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
44unsigned isqrt32(opus_uint32 _val);
45
46#ifndef FIXED_POINT
47
48#define PI 3.141592653f
49#define celt_sqrt(x) ((float)sqrt(x))
50#define celt_rsqrt(x) (1.f/celt_sqrt(x))
51#define celt_rsqrt_norm(x) (celt_rsqrt(x))
52#define celt_cos_norm(x) ((float)cos((.5f*PI)*(x)))
53#define celt_rcp(x) (1.f/(x))
54#define celt_div(a,b) ((a)/(b))
55#define frac_div32(a,b) ((float)(a)/(b))
56
57#ifdef FLOAT_APPROX
58
59/* Note: This assumes radix-2 floating point with the exponent at bits 23..30 and an offset of 127
60         denorm, +/- inf and NaN are *not* handled */
61
62/** Base-2 log approximation (log2(x)). */
63static inline float celt_log2(float x)
64{
65   int integer;
66   float frac;
67   union {
68      float f;
69      opus_uint32 i;
70   } in;
71   in.f = x;
72   integer = (in.i>>23)-127;
73   in.i -= integer<<23;
74   frac = in.f - 1.5f;
75   frac = -0.41445418f + frac*(0.95909232f
76          + frac*(-0.33951290f + frac*0.16541097f));
77   return 1+integer+frac;
78}
79
80/** Base-2 exponential approximation (2^x). */
81static inline float celt_exp2(float x)
82{
83   int integer;
84   float frac;
85   union {
86      float f;
87      opus_uint32 i;
88   } res;
89   integer = floor(x);
90   if (integer < -50)
91      return 0;
92   frac = x-integer;
93   /* K0 = 1, K1 = log(2), K2 = 3-4*log(2), K3 = 3*log(2) - 2 */
94   res.f = 0.99992522f + frac * (0.69583354f
95           + frac * (0.22606716f + 0.078024523f*frac));
96   res.i = (res.i + (integer<<23)) & 0x7fffffff;
97   return res.f;
98}
99
100#else
101#define celt_log2(x) ((float)(1.442695040888963387*log(x)))
102#define celt_exp2(x) ((float)exp(0.6931471805599453094*(x)))
103#endif
104
105#endif
106
107#ifdef FIXED_POINT
108
109#include "os_support.h"
110
111#ifndef OVERRIDE_CELT_ILOG2
112/** Integer log in base2. Undefined for zero and negative numbers */
113static inline opus_int16 celt_ilog2(opus_int32 x)
114{
115   celt_assert2(x>0, "celt_ilog2() only defined for strictly positive numbers");
116   return EC_ILOG(x)-1;
117}
118#endif
119
120#ifndef OVERRIDE_CELT_MAXABS16
121static inline opus_val16 celt_maxabs16(opus_val16 *x, int len)
122{
123   int i;
124   opus_val16 maxval = 0;
125   for (i=0;i<len;i++)
126      maxval = MAX16(maxval, ABS16(x[i]));
127   return maxval;
128}
129#endif
130
131#ifndef OVERRIDE_CELT_MAXABS32
132static inline opus_val32 celt_maxabs32(opus_val32 *x, int len)
133{
134   int i;
135   opus_val32 maxval = 0;
136   for (i=0;i<len;i++)
137      maxval = MAX32(maxval, ABS32(x[i]));
138   return maxval;
139}
140#endif
141
142/** Integer log in base2. Defined for zero, but not for negative numbers */
143static inline opus_int16 celt_zlog2(opus_val32 x)
144{
145   return x <= 0 ? 0 : celt_ilog2(x);
146}
147
148opus_val16 celt_rsqrt_norm(opus_val32 x);
149
150opus_val32 celt_sqrt(opus_val32 x);
151
152opus_val16 celt_cos_norm(opus_val32 x);
153
154static inline opus_val16 celt_log2(opus_val32 x)
155{
156   int i;
157   opus_val16 n, frac;
158   /* -0.41509302963303146, 0.9609890551383969, -0.31836011537636605,
159       0.15530808010959576, -0.08556153059057618 */
160   static const opus_val16 C[5] = {-6801+(1<<(13-DB_SHIFT)), 15746, -5217, 2545, -1401};
161   if (x==0)
162      return -32767;
163   i = celt_ilog2(x);
164   n = VSHR32(x,i-15)-32768-16384;
165   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]))))))));
166   return SHL16(i-13,DB_SHIFT)+SHR16(frac,14-DB_SHIFT);
167}
168
169/*
170 K0 = 1
171 K1 = log(2)
172 K2 = 3-4*log(2)
173 K3 = 3*log(2) - 2
174*/
175#define D0 16383
176#define D1 22804
177#define D2 14819
178#define D3 10204
179/** Base-2 exponential approximation (2^x). (Q10 input, Q16 output) */
180static inline opus_val32 celt_exp2(opus_val16 x)
181{
182   int integer;
183   opus_val16 frac;
184   integer = SHR16(x,10);
185   if (integer>14)
186      return 0x7f000000;
187   else if (integer < -15)
188      return 0;
189   frac = SHL16(x-SHL16(integer,10),4);
190   frac = ADD16(D0, MULT16_16_Q15(frac, ADD16(D1, MULT16_16_Q15(frac, ADD16(D2 , MULT16_16_Q15(D3,frac))))));
191   return VSHR32(EXTEND32(frac), -integer-2);
192}
193
194opus_val32 celt_rcp(opus_val32 x);
195
196#define celt_div(a,b) MULT32_32_Q31((opus_val32)(a),celt_rcp(b))
197
198opus_val32 frac_div32(opus_val32 a, opus_val32 b);
199
200#define M1 32767
201#define M2 -21
202#define M3 -11943
203#define M4 4936
204
205/* Atan approximation using a 4th order polynomial. Input is in Q15 format
206   and normalized by pi/4. Output is in Q15 format */
207static inline opus_val16 celt_atan01(opus_val16 x)
208{
209   return MULT16_16_P15(x, ADD32(M1, MULT16_16_P15(x, ADD32(M2, MULT16_16_P15(x, ADD32(M3, MULT16_16_P15(M4, x)))))));
210}
211
212#undef M1
213#undef M2
214#undef M3
215#undef M4
216
217/* atan2() approximation valid for positive input values */
218static inline opus_val16 celt_atan2p(opus_val16 y, opus_val16 x)
219{
220   if (y < x)
221   {
222      opus_val32 arg;
223      arg = celt_div(SHL32(EXTEND32(y),15),x);
224      if (arg >= 32767)
225         arg = 32767;
226      return SHR16(celt_atan01(EXTRACT16(arg)),1);
227   } else {
228      opus_val32 arg;
229      arg = celt_div(SHL32(EXTEND32(x),15),y);
230      if (arg >= 32767)
231         arg = 32767;
232      return 25736-SHR16(celt_atan01(EXTRACT16(arg)),1);
233   }
234}
235
236#endif /* FIXED_POINT */
237#endif /* MATHOPS_H */
238