#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <math.h>
#include <string.h>
//#include <stdlib.h>
//#include <math.h>
//#include <stdio.h>
//#include "fft_czt.h"
typedef double REAL;
	/* FFT計算用 数表保持構造体 */
typedef struct {
	int  samples;		/* 標本点の数( 4以上の 2の整数乗に限る) */
	int  *bitrev;		/* ビット反転表 - 要素数は(samples) */
	REAL *sintbl;		/* 三角関数表 - 要素数は(samples*3/4) */
} fft_struct;
	/* CZT計算用 数表保持構造体 */
typedef struct {
	fft_struct fft;		/* 下請け FFT計算用 */
	int  samples;		/* 標本点の数 */
	int  samples_out;	/* 出力する標本点の数 */
	int  samples_ex;	/* 2の整数乗で、(samples + samples_out) <= samples_ex
						 * である最小の数 */
	REAL *wr, *wi;		/* 重みデータ - 要素数は(samples) */
	REAL *vr, *vi;		/* インパルス応答データ - 要素数は(samples_ex) */
	REAL *tr, *ti;		/* 作業用領域 - 要素数は(samples_ex) */
} czt_struct;
	/* fft.c */
int fft_init(fft_struct *fftp, int n);
void fft_end(fft_struct *fftp);
//void fft(fft_struct *fftp, int inv, REAL re[], REAL im[]);
void fft(double*,double*,int,int);
void half_fft(double*,double*,int);
void half_ifft(double*,double*,int);
	/* czt.c */
int czt_init(czt_struct *cztp, int n, int no,int *ip,double *ww);
void czt_end(czt_struct *cztp);
void czt(czt_struct *cztp, int inv, REAL re[], REAL im[],int *ip,double *ww);
    /* czttest.c*/
int charp_FFT(int,double*,double*,double*,double*,int *ip, double *ww);
int charp_IFFT(int,double*,double*,double*,double*,int *ip, double *ww);
/*
Fast Fourier/Cosine/Sine Transform
    dimension   :one
    data length :power of 2
    decimation  :frequency
    radix       :split-radix
    data        :inplace
    table       :use
functions
    cdft: Complex Discrete Fourier Transform
    rdft: Real Discrete Fourier Transform
    ddct: Discrete Cosine Transform
    ddst: Discrete Sine Transform
    dfct: Cosine Transform of RDFT (Real Symmetric DFT)
    dfst: Sine Transform of RDFT (Real Anti-symmetric DFT)
function prototypes
    void cdft(int, int, double *, int *, double *);
    void rdft(int, int, double *, int *, double *);
    void ddct(int, int, double *, int *, double *);
    void ddst(int, int, double *, int *, double *);
    void dfct(int, double *, double *, int *, double *);
    void dfst(int, double *, double *, int *, double *);
macro definitions
    USE_CDFT_PTHREADS : default=not defined
        CDFT_THREADS_BEGIN_N  : must be >= 512, default=8192
        CDFT_4THREADS_BEGIN_N : must be >= 512, default=65536
    USE_CDFT_WINTHREADS : default=not defined
        CDFT_THREADS_BEGIN_N  : must be >= 512, default=32768
        CDFT_4THREADS_BEGIN_N : must be >= 512, default=524288


-------- Complex DFT (Discrete Fourier Transform) --------
    [definition]
        <case1>
            X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
        <case2>
            X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
        (notes: sum_j=0^n-1 is a summation from j=0 to n-1)
    [usage]
        <case1>
            ip[0] = 0; // first time only
            cdft(2*n, 1, a, ip, w);
        <case2>
            ip[0] = 0; // first time only
            cdft(2*n, -1, a, ip, w);
    [parameters]
        2*n            :data length (int)
                        n >= 1, n = power of 2
        a[0...2*n-1]   :input/output data (double *)
                        input data
                            a[2*j] = Re(x[j]), 
                            a[2*j+1] = Im(x[j]), 0<=j<n
                        output data
                            a[2*k] = Re(X[k]), 
                            a[2*k+1] = Im(X[k]), 0<=k<n
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n)
                        strictly, 
                        length of ip >= 
                            2+(1<<(int)(log(n+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n/2-1]   :cos/sin table (double *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of 
            cdft(2*n, -1, a, ip, w);
        is 
            cdft(2*n, 1, a, ip, w);
            for (j = 0; j <= 2 * n - 1; j++) {
                a[j] *= 1.0 / n;
            }
        .


-------- Real DFT / Inverse of Real DFT --------
    [definition]
        <case1> RDFT
            R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2
            I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2
        <case2> IRDFT (excluding scale)
            a[k] = (R[0] + R[n/2]*cos(pi*k))/2 + 
                   sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) + 
                   sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n
    [usage]
        <case1>
            ip[0] = 0; // first time only
            rdft(n, 1, a, ip, w);
        <case2>
            ip[0] = 0; // first time only
            rdft(n, -1, a, ip, w);
    [parameters]
        n              :data length (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (double *)
                        <case1>
                            output data
                                a[2*k] = R[k], 0<=k<n/2
                                a[2*k+1] = I[k], 0<k<n/2
                                a[1] = R[n/2]
                        <case2>
                            input data
                                a[2*j] = R[j], 0<=j<n/2
                                a[2*j+1] = I[j], 0<j<n/2
                                a[1] = R[n/2]
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n/2)
                        strictly, 
                        length of ip >= 
                            2+(1<<(int)(log(n/2+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n/2-1]   :cos/sin table (double *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of 
            rdft(n, 1, a, ip, w);
        is 
            rdft(n, -1, a, ip, w);
            for (j = 0; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- DCT (Discrete Cosine Transform) / Inverse of DCT --------
    [definition]
        <case1> IDCT (excluding scale)
            C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n
        <case2> DCT
            C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n
    [usage]
        <case1>
            ip[0] = 0; // first time only
            ddct(n, 1, a, ip, w);
        <case2>
            ip[0] = 0; // first time only
            ddct(n, -1, a, ip, w);
    [parameters]
        n              :data length (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (double *)
                        output data
                            a[k] = C[k], 0<=k<n
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n/2)
                        strictly, 
                        length of ip >= 
                            2+(1<<(int)(log(n/2+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n*5/4-1] :cos/sin table (double *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of 
            ddct(n, -1, a, ip, w);
        is 
            a[0] *= 0.5;
            ddct(n, 1, a, ip, w);
            for (j = 0; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- DST (Discrete Sine Transform) / Inverse of DST --------
    [definition]
        <case1> IDST (excluding scale)
            S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n
        <case2> DST
            S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n
    [usage]
        <case1>
            ip[0] = 0; // first time only
            ddst(n, 1, a, ip, w);
        <case2>
            ip[0] = 0; // first time only
            ddst(n, -1, a, ip, w);
    [parameters]
        n              :data length (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (double *)
                        <case1>
                            input data
                                a[j] = A[j], 0<j<n
                                a[0] = A[n]
                            output data
                                a[k] = S[k], 0<=k<n
                        <case2>
                            output data
                                a[k] = S[k], 0<k<n
                                a[0] = S[n]
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n/2)
                        strictly, 
                        length of ip >= 
                            2+(1<<(int)(log(n/2+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n*5/4-1] :cos/sin table (double *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of 
            ddst(n, -1, a, ip, w);
        is 
            a[0] *= 0.5;
            ddst(n, 1, a, ip, w);
            for (j = 0; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- Cosine Transform of RDFT (Real Symmetric DFT) --------
    [definition]
        C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n
    [usage]
        ip[0] = 0; // first time only
        dfct(n, a, t, ip, w);
    [parameters]
        n              :data length - 1 (int)
                        n >= 2, n = power of 2
        a[0...n]       :input/output data (double *)
                        output data
                            a[k] = C[k], 0<=k<=n
        t[0...n/2]     :work area (double *)
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n/4)
                        strictly, 
                        length of ip >= 
                            2+(1<<(int)(log(n/4+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n*5/8-1] :cos/sin table (double *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of 
            a[0] *= 0.5;
            a[n] *= 0.5;
            dfct(n, a, t, ip, w);
        is 
            a[0] *= 0.5;
            a[n] *= 0.5;
            dfct(n, a, t, ip, w);
            for (j = 0; j <= n; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- Sine Transform of RDFT (Real Anti-symmetric DFT) --------
    [definition]
        S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n
    [usage]
        ip[0] = 0; // first time only
        dfst(n, a, t, ip, w);
    [parameters]
        n              :data length + 1 (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (double *)
                        output data
                            a[k] = S[k], 0<k<n
                        (a[0] is used for work area)
        t[0...n/2-1]   :work area (double *)
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n/4)
                        strictly, 
                        length of ip >= 
                            2+(1<<(int)(log(n/4+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n*5/8-1] :cos/sin table (double *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of 
            dfst(n, a, t, ip, w);
        is 
            dfst(n, a, t, ip, w);
            for (j = 1; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


Appendix :
    The cos/sin table is recalculated when the larger table required.
    w[] and ip[] are compatible with all routines.
*/
//#include "stdafx.h"

void cdft(int n, int isgn, double *a, int *ip, double *w)
{
    void makewt(int nw, int *ip, double *w);
    void cftfsub(int n, double *a, int *ip, int nw, double *w);
    void cftbsub(int n, double *a, int *ip, int nw, double *w);
    int nw;
    
    nw = ip[0];
    if (n > (nw << 2)) {
        nw = n >> 2;
        makewt(nw, ip, w);
    }
    if (isgn >= 0) {
        cftfsub(n, a, ip, nw, w);
    } else {
        cftbsub(n, a, ip, nw, w);
    }
}


void rdft(int n, int isgn, double *a, int *ip, double *w)
{
    void makewt(int nw, int *ip, double *w);
    void makect(int nc, int *ip, double *c);
    void cftfsub(int n, double *a, int *ip, int nw, double *w);
    void cftbsub(int n, double *a, int *ip, int nw, double *w);
    void rftfsub(int n, double *a, int nc, double *c);
    void rftbsub(int n, double *a, int nc, double *c);
    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) {
            cftfsub(n, a, ip, nw, w);
            rftfsub(n, a, nc, w + nw);
        } else if (n == 4) {
            cftfsub(n, a, ip, nw, 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);
            cftbsub(n, a, ip, nw, w);
        } else if (n == 4) {
            cftbsub(n, a, ip, nw, w);
        }
    }
}


void ddct(int n, int isgn, double *a, int *ip, double *w)
{
    void makewt(int nw, int *ip, double *w);
    void makect(int nc, int *ip, double *c);
    void cftfsub(int n, double *a, int *ip, int nw, double *w);
    void cftbsub(int n, double *a, int *ip, int nw, double *w);
    void rftfsub(int n, double *a, int nc, double *c);
    void rftbsub(int n, double *a, int nc, double *c);
    void dctsub(int n, double *a, int nc, double *c);
    int j, nw, nc;
    double xr;
    
    nw = ip[0];
    if (n > (nw << 2)) {
        nw = n >> 2;
        makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n > nc) {
        nc = n;
        makect(nc, ip, w + nw);
    }
    if (isgn < 0) {
        xr = a[n - 1];
        for (j = n - 2; j >= 2; j -= 2) {
            a[j + 1] = a[j] - a[j - 1];
            a[j] += a[j - 1];
        }
        a[1] = a[0] - xr;
        a[0] += xr;
        if (n > 4) {
            rftbsub(n, a, nc, w + nw);
            cftbsub(n, a, ip, nw, w);
        } else if (n == 4) {
            cftbsub(n, a, ip, nw, w);
        }
    }
    dctsub(n, a, nc, w + nw);
    if (isgn >= 0) {
        if (n > 4) {
            cftfsub(n, a, ip, nw, w);
            rftfsub(n, a, nc, w + nw);
        } else if (n == 4) {
            cftfsub(n, a, ip, nw, w);
        }
        xr = a[0] - a[1];
        a[0] += a[1];
        for (j = 2; j < n; j += 2) {
            a[j - 1] = a[j] - a[j + 1];
            a[j] += a[j + 1];
        }
        a[n - 1] = xr;
    }
}


void ddst(int n, int isgn, double *a, int *ip, double *w)
{
    void makewt(int nw, int *ip, double *w);
    void makect(int nc, int *ip, double *c);
    void cftfsub(int n, double *a, int *ip, int nw, double *w);
    void cftbsub(int n, double *a, int *ip, int nw, double *w);
    void rftfsub(int n, double *a, int nc, double *c);
    void rftbsub(int n, double *a, int nc, double *c);
    void dstsub(int n, double *a, int nc, double *c);
    int j, nw, nc;
    double xr;
    
    nw = ip[0];
    if (n > (nw << 2)) {
        nw = n >> 2;
        makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n > nc) {
        nc = n;
        makect(nc, ip, w + nw);
    }
    if (isgn < 0) {
        xr = a[n - 1];
        for (j = n - 2; j >= 2; j -= 2) {
            a[j + 1] = -a[j] - a[j - 1];
            a[j] -= a[j - 1];
        }
        a[1] = a[0] + xr;
        a[0] -= xr;
        if (n > 4) {
            rftbsub(n, a, nc, w + nw);
            cftbsub(n, a, ip, nw, w);
        } else if (n == 4) {
            cftbsub(n, a, ip, nw, w);
        }
    }
    dstsub(n, a, nc, w + nw);
    if (isgn >= 0) {
        if (n > 4) {
            cftfsub(n, a, ip, nw, w);
            rftfsub(n, a, nc, w + nw);
        } else if (n == 4) {
            cftfsub(n, a, ip, nw, w);
        }
        xr = a[0] - a[1];
        a[0] += a[1];
        for (j = 2; j < n; j += 2) {
            a[j - 1] = -a[j] - a[j + 1];
            a[j] -= a[j + 1];
        }
        a[n - 1] = -xr;
    }
}


void dfct(int n, double *a, double *t, int *ip, double *w)
{
    void makewt(int nw, int *ip, double *w);
    void makect(int nc, int *ip, double *c);
    void cftfsub(int n, double *a, int *ip, int nw, double *w);
    void rftfsub(int n, double *a, int nc, double *c);
    void dctsub(int n, double *a, int nc, double *c);
    int j, k, l, m, mh, nw, nc;
    double xr, xi, yr, yi;
    
    nw = ip[0];
    if (n > (nw << 3)) {
        nw = n >> 3;
        makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n > (nc << 1)) {
        nc = n >> 1;
        makect(nc, ip, w + nw);
    }
    m = n >> 1;
    yi = a[m];
    xi = a[0] + a[n];
    a[0] -= a[n];
    t[0] = xi - yi;
    t[m] = xi + yi;
    if (n > 2) {
        mh = m >> 1;
        for (j = 1; j < mh; j++) {
            k = m - j;
            xr = a[j] - a[n - j];
            xi = a[j] + a[n - j];
            yr = a[k] - a[n - k];
            yi = a[k] + a[n - k];
            a[j] = xr;
            a[k] = yr;
            t[j] = xi - yi;
            t[k] = xi + yi;
        }
        t[mh] = a[mh] + a[n - mh];
        a[mh] -= a[n - mh];
        dctsub(m, a, nc, w + nw);
        if (m > 4) {
            cftfsub(m, a, ip, nw, w);
            rftfsub(m, a, nc, w + nw);
        } else if (m == 4) {
            cftfsub(m, a, ip, nw, w);
        }
        a[n - 1] = a[0] - a[1];
        a[1] = a[0] + a[1];
        for (j = m - 2; j >= 2; j -= 2) {
            a[2 * j + 1] = a[j] + a[j + 1];
            a[2 * j - 1] = a[j] - a[j + 1];
        }
        l = 2;
        m = mh;
        while (m >= 2) {
            dctsub(m, t, nc, w + nw);
            if (m > 4) {
                cftfsub(m, t, ip, nw, w);
                rftfsub(m, t, nc, w + nw);
            } else if (m == 4) {
                cftfsub(m, t, ip, nw, w);
            }
            a[n - l] = t[0] - t[1];
            a[l] = t[0] + t[1];
            k = 0;
            for (j = 2; j < m; j += 2) {
                k += l << 2;
                a[k - l] = t[j] - t[j + 1];
                a[k + l] = t[j] + t[j + 1];
            }
            l <<= 1;
            mh = m >> 1;
            for (j = 0; j < mh; j++) {
                k = m - j;
                t[j] = t[m + k] - t[m + j];
                t[k] = t[m + k] + t[m + j];
            }
            t[mh] = t[m + mh];
            m = mh;
        }
        a[l] = t[0];
        a[n] = t[2] - t[1];
        a[0] = t[2] + t[1];
    } else {
        a[1] = a[0];
        a[2] = t[0];
        a[0] = t[1];
    }
}


void dfst(int n, double *a, double *t, int *ip, double *w)
{
    void makewt(int nw, int *ip, double *w);
    void makect(int nc, int *ip, double *c);
    void cftfsub(int n, double *a, int *ip, int nw, double *w);
    void rftfsub(int n, double *a, int nc, double *c);
    void dstsub(int n, double *a, int nc, double *c);
    int j, k, l, m, mh, nw, nc;
    double xr, xi, yr, yi;
    
    nw = ip[0];
    if (n > (nw << 3)) {
        nw = n >> 3;
        makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n > (nc << 1)) {
        nc = n >> 1;
        makect(nc, ip, w + nw);
    }
    if (n > 2) {
        m = n >> 1;
        mh = m >> 1;
        for (j = 1; j < mh; j++) {
            k = m - j;
            xr = a[j] + a[n - j];
            xi = a[j] - a[n - j];
            yr = a[k] + a[n - k];
            yi = a[k] - a[n - k];
            a[j] = xr;
            a[k] = yr;
            t[j] = xi + yi;
            t[k] = xi - yi;
        }
        t[0] = a[mh] - a[n - mh];
        a[mh] += a[n - mh];
        a[0] = a[m];
        dstsub(m, a, nc, w + nw);
        if (m > 4) {
            cftfsub(m, a, ip, nw, w);
            rftfsub(m, a, nc, w + nw);
        } else if (m == 4) {
            cftfsub(m, a, ip, nw, w);
        }
        a[n - 1] = a[1] - a[0];
        a[1] = a[0] + a[1];
        for (j = m - 2; j >= 2; j -= 2) {
            a[2 * j + 1] = a[j] - a[j + 1];
            a[2 * j - 1] = -a[j] - a[j + 1];
        }
        l = 2;
        m = mh;
        while (m >= 2) {
            dstsub(m, t, nc, w + nw);
            if (m > 4) {
                cftfsub(m, t, ip, nw, w);
                rftfsub(m, t, nc, w + nw);
            } else if (m == 4) {
                cftfsub(m, t, ip, nw, w);
            }
            a[n - l] = t[1] - t[0];
            a[l] = t[0] + t[1];
            k = 0;
            for (j = 2; j < m; j += 2) {
                k += l << 2;
                a[k - l] = -t[j] - t[j + 1];
                a[k + l] = t[j] - t[j + 1];
            }
            l <<= 1;
            mh = m >> 1;
            for (j = 1; j < mh; j++) {
                k = m - j;
                t[j] = t[m + k] + t[m + j];
                t[k] = t[m + k] - t[m + j];
            }
            t[0] = t[m + mh];
            m = mh;
        }
        a[l] = t[0];
    }
    a[0] = 0;
}


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


#include <math.h>

void makewt(int nw, int *ip, double *w)
{
    void makeipt(int nw, int *ip);
    int j, nwh, nw0, nw1;
    double delta, wn4r, wk1r, wk1i, wk3r, wk3i;
    
    ip[0] = nw;
    ip[1] = 1;
    if (nw > 2) {
        nwh = nw >> 1;
        delta = atan(1.0) / nwh;
        wn4r = cos(delta * nwh);
        w[0] = 1;
        w[1] = wn4r;
        if (nwh == 4) {
            w[2] = cos(delta * 2);
            w[3] = sin(delta * 2);
        } else if (nwh > 4) {
            makeipt(nw, ip);
            w[2] = 0.5 / cos(delta * 2);
            w[3] = 0.5 / cos(delta * 6);
            for (j = 4; j < nwh; j += 4) {
                w[j] = cos(delta * j);
                w[j + 1] = sin(delta * j);
                w[j + 2] = cos(3 * delta * j);
                w[j + 3] = -sin(3 * delta * j);
            }
        }
        nw0 = 0;
        while (nwh > 2) {
            nw1 = nw0 + nwh;
            nwh >>= 1;
            w[nw1] = 1;
            w[nw1 + 1] = wn4r;
            if (nwh == 4) {
                wk1r = w[nw0 + 4];
                wk1i = w[nw0 + 5];
                w[nw1 + 2] = wk1r;
                w[nw1 + 3] = wk1i;
            } else if (nwh > 4) {
                wk1r = w[nw0 + 4];
                wk3r = w[nw0 + 6];
                w[nw1 + 2] = 0.5 / wk1r;
                w[nw1 + 3] = 0.5 / wk3r;
                for (j = 4; j < nwh; j += 4) {
                    wk1r = w[nw0 + 2 * j];
                    wk1i = w[nw0 + 2 * j + 1];
                    wk3r = w[nw0 + 2 * j + 2];
                    wk3i = w[nw0 + 2 * j + 3];
                    w[nw1 + j] = wk1r;
                    w[nw1 + j + 1] = wk1i;
                    w[nw1 + j + 2] = wk3r;
                    w[nw1 + j + 3] = wk3i;
                }
            }
            nw0 = nw1;
        }
    }
}


void makeipt(int nw, int *ip)
{
    int j, l, m, m2, p, q;
    
    ip[2] = 0;
    ip[3] = 16;
    m = 2;
    for (l = nw; l > 32; l >>= 2) {
        m2 = m << 1;
        q = m2 << 3;
        for (j = m; j < m2; j++) {
            p = ip[j] << 2;
            ip[m + j] = p;
            ip[m2 + j] = p + q;
        }
        m = m2;
    }
}


void makect(int nc, int *ip, double *c)
{
    int j, nch;
    double delta;
    
    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 -------- */


#ifdef USE_CDFT_PTHREADS
#define USE_CDFT_THREADS
#ifndef CDFT_THREADS_BEGIN_N
#define CDFT_THREADS_BEGIN_N 8192
#endif
#ifndef CDFT_4THREADS_BEGIN_N
#define CDFT_4THREADS_BEGIN_N 65536
#endif
#include <pthread.h>
#include <stdio.h>
#include <stdlib.h>
#define cdft_thread_t pthread_t
#define cdft_thread_create(thp,func,argp) { \
    if (pthread_create(thp, NULL, func, (void *) argp) != 0) { \
        fprintf(stderr, "cdft thread error\n"); \
        exit(1); \
    } \
}
#define cdft_thread_wait(th) { \
    if (pthread_join(th, NULL) != 0) { \
        fprintf(stderr, "cdft thread error\n"); \
        exit(1); \
    } \
}
#endif /* USE_CDFT_PTHREADS */


#ifdef USE_CDFT_WINTHREADS
#define USE_CDFT_THREADS
#ifndef CDFT_THREADS_BEGIN_N
#define CDFT_THREADS_BEGIN_N 32768
#endif
#ifndef CDFT_4THREADS_BEGIN_N
#define CDFT_4THREADS_BEGIN_N 524288
#endif
#include <windows.h>
#include <stdio.h>
#include <stdlib.h>
#define cdft_thread_t HANDLE
#define cdft_thread_create(thp,func,argp) { \
    DWORD thid; \
    *(thp) = CreateThread(NULL, 0, (LPTHREAD_START_ROUTINE) func, (LPVOID) argp, 0, &thid); \
    if (*(thp) == 0) { \
        fprintf(stderr, "cdft thread error\n"); \
        exit(1); \
    } \
}
#define cdft_thread_wait(th) { \
    WaitForSingleObject(th, INFINITE); \
    CloseHandle(th); \
}
#endif /* USE_CDFT_WINTHREADS */


void cftfsub(int n, double *a, int *ip, int nw, double *w)
{
    void bitrv2(int n, int *ip, double *a);
    void bitrv216(double *a);
    void bitrv208(double *a);
    void cftf1st(int n, double *a, double *w);
    void cftrec4(int n, double *a, int nw, double *w);
    void cftleaf(int n, int isplt, double *a, int nw, double *w);
    void cftfx41(int n, double *a, int nw, double *w);
    void cftf161(double *a, double *w);
    void cftf081(double *a, double *w);
    void cftf040(double *a);
    void cftx020(double *a);
#ifdef USE_CDFT_THREADS
    void cftrec4_th(int n, double *a, int nw, double *w);
#endif /* USE_CDFT_THREADS */
    
    if (n > 8) {
        if (n > 32) {
            cftf1st(n, a, &w[nw - (n >> 2)]);
#ifdef USE_CDFT_THREADS
            if (n > CDFT_THREADS_BEGIN_N) {
                cftrec4_th(n, a, nw, w);
            } else 
#endif /* USE_CDFT_THREADS */
            if (n > 512) {
                cftrec4(n, a, nw, w);
            } else if (n > 128) {
                cftleaf(n, 1, a, nw, w);
            } else {
                cftfx41(n, a, nw, w);
            }
            bitrv2(n, ip, a);
        } else if (n == 32) {
            cftf161(a, &w[nw - 8]);
            bitrv216(a);
        } else {
            cftf081(a, w);
            bitrv208(a);
        }
    } else if (n == 8) {
        cftf040(a);
    } else if (n == 4) {
        cftx020(a);
    }
}


void cftbsub(int n, double *a, int *ip, int nw, double *w)
{
    void bitrv2conj(int n, int *ip, double *a);
    void bitrv216neg(double *a);
    void bitrv208neg(double *a);
    void cftb1st(int n, double *a, double *w);
    void cftrec4(int n, double *a, int nw, double *w);
    void cftleaf(int n, int isplt, double *a, int nw, double *w);
    void cftfx41(int n, double *a, int nw, double *w);
    void cftf161(double *a, double *w);
    void cftf081(double *a, double *w);
    void cftb040(double *a);
    void cftx020(double *a);
#ifdef USE_CDFT_THREADS
    void cftrec4_th(int n, double *a, int nw, double *w);
#endif /* USE_CDFT_THREADS */
    
    if (n > 8) {
        if (n > 32) {
            cftb1st(n, a, &w[nw - (n >> 2)]);
#ifdef USE_CDFT_THREADS
            if (n > CDFT_THREADS_BEGIN_N) {
                cftrec4_th(n, a, nw, w);
            } else 
#endif /* USE_CDFT_THREADS */
            if (n > 512) {
                cftrec4(n, a, nw, w);
            } else if (n > 128) {
                cftleaf(n, 1, a, nw, w);
            } else {
                cftfx41(n, a, nw, w);
            }
            bitrv2conj(n, ip, a);
        } else if (n == 32) {
            cftf161(a, &w[nw - 8]);
            bitrv216neg(a);
        } else {
            cftf081(a, w);
            bitrv208neg(a);
        }
    } else if (n == 8) {
        cftb040(a);
    } else if (n == 4) {
        cftx020(a);
    }
}


void bitrv2(int n, int *ip, double *a)
{
    int j, j1, k, k1, l, m, nh, nm;
    double xr, xi, yr, yi;
    
    m = 1;
    for (l = n >> 2; l > 8; l >>= 2) {
        m <<= 1;
    }
    nh = n >> 1;
    nm = 4 * m;
    if (l == 8) {
        for (k = 0; k < m; k++) {
            for (j = 0; j < k; j++) {
                j1 = 4 * j + 2 * ip[m + k];
                k1 = 4 * k + 2 * ip[m + 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 += nm;
                k1 += 2 * nm;
                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 += nm;
                k1 -= nm;
                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 += nm;
                k1 += 2 * nm;
                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 += nh;
                k1 += 2;
                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 -= nm;
                k1 -= 2 * nm;
                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 -= nm;
                k1 += nm;
                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 -= nm;
                k1 -= 2 * nm;
                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;
                k1 += nh;
                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 += nm;
                k1 += 2 * nm;
                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 += nm;
                k1 -= nm;
                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 += nm;
                k1 += 2 * nm;
                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 -= nh;
                k1 -= 2;
                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 -= nm;
                k1 -= 2 * nm;
                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 -= nm;
                k1 += nm;
                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 -= nm;
                k1 -= 2 * nm;
                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 = 4 * k + 2 * ip[m + k];
            j1 = k1 + 2;
            k1 += nh;
            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 += nm;
            k1 += 2 * nm;
            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 += nm;
            k1 -= nm;
            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;
            k1 -= nh;
            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 += nh + 2;
            k1 += nh + 2;
            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 -= nh - nm;
            k1 += 2 * nm - 2;
            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 = 0; k < m; k++) {
            for (j = 0; j < k; j++) {
                j1 = 4 * j + ip[m + k];
                k1 = 4 * k + ip[m + 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 += nm;
                k1 += nm;
                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 += nh;
                k1 += 2;
                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 -= nm;
                k1 -= nm;
                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;
                k1 += nh;
                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 += nm;
                k1 += nm;
                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 -= nh;
                k1 -= 2;
                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 -= nm;
                k1 -= nm;
                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 = 4 * k + ip[m + k];
            j1 = k1 + 2;
            k1 += nh;
            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 += nm;
            k1 += nm;
            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 bitrv2conj(int n, int *ip, double *a)
{
    int j, j1, k, k1, l, m, nh, nm;
    double xr, xi, yr, yi;
    
    m = 1;
    for (l = n >> 2; l > 8; l >>= 2) {
        m <<= 1;
    }
    nh = n >> 1;
    nm = 4 * m;
    if (l == 8) {
        for (k = 0; k < m; k++) {
            for (j = 0; j < k; j++) {
                j1 = 4 * j + 2 * ip[m + k];
                k1 = 4 * k + 2 * ip[m + 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 += nm;
                k1 += 2 * nm;
                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 += nm;
                k1 -= nm;
                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 += nm;
                k1 += 2 * nm;
                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 += nh;
                k1 += 2;
                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 -= nm;
                k1 -= 2 * nm;
                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 -= nm;
                k1 += nm;
                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 -= nm;
                k1 -= 2 * nm;
                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;
                k1 += nh;
                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 += nm;
                k1 += 2 * nm;
                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 += nm;
                k1 -= nm;
                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 += nm;
                k1 += 2 * nm;
                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 -= nh;
                k1 -= 2;
                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 -= nm;
                k1 -= 2 * nm;
                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 -= nm;
                k1 += nm;
                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 -= nm;
                k1 -= 2 * nm;
                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 = 4 * k + 2 * ip[m + k];
            j1 = k1 + 2;
            k1 += nh;
            a[j1 - 1] = -a[j1 - 1];
            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;
            a[k1 + 3] = -a[k1 + 3];
            j1 += nm;
            k1 += 2 * nm;
            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 += nm;
            k1 -= nm;
            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;
            k1 -= nh;
            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 += nh + 2;
            k1 += nh + 2;
            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 -= nh - nm;
            k1 += 2 * nm - 2;
            a[j1 - 1] = -a[j1 - 1];
            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;
            a[k1 + 3] = -a[k1 + 3];
        }
    } else {
        for (k = 0; k < m; k++) {
            for (j = 0; j < k; j++) {
                j1 = 4 * j + ip[m + k];
                k1 = 4 * k + ip[m + 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 += nm;
                k1 += nm;
                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 += nh;
                k1 += 2;
                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 -= nm;
                k1 -= nm;
                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;
                k1 += nh;
                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 += nm;
                k1 += nm;
                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 -= nh;
                k1 -= 2;
                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 -= nm;
                k1 -= nm;
                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 = 4 * k + ip[m + k];
            j1 = k1 + 2;
            k1 += nh;
            a[j1 - 1] = -a[j1 - 1];
            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;
            a[k1 + 3] = -a[k1 + 3];
            j1 += nm;
            k1 += nm;
            a[j1 - 1] = -a[j1 - 1];
            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;
            a[k1 + 3] = -a[k1 + 3];
        }
    }
}


void bitrv216(double *a)
{
    double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, 
        x5r, x5i, x7r, x7i, x8r, x8i, x10r, x10i, 
        x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i;
    
    x1r = a[2];
    x1i = a[3];
    x2r = a[4];
    x2i = a[5];
    x3r = a[6];
    x3i = a[7];
    x4r = a[8];
    x4i = a[9];
    x5r = a[10];
    x5i = a[11];
    x7r = a[14];
    x7i = a[15];
    x8r = a[16];
    x8i = a[17];
    x10r = a[20];
    x10i = a[21];
    x11r = a[22];
    x11i = a[23];
    x12r = a[24];
    x12i = a[25];
    x13r = a[26];
    x13i = a[27];
    x14r = a[28];
    x14i = a[29];
    a[2] = x8r;
    a[3] = x8i;
    a[4] = x4r;
    a[5] = x4i;
    a[6] = x12r;
    a[7] = x12i;
    a[8] = x2r;
    a[9] = x2i;
    a[10] = x10r;
    a[11] = x10i;
    a[14] = x14r;
    a[15] = x14i;
    a[16] = x1r;
    a[17] = x1i;
    a[20] = x5r;
    a[21] = x5i;
    a[22] = x13r;
    a[23] = x13i;
    a[24] = x3r;
    a[25] = x3i;
    a[26] = x11r;
    a[27] = x11i;
    a[28] = x7r;
    a[29] = x7i;
}


void bitrv216neg(double *a)
{
    double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, 
        x5r, x5i, x6r, x6i, x7r, x7i, x8r, x8i, 
        x9r, x9i, x10r, x10i, x11r, x11i, x12r, x12i, 
        x13r, x13i, x14r, x14i, x15r, x15i;
    
    x1r = a[2];
    x1i = a[3];
    x2r = a[4];
    x2i = a[5];
    x3r = a[6];
    x3i = a[7];
    x4r = a[8];
    x4i = a[9];
    x5r = a[10];
    x5i = a[11];
    x6r = a[12];
    x6i = a[13];
    x7r = a[14];
    x7i = a[15];
    x8r = a[16];
    x8i = a[17];
    x9r = a[18];
    x9i = a[19];
    x10r = a[20];
    x10i = a[21];
    x11r = a[22];
    x11i = a[23];
    x12r = a[24];
    x12i = a[25];
    x13r = a[26];
    x13i = a[27];
    x14r = a[28];
    x14i = a[29];
    x15r = a[30];
    x15i = a[31];
    a[2] = x15r;
    a[3] = x15i;
    a[4] = x7r;
    a[5] = x7i;
    a[6] = x11r;
    a[7] = x11i;
    a[8] = x3r;
    a[9] = x3i;
    a[10] = x13r;
    a[11] = x13i;
    a[12] = x5r;
    a[13] = x5i;
    a[14] = x9r;
    a[15] = x9i;
    a[16] = x1r;
    a[17] = x1i;
    a[18] = x14r;
    a[19] = x14i;
    a[20] = x6r;
    a[21] = x6i;
    a[22] = x10r;
    a[23] = x10i;
    a[24] = x2r;
    a[25] = x2i;
    a[26] = x12r;
    a[27] = x12i;
    a[28] = x4r;
    a[29] = x4i;
    a[30] = x8r;
    a[31] = x8i;
}


void bitrv208(double *a)
{
    double x1r, x1i, x3r, x3i, x4r, x4i, x6r, x6i;
    
    x1r = a[2];
    x1i = a[3];
    x3r = a[6];
    x3i = a[7];
    x4r = a[8];
    x4i = a[9];
    x6r = a[12];
    x6i = a[13];
    a[2] = x4r;
    a[3] = x4i;
    a[6] = x6r;
    a[7] = x6i;
    a[8] = x1r;
    a[9] = x1i;
    a[12] = x3r;
    a[13] = x3i;
}


void bitrv208neg(double *a)
{
    double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, 
        x5r, x5i, x6r, x6i, x7r, x7i;
    
    x1r = a[2];
    x1i = a[3];
    x2r = a[4];
    x2i = a[5];
    x3r = a[6];
    x3i = a[7];
    x4r = a[8];
    x4i = a[9];
    x5r = a[10];
    x5i = a[11];
    x6r = a[12];
    x6i = a[13];
    x7r = a[14];
    x7i = a[15];
    a[2] = x7r;
    a[3] = x7i;
    a[4] = x3r;
    a[5] = x3i;
    a[6] = x5r;
    a[7] = x5i;
    a[8] = x1r;
    a[9] = x1i;
    a[10] = x6r;
    a[11] = x6i;
    a[12] = x2r;
    a[13] = x2i;
    a[14] = x4r;
    a[15] = x4i;
}


void cftf1st(int n, double *a, double *w)
{
    int j, j0, j1, j2, j3, k, m, mh;
    double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i, 
        wd1r, wd1i, wd3r, wd3i;
    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, 
        y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;
    
    mh = n >> 3;
    m = 2 * mh;
    j1 = m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[0] + a[j2];
    x0i = a[1] + a[j2 + 1];
    x1r = a[0] - a[j2];
    x1i = a[1] - a[j2 + 1];
    x2r = a[j1] + a[j3];
    x2i = a[j1 + 1] + a[j3 + 1];
    x3r = a[j1] - a[j3];
    x3i = a[j1 + 1] - a[j3 + 1];
    a[0] = x0r + x2r;
    a[1] = x0i + x2i;
    a[j1] = x0r - x2r;
    a[j1 + 1] = x0i - x2i;
    a[j2] = x1r - x3i;
    a[j2 + 1] = x1i + x3r;
    a[j3] = x1r + x3i;
    a[j3 + 1] = x1i - x3r;
    wn4r = w[1];
    csc1 = w[2];
    csc3 = w[3];
    wd1r = 1;
    wd1i = 0;
    wd3r = 1;
    wd3i = 0;
    k = 0;
    for (j = 2; j < mh - 2; j += 4) {
        k += 4;
        wk1r = csc1 * (wd1r + w[k]);
        wk1i = csc1 * (wd1i + w[k + 1]);
        wk3r = csc3 * (wd3r + w[k + 2]);
        wk3i = csc3 * (wd3i + w[k + 3]);
        wd1r = w[k];
        wd1i = w[k + 1];
        wd3r = w[k + 2];
        wd3i = w[k + 3];
        j1 = j + m;
        j2 = j1 + m;
        j3 = j2 + m;
        x0r = a[j] + a[j2];
        x0i = a[j + 1] + a[j2 + 1];
        x1r = a[j] - a[j2];
        x1i = a[j + 1] - a[j2 + 1];
        y0r = a[j + 2] + a[j2 + 2];
        y0i = a[j + 3] + a[j2 + 3];
        y1r = a[j + 2] - a[j2 + 2];
        y1i = a[j + 3] - a[j2 + 3];
        x2r = a[j1] + a[j3];
        x2i = a[j1 + 1] + a[j3 + 1];
        x3r = a[j1] - a[j3];
        x3i = a[j1 + 1] - a[j3 + 1];
        y2r = a[j1 + 2] + a[j3 + 2];
        y2i = a[j1 + 3] + a[j3 + 3];
        y3r = a[j1 + 2] - a[j3 + 2];
        y3i = a[j1 + 3] - a[j3 + 3];
        a[j] = x0r + x2r;
        a[j + 1] = x0i + x2i;
        a[j + 2] = y0r + y2r;
        a[j + 3] = y0i + y2i;
        a[j1] = x0r - x2r;
        a[j1 + 1] = x0i - x2i;
        a[j1 + 2] = y0r - y2r;
        a[j1 + 3] = y0i - y2i;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[j2] = wk1r * x0r - wk1i * x0i;
        a[j2 + 1] = wk1r * x0i + wk1i * x0r;
        x0r = y1r - y3i;
        x0i = y1i + y3r;
        a[j2 + 2] = wd1r * x0r - wd1i * x0i;
        a[j2 + 3] = wd1r * x0i + wd1i * x0r;
        x0r = x1r + x3i;
        x0i = x1i - x3r;
        a[j3] = wk3r * x0r + wk3i * x0i;
        a[j3 + 1] = wk3r * x0i - wk3i * x0r;
        x0r = y1r + y3i;
        x0i = y1i - y3r;
        a[j3 + 2] = wd3r * x0r + wd3i * x0i;
        a[j3 + 3] = wd3r * x0i - wd3i * x0r;
        j0 = m - j;
        j1 = j0 + m;
        j2 = j1 + m;
        j3 = j2 + m;
        x0r = a[j0] + a[j2];
        x0i = a[j0 + 1] + a[j2 + 1];
        x1r = a[j0] - a[j2];
        x1i = a[j0 + 1] - a[j2 + 1];
        y0r = a[j0 - 2] + a[j2 - 2];
        y0i = a[j0 - 1] + a[j2 - 1];
        y1r = a[j0 - 2] - a[j2 - 2];
        y1i = a[j0 - 1] - a[j2 - 1];
        x2r = a[j1] + a[j3];
        x2i = a[j1 + 1] + a[j3 + 1];
        x3r = a[j1] - a[j3];
        x3i = a[j1 + 1] - a[j3 + 1];
        y2r = a[j1 - 2] + a[j3 - 2];
        y2i = a[j1 - 1] + a[j3 - 1];
        y3r = a[j1 - 2] - a[j3 - 2];
        y3i = a[j1 - 1] - a[j3 - 1];
        a[j0] = x0r + x2r;
        a[j0 + 1] = x0i + x2i;
        a[j0 - 2] = y0r + y2r;
        a[j0 - 1] = y0i + y2i;
        a[j1] = x0r - x2r;
        a[j1 + 1] = x0i - x2i;
        a[j1 - 2] = y0r - y2r;
        a[j1 - 1] = y0i - y2i;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[j2] = wk1i * x0r - wk1r * x0i;
        a[j2 + 1] = wk1i * x0i + wk1r * x0r;
        x0r = y1r - y3i;
        x0i = y1i + y3r;
        a[j2 - 2] = wd1i * x0r - wd1r * x0i;
        a[j2 - 1] = wd1i * x0i + wd1r * x0r;
        x0r = x1r + x3i;
        x0i = x1i - x3r;
        a[j3] = wk3i * x0r + wk3r * x0i;
        a[j3 + 1] = wk3i * x0i - wk3r * x0r;
        x0r = y1r + y3i;
        x0i = y1i - y3r;
        a[j3 - 2] = wd3i * x0r + wd3r * x0i;
        a[j3 - 1] = wd3i * x0i - wd3r * x0r;
    }
    wk1r = csc1 * (wd1r + wn4r);
    wk1i = csc1 * (wd1i + wn4r);
    wk3r = csc3 * (wd3r - wn4r);
    wk3i = csc3 * (wd3i - wn4r);
    j0 = mh;
    j1 = j0 + m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[j0 - 2] + a[j2 - 2];
    x0i = a[j0 - 1] + a[j2 - 1];
    x1r = a[j0 - 2] - a[j2 - 2];
    x1i = a[j0 - 1] - a[j2 - 1];
    x2r = a[j1 - 2] + a[j3 - 2];
    x2i = a[j1 - 1] + a[j3 - 1];
    x3r = a[j1 - 2] - a[j3 - 2];
    x3i = a[j1 - 1] - a[j3 - 1];
    a[j0 - 2] = x0r + x2r;
    a[j0 - 1] = x0i + x2i;
    a[j1 - 2] = x0r - x2r;
    a[j1 - 1] = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[j2 - 2] = wk1r * x0r - wk1i * x0i;
    a[j2 - 1] = wk1r * x0i + wk1i * x0r;
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    a[j3 - 2] = wk3r * x0r + wk3i * x0i;
    a[j3 - 1] = wk3r * x0i - wk3i * x0r;
    x0r = a[j0] + a[j2];
    x0i = a[j0 + 1] + a[j2 + 1];
    x1r = a[j0] - a[j2];
    x1i = a[j0 + 1] - a[j2 + 1];
    x2r = a[j1] + a[j3];
    x2i = a[j1 + 1] + a[j3 + 1];
    x3r = a[j1] - a[j3];
    x3i = a[j1 + 1] - a[j3 + 1];
    a[j0] = x0r + x2r;
    a[j0 + 1] = x0i + x2i;
    a[j1] = x0r - x2r;
    a[j1 + 1] = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[j2] = wn4r * (x0r - x0i);
    a[j2 + 1] = wn4r * (x0i + x0r);
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    a[j3] = -wn4r * (x0r + x0i);
    a[j3 + 1] = -wn4r * (x0i - x0r);
    x0r = a[j0 + 2] + a[j2 + 2];
    x0i = a[j0 + 3] + a[j2 + 3];
    x1r = a[j0 + 2] - a[j2 + 2];
    x1i = a[j0 + 3] - a[j2 + 3];
    x2r = a[j1 + 2] + a[j3 + 2];
    x2i = a[j1 + 3] + a[j3 + 3];
    x3r = a[j1 + 2] - a[j3 + 2];
    x3i = a[j1 + 3] - a[j3 + 3];
    a[j0 + 2] = x0r + x2r;
    a[j0 + 3] = x0i + x2i;
    a[j1 + 2] = x0r - x2r;
    a[j1 + 3] = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[j2 + 2] = wk1i * x0r - wk1r * x0i;
    a[j2 + 3] = wk1i * x0i + wk1r * x0r;
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    a[j3 + 2] = wk3i * x0r + wk3r * x0i;
    a[j3 + 3] = wk3i * x0i - wk3r * x0r;
}


void cftb1st(int n, double *a, double *w)
{
    int j, j0, j1, j2, j3, k, m, mh;
    double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i, 
        wd1r, wd1i, wd3r, wd3i;
    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, 
        y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;
    
    mh = n >> 3;
    m = 2 * mh;
    j1 = m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[0] + a[j2];
    x0i = -a[1] - a[j2 + 1];
    x1r = a[0] - a[j2];
    x1i = -a[1] + a[j2 + 1];
    x2r = a[j1] + a[j3];
    x2i = a[j1 + 1] + a[j3 + 1];
    x3r = a[j1] - a[j3];
    x3i = a[j1 + 1] - a[j3 + 1];
    a[0] = x0r + x2r;
    a[1] = x0i - x2i;
    a[j1] = x0r - x2r;
    a[j1 + 1] = x0i + x2i;
    a[j2] = x1r + x3i;
    a[j2 + 1] = x1i + x3r;
    a[j3] = x1r - x3i;
    a[j3 + 1] = x1i - x3r;
    wn4r = w[1];
    csc1 = w[2];
    csc3 = w[3];
    wd1r = 1;
    wd1i = 0;
    wd3r = 1;
    wd3i = 0;
    k = 0;
    for (j = 2; j < mh - 2; j += 4) {
        k += 4;
        wk1r = csc1 * (wd1r + w[k]);
        wk1i = csc1 * (wd1i + w[k + 1]);
        wk3r = csc3 * (wd3r + w[k + 2]);
        wk3i = csc3 * (wd3i + w[k + 3]);
        wd1r = w[k];
        wd1i = w[k + 1];
        wd3r = w[k + 2];
        wd3i = w[k + 3];
        j1 = j + m;
        j2 = j1 + m;
        j3 = j2 + m;
        x0r = a[j] + a[j2];
        x0i = -a[j + 1] - a[j2 + 1];
        x1r = a[j] - a[j2];
        x1i = -a[j + 1] + a[j2 + 1];
        y0r = a[j + 2] + a[j2 + 2];
        y0i = -a[j + 3] - a[j2 + 3];
        y1r = a[j + 2] - a[j2 + 2];
        y1i = -a[j + 3] + a[j2 + 3];
        x2r = a[j1] + a[j3];
        x2i = a[j1 + 1] + a[j3 + 1];
        x3r = a[j1] - a[j3];
        x3i = a[j1 + 1] - a[j3 + 1];
        y2r = a[j1 + 2] + a[j3 + 2];
        y2i = a[j1 + 3] + a[j3 + 3];
        y3r = a[j1 + 2] - a[j3 + 2];
        y3i = a[j1 + 3] - a[j3 + 3];
        a[j] = x0r + x2r;
        a[j + 1] = x0i - x2i;
        a[j + 2] = y0r + y2r;
        a[j + 3] = y0i - y2i;
        a[j1] = x0r - x2r;
        a[j1 + 1] = x0i + x2i;
        a[j1 + 2] = y0r - y2r;
        a[j1 + 3] = y0i + y2i;
        x0r = x1r + x3i;
        x0i = x1i + x3r;
        a[j2] = wk1r * x0r - wk1i * x0i;
        a[j2 + 1] = wk1r * x0i + wk1i * x0r;
        x0r = y1r + y3i;
        x0i = y1i + y3r;
        a[j2 + 2] = wd1r * x0r - wd1i * x0i;
        a[j2 + 3] = wd1r * x0i + wd1i * x0r;
        x0r = x1r - x3i;
        x0i = x1i - x3r;
        a[j3] = wk3r * x0r + wk3i * x0i;
        a[j3 + 1] = wk3r * x0i - wk3i * x0r;
        x0r = y1r - y3i;
        x0i = y1i - y3r;
        a[j3 + 2] = wd3r * x0r + wd3i * x0i;
        a[j3 + 3] = wd3r * x0i - wd3i * x0r;
        j0 = m - j;
        j1 = j0 + m;
        j2 = j1 + m;
        j3 = j2 + m;
        x0r = a[j0] + a[j2];
        x0i = -a[j0 + 1] - a[j2 + 1];
        x1r = a[j0] - a[j2];
        x1i = -a[j0 + 1] + a[j2 + 1];
        y0r = a[j0 - 2] + a[j2 - 2];
        y0i = -a[j0 - 1] - a[j2 - 1];
        y1r = a[j0 - 2] - a[j2 - 2];
        y1i = -a[j0 - 1] + a[j2 - 1];
        x2r = a[j1] + a[j3];
        x2i = a[j1 + 1] + a[j3 + 1];
        x3r = a[j1] - a[j3];
        x3i = a[j1 + 1] - a[j3 + 1];
        y2r = a[j1 - 2] + a[j3 - 2];
        y2i = a[j1 - 1] + a[j3 - 1];
        y3r = a[j1 - 2] - a[j3 - 2];
        y3i = a[j1 - 1] - a[j3 - 1];
        a[j0] = x0r + x2r;
        a[j0 + 1] = x0i - x2i;
        a[j0 - 2] = y0r + y2r;
        a[j0 - 1] = y0i - y2i;
        a[j1] = x0r - x2r;
        a[j1 + 1] = x0i + x2i;
        a[j1 - 2] = y0r - y2r;
        a[j1 - 1] = y0i + y2i;
        x0r = x1r + x3i;
        x0i = x1i + x3r;
        a[j2] = wk1i * x0r - wk1r * x0i;
        a[j2 + 1] = wk1i * x0i + wk1r * x0r;
        x0r = y1r + y3i;
        x0i = y1i + y3r;
        a[j2 - 2] = wd1i * x0r - wd1r * x0i;
        a[j2 - 1] = wd1i * x0i + wd1r * x0r;
        x0r = x1r - x3i;
        x0i = x1i - x3r;
        a[j3] = wk3i * x0r + wk3r * x0i;
        a[j3 + 1] = wk3i * x0i - wk3r * x0r;
        x0r = y1r - y3i;
        x0i = y1i - y3r;
        a[j3 - 2] = wd3i * x0r + wd3r * x0i;
        a[j3 - 1] = wd3i * x0i - wd3r * x0r;
    }
    wk1r = csc1 * (wd1r + wn4r);
    wk1i = csc1 * (wd1i + wn4r);
    wk3r = csc3 * (wd3r - wn4r);
    wk3i = csc3 * (wd3i - wn4r);
    j0 = mh;
    j1 = j0 + m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[j0 - 2] + a[j2 - 2];
    x0i = -a[j0 - 1] - a[j2 - 1];
    x1r = a[j0 - 2] - a[j2 - 2];
    x1i = -a[j0 - 1] + a[j2 - 1];
    x2r = a[j1 - 2] + a[j3 - 2];
    x2i = a[j1 - 1] + a[j3 - 1];
    x3r = a[j1 - 2] - a[j3 - 2];
    x3i = a[j1 - 1] - a[j3 - 1];
    a[j0 - 2] = x0r + x2r;
    a[j0 - 1] = x0i - x2i;
    a[j1 - 2] = x0r - x2r;
    a[j1 - 1] = x0i + x2i;
    x0r = x1r + x3i;
    x0i = x1i + x3r;
    a[j2 - 2] = wk1r * x0r - wk1i * x0i;
    a[j2 - 1] = wk1r * x0i + wk1i * x0r;
    x0r = x1r - x3i;
    x0i = x1i - x3r;
    a[j3 - 2] = wk3r * x0r + wk3i * x0i;
    a[j3 - 1] = wk3r * x0i - wk3i * x0r;
    x0r = a[j0] + a[j2];
    x0i = -a[j0 + 1] - a[j2 + 1];
    x1r = a[j0] - a[j2];
    x1i = -a[j0 + 1] + a[j2 + 1];
    x2r = a[j1] + a[j3];
    x2i = a[j1 + 1] + a[j3 + 1];
    x3r = a[j1] - a[j3];
    x3i = a[j1 + 1] - a[j3 + 1];
    a[j0] = x0r + x2r;
    a[j0 + 1] = x0i - x2i;
    a[j1] = x0r - x2r;
    a[j1 + 1] = x0i + x2i;
    x0r = x1r + x3i;
    x0i = x1i + x3r;
    a[j2] = wn4r * (x0r - x0i);
    a[j2 + 1] = wn4r * (x0i + x0r);
    x0r = x1r - x3i;
    x0i = x1i - x3r;
    a[j3] = -wn4r * (x0r + x0i);
    a[j3 + 1] = -wn4r * (x0i - x0r);
    x0r = a[j0 + 2] + a[j2 + 2];
    x0i = -a[j0 + 3] - a[j2 + 3];
    x1r = a[j0 + 2] - a[j2 + 2];
    x1i = -a[j0 + 3] + a[j2 + 3];
    x2r = a[j1 + 2] + a[j3 + 2];
    x2i = a[j1 + 3] + a[j3 + 3];
    x3r = a[j1 + 2] - a[j3 + 2];
    x3i = a[j1 + 3] - a[j3 + 3];
    a[j0 + 2] = x0r + x2r;
    a[j0 + 3] = x0i - x2i;
    a[j1 + 2] = x0r - x2r;
    a[j1 + 3] = x0i + x2i;
    x0r = x1r + x3i;
    x0i = x1i + x3r;
    a[j2 + 2] = wk1i * x0r - wk1r * x0i;
    a[j2 + 3] = wk1i * x0i + wk1r * x0r;
    x0r = x1r - x3i;
    x0i = x1i - x3r;
    a[j3 + 2] = wk3i * x0r + wk3r * x0i;
    a[j3 + 3] = wk3i * x0i - wk3r * x0r;
}


#ifdef USE_CDFT_THREADS
struct cdft_arg_st {
    int n0;
    int n;
    double *a;
    int nw;
    double *w;
};
typedef struct cdft_arg_st cdft_arg_t;


void cftrec4_th(int n, double *a, int nw, double *w)
{
    void *cftrec1_th(void *p);
    void *cftrec2_th(void *p);
    int i, idiv4, m, nthread;
    cdft_thread_t th[4];
    cdft_arg_t ag[4];
    
    nthread = 2;
    idiv4 = 0;
    m = n >> 1;
    if (n > CDFT_4THREADS_BEGIN_N) {
        nthread = 4;
        idiv4 = 1;
        m >>= 1;
    }
    for (i = 0; i < nthread; i++) {
        ag[i].n0 = n;
        ag[i].n = m;
        ag[i].a = &a[i * m];
        ag[i].nw = nw;
        ag[i].w = w;
        if (i != idiv4) {
            cdft_thread_create(&th[i], cftrec1_th, &ag[i]);
        } else {
            cdft_thread_create(&th[i], cftrec2_th, &ag[i]);
        }
    }
    for (i = 0; i < nthread; i++) {
        cdft_thread_wait(th[i]);
    }
}


void *cftrec1_th(void *p)
{
    int cfttree(int n, int j, int k, double *a, int nw, double *w);
    void cftleaf(int n, int isplt, double *a, int nw, double *w);
    void cftmdl1(int n, double *a, double *w);
    int isplt, j, k, m, n, n0, nw;
    double *a, *w;
    
    n0 = ((cdft_arg_t *) p)->n0;
    n = ((cdft_arg_t *) p)->n;
    a = ((cdft_arg_t *) p)->a;
    nw = ((cdft_arg_t *) p)->nw;
    w = ((cdft_arg_t *) p)->w;
    m = n0;
    while (m > 512) {
        m >>= 2;
        cftmdl1(m, &a[n - m], &w[nw - (m >> 1)]);
    }
    cftleaf(m, 1, &a[n - m], nw, w);
    k = 0;
    for (j = n - m; j > 0; j -= m) {
        k++;
        isplt = cfttree(m, j, k, a, nw, w);
        cftleaf(m, isplt, &a[j - m], nw, w);
    }
    return (void *) 0;
}


void *cftrec2_th(void *p)
{
    int cfttree(int n, int j, int k, double *a, int nw, double *w);
    void cftleaf(int n, int isplt, double *a, int nw, double *w);
    void cftmdl2(int n, double *a, double *w);
    int isplt, j, k, m, n, n0, nw;
    double *a, *w;
    
    n0 = ((cdft_arg_t *) p)->n0;
    n = ((cdft_arg_t *) p)->n;
    a = ((cdft_arg_t *) p)->a;
    nw = ((cdft_arg_t *) p)->nw;
    w = ((cdft_arg_t *) p)->w;
    k = 1;
    m = n0;
    while (m > 512) {
        m >>= 2;
        k <<= 2;
        cftmdl2(m, &a[n - m], &w[nw - m]);
    }
    cftleaf(m, 0, &a[n - m], nw, w);
    k >>= 1;
    for (j = n - m; j > 0; j -= m) {
        k++;
        isplt = cfttree(m, j, k, a, nw, w);
        cftleaf(m, isplt, &a[j - m], nw, w);
    }
    return (void *) 0;
}
#endif /* USE_CDFT_THREADS */


void cftrec4(int n, double *a, int nw, double *w)
{
    int cfttree(int n, int j, int k, double *a, int nw, double *w);
    void cftleaf(int n, int isplt, double *a, int nw, double *w);
    void cftmdl1(int n, double *a, double *w);
    int isplt, j, k, m;
    
    m = n;
    while (m > 512) {
        m >>= 2;
        cftmdl1(m, &a[n - m], &w[nw - (m >> 1)]);
    }
    cftleaf(m, 1, &a[n - m], nw, w);
    k = 0;
    for (j = n - m; j > 0; j -= m) {
        k++;
        isplt = cfttree(m, j, k, a, nw, w);
        cftleaf(m, isplt, &a[j - m], nw, w);
    }
}


int cfttree(int n, int j, int k, double *a, int nw, double *w)
{
    void cftmdl1(int n, double *a, double *w);
    void cftmdl2(int n, double *a, double *w);
    int i, isplt, m;
    
    if ((k & 3) != 0) {
        isplt = k & 1;
        if (isplt != 0) {
            cftmdl1(n, &a[j - n], &w[nw - (n >> 1)]);
        } else {
            cftmdl2(n, &a[j - n], &w[nw - n]);
        }
    } else {
        m = n;
        for (i = k; (i & 3) == 0; i >>= 2) {
            m <<= 2;
        }
        isplt = i & 1;
        if (isplt != 0) {
            while (m > 128) {
                cftmdl1(m, &a[j - m], &w[nw - (m >> 1)]);
                m >>= 2;
            }
        } else {
            while (m > 128) {
                cftmdl2(m, &a[j - m], &w[nw - m]);
                m >>= 2;
            }
        }
    }
    return isplt;
}


void cftleaf(int n, int isplt, double *a, int nw, double *w)
{
    void cftmdl1(int n, double *a, double *w);
    void cftmdl2(int n, double *a, double *w);
    void cftf161(double *a, double *w);
    void cftf162(double *a, double *w);
    void cftf081(double *a, double *w);
    void cftf082(double *a, double *w);
    
    if (n == 512) {
        cftmdl1(128, a, &w[nw - 64]);
        cftf161(a, &w[nw - 8]);
        cftf162(&a[32], &w[nw - 32]);
        cftf161(&a[64], &w[nw - 8]);
        cftf161(&a[96], &w[nw - 8]);
        cftmdl2(128, &a[128], &w[nw - 128]);
        cftf161(&a[128], &w[nw - 8]);
        cftf162(&a[160], &w[nw - 32]);
        cftf161(&a[192], &w[nw - 8]);
        cftf162(&a[224], &w[nw - 32]);
        cftmdl1(128, &a[256], &w[nw - 64]);
        cftf161(&a[256], &w[nw - 8]);
        cftf162(&a[288], &w[nw - 32]);
        cftf161(&a[320], &w[nw - 8]);
        cftf161(&a[352], &w[nw - 8]);
        if (isplt != 0) {
            cftmdl1(128, &a[384], &w[nw - 64]);
            cftf161(&a[480], &w[nw - 8]);
        } else {
            cftmdl2(128, &a[384], &w[nw - 128]);
            cftf162(&a[480], &w[nw - 32]);
        }
        cftf161(&a[384], &w[nw - 8]);
        cftf162(&a[416], &w[nw - 32]);
        cftf161(&a[448], &w[nw - 8]);
    } else {
        cftmdl1(64, a, &w[nw - 32]);
        cftf081(a, &w[nw - 8]);
        cftf082(&a[16], &w[nw - 8]);
        cftf081(&a[32], &w[nw - 8]);
        cftf081(&a[48], &w[nw - 8]);
        cftmdl2(64, &a[64], &w[nw - 64]);
        cftf081(&a[64], &w[nw - 8]);
        cftf082(&a[80], &w[nw - 8]);
        cftf081(&a[96], &w[nw - 8]);
        cftf082(&a[112], &w[nw - 8]);
        cftmdl1(64, &a[128], &w[nw - 32]);
        cftf081(&a[128], &w[nw - 8]);
        cftf082(&a[144], &w[nw - 8]);
        cftf081(&a[160], &w[nw - 8]);
        cftf081(&a[176], &w[nw - 8]);
        if (isplt != 0) {
            cftmdl1(64, &a[192], &w[nw - 32]);
            cftf081(&a[240], &w[nw - 8]);
        } else {
            cftmdl2(64, &a[192], &w[nw - 64]);
            cftf082(&a[240], &w[nw - 8]);
        }
        cftf081(&a[192], &w[nw - 8]);
        cftf082(&a[208], &w[nw - 8]);
        cftf081(&a[224], &w[nw - 8]);
    }
}


void cftmdl1(int n, double *a, double *w)
{
    int j, j0, j1, j2, j3, k, m, mh;
    double wn4r, wk1r, wk1i, wk3r, wk3i;
    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
    
    mh = n >> 3;
    m = 2 * mh;
    j1 = m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[0] + a[j2];
    x0i = a[1] + a[j2 + 1];
    x1r = a[0] - a[j2];
    x1i = a[1] - a[j2 + 1];
    x2r = a[j1] + a[j3];
    x2i = a[j1 + 1] + a[j3 + 1];
    x3r = a[j1] - a[j3];
    x3i = a[j1 + 1] - a[j3 + 1];
    a[0] = x0r + x2r;
    a[1] = x0i + x2i;
    a[j1] = x0r - x2r;
    a[j1 + 1] = x0i - x2i;
    a[j2] = x1r - x3i;
    a[j2 + 1] = x1i + x3r;
    a[j3] = x1r + x3i;
    a[j3 + 1] = x1i - x3r;
    wn4r = w[1];
    k = 0;
    for (j = 2; j < mh; j += 2) {
        k += 4;
        wk1r = w[k];
        wk1i = w[k + 1];
        wk3r = w[k + 2];
        wk3i = w[k + 3];
        j1 = j + m;
        j2 = j1 + m;
        j3 = j2 + m;
        x0r = a[j] + a[j2];
        x0i = a[j + 1] + a[j2 + 1];
        x1r = a[j] - a[j2];
        x1i = a[j + 1] - a[j2 + 1];
        x2r = a[j1] + a[j3];
        x2i = a[j1 + 1] + a[j3 + 1];
        x3r = a[j1] - a[j3];
        x3i = a[j1 + 1] - a[j3 + 1];
        a[j] = x0r + x2r;
        a[j + 1] = x0i + x2i;
        a[j1] = x0r - x2r;
        a[j1 + 1] = x0i - x2i;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[j2] = wk1r * x0r - wk1i * x0i;
        a[j2 + 1] = wk1r * x0i + wk1i * x0r;
        x0r = x1r + x3i;
        x0i = x1i - x3r;
        a[j3] = wk3r * x0r + wk3i * x0i;
        a[j3 + 1] = wk3r * x0i - wk3i * x0r;
        j0 = m - j;
        j1 = j0 + m;
        j2 = j1 + m;
        j3 = j2 + m;
        x0r = a[j0] + a[j2];
        x0i = a[j0 + 1] + a[j2 + 1];
        x1r = a[j0] - a[j2];
        x1i = a[j0 + 1] - a[j2 + 1];
        x2r = a[j1] + a[j3];
        x2i = a[j1 + 1] + a[j3 + 1];
        x3r = a[j1] - a[j3];
        x3i = a[j1 + 1] - a[j3 + 1];
        a[j0] = x0r + x2r;
        a[j0 + 1] = x0i + x2i;
        a[j1] = x0r - x2r;
        a[j1 + 1] = x0i - x2i;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[j2] = wk1i * x0r - wk1r * x0i;
        a[j2 + 1] = wk1i * x0i + wk1r * x0r;
        x0r = x1r + x3i;
        x0i = x1i - x3r;
        a[j3] = wk3i * x0r + wk3r * x0i;
        a[j3 + 1] = wk3i * x0i - wk3r * x0r;
    }
    j0 = mh;
    j1 = j0 + m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[j0] + a[j2];
    x0i = a[j0 + 1] + a[j2 + 1];
    x1r = a[j0] - a[j2];
    x1i = a[j0 + 1] - a[j2 + 1];
    x2r = a[j1] + a[j3];
    x2i = a[j1 + 1] + a[j3 + 1];
    x3r = a[j1] - a[j3];
    x3i = a[j1 + 1] - a[j3 + 1];
    a[j0] = x0r + x2r;
    a[j0 + 1] = x0i + x2i;
    a[j1] = x0r - x2r;
    a[j1 + 1] = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[j2] = wn4r * (x0r - x0i);
    a[j2 + 1] = wn4r * (x0i + x0r);
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    a[j3] = -wn4r * (x0r + x0i);
    a[j3 + 1] = -wn4r * (x0i - x0r);
}


void cftmdl2(int n, double *a, double *w)
{
    int j, j0, j1, j2, j3, k, kr, m, mh;
    double wn4r, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i;
    
    mh = n >> 3;
    m = 2 * mh;
    wn4r = w[1];
    j1 = m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[0] - a[j2 + 1];
    x0i = a[1] + a[j2];
    x1r = a[0] + a[j2 + 1];
    x1i = a[1] - a[j2];
    x2r = a[j1] - a[j3 + 1];
    x2i = a[j1 + 1] + a[j3];
    x3r = a[j1] + a[j3 + 1];
    x3i = a[j1 + 1] - a[j3];
    y0r = wn4r * (x2r - x2i);
    y0i = wn4r * (x2i + x2r);
    a[0] = x0r + y0r;
    a[1] = x0i + y0i;
    a[j1] = x0r - y0r;
    a[j1 + 1] = x0i - y0i;
    y0r = wn4r * (x3r - x3i);
    y0i = wn4r * (x3i + x3r);
    a[j2] = x1r - y0i;
    a[j2 + 1] = x1i + y0r;
    a[j3] = x1r + y0i;
    a[j3 + 1] = x1i - y0r;
    k = 0;
    kr = 2 * m;
    for (j = 2; j < mh; j += 2) {
        k += 4;
        wk1r = w[k];
        wk1i = w[k + 1];
        wk3r = w[k + 2];
        wk3i = w[k + 3];
        kr -= 4;
        wd1i = w[kr];
        wd1r = w[kr + 1];
        wd3i = w[kr + 2];
        wd3r = w[kr + 3];
        j1 = j + m;
        j2 = j1 + m;
        j3 = j2 + m;
        x0r = a[j] - a[j2 + 1];
        x0i = a[j + 1] + a[j2];
        x1r = a[j] + a[j2 + 1];
        x1i = a[j + 1] - a[j2];
        x2r = a[j1] - a[j3 + 1];
        x2i = a[j1 + 1] + a[j3];
        x3r = a[j1] + a[j3 + 1];
        x3i = a[j1 + 1] - a[j3];
        y0r = wk1r * x0r - wk1i * x0i;
        y0i = wk1r * x0i + wk1i * x0r;
        y2r = wd1r * x2r - wd1i * x2i;
        y2i = wd1r * x2i + wd1i * x2r;
        a[j] = y0r + y2r;
        a[j + 1] = y0i + y2i;
        a[j1] = y0r - y2r;
        a[j1 + 1] = y0i - y2i;
        y0r = wk3r * x1r + wk3i * x1i;
        y0i = wk3r * x1i - wk3i * x1r;
        y2r = wd3r * x3r + wd3i * x3i;
        y2i = wd3r * x3i - wd3i * x3r;
        a[j2] = y0r + y2r;
        a[j2 + 1] = y0i + y2i;
        a[j3] = y0r - y2r;
        a[j3 + 1] = y0i - y2i;
        j0 = m - j;
        j1 = j0 + m;
        j2 = j1 + m;
        j3 = j2 + m;
        x0r = a[j0] - a[j2 + 1];
        x0i = a[j0 + 1] + a[j2];
        x1r = a[j0] + a[j2 + 1];
        x1i = a[j0 + 1] - a[j2];
        x2r = a[j1] - a[j3 + 1];
        x2i = a[j1 + 1] + a[j3];
        x3r = a[j1] + a[j3 + 1];
        x3i = a[j1 + 1] - a[j3];
        y0r = wd1i * x0r - wd1r * x0i;
        y0i = wd1i * x0i + wd1r * x0r;
        y2r = wk1i * x2r - wk1r * x2i;
        y2i = wk1i * x2i + wk1r * x2r;
        a[j0] = y0r + y2r;
        a[j0 + 1] = y0i + y2i;
        a[j1] = y0r - y2r;
        a[j1 + 1] = y0i - y2i;
        y0r = wd3i * x1r + wd3r * x1i;
        y0i = wd3i * x1i - wd3r * x1r;
        y2r = wk3i * x3r + wk3r * x3i;
        y2i = wk3i * x3i - wk3r * x3r;
        a[j2] = y0r + y2r;
        a[j2 + 1] = y0i + y2i;
        a[j3] = y0r - y2r;
        a[j3 + 1] = y0i - y2i;
    }
    wk1r = w[m];
    wk1i = w[m + 1];
    j0 = mh;
    j1 = j0 + m;
    j2 = j1 + m;
    j3 = j2 + m;
    x0r = a[j0] - a[j2 + 1];
    x0i = a[j0 + 1] + a[j2];
    x1r = a[j0] + a[j2 + 1];
    x1i = a[j0 + 1] - a[j2];
    x2r = a[j1] - a[j3 + 1];
    x2i = a[j1 + 1] + a[j3];
    x3r = a[j1] + a[j3 + 1];
    x3i = a[j1 + 1] - a[j3];
    y0r = wk1r * x0r - wk1i * x0i;
    y0i = wk1r * x0i + wk1i * x0r;
    y2r = wk1i * x2r - wk1r * x2i;
    y2i = wk1i * x2i + wk1r * x2r;
    a[j0] = y0r + y2r;
    a[j0 + 1] = y0i + y2i;
    a[j1] = y0r - y2r;
    a[j1 + 1] = y0i - y2i;
    y0r = wk1i * x1r - wk1r * x1i;
    y0i = wk1i * x1i + wk1r * x1r;
    y2r = wk1r * x3r - wk1i * x3i;
    y2i = wk1r * x3i + wk1i * x3r;
    a[j2] = y0r - y2r;
    a[j2 + 1] = y0i - y2i;
    a[j3] = y0r + y2r;
    a[j3 + 1] = y0i + y2i;
}


void cftfx41(int n, double *a, int nw, double *w)
{
    void cftf161(double *a, double *w);
    void cftf162(double *a, double *w);
    void cftf081(double *a, double *w);
    void cftf082(double *a, double *w);
    
    if (n == 128) {
        cftf161(a, &w[nw - 8]);
        cftf162(&a[32], &w[nw - 32]);
        cftf161(&a[64], &w[nw - 8]);
        cftf161(&a[96], &w[nw - 8]);
    } else {
        cftf081(a, &w[nw - 8]);
        cftf082(&a[16], &w[nw - 8]);
        cftf081(&a[32], &w[nw - 8]);
        cftf081(&a[48], &w[nw - 8]);
    }
}


void cftf161(double *a, double *w)
{
    double wn4r, wk1r, wk1i, 
        x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, 
        y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, 
        y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i, 
        y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i, 
        y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;
    
    wn4r = w[1];
    wk1r = w[2];
    wk1i = w[3];
    x0r = a[0] + a[16];
    x0i = a[1] + a[17];
    x1r = a[0] - a[16];
    x1i = a[1] - a[17];
    x2r = a[8] + a[24];
    x2i = a[9] + a[25];
    x3r = a[8] - a[24];
    x3i = a[9] - a[25];
    y0r = x0r + x2r;
    y0i = x0i + x2i;
    y4r = x0r - x2r;
    y4i = x0i - x2i;
    y8r = x1r - x3i;
    y8i = x1i + x3r;
    y12r = x1r + x3i;
    y12i = x1i - x3r;
    x0r = a[2] + a[18];
    x0i = a[3] + a[19];
    x1r = a[2] - a[18];
    x1i = a[3] - a[19];
    x2r = a[10] + a[26];
    x2i = a[11] + a[27];
    x3r = a[10] - a[26];
    x3i = a[11] - a[27];
    y1r = x0r + x2r;
    y1i = x0i + x2i;
    y5r = x0r - x2r;
    y5i = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    y9r = wk1r * x0r - wk1i * x0i;
    y9i = wk1r * x0i + wk1i * x0r;
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    y13r = wk1i * x0r - wk1r * x0i;
    y13i = wk1i * x0i + wk1r * x0r;
    x0r = a[4] + a[20];
    x0i = a[5] + a[21];
    x1r = a[4] - a[20];
    x1i = a[5] - a[21];
    x2r = a[12] + a[28];
    x2i = a[13] + a[29];
    x3r = a[12] - a[28];
    x3i = a[13] - a[29];
    y2r = x0r + x2r;
    y2i = x0i + x2i;
    y6r = x0r - x2r;
    y6i = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    y10r = wn4r * (x0r - x0i);
    y10i = wn4r * (x0i + x0r);
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    y14r = wn4r * (x0r + x0i);
    y14i = wn4r * (x0i - x0r);
    x0r = a[6] + a[22];
    x0i = a[7] + a[23];
    x1r = a[6] - a[22];
    x1i = a[7] - a[23];
    x2r = a[14] + a[30];
    x2i = a[15] + a[31];
    x3r = a[14] - a[30];
    x3i = a[15] - a[31];
    y3r = x0r + x2r;
    y3i = x0i + x2i;
    y7r = x0r - x2r;
    y7i = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    y11r = wk1i * x0r - wk1r * x0i;
    y11i = wk1i * x0i + wk1r * x0r;
    x0r = x1r + x3i;
    x0i = x1i - x3r;
    y15r = wk1r * x0r - wk1i * x0i;
    y15i = wk1r * x0i + wk1i * x0r;
    x0r = y12r - y14r;
    x0i = y12i - y14i;
    x1r = y12r + y14r;
    x1i = y12i + y14i;
    x2r = y13r - y15r;
    x2i = y13i - y15i;
    x3r = y13r + y15r;
    x3i = y13i + y15i;
    a[24] = x0r + x2r;
    a[25] = x0i + x2i;
    a[26] = x0r - x2r;
    a[27] = x0i - x2i;
    a[28] = x1r - x3i;
    a[29] = x1i + x3r;
    a[30] = x1r + x3i;
    a[31] = x1i - x3r;
    x0r = y8r + y10r;
    x0i = y8i + y10i;
    x1r = y8r - y10r;
    x1i = y8i - y10i;
    x2r = y9r + y11r;
    x2i = y9i + y11i;
    x3r = y9r - y11r;
    x3i = y9i - y11i;
    a[16] = x0r + x2r;
    a[17] = x0i + x2i;
    a[18] = x0r - x2r;
    a[19] = x0i - x2i;
    a[20] = x1r - x3i;
    a[21] = x1i + x3r;
    a[22] = x1r + x3i;
    a[23] = x1i - x3r;
    x0r = y5r - y7i;
    x0i = y5i + y7r;
    x2r = wn4r * (x0r - x0i);
    x2i = wn4r * (x0i + x0r);
    x0r = y5r + y7i;
    x0i = y5i - y7r;
    x3r = wn4r * (x0r - x0i);
    x3i = wn4r * (x0i + x0r);
    x0r = y4r - y6i;
    x0i = y4i + y6r;
    x1r = y4r + y6i;
    x1i = y4i - y6r;
    a[8] = x0r + x2r;
    a[9] = x0i + x2i;
    a[10] = x0r - x2r;
    a[11] = x0i - x2i;
    a[12] = x1r - x3i;
    a[13] = x1i + x3r;
    a[14] = x1r + x3i;
    a[15] = x1i - x3r;
    x0r = y0r + y2r;
    x0i = y0i + y2i;
    x1r = y0r - y2r;
    x1i = y0i - y2i;
    x2r = y1r + y3r;
    x2i = y1i + y3i;
    x3r = y1r - y3r;
    x3i = y1i - y3i;
    a[0] = x0r + x2r;
    a[1] = x0i + x2i;
    a[2] = x0r - x2r;
    a[3] = x0i - x2i;
    a[4] = x1r - x3i;
    a[5] = x1i + x3r;
    a[6] = x1r + x3i;
    a[7] = x1i - x3r;
}


void cftf162(double *a, double *w)
{
    double wn4r, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i, 
        x0r, x0i, x1r, x1i, x2r, x2i, 
        y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, 
        y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i, 
        y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i, 
        y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;
    
    wn4r = w[1];
    wk1r = w[4];
    wk1i = w[5];
    wk3r = w[6];
    wk3i = -w[7];
    wk2r = w[8];
    wk2i = w[9];
    x1r = a[0] - a[17];
    x1i = a[1] + a[16];
    x0r = a[8] - a[25];
    x0i = a[9] + a[24];
    x2r = wn4r * (x0r - x0i);
    x2i = wn4r * (x0i + x0r);
    y0r = x1r + x2r;
    y0i = x1i + x2i;
    y4r = x1r - x2r;
    y4i = x1i - x2i;
    x1r = a[0] + a[17];
    x1i = a[1] - a[16];
    x0r = a[8] + a[25];
    x0i = a[9] - a[24];
    x2r = wn4r * (x0r - x0i);
    x2i = wn4r * (x0i + x0r);
    y8r = x1r - x2i;
    y8i = x1i + x2r;
    y12r = x1r + x2i;
    y12i = x1i - x2r;
    x0r = a[2] - a[19];
    x0i = a[3] + a[18];
    x1r = wk1r * x0r - wk1i * x0i;
    x1i = wk1r * x0i + wk1i * x0r;
    x0r = a[10] - a[27];
    x0i = a[11] + a[26];
    x2r = wk3i * x0r - wk3r * x0i;
    x2i = wk3i * x0i + wk3r * x0r;
    y1r = x1r + x2r;
    y1i = x1i + x2i;
    y5r = x1r - x2r;
    y5i = x1i - x2i;
    x0r = a[2] + a[19];
    x0i = a[3] - a[18];
    x1r = wk3r * x0r - wk3i * x0i;
    x1i = wk3r * x0i + wk3i * x0r;
    x0r = a[10] + a[27];
    x0i = a[11] - a[26];
    x2r = wk1r * x0r + wk1i * x0i;
    x2i = wk1r * x0i - wk1i * x0r;
    y9r = x1r - x2r;
    y9i = x1i - x2i;
    y13r = x1r + x2r;
    y13i = x1i + x2i;
    x0r = a[4] - a[21];
    x0i = a[5] + a[20];
    x1r = wk2r * x0r - wk2i * x0i;
    x1i = wk2r * x0i + wk2i * x0r;
    x0r = a[12] - a[29];
    x0i = a[13] + a[28];
    x2r = wk2i * x0r - wk2r * x0i;
    x2i = wk2i * x0i + wk2r * x0r;
    y2r = x1r + x2r;
    y2i = x1i + x2i;
    y6r = x1r - x2r;
    y6i = x1i - x2i;
    x0r = a[4] + a[21];
    x0i = a[5] - a[20];
    x1r = wk2i * x0r - wk2r * x0i;
    x1i = wk2i * x0i + wk2r * x0r;
    x0r = a[12] + a[29];
    x0i = a[13] - a[28];
    x2r = wk2r * x0r - wk2i * x0i;
    x2i = wk2r * x0i + wk2i * x0r;
    y10r = x1r - x2r;
    y10i = x1i - x2i;
    y14r = x1r + x2r;
    y14i = x1i + x2i;
    x0r = a[6] - a[23];
    x0i = a[7] + a[22];
    x1r = wk3r * x0r - wk3i * x0i;
    x1i = wk3r * x0i + wk3i * x0r;
    x0r = a[14] - a[31];
    x0i = a[15] + a[30];
    x2r = wk1i * x0r - wk1r * x0i;
    x2i = wk1i * x0i + wk1r * x0r;
    y3r = x1r + x2r;
    y3i = x1i + x2i;
    y7r = x1r - x2r;
    y7i = x1i - x2i;
    x0r = a[6] + a[23];
    x0i = a[7] - a[22];
    x1r = wk1i * x0r + wk1r * x0i;
    x1i = wk1i * x0i - wk1r * x0r;
    x0r = a[14] + a[31];
    x0i = a[15] - a[30];
    x2r = wk3i * x0r - wk3r * x0i;
    x2i = wk3i * x0i + wk3r * x0r;
    y11r = x1r + x2r;
    y11i = x1i + x2i;
    y15r = x1r - x2r;
    y15i = x1i - x2i;
    x1r = y0r + y2r;
    x1i = y0i + y2i;
    x2r = y1r + y3r;
    x2i = y1i + y3i;
    a[0] = x1r + x2r;
    a[1] = x1i + x2i;
    a[2] = x1r - x2r;
    a[3] = x1i - x2i;
    x1r = y0r - y2r;
    x1i = y0i - y2i;
    x2r = y1r - y3r;
    x2i = y1i - y3i;
    a[4] = x1r - x2i;
    a[5] = x1i + x2r;
    a[6] = x1r + x2i;
    a[7] = x1i - x2r;
    x1r = y4r - y6i;
    x1i = y4i + y6r;
    x0r = y5r - y7i;
    x0i = y5i + y7r;
    x2r = wn4r * (x0r - x0i);
    x2i = wn4r * (x0i + x0r);
    a[8] = x1r + x2r;
    a[9] = x1i + x2i;
    a[10] = x1r - x2r;
    a[11] = x1i - x2i;
    x1r = y4r + y6i;
    x1i = y4i - y6r;
    x0r = y5r + y7i;
    x0i = y5i - y7r;
    x2r = wn4r * (x0r - x0i);
    x2i = wn4r * (x0i + x0r);
    a[12] = x1r - x2i;
    a[13] = x1i + x2r;
    a[14] = x1r + x2i;
    a[15] = x1i - x2r;
    x1r = y8r + y10r;
    x1i = y8i + y10i;
    x2r = y9r - y11r;
    x2i = y9i - y11i;
    a[16] = x1r + x2r;
    a[17] = x1i + x2i;
    a[18] = x1r - x2r;
    a[19] = x1i - x2i;
    x1r = y8r - y10r;
    x1i = y8i - y10i;
    x2r = y9r + y11r;
    x2i = y9i + y11i;
    a[20] = x1r - x2i;
    a[21] = x1i + x2r;
    a[22] = x1r + x2i;
    a[23] = x1i - x2r;
    x1r = y12r - y14i;
    x1i = y12i + y14r;
    x0r = y13r + y15i;
    x0i = y13i - y15r;
    x2r = wn4r * (x0r - x0i);
    x2i = wn4r * (x0i + x0r);
    a[24] = x1r + x2r;
    a[25] = x1i + x2i;
    a[26] = x1r - x2r;
    a[27] = x1i - x2i;
    x1r = y12r + y14i;
    x1i = y12i - y14r;
    x0r = y13r - y15i;
    x0i = y13i + y15r;
    x2r = wn4r * (x0r - x0i);
    x2i = wn4r * (x0i + x0r);
    a[28] = x1r - x2i;
    a[29] = x1i + x2r;
    a[30] = x1r + x2i;
    a[31] = x1i - x2r;
}


void cftf081(double *a, double *w)
{
    double wn4r, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, 
        y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, 
        y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;
    
    wn4r = w[1];
    x0r = a[0] + a[8];
    x0i = a[1] + a[9];
    x1r = a[0] - a[8];
    x1i = a[1] - a[9];
    x2r = a[4] + a[12];
    x2i = a[5] + a[13];
    x3r = a[4] - a[12];
    x3i = a[5] - a[13];
    y0r = x0r + x2r;
    y0i = x0i + x2i;
    y2r = x0r - x2r;
    y2i = x0i - x2i;
    y1r = x1r - x3i;
    y1i = x1i + x3r;
    y3r = x1r + x3i;
    y3i = x1i - x3r;
    x0r = a[2] + a[10];
    x0i = a[3] + a[11];
    x1r = a[2] - a[10];
    x1i = a[3] - a[11];
    x2r = a[6] + a[14];
    x2i = a[7] + a[15];
    x3r = a[6] - a[14];
    x3i = a[7] - a[15];
    y4r = x0r + x2r;
    y4i = x0i + x2i;
    y6r = x0r - x2r;
    y6i = x0i - x2i;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    x2r = x1r + x3i;
    x2i = x1i - x3r;
    y5r = wn4r * (x0r - x0i);
    y5i = wn4r * (x0r + x0i);
    y7r = wn4r * (x2r - x2i);
    y7i = wn4r * (x2r + x2i);
    a[8] = y1r + y5r;
    a[9] = y1i + y5i;
    a[10] = y1r - y5r;
    a[11] = y1i - y5i;
    a[12] = y3r - y7i;
    a[13] = y3i + y7r;
    a[14] = y3r + y7i;
    a[15] = y3i - y7r;
    a[0] = y0r + y4r;
    a[1] = y0i + y4i;
    a[2] = y0r - y4r;
    a[3] = y0i - y4i;
    a[4] = y2r - y6i;
    a[5] = y2i + y6r;
    a[6] = y2r + y6i;
    a[7] = y2i - y6r;
}


void cftf082(double *a, double *w)
{
    double wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i, 
        y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, 
        y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;
    
    wn4r = w[1];
    wk1r = w[2];
    wk1i = w[3];
    y0r = a[0] - a[9];
    y0i = a[1] + a[8];
    y1r = a[0] + a[9];
    y1i = a[1] - a[8];
    x0r = a[4] - a[13];
    x0i = a[5] + a[12];
    y2r = wn4r * (x0r - x0i);
    y2i = wn4r * (x0i + x0r);
    x0r = a[4] + a[13];
    x0i = a[5] - a[12];
    y3r = wn4r * (x0r - x0i);
    y3i = wn4r * (x0i + x0r);
    x0r = a[2] - a[11];
    x0i = a[3] + a[10];
    y4r = wk1r * x0r - wk1i * x0i;
    y4i = wk1r * x0i + wk1i * x0r;
    x0r = a[2] + a[11];
    x0i = a[3] - a[10];
    y5r = wk1i * x0r - wk1r * x0i;
    y5i = wk1i * x0i + wk1r * x0r;
    x0r = a[6] - a[15];
    x0i = a[7] + a[14];
    y6r = wk1i * x0r - wk1r * x0i;
    y6i = wk1i * x0i + wk1r * x0r;
    x0r = a[6] + a[15];
    x0i = a[7] - a[14];
    y7r = wk1r * x0r - wk1i * x0i;
    y7i = wk1r * x0i + wk1i * x0r;
    x0r = y0r + y2r;
    x0i = y0i + y2i;
    x1r = y4r + y6r;
    x1i = y4i + y6i;
    a[0] = x0r + x1r;
    a[1] = x0i + x1i;
    a[2] = x0r - x1r;
    a[3] = x0i - x1i;
    x0r = y0r - y2r;
    x0i = y0i - y2i;
    x1r = y4r - y6r;
    x1i = y4i - y6i;
    a[4] = x0r - x1i;
    a[5] = x0i + x1r;
    a[6] = x0r + x1i;
    a[7] = x0i - x1r;
    x0r = y1r - y3i;
    x0i = y1i + y3r;
    x1r = y5r - y7r;
    x1i = y5i - y7i;
    a[8] = x0r + x1r;
    a[9] = x0i + x1i;
    a[10] = x0r - x1r;
    a[11] = x0i - x1i;
    x0r = y1r + y3i;
    x0i = y1i - y3r;
    x1r = y5r + y7r;
    x1i = y5i + y7i;
    a[12] = x0r - x1i;
    a[13] = x0i + x1r;
    a[14] = x0r + x1i;
    a[15] = x0i - x1r;
}


void cftf040(double *a)
{
    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
    
    x0r = a[0] + a[4];
    x0i = a[1] + a[5];
    x1r = a[0] - a[4];
    x1i = a[1] - a[5];
    x2r = a[2] + a[6];
    x2i = a[3] + a[7];
    x3r = a[2] - a[6];
    x3i = a[3] - a[7];
    a[0] = x0r + x2r;
    a[1] = x0i + x2i;
    a[2] = x1r - x3i;
    a[3] = x1i + x3r;
    a[4] = x0r - x2r;
    a[5] = x0i - x2i;
    a[6] = x1r + x3i;
    a[7] = x1i - x3r;
}


void cftb040(double *a)
{
    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
    
    x0r = a[0] + a[4];
    x0i = a[1] + a[5];
    x1r = a[0] - a[4];
    x1i = a[1] - a[5];
    x2r = a[2] + a[6];
    x2i = a[3] + a[7];
    x3r = a[2] - a[6];
    x3i = a[3] - a[7];
    a[0] = x0r + x2r;
    a[1] = x0i + x2i;
    a[2] = x1r + x3i;
    a[3] = x1i - x3r;
    a[4] = x0r - x2r;
    a[5] = x0i - x2i;
    a[6] = x1r - x3i;
    a[7] = x1i + x3r;
}


void cftx020(double *a)
{
    double x0r, x0i;
    
    x0r = a[0] - a[2];
    x0i = a[1] - a[3];
    a[0] += a[2];
    a[1] += a[3];
    a[2] = x0r;
    a[3] = x0i;
}


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


void dstsub(int n, double *a, int nc, double *c)
{
    int j, k, kk, ks, m;
    double wkr, wki, xr;
    
    m = n >> 1;
    ks = nc / n;
    kk = 0;
    for (j = 1; j < m; j++) {
        k = n - j;
        kk += ks;
        wkr = c[kk] - c[nc - kk];
        wki = c[kk] + c[nc - kk];
        xr = wki * a[k] - wkr * a[j];
        a[k] = wkr * a[k] + wki * a[j];
        a[j] = xr;
    }
    a[m] *= c[0];
}
/*
**	fft.c -- Fast Fourier Tramsform (FFT)
**	時間軸間引きFFT (Cooley--Tukeyのアルゴリズム)
**
**	『Ｃ言語による最新アルゴリズム事典』（奥村晴彦・著）に掲載の
**	プログラムを改変して利用させて頂きました.
**
**	Revised by MIYASAKA Masaru <alkaid@coral.ocn.ne.jp> (Sep 15, 2003)
**
**	[TAB4]
*/

//#include <stdlib.h>
//#include <math.h>
//#include <stdio.h>

//#include "fft_czt.h"

//#undef PI
//#define PI	3.1415926535897932384626433832795L	/* 円周率(π) */


/*
**	三角関数表を作る.
*/
static void make_sintbl(int n, REAL sintbl[])
{
	/* ↓精度が重要でないなら double でもいいかも */
	double PI;
	PI =(double)atan(1.0)*4.0;
	long double r, d = (2 * PI) / n;
	int i, n2 = n / 2, n4 = n / 4, n8 = n / 8;

	for (i = 0; i <= n8; i++) {
		r = d * i;
		sintbl[i]      = sin(r);			/* sin(2*PI*i/n) */
		sintbl[n4 - i] = cos(r);
	}
	for (i = 0; i < n4; i++) {
		sintbl[n2 - i] =  sintbl[i];
		sintbl[i + n2] = -sintbl[i];
	}
}


/*
**	ビット反転表を作る.
*/
static void make_bitrev(int n, int bitrev[])
{
	int i = 0, j = 0, k;
	int n2 = n / 2;

	for (;;) {
		bitrev[i] = j;
		if (++i >= n) break;
		k = n2;
		while (k <= j) { j -= k; k /= 2; }
		j += k;
	}
}


/*
**	FFT計算用構造体に対し、標本数 n 用の数表データを作成する。
**
**	fftp	= FFT計算用構造体へのポインタ
**	n		= 標本点の数 ( 4以上の 2の整数乗に限る)
**	return	= 0:正常終了 1:nが無効な数 2:メモリ不足
*/
int fft_init(fft_struct *fftp, int n)
{
	int i;

	for (i = 4; i < n; i *= 2) ;
	if (i != n) return 1;

	fftp->samples = n;
	fftp->sintbl  = (REAL*)malloc((n / 4 * 3) * sizeof(REAL));
	fftp->bitrev  = (int*)malloc(n * sizeof(int));
	if (fftp->sintbl == NULL || fftp->bitrev == NULL) {
		fft_end(fftp);
		return 2;
	}
//	make_sintbl(n, fftp->sintbl);
//	make_bitrev(n, fftp->bitrev);

	return 0;
}


/*
**	FFT計算用構造体の数表データを消去してそのメモリ領域を開放する。
**
**	fftp	= FFT計算用構造体へのポインタ
*/
void fft_end(fft_struct *fftp)
{
	if (fftp->sintbl != NULL) { free(fftp->sintbl); fftp->sintbl = NULL; }
	if (fftp->bitrev != NULL) { free(fftp->bitrev); fftp->bitrev = NULL; }

//	fftp->samples = 0;
}


/*
**	高速Fourier変換 (FFT) (Cooley--Tukeyのアルゴリズム).
**	re[] が実部, im[] が虚部. 結果は re[],im[] に上書きされる.
**	inv!=0 (=TRUE) なら逆変換を行う. fftp には, 計算用データが
**	入っている構造体を指定する.
*/
void fft_tukawan(fft_struct *fftp, int inv, REAL re[], REAL im[])
{
	REAL si, co, dr, di, t;
	int i, j, k, ik, h, d, k2, n, n4;

	n  = fftp->samples;
	n4 = n / 4;

	for (i = 0; i < n; i++) {		/* ビット反転 */
		j = fftp->bitrev[i];
		if (i < j) {
			t = re[i];  re[i] = re[j];  re[j] = t;
			t = im[i];  im[i] = im[j];  im[j] = t;
		}
	}
	for (k = 1; k < n; k = k2) {	/* 変換 */
		h = 0;  k2 = k + k;  d = n / k2;
		for (j = 0; j < k; j++) {
			co = fftp->sintbl[h + n4];
			si = fftp->sintbl[h];
			if (inv) si = -si;
			for (i = j; i < n; i += k2) {
				ik = i + k;
				dr = si * im[ik] + co * re[ik];
				di = co * im[ik] - si * re[ik];
				re[ik] = re[i] - dr;  re[i] += dr;
				im[ik] = im[i] - di;  im[i] += di;
			}
			h += d;
		}
	}
	double t1;
	if (!inv) {						/* 逆変換でないならnで割る */
		t = 1.0 / n;			/* 逆数をかける(除算は遅いので) */
        t1 = 0.5 / n;
//		t = (4.3775) / (double)n ;			/* 逆数をかける(除算は遅いので) */
		for (i = 0; i < n; i++) {
			re[i] *= t;
			im[i] *= t;
		}
//		for (i = 0; i < n; i++) {
//			if(i==0){
//			re[i] *= t1;
//			im[i] *= t1;
//			} else { 
//			re[i] *= t;
//			im[i] *= t;
//			}
//		}
	}
}
/*
void fft(double *real,double *imag, int power, int flg)
{
double c,s,t1,t2;
int arg,inc,i,j,k,lmax,lix,j1,j2,pnum,pnum1,nv2;
pnum = (int)((pow(2.0,(float)(power)))+0.5);
double PI = atan(1.0) * 4.0;

lmax = pnum;
inc = 1;
for(i=0;i<power;i++){
lix=lmax;
lmax /= 2;
arg = 0;
for(j=0;j<lmax;j++){
c=cos(2.0*PI*((double)(arg))/((double)(pnum)));
s=flg*sin(2.0*PI*((double)(arg))/((double)(pnum)));
arg += inc;
for(k=lix;k<=pnum;k+=lix){
j1=k-lix+j;
j2=j1+lmax;
t1=(*(real+j1))-(*(real+j2));
t2=(*(imag+j1))-(*(imag+j2));
*(real+j1) += *(real+j2);
*(imag+j1) += *(imag+j2);
*(real+j2) = c*t1+s*t2;
*(imag+j2) = c*t2-s*t1;
}
}
inc *= 2;
}
j=0;
nv2=pnum/2;
pnum1=pnum-1;
for(i=0;i<pnum1;i++){
if(i<j){
t1=*(real+j);
t2=*(imag+j);
*(real+j)=*(real+i);
*(imag+j)=*(imag+i);
*(real+i)=t1;
*(imag+i)=t2;
}
k=nv2;
while(k<j+1){
j -= k;
k /= 2;
}
j+=k;
}
	double sc=1.0/(double)(pnum);
	if(flg==-1){
 		for(i=0;i<pnum;i++){
			*(real+i) *= sc;
			*(imag+i) *= sc;
		}
	}
}
*/

/*
**	czt.c -- Chirp z-Tramsform (CZT)
**	任意データ数での計算が可能な高速 DFT アルゴリズム
**
**	『トランジスタ技術』1993年2月号 P.363〜368 の解説を参考にしています.
**
**	Public domain by MIYASAKA Masaru <alkaid@coral.ocn.ne.jp> (Sep 15, 2003)
**
**	[TAB4]
*/


/*
**	fft_czt.h -- header file for fft.c and czt.c
**
**	Public domain by MIYASAKA Masaru <alkaid@coral.ocn.ne.jp> (Sep 15, 2003)
**
**	[TAB4]
*/

//#ifndef FFT_CZT_H
//#define FFT_CZT_H

	/* データ実数型 REAL の定義 (float or double) */
	/* この型を long double にする場合は、czt.c / fft.c で使われている
	 * 三角関数 sin() / cos() を long double 版 (C99 対応コンパイラでは
	 * sinl / cosl) に変更する必要あり */



//#endif	/* FFT_CZT_H */


//#undef PI
//#define PI	3.1415926535897932384626433832795L	/* 円周率(π) */


/*
**	重みデータ・インパルス応答データを作る
*/
static void make_cztdata(int n, int no, int nx, REAL wr[], REAL wi[],
                         REAL vr[], REAL vi[])
{
	/* ↓精度が重要でないなら double でもいいかも */
	double PI;
	PI = (double)atan(1.0)*4.0;
	long double r, d = PI / n;
	int i, j, n2 = n * 2;

	for (i = j = 0; i < n; i++, j = (j + (2 * i - 1)) % n2) {
		r = d * j;
		wr[i] =  cos(r);					/*  cos(i*i*PI/n) */
		wi[i] = -sin(r);					/* -sin(i*i*PI/n) */
	}

	vr[0] = nx;					/* nx: FFT順変換のスケーリングに対応する補正 */
	vi[0] = 0;
	for (i = 1; i < n; i++) {
		vr[i] = vr[nx - i] =  nx * wr[i];	/* nx * cos(i*i*PI/n) */
		vi[i] = vi[nx - i] = -nx * wi[i];	/* nx * sin(i*i*PI/n) */
	}
	for (i = no, j = nx - n; i <= j; i++, j--) {
		vr[j] = vr[i] = 0;					/* 残りの拡張部には 0 を */
		vi[j] = vi[i] = 0;
	}
}


/*
**	CZT計算用構造体に対し、標本数 n, 出力データ数 no 用の数表データを
**	作成する。
**
**	cztp	= CZT計算用構造体へのポインタ
**	n		= 標本点の数
**	no		= 出力するデータの数
**	return	= 0:正常終了 1:nが無効な数 2:メモリ不足
*/
int czt_init(czt_struct *cztp, int n, int no,int *ip,double *ww)
{
	int i, nx,powe;

	if (n <= 1) return 1;
	if (no <= 1 || n < no) no = n;

	nx = n + no;		/* (n + no)を2の整数乗まで拡張する(nx) */
	for (i = 1; i < nx; i *= 2) ;
	nx = i;//64
	//debug start
	//printf("nx=%d\n",nx);
	//debug end

	if (fft_init(&cztp->fft, nx) != 0) return 2;

	cztp->samples     = n;
	cztp->samples_out = no;
	cztp->samples_ex  = nx;
	cztp->wr = (REAL*)malloc(2 * n  * sizeof(REAL));
	cztp->vr = (REAL*)malloc(2 * nx * sizeof(REAL));
	cztp->tr = (REAL*)malloc(2 * nx * sizeof(REAL));
	if (cztp->wr == NULL || cztp->vr == NULL || cztp->tr == NULL) {
		czt_end(cztp);
		return 2;
	}
	cztp->wi = cztp->wr + n;
	cztp->vi = cztp->vr + nx;
	cztp->ti = cztp->tr + nx;

	make_cztdata(n, no, nx, cztp->wr, cztp->wi, cztp->vr, cztp->vi);
	double *temp/*,*ww*/;
	temp = (double *)malloc(sizeof(double)*nx*2);
//	ww = (double *)malloc(sizeof(double)*nx);
	for(i=0;i<nx;i++){
		temp[2*i] = cztp->vr[i];
		temp[2*i+1] = cztp->vi[i];
	}
//	int *ip;
//	ip = (int *)malloc(sizeof(int)*nx);
//	ip[0] = 0;
//debug s
//debug e
	cdft(2*nx,-1,temp,ip,ww);
	for(i=0;i<nx;i++){
		cztp->vr[i] = temp[2*i]/nx ;
		cztp->vi[i] = temp[2*i+1]/nx ;
	}
	free(temp);

//	fft(&cztp->fft, 0, cztp->vr, cztp->vi);
//	powe = (int)((log((double)(cztp->fft.samples))/log(2.0))+0.5);
	//debug start
//	printf("cztp->fft.samples=%d,powe=%d\n",cztp->fft.samples,powe);
	//debug end
//debug start	
//	double *zzzr,*zzzi;
//	zzzr=(double*)malloc(sizeof(double)*cztp->fft.samples);
//	zzzi=(double*)malloc(sizeof(double)*cztp->fft.samples);
//	for(i=0;i<cztp->fft.samples;i++){
//		zzzr[i] = cztp->vr[i];
//		zzzi[i] = cztp->vi[i];
//	}	
//	half_fft(cztp->vr, cztp->vi,powe);
//	half_fft(zzzr, zzzi,powe);
//	fft(cztp->vr, cztp->vi,powe,-1);
//	for(i=0;i<1024;i++){
//		printf("N= %d %d half %f full %f\n",cztp->fft.samples,i,zzzi[i],cztp->vi[i]);
//	}
//	while(1);
//debug end	
	return 0;
}


/*
**	CZT計算用構造体の数表データを消去してそのメモリ領域を開放する。
**
**	cztp	= CZT計算用構造体へのポインタ
*/
void czt_end(czt_struct *cztp)
{
	if (cztp->wr != NULL) { free(cztp->wr); cztp->wr = NULL; }
	if (cztp->vr != NULL) { free(cztp->vr); cztp->vr = NULL; }
	if (cztp->tr != NULL) { free(cztp->tr); cztp->tr = NULL; }

	cztp->samples     = 0;
	cztp->samples_out = 0;
	cztp->samples_ex  = 0;

	fft_end(&cztp->fft);
}


/*
**	CZT (Chirp z-Tramsform) アルゴリズムによる高速 DFT.
**	re[] が実部, im[] が虚部. 結果は re[],im[] に上書きされる.
**	inv!=0 (=TRUE) なら逆変換を行う. cztp には, 計算用データが
**	入っている構造体を指定する.
*/
void czt(czt_struct *cztp, int inv, REAL re[], REAL im[],int *ip,double *ww)
{
	REAL xr, xi, yr, yi, t;
	int i, n, no, nx, powe;

	n  = cztp->samples;
	no = cztp->samples_out;
	nx = cztp->samples_ex;

	for (i = 0; i < n; i++) {		/* 入力の重みデータ乗算 */
		yr = cztp->wr[i];
		yi = cztp->wi[i];
		if (inv) yi = -yi;
		cztp->tr[i] = re[i] * yr - im[i] * yi;
		cztp->ti[i] = im[i] * yr + re[i] * yi;
	}
	for (; i < nx; i++) {			/* 残りの拡張部には 0 を */
		cztp->tr[i] = 0;
		cztp->ti[i] = 0;
	}
	double *temp/*,*ww*/;
	temp = (double *)malloc(sizeof(double)*nx*2);
//	ww = (double *)malloc(sizeof(double)*nx);
	for(i=0;i<nx;i++){
		temp[2*i] = cztp->tr[i];
		temp[2*i+1] = cztp->ti[i];
	}
//	fft(&cztp->fft, 0, cztp->tr, cztp->ti);
	cdft(2*nx,-1,temp,ip,ww);
	for(i=0;i<nx;i++){
		cztp->tr[i] = temp[2*i]/nx ;
		cztp->ti[i] = temp[2*i+1]/nx ;
	}

//	fft(&cztp->fft, 0, cztp->tr, cztp->ti);
//	powe = (int)((log((double)(cztp->fft.samples))/log(2.0))+0.5);
	//debug start
//	printf("cztp->fft.samples=%d,powe=%d\n",cztp->fft.samples,powe);
	//debug end
//	half_fft(cztp->tr, cztp->ti,powe);
//	fft(cztp->tr, cztp->ti,powe,-1);

	for (i = 0; i < nx; i++) {		/* コンボリューション演算 */
		xr = cztp->tr[i];
		xi = cztp->ti[i];
		yr = cztp->vr[i];
		yi = cztp->vi[i];
		if (inv) yi = -yi;
		cztp->tr[i] = xr * yr - xi * yi;
		cztp->ti[i] = xi * yr + xr * yi;
	}

//	fft(&cztp->fft, 1, cztp->tr, cztp->ti);
//	powe = (int)((log((double)(cztp->fft.samples))/log(2.0))+0.5);
	//debug start
//	printf("cztp->fft.samples=%d,powe=%d\n",cztp->fft.samples,powe);
	//debug end
//	half_ifft(cztp->tr, cztp->ti,powe);
//	fft(cztp->tr, cztp->ti,powe,1);
	for(i=0;i<nx;i++){
		temp[2*i] = cztp->tr[i];
		temp[2*i+1] = cztp->ti[i];
	}
	cdft(2*nx,1,temp,ip,ww);
	for(i=0;i<nx;i++){
		cztp->tr[i] = temp[2*i]/*/nx*/ ;
		cztp->ti[i] = temp[2*i+1]/*/nx*/ ;
	}

	for (i = 0; i < no; i++) {		/* 出力の重みデータ乗算 */
		yr = cztp->wr[i];
		yi = cztp->wi[i];
		if (inv) yi = -yi;
		re[i] = cztp->tr[i] * yr - cztp->ti[i] * yi;
		im[i] = cztp->ti[i] * yr + cztp->tr[i] * yi;
	}

	if (!inv) {						/* 逆変換でないならnで割る */
		t = 1.0 / n;			/* 逆数をかける(除算は遅いので) */
		for (i = 0; i < no; i++) {
			re[i] *= t;
			im[i] *= t;
		}
	}
}
/*
**	czttest.c -- czt.c のテストルーチン
**
**	『Ｃ言語による最新アルゴリズム事典』（奥村晴彦・著）に掲載の
**	fft.c のテストルーチンを参考にさせて頂きました.
**
**	Public domain by MIYASAKA Masaru <alkaid@coral.ocn.ne.jp> (Sep 15, 2003)
**
**	[TAB4]
*/

//#include <stdio.h>
//#include <stdlib.h>
//#include <math.h>

//#include "fft_czt.h"

//#undef PI
//#define PI	3.1415926535897932384626433832795	/* 円周率(π) */

//#define N 8000	/* テスト用データのサンプル数 */


int charp_FFT(int N,double *R,double *I,double *OR, double *OI,int *ip, double *ww)
{
	static REAL  r2[8192], i2[8192];
	czt_struct cztd;
	int i;
	for (i=0;i<N;i++){
		r2[i]=*(R+i);
		i2[i]=*(I+i);
	}
		if (czt_init(&cztd, N, N,ip,ww) != 0) {printf("failure!!!!\n"); while(1); return EXIT_FAILURE;}
	czt(&cztd, 0, r2, i2,ip,ww);		/* 順変換 */
	for(i=0;i<N;i++){
		*(OR+i) = r2[i];
		*(OI+i) = i2[i];
	}
//	czt(&cztd, 1, r3, i3);		/* 逆変換 */
	czt_end(&cztd);


	return EXIT_SUCCESS;
}
		
int charp_IFFT(int N,double *R,double *I,double *OR,double *OI,int *ip, double *ww)
{
	static REAL r2[8192], i2[8192];
	czt_struct cztd;
	int i;
	for (i=0;i<N;i++){
		r2[i]=*(R+i);
		i2[i]=*(I+i);
	}

	if (czt_init(&cztd, N, N,ip,ww) != 0) return EXIT_FAILURE;
//	czt(&cztd, 0, r2, i2);		/* 順変換 */
	for(i=0;i<N;i++){
		*(OR+i) = r2[i];
		*(OI+i) = i2[i];
	}

	czt(&cztd, 1, r2, i2,ip,ww);		/* 逆変換 */
	for(i=0;i<N;i++){
		*(OR+i) = r2[i];
		*(OI+i) = i2[i];
	}
	czt_end(&cztd);


	return EXIT_SUCCESS;
}
#define uchar           unsigned char
#define ushort          unsigned short
#define uint            unsigned int
#define ulong           unsigned long
#define rchar           register char
#define rshort          register short
#define rint            register int
#define rlong           register long
#define ruchar          register uchar
#define rushort         register ushort
#define ruint           register uint
#define rulong          register ulong
#define schar           static char
#define sshhort         static short
#define sint            static int
#define slong           static long
#define suchar          static uchar
#define sushort         static ushort
#define suint           static uint
#define sulong          static ulong
#define ORG_IMAGE_X     720
#define ORG_IMAGE_Y     480

#define BUNBOMAX 32
#define BUNSHIMAX 31
#define TAPMAXY 50
#define TAPMAXC 50

typedef struct control_data {
  uint          sizex;
  uint          sizey;
  uint          startx;
  uint          starty;
  char         InputFileName[128];
  char         InputFileName2[128];
  char         OutputFileName[128];
  uint          hv;
  uint		sm;
  uint          smy;	
  uint          bunshi;
  uint          bunbo;
  uint          norm;
  uint          mado;
  uint          tapnum_y;
  uint          tapnum_c;
  double        Fs;		
} CNTL;
        char inputfile[128];
        char inputfile2[128];
        char outputfile[128];
        int hsize;
        int vsize;
        int org_image_x;
        int org_image_y;
	void coeffhairetsuculc(uint , uint, uint , uint, uint, uint, uint, uint, double, double, double, double, double *,double *, uint,double);
        double INITPHASECULC(uint , uint , uint , uint , uint );
        uint FILPATCULC(uint , uint , uint , double , double *);
        void COEFCULC( uint , uint , uint , uint , uint , uint , uint, double );
  	void normarize(uint ,uint ,uint ,uint , double *, uint  );
	void DFT1DV(int , double *, double *, double *, double *,int *,double *);
	void DFT1DH(int , int  , double *, double*, double *, double *,int *,double *);
	void IDFT1DV(int , double *, double *, double *, double *,int *,double *);
	void IDFT1DH(int , int  , double *, double*, double *, double *,int *,double *);
void resize( int hsize, int vsize, int sizeminus, int smy,  unsigned char *vin_buffer , unsigned char *vout);
void    print_help( void )
{
  fprintf( stderr, "Usage: EVEN FUNCTIONIZED DFT DOWN RESIZE [options]\n" );
  fprintf( stderr, "\toptions: \n" );
  fprintf( stderr, "\t  -help          : Display help\n" );
  fprintf( stderr, "\t  -i             : Input bmp file name\n" );
  fprintf( stderr, "\t  -o             : Output bmp file name(be added .bmp extension\n" );
//  fprintf( stderr, "\t  -x             : 出力補正スペクトルを何倍にするか指定\n" );
//  fprintf( stderr, "\t  -orgx          : 水平画素サイズ(任意の自然数)\n" );
//  fprintf( stderr, "\t  -orgy          : 垂直画素サイズ(任意の自然数)\n" );
  fprintf( stderr, "\t  -hsize         : output horizontal size \n" );
  fprintf( stderr, "\t  -vsize         : output vertical size\n" );
//  fprintf( stderr, "\t  -hv       : 1:水平 2:プログレッシブ垂直 3:インタレース垂直\n" );
//  fprintf( stderr, "\t  -bunshi   : 縮小率分子 max31\n" );
//  fprintf( stderr, "\t  -bunbo    : 縮小率分母 max32\n" );
//  fprintf( stderr, "\t  -tapnum_y : 輝度フィルタタップ数  推奨 21 max50\n" );
//  fprintf( stderr, "\t  -tapnum_c : 色差フィルタタップ数  推奨 11 max50\n" );
//  fprintf( stderr, "\t  -norm     : 総係数合計 推奨4096 サブサンプルプログラムで使う場合\n" );
//  fprintf( stderr, "\t  -mado     : 1:矩形 2:Lanczos 3:hanning(両端が0) 4:hamming\n" );
//  fprintf( stderr, "\t  -Fsc      : サブサンプル後のサンプリング周波数を１としたときカットオフ周波数を指定(推奨0.5)\n" );

}
void    option_set(short argc,char *argv[], CNTL *ptr)
{
  short i;
                                                                                                                                                         
  for(i=1;i < argc;i++) {
    if(argv[i][0] != '-')
      continue;

    if ( !strcmp( &argv[i][1], "h" ) ){
      /* \245\330\245\353\245\327\311\275\274\250 */
      print_help();
      exit(0);
    } else if ( !strcmp( &argv[i][1], "o" ) ){
      /* \275\320\316\317\245\325\245\241\245\244\245\353\314\276 */
      strcpy(ptr->OutputFileName, argv[++i]);
    } else if ( !strcmp( &argv[i][1], "i" ) ){
      strcpy(ptr->InputFileName, argv[++i]);
    } else if ( !strcmp( &argv[i][1], "i2" ) ){
      strcpy(ptr->InputFileName2, argv[++i]);
                                                                                                                                                         
    } else if ( !strcmp( &argv[i][1], "x" ) ){
      ptr->sizex = atoi(argv[++i]);
    } else if ( !strcmp( &argv[i][1], "y" ) ){
      ptr->sizey = atoi(argv[++i]);
                                                                                                                                                         
    } else if ( !strcmp( &argv[i][1], "startx" ) ){
      ptr->startx = atoi(argv[++i]);
    } else if ( !strcmp( &argv[i][1], "starty" ) ){
      ptr->starty = atoi(argv[++i]);
                                                                                                                                                         
    } else if ( !strcmp( &argv[i][1], "hv" ) ){
      ptr->hv = atoi(argv[++i]);
    } else if ( !strcmp( &argv[i][1], "bunshi" ) ){
      ptr->bunshi = atoi(argv[++i]);
    } else if ( !strcmp( &argv[i][1], "bunbo" ) ){
      ptr->bunbo = atoi(argv[++i]);
    } else if ( !strcmp( &argv[i][1], "norm" ) ){
      ptr->norm = atoi(argv[++i]);
    } else if ( !strcmp( &argv[i][1], "mado" ) ){
      ptr->mado = atoi(argv[++i]);
    } else if ( !strcmp( &argv[i][1], "tapnum_y" ) ){
      ptr->tapnum_y = atoi(argv[++i]);
    } else if ( !strcmp( &argv[i][1], "tapnum_c" ) ){
      ptr->tapnum_c = atoi(argv[++i]);
    } else if ( !strcmp( &argv[i][1], "Fsc" ) ){
      ptr->Fs = atof(argv[++i]);
    } else if ( !strcmp( &argv[i][1], "hsize" ) ){
      ptr->sm = atoi(argv[++i]);
    } else if ( !strcmp( &argv[i][1], "vsize" ) ){
      ptr->smy = atoi(argv[++i]);
    } else if ( !strcmp( &argv[i][1], "orgx" ) ){
      /* \277\345\312\277\312\375\270\376\306\376\316\317\262\350\301\374\245\265\245\244\245\272 */
      org_image_x = atoi(argv[++i]);
    } else if ( !strcmp( &argv[i][1], "orgy" ) ){
      /* \277\342\304\276\312\375\270\376\306\376\316\317\262\350\301\374\245\265\245\244\245\272 */
      org_image_y = atoi(argv[++i]);
    } else {
      print_help();
      exit(0);
    }
  }
                                                                                                                                                         
}

int main(int argc, char *argv[]){
FILE *fpr1;
FILE *fpr2;
FILE *fpw;
unsigned char *vin;
unsigned char *vout;
unsigned char *vin_buffer;
#define HSIZE 360
#define VSIZE 288
#define tmp HSIZE*VSIZE 
int i,j,k,l,m,n,o ;
CNTL  *cnt;
int center0;
int sizeminus;
int filesizebyte;
unsigned char *B;
unsigned char *G;
unsigned char *R;
unsigned char *BIN;
unsigned char *GIN;
unsigned char *RIN;
unsigned char *RUPOUT;
unsigned char *GUPOUT;
unsigned char *BUPOUT;
unsigned char temp;
unsigned char temp2;
unsigned int filesize;


  org_image_x = ORG_IMAGE_X;
  org_image_y = ORG_IMAGE_Y;

        if( argc < 2 ) {
                print_help();
                exit(0);
        }
//-----debug-----
//for(;;);
//----------------
        cnt = (CNTL *)malloc( sizeof(CNTL)*sizeof(uchar) );
                                                                                                                                                         
        /* \245\307\245\325\245\251\245\353\245\310\303\315\300\337\304\352 */
        cnt->sizex = ORG_IMAGE_X;    
        cnt->sizey = ORG_IMAGE_Y;     
        cnt->startx = 0;
        cnt->starty = 0;
                                                                                                                                                         
        /* \245\252\245\327\245\267\245\347\245\363\245\301\245\247\245\303\245\257 */
        option_set(argc, argv, cnt);
                                                                                                                                                         
                                                                                                                                                         
        hsize = org_image_x;
        vsize = org_image_y;
        strcpy(inputfile,cnt->InputFileName);
        strcpy(inputfile2,cnt->InputFileName2);
        strcpy(outputfile,cnt->OutputFileName);
//	sizeminus = cnt->sm;
                                                                                                                                                         
/********************************/ 
/*				*/
/*	  MAIN ROUTINE		*/
/*				*/
/********************************/

//	vin_buffer = (unsigned char *)malloc(sizeof(unsigned char)*hsize*vsize);
//	vout = (unsigned char *)malloc(sizeof(unsigned char)*(hsize+sizeminus)*(vsize+smy)*2);

        if((fpr1 = fopen(inputfile,"rb"))==NULL){
                exit(0);
        }
//debug start
//for(;;);
//debug end
/***************************************************/
/* picture size & file size get from bitmap header */
/***************************************************/
	fseek(fpr1,18,SEEK_SET);
	fread(&hsize,sizeof(int),1,fpr1);
//debug start
//printf ("%d\n",hsize);
//for(;;);
//debug end
	fread(&vsize,sizeof(int),1,fpr1);
	fseek(fpr1,2,SEEK_SET);
	fread(&filesizebyte,sizeof(int),1,fpr1);
//debug start
//printf ("%d\n",filesizebyte);
//for(;;);
//debug end
	sizeminus = hsize - cnt->sm;
	cnt->smy  = vsize - cnt->smy;

/***************/
/* picture get */
/***************/
	vin = (unsigned char *)malloc(sizeof(unsigned char)*(filesizebyte-54));
	B = (unsigned char *)malloc(sizeof(unsigned char)*hsize*vsize);
	G = (unsigned char *)malloc(sizeof(unsigned char)*hsize*vsize);
	R = (unsigned char *)malloc(sizeof(unsigned char)*hsize*vsize);
	fseek(fpr1,54,SEEK_SET);
	if(fread(vin,sizeof(unsigned char),filesizebyte - 54,fpr1) != filesizebyte -54 ){
		printf("input file size err!!\n");
		exit(1);
	}
	fclose(fpr1);
//debug start
//for(;;);
//debug end

/***************************************/
/* set to B,G,R array with RGB PICTURE */
/***************************************/
	for(i=0,k=0;i<vsize;i++){
		for(j=0;j<hsize;j++){
			*(B+j*vsize+i) = *(vin+k);
			k++;
			*(G+j*vsize+i) = *(vin+k);
			k++;
			*(R+j*vsize+i) = *(vin+k);
			k++;
		}
		if(((hsize*3)%4) == 1){
			k=k+3;
		}
		if(((hsize*3)%4) == 2){
			k=k+2;
		}
		if(((hsize*3)%4) == 3){
			k=k+1;
		}
		if(((hsize*3)%4) == 0){
			;
		}
	}
//debug start
//for(;;);
//debug end
	BIN = (unsigned char *)malloc(sizeof(unsigned char)*hsize*vsize);
	GIN = (unsigned char *)malloc(sizeof(unsigned char)*hsize*vsize);
	RIN = (unsigned char *)malloc(sizeof(unsigned char)*hsize*vsize);

/*******************/
/* RGB arrangement */	
/*******************/

	for(i=0;i<vsize;i++){
		for(j=0;j<hsize;j++){
			*(RIN+j*vsize+i) = *(R+j*vsize+vsize-1-i);
			*(GIN+j*vsize+i) = *(G+j*vsize+vsize-1-i);
			*(BIN+j*vsize+i) = *(B+j*vsize+vsize-1-i);	
		}
	}

	RUPOUT = (unsigned char *)malloc(sizeof(unsigned char)*(hsize-sizeminus)*(vsize-cnt->smy));
	GUPOUT = (unsigned char *)malloc(sizeof(unsigned char)*(hsize-sizeminus)*(vsize-cnt->smy));
	BUPOUT = (unsigned char *)malloc(sizeof(unsigned char)*(hsize-sizeminus)*(vsize-cnt->smy));

	resize(  hsize,  vsize,  sizeminus,  cnt->smy,   RIN ,  RUPOUT);
	resize(  hsize,  vsize,  sizeminus,  cnt->smy,   GIN ,  GUPOUT);
	resize(  hsize,  vsize,  sizeminus,  cnt->smy,   BIN ,  BUPOUT);

	sprintf(cnt->OutputFileName,"%s.bmp",outputfile);
	fpw = fopen(cnt->OutputFileName,"wb");
	hsize = hsize - sizeminus;
	vsize = vsize - cnt->smy;
/************************/
/* HEADER 54 byte write */
/************************/
	if(((hsize*3)%4) == 0){
		filesize = 0x36 + hsize*vsize*3;
	} else {
		filesize = 0x36 + hsize*vsize*3+(4-(hsize*3)%4)*vsize;
	}

	temp = 0x42; //'B'
	fwrite(&temp,sizeof(unsigned char),1,fpw);
	temp = 0x4D; //'M'
	fwrite(&temp,sizeof(unsigned char),1,fpw);
	fwrite(&filesize,sizeof(unsigned int),1,fpw);
	filesize = 0;
	fwrite(&filesize,sizeof(unsigned int),1,fpw);
	filesize = 0x00000036;
	fwrite(&filesize,sizeof(unsigned int),1,fpw);
	filesize = 0x28;
	fwrite(&filesize,sizeof(unsigned int),1,fpw);
	fwrite(&hsize,sizeof(int),1,fpw);	
	fwrite(&vsize,sizeof(int),1,fpw);
	filesize = 0x00180001;
	fwrite(&filesize,sizeof(unsigned int),1,fpw);
	filesize = 0;
	fwrite(&filesize,sizeof(unsigned int),1,fpw);
	fwrite(&filesize,sizeof(unsigned int),1,fpw);
	filesize = 0x00000EC4;
	fwrite(&filesize,sizeof(unsigned int),1,fpw);
	fwrite(&filesize,sizeof(unsigned int),1,fpw);
	filesize = 0;
	fwrite(&filesize,sizeof(unsigned int),1,fpw);
	fwrite(&filesize,sizeof(unsigned int),1,fpw);
	temp2 =0;

	for(i=0;i<vsize;i++){
		for(j=0;j<hsize;j++){
			fwrite((BUPOUT+j*vsize+vsize-1-i),sizeof(unsigned char),1,fpw);
			fwrite((GUPOUT+j*vsize+vsize-1-i),sizeof(unsigned char),1,fpw);
			fwrite((RUPOUT+j*vsize+vsize-1-i),sizeof(unsigned char),1,fpw);
		}
		temp = 4-((hsize*3)%4) ;
		if(temp != 4 ){
			for(k=0;k<temp;k++){
				fwrite( &temp2,sizeof(unsigned char),1,fpw);
			}
		}
	}	

	fclose(fpw);
        return 0;
}

void resize( int hsize, int vsize, int sizeminus, int smy,  unsigned char *vin_buffer , unsigned char *vout)
{ 

double *VINR;
double *VINI;
double *VOUTR;
double *VOUTI;
double *VINRptr;
double *VINIptr;
double *VOUTRptr;
double *VOUTIptr;
double *kariR;
double *kariI;
int i,j,k,l,m,n,o ;
double PI;
double *fourieR;
double *fourieI;
	PI = atan(1)*4.0;
	kariR = (double *)malloc(sizeof(double)*(hsize)*(vsize)*4);
	kariI = (double *)malloc(sizeof(double)*(hsize)*(vsize)*4);
	VINR = (double *)malloc(sizeof(double)*(hsize)*(vsize)*4);
	VINI = (double *)malloc(sizeof(double)*(hsize)*(vsize)*4);
	VOUTR = (double *)malloc(sizeof(double)*(hsize)*(vsize)*4);
	VOUTI = (double *)malloc(sizeof(double)*(hsize)*(vsize)*4);
	VINRptr = VINR;
	VINIptr = VINI;
	VOUTRptr = VOUTR;
	VOUTIptr = VOUTI;
/************************/
/*			*/
/*      BUFFERING	*/
/*			*/
/************************/
//	for(i=0,k=0;i<vsize;i++){
//		for(j=0;j<hsize;j++){
//			*(vin_buffer+j*vsize+i) = *(vin+k);
//			k++;
//		}
//	}
/*************************/
/*			 */
/*     第一象限代入	 */
/*			 */
/*************************/
	for(i=0;i<vsize;i++){
		for(j=0;j<hsize;j++){
			*(VINR+j*2*vsize+i) = (double)(*(vin_buffer+j*vsize+i));
			*(VINI+j*2*vsize+i) = 0.0;
		}
	}
/*************************/
/*			 */
/*     第二象限代入	 */
/*			 */
/*************************/
	for(i=0;i<vsize;i++){
		for(j=0;j<hsize;j++){
			*(VINR+(j+hsize)*2*vsize+i) = (double)(*(vin_buffer+(hsize-1-j)*vsize+i));
			*(VINI+(j+hsize)*2*vsize+i) = 0.0; 
		}
	}
/*************************/
/*			 */
/*     第三象限代入	 */
/*			 */
/*************************/
	for(i=0;i<vsize;i++){
		for(j=0;j<hsize;j++){
			*(VINR+j*2*vsize+i+vsize) = (double)(*(vin_buffer+j*vsize+(vsize-1-i)));
			*(VINI+j*2*vsize+i+vsize) = 0.0;
		}
	}
/*************************/
/*			 */
/*     第四象限代入	 */
/*			 */
/*************************/
	for(i=0;i<vsize;i++){
		for(j=0;j<hsize;j++){
			*(VINR+(j+hsize)*2*vsize+i+vsize) = (double)(*(vin_buffer+(hsize-1-j)*vsize+(vsize-1-i)));
			*(VINI+(j+hsize)*2*vsize+i+vsize) = 0.0;
		}
	}

//debug
//for(;;);
//------
	fprintf(stderr,"Start Horizontal DFT\n");
	double *ww;
	ww = (double *)malloc(sizeof(double)*8192*4);
	if(ww==NULL){printf("ww no memory!!\n");exit(1);}
	int *ip;
	ip = (int *)malloc(sizeof(int)*8192*4);
	if(ip==NULL){printf("ip no memory!!\n");exit(1);}

	for(i=0;i<vsize*2;i++){
		if(i==0){
			ip[0]=0;
			DFT1DH (hsize*2,vsize*2,VINRptr+i,VINIptr+i,VOUTRptr+i,VOUTIptr+i,ip,ww);
		} else {
			//printf("ip2kaime=%d\n",ip[0]);while(1);
			DFT1DH (hsize*2,vsize*2,VINRptr+i,VINIptr+i,VOUTRptr+i,VOUTIptr+i,ip,ww);
		}
		printf("DFTH%d\n",i);
	}

	fprintf(stderr,"End Horizontal DFT\n");
	for(i=0;i<vsize*hsize*4;i++){
		*(VINR+i) = *(VOUTR+i);
		*(VINI+i) = *(VOUTI+i);
	}
//debug
//for(;;);
//------

	fprintf(stderr,"Start Vertical DFT\n");

	for(i=0;i<hsize*2;i++){
		if(i==0){
			ip[0]=0;
			DFT1DV (vsize*2,VINRptr+(vsize*2)*i,VINIptr+(vsize*2)*i,VOUTRptr+(vsize*2)*i,VOUTIptr+(vsize*2)*i,ip,ww);
		} else {
			DFT1DV (vsize*2,VINRptr+(vsize*2)*i,VINIptr+(vsize*2)*i,VOUTRptr+(vsize*2)*i,VOUTIptr+(vsize*2)*i,ip,ww);
		}
		printf("DFTV%d\n",i);
	}
	fprintf(stderr,"End Vertical DFT\n");


//	fourieR = (double *)malloc(sizeof(double)*(hsize-sizeminus)*vsize);
//	fourieI = (double *)malloc(sizeof(double)*(hsize-sizeminus)*vsize);
	fourieR = (double *)malloc(sizeof(double)*(hsize+sizeminus)*(vsize+smy)*4);
	fourieI = (double *)malloc(sizeof(double)*(hsize+sizeminus)*(vsize+smy)*4);

/*縮小した画像のフーリエ変換像の配列作成*/

	fprintf(stderr,"Start High frequency component removing \n");
	for(i=0;i<vsize*2;i++){
		*(VOUTRptr+((hsize+sizeminus))*vsize*2+i) = *(VOUTRptr+((hsize+sizeminus))*vsize*2+i) * 2.0;
		*(VOUTIptr+((hsize+sizeminus))*vsize*2+i) = 0.0;	
	}

	for(i=0;i<vsize*2;i++){
		for(j=0;j<(hsize-sizeminus);j++){
			*(fourieR+j*vsize*2+i)=*(VOUTRptr+j*vsize*2+i);
			*(fourieI+j*vsize*2+i)=*(VOUTIptr+j*vsize*2+i);
		}
		for(j=0;j<(hsize-sizeminus);j++){
			*(fourieR+((hsize-sizeminus)+j)*vsize*2+i) = *(VOUTRptr+(hsize+sizeminus+j)*vsize*2+i);
			*(fourieI+((hsize-sizeminus)+j)*vsize*2+i) = *(VOUTIptr+(hsize+sizeminus+j)*vsize*2+i);
		}
	}

	for(j=0;j<2*(hsize-sizeminus);j++){
		*(fourieR+j*vsize*2+(vsize+smy)) = *(fourieR+j*vsize*2+(vsize+smy)) * 2.0;
		*(fourieI+j*vsize*2+(vsize+smy)) = 0.0;
	}

	for(j=0;j<2*(hsize-sizeminus);j++){
		for(i=0;i<vsize-smy;i++){
			*(kariR+j*2*(vsize-(smy))+i)=*(fourieR+j*2*vsize+i);
			*(kariI+j*2*(vsize-(smy))+i)=*(fourieI+j*2*vsize+i);
		}
		for(i=0;i<vsize-smy;i++){
			*(kariR+j*2*(vsize-(smy))+i+(vsize-(smy))) =*(fourieR+j*2*vsize+i+vsize+smy);
			*(kariI+j*2*(vsize-(smy))+i+(vsize-(smy))) =*(fourieI+j*2*vsize+i+vsize+smy);
		}
	}
//debug start
//for(i=0;i<2*(vsize-smy);i++){
//	for(j=0;j<2*(hsize-sizeminus);j++){
//		printf("%f\n",*(kariR+j*2*(vsize-smy)+i));
//	}
//}	
//debug end
	for(i=0;i<2*(vsize-smy);i++){
		for(j=0;j<2*(hsize-sizeminus);j++){
			*(fourieR+j*2*(vsize-smy)+i) = *(kariR+j*2*(vsize-smy)+i);
			*(fourieI+j*2*(vsize-smy)+i) = *(kariI+j*2*(vsize-smy)+i);
		}
	}
	fprintf(stderr,"End High Frequency component removing\n");
//debug start
//for(i=0;i<2*(vsize-smy);i++){
//	for(j=0;j<2*(hsize-sizeminus);j++){
//		printf("%f\n",*(fourieR+j*2*(vsize-smy)+i));
//	}
//}	
//debug end
	fprintf(stderr,"Start horizontal IDFT\n");
	
	for(i=0;i<2*(vsize-smy);i++){
		if(i==0){
			ip[0]=0;
			IDFT1DH (2*(hsize-sizeminus),2*(vsize-smy),fourieR+i,fourieI+i,VOUTRptr+i,VOUTIptr+i,ip,ww);
		} else {
			IDFT1DH (2*(hsize-sizeminus),2*(vsize-smy),fourieR+i,fourieI+i,VOUTRptr+i,VOUTIptr+i,ip,ww);
		}
		printf("IDFTH%d\n",i);
	}
	fprintf(stderr,"End horizontal IDFT\n");
//debug start
//for(i=0;i<2*(vsize-smy);i++){
//	for(j=0;j<2*(hsize-sizeminus);j++){
//		printf("%f\n",*(VOUTRptr+j*2*(vsize-smy)+i));
//	}
//}	
//debug end
	fprintf(stderr,"Start vertical IDFT\n");
	for(i=0;i<2*(hsize-sizeminus);i++){
		if(i==0){
			ip[0]=0;
			IDFT1DV (2*(vsize-smy),VOUTRptr+2*(vsize-smy)*i,VOUTIptr+2*(vsize-smy)*i,fourieR+2*(vsize-smy)*i,fourieI+2*(vsize-smy)*i,ip,ww);
		} else {
			IDFT1DV (2*(vsize-smy),VOUTRptr+2*(vsize-smy)*i,VOUTIptr+2*(vsize-smy)*i,fourieR+2*(vsize-smy)*i,fourieI+2*(vsize-smy)*i,ip,ww);
		}
		printf("IDFTV%d\n",i);
	}
	fprintf(stderr,"End vertical IDFT\n");
	
	
	
	for(i=0,k=0;i<vsize-smy;i++){
		for(j=0;j<(hsize-sizeminus);j++){
			if(*(fourieR+j*2*(vsize-smy)+i)/*/(double)(hsize*vsize*4)*/ >= 255.0){
				*(vout+j*(vsize-smy)+i) = 255;
			} else if(*(fourieR+j*2*(vsize-smy)+i)/*/(double)(hsize*vsize*4)*/ <= 0.0){
				*(vout+j*(vsize-smy)+i) = 0;
			} else {
				*(vout+j*(vsize-smy)+i) = (unsigned char)(*(fourieR+j*2*(vsize-smy)+i)/*/(double)(hsize*vsize*4)*/);
//				*(vout+k) = (unsigned char)(*(fourieR+j*(vsize-smy)+i)/(double)(hsize*vsize)/((double)(vsize-smy) * (double)(hsize-sizeminus)));
//				*(vout+k) = (unsigned char)(*(fourieR+j*(vsize-smy)+i)/(double)(hsize*vsize)/(double)(hsize*vsize)*((double)(vsize-smy) * (double)(hsize-sizeminus)));
//				*(vout+k) = (unsigned char)((*(fourieR+j*(vsize-smy)+i))/(sqrt((double)(hsize*vsize)*((double)(vsize-smy) * (double)(hsize-sizeminus)))));
//				*(vout+k) = (unsigned char)((*(fourieR+j*(vsize-smy)+i))*((double)(hsize*vsize)));
			}
//debug
//printf("%f\n",((*(fourieR+j*2*(vsize-smy)+i))/(double)(hsize*vsize*4)));
//
			k++;
		}
	}
}// resize kansuu end	

void DFT1DV(int size, double *VINR, double *VINI, double *VOUTR, double *VOUTI,int *ip,double *ww)
{
	int i,j;
	double PI = atan(1)*4.0;
	for(i=0;i<size;i++){
		*(VOUTR+i) = 0.0;
		*(VOUTI+i) = 0.0;
	}
	charp_FFT(size,VINR,VINI,VOUTR,VOUTI,ip,ww);
//	for(i=0;i<size;i++){
//		for(j=0;j<size;j++){
//			*(VOUTR+i) += (*(VINR+j)*cos(2.0*PI*(double)i*(double)j/(double)size) + *(VINI+j)*sin(2.0*PI*(double)i*(double)j/(double)size));
//			*(VOUTI+i) += (*(VINI+j)*cos(2.0*PI*(double)i*(double)j/(double)size) - *(VINR+j)*sin(2.0*PI*(double)i*(double)j/(double)size));
//		}
//	}	
		
}

void DFT1DH(int hsize, int vsize , double *VINR, double*VINI, double *VOUTR, double *VOUTI,int *ip,double *ww)
{
	int i,j;
        double PI = atan(1)*4.0;
        for(i=0;i<hsize;i++){
                *(VOUTR+i*vsize) = 0.0;
                *(VOUTI+i*vsize) = 0.0;
        }
		double *R,*I,*OR,*OI;
	R= (double*)malloc(sizeof(double)*hsize);
	I= (double*)malloc(sizeof(double)*hsize);
	OR= (double*)malloc(sizeof(double)*hsize);
	OI= (double*)malloc(sizeof(double)*hsize);
	for(i=0;i<hsize;i++){
		*(R+i)= *(VINR+i*vsize);
		*(I+i)= *(VINI+i*vsize);
	}
	charp_FFT(hsize,R,I,OR,OI,ip,ww);
	for(i=0;i<hsize;i++){
		*(VOUTR+i*vsize)=*(OR+i);
		*(VOUTI+i*vsize)=*(OI+i);
//debug start
//		fprintf(stderr,"%d======%f\n",i,*(VOUTR+i*vsize));
//debug end
	}
//	*(VOUTR) /= 1.0;
	free(R);free(I);free(OR);free(OI);
//	for(i=0;i<hsize;i++){
  //              for(j=0;j<hsize;j++){
    //                    *(VOUTR+i*vsize) += (*(VINR+j*vsize)*cos(2.0*PI*(double)i*(double)j/(double)hsize) + *(VINI+j*vsize)*sin(2.0*PI*(double)i*(double)j/(double)hsize));
      //                  *(VOUTI+i*vsize) += (*(VINI+j*vsize)*cos(2.0*PI*(double)i*(double)j/(double)hsize) - *(VINR+j*vsize)*sin(2.0*PI*(double)i*(double)j/(double)hsize));
        //        }
        //}
}
void IDFT1DV(int size, double *VINR, double *VINI, double *VOUTR, double *VOUTI,int *ip,double *ww)
{
	int i,j;
	double PI = atan(1)*4.0;
	for(i=0;i<size;i++){
		*(VOUTR+i) = 0.0;
		*(VOUTI+i) = 0.0;
	}
	charp_IFFT(size,VINR,VINI,VOUTR,VOUTI,ip,ww);
//	for(i=0;i<size;i++){
//		for(j=0;j<size;j++){
//			*(VOUTR+i) += (*(VINR+j)*cos(2.0*PI*(double)i*(double)j/(double)size) - *(VINI+j)*sin(2.0*PI*(double)i*(double)j/(double)size));
//			*(VOUTI+i) += (*(VINI+j)*cos(2.0*PI*(double)i*(double)j/(double)size) + *(VINR+j)*sin(2.0*PI*(double)i*(double)j/(double)size));
//		}
//	}	
		
}

void IDFT1DH(int hsize, int vsize , double *VINR, double*VINI, double *VOUTR, double *VOUTI,int *ip,double *ww)
{
	int i,j;
        double PI = atan(1)*4.0;
        for(i=0;i<hsize;i++){
                *(VOUTR+i*vsize) = 0.0;
                *(VOUTI+i*vsize) = 0.0;
        }
		double *R,*I,*OR,*OI;
	R= (double*)malloc(sizeof(double)*hsize);
	I= (double*)malloc(sizeof(double)*hsize);
	OR= (double*)malloc(sizeof(double)*hsize);
	OI= (double*)malloc(sizeof(double)*hsize);
	for(i=0;i<hsize;i++){
		*(R+i)= *(VINR+i*vsize);
		*(I+i)= *(VINI+i*vsize);
	}
	charp_IFFT(hsize,R,I,OR,OI,ip,ww);
	for(i=0;i<hsize;i++){
		*(VOUTR+i*vsize)=*(OR+i);
		*(VOUTI+i*vsize)=*(OI+i);
		
	}
	free(R);free(I);free(OR);free(OI);
//	for(i=0;i<hsize;i++){
  //              for(j=0;j<hsize;j++){
    //                    *(VOUTR+i*vsize) += (*(VINR+j*vsize)*cos(2.0*PI*(double)i*(double)j/(double)hsize) - *(VINI+j*vsize)*sin(2.0*PI*(double)i*(double)j/(double)hsize));
      //                  *(VOUTI+i*vsize) += (*(VINI+j*vsize)*cos(2.0*PI*(double)i*(double)j/(double)hsize) + *(VINR+j*vsize)*sin(2.0*PI*(double)i*(double)j/(double)hsize));
        //        }
       // }
}