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 */
5 /**
6 @file mathops.h
7 @brief Various math functions
8 */
9 /*
10 Redistribution and use in source and binary forms, with or without
11 modification, are permitted provided that the following conditions
12 are met:
13
14 - Redistributions of source code must retain the above copyright
15 notice, this list of conditions and the following disclaimer.
16
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.
20
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.
32 */
33
34 #ifndef MATHOPS_H
35 #define MATHOPS_H
36
37 #include "arch.h"
38 #include "entcode.h"
39 #include "os_support.h"
40
41 #define PI 3.141592653f
42
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)
45
46 unsigned isqrt32(opus_uint32 _val);
47
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)
fast_atan2f(float y,float x)54 static OPUS_INLINE float fast_atan2f(float y, float x) {
55 float x2, y2;
56 x2 = x*x;
57 y2 = y*y;
58 /* For very small values, we don't care about the answer, so
59 we can just return 0. */
60 if (x2 + y2 < 1e-18f)
61 {
62 return 0;
63 }
64 if(x2<y2){
65 float den = (y2 + cB*x2) * (y2 + cC*x2);
66 return -x*y*(y2 + cA*x2) / den + (y<0 ? -cE : cE);
67 }else{
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);
70 }
71 }
72 #undef cA
73 #undef cB
74 #undef cC
75 #undef cE
76 #endif
77
78
79 #ifndef OVERRIDE_CELT_MAXABS16
celt_maxabs16(const opus_val16 * x,int len)80 static OPUS_INLINE opus_val32 celt_maxabs16(const opus_val16 *x, int len)
81 {
82 int i;
83 opus_val16 maxval = 0;
84 opus_val16 minval = 0;
85 for (i=0;i<len;i++)
86 {
87 maxval = MAX16(maxval, x[i]);
88 minval = MIN16(minval, x[i]);
89 }
90 return MAX32(EXTEND32(maxval),-EXTEND32(minval));
91 }
92 #endif
93
94 #ifndef OVERRIDE_CELT_MAXABS32
95 #ifdef FIXED_POINT
celt_maxabs32(const opus_val32 * x,int len)96 static OPUS_INLINE opus_val32 celt_maxabs32(const opus_val32 *x, int len)
97 {
98 int i;
99 opus_val32 maxval = 0;
100 opus_val32 minval = 0;
101 for (i=0;i<len;i++)
102 {
103 maxval = MAX32(maxval, x[i]);
104 minval = MIN32(minval, x[i]);
105 }
106 return MAX32(maxval, -minval);
107 }
108 #else
109 #define celt_maxabs32(x,len) celt_maxabs16(x,len)
110 #endif
111 #endif
112
113
114 #ifndef FIXED_POINT
115
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))
123
124 #ifdef FLOAT_APPROX
125
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 */
128
129 /** Base-2 log approximation (log2(x)). */
celt_log2(float x)130 static OPUS_INLINE float celt_log2(float x)
131 {
132 int integer;
133 float frac;
134 union {
135 float f;
136 opus_uint32 i;
137 } in;
138 in.f = x;
139 integer = (in.i>>23)-127;
140 in.i -= integer<<23;
141 frac = in.f - 1.5f;
142 frac = -0.41445418f + frac*(0.95909232f
143 + frac*(-0.33951290f + frac*0.16541097f));
144 return 1+integer+frac;
145 }
146
147 /** Base-2 exponential approximation (2^x). */
celt_exp2(float x)148 static OPUS_INLINE float celt_exp2(float x)
149 {
150 int integer;
151 float frac;
152 union {
153 float f;
154 opus_uint32 i;
155 } res;
156 integer = floor(x);
157 if (integer < -50)
158 return 0;
159 frac = x-integer;
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 + (integer<<23)) & 0x7fffffff;
164 return res.f;
165 }
166
167 #else
168 #define celt_log2(x) ((float)(1.442695040888963387*log(x)))
169 #define celt_exp2(x) ((float)exp(0.6931471805599453094*(x)))
170 #endif
171
172 #endif
173
174 #ifdef FIXED_POINT
175
176 #include "os_support.h"
177
178 #ifndef OVERRIDE_CELT_ILOG2
179 /** Integer log in base2. Undefined for zero and negative numbers */
celt_ilog2(opus_int32 x)180 static OPUS_INLINE opus_int16 celt_ilog2(opus_int32 x)
181 {
182 celt_sig_assert(x>0);
183 return EC_ILOG(x)-1;
184 }
185 #endif
186
187
188 /** Integer log in base2. Defined for zero, but not for negative numbers */
celt_zlog2(opus_val32 x)189 static OPUS_INLINE opus_int16 celt_zlog2(opus_val32 x)
190 {
191 return x <= 0 ? 0 : celt_ilog2(x);
192 }
193
194 opus_val16 celt_rsqrt_norm(opus_val32 x);
195
196 opus_val32 celt_sqrt(opus_val32 x);
197
198 opus_val16 celt_cos_norm(opus_val32 x);
199
200 /** Base-2 logarithm approximation (log2(x)). (Q14 input, Q10 output) */
celt_log2(opus_val32 x)201 static OPUS_INLINE opus_val16 celt_log2(opus_val32 x)
202 {
203 int i;
204 opus_val16 n, frac;
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};
208 if (x==0)
209 return -32767;
210 i = celt_ilog2(x);
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);
214 }
215
216 /*
217 K0 = 1
218 K1 = log(2)
219 K2 = 3-4*log(2)
220 K3 = 3*log(2) - 2
221 */
222 #define D0 16383
223 #define D1 22804
224 #define D2 14819
225 #define D3 10204
226
celt_exp2_frac(opus_val16 x)227 static OPUS_INLINE opus_val32 celt_exp2_frac(opus_val16 x)
228 {
229 opus_val16 frac;
230 frac = SHL16(x, 4);
231 return ADD16(D0, MULT16_16_Q15(frac, ADD16(D1, MULT16_16_Q15(frac, ADD16(D2 , MULT16_16_Q15(D3,frac))))));
232 }
233 /** Base-2 exponential approximation (2^x). (Q10 input, Q16 output) */
celt_exp2(opus_val16 x)234 static OPUS_INLINE opus_val32 celt_exp2(opus_val16 x)
235 {
236 int integer;
237 opus_val16 frac;
238 integer = SHR16(x,10);
239 if (integer>14)
240 return 0x7f000000;
241 else if (integer < -15)
242 return 0;
243 frac = celt_exp2_frac(x-SHL16(integer,10));
244 return VSHR32(EXTEND32(frac), -integer-2);
245 }
246
247 opus_val32 celt_rcp(opus_val32 x);
248
249 #define celt_div(a,b) MULT32_32_Q31((opus_val32)(a),celt_rcp(b))
250
251 opus_val32 frac_div32(opus_val32 a, opus_val32 b);
252
253 #define M1 32767
254 #define M2 -21
255 #define M3 -11943
256 #define M4 4936
257
258 /* Atan approximation using a 4th order polynomial. Input is in Q15 format
259 and normalized by pi/4. Output is in Q15 format */
celt_atan01(opus_val16 x)260 static OPUS_INLINE opus_val16 celt_atan01(opus_val16 x)
261 {
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)))))));
263 }
264
265 #undef M1
266 #undef M2
267 #undef M3
268 #undef M4
269
270 /* atan2() approximation valid for positive input values */
celt_atan2p(opus_val16 y,opus_val16 x)271 static OPUS_INLINE opus_val16 celt_atan2p(opus_val16 y, opus_val16 x)
272 {
273 if (y < x)
274 {
275 opus_val32 arg;
276 arg = celt_div(SHL32(EXTEND32(y),15),x);
277 if (arg >= 32767)
278 arg = 32767;
279 return SHR16(celt_atan01(EXTRACT16(arg)),1);
280 } else {
281 opus_val32 arg;
282 arg = celt_div(SHL32(EXTEND32(x),15),y);
283 if (arg >= 32767)
284 arg = 32767;
285 return 25736-SHR16(celt_atan01(EXTRACT16(arg)),1);
286 }
287 }
288
289 #endif /* FIXED_POINT */
290 #endif /* MATHOPS_H */
291