src/gallium/auxiliary/util/u_math.h

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