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
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 int split_radix_permutation(int i, int n, int inverse)
59 if(n <= 2) return i&1;
61 if(!(i&m)) return split_radix_permutation(i, m, inverse)*2;
63 if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
64 else return split_radix_permutation(i, m, inverse)*4 - 1;
67 av_cold void ff_init_ff_cos_tabs(int index)
69 #if !CONFIG_HARDCODED_TABLES
72 double freq = 2*M_PI/m;
73 FFTSample *tab = ff_cos_tabs[index];
81 av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
85 if (nbits < 2 || nbits > 16)
90 s->revtab = av_malloc(n * sizeof(uint16_t));
93 s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
98 s->fft_permute = ff_fft_permute_c;
99 s->fft_calc = ff_fft_calc_c;
101 s->imdct_calc = ff_imdct_calc_c;
102 s->imdct_half = ff_imdct_half_c;
103 s->mdct_calc = ff_mdct_calc_c;
106 if (ARCH_ARM) ff_fft_init_arm(s);
107 if (HAVE_ALTIVEC) ff_fft_init_altivec(s);
108 if (HAVE_MMX) ff_fft_init_mmx(s);
110 for(j=4; j<=nbits; j++) {
111 ff_init_ff_cos_tabs(j);
114 s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = i;
118 av_freep(&s->revtab);
119 av_freep(&s->tmp_buf);
123 void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
126 const uint16_t *revtab = s->revtab;
128 /* TODO: handle split-radix permute in a more optimal way, probably in-place */
129 for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
130 memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
133 av_cold void ff_fft_end(FFTContext *s)
135 av_freep(&s->revtab);
136 av_freep(&s->tmp_buf);
139 #define sqrthalf (float)M_SQRT1_2
141 #define BF(x,y,a,b) {\
146 #define BUTTERFLIES(a0,a1,a2,a3) {\
148 BF(a2.re, a0.re, a0.re, t5);\
149 BF(a3.im, a1.im, a1.im, t3);\
151 BF(a3.re, a1.re, a1.re, t4);\
152 BF(a2.im, a0.im, a0.im, t6);\
155 // force loading all the inputs before storing any.
156 // this is slightly slower for small data, but avoids store->load aliasing
157 // for addresses separated by large powers of 2.
158 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
159 FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
161 BF(a2.re, a0.re, r0, t5);\
162 BF(a3.im, a1.im, i1, t3);\
164 BF(a3.re, a1.re, r1, t4);\
165 BF(a2.im, a0.im, i0, t6);\
168 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
169 t1 = a2.re * wre + a2.im * wim;\
170 t2 = a2.im * wre - a2.re * wim;\
171 t5 = a3.re * wre - a3.im * wim;\
172 t6 = a3.im * wre + a3.re * wim;\
173 BUTTERFLIES(a0,a1,a2,a3)\
176 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
181 BUTTERFLIES(a0,a1,a2,a3)\
184 /* z[0...8n-1], w[1...2n-1] */
186 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
188 FFTSample t1, t2, t3, t4, t5, t6;\
192 const FFTSample *wim = wre+o1;\
195 TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
196 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
201 TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
202 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
208 #define BUTTERFLIES BUTTERFLIES_BIG
211 #define DECL_FFT(n,n2,n4)\
212 static void fft##n(FFTComplex *z)\
217 pass(z,ff_cos_##n,n4/2);\
220 static void fft4(FFTComplex *z)
222 FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
224 BF(t3, t1, z[0].re, z[1].re);
225 BF(t8, t6, z[3].re, z[2].re);
226 BF(z[2].re, z[0].re, t1, t6);
227 BF(t4, t2, z[0].im, z[1].im);
228 BF(t7, t5, z[2].im, z[3].im);
229 BF(z[3].im, z[1].im, t4, t8);
230 BF(z[3].re, z[1].re, t3, t7);
231 BF(z[2].im, z[0].im, t2, t5);
234 static void fft8(FFTComplex *z)
236 FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
240 BF(t1, z[5].re, z[4].re, -z[5].re);
241 BF(t2, z[5].im, z[4].im, -z[5].im);
242 BF(t3, z[7].re, z[6].re, -z[7].re);
243 BF(t4, z[7].im, z[6].im, -z[7].im);
246 BF(z[4].re, z[0].re, z[0].re, t1);
247 BF(z[4].im, z[0].im, z[0].im, t2);
248 BF(z[6].re, z[2].re, z[2].re, t7);
249 BF(z[6].im, z[2].im, z[2].im, t8);
251 TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
255 static void fft16(FFTComplex *z)
257 FFTSample t1, t2, t3, t4, t5, t6;
263 TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
264 TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
265 TRANSFORM(z[1],z[5],z[9],z[13],ff_cos_16[1],ff_cos_16[3]);
266 TRANSFORM(z[3],z[7],z[11],z[15],ff_cos_16[3],ff_cos_16[1]);
275 DECL_FFT(512,256,128)
277 #define pass pass_big
279 DECL_FFT(1024,512,256)
280 DECL_FFT(2048,1024,512)
281 DECL_FFT(4096,2048,1024)
282 DECL_FFT(8192,4096,2048)
283 DECL_FFT(16384,8192,4096)
284 DECL_FFT(32768,16384,8192)
285 DECL_FFT(65536,32768,16384)
287 static void (* const fft_dispatch[])(FFTComplex*) = {
288 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
289 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
292 void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
294 fft_dispatch[s->nbits-2](z);