大浦版FFTをJavaに移植する
今回は、高速な処理で有名な大浦版FFTをJavaに移植してみました。
大浦版FFTとは、Cで書かれた高速フーリエ変換(FFT)で、1次元・2次元・3次元のバージョンがあります。
FFT Package 1-dim / 2-dim
ググってみると、Java移植の話題はちょくちょくあるのですが、ソースコードが載っているものが少ないので、書いてみました。
正直言いますと、こちらのソースをかなり参考にさせていただいております。
要するに、配列をずらしたりする処理を書き換えればいいのです。
大浦版FFTのJava移植
移植での変更点
Javaではポインタが使えないため、配列をそのまま引数として渡さなければなりません。
また、配列をずらす、という動作を行うための処理部分を変更しなければなりません。
Cでは例えば、配列 a [ n ] があったなら、a+2で配列aを2つずらすことができ、これをそのまま関数へ渡すことができます。しかし、Javaにはそのような機能はなく、配列を2つずらすなら、a [ n + 2 ]と書かなければなりません。
この二つの違いを直すと、正常に動くようになります。
今回移植したのは、FFT4gだけです。手抜きですいません。
間違ってたらごめんなさい。勘弁してください。
ということで、ソースコード全体はこちら。
FFT4g.java
package …; import static java.lang.Math.atan; import static java.lang.Math.cos; import static java.lang.Math.sin; public class FFT4g { private int[] ip; private double[] w; private int n; private double t[]; FFT4g(int n) { this.n = n; ip = new int[2+(int)Math.sqrt((double)n/2.0)+1]; w = new double[n*5/4]; t = new double[n/2]; ip[0] = 0; } public void cdft(int isgn, double[] a) { if (n > (ip[0] << 2)) { makewt(n >> 2); } if (n > 4) { if (isgn >= 0) { bitrv2(n, a); cftfsub(n, a); } else { bitrv2conj(n, a); cftbsub(n, a); } } else if (n == 4) { cftfsub(n, a); } } public void rdft(int isgn, double[] a) { int nw, nc; double xi; nw = ip[0]; if (n > (nw << 2)) { nw = n >> 2; makewt(nw); } nc = ip[1]; if (n > (nc << 2)) { nc = n >> 2; makect(nc,w, nw); } if (isgn >= 0) { if (n > 4) { bitrv2(n, a); cftfsub(n, a); rftfsub(n, a, nc, w, nw); } else if (n == 4) { cftfsub(n, a); } xi = a[0] - a[1]; a[0] += a[1]; a[1] = xi; } else { a[1] = 0.5 * (a[0] - a[1]); a[0] -= a[1]; if (n > 4) { rftbsub(n, a, nc, w, nw); bitrv2(n, a); cftbsub(n, a); } else if (n == 4) { cftfsub(n, a); } } } public void ddct(int isgn, double[] a){ int j, nw, nc; double xr; nw = ip[0]; if (n > (nw << 2)) { nw = n >> 2; makewt(nw); } nc = ip[1]; if (n > nc) { nc = n; makect(nc, w, nw); } if (isgn < 0) { xr = a[n - 1]; for (j = n - 2; j >= 2; j -= 2) { a[j + 1] = a[j] - a[j - 1]; a[j] += a[j - 1]; } a[1] = a[0] - xr; a[0] += xr; if (n > 4) { rftbsub(n, a, nc, w, nw); bitrv2(n, a); cftbsub(n, a); } else if (n == 4) { cftfsub(n, a); } } dctsub(n, a, nc, w, nw); if (isgn >= 0) { if (n > 4) { bitrv2(n, a); cftfsub(n, a); rftfsub(n, a, nc, w, nw); } else if (n == 4) { cftfsub(n, a); } xr = a[0] - a[1]; a[0] += a[1]; for (j = 2; j < n; j += 2) { a[j - 1] = a[j] - a[j + 1]; a[j] += a[j + 1]; } a[n - 1] = xr; } } public void ddst(int isgn, double[] a) { int j, nw, nc; double xr; nw = ip[0]; if (n > (nw << 2)) { nw = n >> 2; makewt(nw); } nc = ip[1]; if (n > nc) { nc = n; makect(nc, w, nw); } if (isgn < 0) { xr = a[n - 1]; for (j = n - 2; j >= 2; j -= 2) { a[j + 1] = -a[j] - a[j - 1]; a[j] -= a[j - 1]; } a[1] = a[0] + xr; a[0] -= xr; if (n > 4) { rftbsub(n, a, nc, w, nw); bitrv2(n, a); cftbsub(n, a); } else if (n == 4) { cftfsub(n, a); } } dstsub(n, a, nc, w, nw); if (isgn >= 0) { if (n > 4) { bitrv2(n, a); cftfsub(n, a); rftfsub(n, a, nc, w, nw); } else if (n == 4) { cftfsub(n, a); } xr = a[0] - a[1]; a[0] += a[1]; for (j = 2; j < n; j += 2) { a[j - 1] = -a[j] - a[j + 1]; a[j] -= a[j + 1]; } a[n - 1] = -xr; } } public void dfct(double[] a) { 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); } nc = ip[1]; if (n > (nc << 1)) { nc = n >> 1; makect(nc, w, nw); } m = n >> 1; yi = a[m]; xi = a[0] + a[n]; a[0] -= a[n]; t[0] = xi - yi; t[m] = xi + yi; if (n > 2) { mh = m >> 1; for (j = 1; j < mh; j++) { k = m - j; xr = a[j] - a[n - j]; xi = a[j] + a[n - j]; yr = a[k] - a[n - k]; yi = a[k] + a[n - k]; a[j] = xr; a[k] = yr; t[j] = xi - yi; t[k] = xi + yi; } t[mh] = a[mh] + a[n - mh]; a[mh] -= a[n - mh]; dctsub(m, a, nc, w, nw); if (m > 4) { bitrv2(m, a); cftfsub(m, a); rftfsub(m, a, nc, w, nw); } else if (m == 4) { cftfsub(m, a); } a[n - 1] = a[0] - a[1]; a[1] = a[0] + a[1]; for (j = m - 2; j >= 2; j -= 2) { a[2 * j + 1] = a[j] + a[j + 1]; a[2 * j - 1] = a[j] - a[j + 1]; } l = 2; m = mh; while (m >= 2) { dctsub(m, t, nc, w, nw); if (m > 4) { bitrv2(m, t); cftfsub(m, t); rftfsub(m, t, nc, w, nw); } else if (m == 4) { cftfsub(m, t); } 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]; } } public void dfst(double[] a) { 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); } nc = ip[1]; if (n > (nc << 1)) { nc = n >> 1; makect(nc, w, nw); } if (n > 2) { m = n >> 1; mh = m >> 1; for (j = 1; j < mh; j++) { k = m - j; xr = a[j] + a[n - j]; xi = a[j] - a[n - j]; yr = a[k] + a[n - k]; yi = a[k] - a[n - k]; a[j] = xr; a[k] = yr; t[j] = xi + yi; t[k] = xi - yi; } t[0] = a[mh] - a[n - mh]; a[mh] += a[n - mh]; a[0] = a[m]; dstsub(m, a, nc, w, nw); if (m > 4) { bitrv2(m, a); cftfsub(m, a); rftfsub(m, a, nc, w, nw); } else if (m == 4) { cftfsub(m, a); } a[n - 1] = a[1] - a[0]; a[1] = a[0] + a[1]; for (j = m - 2; j >= 2; j -= 2) { a[2 * j + 1] = a[j] - a[j + 1]; a[2 * j - 1] = -a[j] - a[j + 1]; } l = 2; m = mh; while (m >= 2) { dstsub(m, t, nc, w, nw); if (m > 4) { bitrv2(m, t); cftfsub(m, t); rftfsub(m, t, nc, w, nw); } else if (m == 4) { cftfsub(m, t); } 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 j, nwh; double delta, x, y; ip[0] = nw; ip[1] = 1; if (nw > 2) { nwh = nw >> 1; delta = atan(1.0) / nwh; w[0] = 1; w[1] = 0; w[nwh] = cos(delta * nwh); w[nwh + 1] = w[nwh]; if (nwh > 2) { for (j = 2; j < nwh; j += 2) { x = cos(delta * j); y = sin(delta * j); w[j] = x; w[j + 1] = y; w[nw - j] = y; w[nw - j + 1] = x; } bitrv2(nw, w); } } } private void makect(int nc, double[] c, int nw) { int j, nch; double delta; ip[1] = nc; if (nc > 1) { nch = nc >> 1; delta = atan(1.0) / nch; c[nw + 0] = cos(delta * nch); c[nw + nch] = 0.5 * c[0]; for (j = 1; j < nch; j++) { c[nw + j] = 0.5 * cos(delta * j); c[nw + nc - j] = 0.5 * sin(delta * j); } } } /* -------- child routines -------- */ private void bitrv2(int n, double[] a) { int j, j1, k, k1, l, m, m2; double xr, xi, yr, yi; ip[2 + 0] = 0; l = n; m = 1; while ((m << 3) < l) { l >>= 1; for (j = 0; j < m; j++) { ip[2 + m + j] = ip[2 + 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[2 + k]; k1 = 2 * k + ip[2 + 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[2 + 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[2 + k]; k1 = 2 * k + ip[2 + 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; } } } } private void bitrv2conj(int n, double[] a) { int j, j1, k, k1, l, m, m2; double xr, xi, yr, yi; ip[2 + 0] = 0; l = n; m = 1; while ((m << 3) < l) { l >>= 1; for (j = 0; j < m; j++) { ip[2 + m + j] = ip[2 + 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[2 + k]; k1 = 2 * k + ip[2 + 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[2 + 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[2 + k]; k1 = 2 * k + ip[2 + 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[2 + k]; a[k1 + 1] = -a[k1 + 1]; a[k1 + m2 + 1] = -a[k1 + m2 + 1]; } } } private void cftfsub(int n, double[] a) { int j, j1, j2, j3, l; double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; l = 2; if (n > 8) { cft1st(a); l = 8; while ((l << 2) < n) { cftmdl(l, a); l <<= 2; } } if ((l << 2) == n) { for (j = 0; j < l; j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = a[j + 1] + a[j1 + 1]; x1r = a[j] - a[j1]; x1i = a[j + 1] - a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; a[j2] = x0r - x2r; a[j2 + 1] = x0i - x2i; a[j1] = x1r - x3i; a[j1 + 1] = x1i + x3r; a[j3] = x1r + x3i; a[j3 + 1] = x1i - x3r; } } else { for (j = 0; j < l; j += 2) { j1 = j + l; x0r = a[j] - a[j1]; x0i = a[j + 1] - a[j1 + 1]; a[j] += a[j1]; a[j + 1] += a[j1 + 1]; a[j1] = x0r; a[j1 + 1] = x0i; } } } private void cftbsub(int n, double[] a) { int j, j1, j2, j3, l; double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; l = 2; if (n > 8) { cft1st(a); l = 8; while ((l << 2) < n) { cftmdl(l, a); l <<= 2; } } if ((l << 2) == n) { for (j = 0; j < l; j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = -a[j + 1] - a[j1 + 1]; x1r = a[j] - a[j1]; x1i = -a[j + 1] + a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i - x2i; a[j2] = x0r - x2r; a[j2 + 1] = x0i + x2i; a[j1] = x1r - x3i; a[j1 + 1] = x1i - x3r; a[j3] = x1r + x3i; a[j3 + 1] = x1i + x3r; } } else { for (j = 0; j < l; j += 2) { j1 = j + l; x0r = a[j] - a[j1]; x0i = -a[j + 1] + a[j1 + 1]; a[j] += a[j1]; a[j + 1] = -a[j + 1] - a[j1 + 1]; a[j1] = x0r; a[j1 + 1] = x0i; } } } private void cft1st(double[] a) { int j, k1, k2; double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i; double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; x0r = a[0] + a[2]; x0i = a[1] + a[3]; x1r = a[0] - a[2]; x1i = a[1] - a[3]; x2r = a[4] + a[6]; x2i = a[5] + a[7]; x3r = a[4] - a[6]; x3i = a[5] - a[7]; a[0] = x0r + x2r; a[1] = x0i + x2i; a[4] = x0r - x2r; a[5] = x0i - x2i; a[2] = x1r - x3i; a[3] = x1i + x3r; a[6] = x1r + x3i; a[7] = x1i - x3r; wk1r = w[2]; x0r = a[8] + a[10]; x0i = a[9] + a[11]; x1r = a[8] - a[10]; x1i = a[9] - a[11]; x2r = a[12] + a[14]; x2i = a[13] + a[15]; x3r = a[12] - a[14]; x3i = a[13] - a[15]; a[8] = x0r + x2r; a[9] = x0i + x2i; a[12] = x2i - x0i; a[13] = x0r - x2r; x0r = x1r - x3i; x0i = x1i + x3r; a[10] = wk1r * (x0r - x0i); a[11] = wk1r * (x0r + x0i); x0r = x3i + x1r; x0i = x3r - x1i; a[14] = wk1r * (x0i - x0r); a[15] = wk1r * (x0i + x0r); k1 = 0; for (j = 16; j < n; j += 16) { k1 += 2; k2 = 2 * k1; wk2r = w[k1]; wk2i = w[k1 + 1]; wk1r = w[k2]; wk1i = w[k2 + 1]; wk3r = wk1r - 2 * wk2i * wk1i; wk3i = 2 * wk2i * wk1r - wk1i; x0r = a[j] + a[j + 2]; x0i = a[j + 1] + a[j + 3]; x1r = a[j] - a[j + 2]; x1i = a[j + 1] - a[j + 3]; x2r = a[j + 4] + a[j + 6]; x2i = a[j + 5] + a[j + 7]; x3r = a[j + 4] - a[j + 6]; x3i = a[j + 5] - a[j + 7]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; x0r -= x2r; x0i -= x2i; a[j + 4] = wk2r * x0r - wk2i * x0i; a[j + 5] = wk2r * x0i + wk2i * x0r; x0r = x1r - x3i; x0i = x1i + x3r; a[j + 2] = wk1r * x0r - wk1i * x0i; a[j + 3] = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j + 6] = wk3r * x0r - wk3i * x0i; a[j + 7] = wk3r * x0i + wk3i * x0r; wk1r = w[k2 + 2]; wk1i = w[k2 + 3]; wk3r = wk1r - 2 * wk2r * wk1i; wk3i = 2 * wk2r * wk1r - wk1i; x0r = a[j + 8] + a[j + 10]; x0i = a[j + 9] + a[j + 11]; x1r = a[j + 8] - a[j + 10]; x1i = a[j + 9] - a[j + 11]; x2r = a[j + 12] + a[j + 14]; x2i = a[j + 13] + a[j + 15]; x3r = a[j + 12] - a[j + 14]; x3i = a[j + 13] - a[j + 15]; a[j + 8] = x0r + x2r; a[j + 9] = x0i + x2i; x0r -= x2r; x0i -= x2i; a[j + 12] = -wk2i * x0r - wk2r * x0i; a[j + 13] = -wk2i * x0i + wk2r * x0r; x0r = x1r - x3i; x0i = x1i + x3r; a[j + 10] = wk1r * x0r - wk1i * x0i; a[j + 11] = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j + 14] = wk3r * x0r - wk3i * x0i; a[j + 15] = wk3r * x0i + wk3i * x0r; } } private void cftmdl(int l, double[] a) { int j, j1, j2, j3, k, k1, k2, m, m2; double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i; double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; m = l << 2; for (j = 0; j < l; j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = a[j + 1] + a[j1 + 1]; x1r = a[j] - a[j1]; x1i = a[j + 1] - a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; a[j2] = x0r - x2r; a[j2 + 1] = x0i - x2i; a[j1] = x1r - x3i; a[j1 + 1] = x1i + x3r; a[j3] = x1r + x3i; a[j3 + 1] = x1i - x3r; } wk1r = w[2]; for (j = m; j < l + m; j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = a[j + 1] + a[j1 + 1]; x1r = a[j] - a[j1]; x1i = a[j + 1] - a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; a[j2] = x2i - x0i; a[j2 + 1] = x0r - x2r; x0r = x1r - x3i; x0i = x1i + x3r; a[j1] = wk1r * (x0r - x0i); a[j1 + 1] = wk1r * (x0r + x0i); x0r = x3i + x1r; x0i = x3r - x1i; a[j3] = wk1r * (x0i - x0r); a[j3 + 1] = wk1r * (x0i + x0r); } k1 = 0; m2 = 2 * m; for (k = m2; k < n; k += m2) { k1 += 2; k2 = 2 * k1; wk2r = w[k1]; wk2i = w[k1 + 1]; wk1r = w[k2]; wk1i = w[k2 + 1]; wk3r = wk1r - 2 * wk2i * wk1i; wk3i = 2 * wk2i * wk1r - wk1i; for (j = k; j < l + k; j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = a[j + 1] + a[j1 + 1]; x1r = a[j] - a[j1]; x1i = a[j + 1] - a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; x0r -= x2r; x0i -= x2i; a[j2] = wk2r * x0r - wk2i * x0i; a[j2 + 1] = wk2r * x0i + wk2i * x0r; x0r = x1r - x3i; x0i = x1i + x3r; a[j1] = wk1r * x0r - wk1i * x0i; a[j1 + 1] = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j3] = wk3r * x0r - wk3i * x0i; a[j3 + 1] = wk3r * x0i + wk3i * x0r; } wk1r = w[k2 + 2]; wk1i = w[k2 + 3]; wk3r = wk1r - 2 * wk2r * wk1i; wk3i = 2 * wk2r * wk1r - wk1i; for (j = k + m; j < l + (k + m); j += 2) { j1 = j + l; j2 = j1 + l; j3 = j2 + l; x0r = a[j] + a[j1]; x0i = a[j + 1] + a[j1 + 1]; x1r = a[j] - a[j1]; x1i = a[j + 1] - a[j1 + 1]; x2r = a[j2] + a[j3]; x2i = a[j2 + 1] + a[j3 + 1]; x3r = a[j2] - a[j3]; x3i = a[j2 + 1] - a[j3 + 1]; a[j] = x0r + x2r; a[j + 1] = x0i + x2i; x0r -= x2r; x0i -= x2i; a[j2] = -wk2i * x0r - wk2r * x0i; a[j2 + 1] = -wk2i * x0i + wk2r * x0r; x0r = x1r - x3i; x0i = x1i + x3r; a[j1] = wk1r * x0r - wk1i * x0i; a[j1 + 1] = wk1r * x0i + wk1i * x0r; x0r = x1r + x3i; x0i = x1i - x3r; a[j3] = wk3r * x0r - wk3i * x0i; a[j3 + 1] = wk3r * x0i + wk3i * x0r; } } } private void rftfsub(int n, double[] a, int nc, double[] c, int nw) { 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[nw + nc - kk]; wki = c[nw + 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; } } private void rftbsub(int n, double[] a, int nc, double[] c, int nw) { int j, k, kk, ks, m; double wkr, wki, xr, xi, yr, yi; a[1] = -a[1]; m = n >> 1; ks = 2 * nc / m; kk = 0; for (j = 2; j < m; j += 2) { k = n - j; kk += ks; wkr = 0.5 - c[nw + nc - kk]; wki = c[nw + kk]; xr = a[j] - a[k]; xi = a[j + 1] + a[k + 1]; yr = wkr * xr + wki * xi; yi = wkr * xi - wki * xr; a[j] -= yr; a[j + 1] = yi - a[j + 1]; a[k] += yr; a[k + 1] = yi - a[k + 1]; } a[m + 1] = -a[m + 1]; } private void dctsub(int n, double[] a, int nc, double[] c, int nw) { 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[nw + kk] - c[nw + nc - kk]; wki = c[nw + kk] + c[nw + nc - kk]; xr = wki * a[j] - wkr * a[k]; a[j] = wkr * a[j] + wki * a[k]; a[k] = xr; } a[m] *= c[nw + 0]; } private void dstsub(int n, double[] a, int nc, double[] c, int nw) { 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[nw + kk] - c[nw + nc - kk]; wki = c[nw + kk] + c[nw + nc - kk]; xr = wki * a[k] - wkr * a[j]; a[k] = wkr * a[k] + wki * a[j]; a[j] = xr; } a[m] *= c[nw + 0]; } }
ご自由にお使いください。他人のソースコードを書き換えただけですから。
ではまた。
