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/*
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 * MDCT/IMDCT transforms
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 * Copyright (c) 2002 Fabrice Bellard
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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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#include <stdlib.h>
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#include <string.h>
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#include "libavutil/common.h"
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#include "libavutil/mathematics.h"
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#include "fft.h"
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/**
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 * @file libavcodec/mdct.c
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 * MDCT/IMDCT transforms.
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 */
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// Generate a Kaiser-Bessel Derived Window.
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#define BESSEL_I0_ITER 50 // default: 50 iterations of Bessel I0 approximation
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av_cold void ff_kbd_window_init(float *window, float alpha, int n)
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{
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   int i, j;
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   double sum = 0.0, bessel, tmp;
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   double local_window[n];
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   double alpha2 = (alpha * M_PI / n) * (alpha * M_PI / n);
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   for (i = 0; i < n; i++) {
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       tmp = i * (n - i) * alpha2;
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       bessel = 1.0;
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       for (j = BESSEL_I0_ITER; j > 0; j--)
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           bessel = bessel * tmp / (j * j) + 1;
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       sum += bessel;
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       local_window[i] = sum;
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   }
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   sum++;
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   for (i = 0; i < n; i++)
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       window[i] = sqrt(local_window[i] / sum);
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}
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#include "mdct_tablegen.h"
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/**
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 * init MDCT or IMDCT computation.
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 */
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av_cold int ff_mdct_init(FFTContext *s, int nbits, int inverse, double scale)
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{
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    int n, n4, i;
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    double alpha, theta;
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    int tstep;
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    memset(s, 0, sizeof(*s));
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    n = 1 << nbits;
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    s->mdct_bits = nbits;
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    s->mdct_size = n;
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    n4 = n >> 2;
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    s->permutation = FF_MDCT_PERM_NONE;
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    if (ff_fft_init(s, s->mdct_bits - 2, inverse) < 0)
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        goto fail;
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    s->tcos = av_malloc(n/2 * sizeof(FFTSample));
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    if (!s->tcos)
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        goto fail;
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    switch (s->permutation) {
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    case FF_MDCT_PERM_NONE:
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        s->tsin = s->tcos + n4;
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        tstep = 1;
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        break;
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    case FF_MDCT_PERM_INTERLEAVE:
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        s->tsin = s->tcos + 1;
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        tstep = 2;
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        break;
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    default:
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        goto fail;
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    }
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    theta = 1.0 / 8.0 + (scale < 0 ? n4 : 0);
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    scale = sqrt(fabs(scale));
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    for(i=0;i<n4;i++) {
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        alpha = 2 * M_PI * (i + theta) / n;
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        s->tcos[i*tstep] = -cos(alpha) * scale;
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        s->tsin[i*tstep] = -sin(alpha) * scale;
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    }
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    return 0;
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 fail:
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    ff_mdct_end(s);
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    return -1;
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}
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/* complex multiplication: p = a * b */
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#define CMUL(pre, pim, are, aim, bre, bim) \
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{\
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    FFTSample _are = (are);\
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    FFTSample _aim = (aim);\
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    FFTSample _bre = (bre);\
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    FFTSample _bim = (bim);\
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    (pre) = _are * _bre - _aim * _bim;\
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    (pim) = _are * _bim + _aim * _bre;\
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}
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/**
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 * Compute the middle half of the inverse MDCT of size N = 2^nbits,
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 * thus excluding the parts that can be derived by symmetry
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 * @param output N/2 samples
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 * @param input N/2 samples
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 */
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void ff_imdct_half_c(FFTContext *s, FFTSample *output, const FFTSample *input)
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{
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    int k, n8, n4, n2, n, j;
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    const uint16_t *revtab = s->revtab;
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    const FFTSample *tcos = s->tcos;
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    const FFTSample *tsin = s->tsin;
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    const FFTSample *in1, *in2;
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    FFTComplex *z = (FFTComplex *)output;
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    n = 1 << s->mdct_bits;
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    n2 = n >> 1;
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    n4 = n >> 2;
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    n8 = n >> 3;
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    /* pre rotation */
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    in1 = input;
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    in2 = input + n2 - 1;
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    for(k = 0; k < n4; k++) {
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        j=revtab[k];
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        CMUL(z[j].re, z[j].im, *in2, *in1, tcos[k], tsin[k]);
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        in1 += 2;
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        in2 -= 2;
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    }
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    ff_fft_calc(s, z);
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    /* post rotation + reordering */
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    for(k = 0; k < n8; k++) {
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        FFTSample r0, i0, r1, i1;
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        CMUL(r0, i1, z[n8-k-1].im, z[n8-k-1].re, tsin[n8-k-1], tcos[n8-k-1]);
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        CMUL(r1, i0, z[n8+k  ].im, z[n8+k  ].re, tsin[n8+k  ], tcos[n8+k  ]);
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        z[n8-k-1].re = r0;
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        z[n8-k-1].im = i0;
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        z[n8+k  ].re = r1;
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        z[n8+k  ].im = i1;
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    }
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}
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/**
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 * Compute inverse MDCT of size N = 2^nbits
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 * @param output N samples
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 * @param input N/2 samples
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 */
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void ff_imdct_calc_c(FFTContext *s, FFTSample *output, const FFTSample *input)
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{
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    int k;
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    int n = 1 << s->mdct_bits;
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    int n2 = n >> 1;
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    int n4 = n >> 2;
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    ff_imdct_half_c(s, output+n4, input);
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    for(k = 0; k < n4; k++) {
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        output[k] = -output[n2-k-1];
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        output[n-k-1] = output[n2+k];
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    }
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}
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/**
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 * Compute MDCT of size N = 2^nbits
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 * @param input N samples
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 * @param out N/2 samples
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 */
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void ff_mdct_calc_c(FFTContext *s, FFTSample *out, const FFTSample *input)
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{
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    int i, j, n, n8, n4, n2, n3;
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    FFTSample re, im;
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    const uint16_t *revtab = s->revtab;
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    const FFTSample *tcos = s->tcos;
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    const FFTSample *tsin = s->tsin;
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    FFTComplex *x = (FFTComplex *)out;
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    n = 1 << s->mdct_bits;
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    n2 = n >> 1;
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    n4 = n >> 2;
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    n8 = n >> 3;
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    n3 = 3 * n4;
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    /* pre rotation */
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    for(i=0;i<n8;i++) {
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        re = -input[2*i+3*n4] - input[n3-1-2*i];
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        im = -input[n4+2*i] + input[n4-1-2*i];
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        j = revtab[i];
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        CMUL(x[j].re, x[j].im, re, im, -tcos[i], tsin[i]);
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        re = input[2*i] - input[n2-1-2*i];
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        im = -(input[n2+2*i] + input[n-1-2*i]);
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        j = revtab[n8 + i];
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        CMUL(x[j].re, x[j].im, re, im, -tcos[n8 + i], tsin[n8 + i]);
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    }
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    ff_fft_calc(s, x);
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    /* post rotation */
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    for(i=0;i<n8;i++) {
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        FFTSample r0, i0, r1, i1;
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        CMUL(i1, r0, x[n8-i-1].re, x[n8-i-1].im, -tsin[n8-i-1], -tcos[n8-i-1]);
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        CMUL(i0, r1, x[n8+i  ].re, x[n8+i  ].im, -tsin[n8+i  ], -tcos[n8+i  ]);
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        x[n8-i-1].re = r0;
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        x[n8-i-1].im = i0;
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        x[n8+i  ].re = r1;
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        x[n8+i  ].im = i1;
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    }
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}
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av_cold void ff_mdct_end(FFTContext *s)
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{
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    av_freep(&s->tcos);
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    ff_fft_end(s);
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}