3 * Copyright (c) 2008 Loren Merritt
4 * Copyright (c) 2002 Fabrice Bellard
5 * Partly based on libdjbfft by D. J. Bernstein
7 * This file is part of FFmpeg.
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.
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.
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
25 * @file libavcodec/fft.c
26 * FFT/IFFT transforms.
31 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
32 DECLARE_ALIGNED_16(FFTSample, ff_cos_16[8]);
33 DECLARE_ALIGNED_16(FFTSample, ff_cos_32[16]);
34 DECLARE_ALIGNED_16(FFTSample, ff_cos_64[32]);
35 DECLARE_ALIGNED_16(FFTSample, ff_cos_128[64]);
36 DECLARE_ALIGNED_16(FFTSample, ff_cos_256[128]);
37 DECLARE_ALIGNED_16(FFTSample, ff_cos_512[256]);
38 DECLARE_ALIGNED_16(FFTSample, ff_cos_1024[512]);
39 DECLARE_ALIGNED_16(FFTSample, ff_cos_2048[1024]);
40 DECLARE_ALIGNED_16(FFTSample, ff_cos_4096[2048]);
41 DECLARE_ALIGNED_16(FFTSample, ff_cos_8192[4096]);
42 DECLARE_ALIGNED_16(FFTSample, ff_cos_16384[8192]);
43 DECLARE_ALIGNED_16(FFTSample, ff_cos_32768[16384]);
44 DECLARE_ALIGNED_16(FFTSample, ff_cos_65536[32768]);
45 FFTSample *ff_cos_tabs[] = {
46 ff_cos_16, ff_cos_32, ff_cos_64, ff_cos_128, ff_cos_256, ff_cos_512, ff_cos_1024,
47 ff_cos_2048, ff_cos_4096, ff_cos_8192, ff_cos_16384, ff_cos_32768, ff_cos_65536,
50 static int split_radix_permutation(int i, int n, int inverse)
53 if(n <= 2) return i&1;
55 if(!(i&m)) return split_radix_permutation(i, m, inverse)*2;
57 if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
58 else return split_radix_permutation(i, m, inverse)*4 - 1;
61 av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
64 float alpha, c1, s1, s2;
66 int av_unused has_vectors;
68 if (nbits < 2 || nbits > 16)
74 s->exptab = av_malloc((n / 2) * sizeof(FFTComplex));
77 s->revtab = av_malloc(n * sizeof(uint16_t));
82 s2 = inverse ? 1.0 : -1.0;
84 s->fft_permute = ff_fft_permute_c;
85 s->fft_calc = ff_fft_calc_c;
86 s->imdct_calc = ff_imdct_calc_c;
87 s->imdct_half = ff_imdct_half_c;
90 #if HAVE_MMX && HAVE_YASM
91 has_vectors = mm_support();
92 if (has_vectors & FF_MM_SSE && HAVE_SSE) {
93 /* SSE for P3/P4/K8 */
94 s->imdct_calc = ff_imdct_calc_sse;
95 s->imdct_half = ff_imdct_half_sse;
96 s->fft_permute = ff_fft_permute_sse;
97 s->fft_calc = ff_fft_calc_sse;
98 } else if (has_vectors & FF_MM_3DNOWEXT && HAVE_AMD3DNOWEXT) {
100 s->imdct_calc = ff_imdct_calc_3dn2;
101 s->imdct_half = ff_imdct_half_3dn2;
102 s->fft_calc = ff_fft_calc_3dn2;
103 } else if (has_vectors & FF_MM_3DNOW && HAVE_AMD3DNOW) {
104 /* 3DNow! for K6-2/3 */
105 s->imdct_calc = ff_imdct_calc_3dn;
106 s->imdct_half = ff_imdct_half_3dn;
107 s->fft_calc = ff_fft_calc_3dn;
110 has_vectors = mm_support();
111 if (has_vectors & FF_MM_ALTIVEC) {
112 s->fft_calc = ff_fft_calc_altivec;
118 for(j=4; j<=nbits; j++) {
120 double freq = 2*M_PI/m;
121 FFTSample *tab = ff_cos_tabs[j-4];
122 for(i=0; i<=m/4; i++)
123 tab[i] = cos(i*freq);
128 s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = i;
129 s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
131 int np, nblocks, np2, l;
134 for(i=0; i<(n/2); i++) {
135 alpha = 2 * M_PI * (float)i / (float)n;
137 s1 = sin(alpha) * s2;
138 s->exptab[i].re = c1;
139 s->exptab[i].im = s1;
145 s->exptab1 = av_malloc(np * 2 * sizeof(FFTComplex));
150 for(l = 0; l < np2; l += 2 * nblocks) {
152 *q++ = s->exptab[l + nblocks];
154 q->re = -s->exptab[l].im;
155 q->im = s->exptab[l].re;
157 q->re = -s->exptab[l + nblocks].im;
158 q->im = s->exptab[l + nblocks].re;
161 nblocks = nblocks >> 1;
162 } while (nblocks != 0);
163 av_freep(&s->exptab);
165 /* compute bit reverse table */
168 for(j=0;j<nbits;j++) {
169 m |= ((i >> j) & 1) << (nbits-j-1);
177 av_freep(&s->revtab);
178 av_freep(&s->exptab);
179 av_freep(&s->exptab1);
180 av_freep(&s->tmp_buf);
184 void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
188 const uint16_t *revtab = s->revtab;
192 /* TODO: handle split-radix permute in a more optimal way, probably in-place */
193 for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
194 memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
209 av_cold void ff_fft_end(FFTContext *s)
211 av_freep(&s->revtab);
212 av_freep(&s->exptab);
213 av_freep(&s->exptab1);
214 av_freep(&s->tmp_buf);
217 #define sqrthalf (float)M_SQRT1_2
219 #define BF(x,y,a,b) {\
224 #define BUTTERFLIES(a0,a1,a2,a3) {\
226 BF(a2.re, a0.re, a0.re, t5);\
227 BF(a3.im, a1.im, a1.im, t3);\
229 BF(a3.re, a1.re, a1.re, t4);\
230 BF(a2.im, a0.im, a0.im, t6);\
233 // force loading all the inputs before storing any.
234 // this is slightly slower for small data, but avoids store->load aliasing
235 // for addresses separated by large powers of 2.
236 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
237 FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
239 BF(a2.re, a0.re, r0, t5);\
240 BF(a3.im, a1.im, i1, t3);\
242 BF(a3.re, a1.re, r1, t4);\
243 BF(a2.im, a0.im, i0, t6);\
246 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
247 t1 = a2.re * wre + a2.im * wim;\
248 t2 = a2.im * wre - a2.re * wim;\
249 t5 = a3.re * wre - a3.im * wim;\
250 t6 = a3.im * wre + a3.re * wim;\
251 BUTTERFLIES(a0,a1,a2,a3)\
254 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
259 BUTTERFLIES(a0,a1,a2,a3)\
262 /* z[0...8n-1], w[1...2n-1] */
264 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
266 FFTSample t1, t2, t3, t4, t5, t6;\
270 const FFTSample *wim = wre+o1;\
273 TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
274 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
279 TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
280 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
286 #define BUTTERFLIES BUTTERFLIES_BIG
289 #define DECL_FFT(n,n2,n4)\
290 static void fft##n(FFTComplex *z)\
295 pass(z,ff_cos_##n,n4/2);\
298 static void fft4(FFTComplex *z)
300 FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
302 BF(t3, t1, z[0].re, z[1].re);
303 BF(t8, t6, z[3].re, z[2].re);
304 BF(z[2].re, z[0].re, t1, t6);
305 BF(t4, t2, z[0].im, z[1].im);
306 BF(t7, t5, z[2].im, z[3].im);
307 BF(z[3].im, z[1].im, t4, t8);
308 BF(z[3].re, z[1].re, t3, t7);
309 BF(z[2].im, z[0].im, t2, t5);
312 static void fft8(FFTComplex *z)
314 FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
318 BF(t1, z[5].re, z[4].re, -z[5].re);
319 BF(t2, z[5].im, z[4].im, -z[5].im);
320 BF(t3, z[7].re, z[6].re, -z[7].re);
321 BF(t4, z[7].im, z[6].im, -z[7].im);
324 BF(z[4].re, z[0].re, z[0].re, t1);
325 BF(z[4].im, z[0].im, z[0].im, t2);
326 BF(z[6].re, z[2].re, z[2].re, t7);
327 BF(z[6].im, z[2].im, z[2].im, t8);
329 TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
333 static void fft16(FFTComplex *z)
335 FFTSample t1, t2, t3, t4, t5, t6;
341 TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
342 TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
343 TRANSFORM(z[1],z[5],z[9],z[13],ff_cos_16[1],ff_cos_16[3]);
344 TRANSFORM(z[3],z[7],z[11],z[15],ff_cos_16[3],ff_cos_16[1]);
353 DECL_FFT(512,256,128)
355 #define pass pass_big
357 DECL_FFT(1024,512,256)
358 DECL_FFT(2048,1024,512)
359 DECL_FFT(4096,2048,1024)
360 DECL_FFT(8192,4096,2048)
361 DECL_FFT(16384,8192,4096)
362 DECL_FFT(32768,16384,8192)
363 DECL_FFT(65536,32768,16384)
365 static void (*fft_dispatch[])(FFTComplex*) = {
366 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
367 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
370 void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
372 fft_dispatch[s->nbits-2](z);