src/gallium/auxiliary/util/u_math.h

   1 /**************************************************************************
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   3  * Copyright 2008 VMware, Inc.
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  13  *
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  15  * next paragraph) shall be included in all copies or substantial portions
  16  * of the Software.
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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
  45 #ifdef __cplusplus
  46 extern "C" {
  47 #endif
  48
  49
  50 #include <math.h>
  51 #include <float.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 #define INFINITY (DBL_MAX + DBL_MAX)
 138 #define NAN (INFINITY - INFINITY)
 139
 140 #endif /* _MSC_VER */
 141
 142
 143 #ifdef PIPE_OS_ANDROID
 144
 145 static INLINE
 146 double log2(double d)
 147 {
 148    return log(d) * (1.0 / M_LN2);
 149 }
 150
 151 /* workaround a conflict with main/imports.h */
 152 #ifdef log2f
 153 #undef log2f
 154 #endif
 155
 156 static INLINE
 157 float log2f(float f)
 158 {
 159    return logf(f) * (float) (1.0 / M_LN2);
 160 }
 161
 162 #endif
 163
 164
 165 #if __STDC_VERSION__ < 199901L && (!defined(__cplusplus) || defined(_MSC_VER))
 166 static INLINE long int
 167 lrint(double d)
 168 {
 169    long int rounded = (long int)(d + 0.5);
 170
 171    if (d - floor(d) == 0.5) {
 172       if (rounded % 2 != 0)
 173          rounded += (d > 0) ? -1 : 1;
 174    }
 175
 176    return rounded;
 177 }
 178
 179 static INLINE long int
 180 lrintf(float f)
 181 {
 182    long int rounded = (long int)(f + 0.5f);
 183
 184    if (f - floorf(f) == 0.5f) {
 185       if (rounded % 2 != 0)
 186          rounded += (f > 0) ? -1 : 1;
 187    }
 188
 189    return rounded;
 190 }
 191
 192 static INLINE long long int
 193 llrint(double d)
 194 {
 195    long long int rounded = (long long int)(d + 0.5);
 196
 197    if (d - floor(d) == 0.5) {
 198       if (rounded % 2 != 0)
 199          rounded += (d > 0) ? -1 : 1;
 200    }
 201
 202    return rounded;
 203 }
 204
 205 static INLINE long long int
 206 llrintf(float f)
 207 {
 208    long long int rounded = (long long int)(f + 0.5f);
 209
 210    if (f - floorf(f) == 0.5f) {
 211       if (rounded % 2 != 0)
 212          rounded += (f > 0) ? -1 : 1;
 213    }
 214
 215    return rounded;
 216 }
 217 #endif /* C99 */
 218
 219 #define POW2_TABLE_SIZE_LOG2 9
 220 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
 221 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
 222 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
 223 extern float pow2_table[POW2_TABLE_SIZE];
 224
 225
 226 /**
 227  * Initialize math module.  This should be called before using any
 228  * other functions in this module.
 229  */
 230 extern void
 231 util_init_math(void);
 232
 233
 234 union fi {
 235    float f;
 236    int32_t i;
 237    uint32_t ui;
 238 };
 239
 240
 241 union di {
 242    double d;
 243    int64_t i;
 244    uint64_t ui;
 245 };
 246
 247
 248 /**
 249  * Extract the IEEE float32 exponent.
 250  */
 251 static INLINE signed
 252 util_get_float32_exponent(float x) {
 253    union fi f;
 254
 255    f.f = x;
 256
 257    return ((f.ui >> 23) & 0xff) - 127;
 258 }
 259
 260
 261 /**
 262  * Fast version of 2^x
 263  * Identity: exp2(a + b) = exp2(a) * exp2(b)
 264  * Let ipart = int(x)
 265  * Let fpart = x - ipart;
 266  * So, exp2(x) = exp2(ipart) * exp2(fpart)
 267  * Compute exp2(ipart) with i << ipart
 268  * Compute exp2(fpart) with lookup table.
 269  */
 270 static INLINE float
 271 util_fast_exp2(float x)
 272 {
 273    int32_t ipart;
 274    float fpart, mpart;
 275    union fi epart;
 276
 277    if(x > 129.00000f)
 278       return 3.402823466e+38f;
 279
 280    if (x < -126.99999f)
 281       return 0.0f;
 282
 283    ipart = (int32_t) x;
 284    fpart = x - (float) ipart;
 285
 286    /* same as
 287     *   epart.f = (float) (1 << ipart)
 288     * but faster and without integer overflow for ipart > 31
 289     */
 290    epart.i = (ipart + 127 ) << 23;
 291
 292    mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];
 293
 294    return epart.f * mpart;
 295 }
 296
 297
 298 /**
 299  * Fast approximation to exp(x).
 300  */
 301 static INLINE float
 302 util_fast_exp(float x)
 303 {
 304    const float k = 1.44269f; /* = log2(e) */
 305    return util_fast_exp2(k * x);
 306 }
 307
 308
 309 #define LOG2_TABLE_SIZE_LOG2 16
 310 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
 311 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
 312 extern float log2_table[LOG2_TABLE_SIZE];
 313
 314
 315 /**
 316  * Fast approximation to log2(x).
 317  */
 318 static INLINE float
 319 util_fast_log2(float x)
 320 {
 321    union fi num;
 322    float epart, mpart;
 323    num.f = x;
 324    epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
 325    /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
 326    mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)];
 327    return epart + mpart;
 328 }
 329
 330
 331 /**
 332  * Fast approximation to x^y.
 333  */
 334 static INLINE float
 335 util_fast_pow(float x, float y)
 336 {
 337    return util_fast_exp2(util_fast_log2(x) * y);
 338 }
 339
 340 /* Note that this counts zero as a power of two.
 341  */
 342 static INLINE boolean
 343 util_is_power_of_two( unsigned v )
 344 {
 345    return (v & (v-1)) == 0;
 346 }
 347
 348
 349 /**
 350  * Floor(x), returned as int.
 351  */
 352 static INLINE int
 353 util_ifloor(float f)
 354 {
 355    int ai, bi;
 356    double af, bf;
 357    union fi u;
 358    af = (3 << 22) + 0.5 + (double) f;
 359    bf = (3 << 22) + 0.5 - (double) f;
 360    u.f = (float) af;  ai = u.i;
 361    u.f = (float) bf;  bi = u.i;
 362    return (ai - bi) >> 1;
 363 }
 364
 365
 366 /**
 367  * Round float to nearest int.
 368  */
 369 static INLINE int
 370 util_iround(float f)
 371 {
 372 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
 373    int r;
 374    __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
 375    return r;
 376 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 377    int r;
 378    _asm {
 379       fld f
 380       fistp r
 381    }
 382    return r;
 383 #else
 384    if (f >= 0.0f)
 385       return (int) (f + 0.5f);
 386    else
 387       return (int) (f - 0.5f);
 388 #endif
 389 }
 390
 391
 392 /**
 393  * Approximate floating point comparison
 394  */
 395 static INLINE boolean
 396 util_is_approx(float a, float b, float tol)
 397 {
 398    return fabs(b - a) <= tol;
 399 }
 400
 401
 402 /**
 403  * util_is_X_inf_or_nan = test if x is NaN or +/- Inf
 404  * util_is_X_nan        = test if x is NaN
 405  * util_X_inf_sign      = return +1 for +Inf, -1 for -Inf, or 0 for not Inf
 406  *
 407  * NaN can be checked with x != x, however this fails with the fast math flag
 408  **/
 409
 410
 411 /**
 412  * Single-float
 413  */
 414 static INLINE boolean
 415 util_is_inf_or_nan(float x)
 416 {
 417    union fi tmp;
 418    tmp.f = x;
 419    return (tmp.ui & 0x7f800000) == 0x7f800000;
 420 }
 421
 422
 423 static INLINE boolean
 424 util_is_nan(float x)
 425 {
 426    union fi tmp;
 427    tmp.f = x;
 428    return (tmp.ui & 0x7fffffff) > 0x7f800000;
 429 }
 430
 431
 432 static INLINE int
 433 util_inf_sign(float x)
 434 {
 435    union fi tmp;
 436    tmp.f = x;
 437    if ((tmp.ui & 0x7fffffff) != 0x7f800000) {
 438       return 0;
 439    }
 440
 441    return (x < 0) ? -1 : 1;
 442 }
 443
 444
 445 /**
 446  * Double-float
 447  */
 448 static INLINE boolean
 449 util_is_double_inf_or_nan(double x)
 450 {
 451    union di tmp;
 452    tmp.d = x;
 453    return (tmp.ui & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL;
 454 }
 455
 456
 457 static INLINE boolean
 458 util_is_double_nan(double x)
 459 {
 460    union di tmp;
 461    tmp.d = x;
 462    return (tmp.ui & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL;
 463 }
 464
 465
 466 static INLINE int
 467 util_double_inf_sign(double x)
 468 {
 469    union di tmp;
 470    tmp.d = x;
 471    if ((tmp.ui & 0x7fffffffffffffffULL) != 0x7ff0000000000000ULL) {
 472       return 0;
 473    }
 474
 475    return (x < 0) ? -1 : 1;
 476 }
 477
 478
 479 /**
 480  * Half-float
 481  */
 482 static INLINE boolean
 483 util_is_half_inf_or_nan(int16_t x)
 484 {
 485    return (x & 0x7c00) == 0x7c00;
 486 }
 487
 488
 489 static INLINE boolean
 490 util_is_half_nan(int16_t x)
 491 {
 492    return (x & 0x7fff) > 0x7c00;
 493 }
 494
 495
 496 static INLINE int
 497 util_half_inf_sign(int16_t x)
 498 {
 499    if ((x & 0x7fff) != 0x7c00) {
 500       return 0;
 501    }
 502
 503    return (x < 0) ? -1 : 1;
 504 }
 505
 506
 507 /**
 508  * Find first bit set in word.  Least significant bit is 1.
 509  * Return 0 if no bits set.
 510  */
 511 #ifndef FFS_DEFINED
 512 #define FFS_DEFINED 1
 513
 514 #if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64)
 515 unsigned char _BitScanForward(unsigned long* Index, unsigned long Mask);
 516 #pragma intrinsic(_BitScanForward)
 517 static INLINE
 518 unsigned long ffs( unsigned long u )
 519 {
 520    unsigned long i;
 521    if (_BitScanForward(&i, u))
 522       return i + 1;
 523    else
 524       return 0;
 525 }
 526 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 527 static INLINE
 528 unsigned ffs( unsigned u )
 529 {
 530    unsigned i;
 531
 532    if (u == 0) {
 533       return 0;
 534    }
 535
 536    __asm bsf eax, [u]
 537    __asm inc eax
 538    __asm mov [i], eax
 539
 540    return i;
 541 }
 542 #elif defined(__MINGW32__) || defined(PIPE_OS_ANDROID)
 543 #define ffs __builtin_ffs
 544 #endif
 545
 546 #endif /* FFS_DEFINED */
 547
 548 /**
 549  * Find last bit set in a word.  The least significant bit is 1.
 550  * Return 0 if no bits are set.
 551  */
 552 static INLINE unsigned util_last_bit(unsigned u)
 553 {
 554 #if defined(__GNUC__) && ((__GNUC__ * 100 + __GNUC_MINOR__) >= 304)
 555    return u == 0 ? 0 : 32 - __builtin_clz(u);
 556 #else
 557    unsigned r = 0;
 558    while (u) {
 559        r++;
 560        u >>= 1;
 561    }
 562    return r;
 563 #endif
 564 }
 565
 566
 567 /* Destructively loop over all of the bits in a mask as in:
 568  *
 569  * while (mymask) {
 570  *   int i = u_bit_scan(&mymask);
 571  *   ... process element i
 572  * }
 573  *
 574  */
 575 static INLINE int u_bit_scan(unsigned *mask)
 576 {
 577    int i = ffs(*mask) - 1;
 578    *mask &= ~(1 << i);
 579    return i;
 580 }
 581
 582
 583 /**
 584  * Return float bits.
 585  */
 586 static INLINE unsigned
 587 fui( float f )
 588 {
 589    union fi fi;
 590    fi.f = f;
 591    return fi.ui;
 592 }
 593
 594
 595 /**
 596  * Convert ubyte to float in [0, 1].
 597  * XXX a 256-entry lookup table would be slightly faster.
 598  */
 599 static INLINE float
 600 ubyte_to_float(ubyte ub)
 601 {
 602    return (float) ub * (1.0f / 255.0f);
 603 }
 604
 605
 606 /**
 607  * Convert float in [0,1] to ubyte in [0,255] with clamping.
 608  */
 609 static INLINE ubyte
 610 float_to_ubyte(float f)
 611 {
 612    union fi tmp;
 613
 614    tmp.f = f;
 615    if (tmp.i < 0) {
 616       return (ubyte) 0;
 617    }
 618    else if (tmp.i >= 0x3f800000 /* 1.0f */) {
 619       return (ubyte) 255;
 620    }
 621    else {
 622       tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
 623       return (ubyte) tmp.i;
 624    }
 625 }
 626
 627 static INLINE float
 628 byte_to_float_tex(int8_t b)
 629 {
 630    return (b == -128) ? -1.0F : b * 1.0F / 127.0F;
 631 }
 632
 633 static INLINE int8_t
 634 float_to_byte_tex(float f)
 635 {
 636    return (int8_t) (127.0F * f);
 637 }
 638
 639 /**
 640  * Calc log base 2
 641  */
 642 static INLINE unsigned
 643 util_logbase2(unsigned n)
 644 {
 645 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
 646    return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1));
 647 #else
 648    unsigned pos = 0;
 649    if (n >= 1<<16) { n >>= 16; pos += 16; }
 650    if (n >= 1<< 8) { n >>=  8; pos +=  8; }
 651    if (n >= 1<< 4) { n >>=  4; pos +=  4; }
 652    if (n >= 1<< 2) { n >>=  2; pos +=  2; }
 653    if (n >= 1<< 1) {           pos +=  1; }
 654    return pos;
 655 #endif
 656 }
 657
 658
 659 /**
 660  * Returns the smallest power of two >= x
 661  */
 662 static INLINE unsigned
 663 util_next_power_of_two(unsigned x)
 664 {
 665 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
 666    if (x <= 1)
 667        return 1;
 668
 669    return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1)));
 670 #else
 671    unsigned val = x;
 672
 673    if (x <= 1)
 674       return 1;
 675
 676    if (util_is_power_of_two(x))
 677       return x;
 678
 679    val--;
 680    val = (val >> 1) | val;
 681    val = (val >> 2) | val;
 682    val = (val >> 4) | val;
 683    val = (val >> 8) | val;
 684    val = (val >> 16) | val;
 685    val++;
 686    return val;
 687 #endif
 688 }
 689
 690
 691 /**
 692  * Return number of bits set in n.
 693  */
 694 static INLINE unsigned
 695 util_bitcount(unsigned n)
 696 {
 697 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
 698    return __builtin_popcount(n);
 699 #else
 700    /* K&R classic bitcount.
 701     *
 702     * For each iteration, clear the LSB from the bitfield.
 703     * Requires only one iteration per set bit, instead of
 704     * one iteration per bit less than highest set bit.
 705     */
 706    unsigned bits = 0;
 707    for (bits; n; bits++) {
 708       n &= n - 1;
 709    }
 710    return bits;
 711 #endif
 712 }
 713
 714
 715 /**
 716  * Convert from little endian to CPU byte order.
 717  */
 718
 719 #ifdef PIPE_ARCH_BIG_ENDIAN
 720 #define util_le32_to_cpu(x) util_bswap32(x)
 721 #define util_le16_to_cpu(x) util_bswap16(x)
 722 #else
 723 #define util_le32_to_cpu(x) (x)
 724 #define util_le16_to_cpu(x) (x)
 725 #endif
 726
 727
 728 /**
 729  * Reverse byte order of a 32 bit word.
 730  */
 731 static INLINE uint32_t
 732 util_bswap32(uint32_t n)
 733 {
 734 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 403)
 735    return __builtin_bswap32(n);
 736 #else
 737    return (n >> 24) |
 738           ((n >> 8) & 0x0000ff00) |
 739           ((n << 8) & 0x00ff0000) |
 740           (n << 24);
 741 #endif
 742 }
 743
 744
 745 /**
 746  * Reverse byte order of a 16 bit word.
 747  */
 748 static INLINE uint16_t
 749 util_bswap16(uint16_t n)
 750 {
 751    return (n >> 8) |
 752           (n << 8);
 753 }
 754
 755
 756 /**
 757  * Clamp X to [MIN, MAX].
 758  * This is a macro to allow float, int, uint, etc. types.
 759  */
 760 #define CLAMP( X, MIN, MAX )  ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
 761
 762 #define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
 763 #define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
 764
 765 #define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
 766 #define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))
 767
 768 #define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
 769 #define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))
 770
 771
 772 /**
 773  * Align a value, only works pot alignemnts.
 774  */
 775 static INLINE int
 776 align(int value, int alignment)
 777 {
 778    return (value + alignment - 1) & ~(alignment - 1);
 779 }
 780
 781 /**
 782  * Works like align but on npot alignments.
 783  */
 784 static INLINE size_t
 785 util_align_npot(size_t value, size_t alignment)
 786 {
 787    if (value % alignment)
 788       return value + (alignment - (value % alignment));
 789    return value;
 790 }
 791
 792 static INLINE unsigned
 793 u_minify(unsigned value, unsigned levels)
 794 {
 795     return MAX2(1, value >> levels);
 796 }
 797
 798 #ifndef COPY_4V
 799 #define COPY_4V( DST, SRC )         \
 800 do {                                \
 801    (DST)[0] = (SRC)[0];             \
 802    (DST)[1] = (SRC)[1];             \
 803    (DST)[2] = (SRC)[2];             \
 804    (DST)[3] = (SRC)[3];             \
 805 } while (0)
 806 #endif
 807
 808
 809 #ifndef COPY_4FV
 810 #define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
 811 #endif
 812
 813
 814 #ifndef ASSIGN_4V
 815 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
 816 do {                                     \
 817    (DST)[0] = (V0);                      \
 818    (DST)[1] = (V1);                      \
 819    (DST)[2] = (V2);                      \
 820    (DST)[3] = (V3);                      \
 821 } while (0)
 822 #endif
 823
 824
 825 static INLINE uint32_t util_unsigned_fixed(float value, unsigned frac_bits)
 826 {
 827    return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits));
 828 }
 829
 830 static INLINE int32_t util_signed_fixed(float value, unsigned frac_bits)
 831 {
 832    return (int32_t)(value * (1<<frac_bits));
 833 }
 834
 835 unsigned
 836 util_fpstate_get(void);
 837 unsigned
 838 util_fpstate_set_denorms_to_zero(unsigned current_fpstate);
 839 void
 840 util_fpstate_set(unsigned fpstate);
 841
 842
 843
 844 #ifdef __cplusplus
 845 }
 846 #endif
 847
 848 #endif /* U_MATH_H */