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 extern void
 194 util_init_math(void);
 195
 196
 197 union fi {
 198    float f;
 199    int32_t i;
 200    uint32_t ui;
 201 };
 202
 203
 204 /**
 205  * Fast version of 2^x
 206  * Identity: exp2(a + b) = exp2(a) * exp2(b)
 207  * Let ipart = int(x)
 208  * Let fpart = x - ipart;
 209  * So, exp2(x) = exp2(ipart) * exp2(fpart)
 210  * Compute exp2(ipart) with i << ipart
 211  * Compute exp2(fpart) with lookup table.
 212  */
 213 static INLINE float
 214 util_fast_exp2(float x)
 215 {
 216    int32_t ipart;
 217    float fpart, mpart;
 218    union fi epart;
 219
 220    if(x > 129.00000f)
 221       return 3.402823466e+38f;
 222
 223    if(x < -126.99999f)
 224       return 0.0f;
 225
 226    ipart = (int32_t) x;
 227    fpart = x - (float) ipart;
 228
 229    /* same as
 230     *   epart.f = (float) (1 << ipart)
 231     * but faster and without integer overflow for ipart > 31 */
 232    epart.i = (ipart + 127 ) << 23;
 233
 234    mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];
 235
 236    return epart.f * mpart;
 237 }
 238
 239
 240 /**
 241  * Fast approximation to exp(x).
 242  */
 243 static INLINE float
 244 util_fast_exp(float x)
 245 {
 246    const float k = 1.44269f; /* = log2(e) */
 247    return util_fast_exp2(k * x);
 248 }
 249
 250
 251 #define LOG2_TABLE_SIZE_LOG2 16
 252 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
 253 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
 254 extern float log2_table[LOG2_TABLE_SIZE];
 255
 256
 257 static INLINE float
 258 util_fast_log2(float x)
 259 {
 260    union fi num;
 261    float epart, mpart;
 262    num.f = x;
 263    epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
 264    /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
 265    mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)];
 266    return epart + mpart;
 267 }
 268
 269
 270 static INLINE float
 271 util_fast_pow(float x, float y)
 272 {
 273    return util_fast_exp2(util_fast_log2(x) * y);
 274 }
 275
 276
 277
 278 /**
 279  * Floor(x), returned as int.
 280  */
 281 static INLINE int
 282 util_ifloor(float f)
 283 {
 284    int ai, bi;
 285    double af, bf;
 286    union fi u;
 287    af = (3 << 22) + 0.5 + (double)f;
 288    bf = (3 << 22) + 0.5 - (double)f;
 289    u.f = (float) af;  ai = u.i;
 290    u.f = (float) bf;  bi = u.i;
 291    return (ai - bi) >> 1;
 292 }
 293
 294
 295 /**
 296  * Round float to nearest int.
 297  */
 298 static INLINE int
 299 util_iround(float f)
 300 {
 301 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
 302    int r;
 303    __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
 304    return r;
 305 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 306    int r;
 307    _asm {
 308          fld f
 309          fistp r
 310         }
 311    return r;
 312 #else
 313    if (f >= 0.0f)
 314       return (int) (f + 0.5f);
 315    else
 316       return (int) (f - 0.5f);
 317 #endif
 318 }
 319
 320
 321
 322 /**
 323  * Test if x is NaN or +/- infinity.
 324  */
 325 static INLINE boolean
 326 util_is_inf_or_nan(float x)
 327 {
 328    union fi tmp;
 329    tmp.f = x;
 330    return !(int)((unsigned int)((tmp.i & 0x7fffffff)-0x7f800000) >> 31);
 331 }
 332
 333
 334 /**
 335  * Find first bit set in word.  Least significant bit is 1.
 336  * Return 0 if no bits set.
 337  */
 338 #if defined(_MSC_VER) && _MSC_VER >= 1300
 339 static INLINE
 340 unsigned long ffs( unsigned long u )
 341 {
 342    unsigned long i;
 343    if(_BitScanForward(&i, u))
 344       return i + 1;
 345    else
 346       return 0;
 347 }
 348 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 349 static INLINE
 350 unsigned ffs( unsigned u )
 351 {
 352    unsigned i;
 353
 354    if( u == 0 ) {
 355       return 0;
 356    }
 357
 358    __asm bsf eax, [u]
 359    __asm inc eax
 360    __asm mov [i], eax
 361
 362    return i;
 363 }
 364 #elif defined(__MINGW32__)
 365 #define ffs __builtin_ffs
 366 #endif
 367
 368
 369 /* Could also binary search for the highest bit.
 370  */
 371 static INLINE unsigned
 372 util_unsigned_logbase2(unsigned n)
 373 {
 374    unsigned log2 = 0;
 375    while (n >>= 1)
 376       ++log2;
 377    return log2;
 378 }
 379
 380
 381 /**
 382  * Return float bits.
 383  */
 384 static INLINE unsigned
 385 fui( float f )
 386 {
 387    union fi fi;
 388    fi.f = f;
 389    return fi.ui;
 390 }
 391
 392
 393
 394 static INLINE float
 395 ubyte_to_float(ubyte ub)
 396 {
 397    return (float) ub * (1.0f / 255.0f);
 398 }
 399
 400
 401 /**
 402  * Convert float in [0,1] to ubyte in [0,255] with clamping.
 403  */
 404 static INLINE ubyte
 405 float_to_ubyte(float f)
 406 {
 407    const int ieee_0996 = 0x3f7f0000;   /* 0.996 or so */
 408    union fi tmp;
 409
 410    tmp.f = f;
 411    if (tmp.i < 0) {
 412       return (ubyte) 0;
 413    }
 414    else if (tmp.i >= ieee_0996) {
 415       return (ubyte) 255;
 416    }
 417    else {
 418       tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
 419       return (ubyte) tmp.i;
 420    }
 421 }
 422
 423
 424
 425 #define CLAMP( X, MIN, MAX )  ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
 426
 427 #define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
 428 #define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
 429
 430
 431 static INLINE int
 432 align(int value, int alignment)
 433 {
 434    return (value + alignment - 1) & ~(alignment - 1);
 435 }
 436
 437
 438 #ifndef COPY_4V
 439 #define COPY_4V( DST, SRC )         \
 440 do {                                \
 441    (DST)[0] = (SRC)[0];             \
 442    (DST)[1] = (SRC)[1];             \
 443    (DST)[2] = (SRC)[2];             \
 444    (DST)[3] = (SRC)[3];             \
 445 } while (0)
 446 #endif
 447
 448
 449 #ifndef COPY_4FV
 450 #define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
 451 #endif
 452
 453
 454 #ifndef ASSIGN_4V
 455 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
 456 do {                                     \
 457    (DST)[0] = (V0);                      \
 458    (DST)[1] = (V1);                      \
 459    (DST)[2] = (V2);                      \
 460    (DST)[3] = (V3);                      \
 461 } while (0)
 462 #endif
 463
 464
 465 #ifdef __cplusplus
 466 }
 467 #endif
 468
 469 #endif /* U_MATH_H */