fft.c

MP3编码的完整实现(源代码和使用例子都有)

/*
** FFT and FHT routines
**  Copyright 1988, 1993; Ron Mayer
**  
**  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; [e-mail]
** and added some optimization by
**           Mather    - idea of using lookup table
**           Takehiro  - some dirty hack for speed up
*/

#include <math.h>
#include "util.h"
#include "psymodel.h"
#include "lame.h"

#define TRI_SIZE (5-1) /* 1024 =  4**5 */
static FLOAT costab[TRI_SIZE*2];
static FLOAT window[BLKSIZE / 2], window_s[BLKSIZE_s / 2];

static INLINE void fht(FLOAT *fz, short n)
{
    short k4;
    FLOAT *fi, *fn, *gi;
    FLOAT *tri;

    fn = fz + n;
    tri = &costab[0];
    k4 = 4;
    do {
	FLOAT s1, c1;
	short 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 short 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 ch2(index)  (((FLOAT)(0.5*SQRT2))*(buffer[0][index] + buffer[1][index]))
#define ch3(index)  (((FLOAT)(0.5*SQRT2))*(buffer[0][index] - buffer[1][index]))

#define ml00(f)	(window[i        ] * f(i))
#define ml10(f)	(window[0x1ff - i] * f(i + 0x200))
#define ml20(f)	(window[i + 0x100] * f(i + 0x100))
#define ml30(f)	(window[0x0ff - i] * f(i + 0x300))

#define ml01(f)	(window[i + 0x001] * f(i + 0x001))
#define ml11(f)	(window[0x1fe - i] * f(i + 0x201))
#define ml21(f)	(window[i + 0x101] * f(i + 0x101))
#define ml31(f)	(window[0x0fe - i] * 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(
    FLOAT x_real[3][BLKSIZE_s], int chn, short *buffer[2])
{
    short i, j, b;

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

		i = rv_tbl[j << 2];

		f0 = ms00(ch2); w = ms10(ch2); f1 = f0 - w; f0 = f0 + w;
		f2 = ms20(ch2); w = ms30(ch2); 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(ch2); w = ms11(ch2); f1 = f0 - w; f0 = f0 + w;
		f2 = ms21(ch2); w = ms31(ch2); 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);
	} else {
	    do {
		FLOAT f0,f1,f2,f3, w;

		i = rv_tbl[j << 2];

		f0 = ms00(ch3); w = ms10(ch3); f1 = f0 - w; f0 = f0 + w;
		f2 = ms20(ch3); w = ms30(ch3); 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(ch3); w = ms11(ch3); f1 = f0 - w; f0 = f0 + w;
		f2 = ms21(ch3); w = ms31(ch3); 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);
	}

	fht(x, BLKSIZE_s);
    }
}

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

    if (chn < 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);
    } else if (chn == 2) {
	do {
	    FLOAT f0,f1,f2,f3, w;

	    i = rv_tbl[jj];
	    f0 = ml00(ch2); w = ml10(ch2); f1 = f0 - w; f0 = f0 + w;
	    f2 = ml20(ch2); w = ml30(ch2); 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(ch2); w = ml11(ch2); f1 = f0 - w; f0 = f0 + w;
	    f2 = ml21(ch2); w = ml31(ch2); 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);
    } else {
	do {
	    FLOAT f0,f1,f2,f3, w;

	    i = rv_tbl[jj];
	    f0 = ml00(ch3); w = ml10(ch3); f1 = f0 - w; f0 = f0 + w;
	    f2 = ml20(ch3); w = ml30(ch3); 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(ch3); w = ml11(ch3); f1 = f0 - w; f0 = f0 + w;
	    f2 = ml21(ch3); w = ml31(ch3); 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);
    }

    fht(x, BLKSIZE);
}


void init_fft(void)
{
    int i;

    FLOAT r = PI*0.125;
    for (i = 0; i < TRI_SIZE; i++) {
	costab[i*2  ] = cos(r);
	costab[i*2+1] = sin(r);
	r *= 0.25;
    }

    /*
     * calculate HANN window coefficients 
     */
    for (i = 0; i < BLKSIZE / 2; i++)
	window[i] = 0.5 * (1.0 - cos(2.0 * PI * (i + 0.5) / 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));
}