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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 "pipe/p_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)))
173 static INLINE
double log2( double x
)
175 const double invln2
= 1.442695041;
176 return log( x
) * invln2
;
179 #endif /* _MSC_VER */
185 #define POW2_TABLE_SIZE_LOG2 9
186 #define POW2_TABLE_SIZE (1 << POW2_TABLE_SIZE_LOG2)
187 #define POW2_TABLE_OFFSET (POW2_TABLE_SIZE/2)
188 #define POW2_TABLE_SCALE ((float)(POW2_TABLE_SIZE/2))
189 extern float pow2_table
[POW2_TABLE_SIZE
];
194 util_init_math(void);
205 * Fast version of 2^x
206 * Identity: exp2(a + b) = exp2(a) * exp2(b)
208 * Let fpart = x - ipart;
209 * So, exp2(x) = exp2(ipart) * exp2(fpart)
210 * Compute exp2(ipart) with i << ipart
211 * Compute exp2(fpart) with lookup table.
214 util_fast_exp2(float x
)
221 return 3.402823466e+38f
;
227 fpart
= x
- (float) ipart
;
230 * epart.f = (float) (1 << ipart)
231 * but faster and without integer overflow for ipart > 31 */
232 epart
.i
= (ipart
+ 127 ) << 23;
234 mpart
= pow2_table
[POW2_TABLE_OFFSET
+ (int)(fpart
* POW2_TABLE_SCALE
)];
236 return epart
.f
* mpart
;
241 * Fast approximation to exp(x).
244 util_fast_exp(float x
)
246 const float k
= 1.44269f
; /* = log2(e) */
247 return util_fast_exp2(k
* x
);
251 #define LOG2_TABLE_SIZE_LOG2 16
252 #define LOG2_TABLE_SCALE (1 << LOG2_TABLE_SIZE_LOG2)
253 #define LOG2_TABLE_SIZE (LOG2_TABLE_SCALE + 1)
254 extern float log2_table
[LOG2_TABLE_SIZE
];
258 util_fast_log2(float x
)
263 epart
= (float)(((num
.i
& 0x7f800000) >> 23) - 127);
264 /* mpart = log2_table[mantissa*LOG2_TABLE_SCALE + 0.5] */
265 mpart
= log2_table
[((num
.i
& 0x007fffff) + (1 << (22 - LOG2_TABLE_SIZE_LOG2
))) >> (23 - LOG2_TABLE_SIZE_LOG2
)];
266 return epart
+ mpart
;
271 util_fast_pow(float x
, float y
)
273 return util_fast_exp2(util_fast_log2(x
) * y
);
279 * Floor(x), returned as int.
287 af
= (3 << 22) + 0.5 + (double)f
;
288 bf
= (3 << 22) + 0.5 - (double)f
;
289 u
.f
= (float) af
; ai
= u
.i
;
290 u
.f
= (float) bf
; bi
= u
.i
;
291 return (ai
- bi
) >> 1;
296 * Round float to nearest int.
301 #if defined(PIPE_CC_GCC) && defined(PIPE_ARCH_X86)
303 __asm__ ("fistpl %0" : "=m" (r
) : "t" (f
) : "st");
305 #elif defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
314 return (int) (f
+ 0.5f
);
316 return (int) (f
- 0.5f
);
322 #if defined(PIPE_CC_MSVC) && defined(PIPE_ARCH_X86)
324 * Find first bit set in word. Least significant bit is 1.
325 * Return 0 if no bits set.
328 unsigned ffs( unsigned u
)
348 static INLINE
unsigned
359 ubyte_to_float(ubyte ub
)
361 return (float) ub
* (1.0f
/ 255.0f
);
366 * Convert float in [0,1] to ubyte in [0,255] with clamping.
369 float_to_ubyte(float f
)
371 const int ieee_0996
= 0x3f7f0000; /* 0.996 or so */
378 else if (tmp
.i
>= ieee_0996
) {
382 tmp
.f
= tmp
.f
* (255.0f
/256.0f
) + 32768.0f
;
383 return (ubyte
) tmp
.i
;
389 #define CLAMP( X, MIN, MAX ) ( (X)<(MIN) ? (MIN) : ((X)>(MAX) ? (MAX) : (X)) )
391 #define MIN2( A, B ) ( (A)<(B) ? (A) : (B) )
392 #define MAX2( A, B ) ( (A)>(B) ? (A) : (B) )
396 align(int value
, int alignment
)
398 return (value
+ alignment
- 1) & ~(alignment
- 1);
403 #define COPY_4V( DST, SRC ) \
405 (DST)[0] = (SRC)[0]; \
406 (DST)[1] = (SRC)[1]; \
407 (DST)[2] = (SRC)[2]; \
408 (DST)[3] = (SRC)[3]; \
414 #define COPY_4FV( DST, SRC ) COPY_4V(DST, SRC)
419 #define ASSIGN_4V( DST, V0, V1, V2, V3 ) \
433 #endif /* U_MATH_H */