src/gallium/auxiliary/util/u_math.h

   1 /**************************************************************************
   2  *
   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
  12  * the following conditions:
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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 #include <math.h>
  52 #include <stdarg.h>
  53
  54 #ifdef PIPE_OS_UNIX
  55 #include <strings.h> /* for ffs */
  56 #endif
  57
  58
  59 #ifndef M_SQRT2
  60 #define M_SQRT2 1.41421356237309504880
  61 #endif
  62
  63
  64 #if defined(_MSC_VER)
  65
  66 #if _MSC_VER < 1400 && !defined(__cplusplus)
  67
  68 static INLINE float cosf( float f )
  69 {
  70    return (float) cos( (double) f );
  71 }
  72
  73 static INLINE float sinf( float f )
  74 {
  75    return (float) sin( (double) f );
  76 }
  77
  78 static INLINE float ceilf( float f )
  79 {
  80    return (float) ceil( (double) f );
  81 }
  82
  83 static INLINE float floorf( float f )
  84 {
  85    return (float) floor( (double) f );
  86 }
  87
  88 static INLINE float powf( float f, float g )
  89 {
  90    return (float) pow( (double) f, (double) g );
  91 }
  92
  93 static INLINE float sqrtf( float f )
  94 {
  95    return (float) sqrt( (double) f );
  96 }
  97
  98 static INLINE float fabsf( float f )
  99 {
 100    return (float) fabs( (double) f );
 101 }
 102
 103 static INLINE float logf( float f )
 104 {
 105    return (float) log( (double) f );
 106 }
 107
 108 #else
 109 /* Work-around an extra semi-colon in VS 2005 logf definition */
 110 #ifdef logf
 111 #undef logf
 112 #define logf(x) ((float)log((double)(x)))
 113 #endif /* logf */
 114
 115 #define isfinite(x) _finite((double)(x))
 116 #define isnan(x) _isnan((double)(x))
 117 #endif /* _MSC_VER < 1400 && !defined(__cplusplus) */
 118
 119 static INLINE double log2( double x )
 120 {
 121    const double invln2 = 1.442695041;
 122    return log( x ) * invln2;
 123 }
 124
 125 static INLINE double
 126 round(double x)
 127 {
 128    return x >= 0.0 ? floor(x + 0.5) : ceil(x - 0.5);
 129 }
 130
 131 static INLINE float
 132 roundf(float x)
 133 {
 134    return x >= 0.0f ? floorf(x + 0.5f) : ceilf(x - 0.5f);
 135 }
 136
 137 #endif /* _MSC_VER */
 138
 139
 140 #ifdef PIPE_OS_ANDROID
 141
 142 static INLINE
 143 double log2(double d)
 144 {
 145    return log(d) * (1.0 / M_LN2);
 146 }
 147
 148 /* workaround a conflict with main/imports.h */
 149 #ifdef log2f
 150 #undef log2f
 151 #endif
 152
 153 static INLINE
 154 float log2f(float f)
 155 {
 156    return logf(f) * (float) (1.0 / M_LN2);
 157 }
 158
 159 #endif
 160
 161
 162
 163
 164 #define POW2_TABLE_SIZE_LOG2 9
 165 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
 166 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
 167 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
 168 extern float pow2_table[POW2_TABLE_SIZE];
 169
 170
 171 /**
 172  * Initialize math module.  This should be called before using any
 173  * other functions in this module.
 174  */
 175 extern void
 176 util_init_math(void);
 177
 178
 179 union fi {
 180    float f;
 181    int32_t i;
 182    uint32_t ui;
 183 };
 184
 185
 186 /**
 187  * Fast version of 2^x
 188  * Identity: exp2(a + b) = exp2(a) * exp2(b)
 189  * Let ipart = int(x)
 190  * Let fpart = x - ipart;
 191  * So, exp2(x) = exp2(ipart) * exp2(fpart)
 192  * Compute exp2(ipart) with i << ipart
 193  * Compute exp2(fpart) with lookup table.
 194  */
 195 static INLINE float
 196 util_fast_exp2(float x)
 197 {
 198    int32_t ipart;
 199    float fpart, mpart;
 200    union fi epart;
 201
 202    if(x > 129.00000f)
 203       return 3.402823466e+38f;
 204
 205    if (x < -126.99999f)
 206       return 0.0f;
 207
 208    ipart = (int32_t) x;
 209    fpart = x - (float) ipart;
 210
 211    /* same as
 212     *   epart.f = (float) (1 << ipart)
 213     * but faster and without integer overflow for ipart > 31
 214     */
 215    epart.i = (ipart + 127 ) << 23;
 216
 217    mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];
 218
 219    return epart.f * mpart;
 220 }
 221
 222
 223 /**
 224  * Fast approximation to exp(x).
 225  */
 226 static INLINE float
 227 util_fast_exp(float x)
 228 {
 229    const float k = 1.44269f; /* = log2(e) */
 230    return util_fast_exp2(k * x);
 231 }
 232
 233
 234 #define LOG2_TABLE_SIZE_LOG2 16
 235 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
 236 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
 237 extern float log2_table[LOG2_TABLE_SIZE];
 238
 239
 240 /**
 241  * Fast approximation to log2(x).
 242  */
 243 static INLINE float
 244 util_fast_log2(float x)
 245 {
 246    union fi num;
 247    float epart, mpart;
 248    num.f = x;
 249    epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
 250    /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
 251    mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)];
 252    return epart + mpart;
 253 }
 254
 255
 256 /**
 257  * Fast approximation to x^y.
 258  */
 259 static INLINE float
 260 util_fast_pow(float x, float y)
 261 {
 262    return util_fast_exp2(util_fast_log2(x) * y);
 263 }
 264
 265 /* Note that this counts zero as a power of two.
 266  */
 267 static INLINE boolean
 268 util_is_power_of_two( unsigned v )
 269 {
 270    return (v & (v-1)) == 0;
 271 }
 272
 273
 274 /**
 275  * Floor(x), returned as int.
 276  */
 277 static INLINE int
 278 util_ifloor(float f)
 279 {
 280    int ai, bi;
 281    double af, bf;
 282    union fi u;
 283    af = (3 << 22) + 0.5 + (double) f;
 284    bf = (3 << 22) + 0.5 - (double) f;
 285    u.f = (float) af;  ai = u.i;
 286    u.f = (float) bf;  bi = u.i;
 287    return (ai - bi) >> 1;
 288 }
 289
 290
 291 /**
 292  * Round float to nearest int.
 293  */
 294 static INLINE int
 295 util_iround(float f)
 296 {
 297 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
 298    int r;
 299    __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
 300    return r;
 301 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 302    int r;
 303    _asm {
 304       fld f
 305       fistp r
 306    }
 307    return r;
 308 #else
 309    if (f >= 0.0f)
 310       return (int) (f + 0.5f);
 311    else
 312       return (int) (f - 0.5f);
 313 #endif
 314 }
 315
 316
 317 /**
 318  * Approximate floating point comparison
 319  */
 320 static INLINE boolean
 321 util_is_approx(float a, float b, float tol)
 322 {
 323    return fabs(b - a) <= tol;
 324 }
 325
 326
 327 /**
 328  * Test if x is NaN or +/- infinity.
 329  */
 330 static INLINE boolean
 331 util_is_inf_or_nan(float x)
 332 {
 333    union fi tmp;
 334    tmp.f = x;
 335    return !(int)((unsigned int)((tmp.i & 0x7fffffff)-0x7f800000) >> 31);
 336 }
 337
 338
 339 /**
 340  * Find first bit set in word.  Least significant bit is 1.
 341  * Return 0 if no bits set.
 342  */
 343 #ifndef FFS_DEFINED
 344 #define FFS_DEFINED 1
 345
 346 #if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64)
 347 unsigned char _BitScanForward(unsigned long* Index, unsigned long Mask);
 348 #pragma intrinsic(_BitScanForward)
 349 static INLINE
 350 unsigned long ffs( unsigned long u )
 351 {
 352    unsigned long i;
 353    if (_BitScanForward(&i, u))
 354       return i + 1;
 355    else
 356       return 0;
 357 }
 358 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 359 static INLINE
 360 unsigned ffs( unsigned u )
 361 {
 362    unsigned i;
 363
 364    if (u == 0) {
 365       return 0;
 366    }
 367
 368    __asm bsf eax, [u]
 369    __asm inc eax
 370    __asm mov [i], eax
 371
 372    return i;
 373 }
 374 #elif defined(__MINGW32__) || defined(PIPE_OS_ANDROID)
 375 #define ffs __builtin_ffs
 376 #endif
 377
 378 #endif /* FFS_DEFINED */
 379
 380
 381 /* Destructively loop over all of the bits in a mask as in:
 382  *
 383  * while (mymask) {
 384  *   int i = u_bit_scan(&mymask);
 385  *   ... process element i
 386  * }
 387  *
 388  */
 389 static INLINE int u_bit_scan(unsigned *mask)
 390 {
 391    int i = ffs(*mask) - 1;
 392    *mask &= ~(1 << i);
 393    return i;
 394 }
 395
 396
 397 /**
 398  * Return float bits.
 399  */
 400 static INLINE unsigned
 401 fui( float f )
 402 {
 403    union fi fi;
 404    fi.f = f;
 405    return fi.ui;
 406 }
 407
 408
 409 /**
 410  * Convert ubyte to float in [0, 1].
 411  * XXX a 256-entry lookup table would be slightly faster.
 412  */
 413 static INLINE float
 414 ubyte_to_float(ubyte ub)
 415 {
 416    return (float) ub * (1.0f / 255.0f);
 417 }
 418
 419
 420 /**
 421  * Convert float in [0,1] to ubyte in [0,255] with clamping.
 422  */
 423 static INLINE ubyte
 424 float_to_ubyte(float f)
 425 {
 426    const int ieee_0996 = 0x3f7f0000;   /* 0.996 or so */
 427    union fi tmp;
 428
 429    tmp.f = f;
 430    if (tmp.i < 0) {
 431       return (ubyte) 0;
 432    }
 433    else if (tmp.i >= ieee_0996) {
 434       return (ubyte) 255;
 435    }
 436    else {
 437       tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
 438       return (ubyte) tmp.i;
 439    }
 440 }
 441
 442 static INLINE float
 443 byte_to_float_tex(int8_t b)
 444 {
 445    return (b == -128) ? -1.0F : b * 1.0F / 127.0F;
 446 }
 447
 448 static INLINE int8_t
 449 float_to_byte_tex(float f)
 450 {
 451    return (int8_t) (127.0F * f);
 452 }
 453
 454 /**
 455  * Calc log base 2
 456  */
 457 static INLINE unsigned
 458 util_logbase2(unsigned n)
 459 {
 460 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
 461    return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1));
 462 #else
 463    unsigned pos = 0;
 464    if (n >= 1<<16) { n >>= 16; pos += 16; }
 465    if (n >= 1<< 8) { n >>=  8; pos +=  8; }
 466    if (n >= 1<< 4) { n >>=  4; pos +=  4; }
 467    if (n >= 1<< 2) { n >>=  2; pos +=  2; }
 468    if (n >= 1<< 1) {           pos +=  1; }
 469    return pos;
 470 #endif
 471 }
 472
 473
 474 /**
 475  * Returns the smallest power of two >= x
 476  */
 477 static INLINE unsigned
 478 util_next_power_of_two(unsigned x)
 479 {
 480 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
 481    if (x <= 1)
 482        return 1;
 483
 484    return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1)));
 485 #else
 486    unsigned val = x;
 487
 488    if (x <= 1)
 489       return 1;
 490
 491    if (util_is_power_of_two(x))
 492       return x;
 493
 494    val--;
 495    val = (val >> 1) | val;
 496    val = (val >> 2) | val;
 497    val = (val >> 4) | val;
 498    val = (val >> 8) | val;
 499    val = (val >> 16) | val;
 500    val++;
 501    return val;
 502 #endif
 503 }
 504
 505
 506 /**
 507  * Return number of bits set in n.
 508  */
 509 static INLINE unsigned
 510 util_bitcount(unsigned n)
 511 {
 512 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
 513    return __builtin_popcount(n);
 514 #else
 515    /* K&R classic bitcount.
 516     *
 517     * For each iteration, clear the LSB from the bitfield.
 518     * Requires only one iteration per set bit, instead of
 519     * one iteration per bit less than highest set bit.
 520     */
 521    unsigned bits = 0;
 522    for (bits; n; bits++) {
 523       n &= n - 1;
 524    }
 525    return bits;
 526 #endif
 527 }
 528
 529
 530 /**
 531  * Convert from little endian to CPU byte order.
 532  */
 533
 534 #ifdef PIPE_ARCH_BIG_ENDIAN
 535 #define util_le32_to_cpu(x) util_bswap32(x)
 536 #define util_le16_to_cpu(x) util_bswap16(x)
 537 #else
 538 #define util_le32_to_cpu(x) (x)
 539 #define util_le16_to_cpu(x) (x)
 540 #endif
 541
 542
 543 /**
 544  * Reverse byte order of a 32 bit word.
 545  */
 546 static INLINE uint32_t
 547 util_bswap32(uint32_t n)
 548 {
 549 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 403)
 550    return __builtin_bswap32(n);
 551 #else
 552    return (n >> 24) |
 553           ((n >> 8) & 0x0000ff00) |
 554           ((n << 8) & 0x00ff0000) |
 555           (n << 24);
 556 #endif
 557 }
 558
 559
 560 /**
 561  * Reverse byte order of a 16 bit word.
 562  */
 563 static INLINE uint16_t
 564 util_bswap16(uint16_t n)
 565 {
 566    return (n >> 8) |
 567           (n << 8);
 568 }
 569
 570
 571 /**
 572  * Clamp X to [MIN, MAX].
 573  * This is a macro to allow float, int, uint, etc. types.
 574  */
 575 #define CLAMP( X, MIN, MAX )  ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
 576
 577 #define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
 578 #define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
 579
 580 #define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
 581 #define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))
 582
 583 #define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
 584 #define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))
 585
 586
 587 /**
 588  * Align a value, only works pot alignemnts.
 589  */
 590 static INLINE int
 591 align(int value, int alignment)
 592 {
 593    return (value + alignment - 1) & ~(alignment - 1);
 594 }
 595
 596 /**
 597  * Works like align but on npot alignments.
 598  */
 599 static INLINE size_t
 600 util_align_npot(size_t value, size_t alignment)
 601 {
 602    if (value % alignment)
 603       return value + (alignment - (value % alignment));
 604    return value;
 605 }
 606
 607 static INLINE unsigned
 608 u_minify(unsigned value, unsigned levels)
 609 {
 610     return MAX2(1, value >> levels);
 611 }
 612
 613 #ifndef COPY_4V
 614 #define COPY_4V( DST, SRC )         \
 615 do {                                \
 616    (DST)[0] = (SRC)[0];             \
 617    (DST)[1] = (SRC)[1];             \
 618    (DST)[2] = (SRC)[2];             \
 619    (DST)[3] = (SRC)[3];             \
 620 } while (0)
 621 #endif
 622
 623
 624 #ifndef COPY_4FV
 625 #define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
 626 #endif
 627
 628
 629 #ifndef ASSIGN_4V
 630 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
 631 do {                                     \
 632    (DST)[0] = (V0);                      \
 633    (DST)[1] = (V1);                      \
 634    (DST)[2] = (V2);                      \
 635    (DST)[3] = (V3);                      \
 636 } while (0)
 637 #endif
 638
 639
 640 static INLINE uint32_t util_unsigned_fixed(float value, unsigned frac_bits)
 641 {
 642    return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits));
 643 }
 644
 645 static INLINE int32_t util_signed_fixed(float value, unsigned frac_bits)
 646 {
 647    return (int32_t)(value * (1<<frac_bits));
 648 }
 649
 650
 651
 652 #ifdef __cplusplus
 653 }
 654 #endif
 655
 656 #endif /* U_MATH_H */