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/*
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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 fft.c
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 * FFT/IFFT transforms.
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 */
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#include "dsputil.h"
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/* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
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DECLARE_ALIGNED_16(FFTSample, ff_cos_16[8]);
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DECLARE_ALIGNED_16(FFTSample, ff_cos_32[16]);
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DECLARE_ALIGNED_16(FFTSample, ff_cos_64[32]);
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DECLARE_ALIGNED_16(FFTSample, ff_cos_128[64]);
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DECLARE_ALIGNED_16(FFTSample, ff_cos_256[128]);
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DECLARE_ALIGNED_16(FFTSample, ff_cos_512[256]);
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DECLARE_ALIGNED_16(FFTSample, ff_cos_1024[512]);
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DECLARE_ALIGNED_16(FFTSample, ff_cos_2048[1024]);
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DECLARE_ALIGNED_16(FFTSample, ff_cos_4096[2048]);
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DECLARE_ALIGNED_16(FFTSample, ff_cos_8192[4096]);
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DECLARE_ALIGNED_16(FFTSample, ff_cos_16384[8192]);
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DECLARE_ALIGNED_16(FFTSample, ff_cos_32768[16384]);
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DECLARE_ALIGNED_16(FFTSample, ff_cos_65536[32768]);
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static FFTSample *ff_cos_tabs[] = {
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    ff_cos_16, ff_cos_32, ff_cos_64, ff_cos_128, ff_cos_256, ff_cos_512, ff_cos_1024,
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    ff_cos_2048, ff_cos_4096, ff_cos_8192, ff_cos_16384, ff_cos_32768, ff_cos_65536,
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};
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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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/**
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 * The size of the FFT is 2^nbits. If inverse is TRUE, inverse FFT is
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 * done
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 */
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int ff_fft_init(FFTContext *s, int nbits, int inverse)
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{
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    int i, j, m, n;
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    float alpha, c1, s1, s2;
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    int split_radix = 1;
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    int av_unused has_vectors;
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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->tmp_buf = NULL;
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    s->exptab = av_malloc((n / 2) * sizeof(FFTComplex));
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    if (!s->exptab)
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        goto fail;
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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->inverse = inverse;
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    s2 = inverse ? 1.0 : -1.0;
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    s->fft_permute = ff_fft_permute_c;
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    s->fft_calc = ff_fft_calc_c;
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    s->imdct_calc = ff_imdct_calc;
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    s->imdct_half = ff_imdct_half;
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    s->exptab1 = NULL;
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#if defined HAVE_MMX && defined HAVE_YASM
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    has_vectors = mm_support();
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    if (has_vectors & MM_SSE) {
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        /* SSE for P3/P4/K8 */
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        s->imdct_calc = ff_imdct_calc_sse;
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        s->imdct_half = ff_imdct_half_sse;
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        s->fft_permute = ff_fft_permute_sse;
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        s->fft_calc = ff_fft_calc_sse;
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    } else if (has_vectors & MM_3DNOWEXT) {
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        /* 3DNowEx for K7 */
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        s->imdct_calc = ff_imdct_calc_3dn2;
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        s->imdct_half = ff_imdct_half_3dn2;
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        s->fft_calc = ff_fft_calc_3dn2;
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    } else if (has_vectors & MM_3DNOW) {
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        /* 3DNow! for K6-2/3 */
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        s->fft_calc = ff_fft_calc_3dn;
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    }
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#elif defined HAVE_ALTIVEC && !defined ALTIVEC_USE_REFERENCE_C_CODE
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    has_vectors = mm_support();
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    if (has_vectors & MM_ALTIVEC) {
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        s->fft_calc = ff_fft_calc_altivec;
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        split_radix = 0;
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    }
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#endif
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    if (split_radix) {
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        for(j=4; j<=nbits; j++) {
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            int m = 1<<j;
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            double freq = 2*M_PI/m;
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            FFTSample *tab = ff_cos_tabs[j-4];
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            for(i=0; i<=m/4; i++)
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                tab[i] = 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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        }
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        for(i=0; i<n; i++)
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            s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = i;
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        s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
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    } else {
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        int np, nblocks, np2, l;
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        FFTComplex *q;
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        for(i=0; i<(n/2); i++) {
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            alpha = 2 * M_PI * (float)i / (float)n;
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            c1 = cos(alpha);
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            s1 = sin(alpha) * s2;
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            s->exptab[i].re = c1;
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            s->exptab[i].im = s1;
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        }
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        np = 1 << nbits;
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        nblocks = np >> 3;
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        np2 = np >> 1;
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        s->exptab1 = av_malloc(np * 2 * sizeof(FFTComplex));
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        if (!s->exptab1)
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            goto fail;
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        q = s->exptab1;
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        do {
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            for(l = 0; l < np2; l += 2 * nblocks) {
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                *q++ = s->exptab[l];
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                *q++ = s->exptab[l + nblocks];
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                q->re = -s->exptab[l].im;
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                q->im = s->exptab[l].re;
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                q++;
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                q->re = -s->exptab[l + nblocks].im;
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                q->im = s->exptab[l + nblocks].re;
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                q++;
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            }
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            nblocks = nblocks >> 1;
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        } while (nblocks != 0);
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        av_freep(&s->exptab);
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    /* compute bit reverse table */
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    for(i=0;i<n;i++) {
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        m=0;
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        for(j=0;j<nbits;j++) {
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            m |= ((i >> j) & 1) << (nbits-j-1);
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        }
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        s->revtab[i]=m;
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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->exptab);
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    av_freep(&s->exptab1);
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    av_freep(&s->tmp_buf);
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    return -1;
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}
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/**
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 * Do the permutation needed BEFORE calling ff_fft_calc()
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 */
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void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
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{
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    int j, k, np;
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    FFTComplex tmp;
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    const uint16_t *revtab = s->revtab;
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    np = 1 << s->nbits;
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    if (s->tmp_buf) {
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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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        return;
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    }
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    /* reverse */
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    for(j=0;j<np;j++) {
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        k = revtab[j];
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        if (k < j) {
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            tmp = z[k];
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            z[k] = z[j];
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            z[j] = tmp;
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        }
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    }
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}
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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->exptab);
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    av_freep(&s->exptab1);
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    av_freep(&s->tmp_buf);
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}
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#define sqrthalf (float)M_SQRT1_2
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#define BF(x,y,a,b) {\
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    x = a - b;\
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    y = a + b;\
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}
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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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    t1 = a2.re * wre + a2.im * wim;\
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    t2 = a2.im * wre - a2.re * wim;\
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    t5 = a3.re * wre - a3.im * wim;\
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    t6 = a3.im * wre + a3.re * 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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    FFTSample 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]);\
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    TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
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    do {\
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        z += 2;\
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        wre += 2;\
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        wim -= 2;\
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        TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
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        TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
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    } while(--n);\
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}
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PASS(pass)
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#undef BUTTERFLIES
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#define BUTTERFLIES BUTTERFLIES_BIG
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PASS(pass_big)
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#define DECL_FFT(n,n2,n4)\
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static void fft##n(FFTComplex *z)\
297
{\
298
    fft##n2(z);\
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    fft##n4(z+n4*2);\
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    fft##n4(z+n4*3);\
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    pass(z,ff_cos_##n,n4/2);\
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}
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static void fft4(FFTComplex *z)
305
{
306
    FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
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    BF(t3, t1, z[0].re, z[1].re);
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    BF(t8, t6, z[3].re, z[2].re);
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    BF(z[2].re, z[0].re, t1, t6);
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    BF(t4, t2, z[0].im, z[1].im);
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    BF(t7, t5, z[2].im, z[3].im);
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    BF(z[3].im, z[1].im, t4, t8);
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    BF(z[3].re, z[1].re, t3, t7);
315
    BF(z[2].im, z[0].im, t2, t5);
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}
317

    
318
static void fft8(FFTComplex *z)
319
{
320
    FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
321

    
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    fft4(z);
323

    
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    BF(t1, z[5].re, z[4].re, -z[5].re);
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    BF(t2, z[5].im, z[4].im, -z[5].im);
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    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);
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    BF(t7, t2, t2, t4);
330
    BF(z[4].re, z[0].re, z[0].re, t1);
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    BF(z[4].im, z[0].im, z[0].im, t2);
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    BF(z[6].re, z[2].re, z[2].re, t7);
333
    BF(z[6].im, z[2].im, z[2].im, t8);
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335
    TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
336
}
337

    
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#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