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
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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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  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
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  21  * IN NO EVENT SHALL TUNGSTEN GRAPHICS AND/OR ITS SUPPLIERS BE LIABLE FOR
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  24  * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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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 "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
  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 256
 178 #define POW2_TABLE_SCALE ((float) (POW2_TABLE_SIZE-1))
 179 extern float pow2_table[POW2_TABLE_SIZE];
 180
 181
 182
 183 extern void
 184 util_init_math(void);
 185
 186
 187 union fi {
 188    float f;
 189    int i;
 190    unsigned ui;
 191 };
 192
 193
 194 /**
 195  * Fast approximation to exp(x).
 196  * Compute with base 2 exponents:  exp(x) = exp2(log2(e) * x)
 197  * Note: log2(e) is a constant, k = 1.44269
 198  * So, exp(x) = exp2(k * x);
 199  * Identity: exp2(a + b) = exp2(a) * exp2(b)
 200  * Let ipart = int(k*x)
 201  * Let fpart = k*x - ipart;
 202  * So, exp2(k*x) = exp2(ipart) * exp2(fpart)
 203  * Compute exp2(ipart) with i << ipart
 204  * Compute exp2(fpart) with lookup table.
 205  */
 206 static INLINE float
 207 util_fast_exp(float x)
 208 {
 209    if (x >= 0.0f) {
 210       float k = 1.44269f; /* = log2(e) */
 211       float kx = k * x;
 212       int ipart = (int) kx;
 213       float fpart = kx - (float) ipart;
 214       float y = (float) (1 << ipart)
 215          * pow2_table[(int) (fpart * POW2_TABLE_SCALE)];
 216       return y;
 217    }
 218    else {
 219       /* exp(-x) = 1.0 / exp(x) */
 220       float k = -1.44269f;
 221       float kx = k * x;
 222       int ipart = (int) kx;
 223       float fpart = kx - (float) ipart;
 224       float y = (float) (1 << ipart)
 225          * pow2_table[(int) (fpart * POW2_TABLE_SCALE)];
 226       return 1.0f / y;
 227    }
 228 }
 229
 230
 231 /**
 232  * Fast version of 2^x
 233  * XXX the above function could be implemented in terms of this one.
 234  */
 235 static INLINE float
 236 util_fast_exp2(float x)
 237 {
 238    if (x >= 0.0f) {
 239       int ipart = (int) x;
 240       float fpart = x - (float) ipart;
 241       float y = (float) (1 << ipart)
 242          * pow2_table[(int) (fpart * POW2_TABLE_SCALE)];
 243       return y;
 244    }
 245    else {
 246       /* exp(-x) = 1.0 / exp(x) */
 247       int ipart = (int) -x;
 248       float fpart = -x - (float) ipart;
 249       float y = (float) (1 << ipart)
 250          * pow2_table[(int) (fpart * POW2_TABLE_SCALE)];
 251       return 1.0f / y;
 252    }
 253 }
 254
 255
 256 /**
 257  * Based on code from http://www.flipcode.com/totd/
 258  */
 259 static INLINE float
 260 util_fast_log2(float val)
 261 {
 262    union fi num;
 263    int log_2;
 264    num.f = val;
 265    log_2 = ((num.i >> 23) & 255) - 128;
 266    num.i &= ~(255 << 23);
 267    num.i += 127 << 23;
 268    num.f = ((-1.0f/3) * num.f + 2) * num.f - 2.0f/3;
 269    return num.f + log_2;
 270 }
 271
 272
 273 static INLINE float
 274 util_fast_pow(float x, float y)
 275 {
 276    /* XXX these tests may need adjustment */
 277    if (y >= 3.0f && (-0.02f <= x && x <= 0.02f))
 278       return 0.0f;
 279    if (y >= 50.0f && (-0.9f <= x && x <= 0.9f))
 280       return 0.0f;
 281    return util_fast_exp2(util_fast_log2(x) * y);
 282 }
 283
 284
 285
 286 /**
 287  * Floor(x), returned as int.
 288  */
 289 static INLINE int
 290 util_ifloor(float f)
 291 {
 292    int ai, bi;
 293    double af, bf;
 294    union fi u;
 295    af = (3 << 22) + 0.5 + (double)f;
 296    bf = (3 << 22) + 0.5 - (double)f;
 297    u.f = (float) af;  ai = u.i;
 298    u.f = (float) bf;  bi = u.i;
 299    return (ai - bi) >> 1;
 300 }
 301
 302
 303 /**
 304  * Round float to nearest int.
 305  */
 306 static INLINE int
 307 util_iround(float f)
 308 {
 309 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
 310    int r;
 311    __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
 312    return r;
 313 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 314    int r;
 315    _asm {
 316          fld f
 317          fistp r
 318         }
 319    return r;
 320 #else
 321    if (f >= 0.0f)
 322       return (int) (f + 0.5f);
 323    else
 324       return (int) (f - 0.5f);
 325 #endif
 326 }
 327
 328
 329
 330 #if defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
 331 /**
 332  * Find first bit set in word.  Least significant bit is 1.
 333  * Return 0 if no bits set.
 334  */
 335 static INLINE
 336 unsigned ffs( unsigned u )
 337 {
 338    unsigned i;
 339
 340    if( u == 0 ) {
 341       return 0;
 342    }
 343
 344    __asm bsf eax, [u]
 345    __asm inc eax
 346    __asm mov [i], eax
 347
 348    return i;
 349 }
 350 #endif
 351
 352
 353 /**
 354  * Return float bits.
 355  */
 356 static INLINE unsigned
 357 fui( float f )
 358 {
 359    union fi fi;
 360    fi.f = f;
 361    return fi.ui;
 362 }
 363
 364
 365
 366 static INLINE float
 367 ubyte_to_float(ubyte ub)
 368 {
 369    return (float) ub * (1.0f / 255.0f);
 370 }
 371
 372
 373 /**
 374  * Convert float in [0,1] to ubyte in [0,255] with clamping.
 375  */
 376 static INLINE ubyte
 377 float_to_ubyte(float f)
 378 {
 379    const int ieee_0996 = 0x3f7f0000;   /* 0.996 or so */
 380    union fi tmp;
 381
 382    tmp.f = f;
 383    if (tmp.i < 0) {
 384       return (ubyte) 0;
 385    }
 386    else if (tmp.i >= ieee_0996) {
 387       return (ubyte) 255;
 388    }
 389    else {
 390       tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
 391       return (ubyte) tmp.i;
 392    }
 393 }
 394
 395
 396
 397 #define CLAMP( X, MIN, MAX )  ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
 398
 399 #define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
 400 #define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
 401
 402
 403 static INLINE int
 404 align(int value, int alignment)
 405 {
 406    return (value + alignment - 1) & ~(alignment - 1);
 407 }
 408
 409
 410 #ifndef COPY_4V
 411 #define COPY_4V( DST, SRC )         \
 412 do {                                \
 413    (DST)[0] = (SRC)[0];             \
 414    (DST)[1] = (SRC)[1];             \
 415    (DST)[2] = (SRC)[2];             \
 416    (DST)[3] = (SRC)[3];             \
 417 } while (0)
 418 #endif
 419
 420
 421 #ifndef COPY_4FV
 422 #define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
 423 #endif
 424
 425
 426 #ifndef ASSIGN_4V
 427 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
 428 do {                                     \
 429    (DST)[0] = (V0);                      \
 430    (DST)[1] = (V1);                      \
 431    (DST)[2] = (V2);                      \
 432    (DST)[3] = (V3);                      \
 433 } while (0)
 434 #endif
 435
 436
 437 #ifdef __cplusplus
 438 }
 439 #endif
 440
 441 #endif /* U_MATH_H */