Fourier.cs

using System;
using System.Threading;

namespace DSPUtil
{
    // based on .NET and unmanaged tests, Richard Grimes 2005 (http://www.grimes.demon.co.uk/dotnet/man_unman.htm)

    // The original code is the fft package by Takuya OOURA
    // from http://momonga.t.u-tokyo.ac.jp/~ooura/fft.html

    public unsafe class Fourier
    {
        // Constants
        const double M_PI_2 = 1.570796326794896619231321691639751442098584699687;
        // cos(M_PI_2*0.5000)
        const double WR5000 = 0.707106781186547524400844362104849039284835937688;
        // cos(M_PI_2*0.2500)
        const double WR2500 = 0.923879532511286756128183189396788286822416625863;
        // sin(M_PI_2*0.2500)
        const double WI2500 = 0.382683432365089771728459984030398866761344562485;
        // cos(M_PI_2*0.1250)
        const double WR1250 = 0.980785280403230449126182236134239036973933730893;
        // sin(M_PI_2*0.1250)
        const double WI1250 = 0.195090322016128267848284868477022240927691617751;
        // cos(M_PI_2*0.3750)
        const double WR3750 = 0.831469612302545237078788377617905756738560811987;
        // sin(M_PI_2*0.3750)
        const double WI3750 = 0.555570233019602224742830813948532874374937190754;

        // control of the CDFT's speed & tolerance
        const int CDFT_LOOP_DIV = 32;
        // control of the RDFT's speed & tolerance
        const int RDFT_LOOP_DIV = 64;
        // control of the DCT,DST's speed & tolerance
        const int DCST_LOOP_DIV = 64;

        const int CDFT_THREADS_BEGIN_N = 8192;
        const int CDFT_4THREADS_BEGIN_N = 131072;

        #region inguz extensions

        /// <summary>
        /// In-place FFT of a complex buffer
        /// </summary>
        /// <param name="n"></param>
        /// <param name="data"></param>
        public static void FFT(int n, Complex[] data)
        {
            fixed (Complex* cdata = data)
            {
                double* rawdata = (double*)cdata;
                cfft(2 * n, rawdata);
            }
        }

        /// <summary>
        /// In-place IFFT of a complex buffer
        /// </summary>
        /// <param name="n"></param>
        /// <param name="data"></param>
        /// <param name="gain"></param>
        public static void IFFT(int n, Complex[] data, double gain)
        {
            fixed (Complex* cdata = data)
            {
                double* rawdata = (double*)cdata;
                cifft(n*2, rawdata, gain);
            }
        }

        /// <summary>
        /// In-place IFFT of a complex buffer
        /// </summary>
        /// <param name="n"></param>
        /// <param name="data"></param>
        public static void IFFT(int n, Complex[] data)
        {
            IFFT(n, data, 1.0);
        }

        public static void Convolve(int n, Complex[] impulse, Complex[] data, bool divide)
        {
            fixed (Complex* cout = data, cimpulse = impulse)
            {
                double* a = (double*)cout;
                double* i = (double*)cimpulse;

                int j, k;
                double gem, div;
                int n2 = n << 1;

                // FFT this data chunk in place
                cdft(n2, 1, a);

                if (divide)
                {
                    // Complex multiply in-place output / impulseFFT
                    for (j = 0, k = 1; j < n2; j += 2, k += 2)
                    {
                        div = i[j] * i[j] + i[k] * i[k];
                        if (div == 0)
                        {
                            a[j] = 0;
                            a[k] = 0;
                        }
                        else
                        {
                            gem = (a[j] * i[j] + a[k] * i[k]) / div;
                            a[k] = (a[k] * i[j] - a[j] * i[k]) / div;
                            a[j] = gem;
                        }
                    }
                }
                else
                {
                    // Complex multiply in-place output * impulseFFT
                    for (j = 0, k = 1; j < n2; j += 2, k += 2)
                    {
                        gem = a[j] * i[j] - a[k] * i[k];
                        a[k] = a[j] * i[k] + a[k] * i[j];
                        a[j] = gem;
                    }
                }

                // IFFT to get the convolved output
                cifft(n2, a, 1.0);
            }
        }

        public static void ConvolvePart(int n, int p, int P, Complex[][] impulse, Complex[] src, Complex[][] accum, Complex[] output, bool divide)
        {
            int n2 = n << 1;

            fixed (Complex* csrc = src, cout = output)
            {
                // FFT this data chunk in place
                double* dd = (double*)csrc;
                cfft(n2, dd);

                // Multiply frequency-domain data * each impulseFFT
                // accumulating into accum[] arrays
                if (divide)
                {
                    for (int impulToUse = 0; impulToUse < P; impulToUse++)
                    {
                        int accumToUse = (p + impulToUse) % P;
                        bool accumulate = (impulToUse + 1 != P);
                        // Trace.WriteLine("partition {0}, impulse {1} to accumulator {2}", p, impulToUse, accumToUse);
                        fixed (Complex* cimpulse = impulse[impulToUse], caccum = accum[accumToUse])
                        {
                            carraydiv(n2, accumulate, (double*)cimpulse, dd, (double*)caccum);
                        }
                    }
                }
                else
                {
                    for (int impulToUse = 0; impulToUse < P; impulToUse++)
                    {
                        int accumToUse = (p + impulToUse) % P;
                        bool accumulate = (impulToUse + 1 != P);
                        // Trace.WriteLine("partition {0}, impulse {1} to accumulator {2}", p, impulToUse, accumToUse);
                        fixed (Complex* cimpulse = impulse[impulToUse], caccum = accum[accumToUse])
                        {
                            double* id = (double*)cimpulse;
                            double* ad = (double*)caccum;
                            if (accumulate)
                            {
                                for (int j = 0, k = 1; j < n2; j += 2, k += 2)
                                {
                                    ad[j] += id[j] * dd[j] - id[k] * dd[k];
                                    ad[k] += id[k] * dd[j] + id[j] * dd[k];
                                }
                            }
                            else
                            {
                                for (int j = 0, k = 1; j < n2; j += 2, k += 2)
                                {
                                    ad[j] = id[j] * dd[j] - id[k] * dd[k];
                                    ad[k] = id[k] * dd[j] + id[j] * dd[k];
                                }
                            }
                        }
                    }
                }

                // Copy accumulator[p] to output then IFFT get the convolved result
                Array.Copy(accum[p], output, n);
                cifft(n2, (double*)cout, 1.0);
            }
        }


        static void cfft(int n, double* a)
        {
            cdft(n, 1, a);
        }

        static void cifft(int n, double* a, double gain)
        {
            double inv = gain / (n>>1);
            cdft(n, -1, a);
            for (int j = 0; j < n; j++)
            {
                a[j] *= inv;
            }
        }

        static void carraydiv(int n, bool accumulate, double* a, double* b, double* o)
        {
            double re, im, div;

            // Complex divide a / b
            // Put the result in o; if accumulate, add result to o
            //            double div = c2.Re * c2.Re + c2.Im * c2.Im;
            //            return new Complex((c1.Re * c2.Re + c1.Im * c2.Im) / div,  (c1.Im * c2.Re - c1.Re * c2.Im) / div);

            for (int j = 0; j < n; j += 2)
            {
                div = b[j] * b[j] + b[j + 1] * b[j + 1];
                if (div == 0)
                {
                    if (!accumulate)
                    {
                        o[j] = 0;
                        o[j + 1] = 0;
                    }
                }
                else
                {
                    re = a[j] * b[j] + a[j + 1] * b[j + 1];
                    im = a[j + 1] * b[j] - a[j] * b[j + 1];
                    if (accumulate)
                    {
                        o[j] += re / div;
                        o[j + 1] += im / div;
                    }
                    else
                    {
                        o[j] = re / div;
                        o[j + 1] = im / div;
                    }
                }
            }
        }

        #endregion


        static void cdft(int n, int isgn, double* a)
        {
            if (isgn >= 0)
            {
                cftfsub(n, a);
            }
            else
            {
                cftbsub(n, a);
            }
        }

/*
        static void rdft(int n, int isgn, double* a)
        {
            double xi;

            if (isgn >= 0)
            {
                if (n > 4)
                {
                    cftfsub(n, a);
                    rftfsub(n, a);
                }
                else if (n == 4)
                {
                    cftfsub(n, a);
                }
                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);
                    cftbsub(n, a);
                }
                else if (n == 4)
                {
                    cftbsub(n, a);
                }
            }
        }
*/
/*
        static void ddct(int n, int isgn, double* a)
        {
            int j;
            double xr;

            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);
                    cftbsub(n, a);
                }
                else if (n == 4)
                {
                    cftbsub(n, a);
                }
            }
            if (n > 4)
            {
                dctsub(n, a);
            }
            else
            {
                dctsub4(n, a);
            }
            if (isgn >= 0)
            {
                if (n > 4)
                {
                    cftfsub(n, a);
                    rftfsub(n, a);
                }
                else if (n == 4)
                {
                    cftfsub(n, a);
                }
                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, double* a)
        {
            int j;
            double xr;

            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);
                    cftbsub(n, a);
                }
                else if (n == 4)
                {
                    cftbsub(n, a);
                }
            }
            if (n > 4)
            {
                dstsub(n, a);
            }
            else
            {
                dstsub4(n, a);
            }
            if (isgn >= 0)
            {
                if (n > 4)
                {
                    cftfsub(n, a);
                    rftfsub(n, a);
                }
                else if (n == 4)
                {
                    cftfsub(n, a);
                }
                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, double* a)
        {
            int j, k, m, mh;
            double xr, xi, yr, yi, an;

            m = n >> 1;
            for (j = 0; j < m; j++)
            {
                k = n - j;
                xr = a[j] + a[k];
                a[j] -= a[k];
                a[k] = xr;
            }
            an = a[n];
            while (m >= 2)
            {
                ddct(m, 1, a);
                if (m > 2)
                {
                    bitrv1(m, a);
                }
                mh = m >> 1;
                xi = a[m];
                a[m] = a[0];
                a[0] = an - xi;
                an += xi;
                for (j = 1; j < mh; j++)
                {
                    k = m - j;
                    xr = a[m + k];
                    xi = a[m + j];
                    yr = a[j];
                    yi = a[k];
                    a[m + j] = yr;
                    a[m + k] = yi;
                    a[j] = xr - xi;
                    a[k] = xr + xi;
                }
                xr = a[mh];
                a[mh] = a[m + mh];
                a[m + mh] = xr;
                m = mh;
            }
            xi = a[1];
            a[1] = a[0];
            a[0] = an + xi;
            a[n] = an - xi;
            if (n > 2)
            {
                bitrv1(n, a);
            }
        }
*/
/*
        static void dfst(int n, double* a)
        {
            int j, k, m, mh;
            double xr, xi, yr, yi;

            m = n >> 1;
            for (j = 1; j < m; j++)
            {
                k = n - j;
                xr = a[j] - a[k];
                a[j] += a[k];
                a[k] = xr;
            }
            a[0] = a[m];
            while (m >= 2)
            {
                ddst(m, 1, a);
                if (m > 2)
                {
                    bitrv1(m, a);
                }
                mh = m >> 1;
                for (j = 1; j < mh; j++)
                {
                    k = m - j;
                    xr = a[m + k];
                    xi = a[m + j];
                    yr = a[j];
                    yi = a[k];
                    a[m + j] = yr;
                    a[m + k] = yi;
                    a[j] = xr + xi;
                    a[k] = xr - xi;
                }
                a[m] = a[0];
                a[0] = a[m + mh];
                a[m + mh] = a[mh];
                m = mh;
            }
            a[1] = a[0];
            a[0] = 0;
            if (n > 2)
            {
                bitrv1(n, a);
            }
        }
*/

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


        static void cftfsub(int n, double* a)
        {
            if (n > 8)
            {
                if (n > 32)
                {
                    cftmdl1(n, a);
                    if (n > CDFT_THREADS_BEGIN_N)
                    {
                        cftrec4_th(n, a);
                    }
                    else if (n > 512)
                    {
                        cftrec4(n, a);
                    }
                    else if (n > 128)
                    {
                        cftleaf(n, 1, a);
                    }
                    else
                    {
                        cftfx41(n, a);
                    }
                    bitrv2(n, a);
                }
                else if (n == 32)
                {
                    cftf161(a);
                    bitrv216(a);
                }
                else
                {
                    cftf081(a);
                    bitrv208(a);
                }
            }
            else if (n == 8)
            {
                cftf040(a);
            }
            else if (n == 4)
            {
                cftx020(a);
            }
        }


        static void cftbsub(int n, double* a)
        {
            if (n > 8)
            {
                if (n > 32)
                {
                    cftb1st(n, a);
                    if (n > CDFT_THREADS_BEGIN_N)
                    {
                        cftrec4_th(n, a);
                    }
                    else if (n > 512)
                    {
                        cftrec4(n, a);
                    }
                    else if (n > 128)
                    {
                        cftleaf(n, 1, a);
                    }
                    else
                    {
                        cftfx41(n, a);
                    }
                    bitrv2conj(n, a);
                }
                else if (n == 32)
                {
                    cftf161(a);
                    bitrv216neg(a);
                }
                else
                {
                    cftf081(a);
                    bitrv208neg(a);
                }
            }
            else if (n == 8)
            {
                cftb040(a);
            }
            else if (n == 4)
            {
                cftx020(a);
            }
        }


        static void bitrv2(int n, double* a)
        {
            int j0, k0, j1, k1, l, m, i, j, k, nh;
            double xr, xi, yr, yi;

            m = 4;
            for (l = n >> 2; l > 8; l >>= 2)
            {
                m <<= 1;
            }
            nh = n >> 1;
            if (l == 8)
            {
                j0 = 0;
                for (k0 = 0; k0 < m; k0 += 4)
                {
                    k = k0;
                    for (j = j0; j < j0 + k0; j += 4)
                    {
                        xr = a[j];
                        xi = a[j + 1];
                        yr = a[k];
                        yi = a[k + 1];
                        a[j] = yr;
                        a[j + 1] = yi;
                        a[k] = xr;
                        a[k + 1] = xi;
                        j1 = j + m;
                        k1 = k + 2 * m;
                        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 += m;
                        k1 -= m;
                        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 += m;
                        k1 += 2 * m;
                        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 -= m;
                        k1 -= 2 * m;
                        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 -= m;
                        k1 += m;
                        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 -= m;
                        k1 -= 2 * m;
                        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 += m;
                        k1 += 2 * m;
                        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 += m;
                        k1 -= m;
                        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 += m;
                        k1 += 2 * m;
                        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 -= m;
                        k1 -= 2 * m;
                        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 -= m;
                        k1 += m;
                        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 -= m;
                        k1 -= 2 * m;
                        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;
                        for (i = nh >> 1; i > (k ^= i); i >>= 1) ;
                    }
                    k1 = j0 + k0;
                    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 += m;
                    k1 += 2 * m;
                    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 += m;
                    k1 -= m;
                    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 - m;
                    k1 += 2 * m - 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;
                    for (i = nh >> 1; i > (j0 ^= i); i >>= 1) ;
                }
            }
            else
            {
                j0 = 0;
                for (k0 = 0; k0 < m; k0 += 4)
                {
                    k = k0;
                    for (j = j0; j < j0 + k0; j += 4)
                    {
                        xr = a[j];
                        xi = a[j + 1];
                        yr = a[k];
                        yi = a[k + 1];
                        a[j] = yr;
                        a[j + 1] = yi;
                        a[k] = xr;
                        a[k + 1] = xi;
                        j1 = j + m;
                        k1 = k + m;
                        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 -= m;
                        k1 -= m;
                        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 += m;
                        k1 += m;
                        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 -= m;
                        k1 -= m;
                        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;
                        for (i = nh >> 1; i > (k ^= i); i >>= 1) ;
                    }
                    k1 = j0 + k0;
                    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 += m;
                    k1 += m;
                    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;
                    for (i = nh >> 1; i > (j0 ^= i); i >>= 1) ;
                }
            }
        }


        static void bitrv2conj(int n, double* a)
        {
            int j0, k0, j1, k1, l, m, i, j, k, nh;
            double xr, xi, yr, yi;

            m = 4;
            for (l = n >> 2; l > 8; l >>= 2)
            {
                m <<= 1;
            }
            nh = n >> 1;
            if (l == 8)
            {
                j0 = 0;
                for (k0 = 0; k0 < m; k0 += 4)
                {
                    k = k0;
                    for (j = j0; j < j0 + k0; j += 4)
                    {
                        xr = a[j];
                        xi = -a[j + 1];
                        yr = a[k];
                        yi = -a[k + 1];
                        a[j] = yr;
                        a[j + 1] = yi;
                        a[k] = xr;
                        a[k + 1] = xi;
                        j1 = j + m;
                        k1 = k + 2 * m;
                        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 += m;
                        k1 -= m;
                        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 += m;
                        k1 += 2 * m;
                        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 -= m;
                        k1 -= 2 * m;
                        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 -= m;
                        k1 += m;
                        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 -= m;
                        k1 -= 2 * m;
                        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 += m;
                        k1 += 2 * m;
                        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 += m;
                        k1 -= m;
                        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 += m;
                        k1 += 2 * m;
                        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 -= m;
                        k1 -= 2 * m;
                        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 -= m;
                        k1 += m;
                        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 -= m;
                        k1 -= 2 * m;
                        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;
                        for (i = nh >> 1; i > (k ^= i); i >>= 1) ;
                    }
                    k1 = j0 + k0;
                    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 += m;
                    k1 += 2 * m;
                    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 += m;
                    k1 -= m;
                    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 - m;
                    k1 += 2 * m - 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];
                    for (i = nh >> 1; i > (j0 ^= i); i >>= 1) ;
                }
            }
            else
            {
                j0 = 0;
                for (k0 = 0; k0 < m; k0 += 4)
                {
                    k = k0;
                    for (j = j0; j < j0 + k0; j += 4)
                    {
                        xr = a[j];
                        xi = -a[j + 1];
                        yr = a[k];
                        yi = -a[k + 1];
                        a[j] = yr;
                        a[j + 1] = yi;
                        a[k] = xr;
                        a[k + 1] = xi;
                        j1 = j + m;
                        k1 = k + m;
                        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 -= m;
                        k1 -= m;
                        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 += m;
                        k1 += m;
                        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 -= m;
                        k1 -= m;
                        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;
                        for (i = nh >> 1; i > (k ^= i); i >>= 1) ;
                    }
                    k1 = j0 + k0;
                    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 += m;
                    k1 += m;
                    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];
                    for (i = nh >> 1; i > (j0 ^= i); i >>= 1) ;
                }
            }
        }


        static 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;
        }


        static 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;
        }


        static 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;
        }


        static 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;
        }

/*
        static void bitrv1(int n, double* a)
        {
            int j0, k0, j1, k1, l, m, i, j, k, nh;
            double x;

            nh = n >> 1;
            x = a[1];
            a[1] = a[nh];
            a[nh] = x;
            m = 2;
            for (l = n >> 2; l > 2; l >>= 2)
            {
                m <<= 1;
            }
            if (l == 2)
            {
                j1 = m + 1;
                k1 = m + nh;
                x = a[j1];
                a[j1] = a[k1];
                a[k1] = x;
                j0 = 0;
                for (k0 = 2; k0 < m; k0 += 2)
                {
                    for (i = nh >> 1; i > (j0 ^= i); i >>= 1) ;
                    k = k0;
                    for (j = j0; j < j0 + k0; j += 2)
                    {
                        x = a[j];
                        a[j] = a[k];
                        a[k] = x;
                        j1 = j + m;
                        k1 = k + m;
                        x = a[j1];
                        a[j1] = a[k1];
                        a[k1] = x;
                        j1 += nh;
                        k1++;
                        x = a[j1];
                        a[j1] = a[k1];
                        a[k1] = x;
                        j1 -= m;
                        k1 -= m;
                        x = a[j1];
                        a[j1] = a[k1];
                        a[k1] = x;
                        j1++;
                        k1 += nh;
                        x = a[j1];
                        a[j1] = a[k1];
                        a[k1] = x;
                        j1 += m;
                        k1 += m;
                        x = a[j1];
                        a[j1] = a[k1];
                        a[k1] = x;
                        j1 -= nh;
                        k1--;
                        x = a[j1];
                        a[j1] = a[k1];
                        a[k1] = x;
                        j1 -= m;
                        k1 -= m;
                        x = a[j1];
                        a[j1] = a[k1];
                        a[k1] = x;
                        for (i = nh >> 1; i > (k ^= i); i >>= 1) ;
                    }
                    k1 = j0 + k0;
                    j1 = k1 + 1;
                    k1 += nh;
                    x = a[j1];
                    a[j1] = a[k1];
                    a[k1] = x;
                    j1 += m;
                    k1 += m;
                    x = a[j1];
                    a[j1] = a[k1];
                    a[k1] = x;
                }
            }
            else
            {
                j0 = 0;
                for (k0 = 2; k0 < m; k0 += 2)
                {
                    for (i = nh >> 1; i > (j0 ^= i); i >>= 1) ;
                    k = k0;
                    for (j = j0; j < j0 + k0; j += 2)
                    {
                        x = a[j];
                        a[j] = a[k];
                        a[k] = x;
                        j1 = j + nh;
                        k1 = k + 1;
                        x = a[j1];
                        a[j1] = a[k1];
                        a[k1] = x;
                        j1++;
                        k1 += nh;
                        x = a[j1];
                        a[j1] = a[k1];
                        a[k1] = x;
                        j1 -= nh;
                        k1--;
                        x = a[j1];
                        a[j1] = a[k1];
                        a[k1] = x;
                        for (i = nh >> 1; i > (k ^= i); i >>= 1) ;
                    }
                    k1 = j0 + k0;
                    j1 = k1 + 1;
                    k1 += nh;
                    x = a[j1];
                    a[j1] = a[k1];
                    a[k1] = x;
                }
            }
        }
*/

        static void cftb1st(int n, double* a)
        {
            int i, i0, j, j0, j1, j2, j3, m, mh;
            double ew, w1r, w1i, wk1r, wk1i, wk3r, wk3i,
                wd1r, wd1i, wd3r, wd3i, ss1, ss3;
            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;
            wd1r = 1;
            wd1i = 0;
            wd3r = 1;
            wd3i = 0;
            ew = M_PI_2 / m;
            w1r = Math.Cos(2 * ew);
            w1i = Math.Sin(2 * ew);
            wk1r = w1r;
            wk1i = w1i;
            ss1 = 2 * w1i;
            wk3i = 2 * ss1 * wk1r;
            wk3r = wk1r - wk3i * wk1i;
            wk3i = wk1i - wk3i * wk1r;
            ss3 = 2 * wk3i;
            i = 0;
            for (; ; )
            {
                i0 = i + 4 * CDFT_LOOP_DIV;
                if (i0 > mh - 4)
                {
                    i0 = mh - 4;
                }
                for (j = i + 2; j < i0; j += 4)
                {
                    wd1r -= ss1 * wk1i;
                    wd1i += ss1 * wk1r;
                    wd3r -= ss3 * wk3i;
                    wd3i += ss3 * wk3r;
                    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;
                    x0r = a[j + 2] + a[j2 + 2];
                    x0i = -a[j + 3] - a[j2 + 3];
                    x1r = a[j + 2] - a[j2 + 2];
                    x1i = -a[j + 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[j + 2] = x0r + x2r;
                    a[j + 3] = x0i - x2i;
                    a[j1 + 2] = x0r - x2r;
                    a[j1 + 3] = x0i + x2i;
                    x0r = x1r + x3i;
                    x0i = x1i + x3r;
                    a[j2 + 2] = wd1r * x0r - wd1i * x0i;
                    a[j2 + 3] = wd1r * x0i + wd1i * x0r;
                    x0r = x1r - x3i;
                    x0i = x1i - x3r;
                    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];
                    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;
                    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] = wd1i * x0r - wd1r * x0i;
                    a[j2 - 1] = wd1i * x0i + wd1r * x0r;
                    x0r = x1r - x3i;
                    x0i = x1i - x3r;
                    a[j3 - 2] = wd3i * x0r + wd3r * x0i;
                    a[j3 - 1] = wd3i * x0i - wd3r * x0r;
                    wk1r -= ss1 * wd1i;
                    wk1i += ss1 * wd1r;
                    wk3r -= ss3 * wd3i;
                    wk3i += ss3 * wd3r;
                }
                if (i0 == mh - 4)
                {
                    break;
                }
                wd1r = Math.Cos(ew * i0);
                wd1i = Math.Sin(ew * i0);
                wd3i = 4 * wd1i * wd1r;
                wd3r = wd1r - wd3i * wd1i;
                wd3i = wd1i - wd3i * wd1r;
                wk1r = w1r * wd1r - w1i * wd1i;
                wk1i = w1r * wd1i + w1i * wd1r;
                wk3i = 4 * wk1i * wk1r;
                wk3r = wk1r - wk3i * wk1i;
                wk3i = wk1i - wk3i * wk1r;
                i = i0;
            }
            wd1r = WR5000;
            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] = wd1r * (x0r - x0i);
            a[j2 + 1] = wd1r * (x0i + x0r);
            x0r = x1r - x3i;
            x0i = x1i - x3r;
            a[j3] = -wd1r * (x0r + x0i);
            a[j3 + 1] = -wd1r * (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;
        }


        struct cdft_arg_st
        {
            public int n0;
            public int n;
            public double* a;
            public ManualResetEvent e;
        };

        static void cftrec4_th(int n, double* a)
        {
            int i, idiv4, m, nthread;
//          Thread[] th = new Thread[4];
            cdft_arg_st[] ag = new cdft_arg_st[4];

            nthread = 2;
            idiv4 = 0;
            m = n >> 1;
            if (n > CDFT_4THREADS_BEGIN_N)
            {
                nthread = 4;
                idiv4 = 1;
                m >>= 1;
            }
            ManualResetEvent[] ev = new ManualResetEvent[nthread];

            for (i = 0; i < nthread; i++)
            {
                ev[i] = new ManualResetEvent(false);
                ag[i].n0 = n;
                ag[i].n = m;
                ag[i].a = &a[i * m];
                ag[i].e = ev[i]; 
                if (i != idiv4)
                {
                    ThreadPool.QueueUserWorkItem(cftrec1_th, ag[i]);
                }
                else
                {
                    ThreadPool.QueueUserWorkItem(cftrec2_th, ag[i]);
                }
            }
            WaitHandle.WaitAll(ev);
        }


        public static void cftrec1_th(object p)
        {
            int isplt, j, k, m, n, n0;
            double* a;

            n0 = ((cdft_arg_st)p).n0;
            n = ((cdft_arg_st)p).n;
            a = ((cdft_arg_st)p).a;
            m = n0;
            while (m > 512)
            {
                m >>= 2;
                cftmdl1(m, &a[n - m]);
            }
            cftleaf(m, 1, &a[n - m]);
            k = 0;
            for (j = n - m; j > 0; j -= m)
            {
                k++;
                isplt = cfttree(m, j, k, a);
                cftleaf(m, isplt, &a[j - m]);
            }
            ((cdft_arg_st)p).e.Set();
        }


        public static void cftrec2_th(object p)
        {
            int isplt, j, k, m, n, n0;
            double* a;

            n0 = ((cdft_arg_st)p).n0;
            n = ((cdft_arg_st)p).n;
            a = ((cdft_arg_st)p).a;
            k = 1;
            m = n0;
            while (m > 512)
            {
                m >>= 2;
                k <<= 2;
                cftmdl2(m, &a[n - m]);
            }
            cftleaf(m, 0, &a[n - m]);
            k >>= 1;
            for (j = n - m; j > 0; j -= m)
            {
                k++;
                isplt = cfttree(m, j, k, a);
                cftleaf(m, isplt, &a[j - m]);
            }
            ((cdft_arg_st)p).e.Set();
        }

        static void cftrec4(int n, double* a)
        {
            int isplt, j, k, m;

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


        static int cfttree(int n, int j, int k, double* a)
        {
            int i, isplt, m;

            if ((k & 3) != 0)
            {
                isplt = k & 1;
                if (isplt != 0)
                {
                    cftmdl1(n, &a[j - n]);
                }
                else
                {
                    cftmdl2(n, &a[j - 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]);
                        m >>= 2;
                    }
                }
                else
                {
                    while (m > 128)
                    {
                        cftmdl2(m, &a[j - m]);
                        m >>= 2;
                    }
                }
            }
            return isplt;
        }


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


        static void cftmdl1(int n, double* a)
        {
            int i, i0, j, j0, j1, j2, j3, m, mh;
            double ew, w1r, w1i, wk1r, wk1i, wk3r, wk3i,
                wd1r, wd1i, wd3r, wd3i, ss1, ss3;
            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;
            wd1r = 1;
            wd1i = 0;
            wd3r = 1;
            wd3i = 0;
            ew = M_PI_2 / m;
            w1r = Math.Cos(2 * ew);
            w1i = Math.Sin(2 * ew);
            wk1r = w1r;
            wk1i = w1i;
            ss1 = 2 * w1i;
            wk3i = 2 * ss1 * wk1r;
            wk3r = wk1r - wk3i * wk1i;
            wk3i = wk1i - wk3i * wk1r;
            ss3 = 2 * wk3i;
            i = 0;
            for (; ; )
            {
                i0 = i + 4 * CDFT_LOOP_DIV;
                if (i0 > mh - 4)
                {
                    i0 = mh - 4;
                }
                for (j = i + 2; j < i0; j += 4)
                {
                    wd1r -= ss1 * wk1i;
                    wd1i += ss1 * wk1r;
                    wd3r -= ss3 * wk3i;
                    wd3i += ss3 * wk3r;
                    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;
                    x0r = a[j + 2] + a[j2 + 2];
                    x0i = a[j + 3] + a[j2 + 3];
                    x1r = a[j + 2] - a[j2 + 2];
                    x1i = a[j + 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[j + 2] = x0r + x2r;
                    a[j + 3] = x0i + x2i;
                    a[j1 + 2] = x0r - x2r;
                    a[j1 + 3] = x0i - x2i;
                    x0r = x1r - x3i;
                    x0i = x1i + x3r;
                    a[j2 + 2] = wd1r * x0r - wd1i * x0i;
                    a[j2 + 3] = wd1r * x0i + wd1i * x0r;
                    x0r = x1r + x3i;
                    x0i = x1i - x3r;
                    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];
                    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;
                    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] = wd1i * x0r - wd1r * x0i;
                    a[j2 - 1] = wd1i * x0i + wd1r * x0r;
                    x0r = x1r + x3i;
                    x0i = x1i - x3r;
                    a[j3 - 2] = wd3i * x0r + wd3r * x0i;
                    a[j3 - 1] = wd3i * x0i - wd3r * x0r;
                    wk1r -= ss1 * wd1i;
                    wk1i += ss1 * wd1r;
                    wk3r -= ss3 * wd3i;
                    wk3i += ss3 * wd3r;
                }
                if (i0 == mh - 4)
                {
                    break;
                }
                wd1r = Math.Cos(ew * i0);
                wd1i = Math.Sin(ew * i0);
                wd3i = 4 * wd1i * wd1r;
                wd3r = wd1r - wd3i * wd1i;
                wd3i = wd1i - wd3i * wd1r;
                wk1r = w1r * wd1r - w1i * wd1i;
                wk1i = w1r * wd1i + w1i * wd1r;
                wk3i = 4 * wk1i * wk1r;
                wk3r = wk1r - wk3i * wk1i;
                wk3i = wk1i - wk3i * wk1r;
                i = i0;
            }
            wd1r = WR5000;
            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] = wd1r * (x0r - x0i);
            a[j2 + 1] = wd1r * (x0i + x0r);
            x0r = x1r + x3i;
            x0i = x1i - x3r;
            a[j3] = -wd1r * (x0r + x0i);
            a[j3 + 1] = -wd1r * (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;
        }


        static void cftmdl2(int n, double* a)
        {
            int i, i0, j, j0, j1, j2, j3, m, mh;
            double ew, w1r, w1i, wn4r, wk1r, wk1i, wk3r, wk3i,
                wl1r, wl1i, wl3r, wl3i, wd1r, wd1i, wd3r, wd3i,
                we1r, we1i, we3r, we3i, ss1, ss3;
            double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i;

            mh = n >> 3;
            m = 2 * mh;
            wn4r = WR5000;
            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;
            wl1r = 1;
            wl1i = 0;
            wl3r = 1;
            wl3i = 0;
            we1r = wn4r;
            we1i = wn4r;
            we3r = -wn4r;
            we3i = -wn4r;
            ew = M_PI_2 / (2 * m);
            w1r = Math.Cos(2 * ew);
            w1i = Math.Sin(2 * ew);
            wk1r = w1r;
            wk1i = w1i;
            wd1r = wn4r * (w1r - w1i);
            wd1i = wn4r * (w1i + w1r);
            ss1 = 2 * w1i;
            wk3i = 2 * ss1 * wk1r;
            wk3r = wk1r - wk3i * wk1i;
            wk3i = wk1i - wk3i * wk1r;
            ss3 = 2 * wk3i;
            wd3r = -wn4r * (wk3r - wk3i);
            wd3i = -wn4r * (wk3i + wk3r);
            i = 0;
            for (; ; )
            {
                i0 = i + 4 * CDFT_LOOP_DIV;
                if (i0 > mh - 4)
                {
                    i0 = mh - 4;
                }
                for (j = i + 2; j < i0; j += 4)
                {
                    wl1r -= ss1 * wk1i;
                    wl1i += ss1 * wk1r;
                    wl3r -= ss3 * wk3i;
                    wl3i += ss3 * wk3r;
                    we1r -= ss1 * wd1i;
                    we1i += ss1 * wd1r;
                    we3r -= ss3 * wd3i;
                    we3i += ss3 * wd3r;
                    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;
                    x0r = a[j + 2] - a[j2 + 3];
                    x0i = a[j + 3] + a[j2 + 2];
                    x1r = a[j + 2] + a[j2 + 3];
                    x1i = a[j + 3] - a[j2 + 2];
                    x2r = a[j1 + 2] - a[j3 + 3];
                    x2i = a[j1 + 3] + a[j3 + 2];
                    x3r = a[j1 + 2] + a[j3 + 3];
                    x3i = a[j1 + 3] - a[j3 + 2];
                    y0r = wl1r * x0r - wl1i * x0i;
                    y0i = wl1r * x0i + wl1i * x0r;
                    y2r = we1r * x2r - we1i * x2i;
                    y2i = we1r * x2i + we1i * x2r;
                    a[j + 2] = y0r + y2r;
                    a[j + 3] = y0i + y2i;
                    a[j1 + 2] = y0r - y2r;
                    a[j1 + 3] = y0i - y2i;
                    y0r = wl3r * x1r + wl3i * x1i;
                    y0i = wl3r * x1i - wl3i * x1r;
                    y2r = we3r * x3r + we3i * x3i;
                    y2i = we3r * x3i - we3i * x3r;
                    a[j2 + 2] = y0r + y2r;
                    a[j2 + 3] = y0i + y2i;
                    a[j3 + 2] = y0r - y2r;
                    a[j3 + 3] = 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;
                    x0r = a[j0 - 2] - a[j2 - 1];
                    x0i = a[j0 - 1] + a[j2 - 2];
                    x1r = a[j0 - 2] + a[j2 - 1];
                    x1i = a[j0 - 1] - a[j2 - 2];
                    x2r = a[j1 - 2] - a[j3 - 1];
                    x2i = a[j1 - 1] + a[j3 - 2];
                    x3r = a[j1 - 2] + a[j3 - 1];
                    x3i = a[j1 - 1] - a[j3 - 2];
                    y0r = we1i * x0r - we1r * x0i;
                    y0i = we1i * x0i + we1r * x0r;
                    y2r = wl1i * x2r - wl1r * x2i;
                    y2i = wl1i * x2i + wl1r * x2r;
                    a[j0 - 2] = y0r + y2r;
                    a[j0 - 1] = y0i + y2i;
                    a[j1 - 2] = y0r - y2r;
                    a[j1 - 1] = y0i - y2i;
                    y0r = we3i * x1r + we3r * x1i;
                    y0i = we3i * x1i - we3r * x1r;
                    y2r = wl3i * x3r + wl3r * x3i;
                    y2i = wl3i * x3i - wl3r * x3r;
                    a[j2 - 2] = y0r + y2r;
                    a[j2 - 1] = y0i + y2i;
                    a[j3 - 2] = y0r - y2r;
                    a[j3 - 1] = y0i - y2i;
                    wk1r -= ss1 * wl1i;
                    wk1i += ss1 * wl1r;
                    wk3r -= ss3 * wl3i;
                    wk3i += ss3 * wl3r;
                    wd1r -= ss1 * we1i;
                    wd1i += ss1 * we1r;
                    wd3r -= ss3 * we3i;
                    wd3i += ss3 * we3r;
                }
                if (i0 == mh - 4)
                {
                    break;
                }
                wl1r = Math.Cos(ew * i0);
                wl1i = Math.Sin(ew * i0);
                wl3i = 4 * wl1i * wl1r;
                wl3r = wl1r - wl3i * wl1i;
                wl3i = wl1i - wl3i * wl1r;
                we1r = wn4r * (wl1r - wl1i);
                we1i = wn4r * (wl1i + wl1r);
                we3r = -wn4r * (wl3r - wl3i);
                we3i = -wn4r * (wl3i + wl3r);
                wk1r = w1r * wl1r - w1i * wl1i;
                wk1i = w1r * wl1i + w1i * wl1r;
                wk3i = 4 * wk1i * wk1r;
                wk3r = wk1r - wk3i * wk1i;
                wk3i = wk1i - wk3i * wk1r;
                wd1r = wn4r * (wk1r - wk1i);
                wd1i = wn4r * (wk1i + wk1r);
                wd3r = -wn4r * (wk3r - wk3i);
                wd3i = -wn4r * (wk3i + wk3r);
                i = i0;
            }
            wl1r = WR2500;
            wl1i = WI2500;
            j0 = mh;
            j1 = j0 + m;
            j2 = j1 + m;
            j3 = j2 + m;
            x0r = a[j0 - 2] - a[j2 - 1];
            x0i = a[j0 - 1] + a[j2 - 2];
            x1r = a[j0 - 2] + a[j2 - 1];
            x1i = a[j0 - 1] - a[j2 - 2];
            x2r = a[j1 - 2] - a[j3 - 1];
            x2i = a[j1 - 1] + a[j3 - 2];
            x3r = a[j1 - 2] + a[j3 - 1];
            x3i = a[j1 - 1] - a[j3 - 2];
            y0r = wk1r * x0r - wk1i * x0i;
            y0i = wk1r * x0i + wk1i * x0r;
            y2r = wd1r * x2r - wd1i * x2i;
            y2i = wd1r * x2i + wd1i * x2r;
            a[j0 - 2] = y0r + y2r;
            a[j0 - 1] = y0i + y2i;
            a[j1 - 2] = 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 - 2] = y0r + y2r;
            a[j2 - 1] = y0i + y2i;
            a[j3 - 2] = y0r - y2r;
            a[j3 - 1] = y0i - y2i;
            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 = wl1r * x0r - wl1i * x0i;
            y0i = wl1r * x0i + wl1i * x0r;
            y2r = wl1i * x2r - wl1r * x2i;
            y2i = wl1i * x2i + wl1r * x2r;
            a[j0] = y0r + y2r;
            a[j0 + 1] = y0i + y2i;
            a[j1] = y0r - y2r;
            a[j1 + 1] = y0i - y2i;
            y0r = wl1i * x1r - wl1r * x1i;
            y0i = wl1i * x1i + wl1r * x1r;
            y2r = wl1r * x3r - wl1i * x3i;
            y2i = wl1r * x3i + wl1i * x3r;
            a[j2] = y0r - y2r;
            a[j2 + 1] = y0i - y2i;
            a[j3] = y0r + y2r;
            a[j3 + 1] = y0i + y2i;
            x0r = a[j0 + 2] - a[j2 + 3];
            x0i = a[j0 + 3] + a[j2 + 2];
            x1r = a[j0 + 2] + a[j2 + 3];
            x1i = a[j0 + 3] - a[j2 + 2];
            x2r = a[j1 + 2] - a[j3 + 3];
            x2i = a[j1 + 3] + a[j3 + 2];
            x3r = a[j1 + 2] + a[j3 + 3];
            x3i = a[j1 + 3] - a[j3 + 2];
            y0r = wd1i * x0r - wd1r * x0i;
            y0i = wd1i * x0i + wd1r * x0r;
            y2r = wk1i * x2r - wk1r * x2i;
            y2i = wk1i * x2i + wk1r * x2r;
            a[j0 + 2] = y0r + y2r;
            a[j0 + 3] = y0i + y2i;
            a[j1 + 2] = y0r - y2r;
            a[j1 + 3] = y0i - y2i;
            y0r = wd3i * x1r + wd3r * x1i;
            y0i = wd3i * x1i - wd3r * x1r;
            y2r = wk3i * x3r + wk3r * x3i;
            y2i = wk3i * x3i - wk3r * x3r;
            a[j2 + 2] = y0r + y2r;
            a[j2 + 3] = y0i + y2i;
            a[j3 + 2] = y0r - y2r;
            a[j3 + 3] = y0i - y2i;
        }


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


        static void cftf161(double* a)
        {
            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 = WR5000;
            wk1r = WR2500;
            wk1i = WI2500;
            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;
        }


        static void cftf162(double* a)
        {
            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 = WR5000;
            wk1r = WR1250;
            wk1i = WI1250;
            wk2r = WR2500;
            wk2i = WI2500;
            wk3r = WR3750;
            wk3i = WI3750;
            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;
        }


        static void cftf081(double* a)
        {
            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 = WR5000;
            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;
        }


        static void cftf082(double* a)
        {
            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 = WR5000;
            wk1r = WR2500;
            wk1i = WI2500;
            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;
        }


        static 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;
        }


        static 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;
        }


        static 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;
        }

/*
        static void rftfsub(int n, double* a)
        {
            int i, i0, j, k;
            double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi;

            ec = 2 * M_PI_2 / n;
            wkr = 0;
            wki = 0;
            wdi = Math.Cos(ec);
            wdr = Math.Sin(ec);
            wdi *= wdr;
            wdr *= wdr;
            w1r = 1 - 2 * wdr;
            w1i = 2 * wdi;
            ss = 2 * w1i;
            i = n >> 1;
            for (; ; )
            {
                i0 = i - 4 * RDFT_LOOP_DIV;
                if (i0 < 4)
                {
                    i0 = 4;
                }
                for (j = i - 4; j >= i0; j -= 4)
                {
                    k = n - j;
                    xr = a[j + 2] - a[k - 2];
                    xi = a[j + 3] + a[k - 1];
                    yr = wdr * xr - wdi * xi;
                    yi = wdr * xi + wdi * xr;
                    a[j + 2] -= yr;
                    a[j + 3] -= yi;
                    a[k - 2] += yr;
                    a[k - 1] -= yi;
                    wkr += ss * wdi;
                    wki += ss * (0.5 - wdr);
                    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;
                    wdr += ss * wki;
                    wdi += ss * (0.5 - wkr);
                }
                if (i0 == 4)
                {
                    break;
                }
                wkr = 0.5 * Math.Sin(ec * i0);
                wki = 0.5 * Math.Cos(ec * i0);
                wdr = 0.5 - (wkr * w1r - wki * w1i);
                wdi = wkr * w1i + wki * w1r;
                wkr = 0.5 - wkr;
                i = i0;
            }
            xr = a[2] - a[n - 2];
            xi = a[3] + a[n - 1];
            yr = wdr * xr - wdi * xi;
            yi = wdr * xi + wdi * xr;
            a[2] -= yr;
            a[3] -= yi;
            a[n - 2] += yr;
            a[n - 1] -= yi;
        }


        static void rftbsub(int n, double* a)
        {
            int i, i0, j, k;
            double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi;

            ec = 2 * M_PI_2 / n;
            wkr = 0;
            wki = 0;
            wdi = Math.Cos(ec);
            wdr = Math.Sin(ec);
            wdi *= wdr;
            wdr *= wdr;
            w1r = 1 - 2 * wdr;
            w1i = 2 * wdi;
            ss = 2 * w1i;
            i = n >> 1;
            for (; ; )
            {
                i0 = i - 4 * RDFT_LOOP_DIV;
                if (i0 < 4)
                {
                    i0 = 4;
                }
                for (j = i - 4; j >= i0; j -= 4)
                {
                    k = n - j;
                    xr = a[j + 2] - a[k - 2];
                    xi = a[j + 3] + a[k - 1];
                    yr = wdr * xr + wdi * xi;
                    yi = wdr * xi - wdi * xr;
                    a[j + 2] -= yr;
                    a[j + 3] -= yi;
                    a[k - 2] += yr;
                    a[k - 1] -= yi;
                    wkr += ss * wdi;
                    wki += ss * (0.5 - wdr);
                    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;
                    wdr += ss * wki;
                    wdi += ss * (0.5 - wkr);
                }
                if (i0 == 4)
                {
                    break;
                }
                wkr = 0.5 * Math.Sin(ec * i0);
                wki = 0.5 * Math.Cos(ec * i0);
                wdr = 0.5 - (wkr * w1r - wki * w1i);
                wdi = wkr * w1i + wki * w1r;
                wkr = 0.5 - wkr;
                i = i0;
            }
            xr = a[2] - a[n - 2];
            xi = a[3] + a[n - 1];
            yr = wdr * xr + wdi * xi;
            yi = wdr * xi - wdi * xr;
            a[2] -= yr;
            a[3] -= yi;
            a[n - 2] += yr;
            a[n - 1] -= yi;
        }


        static void dctsub(int n, double* a)
        {
            int i, i0, j, k, m;
            double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi;

            ec = M_PI_2 / n;
            wkr = 0.5;
            wki = 0.5;
            w1r = Math.Cos(ec);
            w1i = Math.Sin(ec);
            wdr = 0.5 * (w1r - w1i);
            wdi = 0.5 * (w1r + w1i);
            ss = 2 * w1i;
            m = n >> 1;
            i = 0;
            for (; ; )
            {
                i0 = i + 2 * DCST_LOOP_DIV;
                if (i0 > m - 2)
                {
                    i0 = m - 2;
                }
                for (j = i + 2; j <= i0; j += 2)
                {
                    k = n - j;
                    xr = wdi * a[j - 1] - wdr * a[k + 1];
                    xi = wdr * a[j - 1] + wdi * a[k + 1];
                    wkr -= ss * wdi;
                    wki += ss * wdr;
                    yr = wki * a[j] - wkr * a[k];
                    yi = wkr * a[j] + wki * a[k];
                    wdr -= ss * wki;
                    wdi += ss * wkr;
                    a[k + 1] = xr;
                    a[k] = yr;
                    a[j - 1] = xi;
                    a[j] = yi;
                }
                if (i0 == m - 2)
                {
                    break;
                }
                wdr = Math.Cos(ec * i0);
                wdi = Math.Sin(ec * i0);
                wkr = 0.5 * (wdr - wdi);
                wki = 0.5 * (wdr + wdi);
                wdr = wkr * w1r - wki * w1i;
                wdi = wkr * w1i + wki * w1r;
                i = i0;
            }
            xr = wdi * a[m - 1] - wdr * a[m + 1];
            a[m - 1] = wdr * a[m - 1] + wdi * a[m + 1];
            a[m + 1] = xr;
            a[m] *= WR5000;
        }


        static void dstsub(int n, double* a)
        {
            int i, i0, j, k, m;
            double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi;

            ec = M_PI_2 / n;
            wkr = 0.5;
            wki = 0.5;
            w1r = Math.Cos(ec);
            w1i = Math.Sin(ec);
            wdr = 0.5 * (w1r - w1i);
            wdi = 0.5 * (w1r + w1i);
            ss = 2 * w1i;
            m = n >> 1;
            i = 0;
            for (; ; )
            {
                i0 = i + 2 * DCST_LOOP_DIV;
                if (i0 > m - 2)
                {
                    i0 = m - 2;
                }
                for (j = i + 2; j <= i0; j += 2)
                {
                    k = n - j;
                    xr = wdi * a[k + 1] - wdr * a[j - 1];
                    xi = wdr * a[k + 1] + wdi * a[j - 1];
                    wkr -= ss * wdi;
                    wki += ss * wdr;
                    yr = wki * a[k] - wkr * a[j];
                    yi = wkr * a[k] + wki * a[j];
                    wdr -= ss * wki;
                    wdi += ss * wkr;
                    a[j - 1] = xr;
                    a[j] = yr;
                    a[k + 1] = xi;
                    a[k] = yi;
                }
                if (i0 == m - 2)
                {
                    break;
                }
                wdr = Math.Cos(ec * i0);
                wdi = Math.Sin(ec * i0);
                wkr = 0.5 * (wdr - wdi);
                wki = 0.5 * (wdr + wdi);
                wdr = wkr * w1r - wki * w1i;
                wdi = wkr * w1i + wki * w1r;
                i = i0;
            }
            xr = wdi * a[m + 1] - wdr * a[m - 1];
            a[m + 1] = wdr * a[m + 1] + wdi * a[m - 1];
            a[m - 1] = xr;
            a[m] *= WR5000;
        }


        static void dctsub4(int n, double* a)
        {
            int m;
            double wki, wdr, wdi, xr;

            wki = WR5000;
            m = n >> 1;
            if (m == 2)
            {
                wdr = wki * WI2500;
                wdi = wki * WR2500;
                xr = wdi * a[1] - wdr * a[3];
                a[1] = wdr * a[1] + wdi * a[3];
                a[3] = xr;
            }
            a[m] *= wki;
        }


        static void dstsub4(int n, double* a)
        {
            int m;
            double wki, wdr, wdi, xr;

            wki = WR5000;
            m = n >> 1;
            if (m == 2)
            {
                wdr = wki * WI2500;
                wdi = wki * WR2500;
                xr = wdi * a[3] - wdr * a[1];
                a[3] = wdr * a[3] + wdi * a[1];
                a[1] = xr;
            }
            a[m] *= wki;
        }
*/
    }
}