src/util/u_math.h

   1 /**************************************************************************
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   3  * Copyright 2008 VMware, Inc.
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  11  * permit persons to whom the Software is furnished to do so, subject to
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  15  * next paragraph) shall be included in all copies or substantial portions
  16  * of the Software.
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  18  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
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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 "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  */
 364 static inline float
 365 ubyte_to_float(ubyte ub)
 366 {
 367    return (float) ub * (1.0f / 255.0f);
 368 }
 369
 370
 371 /**
 372  * Convert float in [0,1] to ubyte in [0,255] with clamping.
 373  */
 374 static inline ubyte
 375 float_to_ubyte(float f)
 376 {
 377    /* return 0 for NaN too */
 378    if (!(f > 0.0f)) {
 379       return (ubyte) 0;
 380    }
 381    else if (f >= 1.0f) {
 382       return (ubyte) 255;
 383    }
 384    else {
 385       union fi tmp;
 386       tmp.f = f;
 387       tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
 388       return (ubyte) tmp.i;
 389    }
 390 }
 391
 392 /**
 393  * Convert ushort to float in [0, 1].
 394  */
 395 static inline float
 396 ushort_to_float(ushort us)
 397 {
 398    return (float) us * (1.0f / 65535.0f);
 399 }
 400
 401
 402 /**
 403  * Convert float in [0,1] to ushort in [0,65535] with clamping.
 404  */
 405 static inline ushort
 406 float_to_ushort(float f)
 407 {
 408    /* return 0 for NaN too */
 409    if (!(f > 0.0f)) {
 410       return (ushort) 0;
 411    }
 412    else if (f >= 1.0f) {
 413       return (ushort) 65535;
 414    }
 415    else {
 416       union fi tmp;
 417       tmp.f = f;
 418       tmp.f = tmp.f * (65535.0f/65536.0f) + 128.0f;
 419       return (ushort) tmp.i;
 420    }
 421 }
 422
 423 static inline float
 424 byte_to_float_tex(int8_t b)
 425 {
 426    return (b == -128) ? -1.0F : b * 1.0F / 127.0F;
 427 }
 428
 429 static inline int8_t
 430 float_to_byte_tex(float f)
 431 {
 432    return (int8_t) (127.0F * f);
 433 }
 434
 435 /**
 436  * Calc log base 2
 437  */
 438 static inline unsigned
 439 util_logbase2(unsigned n)
 440 {
 441 #if defined(HAVE___BUILTIN_CLZ)
 442    return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1));
 443 #else
 444    unsigned pos = 0;
 445    if (n >= 1<<16) { n >>= 16; pos += 16; }
 446    if (n >= 1<< 8) { n >>=  8; pos +=  8; }
 447    if (n >= 1<< 4) { n >>=  4; pos +=  4; }
 448    if (n >= 1<< 2) { n >>=  2; pos +=  2; }
 449    if (n >= 1<< 1) {           pos +=  1; }
 450    return pos;
 451 #endif
 452 }
 453
 454 static inline uint64_t
 455 util_logbase2_64(uint64_t n)
 456 {
 457 #if defined(HAVE___BUILTIN_CLZLL)
 458    return ((sizeof(uint64_t) * 8 - 1) - __builtin_clzll(n | 1));
 459 #else
 460    uint64_t pos = 0ull;
 461    if (n >= 1ull<<32) { n >>= 32; pos += 32; }
 462    if (n >= 1ull<<16) { n >>= 16; pos += 16; }
 463    if (n >= 1ull<< 8) { n >>=  8; pos +=  8; }
 464    if (n >= 1ull<< 4) { n >>=  4; pos +=  4; }
 465    if (n >= 1ull<< 2) { n >>=  2; pos +=  2; }
 466    if (n >= 1ull<< 1) {           pos +=  1; }
 467    return pos;
 468 #endif
 469 }
 470
 471 /**
 472  * Returns the ceiling of log n base 2, and 0 when n == 0. Equivalently,
 473  * returns the smallest x such that n <= 2**x.
 474  */
 475 static inline unsigned
 476 util_logbase2_ceil(unsigned n)
 477 {
 478    if (n <= 1)
 479       return 0;
 480
 481    return 1 + util_logbase2(n - 1);
 482 }
 483
 484 static inline uint64_t
 485 util_logbase2_ceil64(uint64_t n)
 486 {
 487    if (n <= 1)
 488       return 0;
 489
 490    return 1ull + util_logbase2_64(n - 1);
 491 }
 492
 493 /**
 494  * Returns the smallest power of two >= x
 495  */
 496 static inline unsigned
 497 util_next_power_of_two(unsigned x)
 498 {
 499 #if defined(HAVE___BUILTIN_CLZ)
 500    if (x <= 1)
 501        return 1;
 502
 503    return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1)));
 504 #else
 505    unsigned val = x;
 506
 507    if (x <= 1)
 508       return 1;
 509
 510    if (util_is_power_of_two_or_zero(x))
 511       return x;
 512
 513    val--;
 514    val = (val >> 1) | val;
 515    val = (val >> 2) | val;
 516    val = (val >> 4) | val;
 517    val = (val >> 8) | val;
 518    val = (val >> 16) | val;
 519    val++;
 520    return val;
 521 #endif
 522 }
 523
 524 static inline uint64_t
 525 util_next_power_of_two64(uint64_t x)
 526 {
 527 #if defined(HAVE___BUILTIN_CLZLL)
 528    if (x <= 1)
 529        return 1;
 530
 531    return (1ull << ((sizeof(uint64_t) * 8) - __builtin_clzll(x - 1)));
 532 #else
 533    uint64_t val = x;
 534
 535    if (x <= 1)
 536       return 1;
 537
 538    if (util_is_power_of_two_or_zero64(x))
 539       return x;
 540
 541    val--;
 542    val = (val >> 1)  | val;
 543    val = (val >> 2)  | val;
 544    val = (val >> 4)  | val;
 545    val = (val >> 8)  | val;
 546    val = (val >> 16) | val;
 547    val = (val >> 32) | val;
 548    val++;
 549    return val;
 550 #endif
 551 }
 552
 553
 554 /**
 555  * Return number of bits set in n.
 556  */
 557 static inline unsigned
 558 util_bitcount(unsigned n)
 559 {
 560 #if defined(HAVE___BUILTIN_POPCOUNT)
 561    return __builtin_popcount(n);
 562 #else
 563    /* K&R classic bitcount.
 564     *
 565     * For each iteration, clear the LSB from the bitfield.
 566     * Requires only one iteration per set bit, instead of
 567     * one iteration per bit less than highest set bit.
 568     */
 569    unsigned bits;
 570    for (bits = 0; n; bits++) {
 571       n &= n - 1;
 572    }
 573    return bits;
 574 #endif
 575 }
 576
 577
 578 static inline unsigned
 579 util_bitcount64(uint64_t n)
 580 {
 581 #ifdef HAVE___BUILTIN_POPCOUNTLL
 582    return __builtin_popcountll(n);
 583 #else
 584    return util_bitcount(n) + util_bitcount(n >> 32);
 585 #endif
 586 }
 587
 588
 589 /**
 590  * Reverse bits in n
 591  * Algorithm taken from:
 592  * http://stackoverflow.com/questions/9144800/c-reverse-bits-in-unsigned-integer
 593  */
 594 static inline unsigned
 595 util_bitreverse(unsigned n)
 596 {
 597     n = ((n >> 1) & 0x55555555u) | ((n & 0x55555555u) << 1);
 598     n = ((n >> 2) & 0x33333333u) | ((n & 0x33333333u) << 2);
 599     n = ((n >> 4) & 0x0f0f0f0fu) | ((n & 0x0f0f0f0fu) << 4);
 600     n = ((n >> 8) & 0x00ff00ffu) | ((n & 0x00ff00ffu) << 8);
 601     n = ((n >> 16) & 0xffffu) | ((n & 0xffffu) << 16);
 602     return n;
 603 }
 604
 605 /**
 606  * Convert from little endian to CPU byte order.
 607  */
 608
 609 #ifdef PIPE_ARCH_BIG_ENDIAN
 610 #define util_le64_to_cpu(x) util_bswap64(x)
 611 #define util_le32_to_cpu(x) util_bswap32(x)
 612 #define util_le16_to_cpu(x) util_bswap16(x)
 613 #else
 614 #define util_le64_to_cpu(x) (x)
 615 #define util_le32_to_cpu(x) (x)
 616 #define util_le16_to_cpu(x) (x)
 617 #endif
 618
 619 #define util_cpu_to_le64(x) util_le64_to_cpu(x)
 620 #define util_cpu_to_le32(x) util_le32_to_cpu(x)
 621 #define util_cpu_to_le16(x) util_le16_to_cpu(x)
 622
 623 /**
 624  * Reverse byte order of a 32 bit word.
 625  */
 626 static inline uint32_t
 627 util_bswap32(uint32_t n)
 628 {
 629 #if defined(HAVE___BUILTIN_BSWAP32)
 630    return __builtin_bswap32(n);
 631 #else
 632    return (n >> 24) |
 633           ((n >> 8) & 0x0000ff00) |
 634           ((n << 8) & 0x00ff0000) |
 635           (n << 24);
 636 #endif
 637 }
 638
 639 /**
 640  * Reverse byte order of a 64bit word.
 641  */
 642 static inline uint64_t
 643 util_bswap64(uint64_t n)
 644 {
 645 #if defined(HAVE___BUILTIN_BSWAP64)
 646    return __builtin_bswap64(n);
 647 #else
 648    return ((uint64_t)util_bswap32((uint32_t)n) << 32) |
 649           util_bswap32((n >> 32));
 650 #endif
 651 }
 652
 653
 654 /**
 655  * Reverse byte order of a 16 bit word.
 656  */
 657 static inline uint16_t
 658 util_bswap16(uint16_t n)
 659 {
 660    return (n >> 8) |
 661           (n << 8);
 662 }
 663
 664 static inline void*
 665 util_memcpy_cpu_to_le32(void * restrict dest, const void * restrict src, size_t n)
 666 {
 667 #ifdef PIPE_ARCH_BIG_ENDIAN
 668    size_t i, e;
 669    assert(n % 4 == 0);
 670
 671    for (i = 0, e = n / 4; i < e; i++) {
 672       uint32_t * restrict d = (uint32_t* restrict)dest;
 673       const uint32_t * restrict s = (const uint32_t* restrict)src;
 674       d[i] = util_bswap32(s[i]);
 675    }
 676    return dest;
 677 #else
 678    return memcpy(dest, src, n);
 679 #endif
 680 }
 681
 682 /**
 683  * Clamp X to [MIN, MAX].
 684  * This is a macro to allow float, int, uint, etc. types.
 685  * We arbitrarily turn NaN into MIN.
 686  */
 687 #define CLAMP( X, MIN, MAX )  ( (X)>(MIN) ? ((X)>(MAX) ? (MAX) : (X)) : (MIN) )
 688
 689 #define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
 690 #define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
 691
 692 #define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
 693 #define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))
 694
 695 #define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
 696 #define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))
 697
 698
 699 /**
 700  * Align a value, only works pot alignemnts.
 701  */
 702 static inline int
 703 align(int value, int alignment)
 704 {
 705    return (value + alignment - 1) & ~(alignment - 1);
 706 }
 707
 708 static inline uint64_t
 709 align64(uint64_t value, unsigned alignment)
 710 {
 711    return (value + alignment - 1) & ~((uint64_t)alignment - 1);
 712 }
 713
 714 /**
 715  * Works like align but on npot alignments.
 716  */
 717 static inline size_t
 718 util_align_npot(size_t value, size_t alignment)
 719 {
 720    if (value % alignment)
 721       return value + (alignment - (value % alignment));
 722    return value;
 723 }
 724
 725 static inline unsigned
 726 u_minify(unsigned value, unsigned levels)
 727 {
 728     return MAX2(1, value >> levels);
 729 }
 730
 731 #ifndef COPY_4V
 732 #define COPY_4V( DST, SRC )         \
 733 do {                                \
 734    (DST)[0] = (SRC)[0];             \
 735    (DST)[1] = (SRC)[1];             \
 736    (DST)[2] = (SRC)[2];             \
 737    (DST)[3] = (SRC)[3];             \
 738 } while (0)
 739 #endif
 740
 741
 742 #ifndef COPY_4FV
 743 #define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
 744 #endif
 745
 746
 747 #ifndef ASSIGN_4V
 748 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
 749 do {                                     \
 750    (DST)[0] = (V0);                      \
 751    (DST)[1] = (V1);                      \
 752    (DST)[2] = (V2);                      \
 753    (DST)[3] = (V3);                      \
 754 } while (0)
 755 #endif
 756
 757
 758 static inline uint32_t
 759 util_unsigned_fixed(float value, unsigned frac_bits)
 760 {
 761    return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits));
 762 }
 763
 764 static inline int32_t
 765 util_signed_fixed(float value, unsigned frac_bits)
 766 {
 767    return (int32_t)(value * (1<<frac_bits));
 768 }
 769
 770 unsigned
 771 util_fpstate_get(void);
 772 unsigned
 773 util_fpstate_set_denorms_to_zero(unsigned current_fpstate);
 774 void
 775 util_fpstate_set(unsigned fpstate);
 776
 777
 778
 779 #ifdef __cplusplus
 780 }
 781 #endif
 782
 783 #endif /* U_MATH_H */