aboutsummaryrefslogtreecommitdiff
path: root/mesalib/src/gallium/auxiliary/util/u_math.h
blob: 90b421ed841935d3ee430bc15d1bf3d7ed8c90e6 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
/**************************************************************************
 * 
 * Copyright 2008 Tungsten Graphics, Inc., Cedar Park, Texas.
 * All Rights Reserved.
 * 
 * Permission is hereby granted, free of charge, to any person obtaining a
 * copy of this software and associated documentation files (the
 * "Software"), to deal in the Software without restriction, including
 * without limitation the rights to use, copy, modify, merge, publish,
 * distribute, sub license, and/or sell copies of the Software, and to
 * permit persons to whom the Software is furnished to do so, subject to
 * the following conditions:
 * 
 * The above copyright notice and this permission notice (including the
 * next paragraph) shall be included in all copies or substantial portions
 * of the Software.
 * 
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT.
 * IN NO EVENT SHALL TUNGSTEN GRAPHICS AND/OR ITS SUPPLIERS BE LIABLE FOR
 * ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
 * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
 * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 * 
 **************************************************************************/


/**
 * Math utilities and approximations for common math functions.
 * Reduced precision is usually acceptable in shaders...
 *
 * "fast" is used in the names of functions which are low-precision,
 * or at least lower-precision than the normal C lib functions.
 */


#ifndef U_MATH_H
#define U_MATH_H


#include "pipe/p_compiler.h"
#include "util/u_debug.h"


#ifdef __cplusplus
extern "C" {
#endif


#include <math.h>
#include <stdarg.h>

#ifdef PIPE_OS_UNIX
#include <strings.h> /* for ffs */
#endif


#ifndef M_SQRT2
#define M_SQRT2 1.41421356237309504880
#endif


#if defined(_MSC_VER) 

#if _MSC_VER < 1400 && !defined(__cplusplus)
 
static INLINE float cosf( float f ) 
{
   return (float) cos( (double) f );
}

static INLINE float sinf( float f ) 
{
   return (float) sin( (double) f );
}

static INLINE float ceilf( float f ) 
{
   return (float) ceil( (double) f );
}

static INLINE float floorf( float f ) 
{
   return (float) floor( (double) f );
}

static INLINE float powf( float f, float g ) 
{
   return (float) pow( (double) f, (double) g );
}

static INLINE float sqrtf( float f ) 
{
   return (float) sqrt( (double) f );
}

static INLINE float fabsf( float f ) 
{
   return (float) fabs( (double) f );
}

static INLINE float logf( float f ) 
{
   return (float) log( (double) f );
}

#else
/* Work-around an extra semi-colon in VS 2005 logf definition */
#ifdef logf
#undef logf
#define logf(x) ((float)log((double)(x)))
#endif /* logf */

#define isfinite(x) _finite((double)(x))
#define isnan(x) _isnan((double)(x))
#endif /* _MSC_VER < 1400 && !defined(__cplusplus) */

static INLINE double log2( double x )
{
   const double invln2 = 1.442695041;
   return log( x ) * invln2;
}

static INLINE double
round(double x)
{
   return x >= 0.0 ? floor(x + 0.5) : ceil(x - 0.5);
}

static INLINE float
roundf(float x)
{
   return x >= 0.0f ? floorf(x + 0.5f) : ceilf(x - 0.5f);
}

#endif /* _MSC_VER */


#ifdef PIPE_OS_ANDROID

static INLINE
double log2(double d)
{
   return log(d) * (1.0 / M_LN2);
}

/* workaround a conflict with main/imports.h */
#ifdef log2f
#undef log2f
#endif

static INLINE
float log2f(float f)
{
   return logf(f) * (float) (1.0 / M_LN2);
}

#endif




#define POW2_TABLE_SIZE_LOG2 9
#define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
#define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
#define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
extern float pow2_table[POW2_TABLE_SIZE];


/**
 * Initialize math module.  This should be called before using any
 * other functions in this module.
 */
extern void
util_init_math(void);


union fi {
   float f;
   int32_t i;
   uint32_t ui;
};


union di {
   double d;
   int64_t i;
   uint64_t ui;
};


/**
 * Fast version of 2^x
 * Identity: exp2(a + b) = exp2(a) * exp2(b)
 * Let ipart = int(x)
 * Let fpart = x - ipart;
 * So, exp2(x) = exp2(ipart) * exp2(fpart)
 * Compute exp2(ipart) with i << ipart
 * Compute exp2(fpart) with lookup table.
 */
static INLINE float
util_fast_exp2(float x)
{
   int32_t ipart;
   float fpart, mpart;
   union fi epart;

   if(x > 129.00000f)
      return 3.402823466e+38f;

   if (x < -126.99999f)
      return 0.0f;

   ipart = (int32_t) x;
   fpart = x - (float) ipart;

   /* same as
    *   epart.f = (float) (1 << ipart)
    * but faster and without integer overflow for ipart > 31
    */
   epart.i = (ipart + 127 ) << 23;

   mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];

   return epart.f * mpart;
}


/**
 * Fast approximation to exp(x).
 */
static INLINE float
util_fast_exp(float x)
{
   const float k = 1.44269f; /* = log2(e) */
   return util_fast_exp2(k * x);
}


#define LOG2_TABLE_SIZE_LOG2 16
#define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
#define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
extern float log2_table[LOG2_TABLE_SIZE];


/**
 * Fast approximation to log2(x).
 */
static INLINE float
util_fast_log2(float x)
{
   union fi num;
   float epart, mpart;
   num.f = x;
   epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
   /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
   mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)];
   return epart + mpart;
}


/**
 * Fast approximation to x^y.
 */
static INLINE float
util_fast_pow(float x, float y)
{
   return util_fast_exp2(util_fast_log2(x) * y);
}

/* Note that this counts zero as a power of two.
 */
static INLINE boolean
util_is_power_of_two( unsigned v )
{
   return (v & (v-1)) == 0;
}


/**
 * Floor(x), returned as int.
 */
static INLINE int
util_ifloor(float f)
{
   int ai, bi;
   double af, bf;
   union fi u;
   af = (3 << 22) + 0.5 + (double) f;
   bf = (3 << 22) + 0.5 - (double) f;
   u.f = (float) af;  ai = u.i;
   u.f = (float) bf;  bi = u.i;
   return (ai - bi) >> 1;
}


/**
 * Round float to nearest int.
 */
static INLINE int
util_iround(float f)
{
#if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86) 
   int r;
   __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
   return r;
#elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
   int r;
   _asm {
      fld f
      fistp r
   }
   return r;
#else
   if (f >= 0.0f)
      return (int) (f + 0.5f);
   else
      return (int) (f - 0.5f);
#endif
}


/**
 * Approximate floating point comparison
 */
static INLINE boolean
util_is_approx(float a, float b, float tol)
{
   return fabs(b - a) <= tol;
}


/**
 * util_is_X_inf_or_nan = test if x is NaN or +/- Inf
 * util_is_X_nan        = test if x is NaN
 * util_X_inf_sign      = return +1 for +Inf, -1 for -Inf, or 0 for not Inf
 *
 * NaN can be checked with x != x, however this fails with the fast math flag
 **/


/**
 * Single-float
 */
static INLINE boolean
util_is_inf_or_nan(float x)
{
   union fi tmp;
   tmp.f = x;
   return (tmp.ui & 0x7f800000) == 0x7f800000;
}


static INLINE boolean
util_is_nan(float x)
{
   union fi tmp;
   tmp.f = x;
   return (tmp.ui & 0x7fffffff) > 0x7f800000;
}


static INLINE int
util_inf_sign(float x)
{
   union fi tmp;
   tmp.f = x;
   if ((tmp.ui & 0x7fffffff) != 0x7f800000) {
      return 0;
   }

   return (x < 0) ? -1 : 1;
}


/**
 * Double-float
 */
static INLINE boolean
util_is_double_inf_or_nan(double x)
{
   union di tmp;
   tmp.d = x;
   return (tmp.ui & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL;
}


static INLINE boolean
util_is_double_nan(double x)
{
   union di tmp;
   tmp.d = x;
   return (tmp.ui & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL;
}


static INLINE int
util_double_inf_sign(double x)
{
   union di tmp;
   tmp.d = x;
   if ((tmp.ui & 0x7fffffffffffffffULL) != 0x7ff0000000000000ULL) {
      return 0;
   }

   return (x < 0) ? -1 : 1;
}


/**
 * Half-float
 */
static INLINE boolean
util_is_half_inf_or_nan(int16_t x)
{
   return (x & 0x7c00) == 0x7c00;
}


static INLINE boolean
util_is_half_nan(int16_t x)
{
   return (x & 0x7fff) > 0x7c00;
}


static INLINE int
util_half_inf_sign(int16_t x)
{
   if ((x & 0x7fff) != 0x7c00) {
      return 0;
   }

   return (x < 0) ? -1 : 1;
}


/**
 * Find first bit set in word.  Least significant bit is 1.
 * Return 0 if no bits set.
 */
#ifndef FFS_DEFINED
#define FFS_DEFINED 1

#if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64)
unsigned char _BitScanForward(unsigned long* Index, unsigned long Mask);
#pragma intrinsic(_BitScanForward)
static INLINE
unsigned long ffs( unsigned long u )
{
   unsigned long i;
   if (_BitScanForward(&i, u))
      return i + 1;
   else
      return 0;
}
#elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
static INLINE
unsigned ffs( unsigned u )
{
   unsigned i;

   if (u == 0) {
      return 0;
   }

   __asm bsf eax, [u]
   __asm inc eax
   __asm mov [i], eax

   return i;
}
#elif defined(__MINGW32__) || defined(PIPE_OS_ANDROID)
#define ffs __builtin_ffs
#endif

#endif /* FFS_DEFINED */

/**
 * Find last bit set in a word.  The least significant bit is 1.
 * Return 0 if no bits are set.
 */
static INLINE unsigned util_last_bit(unsigned u)
{
   unsigned r = 0;
   while (u) {
       r++;
       u >>= 1;
   }
   return r;
}


/* Destructively loop over all of the bits in a mask as in:
 *
 * while (mymask) {
 *   int i = u_bit_scan(&mymask);
 *   ... process element i
 * }
 * 
 */
static INLINE int u_bit_scan(unsigned *mask)
{
   int i = ffs(*mask) - 1;
   *mask &= ~(1 << i);
   return i;
}


/**
 * Return float bits.
 */
static INLINE unsigned
fui( float f )
{
   union fi fi;
   fi.f = f;
   return fi.ui;
}


/**
 * Convert ubyte to float in [0, 1].
 * XXX a 256-entry lookup table would be slightly faster.
 */
static INLINE float
ubyte_to_float(ubyte ub)
{
   return (float) ub * (1.0f / 255.0f);
}


/**
 * Convert float in [0,1] to ubyte in [0,255] with clamping.
 */
static INLINE ubyte
float_to_ubyte(float f)
{
   const int ieee_0996 = 0x3f7f0000;   /* 0.996 or so */
   union fi tmp;

   tmp.f = f;
   if (tmp.i < 0) {
      return (ubyte) 0;
   }
   else if (tmp.i >= ieee_0996) {
      return (ubyte) 255;
   }
   else {
      tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
      return (ubyte) tmp.i;
   }
}

static INLINE float
byte_to_float_tex(int8_t b)
{
   return (b == -128) ? -1.0F : b * 1.0F / 127.0F;
}

static INLINE int8_t
float_to_byte_tex(float f)
{
   return (int8_t) (127.0F * f);
}

/**
 * Calc log base 2
 */
static INLINE unsigned
util_logbase2(unsigned n)
{
#if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
   return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1));
#else
   unsigned pos = 0;
   if (n >= 1<<16) { n >>= 16; pos += 16; }
   if (n >= 1<< 8) { n >>=  8; pos +=  8; }
   if (n >= 1<< 4) { n >>=  4; pos +=  4; }
   if (n >= 1<< 2) { n >>=  2; pos +=  2; }
   if (n >= 1<< 1) {           pos +=  1; }
   return pos;
#endif
}


/**
 * Returns the smallest power of two >= x
 */
static INLINE unsigned
util_next_power_of_two(unsigned x)
{
#if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
   if (x <= 1)
       return 1;

   return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1)));
#else
   unsigned val = x;

   if (x <= 1)
      return 1;

   if (util_is_power_of_two(x))
      return x;

   val--;
   val = (val >> 1) | val;
   val = (val >> 2) | val;
   val = (val >> 4) | val;
   val = (val >> 8) | val;
   val = (val >> 16) | val;
   val++;
   return val;
#endif
}


/**
 * Return number of bits set in n.
 */
static INLINE unsigned
util_bitcount(unsigned n)
{
#if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
   return __builtin_popcount(n);
#else
   /* K&R classic bitcount.
    *
    * For each iteration, clear the LSB from the bitfield.
    * Requires only one iteration per set bit, instead of
    * one iteration per bit less than highest set bit.
    */
   unsigned bits = 0;
   for (bits; n; bits++) {
      n &= n - 1;
   }
   return bits;
#endif
}


/**
 * Convert from little endian to CPU byte order.
 */

#ifdef PIPE_ARCH_BIG_ENDIAN
#define util_le32_to_cpu(x) util_bswap32(x)
#define util_le16_to_cpu(x) util_bswap16(x)
#else
#define util_le32_to_cpu(x) (x)
#define util_le16_to_cpu(x) (x)
#endif


/**
 * Reverse byte order of a 32 bit word.
 */
static INLINE uint32_t
util_bswap32(uint32_t n)
{
#if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 403)
   return __builtin_bswap32(n);
#else
   return (n >> 24) |
          ((n >> 8) & 0x0000ff00) |
          ((n << 8) & 0x00ff0000) |
          (n << 24);
#endif
}


/**
 * Reverse byte order of a 16 bit word.
 */
static INLINE uint16_t
util_bswap16(uint16_t n)
{
   return (n >> 8) |
          (n << 8);
}


/**
 * Clamp X to [MIN, MAX].
 * This is a macro to allow float, int, uint, etc. types.
 */
#define CLAMP( X, MIN, MAX )  ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )

#define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
#define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )

#define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
#define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))

#define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
#define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))


/**
 * Align a value, only works pot alignemnts.
 */
static INLINE int
align(int value, int alignment)
{
   return (value + alignment - 1) & ~(alignment - 1);
}

/**
 * Works like align but on npot alignments.
 */
static INLINE size_t
util_align_npot(size_t value, size_t alignment)
{
   if (value % alignment)
      return value + (alignment - (value % alignment));
   return value;
}

static INLINE unsigned
u_minify(unsigned value, unsigned levels)
{
    return MAX2(1, value >> levels);
}

#ifndef COPY_4V
#define COPY_4V( DST, SRC )         \
do {                                \
   (DST)[0] = (SRC)[0];             \
   (DST)[1] = (SRC)[1];             \
   (DST)[2] = (SRC)[2];             \
   (DST)[3] = (SRC)[3];             \
} while (0)
#endif


#ifndef COPY_4FV
#define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
#endif


#ifndef ASSIGN_4V
#define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
do {                                     \
   (DST)[0] = (V0);                      \
   (DST)[1] = (V1);                      \
   (DST)[2] = (V2);                      \
   (DST)[3] = (V3);                      \
} while (0)
#endif


static INLINE uint32_t util_unsigned_fixed(float value, unsigned frac_bits)
{
   return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits));
}

static INLINE int32_t util_signed_fixed(float value, unsigned frac_bits)
{
   return (int32_t)(value * (1<<frac_bits));
}



#ifdef __cplusplus
}
#endif

#endif /* U_MATH_H */