1 /* Copyright (c) 2002-2008 Jean-Marc Valin
2 Copyright (c) 2007-2008 CSIRO
3 Copyright (c) 2007-2009 Xiph.Org Foundation
4 Written by Jean-Marc Valin */
7 @brief Various math functions
10 Redistribution and use in source and binary forms, with or without
11 modification, are permitted provided that the following conditions
14 - Redistributions of source code must retain the above copyright
15 notice, this list of conditions and the following disclaimer.
17 - Redistributions in binary form must reproduce the above copyright
18 notice, this list of conditions and the following disclaimer in the
19 documentation and/or other materials provided with the distribution.
21 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
22 ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
23 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
24 A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
25 OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
26 EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
27 PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
28 PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
29 LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
30 NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
31 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
39 #include "os_support.h"
41 #define PI 3.141592653f
43 /* Multiplies two 16-bit fractional values. Bit-exactness of this macro is important */
44 #define FRAC_MUL16(a,b) ((16384+((opus_int32)(opus_int16)(a)*(opus_int16)(b)))>>15)
46 unsigned isqrt32(opus_uint32 _val
);
48 /* CELT doesn't need it for fixed-point, by analysis.c does. */
49 #if !defined(FIXED_POINT) || defined(ANALYSIS_C)
50 #define cA 0.43157974f
51 #define cB 0.67848403f
52 #define cC 0.08595542f
53 #define cE ((float)PI/2)
54 static OPUS_INLINE
float fast_atan2f(float y
, float x
) {
58 /* For very small values, we don't care about the answer, so
59 we can just return 0. */
65 float den
= (y2
+ cB
*x2
) * (y2
+ cC
*x2
);
66 return -x
*y
*(y2
+ cA
*x2
) / den
+ (y
<0 ? -cE
: cE
);
68 float den
= (x2
+ cB
*y2
) * (x2
+ cC
*y2
);
69 return x
*y
*(x2
+ cA
*y2
) / den
+ (y
<0 ? -cE
: cE
) - (x
*y
<0 ? -cE
: cE
);
79 #ifndef OVERRIDE_CELT_MAXABS16
80 static OPUS_INLINE opus_val32
celt_maxabs16(const opus_val16
*x
, int len
)
83 opus_val16 maxval
= 0;
84 opus_val16 minval
= 0;
87 maxval
= MAX16(maxval
, x
[i
]);
88 minval
= MIN16(minval
, x
[i
]);
90 return MAX32(EXTEND32(maxval
),-EXTEND32(minval
));
94 #ifndef OVERRIDE_CELT_MAXABS32
96 static OPUS_INLINE opus_val32
celt_maxabs32(const opus_val32
*x
, int len
)
99 opus_val32 maxval
= 0;
100 opus_val32 minval
= 0;
103 maxval
= MAX32(maxval
, x
[i
]);
104 minval
= MIN32(minval
, x
[i
]);
106 return MAX32(maxval
, -minval
);
109 #define celt_maxabs32(x,len) celt_maxabs16(x,len)
116 #define celt_sqrt(x) ((float)sqrt(x))
117 #define celt_rsqrt(x) (1.f/celt_sqrt(x))
118 #define celt_rsqrt_norm(x) (celt_rsqrt(x))
119 #define celt_cos_norm(x) ((float)cos((.5f*PI)*(x)))
120 #define celt_rcp(x) (1.f/(x))
121 #define celt_div(a,b) ((a)/(b))
122 #define frac_div32(a,b) ((float)(a)/(b))
126 /* Note: This assumes radix-2 floating point with the exponent at bits 23..30 and an offset of 127
127 denorm, +/- inf and NaN are *not* handled */
129 /** Base-2 log approximation (log2(x)). */
130 static OPUS_INLINE
float celt_log2(float x
)
139 integer
= (in
.i
>>23)-127;
140 in
.i
-= (opus_uint32
)integer
<<23;
142 frac
= -0.41445418f
+ frac
*(0.95909232f
143 + frac
*(-0.33951290f
+ frac
*0.16541097f
));
144 return 1+integer
+frac
;
147 /** Base-2 exponential approximation (2^x). */
148 static OPUS_INLINE
float celt_exp2(float x
)
156 integer
= (int)floor(x
);
160 /* K0 = 1, K1 = log(2), K2 = 3-4*log(2), K3 = 3*log(2) - 2 */
161 res
.f
= 0.99992522f
+ frac
* (0.69583354f
162 + frac
* (0.22606716f
+ 0.078024523f
*frac
));
163 res
.i
= (res
.i
+ ((opus_uint32
)integer
<<23)) & 0x7fffffff;
168 #define celt_log2(x) ((float)(1.442695040888963387*log(x)))
169 #define celt_exp2(x) ((float)exp(0.6931471805599453094*(x)))
176 #include "os_support.h"
178 #ifndef OVERRIDE_CELT_ILOG2
179 /** Integer log in base2. Undefined for zero and negative numbers */
180 static OPUS_INLINE opus_int16
celt_ilog2(opus_int32 x
)
182 celt_sig_assert(x
>0);
188 /** Integer log in base2. Defined for zero, but not for negative numbers */
189 static OPUS_INLINE opus_int16
celt_zlog2(opus_val32 x
)
191 return x
<= 0 ? 0 : celt_ilog2(x
);
194 opus_val16
celt_rsqrt_norm(opus_val32 x
);
196 opus_val32
celt_sqrt(opus_val32 x
);
198 opus_val16
celt_cos_norm(opus_val32 x
);
200 /** Base-2 logarithm approximation (log2(x)). (Q14 input, Q10 output) */
201 static OPUS_INLINE opus_val16
celt_log2(opus_val32 x
)
205 /* -0.41509302963303146, 0.9609890551383969, -0.31836011537636605,
206 0.15530808010959576, -0.08556153059057618 */
207 static const opus_val16 C
[5] = {-6801+(1<<(13-DB_SHIFT
)), 15746, -5217, 2545, -1401};
211 n
= VSHR32(x
,i
-15)-32768-16384;
212 frac
= ADD16(C
[0], MULT16_16_Q15(n
, ADD16(C
[1], MULT16_16_Q15(n
, ADD16(C
[2], MULT16_16_Q15(n
, ADD16(C
[3], MULT16_16_Q15(n
, C
[4]))))))));
213 return SHL16(i
-13,DB_SHIFT
)+SHR16(frac
,14-DB_SHIFT
);
227 static OPUS_INLINE opus_val32
celt_exp2_frac(opus_val16 x
)
231 return ADD16(D0
, MULT16_16_Q15(frac
, ADD16(D1
, MULT16_16_Q15(frac
, ADD16(D2
, MULT16_16_Q15(D3
,frac
))))));
233 /** Base-2 exponential approximation (2^x). (Q10 input, Q16 output) */
234 static OPUS_INLINE opus_val32
celt_exp2(opus_val16 x
)
238 integer
= SHR16(x
,10);
241 else if (integer
< -15)
243 frac
= celt_exp2_frac(x
-SHL16(integer
,10));
244 return VSHR32(EXTEND32(frac
), -integer
-2);
247 opus_val32
celt_rcp(opus_val32 x
);
249 #define celt_div(a,b) MULT32_32_Q31((opus_val32)(a),celt_rcp(b))
251 opus_val32
frac_div32(opus_val32 a
, opus_val32 b
);
258 /* Atan approximation using a 4th order polynomial. Input is in Q15 format
259 and normalized by pi/4. Output is in Q15 format */
260 static OPUS_INLINE opus_val16
celt_atan01(opus_val16 x
)
262 return MULT16_16_P15(x
, ADD32(M1
, MULT16_16_P15(x
, ADD32(M2
, MULT16_16_P15(x
, ADD32(M3
, MULT16_16_P15(M4
, x
)))))));
270 /* atan2() approximation valid for positive input values */
271 static OPUS_INLINE opus_val16
celt_atan2p(opus_val16 y
, opus_val16 x
)
276 arg
= celt_div(SHL32(EXTEND32(y
),15),x
);
279 return SHR16(celt_atan01(EXTRACT16(arg
)),1);
282 arg
= celt_div(SHL32(EXTEND32(x
),15),y
);
285 return 25736-SHR16(celt_atan01(EXTRACT16(arg
)),1);
289 #endif /* FIXED_POINT */
290 #endif /* MATHOPS_H */