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 /* Multiplies two 16-bit fractional values. Bit-exactness of this macro is important */
42 #define FRAC_MUL16(a,b) ((16384+((opus_int32)(opus_int16)(a)*(opus_int16)(b)))>>15)
43
44 unsigned isqrt32(opus_uint32 _val);
45
46 #ifndef OVERRIDE_CELT_MAXABS16
celt_maxabs16(const opus_val16 * x,int len)47 static OPUS_INLINE opus_val32 celt_maxabs16(const opus_val16 *x, int len)
48 {
49 int i;
50 opus_val16 maxval = 0;
51 opus_val16 minval = 0;
52 for (i=0;i<len;i++)
53 {
54 maxval = MAX16(maxval, x[i]);
55 minval = MIN16(minval, x[i]);
56 }
57 return MAX32(EXTEND32(maxval),-EXTEND32(minval));
58 }
59 #endif
60
61 #ifndef OVERRIDE_CELT_MAXABS32
62 #ifdef FIXED_POINT
celt_maxabs32(const opus_val32 * x,int len)63 static OPUS_INLINE opus_val32 celt_maxabs32(const opus_val32 *x, int len)
64 {
65 int i;
66 opus_val32 maxval = 0;
67 opus_val32 minval = 0;
68 for (i=0;i<len;i++)
69 {
70 maxval = MAX32(maxval, x[i]);
71 minval = MIN32(minval, x[i]);
72 }
73 return MAX32(maxval, -minval);
74 }
75 #else
76 #define celt_maxabs32(x,len) celt_maxabs16(x,len)
77 #endif
78 #endif
79
80
81 #ifndef FIXED_POINT
82
83 #define PI 3.141592653f
84 #define celt_sqrt(x) ((float)sqrt(x))
85 #define celt_rsqrt(x) (1.f/celt_sqrt(x))
86 #define celt_rsqrt_norm(x) (celt_rsqrt(x))
87 #define celt_cos_norm(x) ((float)cos((.5f*PI)*(x)))
88 #define celt_rcp(x) (1.f/(x))
89 #define celt_div(a,b) ((a)/(b))
90 #define frac_div32(a,b) ((float)(a)/(b))
91
92 #ifdef FLOAT_APPROX
93
94 /* Note: This assumes radix-2 floating point with the exponent at bits 23..30 and an offset of 127
95 denorm, +/- inf and NaN are *not* handled */
96
97 /** Base-2 log approximation (log2(x)). */
celt_log2(float x)98 static OPUS_INLINE float celt_log2(float x)
99 {
100 int integer;
101 float frac;
102 union {
103 float f;
104 opus_uint32 i;
105 } in;
106 in.f = x;
107 integer = (in.i>>23)-127;
108 in.i -= integer<<23;
109 frac = in.f - 1.5f;
110 frac = -0.41445418f + frac*(0.95909232f
111 + frac*(-0.33951290f + frac*0.16541097f));
112 return 1+integer+frac;
113 }
114
115 /** Base-2 exponential approximation (2^x). */
celt_exp2(float x)116 static OPUS_INLINE float celt_exp2(float x)
117 {
118 int integer;
119 float frac;
120 union {
121 float f;
122 opus_uint32 i;
123 } res;
124 integer = floor(x);
125 if (integer < -50)
126 return 0;
127 frac = x-integer;
128 /* K0 = 1, K1 = log(2), K2 = 3-4*log(2), K3 = 3*log(2) - 2 */
129 res.f = 0.99992522f + frac * (0.69583354f
130 + frac * (0.22606716f + 0.078024523f*frac));
131 res.i = (res.i + (integer<<23)) & 0x7fffffff;
132 return res.f;
133 }
134
135 #else
136 #define celt_log2(x) ((float)(1.442695040888963387*log(x)))
137 #define celt_exp2(x) ((float)exp(0.6931471805599453094*(x)))
138 #endif
139
140 #endif
141
142 #ifdef FIXED_POINT
143
144 #include "os_support.h"
145
146 #ifndef OVERRIDE_CELT_ILOG2
147 /** Integer log in base2. Undefined for zero and negative numbers */
celt_ilog2(opus_int32 x)148 static OPUS_INLINE opus_int16 celt_ilog2(opus_int32 x)
149 {
150 celt_assert2(x>0, "celt_ilog2() only defined for strictly positive numbers");
151 return EC_ILOG(x)-1;
152 }
153 #endif
154
155
156 /** Integer log in base2. Defined for zero, but not for negative numbers */
celt_zlog2(opus_val32 x)157 static OPUS_INLINE opus_int16 celt_zlog2(opus_val32 x)
158 {
159 return x <= 0 ? 0 : celt_ilog2(x);
160 }
161
162 opus_val16 celt_rsqrt_norm(opus_val32 x);
163
164 opus_val32 celt_sqrt(opus_val32 x);
165
166 opus_val16 celt_cos_norm(opus_val32 x);
167
168 /** Base-2 logarithm approximation (log2(x)). (Q14 input, Q10 output) */
celt_log2(opus_val32 x)169 static OPUS_INLINE opus_val16 celt_log2(opus_val32 x)
170 {
171 int i;
172 opus_val16 n, frac;
173 /* -0.41509302963303146, 0.9609890551383969, -0.31836011537636605,
174 0.15530808010959576, -0.08556153059057618 */
175 static const opus_val16 C[5] = {-6801+(1<<(13-DB_SHIFT)), 15746, -5217, 2545, -1401};
176 if (x==0)
177 return -32767;
178 i = celt_ilog2(x);
179 n = VSHR32(x,i-15)-32768-16384;
180 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]))))))));
181 return SHL16(i-13,DB_SHIFT)+SHR16(frac,14-DB_SHIFT);
182 }
183
184 /*
185 K0 = 1
186 K1 = log(2)
187 K2 = 3-4*log(2)
188 K3 = 3*log(2) - 2
189 */
190 #define D0 16383
191 #define D1 22804
192 #define D2 14819
193 #define D3 10204
194
celt_exp2_frac(opus_val16 x)195 static OPUS_INLINE opus_val32 celt_exp2_frac(opus_val16 x)
196 {
197 opus_val16 frac;
198 frac = SHL16(x, 4);
199 return ADD16(D0, MULT16_16_Q15(frac, ADD16(D1, MULT16_16_Q15(frac, ADD16(D2 , MULT16_16_Q15(D3,frac))))));
200 }
201 /** Base-2 exponential approximation (2^x). (Q10 input, Q16 output) */
celt_exp2(opus_val16 x)202 static OPUS_INLINE opus_val32 celt_exp2(opus_val16 x)
203 {
204 int integer;
205 opus_val16 frac;
206 integer = SHR16(x,10);
207 if (integer>14)
208 return 0x7f000000;
209 else if (integer < -15)
210 return 0;
211 frac = celt_exp2_frac(x-SHL16(integer,10));
212 return VSHR32(EXTEND32(frac), -integer-2);
213 }
214
215 opus_val32 celt_rcp(opus_val32 x);
216
217 #define celt_div(a,b) MULT32_32_Q31((opus_val32)(a),celt_rcp(b))
218
219 opus_val32 frac_div32(opus_val32 a, opus_val32 b);
220
221 #define M1 32767
222 #define M2 -21
223 #define M3 -11943
224 #define M4 4936
225
226 /* Atan approximation using a 4th order polynomial. Input is in Q15 format
227 and normalized by pi/4. Output is in Q15 format */
celt_atan01(opus_val16 x)228 static OPUS_INLINE opus_val16 celt_atan01(opus_val16 x)
229 {
230 return MULT16_16_P15(x, ADD32(M1, MULT16_16_P15(x, ADD32(M2, MULT16_16_P15(x, ADD32(M3, MULT16_16_P15(M4, x)))))));
231 }
232
233 #undef M1
234 #undef M2
235 #undef M3
236 #undef M4
237
238 /* atan2() approximation valid for positive input values */
celt_atan2p(opus_val16 y,opus_val16 x)239 static OPUS_INLINE opus_val16 celt_atan2p(opus_val16 y, opus_val16 x)
240 {
241 if (y < x)
242 {
243 opus_val32 arg;
244 arg = celt_div(SHL32(EXTEND32(y),15),x);
245 if (arg >= 32767)
246 arg = 32767;
247 return SHR16(celt_atan01(EXTRACT16(arg)),1);
248 } else {
249 opus_val32 arg;
250 arg = celt_div(SHL32(EXTEND32(x),15),y);
251 if (arg >= 32767)
252 arg = 32767;
253 return 25736-SHR16(celt_atan01(EXTRACT16(arg)),1);
254 }
255 }
256
257 #endif /* FIXED_POINT */
258 #endif /* MATHOPS_H */
259