/* ***** BEGIN LICENSE BLOCK *****
 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
 *
 * The contents of this file are subject to the Mozilla Public License Version
 * 1.1 (the "License"); you may not use this file except in compliance with
 * the License. You may obtain a copy of the License at
 * http://www.mozilla.org/MPL/
 *
 * Software distributed under the License is distributed on an "AS IS" basis,
 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
 * for the specific language governing rights and limitations under the
 * License.
 *
 * The Original Code is JTransforms.
 *
 * The Initial Developer of the Original Code is
 * Piotr Wendykier, Emory University.
 * Portions created by the Initial Developer are Copyright (C) 2007-2009
 * the Initial Developer. All Rights Reserved.
 *
 * Alternatively, the contents of this file may be used under the terms of
 * either the GNU General Public License Version 2 or later (the "GPL"), or
 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
 * in which case the provisions of the GPL or the LGPL are applicable instead
 * of those above. If you wish to allow use of your version of this file only
 * under the terms of either the GPL or the LGPL, and not to allow others to
 * use your version of this file under the terms of the MPL, indicate your
 * decision by deleting the provisions above and replace them with the notice
 * and other provisions required by the GPL or the LGPL. If you do not delete
 * the provisions above, a recipient may use your version of this file under
 * the terms of any one of the MPL, the GPL or the LGPL.
 *
 * ***** END LICENSE BLOCK ***** */

package edu.emory.mathcs.jtransforms.fft;

import java.util.concurrent.Future;

import edu.emory.mathcs.utils.ConcurrencyUtils;

/**
 * Computes 1D Discrete Fourier Transform (DFT) of complex and real, double
 * precision data. The size of the data can be an arbitrary number. This is a
 * parallel implementation of split-radix and mixed-radix algorithms optimized
 * for SMP systems. <br>
 * <br>
 * This code is derived from General Purpose FFT Package written by Takuya Ooura
 * (http://www.kurims.kyoto-u.ac.jp/~ooura/fft.html) and from JFFTPack written
 * by Baoshe Zhang (http://jfftpack.sourceforge.net/)
 * 
 * @author Piotr Wendykier (piotr.wendykier@gmail.com)
 * 
 */
public class DoubleFFT_1D {

    private static enum Plans {
        SPLIT_RADIX, MIXED_RADIX, BLUESTEIN
    }

    private int n;

    private int nBluestein;

    private int[] ip;

    private double[] w;

    private int nw;

    private int nc;

    private double[] wtable;

    private double[] wtable_r;

    private double[] bk1;

    private double[] bk2;

    private Plans plan;

    private static final int[] factors = { 4, 2, 3, 5 };

    private static final double PI = 3.14159265358979311599796346854418516;

    private static final double TWO_PI = 6.28318530717958623199592693708837032;

    /**
     * Creates new instance of DoubleFFT_1D.
     * 
     * @param n
     *            size of data
     */
    public DoubleFFT_1D(int n) {
        if (n < 1) {
            throw new IllegalArgumentException("n must be greater than 0");
        }
        this.n = n;

        if (!ConcurrencyUtils.isPowerOf2(n)) {
            if (getReminder(n, factors) >= 211) {
                plan = Plans.BLUESTEIN;
                nBluestein = ConcurrencyUtils.nextPow2(n * 2 - 1);
                bk1 = new double[2 * nBluestein];
                bk2 = new double[2 * nBluestein];
                this.ip = new int[2 + (int) Math.ceil(2 + (1 << (int) (Math.log(nBluestein + 0.5) / Math.log(2)) / 2))];
                this.w = new double[nBluestein];
                int twon = 2 * nBluestein;
                nw = ip[0];
                if (twon > (nw << 2)) {
                    nw = twon >> 2;
                    makewt(nw);
                }
                nc = ip[1];
                if (nBluestein > (nc << 2)) {
                    nc = nBluestein >> 2;
                    makect(nc, w, nw);
                }
                bluesteini();
            } else {
                plan = Plans.MIXED_RADIX;
                wtable = new double[4 * n + 15];
                wtable_r = new double[2 * n + 15];
                cffti();
                rffti();
            }
        } else {
            plan = Plans.SPLIT_RADIX;
            this.ip = new int[2 + (int) Math.ceil(2 + (1 << (int) (Math.log(n + 0.5) / Math.log(2)) / 2))];
            this.w = new double[n];
            int twon = 2 * n;
            nw = ip[0];
            if (twon > (nw << 2)) {
                nw = twon >> 2;
                makewt(nw);
            }
            nc = ip[1];
            if (n > (nc << 2)) {
                nc = n >> 2;
                makect(nc, w, nw);
            }
        }
    }

    /**
     * Computes 1D forward DFT of complex data leaving the result in
     * <code>a</code>. Complex number is stored as two double values in
     * sequence: the real and imaginary part, i.e. the size of the input array
     * must be greater or equal 2*n. The physical layout of the input data has
     * to be as follows:<br>
     * 
     * <pre>
     * a[2*k] = Re[k], 
     * a[2*k+1] = Im[k], 0&lt;=k&lt;n
     * </pre>
     * 
     * @param a
     *            data to transform
     */
    public void complexForward(double[] a) {
        complexForward(a, 0);
    }

    /**
     * Computes 1D forward DFT of complex data leaving the result in
     * <code>a</code>. Complex number is stored as two double values in
     * sequence: the real and imaginary part, i.e. the size of the input array
     * must be greater or equal 2*n. The physical layout of the input data has
     * to be as follows:<br>
     * 
     * <pre>
     * a[offa+2*k] = Re[k], 
     * a[offa+2*k+1] = Im[k], 0&lt;=k&lt;n
     * </pre>
     * 
     * @param a
     *            data to transform
     * @param offa
     *            index of the first element in array <code>a</code>
     */
    public void complexForward(double[] a, int offa) {
        if (n == 1)
            return;
        switch (plan) {
        case SPLIT_RADIX:
            cftbsub(2 * n, a, offa, ip, nw, w);
            break;
        case MIXED_RADIX:
            cfftf(a, offa, -1);
            break;
        case BLUESTEIN:
            bluestein_complex(a, offa, -1);
            break;
        }
    }

    /**
     * Computes 1D inverse DFT of complex data leaving the result in
     * <code>a</code>. Complex number is stored as two double values in
     * sequence: the real and imaginary part, i.e. the size of the input array
     * must be greater or equal 2*n. The physical layout of the input data has
     * to be as follows:<br>
     * 
     * <pre>
     * a[2*k] = Re[k], 
     * a[2*k+1] = Im[k], 0&lt;=k&lt;n
     * </pre>
     * 
     * @param a
     *            data to transform
     * @param scale
     *            if true then scaling is performed
     */
    public void complexInverse(double[] a, boolean scale) {
        complexInverse(a, 0, scale);
    }

    /**
     * Computes 1D inverse DFT of complex data leaving the result in
     * <code>a</code>. Complex number is stored as two double values in
     * sequence: the real and imaginary part, i.e. the size of the input array
     * must be greater or equal 2*n. The physical layout of the input data has
     * to be as follows:<br>
     * 
     * <pre>
     * a[offa+2*k] = Re[k], 
     * a[offa+2*k+1] = Im[k], 0&lt;=k&lt;n
     * </pre>
     * 
     * @param a
     *            data to transform
     * @param offa
     *            index of the first element in array <code>a</code>
     * @param scale
     *            if true then scaling is performed
     */
    public void complexInverse(double[] a, int offa, boolean scale) {
        if (n == 1)
            return;
        switch (plan) {
        case SPLIT_RADIX:
            cftfsub(2 * n, a, offa, ip, nw, w);
            break;
        case MIXED_RADIX:
            cfftf(a, offa, +1);
            break;
        case BLUESTEIN:
            bluestein_complex(a, offa, 1);
            break;
        }
        if (scale) {
            scale(n, a, offa, true);
        }
    }

    /**
     * Computes 1D forward DFT of real data leaving the result in <code>a</code>
     * . The physical layout of the output data is as follows:<br>
     * 
     * if n is even then
     * 
     * <pre>
     * a[2*k] = Re[k], 0&lt;=k&lt;n/2
     * a[2*k+1] = Im[k], 0&lt;k&lt;n/2
     * a[1] = Re[n/2]
     * </pre>
     * 
     * if n is odd then
     * 
     * <pre>
     * a[2*k] = Re[k], 0&lt;=k&lt;(n+1)/2
     * a[2*k+1] = Im[k], 0&lt;k&lt;(n-1)/2
     * a[1] = Im[(n-1)/2]
     * </pre>
     * 
     * This method computes only half of the elements of the real transform. The
     * other half satisfies the symmetry condition. If you want the full real
     * forward transform, use <code>realForwardFull</code>. To get back the
     * original data, use <code>realInverse</code> on the output of this method.
     * 
     * @param a
     *            data to transform
     */
    public void realForward(double[] a) {
        realForward(a, 0);
    }

    /**
     * Computes 1D forward DFT of real data leaving the result in <code>a</code>
     * . The physical layout of the output data is as follows:<br>
     * 
     * if n is even then
     * 
     * <pre>
     * a[offa+2*k] = Re[k], 0&lt;=k&lt;n/2
     * a[offa+2*k+1] = Im[k], 0&lt;k&lt;n/2
     * a[offa+1] = Re[n/2]
     * </pre>
     * 
     * if n is odd then
     * 
     * <pre>
     * a[offa+2*k] = Re[k], 0&lt;=k&lt;(n+1)/2
     * a[offa+2*k+1] = Im[k], 0&lt;k&lt;(n-1)/2
     * a[offa+1] = Im[(n-1)/2]
     * </pre>
     * 
     * This method computes only half of the elements of the real transform. The
     * other half satisfies the symmetry condition. If you want the full real
     * forward transform, use <code>realForwardFull</code>. To get back the
     * original data, use <code>realInverse</code> on the output of this method.
     * 
     * @param a
     *            data to transform
     * @param offa
     *            index of the first element in array <code>a</code>
     */
    public void realForward(double[] a, int offa) {
        if (n == 1)
            return;

        switch (plan) {
        case SPLIT_RADIX:
            double xi;

            if (n > 4) {
                cftfsub(n, a, offa, ip, nw, w);
                rftfsub(n, a, offa, nc, w, nw);
            } else if (n == 4) {
                cftx020(a, offa);
            }
            xi = a[offa] - a[offa + 1];
            a[offa] += a[offa + 1];
            a[offa + 1] = xi;
            break;
        case MIXED_RADIX:
            rfftf(a, offa);
            for (int k = n - 1; k >= 2; k--) {
                int idx = offa + k;
                double tmp = a[idx];
                a[idx] = a[idx - 1];
                a[idx - 1] = tmp;
            }
            break;
        case BLUESTEIN:
            bluestein_real_forward(a, offa);
            break;
        }
    }

    /**
     * Computes 1D forward DFT of real data leaving the result in <code>a</code>
     * . This method computes the full real forward transform, i.e. you will get
     * the same result as from <code>complexForward</code> called with all
     * imaginary parts equal 0. Because the result is stored in <code>a</code>,
     * the size of the input array must greater or equal 2*n, with only the
     * first n elements filled with real data. To get back the original data,
     * use <code>complexInverse</code> on the output of this method.
     * 
     * @param a
     *            data to transform
     */
    public void realForwardFull(double[] a) {
        realForwardFull(a, 0);
    }

    /**
     * Computes 1D forward DFT of real data leaving the result in <code>a</code>
     * . This method computes the full real forward transform, i.e. you will get
     * the same result as from <code>complexForward</code> called with all
     * imaginary part equal 0. Because the result is stored in <code>a</code>,
     * the size of the input array must greater or equal 2*n, with only the
     * first n elements filled with real data. To get back the original data,
     * use <code>complexInverse</code> on the output of this method.
     * 
     * @param a
     *            data to transform
     * @param offa
     *            index of the first element in array <code>a</code>
     */
    public void realForwardFull(final double[] a, final int offa) {

        final int twon = 2 * n;
        switch (plan) {
        case SPLIT_RADIX:
            realForward(a, offa);
            int nthreads = ConcurrencyUtils.getNumberOfThreads();
            if ((nthreads > 1) && (n / 2 > ConcurrencyUtils.getThreadsBeginN_1D_FFT_2Threads())) {
                Future<?>[] futures = new Future[nthreads];
                int k = n / 2 / nthreads;
                for (int i = 0; i < nthreads; i++) {
                    final int firstIdx = i * k;
                    final int lastIdx = (i == (nthreads - 1)) ? n / 2 : firstIdx + k;
                    futures[i] = ConcurrencyUtils.submit(new Runnable() {
                        @Override
                                                public void run() {
                            int idx1, idx2;
                            for (int k = firstIdx; k < lastIdx; k++) {
                                idx1 = 2 * k;
                                idx2 = offa + ((twon - idx1) % twon);
                                a[idx2] = a[offa + idx1];
                                a[idx2 + 1] = -a[offa + idx1 + 1];
                            }
                        }
                    });
                }
                ConcurrencyUtils.waitForCompletion(futures);
            } else {
                int idx1, idx2;
                for (int k = 0; k < n / 2; k++) {
                    idx1 = 2 * k;
                    idx2 = offa + ((twon - idx1) % twon);
                    a[idx2] = a[offa + idx1];
                    a[idx2 + 1] = -a[offa + idx1 + 1];
                }
            }
            a[offa + n] = -a[offa + 1];
            a[offa + 1] = 0;
            break;
        case MIXED_RADIX:
            rfftf(a, offa);
            int m;
            if (n % 2 == 0) {
                m = n / 2;
            } else {
                m = (n + 1) / 2;
            }
            for (int k = 1; k < m; k++) {
                int idx1 = offa + twon - 2 * k;
                int idx2 = offa + 2 * k;
                a[idx1 + 1] = -a[idx2];
                a[idx1] = a[idx2 - 1];
            }
            for (int k = 1; k < n; k++) {
                int idx = offa + n - k;
                double tmp = a[idx + 1];
                a[idx + 1] = a[idx];
                a[idx] = tmp;
            }
            a[offa + 1] = 0;
            break;
        case BLUESTEIN:
            bluestein_real_full(a, offa, -1);
            break;
        }
    }

    /**
     * Computes 1D inverse DFT of real data leaving the result in <code>a</code>
     * . The physical layout of the input data has to be as follows:<br>
     * 
     * if n is even then
     * 
     * <pre>
     * a[2*k] = Re[k], 0&lt;=k&lt;n/2
     * a[2*k+1] = Im[k], 0&lt;k&lt;n/2
     * a[1] = Re[n/2]
     * </pre>
     * 
     * if n is odd then
     * 
     * <pre>
     * a[2*k] = Re[k], 0&lt;=k&lt;(n+1)/2
     * a[2*k+1] = Im[k], 0&lt;k&lt;(n-1)/2
     * a[1] = Im[(n-1)/2]
     * </pre>
     * 
     * This method computes only half of the elements of the real transform. The
     * other half satisfies the symmetry condition. If you want the full real
     * inverse transform, use <code>realInverseFull</code>.
     * 
     * @param a
     *            data to transform
     * 
     * @param scale
     *            if true then scaling is performed
     * 
     */
    public void realInverse(double[] a, boolean scale) {
        realInverse(a, 0, scale);
    }

    /**
     * Computes 1D inverse DFT of real data leaving the result in <code>a</code>
     * . The physical layout of the input data has to be as follows:<br>
     * 
     * if n is even then
     * 
     * <pre>
     * a[offa+2*k] = Re[k], 0&lt;=k&lt;n/2
     * a[offa+2*k+1] = Im[k], 0&lt;k&lt;n/2
     * a[offa+1] = Re[n/2]
     * </pre>
     * 
     * if n is odd then
     * 
     * <pre>
     * a[offa+2*k] = Re[k], 0&lt;=k&lt;(n+1)/2
     * a[offa+2*k+1] = Im[k], 0&lt;k&lt;(n-1)/2
     * a[offa+1] = Im[(n-1)/2]
     * </pre>
     * 
     * This method computes only half of the elements of the real transform. The
     * other half satisfies the symmetry condition. If you want the full real
     * inverse transform, use <code>realInverseFull</code>.
     * 
     * @param a
     *            data to transform
     * @param offa
     *            index of the first element in array <code>a</code>
     * @param scale
     *            if true then scaling is performed
     * 
     */
    public void realInverse(double[] a, int offa, boolean scale) {
        if (n == 1)
            return;
        switch (plan) {
        case SPLIT_RADIX:
            a[offa + 1] = 0.5 * (a[offa] - a[offa + 1]);
            a[offa] -= a[offa + 1];
            if (n > 4) {
                rftfsub(n, a, offa, nc, w, nw);
                cftbsub(n, a, offa, ip, nw, w);
            } else if (n == 4) {
                cftxc020(a, offa);
            }
            if (scale) {
                scale(n / 2, a, offa, false);
            }
            break;
        case MIXED_RADIX:
            for (int k = 2; k < n; k++) {
                int idx = offa + k;
                double tmp = a[idx - 1];
                a[idx - 1] = a[idx];
                a[idx] = tmp;
            }
            rfftb(a, offa);
            if (scale) {
                scale(n, a, offa, false);
            }
            break;
        case BLUESTEIN:
            bluestein_real_inverse(a, offa);
            if (scale) {
                scale(n, a, offa, false);
            }
            break;
        }

    }

    /**
     * Computes 1D inverse DFT of real data leaving the result in <code>a</code>
     * . This method computes the full real inverse transform, i.e. you will get
     * the same result as from <code>complexInverse</code> called with all
     * imaginary part equal 0. Because the result is stored in <code>a</code>,
     * the size of the input array must greater or equal 2*n, with only the
     * first n elements filled with real data.
     * 
     * @param a
     *            data to transform
     * @param scale
     *            if true then scaling is performed
     */
    public void realInverseFull(double[] a, boolean scale) {
        realInverseFull(a, 0, scale);
    }

    /**
     * Computes 1D inverse DFT of real data leaving the result in <code>a</code>
     * . This method computes the full real inverse transform, i.e. you will get
     * the same result as from <code>complexInverse</code> called with all
     * imaginary part equal 0. Because the result is stored in <code>a</code>,
     * the size of the input array must greater or equal 2*n, with only the
     * first n elements filled with real data.
     * 
     * @param a
     *            data to transform
     * @param offa
     *            index of the first element in array <code>a</code>
     * @param scale
     *            if true then scaling is performed
     */
    public void realInverseFull(final double[] a, final int offa, boolean scale) {
        final int twon = 2 * n;
        switch (plan) {
        case SPLIT_RADIX:
            realInverse2(a, offa, scale);
            int nthreads = ConcurrencyUtils.getNumberOfThreads();
            if ((nthreads > 1) && (n / 2 > ConcurrencyUtils.getThreadsBeginN_1D_FFT_2Threads())) {
                Future<?>[] futures = new Future[nthreads];
                int k = n / 2 / nthreads;
                for (int i = 0; i < nthreads; i++) {
                    final int firstIdx = i * k;
                    final int lastIdx = (i == (nthreads - 1)) ? n / 2 : firstIdx + k;
                    futures[i] = ConcurrencyUtils.submit(new Runnable() {
                        @Override
                                                public void run() {
                            int idx1, idx2;
                            for (int k = firstIdx; k < lastIdx; k++) {
                                idx1 = 2 * k;
                                idx2 = offa + ((twon - idx1) % twon);
                                a[idx2] = a[offa + idx1];
                                a[idx2 + 1] = -a[offa + idx1 + 1];
                            }
                        }
                    });
                }
                ConcurrencyUtils.waitForCompletion(futures);
            } else {
                int idx1, idx2;
                for (int k = 0; k < n / 2; k++) {
                    idx1 = 2 * k;
                    idx2 = offa + ((twon - idx1) % twon);
                    a[idx2] = a[offa + idx1];
                    a[idx2 + 1] = -a[offa + idx1 + 1];
                }
            }
            a[offa + n] = -a[offa + 1];
            a[offa + 1] = 0;
            break;
        case MIXED_RADIX:
            rfftf(a, offa);
            if (scale) {
                scale(n, a, offa, false);
            }
            int m;
            if (n % 2 == 0) {
                m = n / 2;
            } else {
                m = (n + 1) / 2;
            }
            for (int k = 1; k < m; k++) {
                int idx1 = offa + 2 * k;
                int idx2 = offa + twon - 2 * k;
                a[idx1] = -a[idx1];
                a[idx2 + 1] = -a[idx1];
                a[idx2] = a[idx1 - 1];
            }
            for (int k = 1; k < n; k++) {
                int idx = offa + n - k;
                double tmp = a[idx + 1];
                a[idx + 1] = a[idx];
                a[idx] = tmp;
            }
            a[offa + 1] = 0;
            break;
        case BLUESTEIN:
            bluestein_real_full(a, offa, 1);
            if (scale) {
                scale(n, a, offa, true);
            }
            break;
        }
    }

    protected void realInverse2(double[] a, int offa, boolean scale) {
        if (n == 1)
            return;
        switch (plan) {
        case SPLIT_RADIX:
            double xi;

            if (n > 4) {
                cftfsub(n, a, offa, ip, nw, w);
                rftbsub(n, a, offa, nc, w, nw);
            } else if (n == 4) {
                cftbsub(n, a, offa, ip, nw, w);
            }
            xi = a[offa] - a[offa + 1];
            a[offa] += a[offa + 1];
            a[offa + 1] = xi;
            if (scale) {
                scale(n, a, offa, false);
            }
            break;
        case MIXED_RADIX:
            rfftf(a, offa);
            for (int k = n - 1; k >= 2; k--) {
                int idx = offa + k;
                double tmp = a[idx];
                a[idx] = a[idx - 1];
                a[idx - 1] = tmp;
            }
            if (scale) {
                scale(n, a, offa, false);
            }
            int m;
            if (n % 2 == 0) {
                m = n / 2;
                for (int i = 1; i < m; i++) {
                    int idx = offa + 2 * i + 1;
                    a[idx] = -a[idx];
                }
            } else {
                m = (n - 1) / 2;
                for (int i = 0; i < m; i++) {
                    int idx = offa + 2 * i + 1;
                    a[idx] = -a[idx];
                }
            }
            break;
        case BLUESTEIN:
            bluestein_real_inverse2(a, offa);
            if (scale) {
                scale(n, a, offa, false);
            }
            break;
        }
    }

    private static int getReminder(int n, int factors[]) {
        int reminder = n;

        if (n <= 0) {
            throw new IllegalArgumentException("n must be positive integer");
        }

        for (int i = 0; i < factors.length && reminder != 1; i++) {
            int factor = factors[i];
            while ((reminder % factor) == 0) {
                reminder /= factor;
            }
        }
        return reminder;
    }

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

    /*---------------------------------------------------------
       cffti: initialization of Complex FFT
      --------------------------------------------------------*/

    void cffti(int n, int offw) {
        if (n == 1)
            return;

        final int twon = 2 * n;
        final int fourn = 4 * n;
        double argh;
        int idot, ntry = 0, i, j;
        double argld;
        int i1, k1, l1, l2, ib;
        double fi;
        int ld, ii, nf, ip, nl, nq, nr;
        double arg;
        int ido, ipm;

        nl = n;
        nf = 0;
        j = 0;

        factorize_loop: while (true) {
            j++;
            if (j <= 4)
                ntry = factors[j - 1];
            else
                ntry += 2;
            do {
                nq = nl / ntry;
                nr = nl - ntry * nq;
                if (nr != 0)
                    continue factorize_loop;
                nf++;
                wtable[offw + nf + 1 + fourn] = ntry;
                nl = nq;
                if (ntry == 2 && nf != 1) {
                    for (i = 2; i <= nf; i++) {
                        ib = nf - i + 2;
                        int idx = ib + fourn;
                        wtable[offw + idx + 1] = wtable[offw + idx];
                    }
                    wtable[offw + 2 + fourn] = 2;
                }
            } while (nl != 1);
            break factorize_loop;
        }
        wtable[offw + fourn] = n;
        wtable[offw + 1 + fourn] = nf;
        argh = TWO_PI / (double) n;
        i = 1;
        l1 = 1;
        for (k1 = 1; k1 <= nf; k1++) {
            ip = (int) wtable[offw + k1 + 1 + fourn];
            ld = 0;
            l2 = l1 * ip;
            ido = n / l2;
            idot = ido + ido + 2;
            ipm = ip - 1;
            for (j = 1; j <= ipm; j++) {
                i1 = i;
                wtable[offw + i - 1 + twon] = 1;
                wtable[offw + i + twon] = 0;
                ld += l1;
                fi = 0;
                argld = ld * argh;
                for (ii = 4; ii <= idot; ii += 2) {
                    i += 2;
                    fi += 1;
                    arg = fi * argld;
                    int idx = i + twon;
                    wtable[offw + idx - 1] = Math.cos(arg);
                    wtable[offw + idx] = Math.sin(arg);
                }
                if (ip > 5) {
                    int idx1 = i1 + twon;
                    int idx2 = i + twon;
                    wtable[offw + idx1 - 1] = wtable[offw + idx2 - 1];
                    wtable[offw + idx1] = wtable[offw + idx2];
                }
            }
            l1 = l2;
        }

    }

    void cffti() {
        if (n == 1)
            return;

        final int twon = 2 * n;
        final int fourn = 4 * n;
        double argh;
        int idot, ntry = 0, i, j;
        double argld;
        int i1, k1, l1, l2, ib;
        double fi;
        int ld, ii, nf, ip, nl, nq, nr;
        double arg;
        int ido, ipm;

        nl = n;
        nf = 0;
        j = 0;

        factorize_loop: while (true) {
            j++;
            if (j <= 4)
                ntry = factors[j - 1];
            else
                ntry += 2;
            do {
                nq = nl / ntry;
                nr = nl - ntry * nq;
                if (nr != 0)
                    continue factorize_loop;
                nf++;
                wtable[nf + 1 + fourn] = ntry;
                nl = nq;
                if (ntry == 2 && nf != 1) {
                    for (i = 2; i <= nf; i++) {
                        ib = nf - i + 2;
                        int idx = ib + fourn;
                        wtable[idx + 1] = wtable[idx];
                    }
                    wtable[2 + fourn] = 2;
                }
            } while (nl != 1);
            break factorize_loop;
        }
        wtable[fourn] = n;
        wtable[1 + fourn] = nf;
        argh = TWO_PI / (double) n;
        i = 1;
        l1 = 1;
        for (k1 = 1; k1 <= nf; k1++) {
            ip = (int) wtable[k1 + 1 + fourn];
            ld = 0;
            l2 = l1 * ip;
            ido = n / l2;
            idot = ido + ido + 2;
            ipm = ip - 1;
            for (j = 1; j <= ipm; j++) {
                i1 = i;
                wtable[i - 1 + twon] = 1;
                wtable[i + twon] = 0;
                ld += l1;
                fi = 0;
                argld = ld * argh;
                for (ii = 4; ii <= idot; ii += 2) {
                    i += 2;
                    fi += 1;
                    arg = fi * argld;
                    int idx = i + twon;
                    wtable[idx - 1] = Math.cos(arg);
                    wtable[idx] = Math.sin(arg);
                }
                if (ip > 5) {
                    int idx1 = i1 + twon;
                    int idx2 = i + twon;
                    wtable[idx1 - 1] = wtable[idx2 - 1];
                    wtable[idx1] = wtable[idx2];
                }
            }
            l1 = l2;
        }

    }

    void rffti() {

        if (n == 1)
            return;
        final int twon = 2 * n;
        double argh;
        int ntry = 0, i, j;
        double argld;
        int k1, l1, l2, ib;
        double fi;
        int ld, ii, nf, ip, nl, is, nq, nr;
        double arg;
        int ido, ipm;
        int nfm1;

        nl = n;
        nf = 0;
        j = 0;

        factorize_loop: while (true) {
            ++j;
            if (j <= 4)
                ntry = factors[j - 1];
            else
                ntry += 2;
            do {
                nq = nl / ntry;
                nr = nl - ntry * nq;
                if (nr != 0)
                    continue factorize_loop;
                ++nf;
                wtable_r[nf + 1 + twon] = ntry;

                nl = nq;
                if (ntry == 2 && nf != 1) {
                    for (i = 2; i <= nf; i++) {
                        ib = nf - i + 2;
                        int idx = ib + twon;
                        wtable_r[idx + 1] = wtable_r[idx];
                    }
                    wtable_r[2 + twon] = 2;
                }
            } while (nl != 1);
            break factorize_loop;
        }
        wtable_r[twon] = n;
        wtable_r[1 + twon] = nf;
        argh = TWO_PI / (double) (n);
        is = 0;
        nfm1 = nf - 1;
        l1 = 1;
        if (nfm1 == 0)
            return;
        for (k1 = 1; k1 <= nfm1; k1++) {
            ip = (int) wtable_r[k1 + 1 + twon];
            ld = 0;
            l2 = l1 * ip;
            ido = n / l2;
            ipm = ip - 1;
            for (j = 1; j <= ipm; ++j) {
                ld += l1;
                i = is;
                argld = (double) ld * argh;

                fi = 0;
                for (ii = 3; ii <= ido; ii += 2) {
                    i += 2;
                    fi += 1;
                    arg = fi * argld;
                    int idx = i + n;
                    wtable_r[idx - 2] = Math.cos(arg);
                    wtable_r[idx - 1] = Math.sin(arg);
                }
                is += ido;
            }
            l1 = l2;
        }
    }

    private void bluesteini() {
        int k = 0;
        double arg;
        double pi_n = PI / n;
        bk1[0] = 1;
        bk1[1] = 0;
        for (int i = 1; i < n; i++) {
            k += 2 * i - 1;
            if (k >= 2 * n)
                k -= 2 * n;
            arg = pi_n * k;
            bk1[2 * i] = Math.cos(arg);
            bk1[2 * i + 1] = Math.sin(arg);
        }
        double scale = 1.0 / nBluestein;
        bk2[0] = bk1[0] * scale;
        bk2[1] = bk1[1] * scale;
        for (int i = 2; i < 2 * n; i += 2) {
            bk2[i] = bk1[i] * scale;
            bk2[i + 1] = bk1[i + 1] * scale;
            bk2[2 * nBluestein - i] = bk2[i];
            bk2[2 * nBluestein - i + 1] = bk2[i + 1];
        }
        cftbsub(2 * nBluestein, bk2, 0, ip, nw, w);
    }

    private void makewt(int nw) {
        int j, nwh, nw0, nw1;
        double delta, wn4r, wk1r, wk1i, wk3r, wk3i;
        double delta2, deltaj, deltaj3;

        ip[0] = nw;
        ip[1] = 1;
        if (nw > 2) {
            nwh = nw >> 1;
            delta = 0.785398163397448278999490867136046290 / nwh;
            delta2 = delta * 2;
            wn4r = Math.cos(delta * nwh);
            w[0] = 1;
            w[1] = wn4r;
            if (nwh == 4) {
                w[2] = Math.cos(delta2);
                w[3] = Math.sin(delta2);
            } else if (nwh > 4) {
                makeipt(nw);
                w[2] = 0.5 / Math.cos(delta2);
                w[3] = 0.5 / Math.cos(delta * 6);
                for (j = 4; j < nwh; j += 4) {
                    deltaj = delta * j;
                    deltaj3 = 3 * deltaj;
                    w[j] = Math.cos(deltaj);
                    w[j + 1] = Math.sin(deltaj);
                    w[j + 2] = Math.cos(deltaj3);
                    w[j + 3] = -Math.sin(deltaj3);
                }
            }
            nw0 = 0;
            while (nwh > 2) {
                nw1 = nw0 + nwh;
                nwh >>= 1;
                w[nw1] = 1;
                w[nw1 + 1] = wn4r;
                if (nwh == 4) {
                    wk1r = w[nw0 + 4];
                    wk1i = w[nw0 + 5];
                    w[nw1 + 2] = wk1r;
                    w[nw1 + 3] = wk1i;
                } else if (nwh > 4) {
                    wk1r = w[nw0 + 4];
                    wk3r = w[nw0 + 6];
                    w[nw1 + 2] = 0.5 / wk1r;
                    w[nw1 + 3] = 0.5 / wk3r;
                    for (j = 4; j < nwh; j += 4) {
                        int idx1 = nw0 + 2 * j;
                        int idx2 = nw1 + j;
                        wk1r = w[idx1];
                        wk1i = w[idx1 + 1];
                        wk3r = w[idx1 + 2];
                        wk3i = w[idx1 + 3];
                        w[idx2] = wk1r;
                        w[idx2 + 1] = wk1i;
                        w[idx2 + 2] = wk3r;
                        w[idx2 + 3] = wk3i;
                    }
                }
                nw0 = nw1;
            }
        }
    }

    private void makeipt(int nw) {
        int j, l, m, m2, p, q;

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

    private void makect(int nc, double[] c, int startc) {
        int j, nch;
        double delta, deltaj;

        ip[1] = nc;
        if (nc > 1) {
            nch = nc >> 1;
            delta = 0.785398163397448278999490867136046290 / nch;
            c[startc] = Math.cos(delta * nch);
            c[startc + nch] = 0.5 * c[startc];
            for (j = 1; j < nch; j++) {
                deltaj = delta * j;
                c[startc + j] = 0.5 * Math.cos(deltaj);
                c[startc + nc - j] = 0.5 * Math.sin(deltaj);
            }
        }
    }

    private void bluestein_complex(final double[] a, final int offa, final int isign) {
        final double[] ak = new double[2 * nBluestein];
        int nthreads = 1;
        int threads = ConcurrencyUtils.getNumberOfThreads();
        if ((threads > 1) && (n > ConcurrencyUtils.getThreadsBeginN_1D_FFT_2Threads())) {
            nthreads = 2;
            if ((threads >= 4) && (n > ConcurrencyUtils.getThreadsBeginN_1D_FFT_4Threads())) {
                nthreads = 4;
            }
            Future<?>[] futures = new Future[nthreads];
            int k = n / nthreads;
            for (int i = 0; i < nthreads; i++) {
                final int firstIdx = i * k;
                final int lastIdx = (i == (nthreads - 1)) ? n : firstIdx + k;
                futures[i] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        if (isign > 0) {
                            for (int i = firstIdx; i < lastIdx; i++) {
                                int idx1 = 2 * i;
                                int idx2 = idx1 + 1;
                                int idx3 = offa + idx1;
                                int idx4 = offa + idx2;
                                ak[idx1] = a[idx3] * bk1[idx1] - a[idx4] * bk1[idx2];
                                ak[idx2] = a[idx3] * bk1[idx2] + a[idx4] * bk1[idx1];
                            }
                        } else {
                            for (int i = firstIdx; i < lastIdx; i++) {
                                int idx1 = 2 * i;
                                int idx2 = idx1 + 1;
                                int idx3 = offa + idx1;
                                int idx4 = offa + idx2;
                                ak[idx1] = a[idx3] * bk1[idx1] + a[idx4] * bk1[idx2];
                                ak[idx2] = -a[idx3] * bk1[idx2] + a[idx4] * bk1[idx1];
                            }
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            cftbsub(2 * nBluestein, ak, 0, ip, nw, w);

            k = nBluestein / nthreads;
            for (int i = 0; i < nthreads; i++) {
                final int firstIdx = i * k;
                final int lastIdx = (i == (nthreads - 1)) ? nBluestein : firstIdx + k;
                futures[i] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        if (isign > 0) {
                            for (int i = firstIdx; i < lastIdx; i++) {
                                int idx1 = 2 * i;
                                int idx2 = idx1 + 1;
                                double im = -ak[idx1] * bk2[idx2] + ak[idx2] * bk2[idx1];
                                ak[idx1] = ak[idx1] * bk2[idx1] + ak[idx2] * bk2[idx2];
                                ak[idx2] = im;
                            }
                        } else {
                            for (int i = firstIdx; i < lastIdx; i++) {
                                int idx1 = 2 * i;
                                int idx2 = idx1 + 1;
                                double im = ak[idx1] * bk2[idx2] + ak[idx2] * bk2[idx1];
                                ak[idx1] = ak[idx1] * bk2[idx1] - ak[idx2] * bk2[idx2];
                                ak[idx2] = im;
                            }
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            cftfsub(2 * nBluestein, ak, 0, ip, nw, w);

            k = n / nthreads;
            for (int i = 0; i < nthreads; i++) {
                final int firstIdx = i * k;
                final int lastIdx = (i == (nthreads - 1)) ? n : firstIdx + k;
                futures[i] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        if (isign > 0) {
                            for (int i = firstIdx; i < lastIdx; i++) {
                                int idx1 = 2 * i;
                                int idx2 = idx1 + 1;
                                int idx3 = offa + idx1;
                                int idx4 = offa + idx2;
                                a[idx3] = bk1[idx1] * ak[idx1] - bk1[idx2] * ak[idx2];
                                a[idx4] = bk1[idx2] * ak[idx1] + bk1[idx1] * ak[idx2];
                            }
                        } else {
                            for (int i = firstIdx; i < lastIdx; i++) {
                                int idx1 = 2 * i;
                                int idx2 = idx1 + 1;
                                int idx3 = offa + idx1;
                                int idx4 = offa + idx2;
                                a[idx3] = bk1[idx1] * ak[idx1] + bk1[idx2] * ak[idx2];
                                a[idx4] = -bk1[idx2] * ak[idx1] + bk1[idx1] * ak[idx2];
                            }
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);
        } else {
            if (isign > 0) {
                for (int i = 0; i < n; i++) {
                    int idx1 = 2 * i;
                    int idx2 = idx1 + 1;
                    int idx3 = offa + idx1;
                    int idx4 = offa + idx2;
                    ak[idx1] = a[idx3] * bk1[idx1] - a[idx4] * bk1[idx2];
                    ak[idx2] = a[idx3] * bk1[idx2] + a[idx4] * bk1[idx1];
                }
            } else {
                for (int i = 0; i < n; i++) {
                    int idx1 = 2 * i;
                    int idx2 = idx1 + 1;
                    int idx3 = offa + idx1;
                    int idx4 = offa + idx2;
                    ak[idx1] = a[idx3] * bk1[idx1] + a[idx4] * bk1[idx2];
                    ak[idx2] = -a[idx3] * bk1[idx2] + a[idx4] * bk1[idx1];
                }
            }

            cftbsub(2 * nBluestein, ak, 0, ip, nw, w);

            if (isign > 0) {
                for (int i = 0; i < nBluestein; i++) {
                    int idx1 = 2 * i;
                    int idx2 = idx1 + 1;
                    double im = -ak[idx1] * bk2[idx2] + ak[idx2] * bk2[idx1];
                    ak[idx1] = ak[idx1] * bk2[idx1] + ak[idx2] * bk2[idx2];
                    ak[idx2] = im;
                }
            } else {
                for (int i = 0; i < nBluestein; i++) {
                    int idx1 = 2 * i;
                    int idx2 = idx1 + 1;
                    double im = ak[idx1] * bk2[idx2] + ak[idx2] * bk2[idx1];
                    ak[idx1] = ak[idx1] * bk2[idx1] - ak[idx2] * bk2[idx2];
                    ak[idx2] = im;
                }
            }

            cftfsub(2 * nBluestein, ak, 0, ip, nw, w);
            if (isign > 0) {
                for (int i = 0; i < n; i++) {
                    int idx1 = 2 * i;
                    int idx2 = idx1 + 1;
                    int idx3 = offa + idx1;
                    int idx4 = offa + idx2;
                    a[idx3] = bk1[idx1] * ak[idx1] - bk1[idx2] * ak[idx2];
                    a[idx4] = bk1[idx2] * ak[idx1] + bk1[idx1] * ak[idx2];
                }
            } else {
                for (int i = 0; i < n; i++) {
                    int idx1 = 2 * i;
                    int idx2 = idx1 + 1;
                    int idx3 = offa + idx1;
                    int idx4 = offa + idx2;
                    a[idx3] = bk1[idx1] * ak[idx1] + bk1[idx2] * ak[idx2];
                    a[idx4] = -bk1[idx2] * ak[idx1] + bk1[idx1] * ak[idx2];
                }
            }
        }
    }

    private void bluestein_real_full(final double[] a, final int offa, final int isign) {
        final double[] ak = new double[2 * nBluestein];
        int nthreads = 1;
        int threads = ConcurrencyUtils.getNumberOfThreads();
        if ((threads > 1) && (n > ConcurrencyUtils.getThreadsBeginN_1D_FFT_2Threads())) {
            nthreads = 2;
            if ((threads >= 4) && (n > ConcurrencyUtils.getThreadsBeginN_1D_FFT_4Threads())) {
                nthreads = 4;
            }
            Future<?>[] futures = new Future[nthreads];
            int k = n / nthreads;
            for (int i = 0; i < nthreads; i++) {
                final int firstIdx = i * k;
                final int lastIdx = (i == (nthreads - 1)) ? n : firstIdx + k;
                futures[i] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        if (isign > 0) {
                            for (int i = firstIdx; i < lastIdx; i++) {
                                int idx1 = 2 * i;
                                int idx2 = idx1 + 1;
                                int idx3 = offa + i;
                                ak[idx1] = a[idx3] * bk1[idx1];
                                ak[idx2] = a[idx3] * bk1[idx2];
                            }
                        } else {
                            for (int i = firstIdx; i < lastIdx; i++) {
                                int idx1 = 2 * i;
                                int idx2 = idx1 + 1;
                                int idx3 = offa + i;
                                ak[idx1] = a[idx3] * bk1[idx1];
                                ak[idx2] = -a[idx3] * bk1[idx2];
                            }
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            cftbsub(2 * nBluestein, ak, 0, ip, nw, w);

            k = nBluestein / nthreads;
            for (int i = 0; i < nthreads; i++) {
                final int firstIdx = i * k;
                final int lastIdx = (i == (nthreads - 1)) ? nBluestein : firstIdx + k;
                futures[i] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        if (isign > 0) {
                            for (int i = firstIdx; i < lastIdx; i++) {
                                int idx1 = 2 * i;
                                int idx2 = idx1 + 1;
                                double im = -ak[idx1] * bk2[idx2] + ak[idx2] * bk2[idx1];
                                ak[idx1] = ak[idx1] * bk2[idx1] + ak[idx2] * bk2[idx2];
                                ak[idx2] = im;
                            }
                        } else {
                            for (int i = firstIdx; i < lastIdx; i++) {
                                int idx1 = 2 * i;
                                int idx2 = idx1 + 1;
                                double im = ak[idx1] * bk2[idx2] + ak[idx2] * bk2[idx1];
                                ak[idx1] = ak[idx1] * bk2[idx1] - ak[idx2] * bk2[idx2];
                                ak[idx2] = im;
                            }
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            cftfsub(2 * nBluestein, ak, 0, ip, nw, w);

            k = n / nthreads;
            for (int i = 0; i < nthreads; i++) {
                final int firstIdx = i * k;
                final int lastIdx = (i == (nthreads - 1)) ? n : firstIdx + k;
                futures[i] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        if (isign > 0) {
                            for (int i = firstIdx; i < lastIdx; i++) {
                                int idx1 = 2 * i;
                                int idx2 = idx1 + 1;
                                a[offa + idx1] = bk1[idx1] * ak[idx1] - bk1[idx2] * ak[idx2];
                                a[offa + idx2] = bk1[idx2] * ak[idx1] + bk1[idx1] * ak[idx2];
                            }
                        } else {
                            for (int i = firstIdx; i < lastIdx; i++) {
                                int idx1 = 2 * i;
                                int idx2 = idx1 + 1;
                                a[offa + idx1] = bk1[idx1] * ak[idx1] + bk1[idx2] * ak[idx2];
                                a[offa + idx2] = -bk1[idx2] * ak[idx1] + bk1[idx1] * ak[idx2];
                            }
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);
        } else {
            if (isign > 0) {
                for (int i = 0; i < n; i++) {
                    int idx1 = 2 * i;
                    int idx2 = idx1 + 1;
                    int idx3 = offa + i;
                    ak[idx1] = a[idx3] * bk1[idx1];
                    ak[idx2] = a[idx3] * bk1[idx2];
                }
            } else {
                for (int i = 0; i < n; i++) {
                    int idx1 = 2 * i;
                    int idx2 = idx1 + 1;
                    int idx3 = offa + i;
                    ak[idx1] = a[idx3] * bk1[idx1];
                    ak[idx2] = -a[idx3] * bk1[idx2];
                }
            }

            cftbsub(2 * nBluestein, ak, 0, ip, nw, w);

            if (isign > 0) {
                for (int i = 0; i < nBluestein; i++) {
                    int idx1 = 2 * i;
                    int idx2 = idx1 + 1;
                    double im = -ak[idx1] * bk2[idx2] + ak[idx2] * bk2[idx1];
                    ak[idx1] = ak[idx1] * bk2[idx1] + ak[idx2] * bk2[idx2];
                    ak[idx2] = im;
                }
            } else {
                for (int i = 0; i < nBluestein; i++) {
                    int idx1 = 2 * i;
                    int idx2 = idx1 + 1;
                    double im = ak[idx1] * bk2[idx2] + ak[idx2] * bk2[idx1];
                    ak[idx1] = ak[idx1] * bk2[idx1] - ak[idx2] * bk2[idx2];
                    ak[idx2] = im;
                }
            }

            cftfsub(2 * nBluestein, ak, 0, ip, nw, w);

            if (isign > 0) {
                for (int i = 0; i < n; i++) {
                    int idx1 = 2 * i;
                    int idx2 = idx1 + 1;
                    a[offa + idx1] = bk1[idx1] * ak[idx1] - bk1[idx2] * ak[idx2];
                    a[offa + idx2] = bk1[idx2] * ak[idx1] + bk1[idx1] * ak[idx2];
                }
            } else {
                for (int i = 0; i < n; i++) {
                    int idx1 = 2 * i;
                    int idx2 = idx1 + 1;
                    a[offa + idx1] = bk1[idx1] * ak[idx1] + bk1[idx2] * ak[idx2];
                    a[offa + idx2] = -bk1[idx2] * ak[idx1] + bk1[idx1] * ak[idx2];
                }
            }
        }
    }

    private void bluestein_real_forward(final double[] a, final int offa) {
        final double[] ak = new double[2 * nBluestein];
        int nthreads = 1;
        int threads = ConcurrencyUtils.getNumberOfThreads();
        if ((threads > 1) && (n > ConcurrencyUtils.getThreadsBeginN_1D_FFT_2Threads())) {
            nthreads = 2;
            if ((threads >= 4) && (n > ConcurrencyUtils.getThreadsBeginN_1D_FFT_4Threads())) {
                nthreads = 4;
            }
            Future<?>[] futures = new Future[nthreads];
            int k = n / nthreads;
            for (int i = 0; i < nthreads; i++) {
                final int firstIdx = i * k;
                final int lastIdx = (i == (nthreads - 1)) ? n : firstIdx + k;
                futures[i] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int i = firstIdx; i < lastIdx; i++) {
                            int idx1 = 2 * i;
                            int idx2 = idx1 + 1;
                            int idx3 = offa + i;
                            ak[idx1] = a[idx3] * bk1[idx1];
                            ak[idx2] = -a[idx3] * bk1[idx2];
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            cftbsub(2 * nBluestein, ak, 0, ip, nw, w);

            k = nBluestein / nthreads;
            for (int i = 0; i < nthreads; i++) {
                final int firstIdx = i * k;
                final int lastIdx = (i == (nthreads - 1)) ? nBluestein : firstIdx + k;
                futures[i] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int i = firstIdx; i < lastIdx; i++) {
                            int idx1 = 2 * i;
                            int idx2 = idx1 + 1;
                            double im = ak[idx1] * bk2[idx2] + ak[idx2] * bk2[idx1];
                            ak[idx1] = ak[idx1] * bk2[idx1] - ak[idx2] * bk2[idx2];
                            ak[idx2] = im;
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

        } else {

            for (int i = 0; i < n; i++) {
                int idx1 = 2 * i;
                int idx2 = idx1 + 1;
                int idx3 = offa + i;
                ak[idx1] = a[idx3] * bk1[idx1];
                ak[idx2] = -a[idx3] * bk1[idx2];
            }

            cftbsub(2 * nBluestein, ak, 0, ip, nw, w);

            for (int i = 0; i < nBluestein; i++) {
                int idx1 = 2 * i;
                int idx2 = idx1 + 1;
                double im = ak[idx1] * bk2[idx2] + ak[idx2] * bk2[idx1];
                ak[idx1] = ak[idx1] * bk2[idx1] - ak[idx2] * bk2[idx2];
                ak[idx2] = im;
            }
        }

        cftfsub(2 * nBluestein, ak, 0, ip, nw, w);

        if (n % 2 == 0) {
            a[offa] = bk1[0] * ak[0] + bk1[1] * ak[1];
            a[offa + 1] = bk1[n] * ak[n] + bk1[n + 1] * ak[n + 1];
            for (int i = 1; i < n / 2; i++) {
                int idx1 = 2 * i;
                int idx2 = idx1 + 1;
                a[offa + idx1] = bk1[idx1] * ak[idx1] + bk1[idx2] * ak[idx2];
                a[offa + idx2] = -bk1[idx2] * ak[idx1] + bk1[idx1] * ak[idx2];
            }
        } else {
            a[offa] = bk1[0] * ak[0] + bk1[1] * ak[1];
            a[offa + 1] = -bk1[n] * ak[n - 1] + bk1[n - 1] * ak[n];
            for (int i = 1; i < (n - 1) / 2; i++) {
                int idx1 = 2 * i;
                int idx2 = idx1 + 1;
                a[offa + idx1] = bk1[idx1] * ak[idx1] + bk1[idx2] * ak[idx2];
                a[offa + idx2] = -bk1[idx2] * ak[idx1] + bk1[idx1] * ak[idx2];
            }
            a[offa + n - 1] = bk1[n - 1] * ak[n - 1] + bk1[n] * ak[n];
        }

    }

    private void bluestein_real_inverse(final double[] a, final int offa) {
        final double[] ak = new double[2 * nBluestein];
        if (n % 2 == 0) {
            ak[0] = a[offa] * bk1[0];
            ak[1] = a[offa] * bk1[1];

            for (int i = 1; i < n / 2; i++) {
                int idx1 = 2 * i;
                int idx2 = idx1 + 1;
                int idx3 = offa + idx1;
                int idx4 = offa + idx2;
                ak[idx1] = a[idx3] * bk1[idx1] - a[idx4] * bk1[idx2];
                ak[idx2] = a[idx3] * bk1[idx2] + a[idx4] * bk1[idx1];
            }

            ak[n] = a[offa + 1] * bk1[n];
            ak[n + 1] = a[offa + 1] * bk1[n + 1];

            for (int i = n / 2 + 1; i < n; i++) {
                int idx1 = 2 * i;
                int idx2 = idx1 + 1;
                int idx3 = offa + 2 * n - idx1;
                int idx4 = idx3 + 1;
                ak[idx1] = a[idx3] * bk1[idx1] + a[idx4] * bk1[idx2];
                ak[idx2] = a[idx3] * bk1[idx2] - a[idx4] * bk1[idx1];
            }

        } else {
            ak[0] = a[offa] * bk1[0];
            ak[1] = a[offa] * bk1[1];

            for (int i = 1; i < (n - 1) / 2; i++) {
                int idx1 = 2 * i;
                int idx2 = idx1 + 1;
                int idx3 = offa + idx1;
                int idx4 = offa + idx2;
                ak[idx1] = a[idx3] * bk1[idx1] - a[idx4] * bk1[idx2];
                ak[idx2] = a[idx3] * bk1[idx2] + a[idx4] * bk1[idx1];
            }

            ak[n - 1] = a[offa + n - 1] * bk1[n - 1] - a[offa + 1] * bk1[n];
            ak[n] = a[offa + n - 1] * bk1[n] + a[offa + 1] * bk1[n - 1];

            ak[n + 1] = a[offa + n - 1] * bk1[n + 1] + a[offa + 1] * bk1[n + 2];
            ak[n + 2] = a[offa + n - 1] * bk1[n + 2] - a[offa + 1] * bk1[n + 1];

            for (int i = (n - 1) / 2 + 2; i < n; i++) {
                int idx1 = 2 * i;
                int idx2 = idx1 + 1;
                int idx3 = offa + 2 * n - idx1;
                int idx4 = idx3 + 1;
                ak[idx1] = a[idx3] * bk1[idx1] + a[idx4] * bk1[idx2];
                ak[idx2] = a[idx3] * bk1[idx2] - a[idx4] * bk1[idx1];
            }
        }

        cftbsub(2 * nBluestein, ak, 0, ip, nw, w);

        int nthreads = 1;
        int threads = ConcurrencyUtils.getNumberOfThreads();
        if ((threads > 1) && (n > ConcurrencyUtils.getThreadsBeginN_1D_FFT_2Threads())) {
            nthreads = 2;
            if ((threads >= 4) && (n > ConcurrencyUtils.getThreadsBeginN_1D_FFT_4Threads())) {
                nthreads = 4;
            }
            Future<?>[] futures = new Future[nthreads];
            int k = nBluestein / nthreads;
            for (int i = 0; i < nthreads; i++) {
                final int firstIdx = i * k;
                final int lastIdx = (i == (nthreads - 1)) ? nBluestein : firstIdx + k;
                futures[i] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int i = firstIdx; i < lastIdx; i++) {
                            int idx1 = 2 * i;
                            int idx2 = idx1 + 1;
                            double im = -ak[idx1] * bk2[idx2] + ak[idx2] * bk2[idx1];
                            ak[idx1] = ak[idx1] * bk2[idx1] + ak[idx2] * bk2[idx2];
                            ak[idx2] = im;
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            cftfsub(2 * nBluestein, ak, 0, ip, nw, w);

            k = n / nthreads;
            for (int i = 0; i < nthreads; i++) {
                final int firstIdx = i * k;
                final int lastIdx = (i == (nthreads - 1)) ? n : firstIdx + k;
                futures[i] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int i = firstIdx; i < lastIdx; i++) {
                            int idx1 = 2 * i;
                            int idx2 = idx1 + 1;
                            a[offa + i] = bk1[idx1] * ak[idx1] - bk1[idx2] * ak[idx2];
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

        } else {

            for (int i = 0; i < nBluestein; i++) {
                int idx1 = 2 * i;
                int idx2 = idx1 + 1;
                double im = -ak[idx1] * bk2[idx2] + ak[idx2] * bk2[idx1];
                ak[idx1] = ak[idx1] * bk2[idx1] + ak[idx2] * bk2[idx2];
                ak[idx2] = im;
            }

            cftfsub(2 * nBluestein, ak, 0, ip, nw, w);

            for (int i = 0; i < n; i++) {
                int idx1 = 2 * i;
                int idx2 = idx1 + 1;
                a[offa + i] = bk1[idx1] * ak[idx1] - bk1[idx2] * ak[idx2];
            }
        }
    }

    private void bluestein_real_inverse2(final double[] a, final int offa) {
        final double[] ak = new double[2 * nBluestein];
        int nthreads = 1;
        int threads = ConcurrencyUtils.getNumberOfThreads();
        if ((threads > 1) && (n > ConcurrencyUtils.getThreadsBeginN_1D_FFT_2Threads())) {
            nthreads = 2;
            if ((threads >= 4) && (n > ConcurrencyUtils.getThreadsBeginN_1D_FFT_4Threads())) {
                nthreads = 4;
            }
            Future<?>[] futures = new Future[nthreads];
            int k = n / nthreads;
            for (int i = 0; i < nthreads; i++) {
                final int firstIdx = i * k;
                final int lastIdx = (i == (nthreads - 1)) ? n : firstIdx + k;
                futures[i] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int i = firstIdx; i < lastIdx; i++) {
                            int idx1 = 2 * i;
                            int idx2 = idx1 + 1;
                            int idx3 = offa + i;
                            ak[idx1] = a[idx3] * bk1[idx1];
                            ak[idx2] = a[idx3] * bk1[idx2];
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

            cftbsub(2 * nBluestein, ak, 0, ip, nw, w);

            k = nBluestein / nthreads;
            for (int i = 0; i < nthreads; i++) {
                final int firstIdx = i * k;
                final int lastIdx = (i == (nthreads - 1)) ? nBluestein : firstIdx + k;
                futures[i] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        for (int i = firstIdx; i < lastIdx; i++) {
                            int idx1 = 2 * i;
                            int idx2 = idx1 + 1;
                            double im = -ak[idx1] * bk2[idx2] + ak[idx2] * bk2[idx1];
                            ak[idx1] = ak[idx1] * bk2[idx1] + ak[idx2] * bk2[idx2];
                            ak[idx2] = im;
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);

        } else {

            for (int i = 0; i < n; i++) {
                int idx1 = 2 * i;
                int idx2 = idx1 + 1;
                int idx3 = offa + i;
                ak[idx1] = a[idx3] * bk1[idx1];
                ak[idx2] = a[idx3] * bk1[idx2];
            }

            cftbsub(2 * nBluestein, ak, 0, ip, nw, w);

            for (int i = 0; i < nBluestein; i++) {
                int idx1 = 2 * i;
                int idx2 = idx1 + 1;
                double im = -ak[idx1] * bk2[idx2] + ak[idx2] * bk2[idx1];
                ak[idx1] = ak[idx1] * bk2[idx1] + ak[idx2] * bk2[idx2];
                ak[idx2] = im;
            }
        }

        cftfsub(2 * nBluestein, ak, 0, ip, nw, w);

        if (n % 2 == 0) {
            a[offa] = bk1[0] * ak[0] - bk1[1] * ak[1];
            a[offa + 1] = bk1[n] * ak[n] - bk1[n + 1] * ak[n + 1];
            for (int i = 1; i < n / 2; i++) {
                int idx1 = 2 * i;
                int idx2 = idx1 + 1;
                a[offa + idx1] = bk1[idx1] * ak[idx1] - bk1[idx2] * ak[idx2];
                a[offa + idx2] = bk1[idx2] * ak[idx1] + bk1[idx1] * ak[idx2];
            }
        } else {
            a[offa] = bk1[0] * ak[0] - bk1[1] * ak[1];
            a[offa + 1] = bk1[n] * ak[n - 1] + bk1[n - 1] * ak[n];
            for (int i = 1; i < (n - 1) / 2; i++) {
                int idx1 = 2 * i;
                int idx2 = idx1 + 1;
                a[offa + idx1] = bk1[idx1] * ak[idx1] - bk1[idx2] * ak[idx2];
                a[offa + idx2] = bk1[idx2] * ak[idx1] + bk1[idx1] * ak[idx2];
            }
            a[offa + n - 1] = bk1[n - 1] * ak[n - 1] - bk1[n] * ak[n];
        }
    }

    /*---------------------------------------------------------
       rfftf1: further processing of Real forward FFT
      --------------------------------------------------------*/
    void rfftf(final double a[], final int offa) {
        if (n == 1)
            return;
        int l1, l2, na, kh, nf, ip, iw, ido, idl1;

        final double[] ch = new double[n];
        final int twon = 2 * n;
        nf = (int) wtable_r[1 + twon];
        na = 1;
        l2 = n;
        iw = twon - 1;
        for (int k1 = 1; k1 <= nf; ++k1) {
            kh = nf - k1;
            ip = (int) wtable_r[kh + 2 + twon];
            l1 = l2 / ip;
            ido = n / l2;
            idl1 = ido * l1;
            iw -= (ip - 1) * ido;
            na = 1 - na;
            switch (ip) {
            case 2:
                if (na == 0) {
                    radf2(ido, l1, a, offa, ch, 0, iw);
                } else {
                    radf2(ido, l1, ch, 0, a, offa, iw);
                }
                break;
            case 3:
                if (na == 0) {
                    radf3(ido, l1, a, offa, ch, 0, iw);
                } else {
                    radf3(ido, l1, ch, 0, a, offa, iw);
                }
                break;
            case 4:
                if (na == 0) {
                    radf4(ido, l1, a, offa, ch, 0, iw);
                } else {
                    radf4(ido, l1, ch, 0, a, offa, iw);
                }
                break;
            case 5:
                if (na == 0) {
                    radf5(ido, l1, a, offa, ch, 0, iw);
                } else {
                    radf5(ido, l1, ch, 0, a, offa, iw);
                }
                break;
            default:
                if (ido == 1)
                    na = 1 - na;
                if (na == 0) {
                    radfg(ido, ip, l1, idl1, a, offa, ch, 0, iw);
                    na = 1;
                } else {
                    radfg(ido, ip, l1, idl1, ch, 0, a, offa, iw);
                    na = 0;
                }
                break;
            }
            l2 = l1;
        }
        if (na == 1)
            return;
        System.arraycopy(ch, 0, a, offa, n);
    }

    /*---------------------------------------------------------
       rfftb1: further processing of Real backward FFT
      --------------------------------------------------------*/
    void rfftb(final double a[], final int offa) {
        if (n == 1)
            return;
        int l1, l2, na, nf, ip, iw, ido, idl1;

        double[] ch = new double[n];
        final int twon = 2 * n;
        nf = (int) wtable_r[1 + twon];
        na = 0;
        l1 = 1;
        iw = n;
        for (int k1 = 1; k1 <= nf; k1++) {
            ip = (int) wtable_r[k1 + 1 + twon];
            l2 = ip * l1;
            ido = n / l2;
            idl1 = ido * l1;
            switch (ip) {
            case 2:
                if (na == 0) {
                    radb2(ido, l1, a, offa, ch, 0, iw);
                } else {
                    radb2(ido, l1, ch, 0, a, offa, iw);
                }
                na = 1 - na;
                break;
            case 3:
                if (na == 0) {
                    radb3(ido, l1, a, offa, ch, 0, iw);
                } else {
                    radb3(ido, l1, ch, 0, a, offa, iw);
                }
                na = 1 - na;
                break;
            case 4:
                if (na == 0) {
                    radb4(ido, l1, a, offa, ch, 0, iw);
                } else {
                    radb4(ido, l1, ch, 0, a, offa, iw);
                }
                na = 1 - na;
                break;
            case 5:
                if (na == 0) {
                    radb5(ido, l1, a, offa, ch, 0, iw);
                } else {
                    radb5(ido, l1, ch, 0, a, offa, iw);
                }
                na = 1 - na;
                break;
            default:
                if (na == 0) {
                    radbg(ido, ip, l1, idl1, a, offa, ch, 0, iw);
                } else {
                    radbg(ido, ip, l1, idl1, ch, 0, a, offa, iw);
                }
                if (ido == 1)
                    na = 1 - na;
                break;
            }
            l1 = l2;
            iw += (ip - 1) * ido;
        }
        if (na == 0)
            return;
        System.arraycopy(ch, 0, a, offa, n);
    }

    /*-------------------------------------------------
       radf2: Real FFT's forward processing of factor 2
      -------------------------------------------------*/
    void radf2(final int ido, final int l1, final double in[], final int in_off, final double out[], final int out_off, final int offset) {
        int i, ic, idx0, idx1, idx2, idx3, idx4;
        double t1i, t1r, w1r, w1i;
        int iw1;
        iw1 = offset;
        idx0 = l1 * ido;
        idx1 = 2 * ido;
        for (int k = 0; k < l1; k++) {
            int oidx1 = out_off + k * idx1;
            int oidx2 = oidx1 + idx1 - 1;
            int iidx1 = in_off + k * ido;
            int iidx2 = iidx1 + idx0;

            double i1r = in[iidx1];
            double i2r = in[iidx2];

            out[oidx1] = i1r + i2r;
            out[oidx2] = i1r - i2r;
        }
        if (ido < 2)
            return;
        if (ido != 2) {
            for (int k = 0; k < l1; k++) {
                idx1 = k * ido;
                idx2 = 2 * idx1;
                idx3 = idx2 + ido;
                idx4 = idx1 + idx0;
                for (i = 2; i < ido; i += 2) {
                    ic = ido - i;
                    int widx1 = i - 1 + iw1;
                    int oidx1 = out_off + i + idx2;
                    int oidx2 = out_off + ic + idx3;
                    int iidx1 = in_off + i + idx1;
                    int iidx2 = in_off + i + idx4;

                    double a1i = in[iidx1 - 1];
                    double a1r = in[iidx1];
                    double a2i = in[iidx2 - 1];
                    double a2r = in[iidx2];

                    w1r = wtable_r[widx1 - 1];
                    w1i = wtable_r[widx1];

                    t1r = w1r * a2i + w1i * a2r;
                    t1i = w1r * a2r - w1i * a2i;

                    out[oidx1] = a1r + t1i;
                    out[oidx1 - 1] = a1i + t1r;

                    out[oidx2] = t1i - a1r;
                    out[oidx2 - 1] = a1i - t1r;
                }
            }
            if (ido % 2 == 1)
                return;
        }
        idx2 = 2 * idx1;
        for (int k = 0; k < l1; k++) {
            idx1 = k * ido;
            int oidx1 = out_off + idx2 + ido;
            int iidx1 = in_off + ido - 1 + idx1;

            out[oidx1] = -in[iidx1 + idx0];
            out[oidx1 - 1] = in[iidx1];
        }
    }

    /*-------------------------------------------------
       radb2: Real FFT's backward processing of factor 2
      -------------------------------------------------*/
    void radb2(final int ido, final int l1, final double in[], final int in_off, final double out[], final int out_off, final int offset) {
        int i, ic;
        double t1i, t1r, w1r, w1i;
        int iw1 = offset;

        int idx0 = l1 * ido;
        for (int k = 0; k < l1; k++) {
            int idx1 = k * ido;
            int idx2 = 2 * idx1;
            int idx3 = idx2 + ido;
            int oidx1 = out_off + idx1;
            int iidx1 = in_off + idx2;
            int iidx2 = in_off + ido - 1 + idx3;
            double i1r = in[iidx1];
            double i2r = in[iidx2];
            out[oidx1] = i1r + i2r;
            out[oidx1 + idx0] = i1r - i2r;
        }
        if (ido < 2)
            return;
        if (ido != 2) {
            for (int k = 0; k < l1; ++k) {
                int idx1 = k * ido;
                int idx2 = 2 * idx1;
                int idx3 = idx2 + ido;
                int idx4 = idx1 + idx0;
                for (i = 2; i < ido; i += 2) {
                    ic = ido - i;
                    int idx5 = i - 1 + iw1;
                    int idx6 = out_off + i;
                    int idx7 = in_off + i;
                    int idx8 = in_off + ic;
                    w1r = wtable_r[idx5 - 1];
                    w1i = wtable_r[idx5];
                    int iidx1 = idx7 + idx2;
                    int iidx2 = idx8 + idx3;
                    int oidx1 = idx6 + idx1;
                    int oidx2 = idx6 + idx4;
                    t1r = in[iidx1 - 1] - in[iidx2 - 1];
                    t1i = in[iidx1] + in[iidx2];
                    double i1i = in[iidx1];
                    double i1r = in[iidx1 - 1];
                    double i2i = in[iidx2];
                    double i2r = in[iidx2 - 1];

                    out[oidx1 - 1] = i1r + i2r;
                    out[oidx1] = i1i - i2i;
                    out[oidx2 - 1] = w1r * t1r - w1i * t1i;
                    out[oidx2] = w1r * t1i + w1i * t1r;
                }
            }
            if (ido % 2 == 1)
                return;
        }
        for (int k = 0; k < l1; k++) {
            int idx1 = k * ido;
            int idx2 = 2 * idx1;
            int oidx1 = out_off + ido - 1 + idx1;
            int iidx1 = in_off + idx2 + ido;
            out[oidx1] = 2 * in[iidx1 - 1];
            out[oidx1 + idx0] = -2 * in[iidx1];
        }
    }

    /*-------------------------------------------------
       radf3: Real FFT's forward processing of factor 3 
      -------------------------------------------------*/
    void radf3(final int ido, final int l1, final double in[], final int in_off, final double out[], final int out_off, final int offset) {
        final double taur = -0.5;
        final double taui = 0.866025403784438707610604524234076962;
        int i, ic;
        double ci2, di2, di3, cr2, dr2, dr3, ti2, ti3, tr2, tr3, w1r, w2r, w1i, w2i;
        int iw1, iw2;
        iw1 = offset;
        iw2 = iw1 + ido;

        int idx0 = l1 * ido;
        for (int k = 0; k < l1; k++) {
            int idx1 = k * ido;
            int idx3 = 2 * idx0;
            int idx4 = (3 * k + 1) * ido;
            int iidx1 = in_off + idx1;
            int iidx2 = iidx1 + idx0;
            int iidx3 = iidx1 + idx3;
            double i1r = in[iidx1];
            double i2r = in[iidx2];
            double i3r = in[iidx3];
            cr2 = i2r + i3r;
            out[out_off + 3 * idx1] = i1r + cr2;
            out[out_off + idx4 + ido] = taui * (i3r - i2r);
            out[out_off + ido - 1 + idx4] = i1r + taur * cr2;
        }
        if (ido == 1)
            return;
        for (int k = 0; k < l1; k++) {
            int idx3 = k * ido;
            int idx4 = 3 * idx3;
            int idx5 = idx3 + idx0;
            int idx6 = idx5 + idx0;
            int idx7 = idx4 + ido;
            int idx8 = idx7 + ido;
            for (i = 2; i < ido; i += 2) {
                ic = ido - i;
                int widx1 = i - 1 + iw1;
                int widx2 = i - 1 + iw2;

                w1r = wtable_r[widx1 - 1];
                w1i = wtable_r[widx1];
                w2r = wtable_r[widx2 - 1];
                w2i = wtable_r[widx2];

                int idx9 = in_off + i;
                int idx10 = out_off + i;
                int idx11 = out_off + ic;
                int iidx1 = idx9 + idx3;
                int iidx2 = idx9 + idx5;
                int iidx3 = idx9 + idx6;

                double i1i = in[iidx1 - 1];
                double i1r = in[iidx1];
                double i2i = in[iidx2 - 1];
                double i2r = in[iidx2];
                double i3i = in[iidx3 - 1];
                double i3r = in[iidx3];

                dr2 = w1r * i2i + w1i * i2r;
                di2 = w1r * i2r - w1i * i2i;
                dr3 = w2r * i3i + w2i * i3r;
                di3 = w2r * i3r - w2i * i3i;
                cr2 = dr2 + dr3;
                ci2 = di2 + di3;
                tr2 = i1i + taur * cr2;
                ti2 = i1r + taur * ci2;
                tr3 = taui * (di2 - di3);
                ti3 = taui * (dr3 - dr2);

                int oidx1 = idx10 + idx4;
                int oidx2 = idx11 + idx7;
                int oidx3 = idx10 + idx8;

                out[oidx1 - 1] = i1i + cr2;
                out[oidx1] = i1r + ci2;
                out[oidx2 - 1] = tr2 - tr3;
                out[oidx2] = ti3 - ti2;
                out[oidx3 - 1] = tr2 + tr3;
                out[oidx3] = ti2 + ti3;
            }
        }
    }

    /*-------------------------------------------------
       radb3: Real FFT's backward processing of factor 3
      -------------------------------------------------*/
    void radb3(final int ido, final int l1, final double in[], final int in_off, final double out[], final int out_off, final int offset) {
        final double taur = -0.5;
        final double taui = 0.866025403784438707610604524234076962;
        int i, ic;
        double ci2, ci3, di2, di3, cr2, cr3, dr2, dr3, ti2, tr2, w1r, w2r, w1i, w2i;
        int iw1, iw2;
        iw1 = offset;
        iw2 = iw1 + ido;

        for (int k = 0; k < l1; k++) {
            int idx1 = k * ido;
            int iidx1 = in_off + 3 * idx1;
            int iidx2 = iidx1 + 2 * ido;
            double i1i = in[iidx1];

            tr2 = 2 * in[iidx2 - 1];
            cr2 = i1i + taur * tr2;
            ci3 = 2 * taui * in[iidx2];

            out[out_off + idx1] = i1i + tr2;
            out[out_off + (k + l1) * ido] = cr2 - ci3;
            out[out_off + (k + 2 * l1) * ido] = cr2 + ci3;
        }
        if (ido == 1)
            return;
        int idx0 = l1 * ido;
        for (int k = 0; k < l1; k++) {
            int idx1 = k * ido;
            int idx2 = 3 * idx1;
            int idx3 = idx2 + ido;
            int idx4 = idx3 + ido;
            int idx5 = idx1 + idx0;
            int idx6 = idx5 + idx0;
            for (i = 2; i < ido; i += 2) {
                ic = ido - i;
                int idx7 = in_off + i;
                int idx8 = in_off + ic;
                int idx9 = out_off + i;
                int iidx1 = idx7 + idx2;
                int iidx2 = idx7 + idx4;
                int iidx3 = idx8 + idx3;

                double i1i = in[iidx1 - 1];
                double i1r = in[iidx1];
                double i2i = in[iidx2 - 1];
                double i2r = in[iidx2];
                double i3i = in[iidx3 - 1];
                double i3r = in[iidx3];

                tr2 = i2i + i3i;
                cr2 = i1i + taur * tr2;
                ti2 = i2r - i3r;
                ci2 = i1r + taur * ti2;
                cr3 = taui * (i2i - i3i);
                ci3 = taui * (i2r + i3r);
                dr2 = cr2 - ci3;
                dr3 = cr2 + ci3;
                di2 = ci2 + cr3;
                di3 = ci2 - cr3;

                int widx1 = i - 1 + iw1;
                int widx2 = i - 1 + iw2;

                w1r = wtable_r[widx1 - 1];
                w1i = wtable_r[widx1];
                w2r = wtable_r[widx2 - 1];
                w2i = wtable_r[widx2];

                int oidx1 = idx9 + idx1;
                int oidx2 = idx9 + idx5;
                int oidx3 = idx9 + idx6;

                out[oidx1 - 1] = i1i + tr2;
                out[oidx1] = i1r + ti2;
                out[oidx2 - 1] = w1r * dr2 - w1i * di2;
                out[oidx2] = w1r * di2 + w1i * dr2;
                out[oidx3 - 1] = w2r * dr3 - w2i * di3;
                out[oidx3] = w2r * di3 + w2i * dr3;
            }
        }
    }

    /*-------------------------------------------------
       radf4: Real FFT's forward processing of factor 4
      -------------------------------------------------*/
    void radf4(final int ido, final int l1, final double in[], final int in_off, final double out[], final int out_off, final int offset) {
        final double hsqt2 = 0.707106781186547572737310929369414225;
        int i, ic;
        double ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4, w1r, w1i, w2r, w2i, w3r, w3i;
        int iw1, iw2, iw3;
        iw1 = offset;
        iw2 = offset + ido;
        iw3 = iw2 + ido;
        int idx0 = l1 * ido;
        for (int k = 0; k < l1; k++) {
            int idx1 = k * ido;
            int idx2 = 4 * idx1;
            int idx3 = idx1 + idx0;
            int idx4 = idx3 + idx0;
            int idx5 = idx4 + idx0;
            int idx6 = idx2 + ido;
            double i1r = in[in_off + idx1];
            double i2r = in[in_off + idx3];
            double i3r = in[in_off + idx4];
            double i4r = in[in_off + idx5];

            tr1 = i2r + i4r;
            tr2 = i1r + i3r;

            int oidx1 = out_off + idx2;
            int oidx2 = out_off + idx6 + ido;

            out[oidx1] = tr1 + tr2;
            out[oidx2 - 1 + ido + ido] = tr2 - tr1;
            out[oidx2 - 1] = i1r - i3r;
            out[oidx2] = i4r - i2r;
        }
        if (ido < 2)
            return;
        if (ido != 2) {
            for (int k = 0; k < l1; k++) {
                int idx1 = k * ido;
                int idx2 = idx1 + idx0;
                int idx3 = idx2 + idx0;
                int idx4 = idx3 + idx0;
                int idx5 = 4 * idx1;
                int idx6 = idx5 + ido;
                int idx7 = idx6 + ido;
                int idx8 = idx7 + ido;
                for (i = 2; i < ido; i += 2) {
                    ic = ido - i;
                    int widx1 = i - 1 + iw1;
                    int widx2 = i - 1 + iw2;
                    int widx3 = i - 1 + iw3;
                    w1r = wtable_r[widx1 - 1];
                    w1i = wtable_r[widx1];
                    w2r = wtable_r[widx2 - 1];
                    w2i = wtable_r[widx2];
                    w3r = wtable_r[widx3 - 1];
                    w3i = wtable_r[widx3];

                    int idx9 = in_off + i;
                    int idx10 = out_off + i;
                    int idx11 = out_off + ic;
                    int iidx1 = idx9 + idx1;
                    int iidx2 = idx9 + idx2;
                    int iidx3 = idx9 + idx3;
                    int iidx4 = idx9 + idx4;

                    double i1i = in[iidx1 - 1];
                    double i1r = in[iidx1];
                    double i2i = in[iidx2 - 1];
                    double i2r = in[iidx2];
                    double i3i = in[iidx3 - 1];
                    double i3r = in[iidx3];
                    double i4i = in[iidx4 - 1];
                    double i4r = in[iidx4];

                    cr2 = w1r * i2i + w1i * i2r;
                    ci2 = w1r * i2r - w1i * i2i;
                    cr3 = w2r * i3i + w2i * i3r;
                    ci3 = w2r * i3r - w2i * i3i;
                    cr4 = w3r * i4i + w3i * i4r;
                    ci4 = w3r * i4r - w3i * i4i;
                    tr1 = cr2 + cr4;
                    tr4 = cr4 - cr2;
                    ti1 = ci2 + ci4;
                    ti4 = ci2 - ci4;
                    ti2 = i1r + ci3;
                    ti3 = i1r - ci3;
                    tr2 = i1i + cr3;
                    tr3 = i1i - cr3;

                    int oidx1 = idx10 + idx5;
                    int oidx2 = idx11 + idx6;
                    int oidx3 = idx10 + idx7;
                    int oidx4 = idx11 + idx8;

                    out[oidx1 - 1] = tr1 + tr2;
                    out[oidx4 - 1] = tr2 - tr1;
                    out[oidx1] = ti1 + ti2;
                    out[oidx4] = ti1 - ti2;
                    out[oidx3 - 1] = ti4 + tr3;
                    out[oidx2 - 1] = tr3 - ti4;
                    out[oidx3] = tr4 + ti3;
                    out[oidx2] = tr4 - ti3;
                }
            }
            if (ido % 2 == 1)
                return;
        }
        for (int k = 0; k < l1; k++) {
            int idx1 = k * ido;
            int idx2 = 4 * idx1;
            int idx3 = idx1 + idx0;
            int idx4 = idx3 + idx0;
            int idx5 = idx4 + idx0;
            int idx6 = idx2 + ido;
            int idx7 = idx6 + ido;
            int idx8 = idx7 + ido;
            int idx9 = in_off + ido;
            int idx10 = out_off + ido;

            double i1i = in[idx9 - 1 + idx1];
            double i2i = in[idx9 - 1 + idx3];
            double i3i = in[idx9 - 1 + idx4];
            double i4i = in[idx9 - 1 + idx5];

            ti1 = -hsqt2 * (i2i + i4i);
            tr1 = hsqt2 * (i2i - i4i);

            out[idx10 - 1 + idx2] = tr1 + i1i;
            out[idx10 - 1 + idx7] = i1i - tr1;
            out[out_off + idx6] = ti1 - i3i;
            out[out_off + idx8] = ti1 + i3i;
        }
    }

    /*-------------------------------------------------
       radb4: Real FFT's backward processing of factor 4
      -------------------------------------------------*/
    void radb4(final int ido, final int l1, final double in[], final int in_off, final double out[], final int out_off, final int offset) {
        final double sqrt2 = 1.41421356237309514547462185873882845;
        int i, ic;
        double ci2, ci3, ci4, cr2, cr3, cr4;
        double ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4, w1r, w1i, w2r, w2i, w3r, w3i;
        int iw1, iw2, iw3;
        iw1 = offset;
        iw2 = iw1 + ido;
        iw3 = iw2 + ido;

        int idx0 = l1 * ido;
        for (int k = 0; k < l1; k++) {
            int idx1 = k * ido;
            int idx2 = 4 * idx1;
            int idx3 = idx1 + idx0;
            int idx4 = idx3 + idx0;
            int idx5 = idx4 + idx0;
            int idx6 = idx2 + ido;
            int idx7 = idx6 + ido;
            int idx8 = idx7 + ido;

            double i1r = in[in_off + idx2];
            double i2r = in[in_off + idx7];
            double i3r = in[in_off + ido - 1 + idx8];
            double i4r = in[in_off + ido - 1 + idx6];

            tr1 = i1r - i3r;
            tr2 = i1r + i3r;
            tr3 = i4r + i4r;
            tr4 = i2r + i2r;

            out[out_off + idx1] = tr2 + tr3;
            out[out_off + idx3] = tr1 - tr4;
            out[out_off + idx4] = tr2 - tr3;
            out[out_off + idx5] = tr1 + tr4;
        }
        if (ido < 2)
            return;
        if (ido != 2) {
            for (int k = 0; k < l1; ++k) {
                int idx1 = k * ido;
                int idx2 = idx1 + idx0;
                int idx3 = idx2 + idx0;
                int idx4 = idx3 + idx0;
                int idx5 = 4 * idx1;
                int idx6 = idx5 + ido;
                int idx7 = idx6 + ido;
                int idx8 = idx7 + ido;
                for (i = 2; i < ido; i += 2) {
                    ic = ido - i;
                    int widx1 = i - 1 + iw1;
                    int widx2 = i - 1 + iw2;
                    int widx3 = i - 1 + iw3;
                    w1r = wtable_r[widx1 - 1];
                    w1i = wtable_r[widx1];
                    w2r = wtable_r[widx2 - 1];
                    w2i = wtable_r[widx2];
                    w3r = wtable_r[widx3 - 1];
                    w3i = wtable_r[widx3];

                    int idx12 = in_off + i;
                    int idx13 = in_off + ic;
                    int idx14 = out_off + i;

                    int iidx1 = idx12 + idx5;
                    int iidx2 = idx13 + idx6;
                    int iidx3 = idx12 + idx7;
                    int iidx4 = idx13 + idx8;

                    double i1i = in[iidx1 - 1];
                    double i1r = in[iidx1];
                    double i2i = in[iidx2 - 1];
                    double i2r = in[iidx2];
                    double i3i = in[iidx3 - 1];
                    double i3r = in[iidx3];
                    double i4i = in[iidx4 - 1];
                    double i4r = in[iidx4];

                    ti1 = i1r + i4r;
                    ti2 = i1r - i4r;
                    ti3 = i3r - i2r;
                    tr4 = i3r + i2r;
                    tr1 = i1i - i4i;
                    tr2 = i1i + i4i;
                    ti4 = i3i - i2i;
                    tr3 = i3i + i2i;
                    cr3 = tr2 - tr3;
                    ci3 = ti2 - ti3;
                    cr2 = tr1 - tr4;
                    cr4 = tr1 + tr4;
                    ci2 = ti1 + ti4;
                    ci4 = ti1 - ti4;

                    int oidx1 = idx14 + idx1;
                    int oidx2 = idx14 + idx2;
                    int oidx3 = idx14 + idx3;
                    int oidx4 = idx14 + idx4;

                    out[oidx1 - 1] = tr2 + tr3;
                    out[oidx1] = ti2 + ti3;
                    out[oidx2 - 1] = w1r * cr2 - w1i * ci2;
                    out[oidx2] = w1r * ci2 + w1i * cr2;
                    out[oidx3 - 1] = w2r * cr3 - w2i * ci3;
                    out[oidx3] = w2r * ci3 + w2i * cr3;
                    out[oidx4 - 1] = w3r * cr4 - w3i * ci4;
                    out[oidx4] = w3r * ci4 + w3i * cr4;
                }
            }
            if (ido % 2 == 1)
                return;
        }
        for (int k = 0; k < l1; k++) {
            int idx1 = k * ido;
            int idx2 = 4 * idx1;
            int idx3 = idx1 + idx0;
            int idx4 = idx3 + idx0;
            int idx5 = idx4 + idx0;
            int idx6 = idx2 + ido;
            int idx7 = idx6 + ido;
            int idx8 = idx7 + ido;
            int idx9 = in_off + ido;
            int idx10 = out_off + ido;

            double i1r = in[idx9 - 1 + idx2];
            double i2r = in[idx9 - 1 + idx7];
            double i3r = in[in_off + idx6];
            double i4r = in[in_off + idx8];

            ti1 = i3r + i4r;
            ti2 = i4r - i3r;
            tr1 = i1r - i2r;
            tr2 = i1r + i2r;

            out[idx10 - 1 + idx1] = tr2 + tr2;
            out[idx10 - 1 + idx3] = sqrt2 * (tr1 - ti1);
            out[idx10 - 1 + idx4] = ti2 + ti2;
            out[idx10 - 1 + idx5] = -sqrt2 * (tr1 + ti1);
        }
    }

    /*-------------------------------------------------
       radf5: Real FFT's forward processing of factor 5
      -------------------------------------------------*/
    void radf5(final int ido, final int l1, final double in[], final int in_off, final double out[], final int out_off, final int offset) {
        final double tr11 = 0.309016994374947451262869435595348477;
        final double ti11 = 0.951056516295153531181938433292089030;
        final double tr12 = -0.809016994374947340240566973079694435;
        final double ti12 = 0.587785252292473248125759255344746634;
        int i, ic;
        double ci2, di2, ci4, ci5, di3, di4, di5, ci3, cr2, cr3, dr2, dr3, dr4, dr5, cr5, cr4, ti2, ti3, ti5, ti4, tr2, tr3, tr4, tr5, w1r, w1i, w2r, w2i, w3r, w3i, w4r, w4i;
        int iw1, iw2, iw3, iw4;
        iw1 = offset;
        iw2 = iw1 + ido;
        iw3 = iw2 + ido;
        iw4 = iw3 + ido;

        int idx0 = l1 * ido;
        for (int k = 0; k < l1; k++) {
            int idx1 = k * ido;
            int idx2 = 5 * idx1;
            int idx3 = idx2 + ido;
            int idx4 = idx3 + ido;
            int idx5 = idx4 + ido;
            int idx6 = idx5 + ido;
            int idx7 = idx1 + idx0;
            int idx8 = idx7 + idx0;
            int idx9 = idx8 + idx0;
            int idx10 = idx9 + idx0;
            int idx11 = out_off + ido - 1;

            double i1r = in[in_off + idx1];
            double i2r = in[in_off + idx7];
            double i3r = in[in_off + idx8];
            double i4r = in[in_off + idx9];
            double i5r = in[in_off + idx10];

            cr2 = i5r + i2r;
            ci5 = i5r - i2r;
            cr3 = i4r + i3r;
            ci4 = i4r - i3r;

            out[out_off + idx2] = i1r + cr2 + cr3;
            out[idx11 + idx3] = i1r + tr11 * cr2 + tr12 * cr3;
            out[out_off + idx4] = ti11 * ci5 + ti12 * ci4;
            out[idx11 + idx5] = i1r + tr12 * cr2 + tr11 * cr3;
            out[out_off + idx6] = ti12 * ci5 - ti11 * ci4;
        }
        if (ido == 1)
            return;
        for (int k = 0; k < l1; ++k) {
            int idx1 = k * ido;
            int idx2 = 5 * idx1;
            int idx3 = idx2 + ido;
            int idx4 = idx3 + ido;
            int idx5 = idx4 + ido;
            int idx6 = idx5 + ido;
            int idx7 = idx1 + idx0;
            int idx8 = idx7 + idx0;
            int idx9 = idx8 + idx0;
            int idx10 = idx9 + idx0;
            for (i = 2; i < ido; i += 2) {
                int widx1 = i - 1 + iw1;
                int widx2 = i - 1 + iw2;
                int widx3 = i - 1 + iw3;
                int widx4 = i - 1 + iw4;
                w1r = wtable_r[widx1 - 1];
                w1i = wtable_r[widx1];
                w2r = wtable_r[widx2 - 1];
                w2i = wtable_r[widx2];
                w3r = wtable_r[widx3 - 1];
                w3i = wtable_r[widx3];
                w4r = wtable_r[widx4 - 1];
                w4i = wtable_r[widx4];

                ic = ido - i;
                int idx15 = in_off + i;
                int idx16 = out_off + i;
                int idx17 = out_off + ic;

                int iidx1 = idx15 + idx1;
                int iidx2 = idx15 + idx7;
                int iidx3 = idx15 + idx8;
                int iidx4 = idx15 + idx9;
                int iidx5 = idx15 + idx10;

                double i1i = in[iidx1 - 1];
                double i1r = in[iidx1];
                double i2i = in[iidx2 - 1];
                double i2r = in[iidx2];
                double i3i = in[iidx3 - 1];
                double i3r = in[iidx3];
                double i4i = in[iidx4 - 1];
                double i4r = in[iidx4];
                double i5i = in[iidx5 - 1];
                double i5r = in[iidx5];

                dr2 = w1r * i2i + w1i * i2r;
                di2 = w1r * i2r - w1i * i2i;
                dr3 = w2r * i3i + w2i * i3r;
                di3 = w2r * i3r - w2i * i3i;
                dr4 = w3r * i4i + w3i * i4r;
                di4 = w3r * i4r - w3i * i4i;
                dr5 = w4r * i5i + w4i * i5r;
                di5 = w4r * i5r - w4i * i5i;

                cr2 = dr2 + dr5;
                ci5 = dr5 - dr2;
                cr5 = di2 - di5;
                ci2 = di2 + di5;
                cr3 = dr3 + dr4;
                ci4 = dr4 - dr3;
                cr4 = di3 - di4;
                ci3 = di3 + di4;

                tr2 = i1i + tr11 * cr2 + tr12 * cr3;
                ti2 = i1r + tr11 * ci2 + tr12 * ci3;
                tr3 = i1i + tr12 * cr2 + tr11 * cr3;
                ti3 = i1r + tr12 * ci2 + tr11 * ci3;
                tr5 = ti11 * cr5 + ti12 * cr4;
                ti5 = ti11 * ci5 + ti12 * ci4;
                tr4 = ti12 * cr5 - ti11 * cr4;
                ti4 = ti12 * ci5 - ti11 * ci4;

                int oidx1 = idx16 + idx2;
                int oidx2 = idx17 + idx3;
                int oidx3 = idx16 + idx4;
                int oidx4 = idx17 + idx5;
                int oidx5 = idx16 + idx6;

                out[oidx1 - 1] = i1i + cr2 + cr3;
                out[oidx1] = i1r + ci2 + ci3;
                out[oidx3 - 1] = tr2 + tr5;
                out[oidx2 - 1] = tr2 - tr5;
                out[oidx3] = ti2 + ti5;
                out[oidx2] = ti5 - ti2;
                out[oidx5 - 1] = tr3 + tr4;
                out[oidx4 - 1] = tr3 - tr4;
                out[oidx5] = ti3 + ti4;
                out[oidx4] = ti4 - ti3;
            }
        }
    }

    /*-------------------------------------------------
       radb5: Real FFT's backward processing of factor 5
      -------------------------------------------------*/
    void radb5(final int ido, final int l1, final double in[], final int in_off, final double out[], final int out_off, final int offset) {
        final double tr11 = 0.309016994374947451262869435595348477;
        final double ti11 = 0.951056516295153531181938433292089030;
        final double tr12 = -0.809016994374947340240566973079694435;
        final double ti12 = 0.587785252292473248125759255344746634;
        int i, ic;
        double ci2, ci3, ci4, ci5, di3, di4, di5, di2, cr2, cr3, cr5, cr4, ti2, ti3, ti4, ti5, dr3, dr4, dr5, dr2, tr2, tr3, tr4, tr5, w1r, w1i, w2r, w2i, w3r, w3i, w4r, w4i;
        int iw1, iw2, iw3, iw4;
        iw1 = offset;
        iw2 = iw1 + ido;
        iw3 = iw2 + ido;
        iw4 = iw3 + ido;

        int idx0 = l1 * ido;
        for (int k = 0; k < l1; k++) {
            int idx1 = k * ido;
            int idx2 = 5 * idx1;
            int idx3 = idx2 + ido;
            int idx4 = idx3 + ido;
            int idx5 = idx4 + ido;
            int idx6 = idx5 + ido;
            int idx7 = idx1 + idx0;
            int idx8 = idx7 + idx0;
            int idx9 = idx8 + idx0;
            int idx10 = idx9 + idx0;
            int idx11 = in_off + ido - 1;

            double i1r = in[in_off + idx2];

            ti5 = 2 * in[in_off + idx4];
            ti4 = 2 * in[in_off + idx6];
            tr2 = 2 * in[idx11 + idx3];
            tr3 = 2 * in[idx11 + idx5];
            cr2 = i1r + tr11 * tr2 + tr12 * tr3;
            cr3 = i1r + tr12 * tr2 + tr11 * tr3;
            ci5 = ti11 * ti5 + ti12 * ti4;
            ci4 = ti12 * ti5 - ti11 * ti4;

            out[out_off + idx1] = i1r + tr2 + tr3;
            out[out_off + idx7] = cr2 - ci5;
            out[out_off + idx8] = cr3 - ci4;
            out[out_off + idx9] = cr3 + ci4;
            out[out_off + idx10] = cr2 + ci5;
        }
        if (ido == 1)
            return;
        for (int k = 0; k < l1; ++k) {
            int idx1 = k * ido;
            int idx2 = 5 * idx1;
            int idx3 = idx2 + ido;
            int idx4 = idx3 + ido;
            int idx5 = idx4 + ido;
            int idx6 = idx5 + ido;
            int idx7 = idx1 + idx0;
            int idx8 = idx7 + idx0;
            int idx9 = idx8 + idx0;
            int idx10 = idx9 + idx0;
            for (i = 2; i < ido; i += 2) {
                ic = ido - i;
                int widx1 = i - 1 + iw1;
                int widx2 = i - 1 + iw2;
                int widx3 = i - 1 + iw3;
                int widx4 = i - 1 + iw4;
                w1r = wtable_r[widx1 - 1];
                w1i = wtable_r[widx1];
                w2r = wtable_r[widx2 - 1];
                w2i = wtable_r[widx2];
                w3r = wtable_r[widx3 - 1];
                w3i = wtable_r[widx3];
                w4r = wtable_r[widx4 - 1];
                w4i = wtable_r[widx4];

                int idx15 = in_off + i;
                int idx16 = in_off + ic;
                int idx17 = out_off + i;

                int iidx1 = idx15 + idx2;
                int iidx2 = idx16 + idx3;
                int iidx3 = idx15 + idx4;
                int iidx4 = idx16 + idx5;
                int iidx5 = idx15 + idx6;

                double i1i = in[iidx1 - 1];
                double i1r = in[iidx1];
                double i2i = in[iidx2 - 1];
                double i2r = in[iidx2];
                double i3i = in[iidx3 - 1];
                double i3r = in[iidx3];
                double i4i = in[iidx4 - 1];
                double i4r = in[iidx4];
                double i5i = in[iidx5 - 1];
                double i5r = in[iidx5];

                ti5 = i3r + i2r;
                ti2 = i3r - i2r;
                ti4 = i5r + i4r;
                ti3 = i5r - i4r;
                tr5 = i3i - i2i;
                tr2 = i3i + i2i;
                tr4 = i5i - i4i;
                tr3 = i5i + i4i;

                cr2 = i1i + tr11 * tr2 + tr12 * tr3;
                ci2 = i1r + tr11 * ti2 + tr12 * ti3;
                cr3 = i1i + tr12 * tr2 + tr11 * tr3;
                ci3 = i1r + tr12 * ti2 + tr11 * ti3;
                cr5 = ti11 * tr5 + ti12 * tr4;
                ci5 = ti11 * ti5 + ti12 * ti4;
                cr4 = ti12 * tr5 - ti11 * tr4;
                ci4 = ti12 * ti5 - ti11 * ti4;
                dr3 = cr3 - ci4;
                dr4 = cr3 + ci4;
                di3 = ci3 + cr4;
                di4 = ci3 - cr4;
                dr5 = cr2 + ci5;
                dr2 = cr2 - ci5;
                di5 = ci2 - cr5;
                di2 = ci2 + cr5;

                int oidx1 = idx17 + idx1;
                int oidx2 = idx17 + idx7;
                int oidx3 = idx17 + idx8;
                int oidx4 = idx17 + idx9;
                int oidx5 = idx17 + idx10;

                out[oidx1 - 1] = i1i + tr2 + tr3;
                out[oidx1] = i1r + ti2 + ti3;
                out[oidx2 - 1] = w1r * dr2 - w1i * di2;
                out[oidx2] = w1r * di2 + w1i * dr2;
                out[oidx3 - 1] = w2r * dr3 - w2i * di3;
                out[oidx3] = w2r * di3 + w2i * dr3;
                out[oidx4 - 1] = w3r * dr4 - w3i * di4;
                out[oidx4] = w3r * di4 + w3i * dr4;
                out[oidx5 - 1] = w4r * dr5 - w4i * di5;
                out[oidx5] = w4r * di5 + w4i * dr5;
            }
        }
    }

    /*---------------------------------------------------------
       radfg: Real FFT's forward processing of general factor
      --------------------------------------------------------*/
    void radfg(final int ido, final int ip, final int l1, final int idl1, final double in[], final int in_off, final double out[], final int out_off, final int offset) {
        int idij, ipph, j2, ic, jc, lc, is, nbd;
        double dc2, ai1, ai2, ar1, ar2, ds2, dcp, arg, dsp, ar1h, ar2h, w1r, w1i;
        int iw1 = offset;

        arg = TWO_PI / (double) ip;
        dcp = Math.cos(arg);
        dsp = Math.sin(arg);
        ipph = (ip + 1) / 2;
        nbd = (ido - 1) / 2;
        if (ido != 1) {
            for (int ik = 0; ik < idl1; ik++)
                out[out_off + ik] = in[in_off + ik];
            for (int j = 1; j < ip; j++) {
                int idx1 = j * l1 * ido;
                for (int k = 0; k < l1; k++) {
                    int idx2 = k * ido + idx1;
                    out[out_off + idx2] = in[in_off + idx2];
                }
            }
            if (nbd <= l1) {
                is = -ido;
                for (int j = 1; j < ip; j++) {
                    is += ido;
                    idij = is - 1;
                    int idx1 = j * l1 * ido;
                    for (int i = 2; i < ido; i += 2) {
                        idij += 2;
                        int idx2 = idij + iw1;
                        int idx4 = in_off + i;
                        int idx5 = out_off + i;
                        w1r = wtable_r[idx2 - 1];
                        w1i = wtable_r[idx2];
                        for (int k = 0; k < l1; k++) {
                            int idx3 = k * ido + idx1;
                            int oidx1 = idx5 + idx3;
                            int iidx1 = idx4 + idx3;
                            double i1i = in[iidx1 - 1];
                            double i1r = in[iidx1];

                            out[oidx1 - 1] = w1r * i1i + w1i * i1r;
                            out[oidx1] = w1r * i1r - w1i * i1i;
                        }
                    }
                }
            } else {
                is = -ido;
                for (int j = 1; j < ip; j++) {
                    is += ido;
                    int idx1 = j * l1 * ido;
                    for (int k = 0; k < l1; k++) {
                        idij = is - 1;
                        int idx3 = k * ido + idx1;
                        for (int i = 2; i < ido; i += 2) {
                            idij += 2;
                            int idx2 = idij + iw1;
                            w1r = wtable_r[idx2 - 1];
                            w1i = wtable_r[idx2];
                            int oidx1 = out_off + i + idx3;
                            int iidx1 = in_off + i + idx3;
                            double i1i = in[iidx1 - 1];
                            double i1r = in[iidx1];

                            out[oidx1 - 1] = w1r * i1i + w1i * i1r;
                            out[oidx1] = w1r * i1r - w1i * i1i;
                        }
                    }
                }
            }
            if (nbd >= l1) {
                for (int j = 1; j < ipph; j++) {
                    jc = ip - j;
                    int idx1 = j * l1 * ido;
                    int idx2 = jc * l1 * ido;
                    for (int k = 0; k < l1; k++) {
                        int idx3 = k * ido + idx1;
                        int idx4 = k * ido + idx2;
                        for (int i = 2; i < ido; i += 2) {
                            int idx5 = in_off + i;
                            int idx6 = out_off + i;
                            int iidx1 = idx5 + idx3;
                            int iidx2 = idx5 + idx4;
                            int oidx1 = idx6 + idx3;
                            int oidx2 = idx6 + idx4;
                            double o1i = out[oidx1 - 1];
                            double o1r = out[oidx1];
                            double o2i = out[oidx2 - 1];
                            double o2r = out[oidx2];

                            in[iidx1 - 1] = o1i + o2i;
                            in[iidx1] = o1r + o2r;

                            in[iidx2 - 1] = o1r - o2r;
                            in[iidx2] = o2i - o1i;
                        }
                    }
                }
            } else {
                for (int j = 1; j < ipph; j++) {
                    jc = ip - j;
                    int idx1 = j * l1 * ido;
                    int idx2 = jc * l1 * ido;
                    for (int i = 2; i < ido; i += 2) {
                        int idx5 = in_off + i;
                        int idx6 = out_off + i;
                        for (int k = 0; k < l1; k++) {
                            int idx3 = k * ido + idx1;
                            int idx4 = k * ido + idx2;
                            int iidx1 = idx5 + idx3;
                            int iidx2 = idx5 + idx4;
                            int oidx1 = idx6 + idx3;
                            int oidx2 = idx6 + idx4;
                            double o1i = out[oidx1 - 1];
                            double o1r = out[oidx1];
                            double o2i = out[oidx2 - 1];
                            double o2r = out[oidx2];

                            in[iidx1 - 1] = o1i + o2i;
                            in[iidx1] = o1r + o2r;
                            in[iidx2 - 1] = o1r - o2r;
                            in[iidx2] = o2i - o1i;
                        }
                    }
                }
            }
        } else {
            System.arraycopy(out, out_off, in, in_off, idl1);
        }
        for (int j = 1; j < ipph; j++) {
            jc = ip - j;
            int idx1 = j * l1 * ido;
            int idx2 = jc * l1 * ido;
            for (int k = 0; k < l1; k++) {
                int idx3 = k * ido + idx1;
                int idx4 = k * ido + idx2;
                int oidx1 = out_off + idx3;
                int oidx2 = out_off + idx4;
                double o1r = out[oidx1];
                double o2r = out[oidx2];

                in[in_off + idx3] = o1r + o2r;
                in[in_off + idx4] = o2r - o1r;
            }
        }

        ar1 = 1;
        ai1 = 0;
        int idx0 = (ip - 1) * idl1;
        for (int l = 1; l < ipph; l++) {
            lc = ip - l;
            ar1h = dcp * ar1 - dsp * ai1;
            ai1 = dcp * ai1 + dsp * ar1;
            ar1 = ar1h;
            int idx1 = l * idl1;
            int idx2 = lc * idl1;
            for (int ik = 0; ik < idl1; ik++) {
                int idx3 = out_off + ik;
                int idx4 = in_off + ik;
                out[idx3 + idx1] = in[idx4] + ar1 * in[idx4 + idl1];
                out[idx3 + idx2] = ai1 * in[idx4 + idx0];
            }
            dc2 = ar1;
            ds2 = ai1;
            ar2 = ar1;
            ai2 = ai1;
            for (int j = 2; j < ipph; j++) {
                jc = ip - j;
                ar2h = dc2 * ar2 - ds2 * ai2;
                ai2 = dc2 * ai2 + ds2 * ar2;
                ar2 = ar2h;
                int idx3 = j * idl1;
                int idx4 = jc * idl1;
                for (int ik = 0; ik < idl1; ik++) {
                    int idx5 = out_off + ik;
                    int idx6 = in_off + ik;
                    out[idx5 + idx1] += ar2 * in[idx6 + idx3];
                    out[idx5 + idx2] += ai2 * in[idx6 + idx4];
                }
            }
        }
        for (int j = 1; j < ipph; j++) {
            int idx1 = j * idl1;
            for (int ik = 0; ik < idl1; ik++) {
                out[out_off + ik] += in[in_off + ik + idx1];
            }
        }

        if (ido >= l1) {
            for (int k = 0; k < l1; k++) {
                int idx1 = k * ido;
                int idx2 = idx1 * ip;
                for (int i = 0; i < ido; i++) {
                    in[in_off + i + idx2] = out[out_off + i + idx1];
                }
            }
        } else {
            for (int i = 0; i < ido; i++) {
                for (int k = 0; k < l1; k++) {
                    int idx1 = k * ido;
                    in[in_off + i + idx1 * ip] = out[out_off + i + idx1];
                }
            }
        }
        int idx01 = ip * ido;
        for (int j = 1; j < ipph; j++) {
            jc = ip - j;
            j2 = 2 * j;
            int idx1 = j * l1 * ido;
            int idx2 = jc * l1 * ido;
            int idx3 = j2 * ido;
            for (int k = 0; k < l1; k++) {
                int idx4 = k * ido;
                int idx5 = idx4 + idx1;
                int idx6 = idx4 + idx2;
                int idx7 = k * idx01;
                in[in_off + ido - 1 + idx3 - ido + idx7] = out[out_off + idx5];
                in[in_off + idx3 + idx7] = out[out_off + idx6];
            }
        }
        if (ido == 1)
            return;
        if (nbd >= l1) {
            for (int j = 1; j < ipph; j++) {
                jc = ip - j;
                j2 = 2 * j;
                int idx1 = j * l1 * ido;
                int idx2 = jc * l1 * ido;
                int idx3 = j2 * ido;
                for (int k = 0; k < l1; k++) {
                    int idx4 = k * idx01;
                    int idx5 = k * ido;
                    for (int i = 2; i < ido; i += 2) {
                        ic = ido - i;
                        int idx6 = in_off + i;
                        int idx7 = in_off + ic;
                        int idx8 = out_off + i;
                        int iidx1 = idx6 + idx3 + idx4;
                        int iidx2 = idx7 + idx3 - ido + idx4;
                        int oidx1 = idx8 + idx5 + idx1;
                        int oidx2 = idx8 + idx5 + idx2;
                        double o1i = out[oidx1 - 1];
                        double o1r = out[oidx1];
                        double o2i = out[oidx2 - 1];
                        double o2r = out[oidx2];

                        in[iidx1 - 1] = o1i + o2i;
                        in[iidx2 - 1] = o1i - o2i;
                        in[iidx1] = o1r + o2r;
                        in[iidx2] = o2r - o1r;
                    }
                }
            }
        } else {
            for (int j = 1; j < ipph; j++) {
                jc = ip - j;
                j2 = 2 * j;
                int idx1 = j * l1 * ido;
                int idx2 = jc * l1 * ido;
                int idx3 = j2 * ido;
                for (int i = 2; i < ido; i += 2) {
                    ic = ido - i;
                    int idx6 = in_off + i;
                    int idx7 = in_off + ic;
                    int idx8 = out_off + i;
                    for (int k = 0; k < l1; k++) {
                        int idx4 = k * idx01;
                        int idx5 = k * ido;
                        int iidx1 = idx6 + idx3 + idx4;
                        int iidx2 = idx7 + idx3 - ido + idx4;
                        int oidx1 = idx8 + idx5 + idx1;
                        int oidx2 = idx8 + idx5 + idx2;
                        double o1i = out[oidx1 - 1];
                        double o1r = out[oidx1];
                        double o2i = out[oidx2 - 1];
                        double o2r = out[oidx2];

                        in[iidx1 - 1] = o1i + o2i;
                        in[iidx2 - 1] = o1i - o2i;
                        in[iidx1] = o1r + o2r;
                        in[iidx2] = o2r - o1r;
                    }
                }
            }
        }
    }

    /*---------------------------------------------------------
       radbg: Real FFT's backward processing of general factor
      --------------------------------------------------------*/
    void radbg(final int ido, final int ip, final int l1, final int idl1, final double in[], final int in_off, final double out[], final int out_off, final int offset) {
        int idij, ipph, j2, ic, jc, lc, is;
        double dc2, ai1, ai2, ar1, ar2, ds2, w1r, w1i;
        int nbd;
        double dcp, arg, dsp, ar1h, ar2h;
        int iw1 = offset;

        arg = TWO_PI / (double) ip;
        dcp = Math.cos(arg);
        dsp = Math.sin(arg);
        nbd = (ido - 1) / 2;
        ipph = (ip + 1) / 2;
        int idx0 = ip * ido;
        if (ido >= l1) {
            for (int k = 0; k < l1; k++) {
                int idx1 = k * ido;
                int idx2 = k * idx0;
                for (int i = 0; i < ido; i++) {
                    out[out_off + i + idx1] = in[in_off + i + idx2];
                }
            }
        } else {
            for (int i = 0; i < ido; i++) {
                int idx1 = out_off + i;
                int idx2 = in_off + i;
                for (int k = 0; k < l1; k++) {
                    out[idx1 + k * ido] = in[idx2 + k * idx0];
                }
            }
        }
        int iidx0 = in_off + ido - 1;
        for (int j = 1; j < ipph; j++) {
            jc = ip - j;
            j2 = 2 * j;
            int idx1 = j * l1 * ido;
            int idx2 = jc * l1 * ido;
            int idx3 = j2 * ido;
            for (int k = 0; k < l1; k++) {
                int idx4 = k * ido;
                int idx5 = idx4 * ip;
                int iidx1 = iidx0 + idx3 + idx5 - ido;
                int iidx2 = in_off + idx3 + idx5;
                double i1r = in[iidx1];
                double i2r = in[iidx2];

                out[out_off + idx4 + idx1] = i1r + i1r;
                out[out_off + idx4 + idx2] = i2r + i2r;
            }
        }

        if (ido != 1) {
            if (nbd >= l1) {
                for (int j = 1; j < ipph; j++) {
                    jc = ip - j;
                    int idx1 = j * l1 * ido;
                    int idx2 = jc * l1 * ido;
                    int idx3 = 2 * j * ido;
                    for (int k = 0; k < l1; k++) {
                        int idx4 = k * ido + idx1;
                        int idx5 = k * ido + idx2;
                        int idx6 = k * ip * ido + idx3;
                        for (int i = 2; i < ido; i += 2) {
                            ic = ido - i;
                            int idx7 = out_off + i;
                            int idx8 = in_off + ic;
                            int idx9 = in_off + i;
                            int oidx1 = idx7 + idx4;
                            int oidx2 = idx7 + idx5;
                            int iidx1 = idx9 + idx6;
                            int iidx2 = idx8 + idx6 - ido;
                            double a1i = in[iidx1 - 1];
                            double a1r = in[iidx1];
                            double a2i = in[iidx2 - 1];
                            double a2r = in[iidx2];

                            out[oidx1 - 1] = a1i + a2i;
                            out[oidx2 - 1] = a1i - a2i;
                            out[oidx1] = a1r - a2r;
                            out[oidx2] = a1r + a2r;
                        }
                    }
                }
            } else {
                for (int j = 1; j < ipph; j++) {
                    jc = ip - j;
                    int idx1 = j * l1 * ido;
                    int idx2 = jc * l1 * ido;
                    int idx3 = 2 * j * ido;
                    for (int i = 2; i < ido; i += 2) {
                        ic = ido - i;
                        int idx7 = out_off + i;
                        int idx8 = in_off + ic;
                        int idx9 = in_off + i;
                        for (int k = 0; k < l1; k++) {
                            int idx4 = k * ido + idx1;
                            int idx5 = k * ido + idx2;
                            int idx6 = k * ip * ido + idx3;
                            int oidx1 = idx7 + idx4;
                            int oidx2 = idx7 + idx5;
                            int iidx1 = idx9 + idx6;
                            int iidx2 = idx8 + idx6 - ido;
                            double a1i = in[iidx1 - 1];
                            double a1r = in[iidx1];
                            double a2i = in[iidx2 - 1];
                            double a2r = in[iidx2];

                            out[oidx1 - 1] = a1i + a2i;
                            out[oidx2 - 1] = a1i - a2i;
                            out[oidx1] = a1r - a2r;
                            out[oidx2] = a1r + a2r;
                        }
                    }
                }
            }
        }

        ar1 = 1;
        ai1 = 0;
        int idx01 = (ip - 1) * idl1;
        for (int l = 1; l < ipph; l++) {
            lc = ip - l;
            ar1h = dcp * ar1 - dsp * ai1;
            ai1 = dcp * ai1 + dsp * ar1;
            ar1 = ar1h;
            int idx1 = l * idl1;
            int idx2 = lc * idl1;
            for (int ik = 0; ik < idl1; ik++) {
                int idx3 = in_off + ik;
                int idx4 = out_off + ik;
                in[idx3 + idx1] = out[idx4] + ar1 * out[idx4 + idl1];
                in[idx3 + idx2] = ai1 * out[idx4 + idx01];
            }
            dc2 = ar1;
            ds2 = ai1;
            ar2 = ar1;
            ai2 = ai1;
            for (int j = 2; j < ipph; j++) {
                jc = ip - j;
                ar2h = dc2 * ar2 - ds2 * ai2;
                ai2 = dc2 * ai2 + ds2 * ar2;
                ar2 = ar2h;
                int idx5 = j * idl1;
                int idx6 = jc * idl1;
                for (int ik = 0; ik < idl1; ik++) {
                    int idx7 = in_off + ik;
                    int idx8 = out_off + ik;
                    in[idx7 + idx1] += ar2 * out[idx8 + idx5];
                    in[idx7 + idx2] += ai2 * out[idx8 + idx6];
                }
            }
        }
        for (int j = 1; j < ipph; j++) {
            int idx1 = j * idl1;
            for (int ik = 0; ik < idl1; ik++) {
                int idx2 = out_off + ik;
                out[idx2] += out[idx2 + idx1];
            }
        }
        for (int j = 1; j < ipph; j++) {
            jc = ip - j;
            int idx1 = j * l1 * ido;
            int idx2 = jc * l1 * ido;
            for (int k = 0; k < l1; k++) {
                int idx3 = k * ido;
                int oidx1 = out_off + idx3;
                int iidx1 = in_off + idx3 + idx1;
                int iidx2 = in_off + idx3 + idx2;
                double i1r = in[iidx1];
                double i2r = in[iidx2];

                out[oidx1 + idx1] = i1r - i2r;
                out[oidx1 + idx2] = i1r + i2r;
            }
        }

        if (ido == 1)
            return;
        if (nbd >= l1) {
            for (int j = 1; j < ipph; j++) {
                jc = ip - j;
                int idx1 = j * l1 * ido;
                int idx2 = jc * l1 * ido;
                for (int k = 0; k < l1; k++) {
                    int idx3 = k * ido;
                    for (int i = 2; i < ido; i += 2) {
                        int idx4 = out_off + i;
                        int idx5 = in_off + i;
                        int oidx1 = idx4 + idx3 + idx1;
                        int oidx2 = idx4 + idx3 + idx2;
                        int iidx1 = idx5 + idx3 + idx1;
                        int iidx2 = idx5 + idx3 + idx2;
                        double i1i = in[iidx1 - 1];
                        double i1r = in[iidx1];
                        double i2i = in[iidx2 - 1];
                        double i2r = in[iidx2];

                        out[oidx1 - 1] = i1i - i2r;
                        out[oidx2 - 1] = i1i + i2r;
                        out[oidx1] = i1r + i2i;
                        out[oidx2] = i1r - i2i;
                    }
                }
            }
        } else {
            for (int j = 1; j < ipph; j++) {
                jc = ip - j;
                int idx1 = j * l1 * ido;
                int idx2 = jc * l1 * ido;
                for (int i = 2; i < ido; i += 2) {
                    int idx4 = out_off + i;
                    int idx5 = in_off + i;
                    for (int k = 0; k < l1; k++) {
                        int idx3 = k * ido;
                        int oidx1 = idx4 + idx3 + idx1;
                        int oidx2 = idx4 + idx3 + idx2;
                        int iidx1 = idx5 + idx3 + idx1;
                        int iidx2 = idx5 + idx3 + idx2;
                        double i1i = in[iidx1 - 1];
                        double i1r = in[iidx1];
                        double i2i = in[iidx2 - 1];
                        double i2r = in[iidx2];

                        out[oidx1 - 1] = i1i - i2r;
                        out[oidx2 - 1] = i1i + i2r;
                        out[oidx1] = i1r + i2i;
                        out[oidx2] = i1r - i2i;
                    }
                }
            }
        }
        System.arraycopy(out, out_off, in, in_off, idl1);
        for (int j = 1; j < ip; j++) {
            int idx1 = j * l1 * ido;
            for (int k = 0; k < l1; k++) {
                int idx2 = k * ido + idx1;
                in[in_off + idx2] = out[out_off + idx2];
            }
        }
        if (nbd <= l1) {
            is = -ido;
            for (int j = 1; j < ip; j++) {
                is += ido;
                idij = is - 1;
                int idx1 = j * l1 * ido;
                for (int i = 2; i < ido; i += 2) {
                    idij += 2;
                    int idx2 = idij + iw1;
                    w1r = wtable_r[idx2 - 1];
                    w1i = wtable_r[idx2];
                    int idx4 = in_off + i;
                    int idx5 = out_off + i;
                    for (int k = 0; k < l1; k++) {
                        int idx3 = k * ido + idx1;
                        int iidx1 = idx4 + idx3;
                        int oidx1 = idx5 + idx3;
                        double o1i = out[oidx1 - 1];
                        double o1r = out[oidx1];

                        in[iidx1 - 1] = w1r * o1i - w1i * o1r;
                        in[iidx1] = w1r * o1r + w1i * o1i;
                    }
                }
            }
        } else {
            is = -ido;
            for (int j = 1; j < ip; j++) {
                is += ido;
                int idx1 = j * l1 * ido;
                for (int k = 0; k < l1; k++) {
                    idij = is - 1;
                    int idx3 = k * ido + idx1;
                    for (int i = 2; i < ido; i += 2) {
                        idij += 2;
                        int idx2 = idij + iw1;
                        w1r = wtable_r[idx2 - 1];
                        w1i = wtable_r[idx2];
                        int idx4 = in_off + i;
                        int idx5 = out_off + i;
                        int iidx1 = idx4 + idx3;
                        int oidx1 = idx5 + idx3;
                        double o1i = out[oidx1 - 1];
                        double o1r = out[oidx1];

                        in[iidx1 - 1] = w1r * o1i - w1i * o1r;
                        in[iidx1] = w1r * o1r + w1i * o1i;

                    }
                }
            }
        }
    }

    /*---------------------------------------------------------
       cfftf1: further processing of Complex forward FFT
      --------------------------------------------------------*/
    void cfftf(double a[], int offa, int isign) {
        int idot;
        int l1, l2;
        int na, nf, ip, iw, ido, idl1;
        int[] nac = new int[1];
        final int twon = 2 * n;

        int iw1, iw2;
        double[] ch = new double[twon];

        iw1 = twon;
        iw2 = 4 * n;
        nac[0] = 0;
        nf = (int) wtable[1 + iw2];
        na = 0;
        l1 = 1;
        iw = iw1;
        for (int k1 = 2; k1 <= nf + 1; k1++) {
            ip = (int) wtable[k1 + iw2];
            l2 = ip * l1;
            ido = n / l2;
            idot = ido + ido;
            idl1 = idot * l1;
            switch (ip) {
            case 4:
                if (na == 0) {
                    passf4(idot, l1, a, offa, ch, 0, iw, isign);
                } else {
                    passf4(idot, l1, ch, 0, a, offa, iw, isign);
                }
                na = 1 - na;
                break;
            case 2:
                if (na == 0) {
                    passf2(idot, l1, a, offa, ch, 0, iw, isign);
                } else {
                    passf2(idot, l1, ch, 0, a, offa, iw, isign);
                }
                na = 1 - na;
                break;
            case 3:
                if (na == 0) {
                    passf3(idot, l1, a, offa, ch, 0, iw, isign);
                } else {
                    passf3(idot, l1, ch, 0, a, offa, iw, isign);
                }
                na = 1 - na;
                break;
            case 5:
                if (na == 0) {
                    passf5(idot, l1, a, offa, ch, 0, iw, isign);
                } else {
                    passf5(idot, l1, ch, 0, a, offa, iw, isign);
                }
                na = 1 - na;
                break;
            default:
                if (na == 0) {
                    passfg(nac, idot, ip, l1, idl1, a, offa, ch, 0, iw, isign);
                } else {
                    passfg(nac, idot, ip, l1, idl1, ch, 0, a, offa, iw, isign);
                }
                if (nac[0] != 0)
                    na = 1 - na;
                break;
            }
            l1 = l2;
            iw += (ip - 1) * idot;
        }
        if (na == 0)
            return;
        System.arraycopy(ch, 0, a, offa, twon);

    }

    /*----------------------------------------------------------------------
       passf2: Complex FFT's forward/backward processing of factor 2;
       isign is +1 for backward and -1 for forward transforms
      ----------------------------------------------------------------------*/

    void passf2(final int ido, final int l1, final double in[], final int in_off, final double out[], final int out_off, final int offset, final int isign) {
        double t1i, t1r;
        int iw1;
        iw1 = offset;
        int idx = ido * l1;
        if (ido <= 2) {
            for (int k = 0; k < l1; k++) {
                int idx0 = k * ido;
                int iidx1 = in_off + 2 * idx0;
                int iidx2 = iidx1 + ido;
                double a1r = in[iidx1];
                double a1i = in[iidx1 + 1];
                double a2r = in[iidx2];
                double a2i = in[iidx2 + 1];

                int oidx1 = out_off + idx0;
                int oidx2 = oidx1 + idx;
                out[oidx1] = a1r + a2r;
                out[oidx1 + 1] = a1i + a2i;
                out[oidx2] = a1r - a2r;
                out[oidx2 + 1] = a1i - a2i;
            }
        } else {
            for (int k = 0; k < l1; k++) {
                for (int i = 0; i < ido - 1; i += 2) {
                    int idx0 = k * ido;
                    int iidx1 = in_off + i + 2 * idx0;
                    int iidx2 = iidx1 + ido;
                    double i1r = in[iidx1];
                    double i1i = in[iidx1 + 1];
                    double i2r = in[iidx2];
                    double i2i = in[iidx2 + 1];

                    int widx1 = i + iw1;
                    double w1r = wtable[widx1];
                    double w1i = isign * wtable[widx1 + 1];

                    t1r = i1r - i2r;
                    t1i = i1i - i2i;

                    int oidx1 = out_off + i + idx0;
                    int oidx2 = oidx1 + idx;
                    out[oidx1] = i1r + i2r;
                    out[oidx1 + 1] = i1i + i2i;
                    out[oidx2] = w1r * t1r - w1i * t1i;
                    out[oidx2 + 1] = w1r * t1i + w1i * t1r;
                }
            }
        }
    }

    /*----------------------------------------------------------------------
       passf3: Complex FFT's forward/backward processing of factor 3;
       isign is +1 for backward and -1 for forward transforms
      ----------------------------------------------------------------------*/
    void passf3(final int ido, final int l1, final double in[], final int in_off, final double out[], final int out_off, final int offset, final int isign) {
        final double taur = -0.5;
        final double taui = 0.866025403784438707610604524234076962;
        double ci2, ci3, di2, di3, cr2, cr3, dr2, dr3, ti2, tr2;
        int iw1, iw2;

        iw1 = offset;
        iw2 = iw1 + ido;

        final int idxt = l1 * ido;

        if (ido == 2) {
            for (int k = 1; k <= l1; k++) {
                int iidx1 = in_off + (3 * k - 2) * ido;
                int iidx2 = iidx1 + ido;
                int iidx3 = iidx1 - ido;
                double i1r = in[iidx1];
                double i1i = in[iidx1 + 1];
                double i2r = in[iidx2];
                double i2i = in[iidx2 + 1];
                double i3r = in[iidx3];
                double i3i = in[iidx3 + 1];

                tr2 = i1r + i2r;
                cr2 = i3r + taur * tr2;
                ti2 = i1i + i2i;
                ci2 = i3i + taur * ti2;
                cr3 = isign * taui * (i1r - i2r);
                ci3 = isign * taui * (i1i - i2i);

                int oidx1 = out_off + (k - 1) * ido;
                int oidx2 = oidx1 + idxt;
                int oidx3 = oidx2 + idxt;
                out[oidx1] = in[iidx3] + tr2;
                out[oidx1 + 1] = i3i + ti2;
                out[oidx2] = cr2 - ci3;
                out[oidx2 + 1] = ci2 + cr3;
                out[oidx3] = cr2 + ci3;
                out[oidx3 + 1] = ci2 - cr3;
            }
        } else {
            for (int k = 1; k <= l1; k++) {
                int idx1 = in_off + (3 * k - 2) * ido;
                int idx2 = out_off + (k - 1) * ido;
                for (int i = 0; i < ido - 1; i += 2) {
                    int iidx1 = i + idx1;
                    int iidx2 = iidx1 + ido;
                    int iidx3 = iidx1 - ido;
                    double a1r = in[iidx1];
                    double a1i = in[iidx1 + 1];
                    double a2r = in[iidx2];
                    double a2i = in[iidx2 + 1];
                    double a3r = in[iidx3];
                    double a3i = in[iidx3 + 1];

                    tr2 = a1r + a2r;
                    cr2 = a3r + taur * tr2;
                    ti2 = a1i + a2i;
                    ci2 = a3i + taur * ti2;
                    cr3 = isign * taui * (a1r - a2r);
                    ci3 = isign * taui * (a1i - a2i);
                    dr2 = cr2 - ci3;
                    dr3 = cr2 + ci3;
                    di2 = ci2 + cr3;
                    di3 = ci2 - cr3;

                    int widx1 = i + iw1;
                    int widx2 = i + iw2;
                    double w1r = wtable[widx1];
                    double w1i = isign * wtable[widx1 + 1];
                    double w2r = wtable[widx2];
                    double w2i = isign * wtable[widx2 + 1];

                    int oidx1 = i + idx2;
                    int oidx2 = oidx1 + idxt;
                    int oidx3 = oidx2 + idxt;
                    out[oidx1] = a3r + tr2;
                    out[oidx1 + 1] = a3i + ti2;
                    out[oidx2] = w1r * dr2 - w1i * di2;
                    out[oidx2 + 1] = w1r * di2 + w1i * dr2;
                    out[oidx3] = w2r * dr3 - w2i * di3;
                    out[oidx3 + 1] = w2r * di3 + w2i * dr3;
                }
            }
        }
    }

    /*----------------------------------------------------------------------
       passf4: Complex FFT's forward/backward processing of factor 4;
       isign is +1 for backward and -1 for forward transforms
      ----------------------------------------------------------------------*/
    void passf4(final int ido, final int l1, final double in[], final int in_off, final double out[], final int out_off, final int offset, final int isign) {
        double ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
        int iw1, iw2, iw3;
        iw1 = offset;
        iw2 = iw1 + ido;
        iw3 = iw2 + ido;

        int idx0 = l1 * ido;
        if (ido == 2) {
            for (int k = 0; k < l1; k++) {
                int idxt1 = k * ido;
                int iidx1 = in_off + 4 * idxt1 + 1;
                int iidx2 = iidx1 + ido;
                int iidx3 = iidx2 + ido;
                int iidx4 = iidx3 + ido;

                double i1i = in[iidx1 - 1];
                double i1r = in[iidx1];
                double i2i = in[iidx2 - 1];
                double i2r = in[iidx2];
                double i3i = in[iidx3 - 1];
                double i3r = in[iidx3];
                double i4i = in[iidx4 - 1];
                double i4r = in[iidx4];

                ti1 = i1r - i3r;
                ti2 = i1r + i3r;
                tr4 = i4r - i2r;
                ti3 = i2r + i4r;
                tr1 = i1i - i3i;
                tr2 = i1i + i3i;
                ti4 = i2i - i4i;
                tr3 = i2i + i4i;

                int oidx1 = out_off + idxt1;
                int oidx2 = oidx1 + idx0;
                int oidx3 = oidx2 + idx0;
                int oidx4 = oidx3 + idx0;
                out[oidx1] = tr2 + tr3;
                out[oidx1 + 1] = ti2 + ti3;
                out[oidx2] = tr1 + isign * tr4;
                out[oidx2 + 1] = ti1 + isign * ti4;
                out[oidx3] = tr2 - tr3;
                out[oidx3 + 1] = ti2 - ti3;
                out[oidx4] = tr1 - isign * tr4;
                out[oidx4 + 1] = ti1 - isign * ti4;
            }
        } else {
            for (int k = 0; k < l1; k++) {
                int idx1 = k * ido;
                int idx2 = in_off + 1 + 4 * idx1;
                for (int i = 0; i < ido - 1; i += 2) {
                    int iidx1 = i + idx2;
                    int iidx2 = iidx1 + ido;
                    int iidx3 = iidx2 + ido;
                    int iidx4 = iidx3 + ido;
                    double i1i = in[iidx1 - 1];
                    double i1r = in[iidx1];
                    double i2i = in[iidx2 - 1];
                    double i2r = in[iidx2];
                    double i3i = in[iidx3 - 1];
                    double i3r = in[iidx3];
                    double i4i = in[iidx4 - 1];
                    double i4r = in[iidx4];

                    ti1 = i1r - i3r;
                    ti2 = i1r + i3r;
                    ti3 = i2r + i4r;
                    tr4 = i4r - i2r;
                    tr1 = i1i - i3i;
                    tr2 = i1i + i3i;
                    ti4 = i2i - i4i;
                    tr3 = i2i + i4i;
                    cr3 = tr2 - tr3;
                    ci3 = ti2 - ti3;
                    cr2 = tr1 + isign * tr4;
                    cr4 = tr1 - isign * tr4;
                    ci2 = ti1 + isign * ti4;
                    ci4 = ti1 - isign * ti4;

                    int widx1 = i + iw1;
                    int widx2 = i + iw2;
                    int widx3 = i + iw3;
                    double w1r = wtable[widx1];
                    double w1i = isign * wtable[widx1 + 1];
                    double w2r = wtable[widx2];
                    double w2i = isign * wtable[widx2 + 1];
                    double w3r = wtable[widx3];
                    double w3i = isign * wtable[widx3 + 1];

                    int oidx1 = out_off + i + idx1;
                    int oidx2 = oidx1 + idx0;
                    int oidx3 = oidx2 + idx0;
                    int oidx4 = oidx3 + idx0;
                    out[oidx1] = tr2 + tr3;
                    out[oidx1 + 1] = ti2 + ti3;
                    out[oidx2] = w1r * cr2 - w1i * ci2;
                    out[oidx2 + 1] = w1r * ci2 + w1i * cr2;
                    out[oidx3] = w2r * cr3 - w2i * ci3;
                    out[oidx3 + 1] = w2r * ci3 + w2i * cr3;
                    out[oidx4] = w3r * cr4 - w3i * ci4;
                    out[oidx4 + 1] = w3r * ci4 + w3i * cr4;
                }
            }
        }
    }

    /*----------------------------------------------------------------------
       passf5: Complex FFT's forward/backward processing of factor 5;
       isign is +1 for backward and -1 for forward transforms
      ----------------------------------------------------------------------*/
    void passf5(final int ido, final int l1, final double in[], final int in_off, final double out[], final int out_off, final int offset, final int isign)
    /* isign==-1 for forward transform and+1 for backward transform */
    {
        final double tr11 = 0.309016994374947451262869435595348477;
        final double ti11 = 0.951056516295153531181938433292089030;
        final double tr12 = -0.809016994374947340240566973079694435;
        final double ti12 = 0.587785252292473248125759255344746634;
        double ci2, ci3, ci4, ci5, di3, di4, di5, di2, cr2, cr3, cr5, cr4, ti2, ti3, ti4, ti5, dr3, dr4, dr5, dr2, tr2, tr3, tr4, tr5;
        int iw1, iw2, iw3, iw4;

        iw1 = offset;
        iw2 = iw1 + ido;
        iw3 = iw2 + ido;
        iw4 = iw3 + ido;

        int idx0 = l1 * ido;

        if (ido == 2) {
            for (int k = 1; k <= l1; ++k) {
                int iidx1 = in_off + (5 * k - 4) * ido + 1;
                int iidx2 = iidx1 + ido;
                int iidx3 = iidx1 - ido;
                int iidx4 = iidx2 + ido;
                int iidx5 = iidx4 + ido;

                double i1i = in[iidx1 - 1];
                double i1r = in[iidx1];
                double i2i = in[iidx2 - 1];
                double i2r = in[iidx2];
                double i3i = in[iidx3 - 1];
                double i3r = in[iidx3];
                double i4i = in[iidx4 - 1];
                double i4r = in[iidx4];
                double i5i = in[iidx5 - 1];
                double i5r = in[iidx5];

                ti5 = i1r - i5r;
                ti2 = i1r + i5r;
                ti4 = i2r - i4r;
                ti3 = i2r + i4r;
                tr5 = i1i - i5i;
                tr2 = i1i + i5i;
                tr4 = i2i - i4i;
                tr3 = i2i + i4i;
                cr2 = i3i + tr11 * tr2 + tr12 * tr3;
                ci2 = i3r + tr11 * ti2 + tr12 * ti3;
                cr3 = i3i + tr12 * tr2 + tr11 * tr3;
                ci3 = i3r + tr12 * ti2 + tr11 * ti3;
                cr5 = isign * (ti11 * tr5 + ti12 * tr4);
                ci5 = isign * (ti11 * ti5 + ti12 * ti4);
                cr4 = isign * (ti12 * tr5 - ti11 * tr4);
                ci4 = isign * (ti12 * ti5 - ti11 * ti4);

                int oidx1 = out_off + (k - 1) * ido;
                int oidx2 = oidx1 + idx0;
                int oidx3 = oidx2 + idx0;
                int oidx4 = oidx3 + idx0;
                int oidx5 = oidx4 + idx0;
                out[oidx1] = i3i + tr2 + tr3;
                out[oidx1 + 1] = i3r + ti2 + ti3;
                out[oidx2] = cr2 - ci5;
                out[oidx2 + 1] = ci2 + cr5;
                out[oidx3] = cr3 - ci4;
                out[oidx3 + 1] = ci3 + cr4;
                out[oidx4] = cr3 + ci4;
                out[oidx4 + 1] = ci3 - cr4;
                out[oidx5] = cr2 + ci5;
                out[oidx5 + 1] = ci2 - cr5;
            }
        } else {
            for (int k = 1; k <= l1; k++) {
                int idx1 = in_off + 1 + (k * 5 - 4) * ido;
                int idx2 = out_off + (k - 1) * ido;
                for (int i = 0; i < ido - 1; i += 2) {
                    int iidx1 = i + idx1;
                    int iidx2 = iidx1 + ido;
                    int iidx3 = iidx1 - ido;
                    int iidx4 = iidx2 + ido;
                    int iidx5 = iidx4 + ido;
                    double i1i = in[iidx1 - 1];
                    double i1r = in[iidx1];
                    double i2i = in[iidx2 - 1];
                    double i2r = in[iidx2];
                    double i3i = in[iidx3 - 1];
                    double i3r = in[iidx3];
                    double i4i = in[iidx4 - 1];
                    double i4r = in[iidx4];
                    double i5i = in[iidx5 - 1];
                    double i5r = in[iidx5];

                    ti5 = i1r - i5r;
                    ti2 = i1r + i5r;
                    ti4 = i2r - i4r;
                    ti3 = i2r + i4r;
                    tr5 = i1i - i5i;
                    tr2 = i1i + i5i;
                    tr4 = i2i - i4i;
                    tr3 = i2i + i4i;
                    cr2 = i3i + tr11 * tr2 + tr12 * tr3;
                    ci2 = i3r + tr11 * ti2 + tr12 * ti3;
                    cr3 = i3i + tr12 * tr2 + tr11 * tr3;
                    ci3 = i3r + tr12 * ti2 + tr11 * ti3;
                    cr5 = isign * (ti11 * tr5 + ti12 * tr4);
                    ci5 = isign * (ti11 * ti5 + ti12 * ti4);
                    cr4 = isign * (ti12 * tr5 - ti11 * tr4);
                    ci4 = isign * (ti12 * ti5 - ti11 * ti4);
                    dr3 = cr3 - ci4;
                    dr4 = cr3 + ci4;
                    di3 = ci3 + cr4;
                    di4 = ci3 - cr4;
                    dr5 = cr2 + ci5;
                    dr2 = cr2 - ci5;
                    di5 = ci2 - cr5;
                    di2 = ci2 + cr5;

                    int widx1 = i + iw1;
                    int widx2 = i + iw2;
                    int widx3 = i + iw3;
                    int widx4 = i + iw4;
                    double w1r = wtable[widx1];
                    double w1i = isign * wtable[widx1 + 1];
                    double w2r = wtable[widx2];
                    double w2i = isign * wtable[widx2 + 1];
                    double w3r = wtable[widx3];
                    double w3i = isign * wtable[widx3 + 1];
                    double w4r = wtable[widx4];
                    double w4i = isign * wtable[widx4 + 1];

                    int oidx1 = i + idx2;
                    int oidx2 = oidx1 + idx0;
                    int oidx3 = oidx2 + idx0;
                    int oidx4 = oidx3 + idx0;
                    int oidx5 = oidx4 + idx0;
                    out[oidx1] = i3i + tr2 + tr3;
                    out[oidx1 + 1] = i3r + ti2 + ti3;
                    out[oidx2] = w1r * dr2 - w1i * di2;
                    out[oidx2 + 1] = w1r * di2 + w1i * dr2;
                    out[oidx3] = w2r * dr3 - w2i * di3;
                    out[oidx3 + 1] = w2r * di3 + w2i * dr3;
                    out[oidx4] = w3r * dr4 - w3i * di4;
                    out[oidx4 + 1] = w3r * di4 + w3i * dr4;
                    out[oidx5] = w4r * dr5 - w4i * di5;
                    out[oidx5 + 1] = w4r * di5 + w4i * dr5;
                }
            }
        }
    }

    /*----------------------------------------------------------------------
       passfg: Complex FFT's forward/backward processing of general factor;
       isign is +1 for backward and -1 for forward transforms
      ----------------------------------------------------------------------*/
    void passfg(final int nac[], final int ido, final int ip, final int l1, final int idl1, final double in[], final int in_off, final double out[], final int out_off, final int offset, final int isign) {
        int idij, idlj, idot, ipph, l, jc, lc, idj, idl, inc, idp;
        double w1r, w1i, w2i, w2r;
        int iw1;

        iw1 = offset;
        idot = ido / 2;
        ipph = (ip + 1) / 2;
        idp = ip * ido;
        if (ido >= l1) {
            for (int j = 1; j < ipph; j++) {
                jc = ip - j;
                int idx1 = j * ido;
                int idx2 = jc * ido;
                for (int k = 0; k < l1; k++) {
                    int idx3 = k * ido;
                    int idx4 = idx3 + idx1 * l1;
                    int idx5 = idx3 + idx2 * l1;
                    int idx6 = idx3 * ip;
                    for (int i = 0; i < ido; i++) {
                        int oidx1 = out_off + i;
                        double i1r = in[in_off + i + idx1 + idx6];
                        double i2r = in[in_off + i + idx2 + idx6];
                        out[oidx1 + idx4] = i1r + i2r;
                        out[oidx1 + idx5] = i1r - i2r;
                    }
                }
            }
            for (int k = 0; k < l1; k++) {
                int idxt1 = k * ido;
                int idxt2 = idxt1 * ip;
                for (int i = 0; i < ido; i++) {
                    out[out_off + i + idxt1] = in[in_off + i + idxt2];
                }
            }
        } else {
            for (int j = 1; j < ipph; j++) {
                jc = ip - j;
                int idxt1 = j * l1 * ido;
                int idxt2 = jc * l1 * ido;
                int idxt3 = j * ido;
                int idxt4 = jc * ido;
                for (int i = 0; i < ido; i++) {
                    for (int k = 0; k < l1; k++) {
                        int idx1 = k * ido;
                        int idx2 = idx1 * ip;
                        int idx3 = out_off + i;
                        int idx4 = in_off + i;
                        double i1r = in[idx4 + idxt3 + idx2];
                        double i2r = in[idx4 + idxt4 + idx2];
                        out[idx3 + idx1 + idxt1] = i1r + i2r;
                        out[idx3 + idx1 + idxt2] = i1r - i2r;
                    }
                }
            }
            for (int i = 0; i < ido; i++) {
                for (int k = 0; k < l1; k++) {
                    int idx1 = k * ido;
                    out[out_off + i + idx1] = in[in_off + i + idx1 * ip];
                }
            }
        }

        idl = 2 - ido;
        inc = 0;
        int idxt0 = (ip - 1) * idl1;
        for (l = 1; l < ipph; l++) {
            lc = ip - l;
            idl += ido;
            int idxt1 = l * idl1;
            int idxt2 = lc * idl1;
            int idxt3 = idl + iw1;
            w1r = wtable[idxt3 - 2];
            w1i = isign * wtable[idxt3 - 1];
            for (int ik = 0; ik < idl1; ik++) {
                int idx1 = in_off + ik;
                int idx2 = out_off + ik;
                in[idx1 + idxt1] = out[idx2] + w1r * out[idx2 + idl1];
                in[idx1 + idxt2] = w1i * out[idx2 + idxt0];
            }
            idlj = idl;
            inc += ido;
            for (int j = 2; j < ipph; j++) {
                jc = ip - j;
                idlj += inc;
                if (idlj > idp)
                    idlj -= idp;
                int idxt4 = idlj + iw1;
                w2r = wtable[idxt4 - 2];
                w2i = isign * wtable[idxt4 - 1];
                int idxt5 = j * idl1;
                int idxt6 = jc * idl1;
                for (int ik = 0; ik < idl1; ik++) {
                    int idx1 = in_off + ik;
                    int idx2 = out_off + ik;
                    in[idx1 + idxt1] += w2r * out[idx2 + idxt5];
                    in[idx1 + idxt2] += w2i * out[idx2 + idxt6];
                }
            }
        }
        for (int j = 1; j < ipph; j++) {
            int idxt1 = j * idl1;
            for (int ik = 0; ik < idl1; ik++) {
                int idx1 = out_off + ik;
                out[idx1] += out[idx1 + idxt1];
            }
        }
        for (int j = 1; j < ipph; j++) {
            jc = ip - j;
            int idx1 = j * idl1;
            int idx2 = jc * idl1;
            for (int ik = 1; ik < idl1; ik += 2) {
                int idx3 = out_off + ik;
                int idx4 = in_off + ik;
                int iidx1 = idx4 + idx1;
                int iidx2 = idx4 + idx2;
                double i1i = in[iidx1 - 1];
                double i1r = in[iidx1];
                double i2i = in[iidx2 - 1];
                double i2r = in[iidx2];

                int oidx1 = idx3 + idx1;
                int oidx2 = idx3 + idx2;
                out[oidx1 - 1] = i1i - i2r;
                out[oidx2 - 1] = i1i + i2r;
                out[oidx1] = i1r + i2i;
                out[oidx2] = i1r - i2i;
            }
        }
        nac[0] = 1;
        if (ido == 2)
            return;
        nac[0] = 0;
        System.arraycopy(out, out_off, in, in_off, idl1);
        int idx0 = l1 * ido;
        for (int j = 1; j < ip; j++) {
            int idx1 = j * idx0;
            for (int k = 0; k < l1; k++) {
                int idx2 = k * ido;
                int oidx1 = out_off + idx2 + idx1;
                int iidx1 = in_off + idx2 + idx1;
                in[iidx1] = out[oidx1];
                in[iidx1 + 1] = out[oidx1 + 1];
            }
        }
        if (idot <= l1) {
            idij = 0;
            for (int j = 1; j < ip; j++) {
                idij += 2;
                int idx1 = j * l1 * ido;
                for (int i = 3; i < ido; i += 2) {
                    idij += 2;
                    int idx2 = idij + iw1 - 1;
                    w1r = wtable[idx2 - 1];
                    w1i = isign * wtable[idx2];
                    int idx3 = in_off + i;
                    int idx4 = out_off + i;
                    for (int k = 0; k < l1; k++) {
                        int idx5 = k * ido + idx1;
                        int iidx1 = idx3 + idx5;
                        int oidx1 = idx4 + idx5;
                        double o1i = out[oidx1 - 1];
                        double o1r = out[oidx1];
                        in[iidx1 - 1] = w1r * o1i - w1i * o1r;
                        in[iidx1] = w1r * o1r + w1i * o1i;
                    }
                }
            }
        } else {
            idj = 2 - ido;
            for (int j = 1; j < ip; j++) {
                idj += ido;
                int idx1 = j * l1 * ido;
                for (int k = 0; k < l1; k++) {
                    idij = idj;
                    int idx3 = k * ido + idx1;
                    for (int i = 3; i < ido; i += 2) {
                        idij += 2;
                        int idx2 = idij - 1 + iw1;
                        w1r = wtable[idx2 - 1];
                        w1i = isign * wtable[idx2];
                        int iidx1 = in_off + i + idx3;
                        int oidx1 = out_off + i + idx3;
                        double o1i = out[oidx1 - 1];
                        double o1r = out[oidx1];
                        in[iidx1 - 1] = w1r * o1i - w1i * o1r;
                        in[iidx1] = w1r * o1r + w1i * o1i;
                    }
                }
            }
        }
    }

    private void cftfsub(int n, double[] a, int offa, int[] ip, int nw, double[] w) {
        if (n > 8) {
            if (n > 32) {
                cftf1st(n, a, offa, w, nw - (n >> 2));
                if ((ConcurrencyUtils.getNumberOfThreads() > 1) && (n > ConcurrencyUtils.getThreadsBeginN_1D_FFT_2Threads())) {
                    cftrec4_th(n, a, offa, nw, w);
                } else if (n > 512) {
                    cftrec4(n, a, offa, nw, w);
                } else if (n > 128) {
                    cftleaf(n, 1, a, offa, nw, w);
                } else {
                    cftfx41(n, a, offa, nw, w);
                }
                bitrv2(n, ip, a, offa);
            } else if (n == 32) {
                cftf161(a, offa, w, nw - 8);
                bitrv216(a, offa);
            } else {
                cftf081(a, offa, w, 0);
                bitrv208(a, offa);
            }
        } else if (n == 8) {
            cftf040(a, offa);
        } else if (n == 4) {
            cftxb020(a, offa);
        }
    }

    private void cftbsub(int n, double[] a, int offa, int[] ip, int nw, double[] w) {
        if (n > 8) {
            if (n > 32) {
                cftb1st(n, a, offa, w, nw - (n >> 2));
                if ((ConcurrencyUtils.getNumberOfThreads() > 1) && (n > ConcurrencyUtils.getThreadsBeginN_1D_FFT_2Threads())) {
                    cftrec4_th(n, a, offa, nw, w);
                } else if (n > 512) {
                    cftrec4(n, a, offa, nw, w);
                } else if (n > 128) {
                    cftleaf(n, 1, a, offa, nw, w);
                } else {
                    cftfx41(n, a, offa, nw, w);
                }
                bitrv2conj(n, ip, a, offa);
            } else if (n == 32) {
                cftf161(a, offa, w, nw - 8);
                bitrv216neg(a, offa);
            } else {
                cftf081(a, offa, w, 0);
                bitrv208neg(a, offa);
            }
        } else if (n == 8) {
            cftb040(a, offa);
        } else if (n == 4) {
            cftxb020(a, offa);
        }
    }

    private void bitrv2(int n, int[] ip, double[] a, int offa) {
        int j1, k1, l, m, nh, nm;
        double xr, xi, yr, yi;
        int idx0, idx1, idx2;

        m = 1;
        for (l = n >> 2; l > 8; l >>= 2) {
            m <<= 1;
        }
        nh = n >> 1;
        nm = 4 * m;
        if (l == 8) {
            for (int k = 0; k < m; k++) {
                idx0 = 4 * k;
                for (int j = 0; j < k; j++) {
                    j1 = 4 * j + 2 * ip[m + k];
                    k1 = idx0 + 2 * ip[m + j];
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nm;
                    k1 += 2 * nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nm;
                    k1 -= nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nm;
                    k1 += 2 * nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nh;
                    k1 += 2;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nm;
                    k1 -= 2 * nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nm;
                    k1 += nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nm;
                    k1 -= 2 * nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += 2;
                    k1 += nh;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nm;
                    k1 += 2 * nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nm;
                    k1 -= nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nm;
                    k1 += 2 * nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nh;
                    k1 -= 2;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nm;
                    k1 -= 2 * nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nm;
                    k1 += nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nm;
                    k1 -= 2 * nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                }
                k1 = idx0 + 2 * ip[m + k];
                j1 = k1 + 2;
                k1 += nh;
                idx1 = offa + j1;
                idx2 = offa + k1;
                xr = a[idx1];
                xi = a[idx1 + 1];
                yr = a[idx2];
                yi = a[idx2 + 1];
                a[idx1] = yr;
                a[idx1 + 1] = yi;
                a[idx2] = xr;
                a[idx2 + 1] = xi;
                j1 += nm;
                k1 += 2 * nm;
                idx1 = offa + j1;
                idx2 = offa + k1;
                xr = a[idx1];
                xi = a[idx1 + 1];
                yr = a[idx2];
                yi = a[idx2 + 1];
                a[idx1] = yr;
                a[idx1 + 1] = yi;
                a[idx2] = xr;
                a[idx2 + 1] = xi;
                j1 += nm;
                k1 -= nm;
                idx1 = offa + j1;
                idx2 = offa + k1;
                xr = a[idx1];
                xi = a[idx1 + 1];
                yr = a[idx2];
                yi = a[idx2 + 1];
                a[idx1] = yr;
                a[idx1 + 1] = yi;
                a[idx2] = xr;
                a[idx2 + 1] = xi;
                j1 -= 2;
                k1 -= nh;
                idx1 = offa + j1;
                idx2 = offa + k1;
                xr = a[idx1];
                xi = a[idx1 + 1];
                yr = a[idx2];
                yi = a[idx2 + 1];
                a[idx1] = yr;
                a[idx1 + 1] = yi;
                a[idx2] = xr;
                a[idx2 + 1] = xi;
                j1 += nh + 2;
                k1 += nh + 2;
                idx1 = offa + j1;
                idx2 = offa + k1;
                xr = a[idx1];
                xi = a[idx1 + 1];
                yr = a[idx2];
                yi = a[idx2 + 1];
                a[idx1] = yr;
                a[idx1 + 1] = yi;
                a[idx2] = xr;
                a[idx2 + 1] = xi;
                j1 -= nh - nm;
                k1 += 2 * nm - 2;
                idx1 = offa + j1;
                idx2 = offa + k1;
                xr = a[idx1];
                xi = a[idx1 + 1];
                yr = a[idx2];
                yi = a[idx2 + 1];
                a[idx1] = yr;
                a[idx1 + 1] = yi;
                a[idx2] = xr;
                a[idx2 + 1] = xi;
            }
        } else {
            for (int k = 0; k < m; k++) {
                idx0 = 4 * k;
                for (int j = 0; j < k; j++) {
                    j1 = 4 * j + ip[m + k];
                    k1 = idx0 + ip[m + j];
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nm;
                    k1 += nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nh;
                    k1 += 2;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nm;
                    k1 -= nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += 2;
                    k1 += nh;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nm;
                    k1 += nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nh;
                    k1 -= 2;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nm;
                    k1 -= nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = a[idx1 + 1];
                    yr = a[idx2];
                    yi = a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                }
                k1 = idx0 + ip[m + k];
                j1 = k1 + 2;
                k1 += nh;
                idx1 = offa + j1;
                idx2 = offa + k1;
                xr = a[idx1];
                xi = a[idx1 + 1];
                yr = a[idx2];
                yi = a[idx2 + 1];
                a[idx1] = yr;
                a[idx1 + 1] = yi;
                a[idx2] = xr;
                a[idx2 + 1] = xi;
                j1 += nm;
                k1 += nm;
                idx1 = offa + j1;
                idx2 = offa + k1;
                xr = a[idx1];
                xi = a[idx1 + 1];
                yr = a[idx2];
                yi = a[idx2 + 1];
                a[idx1] = yr;
                a[idx1 + 1] = yi;
                a[idx2] = xr;
                a[idx2 + 1] = xi;
            }
        }
    }

    private void bitrv2conj(int n, int[] ip, double[] a, int offa) {
        int j1, k1, l, m, nh, nm;
        double xr, xi, yr, yi;
        int idx0, idx1, idx2;

        m = 1;
        for (l = n >> 2; l > 8; l >>= 2) {
            m <<= 1;
        }
        nh = n >> 1;
        nm = 4 * m;
        if (l == 8) {
            for (int k = 0; k < m; k++) {
                idx0 = 4 * k;
                for (int j = 0; j < k; j++) {
                    j1 = 4 * j + 2 * ip[m + k];
                    k1 = idx0 + 2 * ip[m + j];
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nm;
                    k1 += 2 * nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nm;
                    k1 -= nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nm;
                    k1 += 2 * nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nh;
                    k1 += 2;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nm;
                    k1 -= 2 * nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nm;
                    k1 += nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nm;
                    k1 -= 2 * nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += 2;
                    k1 += nh;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nm;
                    k1 += 2 * nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nm;
                    k1 -= nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nm;
                    k1 += 2 * nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nh;
                    k1 -= 2;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nm;
                    k1 -= 2 * nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nm;
                    k1 += nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nm;
                    k1 -= 2 * nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                }
                k1 = idx0 + 2 * ip[m + k];
                j1 = k1 + 2;
                k1 += nh;
                idx1 = offa + j1;
                idx2 = offa + k1;
                a[idx1 - 1] = -a[idx1 - 1];
                xr = a[idx1];
                xi = -a[idx1 + 1];
                yr = a[idx2];
                yi = -a[idx2 + 1];
                a[idx1] = yr;
                a[idx1 + 1] = yi;
                a[idx2] = xr;
                a[idx2 + 1] = xi;
                a[idx2 + 3] = -a[idx2 + 3];
                j1 += nm;
                k1 += 2 * nm;
                idx1 = offa + j1;
                idx2 = offa + k1;
                xr = a[idx1];
                xi = -a[idx1 + 1];
                yr = a[idx2];
                yi = -a[idx2 + 1];
                a[idx1] = yr;
                a[idx1 + 1] = yi;
                a[idx2] = xr;
                a[idx2 + 1] = xi;
                j1 += nm;
                k1 -= nm;
                idx1 = offa + j1;
                idx2 = offa + k1;
                xr = a[idx1];
                xi = -a[idx1 + 1];
                yr = a[idx2];
                yi = -a[idx2 + 1];
                a[idx1] = yr;
                a[idx1 + 1] = yi;
                a[idx2] = xr;
                a[idx2 + 1] = xi;
                j1 -= 2;
                k1 -= nh;
                idx1 = offa + j1;
                idx2 = offa + k1;
                xr = a[idx1];
                xi = -a[idx1 + 1];
                yr = a[idx2];
                yi = -a[idx2 + 1];
                a[idx1] = yr;
                a[idx1 + 1] = yi;
                a[idx2] = xr;
                a[idx2 + 1] = xi;
                j1 += nh + 2;
                k1 += nh + 2;
                idx1 = offa + j1;
                idx2 = offa + k1;
                xr = a[idx1];
                xi = -a[idx1 + 1];
                yr = a[idx2];
                yi = -a[idx2 + 1];
                a[idx1] = yr;
                a[idx1 + 1] = yi;
                a[idx2] = xr;
                a[idx2 + 1] = xi;
                j1 -= nh - nm;
                k1 += 2 * nm - 2;
                idx1 = offa + j1;
                idx2 = offa + k1;
                a[idx1 - 1] = -a[idx1 - 1];
                xr = a[idx1];
                xi = -a[idx1 + 1];
                yr = a[idx2];
                yi = -a[idx2 + 1];
                a[idx1] = yr;
                a[idx1 + 1] = yi;
                a[idx2] = xr;
                a[idx2 + 1] = xi;
                a[idx2 + 3] = -a[idx2 + 3];
            }
        } else {
            for (int k = 0; k < m; k++) {
                idx0 = 4 * k;
                for (int j = 0; j < k; j++) {
                    j1 = 4 * j + ip[m + k];
                    k1 = idx0 + ip[m + j];
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nm;
                    k1 += nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nh;
                    k1 += 2;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nm;
                    k1 -= nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += 2;
                    k1 += nh;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 += nm;
                    k1 += nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nh;
                    k1 -= 2;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                    j1 -= nm;
                    k1 -= nm;
                    idx1 = offa + j1;
                    idx2 = offa + k1;
                    xr = a[idx1];
                    xi = -a[idx1 + 1];
                    yr = a[idx2];
                    yi = -a[idx2 + 1];
                    a[idx1] = yr;
                    a[idx1 + 1] = yi;
                    a[idx2] = xr;
                    a[idx2 + 1] = xi;
                }
                k1 = idx0 + ip[m + k];
                j1 = k1 + 2;
                k1 += nh;
                idx1 = offa + j1;
                idx2 = offa + k1;
                a[idx1 - 1] = -a[idx1 - 1];
                xr = a[idx1];
                xi = -a[idx1 + 1];
                yr = a[idx2];
                yi = -a[idx2 + 1];
                a[idx1] = yr;
                a[idx1 + 1] = yi;
                a[idx2] = xr;
                a[idx2 + 1] = xi;
                a[idx2 + 3] = -a[idx2 + 3];
                j1 += nm;
                k1 += nm;
                idx1 = offa + j1;
                idx2 = offa + k1;
                a[idx1 - 1] = -a[idx1 - 1];
                xr = a[idx1];
                xi = -a[idx1 + 1];
                yr = a[idx2];
                yi = -a[idx2 + 1];
                a[idx1] = yr;
                a[idx1 + 1] = yi;
                a[idx2] = xr;
                a[idx2 + 1] = xi;
                a[idx2 + 3] = -a[idx2 + 3];
            }
        }
    }

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

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

    private void bitrv208(double[] a, int offa) {
        double x1r, x1i, x3r, x3i, x4r, x4i, x6r, x6i;

        x1r = a[offa + 2];
        x1i = a[offa + 3];
        x3r = a[offa + 6];
        x3i = a[offa + 7];
        x4r = a[offa + 8];
        x4i = a[offa + 9];
        x6r = a[offa + 12];
        x6i = a[offa + 13];
        a[offa + 2] = x4r;
        a[offa + 3] = x4i;
        a[offa + 6] = x6r;
        a[offa + 7] = x6i;
        a[offa + 8] = x1r;
        a[offa + 9] = x1i;
        a[offa + 12] = x3r;
        a[offa + 13] = x3i;
    }

    private void bitrv208neg(double[] a, int offa) {
        double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, x5r, x5i, x6r, x6i, x7r, x7i;

        x1r = a[offa + 2];
        x1i = a[offa + 3];
        x2r = a[offa + 4];
        x2i = a[offa + 5];
        x3r = a[offa + 6];
        x3i = a[offa + 7];
        x4r = a[offa + 8];
        x4i = a[offa + 9];
        x5r = a[offa + 10];
        x5i = a[offa + 11];
        x6r = a[offa + 12];
        x6i = a[offa + 13];
        x7r = a[offa + 14];
        x7i = a[offa + 15];
        a[offa + 2] = x7r;
        a[offa + 3] = x7i;
        a[offa + 4] = x3r;
        a[offa + 5] = x3i;
        a[offa + 6] = x5r;
        a[offa + 7] = x5i;
        a[offa + 8] = x1r;
        a[offa + 9] = x1i;
        a[offa + 10] = x6r;
        a[offa + 11] = x6i;
        a[offa + 12] = x2r;
        a[offa + 13] = x2i;
        a[offa + 14] = x4r;
        a[offa + 15] = x4i;
    }

    private void cftf1st(int n, double[] a, int offa, double[] w, int startw) {
        int j0, j1, j2, j3, k, m, mh;
        double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
        double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;
        int idx0, idx1, idx2, idx3, idx4, idx5;
        mh = n >> 3;
        m = 2 * mh;
        j1 = m;
        j2 = j1 + m;
        j3 = j2 + m;
        idx1 = offa + j1;
        idx2 = offa + j2;
        idx3 = offa + j3;
        x0r = a[offa] + a[idx2];
        x0i = a[offa + 1] + a[idx2 + 1];
        x1r = a[offa] - a[idx2];
        x1i = a[offa + 1] - a[idx2 + 1];
        x2r = a[idx1] + a[idx3];
        x2i = a[idx1 + 1] + a[idx3 + 1];
        x3r = a[idx1] - a[idx3];
        x3i = a[idx1 + 1] - a[idx3 + 1];
        a[offa] = x0r + x2r;
        a[offa + 1] = x0i + x2i;
        a[idx1] = x0r - x2r;
        a[idx1 + 1] = x0i - x2i;
        a[idx2] = x1r - x3i;
        a[idx2 + 1] = x1i + x3r;
        a[idx3] = x1r + x3i;
        a[idx3 + 1] = x1i - x3r;
        wn4r = w[startw + 1];
        csc1 = w[startw + 2];
        csc3 = w[startw + 3];
        wd1r = 1;
        wd1i = 0;
        wd3r = 1;
        wd3i = 0;
        k = 0;
        for (int j = 2; j < mh - 2; j += 4) {
            k += 4;
            idx4 = startw + k;
            wk1r = csc1 * (wd1r + w[idx4]);
            wk1i = csc1 * (wd1i + w[idx4 + 1]);
            wk3r = csc3 * (wd3r + w[idx4 + 2]);
            wk3i = csc3 * (wd3i + w[idx4 + 3]);
            wd1r = w[idx4];
            wd1i = w[idx4 + 1];
            wd3r = w[idx4 + 2];
            wd3i = w[idx4 + 3];
            j1 = j + m;
            j2 = j1 + m;
            j3 = j2 + m;
            idx1 = offa + j1;
            idx2 = offa + j2;
            idx3 = offa + j3;
            idx5 = offa + j;
            x0r = a[idx5] + a[idx2];
            x0i = a[idx5 + 1] + a[idx2 + 1];
            x1r = a[idx5] - a[idx2];
            x1i = a[idx5 + 1] - a[idx2 + 1];
            y0r = a[idx5 + 2] + a[idx2 + 2];
            y0i = a[idx5 + 3] + a[idx2 + 3];
            y1r = a[idx5 + 2] - a[idx2 + 2];
            y1i = a[idx5 + 3] - a[idx2 + 3];
            x2r = a[idx1] + a[idx3];
            x2i = a[idx1 + 1] + a[idx3 + 1];
            x3r = a[idx1] - a[idx3];
            x3i = a[idx1 + 1] - a[idx3 + 1];
            y2r = a[idx1 + 2] + a[idx3 + 2];
            y2i = a[idx1 + 3] + a[idx3 + 3];
            y3r = a[idx1 + 2] - a[idx3 + 2];
            y3i = a[idx1 + 3] - a[idx3 + 3];
            a[idx5] = x0r + x2r;
            a[idx5 + 1] = x0i + x2i;
            a[idx5 + 2] = y0r + y2r;
            a[idx5 + 3] = y0i + y2i;
            a[idx1] = x0r - x2r;
            a[idx1 + 1] = x0i - x2i;
            a[idx1 + 2] = y0r - y2r;
            a[idx1 + 3] = y0i - y2i;
            x0r = x1r - x3i;
            x0i = x1i + x3r;
            a[idx2] = wk1r * x0r - wk1i * x0i;
            a[idx2 + 1] = wk1r * x0i + wk1i * x0r;
            x0r = y1r - y3i;
            x0i = y1i + y3r;
            a[idx2 + 2] = wd1r * x0r - wd1i * x0i;
            a[idx2 + 3] = wd1r * x0i + wd1i * x0r;
            x0r = x1r + x3i;
            x0i = x1i - x3r;
            a[idx3] = wk3r * x0r + wk3i * x0i;
            a[idx3 + 1] = wk3r * x0i - wk3i * x0r;
            x0r = y1r + y3i;
            x0i = y1i - y3r;
            a[idx3 + 2] = wd3r * x0r + wd3i * x0i;
            a[idx3 + 3] = wd3r * x0i - wd3i * x0r;
            j0 = m - j;
            j1 = j0 + m;
            j2 = j1 + m;
            j3 = j2 + m;
            idx0 = offa + j0;
            idx1 = offa + j1;
            idx2 = offa + j2;
            idx3 = offa + j3;
            x0r = a[idx0] + a[idx2];
            x0i = a[idx0 + 1] + a[idx2 + 1];
            x1r = a[idx0] - a[idx2];
            x1i = a[idx0 + 1] - a[idx2 + 1];
            y0r = a[idx0 - 2] + a[idx2 - 2];
            y0i = a[idx0 - 1] + a[idx2 - 1];
            y1r = a[idx0 - 2] - a[idx2 - 2];
            y1i = a[idx0 - 1] - a[idx2 - 1];
            x2r = a[idx1] + a[idx3];
            x2i = a[idx1 + 1] + a[idx3 + 1];
            x3r = a[idx1] - a[idx3];
            x3i = a[idx1 + 1] - a[idx3 + 1];
            y2r = a[idx1 - 2] + a[idx3 - 2];
            y2i = a[idx1 - 1] + a[idx3 - 1];
            y3r = a[idx1 - 2] - a[idx3 - 2];
            y3i = a[idx1 - 1] - a[idx3 - 1];
            a[idx0] = x0r + x2r;
            a[idx0 + 1] = x0i + x2i;
            a[idx0 - 2] = y0r + y2r;
            a[idx0 - 1] = y0i + y2i;
            a[idx1] = x0r - x2r;
            a[idx1 + 1] = x0i - x2i;
            a[idx1 - 2] = y0r - y2r;
            a[idx1 - 1] = y0i - y2i;
            x0r = x1r - x3i;
            x0i = x1i + x3r;
            a[idx2] = wk1i * x0r - wk1r * x0i;
            a[idx2 + 1] = wk1i * x0i + wk1r * x0r;
            x0r = y1r - y3i;
            x0i = y1i + y3r;
            a[idx2 - 2] = wd1i * x0r - wd1r * x0i;
            a[idx2 - 1] = wd1i * x0i + wd1r * x0r;
            x0r = x1r + x3i;
            x0i = x1i - x3r;
            a[idx3] = wk3i * x0r + wk3r * x0i;
            a[idx3 + 1] = wk3i * x0i - wk3r * x0r;
            x0r = y1r + y3i;
            x0i = y1i - y3r;
            a[offa + j3 - 2] = wd3i * x0r + wd3r * x0i;
            a[offa + j3 - 1] = wd3i * x0i - wd3r * x0r;
        }
        wk1r = csc1 * (wd1r + wn4r);
        wk1i = csc1 * (wd1i + wn4r);
        wk3r = csc3 * (wd3r - wn4r);
        wk3i = csc3 * (wd3i - wn4r);
        j0 = mh;
        j1 = j0 + m;
        j2 = j1 + m;
        j3 = j2 + m;
        idx0 = offa + j0;
        idx1 = offa + j1;
        idx2 = offa + j2;
        idx3 = offa + j3;
        x0r = a[idx0 - 2] + a[idx2 - 2];
        x0i = a[idx0 - 1] + a[idx2 - 1];
        x1r = a[idx0 - 2] - a[idx2 - 2];
        x1i = a[idx0 - 1] - a[idx2 - 1];
        x2r = a[idx1 - 2] + a[idx3 - 2];
        x2i = a[idx1 - 1] + a[idx3 - 1];
        x3r = a[idx1 - 2] - a[idx3 - 2];
        x3i = a[idx1 - 1] - a[idx3 - 1];
        a[idx0 - 2] = x0r + x2r;
        a[idx0 - 1] = x0i + x2i;
        a[idx1 - 2] = x0r - x2r;
        a[idx1 - 1] = x0i - x2i;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[idx2 - 2] = wk1r * x0r - wk1i * x0i;
        a[idx2 - 1] = wk1r * x0i + wk1i * x0r;
        x0r = x1r + x3i;
        x0i = x1i - x3r;
        a[idx3 - 2] = wk3r * x0r + wk3i * x0i;
        a[idx3 - 1] = wk3r * x0i - wk3i * x0r;
        x0r = a[idx0] + a[idx2];
        x0i = a[idx0 + 1] + a[idx2 + 1];
        x1r = a[idx0] - a[idx2];
        x1i = a[idx0 + 1] - a[idx2 + 1];
        x2r = a[idx1] + a[idx3];
        x2i = a[idx1 + 1] + a[idx3 + 1];
        x3r = a[idx1] - a[idx3];
        x3i = a[idx1 + 1] - a[idx3 + 1];
        a[idx0] = x0r + x2r;
        a[idx0 + 1] = x0i + x2i;
        a[idx1] = x0r - x2r;
        a[idx1 + 1] = x0i - x2i;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[idx2] = wn4r * (x0r - x0i);
        a[idx2 + 1] = wn4r * (x0i + x0r);
        x0r = x1r + x3i;
        x0i = x1i - x3r;
        a[idx3] = -wn4r * (x0r + x0i);
        a[idx3 + 1] = -wn4r * (x0i - x0r);
        x0r = a[idx0 + 2] + a[idx2 + 2];
        x0i = a[idx0 + 3] + a[idx2 + 3];
        x1r = a[idx0 + 2] - a[idx2 + 2];
        x1i = a[idx0 + 3] - a[idx2 + 3];
        x2r = a[idx1 + 2] + a[idx3 + 2];
        x2i = a[idx1 + 3] + a[idx3 + 3];
        x3r = a[idx1 + 2] - a[idx3 + 2];
        x3i = a[idx1 + 3] - a[idx3 + 3];
        a[idx0 + 2] = x0r + x2r;
        a[idx0 + 3] = x0i + x2i;
        a[idx1 + 2] = x0r - x2r;
        a[idx1 + 3] = x0i - x2i;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[idx2 + 2] = wk1i * x0r - wk1r * x0i;
        a[idx2 + 3] = wk1i * x0i + wk1r * x0r;
        x0r = x1r + x3i;
        x0i = x1i - x3r;
        a[idx3 + 2] = wk3i * x0r + wk3r * x0i;
        a[idx3 + 3] = wk3i * x0i - wk3r * x0r;
    }

    private void cftb1st(int n, double[] a, int offa, double[] w, int startw) {
        int j0, j1, j2, j3, k, m, mh;
        double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
        double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;
        int idx0, idx1, idx2, idx3, idx4, idx5;
        mh = n >> 3;
        m = 2 * mh;
        j1 = m;
        j2 = j1 + m;
        j3 = j2 + m;
        idx1 = offa + j1;
        idx2 = offa + j2;
        idx3 = offa + j3;

        x0r = a[offa] + a[idx2];
        x0i = -a[offa + 1] - a[idx2 + 1];
        x1r = a[offa] - a[idx2];
        x1i = -a[offa + 1] + a[idx2 + 1];
        x2r = a[idx1] + a[idx3];
        x2i = a[idx1 + 1] + a[idx3 + 1];
        x3r = a[idx1] - a[idx3];
        x3i = a[idx1 + 1] - a[idx3 + 1];
        a[offa] = x0r + x2r;
        a[offa + 1] = x0i - x2i;
        a[idx1] = x0r - x2r;
        a[idx1 + 1] = x0i + x2i;
        a[idx2] = x1r + x3i;
        a[idx2 + 1] = x1i + x3r;
        a[idx3] = x1r - x3i;
        a[idx3 + 1] = x1i - x3r;
        wn4r = w[startw + 1];
        csc1 = w[startw + 2];
        csc3 = w[startw + 3];
        wd1r = 1;
        wd1i = 0;
        wd3r = 1;
        wd3i = 0;
        k = 0;
        for (int j = 2; j < mh - 2; j += 4) {
            k += 4;
            idx4 = startw + k;
            wk1r = csc1 * (wd1r + w[idx4]);
            wk1i = csc1 * (wd1i + w[idx4 + 1]);
            wk3r = csc3 * (wd3r + w[idx4 + 2]);
            wk3i = csc3 * (wd3i + w[idx4 + 3]);
            wd1r = w[idx4];
            wd1i = w[idx4 + 1];
            wd3r = w[idx4 + 2];
            wd3i = w[idx4 + 3];
            j1 = j + m;
            j2 = j1 + m;
            j3 = j2 + m;
            idx1 = offa + j1;
            idx2 = offa + j2;
            idx3 = offa + j3;
            idx5 = offa + j;
            x0r = a[idx5] + a[idx2];
            x0i = -a[idx5 + 1] - a[idx2 + 1];
            x1r = a[idx5] - a[offa + j2];
            x1i = -a[idx5 + 1] + a[idx2 + 1];
            y0r = a[idx5 + 2] + a[idx2 + 2];
            y0i = -a[idx5 + 3] - a[idx2 + 3];
            y1r = a[idx5 + 2] - a[idx2 + 2];
            y1i = -a[idx5 + 3] + a[idx2 + 3];
            x2r = a[idx1] + a[idx3];
            x2i = a[idx1 + 1] + a[idx3 + 1];
            x3r = a[idx1] - a[idx3];
            x3i = a[idx1 + 1] - a[idx3 + 1];
            y2r = a[idx1 + 2] + a[idx3 + 2];
            y2i = a[idx1 + 3] + a[idx3 + 3];
            y3r = a[idx1 + 2] - a[idx3 + 2];
            y3i = a[idx1 + 3] - a[idx3 + 3];
            a[idx5] = x0r + x2r;
            a[idx5 + 1] = x0i - x2i;
            a[idx5 + 2] = y0r + y2r;
            a[idx5 + 3] = y0i - y2i;
            a[idx1] = x0r - x2r;
            a[idx1 + 1] = x0i + x2i;
            a[idx1 + 2] = y0r - y2r;
            a[idx1 + 3] = y0i + y2i;
            x0r = x1r + x3i;
            x0i = x1i + x3r;
            a[idx2] = wk1r * x0r - wk1i * x0i;
            a[idx2 + 1] = wk1r * x0i + wk1i * x0r;
            x0r = y1r + y3i;
            x0i = y1i + y3r;
            a[idx2 + 2] = wd1r * x0r - wd1i * x0i;
            a[idx2 + 3] = wd1r * x0i + wd1i * x0r;
            x0r = x1r - x3i;
            x0i = x1i - x3r;
            a[idx3] = wk3r * x0r + wk3i * x0i;
            a[idx3 + 1] = wk3r * x0i - wk3i * x0r;
            x0r = y1r - y3i;
            x0i = y1i - y3r;
            a[idx3 + 2] = wd3r * x0r + wd3i * x0i;
            a[idx3 + 3] = wd3r * x0i - wd3i * x0r;
            j0 = m - j;
            j1 = j0 + m;
            j2 = j1 + m;
            j3 = j2 + m;
            idx0 = offa + j0;
            idx1 = offa + j1;
            idx2 = offa + j2;
            idx3 = offa + j3;
            x0r = a[idx0] + a[idx2];
            x0i = -a[idx0 + 1] - a[idx2 + 1];
            x1r = a[idx0] - a[idx2];
            x1i = -a[idx0 + 1] + a[idx2 + 1];
            y0r = a[idx0 - 2] + a[idx2 - 2];
            y0i = -a[idx0 - 1] - a[idx2 - 1];
            y1r = a[idx0 - 2] - a[idx2 - 2];
            y1i = -a[idx0 - 1] + a[idx2 - 1];
            x2r = a[idx1] + a[idx3];
            x2i = a[idx1 + 1] + a[idx3 + 1];
            x3r = a[idx1] - a[idx3];
            x3i = a[idx1 + 1] - a[idx3 + 1];
            y2r = a[idx1 - 2] + a[idx3 - 2];
            y2i = a[idx1 - 1] + a[idx3 - 1];
            y3r = a[idx1 - 2] - a[idx3 - 2];
            y3i = a[idx1 - 1] - a[idx3 - 1];
            a[idx0] = x0r + x2r;
            a[idx0 + 1] = x0i - x2i;
            a[idx0 - 2] = y0r + y2r;
            a[idx0 - 1] = y0i - y2i;
            a[idx1] = x0r - x2r;
            a[idx1 + 1] = x0i + x2i;
            a[idx1 - 2] = y0r - y2r;
            a[idx1 - 1] = y0i + y2i;
            x0r = x1r + x3i;
            x0i = x1i + x3r;
            a[idx2] = wk1i * x0r - wk1r * x0i;
            a[idx2 + 1] = wk1i * x0i + wk1r * x0r;
            x0r = y1r + y3i;
            x0i = y1i + y3r;
            a[idx2 - 2] = wd1i * x0r - wd1r * x0i;
            a[idx2 - 1] = wd1i * x0i + wd1r * x0r;
            x0r = x1r - x3i;
            x0i = x1i - x3r;
            a[idx3] = wk3i * x0r + wk3r * x0i;
            a[idx3 + 1] = wk3i * x0i - wk3r * x0r;
            x0r = y1r - y3i;
            x0i = y1i - y3r;
            a[idx3 - 2] = wd3i * x0r + wd3r * x0i;
            a[idx3 - 1] = wd3i * x0i - wd3r * x0r;
        }
        wk1r = csc1 * (wd1r + wn4r);
        wk1i = csc1 * (wd1i + wn4r);
        wk3r = csc3 * (wd3r - wn4r);
        wk3i = csc3 * (wd3i - wn4r);
        j0 = mh;
        j1 = j0 + m;
        j2 = j1 + m;
        j3 = j2 + m;
        idx0 = offa + j0;
        idx1 = offa + j1;
        idx2 = offa + j2;
        idx3 = offa + j3;
        x0r = a[idx0 - 2] + a[idx2 - 2];
        x0i = -a[idx0 - 1] - a[idx2 - 1];
        x1r = a[idx0 - 2] - a[idx2 - 2];
        x1i = -a[idx0 - 1] + a[idx2 - 1];
        x2r = a[idx1 - 2] + a[idx3 - 2];
        x2i = a[idx1 - 1] + a[idx3 - 1];
        x3r = a[idx1 - 2] - a[idx3 - 2];
        x3i = a[idx1 - 1] - a[idx3 - 1];
        a[idx0 - 2] = x0r + x2r;
        a[idx0 - 1] = x0i - x2i;
        a[idx1 - 2] = x0r - x2r;
        a[idx1 - 1] = x0i + x2i;
        x0r = x1r + x3i;
        x0i = x1i + x3r;
        a[idx2 - 2] = wk1r * x0r - wk1i * x0i;
        a[idx2 - 1] = wk1r * x0i + wk1i * x0r;
        x0r = x1r - x3i;
        x0i = x1i - x3r;
        a[idx3 - 2] = wk3r * x0r + wk3i * x0i;
        a[idx3 - 1] = wk3r * x0i - wk3i * x0r;
        x0r = a[idx0] + a[idx2];
        x0i = -a[idx0 + 1] - a[idx2 + 1];
        x1r = a[idx0] - a[idx2];
        x1i = -a[idx0 + 1] + a[idx2 + 1];
        x2r = a[idx1] + a[idx3];
        x2i = a[idx1 + 1] + a[idx3 + 1];
        x3r = a[idx1] - a[idx3];
        x3i = a[idx1 + 1] - a[idx3 + 1];
        a[idx0] = x0r + x2r;
        a[idx0 + 1] = x0i - x2i;
        a[idx1] = x0r - x2r;
        a[idx1 + 1] = x0i + x2i;
        x0r = x1r + x3i;
        x0i = x1i + x3r;
        a[idx2] = wn4r * (x0r - x0i);
        a[idx2 + 1] = wn4r * (x0i + x0r);
        x0r = x1r - x3i;
        x0i = x1i - x3r;
        a[idx3] = -wn4r * (x0r + x0i);
        a[idx3 + 1] = -wn4r * (x0i - x0r);
        x0r = a[idx0 + 2] + a[idx2 + 2];
        x0i = -a[idx0 + 3] - a[idx2 + 3];
        x1r = a[idx0 + 2] - a[idx2 + 2];
        x1i = -a[idx0 + 3] + a[idx2 + 3];
        x2r = a[idx1 + 2] + a[idx3 + 2];
        x2i = a[idx1 + 3] + a[idx3 + 3];
        x3r = a[idx1 + 2] - a[idx3 + 2];
        x3i = a[idx1 + 3] - a[idx3 + 3];
        a[idx0 + 2] = x0r + x2r;
        a[idx0 + 3] = x0i - x2i;
        a[idx1 + 2] = x0r - x2r;
        a[idx1 + 3] = x0i + x2i;
        x0r = x1r + x3i;
        x0i = x1i + x3r;
        a[idx2 + 2] = wk1i * x0r - wk1r * x0i;
        a[idx2 + 3] = wk1i * x0i + wk1r * x0r;
        x0r = x1r - x3i;
        x0i = x1i - x3r;
        a[idx3 + 2] = wk3i * x0r + wk3r * x0i;
        a[idx3 + 3] = wk3i * x0i - wk3r * x0r;
    }

    private void cftrec4_th(final int n, final double[] a, final int offa, final int nw, final double[] w) {
        int i;
        int idiv4, m, nthreads;
        int idx = 0;
        nthreads = 2;
        idiv4 = 0;
        m = n >> 1;
        if (n > ConcurrencyUtils.getThreadsBeginN_1D_FFT_4Threads()) {
            nthreads = 4;
            idiv4 = 1;
            m >>= 1;
        }
        Future<?>[] futures = new Future[nthreads];
        final int mf = m;
        for (i = 0; i < nthreads; i++) {
            final int firstIdx = offa + i * m;
            if (i != idiv4) {
                futures[idx++] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        int isplt, j, k, m;
                        int idx1 = firstIdx + mf;
                        m = n;
                        while (m > 512) {
                            m >>= 2;
                            cftmdl1(m, a, idx1 - m, w, nw - (m >> 1));
                        }
                        cftleaf(m, 1, a, idx1 - m, nw, w);
                        k = 0;
                        int idx2 = firstIdx - m;
                        for (j = mf - m; j > 0; j -= m) {
                            k++;
                            isplt = cfttree(m, j, k, a, firstIdx, nw, w);
                            cftleaf(m, isplt, a, idx2 + j, nw, w);
                        }
                    }
                });
            } else {
                futures[idx++] = ConcurrencyUtils.submit(new Runnable() {
                    @Override
                                        public void run() {
                        int isplt, j, k, m;
                        int idx1 = firstIdx + mf;
                        k = 1;
                        m = n;
                        while (m > 512) {
                            m >>= 2;
                            k <<= 2;
                            cftmdl2(m, a, idx1 - m, w, nw - m);
                        }
                        cftleaf(m, 0, a, idx1 - m, nw, w);
                        k >>= 1;
                        int idx2 = firstIdx - m;
                        for (j = mf - m; j > 0; j -= m) {
                            k++;
                            isplt = cfttree(m, j, k, a, firstIdx, nw, w);
                            cftleaf(m, isplt, a, idx2 + j, nw, w);
                        }
                    }
                });
            }
        }
        ConcurrencyUtils.waitForCompletion(futures);
    }

    private void cftrec4(int n, double[] a, int offa, int nw, double[] w) {
        int isplt, j, k, m;

        m = n;
        int idx1 = offa + n;
        while (m > 512) {
            m >>= 2;
            cftmdl1(m, a, idx1 - m, w, nw - (m >> 1));
        }
        cftleaf(m, 1, a, idx1 - m, nw, w);
        k = 0;
        int idx2 = offa - m;
        for (j = n - m; j > 0; j -= m) {
            k++;
            isplt = cfttree(m, j, k, a, offa, nw, w);
            cftleaf(m, isplt, a, idx2 + j, nw, w);
        }
    }

    private int cfttree(int n, int j, int k, double[] a, int offa, int nw, double[] w) {
        int i, isplt, m;
        int idx1 = offa - n;
        if ((k & 3) != 0) {
            isplt = k & 1;
            if (isplt != 0) {
                cftmdl1(n, a, idx1 + j, w, nw - (n >> 1));
            } else {
                cftmdl2(n, a, idx1 + j, w, nw - n);
            }
        } else {
            m = n;
            for (i = k; (i & 3) == 0; i >>= 2) {
                m <<= 2;
            }
            isplt = i & 1;
            int idx2 = offa + j;
            if (isplt != 0) {
                while (m > 128) {
                    cftmdl1(m, a, idx2 - m, w, nw - (m >> 1));
                    m >>= 2;
                }
            } else {
                while (m > 128) {
                    cftmdl2(m, a, idx2 - m, w, nw - m);
                    m >>= 2;
                }
            }
        }
        return isplt;
    }

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

    private void cftmdl1(int n, double[] a, int offa, double[] w, int startw) {
        int j0, j1, j2, j3, k, m, mh;
        double wn4r, wk1r, wk1i, wk3r, wk3i;
        double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
        int idx0, idx1, idx2, idx3, idx4, idx5;

        mh = n >> 3;
        m = 2 * mh;
        j1 = m;
        j2 = j1 + m;
        j3 = j2 + m;
        idx1 = offa + j1;
        idx2 = offa + j2;
        idx3 = offa + j3;
        x0r = a[offa] + a[idx2];
        x0i = a[offa + 1] + a[idx2 + 1];
        x1r = a[offa] - a[idx2];
        x1i = a[offa + 1] - a[idx2 + 1];
        x2r = a[idx1] + a[idx3];
        x2i = a[idx1 + 1] + a[idx3 + 1];
        x3r = a[idx1] - a[idx3];
        x3i = a[idx1 + 1] - a[idx3 + 1];
        a[offa] = x0r + x2r;
        a[offa + 1] = x0i + x2i;
        a[idx1] = x0r - x2r;
        a[idx1 + 1] = x0i - x2i;
        a[idx2] = x1r - x3i;
        a[idx2 + 1] = x1i + x3r;
        a[idx3] = x1r + x3i;
        a[idx3 + 1] = x1i - x3r;
        wn4r = w[startw + 1];
        k = 0;
        for (int j = 2; j < mh; j += 2) {
            k += 4;
            idx4 = startw + k;
            wk1r = w[idx4];
            wk1i = w[idx4 + 1];
            wk3r = w[idx4 + 2];
            wk3i = w[idx4 + 3];
            j1 = j + m;
            j2 = j1 + m;
            j3 = j2 + m;
            idx1 = offa + j1;
            idx2 = offa + j2;
            idx3 = offa + j3;
            idx5 = offa + j;
            x0r = a[idx5] + a[idx2];
            x0i = a[idx5 + 1] + a[idx2 + 1];
            x1r = a[idx5] - a[idx2];
            x1i = a[idx5 + 1] - a[idx2 + 1];
            x2r = a[idx1] + a[idx3];
            x2i = a[idx1 + 1] + a[idx3 + 1];
            x3r = a[idx1] - a[idx3];
            x3i = a[idx1 + 1] - a[idx3 + 1];
            a[idx5] = x0r + x2r;
            a[idx5 + 1] = x0i + x2i;
            a[idx1] = x0r - x2r;
            a[idx1 + 1] = x0i - x2i;
            x0r = x1r - x3i;
            x0i = x1i + x3r;
            a[idx2] = wk1r * x0r - wk1i * x0i;
            a[idx2 + 1] = wk1r * x0i + wk1i * x0r;
            x0r = x1r + x3i;
            x0i = x1i - x3r;
            a[idx3] = wk3r * x0r + wk3i * x0i;
            a[idx3 + 1] = wk3r * x0i - wk3i * x0r;
            j0 = m - j;
            j1 = j0 + m;
            j2 = j1 + m;
            j3 = j2 + m;
            idx0 = offa + j0;
            idx1 = offa + j1;
            idx2 = offa + j2;
            idx3 = offa + j3;
            x0r = a[idx0] + a[idx2];
            x0i = a[idx0 + 1] + a[idx2 + 1];
            x1r = a[idx0] - a[idx2];
            x1i = a[idx0 + 1] - a[idx2 + 1];
            x2r = a[idx1] + a[idx3];
            x2i = a[idx1 + 1] + a[idx3 + 1];
            x3r = a[idx1] - a[idx3];
            x3i = a[idx1 + 1] - a[idx3 + 1];
            a[idx0] = x0r + x2r;
            a[idx0 + 1] = x0i + x2i;
            a[idx1] = x0r - x2r;
            a[idx1 + 1] = x0i - x2i;
            x0r = x1r - x3i;
            x0i = x1i + x3r;
            a[idx2] = wk1i * x0r - wk1r * x0i;
            a[idx2 + 1] = wk1i * x0i + wk1r * x0r;
            x0r = x1r + x3i;
            x0i = x1i - x3r;
            a[idx3] = wk3i * x0r + wk3r * x0i;
            a[idx3 + 1] = wk3i * x0i - wk3r * x0r;
        }
        j0 = mh;
        j1 = j0 + m;
        j2 = j1 + m;
        j3 = j2 + m;
        idx0 = offa + j0;
        idx1 = offa + j1;
        idx2 = offa + j2;
        idx3 = offa + j3;
        x0r = a[idx0] + a[idx2];
        x0i = a[idx0 + 1] + a[idx2 + 1];
        x1r = a[idx0] - a[idx2];
        x1i = a[idx0 + 1] - a[idx2 + 1];
        x2r = a[idx1] + a[idx3];
        x2i = a[idx1 + 1] + a[idx3 + 1];
        x3r = a[idx1] - a[idx3];
        x3i = a[idx1 + 1] - a[idx3 + 1];
        a[idx0] = x0r + x2r;
        a[idx0 + 1] = x0i + x2i;
        a[idx1] = x0r - x2r;
        a[idx1 + 1] = x0i - x2i;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[idx2] = wn4r * (x0r - x0i);
        a[idx2 + 1] = wn4r * (x0i + x0r);
        x0r = x1r + x3i;
        x0i = x1i - x3r;
        a[idx3] = -wn4r * (x0r + x0i);
        a[idx3 + 1] = -wn4r * (x0i - x0r);
    }

    private void cftmdl2(int n, double[] a, int offa, double[] w, int startw) {
        int j0, j1, j2, j3, k, kr, m, mh;
        double wn4r, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
        double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i;
        int idx0, idx1, idx2, idx3, idx4, idx5, idx6;

        mh = n >> 3;
        m = 2 * mh;
        wn4r = w[startw + 1];
        j1 = m;
        j2 = j1 + m;
        j3 = j2 + m;
        idx1 = offa + j1;
        idx2 = offa + j2;
        idx3 = offa + j3;
        x0r = a[offa] - a[idx2 + 1];
        x0i = a[offa + 1] + a[idx2];
        x1r = a[offa] + a[idx2 + 1];
        x1i = a[offa + 1] - a[idx2];
        x2r = a[idx1] - a[idx3 + 1];
        x2i = a[idx1 + 1] + a[idx3];
        x3r = a[idx1] + a[idx3 + 1];
        x3i = a[idx1 + 1] - a[idx3];
        y0r = wn4r * (x2r - x2i);
        y0i = wn4r * (x2i + x2r);
        a[offa] = x0r + y0r;
        a[offa + 1] = x0i + y0i;
        a[idx1] = x0r - y0r;
        a[idx1 + 1] = x0i - y0i;
        y0r = wn4r * (x3r - x3i);
        y0i = wn4r * (x3i + x3r);
        a[idx2] = x1r - y0i;
        a[idx2 + 1] = x1i + y0r;
        a[idx3] = x1r + y0i;
        a[idx3 + 1] = x1i - y0r;
        k = 0;
        kr = 2 * m;
        for (int j = 2; j < mh; j += 2) {
            k += 4;
            idx4 = startw + k;
            wk1r = w[idx4];
            wk1i = w[idx4 + 1];
            wk3r = w[idx4 + 2];
            wk3i = w[idx4 + 3];
            kr -= 4;
            idx5 = startw + kr;
            wd1i = w[idx5];
            wd1r = w[idx5 + 1];
            wd3i = w[idx5 + 2];
            wd3r = w[idx5 + 3];
            j1 = j + m;
            j2 = j1 + m;
            j3 = j2 + m;
            idx1 = offa + j1;
            idx2 = offa + j2;
            idx3 = offa + j3;
            idx6 = offa + j;
            x0r = a[idx6] - a[idx2 + 1];
            x0i = a[idx6 + 1] + a[idx2];
            x1r = a[idx6] + a[idx2 + 1];
            x1i = a[idx6 + 1] - a[idx2];
            x2r = a[idx1] - a[idx3 + 1];
            x2i = a[idx1 + 1] + a[idx3];
            x3r = a[idx1] + a[idx3 + 1];
            x3i = a[idx1 + 1] - a[idx3];
            y0r = wk1r * x0r - wk1i * x0i;
            y0i = wk1r * x0i + wk1i * x0r;
            y2r = wd1r * x2r - wd1i * x2i;
            y2i = wd1r * x2i + wd1i * x2r;
            a[idx6] = y0r + y2r;
            a[idx6 + 1] = y0i + y2i;
            a[idx1] = y0r - y2r;
            a[idx1 + 1] = y0i - y2i;
            y0r = wk3r * x1r + wk3i * x1i;
            y0i = wk3r * x1i - wk3i * x1r;
            y2r = wd3r * x3r + wd3i * x3i;
            y2i = wd3r * x3i - wd3i * x3r;
            a[idx2] = y0r + y2r;
            a[idx2 + 1] = y0i + y2i;
            a[idx3] = y0r - y2r;
            a[idx3 + 1] = y0i - y2i;
            j0 = m - j;
            j1 = j0 + m;
            j2 = j1 + m;
            j3 = j2 + m;
            idx0 = offa + j0;
            idx1 = offa + j1;
            idx2 = offa + j2;
            idx3 = offa + j3;
            x0r = a[idx0] - a[idx2 + 1];
            x0i = a[idx0 + 1] + a[idx2];
            x1r = a[idx0] + a[idx2 + 1];
            x1i = a[idx0 + 1] - a[idx2];
            x2r = a[idx1] - a[idx3 + 1];
            x2i = a[idx1 + 1] + a[idx3];
            x3r = a[idx1] + a[idx3 + 1];
            x3i = a[idx1 + 1] - a[idx3];
            y0r = wd1i * x0r - wd1r * x0i;
            y0i = wd1i * x0i + wd1r * x0r;
            y2r = wk1i * x2r - wk1r * x2i;
            y2i = wk1i * x2i + wk1r * x2r;
            a[idx0] = y0r + y2r;
            a[idx0 + 1] = y0i + y2i;
            a[idx1] = y0r - y2r;
            a[idx1 + 1] = y0i - y2i;
            y0r = wd3i * x1r + wd3r * x1i;
            y0i = wd3i * x1i - wd3r * x1r;
            y2r = wk3i * x3r + wk3r * x3i;
            y2i = wk3i * x3i - wk3r * x3r;
            a[idx2] = y0r + y2r;
            a[idx2 + 1] = y0i + y2i;
            a[idx3] = y0r - y2r;
            a[idx3 + 1] = y0i - y2i;
        }
        wk1r = w[startw + m];
        wk1i = w[startw + m + 1];
        j0 = mh;
        j1 = j0 + m;
        j2 = j1 + m;
        j3 = j2 + m;
        idx0 = offa + j0;
        idx1 = offa + j1;
        idx2 = offa + j2;
        idx3 = offa + j3;
        x0r = a[idx0] - a[idx2 + 1];
        x0i = a[idx0 + 1] + a[idx2];
        x1r = a[idx0] + a[idx2 + 1];
        x1i = a[idx0 + 1] - a[idx2];
        x2r = a[idx1] - a[idx3 + 1];
        x2i = a[idx1 + 1] + a[idx3];
        x3r = a[idx1] + a[idx3 + 1];
        x3i = a[idx1 + 1] - a[idx3];
        y0r = wk1r * x0r - wk1i * x0i;
        y0i = wk1r * x0i + wk1i * x0r;
        y2r = wk1i * x2r - wk1r * x2i;
        y2i = wk1i * x2i + wk1r * x2r;
        a[idx0] = y0r + y2r;
        a[idx0 + 1] = y0i + y2i;
        a[idx1] = y0r - y2r;
        a[idx1 + 1] = y0i - y2i;
        y0r = wk1i * x1r - wk1r * x1i;
        y0i = wk1i * x1i + wk1r * x1r;
        y2r = wk1r * x3r - wk1i * x3i;
        y2i = wk1r * x3i + wk1i * x3r;
        a[idx2] = y0r - y2r;
        a[idx2 + 1] = y0i - y2i;
        a[idx3] = y0r + y2r;
        a[idx3 + 1] = y0i + y2i;
    }

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

    private void cftf161(double[] a, int offa, double[] w, int startw) {
        double wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i, y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i, y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;

        wn4r = w[startw + 1];
        wk1r = w[startw + 2];
        wk1i = w[startw + 3];

        x0r = a[offa] + a[offa + 16];
        x0i = a[offa + 1] + a[offa + 17];
        x1r = a[offa] - a[offa + 16];
        x1i = a[offa + 1] - a[offa + 17];
        x2r = a[offa + 8] + a[offa + 24];
        x2i = a[offa + 9] + a[offa + 25];
        x3r = a[offa + 8] - a[offa + 24];
        x3i = a[offa + 9] - a[offa + 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[offa + 2] + a[offa + 18];
        x0i = a[offa + 3] + a[offa + 19];
        x1r = a[offa + 2] - a[offa + 18];
        x1i = a[offa + 3] - a[offa + 19];
        x2r = a[offa + 10] + a[offa + 26];
        x2i = a[offa + 11] + a[offa + 27];
        x3r = a[offa + 10] - a[offa + 26];
        x3i = a[offa + 11] - a[offa + 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[offa + 4] + a[offa + 20];
        x0i = a[offa + 5] + a[offa + 21];
        x1r = a[offa + 4] - a[offa + 20];
        x1i = a[offa + 5] - a[offa + 21];
        x2r = a[offa + 12] + a[offa + 28];
        x2i = a[offa + 13] + a[offa + 29];
        x3r = a[offa + 12] - a[offa + 28];
        x3i = a[offa + 13] - a[offa + 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[offa + 6] + a[offa + 22];
        x0i = a[offa + 7] + a[offa + 23];
        x1r = a[offa + 6] - a[offa + 22];
        x1i = a[offa + 7] - a[offa + 23];
        x2r = a[offa + 14] + a[offa + 30];
        x2i = a[offa + 15] + a[offa + 31];
        x3r = a[offa + 14] - a[offa + 30];
        x3i = a[offa + 15] - a[offa + 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[offa + 24] = x0r + x2r;
        a[offa + 25] = x0i + x2i;
        a[offa + 26] = x0r - x2r;
        a[offa + 27] = x0i - x2i;
        a[offa + 28] = x1r - x3i;
        a[offa + 29] = x1i + x3r;
        a[offa + 30] = x1r + x3i;
        a[offa + 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[offa + 16] = x0r + x2r;
        a[offa + 17] = x0i + x2i;
        a[offa + 18] = x0r - x2r;
        a[offa + 19] = x0i - x2i;
        a[offa + 20] = x1r - x3i;
        a[offa + 21] = x1i + x3r;
        a[offa + 22] = x1r + x3i;
        a[offa + 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[offa + 8] = x0r + x2r;
        a[offa + 9] = x0i + x2i;
        a[offa + 10] = x0r - x2r;
        a[offa + 11] = x0i - x2i;
        a[offa + 12] = x1r - x3i;
        a[offa + 13] = x1i + x3r;
        a[offa + 14] = x1r + x3i;
        a[offa + 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[offa] = x0r + x2r;
        a[offa + 1] = x0i + x2i;
        a[offa + 2] = x0r - x2r;
        a[offa + 3] = x0i - x2i;
        a[offa + 4] = x1r - x3i;
        a[offa + 5] = x1i + x3r;
        a[offa + 6] = x1r + x3i;
        a[offa + 7] = x1i - x3r;
    }

    private void cftf162(double[] a, int offa, double[] w, int startw) {
        double wn4r, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i, x0r, x0i, x1r, x1i, x2r, x2i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i, y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i, y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;

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

    private void cftf081(double[] a, int offa, double[] w, int startw) {
        double wn4r, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;

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

    private void cftf082(double[] a, int offa, double[] w, int startw) {
        double wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;

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

    private void cftf040(double[] a, int offa) {
        double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

        x0r = a[offa] + a[offa + 4];
        x0i = a[offa + 1] + a[offa + 5];
        x1r = a[offa] - a[offa + 4];
        x1i = a[offa + 1] - a[offa + 5];
        x2r = a[offa + 2] + a[offa + 6];
        x2i = a[offa + 3] + a[offa + 7];
        x3r = a[offa + 2] - a[offa + 6];
        x3i = a[offa + 3] - a[offa + 7];
        a[offa] = x0r + x2r;
        a[offa + 1] = x0i + x2i;
        a[offa + 2] = x1r - x3i;
        a[offa + 3] = x1i + x3r;
        a[offa + 4] = x0r - x2r;
        a[offa + 5] = x0i - x2i;
        a[offa + 6] = x1r + x3i;
        a[offa + 7] = x1i - x3r;
    }

    private void cftb040(double[] a, int offa) {
        double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

        x0r = a[offa] + a[offa + 4];
        x0i = a[offa + 1] + a[offa + 5];
        x1r = a[offa] - a[offa + 4];
        x1i = a[offa + 1] - a[offa + 5];
        x2r = a[offa + 2] + a[offa + 6];
        x2i = a[offa + 3] + a[offa + 7];
        x3r = a[offa + 2] - a[offa + 6];
        x3i = a[offa + 3] - a[offa + 7];
        a[offa] = x0r + x2r;
        a[offa + 1] = x0i + x2i;
        a[offa + 2] = x1r + x3i;
        a[offa + 3] = x1i - x3r;
        a[offa + 4] = x0r - x2r;
        a[offa + 5] = x0i - x2i;
        a[offa + 6] = x1r - x3i;
        a[offa + 7] = x1i + x3r;
    }

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

    private void cftxb020(double[] a, int offa) {
        double x0r, x0i;

        x0r = a[offa] - a[offa + 2];
        x0i = a[offa + 1] - a[offa + 3];
        a[offa] += a[offa + 2];
        a[offa + 1] += a[offa + 3];
        a[offa + 2] = x0r;
        a[offa + 3] = x0i;
    }

    private void cftxc020(double[] a, int offa) {
        double x0r, x0i;
        x0r = a[offa] - a[offa + 2];
        x0i = a[offa + 1] + a[offa + 3];
        a[offa] += a[offa + 2];
        a[offa + 1] -= a[offa + 3];
        a[offa + 2] = x0r;
        a[offa + 3] = x0i;
    }

    private void rftfsub(int n, double[] a, int offa, int nc, double[] c, int startc) {
        int k, kk, ks, m;
        double wkr, wki, xr, xi, yr, yi;
        int idx1, idx2;

        m = n >> 1;
        ks = 2 * nc / m;
        kk = 0;
        for (int j = 2; j < m; j += 2) {
            k = n - j;
            kk += ks;
            wkr = 0.5 - c[startc + nc - kk];
            wki = c[startc + kk];
            idx1 = offa + j;
            idx2 = offa + k;
            xr = a[idx1] - a[idx2];
            xi = a[idx1 + 1] + a[idx2 + 1];
            yr = wkr * xr - wki * xi;
            yi = wkr * xi + wki * xr;
            a[idx1] -= yr;
            a[idx1 + 1] = yi - a[idx1 + 1];
            a[idx2] += yr;
            a[idx2 + 1] = yi - a[idx2 + 1];
        }
        a[offa + m + 1] = -a[offa + m + 1];
    }

    private void rftbsub(int n, double[] a, int offa, int nc, double[] c, int startc) {
        int k, kk, ks, m;
        double wkr, wki, xr, xi, yr, yi;
        int idx1, idx2;

        m = n >> 1;
        ks = 2 * nc / m;
        kk = 0;
        for (int j = 2; j < m; j += 2) {
            k = n - j;
            kk += ks;
            wkr = 0.5 - c[startc + nc - kk];
            wki = c[startc + kk];
            idx1 = offa + j;
            idx2 = offa + k;
            xr = a[idx1] - a[idx2];
            xi = a[idx1 + 1] + a[idx2 + 1];
            yr = wkr * xr - wki * xi;
            yi = wkr * xi + wki * xr;
            a[idx1] -= yr;
            a[idx1 + 1] -= yi;
            a[idx2] += yr;
            a[idx2 + 1] -= yi;
        }
    }

    private void scale(final double m, final double[] a, int offa, boolean complex) {
        final double norm = (1.0 / m);
        int n2;
        if (complex) {
            n2 = 2 * n;
        } else {
            n2 = n;
        }
        int nthreads = ConcurrencyUtils.getNumberOfThreads();
        if ((nthreads > 1) && (n2 >= ConcurrencyUtils.getThreadsBeginN_1D_FFT_2Threads())) {
            final int k = n2 / nthreads;
            Future<?>[] futures = new Future[nthreads];
            for (int i = 0; i < nthreads; i++) {
                final int firstIdx = offa + i * k;
                final int lastIdx = (i == (nthreads - 1)) ? offa + n2 : firstIdx + k;
                futures[i] = ConcurrencyUtils.submit(new Runnable() {

                    @Override
                                        public void run() {
                        for (int i = firstIdx; i < lastIdx; i++) {
                            a[i] *= norm;
                        }
                    }
                });
            }
            ConcurrencyUtils.waitForCompletion(futures);
        } else {
            for (int i = offa; i < offa + n2; i++) {
                a[i] *= norm;
            }

        }
    }
}