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 Libav.
8 *
9 * Libav 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 * Libav 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 Libav; 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#include "fft-internal.h"
34
35/* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
36#if !CONFIG_HARDCODED_TABLES
37COSTABLE(16);
38COSTABLE(32);
39COSTABLE(64);
40COSTABLE(128);
41COSTABLE(256);
42COSTABLE(512);
43COSTABLE(1024);
44COSTABLE(2048);
45COSTABLE(4096);
46COSTABLE(8192);
47COSTABLE(16384);
48COSTABLE(32768);
49COSTABLE(65536);
50#endif
51COSTABLE_CONST FFTSample * const FFT_NAME(ff_cos_tabs)[] = {
52    NULL, NULL, NULL, NULL,
53    FFT_NAME(ff_cos_16),
54    FFT_NAME(ff_cos_32),
55    FFT_NAME(ff_cos_64),
56    FFT_NAME(ff_cos_128),
57    FFT_NAME(ff_cos_256),
58    FFT_NAME(ff_cos_512),
59    FFT_NAME(ff_cos_1024),
60    FFT_NAME(ff_cos_2048),
61    FFT_NAME(ff_cos_4096),
62    FFT_NAME(ff_cos_8192),
63    FFT_NAME(ff_cos_16384),
64    FFT_NAME(ff_cos_32768),
65    FFT_NAME(ff_cos_65536),
66};
67
68static void ff_fft_permute_c(FFTContext *s, FFTComplex *z);
69static void ff_fft_calc_c(FFTContext *s, FFTComplex *z);
70
71static int split_radix_permutation(int i, int n, int inverse)
72{
73    int m;
74    if(n <= 2) return i&1;
75    m = n >> 1;
76    if(!(i&m))            return split_radix_permutation(i, m, inverse)*2;
77    m >>= 1;
78    if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
79    else                  return split_radix_permutation(i, m, inverse)*4 - 1;
80}
81
82av_cold void ff_init_ff_cos_tabs(int index)
83{
84#if !CONFIG_HARDCODED_TABLES
85    int i;
86    int m = 1<<index;
87    double freq = 2*M_PI/m;
88    FFTSample *tab = FFT_NAME(ff_cos_tabs)[index];
89    for(i=0; i<=m/4; i++)
90        tab[i] = FIX15(cos(i*freq));
91    for(i=1; i<m/4; i++)
92        tab[m/2-i] = tab[i];
93#endif
94}
95
96static const int avx_tab[] = {
97    0, 4, 1, 5, 8, 12, 9, 13, 2, 6, 3, 7, 10, 14, 11, 15
98};
99
100static int is_second_half_of_fft32(int i, int n)
101{
102    if (n <= 32)
103        return i >= 16;
104    else if (i < n/2)
105        return is_second_half_of_fft32(i, n/2);
106    else if (i < 3*n/4)
107        return is_second_half_of_fft32(i - n/2, n/4);
108    else
109        return is_second_half_of_fft32(i - 3*n/4, n/4);
110}
111
112static av_cold void fft_perm_avx(FFTContext *s)
113{
114    int i;
115    int n = 1 << s->nbits;
116
117    for (i = 0; i < n; i += 16) {
118        int k;
119        if (is_second_half_of_fft32(i, n)) {
120            for (k = 0; k < 16; k++)
121                s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] =
122                    i + avx_tab[k];
123
124        } else {
125            for (k = 0; k < 16; k++) {
126                int j = i + k;
127                j = (j & ~7) | ((j >> 1) & 3) | ((j << 2) & 4);
128                s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] = j;
129            }
130        }
131    }
132}
133
134av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
135{
136    int i, j, n;
137
138    if (nbits < 2 || nbits > 16)
139        goto fail;
140    s->nbits = nbits;
141    n = 1 << nbits;
142
143    s->revtab = av_malloc(n * sizeof(uint16_t));
144    if (!s->revtab)
145        goto fail;
146    s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
147    if (!s->tmp_buf)
148        goto fail;
149    s->inverse = inverse;
150    s->fft_permutation = FF_FFT_PERM_DEFAULT;
151
152    s->fft_permute = ff_fft_permute_c;
153    s->fft_calc    = ff_fft_calc_c;
154#if CONFIG_MDCT
155    s->imdct_calc  = ff_imdct_calc_c;
156    s->imdct_half  = ff_imdct_half_c;
157    s->mdct_calc   = ff_mdct_calc_c;
158#endif
159
160#if CONFIG_FFT_FLOAT
161    if (ARCH_ARM)     ff_fft_init_arm(s);
162    if (HAVE_ALTIVEC) ff_fft_init_altivec(s);
163    if (HAVE_MMX)     ff_fft_init_mmx(s);
164    if (CONFIG_MDCT)  s->mdct_calcw = s->mdct_calc;
165#else
166    if (CONFIG_MDCT)  s->mdct_calcw = ff_mdct_calcw_c;
167    if (ARCH_ARM)     ff_fft_fixed_init_arm(s);
168#endif
169
170    for(j=4; j<=nbits; j++) {
171        ff_init_ff_cos_tabs(j);
172    }
173
174    if (s->fft_permutation == FF_FFT_PERM_AVX) {
175        fft_perm_avx(s);
176    } else {
177        for(i=0; i<n; i++) {
178            int j = i;
179            if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS)
180                j = (j&~3) | ((j>>1)&1) | ((j<<1)&2);
181            s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = j;
182        }
183    }
184
185    return 0;
186 fail:
187    av_freep(&s->revtab);
188    av_freep(&s->tmp_buf);
189    return -1;
190}
191
192static void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
193{
194    int j, np;
195    const uint16_t *revtab = s->revtab;
196    np = 1 << s->nbits;
197    /* TODO: handle split-radix permute in a more optimal way, probably in-place */
198    for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
199    memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
200}
201
202av_cold void ff_fft_end(FFTContext *s)
203{
204    av_freep(&s->revtab);
205    av_freep(&s->tmp_buf);
206}
207
208#define BUTTERFLIES(a0,a1,a2,a3) {\
209    BF(t3, t5, t5, t1);\
210    BF(a2.re, a0.re, a0.re, t5);\
211    BF(a3.im, a1.im, a1.im, t3);\
212    BF(t4, t6, t2, t6);\
213    BF(a3.re, a1.re, a1.re, t4);\
214    BF(a2.im, a0.im, a0.im, t6);\
215}
216
217// force loading all the inputs before storing any.
218// this is slightly slower for small data, but avoids store->load aliasing
219// for addresses separated by large powers of 2.
220#define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
221    FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
222    BF(t3, t5, t5, t1);\
223    BF(a2.re, a0.re, r0, t5);\
224    BF(a3.im, a1.im, i1, t3);\
225    BF(t4, t6, t2, t6);\
226    BF(a3.re, a1.re, r1, t4);\
227    BF(a2.im, a0.im, i0, t6);\
228}
229
230#define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
231    CMUL(t1, t2, a2.re, a2.im, wre, -wim);\
232    CMUL(t5, t6, a3.re, a3.im, wre,  wim);\
233    BUTTERFLIES(a0,a1,a2,a3)\
234}
235
236#define TRANSFORM_ZERO(a0,a1,a2,a3) {\
237    t1 = a2.re;\
238    t2 = a2.im;\
239    t5 = a3.re;\
240    t6 = a3.im;\
241    BUTTERFLIES(a0,a1,a2,a3)\
242}
243
244/* z[0...8n-1], w[1...2n-1] */
245#define PASS(name)\
246static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
247{\
248    FFTDouble t1, t2, t3, t4, t5, t6;\
249    int o1 = 2*n;\
250    int o2 = 4*n;\
251    int o3 = 6*n;\
252    const FFTSample *wim = wre+o1;\
253    n--;\
254\
255    TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
256    TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
257    do {\
258        z += 2;\
259        wre += 2;\
260        wim -= 2;\
261        TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
262        TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
263    } while(--n);\
264}
265
266PASS(pass)
267#undef BUTTERFLIES
268#define BUTTERFLIES BUTTERFLIES_BIG
269PASS(pass_big)
270
271#define DECL_FFT(n,n2,n4)\
272static void fft##n(FFTComplex *z)\
273{\
274    fft##n2(z);\
275    fft##n4(z+n4*2);\
276    fft##n4(z+n4*3);\
277    pass(z,FFT_NAME(ff_cos_##n),n4/2);\
278}
279
280static void fft4(FFTComplex *z)
281{
282    FFTDouble t1, t2, t3, t4, t5, t6, t7, t8;
283
284    BF(t3, t1, z[0].re, z[1].re);
285    BF(t8, t6, z[3].re, z[2].re);
286    BF(z[2].re, z[0].re, t1, t6);
287    BF(t4, t2, z[0].im, z[1].im);
288    BF(t7, t5, z[2].im, z[3].im);
289    BF(z[3].im, z[1].im, t4, t8);
290    BF(z[3].re, z[1].re, t3, t7);
291    BF(z[2].im, z[0].im, t2, t5);
292}
293
294static void fft8(FFTComplex *z)
295{
296    FFTDouble t1, t2, t3, t4, t5, t6;
297
298    fft4(z);
299
300    BF(t1, z[5].re, z[4].re, -z[5].re);
301    BF(t2, z[5].im, z[4].im, -z[5].im);
302    BF(t5, z[7].re, z[6].re, -z[7].re);
303    BF(t6, z[7].im, z[6].im, -z[7].im);
304
305    BUTTERFLIES(z[0],z[2],z[4],z[6]);
306    TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
307}
308
309#if !CONFIG_SMALL
310static void fft16(FFTComplex *z)
311{
312    FFTDouble t1, t2, t3, t4, t5, t6;
313    FFTSample cos_16_1 = FFT_NAME(ff_cos_16)[1];
314    FFTSample cos_16_3 = FFT_NAME(ff_cos_16)[3];
315
316    fft8(z);
317    fft4(z+8);
318    fft4(z+12);
319
320    TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
321    TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
322    TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3);
323    TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1);
324}
325#else
326DECL_FFT(16,8,4)
327#endif
328DECL_FFT(32,16,8)
329DECL_FFT(64,32,16)
330DECL_FFT(128,64,32)
331DECL_FFT(256,128,64)
332DECL_FFT(512,256,128)
333#if !CONFIG_SMALL
334#define pass pass_big
335#endif
336DECL_FFT(1024,512,256)
337DECL_FFT(2048,1024,512)
338DECL_FFT(4096,2048,1024)
339DECL_FFT(8192,4096,2048)
340DECL_FFT(16384,8192,4096)
341DECL_FFT(32768,16384,8192)
342DECL_FFT(65536,32768,16384)
343
344static void (* const fft_dispatch[])(FFTComplex*) = {
345    fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
346    fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
347};
348
349static void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
350{
351    fft_dispatch[s->nbits-2](z);
352}
353
354