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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
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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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/* 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 ff_cos_tabs[] = {
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    NULL, NULL, NULL, NULL,
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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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av_cold void ff_init_ff_cos_tabs(int index)
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{
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#if !CONFIG_HARDCODED_TABLES
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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 = ff_cos_tabs[index];
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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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#endif
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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_permute = ff_fft_permute_c;
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    s->fft_calc    = ff_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 (ARCH_ARM)     ff_fft_init_arm(s);
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    if (HAVE_ALTIVEC) ff_fft_init_altivec(s);
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    if (HAVE_MMX)     ff_fft_init_mmx(s);
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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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    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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    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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void ff_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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#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)\
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{\
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    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)
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{
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    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);
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    BF(z[2].im, z[0].im, t2, t5);
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}
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static void fft8(FFTComplex *z)
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{
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    FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
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    fft4(z);
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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);
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    BF(t4, z[7].im, z[6].im, -z[7].im);
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    BF(t8, t1, t3, t1);
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    BF(t7, t2, t2, t4);
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    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);
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    BF(z[6].im, z[2].im, z[2].im, t8);
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    TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
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}
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#if !CONFIG_SMALL
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static void fft16(FFTComplex *z)
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{
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    FFTSample t1, t2, t3, t4, t5, t6;
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    fft8(z);
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    fft4(z+8);
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    fft4(z+12);
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    TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
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    TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
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    TRANSFORM(z[1],z[5],z[9],z[13],ff_cos_16[1],ff_cos_16[3]);
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    TRANSFORM(z[3],z[7],z[11],z[15],ff_cos_16[3],ff_cos_16[1]);
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}
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#else
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DECL_FFT(16,8,4)
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#endif
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DECL_FFT(32,16,8)
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DECL_FFT(64,32,16)
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DECL_FFT(128,64,32)
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DECL_FFT(256,128,64)
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DECL_FFT(512,256,128)
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#if !CONFIG_SMALL
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#define pass pass_big
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#endif
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DECL_FFT(1024,512,256)
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DECL_FFT(2048,1024,512)
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DECL_FFT(4096,2048,1024)
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DECL_FFT(8192,4096,2048)
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DECL_FFT(16384,8192,4096)
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DECL_FFT(32768,16384,8192)
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DECL_FFT(65536,32768,16384)
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static void (* const fft_dispatch[])(FFTComplex*) = {
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    fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
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    fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
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};
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void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
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{
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    fft_dispatch[s->nbits-2](z);
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}
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