4e58e505572e6d9280d3993d4225c373b6ab7cbf
[mesa.git] / src / gallium / auxiliary / util / u_math.h
1 /**************************************************************************
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3 * Copyright 2008 VMware, Inc.
4 * All Rights Reserved.
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13 *
14 * The above copyright notice and this permission notice (including the
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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
44 #include "c99_math.h"
45 #include <assert.h>
46 #include <float.h>
47 #include <stdarg.h>
48
49 #ifdef PIPE_OS_UNIX
50 #include <strings.h> /* for ffs */
51 #endif
52
53 #if defined(_MSC_VER)
54 #include <intrin.h>
55 #endif
56
57
58 #ifdef __cplusplus
59 extern "C" {
60 #endif
61
62
63 #ifndef M_SQRT2
64 #define M_SQRT2 1.41421356237309504880
65 #endif
66
67 #define POW2_TABLE_SIZE_LOG2 9
68 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
69 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
70 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
71 extern float pow2_table[POW2_TABLE_SIZE];
72
73
74 /**
75 * Initialize math module. This should be called before using any
76 * other functions in this module.
77 */
78 extern void
79 util_init_math(void);
80
81
82 union fi {
83 float f;
84 int32_t i;
85 uint32_t ui;
86 };
87
88
89 union di {
90 double d;
91 int64_t i;
92 uint64_t ui;
93 };
94
95
96 /**
97 * Extract the IEEE float32 exponent.
98 */
99 static inline signed
100 util_get_float32_exponent(float x)
101 {
102 union fi f;
103
104 f.f = x;
105
106 return ((f.ui >> 23) & 0xff) - 127;
107 }
108
109
110 /**
111 * Fast version of 2^x
112 * Identity: exp2(a + b) = exp2(a) * exp2(b)
113 * Let ipart = int(x)
114 * Let fpart = x - ipart;
115 * So, exp2(x) = exp2(ipart) * exp2(fpart)
116 * Compute exp2(ipart) with i << ipart
117 * Compute exp2(fpart) with lookup table.
118 */
119 static inline float
120 util_fast_exp2(float x)
121 {
122 int32_t ipart;
123 float fpart, mpart;
124 union fi epart;
125
126 if(x > 129.00000f)
127 return 3.402823466e+38f;
128
129 if (x < -126.99999f)
130 return 0.0f;
131
132 ipart = (int32_t) x;
133 fpart = x - (float) ipart;
134
135 /* same as
136 * epart.f = (float) (1 << ipart)
137 * but faster and without integer overflow for ipart > 31
138 */
139 epart.i = (ipart + 127 ) << 23;
140
141 mpart = pow2_table[POW2_TABLE_OFFSET + (int)(fpart * POW2_TABLE_SCALE)];
142
143 return epart.f * mpart;
144 }
145
146
147 /**
148 * Fast approximation to exp(x).
149 */
150 static inline float
151 util_fast_exp(float x)
152 {
153 const float k = 1.44269f; /* = log2(e) */
154 return util_fast_exp2(k * x);
155 }
156
157
158 #define LOG2_TABLE_SIZE_LOG2 16
159 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
160 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
161 extern float log2_table[LOG2_TABLE_SIZE];
162
163
164 /**
165 * Fast approximation to log2(x).
166 */
167 static inline float
168 util_fast_log2(float x)
169 {
170 union fi num;
171 float epart, mpart;
172 num.f = x;
173 epart = (float)(((num.i & 0x7f800000) >> 23) - 127);
174 /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
175 mpart = log2_table[((num.i & 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2))) >> (23 - LOG2_TABLE_SIZE_LOG2)];
176 return epart + mpart;
177 }
178
179
180 /**
181 * Fast approximation to x^y.
182 */
183 static inline float
184 util_fast_pow(float x, float y)
185 {
186 return util_fast_exp2(util_fast_log2(x) * y);
187 }
188
189 /* Note that this counts zero as a power of two.
190 */
191 static inline boolean
192 util_is_power_of_two( unsigned v )
193 {
194 return (v & (v-1)) == 0;
195 }
196
197
198 /**
199 * Floor(x), returned as int.
200 */
201 static inline int
202 util_ifloor(float f)
203 {
204 int ai, bi;
205 double af, bf;
206 union fi u;
207 af = (3 << 22) + 0.5 + (double) f;
208 bf = (3 << 22) + 0.5 - (double) f;
209 u.f = (float) af; ai = u.i;
210 u.f = (float) bf; bi = u.i;
211 return (ai - bi) >> 1;
212 }
213
214
215 /**
216 * Round float to nearest int.
217 */
218 static inline int
219 util_iround(float f)
220 {
221 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
222 int r;
223 __asm__ ("fistpl %0" : "=m" (r) : "t" (f) : "st");
224 return r;
225 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
226 int r;
227 _asm {
228 fld f
229 fistp r
230 }
231 return r;
232 #else
233 if (f >= 0.0f)
234 return (int) (f + 0.5f);
235 else
236 return (int) (f - 0.5f);
237 #endif
238 }
239
240
241 /**
242 * Approximate floating point comparison
243 */
244 static inline boolean
245 util_is_approx(float a, float b, float tol)
246 {
247 return fabsf(b - a) <= tol;
248 }
249
250
251 /**
252 * util_is_X_inf_or_nan = test if x is NaN or +/- Inf
253 * util_is_X_nan = test if x is NaN
254 * util_X_inf_sign = return +1 for +Inf, -1 for -Inf, or 0 for not Inf
255 *
256 * NaN can be checked with x != x, however this fails with the fast math flag
257 **/
258
259
260 /**
261 * Single-float
262 */
263 static inline boolean
264 util_is_inf_or_nan(float x)
265 {
266 union fi tmp;
267 tmp.f = x;
268 return (tmp.ui & 0x7f800000) == 0x7f800000;
269 }
270
271
272 static inline boolean
273 util_is_nan(float x)
274 {
275 union fi tmp;
276 tmp.f = x;
277 return (tmp.ui & 0x7fffffff) > 0x7f800000;
278 }
279
280
281 static inline int
282 util_inf_sign(float x)
283 {
284 union fi tmp;
285 tmp.f = x;
286 if ((tmp.ui & 0x7fffffff) != 0x7f800000) {
287 return 0;
288 }
289
290 return (x < 0) ? -1 : 1;
291 }
292
293
294 /**
295 * Double-float
296 */
297 static inline boolean
298 util_is_double_inf_or_nan(double x)
299 {
300 union di tmp;
301 tmp.d = x;
302 return (tmp.ui & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL;
303 }
304
305
306 static inline boolean
307 util_is_double_nan(double x)
308 {
309 union di tmp;
310 tmp.d = x;
311 return (tmp.ui & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL;
312 }
313
314
315 static inline int
316 util_double_inf_sign(double x)
317 {
318 union di tmp;
319 tmp.d = x;
320 if ((tmp.ui & 0x7fffffffffffffffULL) != 0x7ff0000000000000ULL) {
321 return 0;
322 }
323
324 return (x < 0) ? -1 : 1;
325 }
326
327
328 /**
329 * Half-float
330 */
331 static inline boolean
332 util_is_half_inf_or_nan(int16_t x)
333 {
334 return (x & 0x7c00) == 0x7c00;
335 }
336
337
338 static inline boolean
339 util_is_half_nan(int16_t x)
340 {
341 return (x & 0x7fff) > 0x7c00;
342 }
343
344
345 static inline int
346 util_half_inf_sign(int16_t x)
347 {
348 if ((x & 0x7fff) != 0x7c00) {
349 return 0;
350 }
351
352 return (x < 0) ? -1 : 1;
353 }
354
355
356 /**
357 * Find first bit set in word. Least significant bit is 1.
358 * Return 0 if no bits set.
359 */
360 #ifndef FFS_DEFINED
361 #define FFS_DEFINED 1
362
363 #if defined(_MSC_VER) && (_M_IX86 || _M_AMD64 || _M_IA64)
364 static inline
365 unsigned long ffs( unsigned long u )
366 {
367 unsigned long i;
368 if (_BitScanForward(&i, u))
369 return i + 1;
370 else
371 return 0;
372 }
373 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
374 static inline
375 unsigned ffs( unsigned u )
376 {
377 unsigned i;
378
379 if (u == 0) {
380 return 0;
381 }
382
383 __asm bsf eax, [u]
384 __asm inc eax
385 __asm mov [i], eax
386
387 return i;
388 }
389 #elif defined(__MINGW32__) || defined(PIPE_OS_ANDROID) || \
390 defined(HAVE___BUILTIN_FFS)
391 #define ffs __builtin_ffs
392 #endif
393
394 #ifdef HAVE___BUILTIN_FFSLL
395 #define ffsll __builtin_ffsll
396 #else
397 static inline int
398 ffsll(long long int val)
399 {
400 int bit;
401
402 bit = ffs((unsigned) (val & 0xffffffff));
403 if (bit != 0)
404 return bit;
405
406 bit = ffs((unsigned) (val >> 32));
407 if (bit != 0)
408 return 32 + bit;
409
410 return 0;
411 }
412 #endif
413
414 #endif /* FFS_DEFINED */
415
416 /**
417 * Find first bit set in long long. Least significant bit is 1.
418 * Return 0 if no bits set.
419 */
420 #ifndef FFSLL_DEFINED
421 #define FFSLL_DEFINED 1
422
423 #if defined(__MINGW32__) || defined(PIPE_OS_ANDROID) || \
424 defined(HAVE___BUILTIN_FFSLL)
425 #define ffsll __builtin_ffsll
426 #endif
427
428 #endif /* FFSLL_DEFINED */
429
430 /**
431 * Find last bit set in a word. The least significant bit is 1.
432 * Return 0 if no bits are set.
433 */
434 static inline unsigned
435 util_last_bit(unsigned u)
436 {
437 #if defined(HAVE___BUILTIN_CLZ)
438 return u == 0 ? 0 : 32 - __builtin_clz(u);
439 #else
440 unsigned r = 0;
441 while (u) {
442 r++;
443 u >>= 1;
444 }
445 return r;
446 #endif
447 }
448
449 /**
450 * Find last bit set in a word. The least significant bit is 1.
451 * Return 0 if no bits are set.
452 */
453 static inline unsigned
454 util_last_bit64(uint64_t u)
455 {
456 #if defined(HAVE___BUILTIN_CLZLL)
457 return u == 0 ? 0 : 64 - __builtin_clzll(u);
458 #else
459 unsigned r = 0;
460 while (u) {
461 r++;
462 u >>= 1;
463 }
464 return r;
465 #endif
466 }
467
468 /**
469 * Find last bit in a word that does not match the sign bit. The least
470 * significant bit is 1.
471 * Return 0 if no bits are set.
472 */
473 static inline unsigned
474 util_last_bit_signed(int i)
475 {
476 if (i >= 0)
477 return util_last_bit(i);
478 else
479 return util_last_bit(~(unsigned)i);
480 }
481
482 /* Destructively loop over all of the bits in a mask as in:
483 *
484 * while (mymask) {
485 * int i = u_bit_scan(&mymask);
486 * ... process element i
487 * }
488 *
489 */
490 static inline int
491 u_bit_scan(unsigned *mask)
492 {
493 int i = ffs(*mask) - 1;
494 *mask &= ~(1u << i);
495 return i;
496 }
497
498 #ifndef _MSC_VER
499 static inline int
500 u_bit_scan64(uint64_t *mask)
501 {
502 int i = ffsll(*mask) - 1;
503 *mask &= ~(1llu << i);
504 return i;
505 }
506 #endif
507
508 /* For looping over a bitmask when you want to loop over consecutive bits
509 * manually, for example:
510 *
511 * while (mask) {
512 * int start, count, i;
513 *
514 * u_bit_scan_consecutive_range(&mask, &start, &count);
515 *
516 * for (i = 0; i < count; i++)
517 * ... process element (start+i)
518 * }
519 */
520 static inline void
521 u_bit_scan_consecutive_range(unsigned *mask, int *start, int *count)
522 {
523 if (*mask == 0xffffffff) {
524 *start = 0;
525 *count = 32;
526 *mask = 0;
527 return;
528 }
529 *start = ffs(*mask) - 1;
530 *count = ffs(~(*mask >> *start)) - 1;
531 *mask &= ~(((1u << *count) - 1) << *start);
532 }
533
534 static inline void
535 u_bit_scan_consecutive_range64(uint64_t *mask, int *start, int *count)
536 {
537 if (*mask == ~0llu) {
538 *start = 0;
539 *count = 64;
540 *mask = 0;
541 return;
542 }
543 *start = ffsll(*mask) - 1;
544 *count = ffsll(~(*mask >> *start)) - 1;
545 *mask &= ~(((1llu << *count) - 1) << *start);
546 }
547
548 /**
549 * Return float bits.
550 */
551 static inline unsigned
552 fui( float f )
553 {
554 union fi fi;
555 fi.f = f;
556 return fi.ui;
557 }
558
559 static inline float
560 uif(uint32_t ui)
561 {
562 union fi fi;
563 fi.ui = ui;
564 return fi.f;
565 }
566
567
568 /**
569 * Convert ubyte to float in [0, 1].
570 * XXX a 256-entry lookup table would be slightly faster.
571 */
572 static inline float
573 ubyte_to_float(ubyte ub)
574 {
575 return (float) ub * (1.0f / 255.0f);
576 }
577
578
579 /**
580 * Convert float in [0,1] to ubyte in [0,255] with clamping.
581 */
582 static inline ubyte
583 float_to_ubyte(float f)
584 {
585 union fi tmp;
586
587 tmp.f = f;
588 if (tmp.i < 0) {
589 return (ubyte) 0;
590 }
591 else if (tmp.i >= 0x3f800000 /* 1.0f */) {
592 return (ubyte) 255;
593 }
594 else {
595 tmp.f = tmp.f * (255.0f/256.0f) + 32768.0f;
596 return (ubyte) tmp.i;
597 }
598 }
599
600 static inline float
601 byte_to_float_tex(int8_t b)
602 {
603 return (b == -128) ? -1.0F : b * 1.0F / 127.0F;
604 }
605
606 static inline int8_t
607 float_to_byte_tex(float f)
608 {
609 return (int8_t) (127.0F * f);
610 }
611
612 /**
613 * Calc log base 2
614 */
615 static inline unsigned
616 util_logbase2(unsigned n)
617 {
618 #if defined(HAVE___BUILTIN_CLZ)
619 return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n | 1));
620 #else
621 unsigned pos = 0;
622 if (n >= 1<<16) { n >>= 16; pos += 16; }
623 if (n >= 1<< 8) { n >>= 8; pos += 8; }
624 if (n >= 1<< 4) { n >>= 4; pos += 4; }
625 if (n >= 1<< 2) { n >>= 2; pos += 2; }
626 if (n >= 1<< 1) { pos += 1; }
627 return pos;
628 #endif
629 }
630
631
632 /**
633 * Returns the smallest power of two >= x
634 */
635 static inline unsigned
636 util_next_power_of_two(unsigned x)
637 {
638 #if defined(HAVE___BUILTIN_CLZ)
639 if (x <= 1)
640 return 1;
641
642 return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x - 1)));
643 #else
644 unsigned val = x;
645
646 if (x <= 1)
647 return 1;
648
649 if (util_is_power_of_two(x))
650 return x;
651
652 val--;
653 val = (val >> 1) | val;
654 val = (val >> 2) | val;
655 val = (val >> 4) | val;
656 val = (val >> 8) | val;
657 val = (val >> 16) | val;
658 val++;
659 return val;
660 #endif
661 }
662
663
664 /**
665 * Return number of bits set in n.
666 */
667 static inline unsigned
668 util_bitcount(unsigned n)
669 {
670 #if defined(HAVE___BUILTIN_POPCOUNT)
671 return __builtin_popcount(n);
672 #else
673 /* K&R classic bitcount.
674 *
675 * For each iteration, clear the LSB from the bitfield.
676 * Requires only one iteration per set bit, instead of
677 * one iteration per bit less than highest set bit.
678 */
679 unsigned bits;
680 for (bits = 0; n; bits++) {
681 n &= n - 1;
682 }
683 return bits;
684 #endif
685 }
686
687
688 static inline unsigned
689 util_bitcount64(uint64_t n)
690 {
691 #ifdef HAVE___BUILTIN_POPCOUNTLL
692 return __builtin_popcountll(n);
693 #else
694 return util_bitcount(n) + util_bitcount(n >> 32);
695 #endif
696 }
697
698
699 /**
700 * Reverse bits in n
701 * Algorithm taken from:
702 * http://stackoverflow.com/questions/9144800/c-reverse-bits-in-unsigned-integer
703 */
704 static inline unsigned
705 util_bitreverse(unsigned n)
706 {
707 n = ((n >> 1) & 0x55555555u) | ((n & 0x55555555u) << 1);
708 n = ((n >> 2) & 0x33333333u) | ((n & 0x33333333u) << 2);
709 n = ((n >> 4) & 0x0f0f0f0fu) | ((n & 0x0f0f0f0fu) << 4);
710 n = ((n >> 8) & 0x00ff00ffu) | ((n & 0x00ff00ffu) << 8);
711 n = ((n >> 16) & 0xffffu) | ((n & 0xffffu) << 16);
712 return n;
713 }
714
715 /**
716 * Convert from little endian to CPU byte order.
717 */
718
719 #ifdef PIPE_ARCH_BIG_ENDIAN
720 #define util_le64_to_cpu(x) util_bswap64(x)
721 #define util_le32_to_cpu(x) util_bswap32(x)
722 #define util_le16_to_cpu(x) util_bswap16(x)
723 #else
724 #define util_le64_to_cpu(x) (x)
725 #define util_le32_to_cpu(x) (x)
726 #define util_le16_to_cpu(x) (x)
727 #endif
728
729 #define util_cpu_to_le64(x) util_le64_to_cpu(x)
730 #define util_cpu_to_le32(x) util_le32_to_cpu(x)
731 #define util_cpu_to_le16(x) util_le16_to_cpu(x)
732
733 /**
734 * Reverse byte order of a 32 bit word.
735 */
736 static inline uint32_t
737 util_bswap32(uint32_t n)
738 {
739 #if defined(HAVE___BUILTIN_BSWAP32)
740 return __builtin_bswap32(n);
741 #else
742 return (n >> 24) |
743 ((n >> 8) & 0x0000ff00) |
744 ((n << 8) & 0x00ff0000) |
745 (n << 24);
746 #endif
747 }
748
749 /**
750 * Reverse byte order of a 64bit word.
751 */
752 static inline uint64_t
753 util_bswap64(uint64_t n)
754 {
755 #if defined(HAVE___BUILTIN_BSWAP64)
756 return __builtin_bswap64(n);
757 #else
758 return ((uint64_t)util_bswap32((uint32_t)n) << 32) |
759 util_bswap32((n >> 32));
760 #endif
761 }
762
763
764 /**
765 * Reverse byte order of a 16 bit word.
766 */
767 static inline uint16_t
768 util_bswap16(uint16_t n)
769 {
770 return (n >> 8) |
771 (n << 8);
772 }
773
774 static inline void*
775 util_memcpy_cpu_to_le32(void * restrict dest, const void * restrict src, size_t n)
776 {
777 #ifdef PIPE_ARCH_BIG_ENDIAN
778 size_t i, e;
779 assert(n % 4 == 0);
780
781 for (i = 0, e = n / 4; i < e; i++) {
782 uint32_t * restrict d = (uint32_t* restrict)dest;
783 const uint32_t * restrict s = (const uint32_t* restrict)src;
784 d[i] = util_bswap32(s[i]);
785 }
786 return dest;
787 #else
788 return memcpy(dest, src, n);
789 #endif
790 }
791
792 /**
793 * Clamp X to [MIN, MAX].
794 * This is a macro to allow float, int, uint, etc. types.
795 */
796 #define CLAMP( X, MIN, MAX ) ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
797
798 #define MIN2( A, B ) ( (A)<(B) ? (A) : (B) )
799 #define MAX2( A, B ) ( (A)>(B) ? (A) : (B) )
800
801 #define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
802 #define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))
803
804 #define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
805 #define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))
806
807
808 /**
809 * Align a value, only works pot alignemnts.
810 */
811 static inline int
812 align(int value, int alignment)
813 {
814 return (value + alignment - 1) & ~(alignment - 1);
815 }
816
817 static inline uint64_t
818 align64(uint64_t value, unsigned alignment)
819 {
820 return (value + alignment - 1) & ~(alignment - 1);
821 }
822
823 /**
824 * Works like align but on npot alignments.
825 */
826 static inline size_t
827 util_align_npot(size_t value, size_t alignment)
828 {
829 if (value % alignment)
830 return value + (alignment - (value % alignment));
831 return value;
832 }
833
834 static inline unsigned
835 u_minify(unsigned value, unsigned levels)
836 {
837 return MAX2(1, value >> levels);
838 }
839
840 #ifndef COPY_4V
841 #define COPY_4V( DST, SRC ) \
842 do { \
843 (DST)[0] = (SRC)[0]; \
844 (DST)[1] = (SRC)[1]; \
845 (DST)[2] = (SRC)[2]; \
846 (DST)[3] = (SRC)[3]; \
847 } while (0)
848 #endif
849
850
851 #ifndef COPY_4FV
852 #define COPY_4FV( DST, SRC ) COPY_4V(DST, SRC)
853 #endif
854
855
856 #ifndef ASSIGN_4V
857 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
858 do { \
859 (DST)[0] = (V0); \
860 (DST)[1] = (V1); \
861 (DST)[2] = (V2); \
862 (DST)[3] = (V3); \
863 } while (0)
864 #endif
865
866
867 static inline uint32_t
868 util_unsigned_fixed(float value, unsigned frac_bits)
869 {
870 return value < 0 ? 0 : (uint32_t)(value * (1<<frac_bits));
871 }
872
873 static inline int32_t
874 util_signed_fixed(float value, unsigned frac_bits)
875 {
876 return (int32_t)(value * (1<<frac_bits));
877 }
878
879 unsigned
880 util_fpstate_get(void);
881 unsigned
882 util_fpstate_set_denorms_to_zero(unsigned current_fpstate);
883 void
884 util_fpstate_set(unsigned fpstate);
885
886
887
888 #ifdef __cplusplus
889 }
890 #endif
891
892 #endif /* U_MATH_H */