 601 602 if (x <= 1) 603 return 1; 604 605 if (util_is_power_of_two(x)) 606 return x; 607 608 val--; 609 val = (val >> 1) | val; 610 val = (val >> 2) | val; 611 val = (val >> 4) | val; 612 val = (val >> 8) | val; 613 val = (val >> 16) | val; 614 val++; 615 return val; 616 #endif 617 } 618 619 620 /** 621 * Return number of bits set in n. 622 */ 623 static INLINE unsigned 624 util_bitcount(unsigned n) 625 { 626 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304) 627 return __builtin_popcount(n); 628 #else 629 /* K&R classic bitcount. 630 * 631 * For each iteration, clear the LSB from the bitfield. 632 * Requires only one iteration per set bit, instead of 633 * one iteration per bit less than highest set bit. 634 */ 635 unsigned bits = 0; 636 for (bits; n; bits++) { 637 n &= n - 1; 638 } 639 return bits; 640 #endif 641 } 642 643 644 /** 645 * Convert from little endian to CPU byte order. 646 */ 647 648 #ifdef PIPE_ARCH_BIG_ENDIAN 649 #define util_le32_to_cpu(x) util_bswap32(x) 650 #define util_le16_to_cpu(x) util_bswap16(x) 651 #else 652 #define util_le32_to_cpu(x) (x) 653 #define util_le16_to_cpu(x) (x) 654 #endif 655 656 657 /** 658 * Reverse byte order of a 32 bit word. 659 */ 660 static INLINE uint32_t 661 util_bswap32(uint32_t n) 662 { 663 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 403) 664 return __builtin_bswap32(n); 665 #else 666 return (n >> 24) | 667 ((n >> 8) & 0x0000ff00) | 668 ((n << 8) & 0x00ff0000) | 669 (n << 24); 670 #endif 671 } 672 673 674 /** 675 * Reverse byte order of a 16 bit word. 676 */ 677 static INLINE uint16_t 678 util_bswap16(uint16_t n) 679 { 680 return (n >> 8) | 681 (n << 8); 682 } 683 684 685 /** 686 * Clamp X to [MIN, MAX]. 687 * This is a macro to allow float, int, uint, etc. types. 688 */ 689 #define CLAMP( X, MIN, MAX ) ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) ) 690 691 #define MIN2( A, B ) ( (A)<(B) ? (A) : (B) ) 692 #define MAX2( A, B ) ( (A)>(B) ? (A) : (B) ) 693 694 #define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C)) 695 #define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C)) 696 697 #define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D)) 698 #define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D)) 699 700 701 /** 702 * Align a value, only works pot alignemnts. 703 */ 704 static INLINE int 705 align(int value, int alignment) 706 { 707 return (value + alignment - 1) & ~(alignment - 1); 708 } 709 710 /** 711 * Works like align but on npot alignments. 712 */ 713 static INLINE size_t 714 util_align_npot(size_t value, size_t alignment) 715 { 716 if (value % alignment) 717 return value + (alignment - (value % alignment)); 718 return value; 719 } 720 721 static INLINE unsigned 722 u_minify(unsigned value, unsigned levels) 723 { 724 return MAX2(1, value >> levels); 725 } 726 727 #ifndef COPY_4V 728 #define COPY_4V( DST, SRC ) \ 729 do { \ 730 (DST)[0] = (SRC)[0]; \ 731 (DST)[1] = (SRC)[1]; \ 732 (DST)[2] = (SRC)[2]; \ 733 (DST)[3] = (SRC)[3]; \ 734 } while (0) 735 #endif 736 737 738 #ifndef COPY_4FV 739 #define COPY_4FV( DST, SRC ) COPY_4V(DST, SRC) 740 #endif 741 742 743 #ifndef ASSIGN_4V 744 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \ 745 do { \ 746 (DST)[0] = (V0); \ 747 (DST)[1] = (V1); \ 748 (DST)[2] = (V2); \ 749 (DST)[3] = (V3); \ 750 } while (0) 751 #endif 752 753 754 static INLINE uint32_t util_unsigned_fixed(float value, unsigned frac_bits) 755 { 756 return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits)); 757 } 758 759 static INLINE int32_t util_signed_fixed(float value, unsigned frac_bits) 760 { 761 return (int32_t)(value * (1<<frac_bits)); 762 } 763 764 765 766 #ifdef __cplusplus 767 } 768 #endif 769 770 #endif /* U_MATH_H */ 771
