src/gallium/auxiliary/util/u_math.h

   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
  44
  45 #ifdef __cplusplus
  46 extern "C" {
  47 #endif
  48
  49
  50 #include <math.h>
  51 #include <stdarg.h>
  52
  53 #ifdef PIPE_OS_UNIX
  54 #include <strings.h> /* for ffs */
  55 #endif
  56
  57
  58 #ifndef M_SQRT2
  59 #define M_SQRT2 1.41421356237309504880
  60 #endif
  61
  62
  63 #if defined(_MSC_VER)
  64
  65 #if _MSC_VER < 1400 && !defined(__cplusplus)
  66
  67 static INLINE float cosf( float f )
  68 {
  69    return (float) cos( (double) f );
  70 }
  71
  72 static INLINE float sinf( float f )
  73 {
  74    return (float) sin( (double) f );
  75 }
  76
  77 static INLINE float ceilf( float f )
  78 {
  79    return (float) ceil( (double) f );
  80 }
  81
  82 static INLINE float floorf( float f )
  83 {
  84    return (float) floor( (double) f );
  85 }
  86
  87 static INLINE float powf( float f, float g )
  88 {
  89    return (float) pow( (double) f, (double) g );
  90 }
  91
  92 static INLINE float sqrtf( float f )
  93 {
  94    return (float) sqrt( (double) f );
  95 }
  96
  97 static INLINE float fabsf( float f )
  98 {
  99    return (float) fabs( (double) f );
 100 }
 101
 102 static INLINE float logf( float f )
 103 {
 104    return (float) log( (double) f );
 105 }
 106
 107 #else
 108 /* Work-around an extra semi-colon in VS 2005 logf definition */
 109 #ifdef logf
 110 #undef logf
 111 #define logf(x) ((float)log((double)(x)))
 112 #endif /* logf */
 113
 114 #define isfinite(x) _finite((double)(x))
 115 #define isnan(x) _isnan((double)(x))
 116 #endif /* _MSC_VER < 1400 && !defined(__cplusplus) */
 117
 118 static INLINE double log2( double x )
 119 {
 120    const double invln2 = 1.442695041;
 121    return log( x ) * invln2;
 122 }
 123
 124 static INLINE double
 125 round(double x)
 126 {
 127    return x >= 0.0 ? floor(x + 0.5) : ceil(x - 0.5);
 128 }
 129
 130 static INLINE float
 131 roundf(float x)
 132 {
 133    return x >= 0.0f ? floorf(x + 0.5f) : ceilf(x - 0.5f);
 134 }
 135
 136 #endif /* _MSC_VER */
 137
 138
 139 #ifdef PIPE_OS_ANDROID
 140
 141 static INLINE
 142 double log2(double d)
 143 {
 144    return log(d) * (1.0 / M_LN2);
 145 }
 146
 147 /* workaround a conflict with main/imports.h */
 148 #ifdef log2f
 149 #undef log2f
 150 #endif
 151
 152 static INLINE
 153 float log2f(float f)
 154 {
 155    return logf(f) * (float) (1.0 / M_LN2);
 156 }
 157
 158 #endif
 159
 160
 161
 162
 163 #define POW2_TABLE_SIZE_LOG2 9
 164 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
 165 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
 166 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
 167 extern float pow2_table[POW2_TABLE_SIZE];
 168
 169
 170 /**
 171  * Initialize math module.  This should be called before using any
 172  * other functions in this module.
 173  */
 174 extern void
 175 util_init_math(void);
 176
 177
 178 union fi {
 179    float f;
 180    int32_t i;
 181    uint32_t ui;
 182 };
 183
 184
 185 union di {
 186    double d;
 187    int64_t i;
 188    uint64_t ui;
 189 };
 190
 191
 192 /**
 193  * Fast version of 2^x
 194  * Identity: exp2(a + b) = exp2(a) * exp2(b)
 195  * Let ipart = int(x)
 196  * Let fpart = x - ipart;
 197  * So, exp2(x) = exp2(ipart) * exp2(fpart)
 198  * Compute exp2(ipart) with i << ipart
 199  * Compute exp2(fpart) with lookup table.
 200  */
 201 static INLINE float
 202 util_fast_exp2(float x)
 203 {
 204    int32_t ipart;
 205    float fpart, mpart;
 206    union fi epart;
 207
 208    if(x > 129.00000f)
 209       return 3.402823466e+38f;
 210
 211    if (x < -126.99999f)
 212       return 0.0f;
 213
 214    ipart = (int32_t) x;
 215    fpart = x - (float) ipart;
 216
 217    /* same as
 218     *   epart.f = (float) (1 << ipart)
 219     * but faster and without integer overflow for ipart > 31
 220     */
 221    epart.i = (ipart + 127 ) << 23;
 222
 223    mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];
 224
 225    return epart.f * mpart;
 226 }
 227
 228
 229 /**
 230  * Fast approximation to exp(x).
 231  */
 232 static INLINE float
 233 util_fast_exp(float x)
 234 {
 235    const float k = 1.44269f; /* = log2(e) */
 236    return util_fast_exp2(k * x);
 237 }
 238
 239
 240 #define LOG2_TABLE_SIZE_LOG2 16
 241 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
 242 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
 243 extern float log2_table[LOG2_TABLE_SIZE];
 244
 245
 246 /**
 247  * Fast approximation to log2(x).
 248  */
 249 static INLINE float
 250 util_fast_log2(float x)
 251 {
 252    union fi num;
 253    float epart, mpart;
 254    num.f = x;
 255    epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
 256    /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
 257    mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)];
 258    return epart + mpart;
 259 }
 260
 261
 262 /**
 263  * Fast approximation to x^y.
 264  */
 265 static INLINE float
 266 util_fast_pow(float x, float y)
 267 {
 268    return util_fast_exp2(util_fast_log2(x) * y);
 269 }
 270
 271 /* Note that this counts zero as a power of two.
 272  */
 273 static INLINE boolean
 274 util_is_power_of_two( unsigned v )
 275 {
 276    return (v & (v-1)) == 0;
 277 }
 278
 279
 280 /**
 281  * Floor(x), returned as int.
 282  */
 283 static INLINE int
 284 util_ifloor(float f)
 285 {
 286    int ai, bi;
 287    double af, bf;
 288    union fi u;
 289    af = (3 << 22) + 0.5 + (double) f;
 290    bf = (3 << 22) + 0.5 - (double) f;
 291    u.f = (float) af;  ai = u.i;
 292    u.f = (float) bf;  bi = u.i;
 293    return (ai - bi) >> 1;
 294 }
 295
 296
 297 /**
 298  * Round float to nearest int.
 299  */
 300 static INLINE int
 301 util_iround(float f)
 302 {
 303 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
 304    int r;
 305    __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
 306    return r;
 307 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 308    int r;
 309    _asm {
 310       fld f
 311       fistp r
 312    }
 313    return r;
 314 #else
 315    if (f >= 0.0f)
 316       return (int) (f + 0.5f);
 317    else
 318       return (int) (f - 0.5f);
 319 #endif
 320 }
 321
 322
 323 /**
 324  * Approximate floating point comparison
 325  */
 326 static INLINE boolean
 327 util_is_approx(float a, float b, float tol)
 328 {
 329    return fabs(b - a) <= tol;
 330 }
 331
 332
 333 /**
 334  * util_is_X_inf_or_nan = test if x is NaN or +/- Inf
 335  * util_is_X_nan        = test if x is NaN
 336  * util_X_inf_sign      = return +1 for +Inf, -1 for -Inf, or 0 for not Inf
 337  *
 338  * NaN can be checked with x != x, however this fails with the fast math flag
 339  **/
 340
 341
 342 /**
 343  * Single-float
 344  */
 345 static INLINE boolean
 346 util_is_inf_or_nan(float x)
 347 {
 348    union fi tmp;
 349    tmp.f = x;
 350    return (tmp.ui & 0x7f800000) == 0x7f800000;
 351 }
 352
 353
 354 static INLINE boolean
 355 util_is_nan(float x)
 356 {
 357    union fi tmp;
 358    tmp.f = x;
 359    return (tmp.ui & 0x7fffffff) > 0x7f800000;
 360 }
 361
 362
 363 static INLINE int
 364 util_inf_sign(float x)
 365 {
 366    union fi tmp;
 367    tmp.f = x;
 368    if ((tmp.ui & 0x7fffffff) != 0x7f800000) {
 369       return 0;
 370    }
 371
 372    return (x < 0) ? -1 : 1;
 373 }
 374
 375
 376 /**
 377  * Double-float
 378  */
 379 static INLINE boolean
 380 util_is_double_inf_or_nan(double x)
 381 {
 382    union di tmp;
 383    tmp.d = x;
 384    return (tmp.ui & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL;
 385 }
 386
 387
 388 static INLINE boolean
 389 util_is_double_nan(double x)
 390 {
 391    union di tmp;
 392    tmp.d = x;
 393    return (tmp.ui & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL;
 394 }
 395
 396
 397 static INLINE int
 398 util_double_inf_sign(double x)
 399 {
 400    union di tmp;
 401    tmp.d = x;
 402    if ((tmp.ui & 0x7fffffffffffffffULL) != 0x7ff0000000000000ULL) {
 403       return 0;
 404    }
 405
 406    return (x < 0) ? -1 : 1;
 407 }
 408
 409
 410 /**
 411  * Half-float
 412  */
 413 static INLINE boolean
 414 util_is_half_inf_or_nan(int16_t x)
 415 {
 416    return (x & 0x7c00) == 0x7c00;
 417 }
 418
 419
 420 static INLINE boolean
 421 util_is_half_nan(int16_t x)
 422 {
 423    return (x & 0x7fff) > 0x7c00;
 424 }
 425
 426
 427 static INLINE int
 428 util_half_inf_sign(int16_t x)
 429 {
 430    if ((x & 0x7fff) != 0x7c00) {
 431       return 0;
 432    }
 433
 434    return (x < 0) ? -1 : 1;
 435 }
 436
 437
 438 /**
 439  * Find first bit set in word.  Least significant bit is 1.
 440  * Return 0 if no bits set.
 441  */
 442 #ifndef FFS_DEFINED
 443 #define FFS_DEFINED 1
 444
 445 #if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64)
 446 unsigned char _BitScanForward(unsigned long* Index, unsigned long Mask);
 447 #pragma intrinsic(_BitScanForward)
 448 static INLINE
 449 unsigned long ffs( unsigned long u )
 450 {
 451    unsigned long i;
 452    if (_BitScanForward(&i, u))
 453       return i + 1;
 454    else
 455       return 0;
 456 }
 457 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 458 static INLINE
 459 unsigned ffs( unsigned u )
 460 {
 461    unsigned i;
 462
 463    if (u == 0) {
 464       return 0;
 465    }
 466
 467    __asm bsf eax, [u]
 468    __asm inc eax
 469    __asm mov [i], eax
 470
 471    return i;
 472 }
 473 #elif defined(__MINGW32__) || defined(PIPE_OS_ANDROID)
 474 #define ffs __builtin_ffs
 475 #endif
 476
 477 #endif /* FFS_DEFINED */
 478
 479 /**
 480  * Find last bit set in a word.  The least significant bit is 1.
 481  * Return 0 if no bits are set.
 482  */
 483 static INLINE unsigned util_last_bit(unsigned u)
 484 {
 485 #if defined(__GNUC__) && ((__GNUC__ * 100 + __GNUC_MINOR__) >= 304)
 486    return u == 0 ? 0 : 32 - __builtin_clz(u);
 487 #else
 488    unsigned r = 0;
 489    while (u) {
 490        r++;
 491        u >>= 1;
 492    }
 493    return r;
 494 #endif
 495 }
 496
 497
 498 /* Destructively loop over all of the bits in a mask as in:
 499  *
 500  * while (mymask) {
 501  *   int i = u_bit_scan(&mymask);
 502  *   ... process element i
 503  * }
 504  *
 505  */
 506 static INLINE int u_bit_scan(unsigned *mask)
 507 {
 508    int i = ffs(*mask) - 1;
 509    *mask &= ~(1 << i);
 510    return i;
 511 }
 512
 513
 514 /**
 515  * Return float bits.
 516  */
 517 static INLINE unsigned
 518 fui( float f )
 519 {
 520    union fi fi;
 521    fi.f = f;
 522    return fi.ui;
 523 }
 524
 525
 526 /**
 527  * Convert ubyte to float in [0, 1].
 528  * XXX a 256-entry lookup table would be slightly faster.
 529  */
 530 static INLINE float
 531 ubyte_to_float(ubyte ub)
 532 {
 533    return (float) ub * (1.0f / 255.0f);
 534 }
 535
 536
 537 /**
 538  * Convert float in [0,1] to ubyte in [0,255] with clamping.
 539  */
 540 static INLINE ubyte
 541 float_to_ubyte(float f)
 542 {
 543    const int ieee_0996 = 0x3f7f0000;   /* 0.996 or so */
 544    union fi tmp;
 545
 546    tmp.f = f;
 547    if (tmp.i < 0) {
 548       return (ubyte) 0;
 549    }
 550    else if (tmp.i >= ieee_0996) {
 551       return (ubyte) 255;
 552    }
 553    else {
 554       tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
 555       return (ubyte) tmp.i;
 556    }
 557 }
 558
 559 static INLINE float
 560 byte_to_float_tex(int8_t b)
 561 {
 562    return (b == -128) ? -1.0F : b * 1.0F / 127.0F;
 563 }
 564
 565 static INLINE int8_t
 566 float_to_byte_tex(float f)
 567 {
 568    return (int8_t) (127.0F * f);
 569 }
 570
 571 /**
 572  * Calc log base 2
 573  */
 574 static INLINE unsigned
 575 util_logbase2(unsigned n)
 576 {
 577 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
 578    return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1));
 579 #else
 580    unsigned pos = 0;
 581    if (n >= 1<<16) { n >>= 16; pos += 16; }
 582    if (n >= 1<< 8) { n >>=  8; pos +=  8; }
 583    if (n >= 1<< 4) { n >>=  4; pos +=  4; }
 584    if (n >= 1<< 2) { n >>=  2; pos +=  2; }
 585    if (n >= 1<< 1) {           pos +=  1; }
 586    return pos;
 587 #endif
 588 }
 589
 590
 591 /**
 592  * Returns the smallest power of two >= x
 593  */
 594 static INLINE unsigned
 595 util_next_power_of_two(unsigned x)
 596 {
 597 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
 598    if (x <= 1)
 599        return 1;
 600
 601    return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1)));
 602 #else
 603    unsigned val = x;
 604
 605    if (x <= 1)
 606       return 1;
 607
 608    if (util_is_power_of_two(x))
 609       return x;
 610
 611    val--;
 612    val = (val >> 1) | val;
 613    val = (val >> 2) | val;
 614    val = (val >> 4) | val;
 615    val = (val >> 8) | val;
 616    val = (val >> 16) | val;
 617    val++;
 618    return val;
 619 #endif
 620 }
 621
 622
 623 /**
 624  * Return number of bits set in n.
 625  */
 626 static INLINE unsigned
 627 util_bitcount(unsigned n)
 628 {
 629 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
 630    return __builtin_popcount(n);
 631 #else
 632    /* K&R classic bitcount.
 633     *
 634     * For each iteration, clear the LSB from the bitfield.
 635     * Requires only one iteration per set bit, instead of
 636     * one iteration per bit less than highest set bit.
 637     */
 638    unsigned bits = 0;
 639    for (bits; n; bits++) {
 640       n &= n - 1;
 641    }
 642    return bits;
 643 #endif
 644 }
 645
 646
 647 /**
 648  * Convert from little endian to CPU byte order.
 649  */
 650
 651 #ifdef PIPE_ARCH_BIG_ENDIAN
 652 #define util_le32_to_cpu(x) util_bswap32(x)
 653 #define util_le16_to_cpu(x) util_bswap16(x)
 654 #else
 655 #define util_le32_to_cpu(x) (x)
 656 #define util_le16_to_cpu(x) (x)
 657 #endif
 658
 659
 660 /**
 661  * Reverse byte order of a 32 bit word.
 662  */
 663 static INLINE uint32_t
 664 util_bswap32(uint32_t n)
 665 {
 666 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 403)
 667    return __builtin_bswap32(n);
 668 #else
 669    return (n >> 24) |
 670           ((n >> 8) & 0x0000ff00) |
 671           ((n << 8) & 0x00ff0000) |
 672           (n << 24);
 673 #endif
 674 }
 675
 676
 677 /**
 678  * Reverse byte order of a 16 bit word.
 679  */
 680 static INLINE uint16_t
 681 util_bswap16(uint16_t n)
 682 {
 683    return (n >> 8) |
 684           (n << 8);
 685 }
 686
 687
 688 /**
 689  * Clamp X to [MIN, MAX].
 690  * This is a macro to allow float, int, uint, etc. types.
 691  */
 692 #define CLAMP( X, MIN, MAX )  ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
 693
 694 #define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
 695 #define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
 696
 697 #define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
 698 #define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))
 699
 700 #define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
 701 #define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))
 702
 703
 704 /**
 705  * Align a value, only works pot alignemnts.
 706  */
 707 static INLINE int
 708 align(int value, int alignment)
 709 {
 710    return (value + alignment - 1) & ~(alignment - 1);
 711 }
 712
 713 /**
 714  * Works like align but on npot alignments.
 715  */
 716 static INLINE size_t
 717 util_align_npot(size_t value, size_t alignment)
 718 {
 719    if (value % alignment)
 720       return value + (alignment - (value % alignment));
 721    return value;
 722 }
 723
 724 static INLINE unsigned
 725 u_minify(unsigned value, unsigned levels)
 726 {
 727     return MAX2(1, value >> levels);
 728 }
 729
 730 #ifndef COPY_4V
 731 #define COPY_4V( DST, SRC )         \
 732 do {                                \
 733    (DST)[0] = (SRC)[0];             \
 734    (DST)[1] = (SRC)[1];             \
 735    (DST)[2] = (SRC)[2];             \
 736    (DST)[3] = (SRC)[3];             \
 737 } while (0)
 738 #endif
 739
 740
 741 #ifndef COPY_4FV
 742 #define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
 743 #endif
 744
 745
 746 #ifndef ASSIGN_4V
 747 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
 748 do {                                     \
 749    (DST)[0] = (V0);                      \
 750    (DST)[1] = (V1);                      \
 751    (DST)[2] = (V2);                      \
 752    (DST)[3] = (V3);                      \
 753 } while (0)
 754 #endif
 755
 756
 757 static INLINE uint32_t util_unsigned_fixed(float value, unsigned frac_bits)
 758 {
 759    return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits));
 760 }
 761
 762 static INLINE int32_t util_signed_fixed(float value, unsigned frac_bits)
 763 {
 764    return (int32_t)(value * (1<<frac_bits));
 765 }
 766
 767
 768
 769 #ifdef __cplusplus
 770 }
 771 #endif
 772
 773 #endif /* U_MATH_H */