1/*
2 * FFT/IFFT transforms
3 * Copyright (c) 2008 Loren Merritt
4 * Copyright (c) 2002 Fabrice Bellard
5 * Partly based on libdjbfft by D. J. Bernstein
6 *
7 * This file is part of FFmpeg.
8 *
9 * FFmpeg is free software; you can redistribute it and/or
10 * modify it under the terms of the GNU Lesser General Public
11 * License as published by the Free Software Foundation; either
12 * version 2.1 of the License, or (at your option) any later version.
13 *
14 * FFmpeg is distributed in the hope that it will be useful,
15 * but WITHOUT ANY WARRANTY; without even the implied warranty of
16 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
17 * Lesser General Public License for more details.
18 *
19 * You should have received a copy of the GNU Lesser General Public
20 * License along with FFmpeg; if not, write to the Free Software
21 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
22 */
23
24/**
25 * @file
26 * FFT/IFFT transforms.
27 */
28
29#include <stdlib.h>
30#include <string.h>
31#include "libavutil/mathematics.h"
32#include "fft.h"
33
34/* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
35#if !CONFIG_HARDCODED_TABLES
36COSTABLE(16);
37COSTABLE(32);
38COSTABLE(64);
39COSTABLE(128);
40COSTABLE(256);
41COSTABLE(512);
42COSTABLE(1024);
43COSTABLE(2048);
44COSTABLE(4096);
45COSTABLE(8192);
46COSTABLE(16384);
47COSTABLE(32768);
48COSTABLE(65536);
49#endif
50COSTABLE_CONST FFTSample * const ff_cos_tabs[] = {
51    NULL, NULL, NULL, NULL,
52    ff_cos_16, ff_cos_32, ff_cos_64, ff_cos_128, ff_cos_256, ff_cos_512, ff_cos_1024,
53    ff_cos_2048, ff_cos_4096, ff_cos_8192, ff_cos_16384, ff_cos_32768, ff_cos_65536,
54};
55
56static int split_radix_permutation(int i, int n, int inverse)
57{
58    int m;
59    if(n <= 2) return i&1;
60    m = n >> 1;
61    if(!(i&m))            return split_radix_permutation(i, m, inverse)*2;
62    m >>= 1;
63    if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
64    else                  return split_radix_permutation(i, m, inverse)*4 - 1;
65}
66
67av_cold void ff_init_ff_cos_tabs(int index)
68{
69#if !CONFIG_HARDCODED_TABLES
70    int i;
71    int m = 1<<index;
72    double freq = 2*M_PI/m;
73    FFTSample *tab = ff_cos_tabs[index];
74    for(i=0; i<=m/4; i++)
75        tab[i] = cos(i*freq);
76    for(i=1; i<m/4; i++)
77        tab[m/2-i] = tab[i];
78#endif
79}
80
81av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
82{
83    int i, j, m, n;
84    float alpha, c1, s1, s2;
85    int av_unused has_vectors;
86
87    if (nbits < 2 || nbits > 16)
88        goto fail;
89    s->nbits = nbits;
90    n = 1 << nbits;
91
92    s->tmp_buf = NULL;
93    s->exptab  = av_malloc((n / 2) * sizeof(FFTComplex));
94    if (!s->exptab)
95        goto fail;
96    s->revtab = av_malloc(n * sizeof(uint16_t));
97    if (!s->revtab)
98        goto fail;
99    s->inverse = inverse;
100
101    s2 = inverse ? 1.0 : -1.0;
102
103    s->fft_permute = ff_fft_permute_c;
104    s->fft_calc    = ff_fft_calc_c;
105#if CONFIG_MDCT
106    s->imdct_calc  = ff_imdct_calc_c;
107    s->imdct_half  = ff_imdct_half_c;
108    s->mdct_calc   = ff_mdct_calc_c;
109#endif
110    s->exptab1     = NULL;
111    s->split_radix = 1;
112
113    if (ARCH_ARM)     ff_fft_init_arm(s);
114    if (HAVE_ALTIVEC) ff_fft_init_altivec(s);
115    if (HAVE_MMX)     ff_fft_init_mmx(s);
116
117    if (s->split_radix) {
118        for(j=4; j<=nbits; j++) {
119            ff_init_ff_cos_tabs(j);
120        }
121        for(i=0; i<n; i++)
122            s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = i;
123        s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
124    } else {
125        int np, nblocks, np2, l;
126        FFTComplex *q;
127
128        for(i=0; i<(n/2); i++) {
129            alpha = 2 * M_PI * (float)i / (float)n;
130            c1 = cos(alpha);
131            s1 = sin(alpha) * s2;
132            s->exptab[i].re = c1;
133            s->exptab[i].im = s1;
134        }
135
136        np = 1 << nbits;
137        nblocks = np >> 3;
138        np2 = np >> 1;
139        s->exptab1 = av_malloc(np * 2 * sizeof(FFTComplex));
140        if (!s->exptab1)
141            goto fail;
142        q = s->exptab1;
143        do {
144            for(l = 0; l < np2; l += 2 * nblocks) {
145                *q++ = s->exptab[l];
146                *q++ = s->exptab[l + nblocks];
147
148                q->re = -s->exptab[l].im;
149                q->im = s->exptab[l].re;
150                q++;
151                q->re = -s->exptab[l + nblocks].im;
152                q->im = s->exptab[l + nblocks].re;
153                q++;
154            }
155            nblocks = nblocks >> 1;
156        } while (nblocks != 0);
157        av_freep(&s->exptab);
158
159        /* compute bit reverse table */
160        for(i=0;i<n;i++) {
161            m=0;
162            for(j=0;j<nbits;j++) {
163                m |= ((i >> j) & 1) << (nbits-j-1);
164            }
165            s->revtab[i]=m;
166        }
167    }
168
169    return 0;
170 fail:
171    av_freep(&s->revtab);
172    av_freep(&s->exptab);
173    av_freep(&s->exptab1);
174    av_freep(&s->tmp_buf);
175    return -1;
176}
177
178void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
179{
180    int j, k, np;
181    FFTComplex tmp;
182    const uint16_t *revtab = s->revtab;
183    np = 1 << s->nbits;
184
185    if (s->tmp_buf) {
186        /* TODO: handle split-radix permute in a more optimal way, probably in-place */
187        for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
188        memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
189        return;
190    }
191
192    /* reverse */
193    for(j=0;j<np;j++) {
194        k = revtab[j];
195        if (k < j) {
196            tmp = z[k];
197            z[k] = z[j];
198            z[j] = tmp;
199        }
200    }
201}
202
203av_cold void ff_fft_end(FFTContext *s)
204{
205    av_freep(&s->revtab);
206    av_freep(&s->exptab);
207    av_freep(&s->exptab1);
208    av_freep(&s->tmp_buf);
209}
210
211#define sqrthalf (float)M_SQRT1_2
212
213#define BF(x,y,a,b) {\
214    x = a - b;\
215    y = a + b;\
216}
217
218#define BUTTERFLIES(a0,a1,a2,a3) {\
219    BF(t3, t5, t5, t1);\
220    BF(a2.re, a0.re, a0.re, t5);\
221    BF(a3.im, a1.im, a1.im, t3);\
222    BF(t4, t6, t2, t6);\
223    BF(a3.re, a1.re, a1.re, t4);\
224    BF(a2.im, a0.im, a0.im, t6);\
225}
226
227// force loading all the inputs before storing any.
228// this is slightly slower for small data, but avoids store->load aliasing
229// for addresses separated by large powers of 2.
230#define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
231    FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
232    BF(t3, t5, t5, t1);\
233    BF(a2.re, a0.re, r0, t5);\
234    BF(a3.im, a1.im, i1, t3);\
235    BF(t4, t6, t2, t6);\
236    BF(a3.re, a1.re, r1, t4);\
237    BF(a2.im, a0.im, i0, t6);\
238}
239
240#define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
241    t1 = a2.re * wre + a2.im * wim;\
242    t2 = a2.im * wre - a2.re * wim;\
243    t5 = a3.re * wre - a3.im * wim;\
244    t6 = a3.im * wre + a3.re * wim;\
245    BUTTERFLIES(a0,a1,a2,a3)\
246}
247
248#define TRANSFORM_ZERO(a0,a1,a2,a3) {\
249    t1 = a2.re;\
250    t2 = a2.im;\
251    t5 = a3.re;\
252    t6 = a3.im;\
253    BUTTERFLIES(a0,a1,a2,a3)\
254}
255
256/* z[0...8n-1], w[1...2n-1] */
257#define PASS(name)\
258static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
259{\
260    FFTSample t1, t2, t3, t4, t5, t6;\
261    int o1 = 2*n;\
262    int o2 = 4*n;\
263    int o3 = 6*n;\
264    const FFTSample *wim = wre+o1;\
265    n--;\
266\
267    TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
268    TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
269    do {\
270        z += 2;\
271        wre += 2;\
272        wim -= 2;\
273        TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
274        TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
275    } while(--n);\
276}
277
278PASS(pass)
279#undef BUTTERFLIES
280#define BUTTERFLIES BUTTERFLIES_BIG
281PASS(pass_big)
282
283#define DECL_FFT(n,n2,n4)\
284static void fft##n(FFTComplex *z)\
285{\
286    fft##n2(z);\
287    fft##n4(z+n4*2);\
288    fft##n4(z+n4*3);\
289    pass(z,ff_cos_##n,n4/2);\
290}
291
292static void fft4(FFTComplex *z)
293{
294    FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
295
296    BF(t3, t1, z[0].re, z[1].re);
297    BF(t8, t6, z[3].re, z[2].re);
298    BF(z[2].re, z[0].re, t1, t6);
299    BF(t4, t2, z[0].im, z[1].im);
300    BF(t7, t5, z[2].im, z[3].im);
301    BF(z[3].im, z[1].im, t4, t8);
302    BF(z[3].re, z[1].re, t3, t7);
303    BF(z[2].im, z[0].im, t2, t5);
304}
305
306static void fft8(FFTComplex *z)
307{
308    FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
309
310    fft4(z);
311
312    BF(t1, z[5].re, z[4].re, -z[5].re);
313    BF(t2, z[5].im, z[4].im, -z[5].im);
314    BF(t3, z[7].re, z[6].re, -z[7].re);
315    BF(t4, z[7].im, z[6].im, -z[7].im);
316    BF(t8, t1, t3, t1);
317    BF(t7, t2, t2, t4);
318    BF(z[4].re, z[0].re, z[0].re, t1);
319    BF(z[4].im, z[0].im, z[0].im, t2);
320    BF(z[6].re, z[2].re, z[2].re, t7);
321    BF(z[6].im, z[2].im, z[2].im, t8);
322
323    TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
324}
325
326#if !CONFIG_SMALL
327static void fft16(FFTComplex *z)
328{
329    FFTSample t1, t2, t3, t4, t5, t6;
330
331    fft8(z);
332    fft4(z+8);
333    fft4(z+12);
334
335    TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
336    TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
337    TRANSFORM(z[1],z[5],z[9],z[13],ff_cos_16[1],ff_cos_16[3]);
338    TRANSFORM(z[3],z[7],z[11],z[15],ff_cos_16[3],ff_cos_16[1]);
339}
340#else
341DECL_FFT(16,8,4)
342#endif
343DECL_FFT(32,16,8)
344DECL_FFT(64,32,16)
345DECL_FFT(128,64,32)
346DECL_FFT(256,128,64)
347DECL_FFT(512,256,128)
348#if !CONFIG_SMALL
349#define pass pass_big
350#endif
351DECL_FFT(1024,512,256)
352DECL_FFT(2048,1024,512)
353DECL_FFT(4096,2048,1024)
354DECL_FFT(8192,4096,2048)
355DECL_FFT(16384,8192,4096)
356DECL_FFT(32768,16384,8192)
357DECL_FFT(65536,32768,16384)
358
359static void (* const fft_dispatch[])(FFTComplex*) = {
360    fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
361    fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
362};
363
364void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
365{
366    fft_dispatch[s->nbits-2](z);
367}
368
369