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
47extern "C" {
48#endif
49
50
51#include <math.h>
52#include <stdarg.h>
53
54#ifdef PIPE_OS_UNIX
55#include <strings.h> /* for ffs */
56#endif
57
58
59#ifndef M_SQRT2
60#define M_SQRT2 1.41421356237309504880
61#endif
62
63
64#if defined(_MSC_VER)
65
66#if _MSC_VER < 1400 && !defined(__cplusplus)
67
68static INLINE float cosf( float f )
69{
70   return (float) cos( (double) f );
71}
72
73static INLINE float sinf( float f )
74{
75   return (float) sin( (double) f );
76}
77
78static INLINE float ceilf( float f )
79{
80   return (float) ceil( (double) f );
81}
82
83static INLINE float floorf( float f )
84{
85   return (float) floor( (double) f );
86}
87
88static INLINE float powf( float f, float g )
89{
90   return (float) pow( (double) f, (double) g );
91}
92
93static INLINE float sqrtf( float f )
94{
95   return (float) sqrt( (double) f );
96}
97
98static INLINE float fabsf( float f )
99{
100   return (float) fabs( (double) f );
101}
102
103static INLINE float logf( float f )
104{
105   return (float) log( (double) f );
106}
107
108#else
109/* Work-around an extra semi-colon in VS 2005 logf definition */
110#ifdef logf
111#undef logf
112#define logf(x) ((float)log((double)(x)))
113#endif /* logf */
114
115#if _MSC_VER < 1800
116#define isfinite(x) _finite((double)(x))
117#define isnan(x) _isnan((double)(x))
118#endif /* _MSC_VER < 1800 */
119#endif /* _MSC_VER < 1400 && !defined(__cplusplus) */
120
121#if _MSC_VER < 1800
122static INLINE double log2( double x )
123{
124   const double invln2 = 1.442695041;
125   return log( x ) * invln2;
126}
127
128static INLINE double
129round(double x)
130{
131   return x >= 0.0 ? floor(x + 0.5) : ceil(x - 0.5);
132}
133
134static INLINE float
135roundf(float x)
136{
137   return x >= 0.0f ? floorf(x + 0.5f) : ceilf(x - 0.5f);
138}
139#endif
140
141#endif /* _MSC_VER */
142
143#define POW2_TABLE_SIZE_LOG2 9
144#define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
145#define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
146#define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
147extern float pow2_table[POW2_TABLE_SIZE];
148
149
150/**
151 * Initialize math module.  This should be called before using any
152 * other functions in this module.
153 */
154extern void
155util_init_math(void);
156
157
158union fi {
159   float f;
160   int32_t i;
161   uint32_t ui;
162};
163
164
165union di {
166   double d;
167   int64_t i;
168   uint64_t ui;
169};
170
171
172/**
173 * Fast version of 2^x
174 * Identity: exp2(a + b) = exp2(a) * exp2(b)
175 * Let ipart = int(x)
176 * Let fpart = x - ipart;
177 * So, exp2(x) = exp2(ipart) * exp2(fpart)
178 * Compute exp2(ipart) with i << ipart
179 * Compute exp2(fpart) with lookup table.
180 */
181static INLINE float
182util_fast_exp2(float x)
183{
184   int32_t ipart;
185   float fpart, mpart;
186   union fi epart;
187
188   if(x > 129.00000f)
189      return 3.402823466e+38f;
190
191   if (x < -126.99999f)
192      return 0.0f;
193
194   ipart = (int32_t) x;
195   fpart = x - (float) ipart;
196
197   /* same as
198    *   epart.f = (float) (1 << ipart)
199    * but faster and without integer overflow for ipart > 31
200    */
201   epart.i = (ipart + 127 ) << 23;
202
203   mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];
204
205   return epart.f * mpart;
206}
207
208
209/**
210 * Fast approximation to exp(x).
211 */
212static INLINE float
213util_fast_exp(float x)
214{
215   const float k = 1.44269f; /* = log2(e) */
216   return util_fast_exp2(k * x);
217}
218
219
220#define LOG2_TABLE_SIZE_LOG2 16
221#define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
222#define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
223extern float log2_table[LOG2_TABLE_SIZE];
224
225
226/**
227 * Fast approximation to log2(x).
228 */
229static INLINE float
230util_fast_log2(float x)
231{
232   union fi num;
233   float epart, mpart;
234   num.f = x;
235   epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
236   /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
237   mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)];
238   return epart + mpart;
239}
240
241
242/**
243 * Fast approximation to x^y.
244 */
245static INLINE float
246util_fast_pow(float x, float y)
247{
248   return util_fast_exp2(util_fast_log2(x) * y);
249}
250
251/* Note that this counts zero as a power of two.
252 */
253static INLINE boolean
254util_is_power_of_two( unsigned v )
255{
256   return (v & (v-1)) == 0;
257}
258
259
260/**
261 * Floor(x), returned as int.
262 */
263static INLINE int
264util_ifloor(float f)
265{
266   int ai, bi;
267   double af, bf;
268   union fi u;
269   af = (3 << 22) + 0.5 + (double) f;
270   bf = (3 << 22) + 0.5 - (double) f;
271   u.f = (float) af;  ai = u.i;
272   u.f = (float) bf;  bi = u.i;
273   return (ai - bi) >> 1;
274}
275
276
277/**
278 * Round float to nearest int.
279 */
280static INLINE int
281util_iround(float f)
282{
283#if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
284   int r;
285   __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
286   return r;
287#elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
288   int r;
289   _asm {
290      fld f
291      fistp r
292   }
293   return r;
294#else
295   if (f >= 0.0f)
296      return (int) (f + 0.5f);
297   else
298      return (int) (f - 0.5f);
299#endif
300}
301
302
303/**
304 * Approximate floating point comparison
305 */
306static INLINE boolean
307util_is_approx(float a, float b, float tol)
308{
309   return fabs(b - a) <= tol;
310}
311
312
313/**
314 * util_is_X_inf_or_nan = test if x is NaN or +/- Inf
315 * util_is_X_nan        = test if x is NaN
316 * util_X_inf_sign      = return +1 for +Inf, -1 for -Inf, or 0 for not Inf
317 *
318 * NaN can be checked with x != x, however this fails with the fast math flag
319 **/
320
321
322/**
323 * Single-float
324 */
325static INLINE boolean
326util_is_inf_or_nan(float x)
327{
328   union fi tmp;
329   tmp.f = x;
330   return (tmp.ui & 0x7f800000) == 0x7f800000;
331}
332
333
334static INLINE boolean
335util_is_nan(float x)
336{
337   union fi tmp;
338   tmp.f = x;
339   return (tmp.ui & 0x7fffffff) > 0x7f800000;
340}
341
342
343static INLINE int
344util_inf_sign(float x)
345{
346   union fi tmp;
347   tmp.f = x;
348   if ((tmp.ui & 0x7fffffff) != 0x7f800000) {
349      return 0;
350   }
351
352   return (x < 0) ? -1 : 1;
353}
354
355
356/**
357 * Double-float
358 */
359static INLINE boolean
360util_is_double_inf_or_nan(double x)
361{
362   union di tmp;
363   tmp.d = x;
364   return (tmp.ui & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL;
365}
366
367
368static INLINE boolean
369util_is_double_nan(double x)
370{
371   union di tmp;
372   tmp.d = x;
373   return (tmp.ui & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL;
374}
375
376
377static INLINE int
378util_double_inf_sign(double x)
379{
380   union di tmp;
381   tmp.d = x;
382   if ((tmp.ui & 0x7fffffffffffffffULL) != 0x7ff0000000000000ULL) {
383      return 0;
384   }
385
386   return (x < 0) ? -1 : 1;
387}
388
389
390/**
391 * Half-float
392 */
393static INLINE boolean
394util_is_half_inf_or_nan(int16_t x)
395{
396   return (x & 0x7c00) == 0x7c00;
397}
398
399
400static INLINE boolean
401util_is_half_nan(int16_t x)
402{
403   return (x & 0x7fff) > 0x7c00;
404}
405
406
407static INLINE int
408util_half_inf_sign(int16_t x)
409{
410   if ((x & 0x7fff) != 0x7c00) {
411      return 0;
412   }
413
414   return (x < 0) ? -1 : 1;
415}
416
417
418/**
419 * Find first bit set in word.  Least significant bit is 1.
420 * Return 0 if no bits set.
421 */
422#ifndef FFS_DEFINED
423#define FFS_DEFINED 1
424
425#if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64)
426unsigned char _BitScanForward(unsigned long* Index, unsigned long Mask);
427#pragma intrinsic(_BitScanForward)
428static INLINE
429unsigned long ffs( unsigned long u )
430{
431   unsigned long i;
432   if (_BitScanForward(&i, u))
433      return i + 1;
434   else
435      return 0;
436}
437#elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
438static INLINE
439unsigned ffs( unsigned u )
440{
441   unsigned i;
442
443   if (u == 0) {
444      return 0;
445   }
446
447   __asm bsf eax, [u]
448   __asm inc eax
449   __asm mov [i], eax
450
451   return i;
452}
453#elif defined(__MINGW32__) || defined(PIPE_OS_ANDROID)
454#define ffs __builtin_ffs
455#endif
456
457#endif /* FFS_DEFINED */
458
459/**
460 * Find last bit set in a word.  The least significant bit is 1.
461 * Return 0 if no bits are set.
462 */
463static INLINE unsigned util_last_bit(unsigned u)
464{
465   unsigned r = 0;
466   while (u) {
467       r++;
468       u >>= 1;
469   }
470   return r;
471}
472
473
474/* Destructively loop over all of the bits in a mask as in:
475 *
476 * while (mymask) {
477 *   int i = u_bit_scan(&mymask);
478 *   ... process element i
479 * }
480 *
481 */
482static INLINE int u_bit_scan(unsigned *mask)
483{
484   int i = ffs(*mask) - 1;
485   *mask &= ~(1 << i);
486   return i;
487}
488
489
490/**
491 * Return float bits.
492 */
493static INLINE unsigned
494fui( float f )
495{
496   union fi fi;
497   fi.f = f;
498   return fi.ui;
499}
500
501
502/**
503 * Convert ubyte to float in [0, 1].
504 * XXX a 256-entry lookup table would be slightly faster.
505 */
506static INLINE float
507ubyte_to_float(ubyte ub)
508{
509   return (float) ub * (1.0f / 255.0f);
510}
511
512
513/**
514 * Convert float in [0,1] to ubyte in [0,255] with clamping.
515 */
516static INLINE ubyte
517float_to_ubyte(float f)
518{
519   const int ieee_0996 = 0x3f7f0000;   /* 0.996 or so */
520   union fi tmp;
521
522   tmp.f = f;
523   if (tmp.i < 0) {
524      return (ubyte) 0;
525   }
526   else if (tmp.i >= ieee_0996) {
527      return (ubyte) 255;
528   }
529   else {
530      tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
531      return (ubyte) tmp.i;
532   }
533}
534
535static INLINE float
536byte_to_float_tex(int8_t b)
537{
538   return (b == -128) ? -1.0F : b * 1.0F / 127.0F;
539}
540
541static INLINE int8_t
542float_to_byte_tex(float f)
543{
544   return (int8_t) (127.0F * f);
545}
546
547/**
548 * Calc log base 2
549 */
550static INLINE unsigned
551util_logbase2(unsigned n)
552{
553#if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
554   return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1));
555#else
556   unsigned pos = 0;
557   if (n >= 1<<16) { n >>= 16; pos += 16; }
558   if (n >= 1<< 8) { n >>=  8; pos +=  8; }
559   if (n >= 1<< 4) { n >>=  4; pos +=  4; }
560   if (n >= 1<< 2) { n >>=  2; pos +=  2; }
561   if (n >= 1<< 1) {           pos +=  1; }
562   return pos;
563#endif
564}
565
566
567/**
568 * Returns the smallest power of two >= x
569 */
570static INLINE unsigned
571util_next_power_of_two(unsigned x)
572{
573#if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
574   if (x <= 1)
575       return 1;
576
577   return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1)));
578#else
579   unsigned val = x;
580
581   if (x <= 1)
582      return 1;
583
584   if (util_is_power_of_two(x))
585      return x;
586
587   val--;
588   val = (val >> 1) | val;
589   val = (val >> 2) | val;
590   val = (val >> 4) | val;
591   val = (val >> 8) | val;
592   val = (val >> 16) | val;
593   val++;
594   return val;
595#endif
596}
597
598
599/**
600 * Return number of bits set in n.
601 */
602static INLINE unsigned
603util_bitcount(unsigned n)
604{
605#if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 304)
606   return __builtin_popcount(n);
607#else
608   /* K&R classic bitcount.
609    *
610    * For each iteration, clear the LSB from the bitfield.
611    * Requires only one iteration per set bit, instead of
612    * one iteration per bit less than highest set bit.
613    */
614   unsigned bits = 0;
615   for (bits; n; bits++) {
616      n &= n - 1;
617   }
618   return bits;
619#endif
620}
621
622
623/**
624 * Convert from little endian to CPU byte order.
625 */
626
627#ifdef PIPE_ARCH_BIG_ENDIAN
628#define util_le32_to_cpu(x) util_bswap32(x)
629#define util_le16_to_cpu(x) util_bswap16(x)
630#else
631#define util_le32_to_cpu(x) (x)
632#define util_le16_to_cpu(x) (x)
633#endif
634
635
636/**
637 * Reverse byte order of a 32 bit word.
638 */
639static INLINE uint32_t
640util_bswap32(uint32_t n)
641{
642#if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 403)
643   return __builtin_bswap32(n);
644#else
645   return (n >> 24) |
646          ((n >> 8) & 0x0000ff00) |
647          ((n << 8) & 0x00ff0000) |
648          (n << 24);
649#endif
650}
651
652
653/**
654 * Reverse byte order of a 16 bit word.
655 */
656static INLINE uint16_t
657util_bswap16(uint16_t n)
658{
659   return (n >> 8) |
660          (n << 8);
661}
662
663
664/**
665 * Clamp X to [MIN, MAX].
666 * This is a macro to allow float, int, uint, etc. types.
667 */
668#define CLAMP( X, MIN, MAX )  ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
669
670#define MIN2( A, B )   ( (A)<(B) ? (A) : (B) )
671#define MAX2( A, B )   ( (A)>(B) ? (A) : (B) )
672
673#define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
674#define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))
675
676#define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
677#define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))
678
679
680/**
681 * Align a value, only works pot alignemnts.
682 */
683static INLINE int
684align(int value, int alignment)
685{
686   return (value + alignment - 1) & ~(alignment - 1);
687}
688
689/**
690 * Works like align but on npot alignments.
691 */
692static INLINE size_t
693util_align_npot(size_t value, size_t alignment)
694{
695   if (value % alignment)
696      return value + (alignment - (value % alignment));
697   return value;
698}
699
700static INLINE unsigned
701u_minify(unsigned value, unsigned levels)
702{
703    return MAX2(1, value >> levels);
704}
705
706#ifndef COPY_4V
707#define COPY_4V( DST, SRC )         \
708do {                                \
709   (DST)[0] = (SRC)[0];             \
710   (DST)[1] = (SRC)[1];             \
711   (DST)[2] = (SRC)[2];             \
712   (DST)[3] = (SRC)[3];             \
713} while (0)
714#endif
715
716
717#ifndef COPY_4FV
718#define COPY_4FV( DST, SRC )  COPY_4V(DST, SRC)
719#endif
720
721
722#ifndef ASSIGN_4V
723#define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
724do {                                     \
725   (DST)[0] = (V0);                      \
726   (DST)[1] = (V1);                      \
727   (DST)[2] = (V2);                      \
728   (DST)[3] = (V3);                      \
729} while (0)
730#endif
731
732
733static INLINE uint32_t util_unsigned_fixed(float value, unsigned frac_bits)
734{
735   return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits));
736}
737
738static INLINE int32_t util_signed_fixed(float value, unsigned frac_bits)
739{
740   return (int32_t)(value * (1<<frac_bits));
741}
742
743
744
745#ifdef __cplusplus
746}
747#endif
748
749#endif /* U_MATH_H */
750