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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 libavcodec/fft.c
26 * FFT/IFFT transforms.
27 */
28
29#include "dsputil.h"
30#include "fft.h"
31#ifndef M_PI
32#define M_PI 3.14159265358979323846 /* pi */
33#endif
34#ifndef M_SQRT1_2
35#define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
36#endif
37#ifndef M_SQRT2
38#define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
39#endif
40
41/* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
42DECLARE_ALIGNED_16(FFTSample, ff_cos_16[8]);
43DECLARE_ALIGNED_16(FFTSample, ff_cos_32[16]);
44DECLARE_ALIGNED_16(FFTSample, ff_cos_64[32]);
45DECLARE_ALIGNED_16(FFTSample, ff_cos_128[64]);
46DECLARE_ALIGNED_16(FFTSample, ff_cos_256[128]);
47DECLARE_ALIGNED_16(FFTSample, ff_cos_512[256]);
48DECLARE_ALIGNED_16(FFTSample, ff_cos_1024[512]);
49DECLARE_ALIGNED_16(FFTSample, ff_cos_2048[1024]);
50DECLARE_ALIGNED_16(FFTSample, ff_cos_4096[2048]);
51DECLARE_ALIGNED_16(FFTSample, ff_cos_8192[4096]);
52DECLARE_ALIGNED_16(FFTSample, ff_cos_16384[8192]);
53DECLARE_ALIGNED_16(FFTSample, ff_cos_32768[16384]);
54DECLARE_ALIGNED_16(FFTSample, ff_cos_65536[32768]);
55
56FFTSample *ff_cos_tabs[] = {
57 ff_cos_16, ff_cos_32, ff_cos_64, ff_cos_128, ff_cos_256, ff_cos_512, ff_cos_1024,
58 ff_cos_2048, ff_cos_4096, ff_cos_8192, ff_cos_16384, ff_cos_32768, ff_cos_65536,
59};
60
61static int split_radix_permutation(int i, int n, int inverse)
62{
63 int m;
64 if(n <= 2) return i&1;
65 m = n >> 1;
66 if(!(i&m)) return split_radix_permutation(i, m, inverse)*2;
67 m >>= 1;
68 if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
69 else return split_radix_permutation(i, m, inverse)*4 - 1;
70}
71
72av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
73{
74 int i, j, m, n;
75 float alpha, c1, s1, s2;
76 int split_radix = 1;
77 int av_unused has_vectors;
78
79 if (nbits < 2 || nbits > 16)
80 goto fail;
81 s->nbits = nbits;
82 n = 1 << nbits;
83
84 s->tmp_buf = NULL;
85 s->exptab = av_malloc((n / 2) * sizeof(FFTComplex));
86 if (!s->exptab)
87 goto fail;
88 s->revtab = av_malloc(n * sizeof(uint16_t));
89 if (!s->revtab)
90 goto fail;
91 s->inverse = inverse;
92
93 s2 = inverse ? 1.0 : -1.0;
94
95 s->fft_permute = ff_fft_permute_c;
96 s->fft_calc = ff_fft_calc_c;
97 s->imdct_calc = ff_imdct_calc_c;
98 s->imdct_half = ff_imdct_half_c;
99 s->exptab1 = NULL;
100
101#if HAVE_MMX && HAVE_YASM
102 has_vectors = mm_support();
103 if (has_vectors & FF_MM_SSE && HAVE_SSE) {
104 /* SSE for P3/P4/K8 */
105 s->imdct_calc = ff_imdct_calc_sse;
106 s->imdct_half = ff_imdct_half_sse;
107 s->fft_permute = ff_fft_permute_sse;
108 s->fft_calc = ff_fft_calc_sse;
109 } else if (has_vectors & FF_MM_3DNOWEXT && HAVE_AMD3DNOWEXT) {
110 /* 3DNowEx for K7 */
111 s->imdct_calc = ff_imdct_calc_3dn2;
112 s->imdct_half = ff_imdct_half_3dn2;
113 s->fft_calc = ff_fft_calc_3dn2;
114 } else if (has_vectors & FF_MM_3DNOW && HAVE_AMD3DNOW) {
115 /* 3DNow! for K6-2/3 */
116 s->imdct_calc = ff_imdct_calc_3dn;
117 s->imdct_half = ff_imdct_half_3dn;
118 s->fft_calc = ff_fft_calc_3dn;
119 }
120#elif HAVE_ALTIVEC
121 has_vectors = mm_support();
122 if (has_vectors & FF_MM_ALTIVEC) {
123 s->fft_calc = ff_fft_calc_altivec;
124 split_radix = 0;
125 }
126#endif
127
128 if (split_radix) {
129 for(j=4; j<=nbits; j++) {
130 int m = 1<<j;
131 double freq = 2*M_PI/m;
132 FFTSample *tab = ff_cos_tabs[j-4];
133 for(i=0; i<=m/4; i++)
134 tab[i] = cos(i*freq);
135 for(i=1; i<m/4; i++)
136 tab[m/2-i] = tab[i];
137 }
138 for(i=0; i<n; i++)
139 s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = i;
140 s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
141 } else {
142 int np, nblocks, np2, l;
143 FFTComplex *q;
144
145 for(i=0; i<(n/2); i++) {
146 alpha = 2 * M_PI * (float)i / (float)n;
147 c1 = cos(alpha);
148 s1 = sin(alpha) * s2;
149 s->exptab[i].re = c1;
150 s->exptab[i].im = s1;
151 }
152
153 np = 1 << nbits;
154 nblocks = np >> 3;
155 np2 = np >> 1;
156 s->exptab1 = av_malloc(np * 2 * sizeof(FFTComplex));
157 if (!s->exptab1)
158 goto fail;
159 q = s->exptab1;
160 do {
161 for(l = 0; l < np2; l += 2 * nblocks) {
162 *q++ = s->exptab[l];
163 *q++ = s->exptab[l + nblocks];
164
165 q->re = -s->exptab[l].im;
166 q->im = s->exptab[l].re;
167 q++;
168 q->re = -s->exptab[l + nblocks].im;
169 q->im = s->exptab[l + nblocks].re;
170 q++;
171 }
172 nblocks = nblocks >> 1;
173 } while (nblocks != 0);
174 av_freep(&s->exptab);
175
176 /* compute bit reverse table */
177 for(i=0;i<n;i++) {
178 m=0;
179 for(j=0;j<nbits;j++) {
180 m |= ((i >> j) & 1) << (nbits-j-1);
181 }
182 s->revtab[i]=m;
183 }
184 }
185
186 return 0;
187 fail:
188 av_freep(&s->revtab);
189 av_freep(&s->exptab);
190 av_freep(&s->exptab1);
191 av_freep(&s->tmp_buf);
192 return -1;
193}
194
195void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
196{
197 int j, k, np;
198 FFTComplex tmp;
199 const uint16_t *revtab = s->revtab;
200 np = 1 << s->nbits;
201
202 if (s->tmp_buf) {
203 /* TODO: handle split-radix permute in a more optimal way, probably in-place */
204 for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
205 memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
206 return;
207 }
208
209 /* reverse */
210 for(j=0;j<np;j++) {
211 k = revtab[j];
212 if (k < j) {
213 tmp = z[k];
214 z[k] = z[j];
215 z[j] = tmp;
216 }
217 }
218}
219
220av_cold void ff_fft_end(FFTContext *s)
221{
222 av_freep(&s->revtab);
223 av_freep(&s->exptab);
224 av_freep(&s->exptab1);
225 av_freep(&s->tmp_buf);
226}
227
228#define sqrthalf (float)M_SQRT1_2
229
230#define BF(x,y,a,b) {\
231 x = a - b;\
232 y = a + b;\
233}
234
235#define BUTTERFLIES(a0,a1,a2,a3) {\
236 BF(t3, t5, t5, t1);\
237 BF(a2.re, a0.re, a0.re, t5);\
238 BF(a3.im, a1.im, a1.im, t3);\
239 BF(t4, t6, t2, t6);\
240 BF(a3.re, a1.re, a1.re, t4);\
241 BF(a2.im, a0.im, a0.im, t6);\
242}
243
244// force loading all the inputs before storing any.
245// this is slightly slower for small data, but avoids store->load aliasing
246// for addresses separated by large powers of 2.
247#define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
248 FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
249 BF(t3, t5, t5, t1);\
250 BF(a2.re, a0.re, r0, t5);\
251 BF(a3.im, a1.im, i1, t3);\
252 BF(t4, t6, t2, t6);\
253 BF(a3.re, a1.re, r1, t4);\
254 BF(a2.im, a0.im, i0, t6);\
255}
256
257#define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
258 t1 = a2.re * wre + a2.im * wim;\
259 t2 = a2.im * wre - a2.re * wim;\
260 t5 = a3.re * wre - a3.im * wim;\
261 t6 = a3.im * wre + a3.re * wim;\
262 BUTTERFLIES(a0,a1,a2,a3)\
263}
264
265#define TRANSFORM_ZERO(a0,a1,a2,a3) {\
266 t1 = a2.re;\
267 t2 = a2.im;\
268 t5 = a3.re;\
269 t6 = a3.im;\
270 BUTTERFLIES(a0,a1,a2,a3)\
271}
272
273/* z[0...8n-1], w[1...2n-1] */
274#define PASS(name)\
275static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
276{\
277 FFTSample t1, t2, t3, t4, t5, t6;\
278 int o1 = 2*n;\
279 int o2 = 4*n;\
280 int o3 = 6*n;\
281 const FFTSample *wim = wre+o1;\
282 n--;\
283\
284 TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
285 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
286 do {\
287 z += 2;\
288 wre += 2;\
289 wim -= 2;\
290 TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
291 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
292 } while(--n);\
293}
294
295PASS(pass)
296#undef BUTTERFLIES
297#define BUTTERFLIES BUTTERFLIES_BIG
298PASS(pass_big)
299
300#define DECL_FFT(n,n2,n4)\
301static void fft##n(FFTComplex *z)\
302{\
303 fft##n2(z);\
304 fft##n4(z+n4*2);\
305 fft##n4(z+n4*3);\
306 pass(z,ff_cos_##n,n4/2);\
307}
308
309static void fft4(FFTComplex *z)
310{
311 FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
312
313 BF(t3, t1, z[0].re, z[1].re);
314 BF(t8, t6, z[3].re, z[2].re);
315 BF(z[2].re, z[0].re, t1, t6);
316 BF(t4, t2, z[0].im, z[1].im);
317 BF(t7, t5, z[2].im, z[3].im);
318 BF(z[3].im, z[1].im, t4, t8);
319 BF(z[3].re, z[1].re, t3, t7);
320 BF(z[2].im, z[0].im, t2, t5);
321}
322
323static void fft8(FFTComplex *z)
324{
325 FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
326
327 fft4(z);
328
329 BF(t1, z[5].re, z[4].re, -z[5].re);
330 BF(t2, z[5].im, z[4].im, -z[5].im);
331 BF(t3, z[7].re, z[6].re, -z[7].re);
332 BF(t4, z[7].im, z[6].im, -z[7].im);
333 BF(t8, t1, t3, t1);
334 BF(t7, t2, t2, t4);
335 BF(z[4].re, z[0].re, z[0].re, t1);
336 BF(z[4].im, z[0].im, z[0].im, t2);
337 BF(z[6].re, z[2].re, z[2].re, t7);
338 BF(z[6].im, z[2].im, z[2].im, t8);
339
340 TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
341}
342
343#if !CONFIG_SMALL
344static void fft16(FFTComplex *z)
345{
346 FFTSample t1, t2, t3, t4, t5, t6;
347
348 fft8(z);
349 fft4(z+8);
350 fft4(z+12);
351
352 TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
353 TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
354 TRANSFORM(z[1],z[5],z[9],z[13],ff_cos_16[1],ff_cos_16[3]);
355 TRANSFORM(z[3],z[7],z[11],z[15],ff_cos_16[3],ff_cos_16[1]);
356}
357#else
358DECL_FFT(16,8,4)
359#endif
360DECL_FFT(32,16,8)
361DECL_FFT(64,32,16)
362DECL_FFT(128,64,32)
363DECL_FFT(256,128,64)
364DECL_FFT(512,256,128)
365#if !CONFIG_SMALL
366#define pass pass_big
367#endif
368DECL_FFT(1024,512,256)
369DECL_FFT(2048,1024,512)
370DECL_FFT(4096,2048,1024)
371DECL_FFT(8192,4096,2048)
372DECL_FFT(16384,8192,4096)
373DECL_FFT(32768,16384,8192)
374DECL_FFT(65536,32768,16384)
375
376static void (*fft_dispatch[])(FFTComplex*) = {
377 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
378 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
379};
380
381void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
382{
383 fft_dispatch[s->nbits-2](z);
384}
385