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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"
43 #include "util/u_debug.h"
56 #include <strings.h> /* for ffs */
61 #define M_SQRT2 1.41421356237309504880
67 #if _MSC_VER < 1400 && !defined(__cplusplus)
69 static INLINE
float cosf( float f
)
71 return (float) cos( (double) f
);
74 static INLINE
float sinf( float f
)
76 return (float) sin( (double) f
);
79 static INLINE
float ceilf( float f
)
81 return (float) ceil( (double) f
);
84 static INLINE
float floorf( float f
)
86 return (float) floor( (double) f
);
89 static INLINE
float powf( float f
, float g
)
91 return (float) pow( (double) f
, (double) g
);
94 static INLINE
float sqrtf( float f
)
96 return (float) sqrt( (double) f
);
99 static INLINE
float fabsf( float f
)
101 return (float) fabs( (double) f
);
104 static INLINE
float logf( float f
)
106 return (float) log( (double) f
);
110 /* Work-around an extra semi-colon in VS 2005 logf definition */
113 #define logf(x) ((float)log((double)(x)))
117 #define isfinite(x) _finite((double)(x))
118 #define isnan(x) _isnan((double)(x))
119 #endif /* _MSC_VER < 1800 */
120 #endif /* _MSC_VER < 1400 && !defined(__cplusplus) */
123 static INLINE
double log2( double x
)
125 const double invln2
= 1.442695041;
126 return log( x
) * invln2
;
132 return x
>= 0.0 ? floor(x
+ 0.5) : ceil(x
- 0.5);
138 return x
>= 0.0f
? floorf(x
+ 0.5f
) : ceilf(x
- 0.5f
);
143 #define INFINITY (DBL_MAX + DBL_MAX)
147 #define NAN (INFINITY - INFINITY)
150 #endif /* _MSC_VER */
153 #if __STDC_VERSION__ < 199901L && (!defined(__cplusplus) || defined(_MSC_VER))
154 static INLINE
long int
157 long int rounded
= (long int)(d
+ 0.5);
159 if (d
- floor(d
) == 0.5) {
160 if (rounded
% 2 != 0)
161 rounded
+= (d
> 0) ? -1 : 1;
167 static INLINE
long int
170 long int rounded
= (long int)(f
+ 0.5f
);
172 if (f
- floorf(f
) == 0.5f
) {
173 if (rounded
% 2 != 0)
174 rounded
+= (f
> 0) ? -1 : 1;
180 static INLINE
long long int
183 long long int rounded
= (long long int)(d
+ 0.5);
185 if (d
- floor(d
) == 0.5) {
186 if (rounded
% 2 != 0)
187 rounded
+= (d
> 0) ? -1 : 1;
193 static INLINE
long long int
196 long long int rounded
= (long long int)(f
+ 0.5f
);
198 if (f
- floorf(f
) == 0.5f
) {
199 if (rounded
% 2 != 0)
200 rounded
+= (f
> 0) ? -1 : 1;
207 #define POW2_TABLE_SIZE_LOG2 9
208 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
209 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
210 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
211 extern float pow2_table
[POW2_TABLE_SIZE
];
215 * Initialize math module. This should be called before using any
216 * other functions in this module.
219 util_init_math(void);
237 * Extract the IEEE float32 exponent.
240 util_get_float32_exponent(float x
)
246 return ((f
.ui
>> 23) & 0xff) - 127;
251 * Fast version of 2^x
252 * Identity: exp2(a + b) = exp2(a) * exp2(b)
254 * Let fpart = x - ipart;
255 * So, exp2(x) = exp2(ipart) * exp2(fpart)
256 * Compute exp2(ipart) with i << ipart
257 * Compute exp2(fpart) with lookup table.
260 util_fast_exp2(float x
)
267 return 3.402823466e+38f
;
273 fpart
= x
- (float) ipart
;
276 * epart.f = (float) (1 << ipart)
277 * but faster and without integer overflow for ipart > 31
279 epart
.i
= (ipart
+ 127 ) << 23;
281 mpart
= pow2_table
[POW2_TABLE_OFFSET
+ (int)(fpart
* POW2_TABLE_SCALE
)];
283 return epart
.f
* mpart
;
288 * Fast approximation to exp(x).
291 util_fast_exp(float x
)
293 const float k
= 1.44269f
; /* = log2(e) */
294 return util_fast_exp2(k
* x
);
298 #define LOG2_TABLE_SIZE_LOG2 16
299 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
300 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
301 extern float log2_table
[LOG2_TABLE_SIZE
];
305 * Fast approximation to log2(x).
308 util_fast_log2(float x
)
313 epart
= (float)(((num
.i
& 0x7f800000) >> 23) - 127);
314 /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
315 mpart
= log2_table
[((num
.i
& 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2
))) >> (23 - LOG2_TABLE_SIZE_LOG2
)];
316 return epart
+ mpart
;
321 * Fast approximation to x^y.
324 util_fast_pow(float x
, float y
)
326 return util_fast_exp2(util_fast_log2(x
) * y
);
329 /* Note that this counts zero as a power of two.
331 static INLINE boolean
332 util_is_power_of_two( unsigned v
)
334 return (v
& (v
-1)) == 0;
339 * Floor(x), returned as int.
347 af
= (3 << 22) + 0.5 + (double) f
;
348 bf
= (3 << 22) + 0.5 - (double) f
;
349 u
.f
= (float) af
; ai
= u
.i
;
350 u
.f
= (float) bf
; bi
= u
.i
;
351 return (ai
- bi
) >> 1;
356 * Round float to nearest int.
361 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
363 __asm__ ("fistpl %0" : "=m" (r
) : "t" (f
) : "st");
365 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
374 return (int) (f
+ 0.5f
);
376 return (int) (f
- 0.5f
);
382 * Approximate floating point comparison
384 static INLINE boolean
385 util_is_approx(float a
, float b
, float tol
)
387 return fabs(b
- a
) <= tol
;
392 * util_is_X_inf_or_nan = test if x is NaN or +/- Inf
393 * util_is_X_nan = test if x is NaN
394 * util_X_inf_sign = return +1 for +Inf, -1 for -Inf, or 0 for not Inf
396 * NaN can be checked with x != x, however this fails with the fast math flag
403 static INLINE boolean
404 util_is_inf_or_nan(float x
)
408 return (tmp
.ui
& 0x7f800000) == 0x7f800000;
412 static INLINE boolean
417 return (tmp
.ui
& 0x7fffffff) > 0x7f800000;
422 util_inf_sign(float x
)
426 if ((tmp
.ui
& 0x7fffffff) != 0x7f800000) {
430 return (x
< 0) ? -1 : 1;
437 static INLINE boolean
438 util_is_double_inf_or_nan(double x
)
442 return (tmp
.ui
& 0x7ff0000000000000ULL
) == 0x7ff0000000000000ULL
;
446 static INLINE boolean
447 util_is_double_nan(double x
)
451 return (tmp
.ui
& 0x7fffffffffffffffULL
) > 0x7ff0000000000000ULL
;
456 util_double_inf_sign(double x
)
460 if ((tmp
.ui
& 0x7fffffffffffffffULL
) != 0x7ff0000000000000ULL
) {
464 return (x
< 0) ? -1 : 1;
471 static INLINE boolean
472 util_is_half_inf_or_nan(int16_t x
)
474 return (x
& 0x7c00) == 0x7c00;
478 static INLINE boolean
479 util_is_half_nan(int16_t x
)
481 return (x
& 0x7fff) > 0x7c00;
486 util_half_inf_sign(int16_t x
)
488 if ((x
& 0x7fff) != 0x7c00) {
492 return (x
< 0) ? -1 : 1;
497 * Find first bit set in word. Least significant bit is 1.
498 * Return 0 if no bits set.
501 #define FFS_DEFINED 1
503 #if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64)
504 unsigned char _BitScanForward(unsigned long* Index
, unsigned long Mask
);
505 #pragma intrinsic(_BitScanForward)
507 unsigned long ffs( unsigned long u
)
510 if (_BitScanForward(&i
, u
))
515 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
517 unsigned ffs( unsigned u
)
531 #elif defined(__MINGW32__) || defined(PIPE_OS_ANDROID)
532 #define ffs __builtin_ffs
533 #define ffsll __builtin_ffsll
536 #endif /* FFS_DEFINED */
539 * Find last bit set in a word. The least significant bit is 1.
540 * Return 0 if no bits are set.
542 static INLINE
unsigned
543 util_last_bit(unsigned u
)
545 #if defined(__GNUC__)
546 return u
== 0 ? 0 : 32 - __builtin_clz(u
);
558 * Find last bit in a word that does not match the sign bit. The least
559 * significant bit is 1.
560 * Return 0 if no bits are set.
562 static INLINE
unsigned
563 util_last_bit_signed(int i
)
566 return util_last_bit(i
);
568 return util_last_bit(~(unsigned)i
);
571 /* Destructively loop over all of the bits in a mask as in:
574 * int i = u_bit_scan(&mymask);
575 * ... process element i
580 u_bit_scan(unsigned *mask
)
582 int i
= ffs(*mask
) - 1;
588 u_bit_scan64(uint64_t *mask
)
590 int i
= ffsll(*mask
) - 1;
591 *mask
&= ~(1llu << i
);
598 static INLINE
unsigned
616 * Convert ubyte to float in [0, 1].
617 * XXX a 256-entry lookup table would be slightly faster.
620 ubyte_to_float(ubyte ub
)
622 return (float) ub
* (1.0f
/ 255.0f
);
627 * Convert float in [0,1] to ubyte in [0,255] with clamping.
630 float_to_ubyte(float f
)
638 else if (tmp
.i
>= 0x3f800000 /* 1.0f */) {
642 tmp
.f
= tmp
.f
* (255.0f
/256.0f
) + 32768.0f
;
643 return (ubyte
) tmp
.i
;
648 byte_to_float_tex(int8_t b
)
650 return (b
== -128) ? -1.0F
: b
* 1.0F
/ 127.0F
;
654 float_to_byte_tex(float f
)
656 return (int8_t) (127.0F
* f
);
662 static INLINE
unsigned
663 util_logbase2(unsigned n
)
665 #if defined(PIPE_CC_GCC)
666 return ((sizeof(unsigned) * 8 - 1) - __builtin_clz(n
| 1));
669 if (n
>= 1<<16) { n
>>= 16; pos
+= 16; }
670 if (n
>= 1<< 8) { n
>>= 8; pos
+= 8; }
671 if (n
>= 1<< 4) { n
>>= 4; pos
+= 4; }
672 if (n
>= 1<< 2) { n
>>= 2; pos
+= 2; }
673 if (n
>= 1<< 1) { pos
+= 1; }
680 * Returns the smallest power of two >= x
682 static INLINE
unsigned
683 util_next_power_of_two(unsigned x
)
685 #if defined(PIPE_CC_GCC)
689 return (1 << ((sizeof(unsigned) * 8) - __builtin_clz(x
- 1)));
696 if (util_is_power_of_two(x
))
700 val
= (val
>> 1) | val
;
701 val
= (val
>> 2) | val
;
702 val
= (val
>> 4) | val
;
703 val
= (val
>> 8) | val
;
704 val
= (val
>> 16) | val
;
712 * Return number of bits set in n.
714 static INLINE
unsigned
715 util_bitcount(unsigned n
)
717 #if defined(PIPE_CC_GCC)
718 return __builtin_popcount(n
);
720 /* K&R classic bitcount.
722 * For each iteration, clear the LSB from the bitfield.
723 * Requires only one iteration per set bit, instead of
724 * one iteration per bit less than highest set bit.
727 for (bits
; n
; bits
++) {
735 static INLINE
unsigned
736 util_bitcount64(uint64_t n
)
738 #ifdef HAVE___BUILTIN_POPCOUNTLL
739 return __builtin_popcountll(n
);
741 return util_bitcount(n
) + util_bitcount(n
>> 32);
748 * Algorithm taken from:
749 * http://stackoverflow.com/questions/9144800/c-reverse-bits-in-unsigned-integer
751 static INLINE
unsigned
752 util_bitreverse(unsigned n
)
754 n
= ((n
>> 1) & 0x55555555u
) | ((n
& 0x55555555u
) << 1);
755 n
= ((n
>> 2) & 0x33333333u
) | ((n
& 0x33333333u
) << 2);
756 n
= ((n
>> 4) & 0x0f0f0f0fu
) | ((n
& 0x0f0f0f0fu
) << 4);
757 n
= ((n
>> 8) & 0x00ff00ffu
) | ((n
& 0x00ff00ffu
) << 8);
758 n
= ((n
>> 16) & 0xffffu
) | ((n
& 0xffffu
) << 16);
763 * Convert from little endian to CPU byte order.
766 #ifdef PIPE_ARCH_BIG_ENDIAN
767 #define util_le64_to_cpu(x) util_bswap64(x)
768 #define util_le32_to_cpu(x) util_bswap32(x)
769 #define util_le16_to_cpu(x) util_bswap16(x)
771 #define util_le64_to_cpu(x) (x)
772 #define util_le32_to_cpu(x) (x)
773 #define util_le16_to_cpu(x) (x)
776 #define util_cpu_to_le64(x) util_le64_to_cpu(x)
777 #define util_cpu_to_le32(x) util_le32_to_cpu(x)
778 #define util_cpu_to_le16(x) util_le16_to_cpu(x)
781 * Reverse byte order of a 32 bit word.
783 static INLINE
uint32_t
784 util_bswap32(uint32_t n
)
786 /* We need the gcc version checks for non-autoconf build system */
787 #if defined(HAVE___BUILTIN_BSWAP32) || (defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 403))
788 return __builtin_bswap32(n
);
791 ((n
>> 8) & 0x0000ff00) |
792 ((n
<< 8) & 0x00ff0000) |
798 * Reverse byte order of a 64bit word.
800 static INLINE
uint64_t
801 util_bswap64(uint64_t n
)
803 #if defined(HAVE___BUILTIN_BSWAP64)
804 return __builtin_bswap64(n
);
806 return ((uint64_t)util_bswap32((uint32_t)n
) << 32) |
807 util_bswap32((n
>> 32));
813 * Reverse byte order of a 16 bit word.
815 static INLINE
uint16_t
816 util_bswap16(uint16_t n
)
823 util_memcpy_cpu_to_le32(void * restrict dest
, const void * restrict src
, size_t n
)
825 #ifdef PIPE_ARCH_BIG_ENDIAN
829 for (i
= 0, e
= n
/ 4; i
< e
; i
++) {
830 uint32_t * restrict d
= (uint32_t* restrict
)dest
;
831 const uint32_t * restrict s
= (const uint32_t* restrict
)src
;
832 d
[i
] = util_bswap32(s
[i
]);
836 return memcpy(dest
, src
, n
);
841 * Clamp X to [MIN, MAX].
842 * This is a macro to allow float, int, uint, etc. types.
844 #define CLAMP( X, MIN, MAX ) ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
846 #define MIN2( A, B ) ( (A)<(B) ? (A) : (B) )
847 #define MAX2( A, B ) ( (A)>(B) ? (A) : (B) )
849 #define MIN3( A, B, C ) ((A) < (B) ? MIN2(A, C) : MIN2(B, C))
850 #define MAX3( A, B, C ) ((A) > (B) ? MAX2(A, C) : MAX2(B, C))
852 #define MIN4( A, B, C, D ) ((A) < (B) ? MIN3(A, C, D) : MIN3(B, C, D))
853 #define MAX4( A, B, C, D ) ((A) > (B) ? MAX3(A, C, D) : MAX3(B, C, D))
857 * Align a value, only works pot alignemnts.
860 align(int value
, int alignment
)
862 return (value
+ alignment
- 1) & ~(alignment
- 1);
866 * Works like align but on npot alignments.
869 util_align_npot(size_t value
, size_t alignment
)
871 if (value
% alignment
)
872 return value
+ (alignment
- (value
% alignment
));
876 static INLINE
unsigned
877 u_minify(unsigned value
, unsigned levels
)
879 return MAX2(1, value
>> levels
);
883 #define COPY_4V( DST, SRC ) \
885 (DST)[0] = (SRC)[0]; \
886 (DST)[1] = (SRC)[1]; \
887 (DST)[2] = (SRC)[2]; \
888 (DST)[3] = (SRC)[3]; \
894 #define COPY_4FV( DST, SRC ) COPY_4V(DST, SRC)
899 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
909 static INLINE
uint32_t
910 util_unsigned_fixed(float value
, unsigned frac_bits
)
912 return value
< 0 ? 0 : (uint32_t)(value
* (1<<frac_bits
));
915 static INLINE
int32_t
916 util_signed_fixed(float value
, unsigned frac_bits
)
918 return (int32_t)(value
* (1<<frac_bits
));
922 util_fpstate_get(void);
924 util_fpstate_set_denorms_to_zero(unsigned current_fpstate
);
926 util_fpstate_set(unsigned fpstate
);
934 #endif /* U_MATH_H */