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 #if !CONFIG_HARDCODED_TABLES
47 COSTABLE_CONST FFTSample * const ff_cos_tabs[] = {
48 ff_cos_16, ff_cos_32, ff_cos_64, ff_cos_128, ff_cos_256, ff_cos_512, ff_cos_1024,
49 ff_cos_2048, ff_cos_4096, ff_cos_8192, ff_cos_16384, ff_cos_32768, ff_cos_65536,
52 static int split_radix_permutation(int i, int n, int inverse)
55 if(n <= 2) return i&1;
57 if(!(i&m)) return split_radix_permutation(i, m, inverse)*2;
59 if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
60 else return split_radix_permutation(i, m, inverse)*4 - 1;
63 av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
66 float alpha, c1, s1, s2;
67 int av_unused has_vectors;
69 if (nbits < 2 || nbits > 16)
75 s->exptab = av_malloc((n / 2) * sizeof(FFTComplex));
78 s->revtab = av_malloc(n * sizeof(uint16_t));
83 s2 = inverse ? 1.0 : -1.0;
85 s->fft_permute = ff_fft_permute_c;
86 s->fft_calc = ff_fft_calc_c;
87 s->imdct_calc = ff_imdct_calc_c;
88 s->imdct_half = ff_imdct_half_c;
89 s->mdct_calc = ff_mdct_calc_c;
93 if (ARCH_ARM) ff_fft_init_arm(s);
94 if (HAVE_ALTIVEC) ff_fft_init_altivec(s);
95 if (HAVE_MMX) ff_fft_init_mmx(s);
98 #if !CONFIG_HARDCODED_TABLES
99 for(j=4; j<=nbits; j++) {
101 double freq = 2*M_PI/m;
102 FFTSample *tab = ff_cos_tabs[j-4];
103 for(i=0; i<=m/4; i++)
104 tab[i] = cos(i*freq);
110 s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = i;
111 s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
113 int np, nblocks, np2, l;
116 for(i=0; i<(n/2); i++) {
117 alpha = 2 * M_PI * (float)i / (float)n;
119 s1 = sin(alpha) * s2;
120 s->exptab[i].re = c1;
121 s->exptab[i].im = s1;
127 s->exptab1 = av_malloc(np * 2 * sizeof(FFTComplex));
132 for(l = 0; l < np2; l += 2 * nblocks) {
134 *q++ = s->exptab[l + nblocks];
136 q->re = -s->exptab[l].im;
137 q->im = s->exptab[l].re;
139 q->re = -s->exptab[l + nblocks].im;
140 q->im = s->exptab[l + nblocks].re;
143 nblocks = nblocks >> 1;
144 } while (nblocks != 0);
145 av_freep(&s->exptab);
147 /* compute bit reverse table */
150 for(j=0;j<nbits;j++) {
151 m |= ((i >> j) & 1) << (nbits-j-1);
159 av_freep(&s->revtab);
160 av_freep(&s->exptab);
161 av_freep(&s->exptab1);
162 av_freep(&s->tmp_buf);
166 void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
170 const uint16_t *revtab = s->revtab;
174 /* TODO: handle split-radix permute in a more optimal way, probably in-place */
175 for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
176 memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
191 av_cold void ff_fft_end(FFTContext *s)
193 av_freep(&s->revtab);
194 av_freep(&s->exptab);
195 av_freep(&s->exptab1);
196 av_freep(&s->tmp_buf);
199 #define sqrthalf (float)M_SQRT1_2
201 #define BF(x,y,a,b) {\
206 #define BUTTERFLIES(a0,a1,a2,a3) {\
208 BF(a2.re, a0.re, a0.re, t5);\
209 BF(a3.im, a1.im, a1.im, t3);\
211 BF(a3.re, a1.re, a1.re, t4);\
212 BF(a2.im, a0.im, a0.im, t6);\
215 // force loading all the inputs before storing any.
216 // this is slightly slower for small data, but avoids store->load aliasing
217 // for addresses separated by large powers of 2.
218 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
219 FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
221 BF(a2.re, a0.re, r0, t5);\
222 BF(a3.im, a1.im, i1, t3);\
224 BF(a3.re, a1.re, r1, t4);\
225 BF(a2.im, a0.im, i0, t6);\
228 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
229 t1 = a2.re * wre + a2.im * wim;\
230 t2 = a2.im * wre - a2.re * wim;\
231 t5 = a3.re * wre - a3.im * wim;\
232 t6 = a3.im * wre + a3.re * wim;\
233 BUTTERFLIES(a0,a1,a2,a3)\
236 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
241 BUTTERFLIES(a0,a1,a2,a3)\
244 /* z[0...8n-1], w[1...2n-1] */
246 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
248 FFTSample t1, t2, t3, t4, t5, t6;\
252 const FFTSample *wim = wre+o1;\
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]);\
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]);\
268 #define BUTTERFLIES BUTTERFLIES_BIG
271 #define DECL_FFT(n,n2,n4)\
272 static void fft##n(FFTComplex *z)\
277 pass(z,ff_cos_##n,n4/2);\
280 static void fft4(FFTComplex *z)
282 FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
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);
294 static void fft8(FFTComplex *z)
296 FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
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(t3, z[7].re, z[6].re, -z[7].re);
303 BF(t4, z[7].im, z[6].im, -z[7].im);
306 BF(z[4].re, z[0].re, z[0].re, t1);
307 BF(z[4].im, z[0].im, z[0].im, t2);
308 BF(z[6].re, z[2].re, z[2].re, t7);
309 BF(z[6].im, z[2].im, z[2].im, t8);
311 TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
315 static void fft16(FFTComplex *z)
317 FFTSample t1, t2, t3, t4, t5, t6;
323 TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
324 TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
325 TRANSFORM(z[1],z[5],z[9],z[13],ff_cos_16[1],ff_cos_16[3]);
326 TRANSFORM(z[3],z[7],z[11],z[15],ff_cos_16[3],ff_cos_16[1]);
335 DECL_FFT(512,256,128)
337 #define pass pass_big
339 DECL_FFT(1024,512,256)
340 DECL_FFT(2048,1024,512)
341 DECL_FFT(4096,2048,1024)
342 DECL_FFT(8192,4096,2048)
343 DECL_FFT(16384,8192,4096)
344 DECL_FFT(32768,16384,8192)
345 DECL_FFT(65536,32768,16384)
347 static void (* const fft_dispatch[])(FFTComplex*) = {
348 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
349 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
352 void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
354 fft_dispatch[s->nbits-2](z);