1/************************************************************************** 2 * 3 * Copyright 2008 VMware, Inc. 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 VMWARE 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 44#include "c99_math.h" 45#include <assert.h> 46#include <float.h> 47#include <stdarg.h> 48 49#include "util/bitscan.h" 50 51#ifdef __cplusplus 52extern "C" { 53#endif 54 55 56#ifndef M_SQRT2 57#define M_SQRT2 1.41421356237309504880 58#endif 59 60#define POW2_TABLE_SIZE_LOG2 9 61#define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2) 62#define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2) 63#define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2)) 64extern float pow2_table[POW2_TABLE_SIZE]; 65 66 67/** 68 * Initialize math module. This should be called before using any 69 * other functions in this module. 70 */ 71extern void 72util_init_math(void); 73 74 75union fi { 76 float f; 77 int32_t i; 78 uint32_t ui; 79}; 80 81 82union di { 83 double d; 84 int64_t i; 85 uint64_t ui; 86}; 87 88 89/** 90 * Extract the IEEE float32 exponent. 91 */ 92static inline signed 93util_get_float32_exponent(float x) 94{ 95 union fi f; 96 97 f.f = x; 98 99 return ((f.ui >> 23) & 0xff) - 127; 100} 101 102 103/** 104 * Fast version of 2^x 105 * Identity: exp2(a + b) = exp2(a) * exp2(b) 106 * Let ipart = int(x) 107 * Let fpart = x - ipart; 108 * So, exp2(x) = exp2(ipart) * exp2(fpart) 109 * Compute exp2(ipart) with i << ipart 110 * Compute exp2(fpart) with lookup table. 111 */ 112static inline float 113util_fast_exp2(float x) 114{ 115 int32_t ipart; 116 float fpart, mpart; 117 union fi epart; 118 119 if(x > 129.00000f) 120 return 3.402823466e+38f; 121 122 if (x < -126.99999f) 123 return 0.0f; 124 125 ipart = (int32_t) x; 126 fpart = x - (float) ipart; 127 128 /* same as 129 * epart.f = (float) (1 << ipart) 130 * but faster and without integer overflow for ipart > 31 131 */ 132 epart.i = (ipart + 127 ) << 23; 133 134 mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)]; 135 136 return epart.f * mpart; 137} 138 139 140/** 141 * Fast approximation to exp(x). 142 */ 143static inline float 144util_fast_exp(float x) 145{ 146 const float k = 1.44269f; /* = log2(e) */ 147 return util_fast_exp2(k * x); 148} 149 150 151#define LOG2_TABLE_SIZE_LOG2 16 152#define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2) 153#define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1) 154extern float log2_table[LOG2_TABLE_SIZE]; 155 156 157/** 158 * Fast approximation to log2(x). 159 */ 160static inline float 161util_fast_log2(float x) 162{ 163 union fi num; 164 float epart, mpart; 165 num.f = x; 166 epart = (float)(((num.i & 0x7f800000) >> 23) - 127); 167 /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */ 168 mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)]; 169 return epart + mpart; 170} 171 172 173/** 174 * Fast approximation to x^y. 175 */ 176static inline float 177util_fast_pow(float x, float y) 178{ 179 return util_fast_exp2(util_fast_log2(x) * y); 180} 181 182/* Note that this counts zero as a power of two. 183 */ 184static inline boolean 185util_is_power_of_two( unsigned v ) 186{ 187 return (v & (v-1)) == 0; 188} 189 190 191/** 192 * Floor(x), returned as int. 193 */ 194static inline int 195util_ifloor(float f) 196{ 197 int ai, bi; 198 double af, bf; 199 union fi u; 200 af = (3 << 22) + 0.5 + (double) f; 201 bf = (3 << 22) + 0.5 - (double) f; 202 u.f = (float) af; ai = u.i; 203 u.f = (float) bf; bi = u.i; 204 return (ai - bi) >> 1; 205} 206 207 208/** 209 * Round float to nearest int. 210 */ 211static inline int 212util_iround(float f) 213{ 214#if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86) 215 int r; 216 __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st"); 217 return r; 218#elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86) 219 int r; 220 _asm { 221 fld f 222 fistp r 223 } 224 return r; 225#else 226 if (f >= 0.0f) 227 return (int) (f + 0.5f); 228 else 229 return (int) (f - 0.5f); 230#endif 231} 232 233 234/** 235 * Approximate floating point comparison 236 */ 237static inline boolean 238util_is_approx(float a, float b, float tol) 239{ 240 return fabsf(b - a) <= tol; 241} 242 243 244/** 245 * util_is_X_inf_or_nan = test if x is NaN or +/- Inf 246 * util_is_X_nan = test if x is NaN 247 * util_X_inf_sign = return +1 for +Inf, -1 for -Inf, or 0 for not Inf 248 * 249 * NaN can be checked with x != x, however this fails with the fast math flag 250 **/ 251 252 253/** 254 * Single-float 255 */ 256static inline boolean 257util_is_inf_or_nan(float x) 258{ 259 union fi tmp; 260 tmp.f = x; 261 return (tmp.ui & 0x7f800000) == 0x7f800000; 262} 263 264 265static inline boolean 266util_is_nan(float x) 267{ 268 union fi tmp; 269 tmp.f = x; 270 return (tmp.ui & 0x7fffffff) > 0x7f800000; 271} 272 273 274static inline int 275util_inf_sign(float x) 276{ 277 union fi tmp; 278 tmp.f = x; 279 if ((tmp.ui & 0x7fffffff) != 0x7f800000) { 280 return 0; 281 } 282 283 return (x < 0) ? -1 : 1; 284} 285 286 287/** 288 * Double-float 289 */ 290static inline boolean 291util_is_double_inf_or_nan(double x) 292{ 293 union di tmp; 294 tmp.d = x; 295 return (tmp.ui & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL; 296} 297 298 299static inline boolean 300util_is_double_nan(double x) 301{ 302 union di tmp; 303 tmp.d = x; 304 return (tmp.ui & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL; 305} 306 307 308static inline int 309util_double_inf_sign(double x) 310{ 311 union di tmp; 312 tmp.d = x; 313 if ((tmp.ui & 0x7fffffffffffffffULL) != 0x7ff0000000000000ULL) { 314 return 0; 315 } 316 317 return (x < 0) ? -1 : 1; 318} 319 320 321/** 322 * Half-float 323 */ 324static inline boolean 325util_is_half_inf_or_nan(int16_t x) 326{ 327 return (x & 0x7c00) == 0x7c00; 328} 329 330 331static inline boolean 332util_is_half_nan(int16_t x) 333{ 334 return (x & 0x7fff) > 0x7c00; 335} 336 337 338static inline int 339util_half_inf_sign(int16_t x) 340{ 341 if ((x & 0x7fff) != 0x7c00) { 342 return 0; 343 } 344 345 return (x < 0) ? -1 : 1; 346} 347 348 349/** 350 * Return float bits. 351 */ 352static inline unsigned 353fui( float f ) 354{ 355 union fi fi; 356 fi.f = f; 357 return fi.ui; 358} 359 360static inline float 361uif(uint32_t ui) 362{ 363 union fi fi; 364 fi.ui = ui; 365 return fi.f; 366} 367 368 369/** 370 * Convert ubyte to float in [0, 1]. 371 * XXX a 256-entry lookup table would be slightly faster. 372 */ 373static inline float 374ubyte_to_float(ubyte ub) 375{ 376 return (float) ub * (1.0f / 255.0f); 377} 378 379 380/** 381 * Convert float in [0,1] to ubyte in [0,255] with clamping. 382 */ 383static inline ubyte 384float_to_ubyte(float f) 385{ 386 union fi tmp; 387 388 tmp.f = f; 389 if (tmp.i < 0) { 390 return (ubyte) 0; 391 } 392 else if (tmp.i >= 0x3f800000 /* 1.0f */) { 393 return (ubyte) 255; 394 } 395 else { 396 tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f; 397 return (ubyte) tmp.i; 398 } 399} 400 401static inline float 402byte_to_float_tex(int8_t b) 403{ 404 return (b == -128) ? -1.0F : b * 1.0F / 127.0F; 405} 406 407static inline int8_t 408float_to_byte_tex(float f) 409{ 410 return (int8_t) (127.0F * f); 411} 412 413/** 414 * Calc log base 2 415 */ 416static inline unsigned 417util_logbase2(unsigned n) 418{ 419#if defined(HAVE___BUILTIN_CLZ) 420 return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1)); 421#else 422 unsigned pos = 0; 423 if (n >= 1<<16) { n >>= 16; pos += 16; } 424 if (n >= 1<< 8) { n >>= 8; pos += 8; } 425 if (n >= 1<< 4) { n >>= 4; pos += 4; } 426 if (n >= 1<< 2) { n >>= 2; pos += 2; } 427 if (n >= 1<< 1) { pos += 1; } 428 return pos; 429#endif 430} 431 432/** 433 * Returns the ceiling of log n base 2, and 0 when n == 0. Equivalently, 434 * returns the smallest x such that n <= 2**x. 435 */ 436static inline unsigned 437util_logbase2_ceil(unsigned n) 438{ 439 if (n <= 1) 440 return 0; 441 442 return 1 + util_logbase2(n - 1); 443} 444 445/** 446 * Returns the smallest power of two >= x 447 */ 448static inline unsigned 449util_next_power_of_two(unsigned x) 450{ 451#if defined(HAVE___BUILTIN_CLZ) 452 if (x <= 1) 453 return 1; 454 455 return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1))); 456#else 457 unsigned val = x; 458 459 if (x <= 1) 460 return 1; 461 462 if (util_is_power_of_two(x)) 463 return x; 464 465 val--; 466 val = (val >> 1) | val; 467 val = (val >> 2) | val; 468 val = (val >> 4) | val; 469 val = (val >> 8) | val; 470 val = (val >> 16) | val; 471 val++; 472 return val; 473#endif 474} 475 476 477/** 478 * Return number of bits set in n. 479 */ 480static inline unsigned 481util_bitcount(unsigned n) 482{ 483#if defined(HAVE___BUILTIN_POPCOUNT) 484 return __builtin_popcount(n); 485#else 486 /* K&R classic bitcount. 487 * 488 * For each iteration, clear the LSB from the bitfield. 489 * Requires only one iteration per set bit, instead of 490 * one iteration per bit less than highest set bit. 491 */ 492 unsigned bits; 493 for (bits = 0; n; bits++) { 494 n &= n - 1; 495 } 496 return bits; 497#endif 498} 499 500 501static inline unsigned 502util_bitcount64(uint64_t n) 503{ 504#ifdef HAVE___BUILTIN_POPCOUNTLL 505 return __builtin_popcountll(n); 506#else 507 return util_bitcount(n) + util_bitcount(n >> 32); 508#endif 509} 510 511 512/** 513 * Reverse bits in n 514 * Algorithm taken from: 515 * http://stackoverflow.com/questions/9144800/c-reverse-bits-in-unsigned-integer 516 */ 517static inline unsigned 518util_bitreverse(unsigned n) 519{ 520 n = ((n >> 1) & 0x55555555u) | ((n & 0x55555555u) << 1); 521 n = ((n >> 2) & 0x33333333u) | ((n & 0x33333333u) << 2); 522 n = ((n >> 4) & 0x0f0f0f0fu) | ((n & 0x0f0f0f0fu) << 4); 523 n = ((n >> 8) & 0x00ff00ffu) | ((n & 0x00ff00ffu) << 8); 524 n = ((n >> 16) & 0xffffu) | ((n & 0xffffu) << 16); 525 return n; 526} 527 528/** 529 * Convert from little endian to CPU byte order. 530 */ 531 532#ifdef PIPE_ARCH_BIG_ENDIAN 533#define util_le64_to_cpu(x) util_bswap64(x) 534#define util_le32_to_cpu(x) util_bswap32(x) 535#define util_le16_to_cpu(x) util_bswap16(x) 536#else 537#define util_le64_to_cpu(x) (x) 538#define util_le32_to_cpu(x) (x) 539#define util_le16_to_cpu(x) (x) 540#endif 541 542#define util_cpu_to_le64(x) util_le64_to_cpu(x) 543#define util_cpu_to_le32(x) util_le32_to_cpu(x) 544#define util_cpu_to_le16(x) util_le16_to_cpu(x) 545 546/** 547 * Reverse byte order of a 32 bit word. 548 */ 549static inline uint32_t 550util_bswap32(uint32_t n) 551{ 552#if defined(HAVE___BUILTIN_BSWAP32) 553 return __builtin_bswap32(n); 554#else 555 return (n >> 24) | 556 ((n >> 8) & 0x0000ff00) | 557 ((n << 8) & 0x00ff0000) | 558 (n << 24); 559#endif 560} 561 562/** 563 * Reverse byte order of a 64bit word. 564 */ 565static inline uint64_t 566util_bswap64(uint64_t n) 567{ 568#if defined(HAVE___BUILTIN_BSWAP64) 569 return __builtin_bswap64(n); 570#else 571 return ((uint64_t)util_bswap32((uint32_t)n) << 32) | 572 util_bswap32((n >> 32)); 573#endif 574} 575 576 577/** 578 * Reverse byte order of a 16 bit word. 579 */ 580static inline uint16_t 581util_bswap16(uint16_t n) 582{ 583 return (n >> 8) | 584 (n << 8); 585} 586 587static inline void* 588util_memcpy_cpu_to_le32(void * restrict dest, const void * restrict src, size_t n) 589{ 590#ifdef PIPE_ARCH_BIG_ENDIAN 591 size_t i, e; 592 assert(n % 4 == 0); 593 594 for (i = 0, e = n / 4; i < e; i++) { 595 uint32_t * restrict d = (uint32_t* restrict)dest; 596 const uint32_t * restrict s = (const uint32_t* restrict)src; 597 d[i] = util_bswap32(s[i]); 598 } 599 return dest; 600#else 601 return memcpy(dest, src, n); 602#endif 603} 604 605/** 606 * Clamp X to [MIN, MAX]. 607 * This is a macro to allow float, int, uint, etc. types. 608 */ 609#define CLAMP( X, MIN, MAX ) ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) ) 610 611#define MIN2( A, B ) ( (A)<(B) ? (A) : (B) ) 612#define MAX2( A, B ) ( (A)>(B) ? (A) : (B) ) 613 614#define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C)) 615#define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C)) 616 617#define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D)) 618#define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D)) 619 620 621/** 622 * Align a value, only works pot alignemnts. 623 */ 624static inline int 625align(int value, int alignment) 626{ 627 return (value + alignment - 1) & ~(alignment - 1); 628} 629 630static inline uint64_t 631align64(uint64_t value, unsigned alignment) 632{ 633 return (value + alignment - 1) & ~((uint64_t)alignment - 1); 634} 635 636/** 637 * Works like align but on npot alignments. 638 */ 639static inline size_t 640util_align_npot(size_t value, size_t alignment) 641{ 642 if (value % alignment) 643 return value + (alignment - (value % alignment)); 644 return value; 645} 646 647static inline unsigned 648u_minify(unsigned value, unsigned levels) 649{ 650 return MAX2(1, value >> levels); 651} 652 653#ifndef COPY_4V 654#define COPY_4V( DST, SRC ) \ 655do { \ 656 (DST)[0] = (SRC)[0]; \ 657 (DST)[1] = (SRC)[1]; \ 658 (DST)[2] = (SRC)[2]; \ 659 (DST)[3] = (SRC)[3]; \ 660} while (0) 661#endif 662 663 664#ifndef COPY_4FV 665#define COPY_4FV( DST, SRC ) COPY_4V(DST, SRC) 666#endif 667 668 669#ifndef ASSIGN_4V 670#define ASSIGN_4V( DST, V0, V1, V2, V3 ) \ 671do { \ 672 (DST)[0] = (V0); \ 673 (DST)[1] = (V1); \ 674 (DST)[2] = (V2); \ 675 (DST)[3] = (V3); \ 676} while (0) 677#endif 678 679 680static inline uint32_t 681util_unsigned_fixed(float value, unsigned frac_bits) 682{ 683 return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits)); 684} 685 686static inline int32_t 687util_signed_fixed(float value, unsigned frac_bits) 688{ 689 return (int32_t)(value * (1<<frac_bits)); 690} 691 692unsigned 693util_fpstate_get(void); 694unsigned 695util_fpstate_set_denorms_to_zero(unsigned current_fpstate); 696void 697util_fpstate_set(unsigned fpstate); 698 699 700 701#ifdef __cplusplus 702} 703#endif 704 705#endif /* U_MATH_H */ 706