src/util/u_math.h

   1 /**************************************************************************
   2  *
   3  * Copyright 2008 VMware, Inc.
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   7  * copy of this software and associated documentation files (the
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  11  * permit persons to whom the Software is furnished to do so, subject to
  12  * the following conditions:
  13  *
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  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
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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 "c99_math.h"
  43 #include <assert.h>
  44 #include <float.h>
  45 #include <stdarg.h>
  46
  47 #include "bitscan.h"
  48 #include "u_endian.h" /* for PIPE_ARCH_BIG_ENDIAN */
  49
  50 #ifdef __cplusplus
  51 extern "C" {
  52 #endif
  53
  54
  55 #ifndef M_SQRT2
  56 #define M_SQRT2 1.41421356237309504880
  57 #endif
  58
  59 #define POW2_TABLE_SIZE_LOG2 9
  60 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
  61 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
  62 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
  63 extern float pow2_table[POW2_TABLE_SIZE];
  64
  65
  66 /**
  67  * Initialize math module.  This should be called before using any
  68  * other functions in this module.
  69  */
  70 extern void
  71 util_init_math(void);
  72
  73
  74 union fi {
  75    float f;
  76    int32_t i;
  77    uint32_t ui;
  78 };
  79
  80
  81 union di {
  82    double d;
  83    int64_t i;
  84    uint64_t ui;
  85 };
  86
  87
  88 /**
  89  * Extract the IEEE float32 exponent.
  90  */
  91 static inline signed
  92 util_get_float32_exponent(float x)
  93 {
  94    union fi f;
  95
  96    f.f = x;
  97
  98    return ((f.ui >> 23) & 0xff) - 127;
  99 }
 100
 101
 102 /**
 103  * Fast version of 2^x
 104  * Identity: exp2(a + b) = exp2(a) * exp2(b)
 105  * Let ipart = int(x)
 106  * Let fpart = x - ipart;
 107  * So, exp2(x) = exp2(ipart) * exp2(fpart)
 108  * Compute exp2(ipart) with i << ipart
 109  * Compute exp2(fpart) with lookup table.
 110  */
 111 static inline float
 112 util_fast_exp2(float x)
 113 {
 114    int32_t ipart;
 115    float fpart, mpart;
 116    union fi epart;
 117
 118    if(x > 129.00000f)
 119       return 3.402823466e+38f;
 120
 121    if (x < -126.99999f)
 122       return 0.0f;
 123
 124    ipart = (int32_t) x;
 125    fpart = x - (float) ipart;
 126
 127    /* same as
 128     *   epart.f = (float) (1 << ipart)
 129     * but faster and without integer overflow for ipart > 31
 130     */
 131    epart.i = (ipart + 127 ) << 23;
 132
 133    mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];
 134
 135    return epart.f * mpart;
 136 }
 137
 138
 139 /**
 140  * Fast approximation to exp(x).
 141  */
 142 static inline float
 143 util_fast_exp(float x)
 144 {
 145    const float k = 1.44269f; /* = log2(e) */
 146    return util_fast_exp2(k * x);
 147 }
 148
 149
 150 #define LOG2_TABLE_SIZE_LOG2 16
 151 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
 152 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
 153 extern float log2_table[LOG2_TABLE_SIZE];
 154
 155
 156 /**
 157  * Fast approximation to log2(x).
 158  */
 159 static inline float
 160 util_fast_log2(float x)
 161 {
 162    union fi num;
 163    float epart, mpart;
 164    num.f = x;
 165    epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
 166    /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
 167    mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)];
 168    return epart + mpart;
 169 }
 170
 171
 172 /**
 173  * Fast approximation to x^y.
 174  */
 175 static inline float
 176 util_fast_pow(float x, float y)
 177 {
 178    return util_fast_exp2(util_fast_log2(x) * y);
 179 }
 180
 181
 182 /**
 183  * Floor(x), returned as int.
 184  */
 185 static inline int
 186 util_ifloor(float f)
 187 {
 188    int ai, bi;
 189    double af, bf;
 190    union fi u;
 191    af = (3 << 22) + 0.5 + (double) f;
 192    bf = (3 << 22) + 0.5 - (double) f;
 193    u.f = (float) af;  ai = u.i;
 194    u.f = (float) bf;  bi = u.i;
 195    return (ai - bi) >> 1;
 196 }
 197
 198
 199 /**
 200  * Round float to nearest int.
 201  */
 202 static inline int
 203 util_iround(float f)
 204 {
 205 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
 206    int r;
 207    __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
 208    return r;
 209 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 210    int r;
 211    _asm {
 212       fld f
 213       fistp r
 214    }
 215    return r;
 216 #else
 217    if (f >= 0.0f)
 218       return (int) (f + 0.5f);
 219    else
 220       return (int) (f - 0.5f);
 221 #endif
 222 }
 223
 224
 225 /**
 226  * Approximate floating point comparison
 227  */
 228 static inline bool
 229 util_is_approx(float a, float b, float tol)
 230 {
 231    return fabsf(b - a) <= tol;
 232 }
 233
 234
 235 /**
 236  * util_is_X_inf_or_nan = test if x is NaN or +/- Inf
 237  * util_is_X_nan        = test if x is NaN
 238  * util_X_inf_sign      = return +1 for +Inf, -1 for -Inf, or 0 for not Inf
 239  *
 240  * NaN can be checked with x != x, however this fails with the fast math flag
 241  **/
 242
 243
 244 /**
 245  * Single-float
 246  */
 247 static inline bool
 248 util_is_inf_or_nan(float x)
 249 {
 250    union fi tmp;
 251    tmp.f = x;
 252    return (tmp.ui & 0x7f800000) == 0x7f800000;
 253 }
 254
 255
 256 static inline bool
 257 util_is_nan(float x)
 258 {
 259    union fi tmp;
 260    tmp.f = x;
 261    return (tmp.ui & 0x7fffffff) > 0x7f800000;
 262 }
 263
 264
 265 static inline int
 266 util_inf_sign(float x)
 267 {
 268    union fi tmp;
 269    tmp.f = x;
 270    if ((tmp.ui & 0x7fffffff) != 0x7f800000) {
 271       return 0;
 272    }
 273
 274    return (x < 0) ? -1 : 1;
 275 }
 276
 277
 278 /**
 279  * Double-float
 280  */
 281 static inline bool
 282 util_is_double_inf_or_nan(double x)
 283 {
 284    union di tmp;
 285    tmp.d = x;
 286    return (tmp.ui & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL;
 287 }
 288
 289
 290 static inline bool
 291 util_is_double_nan(double x)
 292 {
 293    union di tmp;
 294    tmp.d = x;
 295    return (tmp.ui & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL;
 296 }
 297
 298
 299 static inline int
 300 util_double_inf_sign(double x)
 301 {
 302    union di tmp;
 303    tmp.d = x;
 304    if ((tmp.ui & 0x7fffffffffffffffULL) != 0x7ff0000000000000ULL) {
 305       return 0;
 306    }
 307
 308    return (x < 0) ? -1 : 1;
 309 }
 310
 311
 312 /**
 313  * Half-float
 314  */
 315 static inline bool
 316 util_is_half_inf_or_nan(int16_t x)
 317 {
 318    return (x & 0x7c00) == 0x7c00;
 319 }
 320
 321
 322 static inline bool
 323 util_is_half_nan(int16_t x)
 324 {
 325    return (x & 0x7fff) > 0x7c00;
 326 }
 327
 328
 329 static inline int
 330 util_half_inf_sign(int16_t x)
 331 {
 332    if ((x & 0x7fff) != 0x7c00) {
 333       return 0;
 334    }
 335
 336    return (x < 0) ? -1 : 1;
 337 }
 338
 339
 340 /**
 341  * Return float bits.
 342  */
 343 static inline unsigned
 344 fui( float f )
 345 {
 346    union fi fi;
 347    fi.f = f;
 348    return fi.ui;
 349 }
 350
 351 static inline float
 352 uif(uint32_t ui)
 353 {
 354    union fi fi;
 355    fi.ui = ui;
 356    return fi.f;
 357 }
 358
 359
 360 /**
 361  * Convert uint8_t to float in [0, 1].
 362  */
 363 static inline float
 364 ubyte_to_float(uint8_t ub)
 365 {
 366    return (float) ub * (1.0f / 255.0f);
 367 }
 368
 369
 370 /**
 371  * Convert float in [0,1] to uint8_t in [0,255] with clamping.
 372  */
 373 static inline uint8_t
 374 float_to_ubyte(float f)
 375 {
 376    /* return 0 for NaN too */
 377    if (!(f > 0.0f)) {
 378       return (uint8_t) 0;
 379    }
 380    else if (f >= 1.0f) {
 381       return (uint8_t) 255;
 382    }
 383    else {
 384       union fi tmp;
 385       tmp.f = f;
 386       tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
 387       return (uint8_t) tmp.i;
 388    }
 389 }
 390
 391 /**
 392  * Convert uint16_t to float in [0, 1].
 393  */
 394 static inline float
 395 ushort_to_float(uint16_t us)
 396 {
 397    return (float) us * (1.0f / 65535.0f);
 398 }
 399
 400
 401 /**
 402  * Convert float in [0,1] to uint16_t in [0,65535] with clamping.
 403  */
 404 static inline uint16_t
 405 float_to_ushort(float f)
 406 {
 407    /* return 0 for NaN too */
 408    if (!(f > 0.0f)) {
 409       return (uint16_t) 0;
 410    }
 411    else if (f >= 1.0f) {
 412       return (uint16_t) 65535;
 413    }
 414    else {
 415       union fi tmp;
 416       tmp.f = f;
 417       tmp.f = tmp.f * (65535.0f/65536.0f) + 128.0f;
 418       return (uint16_t) tmp.i;
 419    }
 420 }
 421
 422 static inline float
 423 byte_to_float_tex(int8_t b)
 424 {
 425    return (b == -128) ? -1.0F : b * 1.0F / 127.0F;
 426 }
 427
 428 static inline int8_t
 429 float_to_byte_tex(float f)
 430 {
 431    return (int8_t) (127.0F * f);
 432 }
 433
 434 /**
 435  * Calc log base 2
 436  */
 437 static inline unsigned
 438 util_logbase2(unsigned n)
 439 {
 440 #if defined(HAVE___BUILTIN_CLZ)
 441    return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1));
 442 #else
 443    unsigned pos = 0;
 444    if (n >= 1<<16) { n >>= 16; pos += 16; }
 445    if (n >= 1<< 8) { n >>=  8; pos +=  8; }
 446    if (n >= 1<< 4) { n >>=  4; pos +=  4; }
 447    if (n >= 1<< 2) { n >>=  2; pos +=  2; }
 448    if (n >= 1<< 1) {           pos +=  1; }
 449    return pos;
 450 #endif
 451 }
 452
 453 static inline uint64_t
 454 util_logbase2_64(uint64_t n)
 455 {
 456 #if defined(HAVE___BUILTIN_CLZLL)
 457    return ((sizeof(uint64_t) * 8 - 1) - __builtin_clzll(n | 1));
 458 #else
 459    uint64_t pos = 0ull;
 460    if (n >= 1ull<<32) { n >>= 32; pos += 32; }
 461    if (n >= 1ull<<16) { n >>= 16; pos += 16; }
 462    if (n >= 1ull<< 8) { n >>=  8; pos +=  8; }
 463    if (n >= 1ull<< 4) { n >>=  4; pos +=  4; }
 464    if (n >= 1ull<< 2) { n >>=  2; pos +=  2; }
 465    if (n >= 1ull<< 1) {           pos +=  1; }
 466    return pos;
 467 #endif
 468 }
 469
 470 /**
 471  * Returns the ceiling of log n base 2, and 0 when n == 0. Equivalently,
 472  * returns the smallest x such that n <= 2**x.
 473  */
 474 static inline unsigned
 475 util_logbase2_ceil(unsigned n)
 476 {
 477    if (n <= 1)
 478       return 0;
 479
 480    return 1 + util_logbase2(n - 1);
 481 }
 482
 483 static inline uint64_t
 484 util_logbase2_ceil64(uint64_t n)
 485 {
 486    if (n <= 1)
 487       return 0;
 488
 489    return 1ull + util_logbase2_64(n - 1);
 490 }
 491
 492 /**
 493  * Returns the smallest power of two >= x
 494  */
 495 static inline unsigned
 496 util_next_power_of_two(unsigned x)
 497 {
 498 #if defined(HAVE___BUILTIN_CLZ)
 499    if (x <= 1)
 500        return 1;
 501
 502    return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1)));
 503 #else
 504    unsigned val = x;
 505
 506    if (x <= 1)
 507       return 1;
 508
 509    if (util_is_power_of_two_or_zero(x))
 510       return x;
 511
 512    val--;
 513    val = (val >> 1) | val;
 514    val = (val >> 2) | val;
 515    val = (val >> 4) | val;
 516    val = (val >> 8) | val;
 517    val = (val >> 16) | val;
 518    val++;
 519    return val;
 520 #endif
 521 }
 522
 523 static inline uint64_t
 524 util_next_power_of_two64(uint64_t x)
 525 {
 526 #if defined(HAVE___BUILTIN_CLZLL)
 527    if (x <= 1)
 528        return 1;
 529
 530    return (1ull << ((sizeof(uint64_t) * 8) - __builtin_clzll(x - 1)));
 531 #else
 532    uint64_t val = x;
 533
 534    if (x <= 1)
 535       return 1;
 536
 537    if (util_is_power_of_two_or_zero64(x))
 538       return x;
 539
 540    val--;
 541    val = (val >> 1)  | val;
 542    val = (val >> 2)  | val;
 543    val = (val >> 4)  | val;
 544    val = (val >> 8)  | val;
 545    val = (val >> 16) | val;
 546    val = (val >> 32) | val;
 547    val++;
 548    return val;
 549 #endif
 550 }
 551
 552 /**
 553  * Reverse bits in n
 554  * Algorithm taken from:
 555  * http://stackoverflow.com/questions/9144800/c-reverse-bits-in-unsigned-integer
 556  */
 557 static inline unsigned
 558 util_bitreverse(unsigned n)
 559 {
 560     n = ((n >> 1) & 0x55555555u) | ((n & 0x55555555u) << 1);
 561     n = ((n >> 2) & 0x33333333u) | ((n & 0x33333333u) << 2);
 562     n = ((n >> 4) & 0x0f0f0f0fu) | ((n & 0x0f0f0f0fu) << 4);
 563     n = ((n >> 8) & 0x00ff00ffu) | ((n & 0x00ff00ffu) << 8);
 564     n = ((n >> 16) & 0xffffu) | ((n & 0xffffu) << 16);
 565     return n;
 566 }
 567
 568 /**
 569  * Convert from little endian to CPU byte order.
 570  */
 571
 572 #ifdef PIPE_ARCH_BIG_ENDIAN
 573 #define util_le64_to_cpu(x) util_bswap64(x)
 574 #define util_le32_to_cpu(x) util_bswap32(x)
 575 #define util_le16_to_cpu(x) util_bswap16(x)
 576 #else
 577 #define util_le64_to_cpu(x) (x)
 578 #define util_le32_to_cpu(x) (x)
 579 #define util_le16_to_cpu(x) (x)
 580 #endif
 581
 582 #define util_cpu_to_le64(x) util_le64_to_cpu(x)
 583 #define util_cpu_to_le32(x) util_le32_to_cpu(x)
 584 #define util_cpu_to_le16(x) util_le16_to_cpu(x)
 585
 586 /**
 587  * Reverse byte order of a 32 bit word.
 588  */
 589 static inline uint32_t
 590 util_bswap32(uint32_t n)
 591 {
 592 #if defined(HAVE___BUILTIN_BSWAP32)
 593    return __builtin_bswap32(n);
 594 #else
 595    return (n >> 24) |
 596           ((n >> 8) & 0x0000ff00) |
 597           ((n << 8) & 0x00ff0000) |
 598           (n << 24);
 599 #endif
 600 }
 601
 602 /**
 603  * Reverse byte order of a 64bit word.
 604  */
 605 static inline uint64_t
 606 util_bswap64(uint64_t n)
 607 {
 608 #if defined(HAVE___BUILTIN_BSWAP64)
 609    return __builtin_bswap64(n);
 610 #else
 611    return ((uint64_t)util_bswap32((uint32_t)n) << 32) |
 612           util_bswap32((n >> 32));
 613 #endif
 614 }
 615
 616
 617 /**
 618  * Reverse byte order of a 16 bit word.
 619  */
 620 static inline uint16_t
 621 util_bswap16(uint16_t n)
 622 {
 623    return (n >> 8) |
 624           (n << 8);
 625 }
 626
 627 static inline void*
 628 util_memcpy_cpu_to_le32(void * restrict dest, const void * restrict src, size_t n)
 629 {
 630 #ifdef PIPE_ARCH_BIG_ENDIAN
 631    size_t i, e;
 632    assert(n % 4 == 0);
 633
 634    for (i = 0, e = n / 4; i < e; i++) {
 635       uint32_t * restrict d = (uint32_t* restrict)dest;
 636       const uint32_t * restrict s = (const uint32_t* restrict)src;
 637       d[i] = util_bswap32(s[i]);
 638    }
 639    return dest;
 640 #else
 641    return memcpy(dest, src, n);
 642 #endif
 643 }
 644
 645 /**
 646  * Clamp X to [MIN, MAX].
 647  * This is a macro to allow float, int, uint, etc. types.
 648  * We arbitrarily turn NaN into MIN.
 649  */
 650 #define CLAMP( X, MIN, MAX )  ( (X)>(MIN) ? ((X)>(MAX) ? (MAX) : (X)) : (MIN) )
 651
 652 #define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
 653 #define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
 654
 655 #define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
 656 #define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))
 657
 658 #define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
 659 #define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))
 660
 661
 662 /**
 663  * Align a value, only works pot alignemnts.
 664  */
 665 static inline int
 666 align(int value, int alignment)
 667 {
 668    return (value + alignment - 1) & ~(alignment - 1);
 669 }
 670
 671 static inline uint64_t
 672 align64(uint64_t value, unsigned alignment)
 673 {
 674    return (value + alignment - 1) & ~((uint64_t)alignment - 1);
 675 }
 676
 677 /**
 678  * Works like align but on npot alignments.
 679  */
 680 static inline size_t
 681 util_align_npot(size_t value, size_t alignment)
 682 {
 683    if (value % alignment)
 684       return value + (alignment - (value % alignment));
 685    return value;
 686 }
 687
 688 static inline unsigned
 689 u_minify(unsigned value, unsigned levels)
 690 {
 691     return MAX2(1, value >> levels);
 692 }
 693
 694 #ifndef COPY_4V
 695 #define COPY_4V( DST, SRC )         \
 696 do {                                \
 697    (DST)[0] = (SRC)[0];             \
 698    (DST)[1] = (SRC)[1];             \
 699    (DST)[2] = (SRC)[2];             \
 700    (DST)[3] = (SRC)[3];             \
 701 } while (0)
 702 #endif
 703
 704
 705 #ifndef COPY_4FV
 706 #define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
 707 #endif
 708
 709
 710 #ifndef ASSIGN_4V
 711 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
 712 do {                                     \
 713    (DST)[0] = (V0);                      \
 714    (DST)[1] = (V1);                      \
 715    (DST)[2] = (V2);                      \
 716    (DST)[3] = (V3);                      \
 717 } while (0)
 718 #endif
 719
 720
 721 static inline uint32_t
 722 util_unsigned_fixed(float value, unsigned frac_bits)
 723 {
 724    return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits));
 725 }
 726
 727 static inline int32_t
 728 util_signed_fixed(float value, unsigned frac_bits)
 729 {
 730    return (int32_t)(value * (1<<frac_bits));
 731 }
 732
 733 unsigned
 734 util_fpstate_get(void);
 735 unsigned
 736 util_fpstate_set_denorms_to_zero(unsigned current_fpstate);
 737 void
 738 util_fpstate_set(unsigned fpstate);
 739
 740
 741
 742 #ifdef __cplusplus
 743 }
 744 #endif
 745
 746 #endif /* U_MATH_H */