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rdft.c
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1 /*
2  * (I)RDFT transforms
3  * Copyright (c) 2009 Alex Converse <alex dot converse at gmail dot com>
4  *
5  * This file is part of FFmpeg.
6  *
7  * FFmpeg is free software; you can redistribute it and/or
8  * modify it under the terms of the GNU Lesser General Public
9  * License as published by the Free Software Foundation; either
10  * version 2.1 of the License, or (at your option) any later version.
11  *
12  * FFmpeg is distributed in the hope that it will be useful,
13  * but WITHOUT ANY WARRANTY; without even the implied warranty of
14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
15  * Lesser General Public License for more details.
16  *
17  * You should have received a copy of the GNU Lesser General Public
18  * License along with FFmpeg; if not, write to the Free Software
19  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
20  */
21 #include <stdlib.h>
22 #include <math.h>
23 #include "libavutil/mathematics.h"
24 #include "rdft.h"
25 
26 /**
27  * @file
28  * (Inverse) Real Discrete Fourier Transforms.
29  */
30 
31 /* sin(2*pi*x/n) for 0<=x<n/4, followed by n/2<=x<3n/4 */
32 #if !CONFIG_HARDCODED_TABLES
33 SINTABLE(16);
34 SINTABLE(32);
35 SINTABLE(64);
36 SINTABLE(128);
37 SINTABLE(256);
38 SINTABLE(512);
39 SINTABLE(1024);
40 SINTABLE(2048);
41 SINTABLE(4096);
42 SINTABLE(8192);
43 SINTABLE(16384);
44 SINTABLE(32768);
45 SINTABLE(65536);
46 #endif
47 static SINTABLE_CONST FFTSample * const ff_sin_tabs[] = {
48  NULL, NULL, NULL, NULL,
49  ff_sin_16, ff_sin_32, ff_sin_64, ff_sin_128, ff_sin_256, ff_sin_512, ff_sin_1024,
50  ff_sin_2048, ff_sin_4096, ff_sin_8192, ff_sin_16384, ff_sin_32768, ff_sin_65536,
51 };
52 
53 /** Map one real FFT into two parallel real even and odd FFTs. Then interleave
54  * the two real FFTs into one complex FFT. Unmangle the results.
55  * ref: http://www.engineeringproductivitytools.com/stuff/T0001/PT10.HTM
56  */
58 {
59  int i, i1, i2;
60  FFTComplex ev, od;
61  const int n = 1 << s->nbits;
62  const float k1 = 0.5;
63  const float k2 = 0.5 - s->inverse;
64  const FFTSample *tcos = s->tcos;
65  const FFTSample *tsin = s->tsin;
66 
67  if (!s->inverse) {
68  s->fft.fft_permute(&s->fft, (FFTComplex*)data);
69  s->fft.fft_calc(&s->fft, (FFTComplex*)data);
70  }
71  /* i=0 is a special case because of packing, the DC term is real, so we
72  are going to throw the N/2 term (also real) in with it. */
73  ev.re = data[0];
74  data[0] = ev.re+data[1];
75  data[1] = ev.re-data[1];
76  for (i = 1; i < (n>>2); i++) {
77  i1 = 2*i;
78  i2 = n-i1;
79  /* Separate even and odd FFTs */
80  ev.re = k1*(data[i1 ]+data[i2 ]);
81  od.im = -k2*(data[i1 ]-data[i2 ]);
82  ev.im = k1*(data[i1+1]-data[i2+1]);
83  od.re = k2*(data[i1+1]+data[i2+1]);
84  /* Apply twiddle factors to the odd FFT and add to the even FFT */
85  data[i1 ] = ev.re + od.re*tcos[i] - od.im*tsin[i];
86  data[i1+1] = ev.im + od.im*tcos[i] + od.re*tsin[i];
87  data[i2 ] = ev.re - od.re*tcos[i] + od.im*tsin[i];
88  data[i2+1] = -ev.im + od.im*tcos[i] + od.re*tsin[i];
89  }
90  data[2*i+1]=s->sign_convention*data[2*i+1];
91  if (s->inverse) {
92  data[0] *= k1;
93  data[1] *= k1;
94  s->fft.fft_permute(&s->fft, (FFTComplex*)data);
95  s->fft.fft_calc(&s->fft, (FFTComplex*)data);
96  }
97 }
98 
99 av_cold int ff_rdft_init(RDFTContext *s, int nbits, enum RDFTransformType trans)
100 {
101  int n = 1 << nbits;
102 
103  s->nbits = nbits;
104  s->inverse = trans == IDFT_C2R || trans == DFT_C2R;
105  s->sign_convention = trans == IDFT_R2C || trans == DFT_C2R ? 1 : -1;
106 
107  if (nbits < 4 || nbits > 16)
108  return -1;
109 
110  if (ff_fft_init(&s->fft, nbits-1, trans == IDFT_C2R || trans == IDFT_R2C) < 0)
111  return -1;
112 
113  ff_init_ff_cos_tabs(nbits);
114  s->tcos = ff_cos_tabs[nbits];
115  s->tsin = ff_sin_tabs[nbits]+(trans == DFT_R2C || trans == DFT_C2R)*(n>>2);
116 #if !CONFIG_HARDCODED_TABLES
117  {
118  int i;
119  const double theta = (trans == DFT_R2C || trans == DFT_C2R ? -1 : 1) * 2 * M_PI / n;
120  for (i = 0; i < (n >> 2); i++)
121  s->tsin[i] = sin(i * theta);
122  }
123 #endif
124  s->rdft_calc = rdft_calc_c;
125 
126  if (ARCH_ARM) ff_rdft_init_arm(s);
127 
128  return 0;
129 }
130 
132 {
133  ff_fft_end(&s->fft);
134 }