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 "fft.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
33SINTABLE(16);
34SINTABLE(32);
35SINTABLE(64);
36SINTABLE(128);
37SINTABLE(256);
38SINTABLE(512);
39SINTABLE(1024);
40SINTABLE(2048);
41SINTABLE(4096);
42SINTABLE(8192);
43SINTABLE(16384);
44SINTABLE(32768);
45SINTABLE(65536);
46#endif
47SINTABLE_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 */
57static void ff_rdft_calc_c(RDFTContext* s, FFTSample* data)
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        ff_fft_permute(&s->fft, (FFTComplex*)data);
69        ff_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        ff_fft_permute(&s->fft, (FFTComplex*)data);
95        ff_fft_calc(&s->fft, (FFTComplex*)data);
96    }
97}
98
99av_cold int ff_rdft_init(RDFTContext *s, int nbits, enum RDFTransformType trans)
100{
101    int n = 1 << nbits;
102    int i;
103    const double theta = (trans == DFT_R2C || trans == DFT_C2R ? -1 : 1)*2*M_PI/n;
104
105    s->nbits           = nbits;
106    s->inverse         = trans == IDFT_C2R || trans == DFT_C2R;
107    s->sign_convention = trans == IDFT_R2C || trans == DFT_C2R ? 1 : -1;
108
109    if (nbits < 4 || nbits > 16)
110        return -1;
111
112    if (ff_fft_init(&s->fft, nbits-1, trans == IDFT_C2R || trans == IDFT_R2C) < 0)
113        return -1;
114
115    ff_init_ff_cos_tabs(nbits);
116    s->tcos = ff_cos_tabs[nbits];
117    s->tsin = ff_sin_tabs[nbits]+(trans == DFT_R2C || trans == DFT_C2R)*(n>>2);
118#if !CONFIG_HARDCODED_TABLES
119    for (i = 0; i < (n>>2); i++) {
120        s->tsin[i] = sin(i*theta);
121    }
122#endif
123    s->rdft_calc   = ff_rdft_calc_c;
124
125    if (ARCH_ARM) ff_rdft_init_arm(s);
126
127    return 0;
128}
129
130av_cold void ff_rdft_end(RDFTContext *s)
131{
132    ff_fft_end(&s->fft);
133}
134