src/gallium/auxiliary/util/u_math.h

   1 /**************************************************************************
   2  *
   3  * Copyright 2008 Tungsten Graphics, Inc., Cedar Park, Texas.
   4  * All Rights Reserved.
   5  *
   6  * Permission is hereby granted, free of charge, to any person obtaining a
   7  * copy of this software and associated documentation files (the
   8  * "Software"), to deal in the Software without restriction, including
   9  * without limitation the rights to use, copy, modify, merge, publish,
  10  * distribute, sub license, and/or sell copies of the Software, and to
  11  * permit persons to whom the Software is furnished to do so, subject to
  12  * the following conditions:
  13  *
  14  * The above copyright notice and this permission notice (including the
  15  * next paragraph) shall be included in all copies or substantial portions
  16  * of the Software.
  17  *
  18  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
  19  * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
  20  * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT.
  21  * IN NO EVENT SHALL TUNGSTEN GRAPHICS AND/OR ITS SUPPLIERS BE LIABLE FOR
  22  * ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
  23  * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
  24  * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
  25  *
  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 #endif
 172
 173 static INLINE double log2( double x )
 174 {
 175    const double invln2 = 1.442695041;
 176    return log( x ) * invln2;
 177 }
 178
 179 #endif /* _MSC_VER */
 180
 181
 182
 183
 184
 185 #define POW2_TABLE_SIZE_LOG2 9
 186 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
 187 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
 188 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
 189 extern float pow2_table[POW2_TABLE_SIZE];
 190
 191
 192 /**
 193  * Initialize math module.  This should be called before using any
 194  * other functions in this module.
 195  */
 196 extern void
 197 util_init_math(void);
 198
 199
 200 union fi {
 201    float f;
 202    int32_t i;
 203    uint32_t ui;
 204 };
 205
 206
 207 /**
 208  * Fast version of 2^x
 209  * Identity: exp2(a + b) = exp2(a) * exp2(b)
 210  * Let ipart = int(x)
 211  * Let fpart = x - ipart;
 212  * So, exp2(x) = exp2(ipart) * exp2(fpart)
 213  * Compute exp2(ipart) with i << ipart
 214  * Compute exp2(fpart) with lookup table.
 215  */
 216 static INLINE float
 217 util_fast_exp2(float x)
 218 {
 219    int32_t ipart;
 220    float fpart, mpart;
 221    union fi epart;
 222
 223    if(x > 129.00000f)
 224       return 3.402823466e+38f;
 225
 226    if (x < -126.99999f)
 227       return 0.0f;
 228
 229    ipart = (int32_t) x;
 230    fpart = x - (float) ipart;
 231
 232    /* same as
 233     *   epart.f = (float) (1 << ipart)
 234     * but faster and without integer overflow for ipart > 31
 235     */
 236    epart.i = (ipart + 127 ) << 23;
 237
 238    mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];
 239
 240    return epart.f * mpart;
 241 }
 242
 243
 244 /**
 245  * Fast approximation to exp(x).
 246  */
 247 static INLINE float
 248 util_fast_exp(float x)
 249 {
 250    const float k = 1.44269f; /* = log2(e) */
 251    return util_fast_exp2(k * x);
 252 }
 253
 254
 255 #define LOG2_TABLE_SIZE_LOG2 16
 256 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
 257 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
 258 extern float log2_table[LOG2_TABLE_SIZE];
 259
 260
 261 /**
 262  * Fast approximation to log2(x).
 263  */
 264 static INLINE float
 265 util_fast_log2(float x)
 266 {
 267    union fi num;
 268    float epart, mpart;
 269    num.f = x;
 270    epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
 271    /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
 272    mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)];
 273    return epart + mpart;
 274 }
 275
 276
 277 /**
 278  * Fast approximation to x^y.
 279  */
 280 static INLINE float
 281 util_fast_pow(float x, float y)
 282 {
 283    return util_fast_exp2(util_fast_log2(x) * y);
 284 }
 285
 286 /* Note that this counts zero as a power of two.
 287  */
 288 static INLINE boolean
 289 util_is_power_of_two( unsigned v )
 290 {
 291    return (v & (v-1)) == 0;
 292 }
 293
 294
 295 /**
 296  * Floor(x), returned as int.
 297  */
 298 static INLINE int
 299 util_ifloor(float f)
 300 {
 301    int ai, bi;
 302    double af, bf;
 303    union fi u;
 304    af = (3 << 22) + 0.5 + (double) f;
 305    bf = (3 << 22) + 0.5 - (double) f;
 306    u.f = (float) af;  ai = u.i;
 307    u.f = (float) bf;  bi = u.i;
 308    return (ai - bi) >> 1;
 309 }
 310
 311
 312 /**
 313  * Round float to nearest int.
 314  */
 315 static INLINE int
 316 util_iround(float f)
 317 {
 318 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
 319    int r;
 320    __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
 321    return r;
 322 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 323    int r;
 324    _asm {
 325       fld f
 326       fistp r
 327    }
 328    return r;
 329 #else
 330    if (f >= 0.0f)
 331       return (int) (f + 0.5f);
 332    else
 333       return (int) (f - 0.5f);
 334 #endif
 335 }
 336
 337
 338
 339 /**
 340  * Test if x is NaN or +/- infinity.
 341  */
 342 static INLINE boolean
 343 util_is_inf_or_nan(float x)
 344 {
 345    union fi tmp;
 346    tmp.f = x;
 347    return !(int)((unsigned int)((tmp.i & 0x7fffffff)-0x7f800000) >> 31);
 348 }
 349
 350
 351 /**
 352  * Test whether x is a power of two.
 353  */
 354 static INLINE boolean
 355 util_is_pot(unsigned x)
 356 {
 357    return (x & (x - 1)) == 0;
 358 }
 359
 360
 361 /**
 362  * Find first bit set in word.  Least significant bit is 1.
 363  * Return 0 if no bits set.
 364  */
 365 #if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64)
 366 unsigned char _BitScanForward(unsigned long* Index, unsigned long Mask);
 367 #pragma intrinsic(_BitScanForward)
 368 static INLINE
 369 unsigned long ffs( unsigned long u )
 370 {
 371    unsigned long i;
 372    if (_BitScanForward(&i, u))
 373       return i + 1;
 374    else
 375       return 0;
 376 }
 377 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 378 static INLINE
 379 unsigned ffs( unsigned u )
 380 {
 381    unsigned i;
 382
 383    if (u == 0) {
 384       return 0;
 385    }
 386
 387    __asm bsf eax, [u]
 388    __asm inc eax
 389    __asm mov [i], eax
 390
 391    return i;
 392 }
 393 #elif defined(__MINGW32__)
 394 #define ffs __builtin_ffs
 395 #endif
 396
 397 #ifdef __MINGW32__
 398 #define ffs __builtin_ffs
 399 #endif
 400
 401
 402 /* Could also binary search for the highest bit.
 403  */
 404 static INLINE unsigned
 405 util_unsigned_logbase2(unsigned n)
 406 {
 407    unsigned log2 = 0;
 408    while (n >>= 1)
 409       ++log2;
 410    return log2;
 411 }
 412
 413
 414 /**
 415  * Return float bits.
 416  */
 417 static INLINE unsigned
 418 fui( float f )
 419 {
 420    union fi fi;
 421    fi.f = f;
 422    return fi.ui;
 423 }
 424
 425
 426 /**
 427  * Convert ubyte to float in [0, 1].
 428  * XXX a 256-entry lookup table would be slightly faster.
 429  */
 430 static INLINE float
 431 ubyte_to_float(ubyte ub)
 432 {
 433    return (float) ub * (1.0f / 255.0f);
 434 }
 435
 436
 437 /**
 438  * Convert float in [0,1] to ubyte in [0,255] with clamping.
 439  */
 440 static INLINE ubyte
 441 float_to_ubyte(float f)
 442 {
 443    const int ieee_0996 = 0x3f7f0000;   /* 0.996 or so */
 444    union fi tmp;
 445
 446    tmp.f = f;
 447    if (tmp.i < 0) {
 448       return (ubyte) 0;
 449    }
 450    else if (tmp.i >= ieee_0996) {
 451       return (ubyte) 255;
 452    }
 453    else {
 454       tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
 455       return (ubyte) tmp.i;
 456    }
 457 }
 458
 459
 460 /**
 461  * Calc log base 2
 462  */
 463 static INLINE unsigned
 464 util_logbase2(unsigned n)
 465 {
 466    unsigned log2 = 0;
 467    while (n >>= 1)
 468       ++log2;
 469    return log2;
 470 }
 471
 472
 473 /**
 474  * Returns the smallest power of two >= x
 475  */
 476 static INLINE unsigned
 477 util_next_power_of_two(unsigned x)
 478 {
 479    unsigned i;
 480
 481    if (x == 0)
 482       return 1;
 483
 484    --x;
 485
 486    for (i = 1; i < sizeof(unsigned) * 8; i <<= 1)
 487       x |= x >> i;
 488
 489    return x + 1;
 490 }
 491
 492
 493 /**
 494  * Clamp X to [MIN, MAX].
 495  * This is a macro to allow float, int, uint, etc. types.
 496  */
 497 #define CLAMP( X, MIN, MAX )  ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
 498
 499 #define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
 500 #define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
 501
 502
 503 static INLINE int
 504 align(int value, int alignment)
 505 {
 506    return (value + alignment - 1) & ~(alignment - 1);
 507 }
 508
 509 static INLINE unsigned
 510 minify(unsigned value)
 511 {
 512     return MAX2(1, value >> 1);
 513 }
 514
 515 #ifndef COPY_4V
 516 #define COPY_4V( DST, SRC )         \
 517 do {                                \
 518    (DST)[0] = (SRC)[0];             \
 519    (DST)[1] = (SRC)[1];             \
 520    (DST)[2] = (SRC)[2];             \
 521    (DST)[3] = (SRC)[3];             \
 522 } while (0)
 523 #endif
 524
 525
 526 #ifndef COPY_4FV
 527 #define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
 528 #endif
 529
 530
 531 #ifndef ASSIGN_4V
 532 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
 533 do {                                     \
 534    (DST)[0] = (V0);                      \
 535    (DST)[1] = (V1);                      \
 536    (DST)[2] = (V2);                      \
 537    (DST)[3] = (V3);                      \
 538 } while (0)
 539 #endif
 540
 541
 542 #ifdef __cplusplus
 543 }
 544 #endif
 545
 546 #endif /* U_MATH_H */