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/*

 * FFT/IFFT transforms

 * Copyright (c) 2008 Loren Merritt

 * Copyright (c) 2002 Fabrice Bellard

 * Partly based on libdjbfft by D. J. Bernstein

 *

 * This file is part of FFmpeg.

 *

 * FFmpeg is free software; you can redistribute it and/or

 * modify it under the terms of the GNU Lesser General Public

 * License as published by the Free Software Foundation; either

 * version 2.1 of the License, or (at your option) any later version.

 *

 * FFmpeg is distributed in the hope that it will be useful,

 * but WITHOUT ANY WARRANTY; without even the implied warranty of

 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

 * Lesser General Public License for more details.

 *

 * You should have received a copy of the GNU Lesser General Public

 * License along with FFmpeg; if not, write to the Free Software

 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA

 */

/**

 * @file

 * FFT/IFFT transforms.

 */

#include 

#include 

#include "libavutil/mathematics.h"

#include "fft.h"

#include "fft-internal.h"

#if CONFIG_FFT_FIXED_32

#include "fft_table.h"

#else /* CONFIG_FFT_FIXED_32 */

/* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */

#if !CONFIG_HARDCODED_TABLES

COSTABLE(16);

COSTABLE(32);

COSTABLE(64);

COSTABLE(128);

COSTABLE(256);

COSTABLE(512);

COSTABLE(1024);

COSTABLE(2048);

COSTABLE(4096);

COSTABLE(8192);

COSTABLE(16384);

COSTABLE(32768);

COSTABLE(65536);

#endif

COSTABLE_CONST FFTSample * const FFT_NAME(ff_cos_tabs)[] = {

    NULL, NULL, NULL, NULL,

    FFT_NAME(ff_cos_16),

    FFT_NAME(ff_cos_32),

    FFT_NAME(ff_cos_64),

    FFT_NAME(ff_cos_128),

    FFT_NAME(ff_cos_256),

    FFT_NAME(ff_cos_512),

    FFT_NAME(ff_cos_1024),

    FFT_NAME(ff_cos_2048),

    FFT_NAME(ff_cos_4096),

    FFT_NAME(ff_cos_8192),

    FFT_NAME(ff_cos_16384),

    FFT_NAME(ff_cos_32768),

    FFT_NAME(ff_cos_65536),

};

#endif /* CONFIG_FFT_FIXED_32 */

static void fft_permute_c(FFTContext *s, FFTComplex *z);

static void fft_calc_c(FFTContext *s, FFTComplex *z);

static int split_radix_permutation(int i, int n, int inverse)

{

    int m;

    if(n <= 2) return i&1;

    m = n >> 1;

    if(!(i&m))            return split_radix_permutation(i, m, inverse)*2;

    m >>= 1;

    if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;

    else                  return split_radix_permutation(i, m, inverse)*4 - 1;

}

av_cold void ff_init_ff_cos_tabs(int index)

{

#if (!CONFIG_HARDCODED_TABLES) && (!CONFIG_FFT_FIXED_32)

    int i;

    int m = 1<

    double freq = 2*M_PI/m;

    FFTSample *tab = FFT_NAME(ff_cos_tabs)[index];

    for(i=0; i<=m/4; i++)

        tab[i] = FIX15(cos(i*freq));

    for(i=1; i

        tab[m/2-i] = tab[i];

#endif

}

static const int avx_tab[] = {

    0, 4, 1, 5, 8, 12, 9, 13, 2, 6, 3, 7, 10, 14, 11, 15

};

static int is_second_half_of_fft32(int i, int n)

{

    if (n <= 32)

        return i >= 16;

    else if (i < n/2)

        return is_second_half_of_fft32(i, n/2);

    else if (i < 3*n/4)

        return is_second_half_of_fft32(i - n/2, n/4);

    else

        return is_second_half_of_fft32(i - 3*n/4, n/4);

}

static av_cold void fft_perm_avx(FFTContext *s)

{

    int i;

    int n = 1 << s->nbits;

    for (i = 0; i < n; i += 16) {

        int k;

        if (is_second_half_of_fft32(i, n)) {

            for (k = 0; k < 16; k++)

                s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] =

                    i + avx_tab[k];

        } else {

            for (k = 0; k < 16; k++) {

                int j = i + k;

                j = (j & ~7) | ((j >> 1) & 3) | ((j << 2) & 4);

                s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] = j;

            }

        }

    }

}

av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)

{

    int i, j, n;

    if (nbits < 2 || nbits > 16)

        goto fail;

    s->nbits = nbits;

    n = 1 << nbits;

    s->revtab = av_malloc(n * sizeof(uint16_t));

    if (!s->revtab)

        goto fail;

    s->tmp_buf = av_malloc(n * sizeof(FFTComplex));

    if (!s->tmp_buf)

        goto fail;

    s->inverse = inverse;

    s->fft_permutation = FF_FFT_PERM_DEFAULT;

    s->fft_permute = fft_permute_c;

    s->fft_calc    = fft_calc_c;

#if CONFIG_MDCT

    s->imdct_calc  = ff_imdct_calc_c;

    s->imdct_half  = ff_imdct_half_c;

    s->mdct_calc   = ff_mdct_calc_c;

#endif

#if CONFIG_FFT_FIXED_32

    {

        int n=0;

        ff_fft_lut_init(fft_offsets_lut, 0, 1 << 16, &n);

    }

#else /* CONFIG_FFT_FIXED_32 */

#if CONFIG_FFT_FLOAT

    if (ARCH_ARM)     ff_fft_init_arm(s);

    if (ARCH_PPC)     ff_fft_init_ppc(s);

    if (ARCH_X86)     ff_fft_init_x86(s);

    if (CONFIG_MDCT)  s->mdct_calcw = s->mdct_calc;

    if (HAVE_MIPSFPU) ff_fft_init_mips(s);

#else

    if (CONFIG_MDCT)  s->mdct_calcw = ff_mdct_calcw_c;

    if (ARCH_ARM)     ff_fft_fixed_init_arm(s);

#endif

    for(j=4; j<=nbits; j++) {

        ff_init_ff_cos_tabs(j);

    }

#endif /* CONFIG_FFT_FIXED_32 */

    if (s->fft_permutation == FF_FFT_PERM_AVX) {

        fft_perm_avx(s);

    } else {

        for(i=0; i

            j = i;

            if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS)

                j = (j&~3) | ((j>>1)&1) | ((j<<1)&2);

            s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = j;

        }

    }

    return 0;

 fail:

    av_freep(&s->revtab);

    av_freep(&s->tmp_buf);

    return -1;

}

static void fft_permute_c(FFTContext *s, FFTComplex *z)

{

    int j, np;

    const uint16_t *revtab = s->revtab;

    np = 1 << s->nbits;

    /* TODO: handle split-radix permute in a more optimal way, probably in-place */

    for(j=0;jtmp_buf[revtab[j]] = z[j];

    memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));

}

av_cold void ff_fft_end(FFTContext *s)

{

    av_freep(&s->revtab);

    av_freep(&s->tmp_buf);

}

#if CONFIG_FFT_FIXED_32

static void fft_calc_c(FFTContext *s, FFTComplex *z) {

    int nbits, i, n, num_transforms, offset, step;

    int n4, n2, n34;

    FFTSample tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8;

    FFTComplex *tmpz;

    FFTSample w_re, w_im;

    FFTSample *w_re_ptr, *w_im_ptr;

    const int fft_size = (1 << s->nbits);

    int64_t accu;

    num_transforms = (0x2aab >> (16 - s->nbits)) | 1;

    for (n=0; n

        offset = fft_offsets_lut[n] << 2;

        tmpz = z + offset;

        tmp1 = tmpz[0].re + tmpz[1].re;

        tmp5 = tmpz[2].re + tmpz[3].re;

        tmp2 = tmpz[0].im + tmpz[1].im;

        tmp6 = tmpz[2].im + tmpz[3].im;

        tmp3 = tmpz[0].re - tmpz[1].re;

        tmp8 = tmpz[2].im - tmpz[3].im;

        tmp4 = tmpz[0].im - tmpz[1].im;

        tmp7 = tmpz[2].re - tmpz[3].re;

        tmpz[0].re = tmp1 + tmp5;

        tmpz[2].re = tmp1 - tmp5;

        tmpz[0].im = tmp2 + tmp6;

        tmpz[2].im = tmp2 - tmp6;

        tmpz[1].re = tmp3 + tmp8;

        tmpz[3].re = tmp3 - tmp8;

        tmpz[1].im = tmp4 - tmp7;

        tmpz[3].im = tmp4 + tmp7;

    }

    if (fft_size < 8)

        return;

    num_transforms = (num_transforms >> 1) | 1;

    for (n=0; n

        offset = fft_offsets_lut[n] << 3;

        tmpz = z + offset;

        tmp1 = tmpz[4].re + tmpz[5].re;

        tmp3 = tmpz[6].re + tmpz[7].re;

        tmp2 = tmpz[4].im + tmpz[5].im;

        tmp4 = tmpz[6].im + tmpz[7].im;

        tmp5 = tmp1 + tmp3;

        tmp7 = tmp1 - tmp3;

        tmp6 = tmp2 + tmp4;

        tmp8 = tmp2 - tmp4;

        tmp1 = tmpz[4].re - tmpz[5].re;

        tmp2 = tmpz[4].im - tmpz[5].im;

        tmp3 = tmpz[6].re - tmpz[7].re;

        tmp4 = tmpz[6].im - tmpz[7].im;

        tmpz[4].re = tmpz[0].re - tmp5;

        tmpz[0].re = tmpz[0].re + tmp5;

        tmpz[4].im = tmpz[0].im - tmp6;

        tmpz[0].im = tmpz[0].im + tmp6;

        tmpz[6].re = tmpz[2].re - tmp8;

        tmpz[2].re = tmpz[2].re + tmp8;

        tmpz[6].im = tmpz[2].im + tmp7;

        tmpz[2].im = tmpz[2].im - tmp7;

        accu = (int64_t)Q31(M_SQRT1_2)*(tmp1 + tmp2);

        tmp5 = (int32_t)((accu + 0x40000000) >> 31);

        accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 - tmp4);

        tmp7 = (int32_t)((accu + 0x40000000) >> 31);

        accu = (int64_t)Q31(M_SQRT1_2)*(tmp2 - tmp1);

        tmp6 = (int32_t)((accu + 0x40000000) >> 31);

        accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 + tmp4);

        tmp8 = (int32_t)((accu + 0x40000000) >> 31);

        tmp1 = tmp5 + tmp7;

        tmp3 = tmp5 - tmp7;

        tmp2 = tmp6 + tmp8;

        tmp4 = tmp6 - tmp8;

        tmpz[5].re = tmpz[1].re - tmp1;

        tmpz[1].re = tmpz[1].re + tmp1;

        tmpz[5].im = tmpz[1].im - tmp2;

        tmpz[1].im = tmpz[1].im + tmp2;

        tmpz[7].re = tmpz[3].re - tmp4;

        tmpz[3].re = tmpz[3].re + tmp4;

        tmpz[7].im = tmpz[3].im + tmp3;

        tmpz[3].im = tmpz[3].im - tmp3;

    }

    step = 1 << ((MAX_LOG2_NFFT-4) - 4);

    n4 = 4;

    for (nbits=4; nbits<=s->nbits; nbits++){

        n2  = 2*n4;

        n34 = 3*n4;

        num_transforms = (num_transforms >> 1) | 1;

        for (n=0; n

            offset = fft_offsets_lut[n] << nbits;

            tmpz = z + offset;

            tmp5 = tmpz[ n2].re + tmpz[n34].re;

            tmp1 = tmpz[ n2].re - tmpz[n34].re;

            tmp6 = tmpz[ n2].im + tmpz[n34].im;

            tmp2 = tmpz[ n2].im - tmpz[n34].im;

            tmpz[ n2].re = tmpz[ 0].re - tmp5;

            tmpz[  0].re = tmpz[ 0].re + tmp5;

            tmpz[ n2].im = tmpz[ 0].im - tmp6;

            tmpz[  0].im = tmpz[ 0].im + tmp6;

            tmpz[n34].re = tmpz[n4].re - tmp2;

            tmpz[ n4].re = tmpz[n4].re + tmp2;

            tmpz[n34].im = tmpz[n4].im + tmp1;

            tmpz[ n4].im = tmpz[n4].im - tmp1;

            w_re_ptr = w_tab_sr + step;

            w_im_ptr = w_tab_sr + MAX_FFT_SIZE/(4*16) - step;

            for (i=1; i

                w_re = w_re_ptr[0];

                w_im = w_im_ptr[0];

                accu  = (int64_t)w_re*tmpz[ n2+i].re;

                accu += (int64_t)w_im*tmpz[ n2+i].im;

                tmp1 = (int32_t)((accu + 0x40000000) >> 31);

                accu  = (int64_t)w_re*tmpz[ n2+i].im;

                accu -= (int64_t)w_im*tmpz[ n2+i].re;

                tmp2 = (int32_t)((accu + 0x40000000) >> 31);

                accu  = (int64_t)w_re*tmpz[n34+i].re;

                accu -= (int64_t)w_im*tmpz[n34+i].im;

                tmp3 = (int32_t)((accu + 0x40000000) >> 31);

                accu  = (int64_t)w_re*tmpz[n34+i].im;

                accu += (int64_t)w_im*tmpz[n34+i].re;

                tmp4 = (int32_t)((accu + 0x40000000) >> 31);

                tmp5 = tmp1 + tmp3;

                tmp1 = tmp1 - tmp3;

                tmp6 = tmp2 + tmp4;

                tmp2 = tmp2 - tmp4;

                tmpz[ n2+i].re = tmpz[   i].re - tmp5;

                tmpz[    i].re = tmpz[   i].re + tmp5;

                tmpz[ n2+i].im = tmpz[   i].im - tmp6;

                tmpz[    i].im = tmpz[   i].im + tmp6;

                tmpz[n34+i].re = tmpz[n4+i].re - tmp2;

                tmpz[ n4+i].re = tmpz[n4+i].re + tmp2;

                tmpz[n34+i].im = tmpz[n4+i].im + tmp1;

                tmpz[ n4+i].im = tmpz[n4+i].im - tmp1;

                w_re_ptr += step;

                w_im_ptr -= step;

            }

        }

        step >>= 1;

        n4   <<= 1;

    }

}

#else /* CONFIG_FFT_FIXED_32 */

#define BUTTERFLIES(a0,a1,a2,a3) {\

    BF(t3, t5, t5, t1);\

    BF(a2.re, a0.re, a0.re, t5);\

    BF(a3.im, a1.im, a1.im, t3);\

    BF(t4, t6, t2, t6);\

    BF(a3.re, a1.re, a1.re, t4);\

    BF(a2.im, a0.im, a0.im, t6);\

}

// force loading all the inputs before storing any.

// this is slightly slower for small data, but avoids store->load aliasing

// for addresses separated by large powers of 2.

#define BUTTERFLIES_BIG(a0,a1,a2,a3) {\

    FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\

    BF(t3, t5, t5, t1);\

    BF(a2.re, a0.re, r0, t5);\

    BF(a3.im, a1.im, i1, t3);\

    BF(t4, t6, t2, t6);\

    BF(a3.re, a1.re, r1, t4);\

    BF(a2.im, a0.im, i0, t6);\

}

#define TRANSFORM(a0,a1,a2,a3,wre,wim) {\

    CMUL(t1, t2, a2.re, a2.im, wre, -wim);\

    CMUL(t5, t6, a3.re, a3.im, wre,  wim);\

    BUTTERFLIES(a0,a1,a2,a3)\

}

#define TRANSFORM_ZERO(a0,a1,a2,a3) {\

    t1 = a2.re;\

    t2 = a2.im;\

    t5 = a3.re;\

    t6 = a3.im;\

    BUTTERFLIES(a0,a1,a2,a3)\

}

/* z[0...8n-1], w[1...2n-1] */

#define PASS(name)\

static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\

{\

    FFTDouble t1, t2, t3, t4, t5, t6;\

    int o1 = 2*n;\

    int o2 = 4*n;\

    int o3 = 6*n;\

    const FFTSample *wim = wre+o1;\

    n--;\

\

    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 /* CONFIG_FFT_FIXED_32 */