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 "pipe/p_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 #if _MSC_VER < 1400 && !defined(__cplusplus) || defined(PIPE_SUBSYSTEM_WINDOWS_CE)
 123
 124 static INLINE float cosf( float f )
 125 {
 126    return (float) cos( (double) f );
 127 }
 128
 129 static INLINE float sinf( float f )
 130 {
 131    return (float) sin( (double) f );
 132 }
 133
 134 static INLINE float ceilf( float f )
 135 {
 136    return (float) ceil( (double) f );
 137 }
 138
 139 static INLINE float floorf( float f )
 140 {
 141    return (float) floor( (double) f );
 142 }
 143
 144 static INLINE float powf( float f, float g )
 145 {
 146    return (float) pow( (double) f, (double) g );
 147 }
 148
 149 static INLINE float sqrtf( float f )
 150 {
 151    return (float) sqrt( (double) f );
 152 }
 153
 154 static INLINE float fabsf( float f )
 155 {
 156    return (float) fabs( (double) f );
 157 }
 158
 159 static INLINE float logf( float f )
 160 {
 161    return (float) log( (double) f );
 162 }
 163
 164 #else
 165 /* Work-around an extra semi-colon in VS 2005 logf definition */
 166 #ifdef logf
 167 #undef logf
 168 #define logf(x) ((float)log((double)(x)))
 169 #endif /* logf */
 170 #endif
 171 #endif /* _MSC_VER */
 172
 173
 174
 175
 176
 177 #define POW2_TABLE_SIZE_LOG2 9
 178 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
 179 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
 180 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
 181 extern float pow2_table[POW2_TABLE_SIZE];
 182
 183
 184
 185 extern void
 186 util_init_math(void);
 187
 188
 189 union fi {
 190    float f;
 191    int32_t i;
 192    uint32_t ui;
 193 };
 194
 195
 196 /**
 197  * Fast version of 2^x
 198  * Identity: exp2(a + b) = exp2(a) * exp2(b)
 199  * Let ipart = int(x)
 200  * Let fpart = x - ipart;
 201  * So, exp2(x) = exp2(ipart) * exp2(fpart)
 202  * Compute exp2(ipart) with i << ipart
 203  * Compute exp2(fpart) with lookup table.
 204  */
 205 static INLINE float
 206 util_fast_exp2(float x)
 207 {
 208    int32_t ipart;
 209    float fpart, mpart;
 210    union fi epart;
 211
 212    if(x > 129.00000f)
 213       return 3.402823466e+38f;
 214
 215    if(x < -126.99999f)
 216       return 0.0f;
 217
 218    ipart = (int32_t) x;
 219    fpart = x - (float) ipart;
 220
 221    /* same as
 222     *   epart.f = (float) (1 << ipart)
 223     * but faster and without integer overflow for ipart > 31 */
 224    epart.i = (ipart + 127 ) << 23;
 225
 226    mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];
 227
 228    return epart.f * mpart;
 229 }
 230
 231
 232 /**
 233  * Fast approximation to exp(x).
 234  */
 235 static INLINE float
 236 util_fast_exp(float x)
 237 {
 238    const float k = 1.44269f; /* = log2(e) */
 239    return util_fast_exp2(k * x);
 240 }
 241
 242
 243 #define LOG2_TABLE_SIZE_LOG2 8
 244 #define LOG2_TABLE_SIZE (1 << LOG2_TABLE_SIZE_LOG2)
 245 extern float log2_table[LOG2_TABLE_SIZE];
 246
 247
 248 static INLINE float
 249 util_fast_log2(float x)
 250 {
 251    union fi num;
 252    float epart, mpart;
 253    num.f = x;
 254    epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
 255    mpart = log2_table[(num.i & 0x007fffff) >> (23 - LOG2_TABLE_SIZE_LOG2)];
 256    return epart + mpart;
 257 }
 258
 259
 260 static INLINE float
 261 util_fast_pow(float x, float y)
 262 {
 263    return util_fast_exp2(util_fast_log2(x) * y);
 264 }
 265
 266
 267
 268 /**
 269  * Floor(x), returned as int.
 270  */
 271 static INLINE int
 272 util_ifloor(float f)
 273 {
 274    int ai, bi;
 275    double af, bf;
 276    union fi u;
 277    af = (3 << 22) + 0.5 + (double)f;
 278    bf = (3 << 22) + 0.5 - (double)f;
 279    u.f = (float) af;  ai = u.i;
 280    u.f = (float) bf;  bi = u.i;
 281    return (ai - bi) >> 1;
 282 }
 283
 284
 285 /**
 286  * Round float to nearest int.
 287  */
 288 static INLINE int
 289 util_iround(float f)
 290 {
 291 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
 292    int r;
 293    __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
 294    return r;
 295 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 296    int r;
 297    _asm {
 298          fld f
 299          fistp r
 300         }
 301    return r;
 302 #else
 303    if (f >= 0.0f)
 304       return (int) (f + 0.5f);
 305    else
 306       return (int) (f - 0.5f);
 307 #endif
 308 }
 309
 310
 311
 312 #if defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 313 /**
 314  * Find first bit set in word.  Least significant bit is 1.
 315  * Return 0 if no bits set.
 316  */
 317 static INLINE
 318 unsigned ffs( unsigned u )
 319 {
 320    unsigned i;
 321
 322    if( u == 0 ) {
 323       return 0;
 324    }
 325
 326    __asm bsf eax, [u]
 327    __asm inc eax
 328    __asm mov [i], eax
 329
 330    return i;
 331 }
 332 #endif
 333
 334
 335 /**
 336  * Return float bits.
 337  */
 338 static INLINE unsigned
 339 fui( float f )
 340 {
 341    union fi fi;
 342    fi.f = f;
 343    return fi.ui;
 344 }
 345
 346
 347
 348 static INLINE float
 349 ubyte_to_float(ubyte ub)
 350 {
 351    return (float) ub * (1.0f / 255.0f);
 352 }
 353
 354
 355 /**
 356  * Convert float in [0,1] to ubyte in [0,255] with clamping.
 357  */
 358 static INLINE ubyte
 359 float_to_ubyte(float f)
 360 {
 361    const int ieee_0996 = 0x3f7f0000;   /* 0.996 or so */
 362    union fi tmp;
 363
 364    tmp.f = f;
 365    if (tmp.i < 0) {
 366       return (ubyte) 0;
 367    }
 368    else if (tmp.i >= ieee_0996) {
 369       return (ubyte) 255;
 370    }
 371    else {
 372       tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
 373       return (ubyte) tmp.i;
 374    }
 375 }
 376
 377
 378
 379 #define CLAMP( X, MIN, MAX )  ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
 380
 381 #define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
 382 #define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
 383
 384
 385 static INLINE int
 386 align(int value, int alignment)
 387 {
 388    return (value + alignment - 1) & ~(alignment - 1);
 389 }
 390
 391
 392 #ifndef COPY_4V
 393 #define COPY_4V( DST, SRC )         \
 394 do {                                \
 395    (DST)[0] = (SRC)[0];             \
 396    (DST)[1] = (SRC)[1];             \
 397    (DST)[2] = (SRC)[2];             \
 398    (DST)[3] = (SRC)[3];             \
 399 } while (0)
 400 #endif
 401
 402
 403 #ifndef COPY_4FV
 404 #define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
 405 #endif
 406
 407
 408 #ifndef ASSIGN_4V
 409 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
 410 do {                                     \
 411    (DST)[0] = (V0);                      \
 412    (DST)[1] = (V1);                      \
 413    (DST)[2] = (V2);                      \
 414    (DST)[3] = (V3);                      \
 415 } while (0)
 416 #endif
 417
 418
 419 #ifdef __cplusplus
 420 }
 421 #endif
 422
 423 #endif /* U_MATH_H */