src/gallium/auxiliary/util/u_math.h

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   3  * Copyright 2008 VMware, Inc.
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  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
  52 extern "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))
  64 extern 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  */
  71 extern void
  72 util_init_math(void);
  73
  74
  75 union fi {
  76    float f;
  77    int32_t i;
  78    uint32_t ui;
  79 };
  80
  81
  82 union di {
  83    double d;
  84    int64_t i;
  85    uint64_t ui;
  86 };
  87
  88
  89 /**
  90  * Extract the IEEE float32 exponent.
  91  */
  92 static inline signed
  93 util_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  */
 112 static inline float
 113 util_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  */
 143 static inline float
 144 util_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)
 154 extern float log2_table[LOG2_TABLE_SIZE];
 155
 156
 157 /**
 158  * Fast approximation to log2(x).
 159  */
 160 static inline float
 161 util_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  */
 176 static inline float
 177 util_fast_pow(float x, float y)
 178 {
 179    return util_fast_exp2(util_fast_log2(x) * y);
 180 }
 181
 182
 183 /**
 184  * Floor(x), returned as int.
 185  */
 186 static inline int
 187 util_ifloor(float f)
 188 {
 189    int ai, bi;
 190    double af, bf;
 191    union fi u;
 192    af = (3 << 22) + 0.5 + (double) f;
 193    bf = (3 << 22) + 0.5 - (double) f;
 194    u.f = (float) af;  ai = u.i;
 195    u.f = (float) bf;  bi = u.i;
 196    return (ai - bi) >> 1;
 197 }
 198
 199
 200 /**
 201  * Round float to nearest int.
 202  */
 203 static inline int
 204 util_iround(float f)
 205 {
 206 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
 207    int r;
 208    __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
 209    return r;
 210 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 211    int r;
 212    _asm {
 213       fld f
 214       fistp r
 215    }
 216    return r;
 217 #else
 218    if (f >= 0.0f)
 219       return (int) (f + 0.5f);
 220    else
 221       return (int) (f - 0.5f);
 222 #endif
 223 }
 224
 225
 226 /**
 227  * Approximate floating point comparison
 228  */
 229 static inline boolean
 230 util_is_approx(float a, float b, float tol)
 231 {
 232    return fabsf(b - a) <= tol;
 233 }
 234
 235
 236 /**
 237  * util_is_X_inf_or_nan = test if x is NaN or +/- Inf
 238  * util_is_X_nan        = test if x is NaN
 239  * util_X_inf_sign      = return +1 for +Inf, -1 for -Inf, or 0 for not Inf
 240  *
 241  * NaN can be checked with x != x, however this fails with the fast math flag
 242  **/
 243
 244
 245 /**
 246  * Single-float
 247  */
 248 static inline boolean
 249 util_is_inf_or_nan(float x)
 250 {
 251    union fi tmp;
 252    tmp.f = x;
 253    return (tmp.ui & 0x7f800000) == 0x7f800000;
 254 }
 255
 256
 257 static inline boolean
 258 util_is_nan(float x)
 259 {
 260    union fi tmp;
 261    tmp.f = x;
 262    return (tmp.ui & 0x7fffffff) > 0x7f800000;
 263 }
 264
 265
 266 static inline int
 267 util_inf_sign(float x)
 268 {
 269    union fi tmp;
 270    tmp.f = x;
 271    if ((tmp.ui & 0x7fffffff) != 0x7f800000) {
 272       return 0;
 273    }
 274
 275    return (x < 0) ? -1 : 1;
 276 }
 277
 278
 279 /**
 280  * Double-float
 281  */
 282 static inline boolean
 283 util_is_double_inf_or_nan(double x)
 284 {
 285    union di tmp;
 286    tmp.d = x;
 287    return (tmp.ui & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL;
 288 }
 289
 290
 291 static inline boolean
 292 util_is_double_nan(double x)
 293 {
 294    union di tmp;
 295    tmp.d = x;
 296    return (tmp.ui & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL;
 297 }
 298
 299
 300 static inline int
 301 util_double_inf_sign(double x)
 302 {
 303    union di tmp;
 304    tmp.d = x;
 305    if ((tmp.ui & 0x7fffffffffffffffULL) != 0x7ff0000000000000ULL) {
 306       return 0;
 307    }
 308
 309    return (x < 0) ? -1 : 1;
 310 }
 311
 312
 313 /**
 314  * Half-float
 315  */
 316 static inline boolean
 317 util_is_half_inf_or_nan(int16_t x)
 318 {
 319    return (x & 0x7c00) == 0x7c00;
 320 }
 321
 322
 323 static inline boolean
 324 util_is_half_nan(int16_t x)
 325 {
 326    return (x & 0x7fff) > 0x7c00;
 327 }
 328
 329
 330 static inline int
 331 util_half_inf_sign(int16_t x)
 332 {
 333    if ((x & 0x7fff) != 0x7c00) {
 334       return 0;
 335    }
 336
 337    return (x < 0) ? -1 : 1;
 338 }
 339
 340
 341 /**
 342  * Return float bits.
 343  */
 344 static inline unsigned
 345 fui( float f )
 346 {
 347    union fi fi;
 348    fi.f = f;
 349    return fi.ui;
 350 }
 351
 352 static inline float
 353 uif(uint32_t ui)
 354 {
 355    union fi fi;
 356    fi.ui = ui;
 357    return fi.f;
 358 }
 359
 360
 361 /**
 362  * Convert ubyte to float in [0, 1].
 363  * XXX a 256-entry lookup table would be slightly faster.
 364  */
 365 static inline float
 366 ubyte_to_float(ubyte ub)
 367 {
 368    return (float) ub * (1.0f / 255.0f);
 369 }
 370
 371
 372 /**
 373  * Convert float in [0,1] to ubyte in [0,255] with clamping.
 374  */
 375 static inline ubyte
 376 float_to_ubyte(float f)
 377 {
 378    union fi tmp;
 379
 380    tmp.f = f;
 381    if (tmp.i < 0) {
 382       return (ubyte) 0;
 383    }
 384    else if (tmp.i >= 0x3f800000 /* 1.0f */) {
 385       return (ubyte) 255;
 386    }
 387    else {
 388       tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
 389       return (ubyte) tmp.i;
 390    }
 391 }
 392
 393 static inline float
 394 byte_to_float_tex(int8_t b)
 395 {
 396    return (b == -128) ? -1.0F : b * 1.0F / 127.0F;
 397 }
 398
 399 static inline int8_t
 400 float_to_byte_tex(float f)
 401 {
 402    return (int8_t) (127.0F * f);
 403 }
 404
 405 /**
 406  * Calc log base 2
 407  */
 408 static inline unsigned
 409 util_logbase2(unsigned n)
 410 {
 411 #if defined(HAVE___BUILTIN_CLZ)
 412    return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1));
 413 #else
 414    unsigned pos = 0;
 415    if (n >= 1<<16) { n >>= 16; pos += 16; }
 416    if (n >= 1<< 8) { n >>=  8; pos +=  8; }
 417    if (n >= 1<< 4) { n >>=  4; pos +=  4; }
 418    if (n >= 1<< 2) { n >>=  2; pos +=  2; }
 419    if (n >= 1<< 1) {           pos +=  1; }
 420    return pos;
 421 #endif
 422 }
 423
 424 static inline uint64_t
 425 util_logbase2_64(uint64_t n)
 426 {
 427 #if defined(HAVE___BUILTIN_CLZLL)
 428    return ((sizeof(uint64_t) * 8 - 1) - __builtin_clzll(n | 1));
 429 #else
 430    uint64_t pos = 0ull;
 431    if (n >= 1ull<<32) { n >>= 32; pos += 32; }
 432    if (n >= 1ull<<16) { n >>= 16; pos += 16; }
 433    if (n >= 1ull<< 8) { n >>=  8; pos +=  8; }
 434    if (n >= 1ull<< 4) { n >>=  4; pos +=  4; }
 435    if (n >= 1ull<< 2) { n >>=  2; pos +=  2; }
 436    if (n >= 1ull<< 1) {           pos +=  1; }
 437    return pos;
 438 #endif
 439 }
 440
 441 /**
 442  * Returns the ceiling of log n base 2, and 0 when n == 0. Equivalently,
 443  * returns the smallest x such that n <= 2**x.
 444  */
 445 static inline unsigned
 446 util_logbase2_ceil(unsigned n)
 447 {
 448    if (n <= 1)
 449       return 0;
 450
 451    return 1 + util_logbase2(n - 1);
 452 }
 453
 454 static inline uint64_t
 455 util_logbase2_ceil64(uint64_t n)
 456 {
 457    if (n <= 1)
 458       return 0;
 459
 460    return 1ull + util_logbase2_64(n - 1);
 461 }
 462
 463 /**
 464  * Returns the smallest power of two >= x
 465  */
 466 static inline unsigned
 467 util_next_power_of_two(unsigned x)
 468 {
 469 #if defined(HAVE___BUILTIN_CLZ)
 470    if (x <= 1)
 471        return 1;
 472
 473    return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1)));
 474 #else
 475    unsigned val = x;
 476
 477    if (x <= 1)
 478       return 1;
 479
 480    if (util_is_power_of_two_or_zero(x))
 481       return x;
 482
 483    val--;
 484    val = (val >> 1) | val;
 485    val = (val >> 2) | val;
 486    val = (val >> 4) | val;
 487    val = (val >> 8) | val;
 488    val = (val >> 16) | val;
 489    val++;
 490    return val;
 491 #endif
 492 }
 493
 494 static inline uint64_t
 495 util_next_power_of_two64(uint64_t x)
 496 {
 497 #if defined(HAVE___BUILTIN_CLZLL)
 498    if (x <= 1)
 499        return 1;
 500
 501    return (1ull << ((sizeof(uint64_t) * 8) - __builtin_clzll(x - 1)));
 502 #else
 503    uint64_t val = x;
 504
 505    if (x <= 1)
 506       return 1;
 507
 508    if (util_is_power_of_two_or_zero64(x))
 509       return x;
 510
 511    val--;
 512    val = (val >> 1)  | val;
 513    val = (val >> 2)  | val;
 514    val = (val >> 4)  | val;
 515    val = (val >> 8)  | val;
 516    val = (val >> 16) | val;
 517    val = (val >> 32) | val;
 518    val++;
 519    return val;
 520 #endif
 521 }
 522
 523
 524 /**
 525  * Return number of bits set in n.
 526  */
 527 static inline unsigned
 528 util_bitcount(unsigned n)
 529 {
 530 #if defined(HAVE___BUILTIN_POPCOUNT)
 531    return __builtin_popcount(n);
 532 #else
 533    /* K&R classic bitcount.
 534     *
 535     * For each iteration, clear the LSB from the bitfield.
 536     * Requires only one iteration per set bit, instead of
 537     * one iteration per bit less than highest set bit.
 538     */
 539    unsigned bits;
 540    for (bits = 0; n; bits++) {
 541       n &= n - 1;
 542    }
 543    return bits;
 544 #endif
 545 }
 546
 547
 548 static inline unsigned
 549 util_bitcount64(uint64_t n)
 550 {
 551 #ifdef HAVE___BUILTIN_POPCOUNTLL
 552    return __builtin_popcountll(n);
 553 #else
 554    return util_bitcount(n) + util_bitcount(n >> 32);
 555 #endif
 556 }
 557
 558
 559 /**
 560  * Reverse bits in n
 561  * Algorithm taken from:
 562  * http://stackoverflow.com/questions/9144800/c-reverse-bits-in-unsigned-integer
 563  */
 564 static inline unsigned
 565 util_bitreverse(unsigned n)
 566 {
 567     n = ((n >> 1) & 0x55555555u) | ((n & 0x55555555u) << 1);
 568     n = ((n >> 2) & 0x33333333u) | ((n & 0x33333333u) << 2);
 569     n = ((n >> 4) & 0x0f0f0f0fu) | ((n & 0x0f0f0f0fu) << 4);
 570     n = ((n >> 8) & 0x00ff00ffu) | ((n & 0x00ff00ffu) << 8);
 571     n = ((n >> 16) & 0xffffu) | ((n & 0xffffu) << 16);
 572     return n;
 573 }
 574
 575 /**
 576  * Convert from little endian to CPU byte order.
 577  */
 578
 579 #ifdef PIPE_ARCH_BIG_ENDIAN
 580 #define util_le64_to_cpu(x) util_bswap64(x)
 581 #define util_le32_to_cpu(x) util_bswap32(x)
 582 #define util_le16_to_cpu(x) util_bswap16(x)
 583 #else
 584 #define util_le64_to_cpu(x) (x)
 585 #define util_le32_to_cpu(x) (x)
 586 #define util_le16_to_cpu(x) (x)
 587 #endif
 588
 589 #define util_cpu_to_le64(x) util_le64_to_cpu(x)
 590 #define util_cpu_to_le32(x) util_le32_to_cpu(x)
 591 #define util_cpu_to_le16(x) util_le16_to_cpu(x)
 592
 593 /**
 594  * Reverse byte order of a 32 bit word.
 595  */
 596 static inline uint32_t
 597 util_bswap32(uint32_t n)
 598 {
 599 #if defined(HAVE___BUILTIN_BSWAP32)
 600    return __builtin_bswap32(n);
 601 #else
 602    return (n >> 24) |
 603           ((n >> 8) & 0x0000ff00) |
 604           ((n << 8) & 0x00ff0000) |
 605           (n << 24);
 606 #endif
 607 }
 608
 609 /**
 610  * Reverse byte order of a 64bit word.
 611  */
 612 static inline uint64_t
 613 util_bswap64(uint64_t n)
 614 {
 615 #if defined(HAVE___BUILTIN_BSWAP64)
 616    return __builtin_bswap64(n);
 617 #else
 618    return ((uint64_t)util_bswap32((uint32_t)n) << 32) |
 619           util_bswap32((n >> 32));
 620 #endif
 621 }
 622
 623
 624 /**
 625  * Reverse byte order of a 16 bit word.
 626  */
 627 static inline uint16_t
 628 util_bswap16(uint16_t n)
 629 {
 630    return (n >> 8) |
 631           (n << 8);
 632 }
 633
 634 static inline void*
 635 util_memcpy_cpu_to_le32(void * restrict dest, const void * restrict src, size_t n)
 636 {
 637 #ifdef PIPE_ARCH_BIG_ENDIAN
 638    size_t i, e;
 639    assert(n % 4 == 0);
 640
 641    for (i = 0, e = n / 4; i < e; i++) {
 642       uint32_t * restrict d = (uint32_t* restrict)dest;
 643       const uint32_t * restrict s = (const uint32_t* restrict)src;
 644       d[i] = util_bswap32(s[i]);
 645    }
 646    return dest;
 647 #else
 648    return memcpy(dest, src, n);
 649 #endif
 650 }
 651
 652 /**
 653  * Clamp X to [MIN, MAX].
 654  * This is a macro to allow float, int, uint, etc. types.
 655  * We arbitrarily turn NaN into MIN.
 656  */
 657 #define CLAMP( X, MIN, MAX )  ( (X)>(MIN) ? ((X)>(MAX) ? (MAX) : (X)) : (MIN) )
 658
 659 #define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
 660 #define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
 661
 662 #define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
 663 #define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))
 664
 665 #define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
 666 #define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))
 667
 668
 669 /**
 670  * Align a value, only works pot alignemnts.
 671  */
 672 static inline int
 673 align(int value, int alignment)
 674 {
 675    return (value + alignment - 1) & ~(alignment - 1);
 676 }
 677
 678 static inline uint64_t
 679 align64(uint64_t value, unsigned alignment)
 680 {
 681    return (value + alignment - 1) & ~((uint64_t)alignment - 1);
 682 }
 683
 684 /**
 685  * Works like align but on npot alignments.
 686  */
 687 static inline size_t
 688 util_align_npot(size_t value, size_t alignment)
 689 {
 690    if (value % alignment)
 691       return value + (alignment - (value % alignment));
 692    return value;
 693 }
 694
 695 static inline unsigned
 696 u_minify(unsigned value, unsigned levels)
 697 {
 698     return MAX2(1, value >> levels);
 699 }
 700
 701 #ifndef COPY_4V
 702 #define COPY_4V( DST, SRC )         \
 703 do {                                \
 704    (DST)[0] = (SRC)[0];             \
 705    (DST)[1] = (SRC)[1];             \
 706    (DST)[2] = (SRC)[2];             \
 707    (DST)[3] = (SRC)[3];             \
 708 } while (0)
 709 #endif
 710
 711
 712 #ifndef COPY_4FV
 713 #define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
 714 #endif
 715
 716
 717 #ifndef ASSIGN_4V
 718 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
 719 do {                                     \
 720    (DST)[0] = (V0);                      \
 721    (DST)[1] = (V1);                      \
 722    (DST)[2] = (V2);                      \
 723    (DST)[3] = (V3);                      \
 724 } while (0)
 725 #endif
 726
 727
 728 static inline uint32_t
 729 util_unsigned_fixed(float value, unsigned frac_bits)
 730 {
 731    return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits));
 732 }
 733
 734 static inline int32_t
 735 util_signed_fixed(float value, unsigned frac_bits)
 736 {
 737    return (int32_t)(value * (1<<frac_bits));
 738 }
 739
 740 unsigned
 741 util_fpstate_get(void);
 742 unsigned
 743 util_fpstate_set_denorms_to_zero(unsigned current_fpstate);
 744 void
 745 util_fpstate_set(unsigned fpstate);
 746
 747
 748
 749 #ifdef __cplusplus
 750 }
 751 #endif
 752
 753 #endif /* U_MATH_H */