/* EAW - May 11th, 2001:    Changed all doubles to floats */

/*
Copyright:
    Copyright(C) 1996-1999 Takuya OOURA
    email: ooura@mmm.t.u-tokyo.ac.jp
    download: http://momonga.t.u-tokyo.ac.jp/~ooura/fft.html
    You may use, copy, modify this code for any purpose and
    without fee. You may distribute this ORIGINAL package.
*/

/*
Fast Fourier/Cosine/Sine Transform
    dimension   :one
    data length :power of 2
    decimation  :frequency
    radix       :4, 2
    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, float *, int *, float *);
    void rdft(int, int, float *, int *, float *);
    void ddct(int, int, float *, int *, float *);
    void ddst(int, int, float *, int *, float *);
    void dfct(int, float *, float *, int *, float *);
    void dfst(int, float *, float *, int *, float *);


-------- 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 (float *)
                        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 (float *)
                        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 (float *)
                        <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 (float *)
                        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 (float *)
                        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 (float *)
                        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 (float *)
                        <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 (float *)
                        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 (float *)
                        output data
                            a[k] = C[k], 0<=k<=n
        t[0...n/2]     :work area (float *)
        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 (float *)
                        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 (float *)
                        output data
                            a[k] = S[k], 0<k<n
                        (a[0] is used for work area)
        t[0...n/2-1]   :work area (float *)
        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 (float *)
                        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 <math.h>


namespace TimidityPlus
{
	void makewt(int nw, int *ip, float *w);
	void bitrv2(int n, int *ip, float *a);
	void bitrv2conj(int n, int *ip, float *a);
	void cftfsub(int n, float *a, float *w);
	void cftbsub(int n, float *a, float *w);
	void makect(int nc, int *ip, float *c);
	void rftfsub(int n, float *a, int nc, float *c);
	void rftbsub(int n, float *a, int nc, float *c);
	void dctsub(int n, float *a, int nc, float *c);
	void dstsub(int n, float *a, int nc, float *c);
	void cft1st(int n, float *a, float *w);
	void cftmdl(int n, int l, float *a, float *w);



#ifdef _MSC_VER
#pragma warning(disable:4244) // conversion from 'double' to 'float', possible loss of data
#endif


void cdft(int n, int isgn, float *a, int *ip, float *w)
{
	if (n > (ip[0] << 2)) {
		makewt(n >> 2, ip, w);
	}
	if (n > 4) {
		if (isgn >= 0) {
			bitrv2(n, ip + 2, a);
			cftfsub(n, a, w);
		}
		else {
			bitrv2conj(n, ip + 2, a);
			cftbsub(n, a, w);
		}
	}
	else if (n == 4) {
		cftfsub(n, a, w);
	}
}


void rdft(int n, int isgn, float *a, int *ip, float *w)
{
	int nw, nc;
	float xi;

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


void ddct(int n, int isgn, float *a, int *ip, float *w)
{
	int j, nw, nc;
	float 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);
			bitrv2(n, ip + 2, a);
			cftbsub(n, a, w);
		}
		else if (n == 4) {
			cftfsub(n, a, w);
		}
	}
	dctsub(n, a, nc, w + nw);
	if (isgn >= 0) {
		if (n > 4) {
			bitrv2(n, ip + 2, a);
			cftfsub(n, a, w);
			rftfsub(n, a, nc, w + nw);
		}
		else if (n == 4) {
			cftfsub(n, a, w);
		}
		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, float *a, int *ip, float *w)
{
	int j, nw, nc;
	float 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);
			bitrv2(n, ip + 2, a);
			cftbsub(n, a, w);
		}
		else if (n == 4) {
			cftfsub(n, a, w);
		}
	}
	dstsub(n, a, nc, w + nw);
	if (isgn >= 0) {
		if (n > 4) {
			bitrv2(n, ip + 2, a);
			cftfsub(n, a, w);
			rftfsub(n, a, nc, w + nw);
		}
		else if (n == 4) {
			cftfsub(n, a, w);
		}
		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, float *a, float *t, int *ip, float *w)
{
	int j, k, l, m, mh, nw, nc;
	float 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) {
			bitrv2(m, ip + 2, a);
			cftfsub(m, a, w);
			rftfsub(m, a, nc, w + nw);
		}
		else if (m == 4) {
			cftfsub(m, a, 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) {
				bitrv2(m, ip + 2, t);
				cftfsub(m, t, w);
				rftfsub(m, t, nc, w + nw);
			}
			else if (m == 4) {
				cftfsub(m, t, 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, float *a, float *t, int *ip, float *w)
{
	int j, k, l, m, mh, nw, nc;
	float 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) {
			bitrv2(m, ip + 2, a);
			cftfsub(m, a, w);
			rftfsub(m, a, nc, w + nw);
		}
		else if (m == 4) {
			cftfsub(m, a, 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) {
				bitrv2(m, ip + 2, t);
				cftfsub(m, t, w);
				rftfsub(m, t, nc, w + nw);
			}
			else if (m == 4) {
				cftfsub(m, t, 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 -------- */



void makewt(int nw, int *ip, float *w)
{
	void bitrv2(int n, int *ip, float *a);
	int j, nwh;
	float delta, x, y;

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


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


void bitrv2(int n, int *ip, float *a)
{
	int j, j1, k, k1, l, m, m2;
	float xr, xi, yr, yi;

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


void bitrv2conj(int n, int *ip, float *a)
{
	int j, j1, k, k1, l, m, m2;
	float xr, xi, yr, yi;

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


void cftfsub(int n, float *a, float *w)
{
	int j, j1, j2, j3, l;
	float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

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


void cftbsub(int n, float *a, float *w)
{
	int j, j1, j2, j3, l;
	float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

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


void cft1st(int n, float *a, float *w)
{
	int j, k1, k2;
	float wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
	float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

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


void cftmdl(int n, int l, float *a, float *w)
{
	int j, j1, j2, j3, k, k1, k2, m, m2;
	float wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
	float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

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


void rftfsub(int n, float *a, int nc, float *c)
{
	int j, k, kk, ks, m;
	float 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, float *a, int nc, float *c)
{
	int j, k, kk, ks, m;
	float wkr, wki, xr, xi, yr, yi;

	a[1] = -a[1];
	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[j + 1];
		a[k] += yr;
		a[k + 1] = yi - a[k + 1];
	}
	a[m + 1] = -a[m + 1];
}


void dctsub(int n, float *a, int nc, float *c)
{
	int j, k, kk, ks, m;
	float 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, float *a, int nc, float *c)
{
	int j, k, kk, ks, m;
	float 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];
}

}
