PeerStreamer

/*

 * 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 Libav.

 *

 * Libav 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.

 *

 * Libav 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 Libav; if not, write to the Free Software

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

 */

/**

 * @file

 * FFT/IFFT transforms.

 */

#include <stdlib.h>

#include <string.h>

#include "libavutil/mathematics.h"

#include "fft.h"

#include "fft-internal.h"

/* 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),

};

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

static void ff_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

    int i;

    int m = 1<<index;

    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<m/4; i++)

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

#endif

}

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 = ff_fft_permute_c;

    s->fft_calc    = ff_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_FLOAT

    if (ARCH_ARM)     ff_fft_init_arm(s);

    if (HAVE_ALTIVEC) ff_fft_init_altivec(s);

    if (HAVE_MMX)     ff_fft_init_mmx(s);

#endif

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

        ff_init_ff_cos_tabs(j);

    }

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

        int 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 ff_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;j<np;j++) s->tmp_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);

}

#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, t7, t8;

    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(t3, z[7].re, z[6].re, -z[7].re);

    BF(t4, z[7].im, z[6].im, -z[7].im);

    BF(t8, t1, t3, t1);

    BF(t7, t2, t2, t4);

    BF(z[4].re, z[0].re, z[0].re, t1);

    BF(z[4].im, z[0].im, z[0].im, t2);

    BF(z[6].re, z[2].re, z[2].re, t7);

    BF(z[6].im, z[2].im, z[2].im, t8);

    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 ff_fft_calc_c(FFTContext *s, FFTComplex *z)

{

    fft_dispatch[s->nbits-2](z);

}