//===========================================================================
// Real Discrete Fourier Transform
//     dimension   :one
//     data length :power of 2, must be larger than 4
//     decimation  :frequency
//     radix       :4, 2
//     data        :inplace
// classes:
//	 Cfft: real discrete fourier transform class
// functions:
//	 Cfft::rdft  : compute the forward real discrete fourier transform
//   Cfft::cdft  : compute the forward double discrete fourier transform
//   Cfft::icdft : compute the reverse double discrete fourier transform 
//   Cfft::fft   : compute the forward real dft on a set of integer values
//	
//	 This class is derived from the work of Takuya Ooura, who has kindly put his
//	 fft algorithims in the public domain.  Thank you Takuya Ooura!
//===========================================================================

#include <config.h>

#include "misc.h"
#include "fft.h"

// n = size of fourier transform in complex pairs
// fftsiz = size of fourier transform in real (double) values

Cfft::Cfft(int n)
{
	int tablesize = (int)(sqrt(n*1.0)+0.5) + 2;
	fftlen = n;
	fftsiz = 2 * n;
	ip = new int[tablesize];
	w = new double[fftlen];
	fftwin = new double[fftlen*2];
    makewt();
    makect();
    wintype = FFT_NONE;
    RectWindow(fftwin, fftlen*2);
}
	
Cfft::~Cfft()
{
	if (ip) delete [] ip;
	if (w) delete [] w;
	if (fftwin) delete [] fftwin;
}

void Cfft::resize(int n)
{
	int tablesize = (int)(sqrt(n*1.0)+0.5) + 2;
	fftlen = n;
	fftsiz = 2 * n;
	if (ip) delete [] ip;
	ip	= new int[tablesize];
	if (w) delete [] w;
	w 	= new double[fftlen];
	if (fftwin) delete [] fftwin;
	fftwin = new double[fftlen*2];
    makewt();
    makect();
    wintype = FFT_NONE;
    RectWindow(fftwin, fftlen*2);
}

void Cfft::cdft(double *aCmpx)
{
	if (wintype != FFT_NONE)
		for (int i = 0; i < fftlen; i++) {
			aCmpx[2*i] *= fftwin[2*i];
			aCmpx[2*i+1] *= fftwin[2*i];
		}
	bitrv2(fftsiz, ip + 2, aCmpx);
	cftfsub(fftsiz, aCmpx);
	double scale = 1.0 / fftlen;
	for (int i = 0; i < fftsiz; i++) aCmpx[i] = aCmpx[i] * scale;
}

void Cfft::icdft(double *aCmpx)
{
	bitrv2conj(fftsiz, ip + 2, aCmpx);
	cftbsub(fftsiz, aCmpx);
}

// FFT of an array of short integers
// siData = array (size n) of unsigned integers such as the output of a soundcard
// operating in 16 bit mode
// out = array (size n) of double pairs

void Cfft::sifft(short int *siData, double *out)
{
	for (int i = 0; i < fftlen; i++) {
		out[2*i] = siData[i];
		out[2*i+1] = 0.0;
	}
	cdft(out);
	return;
}


void Cfft::rdft(double *RealData) // RealData is 2N long
{
	if (wintype != FFT_NONE)
		for (int i = 0; i < fftlen*2; i++) {
			RealData[i] *= fftwin[i];
		}

    if (fftsiz > 4) {
        bitrv2(fftsiz, ip + 2, RealData);
        cftfsub(fftsiz, RealData);
        rftfsub(fftsiz, RealData);
    } else if (fftsiz == 4) {
        cftfsub(fftsiz, RealData);
    }
    double xi = RealData[0] - RealData[1];
    RealData[0] += RealData[1];
    RealData[1] = xi;
	double scale = 1.0 / fftlen;
	for (int i = 0; i < fftsiz; i++) RealData[i] *= scale;

}

void Cfft::irdft(double *RealData)
{
/*
    int nw, nc;
    double xi;
    
    nw = ip[0];
    if (n > (nw << 2)) {
        nw = n >> 2;
        makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n > (nc << 2)) {
        nc = n >> 2;
        makect(nc, ip, w + nw);
    }
    if (isgn >= 0) {
        if (n > 4) {
            bitrv2(n, ip + 2, a);
            cftfsub(n, a, w);
            rftfsub(n, a, nc, w + nw);
        } else if (n == 4) {
            cftfsub(n, a, w);
        }
        xi = a[0] - a[1];
        a[0] += a[1];
        a[1] = xi;
    } else {
        a[1] = 0.5 * (a[0] - a[1]);
        a[0] -= a[1];
        if (n > 4) {
            rftbsub(n, a, nc, w + nw);
            bitrv2(n, ip + 2, a);
            cftbsub(n, a, w);
        } else if (n == 4) {
            cftfsub(n, a, w);
        }
    }
*/
}

void Cfft::setWindow(fftPrefilter pf)
{
	wintype = pf;
	if (wintype == FFT_TRIANGULAR)
		TriangularWindow(fftwin, fftlen*2);
	else if (wintype == FFT_HAMMING)
		HammingWindow(fftwin, fftlen*2);
	else if (wintype == FFT_HANNING)
		HanningWindow(fftwin, fftlen*2);
	else if (wintype == FFT_BLACKMAN)
		BlackmanWindow(fftwin, fftlen*2);
	else
		RectWindow(fftwin, fftlen*2);
}

/* -------- initializing routines -------- */


void Cfft::makewt()
{
    int j, 
		nwh, nw = fftsiz / 4;
    double delta, x, y;
    
    ip[0] = nw;
    ip[1] = 1;
    if (nw > 2) {
        nwh = nw >> 1;
        delta = atan(1.0) / nwh;
        w[0] = 1;
        w[1] = 0;
        w[nwh] = cos(delta * nwh);
        w[nwh + 1] = w[nwh];
        if (nwh > 2) {
            for (j = 2; j < nwh; j += 2) {
                x = cos(delta * j);
                y = sin(delta * j);
                w[j] = x;
                w[j + 1] = y;
                w[nw - j] = y;
                w[nw - j + 1] = x;
            }
            bitrv2(nw, ip + 2, w);
        }
    }
}

void Cfft::makect()
{
    int j, nch, nc = fftsiz / 4;
    double delta;
    double *c = w + fftsiz / 4;
	c = w + fftsiz / 4;
    ip[1] = nc;
    if (nc > 1) {
        nch = nc >> 1;
        delta = atan(1.0) / nch;
        c[0] = cos(delta * nch);
        c[nch] = 0.5 * c[0];
        for (j = 1; j < nch; j++) {
            c[j] = 0.5 * cos(delta * j);
            c[nc - j] = 0.5 * sin(delta * j);
        }
    }
}


/* -------- child routines -------- */


void Cfft::bitrv2(int n, int *ip, double *a)
{
    int j, j1, k, k1, l, m, m2;
    double xr, xi, yr, yi;
    
    ip[0] = 0;
    l = n;
    m = 1;
    while ((m << 3) < l) {
        l >>= 1;
        for (j = 0; j < m; j++) {
            ip[m + j] = ip[j] + l;
        }
        m <<= 1;
    }
    m2 = 2 * m;
    if ((m << 3) == l) {
        for (k = 0; k < m; k++) {
            for (j = 0; j < k; j++) {
                j1 = 2 * j + ip[k];
                k1 = 2 * k + ip[j];
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m2;
                k1 += 2 * m2;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m2;
                k1 -= m2;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m2;
                k1 += 2 * m2;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
            }
            j1 = 2 * k + m2 + ip[k];
            k1 = j1 + m2;
            xr = a[j1];
            xi = a[j1 + 1];
            yr = a[k1];
            yi = a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
        }
    } else {
        for (k = 1; k < m; k++) {
            for (j = 0; j < k; j++) {
                j1 = 2 * j + ip[k];
                k1 = 2 * k + ip[j];
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m2;
                k1 += m2;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
            }
        }
    }
}


void Cfft::cftfsub(int n, double *a)
{
    int j, j1, j2, j3, l;
    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
    
    l = 2;
    if (n > 8) {
        cft1st(n, a);
        l = 8;
        while ((l << 2) < n) {
            cftmdl(n, l, a);
            l <<= 2;
        }
    }
    if ((l << 2) == n) {
        for (j = 0; j < l; j += 2) {
            j1 = j + l;
            j2 = j1 + l;
            j3 = j2 + l;
            x0r = a[j] + a[j1];
            x0i = a[j + 1] + a[j1 + 1];
            x1r = a[j] - a[j1];
            x1i = a[j + 1] - a[j1 + 1];
            x2r = a[j2] + a[j3];
            x2i = a[j2 + 1] + a[j3 + 1];
            x3r = a[j2] - a[j3];
            x3i = a[j2 + 1] - a[j3 + 1];
            a[j] = x0r + x2r;
            a[j + 1] = x0i + x2i;
            a[j2] = x0r - x2r;
            a[j2 + 1] = x0i - x2i;
            a[j1] = x1r - x3i;
            a[j1 + 1] = x1i + x3r;
            a[j3] = x1r + x3i;
            a[j3 + 1] = x1i - x3r;
        }
    } else {
        for (j = 0; j < l; j += 2) {
            j1 = j + l;
            x0r = a[j] - a[j1];
            x0i = a[j + 1] - a[j1 + 1];
            a[j] += a[j1];
            a[j + 1] += a[j1 + 1];
            a[j1] = x0r;
            a[j1 + 1] = x0i;
        }
    }
}


void Cfft::cft1st(int n, double *a)
{
    int j, k1, k2;
    double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
    
    x0r = a[0] + a[2];
    x0i = a[1] + a[3];
    x1r = a[0] - a[2];
    x1i = a[1] - a[3];
    x2r = a[4] + a[6];
    x2i = a[5] + a[7];
    x3r = a[4] - a[6];
    x3i = a[5] - a[7];
    a[0] = x0r + x2r;
    a[1] = x0i + x2i;
    a[4] = x0r - x2r;
    a[5] = x0i - x2i;
    a[2] = x1r - x3i;
    a[3] = x1i + x3r;
    a[6] = x1r + x3i;
    a[7] = x1i - x3r;
    wk1r = w[2];
    x0r = a[8] + a[10];
    x0i = a[9] + a[11];
    x1r = a[8] - a[10];
    x1i = a[9] - a[11];
    x2r = a[12] + a[14];
    x2i = a[13] + a[15];
    x3r = a[12] - a[14];
    x3i = a[13] - a[15];
    a[8] = x0r + x2r;
    a[9] = x0i + x2i;
    a[12] = x2i - x0i;
    a[13] = x0r - x2r;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[10] = wk1r * (x0r - x0i);
    a[11] = wk1r * (x0r + x0i);
    x0r = x3i + x1r;
    x0i = x3r - x1i;
    a[14] = wk1r * (x0i - x0r);
    a[15] = wk1r * (x0i + x0r);
    k1 = 0;
    for (j = 16; j < n; j += 16) {
        k1 += 2;
        k2 = 2 * k1;
        wk2r = w[k1];
        wk2i = w[k1 + 1];
        wk1r = w[k2];
        wk1i = w[k2 + 1];
        wk3r = wk1r - 2 * wk2i * wk1i;
        wk3i = 2 * wk2i * wk1r - wk1i;
        x0r = a[j] + a[j + 2];
        x0i = a[j + 1] + a[j + 3];
        x1r = a[j] - a[j + 2];
        x1i = a[j + 1] - a[j + 3];
        x2r = a[j + 4] + a[j + 6];
        x2i = a[j + 5] + a[j + 7];
        x3r = a[j + 4] - a[j + 6];
        x3i = a[j + 5] - a[j + 7];
        a[j] = x0r + x2r;
        a[j + 1] = x0i + x2i;
        x0r -= x2r;
        x0i -= x2i;
        a[j + 4] = wk2r * x0r - wk2i * x0i;
        a[j + 5] = wk2r * x0i + wk2i * x0r;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[j + 2] = wk1r * x0r - wk1i * x0i;
        a[j + 3] = wk1r * x0i + wk1i * x0r;
        x0r = x1r + x3i;
        x0i = x1i - x3r;
        a[j + 6] = wk3r * x0r - wk3i * x0i;
        a[j + 7] = wk3r * x0i + wk3i * x0r;
        wk1r = w[k2 + 2];
        wk1i = w[k2 + 3];
        wk3r = wk1r - 2 * wk2r * wk1i;
        wk3i = 2 * wk2r * wk1r - wk1i;
        x0r = a[j + 8] + a[j + 10];
        x0i = a[j + 9] + a[j + 11];
        x1r = a[j + 8] - a[j + 10];
        x1i = a[j + 9] - a[j + 11];
        x2r = a[j + 12] + a[j + 14];
        x2i = a[j + 13] + a[j + 15];
        x3r = a[j + 12] - a[j + 14];
        x3i = a[j + 13] - a[j + 15];
        a[j + 8] = x0r + x2r;
        a[j + 9] = x0i + x2i;
        x0r -= x2r;
        x0i -= x2i;
        a[j + 12] = -wk2i * x0r - wk2r * x0i;
        a[j + 13] = -wk2i * x0i + wk2r * x0r;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[j + 10] = wk1r * x0r - wk1i * x0i;
        a[j + 11] = wk1r * x0i + wk1i * x0r;
        x0r = x1r + x3i;
        x0i = x1i - x3r;
        a[j + 14] = wk3r * x0r - wk3i * x0i;
        a[j + 15] = wk3r * x0i + wk3i * x0r;
    }
}


void Cfft::cftmdl(int n, int l, double *a)
{
    int j, j1, j2, j3, k, k1, k2, m, m2;
    double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
    
    m = l << 2;
    for (j = 0; j < l; j += 2) {
        j1 = j + l;
        j2 = j1 + l;
        j3 = j2 + l;
        x0r = a[j] + a[j1];
        x0i = a[j + 1] + a[j1 + 1];
        x1r = a[j] - a[j1];
        x1i = a[j + 1] - a[j1 + 1];
        x2r = a[j2] + a[j3];
        x2i = a[j2 + 1] + a[j3 + 1];
        x3r = a[j2] - a[j3];
        x3i = a[j2 + 1] - a[j3 + 1];
        a[j] = x0r + x2r;
        a[j + 1] = x0i + x2i;
        a[j2] = x0r - x2r;
        a[j2 + 1] = x0i - x2i;
        a[j1] = x1r - x3i;
        a[j1 + 1] = x1i + x3r;
        a[j3] = x1r + x3i;
        a[j3 + 1] = x1i - x3r;
    }
    wk1r = w[2];
    for (j = m; j < l + m; j += 2) {
        j1 = j + l;
        j2 = j1 + l;
        j3 = j2 + l;
        x0r = a[j] + a[j1];
        x0i = a[j + 1] + a[j1 + 1];
        x1r = a[j] - a[j1];
        x1i = a[j + 1] - a[j1 + 1];
        x2r = a[j2] + a[j3];
        x2i = a[j2 + 1] + a[j3 + 1];
        x3r = a[j2] - a[j3];
        x3i = a[j2 + 1] - a[j3 + 1];
        a[j] = x0r + x2r;
        a[j + 1] = x0i + x2i;
        a[j2] = x2i - x0i;
        a[j2 + 1] = x0r - x2r;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[j1] = wk1r * (x0r - x0i);
        a[j1 + 1] = wk1r * (x0r + x0i);
        x0r = x3i + x1r;
        x0i = x3r - x1i;
        a[j3] = wk1r * (x0i - x0r);
        a[j3 + 1] = wk1r * (x0i + x0r);
    }
    k1 = 0;
    m2 = 2 * m;
    for (k = m2; k < n; k += m2) {
        k1 += 2;
        k2 = 2 * k1;
        wk2r = w[k1];
        wk2i = w[k1 + 1];
        wk1r = w[k2];
        wk1i = w[k2 + 1];
        wk3r = wk1r - 2 * wk2i * wk1i;
        wk3i = 2 * wk2i * wk1r - wk1i;
        for (j = k; j < l + k; j += 2) {
            j1 = j + l;
            j2 = j1 + l;
            j3 = j2 + l;
            x0r = a[j] + a[j1];
            x0i = a[j + 1] + a[j1 + 1];
            x1r = a[j] - a[j1];
            x1i = a[j + 1] - a[j1 + 1];
            x2r = a[j2] + a[j3];
            x2i = a[j2 + 1] + a[j3 + 1];
            x3r = a[j2] - a[j3];
            x3i = a[j2 + 1] - a[j3 + 1];
            a[j] = x0r + x2r;
            a[j + 1] = x0i + x2i;
            x0r -= x2r;
            x0i -= x2i;
            a[j2] = wk2r * x0r - wk2i * x0i;
            a[j2 + 1] = wk2r * x0i + wk2i * x0r;
            x0r = x1r - x3i;
            x0i = x1i + x3r;
            a[j1] = wk1r * x0r - wk1i * x0i;
            a[j1 + 1] = wk1r * x0i + wk1i * x0r;
            x0r = x1r + x3i;
            x0i = x1i - x3r;
            a[j3] = wk3r * x0r - wk3i * x0i;
            a[j3 + 1] = wk3r * x0i + wk3i * x0r;
        }
        wk1r = w[k2 + 2];
        wk1i = w[k2 + 3];
        wk3r = wk1r - 2 * wk2r * wk1i;
        wk3i = 2 * wk2r * wk1r - wk1i;
        for (j = k + m; j < l + (k + m); j += 2) {
            j1 = j + l;
            j2 = j1 + l;
            j3 = j2 + l;
            x0r = a[j] + a[j1];
            x0i = a[j + 1] + a[j1 + 1];
            x1r = a[j] - a[j1];
            x1i = a[j + 1] - a[j1 + 1];
            x2r = a[j2] + a[j3];
            x2i = a[j2 + 1] + a[j3 + 1];
            x3r = a[j2] - a[j3];
            x3i = a[j2 + 1] - a[j3 + 1];
            a[j] = x0r + x2r;
            a[j + 1] = x0i + x2i;
            x0r -= x2r;
            x0i -= x2i;
            a[j2] = -wk2i * x0r - wk2r * x0i;
            a[j2 + 1] = -wk2i * x0i + wk2r * x0r;
            x0r = x1r - x3i;
            x0i = x1i + x3r;
            a[j1] = wk1r * x0r - wk1i * x0i;
            a[j1 + 1] = wk1r * x0i + wk1i * x0r;
            x0r = x1r + x3i;
            x0i = x1i - x3r;
            a[j3] = wk3r * x0r - wk3i * x0i;
            a[j3 + 1] = wk3r * x0i + wk3i * x0r;
        }
    }
}


void Cfft::cftbsub(int n, double *a)
{
    int j, j1, j2, j3, l;
    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
    
    l = 2;
    if (n > 8) {
        cft1st(n, a);
        l = 8;
        while ((l << 2) < n) {
            cftmdl(n, l, a);
            l <<= 2;
        }
    }
    if ((l << 2) == n) {
        for (j = 0; j < l; j += 2) {
            j1 = j + l;
            j2 = j1 + l;
            j3 = j2 + l;
            x0r = a[j] + a[j1];
            x0i = -a[j + 1] - a[j1 + 1];
            x1r = a[j] - a[j1];
            x1i = -a[j + 1] + a[j1 + 1];
            x2r = a[j2] + a[j3];
            x2i = a[j2 + 1] + a[j3 + 1];
            x3r = a[j2] - a[j3];
            x3i = a[j2 + 1] - a[j3 + 1];
            a[j] = x0r + x2r;
            a[j + 1] = x0i - x2i;
            a[j2] = x0r - x2r;
            a[j2 + 1] = x0i + x2i;
            a[j1] = x1r - x3i;
            a[j1 + 1] = x1i - x3r;
            a[j3] = x1r + x3i;
            a[j3 + 1] = x1i + x3r;
        }
    } else {
        for (j = 0; j < l; j += 2) {
            j1 = j + l;
            x0r = a[j] - a[j1];
            x0i = -a[j + 1] + a[j1 + 1];
            a[j] += a[j1];
            a[j + 1] = -a[j + 1] - a[j1 + 1];
            a[j1] = x0r;
            a[j1 + 1] = x0i;
        }
    }
}

void Cfft::bitrv2conj(int n, int *ip, double *a)
{
    int j, j1, k, k1, l, m, m2;
    double xr, xi, yr, yi;
    
    ip[0] = 0;
    l = n;
    m = 1;
    while ((m << 3) < l) {
        l >>= 1;
        for (j = 0; j < m; j++) {
            ip[m + j] = ip[j] + l;
        }
        m <<= 1;
    }
    m2 = 2 * m;
    if ((m << 3) == l) {
        for (k = 0; k < m; k++) {
            for (j = 0; j < k; j++) {
                j1 = 2 * j + ip[k];
                k1 = 2 * k + ip[j];
                xr = a[j1];
                xi = -a[j1 + 1];
                yr = a[k1];
                yi = -a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m2;
                k1 += 2 * m2;
                xr = a[j1];
                xi = -a[j1 + 1];
                yr = a[k1];
                yi = -a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m2;
                k1 -= m2;
                xr = a[j1];
                xi = -a[j1 + 1];
                yr = a[k1];
                yi = -a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m2;
                k1 += 2 * m2;
                xr = a[j1];
                xi = -a[j1 + 1];
                yr = a[k1];
                yi = -a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
            }
            k1 = 2 * k + ip[k];
            a[k1 + 1] = -a[k1 + 1];
            j1 = k1 + m2;
            k1 = j1 + m2;
            xr = a[j1];
            xi = -a[j1 + 1];
            yr = a[k1];
            yi = -a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
            k1 += m2;
            a[k1 + 1] = -a[k1 + 1];
        }
    } else {
        a[1] = -a[1];
        a[m2 + 1] = -a[m2 + 1];
        for (k = 1; k < m; k++) {
            for (j = 0; j < k; j++) {
                j1 = 2 * j + ip[k];
                k1 = 2 * k + ip[j];
                xr = a[j1];
                xi = -a[j1 + 1];
                yr = a[k1];
                yi = -a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m2;
                k1 += m2;
                xr = a[j1];
                xi = -a[j1 + 1];
                yr = a[k1];
                yi = -a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
            }
            k1 = 2 * k + ip[k];
            a[k1 + 1] = -a[k1 + 1];
            a[k1 + m2 + 1] = -a[k1 + m2 + 1];
        }
    }
}

void Cfft::rftfsub(int n, double *a)
{
    int j, k, kk, ks, m;
    double wkr, wki, xr, xi, yr, yi;
	double *c = w + fftsiz / 4;
    int nc = n >> 2;
	
    m = n >> 1;
    ks = 2 * nc / m;
    kk = 0;
    for (j = 2; j < m; j += 2) {
        k = n - j;
        kk += ks;
        wkr = 0.5 - c[nc - kk];
        wki = c[kk];
        xr = a[j] - a[k];
        xi = a[j + 1] + a[k + 1];
        yr = wkr * xr - wki * xi;
        yi = wkr * xi + wki * xr;
        a[j] -= yr;
        a[j + 1] -= yi;
        a[k] += yr;
        a[k + 1] -= yi;
    }
}

void Cfft::rftbsub(int n, double *a)
{
}



