src/gallium/auxiliary/util/u_math.h

   1 /**************************************************************************
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   3  * Copyright 2008 Tungsten Graphics, Inc., Cedar Park, Texas.
   4  * All Rights Reserved.
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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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  19  * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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  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 #include "util/u_debug.h"
  44
  45
  46 #ifdef __cplusplus
  47 extern "C" {
  48 #endif
  49
  50
  51 #if defined(PIPE_SUBSYSTEM_WINDOWS_MINIPORT)
  52 __inline double ceil(double val)
  53 {
  54    double ceil_val;
  55
  56    if ((val - (long) val) == 0) {
  57       ceil_val = val;
  58    }
  59    else {
  60       if (val > 0) {
  61          ceil_val = (long) val + 1;
  62       }
  63       else {
  64          ceil_val = (long) val;
  65       }
  66    }
  67
  68    return ceil_val;
  69 }
  70
  71 #ifndef PIPE_SUBSYSTEM_WINDOWS_CE_OGL
  72 __inline double floor(double val)
  73 {
  74    double floor_val;
  75
  76    if ((val - (long) val) == 0) {
  77       floor_val = val;
  78    }
  79    else {
  80       if (val > 0) {
  81          floor_val = (long) val;
  82       }
  83       else {
  84          floor_val = (long) val - 1;
  85       }
  86    }
  87
  88    return floor_val;
  89 }
  90 #endif
  91
  92 #pragma function(pow)
  93 __inline double __cdecl pow(double val, double exponent)
  94 {
  95    /* XXX */
  96    assert(0);
  97    return 0;
  98 }
  99
 100 #pragma function(log)
 101 __inline double __cdecl log(double val)
 102 {
 103    /* XXX */
 104    assert(0);
 105    return 0;
 106 }
 107
 108 #pragma function(atan2)
 109 __inline double __cdecl atan2(double val)
 110 {
 111    /* XXX */
 112    assert(0);
 113    return 0;
 114 }
 115 #else
 116 #include <math.h>
 117 #include <stdarg.h>
 118 #endif
 119
 120
 121 #ifndef M_SQRT2
 122 #define M_SQRT2 1.41421356237309504880
 123 #endif
 124
 125
 126 #if defined(_MSC_VER)
 127
 128 #if _MSC_VER < 1400 && !defined(__cplusplus) || defined(PIPE_SUBSYSTEM_WINDOWS_CE)
 129
 130 static INLINE float cosf( float f )
 131 {
 132    return (float) cos( (double) f );
 133 }
 134
 135 static INLINE float sinf( float f )
 136 {
 137    return (float) sin( (double) f );
 138 }
 139
 140 static INLINE float ceilf( float f )
 141 {
 142    return (float) ceil( (double) f );
 143 }
 144
 145 static INLINE float floorf( float f )
 146 {
 147    return (float) floor( (double) f );
 148 }
 149
 150 static INLINE float powf( float f, float g )
 151 {
 152    return (float) pow( (double) f, (double) g );
 153 }
 154
 155 static INLINE float sqrtf( float f )
 156 {
 157    return (float) sqrt( (double) f );
 158 }
 159
 160 static INLINE float fabsf( float f )
 161 {
 162    return (float) fabs( (double) f );
 163 }
 164
 165 static INLINE float logf( float f )
 166 {
 167    return (float) log( (double) f );
 168 }
 169
 170 #else
 171 /* Work-around an extra semi-colon in VS 2005 logf definition */
 172 #ifdef logf
 173 #undef logf
 174 #define logf(x) ((float)log((double)(x)))
 175 #endif /* logf */
 176
 177 #define isfinite(x) _finite((double)(x))
 178 #define isnan(x) _isnan((double)(x))
 179 #endif
 180
 181 static INLINE double log2( double x )
 182 {
 183    const double invln2 = 1.442695041;
 184    return log( x ) * invln2;
 185 }
 186
 187 #endif /* _MSC_VER */
 188
 189
 190
 191
 192
 193 #define POW2_TABLE_SIZE_LOG2 9
 194 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
 195 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
 196 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
 197 extern float pow2_table[POW2_TABLE_SIZE];
 198
 199
 200 /**
 201  * Initialize math module.  This should be called before using any
 202  * other functions in this module.
 203  */
 204 extern void
 205 util_init_math(void);
 206
 207
 208 union fi {
 209    float f;
 210    int32_t i;
 211    uint32_t ui;
 212 };
 213
 214
 215 /**
 216  * Fast version of 2^x
 217  * Identity: exp2(a + b) = exp2(a) * exp2(b)
 218  * Let ipart = int(x)
 219  * Let fpart = x - ipart;
 220  * So, exp2(x) = exp2(ipart) * exp2(fpart)
 221  * Compute exp2(ipart) with i << ipart
 222  * Compute exp2(fpart) with lookup table.
 223  */
 224 static INLINE float
 225 util_fast_exp2(float x)
 226 {
 227    int32_t ipart;
 228    float fpart, mpart;
 229    union fi epart;
 230
 231    if(x > 129.00000f)
 232       return 3.402823466e+38f;
 233
 234    if (x < -126.99999f)
 235       return 0.0f;
 236
 237    ipart = (int32_t) x;
 238    fpart = x - (float) ipart;
 239
 240    /* same as
 241     *   epart.f = (float) (1 << ipart)
 242     * but faster and without integer overflow for ipart > 31
 243     */
 244    epart.i = (ipart + 127 ) << 23;
 245
 246    mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];
 247
 248    return epart.f * mpart;
 249 }
 250
 251
 252 /**
 253  * Fast approximation to exp(x).
 254  */
 255 static INLINE float
 256 util_fast_exp(float x)
 257 {
 258    const float k = 1.44269f; /* = log2(e) */
 259    return util_fast_exp2(k * x);
 260 }
 261
 262
 263 #define LOG2_TABLE_SIZE_LOG2 16
 264 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
 265 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
 266 extern float log2_table[LOG2_TABLE_SIZE];
 267
 268
 269 /**
 270  * Fast approximation to log2(x).
 271  */
 272 static INLINE float
 273 util_fast_log2(float x)
 274 {
 275    union fi num;
 276    float epart, mpart;
 277    num.f = x;
 278    epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
 279    /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
 280    mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)];
 281    return epart + mpart;
 282 }
 283
 284
 285 /**
 286  * Fast approximation to x^y.
 287  */
 288 static INLINE float
 289 util_fast_pow(float x, float y)
 290 {
 291    return util_fast_exp2(util_fast_log2(x) * y);
 292 }
 293
 294 /* Note that this counts zero as a power of two.
 295  */
 296 static INLINE boolean
 297 util_is_power_of_two( unsigned v )
 298 {
 299    return (v & (v-1)) == 0;
 300 }
 301
 302
 303 /**
 304  * Floor(x), returned as int.
 305  */
 306 static INLINE int
 307 util_ifloor(float f)
 308 {
 309    int ai, bi;
 310    double af, bf;
 311    union fi u;
 312    af = (3 << 22) + 0.5 + (double) f;
 313    bf = (3 << 22) + 0.5 - (double) f;
 314    u.f = (float) af;  ai = u.i;
 315    u.f = (float) bf;  bi = u.i;
 316    return (ai - bi) >> 1;
 317 }
 318
 319
 320 /**
 321  * Round float to nearest int.
 322  */
 323 static INLINE int
 324 util_iround(float f)
 325 {
 326 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
 327    int r;
 328    __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
 329    return r;
 330 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 331    int r;
 332    _asm {
 333       fld f
 334       fistp r
 335    }
 336    return r;
 337 #else
 338    if (f >= 0.0f)
 339       return (int) (f + 0.5f);
 340    else
 341       return (int) (f - 0.5f);
 342 #endif
 343 }
 344
 345
 346 /**
 347  * Approximate floating point comparison
 348  */
 349 static INLINE boolean
 350 util_is_approx(float a, float b, float tol)
 351 {
 352    return fabs(b - a) <= tol;
 353 }
 354
 355
 356 /**
 357  * Test if x is NaN or +/- infinity.
 358  */
 359 static INLINE boolean
 360 util_is_inf_or_nan(float x)
 361 {
 362    union fi tmp;
 363    tmp.f = x;
 364    return !(int)((unsigned int)((tmp.i & 0x7fffffff)-0x7f800000) >> 31);
 365 }
 366
 367
 368 /**
 369  * Find first bit set in word.  Least significant bit is 1.
 370  * Return 0 if no bits set.
 371  */
 372 #if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64)
 373 unsigned char _BitScanForward(unsigned long* Index, unsigned long Mask);
 374 #pragma intrinsic(_BitScanForward)
 375 static INLINE
 376 unsigned long ffs( unsigned long u )
 377 {
 378    unsigned long i;
 379    if (_BitScanForward(&i, u))
 380       return i + 1;
 381    else
 382       return 0;
 383 }
 384 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 385 static INLINE
 386 unsigned ffs( unsigned u )
 387 {
 388    unsigned i;
 389
 390    if (u == 0) {
 391       return 0;
 392    }
 393
 394    __asm bsf eax, [u]
 395    __asm inc eax
 396    __asm mov [i], eax
 397
 398    return i;
 399 }
 400 #elif defined(__MINGW32__)
 401 #define ffs __builtin_ffs
 402 #endif
 403
 404 #ifdef __MINGW32__
 405 #define ffs __builtin_ffs
 406 #endif
 407
 408
 409 /* Could also binary search for the highest bit.
 410  */
 411 static INLINE unsigned
 412 util_unsigned_logbase2(unsigned n)
 413 {
 414    unsigned log2 = 0;
 415    while (n >>= 1)
 416       ++log2;
 417    return log2;
 418 }
 419
 420
 421 /**
 422  * Return float bits.
 423  */
 424 static INLINE unsigned
 425 fui( float f )
 426 {
 427    union fi fi;
 428    fi.f = f;
 429    return fi.ui;
 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    const int ieee_0996 = 0x3f7f0000;   /* 0.996 or so */
 451    union fi tmp;
 452
 453    tmp.f = f;
 454    if (tmp.i < 0) {
 455       return (ubyte) 0;
 456    }
 457    else if (tmp.i >= ieee_0996) {
 458       return (ubyte) 255;
 459    }
 460    else {
 461       tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
 462       return (ubyte) tmp.i;
 463    }
 464 }
 465
 466
 467 /**
 468  * Calc log base 2
 469  */
 470 static INLINE unsigned
 471 util_logbase2(unsigned n)
 472 {
 473    unsigned log2 = 0;
 474    while (n >>= 1)
 475       ++log2;
 476    return log2;
 477 }
 478
 479
 480 /**
 481  * Returns the smallest power of two >= x
 482  */
 483 static INLINE unsigned
 484 util_next_power_of_two(unsigned x)
 485 {
 486    unsigned i;
 487
 488    if (x == 0)
 489       return 1;
 490
 491    --x;
 492
 493    for (i = 1; i < sizeof(unsigned) * 8; i <<= 1)
 494       x |= x >> i;
 495
 496    return x + 1;
 497 }
 498
 499
 500 /**
 501  * Return number of bits set in n.
 502  */
 503 static INLINE unsigned
 504 util_bitcount(unsigned n)
 505 {
 506 #if defined(PIPE_CC_GCC)
 507    return __builtin_popcount(n);
 508 #else
 509    /* K&R classic bitcount.
 510     *
 511     * For each iteration, clear the LSB from the bitfield.
 512     * Requires only one iteration per set bit, instead of
 513     * one iteration per bit less than highest set bit.
 514     */
 515    unsigned bits = 0;
 516    for (bits; n; bits++) {
 517       n &= n - 1;
 518    }
 519    return bits;
 520 #endif
 521 }
 522
 523
 524 /**
 525  * Reverse byte order of a 32 bit word.
 526  */
 527 static INLINE uint32_t
 528 util_bswap32(uint32_t n)
 529 {
 530 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 403)
 531    return __builtin_bswap32(n);
 532 #else
 533    return (n >> 24) |
 534           ((n >> 8) & 0x0000ff00) |
 535           ((n << 8) & 0x00ff0000) |
 536           (n << 24);
 537 #endif
 538 }
 539
 540
 541 /**
 542  * Reverse byte order of a 16 bit word.
 543  */
 544 static INLINE uint16_t
 545 util_bswap16(uint16_t n)
 546 {
 547    return (n >> 8) |
 548           (n << 8);
 549 }
 550
 551
 552 /**
 553  * Clamp X to [MIN, MAX].
 554  * This is a macro to allow float, int, uint, etc. types.
 555  */
 556 #define CLAMP( X, MIN, MAX )  ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
 557
 558 #define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
 559 #define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
 560
 561 #define MIN3( A, B, C ) MIN2( MIN2( A, B ), C )
 562 #define MAX3( A, B, C ) MAX2( MAX2( A, B ), C )
 563
 564 #define MIN4( A, B, C, D ) MIN2( MIN2( A, B ), MIN2(C, D) )
 565 #define MAX4( A, B, C, D ) MAX2( MAX2( A, B ), MAX2(C, D) )
 566
 567
 568 /**
 569  * Align a value, only works pot alignemnts.
 570  */
 571 static INLINE int
 572 align(int value, int alignment)
 573 {
 574    return (value + alignment - 1) & ~(alignment - 1);
 575 }
 576
 577 /**
 578  * Works like align but on npot alignments.
 579  */
 580 static INLINE size_t
 581 util_align_npot(size_t value, size_t alignment)
 582 {
 583    if (value % alignment)
 584       return value + (alignment - (value % alignment));
 585    return value;
 586 }
 587
 588 static INLINE unsigned
 589 u_minify(unsigned value, unsigned levels)
 590 {
 591     return MAX2(1, value >> levels);
 592 }
 593
 594 #ifndef COPY_4V
 595 #define COPY_4V( DST, SRC )         \
 596 do {                                \
 597    (DST)[0] = (SRC)[0];             \
 598    (DST)[1] = (SRC)[1];             \
 599    (DST)[2] = (SRC)[2];             \
 600    (DST)[3] = (SRC)[3];             \
 601 } while (0)
 602 #endif
 603
 604
 605 #ifndef COPY_4FV
 606 #define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
 607 #endif
 608
 609
 610 #ifndef ASSIGN_4V
 611 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
 612 do {                                     \
 613    (DST)[0] = (V0);                      \
 614    (DST)[1] = (V1);                      \
 615    (DST)[2] = (V2);                      \
 616    (DST)[3] = (V3);                      \
 617 } while (0)
 618 #endif
 619
 620
 621 static INLINE uint32_t util_unsigned_fixed(float value, unsigned frac_bits)
 622 {
 623    return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits));
 624 }
 625
 626 static INLINE int32_t util_signed_fixed(float value, unsigned frac_bits)
 627 {
 628    return (int32_t)(value * (1<<frac_bits));
 629 }
 630
 631
 632
 633 #ifdef __cplusplus
 634 }
 635 #endif
 636
 637 #endif /* U_MATH_H */