split-radix FFT
[libav.git] / libavcodec / fft.c
1 /*
2 * FFT/IFFT transforms
3 * Copyright (c) 2008 Loren Merritt
4 * Copyright (c) 2002 Fabrice Bellard.
5 * Partly based on libdjbfft by D. J. Bernstein
6 *
7 * This file is part of FFmpeg.
8 *
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.
13 *
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.
18 *
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
22 */
23
24 /**
25 * @file fft.c
26 * FFT/IFFT transforms.
27 */
28
29 #include "dsputil.h"
30
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 static 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,
48 };
49
50 static int split_radix_permutation(int i, int n, int inverse)
51 {
52 int m;
53 if(n <= 2) return i&1;
54 m = n >> 1;
55 if(!(i&m)) return split_radix_permutation(i, m, inverse)*2;
56 m >>= 1;
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;
59 }
60
61 /**
62 * The size of the FFT is 2^nbits. If inverse is TRUE, inverse FFT is
63 * done
64 */
65 int ff_fft_init(FFTContext *s, int nbits, int inverse)
66 {
67 int i, j, m, n;
68 float alpha, c1, s1, s2;
69 int split_radix = 1;
70 int av_unused has_vectors;
71
72 if (nbits < 2 || nbits > 16)
73 goto fail;
74 s->nbits = nbits;
75 n = 1 << nbits;
76
77 s->tmp_buf = NULL;
78 s->exptab = av_malloc((n / 2) * sizeof(FFTComplex));
79 if (!s->exptab)
80 goto fail;
81 s->revtab = av_malloc(n * sizeof(uint16_t));
82 if (!s->revtab)
83 goto fail;
84 s->inverse = inverse;
85
86 s2 = inverse ? 1.0 : -1.0;
87
88 s->fft_permute = ff_fft_permute_c;
89 s->fft_calc = ff_fft_calc_c;
90 s->imdct_calc = ff_imdct_calc;
91 s->imdct_half = ff_imdct_half;
92 s->exptab1 = NULL;
93
94 #if defined HAVE_MMX && defined HAVE_YASM
95 has_vectors = mm_support();
96 if (has_vectors & MM_SSE) {
97 /* SSE for P3/P4/K8 */
98 s->imdct_calc = ff_imdct_calc_sse;
99 s->imdct_half = ff_imdct_half_sse;
100 s->fft_permute = ff_fft_permute_sse;
101 s->fft_calc = ff_fft_calc_sse;
102 } else if (has_vectors & MM_3DNOWEXT) {
103 /* 3DNowEx for K7 */
104 s->imdct_calc = ff_imdct_calc_3dn2;
105 s->imdct_half = ff_imdct_half_3dn2;
106 s->fft_calc = ff_fft_calc_3dn2;
107 } else if (has_vectors & MM_3DNOW) {
108 /* 3DNow! for K6-2/3 */
109 s->fft_calc = ff_fft_calc_3dn;
110 }
111 #elif defined HAVE_ALTIVEC && !defined ALTIVEC_USE_REFERENCE_C_CODE
112 has_vectors = mm_support();
113 if (has_vectors & MM_ALTIVEC) {
114 s->fft_calc = ff_fft_calc_altivec;
115 split_radix = 0;
116 }
117 #endif
118
119 if (split_radix) {
120 for(j=4; j<=nbits; j++) {
121 int m = 1<<j;
122 double freq = 2*M_PI/m;
123 FFTSample *tab = ff_cos_tabs[j-4];
124 for(i=0; i<=m/4; i++)
125 tab[i] = cos(i*freq);
126 for(i=1; i<m/4; i++)
127 tab[m/2-i] = tab[i];
128 }
129 for(i=0; i<n; i++)
130 s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = i;
131 s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
132 } else {
133 int np, nblocks, np2, l;
134 FFTComplex *q;
135
136 for(i=0; i<(n/2); i++) {
137 alpha = 2 * M_PI * (float)i / (float)n;
138 c1 = cos(alpha);
139 s1 = sin(alpha) * s2;
140 s->exptab[i].re = c1;
141 s->exptab[i].im = s1;
142 }
143
144 np = 1 << nbits;
145 nblocks = np >> 3;
146 np2 = np >> 1;
147 s->exptab1 = av_malloc(np * 2 * sizeof(FFTComplex));
148 if (!s->exptab1)
149 goto fail;
150 q = s->exptab1;
151 do {
152 for(l = 0; l < np2; l += 2 * nblocks) {
153 *q++ = s->exptab[l];
154 *q++ = s->exptab[l + nblocks];
155
156 q->re = -s->exptab[l].im;
157 q->im = s->exptab[l].re;
158 q++;
159 q->re = -s->exptab[l + nblocks].im;
160 q->im = s->exptab[l + nblocks].re;
161 q++;
162 }
163 nblocks = nblocks >> 1;
164 } while (nblocks != 0);
165 av_freep(&s->exptab);
166
167 /* compute bit reverse table */
168
169 for(i=0;i<n;i++) {
170 m=0;
171 for(j=0;j<nbits;j++) {
172 m |= ((i >> j) & 1) << (nbits-j-1);
173 }
174 s->revtab[i]=m;
175 }
176 }
177
178 return 0;
179 fail:
180 av_freep(&s->revtab);
181 av_freep(&s->exptab);
182 av_freep(&s->exptab1);
183 av_freep(&s->tmp_buf);
184 return -1;
185 }
186
187 /**
188 * Do the permutation needed BEFORE calling ff_fft_calc()
189 */
190 void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
191 {
192 int j, k, np;
193 FFTComplex tmp;
194 const uint16_t *revtab = s->revtab;
195 np = 1 << s->nbits;
196
197 if (s->tmp_buf) {
198 /* TODO: handle split-radix permute in a more optimal way, probably in-place */
199 for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
200 memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
201 return;
202 }
203
204 /* reverse */
205 for(j=0;j<np;j++) {
206 k = revtab[j];
207 if (k < j) {
208 tmp = z[k];
209 z[k] = z[j];
210 z[j] = tmp;
211 }
212 }
213 }
214
215 void ff_fft_end(FFTContext *s)
216 {
217 av_freep(&s->revtab);
218 av_freep(&s->exptab);
219 av_freep(&s->exptab1);
220 av_freep(&s->tmp_buf);
221 }
222
223 #define sqrthalf (float)M_SQRT1_2
224
225 #define BF(x,y,a,b) {\
226 x = a - b;\
227 y = a + b;\
228 }
229
230 #define BUTTERFLIES(a0,a1,a2,a3) {\
231 BF(t3, t5, t5, t1);\
232 BF(a2.re, a0.re, a0.re, t5);\
233 BF(a3.im, a1.im, a1.im, t3);\
234 BF(t4, t6, t2, t6);\
235 BF(a3.re, a1.re, a1.re, t4);\
236 BF(a2.im, a0.im, a0.im, t6);\
237 }
238
239 // force loading all the inputs before storing any.
240 // this is slightly slower for small data, but avoids store->load aliasing
241 // for addresses separated by large powers of 2.
242 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
243 FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
244 BF(t3, t5, t5, t1);\
245 BF(a2.re, a0.re, r0, t5);\
246 BF(a3.im, a1.im, i1, t3);\
247 BF(t4, t6, t2, t6);\
248 BF(a3.re, a1.re, r1, t4);\
249 BF(a2.im, a0.im, i0, t6);\
250 }
251
252 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
253 t1 = a2.re * wre + a2.im * wim;\
254 t2 = a2.im * wre - a2.re * wim;\
255 t5 = a3.re * wre - a3.im * wim;\
256 t6 = a3.im * wre + a3.re * wim;\
257 BUTTERFLIES(a0,a1,a2,a3)\
258 }
259
260 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
261 t1 = a2.re;\
262 t2 = a2.im;\
263 t5 = a3.re;\
264 t6 = a3.im;\
265 BUTTERFLIES(a0,a1,a2,a3)\
266 }
267
268 /* z[0...8n-1], w[1...2n-1] */
269 #define PASS(name)\
270 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
271 {\
272 FFTSample t1, t2, t3, t4, t5, t6;\
273 int o1 = 2*n;\
274 int o2 = 4*n;\
275 int o3 = 6*n;\
276 const FFTSample *wim = wre+o1;\
277 n--;\
278 \
279 TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
280 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
281 do {\
282 z += 2;\
283 wre += 2;\
284 wim -= 2;\
285 TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
286 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
287 } while(--n);\
288 }
289
290 PASS(pass)
291 #undef BUTTERFLIES
292 #define BUTTERFLIES BUTTERFLIES_BIG
293 PASS(pass_big)
294
295 #define DECL_FFT(n,n2,n4)\
296 static void fft##n(FFTComplex *z)\
297 {\
298 fft##n2(z);\
299 fft##n4(z+n4*2);\
300 fft##n4(z+n4*3);\
301 pass(z,ff_cos_##n,n4/2);\
302 }
303
304 static void fft4(FFTComplex *z)
305 {
306 FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
307
308 BF(t3, t1, z[0].re, z[1].re);
309 BF(t8, t6, z[3].re, z[2].re);
310 BF(z[2].re, z[0].re, t1, t6);
311 BF(t4, t2, z[0].im, z[1].im);
312 BF(t7, t5, z[2].im, z[3].im);
313 BF(z[3].im, z[1].im, t4, t8);
314 BF(z[3].re, z[1].re, t3, t7);
315 BF(z[2].im, z[0].im, t2, t5);
316 }
317
318 static void fft8(FFTComplex *z)
319 {
320 FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
321
322 fft4(z);
323
324 BF(t1, z[5].re, z[4].re, -z[5].re);
325 BF(t2, z[5].im, z[4].im, -z[5].im);
326 BF(t3, z[7].re, z[6].re, -z[7].re);
327 BF(t4, z[7].im, z[6].im, -z[7].im);
328 BF(t8, t1, t3, t1);
329 BF(t7, t2, t2, t4);
330 BF(z[4].re, z[0].re, z[0].re, t1);
331 BF(z[4].im, z[0].im, z[0].im, t2);
332 BF(z[6].re, z[2].re, z[2].re, t7);
333 BF(z[6].im, z[2].im, z[2].im, t8);
334
335 TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
336 }
337
338 #ifndef CONFIG_SMALL
339 static void fft16(FFTComplex *z)
340 {
341 FFTSample t1, t2, t3, t4, t5, t6;
342
343 fft8(z);
344 fft4(z+8);
345 fft4(z+12);
346
347 TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
348 TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
349 TRANSFORM(z[1],z[5],z[9],z[13],ff_cos_16[1],ff_cos_16[3]);
350 TRANSFORM(z[3],z[7],z[11],z[15],ff_cos_16[3],ff_cos_16[1]);
351 }
352 #else
353 DECL_FFT(16,8,4)
354 #endif
355 DECL_FFT(32,16,8)
356 DECL_FFT(64,32,16)
357 DECL_FFT(128,64,32)
358 DECL_FFT(256,128,64)
359 DECL_FFT(512,256,128)
360 #ifndef CONFIG_SMALL
361 #define pass pass_big
362 #endif
363 DECL_FFT(1024,512,256)
364 DECL_FFT(2048,1024,512)
365 DECL_FFT(4096,2048,1024)
366 DECL_FFT(8192,4096,2048)
367 DECL_FFT(16384,8192,4096)
368 DECL_FFT(32768,16384,8192)
369 DECL_FFT(65536,32768,16384)
370
371 static void (*fft_dispatch[])(FFTComplex*) = {
372 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
373 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
374 };
375
376 /**
377 * Do a complex FFT with the parameters defined in ff_fft_init(). The
378 * input data must be permuted before with s->revtab table. No
379 * 1.0/sqrt(n) normalization is done.
380 */
381 void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
382 {
383 fft_dispatch[s->nbits-2](z);
384 }
385