//$ nobt
//$ nocpp

/**
 * @file fft4g.h
 *
 * @brief Wrapper class for Takuya OOURA's FFT functions.
 *
 * Functions from the FFT package by: Copyright(C) 1996-2001 Takuya OOURA
 * http://www.kurims.kyoto-u.ac.jp/~ooura/fft.html
 *
 * Modified and used with permission granted by the license.
 *
 * Here, the original "fft4g.c" file was wrapped into the "ooura_fft" class.
 */

#ifndef R8B_FFT4G_INCLUDED
#define R8B_FFT4G_INCLUDED

/*
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, FPType *, int *, FPType *);
    void rdft(int, int, FPType *, int *, FPType *);
    void ddct(int, int, FPType *, int *, FPType *);
    void ddst(int, int, FPType *, int *, FPType *);
    void dfct(int, FPType *, FPType *, int *, FPType *);
    void dfst(int, FPType *, FPType *, int *, FPType *);


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

namespace r8b
{

	/**
	 * @brief A wrapper class around Takuya OOURA's FFT functions.
	 *
	 * A wrapper class around fft4g.c file's FFT functions by Takuya OOURA.
	 * Provides static private functions for use by the CDSPRealFFT class.
	 */

	class ooura_fft
	{
		friend class CDSPRealFFT;

		typedef double FPType;

		static void cdft(int n, int isgn, FPType* a, int* ip, FPType* 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); }
		}

		static void rdft(int n, int isgn, FPType* a, int* ip, FPType* w)
		{
			int nw = ip[0];
			if (n > (nw << 2))
			{
				nw = n >> 2;
				makewt(nw, ip, w);
			}
			int 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); }
				double 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); }
			}
		}

		static void ddct(int n, int isgn, FPType* a, int* ip, FPType* w)
		{
			int j;
			double xr;

			int nw = ip[0];
			if (n > (nw << 2))
			{
				nw = n >> 2;
				makewt(nw, ip, w);
			}
			int 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;
			}
		}

		static void ddst(int n, int isgn, FPType* a, int* ip, FPType* w)
		{
			int j;
			double xr;

			int nw = ip[0];
			if (n > (nw << 2))
			{
				nw = n >> 2;
				makewt(nw, ip, w);
			}
			int 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;
			}
		}

		static void dfct(int n, FPType* a, FPType* t, int* ip, FPType* w)
		{
			int j, k;

			int nw = ip[0];
			if (n > (nw << 3))
			{
				nw = n >> 3;
				makewt(nw, ip, w);
			}
			int nc = ip[1];
			if (n > (nc << 1))
			{
				nc = n >> 1;
				makect(nc, ip, w + nw);
			}
			int m     = n >> 1;
			double yi = a[m];
			double xi = a[0] + a[n];
			a[0] -= a[n];
			t[0] = xi - yi;
			t[m] = xi + yi;
			if (n > 2)
			{
				int mh = m >> 1;
				for (j = 1; j < mh; ++j)
				{
					k         = m - j;
					double xr = a[j] - a[n - j];
					xi        = a[j] + a[n - j];
					double 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];
				}
				int 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];
			}
		}

		static void dfst(int n, FPType* a, FPType* t, int* ip, FPType* w)
		{
			int j, k;

			int nw = ip[0];
			if (n > (nw << 3))
			{
				nw = n >> 3;
				makewt(nw, ip, w);
			}
			int nc = ip[1];
			if (n > (nc << 1))
			{
				nc = n >> 1;
				makect(nc, ip, w + nw);
			}
			if (n > 2)
			{
				int m  = n >> 1;
				int mh = m >> 1;
				for (j = 1; j < mh; ++j)
				{
					k         = m - j;
					double xr = a[j] + a[n - j];
					double xi = a[j] - a[n - j];
					double yr = a[k] + a[n - k];
					double 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];
				}
				int 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 -------- */

		static void makewt(int nw, int* ip, FPType* w)
		{
			ip[0] = nw;
			ip[1] = 1;
			if (nw > 2)
			{
				int nwh      = nw >> 1;
				double 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 (int j = 2; j < nwh; j += 2)
					{
						double x      = cos(delta * j);
						double 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);
				}
			}
		}

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

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

		static void bitrv2(int n, int* ip, FPType* a)
		{
			int j, j1, k, k1;
			double xr, xi, yr, yi;

			ip[0] = 0;
			int l = n;
			int m = 1;
			while ((m << 3) < l)
			{
				l >>= 1;
				for (j = 0; j < m; ++j) { ip[m + j] = ip[j] + l; }
				m <<= 1;
			}
			int 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;
					}
				}
			}
		}

		static void bitrv2conj(int n, int* ip, FPType* a)
		{
			int j, j1, k, k1;
			double xr, xi, yr, yi;

			ip[0] = 0;
			int l = n;
			int m = 1;
			while ((m << 3) < l)
			{
				l >>= 1;
				for (j = 0; j < m; ++j) { ip[m + j] = ip[j] + l; }
				m <<= 1;
			}
			int 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];
				}
			}
		}

		static void cftfsub(int n, FPType* a, const FPType* w)
		{
			int j, j1;
			double x0r, x0i;

			int 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;
					int j2     = j1 + l;
					int j3     = j2 + l;
					x0r        = a[j] + a[j1];
					x0i        = a[j + 1] + a[j1 + 1];
					double x1r = a[j] - a[j1];
					double x1i = a[j + 1] - a[j1 + 1];
					double x2r = a[j2] + a[j3];
					double x2i = a[j2 + 1] + a[j3 + 1];
					double x3r = a[j2] - a[j3];
					double 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;
				}
			}
		}

		static void cftbsub(int n, FPType* a, const FPType* w)
		{
			int j, j1;
			double x0r, x0i;

			int 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;
					int j2     = j1 + l;
					int j3     = j2 + l;
					x0r        = a[j] + a[j1];
					x0i        = -a[j + 1] - a[j1 + 1];
					double x1r = a[j] - a[j1];
					double x1i = -a[j + 1] + a[j1 + 1];
					double x2r = a[j2] + a[j3];
					double x2i = a[j2 + 1] + a[j3 + 1];
					double x3r = a[j2] - a[j3];
					double 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;
				}
			}
		}

		static void cft1st(int n, FPType* a, const FPType* w)
		{
			double x0r  = a[0] + a[2];
			double x0i  = a[1] + a[3];
			double x1r  = a[0] - a[2];
			double x1i  = a[1] - a[3];
			double x2r  = a[4] + a[6];
			double x2i  = a[5] + a[7];
			double x3r  = a[4] - a[6];
			double 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;
			double 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);
			int k1      = 0;
			for (int j = 16; j < n; j += 16)
			{
				k1 += 2;
				int k2      = 2 * k1;
				double wk2r = w[k1];
				double wk2i = w[k1 + 1];
				wk1r        = w[k2];
				double wk1i = w[k2 + 1];
				double wk3r = wk1r - 2 * wk2i * wk1i;
				double 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;
			}
		}

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

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

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

		static void rftbsub(int n, FPType* a, int nc, const FPType* c)
		{
			a[1]   = -a[1];
			int m  = n >> 1;
			int ks = 2 * nc / m;
			int kk = 0;
			for (int j = 2; j < m; j += 2)
			{
				int k = n - j;
				kk += ks;
				double wkr = 0.5 - c[nc - kk];
				double wki = c[kk];
				double xr  = a[j] - a[k];
				double xi  = a[j + 1] + a[k + 1];
				double yr  = wkr * xr + wki * xi;
				double 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];
		}

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

		static void dstsub(int n, FPType* a, int nc, const FPType* c)
		{
			int m  = n >> 1;
			int ks = nc / n;
			int kk = 0;
			for (int j = 1; j < m; ++j)
			{
				int k = n - j;
				kk += ks;
				double wkr = c[kk] - c[nc - kk];
				double wki = c[kk] + c[nc - kk];
				double xr  = wki * a[k] - wkr * a[j];
				a[k]       = wkr * a[k] + wki * a[j];
				a[j]       = xr;
			}
			a[m] *= c[0];
		}
	};
} // namespace r8b

#endif // R8B_FFT4G_INCLUDED