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 Libav.
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.
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.
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
26 * FFT/IFFT transforms.
31 #include "libavutil/mathematics.h"
34 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
35 #if !CONFIG_HARDCODED_TABLES
50 COSTABLE_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,
56 static void ff_fft_permute_c(FFTContext *s, FFTComplex *z);
57 static void ff_fft_calc_c(FFTContext *s, FFTComplex *z);
59 static int split_radix_permutation(int i, int n, int inverse)
62 if(n <= 2) return i&1;
64 if(!(i&m)) return split_radix_permutation(i, m, inverse)*2;
66 if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
67 else return split_radix_permutation(i, m, inverse)*4 - 1;
70 av_cold void ff_init_ff_cos_tabs(int index)
72 #if !CONFIG_HARDCODED_TABLES
75 double freq = 2*M_PI/m;
76 FFTSample *tab = ff_cos_tabs[index];
84 av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
88 if (nbits < 2 || nbits > 16)
93 s->revtab = av_malloc(n * sizeof(uint16_t));
96 s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
100 s->fft_permutation = FF_FFT_PERM_DEFAULT;
102 s->fft_permute = ff_fft_permute_c;
103 s->fft_calc = ff_fft_calc_c;
105 s->imdct_calc = ff_imdct_calc_c;
106 s->imdct_half = ff_imdct_half_c;
107 s->mdct_calc = ff_mdct_calc_c;
110 if (ARCH_ARM) ff_fft_init_arm(s);
111 if (HAVE_ALTIVEC) ff_fft_init_altivec(s);
112 if (HAVE_MMX) ff_fft_init_mmx(s);
114 for(j=4; j<=nbits; j++) {
115 ff_init_ff_cos_tabs(j);
119 if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS)
120 j = (j&~3) | ((j>>1)&1) | ((j<<1)&2);
121 s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = j;
126 av_freep(&s->revtab);
127 av_freep(&s->tmp_buf);
131 static void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
134 const uint16_t *revtab = s->revtab;
136 /* TODO: handle split-radix permute in a more optimal way, probably in-place */
137 for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
138 memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
141 av_cold void ff_fft_end(FFTContext *s)
143 av_freep(&s->revtab);
144 av_freep(&s->tmp_buf);
147 #define sqrthalf (float)M_SQRT1_2
149 #define BF(x,y,a,b) {\
154 #define BUTTERFLIES(a0,a1,a2,a3) {\
156 BF(a2.re, a0.re, a0.re, t5);\
157 BF(a3.im, a1.im, a1.im, t3);\
159 BF(a3.re, a1.re, a1.re, t4);\
160 BF(a2.im, a0.im, a0.im, t6);\
163 // force loading all the inputs before storing any.
164 // this is slightly slower for small data, but avoids store->load aliasing
165 // for addresses separated by large powers of 2.
166 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
167 FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
169 BF(a2.re, a0.re, r0, t5);\
170 BF(a3.im, a1.im, i1, t3);\
172 BF(a3.re, a1.re, r1, t4);\
173 BF(a2.im, a0.im, i0, t6);\
176 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
177 t1 = a2.re * wre + a2.im * wim;\
178 t2 = a2.im * wre - a2.re * wim;\
179 t5 = a3.re * wre - a3.im * wim;\
180 t6 = a3.im * wre + a3.re * wim;\
181 BUTTERFLIES(a0,a1,a2,a3)\
184 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
189 BUTTERFLIES(a0,a1,a2,a3)\
192 /* z[0...8n-1], w[1...2n-1] */
194 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
196 FFTSample t1, t2, t3, t4, t5, t6;\
200 const FFTSample *wim = wre+o1;\
203 TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
204 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
209 TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
210 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
216 #define BUTTERFLIES BUTTERFLIES_BIG
219 #define DECL_FFT(n,n2,n4)\
220 static void fft##n(FFTComplex *z)\
225 pass(z,ff_cos_##n,n4/2);\
228 static void fft4(FFTComplex *z)
230 FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
232 BF(t3, t1, z[0].re, z[1].re);
233 BF(t8, t6, z[3].re, z[2].re);
234 BF(z[2].re, z[0].re, t1, t6);
235 BF(t4, t2, z[0].im, z[1].im);
236 BF(t7, t5, z[2].im, z[3].im);
237 BF(z[3].im, z[1].im, t4, t8);
238 BF(z[3].re, z[1].re, t3, t7);
239 BF(z[2].im, z[0].im, t2, t5);
242 static void fft8(FFTComplex *z)
244 FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
248 BF(t1, z[5].re, z[4].re, -z[5].re);
249 BF(t2, z[5].im, z[4].im, -z[5].im);
250 BF(t3, z[7].re, z[6].re, -z[7].re);
251 BF(t4, z[7].im, z[6].im, -z[7].im);
254 BF(z[4].re, z[0].re, z[0].re, t1);
255 BF(z[4].im, z[0].im, z[0].im, t2);
256 BF(z[6].re, z[2].re, z[2].re, t7);
257 BF(z[6].im, z[2].im, z[2].im, t8);
259 TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
263 static void fft16(FFTComplex *z)
265 FFTSample t1, t2, t3, t4, t5, t6;
271 TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
272 TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
273 TRANSFORM(z[1],z[5],z[9],z[13],ff_cos_16[1],ff_cos_16[3]);
274 TRANSFORM(z[3],z[7],z[11],z[15],ff_cos_16[3],ff_cos_16[1]);
283 DECL_FFT(512,256,128)
285 #define pass pass_big
287 DECL_FFT(1024,512,256)
288 DECL_FFT(2048,1024,512)
289 DECL_FFT(4096,2048,1024)
290 DECL_FFT(8192,4096,2048)
291 DECL_FFT(16384,8192,4096)
292 DECL_FFT(32768,16384,8192)
293 DECL_FFT(65536,32768,16384)
295 static void (* const fft_dispatch[])(FFTComplex*) = {
296 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
297 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
300 static void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
302 fft_dispatch[s->nbits-2](z);