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
);