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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  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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  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 #if defined(_MSC_VER)
 122
 123 #if _MSC_VER < 1400 && !defined(__cplusplus) || defined(PIPE_SUBSYSTEM_WINDOWS_CE)
 124
 125 static INLINE float cosf( float f )
 126 {
 127    return (float) cos( (double) f );
 128 }
 129
 130 static INLINE float sinf( float f )
 131 {
 132    return (float) sin( (double) f );
 133 }
 134
 135 static INLINE float ceilf( float f )
 136 {
 137    return (float) ceil( (double) f );
 138 }
 139
 140 static INLINE float floorf( float f )
 141 {
 142    return (float) floor( (double) f );
 143 }
 144
 145 static INLINE float powf( float f, float g )
 146 {
 147    return (float) pow( (double) f, (double) g );
 148 }
 149
 150 static INLINE float sqrtf( float f )
 151 {
 152    return (float) sqrt( (double) f );
 153 }
 154
 155 static INLINE float fabsf( float f )
 156 {
 157    return (float) fabs( (double) f );
 158 }
 159
 160 static INLINE float logf( float f )
 161 {
 162    return (float) log( (double) f );
 163 }
 164
 165 #else
 166 /* Work-around an extra semi-colon in VS 2005 logf definition */
 167 #ifdef logf
 168 #undef logf
 169 #define logf(x) ((float)log((double)(x)))
 170 #endif /* logf */
 171
 172 #define isfinite(x) _finite((double)(x))
 173 #define isnan(x) _isnan((double)(x))
 174 #endif
 175
 176 static INLINE double log2( double x )
 177 {
 178    const double invln2 = 1.442695041;
 179    return log( x ) * invln2;
 180 }
 181
 182 #endif /* _MSC_VER */
 183
 184
 185
 186
 187
 188 #define POW2_TABLE_SIZE_LOG2 9
 189 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
 190 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
 191 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
 192 extern float pow2_table[POW2_TABLE_SIZE];
 193
 194
 195 /**
 196  * Initialize math module.  This should be called before using any
 197  * other functions in this module.
 198  */
 199 extern void
 200 util_init_math(void);
 201
 202
 203 union fi {
 204    float f;
 205    int32_t i;
 206    uint32_t ui;
 207 };
 208
 209
 210 /**
 211  * Fast version of 2^x
 212  * Identity: exp2(a + b) = exp2(a) * exp2(b)
 213  * Let ipart = int(x)
 214  * Let fpart = x - ipart;
 215  * So, exp2(x) = exp2(ipart) * exp2(fpart)
 216  * Compute exp2(ipart) with i << ipart
 217  * Compute exp2(fpart) with lookup table.
 218  */
 219 static INLINE float
 220 util_fast_exp2(float x)
 221 {
 222    int32_t ipart;
 223    float fpart, mpart;
 224    union fi epart;
 225
 226    if(x > 129.00000f)
 227       return 3.402823466e+38f;
 228
 229    if (x < -126.99999f)
 230       return 0.0f;
 231
 232    ipart = (int32_t) x;
 233    fpart = x - (float) ipart;
 234
 235    /* same as
 236     *   epart.f = (float) (1 << ipart)
 237     * but faster and without integer overflow for ipart > 31
 238     */
 239    epart.i = (ipart + 127 ) << 23;
 240
 241    mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];
 242
 243    return epart.f * mpart;
 244 }
 245
 246
 247 /**
 248  * Fast approximation to exp(x).
 249  */
 250 static INLINE float
 251 util_fast_exp(float x)
 252 {
 253    const float k = 1.44269f; /* = log2(e) */
 254    return util_fast_exp2(k * x);
 255 }
 256
 257
 258 #define LOG2_TABLE_SIZE_LOG2 16
 259 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
 260 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
 261 extern float log2_table[LOG2_TABLE_SIZE];
 262
 263
 264 /**
 265  * Fast approximation to log2(x).
 266  */
 267 static INLINE float
 268 util_fast_log2(float x)
 269 {
 270    union fi num;
 271    float epart, mpart;
 272    num.f = x;
 273    epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
 274    /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
 275    mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)];
 276    return epart + mpart;
 277 }
 278
 279
 280 /**
 281  * Fast approximation to x^y.
 282  */
 283 static INLINE float
 284 util_fast_pow(float x, float y)
 285 {
 286    return util_fast_exp2(util_fast_log2(x) * y);
 287 }
 288
 289 /* Note that this counts zero as a power of two.
 290  */
 291 static INLINE boolean
 292 util_is_power_of_two( unsigned v )
 293 {
 294    return (v & (v-1)) == 0;
 295 }
 296
 297
 298 /**
 299  * Floor(x), returned as int.
 300  */
 301 static INLINE int
 302 util_ifloor(float f)
 303 {
 304    int ai, bi;
 305    double af, bf;
 306    union fi u;
 307    af = (3 << 22) + 0.5 + (double) f;
 308    bf = (3 << 22) + 0.5 - (double) f;
 309    u.f = (float) af;  ai = u.i;
 310    u.f = (float) bf;  bi = u.i;
 311    return (ai - bi) >> 1;
 312 }
 313
 314
 315 /**
 316  * Round float to nearest int.
 317  */
 318 static INLINE int
 319 util_iround(float f)
 320 {
 321 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
 322    int r;
 323    __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
 324    return r;
 325 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 326    int r;
 327    _asm {
 328       fld f
 329       fistp r
 330    }
 331    return r;
 332 #else
 333    if (f >= 0.0f)
 334       return (int) (f + 0.5f);
 335    else
 336       return (int) (f - 0.5f);
 337 #endif
 338 }
 339
 340
 341 /**
 342  * Approximate floating point comparison
 343  */
 344 static INLINE boolean
 345 util_is_approx(float a, float b, float tol)
 346 {
 347    return fabs(b - a) <= tol;
 348 }
 349
 350
 351 /**
 352  * Test if x is NaN or +/- infinity.
 353  */
 354 static INLINE boolean
 355 util_is_inf_or_nan(float x)
 356 {
 357    union fi tmp;
 358    tmp.f = x;
 359    return !(int)((unsigned int)((tmp.i & 0x7fffffff)-0x7f800000) >> 31);
 360 }
 361
 362
 363 /**
 364  * Find first bit set in word.  Least significant bit is 1.
 365  * Return 0 if no bits set.
 366  */
 367 #if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64)
 368 unsigned char _BitScanForward(unsigned long* Index, unsigned long Mask);
 369 #pragma intrinsic(_BitScanForward)
 370 static INLINE
 371 unsigned long ffs( unsigned long u )
 372 {
 373    unsigned long i;
 374    if (_BitScanForward(&i, u))
 375       return i + 1;
 376    else
 377       return 0;
 378 }
 379 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 380 static INLINE
 381 unsigned ffs( unsigned u )
 382 {
 383    unsigned i;
 384
 385    if (u == 0) {
 386       return 0;
 387    }
 388
 389    __asm bsf eax, [u]
 390    __asm inc eax
 391    __asm mov [i], eax
 392
 393    return i;
 394 }
 395 #elif defined(__MINGW32__)
 396 #define ffs __builtin_ffs
 397 #endif
 398
 399 #ifdef __MINGW32__
 400 #define ffs __builtin_ffs
 401 #endif
 402
 403
 404 /* Could also binary search for the highest bit.
 405  */
 406 static INLINE unsigned
 407 util_unsigned_logbase2(unsigned n)
 408 {
 409    unsigned log2 = 0;
 410    while (n >>= 1)
 411       ++log2;
 412    return log2;
 413 }
 414
 415
 416 /**
 417  * Return float bits.
 418  */
 419 static INLINE unsigned
 420 fui( float f )
 421 {
 422    union fi fi;
 423    fi.f = f;
 424    return fi.ui;
 425 }
 426
 427
 428 /**
 429  * Convert ubyte to float in [0, 1].
 430  * XXX a 256-entry lookup table would be slightly faster.
 431  */
 432 static INLINE float
 433 ubyte_to_float(ubyte ub)
 434 {
 435    return (float) ub * (1.0f / 255.0f);
 436 }
 437
 438
 439 /**
 440  * Convert float in [0,1] to ubyte in [0,255] with clamping.
 441  */
 442 static INLINE ubyte
 443 float_to_ubyte(float f)
 444 {
 445    const int ieee_0996 = 0x3f7f0000;   /* 0.996 or so */
 446    union fi tmp;
 447
 448    tmp.f = f;
 449    if (tmp.i < 0) {
 450       return (ubyte) 0;
 451    }
 452    else if (tmp.i >= ieee_0996) {
 453       return (ubyte) 255;
 454    }
 455    else {
 456       tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
 457       return (ubyte) tmp.i;
 458    }
 459 }
 460
 461
 462 /**
 463  * Calc log base 2
 464  */
 465 static INLINE unsigned
 466 util_logbase2(unsigned n)
 467 {
 468    unsigned log2 = 0;
 469    while (n >>= 1)
 470       ++log2;
 471    return log2;
 472 }
 473
 474
 475 /**
 476  * Returns the smallest power of two >= x
 477  */
 478 static INLINE unsigned
 479 util_next_power_of_two(unsigned x)
 480 {
 481    unsigned i;
 482
 483    if (x == 0)
 484       return 1;
 485
 486    --x;
 487
 488    for (i = 1; i < sizeof(unsigned) * 8; i <<= 1)
 489       x |= x >> i;
 490
 491    return x + 1;
 492 }
 493
 494
 495 /**
 496  * Return number of bits set in n.
 497  */
 498 static INLINE unsigned
 499 util_bitcount(unsigned n)
 500 {
 501 #if defined(PIPE_CC_GCC)
 502    return __builtin_popcount(n);
 503 #else
 504    /* K&R classic bitcount.
 505     *
 506     * For each iteration, clear the LSB from the bitfield.
 507     * Requires only one iteration per set bit, instead of
 508     * one iteration per bit less than highest set bit.
 509     */
 510    unsigned bits = 0;
 511    for (bits; n; bits++) {
 512       n &= n - 1;
 513    }
 514    return bits;
 515 #endif
 516 }
 517
 518
 519 /**
 520  * Reverse byte order of a 32 bit word.
 521  */
 522 static INLINE uint32_t
 523 util_bswap32(uint32_t n)
 524 {
 525 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 403)
 526    return __builtin_bswap32(n);
 527 #else
 528    return (n >> 24) |
 529           ((n >> 8) & 0x0000ff00) |
 530           ((n << 8) & 0x00ff0000) |
 531           (n << 24);
 532 #endif
 533 }
 534
 535
 536 /**
 537  * Reverse byte order of a 16 bit word.
 538  */
 539 static INLINE uint16_t
 540 util_bswap16(uint16_t n)
 541 {
 542    return (n >> 8) |
 543           (n << 8);
 544 }
 545
 546
 547 /**
 548  * Clamp X to [MIN, MAX].
 549  * This is a macro to allow float, int, uint, etc. types.
 550  */
 551 #define CLAMP( X, MIN, MAX )  ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
 552
 553 #define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
 554 #define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
 555
 556 #define MIN3( A, B, C ) MIN2( MIN2( A, B ), C )
 557 #define MAX3( A, B, C ) MAX2( MAX2( A, B ), C )
 558
 559 #define MIN4( A, B, C, D ) MIN2( MIN2( A, B ), MIN2(C, D) )
 560 #define MAX4( A, B, C, D ) MAX2( MAX2( A, B ), MAX2(C, D) )
 561
 562
 563 /**
 564  * Align a value, only works pot alignemnts.
 565  */
 566 static INLINE int
 567 align(int value, int alignment)
 568 {
 569    return (value + alignment - 1) & ~(alignment - 1);
 570 }
 571
 572 /**
 573  * Works like align but on npot alignments.
 574  */
 575 static INLINE size_t
 576 util_align_npot(size_t value, size_t alignment)
 577 {
 578    if (value % alignment)
 579       return value + (alignment - (value % alignment));
 580    return value;
 581 }
 582
 583 static INLINE unsigned
 584 u_minify(unsigned value, unsigned levels)
 585 {
 586     return MAX2(1, value >> levels);
 587 }
 588
 589 #ifndef COPY_4V
 590 #define COPY_4V( DST, SRC )         \
 591 do {                                \
 592    (DST)[0] = (SRC)[0];             \
 593    (DST)[1] = (SRC)[1];             \
 594    (DST)[2] = (SRC)[2];             \
 595    (DST)[3] = (SRC)[3];             \
 596 } while (0)
 597 #endif
 598
 599
 600 #ifndef COPY_4FV
 601 #define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
 602 #endif
 603
 604
 605 #ifndef ASSIGN_4V
 606 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
 607 do {                                     \
 608    (DST)[0] = (V0);                      \
 609    (DST)[1] = (V1);                      \
 610    (DST)[2] = (V2);                      \
 611    (DST)[3] = (V3);                      \
 612 } while (0)
 613 #endif
 614
 615
 616 static INLINE uint32_t util_unsigned_fixed(float value, unsigned frac_bits)
 617 {
 618    return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits));
 619 }
 620
 621 static INLINE int32_t util_signed_fixed(float value, unsigned frac_bits)
 622 {
 623    return (int32_t)(value * (1<<frac_bits));
 624 }
 625
 626
 627
 628 #ifdef __cplusplus
 629 }
 630 #endif
 631
 632 #endif /* U_MATH_H */