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"
33 #include "fft-internal.h"
35 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
36 #if !CONFIG_HARDCODED_TABLES
51 COSTABLE_CONST FFTSample * const FFT_NAME(ff_cos_tabs)[] = {
52 NULL, NULL, NULL, NULL,
59 FFT_NAME(ff_cos_1024),
60 FFT_NAME(ff_cos_2048),
61 FFT_NAME(ff_cos_4096),
62 FFT_NAME(ff_cos_8192),
63 FFT_NAME(ff_cos_16384),
64 FFT_NAME(ff_cos_32768),
65 FFT_NAME(ff_cos_65536),
68 static void ff_fft_permute_c(FFTContext *s, FFTComplex *z);
69 static void ff_fft_calc_c(FFTContext *s, FFTComplex *z);
71 static int split_radix_permutation(int i, int n, int inverse)
74 if(n <= 2) return i&1;
76 if(!(i&m)) return split_radix_permutation(i, m, inverse)*2;
78 if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
79 else return split_radix_permutation(i, m, inverse)*4 - 1;
82 av_cold void ff_init_ff_cos_tabs(int index)
84 #if !CONFIG_HARDCODED_TABLES
87 double freq = 2*M_PI/m;
88 FFTSample *tab = FFT_NAME(ff_cos_tabs)[index];
90 tab[i] = FIX15(cos(i*freq));
96 static const int avx_tab[] = {
97 0, 4, 1, 5, 8, 12, 9, 13, 2, 6, 3, 7, 10, 14, 11, 15
100 static int is_second_half_of_fft32(int i, int n)
105 return is_second_half_of_fft32(i, n/2);
107 return is_second_half_of_fft32(i - n/2, n/4);
109 return is_second_half_of_fft32(i - 3*n/4, n/4);
112 static av_cold void fft_perm_avx(FFTContext *s)
115 int n = 1 << s->nbits;
117 for (i = 0; i < n; i += 16) {
119 if (is_second_half_of_fft32(i, n)) {
120 for (k = 0; k < 16; k++)
121 s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] =
125 for (k = 0; k < 16; k++) {
127 j = (j & ~7) | ((j >> 1) & 3) | ((j << 2) & 4);
128 s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] = j;
134 av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
138 if (nbits < 2 || nbits > 16)
143 s->revtab = av_malloc(n * sizeof(uint16_t));
146 s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
149 s->inverse = inverse;
150 s->fft_permutation = FF_FFT_PERM_DEFAULT;
152 s->fft_permute = ff_fft_permute_c;
153 s->fft_calc = ff_fft_calc_c;
155 s->imdct_calc = ff_imdct_calc_c;
156 s->imdct_half = ff_imdct_half_c;
157 s->mdct_calc = ff_mdct_calc_c;
161 if (ARCH_ARM) ff_fft_init_arm(s);
162 if (HAVE_ALTIVEC) ff_fft_init_altivec(s);
163 if (ARCH_X86) ff_fft_init_x86(s);
164 if (CONFIG_MDCT) s->mdct_calcw = s->mdct_calc;
165 if (HAVE_MIPSFPU) ff_fft_init_mips(s);
167 if (CONFIG_MDCT) s->mdct_calcw = ff_mdct_calcw_c;
168 if (ARCH_ARM) ff_fft_fixed_init_arm(s);
171 for(j=4; j<=nbits; j++) {
172 ff_init_ff_cos_tabs(j);
175 if (s->fft_permutation == FF_FFT_PERM_AVX) {
180 if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS)
181 j = (j&~3) | ((j>>1)&1) | ((j<<1)&2);
182 s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = j;
188 av_freep(&s->revtab);
189 av_freep(&s->tmp_buf);
193 static void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
196 const uint16_t *revtab = s->revtab;
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));
203 av_cold void ff_fft_end(FFTContext *s)
205 av_freep(&s->revtab);
206 av_freep(&s->tmp_buf);
209 #define BUTTERFLIES(a0,a1,a2,a3) {\
211 BF(a2.re, a0.re, a0.re, t5);\
212 BF(a3.im, a1.im, a1.im, t3);\
214 BF(a3.re, a1.re, a1.re, t4);\
215 BF(a2.im, a0.im, a0.im, t6);\
218 // force loading all the inputs before storing any.
219 // this is slightly slower for small data, but avoids store->load aliasing
220 // for addresses separated by large powers of 2.
221 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
222 FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
224 BF(a2.re, a0.re, r0, t5);\
225 BF(a3.im, a1.im, i1, t3);\
227 BF(a3.re, a1.re, r1, t4);\
228 BF(a2.im, a0.im, i0, t6);\
231 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
232 CMUL(t1, t2, a2.re, a2.im, wre, -wim);\
233 CMUL(t5, t6, a3.re, a3.im, wre, wim);\
234 BUTTERFLIES(a0,a1,a2,a3)\
237 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
242 BUTTERFLIES(a0,a1,a2,a3)\
245 /* z[0...8n-1], w[1...2n-1] */
247 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
249 FFTDouble t1, t2, t3, t4, t5, t6;\
253 const FFTSample *wim = wre+o1;\
256 TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
257 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
262 TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
263 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
269 #define BUTTERFLIES BUTTERFLIES_BIG
272 #define DECL_FFT(n,n2,n4)\
273 static void fft##n(FFTComplex *z)\
278 pass(z,FFT_NAME(ff_cos_##n),n4/2);\
281 static void fft4(FFTComplex *z)
283 FFTDouble t1, t2, t3, t4, t5, t6, t7, t8;
285 BF(t3, t1, z[0].re, z[1].re);
286 BF(t8, t6, z[3].re, z[2].re);
287 BF(z[2].re, z[0].re, t1, t6);
288 BF(t4, t2, z[0].im, z[1].im);
289 BF(t7, t5, z[2].im, z[3].im);
290 BF(z[3].im, z[1].im, t4, t8);
291 BF(z[3].re, z[1].re, t3, t7);
292 BF(z[2].im, z[0].im, t2, t5);
295 static void fft8(FFTComplex *z)
297 FFTDouble t1, t2, t3, t4, t5, t6;
301 BF(t1, z[5].re, z[4].re, -z[5].re);
302 BF(t2, z[5].im, z[4].im, -z[5].im);
303 BF(t5, z[7].re, z[6].re, -z[7].re);
304 BF(t6, z[7].im, z[6].im, -z[7].im);
306 BUTTERFLIES(z[0],z[2],z[4],z[6]);
307 TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
311 static void fft16(FFTComplex *z)
313 FFTDouble t1, t2, t3, t4, t5, t6;
314 FFTSample cos_16_1 = FFT_NAME(ff_cos_16)[1];
315 FFTSample cos_16_3 = FFT_NAME(ff_cos_16)[3];
321 TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
322 TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
323 TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3);
324 TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1);
333 DECL_FFT(512,256,128)
335 #define pass pass_big
337 DECL_FFT(1024,512,256)
338 DECL_FFT(2048,1024,512)
339 DECL_FFT(4096,2048,1024)
340 DECL_FFT(8192,4096,2048)
341 DECL_FFT(16384,8192,4096)
342 DECL_FFT(32768,16384,8192)
343 DECL_FFT(65536,32768,16384)
345 static void (* const fft_dispatch[])(FFTComplex*) = {
346 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
347 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
350 static void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
352 fft_dispatch[s->nbits-2](z);