/*** 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; mayer@acuson.com** 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, int 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));}