/* * Copyright Takuya OOURA, 1996-2001 * * You may use, copy, modify and distribute this code * for any purpose (include commercial use) and without fee. * Please refer to this package when you modify this code. */ package vavi.util; /** * Fast Fourier/Cosine/Sine Transform. * <pre> * dimension :one * data length :power of 2 * decimation :frequency * radix :<b>split-radix</b> * data :inplace * table :use * </pre> * <h4>Appendix:</h4> * <p> * The cos/sin table is recalculated when the larger table required. * w[] and ip[] are compatible with all routines. * </p> * @author <a href="mailto:ooura@mmm.t.u-tokyo.ac.jp">Takuya OOURA</a> * @author <a href="mailto:vavivavi@yahoo.co.jp">Naohide Sano</a> (nsano) * @version 0.00 060127 nsano port to java version <br> */ public class SplitRadixFft { /** */ private static final int CDFT_RECURSIVE_N = 512; /** * Complex Discrete Fourier Transform. * <pre> * [definition] * <case1> * X[k] = sum_j=0&circ;n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n * <case2> * X[k] = sum_j=0&circ;n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n * (notes: sum_j=0&circ;n-1 is a summation from j=0 to n-1) * [usage] * <case1> * ip[0] = 0; // first time only * cdft(2*n, 1, a, ip, w); * <case2> * ip[0] = 0; // first time only * cdft(2*n, -1, a, ip, w); * [remark] * Inverse of * cdft(2*n, -1, a, ip, w); * is * cdft(2*n, 1, a, ip, w); * for (j = 0; j <= 2 * n - 1; j++) { * a[j] *= 1.0 / n; * } * . * </pre> * @param n 2*n data length (int) * n >= 1, n = power of 2 * @param isgn * @param a a[0...2*n-1] input/output data (REAL *) * input data * a[2*j] = Re(x[j]), * a[2*j+1] = Im(x[j]), 0<=j<n * output data * a[2*k] = Re(X[k]), * a[2*k+1] = Im(X[k]), 0<=k<n * @param ip ip[0...*] work area for bit reversal (int *) * length of ip >= 2+sqrt(n) * strictly, * length of ip >= * 2+(1<<(int)(log(n+0.5)/log(2))/2). * ip[0],ip[1] are pointers of the cos/sin table. * @param w w[0...n/2-1] cos/sin table (REAL *) * w[],ip[] are initialized if ip[0] == 0. */ public void cdft(int n, int isgn, double[] a, int[] ip, double[] w) { int nw; nw = ip[0]; if (n > (nw << 2)) { nw = n >> 2; makewt(nw, ip, w); } if (isgn >= 0) { cftfsub(n, a, ip, 2, nw, w); } else { cftbsub(n, a, ip, 2, nw, w); } } /** * Real Discrete Fourier Transform. * <pre> * [definition] * <case1> RDFT * R[k] = sum_j = 0 & ˆ (n - 1) a[j] * cos(2 * pi * j * k / n), 0 <= k <= n / 2 * I[k] = sum_j = 0 & ˆ (n - 1) a[j] * sin(2 * pi * j * k / n), 0 < k < n / 2 * <case2> IRDFT (excluding scale) * a[k] = (R[0] + R[n / 2] * cos(pi * k)) / 2 + * sum_j = 1 & ˆ (n / 2 - 1) R[j] * cos(2 * pi * j * k / n) + * sum_j = 1 & ˆ (n / 2 - 1) I[j] * sin(2 * pi * j * k / n), 0 <= k < n * [usage] * <case1> * ip[0] = 0; // first time only * rdft(n, 1, a, ip, w); * <case2> * ip[0] = 0; // first time only * rdft(n, -1, a, ip, w); * [remark] * Inverse of * rdft(n, 1, a, ip, w); * is * rdft(n, -1, a, ip, w); * for (j = 0; j <= n - 1; j++) { * a[j] *= 2.0 / n; * } * . * </pre> * @param n data length <br> * n >= 2, n = power of 2 * @param isgn * @param a [0...n-1] input/output data * <pre> * <case1> * output data * a[2 * k] = R[k], 0 <= k < n / 2 * a[2 * k + 1] = I[k], 0 < k < n / 2 * a[1] = R[n/2] * <case2> * input data * a[2 * j] = R[j], 0 <= j < n / 2 * a[2 * j + 1] = I[j], 0 < j < n / 2 * a[1] = R[n / 2] * </pre> * @param ip [0...*] work area for bit reversal * <pre> * length of ip >= 2 + sqrt(n / 2) * strictly, * length of ip >= * 2 + (1 << (int) (log(n / 2 + 0.5) / log(2)) / 2). * </pre> * ip[0],ip[1] are pointers of the cos/sin table. * @param w [0...n/2-1] cos/sin table <br> * w[],ip[] are initialized if ip[0] == 0. */ public void rdft(int n, int isgn, double[] a, int[] ip, double[] w) { int nw, nc; double xi; nw = ip[0]; if (n > (nw << 2)) { nw = n >> 2; makewt(nw, ip, w); } nc = ip[1]; if (n > (nc << 2)) { nc = n >> 2; makect(nc, ip, w, nw); } if (isgn >= 0) { if (n > 4) { cftfsub(n, a, ip, 2, nw, w); rftfsub(n, a, nc, w, nw); } else if (n == 4) { cftfsub(n, a, ip, 2, nw, w); } xi = a[0] - a[1]; a[0] += a[1]; a[1] = xi; } else { a[1] = 0.5 * (a[0] - a[1]); a[0] -= a[1]; if (n > 4) { rftbsub(n, a, nc, w, nw); cftbsub(n, a, ip, 2, nw, w); } else if (n == 4) { cftbsub(n, a, ip, 2, nw, w); } } } /** * Discrete Cosine Transform. * <pre> * [definition] * <case1> IDCT (excluding scale) * C[k] = sum_j=0&circ;n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n * <case2> DCT * C[k] = sum_j=0&circ;n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n * [usage] * <case1> * ip[0] = 0; // first time only * ddct(n, 1, a, ip, w); * <case2> * ip[0] = 0; // first time only * ddct(n, -1, a, ip, w); * [remark] * Inverse of * ddct(n, -1, a, ip, w); * is * a[0] *= 0.5; * ddct(n, 1, a, ip, w); * for (j = 0; j <= n - 1; j++) { * a[j] *= 2.0 / n; * } * . * </pre> * @param n data length (int) * <pre> * n >= 2, n = power of 2 * </pre> * @param isgn * @param a [0...n-1] input/output data (REAL *) * <pre> * output data * a[k] = C[k], 0<=k<n * </pre> * @param ip [0...*] work area for bit reversal (int *) * <pre> * length of ip >= 2+sqrt(n/2) * strictly, * length of ip >= * 2+(1<<(int)(log(n/2+0.5)/log(2))/2). * ip[0],ip[1] are pointers of the cos/sin table. * </pre> * @param w [0...n*5/4-1] cos/sin table (REAL *) * <pre> * w[],ip[] are initialized if ip[0] == 0. * </pre> */ public void ddct(int n, int isgn, double[] a, int[] ip, double[] w) { int j, nw, nc; double xr; nw = ip[0]; if (n > (nw << 2)) { nw = n >> 2; makewt(nw, ip, w); } nc = ip[1]; if (n > nc) { nc = n; makect(nc, ip, w, nw); } if (isgn < 0) { xr = a[n - 1]; for (j = n - 2; j >= 2; j -= 2) { a[j + 1] = a[j] - a[j - 1]; a[j] += a[j - 1]; } a[1] = a[0] - xr; a[0] += xr; if (n > 4) { rftbsub(n, a, nc, w, nw); cftbsub(n, a, ip, 2, nw, w); } else if (n == 4) { cftbsub(n, a, ip, 2, nw, w); } } dctsub(n, a, nc, w, nw); if (isgn >= 0) { if (n > 4) { cftfsub(n, a, ip, 2, nw, w); rftfsub(n, a, nc, w, nw); } else if (n == 4) { cftfsub(n, a, ip, 2, nw, w); } xr = a[0] - a[1]; a[0] += a[1]; for (j = 2; j < n; j += 2) { a[j - 1] = a[j] - a[j + 1]; a[j] += a[j + 1]; } a[n - 1] = xr; } } /** * Discrete Sine Transform. * <pre> * [definition] * <case1> IDST (excluding scale) * S[k] = sum_j=1ˆn A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n * <case2> DST * S[k] = sum_j=0ˆn-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n * [usage] * <case1> * ip[0] = 0; // first time only * ddst(n, 1, a, ip, w); * <case2> * ip[0] = 0; // first time only * ddst(n, -1, a, ip, w); * [remark] * Inverse of * ddst(n, -1, a, ip, w); * is * a[0] *= 0.5; * ddst(n, 1, a, ip, w); * for (j = 0; j <= n - 1; j++) { * a[j] *= 2.0 / n; * } * . * </pre> * @param n data length (int) * n >= 2, n = power of 2 * @param isgn * @param a [0...n-1] input/output data (REAL *) * <case1> * input data * a[j] = A[j], 0<j<n * a[0] = A[n] * output data * a[k] = S[k], 0<=k<n * <case2> * output data * a[k] = S[k], 0<k<n * a[0] = S[n] * @param ip [0...*] work area for bit reversal (int *) * length of ip >= 2+sqrt(n/2) * strictly, * length of ip >= * 2+(1<<(int)(log(n/2+0.5)/log(2))/2). * ip[0],ip[1] are pointers of the cos/sin table. * @param w [0...n*5/4-1] cos/sin table (REAL *) * w[],ip[] are initialized if ip[0] == 0. */ public void ddst(int n, int isgn, double[] a, int[] ip, double[] w) { int j, nw, nc; double xr; nw = ip[0]; if (n > (nw << 2)) { nw = n >> 2; makewt(nw, ip, w); } nc = ip[1]; if (n > nc) { nc = n; makect(nc, ip, w, nw); } if (isgn < 0) { xr = a[n - 1]; for (j = n - 2; j >= 2; j -= 2) { a[j + 1] = -a[j] - a[j - 1]; a[j] -= a[j - 1]; } a[1] = a[0] + xr; a[0] -= xr; if (n > 4) { rftbsub(n, a, nc, w, nw); cftbsub(n, a, ip, 2, nw, w); } else if (n == 4) { cftbsub(n, a, ip, 2, nw, w); } } dstsub(n, a, nc, w, nw); if (isgn >= 0) { if (n > 4) { cftfsub(n, a, ip, 2, nw, w); rftfsub(n, a, nc, w, nw); } else if (n == 4) { cftfsub(n, a, ip, 2, nw, w); } xr = a[0] - a[1]; a[0] += a[1]; for (j = 2; j < n; j += 2) { a[j - 1] = -a[j] - a[j + 1]; a[j] -= a[j + 1]; } a[n - 1] = -xr; } } /** * Cosine Transform of RDFT (Real Symmetric DFT). * <pre> * [definition] * C[k] = sum_j=0ˆn a[j]*cos(pi*j*k/n), 0<=k<=n * [usage] * ip[0] = 0; // first time only * dfct(n, a, t, ip, w); * [parameters] * [remark] * Inverse of * a[0] *= 0.5; * a[n] *= 0.5; * dfct(n, a, t, ip, w); * is * a[0] *= 0.5; * a[n] *= 0.5; * dfct(n, a, t, ip, w); * for (j = 0; j <= n; j++) { * a[j] *= 2.0 / n; * } * . * </pre> * @param n data length - 1 (int) * <pre> * n >= 2, n = power of 2 * </pre> * @param a [0...n] input/output data (REAL *) * <pre> * output data * a[k] = C[k], 0<=k<=n * </pre> * @param t [0...n/2] work area (REAL *) * @param ip [0...*] work area for bit reversal (int *) * <pre> * length of ip >= 2+sqrt(n/4) * strictly, * length of ip >= * 2+(1<<(int)(log(n/4+0.5)/log(2))/2). * ip[0],ip[1] are pointers of the cos/sin table. * </pre> * @param w [0...n*5/8-1] cos/sin table (REAL *) * <pre> * w[],ip[] are initialized if ip[0] == 0. * </pre> */ public void dfct(int n, double[] a, double[] t, int[] ip, double[] w) { int j, k, l, m, mh, nw, nc; double xr, xi, yr, yi; nw = ip[0]; if (n > (nw << 3)) { nw = n >> 3; makewt(nw, ip, w); } nc = ip[1]; if (n > (nc << 1)) { nc = n >> 1; makect(nc, ip, w, nw); } m = n >> 1; yi = a[m]; xi = a[0] + a[n]; a[0] -= a[n]; t[0] = xi - yi; t[m] = xi + yi; if (n > 2) { mh = m >> 1; for (j = 1; j < mh; j++) { k = m - j; xr = a[j] - a[n - j]; xi = a[j] + a[n - j]; yr = a[k] - a[n - k]; yi = a[k] + a[n - k]; a[j] = xr; a[k] = yr; t[j] = xi - yi; t[k] = xi + yi; } t[mh] = a[mh] + a[n - mh]; a[mh] -= a[n - mh]; dctsub(m, a, nc, w, nw); if (m > 4) { cftfsub(m, a, ip, 2, nw, w); rftfsub(m, a, nc, w, nw); } else if (m == 4) { cftfsub(m, a, ip, 2, nw, w); } a[n - 1] = a[0] - a[1]; a[1] = a[0] + a[1]; for (j = m - 2; j >= 2; j -= 2) { a[2 * j + 1] = a[j] + a[j + 1]; a[2 * j - 1] = a[j] - a[j + 1]; } l = 2; m = mh; while (m >= 2) { dctsub(m, t, nc, w, nw); if (m > 4) { cftfsub(m, t, ip, 2, nw, w); rftfsub(m, t, nc, w, nw); } else if (m == 4) { cftfsub(m, t, ip, 2, nw, w); } a[n - l] = t[0] - t[1]; a[l] = t[0] + t[1]; k = 0; for (j = 2; j < m; j += 2) { k += l << 2; a[k - l] = t[j] - t[j + 1]; a[k + l] = t[j] + t[j + 1]; } l <<= 1; mh = m >> 1; for (j = 0; j < mh; j++) { k = m - j; t[j] = t[m + k] - t[m + j]; t[k] = t[m + k] + t[m + j]; } t[mh] = t[m + mh]; m = mh; } a[l] = t[0]; a[n] = t[2] - t[1]; a[0] = t[2] + t[1]; } else { a[1] = a[0]; a[2] = t[0]; a[0] = t[1]; } } /** * Sine Transform of RDFT (Real Anti-symmetric DFT). * <pre> * [definition] * S[k] = sum_j=1&circ;n-1 a[j]*sin(pi*j*k/n), 0<k<n * [usage] * ip[0] = 0; // first time only * dfst(n, a, t, ip, w); * [remark] * Inverse of * dfst(n, a, t, ip, w); * is * dfst(n, a, t, ip, w); * for (j = 1; j <= n - 1; j++) { * a[j] *= 2.0 / n; * } * . * </pre> * @param n data length + 1 (int) * <pre> * n >= 2, n = power of 2 * </pre> * @param a [0...n-1] input/output data (REAL *) * <pre> * output data * a[k] = S[k], 0<k<n * (a[0] is used for work area) * </pre> * @param t [0...n/2-1] work area (REAL *) * @param ip [0...*] work area for bit reversal (int *) * <pre> * length of ip >= 2+sqrt(n/4) * strictly, * length of ip >= * 2+(1<<(int)(log(n/4+0.5)/log(2))/2). * ip[0],ip[1] are pointers of the cos/sin table. * </pre> * @param w [0...n*5/8-1] cos/sin table (REAL *) * <pre> * w[],ip[] are initialized if ip[0] == 0. * </pre> */ public void dfst(int n, double[] a, double[] t, int[] ip, double[] w) { int j, k, l, m, mh, nw, nc; double xr, xi, yr, yi; nw = ip[0]; if (n > (nw << 3)) { nw = n >> 3; makewt(nw, ip, w); } nc = ip[1]; if (n > (nc << 1)) { nc = n >> 1; makect(nc, ip, w, nw); } if (n > 2) { m = n >> 1; mh = m >> 1; for (j = 1; j < mh; j++) { k = m - j; xr = a[j] + a[n - j]; xi = a[j] - a[n - j]; yr = a[k] + a[n - k]; yi = a[k] - a[n - k]; a[j] = xr; a[k] = yr; t[j] = xi + yi; t[k] = xi - yi; } t[0] = a[mh] - a[n - mh]; a[mh] += a[n - mh]; a[0] = a[m]; dstsub(m, a, nc, w, nw); if (m > 4) { cftfsub(m, a, ip, 2, nw, w); rftfsub(m, a, nc, w, nw); } else if (m == 4) { cftfsub(m, a, ip, 2, nw, w); } a[n - 1] = a[1] - a[0]; a[1] = a[0] + a[1]; for (j = m - 2; j >= 2; j -= 2) { a[2 * j + 1] = a[j] - a[j + 1]; a[2 * j - 1] = -a[j] - a[j + 1]; } l = 2; m = mh; while (m >= 2) { dstsub(m, t, nc, w, nw); if (m > 4) { cftfsub(m, t, ip, 2, nw, w); rftfsub(m, t, nc, w, nw); } else if (m == 4) { cftfsub(m, t, ip, 2, nw, w); } a[n - l] = t[1] - t[0]; a[l] = t[0] + t[1]; k = 0; for (j = 2; j < m; j += 2) { k += l << 2; a[k - l] = -t[j] - t[j + 1]; a[k + l] = t[j] - t[j + 1]; } l <<= 1; mh = m >> 1; for (j = 1; j < mh; j++) { k = m - j; t[j] = t[m + k] + t[m + j]; t[k] = t[m + k] - t[m + j]; } t[0] = t[m + mh]; m = mh; } a[l] = t[0]; } a[0] = 0; } // -------- initializing routines -------- /** */ private void makewt(int nw, int[] ip, double[] w) { int j, nwh, nw0, nw1; double delta, wn4r, wk1r, wk1i, wk3r, wk3i; ip[0] = nw; ip[1] = 1; if (nw > 2) { nwh = nw >> 1; // delta = Math.atan(1.0) / nwh; delta = Math.PI / 4 / nwh; wn4r = Math.cos(delta * nwh); w[0] = 1; w[1] = wn4r; if (nwh >= 4) { w[2] = 0.5 / Math.cos(delta * 2); w[3] = 0.5 / Math.cos(delta * 6); } for (j = 4; j < nwh; j += 4) { w[j] = Math.cos(delta * j); w[j + 1] = Math.sin(delta * j); w[j + 2] = Math.cos(3 * delta * j); w[j + 3] = Math.sin(3 * delta * j); } nw0 = 0; while (nwh > 2) { nw1 = nw0 + nwh; nwh >>= 1; w[nw1] = 1; w[nw1 + 1] = wn4r; if (nwh >= 4) { wk1r = w[nw0 + 4]; wk3r = w[nw0 + 6]; w[nw1 + 2] = 0.5 / wk1r; w[nw1 + 3] = 0.5 / wk3r; } for (j = 4; j < nwh; j += 4) { wk1r = w[nw0 + 2 * j]; wk1i = w[nw0 + 2 * j + 1]; wk3r = w[nw0 + 2 * j + 2]; wk3i = w[nw0 + 2 * j + 3]; w[nw1 + j] = wk1r; w[nw1 + j + 1] = wk1i; w[nw1 + j + 2] = wk3r; w[nw1 + j + 3] = wk3i; } nw0 = nw1; } } } /** */ private void makect(int nc, int[] ip, double[] c, int cP) { int j, nch; double delta; ip[1] = nc; if (nc > 1) { nch = nc >> 1; // delta = Math.atan(1.0) / nch; delta = Math.PI / 4 / nch; c[cP + 0] = Math.cos(delta * nch); c[cP + nch] = 0.5 * c[cP + 0]; for (j = 1; j < nch; j++) { c[cP + j] = 0.5 * Math.cos(delta * j); c[cP + nc - j] = 0.5 * Math.sin(delta * j); } } } // -------- child routines -------- /** * 2nd * @see #rdft(int, int, double[], int[], double[]) * @see #ddct(int, int, double[], int[], double[]) * @see #cdft(int, int, double[], int[], double[]) * @see #ddst(int, int, double[], int[], double[]) * @see #dfst(int, double[], double[], int[], double[]) * @see #dfct(int, double[], double[], int[], double[]) */ private void cftfsub(int n, double[] a, int[] ip, int ipP, int nw, double[] w) { int m; if (n > 32) { m = n >> 2; cftf1st(n, a, w, nw - m); if (n > CDFT_RECURSIVE_N) { cftrec1(m, a, 0, nw, w); cftrec2(m, a, m, nw, w); cftrec1(m, a, 2 * m, nw, w); cftrec1(m, a, 3 * m, nw, w); } else if (m > 32) { cftexp1(n, a, 0, nw, w); } else { cftfx41(n, a, 0, nw, w); } bitrv2(n, ip, ipP, a); } else if (n > 8) { if (n == 32) { cftf161(a, 0, w, nw - 8); bitrv216(a); } else { cftf081(a, 0, w, 0); bitrv208(a); } } else if (n == 8) { cftf040(a); } else if (n == 4) { cftx020(a); } } /** * 2nd * @see #rdft(int, int, double[], int[], double[]) * @see #ddct(int, int, double[], int[], double[]) * @see #cdft(int, int, double[], int[], double[]) * @see #ddst(int, int, double[], int[], double[]) */ private void cftbsub(int n, double[] a, int[] ip, int ipP, int nw, double[] w) { int m; if (n > 32) { m = n >> 2; cftb1st(n, a, w, nw - m); if (n > CDFT_RECURSIVE_N) { cftrec1(m, a, 0, nw, w); cftrec2(m, a, m, nw, w); cftrec1(m, a, 2 * m, nw, w); cftrec1(m, a, 3 * m, nw, w); } else if (m > 32) { cftexp1(n, a, 0, nw, w); } else { cftfx41(n, a, 0, nw, w); } bitrv2conj(n, ip, ipP, a); } else if (n > 8) { if (n == 32) { cftf161(a, 0, w, nw - 8); bitrv216neg(a); } else { cftf081(a, 0, w, 0); bitrv208neg(a); } } else if (n == 8) { cftb040(a); } else if (n == 4) { cftx020(a); } } /** * 3rd * @see #cftfsub(int, double[], int[], int, int, double[]) */ private final void bitrv2(int n, int[] ip, int ipP, double[] a) { int j, j1, k, k1, l, m, m2; double xr, xi, yr, yi; ip[ipP + 0] = 0; l = n; m = 1; while ((m << 3) < l) { l >>= 1; for (j = 0; j < m; j++) { ip[ipP + m + j] = ip[ipP + j] + l; } m <<= 1; } m2 = 2 * m; if ((m << 3) == l) { for (k = 0; k < m; k++) { for (j = 0; j < k; j++) { j1 = 2 * j + ip[ipP + k]; k1 = 2 * k + ip[ipP + j]; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 += 2 * m2; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 -= m2; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 += 2 * m2; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; } j1 = 2 * k + m2 + ip[ipP + k]; k1 = j1 + m2; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; } } else { for (k = 1; k < m; k++) { for (j = 0; j < k; j++) { j1 = 2 * j + ip[ipP + k]; k1 = 2 * k + ip[ipP + j]; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 += m2; xr = a[j1]; xi = a[j1 + 1]; yr = a[k1]; yi = a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; } } } } /** * 3rd * @see #cftbsub(int, double[], int[], int, int, double[]) */ private final void bitrv2conj(int n, int[] ip, int ipP, double[] a) { int j, j1, k, k1, l, m, m2; double xr, xi, yr, yi; ip[ipP + 0] = 0; l = n; m = 1; while ((m << 3) < l) { l >>= 1; for (j = 0; j < m; j++) { ip[ipP + m + j] = ip[ipP + j] + l; } m <<= 1; } m2 = 2 * m; if ((m << 3) == l) { for (k = 0; k < m; k++) { for (j = 0; j < k; j++) { j1 = 2 * j + ip[ipP + k]; k1 = 2 * k + ip[ipP + j]; xr = a[j1]; xi = -a[j1 + 1]; yr = a[k1]; yi = -a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 += 2 * m2; xr = a[j1]; xi = -a[j1 + 1]; yr = a[k1]; yi = -a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 -= m2; xr = a[j1]; xi = -a[j1 + 1]; yr = a[k1]; yi = -a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 += 2 * m2; xr = a[j1]; xi = -a[j1 + 1]; yr = a[k1]; yi = -a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; } k1 = 2 * k + ip[ipP + k]; a[k1 + 1] = -a[k1 + 1]; j1 = k1 + m2; k1 = j1 + m2; xr = a[j1]; xi = -a[j1 + 1]; yr = a[k1]; yi = -a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; k1 += m2; a[k1 + 1] = -a[k1 + 1]; } } else { a[1] = -a[1]; a[m2 + 1] = -a[m2 + 1]; for (k = 1; k < m; k++) { for (j = 0; j < k; j++) { j1 = 2 * j + ip[ipP + k]; k1 = 2 * k + ip[ipP + j]; xr = a[j1]; xi = -a[j1 + 1]; yr = a[k1]; yi = -a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; j1 += m2; k1 += m2; xr = a[j1]; xi = -a[j1 + 1]; yr = a[k1]; yi = -a[k1 + 1]; a[j1] = yr; a[j1 + 1] = yi; a[k1] = xr; a[k1 + 1] = xi; } k1 = 2 * k + ip[ipP + k]; a[k1 + 1] = -a[k1 + 1]; a[k1 + m2 + 1] = -a[k1 + m2 + 1]; } } } /** * 3rd * @see #cftfsub(int, double[], int[], int, int, double[]) */ private void bitrv216(double[] a) { double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, x5r, x5i, x7r, x7i, x8r, x8i, x10r, x10i, x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i; x1r = a[2]; x1i = a[3]; x2r = a[4]; x2i = a[5]; x3r = a[6]; x3i = a[7]; x4r = a[8]; x4i = a[9]; x5r = a[10]; x5i = a[11]; x7r = a[14]; x7i = a[15]; x8r = a[16]; x8i = a[17]; x10r = a[20]; x10i = a[21]; x11r = a[22]; x11i = a[23]; x12r = a[24]; x12i = a[25]; x13r = a[26]; x13i = a[27]; x14r = a[28]; x14i = a[29]; a[2] = x8r; a[3] = x8i; a[4] = x4r; a[5] = x4i; a[6] = x12r; a[7] = x12i; a[8] = x2r; a[9] = x2i; a[10] = x10r; a[11] = x10i; a[14] = x14r; a[15] = x14i; a[16] = x1r; a[17] = x1i; a[20] = x5r; a[21] = x5i; a[22] = x13r; a[23] = x13i; a[24] = x3r; a[25] = x3i; a[26] = x11r; a[27] = x11i; a[28] = x7r; a[29] = x7i; } /** * 3rd * @see #cftbsub(int, double[], int[], int, int, double[]) */ private void bitrv216neg(double[] a) { double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, x5r, x5i, x6r, x6i, x7r, x7i, x8r, x8i, x9r, x9i, x10r, x10i, x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i, x15r, x15i; x1r = a[2]; x1i = a[3]; x2r = a[4]; x2i = a[5]; x3r = a[6]; x3i = a[7]; x4r = a[8]; x4i = a[9]; x5r = a[10]; x5i = a[11]; x6r = a[12]; x6i = a[13]; x7r = a[14]; x7i = a[15]; x8r = a[16]; x8i = a[17]; x9r = a[18]; x9i = a[19]; x10r = a[20]; x10i = a[21]; x11r = a[22]; x11i = a[23]; x12r = a[24]; x12i = a[25]; x13r = a[26]; x13i = a[27]; x14r = a[28]; x14i = a[29]; x15r = a[30]; x15i = a[31]; a[2] = x15r; a[3] = x15i; a[4] = x7r; a[5] = x7i; a[6] = x11r; a[7] = x11i; a[8] = x3r; a[9] = x3i; a[10] = x13r; a[11] = x13i; a[12] = x5r; a[13] = x5i; a[14] = x9r; a[15] = x9i; a[16] = x1r; a[17] = x1i; a[18] = x14r; a[19] = x14i; a[20] = x6r; a[21] = x6i; a[22] = x10r; a[23] = x10i; a[24] = x2r; a[25] = x2i; a[26] = x12r; a[27] = x12i; a[28] = x4r; a[29] = x4i; a[30] = x8r; a[31] = x8i; } /** * 3rd * @see #cftfsub(int, double[], int[], int, int, double[]) */ private void bitrv208(double[] a) { double x1r, x1i, x3r, x3i, x4r, x4i, x6r, x6i; x1r = a[2]; x1i = a[3]; x3r = a[6]; x3i = a[7]; x4r = a[8]; x4i = a[9]; x6r = a[12]; x6i = a[13]; a[2] = x4r; a[3] = x4i; a[6] = x6r; a[7] = x6i; a[8] = x1r; a[9] = x1i; a[12] = x3r; a[13] = x3i; } /** * 3rd * @see #cftbsub(int, double[], int[], int, int, double[]) */ private void bitrv208neg(double[] a) { double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, x5r, x5i, x6r, x6i, x7r, x7i; x1r = a[2]; x1i = a[3]; x2r = a[4]; x2i = a[5]; x3r = a[6]; x3i = a[7]; x4r = a[8]; x4i = a[9]; x5r = a[10]; x5i = a[11]; x6r = a[12]; x6i = a[13]; x7r = a[14]; x7i = a[15]; a[2] = x7r; a[3] = x7i; a[4] = x3r; a[5] = x3i; a[6] = x5r; a[7] = x5i; a[8] = x1r; a[9] = x1i; a[10] = x6r; a[11] = x6i; a[12] = x2r; a[13] = x2i; a[14] = x4r; a[15] = x4i; } /** * 3rd * @see #cftfsub(int, double[], int[], int, int, double[]) */ private void cftf1st(int n, double[] a, double[] w, int wP) { int j, j0, j1, j2, j3, k, m, mh; double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i; double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i; mh = n >> 3; m = 2 * mh; j1 = m; j2 = j1 + m; j3 = j2 + m; x0r = a[0] + a[j2]; x0i = a[1] + a[j2 + 1]; x1r = a[0] - a[j2]; x1i = a[1] - a[j2 + 1]; x2r = a[j1] + a[j3]; x2i = a[j1 + 1] + a[j3 + 1]; x3r = a[j1] - a[j3]; x3i = a[j1 + 1] - a[j3 + 1]; a[0] = x0r + x2r; a[1] = x0i + x2i; a[j1] = x0r - x2r; a[j1 + 1] = x0i - x2i; a[j2] = x1r - x3i; a[j2 + 1] = x1i + x3r; a[j3] = x1r + x3i; a[j3 + 1] = x1i - x3r; wn4r = w[wP + 1]; csc1 = w[wP + 2]; csc3 = w[wP + 3]; wd1r = 1; wd1i = 0; wd3r = 1; wd3i = 0; k = 0; for (j = 2; j < mh - 2; j += 4) { k += 4; wk1r = csc1 * (wd1r + w[wP + k]); wk1i = csc1 * (wd1i + w[wP + k + 1]); wk3r = csc3 * (wd3r + w[wP + k + 2]); wk3i = csc3 * (wd3i - w[wP + k + 3]); wd1r = w[wP + k]; wd1i = w[wP + k + 1]; wd3r = w[wP + k + 2]; wd3i = -w[wP + k + 3]; j1 = j + m; j2 = j1 + m; j3 = j2 + m; x0r = a[j] + a[j2]; x0i = a[j + 1] + a[j2 + 1]; x1r = a[j] - a[j2]; x1i = a[j + 1] - a[j2 + 1]; y0r = a[j + 2] + a[j2 + 2]; y0i = a[j + 3] + a[j2 + 3]; y1r = a[j + 2] - a[j2 + 2]; y1i = a[j + 3] - a[j2 + 3]; x2r = a[j1] + a[j3]; x2i = a[j1 + 1] + a[j3 + 1]; x3r = a[j1] - a[j3]; x3i = a[j1 + 1] - a[j3 + 1]; y2r = a[j1 + 2] + a[j3 + 2]; y2i = a[j1 + 3] + a[j3 + 3]; y3r = a[j1 + 2] - a[j3 + 2]; y3i = a[j1 + 3] - a[j3 + 3]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; a[j + 2] = y0r + y2r; a[j + 3] = y0i + y2i; a[j1] = x0r - x2r; a[j1 + 1] = x0i - x2i; a[j1 + 2] = y0r - y2r; a[j1 + 3] = y0i - y2i; x0r = x1r - x3i; x0i = x1i + x3r; a[j2] = wk1r * x0r - wk1i * x0i; a[j2 + 1] = wk1r * x0i + wk1i * x0r; x0r = y1r - y3i; x0i = y1i + y3r; a[j2 + 2] = wd1r * x0r - wd1i * x0i; a[j2 + 3] = wd1r * x0i + wd1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j3] = wk3r * x0r + wk3i * x0i; a[j3 + 1] = wk3r * x0i - wk3i * x0r; x0r = y1r + y3i; x0i = y1i - y3r; a[j3 + 2] = wd3r * x0r + wd3i * x0i; a[j3 + 3] = wd3r * x0i - wd3i * x0r; j0 = m - j; j1 = j0 + m; j2 = j1 + m; j3 = j2 + m; x0r = a[j0] + a[j2]; x0i = a[j0 + 1] + a[j2 + 1]; x1r = a[j0] - a[j2]; x1i = a[j0 + 1] - a[j2 + 1]; y0r = a[j0 - 2] + a[j2 - 2]; y0i = a[j0 - 1] + a[j2 - 1]; y1r = a[j0 - 2] - a[j2 - 2]; y1i = a[j0 - 1] - a[j2 - 1]; x2r = a[j1] + a[j3]; x2i = a[j1 + 1] + a[j3 + 1]; x3r = a[j1] - a[j3]; x3i = a[j1 + 1] - a[j3 + 1]; y2r = a[j1 - 2] + a[j3 - 2]; y2i = a[j1 - 1] + a[j3 - 1]; y3r = a[j1 - 2] - a[j3 - 2]; y3i = a[j1 - 1] - a[j3 - 1]; a[j0] = x0r + x2r; a[j0 + 1] = x0i + x2i; a[j0 - 2] = y0r + y2r; a[j0 - 1] = y0i + y2i; a[j1] = x0r - x2r; a[j1 + 1] = x0i - x2i; a[j1 - 2] = y0r - y2r; a[j1 - 1] = y0i - y2i; x0r = x1r - x3i; x0i = x1i + x3r; a[j2] = wk1i * x0r - wk1r * x0i; a[j2 + 1] = wk1i * x0i + wk1r * x0r; x0r = y1r - y3i; x0i = y1i + y3r; a[j2 - 2] = wd1i * x0r - wd1r * x0i; a[j2 - 1] = wd1i * x0i + wd1r * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j3] = wk3i * x0r + wk3r * x0i; a[j3 + 1] = wk3i * x0i - wk3r * x0r; x0r = y1r + y3i; x0i = y1i - y3r; a[j3 - 2] = wd3i * x0r + wd3r * x0i; a[j3 - 1] = wd3i * x0i - wd3r * x0r; } wk1r = csc1 * (wd1r + wn4r); wk1i = csc1 * (wd1i + wn4r); wk3r = csc3 * (wd3r - wn4r); wk3i = csc3 * (wd3i - wn4r); j0 = mh; j1 = j0 + m; j2 = j1 + m; j3 = j2 + m; x0r = a[j0 - 2] + a[j2 - 2]; x0i = a[j0 - 1] + a[j2 - 1]; x1r = a[j0 - 2] - a[j2 - 2]; x1i = a[j0 - 1] - a[j2 - 1]; x2r = a[j1 - 2] + a[j3 - 2]; x2i = a[j1 - 1] + a[j3 - 1]; x3r = a[j1 - 2] - a[j3 - 2]; x3i = a[j1 - 1] - a[j3 - 1]; a[j0 - 2] = x0r + x2r; a[j0 - 1] = x0i + x2i; a[j1 - 2] = x0r - x2r; a[j1 - 1] = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; a[j2 - 2] = wk1r * x0r - wk1i * x0i; a[j2 - 1] = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j3 - 2] = wk3r * x0r + wk3i * x0i; a[j3 - 1] = wk3r * x0i - wk3i * x0r; x0r = a[j0] + a[j2]; x0i = a[j0 + 1] + a[j2 + 1]; x1r = a[j0] - a[j2]; x1i = a[j0 + 1] - a[j2 + 1]; x2r = a[j1] + a[j3]; x2i = a[j1 + 1] + a[j3 + 1]; x3r = a[j1] - a[j3]; x3i = a[j1 + 1] - a[j3 + 1]; a[j0] = x0r + x2r; a[j0 + 1] = x0i + x2i; a[j1] = x0r - x2r; a[j1 + 1] = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; a[j2] = wn4r * (x0r - x0i); a[j2 + 1] = wn4r * (x0i + x0r); x0r = x1r + x3i; x0i = x1i - x3r; a[j3] = -wn4r * (x0r + x0i); a[j3 + 1] = -wn4r * (x0i - x0r); x0r = a[j0 + 2] + a[j2 + 2]; x0i = a[j0 + 3] + a[j2 + 3]; x1r = a[j0 + 2] - a[j2 + 2]; x1i = a[j0 + 3] - a[j2 + 3]; x2r = a[j1 + 2] + a[j3 + 2]; x2i = a[j1 + 3] + a[j3 + 3]; x3r = a[j1 + 2] - a[j3 + 2]; x3i = a[j1 + 3] - a[j3 + 3]; a[j0 + 2] = x0r + x2r; a[j0 + 3] = x0i + x2i; a[j1 + 2] = x0r - x2r; a[j1 + 3] = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; a[j2 + 2] = wk1i * x0r - wk1r * x0i; a[j2 + 3] = wk1i * x0i + wk1r * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j3 + 2] = wk3i * x0r + wk3r * x0i; a[j3 + 3] = wk3i * x0i - wk3r * x0r; } /** * 3rd * @see #cftbsub(int, double[], int[], int, int, double[]) */ private final void cftb1st(int n, double[] a, double[] w, int wP) { int j, j0, j1, j2, j3, k, m, mh; double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i; double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i; mh = n >> 3; m = 2 * mh; j1 = m; j2 = j1 + m; j3 = j2 + m; x0r = a[0] + a[j2]; x0i = -a[1] - a[j2 + 1]; x1r = a[0] - a[j2]; x1i = -a[1] + a[j2 + 1]; x2r = a[j1] + a[j3]; x2i = a[j1 + 1] + a[j3 + 1]; x3r = a[j1] - a[j3]; x3i = a[j1 + 1] - a[j3 + 1]; a[0] = x0r + x2r; a[1] = x0i - x2i; a[j1] = x0r - x2r; a[j1 + 1] = x0i + x2i; a[j2] = x1r + x3i; a[j2 + 1] = x1i + x3r; a[j3] = x1r - x3i; a[j3 + 1] = x1i - x3r; wn4r = w[wP + 1]; csc1 = w[wP + 2]; csc3 = w[wP + 3]; wd1r = 1; wd1i = 0; wd3r = 1; wd3i = 0; k = 0; for (j = 2; j < mh - 2; j += 4) { k += 4; wk1r = csc1 * (wd1r + w[wP + k]); wk1i = csc1 * (wd1i + w[wP + k + 1]); wk3r = csc3 * (wd3r + w[wP + k + 2]); wk3i = csc3 * (wd3i - w[wP + k + 3]); wd1r = w[wP + k]; wd1i = w[wP + k + 1]; wd3r = w[wP + k + 2]; wd3i = -w[wP + k + 3]; j1 = j + m; j2 = j1 + m; j3 = j2 + m; x0r = a[j] + a[j2]; x0i = -a[j + 1] - a[j2 + 1]; x1r = a[j] - a[j2]; x1i = -a[j + 1] + a[j2 + 1]; y0r = a[j + 2] + a[j2 + 2]; y0i = -a[j + 3] - a[j2 + 3]; y1r = a[j + 2] - a[j2 + 2]; y1i = -a[j + 3] + a[j2 + 3]; x2r = a[j1] + a[j3]; x2i = a[j1 + 1] + a[j3 + 1]; x3r = a[j1] - a[j3]; x3i = a[j1 + 1] - a[j3 + 1]; y2r = a[j1 + 2] + a[j3 + 2]; y2i = a[j1 + 3] + a[j3 + 3]; y3r = a[j1 + 2] - a[j3 + 2]; y3i = a[j1 + 3] - a[j3 + 3]; a[j] = x0r + x2r; a[j + 1] = x0i - x2i; a[j + 2] = y0r + y2r; a[j + 3] = y0i - y2i; a[j1] = x0r - x2r; a[j1 + 1] = x0i + x2i; a[j1 + 2] = y0r - y2r; a[j1 + 3] = y0i + y2i; x0r = x1r + x3i; x0i = x1i + x3r; a[j2] = wk1r * x0r - wk1i * x0i; a[j2 + 1] = wk1r * x0i + wk1i * x0r; x0r = y1r + y3i; x0i = y1i + y3r; a[j2 + 2] = wd1r * x0r - wd1i * x0i; a[j2 + 3] = wd1r * x0i + wd1i * x0r; x0r = x1r - x3i; x0i = x1i - x3r; a[j3] = wk3r * x0r + wk3i * x0i; a[j3 + 1] = wk3r * x0i - wk3i * x0r; x0r = y1r - y3i; x0i = y1i - y3r; a[j3 + 2] = wd3r * x0r + wd3i * x0i; a[j3 + 3] = wd3r * x0i - wd3i * x0r; j0 = m - j; j1 = j0 + m; j2 = j1 + m; j3 = j2 + m; x0r = a[j0] + a[j2]; x0i = -a[j0 + 1] - a[j2 + 1]; x1r = a[j0] - a[j2]; x1i = -a[j0 + 1] + a[j2 + 1]; y0r = a[j0 - 2] + a[j2 - 2]; y0i = -a[j0 - 1] - a[j2 - 1]; y1r = a[j0 - 2] - a[j2 - 2]; y1i = -a[j0 - 1] + a[j2 - 1]; x2r = a[j1] + a[j3]; x2i = a[j1 + 1] + a[j3 + 1]; x3r = a[j1] - a[j3]; x3i = a[j1 + 1] - a[j3 + 1]; y2r = a[j1 - 2] + a[j3 - 2]; y2i = a[j1 - 1] + a[j3 - 1]; y3r = a[j1 - 2] - a[j3 - 2]; y3i = a[j1 - 1] - a[j3 - 1]; a[j0] = x0r + x2r; a[j0 + 1] = x0i - x2i; a[j0 - 2] = y0r + y2r; a[j0 - 1] = y0i - y2i; a[j1] = x0r - x2r; a[j1 + 1] = x0i + x2i; a[j1 - 2] = y0r - y2r; a[j1 - 1] = y0i + y2i; x0r = x1r + x3i; x0i = x1i + x3r; a[j2] = wk1i * x0r - wk1r * x0i; a[j2 + 1] = wk1i * x0i + wk1r * x0r; x0r = y1r + y3i; x0i = y1i + y3r; a[j2 - 2] = wd1i * x0r - wd1r * x0i; a[j2 - 1] = wd1i * x0i + wd1r * x0r; x0r = x1r - x3i; x0i = x1i - x3r; a[j3] = wk3i * x0r + wk3r * x0i; a[j3 + 1] = wk3i * x0i - wk3r * x0r; x0r = y1r - y3i; x0i = y1i - y3r; a[j3 - 2] = wd3i * x0r + wd3r * x0i; a[j3 - 1] = wd3i * x0i - wd3r * x0r; } wk1r = csc1 * (wd1r + wn4r); wk1i = csc1 * (wd1i + wn4r); wk3r = csc3 * (wd3r - wn4r); wk3i = csc3 * (wd3i - wn4r); j0 = mh; j1 = j0 + m; j2 = j1 + m; j3 = j2 + m; x0r = a[j0 - 2] + a[j2 - 2]; x0i = -a[j0 - 1] - a[j2 - 1]; x1r = a[j0 - 2] - a[j2 - 2]; x1i = -a[j0 - 1] + a[j2 - 1]; x2r = a[j1 - 2] + a[j3 - 2]; x2i = a[j1 - 1] + a[j3 - 1]; x3r = a[j1 - 2] - a[j3 - 2]; x3i = a[j1 - 1] - a[j3 - 1]; a[j0 - 2] = x0r + x2r; a[j0 - 1] = x0i - x2i; a[j1 - 2] = x0r - x2r; a[j1 - 1] = x0i + x2i; x0r = x1r + x3i; x0i = x1i + x3r; a[j2 - 2] = wk1r * x0r - wk1i * x0i; a[j2 - 1] = wk1r * x0i + wk1i * x0r; x0r = x1r - x3i; x0i = x1i - x3r; a[j3 - 2] = wk3r * x0r + wk3i * x0i; a[j3 - 1] = wk3r * x0i - wk3i * x0r; x0r = a[j0] + a[j2]; x0i = -a[j0 + 1] - a[j2 + 1]; x1r = a[j0] - a[j2]; x1i = -a[j0 + 1] + a[j2 + 1]; x2r = a[j1] + a[j3]; x2i = a[j1 + 1] + a[j3 + 1]; x3r = a[j1] - a[j3]; x3i = a[j1 + 1] - a[j3 + 1]; a[j0] = x0r + x2r; a[j0 + 1] = x0i - x2i; a[j1] = x0r - x2r; a[j1 + 1] = x0i + x2i; x0r = x1r + x3i; x0i = x1i + x3r; a[j2] = wn4r * (x0r - x0i); a[j2 + 1] = wn4r * (x0i + x0r); x0r = x1r - x3i; x0i = x1i - x3r; a[j3] = -wn4r * (x0r + x0i); a[j3 + 1] = -wn4r * (x0i - x0r); x0r = a[j0 + 2] + a[j2 + 2]; x0i = -a[j0 + 3] - a[j2 + 3]; x1r = a[j0 + 2] - a[j2 + 2]; x1i = -a[j0 + 3] + a[j2 + 3]; x2r = a[j1 + 2] + a[j3 + 2]; x2i = a[j1 + 3] + a[j3 + 3]; x3r = a[j1 + 2] - a[j3 + 2]; x3i = a[j1 + 3] - a[j3 + 3]; a[j0 + 2] = x0r + x2r; a[j0 + 3] = x0i - x2i; a[j1 + 2] = x0r - x2r; a[j1 + 3] = x0i + x2i; x0r = x1r + x3i; x0i = x1i + x3r; a[j2 + 2] = wk1i * x0r - wk1r * x0i; a[j2 + 3] = wk1i * x0i + wk1r * x0r; x0r = x1r - x3i; x0i = x1i - x3r; a[j3 + 2] = wk3i * x0r + wk3r * x0i; a[j3 + 3] = wk3i * x0i - wk3r * x0r; } /** */ private void cftrec1(int n, double[] a, int aP, int nw, double[] w) { int m; m = n >> 2; cftmdl1(n, a, aP, w, nw - 2 * m); if (n > CDFT_RECURSIVE_N) { cftrec1(m, a, aP, nw, w); cftrec2(m, a, aP + m, nw, w); cftrec1(m, a, aP + 2 * m, nw, w); cftrec1(m, a, aP + 3 * m, nw, w); } else { cftexp1(n, a, aP, nw, w); } } /** */ private void cftrec2(int n, double[] a, int aP, int nw, double[] w) { int m; m = n >> 2; cftmdl2(n, a, aP, w, nw - n); if (n > CDFT_RECURSIVE_N) { cftrec1(m, a, aP, nw, w); cftrec2(m, a, aP + m, nw, w); cftrec1(m, a, aP + 2 * m, nw, w); cftrec2(m, a, aP + 3 * m, nw, w); } else { cftexp2(n, a, aP, nw, w); } } /** */ private void cftexp1(int n, double[] a, int aP, int nw, double[] w) { int j, k, l; l = n >> 2; while (l > 128) { for (k = l; k < n; k <<= 2) { for (j = k - l; j < n; j += 4 * k) { cftmdl1(l, a, aP + j, w, nw - (l >> 1)); cftmdl2(l, a, aP + k + j, w, nw - l); cftmdl1(l, a, aP + 2 * k + j, w, nw - (l >> 1)); } } cftmdl1(l, a, aP + n - l, w, nw - (l >> 1)); l >>= 2; } for (k = l; k < n; k <<= 2) { for (j = k - l; j < n; j += 4 * k) { cftmdl1(l, a, aP + j, w, nw - (l >> 1)); cftfx41(l, a, aP + j, nw, w); cftmdl2(l, a, aP + k + j, w, nw - l); cftfx42(l, a, aP + k + j, nw, w); cftmdl1(l, a, aP + 2 * k + j, w, nw - (l >> 1)); cftfx41(l, a, aP + 2 * k + j, nw, w); } } cftmdl1(l, a, aP + n - l, w, nw - (l >> 1)); cftfx41(l, a, aP + n - l, nw, w); } /** */ private void cftexp2(int n, double[] a, int aP, int nw, double[] w) { int j, k, l, m; m = n >> 1; l = n >> 2; while (l > 128) { for (k = l; k < m; k <<= 2) { for (j = k - l; j < m; j += 2 * k) { cftmdl1(l, a, aP + j, w, nw - (l >> 1)); cftmdl1(l, a, aP + m + j, w, nw - (l >> 1)); } for (j = 2 * k - l; j < m; j += 4 * k) { cftmdl2(l, a, aP + j, w, nw - l); cftmdl2(l, a, aP + m + j, w, nw - l); } } l >>= 2; } for (k = l; k < m; k <<= 2) { for (j = k - l; j < m; j += 2 * k) { cftmdl1(l, a, aP + j, w, nw - (l >> 1)); cftfx41(l, a, aP + j, nw, w); cftmdl1(l, a, aP + m + j, w, nw - (l >> 1)); cftfx41(l, a, aP + m + j, nw, w); } for (j = 2 * k - l; j < m; j += 4 * k) { cftmdl2(l, a, aP + j, w, nw - l); cftfx42(l, a, aP + j, nw, w); cftmdl2(l, a, aP + m + j, w, nw - l); cftfx42(l, a, aP + m + j, nw, w); } } } /** */ private final void cftmdl1(int n, double[] a, int aP, double[] w, int wP) { int j, j0, j1, j2, j3, k, m, mh; double wn4r, wk1r, wk1i, wk3r, wk3i; double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; mh = n >> 3; m = 2 * mh; j1 = m; j2 = j1 + m; j3 = j2 + m; x0r = a[aP + 0] + a[aP + j2]; x0i = a[aP + 1] + a[aP + j2 + 1]; x1r = a[aP + 0] - a[aP + j2]; x1i = a[aP + 1] - a[aP + j2 + 1]; x2r = a[aP + j1] + a[aP + j3]; x2i = a[aP + j1 + 1] + a[aP + j3 + 1]; x3r = a[aP + j1] - a[aP + j3]; x3i = a[aP + j1 + 1] - a[aP + j3 + 1]; a[aP + 0] = x0r + x2r; a[aP + 1] = x0i + x2i; a[aP + j1] = x0r - x2r; a[aP + j1 + 1] = x0i - x2i; a[aP + j2] = x1r - x3i; a[aP + j2 + 1] = x1i + x3r; a[aP + j3] = x1r + x3i; a[aP + j3 + 1] = x1i - x3r; wn4r = w[wP + 1]; k = 0; for (j = 2; j < mh; j += 2) { k += 4; wk1r = w[wP + k]; wk1i = w[wP + k + 1]; wk3r = w[wP + k + 2]; wk3i = -w[wP + k + 3]; j1 = j + m; j2 = j1 + m; j3 = j2 + m; x0r = a[aP + j] + a[aP + j2]; x0i = a[aP + j + 1] + a[aP + j2 + 1]; x1r = a[aP + j] - a[aP + j2]; x1i = a[aP + j + 1] - a[aP + j2 + 1]; x2r = a[aP + j1] + a[aP + j3]; x2i = a[aP + j1 + 1] + a[aP + j3 + 1]; x3r = a[aP + j1] - a[aP + j3]; x3i = a[aP + j1 + 1] - a[aP + j3 + 1]; a[aP + j] = x0r + x2r; a[aP + j + 1] = x0i + x2i; a[aP + j1] = x0r - x2r; a[aP + j1 + 1] = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; a[aP + j2] = wk1r * x0r - wk1i * x0i; a[aP + j2 + 1] = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[aP + j3] = wk3r * x0r + wk3i * x0i; a[aP + j3 + 1] = wk3r * x0i - wk3i * x0r; j0 = m - j; j1 = j0 + m; j2 = j1 + m; j3 = j2 + m; x0r = a[aP + j0] + a[aP + j2]; x0i = a[aP + j0 + 1] + a[aP + j2 + 1]; x1r = a[aP + j0] - a[aP + j2]; x1i = a[aP + j0 + 1] - a[aP + j2 + 1]; x2r = a[aP + j1] + a[aP + j3]; x2i = a[aP + j1 + 1] + a[aP + j3 + 1]; x3r = a[aP + j1] - a[aP + j3]; x3i = a[aP + j1 + 1] - a[aP + j3 + 1]; a[aP + j0] = x0r + x2r; a[aP + j0 + 1] = x0i + x2i; a[aP + j1] = x0r - x2r; a[aP + j1 + 1] = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; a[aP + j2] = wk1i * x0r - wk1r * x0i; a[aP + j2 + 1] = wk1i * x0i + wk1r * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[aP + j3] = wk3i * x0r + wk3r * x0i; a[aP + j3 + 1] = wk3i * x0i - wk3r * x0r; } j0 = mh; j1 = j0 + m; j2 = j1 + m; j3 = j2 + m; x0r = a[aP + j0] + a[aP + j2]; x0i = a[aP + j0 + 1] + a[aP + j2 + 1]; x1r = a[aP + j0] - a[aP + j2]; x1i = a[aP + j0 + 1] - a[aP + j2 + 1]; x2r = a[aP + j1] + a[aP + j3]; x2i = a[aP + j1 + 1] + a[aP + j3 + 1]; x3r = a[aP + j1] - a[aP + j3]; x3i = a[aP + j1 + 1] - a[aP + j3 + 1]; a[aP + j0] = x0r + x2r; a[aP + j0 + 1] = x0i + x2i; a[aP + j1] = x0r - x2r; a[aP + j1 + 1] = x0i - x2i; x0r = x1r - x3i; x0i = x1i + x3r; a[aP + j2] = wn4r * (x0r - x0i); a[aP + j2 + 1] = wn4r * (x0i + x0r); x0r = x1r + x3i; x0i = x1i - x3r; a[aP + j3] = -wn4r * (x0r + x0i); a[aP + j3 + 1] = -wn4r * (x0i - x0r); } /** */ private final void cftmdl2(int n, double[] a, int aP, double[] w, int wP) { int j, j0, j1, j2, j3, k, kr, m, mh; double wn4r, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i; double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i; mh = n >> 3; m = 2 * mh; wn4r = w[wP + 1]; j1 = m; j2 = j1 + m; j3 = j2 + m; x0r = a[aP + 0] - a[aP + j2 + 1]; x0i = a[aP + 1] + a[aP + j2]; x1r = a[aP + 0] + a[aP + j2 + 1]; x1i = a[aP + 1] - a[aP + j2]; x2r = a[aP + j1] - a[aP + j3 + 1]; x2i = a[aP + j1 + 1] + a[aP + j3]; x3r = a[aP + j1] + a[aP + j3 + 1]; x3i = a[aP + j1 + 1] - a[aP + j3]; y0r = wn4r * (x2r - x2i); y0i = wn4r * (x2i + x2r); a[aP + 0] = x0r + y0r; a[aP + 1] = x0i + y0i; a[aP + j1] = x0r - y0r; a[aP + j1 + 1] = x0i - y0i; y0r = wn4r * (x3r - x3i); y0i = wn4r * (x3i + x3r); a[aP + j2] = x1r - y0i; a[aP + j2 + 1] = x1i + y0r; a[aP + j3] = x1r + y0i; a[aP + j3 + 1] = x1i - y0r; k = 0; kr = 2 * m; for (j = 2; j < mh; j += 2) { k += 4; wk1r = w[wP + k]; wk1i = w[wP + k + 1]; wk3r = w[wP + k + 2]; wk3i = -w[wP + k + 3]; kr -= 4; wd1i = w[wP + kr]; wd1r = w[wP + kr + 1]; wd3i = w[wP + kr + 2]; wd3r = -w[wP + kr + 3]; j1 = j + m; j2 = j1 + m; j3 = j2 + m; x0r = a[aP + j] - a[aP + j2 + 1]; x0i = a[aP + j + 1] + a[aP + j2]; x1r = a[aP + j] + a[aP + j2 + 1]; x1i = a[aP + j + 1] - a[aP + j2]; x2r = a[aP + j1] - a[aP + j3 + 1]; x2i = a[aP + j1 + 1] + a[aP + j3]; x3r = a[aP + j1] + a[aP + j3 + 1]; x3i = a[aP + j1 + 1] - a[aP + j3]; y0r = wk1r * x0r - wk1i * x0i; y0i = wk1r * x0i + wk1i * x0r; y2r = wd1r * x2r - wd1i * x2i; y2i = wd1r * x2i + wd1i * x2r; a[aP + j] = y0r + y2r; a[aP + j + 1] = y0i + y2i; a[aP + j1] = y0r - y2r; a[aP + j1 + 1] = y0i - y2i; y0r = wk3r * x1r + wk3i * x1i; y0i = wk3r * x1i - wk3i * x1r; y2r = wd3r * x3r + wd3i * x3i; y2i = wd3r * x3i - wd3i * x3r; a[aP + j2] = y0r + y2r; a[aP + j2 + 1] = y0i + y2i; a[aP + j3] = y0r - y2r; a[aP + j3 + 1] = y0i - y2i; j0 = m - j; j1 = j0 + m; j2 = j1 + m; j3 = j2 + m; x0r = a[aP + j0] - a[aP + j2 + 1]; x0i = a[aP + j0 + 1] + a[aP + j2]; x1r = a[aP + j0] + a[aP + j2 + 1]; x1i = a[aP + j0 + 1] - a[aP + j2]; x2r = a[aP + j1] - a[aP + j3 + 1]; x2i = a[aP + j1 + 1] + a[aP + j3]; x3r = a[aP + j1] + a[aP + j3 + 1]; x3i = a[aP + j1 + 1] - a[aP + j3]; y0r = wd1i * x0r - wd1r * x0i; y0i = wd1i * x0i + wd1r * x0r; y2r = wk1i * x2r - wk1r * x2i; y2i = wk1i * x2i + wk1r * x2r; a[aP + j0] = y0r + y2r; a[aP + j0 + 1] = y0i + y2i; a[aP + j1] = y0r - y2r; a[aP + j1 + 1] = y0i - y2i; y0r = wd3i * x1r + wd3r * x1i; y0i = wd3i * x1i - wd3r * x1r; y2r = wk3i * x3r + wk3r * x3i; y2i = wk3i * x3i - wk3r * x3r; a[aP + j2] = y0r + y2r; a[aP + j2 + 1] = y0i + y2i; a[aP + j3] = y0r - y2r; a[aP + j3 + 1] = y0i - y2i; } wk1r = w[wP + m]; wk1i = w[wP + m + 1]; j0 = mh; j1 = j0 + m; j2 = j1 + m; j3 = j2 + m; x0r = a[aP + j0] - a[aP + j2 + 1]; x0i = a[aP + j0 + 1] + a[aP + j2]; x1r = a[aP + j0] + a[aP + j2 + 1]; x1i = a[aP + j0 + 1] - a[aP + j2]; x2r = a[aP + j1] - a[aP + j3 + 1]; x2i = a[aP + j1 + 1] + a[aP + j3]; x3r = a[aP + j1] + a[aP + j3 + 1]; x3i = a[aP + j1 + 1] - a[aP + j3]; y0r = wk1r * x0r - wk1i * x0i; y0i = wk1r * x0i + wk1i * x0r; y2r = wk1i * x2r - wk1r * x2i; y2i = wk1i * x2i + wk1r * x2r; a[aP + j0] = y0r + y2r; a[aP + j0 + 1] = y0i + y2i; a[aP + j1] = y0r - y2r; a[aP + j1 + 1] = y0i - y2i; y0r = wk1i * x1r - wk1r * x1i; y0i = wk1i * x1i + wk1r * x1r; y2r = wk1r * x3r - wk1i * x3i; y2i = wk1r * x3i + wk1i * x3r; a[aP + j2] = y0r - y2r; a[aP + j2 + 1] = y0i - y2i; a[aP + j3] = y0r + y2r; a[aP + j3 + 1] = y0i + y2i; } /** */ private void cftfx41(int n, double[] a, int aP, int nw, double[] w) { if (n == 128) { cftf161(a, aP, w, nw - 8); cftf162(a, aP + 32, w, nw - 32); cftf161(a, aP + 64, w, nw - 8); cftf161(a, aP + 96, w, nw - 8); } else { cftf081(a, aP, w, nw - 16); cftf082(a, aP + 16, w, nw - 16); cftf081(a, aP + 32, w, nw - 16); cftf081(a, aP + 48, w, nw - 16); } } /** */ private void cftfx42(int n, double[] a, int aP, int nw, double[] w) { if (n == 128) { cftf161(a, aP, w, nw - 8); cftf162(a, aP + 32, w, nw - 32); cftf161(a, aP + 64, w, nw - 8); cftf162(a, aP + 96, w, nw - 32); } else { cftf081(a, aP, w, nw - 16); cftf082(a, aP + 16, w, nw - 16); cftf081(a, aP + 32, w, nw - 16); cftf082(a, aP + 48, w, nw - 16); } } /** */ private void cftf161(double[] a, int aP, double[] w, int wP) { 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[wP + 1]; wk1i = wn4r * w[wP + 2]; wk1r = wk1i + w[wP + 2]; x0r = a[aP + 0] + a[aP + 16]; x0i = a[aP + 1] + a[aP + 17]; x1r = a[aP + 0] - a[aP + 16]; x1i = a[aP + 1] - a[aP + 17]; x2r = a[aP + 8] + a[aP + 24]; x2i = a[aP + 9] + a[aP + 25]; x3r = a[aP + 8] - a[aP + 24]; x3i = a[aP + 9] - a[aP + 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[aP + 2] + a[aP + 18]; x0i = a[aP + 3] + a[aP + 19]; x1r = a[aP + 2] - a[aP + 18]; x1i = a[aP + 3] - a[aP + 19]; x2r = a[aP + 10] + a[aP + 26]; x2i = a[aP + 11] + a[aP + 27]; x3r = a[aP + 10] - a[aP + 26]; x3i = a[aP + 11] - a[aP + 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[aP + 4] + a[aP + 20]; x0i = a[aP + 5] + a[aP + 21]; x1r = a[aP + 4] - a[aP + 20]; x1i = a[aP + 5] - a[aP + 21]; x2r = a[aP + 12] + a[aP + 28]; x2i = a[aP + 13] + a[aP + 29]; x3r = a[aP + 12] - a[aP + 28]; x3i = a[aP + 13] - a[aP + 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[aP + 6] + a[aP + 22]; x0i = a[aP + 7] + a[aP + 23]; x1r = a[aP + 6] - a[aP + 22]; x1i = a[aP + 7] - a[aP + 23]; x2r = a[aP + 14] + a[aP + 30]; x2i = a[aP + 15] + a[aP + 31]; x3r = a[aP + 14] - a[aP + 30]; x3i = a[aP + 15] - a[aP + 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[aP + 24] = x0r + x2r; a[aP + 25] = x0i + x2i; a[aP + 26] = x0r - x2r; a[aP + 27] = x0i - x2i; a[aP + 28] = x1r - x3i; a[aP + 29] = x1i + x3r; a[aP + 30] = x1r + x3i; a[aP + 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[aP + 16] = x0r + x2r; a[aP + 17] = x0i + x2i; a[aP + 18] = x0r - x2r; a[aP + 19] = x0i - x2i; a[aP + 20] = x1r - x3i; a[aP + 21] = x1i + x3r; a[aP + 22] = x1r + x3i; a[aP + 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[aP + 8] = x0r + x2r; a[aP + 9] = x0i + x2i; a[aP + 10] = x0r - x2r; a[aP + 11] = x0i - x2i; a[aP + 12] = x1r - x3i; a[aP + 13] = x1i + x3r; a[aP + 14] = x1r + x3i; a[aP + 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[aP + 0] = x0r + x2r; a[aP + 1] = x0i + x2i; a[aP + 2] = x0r - x2r; a[aP + 3] = x0i - x2i; a[aP + 4] = x1r - x3i; a[aP + 5] = x1i + x3r; a[aP + 6] = x1r + x3i; a[aP + 7] = x1i - x3r; } /** */ private void cftf162(double[] a, int aP, double[] w, int wP) { 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[wP + 1]; wk1r = w[wP + 4]; wk1i = w[wP + 5]; wk3r = w[wP + 6]; wk3i = w[wP + 7]; wk2r = w[wP + 8]; wk2i = w[wP + 9]; x1r = a[aP + 0] - a[aP + 17]; x1i = a[aP + 1] + a[aP + 16]; x0r = a[aP + 8] - a[aP + 25]; x0i = a[aP + 9] + a[aP + 24]; x2r = wn4r * (x0r - x0i); x2i = wn4r * (x0i + x0r); y0r = x1r + x2r; y0i = x1i + x2i; y4r = x1r - x2r; y4i = x1i - x2i; x1r = a[aP + 0] + a[aP + 17]; x1i = a[aP + 1] - a[aP + 16]; x0r = a[aP + 8] + a[aP + 25]; x0i = a[aP + 9] - a[aP + 24]; x2r = wn4r * (x0r - x0i); x2i = wn4r * (x0i + x0r); y8r = x1r - x2i; y8i = x1i + x2r; y12r = x1r + x2i; y12i = x1i - x2r; x0r = a[aP + 2] - a[aP + 19]; x0i = a[aP + 3] + a[aP + 18]; x1r = wk1r * x0r - wk1i * x0i; x1i = wk1r * x0i + wk1i * x0r; x0r = a[aP + 10] - a[aP + 27]; x0i = a[aP + 11] + a[aP + 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[aP + 2] + a[aP + 19]; x0i = a[aP + 3] - a[aP + 18]; x1r = wk3r * x0r - wk3i * x0i; x1i = wk3r * x0i + wk3i * x0r; x0r = a[aP + 10] + a[aP + 27]; x0i = a[aP + 11] - a[aP + 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[aP + 4] - a[aP + 21]; x0i = a[aP + 5] + a[aP + 20]; x1r = wk2r * x0r - wk2i * x0i; x1i = wk2r * x0i + wk2i * x0r; x0r = a[aP + 12] - a[aP + 29]; x0i = a[aP + 13] + a[aP + 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[aP + 4] + a[aP + 21]; x0i = a[aP + 5] - a[aP + 20]; x1r = wk2i * x0r - wk2r * x0i; x1i = wk2i * x0i + wk2r * x0r; x0r = a[aP + 12] + a[aP + 29]; x0i = a[aP + 13] - a[aP + 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[aP + 6] - a[aP + 23]; x0i = a[aP + 7] + a[aP + 22]; x1r = wk3r * x0r - wk3i * x0i; x1i = wk3r * x0i + wk3i * x0r; x0r = a[aP + 14] - a[aP + 31]; x0i = a[aP + 15] + a[aP + 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[aP + 6] + a[aP + 23]; x0i = a[aP + 7] - a[aP + 22]; x1r = wk1i * x0r + wk1r * x0i; x1i = wk1i * x0i - wk1r * x0r; x0r = a[aP + 14] + a[aP + 31]; x0i = a[aP + 15] - a[aP + 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[aP + 0] = x1r + x2r; a[aP + 1] = x1i + x2i; a[aP + 2] = x1r - x2r; a[aP + 3] = x1i - x2i; x1r = y0r - y2r; x1i = y0i - y2i; x2r = y1r - y3r; x2i = y1i - y3i; a[aP + 4] = x1r - x2i; a[aP + 5] = x1i + x2r; a[aP + 6] = x1r + x2i; a[aP + 7] = x1i - x2r; x1r = y4r - y6i; x1i = y4i + y6r; x0r = y5r - y7i; x0i = y5i + y7r; x2r = wn4r * (x0r - x0i); x2i = wn4r * (x0i + x0r); a[aP + 8] = x1r + x2r; a[aP + 9] = x1i + x2i; a[aP + 10] = x1r - x2r; a[aP + 11] = x1i - x2i; x1r = y4r + y6i; x1i = y4i - y6r; x0r = y5r + y7i; x0i = y5i - y7r; x2r = wn4r * (x0r - x0i); x2i = wn4r * (x0i + x0r); a[aP + 12] = x1r - x2i; a[aP + 13] = x1i + x2r; a[aP + 14] = x1r + x2i; a[aP + 15] = x1i - x2r; x1r = y8r + y10r; x1i = y8i + y10i; x2r = y9r - y11r; x2i = y9i - y11i; a[aP + 16] = x1r + x2r; a[aP + 17] = x1i + x2i; a[aP + 18] = x1r - x2r; a[aP + 19] = x1i - x2i; x1r = y8r - y10r; x1i = y8i - y10i; x2r = y9r + y11r; x2i = y9i + y11i; a[aP + 20] = x1r - x2i; a[aP + 21] = x1i + x2r; a[aP + 22] = x1r + x2i; a[aP + 23] = x1i - x2r; x1r = y12r - y14i; x1i = y12i + y14r; x0r = y13r + y15i; x0i = y13i - y15r; x2r = wn4r * (x0r - x0i); x2i = wn4r * (x0i + x0r); a[aP + 24] = x1r + x2r; a[aP + 25] = x1i + x2i; a[aP + 26] = x1r - x2r; a[aP + 27] = x1i - x2i; x1r = y12r + y14i; x1i = y12i - y14r; x0r = y13r - y15i; x0i = y13i + y15r; x2r = wn4r * (x0r - x0i); x2i = wn4r * (x0i + x0r); a[aP + 28] = x1r - x2i; a[aP + 29] = x1i + x2r; a[aP + 30] = x1r + x2i; a[aP + 31] = x1i - x2r; } /** */ private void cftf081(double[] a, int aP, double[] w, int wP) { 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[wP + 1]; x0r = a[aP + 0] + a[aP + 8]; x0i = a[aP + 1] + a[aP + 9]; x1r = a[aP + 0] - a[aP + 8]; x1i = a[aP + 1] - a[aP + 9]; x2r = a[aP + 4] + a[aP + 12]; x2i = a[aP + 5] + a[aP + 13]; x3r = a[aP + 4] - a[aP + 12]; x3i = a[aP + 5] - a[aP + 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[aP + 2] + a[aP + 10]; x0i = a[aP + 3] + a[aP + 11]; x1r = a[aP + 2] - a[aP + 10]; x1i = a[aP + 3] - a[aP + 11]; x2r = a[aP + 6] + a[aP + 14]; x2i = a[aP + 7] + a[aP + 15]; x3r = a[aP + 6] - a[aP + 14]; x3i = a[aP + 7] - a[aP + 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[aP + 8] = y1r + y5r; a[aP + 9] = y1i + y5i; a[aP + 10] = y1r - y5r; a[aP + 11] = y1i - y5i; a[aP + 12] = y3r - y7i; a[aP + 13] = y3i + y7r; a[aP + 14] = y3r + y7i; a[aP + 15] = y3i - y7r; a[aP + 0] = y0r + y4r; a[aP + 1] = y0i + y4i; a[aP + 2] = y0r - y4r; a[aP + 3] = y0i - y4i; a[aP + 4] = y2r - y6i; a[aP + 5] = y2i + y6r; a[aP + 6] = y2r + y6i; a[aP + 7] = y2i - y6r; } /** */ private void cftf082(double[] a, int aP, double[] w, int wP) { 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[wP + 1]; wk1r = w[wP + 4]; wk1i = w[wP + 5]; y0r = a[aP + 0] - a[aP + 9]; y0i = a[aP + 1] + a[aP + 8]; y1r = a[aP + 0] + a[aP + 9]; y1i = a[aP + 1] - a[aP + 8]; x0r = a[aP + 4] - a[aP + 13]; x0i = a[aP + 5] + a[aP + 12]; y2r = wn4r * (x0r - x0i); y2i = wn4r * (x0i + x0r); x0r = a[aP + 4] + a[aP + 13]; x0i = a[aP + 5] - a[aP + 12]; y3r = wn4r * (x0r - x0i); y3i = wn4r * (x0i + x0r); x0r = a[aP + 2] - a[aP + 11]; x0i = a[aP + 3] + a[aP + 10]; y4r = wk1r * x0r - wk1i * x0i; y4i = wk1r * x0i + wk1i * x0r; x0r = a[aP + 2] + a[aP + 11]; x0i = a[aP + 3] - a[aP + 10]; y5r = wk1i * x0r - wk1r * x0i; y5i = wk1i * x0i + wk1r * x0r; x0r = a[aP + 6] - a[aP + 15]; x0i = a[aP + 7] + a[aP + 14]; y6r = wk1i * x0r - wk1r * x0i; y6i = wk1i * x0i + wk1r * x0r; x0r = a[aP + 6] + a[aP + 15]; x0i = a[aP + 7] - a[aP + 14]; y7r = wk1r * x0r - wk1i * x0i; y7i = wk1r * x0i + wk1i * x0r; x0r = y0r + y2r; x0i = y0i + y2i; x1r = y4r + y6r; x1i = y4i + y6i; a[aP + 0] = x0r + x1r; a[aP + 1] = x0i + x1i; a[aP + 2] = x0r - x1r; a[aP + 3] = x0i - x1i; x0r = y0r - y2r; x0i = y0i - y2i; x1r = y4r - y6r; x1i = y4i - y6i; a[aP + 4] = x0r - x1i; a[aP + 5] = x0i + x1r; a[aP + 6] = x0r + x1i; a[aP + 7] = x0i - x1r; x0r = y1r - y3i; x0i = y1i + y3r; x1r = y5r - y7r; x1i = y5i - y7i; a[aP + 8] = x0r + x1r; a[aP + 9] = x0i + x1i; a[aP + 10] = x0r - x1r; a[aP + 11] = x0i - x1i; x0r = y1r + y3i; x0i = y1i - y3r; x1r = y5r + y7r; x1i = y5i + y7i; a[aP + 12] = x0r - x1i; a[aP + 13] = x0i + x1r; a[aP + 14] = x0r + x1i; a[aP + 15] = x0i - x1r; } /** * 3rd * when n = 8. * @see #cftfsub(int, double[], int[], int, int, double[]) */ private void cftf040(double[] a) { double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; x0r = a[0] + a[4]; x0i = a[1] + a[5]; x1r = a[0] - a[4]; x1i = a[1] - a[5]; x2r = a[2] + a[6]; x2i = a[3] + a[7]; x3r = a[2] - a[6]; x3i = a[3] - a[7]; a[0] = x0r + x2r; a[1] = x0i + x2i; a[4] = x0r - x2r; a[5] = x0i - x2i; a[2] = x1r - x3i; a[3] = x1i + x3r; a[6] = x1r + x3i; a[7] = x1i - x3r; } /** * 3rd * when n = 8. * @see #cftbsub(int, double[], int[], int, int, double[]) */ private void cftb040(double[] a) { double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; x0r = a[0] + a[4]; x0i = a[1] + a[5]; x1r = a[0] - a[4]; x1i = a[1] - a[5]; x2r = a[2] + a[6]; x2i = a[3] + a[7]; x3r = a[2] - a[6]; x3i = a[3] - a[7]; a[0] = x0r + x2r; a[1] = x0i + x2i; a[4] = x0r - x2r; a[5] = x0i - x2i; a[2] = x1r + x3i; a[3] = x1i - x3r; a[6] = x1r - x3i; a[7] = x1i + x3r; } /** * 3rd * when n = 4. * @see #cftbsub(int, double[], int[], int, int, double[]) * @see #cftfsub(int, double[], int[], int, int, double[]) */ private void cftx020(double[] a) { double x0r, x0i; x0r = a[0] - a[2]; x0i = a[1] - a[3]; a[0] += a[2]; a[1] += a[3]; a[2] = x0r; a[3] = x0i; } /** * 2nd * @see #rdft(int, int, double[], int[], double[]) * @see #ddct(int, int, double[], int[], double[]) * @see #ddst(int, int, double[], int[], double[]) * @see #dfst(int, double[], double[], int[], double[]) * @see #dfct(int, double[], double[], int[], double[]) */ private void rftfsub(int n, double[] a, int nc, double[] c, int cP) { int j, k, kk, ks, m; double wkr, wki, xr, xi, yr, yi; m = n >> 1; ks = 2 * nc / m; kk = 0; for (j = 2; j < m; j += 2) { k = n - j; kk += ks; wkr = 0.5 - c[cP + nc - kk]; wki = c[cP + kk]; xr = a[j] - a[k]; xi = a[j + 1] + a[k + 1]; yr = wkr * xr - wki * xi; yi = wkr * xi + wki * xr; a[j] -= yr; a[j + 1] -= yi; a[k] += yr; a[k + 1] -= yi; } } /** * 2nd * @see #rdft(int, int, double[], int[], double[]) * @see #ddct(int, int, double[], int[], double[]) * @see #ddst(int, int, double[], int[], double[]) */ private void rftbsub(int n, double[] a, int nc, double[] c, int cP) { int j, k, kk, ks, m; double wkr, wki, xr, xi, yr, yi; m = n >> 1; ks = 2 * nc / m; kk = 0; for (j = 2; j < m; j += 2) { k = n - j; kk += ks; wkr = 0.5 - c[cP + nc - kk]; wki = c[cP + kk]; xr = a[j] - a[k]; xi = a[j + 1] + a[k + 1]; yr = wkr * xr + wki * xi; yi = wkr * xi - wki * xr; a[j] -= yr; a[j + 1] -= yi; a[k] += yr; a[k + 1] -= yi; } } /** * 2nd * @see #ddct(int, int, double[], int[], double[]) * @see #dfct(int, double[], double[], int[], double[]) */ private void dctsub(int n, double[] a, int nc, double[] c, int cP) { int j, k, kk, ks, m; double wkr, wki, xr; m = n >> 1; ks = nc / n; kk = 0; for (j = 1; j < m; j++) { k = n - j; kk += ks; wkr = c[cP + kk] - c[cP + nc - kk]; wki = c[cP + kk] + c[cP + nc - kk]; xr = wki * a[j] - wkr * a[k]; a[j] = wkr * a[j] + wki * a[k]; a[k] = xr; } a[m] *= c[cP + 0]; } /** * 2nd * @see #ddst(int, int, double[], int[], double[]) * @see #dfst(int, double[], double[], int[], double[]) */ private void dstsub(int n, double[] a, int nc, double[] c, int cP) { int j, k, kk, ks, m; double wkr, wki, xr; m = n >> 1; ks = nc / n; kk = 0; for (j = 1; j < m; j++) { k = n - j; kk += ks; wkr = c[cP + kk] - c[cP + nc - kk]; wki = c[cP + kk] + c[cP + nc - kk]; xr = wki * a[k] - wkr * a[j]; a[k] = wkr * a[k] + wki * a[j]; a[j] = xr; } a[m] *= c[cP + 0]; } } /* */