1 /**************************************************************************
3 * Copyright 2008 Tungsten Graphics, Inc., Cedar Park, Texas.
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 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.
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"
43 #include "util/u_debug.h"
51 #if defined(PIPE_SUBSYSTEM_WINDOWS_MINIPORT)
52 __inline
double ceil(double val
)
56 if ((val
- (long) val
) == 0) {
61 ceil_val
= (long) val
+ 1;
64 ceil_val
= (long) val
;
71 #ifndef PIPE_SUBSYSTEM_WINDOWS_CE_OGL
72 __inline
double floor(double val
)
76 if ((val
- (long) val
) == 0) {
81 floor_val
= (long) val
;
84 floor_val
= (long) val
- 1;
93 __inline
double __cdecl
pow(double val
, double exponent
)
100 #pragma function(log)
101 __inline
double __cdecl
log(double val
)
108 #pragma function(atan2)
109 __inline
double __cdecl
atan2(double val
)
121 #if defined(_MSC_VER)
123 #if _MSC_VER < 1400 && !defined(__cplusplus) || defined(PIPE_SUBSYSTEM_WINDOWS_CE)
125 static INLINE
float cosf( float f
)
127 return (float) cos( (double) f
);
130 static INLINE
float sinf( float f
)
132 return (float) sin( (double) f
);
135 static INLINE
float ceilf( float f
)
137 return (float) ceil( (double) f
);
140 static INLINE
float floorf( float f
)
142 return (float) floor( (double) f
);
145 static INLINE
float powf( float f
, float g
)
147 return (float) pow( (double) f
, (double) g
);
150 static INLINE
float sqrtf( float f
)
152 return (float) sqrt( (double) f
);
155 static INLINE
float fabsf( float f
)
157 return (float) fabs( (double) f
);
160 static INLINE
float logf( float f
)
162 return (float) log( (double) f
);
166 /* Work-around an extra semi-colon in VS 2005 logf definition */
169 #define logf(x) ((float)log((double)(x)))
172 #define isfinite(x) _finite((double)(x))
173 #define isnan(x) _isnan((double)(x))
176 static INLINE
double log2( double x
)
178 const double invln2
= 1.442695041;
179 return log( x
) * invln2
;
182 #endif /* _MSC_VER */
188 #define POW2_TABLE_SIZE_LOG2 9
189 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
190 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
191 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
192 extern float pow2_table
[POW2_TABLE_SIZE
];
196 * Initialize math module. This should be called before using any
197 * other functions in this module.
200 util_init_math(void);
211 * Fast version of 2^x
212 * Identity: exp2(a + b) = exp2(a) * exp2(b)
214 * Let fpart = x - ipart;
215 * So, exp2(x) = exp2(ipart) * exp2(fpart)
216 * Compute exp2(ipart) with i << ipart
217 * Compute exp2(fpart) with lookup table.
220 util_fast_exp2(float x
)
227 return 3.402823466e+38f
;
233 fpart
= x
- (float) ipart
;
236 * epart.f = (float) (1 << ipart)
237 * but faster and without integer overflow for ipart > 31
239 epart
.i
= (ipart
+ 127 ) << 23;
241 mpart
= pow2_table
[POW2_TABLE_OFFSET
+ (int)(fpart
* POW2_TABLE_SCALE
)];
243 return epart
.f
* mpart
;
248 * Fast approximation to exp(x).
251 util_fast_exp(float x
)
253 const float k
= 1.44269f
; /* = log2(e) */
254 return util_fast_exp2(k
* x
);
258 #define LOG2_TABLE_SIZE_LOG2 16
259 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
260 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
261 extern float log2_table
[LOG2_TABLE_SIZE
];
265 * Fast approximation to log2(x).
268 util_fast_log2(float x
)
273 epart
= (float)(((num
.i
& 0x7f800000) >> 23) - 127);
274 /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
275 mpart
= log2_table
[((num
.i
& 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2
))) >> (23 - LOG2_TABLE_SIZE_LOG2
)];
276 return epart
+ mpart
;
281 * Fast approximation to x^y.
284 util_fast_pow(float x
, float y
)
286 return util_fast_exp2(util_fast_log2(x
) * y
);
289 /* Note that this counts zero as a power of two.
291 static INLINE boolean
292 util_is_power_of_two( unsigned v
)
294 return (v
& (v
-1)) == 0;
299 * Floor(x), returned as int.
307 af
= (3 << 22) + 0.5 + (double) f
;
308 bf
= (3 << 22) + 0.5 - (double) f
;
309 u
.f
= (float) af
; ai
= u
.i
;
310 u
.f
= (float) bf
; bi
= u
.i
;
311 return (ai
- bi
) >> 1;
316 * Round float to nearest int.
321 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
323 __asm__ ("fistpl %0" : "=m" (r
) : "t" (f
) : "st");
325 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
334 return (int) (f
+ 0.5f
);
336 return (int) (f
- 0.5f
);
342 * Approximate floating point comparison
344 static INLINE boolean
345 util_is_approx(float a
, float b
, float tol
)
347 return fabs(b
- a
) <= tol
;
352 * Test if x is NaN or +/- infinity.
354 static INLINE boolean
355 util_is_inf_or_nan(float x
)
359 return !(int)((unsigned int)((tmp
.i
& 0x7fffffff)-0x7f800000) >> 31);
364 * Test whether x is a power of two.
366 static INLINE boolean
367 util_is_pot(unsigned x
)
369 return (x
& (x
- 1)) == 0;
374 * Find first bit set in word. Least significant bit is 1.
375 * Return 0 if no bits set.
377 #if defined(_MSC_VER) && _MSC_VER >= 1300 && (_M_IX86 || _M_AMD64 || _M_IA64)
378 unsigned char _BitScanForward(unsigned long* Index
, unsigned long Mask
);
379 #pragma intrinsic(_BitScanForward)
381 unsigned long ffs( unsigned long u
)
384 if (_BitScanForward(&i
, u
))
389 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
391 unsigned ffs( unsigned u
)
405 #elif defined(__MINGW32__)
406 #define ffs __builtin_ffs
410 #define ffs __builtin_ffs
414 /* Could also binary search for the highest bit.
416 static INLINE
unsigned
417 util_unsigned_logbase2(unsigned n
)
429 static INLINE
unsigned
439 * Convert ubyte to float in [0, 1].
440 * XXX a 256-entry lookup table would be slightly faster.
443 ubyte_to_float(ubyte ub
)
445 return (float) ub
* (1.0f
/ 255.0f
);
450 * Convert float in [0,1] to ubyte in [0,255] with clamping.
453 float_to_ubyte(float f
)
455 const int ieee_0996
= 0x3f7f0000; /* 0.996 or so */
462 else if (tmp
.i
>= ieee_0996
) {
466 tmp
.f
= tmp
.f
* (255.0f
/256.0f
) + 32768.0f
;
467 return (ubyte
) tmp
.i
;
475 static INLINE
unsigned
476 util_logbase2(unsigned n
)
486 * Returns the smallest power of two >= x
488 static INLINE
unsigned
489 util_next_power_of_two(unsigned x
)
498 for (i
= 1; i
< sizeof(unsigned) * 8; i
<<= 1)
506 * Return number of bits set in n.
508 static INLINE
unsigned
509 util_bitcount(unsigned n
)
511 #if defined(PIPE_CC_GCC)
512 return __builtin_popcount(n
);
514 /* K&R classic bitcount.
516 * For each iteration, clear the LSB from the bitfield.
517 * Requires only one iteration per set bit, instead of
518 * one iteration per bit less than highest set bit.
521 for (bits
; n
; bits
++) {
530 * Reverse byte order of a 32 bit word.
532 static INLINE
uint32_t
533 util_bswap32(uint32_t n
)
535 #if defined(PIPE_CC_GCC) && (PIPE_CC_GCC_VERSION >= 403)
536 return __builtin_bswap32(n
);
539 ((n
>> 8) & 0x0000ff00) |
540 ((n
<< 8) & 0x00ff0000) |
547 * Reverse byte order of a 16 bit word.
549 static INLINE
uint16_t
550 util_bswap16(uint16_t n
)
558 * Clamp X to [MIN, MAX].
559 * This is a macro to allow float, int, uint, etc. types.
561 #define CLAMP( X, MIN, MAX ) ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
563 #define MIN2( A, B ) ( (A)<(B) ? (A) : (B) )
564 #define MAX2( A, B ) ( (A)>(B) ? (A) : (B) )
566 #define MIN3( A, B, C ) MIN2( MIN2( A, B ), C )
567 #define MAX3( A, B, C ) MAX2( MAX2( A, B ), C )
569 #define MIN4( A, B, C, D ) MIN2( MIN2( A, B ), MIN2(C, D) )
570 #define MAX4( A, B, C, D ) MAX2( MAX2( A, B ), MIN2(C, D) )
574 * Align a value, only works pot alignemnts.
577 align(int value
, int alignment
)
579 return (value
+ alignment
- 1) & ~(alignment
- 1);
583 * Works like align but on npot alignments.
586 util_align_npot(size_t value
, size_t alignment
)
588 if (value
% alignment
)
589 return value
+ (alignment
- (value
% alignment
));
593 static INLINE
unsigned
594 u_minify(unsigned value
, unsigned levels
)
596 return MAX2(1, value
>> levels
);
600 #define COPY_4V( DST, SRC ) \
602 (DST)[0] = (SRC)[0]; \
603 (DST)[1] = (SRC)[1]; \
604 (DST)[2] = (SRC)[2]; \
605 (DST)[3] = (SRC)[3]; \
611 #define COPY_4FV( DST, SRC ) COPY_4V(DST, SRC)
616 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
626 static INLINE
uint32_t util_unsigned_fixed(float value
, unsigned frac_bits
)
628 return value
< 0 ? 0 : (uint32_t)(value
* (1<<frac_bits
));
631 static INLINE
int32_t util_signed_fixed(float value
, unsigned frac_bits
)
633 return (int32_t)(value
* (1<<frac_bits
));
642 #endif /* U_MATH_H */