1 /**************************************************************************
3 * Copyright 2008 VMware, Inc.
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:
14 * The above copyright notice and this permission notice (including the
15 * next paragraph) shall be included in all copies or substantial portions
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 VMWARE 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.
26 **************************************************************************/
30 * Math utilities and approximations for common math functions.
31 * Reduced precision is usually acceptable in shaders...
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.
55 #define M_SQRT2 1.41421356237309504880
58 #define POW2_TABLE_SIZE_LOG2 9
59 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
60 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
61 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
62 extern float pow2_table
[POW2_TABLE_SIZE
];
66 * Initialize math module. This should be called before using any
67 * other functions in this module.
88 * Extract the IEEE float32 exponent.
91 util_get_float32_exponent(float x
)
97 return ((f
.ui
>> 23) & 0xff) - 127;
102 * Fast version of 2^x
103 * Identity: exp2(a + b) = exp2(a) * exp2(b)
105 * Let fpart = x - ipart;
106 * So, exp2(x) = exp2(ipart) * exp2(fpart)
107 * Compute exp2(ipart) with i << ipart
108 * Compute exp2(fpart) with lookup table.
111 util_fast_exp2(float x
)
118 return 3.402823466e+38f
;
124 fpart
= x
- (float) ipart
;
127 * epart.f = (float) (1 << ipart)
128 * but faster and without integer overflow for ipart > 31
130 epart
.i
= (ipart
+ 127 ) << 23;
132 mpart
= pow2_table
[POW2_TABLE_OFFSET
+ (int)(fpart
* POW2_TABLE_SCALE
)];
134 return epart
.f
* mpart
;
139 * Fast approximation to exp(x).
142 util_fast_exp(float x
)
144 const float k
= 1.44269f
; /* = log2(e) */
145 return util_fast_exp2(k
* x
);
149 #define LOG2_TABLE_SIZE_LOG2 16
150 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
151 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
152 extern float log2_table
[LOG2_TABLE_SIZE
];
156 * Fast approximation to log2(x).
159 util_fast_log2(float x
)
164 epart
= (float)(((num
.i
& 0x7f800000) >> 23) - 127);
165 /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
166 mpart
= log2_table
[((num
.i
& 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2
))) >> (23 - LOG2_TABLE_SIZE_LOG2
)];
167 return epart
+ mpart
;
172 * Fast approximation to x^y.
175 util_fast_pow(float x
, float y
)
177 return util_fast_exp2(util_fast_log2(x
) * y
);
182 * Floor(x), returned as int.
190 af
= (3 << 22) + 0.5 + (double) f
;
191 bf
= (3 << 22) + 0.5 - (double) f
;
192 u
.f
= (float) af
; ai
= u
.i
;
193 u
.f
= (float) bf
; bi
= u
.i
;
194 return (ai
- bi
) >> 1;
199 * Round float to nearest int.
204 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
206 __asm__ ("fistpl %0" : "=m" (r
) : "t" (f
) : "st");
208 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
217 return (int) (f
+ 0.5f
);
219 return (int) (f
- 0.5f
);
225 * Approximate floating point comparison
228 util_is_approx(float a
, float b
, float tol
)
230 return fabsf(b
- a
) <= tol
;
235 * util_is_X_inf_or_nan = test if x is NaN or +/- Inf
236 * util_is_X_nan = test if x is NaN
237 * util_X_inf_sign = return +1 for +Inf, -1 for -Inf, or 0 for not Inf
239 * NaN can be checked with x != x, however this fails with the fast math flag
247 util_is_inf_or_nan(float x
)
251 return (tmp
.ui
& 0x7f800000) == 0x7f800000;
260 return (tmp
.ui
& 0x7fffffff) > 0x7f800000;
265 util_inf_sign(float x
)
269 if ((tmp
.ui
& 0x7fffffff) != 0x7f800000) {
273 return (x
< 0) ? -1 : 1;
281 util_is_double_inf_or_nan(double x
)
285 return (tmp
.ui
& 0x7ff0000000000000ULL
) == 0x7ff0000000000000ULL
;
290 util_is_double_nan(double x
)
294 return (tmp
.ui
& 0x7fffffffffffffffULL
) > 0x7ff0000000000000ULL
;
299 util_double_inf_sign(double x
)
303 if ((tmp
.ui
& 0x7fffffffffffffffULL
) != 0x7ff0000000000000ULL
) {
307 return (x
< 0) ? -1 : 1;
315 util_is_half_inf_or_nan(int16_t x
)
317 return (x
& 0x7c00) == 0x7c00;
322 util_is_half_nan(int16_t x
)
324 return (x
& 0x7fff) > 0x7c00;
329 util_half_inf_sign(int16_t x
)
331 if ((x
& 0x7fff) != 0x7c00) {
335 return (x
< 0) ? -1 : 1;
342 static inline unsigned
360 * Convert uint8_t to float in [0, 1].
363 ubyte_to_float(uint8_t ub
)
365 return (float) ub
* (1.0f
/ 255.0f
);
370 * Convert float in [0,1] to uint8_t in [0,255] with clamping.
372 static inline uint8_t
373 float_to_ubyte(float f
)
375 /* return 0 for NaN too */
379 else if (f
>= 1.0f
) {
380 return (uint8_t) 255;
385 tmp
.f
= tmp
.f
* (255.0f
/256.0f
) + 32768.0f
;
386 return (uint8_t) tmp
.i
;
391 * Convert uint16_t to float in [0, 1].
394 ushort_to_float(uint16_t us
)
396 return (float) us
* (1.0f
/ 65535.0f
);
401 * Convert float in [0,1] to uint16_t in [0,65535] with clamping.
403 static inline uint16_t
404 float_to_ushort(float f
)
406 /* return 0 for NaN too */
410 else if (f
>= 1.0f
) {
411 return (uint16_t) 65535;
416 tmp
.f
= tmp
.f
* (65535.0f
/65536.0f
) + 128.0f
;
417 return (uint16_t) tmp
.i
;
422 byte_to_float_tex(int8_t b
)
424 return (b
== -128) ? -1.0F
: b
* 1.0F
/ 127.0F
;
428 float_to_byte_tex(float f
)
430 return (int8_t) (127.0F
* f
);
436 static inline unsigned
437 util_logbase2(unsigned n
)
439 #if defined(HAVE___BUILTIN_CLZ)
440 return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n
| 1));
443 if (n
>= 1<<16) { n
>>= 16; pos
+= 16; }
444 if (n
>= 1<< 8) { n
>>= 8; pos
+= 8; }
445 if (n
>= 1<< 4) { n
>>= 4; pos
+= 4; }
446 if (n
>= 1<< 2) { n
>>= 2; pos
+= 2; }
447 if (n
>= 1<< 1) { pos
+= 1; }
452 static inline uint64_t
453 util_logbase2_64(uint64_t n
)
455 #if defined(HAVE___BUILTIN_CLZLL)
456 return ((sizeof(uint64_t) * 8 - 1) - __builtin_clzll(n
| 1));
459 if (n
>= 1ull<<32) { n
>>= 32; pos
+= 32; }
460 if (n
>= 1ull<<16) { n
>>= 16; pos
+= 16; }
461 if (n
>= 1ull<< 8) { n
>>= 8; pos
+= 8; }
462 if (n
>= 1ull<< 4) { n
>>= 4; pos
+= 4; }
463 if (n
>= 1ull<< 2) { n
>>= 2; pos
+= 2; }
464 if (n
>= 1ull<< 1) { pos
+= 1; }
470 * Returns the ceiling of log n base 2, and 0 when n == 0. Equivalently,
471 * returns the smallest x such that n <= 2**x.
473 static inline unsigned
474 util_logbase2_ceil(unsigned n
)
479 return 1 + util_logbase2(n
- 1);
482 static inline uint64_t
483 util_logbase2_ceil64(uint64_t n
)
488 return 1ull + util_logbase2_64(n
- 1);
492 * Returns the smallest power of two >= x
494 static inline unsigned
495 util_next_power_of_two(unsigned x
)
497 #if defined(HAVE___BUILTIN_CLZ)
501 return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x
- 1)));
508 if (util_is_power_of_two_or_zero(x
))
512 val
= (val
>> 1) | val
;
513 val
= (val
>> 2) | val
;
514 val
= (val
>> 4) | val
;
515 val
= (val
>> 8) | val
;
516 val
= (val
>> 16) | val
;
522 static inline uint64_t
523 util_next_power_of_two64(uint64_t x
)
525 #if defined(HAVE___BUILTIN_CLZLL)
529 return (1ull << ((sizeof(uint64_t) * 8) - __builtin_clzll(x
- 1)));
536 if (util_is_power_of_two_or_zero64(x
))
540 val
= (val
>> 1) | val
;
541 val
= (val
>> 2) | val
;
542 val
= (val
>> 4) | val
;
543 val
= (val
>> 8) | val
;
544 val
= (val
>> 16) | val
;
545 val
= (val
>> 32) | val
;
553 * Algorithm taken from:
554 * http://stackoverflow.com/questions/9144800/c-reverse-bits-in-unsigned-integer
556 static inline unsigned
557 util_bitreverse(unsigned n
)
559 n
= ((n
>> 1) & 0x55555555u
) | ((n
& 0x55555555u
) << 1);
560 n
= ((n
>> 2) & 0x33333333u
) | ((n
& 0x33333333u
) << 2);
561 n
= ((n
>> 4) & 0x0f0f0f0fu
) | ((n
& 0x0f0f0f0fu
) << 4);
562 n
= ((n
>> 8) & 0x00ff00ffu
) | ((n
& 0x00ff00ffu
) << 8);
563 n
= ((n
>> 16) & 0xffffu
) | ((n
& 0xffffu
) << 16);
568 * Convert from little endian to CPU byte order.
571 #ifdef PIPE_ARCH_BIG_ENDIAN
572 #define util_le64_to_cpu(x) util_bswap64(x)
573 #define util_le32_to_cpu(x) util_bswap32(x)
574 #define util_le16_to_cpu(x) util_bswap16(x)
576 #define util_le64_to_cpu(x) (x)
577 #define util_le32_to_cpu(x) (x)
578 #define util_le16_to_cpu(x) (x)
581 #define util_cpu_to_le64(x) util_le64_to_cpu(x)
582 #define util_cpu_to_le32(x) util_le32_to_cpu(x)
583 #define util_cpu_to_le16(x) util_le16_to_cpu(x)
586 * Reverse byte order of a 32 bit word.
588 static inline uint32_t
589 util_bswap32(uint32_t n
)
591 #if defined(HAVE___BUILTIN_BSWAP32)
592 return __builtin_bswap32(n
);
595 ((n
>> 8) & 0x0000ff00) |
596 ((n
<< 8) & 0x00ff0000) |
602 * Reverse byte order of a 64bit word.
604 static inline uint64_t
605 util_bswap64(uint64_t n
)
607 #if defined(HAVE___BUILTIN_BSWAP64)
608 return __builtin_bswap64(n
);
610 return ((uint64_t)util_bswap32((uint32_t)n
) << 32) |
611 util_bswap32((n
>> 32));
617 * Reverse byte order of a 16 bit word.
619 static inline uint16_t
620 util_bswap16(uint16_t n
)
627 util_memcpy_cpu_to_le32(void * restrict dest
, const void * restrict src
, size_t n
)
629 #ifdef PIPE_ARCH_BIG_ENDIAN
633 for (i
= 0, e
= n
/ 4; i
< e
; i
++) {
634 uint32_t * restrict d
= (uint32_t* restrict
)dest
;
635 const uint32_t * restrict s
= (const uint32_t* restrict
)src
;
636 d
[i
] = util_bswap32(s
[i
]);
640 return memcpy(dest
, src
, n
);
645 * Clamp X to [MIN, MAX].
646 * This is a macro to allow float, int, uint, etc. types.
647 * We arbitrarily turn NaN into MIN.
649 #define CLAMP( X, MIN, MAX ) ( (X)>(MIN) ? ((X)>(MAX) ? (MAX) : (X)) : (MIN) )
651 #define MIN2( A, B ) ( (A)<(B) ? (A) : (B) )
652 #define MAX2( A, B ) ( (A)>(B) ? (A) : (B) )
654 #define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
655 #define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))
657 #define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
658 #define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))
662 * Align a value, only works pot alignemnts.
665 align(int value
, int alignment
)
667 return (value
+ alignment
- 1) & ~(alignment
- 1);
670 static inline uint64_t
671 align64(uint64_t value
, unsigned alignment
)
673 return (value
+ alignment
- 1) & ~((uint64_t)alignment
- 1);
677 * Works like align but on npot alignments.
680 util_align_npot(size_t value
, size_t alignment
)
682 if (value
% alignment
)
683 return value
+ (alignment
- (value
% alignment
));
687 static inline unsigned
688 u_minify(unsigned value
, unsigned levels
)
690 return MAX2(1, value
>> levels
);
694 #define COPY_4V( DST, SRC ) \
696 (DST)[0] = (SRC)[0]; \
697 (DST)[1] = (SRC)[1]; \
698 (DST)[2] = (SRC)[2]; \
699 (DST)[3] = (SRC)[3]; \
705 #define COPY_4FV( DST, SRC ) COPY_4V(DST, SRC)
710 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
720 static inline uint32_t
721 util_unsigned_fixed(float value
, unsigned frac_bits
)
723 return value
< 0 ? 0 : (uint32_t)(value
* (1<<frac_bits
));
726 static inline int32_t
727 util_signed_fixed(float value
, unsigned frac_bits
)
729 return (int32_t)(value
* (1<<frac_bits
));
733 util_fpstate_get(void);
735 util_fpstate_set_denorms_to_zero(unsigned current_fpstate
);
737 util_fpstate_set(unsigned fpstate
);
745 #endif /* U_MATH_H */