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.
   5  *
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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 #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 /* _MSC_VER < 1400 && !defined(__cplusplus) */
 180
 181 static INLINE double log2( double x )
 182 {
 183    const double invln2 = 1.442695041;
 184    return log( x ) * invln2;
 185 }
 186
 187 static INLINE double
 188 round(double x)
 189 {
 190    return x >= 0.0 ? floor(x + 0.5) : ceil(x - 0.5);
 191 }
 192
 193 static INLINE float
 194 roundf(float x)
 195 {
 196    return x >= 0.0f ? floorf(x + 0.5f) : ceilf(x - 0.5f);
 197 }
 198
 199 #endif /* _MSC_VER */
 200
 201
 202 #ifdef PIPE_OS_ANDROID
 203
 204 static INLINE
 205 double log2(double d)
 206 {
 207    return log(d) * (1.0 / M_LN2);
 208 }
 209
 210 /* workaround a conflict with main/imports.h */
 211 #ifdef log2f
 212 #undef log2f
 213 #endif
 214
 215 static INLINE
 216 float log2f(float f)
 217 {
 218    return logf(f) * (float) (1.0 / M_LN2);
 219 }
 220
 221 #endif
 222
 223
 224
 225
 226 #define POW2_TABLE_SIZE_LOG2 9
 227 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
 228 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
 229 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
 230 extern float pow2_table[POW2_TABLE_SIZE];
 231
 232
 233 /**
 234  * Initialize math module.  This should be called before using any
 235  * other functions in this module.
 236  */
 237 extern void
 238 util_init_math(void);
 239
 240
 241 union fi {
 242    float f;
 243    int32_t i;
 244    uint32_t ui;
 245 };
 246
 247
 248 /**
 249  * Fast version of 2^x
 250  * Identity: exp2(a + b) = exp2(a) * exp2(b)
 251  * Let ipart = int(x)
 252  * Let fpart = x - ipart;
 253  * So, exp2(x) = exp2(ipart) * exp2(fpart)
 254  * Compute exp2(ipart) with i << ipart
 255  * Compute exp2(fpart) with lookup table.
 256  */
 257 static INLINE float
 258 util_fast_exp2(float x)
 259 {
 260    int32_t ipart;
 261    float fpart, mpart;
 262    union fi epart;
 263
 264    if(x > 129.00000f)
 265       return 3.402823466e+38f;
 266
 267    if (x < -126.99999f)
 268       return 0.0f;
 269
 270    ipart = (int32_t) x;
 271    fpart = x - (float) ipart;
 272
 273    /* same as
 274     *   epart.f = (float) (1 << ipart)
 275     * but faster and without integer overflow for ipart > 31
 276     */
 277    epart.i = (ipart + 127 ) << 23;
 278
 279    mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];
 280
 281    return epart.f * mpart;
 282 }
 283
 284
 285 /**
 286  * Fast approximation to exp(x).
 287  */
 288 static INLINE float
 289 util_fast_exp(float x)
 290 {
 291    const float k = 1.44269f; /* = log2(e) */
 292    return util_fast_exp2(k * x);
 293 }
 294
 295
 296 #define LOG2_TABLE_SIZE_LOG2 16
 297 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
 298 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
 299 extern float log2_table[LOG2_TABLE_SIZE];
 300
 301
 302 /**
 303  * Fast approximation to log2(x).
 304  */
 305 static INLINE float
 306 util_fast_log2(float x)
 307 {
 308    union fi num;
 309    float epart, mpart;
 310    num.f = x;
 311    epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
 312    /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
 313    mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)];
 314    return epart + mpart;
 315 }
 316
 317
 318 /**
 319  * Fast approximation to x^y.
 320  */
 321 static INLINE float
 322 util_fast_pow(float x, float y)
 323 {
 324    return util_fast_exp2(util_fast_log2(x) * y);
 325 }
 326
 327 /* Note that this counts zero as a power of two.
 328  */
 329 static INLINE boolean
 330 util_is_power_of_two( unsigned v )
 331 {
 332    return (v & (v-1)) == 0;
 333 }
 334
 335
 336 /**
 337  * Floor(x), returned as int.
 338  */
 339 static INLINE int
 340 util_ifloor(float f)
 341 {
 342    int ai, bi;
 343    double af, bf;
 344    union fi u;
 345    af = (3 << 22) + 0.5 + (double) f;
 346    bf = (3 << 22) + 0.5 - (double) f;
 347    u.f = (float) af;  ai = u.i;
 348    u.f = (float) bf;  bi = u.i;
 349    return (ai - bi) >> 1;
 350 }
 351
 352
 353 /**
 354  * Round float to nearest int.
 355  */
 356 static INLINE int
 357 util_iround(float f)
 358 {
 359 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
 360    int r;
 361    __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
 362    return r;
 363 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 364    int r;
 365    _asm {
 366       fld f
 367       fistp r
 368    }
 369    return r;
 370 #else
 371    if (f >= 0.0f)
 372       return (int) (f + 0.5f);
 373    else
 374       return (int) (f - 0.5f);
 375 #endif
 376 }
 377
 378
 379 /**
 380  * Approximate floating point comparison
 381  */
 382 static INLINE boolean
 383 util_is_approx(float a, float b, float tol)
 384 {
 385    return fabs(b - a) <= tol;
 386 }
 387
 388
 389 /**
 390  * Test if x is NaN or +/- infinity.
 391  */
 392 static INLINE boolean
 393 util_is_inf_or_nan(float x)
 394 {
 395    union fi tmp;
 396    tmp.f = x;
 397    return !(int)((unsigned int)((tmp.i & 0x7fffffff)-0x7f800000) >> 31);
 398 }
 399
 400
 401 /**
 402  * Find first bit set in word.  Least significant bit is 1.
 403  * Return 0 if no bits set.
 404  */
 405 #if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64)
 406 unsigned char _BitScanForward(unsigned long* Index, unsigned long Mask);
 407 #pragma intrinsic(_BitScanForward)
 408 static INLINE
 409 unsigned long ffs( unsigned long u )
 410 {
 411    unsigned long i;
 412    if (_BitScanForward(&i, u))
 413       return i + 1;
 414    else
 415       return 0;
 416 }
 417 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 418 static INLINE
 419 unsigned ffs( unsigned u )
 420 {
 421    unsigned i;
 422
 423    if (u == 0) {
 424       return 0;
 425    }
 426
 427    __asm bsf eax, [u]
 428    __asm inc eax
 429    __asm mov [i], eax
 430
 431    return i;
 432 }
 433 #elif defined(__MINGW32__) || defined(PIPE_OS_ANDROID)
 434 #define ffs __builtin_ffs
 435 #endif
 436
 437
 438 /* Destructively loop over all of the bits in a mask as in:
 439  *
 440  * while (mymask) {
 441  *   int i = u_bit_scan(&mymask);
 442  *   ... process element i
 443  * }
 444  *
 445  */
 446 static INLINE int u_bit_scan(unsigned *mask)
 447 {
 448    int i = ffs(*mask) - 1;
 449    *mask &= ~(1 << i);
 450    return i;
 451 }
 452
 453
 454 /**
 455  * Return float bits.
 456  */
 457 static INLINE unsigned
 458 fui( float f )
 459 {
 460    union fi fi;
 461    fi.f = f;
 462    return fi.ui;
 463 }
 464
 465
 466 /**
 467  * Convert ubyte to float in [0, 1].
 468  * XXX a 256-entry lookup table would be slightly faster.
 469  */
 470 static INLINE float
 471 ubyte_to_float(ubyte ub)
 472 {
 473    return (float) ub * (1.0f / 255.0f);
 474 }
 475
 476
 477 /**
 478  * Convert float in [0,1] to ubyte in [0,255] with clamping.
 479  */
 480 static INLINE ubyte
 481 float_to_ubyte(float f)
 482 {
 483    const int ieee_0996 = 0x3f7f0000;   /* 0.996 or so */
 484    union fi tmp;
 485
 486    tmp.f = f;
 487    if (tmp.i < 0) {
 488       return (ubyte) 0;
 489    }
 490    else if (tmp.i >= ieee_0996) {
 491       return (ubyte) 255;
 492    }
 493    else {
 494       tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
 495       return (ubyte) tmp.i;
 496    }
 497 }
 498
 499 static INLINE float
 500 byte_to_float_tex(int8_t b)
 501 {
 502    return (b == -128) ? -1.0F : b * 1.0F / 127.0F;
 503 }
 504
 505 static INLINE int8_t
 506 float_to_byte_tex(float f)
 507 {
 508    return (int8_t) (127.0F * f);
 509 }
 510
 511 /**
 512  * Calc log base 2
 513  */
 514 static INLINE unsigned
 515 util_logbase2(unsigned n)
 516 {
 517 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
 518    return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1));
 519 #else
 520    unsigned pos = 0;
 521    if (n >= 1<<16) { n >>= 16; pos += 16; }
 522    if (n >= 1<< 8) { n >>=  8; pos +=  8; }
 523    if (n >= 1<< 4) { n >>=  4; pos +=  4; }
 524    if (n >= 1<< 2) { n >>=  2; pos +=  2; }
 525    if (n >= 1<< 1) {           pos +=  1; }
 526    return pos;
 527 #endif
 528 }
 529
 530
 531 /**
 532  * Returns the smallest power of two >= x
 533  */
 534 static INLINE unsigned
 535 util_next_power_of_two(unsigned x)
 536 {
 537 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
 538    if (x <= 1)
 539        return 1;
 540
 541    return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1)));
 542 #else
 543    unsigned val = x;
 544
 545    if (x <= 1)
 546       return 1;
 547
 548    if (util_is_power_of_two(x))
 549       return x;
 550
 551    val--;
 552    val = (val >> 1) | val;
 553    val = (val >> 2) | val;
 554    val = (val >> 4) | val;
 555    val = (val >> 8) | val;
 556    val = (val >> 16) | val;
 557    val++;
 558    return val;
 559 #endif
 560 }
 561
 562
 563 /**
 564  * Return number of bits set in n.
 565  */
 566 static INLINE unsigned
 567 util_bitcount(unsigned n)
 568 {
 569 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
 570    return __builtin_popcount(n);
 571 #else
 572    /* K&R classic bitcount.
 573     *
 574     * For each iteration, clear the LSB from the bitfield.
 575     * Requires only one iteration per set bit, instead of
 576     * one iteration per bit less than highest set bit.
 577     */
 578    unsigned bits = 0;
 579    for (bits; n; bits++) {
 580       n &= n - 1;
 581    }
 582    return bits;
 583 #endif
 584 }
 585
 586
 587 /**
 588  * Convert from little endian to CPU byte order.
 589  */
 590
 591 #ifdef PIPE_ARCH_BIG_ENDIAN
 592 #define util_le32_to_cpu(x) util_bswap32(x)
 593 #define util_le16_to_cpu(x) util_bswap16(x)
 594 #else
 595 #define util_le32_to_cpu(x) (x)
 596 #define util_le16_to_cpu(x) (x)
 597 #endif
 598
 599
 600 /**
 601  * Reverse byte order of a 32 bit word.
 602  */
 603 static INLINE uint32_t
 604 util_bswap32(uint32_t n)
 605 {
 606 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 403)
 607    return __builtin_bswap32(n);
 608 #else
 609    return (n >> 24) |
 610           ((n >> 8) & 0x0000ff00) |
 611           ((n << 8) & 0x00ff0000) |
 612           (n << 24);
 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
 628 /**
 629  * Clamp X to [MIN, MAX].
 630  * This is a macro to allow float, int, uint, etc. types.
 631  */
 632 #define CLAMP( X, MIN, MAX )  ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
 633
 634 #define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
 635 #define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
 636
 637 #define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
 638 #define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))
 639
 640 #define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
 641 #define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))
 642
 643
 644 /**
 645  * Align a value, only works pot alignemnts.
 646  */
 647 static INLINE int
 648 align(int value, int alignment)
 649 {
 650    return (value + alignment - 1) & ~(alignment - 1);
 651 }
 652
 653 /**
 654  * Works like align but on npot alignments.
 655  */
 656 static INLINE size_t
 657 util_align_npot(size_t value, size_t alignment)
 658 {
 659    if (value % alignment)
 660       return value + (alignment - (value % alignment));
 661    return value;
 662 }
 663
 664 static INLINE unsigned
 665 u_minify(unsigned value, unsigned levels)
 666 {
 667     return MAX2(1, value >> levels);
 668 }
 669
 670 #ifndef COPY_4V
 671 #define COPY_4V( DST, SRC )         \
 672 do {                                \
 673    (DST)[0] = (SRC)[0];             \
 674    (DST)[1] = (SRC)[1];             \
 675    (DST)[2] = (SRC)[2];             \
 676    (DST)[3] = (SRC)[3];             \
 677 } while (0)
 678 #endif
 679
 680
 681 #ifndef COPY_4FV
 682 #define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
 683 #endif
 684
 685
 686 #ifndef ASSIGN_4V
 687 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
 688 do {                                     \
 689    (DST)[0] = (V0);                      \
 690    (DST)[1] = (V1);                      \
 691    (DST)[2] = (V2);                      \
 692    (DST)[3] = (V3);                      \
 693 } while (0)
 694 #endif
 695
 696
 697 static INLINE uint32_t util_unsigned_fixed(float value, unsigned frac_bits)
 698 {
 699    return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits));
 700 }
 701
 702 static INLINE int32_t util_signed_fixed(float value, unsigned frac_bits)
 703 {
 704    return (int32_t)(value * (1<<frac_bits));
 705 }
 706
 707
 708
 709 #ifdef __cplusplus
 710 }
 711 #endif
 712
 713 #endif /* U_MATH_H */