src/gallium/auxiliary/util/u_math.h

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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  * Find last bit set in a word.  The least significant bit is 1.
 351  * Return 0 if no bits are set.
 352  */
 353 static inline unsigned
 354 util_last_bit(unsigned u)
 355 {
 356 #if defined(HAVE___BUILTIN_CLZ)
 357    return u == 0 ? 0 : 32 - __builtin_clz(u);
 358 #else
 359    unsigned r = 0;
 360    while (u) {
 361        r++;
 362        u >>= 1;
 363    }
 364    return r;
 365 #endif
 366 }
 367
 368 /**
 369  * Find last bit set in a word.  The least significant bit is 1.
 370  * Return 0 if no bits are set.
 371  */
 372 static inline unsigned
 373 util_last_bit64(uint64_t u)
 374 {
 375 #if defined(HAVE___BUILTIN_CLZLL)
 376    return u == 0 ? 0 : 64 - __builtin_clzll(u);
 377 #else
 378    unsigned r = 0;
 379    while (u) {
 380        r++;
 381        u >>= 1;
 382    }
 383    return r;
 384 #endif
 385 }
 386
 387 /**
 388  * Find last bit in a word that does not match the sign bit. The least
 389  * significant bit is 1.
 390  * Return 0 if no bits are set.
 391  */
 392 static inline unsigned
 393 util_last_bit_signed(int i)
 394 {
 395    if (i >= 0)
 396       return util_last_bit(i);
 397    else
 398       return util_last_bit(~(unsigned)i);
 399 }
 400
 401 /* Returns a bitfield in which the first count bits starting at start are
 402  * set.
 403  */
 404 static inline unsigned
 405 u_bit_consecutive(unsigned start, unsigned count)
 406 {
 407    assert(start + count <= 32);
 408    if (count == 32)
 409       return ~0;
 410    return ((1u << count) - 1) << start;
 411 }
 412
 413 /**
 414  * Return float bits.
 415  */
 416 static inline unsigned
 417 fui( float f )
 418 {
 419    union fi fi;
 420    fi.f = f;
 421    return fi.ui;
 422 }
 423
 424 static inline float
 425 uif(uint32_t ui)
 426 {
 427    union fi fi;
 428    fi.ui = ui;
 429    return fi.f;
 430 }
 431
 432
 433 /**
 434  * Convert ubyte to float in [0, 1].
 435  * XXX a 256-entry lookup table would be slightly faster.
 436  */
 437 static inline float
 438 ubyte_to_float(ubyte ub)
 439 {
 440    return (float) ub * (1.0f / 255.0f);
 441 }
 442
 443
 444 /**
 445  * Convert float in [0,1] to ubyte in [0,255] with clamping.
 446  */
 447 static inline ubyte
 448 float_to_ubyte(float f)
 449 {
 450    union fi tmp;
 451
 452    tmp.f = f;
 453    if (tmp.i < 0) {
 454       return (ubyte) 0;
 455    }
 456    else if (tmp.i >= 0x3f800000 /* 1.0f */) {
 457       return (ubyte) 255;
 458    }
 459    else {
 460       tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
 461       return (ubyte) tmp.i;
 462    }
 463 }
 464
 465 static inline float
 466 byte_to_float_tex(int8_t b)
 467 {
 468    return (b == -128) ? -1.0F : b * 1.0F / 127.0F;
 469 }
 470
 471 static inline int8_t
 472 float_to_byte_tex(float f)
 473 {
 474    return (int8_t) (127.0F * f);
 475 }
 476
 477 /**
 478  * Calc log base 2
 479  */
 480 static inline unsigned
 481 util_logbase2(unsigned n)
 482 {
 483 #if defined(HAVE___BUILTIN_CLZ)
 484    return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1));
 485 #else
 486    unsigned pos = 0;
 487    if (n >= 1<<16) { n >>= 16; pos += 16; }
 488    if (n >= 1<< 8) { n >>=  8; pos +=  8; }
 489    if (n >= 1<< 4) { n >>=  4; pos +=  4; }
 490    if (n >= 1<< 2) { n >>=  2; pos +=  2; }
 491    if (n >= 1<< 1) {           pos +=  1; }
 492    return pos;
 493 #endif
 494 }
 495
 496
 497 /**
 498  * Returns the smallest power of two >= x
 499  */
 500 static inline unsigned
 501 util_next_power_of_two(unsigned x)
 502 {
 503 #if defined(HAVE___BUILTIN_CLZ)
 504    if (x <= 1)
 505        return 1;
 506
 507    return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1)));
 508 #else
 509    unsigned val = x;
 510
 511    if (x <= 1)
 512       return 1;
 513
 514    if (util_is_power_of_two(x))
 515       return x;
 516
 517    val--;
 518    val = (val >> 1) | val;
 519    val = (val >> 2) | val;
 520    val = (val >> 4) | val;
 521    val = (val >> 8) | val;
 522    val = (val >> 16) | val;
 523    val++;
 524    return val;
 525 #endif
 526 }
 527
 528
 529 /**
 530  * Return number of bits set in n.
 531  */
 532 static inline unsigned
 533 util_bitcount(unsigned n)
 534 {
 535 #if defined(HAVE___BUILTIN_POPCOUNT)
 536    return __builtin_popcount(n);
 537 #else
 538    /* K&R classic bitcount.
 539     *
 540     * For each iteration, clear the LSB from the bitfield.
 541     * Requires only one iteration per set bit, instead of
 542     * one iteration per bit less than highest set bit.
 543     */
 544    unsigned bits;
 545    for (bits = 0; n; bits++) {
 546       n &= n - 1;
 547    }
 548    return bits;
 549 #endif
 550 }
 551
 552
 553 static inline unsigned
 554 util_bitcount64(uint64_t n)
 555 {
 556 #ifdef HAVE___BUILTIN_POPCOUNTLL
 557    return __builtin_popcountll(n);
 558 #else
 559    return util_bitcount(n) + util_bitcount(n >> 32);
 560 #endif
 561 }
 562
 563
 564 /**
 565  * Reverse bits in n
 566  * Algorithm taken from:
 567  * http://stackoverflow.com/questions/9144800/c-reverse-bits-in-unsigned-integer
 568  */
 569 static inline unsigned
 570 util_bitreverse(unsigned n)
 571 {
 572     n = ((n >> 1) & 0x55555555u) | ((n & 0x55555555u) << 1);
 573     n = ((n >> 2) & 0x33333333u) | ((n & 0x33333333u) << 2);
 574     n = ((n >> 4) & 0x0f0f0f0fu) | ((n & 0x0f0f0f0fu) << 4);
 575     n = ((n >> 8) & 0x00ff00ffu) | ((n & 0x00ff00ffu) << 8);
 576     n = ((n >> 16) & 0xffffu) | ((n & 0xffffu) << 16);
 577     return n;
 578 }
 579
 580 /**
 581  * Convert from little endian to CPU byte order.
 582  */
 583
 584 #ifdef PIPE_ARCH_BIG_ENDIAN
 585 #define util_le64_to_cpu(x) util_bswap64(x)
 586 #define util_le32_to_cpu(x) util_bswap32(x)
 587 #define util_le16_to_cpu(x) util_bswap16(x)
 588 #else
 589 #define util_le64_to_cpu(x) (x)
 590 #define util_le32_to_cpu(x) (x)
 591 #define util_le16_to_cpu(x) (x)
 592 #endif
 593
 594 #define util_cpu_to_le64(x) util_le64_to_cpu(x)
 595 #define util_cpu_to_le32(x) util_le32_to_cpu(x)
 596 #define util_cpu_to_le16(x) util_le16_to_cpu(x)
 597
 598 /**
 599  * Reverse byte order of a 32 bit word.
 600  */
 601 static inline uint32_t
 602 util_bswap32(uint32_t n)
 603 {
 604 #if defined(HAVE___BUILTIN_BSWAP32)
 605    return __builtin_bswap32(n);
 606 #else
 607    return (n >> 24) |
 608           ((n >> 8) & 0x0000ff00) |
 609           ((n << 8) & 0x00ff0000) |
 610           (n << 24);
 611 #endif
 612 }
 613
 614 /**
 615  * Reverse byte order of a 64bit word.
 616  */
 617 static inline uint64_t
 618 util_bswap64(uint64_t n)
 619 {
 620 #if defined(HAVE___BUILTIN_BSWAP64)
 621    return __builtin_bswap64(n);
 622 #else
 623    return ((uint64_t)util_bswap32((uint32_t)n) << 32) |
 624           util_bswap32((n >> 32));
 625 #endif
 626 }
 627
 628
 629 /**
 630  * Reverse byte order of a 16 bit word.
 631  */
 632 static inline uint16_t
 633 util_bswap16(uint16_t n)
 634 {
 635    return (n >> 8) |
 636           (n << 8);
 637 }
 638
 639 static inline void*
 640 util_memcpy_cpu_to_le32(void * restrict dest, const void * restrict src, size_t n)
 641 {
 642 #ifdef PIPE_ARCH_BIG_ENDIAN
 643    size_t i, e;
 644    assert(n % 4 == 0);
 645
 646    for (i = 0, e = n / 4; i < e; i++) {
 647       uint32_t * restrict d = (uint32_t* restrict)dest;
 648       const uint32_t * restrict s = (const uint32_t* restrict)src;
 649       d[i] = util_bswap32(s[i]);
 650    }
 651    return dest;
 652 #else
 653    return memcpy(dest, src, n);
 654 #endif
 655 }
 656
 657 /**
 658  * Clamp X to [MIN, MAX].
 659  * This is a macro to allow float, int, uint, etc. types.
 660  */
 661 #define CLAMP( X, MIN, MAX )  ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
 662
 663 #define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
 664 #define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
 665
 666 #define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
 667 #define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))
 668
 669 #define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
 670 #define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))
 671
 672
 673 /**
 674  * Align a value, only works pot alignemnts.
 675  */
 676 static inline int
 677 align(int value, int alignment)
 678 {
 679    return (value + alignment - 1) & ~(alignment - 1);
 680 }
 681
 682 static inline uint64_t
 683 align64(uint64_t value, unsigned alignment)
 684 {
 685    return (value + alignment - 1) & ~(alignment - 1);
 686 }
 687
 688 /**
 689  * Works like align but on npot alignments.
 690  */
 691 static inline size_t
 692 util_align_npot(size_t value, size_t alignment)
 693 {
 694    if (value % alignment)
 695       return value + (alignment - (value % alignment));
 696    return value;
 697 }
 698
 699 static inline unsigned
 700 u_minify(unsigned value, unsigned levels)
 701 {
 702     return MAX2(1, value >> levels);
 703 }
 704
 705 #ifndef COPY_4V
 706 #define COPY_4V( DST, SRC )         \
 707 do {                                \
 708    (DST)[0] = (SRC)[0];             \
 709    (DST)[1] = (SRC)[1];             \
 710    (DST)[2] = (SRC)[2];             \
 711    (DST)[3] = (SRC)[3];             \
 712 } while (0)
 713 #endif
 714
 715
 716 #ifndef COPY_4FV
 717 #define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
 718 #endif
 719
 720
 721 #ifndef ASSIGN_4V
 722 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
 723 do {                                     \
 724    (DST)[0] = (V0);                      \
 725    (DST)[1] = (V1);                      \
 726    (DST)[2] = (V2);                      \
 727    (DST)[3] = (V3);                      \
 728 } while (0)
 729 #endif
 730
 731
 732 static inline uint32_t
 733 util_unsigned_fixed(float value, unsigned frac_bits)
 734 {
 735    return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits));
 736 }
 737
 738 static inline int32_t
 739 util_signed_fixed(float value, unsigned frac_bits)
 740 {
 741    return (int32_t)(value * (1<<frac_bits));
 742 }
 743
 744 unsigned
 745 util_fpstate_get(void);
 746 unsigned
 747 util_fpstate_set_denorms_to_zero(unsigned current_fpstate);
 748 void
 749 util_fpstate_set(unsigned fpstate);
 750
 751
 752
 753 #ifdef __cplusplus
 754 }
 755 #endif
 756
 757 #endif /* U_MATH_H */