529 lines
15 KiB
C
529 lines
15 KiB
C
/*
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* FFT/IFFT transforms
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* Copyright (c) 2008 Loren Merritt
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* Copyright (c) 2002 Fabrice Bellard
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* Partly based on libdjbfft by D. J. Bernstein
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*
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* This file is part of FFmpeg.
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*
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* FFmpeg is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* FFmpeg is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with FFmpeg; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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*/
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/**
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* @file
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* FFT/IFFT transforms.
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*/
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#include <stdlib.h>
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#include <string.h>
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#include "libavutil/mathematics.h"
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#include "fft.h"
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#include "fft-internal.h"
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#if FFT_FIXED_32
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#include "fft_table.h"
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#else /* FFT_FIXED_32 */
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/* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
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#if !CONFIG_HARDCODED_TABLES
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COSTABLE(16);
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COSTABLE(32);
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COSTABLE(64);
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COSTABLE(128);
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COSTABLE(256);
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COSTABLE(512);
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COSTABLE(1024);
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COSTABLE(2048);
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COSTABLE(4096);
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COSTABLE(8192);
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COSTABLE(16384);
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COSTABLE(32768);
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COSTABLE(65536);
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#endif
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COSTABLE_CONST FFTSample * const FFT_NAME(ff_cos_tabs)[] = {
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NULL, NULL, NULL, NULL,
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FFT_NAME(ff_cos_16),
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FFT_NAME(ff_cos_32),
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FFT_NAME(ff_cos_64),
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FFT_NAME(ff_cos_128),
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FFT_NAME(ff_cos_256),
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FFT_NAME(ff_cos_512),
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FFT_NAME(ff_cos_1024),
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FFT_NAME(ff_cos_2048),
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FFT_NAME(ff_cos_4096),
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FFT_NAME(ff_cos_8192),
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FFT_NAME(ff_cos_16384),
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FFT_NAME(ff_cos_32768),
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FFT_NAME(ff_cos_65536),
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};
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#endif /* FFT_FIXED_32 */
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static void fft_permute_c(FFTContext *s, FFTComplex *z);
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static void fft_calc_c(FFTContext *s, FFTComplex *z);
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static int split_radix_permutation(int i, int n, int inverse)
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{
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int m;
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if(n <= 2) return i&1;
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m = n >> 1;
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if(!(i&m)) return split_radix_permutation(i, m, inverse)*2;
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m >>= 1;
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if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
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else return split_radix_permutation(i, m, inverse)*4 - 1;
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}
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av_cold void ff_init_ff_cos_tabs(int index)
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{
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#if (!CONFIG_HARDCODED_TABLES) && (!FFT_FIXED_32)
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int i;
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int m = 1<<index;
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double freq = 2*M_PI/m;
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FFTSample *tab = FFT_NAME(ff_cos_tabs)[index];
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for(i=0; i<=m/4; i++)
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tab[i] = FIX15(cos(i*freq));
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for(i=1; i<m/4; i++)
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tab[m/2-i] = tab[i];
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#endif
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}
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static const int avx_tab[] = {
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0, 4, 1, 5, 8, 12, 9, 13, 2, 6, 3, 7, 10, 14, 11, 15
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};
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static int is_second_half_of_fft32(int i, int n)
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{
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if (n <= 32)
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return i >= 16;
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else if (i < n/2)
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return is_second_half_of_fft32(i, n/2);
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else if (i < 3*n/4)
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return is_second_half_of_fft32(i - n/2, n/4);
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else
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return is_second_half_of_fft32(i - 3*n/4, n/4);
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}
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static av_cold void fft_perm_avx(FFTContext *s)
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{
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int i;
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int n = 1 << s->nbits;
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for (i = 0; i < n; i += 16) {
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int k;
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if (is_second_half_of_fft32(i, n)) {
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for (k = 0; k < 16; k++)
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s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] =
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i + avx_tab[k];
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} else {
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for (k = 0; k < 16; k++) {
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int j = i + k;
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j = (j & ~7) | ((j >> 1) & 3) | ((j << 2) & 4);
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s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] = j;
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}
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}
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}
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}
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av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
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{
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int i, j, n;
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if (nbits < 2 || nbits > 16)
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goto fail;
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s->nbits = nbits;
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n = 1 << nbits;
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s->revtab = av_malloc(n * sizeof(uint16_t));
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if (!s->revtab)
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goto fail;
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s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
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if (!s->tmp_buf)
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goto fail;
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s->inverse = inverse;
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s->fft_permutation = FF_FFT_PERM_DEFAULT;
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s->fft_permute = fft_permute_c;
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s->fft_calc = fft_calc_c;
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#if CONFIG_MDCT
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s->imdct_calc = ff_imdct_calc_c;
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s->imdct_half = ff_imdct_half_c;
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s->mdct_calc = ff_mdct_calc_c;
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#endif
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#if FFT_FIXED_32
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{
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int n=0;
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ff_fft_lut_init(ff_fft_offsets_lut, 0, 1 << 16, &n);
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}
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#else /* FFT_FIXED_32 */
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#if FFT_FLOAT
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if (ARCH_AARCH64) ff_fft_init_aarch64(s);
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if (ARCH_ARM) ff_fft_init_arm(s);
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if (ARCH_PPC) ff_fft_init_ppc(s);
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if (ARCH_X86) ff_fft_init_x86(s);
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if (CONFIG_MDCT) s->mdct_calcw = s->mdct_calc;
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if (HAVE_MIPSFPU) ff_fft_init_mips(s);
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#else
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if (CONFIG_MDCT) s->mdct_calcw = ff_mdct_calcw_c;
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if (ARCH_ARM) ff_fft_fixed_init_arm(s);
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#endif
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for(j=4; j<=nbits; j++) {
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ff_init_ff_cos_tabs(j);
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}
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#endif /* FFT_FIXED_32 */
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if (s->fft_permutation == FF_FFT_PERM_AVX) {
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fft_perm_avx(s);
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} else {
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for(i=0; i<n; i++) {
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j = i;
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if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS)
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j = (j&~3) | ((j>>1)&1) | ((j<<1)&2);
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s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = j;
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}
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}
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return 0;
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fail:
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av_freep(&s->revtab);
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av_freep(&s->tmp_buf);
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return -1;
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}
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static void fft_permute_c(FFTContext *s, FFTComplex *z)
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{
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int j, np;
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const uint16_t *revtab = s->revtab;
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np = 1 << s->nbits;
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/* TODO: handle split-radix permute in a more optimal way, probably in-place */
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for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
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memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
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}
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av_cold void ff_fft_end(FFTContext *s)
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{
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av_freep(&s->revtab);
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av_freep(&s->tmp_buf);
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}
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#if FFT_FIXED_32
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static void fft_calc_c(FFTContext *s, FFTComplex *z) {
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int nbits, i, n, num_transforms, offset, step;
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int n4, n2, n34;
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FFTSample tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8;
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FFTComplex *tmpz;
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const int fft_size = (1 << s->nbits);
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int64_t accu;
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num_transforms = (0x2aab >> (16 - s->nbits)) | 1;
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for (n=0; n<num_transforms; n++){
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offset = ff_fft_offsets_lut[n] << 2;
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tmpz = z + offset;
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tmp1 = tmpz[0].re + tmpz[1].re;
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tmp5 = tmpz[2].re + tmpz[3].re;
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tmp2 = tmpz[0].im + tmpz[1].im;
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tmp6 = tmpz[2].im + tmpz[3].im;
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tmp3 = tmpz[0].re - tmpz[1].re;
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tmp8 = tmpz[2].im - tmpz[3].im;
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tmp4 = tmpz[0].im - tmpz[1].im;
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tmp7 = tmpz[2].re - tmpz[3].re;
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tmpz[0].re = tmp1 + tmp5;
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tmpz[2].re = tmp1 - tmp5;
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tmpz[0].im = tmp2 + tmp6;
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tmpz[2].im = tmp2 - tmp6;
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tmpz[1].re = tmp3 + tmp8;
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tmpz[3].re = tmp3 - tmp8;
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tmpz[1].im = tmp4 - tmp7;
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tmpz[3].im = tmp4 + tmp7;
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}
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if (fft_size < 8)
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return;
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num_transforms = (num_transforms >> 1) | 1;
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for (n=0; n<num_transforms; n++){
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offset = ff_fft_offsets_lut[n] << 3;
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tmpz = z + offset;
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tmp1 = tmpz[4].re + tmpz[5].re;
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tmp3 = tmpz[6].re + tmpz[7].re;
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tmp2 = tmpz[4].im + tmpz[5].im;
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tmp4 = tmpz[6].im + tmpz[7].im;
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tmp5 = tmp1 + tmp3;
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tmp7 = tmp1 - tmp3;
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tmp6 = tmp2 + tmp4;
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tmp8 = tmp2 - tmp4;
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tmp1 = tmpz[4].re - tmpz[5].re;
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tmp2 = tmpz[4].im - tmpz[5].im;
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tmp3 = tmpz[6].re - tmpz[7].re;
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tmp4 = tmpz[6].im - tmpz[7].im;
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tmpz[4].re = tmpz[0].re - tmp5;
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tmpz[0].re = tmpz[0].re + tmp5;
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tmpz[4].im = tmpz[0].im - tmp6;
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tmpz[0].im = tmpz[0].im + tmp6;
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tmpz[6].re = tmpz[2].re - tmp8;
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tmpz[2].re = tmpz[2].re + tmp8;
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tmpz[6].im = tmpz[2].im + tmp7;
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tmpz[2].im = tmpz[2].im - tmp7;
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accu = (int64_t)Q31(M_SQRT1_2)*(tmp1 + tmp2);
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tmp5 = (int32_t)((accu + 0x40000000) >> 31);
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accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 - tmp4);
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tmp7 = (int32_t)((accu + 0x40000000) >> 31);
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accu = (int64_t)Q31(M_SQRT1_2)*(tmp2 - tmp1);
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tmp6 = (int32_t)((accu + 0x40000000) >> 31);
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accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 + tmp4);
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tmp8 = (int32_t)((accu + 0x40000000) >> 31);
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tmp1 = tmp5 + tmp7;
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tmp3 = tmp5 - tmp7;
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tmp2 = tmp6 + tmp8;
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tmp4 = tmp6 - tmp8;
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tmpz[5].re = tmpz[1].re - tmp1;
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tmpz[1].re = tmpz[1].re + tmp1;
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tmpz[5].im = tmpz[1].im - tmp2;
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tmpz[1].im = tmpz[1].im + tmp2;
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tmpz[7].re = tmpz[3].re - tmp4;
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tmpz[3].re = tmpz[3].re + tmp4;
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tmpz[7].im = tmpz[3].im + tmp3;
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tmpz[3].im = tmpz[3].im - tmp3;
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}
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step = 1 << ((MAX_LOG2_NFFT-4) - 4);
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n4 = 4;
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for (nbits=4; nbits<=s->nbits; nbits++){
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n2 = 2*n4;
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n34 = 3*n4;
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num_transforms = (num_transforms >> 1) | 1;
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for (n=0; n<num_transforms; n++){
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const FFTSample *w_re_ptr = ff_w_tab_sr + step;
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const FFTSample *w_im_ptr = ff_w_tab_sr + MAX_FFT_SIZE/(4*16) - step;
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offset = ff_fft_offsets_lut[n] << nbits;
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tmpz = z + offset;
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tmp5 = tmpz[ n2].re + tmpz[n34].re;
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tmp1 = tmpz[ n2].re - tmpz[n34].re;
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tmp6 = tmpz[ n2].im + tmpz[n34].im;
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tmp2 = tmpz[ n2].im - tmpz[n34].im;
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tmpz[ n2].re = tmpz[ 0].re - tmp5;
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tmpz[ 0].re = tmpz[ 0].re + tmp5;
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tmpz[ n2].im = tmpz[ 0].im - tmp6;
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tmpz[ 0].im = tmpz[ 0].im + tmp6;
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tmpz[n34].re = tmpz[n4].re - tmp2;
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tmpz[ n4].re = tmpz[n4].re + tmp2;
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tmpz[n34].im = tmpz[n4].im + tmp1;
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tmpz[ n4].im = tmpz[n4].im - tmp1;
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for (i=1; i<n4; i++){
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FFTSample w_re = w_re_ptr[0];
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FFTSample w_im = w_im_ptr[0];
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accu = (int64_t)w_re*tmpz[ n2+i].re;
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accu += (int64_t)w_im*tmpz[ n2+i].im;
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tmp1 = (int32_t)((accu + 0x40000000) >> 31);
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accu = (int64_t)w_re*tmpz[ n2+i].im;
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accu -= (int64_t)w_im*tmpz[ n2+i].re;
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tmp2 = (int32_t)((accu + 0x40000000) >> 31);
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accu = (int64_t)w_re*tmpz[n34+i].re;
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accu -= (int64_t)w_im*tmpz[n34+i].im;
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tmp3 = (int32_t)((accu + 0x40000000) >> 31);
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accu = (int64_t)w_re*tmpz[n34+i].im;
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accu += (int64_t)w_im*tmpz[n34+i].re;
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tmp4 = (int32_t)((accu + 0x40000000) >> 31);
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tmp5 = tmp1 + tmp3;
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tmp1 = tmp1 - tmp3;
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tmp6 = tmp2 + tmp4;
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tmp2 = tmp2 - tmp4;
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tmpz[ n2+i].re = tmpz[ i].re - tmp5;
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tmpz[ i].re = tmpz[ i].re + tmp5;
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tmpz[ n2+i].im = tmpz[ i].im - tmp6;
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tmpz[ i].im = tmpz[ i].im + tmp6;
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tmpz[n34+i].re = tmpz[n4+i].re - tmp2;
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tmpz[ n4+i].re = tmpz[n4+i].re + tmp2;
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tmpz[n34+i].im = tmpz[n4+i].im + tmp1;
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tmpz[ n4+i].im = tmpz[n4+i].im - tmp1;
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w_re_ptr += step;
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w_im_ptr -= step;
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}
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}
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step >>= 1;
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n4 <<= 1;
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}
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}
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#else /* FFT_FIXED_32 */
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#define BUTTERFLIES(a0,a1,a2,a3) {\
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BF(t3, t5, t5, t1);\
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BF(a2.re, a0.re, a0.re, t5);\
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BF(a3.im, a1.im, a1.im, t3);\
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BF(t4, t6, t2, t6);\
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BF(a3.re, a1.re, a1.re, t4);\
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BF(a2.im, a0.im, a0.im, t6);\
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}
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// force loading all the inputs before storing any.
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// this is slightly slower for small data, but avoids store->load aliasing
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// for addresses separated by large powers of 2.
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#define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
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FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
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BF(t3, t5, t5, t1);\
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BF(a2.re, a0.re, r0, t5);\
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BF(a3.im, a1.im, i1, t3);\
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BF(t4, t6, t2, t6);\
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BF(a3.re, a1.re, r1, t4);\
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BF(a2.im, a0.im, i0, t6);\
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}
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#define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
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CMUL(t1, t2, a2.re, a2.im, wre, -wim);\
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CMUL(t5, t6, a3.re, a3.im, wre, wim);\
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BUTTERFLIES(a0,a1,a2,a3)\
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}
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#define TRANSFORM_ZERO(a0,a1,a2,a3) {\
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t1 = a2.re;\
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t2 = a2.im;\
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t5 = a3.re;\
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t6 = a3.im;\
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BUTTERFLIES(a0,a1,a2,a3)\
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}
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/* z[0...8n-1], w[1...2n-1] */
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#define PASS(name)\
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static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
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{\
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FFTDouble t1, t2, t3, t4, t5, t6;\
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int o1 = 2*n;\
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int o2 = 4*n;\
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int o3 = 6*n;\
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const FFTSample *wim = wre+o1;\
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n--;\
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\
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TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
|
|
TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
|
|
do {\
|
|
z += 2;\
|
|
wre += 2;\
|
|
wim -= 2;\
|
|
TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
|
|
TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
|
|
} while(--n);\
|
|
}
|
|
|
|
PASS(pass)
|
|
#undef BUTTERFLIES
|
|
#define BUTTERFLIES BUTTERFLIES_BIG
|
|
PASS(pass_big)
|
|
|
|
#define DECL_FFT(n,n2,n4)\
|
|
static void fft##n(FFTComplex *z)\
|
|
{\
|
|
fft##n2(z);\
|
|
fft##n4(z+n4*2);\
|
|
fft##n4(z+n4*3);\
|
|
pass(z,FFT_NAME(ff_cos_##n),n4/2);\
|
|
}
|
|
|
|
static void fft4(FFTComplex *z)
|
|
{
|
|
FFTDouble t1, t2, t3, t4, t5, t6, t7, t8;
|
|
|
|
BF(t3, t1, z[0].re, z[1].re);
|
|
BF(t8, t6, z[3].re, z[2].re);
|
|
BF(z[2].re, z[0].re, t1, t6);
|
|
BF(t4, t2, z[0].im, z[1].im);
|
|
BF(t7, t5, z[2].im, z[3].im);
|
|
BF(z[3].im, z[1].im, t4, t8);
|
|
BF(z[3].re, z[1].re, t3, t7);
|
|
BF(z[2].im, z[0].im, t2, t5);
|
|
}
|
|
|
|
static void fft8(FFTComplex *z)
|
|
{
|
|
FFTDouble t1, t2, t3, t4, t5, t6;
|
|
|
|
fft4(z);
|
|
|
|
BF(t1, z[5].re, z[4].re, -z[5].re);
|
|
BF(t2, z[5].im, z[4].im, -z[5].im);
|
|
BF(t5, z[7].re, z[6].re, -z[7].re);
|
|
BF(t6, z[7].im, z[6].im, -z[7].im);
|
|
|
|
BUTTERFLIES(z[0],z[2],z[4],z[6]);
|
|
TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
|
|
}
|
|
|
|
#if !CONFIG_SMALL
|
|
static void fft16(FFTComplex *z)
|
|
{
|
|
FFTDouble t1, t2, t3, t4, t5, t6;
|
|
FFTSample cos_16_1 = FFT_NAME(ff_cos_16)[1];
|
|
FFTSample cos_16_3 = FFT_NAME(ff_cos_16)[3];
|
|
|
|
fft8(z);
|
|
fft4(z+8);
|
|
fft4(z+12);
|
|
|
|
TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
|
|
TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
|
|
TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3);
|
|
TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1);
|
|
}
|
|
#else
|
|
DECL_FFT(16,8,4)
|
|
#endif
|
|
DECL_FFT(32,16,8)
|
|
DECL_FFT(64,32,16)
|
|
DECL_FFT(128,64,32)
|
|
DECL_FFT(256,128,64)
|
|
DECL_FFT(512,256,128)
|
|
#if !CONFIG_SMALL
|
|
#define pass pass_big
|
|
#endif
|
|
DECL_FFT(1024,512,256)
|
|
DECL_FFT(2048,1024,512)
|
|
DECL_FFT(4096,2048,1024)
|
|
DECL_FFT(8192,4096,2048)
|
|
DECL_FFT(16384,8192,4096)
|
|
DECL_FFT(32768,16384,8192)
|
|
DECL_FFT(65536,32768,16384)
|
|
|
|
static void (* const fft_dispatch[])(FFTComplex*) = {
|
|
fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
|
|
fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
|
|
};
|
|
|
|
static void fft_calc_c(FFTContext *s, FFTComplex *z)
|
|
{
|
|
fft_dispatch[s->nbits-2](z);
|
|
}
|
|
#endif /* FFT_FIXED_32 */
|