1/*
2 * MDCT/IMDCT transforms
3 * Copyright (c) 2002 Fabrice Bellard
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
22#include <stdlib.h>
23#include <string.h>
24#include "libavutil/common.h"
25#include "libavutil/mathematics.h"
26#include "fft.h"
27
28/**
29 * @file
30 * MDCT/IMDCT transforms.
31 */
32
33// Generate a Kaiser-Bessel Derived Window.
34#define BESSEL_I0_ITER 50 // default: 50 iterations of Bessel I0 approximation
35av_cold void ff_kbd_window_init(float *window, float alpha, int n)
36{
37   int i, j;
38   double sum = 0.0, bessel, tmp;
39   double local_window[n];
40   double alpha2 = (alpha * M_PI / n) * (alpha * M_PI / n);
41
42   for (i = 0; i < n; i++) {
43       tmp = i * (n - i) * alpha2;
44       bessel = 1.0;
45       for (j = BESSEL_I0_ITER; j > 0; j--)
46           bessel = bessel * tmp / (j * j) + 1;
47       sum += bessel;
48       local_window[i] = sum;
49   }
50
51   sum++;
52   for (i = 0; i < n; i++)
53       window[i] = sqrt(local_window[i] / sum);
54}
55
56#include "mdct_tablegen.h"
57
58/**
59 * init MDCT or IMDCT computation.
60 */
61av_cold int ff_mdct_init(FFTContext *s, int nbits, int inverse, double scale)
62{
63    int n, n4, i;
64    double alpha, theta;
65    int tstep;
66
67    memset(s, 0, sizeof(*s));
68    n = 1 << nbits;
69    s->mdct_bits = nbits;
70    s->mdct_size = n;
71    n4 = n >> 2;
72    s->permutation = FF_MDCT_PERM_NONE;
73
74    if (ff_fft_init(s, s->mdct_bits - 2, inverse) < 0)
75        goto fail;
76
77    s->tcos = av_malloc(n/2 * sizeof(FFTSample));
78    if (!s->tcos)
79        goto fail;
80
81    switch (s->permutation) {
82    case FF_MDCT_PERM_NONE:
83        s->tsin = s->tcos + n4;
84        tstep = 1;
85        break;
86    case FF_MDCT_PERM_INTERLEAVE:
87        s->tsin = s->tcos + 1;
88        tstep = 2;
89        break;
90    default:
91        goto fail;
92    }
93
94    theta = 1.0 / 8.0 + (scale < 0 ? n4 : 0);
95    scale = sqrt(fabs(scale));
96    for(i=0;i<n4;i++) {
97        alpha = 2 * M_PI * (i + theta) / n;
98        s->tcos[i*tstep] = -cos(alpha) * scale;
99        s->tsin[i*tstep] = -sin(alpha) * scale;
100    }
101    return 0;
102 fail:
103    ff_mdct_end(s);
104    return -1;
105}
106
107/* complex multiplication: p = a * b */
108#define CMUL(pre, pim, are, aim, bre, bim) \
109{\
110    FFTSample _are = (are);\
111    FFTSample _aim = (aim);\
112    FFTSample _bre = (bre);\
113    FFTSample _bim = (bim);\
114    (pre) = _are * _bre - _aim * _bim;\
115    (pim) = _are * _bim + _aim * _bre;\
116}
117
118/**
119 * Compute the middle half of the inverse MDCT of size N = 2^nbits,
120 * thus excluding the parts that can be derived by symmetry
121 * @param output N/2 samples
122 * @param input N/2 samples
123 */
124void ff_imdct_half_c(FFTContext *s, FFTSample *output, const FFTSample *input)
125{
126    int k, n8, n4, n2, n, j;
127    const uint16_t *revtab = s->revtab;
128    const FFTSample *tcos = s->tcos;
129    const FFTSample *tsin = s->tsin;
130    const FFTSample *in1, *in2;
131    FFTComplex *z = (FFTComplex *)output;
132
133    n = 1 << s->mdct_bits;
134    n2 = n >> 1;
135    n4 = n >> 2;
136    n8 = n >> 3;
137
138    /* pre rotation */
139    in1 = input;
140    in2 = input + n2 - 1;
141    for(k = 0; k < n4; k++) {
142        j=revtab[k];
143        CMUL(z[j].re, z[j].im, *in2, *in1, tcos[k], tsin[k]);
144        in1 += 2;
145        in2 -= 2;
146    }
147    ff_fft_calc(s, z);
148
149    /* post rotation + reordering */
150    for(k = 0; k < n8; k++) {
151        FFTSample r0, i0, r1, i1;
152        CMUL(r0, i1, z[n8-k-1].im, z[n8-k-1].re, tsin[n8-k-1], tcos[n8-k-1]);
153        CMUL(r1, i0, z[n8+k  ].im, z[n8+k  ].re, tsin[n8+k  ], tcos[n8+k  ]);
154        z[n8-k-1].re = r0;
155        z[n8-k-1].im = i0;
156        z[n8+k  ].re = r1;
157        z[n8+k  ].im = i1;
158    }
159}
160
161/**
162 * Compute inverse MDCT of size N = 2^nbits
163 * @param output N samples
164 * @param input N/2 samples
165 */
166void ff_imdct_calc_c(FFTContext *s, FFTSample *output, const FFTSample *input)
167{
168    int k;
169    int n = 1 << s->mdct_bits;
170    int n2 = n >> 1;
171    int n4 = n >> 2;
172
173    ff_imdct_half_c(s, output+n4, input);
174
175    for(k = 0; k < n4; k++) {
176        output[k] = -output[n2-k-1];
177        output[n-k-1] = output[n2+k];
178    }
179}
180
181/**
182 * Compute MDCT of size N = 2^nbits
183 * @param input N samples
184 * @param out N/2 samples
185 */
186void ff_mdct_calc_c(FFTContext *s, FFTSample *out, const FFTSample *input)
187{
188    int i, j, n, n8, n4, n2, n3;
189    FFTSample re, im;
190    const uint16_t *revtab = s->revtab;
191    const FFTSample *tcos = s->tcos;
192    const FFTSample *tsin = s->tsin;
193    FFTComplex *x = (FFTComplex *)out;
194
195    n = 1 << s->mdct_bits;
196    n2 = n >> 1;
197    n4 = n >> 2;
198    n8 = n >> 3;
199    n3 = 3 * n4;
200
201    /* pre rotation */
202    for(i=0;i<n8;i++) {
203        re = -input[2*i+3*n4] - input[n3-1-2*i];
204        im = -input[n4+2*i] + input[n4-1-2*i];
205        j = revtab[i];
206        CMUL(x[j].re, x[j].im, re, im, -tcos[i], tsin[i]);
207
208        re = input[2*i] - input[n2-1-2*i];
209        im = -(input[n2+2*i] + input[n-1-2*i]);
210        j = revtab[n8 + i];
211        CMUL(x[j].re, x[j].im, re, im, -tcos[n8 + i], tsin[n8 + i]);
212    }
213
214    ff_fft_calc(s, x);
215
216    /* post rotation */
217    for(i=0;i<n8;i++) {
218        FFTSample r0, i0, r1, i1;
219        CMUL(i1, r0, x[n8-i-1].re, x[n8-i-1].im, -tsin[n8-i-1], -tcos[n8-i-1]);
220        CMUL(i0, r1, x[n8+i  ].re, x[n8+i  ].im, -tsin[n8+i  ], -tcos[n8+i  ]);
221        x[n8-i-1].re = r0;
222        x[n8-i-1].im = i0;
223        x[n8+i  ].re = r1;
224        x[n8+i  ].im = i1;
225    }
226}
227
228av_cold void ff_mdct_end(FFTContext *s)
229{
230    av_freep(&s->tcos);
231    ff_fft_end(s);
232}
233