1 /**************************************************************************
3 * Copyright 2008 VMware, Inc.
6 * Permission is hereby granted, free of charge, to any person obtaining a
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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
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18 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
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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.
42 #include "pipe/p_compiler.h"
49 #include "util/bitscan.h"
57 #define M_SQRT2 1.41421356237309504880
60 #define POW2_TABLE_SIZE_LOG2 9
61 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
62 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
63 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
64 extern float pow2_table
[POW2_TABLE_SIZE
];
68 * Initialize math module. This should be called before using any
69 * other functions in this module.
90 * Extract the IEEE float32 exponent.
93 util_get_float32_exponent(float x
)
99 return ((f
.ui
>> 23) & 0xff) - 127;
104 * Fast version of 2^x
105 * Identity: exp2(a + b) = exp2(a) * exp2(b)
107 * Let fpart = x - ipart;
108 * So, exp2(x) = exp2(ipart) * exp2(fpart)
109 * Compute exp2(ipart) with i << ipart
110 * Compute exp2(fpart) with lookup table.
113 util_fast_exp2(float x
)
120 return 3.402823466e+38f
;
126 fpart
= x
- (float) ipart
;
129 * epart.f = (float) (1 << ipart)
130 * but faster and without integer overflow for ipart > 31
132 epart
.i
= (ipart
+ 127 ) << 23;
134 mpart
= pow2_table
[POW2_TABLE_OFFSET
+ (int)(fpart
* POW2_TABLE_SCALE
)];
136 return epart
.f
* mpart
;
141 * Fast approximation to exp(x).
144 util_fast_exp(float x
)
146 const float k
= 1.44269f
; /* = log2(e) */
147 return util_fast_exp2(k
* x
);
151 #define LOG2_TABLE_SIZE_LOG2 16
152 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
153 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
154 extern float log2_table
[LOG2_TABLE_SIZE
];
158 * Fast approximation to log2(x).
161 util_fast_log2(float x
)
166 epart
= (float)(((num
.i
& 0x7f800000) >> 23) - 127);
167 /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
168 mpart
= log2_table
[((num
.i
& 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2
))) >> (23 - LOG2_TABLE_SIZE_LOG2
)];
169 return epart
+ mpart
;
174 * Fast approximation to x^y.
177 util_fast_pow(float x
, float y
)
179 return util_fast_exp2(util_fast_log2(x
) * y
);
182 /* Note that this counts zero as a power of two.
184 static inline boolean
185 util_is_power_of_two( unsigned v
)
187 return (v
& (v
-1)) == 0;
192 * Floor(x), returned as int.
200 af
= (3 << 22) + 0.5 + (double) f
;
201 bf
= (3 << 22) + 0.5 - (double) f
;
202 u
.f
= (float) af
; ai
= u
.i
;
203 u
.f
= (float) bf
; bi
= u
.i
;
204 return (ai
- bi
) >> 1;
209 * Round float to nearest int.
214 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
216 __asm__ ("fistpl %0" : "=m" (r
) : "t" (f
) : "st");
218 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
227 return (int) (f
+ 0.5f
);
229 return (int) (f
- 0.5f
);
235 * Approximate floating point comparison
237 static inline boolean
238 util_is_approx(float a
, float b
, float tol
)
240 return fabsf(b
- a
) <= tol
;
245 * util_is_X_inf_or_nan = test if x is NaN or +/- Inf
246 * util_is_X_nan = test if x is NaN
247 * util_X_inf_sign = return +1 for +Inf, -1 for -Inf, or 0 for not Inf
249 * NaN can be checked with x != x, however this fails with the fast math flag
256 static inline boolean
257 util_is_inf_or_nan(float x
)
261 return (tmp
.ui
& 0x7f800000) == 0x7f800000;
265 static inline boolean
270 return (tmp
.ui
& 0x7fffffff) > 0x7f800000;
275 util_inf_sign(float x
)
279 if ((tmp
.ui
& 0x7fffffff) != 0x7f800000) {
283 return (x
< 0) ? -1 : 1;
290 static inline boolean
291 util_is_double_inf_or_nan(double x
)
295 return (tmp
.ui
& 0x7ff0000000000000ULL
) == 0x7ff0000000000000ULL
;
299 static inline boolean
300 util_is_double_nan(double x
)
304 return (tmp
.ui
& 0x7fffffffffffffffULL
) > 0x7ff0000000000000ULL
;
309 util_double_inf_sign(double x
)
313 if ((tmp
.ui
& 0x7fffffffffffffffULL
) != 0x7ff0000000000000ULL
) {
317 return (x
< 0) ? -1 : 1;
324 static inline boolean
325 util_is_half_inf_or_nan(int16_t x
)
327 return (x
& 0x7c00) == 0x7c00;
331 static inline boolean
332 util_is_half_nan(int16_t x
)
334 return (x
& 0x7fff) > 0x7c00;
339 util_half_inf_sign(int16_t x
)
341 if ((x
& 0x7fff) != 0x7c00) {
345 return (x
< 0) ? -1 : 1;
352 static inline unsigned
370 * Convert ubyte to float in [0, 1].
371 * XXX a 256-entry lookup table would be slightly faster.
374 ubyte_to_float(ubyte ub
)
376 return (float) ub
* (1.0f
/ 255.0f
);
381 * Convert float in [0,1] to ubyte in [0,255] with clamping.
384 float_to_ubyte(float f
)
392 else if (tmp
.i
>= 0x3f800000 /* 1.0f */) {
396 tmp
.f
= tmp
.f
* (255.0f
/256.0f
) + 32768.0f
;
397 return (ubyte
) tmp
.i
;
402 byte_to_float_tex(int8_t b
)
404 return (b
== -128) ? -1.0F
: b
* 1.0F
/ 127.0F
;
408 float_to_byte_tex(float f
)
410 return (int8_t) (127.0F
* f
);
416 static inline unsigned
417 util_logbase2(unsigned n
)
419 #if defined(HAVE___BUILTIN_CLZ)
420 return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n
| 1));
423 if (n
>= 1<<16) { n
>>= 16; pos
+= 16; }
424 if (n
>= 1<< 8) { n
>>= 8; pos
+= 8; }
425 if (n
>= 1<< 4) { n
>>= 4; pos
+= 4; }
426 if (n
>= 1<< 2) { n
>>= 2; pos
+= 2; }
427 if (n
>= 1<< 1) { pos
+= 1; }
433 * Returns the ceiling of log n base 2, and 0 when n == 0. Equivalently,
434 * returns the smallest x such that n <= 2**x.
436 static inline unsigned
437 util_logbase2_ceil(unsigned n
)
442 return 1 + util_logbase2(n
- 1);
446 * Returns the smallest power of two >= x
448 static inline unsigned
449 util_next_power_of_two(unsigned x
)
451 #if defined(HAVE___BUILTIN_CLZ)
455 return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x
- 1)));
462 if (util_is_power_of_two(x
))
466 val
= (val
>> 1) | val
;
467 val
= (val
>> 2) | val
;
468 val
= (val
>> 4) | val
;
469 val
= (val
>> 8) | val
;
470 val
= (val
>> 16) | val
;
478 * Return number of bits set in n.
480 static inline unsigned
481 util_bitcount(unsigned n
)
483 #if defined(HAVE___BUILTIN_POPCOUNT)
484 return __builtin_popcount(n
);
486 /* K&R classic bitcount.
488 * For each iteration, clear the LSB from the bitfield.
489 * Requires only one iteration per set bit, instead of
490 * one iteration per bit less than highest set bit.
493 for (bits
= 0; n
; bits
++) {
501 static inline unsigned
502 util_bitcount64(uint64_t n
)
504 #ifdef HAVE___BUILTIN_POPCOUNTLL
505 return __builtin_popcountll(n
);
507 return util_bitcount(n
) + util_bitcount(n
>> 32);
514 * Algorithm taken from:
515 * http://stackoverflow.com/questions/9144800/c-reverse-bits-in-unsigned-integer
517 static inline unsigned
518 util_bitreverse(unsigned n
)
520 n
= ((n
>> 1) & 0x55555555u
) | ((n
& 0x55555555u
) << 1);
521 n
= ((n
>> 2) & 0x33333333u
) | ((n
& 0x33333333u
) << 2);
522 n
= ((n
>> 4) & 0x0f0f0f0fu
) | ((n
& 0x0f0f0f0fu
) << 4);
523 n
= ((n
>> 8) & 0x00ff00ffu
) | ((n
& 0x00ff00ffu
) << 8);
524 n
= ((n
>> 16) & 0xffffu
) | ((n
& 0xffffu
) << 16);
529 * Convert from little endian to CPU byte order.
532 #ifdef PIPE_ARCH_BIG_ENDIAN
533 #define util_le64_to_cpu(x) util_bswap64(x)
534 #define util_le32_to_cpu(x) util_bswap32(x)
535 #define util_le16_to_cpu(x) util_bswap16(x)
537 #define util_le64_to_cpu(x) (x)
538 #define util_le32_to_cpu(x) (x)
539 #define util_le16_to_cpu(x) (x)
542 #define util_cpu_to_le64(x) util_le64_to_cpu(x)
543 #define util_cpu_to_le32(x) util_le32_to_cpu(x)
544 #define util_cpu_to_le16(x) util_le16_to_cpu(x)
547 * Reverse byte order of a 32 bit word.
549 static inline uint32_t
550 util_bswap32(uint32_t n
)
552 #if defined(HAVE___BUILTIN_BSWAP32)
553 return __builtin_bswap32(n
);
556 ((n
>> 8) & 0x0000ff00) |
557 ((n
<< 8) & 0x00ff0000) |
563 * Reverse byte order of a 64bit word.
565 static inline uint64_t
566 util_bswap64(uint64_t n
)
568 #if defined(HAVE___BUILTIN_BSWAP64)
569 return __builtin_bswap64(n
);
571 return ((uint64_t)util_bswap32((uint32_t)n
) << 32) |
572 util_bswap32((n
>> 32));
578 * Reverse byte order of a 16 bit word.
580 static inline uint16_t
581 util_bswap16(uint16_t n
)
588 util_memcpy_cpu_to_le32(void * restrict dest
, const void * restrict src
, size_t n
)
590 #ifdef PIPE_ARCH_BIG_ENDIAN
594 for (i
= 0, e
= n
/ 4; i
< e
; i
++) {
595 uint32_t * restrict d
= (uint32_t* restrict
)dest
;
596 const uint32_t * restrict s
= (const uint32_t* restrict
)src
;
597 d
[i
] = util_bswap32(s
[i
]);
601 return memcpy(dest
, src
, n
);
606 * Clamp X to [MIN, MAX].
607 * This is a macro to allow float, int, uint, etc. types.
608 * We arbitrarily turn NaN into MIN.
610 #define CLAMP( X, MIN, MAX ) ( (X)>(MIN) ? ((X)>(MAX) ? (MAX) : (X)) : (MIN) )
612 #define MIN2( A, B ) ( (A)<(B) ? (A) : (B) )
613 #define MAX2( A, B ) ( (A)>(B) ? (A) : (B) )
615 #define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
616 #define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))
618 #define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
619 #define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))
623 * Align a value, only works pot alignemnts.
626 align(int value
, int alignment
)
628 return (value
+ alignment
- 1) & ~(alignment
- 1);
631 static inline uint64_t
632 align64(uint64_t value
, unsigned alignment
)
634 return (value
+ alignment
- 1) & ~((uint64_t)alignment
- 1);
638 * Works like align but on npot alignments.
641 util_align_npot(size_t value
, size_t alignment
)
643 if (value
% alignment
)
644 return value
+ (alignment
- (value
% alignment
));
648 static inline unsigned
649 u_minify(unsigned value
, unsigned levels
)
651 return MAX2(1, value
>> levels
);
655 #define COPY_4V( DST, SRC ) \
657 (DST)[0] = (SRC)[0]; \
658 (DST)[1] = (SRC)[1]; \
659 (DST)[2] = (SRC)[2]; \
660 (DST)[3] = (SRC)[3]; \
666 #define COPY_4FV( DST, SRC ) COPY_4V(DST, SRC)
671 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
681 static inline uint32_t
682 util_unsigned_fixed(float value
, unsigned frac_bits
)
684 return value
< 0 ? 0 : (uint32_t)(value
* (1<<frac_bits
));
687 static inline int32_t
688 util_signed_fixed(float value
, unsigned frac_bits
)
690 return (int32_t)(value
* (1<<frac_bits
));
694 util_fpstate_get(void);
696 util_fpstate_set_denorms_to_zero(unsigned current_fpstate
);
698 util_fpstate_set(unsigned fpstate
);
706 #endif /* U_MATH_H */