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fft.c

/*
** FFT and FHT routines
**  Copyright 1988, 1993; Ron Mayer
**      Copyright (c) 1999-2000 Takehiro Tominaga
**
**  fht(fz,n);
**      Does a hartley transform of "n" points in the array "fz".
**
** NOTE: This routine uses at least 2 patented algorithms, and may be
**       under the restrictions of a bunch of different organizations.
**       Although I wrote it completely myself; it is kind of a derivative
**       of a routine I once authored and released under the GPL, so it
**       may fall under the free software foundation's restrictions;
**       it was worked on as a Stanford Univ project, so they claim
**       some rights to it; it was further optimized at work here, so
**       I think this company claims parts of it.  The patents are
**       held by R. Bracewell (the FHT algorithm) and O. Buneman (the
**       trig generator), both at Stanford Univ.
**       If it were up to me, I'd say go do whatever you want with it;
**       but it would be polite to give credit to the following people
**       if you use this anywhere:
**           Euler     - probable inventor of the fourier transform.
**           Gauss     - probable inventor of the FFT.
**           Hartley   - probable inventor of the hartley transform.
**           Buneman   - for a really cool trig generator
**           Mayer(me) - for authoring this particular version and
**                       including all the optimizations in one package.
**       Thanks,
**       Ron Mayer; mayer@acuson.com
** and added some optimization by
**           Mather    - idea of using lookup table
**           Takehiro  - some dirty hack for speed up
*/

/* $Id: fft.c,v 1.33 2008/04/12 18:18:06 robert Exp $ */

#ifdef HAVE_CONFIG_H
# include <config.h>
#endif

#include "lame.h"
#include "machine.h"
#include "encoder.h"
#include "util.h"
#include "fft.h"





#define TRI_SIZE (5-1)  /* 1024 =  4**5 */

/* fft.c    */
static FLOAT window[BLKSIZE], window_s[BLKSIZE_s / 2];

static const FLOAT costab[TRI_SIZE * 2] = {
    9.238795325112867e-01, 3.826834323650898e-01,
    9.951847266721969e-01, 9.801714032956060e-02,
    9.996988186962042e-01, 2.454122852291229e-02,
    9.999811752826011e-01, 6.135884649154475e-03
};

static void
fht(FLOAT * fz, int n)
{
    const FLOAT *tri = costab;
    int     k4;
    FLOAT  *fi, *gi;
    FLOAT const *fn;

    n <<= 1;            /* to get BLKSIZE, because of 3DNow! ASM routine */
    fn = fz + n;
    k4 = 4;
    do {
        FLOAT   s1, c1;
        int     i, k1, k2, k3, kx;
        kx = k4 >> 1;
        k1 = k4;
        k2 = k4 << 1;
        k3 = k2 + k1;
        k4 = k2 << 1;
        fi = fz;
        gi = fi + kx;
        do {
            FLOAT   f0, f1, f2, f3;
            f1 = fi[0] - fi[k1];
            f0 = fi[0] + fi[k1];
            f3 = fi[k2] - fi[k3];
            f2 = fi[k2] + fi[k3];
            fi[k2] = f0 - f2;
            fi[0] = f0 + f2;
            fi[k3] = f1 - f3;
            fi[k1] = f1 + f3;
            f1 = gi[0] - gi[k1];
            f0 = gi[0] + gi[k1];
            f3 = SQRT2 * gi[k3];
            f2 = SQRT2 * gi[k2];
            gi[k2] = f0 - f2;
            gi[0] = f0 + f2;
            gi[k3] = f1 - f3;
            gi[k1] = f1 + f3;
            gi += k4;
            fi += k4;
        } while (fi < fn);
        c1 = tri[0];
        s1 = tri[1];
        for (i = 1; i < kx; i++) {
            FLOAT   c2, s2;
            c2 = 1 - (2 * s1) * s1;
            s2 = (2 * s1) * c1;
            fi = fz + i;
            gi = fz + k1 - i;
            do {
                FLOAT   a, b, g0, f0, f1, g1, f2, g2, f3, g3;
                b = s2 * fi[k1] - c2 * gi[k1];
                a = c2 * fi[k1] + s2 * gi[k1];
                f1 = fi[0] - a;
                f0 = fi[0] + a;
                g1 = gi[0] - b;
                g0 = gi[0] + b;
                b = s2 * fi[k3] - c2 * gi[k3];
                a = c2 * fi[k3] + s2 * gi[k3];
                f3 = fi[k2] - a;
                f2 = fi[k2] + a;
                g3 = gi[k2] - b;
                g2 = gi[k2] + b;
                b = s1 * f2 - c1 * g3;
                a = c1 * f2 + s1 * g3;
                fi[k2] = f0 - a;
                fi[0] = f0 + a;
                gi[k3] = g1 - b;
                gi[k1] = g1 + b;
                b = c1 * g2 - s1 * f3;
                a = s1 * g2 + c1 * f3;
                gi[k2] = g0 - a;
                gi[0] = g0 + a;
                fi[k3] = f1 - b;
                fi[k1] = f1 + b;
                gi += k4;
                fi += k4;
            } while (fi < fn);
            c2 = c1;
            c1 = c2 * tri[0] - s1 * tri[1];
            s1 = c2 * tri[1] + s1 * tri[0];
        }
        tri += 2;
    } while (k4 < n);
}

static const unsigned char rv_tbl[] = {
    0x00, 0x80, 0x40, 0xc0, 0x20, 0xa0, 0x60, 0xe0,
    0x10, 0x90, 0x50, 0xd0, 0x30, 0xb0, 0x70, 0xf0,
    0x08, 0x88, 0x48, 0xc8, 0x28, 0xa8, 0x68, 0xe8,
    0x18, 0x98, 0x58, 0xd8, 0x38, 0xb8, 0x78, 0xf8,
    0x04, 0x84, 0x44, 0xc4, 0x24, 0xa4, 0x64, 0xe4,
    0x14, 0x94, 0x54, 0xd4, 0x34, 0xb4, 0x74, 0xf4,
    0x0c, 0x8c, 0x4c, 0xcc, 0x2c, 0xac, 0x6c, 0xec,
    0x1c, 0x9c, 0x5c, 0xdc, 0x3c, 0xbc, 0x7c, 0xfc,
    0x02, 0x82, 0x42, 0xc2, 0x22, 0xa2, 0x62, 0xe2,
    0x12, 0x92, 0x52, 0xd2, 0x32, 0xb2, 0x72, 0xf2,
    0x0a, 0x8a, 0x4a, 0xca, 0x2a, 0xaa, 0x6a, 0xea,
    0x1a, 0x9a, 0x5a, 0xda, 0x3a, 0xba, 0x7a, 0xfa,
    0x06, 0x86, 0x46, 0xc6, 0x26, 0xa6, 0x66, 0xe6,
    0x16, 0x96, 0x56, 0xd6, 0x36, 0xb6, 0x76, 0xf6,
    0x0e, 0x8e, 0x4e, 0xce, 0x2e, 0xae, 0x6e, 0xee,
    0x1e, 0x9e, 0x5e, 0xde, 0x3e, 0xbe, 0x7e, 0xfe
};

#define ch01(index)  (buffer[chn][index])

#define ml00(f) (window[i        ] * f(i))
#define ml10(f) (window[i + 0x200] * f(i + 0x200))
#define ml20(f) (window[i + 0x100] * f(i + 0x100))
#define ml30(f) (window[i + 0x300] * f(i + 0x300))

#define ml01(f) (window[i + 0x001] * f(i + 0x001))
#define ml11(f) (window[i + 0x201] * f(i + 0x201))
#define ml21(f) (window[i + 0x101] * f(i + 0x101))
#define ml31(f) (window[i + 0x301] * f(i + 0x301))

#define ms00(f) (window_s[i       ] * f(i + k))
#define ms10(f) (window_s[0x7f - i] * f(i + k + 0x80))
#define ms20(f) (window_s[i + 0x40] * f(i + k + 0x40))
#define ms30(f) (window_s[0x3f - i] * f(i + k + 0xc0))

#define ms01(f) (window_s[i + 0x01] * f(i + k + 0x01))
#define ms11(f) (window_s[0x7e - i] * f(i + k + 0x81))
#define ms21(f) (window_s[i + 0x41] * f(i + k + 0x41))
#define ms31(f) (window_s[0x3e - i] * f(i + k + 0xc1))


void
fft_short(lame_internal_flags const *const gfc,
          FLOAT x_real[3][BLKSIZE_s], int chn, const sample_t * buffer[2])
{
    int     i;
    int     j;
    int     b;

    for (b = 0; b < 3; b++) {
        FLOAT  *x = &x_real[b][BLKSIZE_s / 2];
        short const k = (576 / 3) * (b + 1);
        j = BLKSIZE_s / 8 - 1;
        do {
            FLOAT   f0, f1, f2, f3, w;

            i = rv_tbl[j << 2];

            f0 = ms00(ch01);
            w = ms10(ch01);
            f1 = f0 - w;
            f0 = f0 + w;
            f2 = ms20(ch01);
            w = ms30(ch01);
            f3 = f2 - w;
            f2 = f2 + w;

            x -= 4;
            x[0] = f0 + f2;
            x[2] = f0 - f2;
            x[1] = f1 + f3;
            x[3] = f1 - f3;

            f0 = ms01(ch01);
            w = ms11(ch01);
            f1 = f0 - w;
            f0 = f0 + w;
            f2 = ms21(ch01);
            w = ms31(ch01);
            f3 = f2 - w;
            f2 = f2 + w;

            x[BLKSIZE_s / 2 + 0] = f0 + f2;
            x[BLKSIZE_s / 2 + 2] = f0 - f2;
            x[BLKSIZE_s / 2 + 1] = f1 + f3;
            x[BLKSIZE_s / 2 + 3] = f1 - f3;
        } while (--j >= 0);

        gfc->fft_fht(x, BLKSIZE_s / 2);
        /* BLKSIZE_s/2 because of 3DNow! ASM routine */
    }
}

void
fft_long(lame_internal_flags const *const gfc,
         FLOAT x[BLKSIZE], int chn, const sample_t * buffer[2])
{
    int     i;
    int     jj = BLKSIZE / 8 - 1;
    x += BLKSIZE / 2;

    do {
        FLOAT   f0, f1, f2, f3, w;

        i = rv_tbl[jj];
        f0 = ml00(ch01);
        w = ml10(ch01);
        f1 = f0 - w;
        f0 = f0 + w;
        f2 = ml20(ch01);
        w = ml30(ch01);
        f3 = f2 - w;
        f2 = f2 + w;

        x -= 4;
        x[0] = f0 + f2;
        x[2] = f0 - f2;
        x[1] = f1 + f3;
        x[3] = f1 - f3;

        f0 = ml01(ch01);
        w = ml11(ch01);
        f1 = f0 - w;
        f0 = f0 + w;
        f2 = ml21(ch01);
        w = ml31(ch01);
        f3 = f2 - w;
        f2 = f2 + w;

        x[BLKSIZE / 2 + 0] = f0 + f2;
        x[BLKSIZE / 2 + 2] = f0 - f2;
        x[BLKSIZE / 2 + 1] = f1 + f3;
        x[BLKSIZE / 2 + 3] = f1 - f3;
    } while (--jj >= 0);

    gfc->fft_fht(x, BLKSIZE / 2);
    /* BLKSIZE/2 because of 3DNow! ASM routine */
}

#ifdef HAVE_NASM
extern void fht_3DN(FLOAT * fz, int n);
extern void fht_SSE(FLOAT * fz, int n);
#endif

void
init_fft(lame_internal_flags * const gfc)
{
    int     i;

    /* The type of window used here will make no real difference, but */
    /* in the interest of merging nspsytune stuff - switch to blackman window */
    for (i = 0; i < BLKSIZE; i++)
        /* blackman window */
        window[i] = 0.42 - 0.5 * cos(2 * PI * (i + .5) / BLKSIZE) +
            0.08 * cos(4 * PI * (i + .5) / BLKSIZE);

    for (i = 0; i < BLKSIZE_s / 2; i++)
        window_s[i] = 0.5 * (1.0 - cos(2.0 * PI * (i + 0.5) / BLKSIZE_s));

#ifdef HAVE_NASM
    if (gfc->CPU_features.AMD_3DNow) {
        gfc->fft_fht = fht_3DN;
    }
    else if (gfc->CPU_features.SSE) {
        gfc->fft_fht = fht_SSE;
    }
    else
#endif
    {
        gfc->fft_fht = fht;
    }
}

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