src/gallium/auxiliary/util/u_math.h

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   3  * Copyright 2008 Tungsten Graphics, Inc., Cedar Park, Texas.
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  15  * next paragraph) shall be included in all copies or substantial portions
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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 #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
 203
 204
 205 #define POW2_TABLE_SIZE_LOG2 9
 206 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
 207 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
 208 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
 209 extern float pow2_table[POW2_TABLE_SIZE];
 210
 211
 212 /**
 213  * Initialize math module.  This should be called before using any
 214  * other functions in this module.
 215  */
 216 extern void
 217 util_init_math(void);
 218
 219
 220 union fi {
 221    float f;
 222    int32_t i;
 223    uint32_t ui;
 224 };
 225
 226
 227 /**
 228  * Fast version of 2^x
 229  * Identity: exp2(a + b) = exp2(a) * exp2(b)
 230  * Let ipart = int(x)
 231  * Let fpart = x - ipart;
 232  * So, exp2(x) = exp2(ipart) * exp2(fpart)
 233  * Compute exp2(ipart) with i << ipart
 234  * Compute exp2(fpart) with lookup table.
 235  */
 236 static INLINE float
 237 util_fast_exp2(float x)
 238 {
 239    int32_t ipart;
 240    float fpart, mpart;
 241    union fi epart;
 242
 243    if(x > 129.00000f)
 244       return 3.402823466e+38f;
 245
 246    if (x < -126.99999f)
 247       return 0.0f;
 248
 249    ipart = (int32_t) x;
 250    fpart = x - (float) ipart;
 251
 252    /* same as
 253     *   epart.f = (float) (1 << ipart)
 254     * but faster and without integer overflow for ipart > 31
 255     */
 256    epart.i = (ipart + 127 ) << 23;
 257
 258    mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];
 259
 260    return epart.f * mpart;
 261 }
 262
 263
 264 /**
 265  * Fast approximation to exp(x).
 266  */
 267 static INLINE float
 268 util_fast_exp(float x)
 269 {
 270    const float k = 1.44269f; /* = log2(e) */
 271    return util_fast_exp2(k * x);
 272 }
 273
 274
 275 #define LOG2_TABLE_SIZE_LOG2 16
 276 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
 277 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
 278 extern float log2_table[LOG2_TABLE_SIZE];
 279
 280
 281 /**
 282  * Fast approximation to log2(x).
 283  */
 284 static INLINE float
 285 util_fast_log2(float x)
 286 {
 287    union fi num;
 288    float epart, mpart;
 289    num.f = x;
 290    epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
 291    /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
 292    mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)];
 293    return epart + mpart;
 294 }
 295
 296
 297 /**
 298  * Fast approximation to x^y.
 299  */
 300 static INLINE float
 301 util_fast_pow(float x, float y)
 302 {
 303    return util_fast_exp2(util_fast_log2(x) * y);
 304 }
 305
 306 /* Note that this counts zero as a power of two.
 307  */
 308 static INLINE boolean
 309 util_is_power_of_two( unsigned v )
 310 {
 311    return (v & (v-1)) == 0;
 312 }
 313
 314
 315 /**
 316  * Floor(x), returned as int.
 317  */
 318 static INLINE int
 319 util_ifloor(float f)
 320 {
 321    int ai, bi;
 322    double af, bf;
 323    union fi u;
 324    af = (3 << 22) + 0.5 + (double) f;
 325    bf = (3 << 22) + 0.5 - (double) f;
 326    u.f = (float) af;  ai = u.i;
 327    u.f = (float) bf;  bi = u.i;
 328    return (ai - bi) >> 1;
 329 }
 330
 331
 332 /**
 333  * Round float to nearest int.
 334  */
 335 static INLINE int
 336 util_iround(float f)
 337 {
 338 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
 339    int r;
 340    __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
 341    return r;
 342 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 343    int r;
 344    _asm {
 345       fld f
 346       fistp r
 347    }
 348    return r;
 349 #else
 350    if (f >= 0.0f)
 351       return (int) (f + 0.5f);
 352    else
 353       return (int) (f - 0.5f);
 354 #endif
 355 }
 356
 357
 358 /**
 359  * Approximate floating point comparison
 360  */
 361 static INLINE boolean
 362 util_is_approx(float a, float b, float tol)
 363 {
 364    return fabs(b - a) <= tol;
 365 }
 366
 367
 368 /**
 369  * Test if x is NaN or +/- infinity.
 370  */
 371 static INLINE boolean
 372 util_is_inf_or_nan(float x)
 373 {
 374    union fi tmp;
 375    tmp.f = x;
 376    return !(int)((unsigned int)((tmp.i & 0x7fffffff)-0x7f800000) >> 31);
 377 }
 378
 379
 380 /**
 381  * Find first bit set in word.  Least significant bit is 1.
 382  * Return 0 if no bits set.
 383  */
 384 #if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64)
 385 unsigned char _BitScanForward(unsigned long* Index, unsigned long Mask);
 386 #pragma intrinsic(_BitScanForward)
 387 static INLINE
 388 unsigned long ffs( unsigned long u )
 389 {
 390    unsigned long i;
 391    if (_BitScanForward(&i, u))
 392       return i + 1;
 393    else
 394       return 0;
 395 }
 396 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 397 static INLINE
 398 unsigned ffs( unsigned u )
 399 {
 400    unsigned i;
 401
 402    if (u == 0) {
 403       return 0;
 404    }
 405
 406    __asm bsf eax, [u]
 407    __asm inc eax
 408    __asm mov [i], eax
 409
 410    return i;
 411 }
 412 #elif defined(__MINGW32__)
 413 #define ffs __builtin_ffs
 414 #endif
 415
 416 #ifdef __MINGW32__
 417 #define ffs __builtin_ffs
 418 #endif
 419
 420
 421 /* Could also binary search for the highest bit.
 422  */
 423 static INLINE unsigned
 424 util_unsigned_logbase2(unsigned n)
 425 {
 426    unsigned log2 = 0;
 427    while (n >>= 1)
 428       ++log2;
 429    return log2;
 430 }
 431
 432
 433 /**
 434  * Return float bits.
 435  */
 436 static INLINE unsigned
 437 fui( float f )
 438 {
 439    union fi fi;
 440    fi.f = f;
 441    return fi.ui;
 442 }
 443
 444
 445 /**
 446  * Convert ubyte to float in [0, 1].
 447  * XXX a 256-entry lookup table would be slightly faster.
 448  */
 449 static INLINE float
 450 ubyte_to_float(ubyte ub)
 451 {
 452    return (float) ub * (1.0f / 255.0f);
 453 }
 454
 455
 456 /**
 457  * Convert float in [0,1] to ubyte in [0,255] with clamping.
 458  */
 459 static INLINE ubyte
 460 float_to_ubyte(float f)
 461 {
 462    const int ieee_0996 = 0x3f7f0000;   /* 0.996 or so */
 463    union fi tmp;
 464
 465    tmp.f = f;
 466    if (tmp.i < 0) {
 467       return (ubyte) 0;
 468    }
 469    else if (tmp.i >= ieee_0996) {
 470       return (ubyte) 255;
 471    }
 472    else {
 473       tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
 474       return (ubyte) tmp.i;
 475    }
 476 }
 477
 478 static INLINE float
 479 byte_to_float_tex(int8_t b)
 480 {
 481    return (b == -128) ? -1.0F : b * 1.0F / 127.0F;
 482 }
 483
 484 static INLINE int8_t
 485 float_to_byte_tex(float f)
 486 {
 487    return (int8_t) (127.0F * f);
 488 }
 489
 490 /**
 491  * Calc log base 2
 492  */
 493 static INLINE unsigned
 494 util_logbase2(unsigned n)
 495 {
 496    unsigned log2 = 0;
 497    while (n >>= 1)
 498       ++log2;
 499    return log2;
 500 }
 501
 502
 503 /**
 504  * Returns the smallest power of two >= x
 505  */
 506 static INLINE unsigned
 507 util_next_power_of_two(unsigned x)
 508 {
 509    unsigned i;
 510
 511    if (x == 0)
 512       return 1;
 513
 514    --x;
 515
 516    for (i = 1; i < sizeof(unsigned) * 8; i <<= 1)
 517       x |= x >> i;
 518
 519    return x + 1;
 520 }
 521
 522
 523 /**
 524  * Return number of bits set in n.
 525  */
 526 static INLINE unsigned
 527 util_bitcount(unsigned n)
 528 {
 529 #if defined(PIPE_CC_GCC)
 530    return __builtin_popcount(n);
 531 #else
 532    /* K&R classic bitcount.
 533     *
 534     * For each iteration, clear the LSB from the bitfield.
 535     * Requires only one iteration per set bit, instead of
 536     * one iteration per bit less than highest set bit.
 537     */
 538    unsigned bits = 0;
 539    for (bits; n; bits++) {
 540       n &= n - 1;
 541    }
 542    return bits;
 543 #endif
 544 }
 545
 546
 547 /**
 548  * Reverse byte order of a 32 bit word.
 549  */
 550 static INLINE uint32_t
 551 util_bswap32(uint32_t n)
 552 {
 553 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 403)
 554    return __builtin_bswap32(n);
 555 #else
 556    return (n >> 24) |
 557           ((n >> 8) & 0x0000ff00) |
 558           ((n << 8) & 0x00ff0000) |
 559           (n << 24);
 560 #endif
 561 }
 562
 563
 564 /**
 565  * Reverse byte order of a 16 bit word.
 566  */
 567 static INLINE uint16_t
 568 util_bswap16(uint16_t n)
 569 {
 570    return (n >> 8) |
 571           (n << 8);
 572 }
 573
 574
 575 /**
 576  * Clamp X to [MIN, MAX].
 577  * This is a macro to allow float, int, uint, etc. types.
 578  */
 579 #define CLAMP( X, MIN, MAX )  ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
 580
 581 #define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
 582 #define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
 583
 584 #define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
 585 #define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))
 586
 587 #define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
 588 #define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))
 589
 590
 591 /**
 592  * Align a value, only works pot alignemnts.
 593  */
 594 static INLINE int
 595 align(int value, int alignment)
 596 {
 597    return (value + alignment - 1) & ~(alignment - 1);
 598 }
 599
 600 /**
 601  * Works like align but on npot alignments.
 602  */
 603 static INLINE size_t
 604 util_align_npot(size_t value, size_t alignment)
 605 {
 606    if (value % alignment)
 607       return value + (alignment - (value % alignment));
 608    return value;
 609 }
 610
 611 static INLINE unsigned
 612 u_minify(unsigned value, unsigned levels)
 613 {
 614     return MAX2(1, value >> levels);
 615 }
 616
 617 #ifndef COPY_4V
 618 #define COPY_4V( DST, SRC )         \
 619 do {                                \
 620    (DST)[0] = (SRC)[0];             \
 621    (DST)[1] = (SRC)[1];             \
 622    (DST)[2] = (SRC)[2];             \
 623    (DST)[3] = (SRC)[3];             \
 624 } while (0)
 625 #endif
 626
 627
 628 #ifndef COPY_4FV
 629 #define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
 630 #endif
 631
 632
 633 #ifndef ASSIGN_4V
 634 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
 635 do {                                     \
 636    (DST)[0] = (V0);                      \
 637    (DST)[1] = (V1);                      \
 638    (DST)[2] = (V2);                      \
 639    (DST)[3] = (V3);                      \
 640 } while (0)
 641 #endif
 642
 643
 644 static INLINE uint32_t util_unsigned_fixed(float value, unsigned frac_bits)
 645 {
 646    return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits));
 647 }
 648
 649 static INLINE int32_t util_signed_fixed(float value, unsigned frac_bits)
 650 {
 651    return (int32_t)(value * (1<<frac_bits));
 652 }
 653
 654
 655
 656 #ifdef __cplusplus
 657 }
 658 #endif
 659
 660 #endif /* U_MATH_H */