1299582047
* ci(performance): Add performance tests to CI * ci(req): Fix requirements * ci(pre-commit): Apply automatic fixes * ci(pre-commit): Increase maximum allowed complexity for python --------- Co-authored-by: pre-commit-ci-lite[bot] <117423508+pre-commit-ci-lite[bot]@users.noreply.github.com> Co-authored-by: Jan Procházka <90197375+P-R-O-C-H-Y@users.noreply.github.com>
2329 lines
51 KiB
C++
2329 lines
51 KiB
C++
/*
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Based on "Calculation of PI(= 3.14159...) using FFT and AGM" by T.Ooura, Nov. 1999.
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https://github.com/Fibonacci43/SuperPI
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Modified for Arduino by Lucas Saavedra Vaz, 2024.
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*/
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#include <fftsg_h.h>
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void cdft(int n, int isgn, double *a) {
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if (isgn >= 0) {
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cftfsub(n, a);
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} else {
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cftbsub(n, a);
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}
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}
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void rdft(int n, int isgn, double *a) {
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double xi;
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if (isgn >= 0) {
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if (n > 4) {
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cftfsub(n, a);
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rftfsub(n, a);
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} else if (n == 4) {
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cftfsub(n, a);
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}
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xi = a[0] - a[1];
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a[0] += a[1];
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a[1] = xi;
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} else {
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a[1] = 0.5 * (a[0] - a[1]);
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a[0] -= a[1];
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if (n > 4) {
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rftbsub(n, a);
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cftbsub(n, a);
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} else if (n == 4) {
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cftbsub(n, a);
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}
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}
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}
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void ddct(int n, int isgn, double *a) {
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int j;
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double xr;
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if (isgn < 0) {
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xr = a[n - 1];
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for (j = n - 2; j >= 2; j -= 2) {
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a[j + 1] = a[j] - a[j - 1];
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a[j] += a[j - 1];
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}
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a[1] = a[0] - xr;
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a[0] += xr;
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if (n > 4) {
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rftbsub(n, a);
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cftbsub(n, a);
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} else if (n == 4) {
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cftbsub(n, a);
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}
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}
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if (n > 4) {
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dctsub(n, a);
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} else {
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dctsub4(n, a);
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}
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if (isgn >= 0) {
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if (n > 4) {
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cftfsub(n, a);
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rftfsub(n, a);
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} else if (n == 4) {
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cftfsub(n, a);
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}
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xr = a[0] - a[1];
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a[0] += a[1];
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for (j = 2; j < n; j += 2) {
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a[j - 1] = a[j] - a[j + 1];
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a[j] += a[j + 1];
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}
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a[n - 1] = xr;
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}
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}
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void ddst(int n, int isgn, double *a) {
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int j;
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double xr;
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if (isgn < 0) {
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xr = a[n - 1];
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for (j = n - 2; j >= 2; j -= 2) {
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a[j + 1] = -a[j] - a[j - 1];
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a[j] -= a[j - 1];
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}
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a[1] = a[0] + xr;
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a[0] -= xr;
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if (n > 4) {
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rftbsub(n, a);
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cftbsub(n, a);
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} else if (n == 4) {
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cftbsub(n, a);
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}
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}
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if (n > 4) {
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dstsub(n, a);
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} else {
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dstsub4(n, a);
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}
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if (isgn >= 0) {
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if (n > 4) {
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cftfsub(n, a);
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rftfsub(n, a);
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} else if (n == 4) {
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cftfsub(n, a);
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}
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xr = a[0] - a[1];
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a[0] += a[1];
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for (j = 2; j < n; j += 2) {
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a[j - 1] = -a[j] - a[j + 1];
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a[j] -= a[j + 1];
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}
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a[n - 1] = -xr;
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}
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}
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void dfct(int n, double *a) {
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int j, k, m, mh;
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double xr, xi, yr, yi, an;
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m = n >> 1;
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for (j = 0; j < m; j++) {
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k = n - j;
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xr = a[j] + a[k];
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a[j] -= a[k];
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a[k] = xr;
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}
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an = a[n];
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while (m >= 2) {
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ddct(m, 1, a);
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bitrv1(m, a);
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mh = m >> 1;
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xi = a[m];
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a[m] = a[0];
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a[0] = an - xi;
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an += xi;
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for (j = 1; j < mh; j++) {
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k = m - j;
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xr = a[m + k];
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xi = a[m + j];
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yr = a[j];
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yi = a[k];
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a[m + j] = yr;
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a[m + k] = yi;
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a[j] = xr - xi;
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a[k] = xr + xi;
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}
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xr = a[mh];
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a[mh] = a[m + mh];
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a[m + mh] = xr;
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m = mh;
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}
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xi = a[1];
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a[1] = a[0];
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a[0] = an + xi;
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a[n] = an - xi;
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bitrv1(n, a);
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}
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void dfst(int n, double *a) {
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int j, k, m, mh;
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double xr, xi, yr, yi;
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m = n >> 1;
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for (j = 1; j < m; j++) {
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k = n - j;
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xr = a[j] - a[k];
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a[j] += a[k];
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a[k] = xr;
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}
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a[0] = a[m];
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while (m >= 2) {
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ddst(m, 1, a);
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bitrv1(m, a);
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mh = m >> 1;
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for (j = 1; j < mh; j++) {
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k = m - j;
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xr = a[m + k];
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xi = a[m + j];
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yr = a[j];
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yi = a[k];
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a[m + j] = yr;
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a[m + k] = yi;
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a[j] = xr + xi;
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a[k] = xr - xi;
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}
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a[m] = a[0];
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a[0] = a[m + mh];
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a[m + mh] = a[mh];
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m = mh;
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}
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a[1] = a[0];
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a[0] = 0;
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bitrv1(n, a);
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}
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/* -------- child routines -------- */
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void cftfsub(int n, double *a) {
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int m;
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if (n > 32) {
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m = n >> 2;
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cftmdl1(n, a);
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if (n > CDFT_RECURSIVE_N) {
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cftrec1(m, a);
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cftrec2(m, &a[m]);
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cftrec1(m, &a[2 * m]);
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cftrec1(m, &a[3 * m]);
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} else if (m > 32) {
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cftexp1(n, a);
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} else {
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cftfx41(n, a);
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}
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bitrv2(n, a);
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} else if (n > 8) {
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if (n == 32) {
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cftf161(a);
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bitrv216(a);
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} else {
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cftf081(a);
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bitrv208(a);
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}
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} else if (n == 8) {
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cftf040(a);
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} else if (n == 4) {
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cftx020(a);
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}
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}
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void cftbsub(int n, double *a) {
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int m;
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if (n > 32) {
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m = n >> 2;
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cftb1st(n, a);
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if (n > CDFT_RECURSIVE_N) {
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cftrec1(m, a);
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cftrec2(m, &a[m]);
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cftrec1(m, &a[2 * m]);
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cftrec1(m, &a[3 * m]);
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} else if (m > 32) {
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cftexp1(n, a);
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} else {
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cftfx41(n, a);
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}
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bitrv2conj(n, a);
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} else if (n > 8) {
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if (n == 32) {
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cftf161(a);
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bitrv216neg(a);
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} else {
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cftf081(a);
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bitrv208neg(a);
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}
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} else if (n == 8) {
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cftb040(a);
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} else if (n == 4) {
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cftx020(a);
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}
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}
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void bitrv2(int n, double *a) {
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int j0, k0, j1, k1, l, m, i, j, k;
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double xr, xi, yr, yi;
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l = n >> 2;
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m = 2;
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while (m < l) {
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l >>= 1;
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m <<= 1;
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}
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if (m == l) {
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j0 = 0;
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for (k0 = 0; k0 < m; k0 += 2) {
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k = k0;
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for (j = j0; j < j0 + k0; j += 2) {
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xr = a[j];
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xi = a[j + 1];
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yr = a[k];
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yi = a[k + 1];
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a[j] = yr;
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a[j + 1] = yi;
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a[k] = xr;
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a[k + 1] = xi;
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j1 = j + m;
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k1 = k + 2 * m;
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xr = a[j1];
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xi = a[j1 + 1];
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yr = a[k1];
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yi = a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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j1 += m;
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k1 -= m;
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xr = a[j1];
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xi = a[j1 + 1];
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yr = a[k1];
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yi = a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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j1 += m;
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k1 += 2 * m;
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xr = a[j1];
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xi = a[j1 + 1];
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yr = a[k1];
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yi = a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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for (i = n >> 1; i > (k ^= i); i >>= 1);
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}
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j1 = j0 + k0 + m;
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k1 = j1 + m;
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xr = a[j1];
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xi = a[j1 + 1];
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yr = a[k1];
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yi = a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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for (i = n >> 1; i > (j0 ^= i); i >>= 1);
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}
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} else {
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j0 = 0;
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for (k0 = 2; k0 < m; k0 += 2) {
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for (i = n >> 1; i > (j0 ^= i); i >>= 1);
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k = k0;
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for (j = j0; j < j0 + k0; j += 2) {
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xr = a[j];
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xi = a[j + 1];
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yr = a[k];
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yi = a[k + 1];
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a[j] = yr;
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a[j + 1] = yi;
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a[k] = xr;
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a[k + 1] = xi;
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j1 = j + m;
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k1 = k + m;
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xr = a[j1];
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xi = a[j1 + 1];
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yr = a[k1];
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yi = a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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for (i = n >> 1; i > (k ^= i); i >>= 1);
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}
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}
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}
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}
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void bitrv2conj(int n, double *a) {
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int j0, k0, j1, k1, l, m, i, j, k;
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double xr, xi, yr, yi;
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l = n >> 2;
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m = 2;
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while (m < l) {
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l >>= 1;
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m <<= 1;
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}
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if (m == l) {
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j0 = 0;
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for (k0 = 0; k0 < m; k0 += 2) {
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k = k0;
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for (j = j0; j < j0 + k0; j += 2) {
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xr = a[j];
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xi = -a[j + 1];
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yr = a[k];
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yi = -a[k + 1];
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a[j] = yr;
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a[j + 1] = yi;
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a[k] = xr;
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a[k + 1] = xi;
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j1 = j + m;
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k1 = k + 2 * m;
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xr = a[j1];
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xi = -a[j1 + 1];
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yr = a[k1];
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yi = -a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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j1 += m;
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k1 -= m;
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xr = a[j1];
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xi = -a[j1 + 1];
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yr = a[k1];
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yi = -a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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j1 += m;
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k1 += 2 * m;
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xr = a[j1];
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xi = -a[j1 + 1];
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yr = a[k1];
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yi = -a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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for (i = n >> 1; i > (k ^= i); i >>= 1);
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}
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k1 = j0 + k0;
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a[k1 + 1] = -a[k1 + 1];
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j1 = k1 + m;
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k1 = j1 + m;
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xr = a[j1];
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xi = -a[j1 + 1];
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yr = a[k1];
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yi = -a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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k1 += m;
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a[k1 + 1] = -a[k1 + 1];
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for (i = n >> 1; i > (j0 ^= i); i >>= 1);
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}
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} else {
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a[1] = -a[1];
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a[m + 1] = -a[m + 1];
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j0 = 0;
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for (k0 = 2; k0 < m; k0 += 2) {
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for (i = n >> 1; i > (j0 ^= i); i >>= 1);
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k = k0;
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for (j = j0; j < j0 + k0; j += 2) {
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xr = a[j];
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xi = -a[j + 1];
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yr = a[k];
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yi = -a[k + 1];
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a[j] = yr;
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a[j + 1] = yi;
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a[k] = xr;
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a[k + 1] = xi;
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j1 = j + m;
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k1 = k + m;
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xr = a[j1];
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xi = -a[j1 + 1];
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yr = a[k1];
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yi = -a[k1 + 1];
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a[j1] = yr;
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a[j1 + 1] = yi;
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a[k1] = xr;
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a[k1 + 1] = xi;
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for (i = n >> 1; i > (k ^= i); i >>= 1);
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}
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k1 = j0 + k0;
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a[k1 + 1] = -a[k1 + 1];
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a[k1 + m + 1] = -a[k1 + m + 1];
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}
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}
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}
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void bitrv216(double *a) {
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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;
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x1r = a[2];
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x1i = a[3];
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x2r = a[4];
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x2i = a[5];
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x3r = a[6];
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x3i = a[7];
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x4r = a[8];
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x4i = a[9];
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x5r = a[10];
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x5i = a[11];
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x7r = a[14];
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x7i = a[15];
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x8r = a[16];
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x8i = a[17];
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x10r = a[20];
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x10i = a[21];
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x11r = a[22];
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x11i = a[23];
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x12r = a[24];
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x12i = a[25];
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x13r = a[26];
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x13i = a[27];
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x14r = a[28];
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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;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
void bitrv1(int n, double *a) {
|
|
int j0, k0, j1, k1, l, m, i, j, k;
|
|
double x;
|
|
|
|
l = n >> 2;
|
|
m = 1;
|
|
while (m < l) {
|
|
l >>= 1;
|
|
m <<= 1;
|
|
}
|
|
if (m == l) {
|
|
j0 = 0;
|
|
for (k0 = 0; k0 < m; k0++) {
|
|
k = k0;
|
|
for (j = j0; j < j0 + k0; j++) {
|
|
x = a[j];
|
|
a[j] = a[k];
|
|
a[k] = x;
|
|
j1 = j + m;
|
|
k1 = k + 2 * m;
|
|
x = a[j1];
|
|
a[j1] = a[k1];
|
|
a[k1] = x;
|
|
j1 += m;
|
|
k1 -= m;
|
|
x = a[j1];
|
|
a[j1] = a[k1];
|
|
a[k1] = x;
|
|
j1 += m;
|
|
k1 += 2 * m;
|
|
x = a[j1];
|
|
a[j1] = a[k1];
|
|
a[k1] = x;
|
|
for (i = n >> 1; i > (k ^= i); i >>= 1);
|
|
}
|
|
j1 = j0 + k0 + m;
|
|
k1 = j1 + m;
|
|
x = a[j1];
|
|
a[j1] = a[k1];
|
|
a[k1] = x;
|
|
for (i = n >> 1; i > (j0 ^= i); i >>= 1);
|
|
}
|
|
} else {
|
|
j0 = 0;
|
|
for (k0 = 1; k0 < m; k0++) {
|
|
for (i = n >> 1; i > (j0 ^= i); i >>= 1);
|
|
k = k0;
|
|
for (j = j0; j < j0 + k0; j++) {
|
|
x = a[j];
|
|
a[j] = a[k];
|
|
a[k] = x;
|
|
j1 = j + m;
|
|
k1 = k + m;
|
|
x = a[j1];
|
|
a[j1] = a[k1];
|
|
a[k1] = x;
|
|
for (i = n >> 1; i > (k ^= i); i >>= 1);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void cftb1st(int n, double *a) {
|
|
int i, i0, j, j0, j1, j2, j3, m, mh;
|
|
double ew, w1r, w1i, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i, ss1, ss3;
|
|
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
|
|
|
|
mh = n >> 3;
|
|
m = 2 * mh;
|
|
j1 = m;
|
|
j2 = j1 + m;
|
|
j3 = j2 + m;
|
|
x0r = a[0] + a[j2];
|
|
x0i = -a[1] - a[j2 + 1];
|
|
x1r = a[0] - a[j2];
|
|
x1i = -a[1] + a[j2 + 1];
|
|
x2r = a[j1] + a[j3];
|
|
x2i = a[j1 + 1] + a[j3 + 1];
|
|
x3r = a[j1] - a[j3];
|
|
x3i = a[j1 + 1] - a[j3 + 1];
|
|
a[0] = x0r + x2r;
|
|
a[1] = x0i - x2i;
|
|
a[j1] = x0r - x2r;
|
|
a[j1 + 1] = x0i + x2i;
|
|
a[j2] = x1r + x3i;
|
|
a[j2 + 1] = x1i + x3r;
|
|
a[j3] = x1r - x3i;
|
|
a[j3 + 1] = x1i - x3r;
|
|
wd1r = 1;
|
|
wd1i = 0;
|
|
wd3r = 1;
|
|
wd3i = 0;
|
|
ew = M_PI_2 / m;
|
|
w1r = cos(2 * ew);
|
|
w1i = sin(2 * ew);
|
|
wk1r = w1r;
|
|
wk1i = w1i;
|
|
ss1 = 2 * w1i;
|
|
wk3i = 2 * ss1 * wk1r;
|
|
wk3r = wk1r - wk3i * wk1i;
|
|
wk3i = wk1i - wk3i * wk1r;
|
|
ss3 = 2 * wk3i;
|
|
i = 0;
|
|
for (;;) {
|
|
i0 = i + 4 * CDFT_LOOP_DIV;
|
|
if (i0 > mh - 4) {
|
|
i0 = mh - 4;
|
|
}
|
|
for (j = i + 2; j < i0; j += 4) {
|
|
wd1r -= ss1 * wk1i;
|
|
wd1i += ss1 * wk1r;
|
|
wd3r -= ss3 * wk3i;
|
|
wd3i += ss3 * wk3r;
|
|
j1 = j + m;
|
|
j2 = j1 + m;
|
|
j3 = j2 + m;
|
|
x0r = a[j] + a[j2];
|
|
x0i = -a[j + 1] - a[j2 + 1];
|
|
x1r = a[j] - a[j2];
|
|
x1i = -a[j + 1] + a[j2 + 1];
|
|
x2r = a[j1] + a[j3];
|
|
x2i = a[j1 + 1] + a[j3 + 1];
|
|
x3r = a[j1] - a[j3];
|
|
x3i = a[j1 + 1] - a[j3 + 1];
|
|
a[j] = x0r + x2r;
|
|
a[j + 1] = x0i - x2i;
|
|
a[j1] = x0r - x2r;
|
|
a[j1 + 1] = x0i + x2i;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i + x3r;
|
|
a[j2] = wk1r * x0r - wk1i * x0i;
|
|
a[j2 + 1] = wk1r * x0i + wk1i * x0r;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3] = wk3r * x0r + wk3i * x0i;
|
|
a[j3 + 1] = wk3r * x0i - wk3i * x0r;
|
|
x0r = a[j + 2] + a[j2 + 2];
|
|
x0i = -a[j + 3] - a[j2 + 3];
|
|
x1r = a[j + 2] - a[j2 + 2];
|
|
x1i = -a[j + 3] + a[j2 + 3];
|
|
x2r = a[j1 + 2] + a[j3 + 2];
|
|
x2i = a[j1 + 3] + a[j3 + 3];
|
|
x3r = a[j1 + 2] - a[j3 + 2];
|
|
x3i = a[j1 + 3] - a[j3 + 3];
|
|
a[j + 2] = x0r + x2r;
|
|
a[j + 3] = x0i - x2i;
|
|
a[j1 + 2] = x0r - x2r;
|
|
a[j1 + 3] = x0i + x2i;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i + x3r;
|
|
a[j2 + 2] = wd1r * x0r - wd1i * x0i;
|
|
a[j2 + 3] = wd1r * x0i + wd1i * x0r;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3 + 2] = wd3r * x0r + wd3i * x0i;
|
|
a[j3 + 3] = wd3r * x0i - wd3i * x0r;
|
|
j0 = m - j;
|
|
j1 = j0 + m;
|
|
j2 = j1 + m;
|
|
j3 = j2 + m;
|
|
x0r = a[j0] + a[j2];
|
|
x0i = -a[j0 + 1] - a[j2 + 1];
|
|
x1r = a[j0] - a[j2];
|
|
x1i = -a[j0 + 1] + a[j2 + 1];
|
|
x2r = a[j1] + a[j3];
|
|
x2i = a[j1 + 1] + a[j3 + 1];
|
|
x3r = a[j1] - a[j3];
|
|
x3i = a[j1 + 1] - a[j3 + 1];
|
|
a[j0] = x0r + x2r;
|
|
a[j0 + 1] = x0i - x2i;
|
|
a[j1] = x0r - x2r;
|
|
a[j1 + 1] = x0i + x2i;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i + x3r;
|
|
a[j2] = wk1i * x0r - wk1r * x0i;
|
|
a[j2 + 1] = wk1i * x0i + wk1r * x0r;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3] = wk3i * x0r + wk3r * x0i;
|
|
a[j3 + 1] = wk3i * x0i - wk3r * x0r;
|
|
x0r = a[j0 - 2] + a[j2 - 2];
|
|
x0i = -a[j0 - 1] - a[j2 - 1];
|
|
x1r = a[j0 - 2] - a[j2 - 2];
|
|
x1i = -a[j0 - 1] + a[j2 - 1];
|
|
x2r = a[j1 - 2] + a[j3 - 2];
|
|
x2i = a[j1 - 1] + a[j3 - 1];
|
|
x3r = a[j1 - 2] - a[j3 - 2];
|
|
x3i = a[j1 - 1] - a[j3 - 1];
|
|
a[j0 - 2] = x0r + x2r;
|
|
a[j0 - 1] = x0i - x2i;
|
|
a[j1 - 2] = x0r - x2r;
|
|
a[j1 - 1] = x0i + x2i;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i + x3r;
|
|
a[j2 - 2] = wd1i * x0r - wd1r * x0i;
|
|
a[j2 - 1] = wd1i * x0i + wd1r * x0r;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3 - 2] = wd3i * x0r + wd3r * x0i;
|
|
a[j3 - 1] = wd3i * x0i - wd3r * x0r;
|
|
wk1r -= ss1 * wd1i;
|
|
wk1i += ss1 * wd1r;
|
|
wk3r -= ss3 * wd3i;
|
|
wk3i += ss3 * wd3r;
|
|
}
|
|
if (i0 == mh - 4) {
|
|
break;
|
|
}
|
|
wd1r = cos(ew * i0);
|
|
wd1i = sin(ew * i0);
|
|
wd3i = 4 * wd1i * wd1r;
|
|
wd3r = wd1r - wd3i * wd1i;
|
|
wd3i = wd1i - wd3i * wd1r;
|
|
wk1r = w1r * wd1r - w1i * wd1i;
|
|
wk1i = w1r * wd1i + w1i * wd1r;
|
|
wk3i = 4 * wk1i * wk1r;
|
|
wk3r = wk1r - wk3i * wk1i;
|
|
wk3i = wk1i - wk3i * wk1r;
|
|
i = i0;
|
|
}
|
|
wd1r -= ss1 * wk1i;
|
|
j0 = mh;
|
|
j1 = j0 + m;
|
|
j2 = j1 + m;
|
|
j3 = j2 + m;
|
|
x0r = a[j0 - 2] + a[j2 - 2];
|
|
x0i = -a[j0 - 1] - a[j2 - 1];
|
|
x1r = a[j0 - 2] - a[j2 - 2];
|
|
x1i = -a[j0 - 1] + a[j2 - 1];
|
|
x2r = a[j1 - 2] + a[j3 - 2];
|
|
x2i = a[j1 - 1] + a[j3 - 1];
|
|
x3r = a[j1 - 2] - a[j3 - 2];
|
|
x3i = a[j1 - 1] - a[j3 - 1];
|
|
a[j0 - 2] = x0r + x2r;
|
|
a[j0 - 1] = x0i - x2i;
|
|
a[j1 - 2] = x0r - x2r;
|
|
a[j1 - 1] = x0i + x2i;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i + x3r;
|
|
a[j2 - 2] = wk1r * x0r - wk1i * x0i;
|
|
a[j2 - 1] = wk1r * x0i + wk1i * x0r;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3 - 2] = wk3r * x0r + wk3i * x0i;
|
|
a[j3 - 1] = wk3r * x0i - wk3i * x0r;
|
|
x0r = a[j0] + a[j2];
|
|
x0i = -a[j0 + 1] - a[j2 + 1];
|
|
x1r = a[j0] - a[j2];
|
|
x1i = -a[j0 + 1] + a[j2 + 1];
|
|
x2r = a[j1] + a[j3];
|
|
x2i = a[j1 + 1] + a[j3 + 1];
|
|
x3r = a[j1] - a[j3];
|
|
x3i = a[j1 + 1] - a[j3 + 1];
|
|
a[j0] = x0r + x2r;
|
|
a[j0 + 1] = x0i - x2i;
|
|
a[j1] = x0r - x2r;
|
|
a[j1 + 1] = x0i + x2i;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i + x3r;
|
|
a[j2] = wd1r * (x0r - x0i);
|
|
a[j2 + 1] = wd1r * (x0i + x0r);
|
|
x0r = x1r - x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3] = -wd1r * (x0r + x0i);
|
|
a[j3 + 1] = -wd1r * (x0i - x0r);
|
|
x0r = a[j0 + 2] + a[j2 + 2];
|
|
x0i = -a[j0 + 3] - a[j2 + 3];
|
|
x1r = a[j0 + 2] - a[j2 + 2];
|
|
x1i = -a[j0 + 3] + a[j2 + 3];
|
|
x2r = a[j1 + 2] + a[j3 + 2];
|
|
x2i = a[j1 + 3] + a[j3 + 3];
|
|
x3r = a[j1 + 2] - a[j3 + 2];
|
|
x3i = a[j1 + 3] - a[j3 + 3];
|
|
a[j0 + 2] = x0r + x2r;
|
|
a[j0 + 3] = x0i - x2i;
|
|
a[j1 + 2] = x0r - x2r;
|
|
a[j1 + 3] = x0i + x2i;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i + x3r;
|
|
a[j2 + 2] = wk1i * x0r - wk1r * x0i;
|
|
a[j2 + 3] = wk1i * x0i + wk1r * x0r;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3 + 2] = wk3i * x0r + wk3r * x0i;
|
|
a[j3 + 3] = wk3i * x0i - wk3r * x0r;
|
|
}
|
|
|
|
void cftrec1(int n, double *a) {
|
|
int m;
|
|
|
|
m = n >> 2;
|
|
cftmdl1(n, a);
|
|
if (n > CDFT_RECURSIVE_N) {
|
|
cftrec1(m, a);
|
|
cftrec2(m, &a[m]);
|
|
cftrec1(m, &a[2 * m]);
|
|
cftrec1(m, &a[3 * m]);
|
|
} else {
|
|
cftexp1(n, a);
|
|
}
|
|
}
|
|
|
|
void cftrec2(int n, double *a) {
|
|
int m;
|
|
|
|
m = n >> 2;
|
|
cftmdl2(n, a);
|
|
if (n > CDFT_RECURSIVE_N) {
|
|
cftrec1(m, a);
|
|
cftrec2(m, &a[m]);
|
|
cftrec1(m, &a[2 * m]);
|
|
cftrec2(m, &a[3 * m]);
|
|
} else {
|
|
cftexp2(n, a);
|
|
}
|
|
}
|
|
|
|
void cftexp1(int n, double *a) {
|
|
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[j]);
|
|
cftmdl2(l, &a[k + j]);
|
|
cftmdl1(l, &a[2 * k + j]);
|
|
}
|
|
}
|
|
cftmdl1(l, &a[n - l]);
|
|
l >>= 2;
|
|
}
|
|
for (k = l; k < n; k <<= 2) {
|
|
for (j = k - l; j < n; j += 4 * k) {
|
|
cftmdl1(l, &a[j]);
|
|
cftfx41(l, &a[j]);
|
|
cftmdl2(l, &a[k + j]);
|
|
cftfx42(l, &a[k + j]);
|
|
cftmdl1(l, &a[2 * k + j]);
|
|
cftfx41(l, &a[2 * k + j]);
|
|
}
|
|
}
|
|
cftmdl1(l, &a[n - l]);
|
|
cftfx41(l, &a[n - l]);
|
|
}
|
|
|
|
void cftexp2(int n, double *a) {
|
|
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[j]);
|
|
cftmdl1(l, &a[m + j]);
|
|
}
|
|
for (j = 2 * k - l; j < m; j += 4 * k) {
|
|
cftmdl2(l, &a[j]);
|
|
cftmdl2(l, &a[m + j]);
|
|
}
|
|
}
|
|
l >>= 2;
|
|
}
|
|
for (k = l; k < m; k <<= 2) {
|
|
for (j = k - l; j < m; j += 2 * k) {
|
|
cftmdl1(l, &a[j]);
|
|
cftfx41(l, &a[j]);
|
|
cftmdl1(l, &a[m + j]);
|
|
cftfx41(l, &a[m + j]);
|
|
}
|
|
for (j = 2 * k - l; j < m; j += 4 * k) {
|
|
cftmdl2(l, &a[j]);
|
|
cftfx42(l, &a[j]);
|
|
cftmdl2(l, &a[m + j]);
|
|
cftfx42(l, &a[m + j]);
|
|
}
|
|
}
|
|
}
|
|
|
|
void cftmdl1(int n, double *a) {
|
|
int i, i0, j, j0, j1, j2, j3, m, mh;
|
|
double ew, w1r, w1i, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i, ss1, ss3;
|
|
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
|
|
|
|
mh = n >> 3;
|
|
m = 2 * mh;
|
|
j1 = m;
|
|
j2 = j1 + m;
|
|
j3 = j2 + m;
|
|
x0r = a[0] + a[j2];
|
|
x0i = a[1] + a[j2 + 1];
|
|
x1r = a[0] - a[j2];
|
|
x1i = a[1] - a[j2 + 1];
|
|
x2r = a[j1] + a[j3];
|
|
x2i = a[j1 + 1] + a[j3 + 1];
|
|
x3r = a[j1] - a[j3];
|
|
x3i = a[j1 + 1] - a[j3 + 1];
|
|
a[0] = x0r + x2r;
|
|
a[1] = x0i + x2i;
|
|
a[j1] = x0r - x2r;
|
|
a[j1 + 1] = x0i - x2i;
|
|
a[j2] = x1r - x3i;
|
|
a[j2 + 1] = x1i + x3r;
|
|
a[j3] = x1r + x3i;
|
|
a[j3 + 1] = x1i - x3r;
|
|
wd1r = 1;
|
|
wd1i = 0;
|
|
wd3r = 1;
|
|
wd3i = 0;
|
|
ew = M_PI_2 / m;
|
|
w1r = cos(2 * ew);
|
|
w1i = sin(2 * ew);
|
|
wk1r = w1r;
|
|
wk1i = w1i;
|
|
ss1 = 2 * w1i;
|
|
wk3i = 2 * ss1 * wk1r;
|
|
wk3r = wk1r - wk3i * wk1i;
|
|
wk3i = wk1i - wk3i * wk1r;
|
|
ss3 = 2 * wk3i;
|
|
i = 0;
|
|
for (;;) {
|
|
i0 = i + 4 * CDFT_LOOP_DIV;
|
|
if (i0 > mh - 4) {
|
|
i0 = mh - 4;
|
|
}
|
|
for (j = i + 2; j < i0; j += 4) {
|
|
wd1r -= ss1 * wk1i;
|
|
wd1i += ss1 * wk1r;
|
|
wd3r -= ss3 * wk3i;
|
|
wd3i += ss3 * wk3r;
|
|
j1 = j + m;
|
|
j2 = j1 + m;
|
|
j3 = j2 + m;
|
|
x0r = a[j] + a[j2];
|
|
x0i = a[j + 1] + a[j2 + 1];
|
|
x1r = a[j] - a[j2];
|
|
x1i = a[j + 1] - a[j2 + 1];
|
|
x2r = a[j1] + a[j3];
|
|
x2i = a[j1 + 1] + a[j3 + 1];
|
|
x3r = a[j1] - a[j3];
|
|
x3i = a[j1 + 1] - a[j3 + 1];
|
|
a[j] = x0r + x2r;
|
|
a[j + 1] = x0i + x2i;
|
|
a[j1] = x0r - x2r;
|
|
a[j1 + 1] = x0i - x2i;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[j2] = wk1r * x0r - wk1i * x0i;
|
|
a[j2 + 1] = wk1r * x0i + wk1i * x0r;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3] = wk3r * x0r + wk3i * x0i;
|
|
a[j3 + 1] = wk3r * x0i - wk3i * x0r;
|
|
x0r = a[j + 2] + a[j2 + 2];
|
|
x0i = a[j + 3] + a[j2 + 3];
|
|
x1r = a[j + 2] - a[j2 + 2];
|
|
x1i = a[j + 3] - a[j2 + 3];
|
|
x2r = a[j1 + 2] + a[j3 + 2];
|
|
x2i = a[j1 + 3] + a[j3 + 3];
|
|
x3r = a[j1 + 2] - a[j3 + 2];
|
|
x3i = a[j1 + 3] - a[j3 + 3];
|
|
a[j + 2] = x0r + x2r;
|
|
a[j + 3] = x0i + x2i;
|
|
a[j1 + 2] = x0r - x2r;
|
|
a[j1 + 3] = x0i - x2i;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[j2 + 2] = wd1r * x0r - wd1i * x0i;
|
|
a[j2 + 3] = wd1r * x0i + wd1i * x0r;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3 + 2] = wd3r * x0r + wd3i * x0i;
|
|
a[j3 + 3] = wd3r * x0i - wd3i * x0r;
|
|
j0 = m - j;
|
|
j1 = j0 + m;
|
|
j2 = j1 + m;
|
|
j3 = j2 + m;
|
|
x0r = a[j0] + a[j2];
|
|
x0i = a[j0 + 1] + a[j2 + 1];
|
|
x1r = a[j0] - a[j2];
|
|
x1i = a[j0 + 1] - a[j2 + 1];
|
|
x2r = a[j1] + a[j3];
|
|
x2i = a[j1 + 1] + a[j3 + 1];
|
|
x3r = a[j1] - a[j3];
|
|
x3i = a[j1 + 1] - a[j3 + 1];
|
|
a[j0] = x0r + x2r;
|
|
a[j0 + 1] = x0i + x2i;
|
|
a[j1] = x0r - x2r;
|
|
a[j1 + 1] = x0i - x2i;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[j2] = wk1i * x0r - wk1r * x0i;
|
|
a[j2 + 1] = wk1i * x0i + wk1r * x0r;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3] = wk3i * x0r + wk3r * x0i;
|
|
a[j3 + 1] = wk3i * x0i - wk3r * x0r;
|
|
x0r = a[j0 - 2] + a[j2 - 2];
|
|
x0i = a[j0 - 1] + a[j2 - 1];
|
|
x1r = a[j0 - 2] - a[j2 - 2];
|
|
x1i = a[j0 - 1] - a[j2 - 1];
|
|
x2r = a[j1 - 2] + a[j3 - 2];
|
|
x2i = a[j1 - 1] + a[j3 - 1];
|
|
x3r = a[j1 - 2] - a[j3 - 2];
|
|
x3i = a[j1 - 1] - a[j3 - 1];
|
|
a[j0 - 2] = x0r + x2r;
|
|
a[j0 - 1] = x0i + x2i;
|
|
a[j1 - 2] = x0r - x2r;
|
|
a[j1 - 1] = x0i - x2i;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[j2 - 2] = wd1i * x0r - wd1r * x0i;
|
|
a[j2 - 1] = wd1i * x0i + wd1r * x0r;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3 - 2] = wd3i * x0r + wd3r * x0i;
|
|
a[j3 - 1] = wd3i * x0i - wd3r * x0r;
|
|
wk1r -= ss1 * wd1i;
|
|
wk1i += ss1 * wd1r;
|
|
wk3r -= ss3 * wd3i;
|
|
wk3i += ss3 * wd3r;
|
|
}
|
|
if (i0 == mh - 4) {
|
|
break;
|
|
}
|
|
wd1r = cos(ew * i0);
|
|
wd1i = sin(ew * i0);
|
|
wd3i = 4 * wd1i * wd1r;
|
|
wd3r = wd1r - wd3i * wd1i;
|
|
wd3i = wd1i - wd3i * wd1r;
|
|
wk1r = w1r * wd1r - w1i * wd1i;
|
|
wk1i = w1r * wd1i + w1i * wd1r;
|
|
wk3i = 4 * wk1i * wk1r;
|
|
wk3r = wk1r - wk3i * wk1i;
|
|
wk3i = wk1i - wk3i * wk1r;
|
|
i = i0;
|
|
}
|
|
wd1r -= ss1 * wk1i;
|
|
j0 = mh;
|
|
j1 = j0 + m;
|
|
j2 = j1 + m;
|
|
j3 = j2 + m;
|
|
x0r = a[j0 - 2] + a[j2 - 2];
|
|
x0i = a[j0 - 1] + a[j2 - 1];
|
|
x1r = a[j0 - 2] - a[j2 - 2];
|
|
x1i = a[j0 - 1] - a[j2 - 1];
|
|
x2r = a[j1 - 2] + a[j3 - 2];
|
|
x2i = a[j1 - 1] + a[j3 - 1];
|
|
x3r = a[j1 - 2] - a[j3 - 2];
|
|
x3i = a[j1 - 1] - a[j3 - 1];
|
|
a[j0 - 2] = x0r + x2r;
|
|
a[j0 - 1] = x0i + x2i;
|
|
a[j1 - 2] = x0r - x2r;
|
|
a[j1 - 1] = x0i - x2i;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[j2 - 2] = wk1r * x0r - wk1i * x0i;
|
|
a[j2 - 1] = wk1r * x0i + wk1i * x0r;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3 - 2] = wk3r * x0r + wk3i * x0i;
|
|
a[j3 - 1] = wk3r * x0i - wk3i * x0r;
|
|
x0r = a[j0] + a[j2];
|
|
x0i = a[j0 + 1] + a[j2 + 1];
|
|
x1r = a[j0] - a[j2];
|
|
x1i = a[j0 + 1] - a[j2 + 1];
|
|
x2r = a[j1] + a[j3];
|
|
x2i = a[j1 + 1] + a[j3 + 1];
|
|
x3r = a[j1] - a[j3];
|
|
x3i = a[j1 + 1] - a[j3 + 1];
|
|
a[j0] = x0r + x2r;
|
|
a[j0 + 1] = x0i + x2i;
|
|
a[j1] = x0r - x2r;
|
|
a[j1 + 1] = x0i - x2i;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[j2] = wd1r * (x0r - x0i);
|
|
a[j2 + 1] = wd1r * (x0i + x0r);
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3] = -wd1r * (x0r + x0i);
|
|
a[j3 + 1] = -wd1r * (x0i - x0r);
|
|
x0r = a[j0 + 2] + a[j2 + 2];
|
|
x0i = a[j0 + 3] + a[j2 + 3];
|
|
x1r = a[j0 + 2] - a[j2 + 2];
|
|
x1i = a[j0 + 3] - a[j2 + 3];
|
|
x2r = a[j1 + 2] + a[j3 + 2];
|
|
x2i = a[j1 + 3] + a[j3 + 3];
|
|
x3r = a[j1 + 2] - a[j3 + 2];
|
|
x3i = a[j1 + 3] - a[j3 + 3];
|
|
a[j0 + 2] = x0r + x2r;
|
|
a[j0 + 3] = x0i + x2i;
|
|
a[j1 + 2] = x0r - x2r;
|
|
a[j1 + 3] = x0i - x2i;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[j2 + 2] = wk1i * x0r - wk1r * x0i;
|
|
a[j2 + 3] = wk1i * x0i + wk1r * x0r;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3 + 2] = wk3i * x0r + wk3r * x0i;
|
|
a[j3 + 3] = wk3i * x0i - wk3r * x0r;
|
|
}
|
|
|
|
void cftmdl2(int n, double *a) {
|
|
int i, i0, j, j0, j1, j2, j3, m, mh;
|
|
double ew, w1r, w1i, wn4r, wk1r, wk1i, wk3r, wk3i, wl1r, wl1i, wl3r, wl3i, wd1r, wd1i, wd3r, wd3i, we1r, we1i, we3r, we3i, ss1, ss3;
|
|
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i;
|
|
|
|
mh = n >> 3;
|
|
m = 2 * mh;
|
|
wn4r = WR5000;
|
|
j1 = m;
|
|
j2 = j1 + m;
|
|
j3 = j2 + m;
|
|
x0r = a[0] - a[j2 + 1];
|
|
x0i = a[1] + a[j2];
|
|
x1r = a[0] + a[j2 + 1];
|
|
x1i = a[1] - a[j2];
|
|
x2r = a[j1] - a[j3 + 1];
|
|
x2i = a[j1 + 1] + a[j3];
|
|
x3r = a[j1] + a[j3 + 1];
|
|
x3i = a[j1 + 1] - a[j3];
|
|
y0r = wn4r * (x2r - x2i);
|
|
y0i = wn4r * (x2i + x2r);
|
|
a[0] = x0r + y0r;
|
|
a[1] = x0i + y0i;
|
|
a[j1] = x0r - y0r;
|
|
a[j1 + 1] = x0i - y0i;
|
|
y0r = wn4r * (x3r - x3i);
|
|
y0i = wn4r * (x3i + x3r);
|
|
a[j2] = x1r - y0i;
|
|
a[j2 + 1] = x1i + y0r;
|
|
a[j3] = x1r + y0i;
|
|
a[j3 + 1] = x1i - y0r;
|
|
wl1r = 1;
|
|
wl1i = 0;
|
|
wl3r = 1;
|
|
wl3i = 0;
|
|
we1r = wn4r;
|
|
we1i = wn4r;
|
|
we3r = -wn4r;
|
|
we3i = -wn4r;
|
|
ew = M_PI_2 / (2 * m);
|
|
w1r = cos(2 * ew);
|
|
w1i = sin(2 * ew);
|
|
wk1r = w1r;
|
|
wk1i = w1i;
|
|
wd1r = wn4r * (w1r - w1i);
|
|
wd1i = wn4r * (w1i + w1r);
|
|
ss1 = 2 * w1i;
|
|
wk3i = 2 * ss1 * wk1r;
|
|
wk3r = wk1r - wk3i * wk1i;
|
|
wk3i = wk1i - wk3i * wk1r;
|
|
ss3 = 2 * wk3i;
|
|
wd3r = -wn4r * (wk3r - wk3i);
|
|
wd3i = -wn4r * (wk3i + wk3r);
|
|
i = 0;
|
|
for (;;) {
|
|
i0 = i + 4 * CDFT_LOOP_DIV;
|
|
if (i0 > mh - 4) {
|
|
i0 = mh - 4;
|
|
}
|
|
for (j = i + 2; j < i0; j += 4) {
|
|
wl1r -= ss1 * wk1i;
|
|
wl1i += ss1 * wk1r;
|
|
wl3r -= ss3 * wk3i;
|
|
wl3i += ss3 * wk3r;
|
|
we1r -= ss1 * wd1i;
|
|
we1i += ss1 * wd1r;
|
|
we3r -= ss3 * wd3i;
|
|
we3i += ss3 * wd3r;
|
|
j1 = j + m;
|
|
j2 = j1 + m;
|
|
j3 = j2 + m;
|
|
x0r = a[j] - a[j2 + 1];
|
|
x0i = a[j + 1] + a[j2];
|
|
x1r = a[j] + a[j2 + 1];
|
|
x1i = a[j + 1] - a[j2];
|
|
x2r = a[j1] - a[j3 + 1];
|
|
x2i = a[j1 + 1] + a[j3];
|
|
x3r = a[j1] + a[j3 + 1];
|
|
x3i = a[j1 + 1] - a[j3];
|
|
y0r = wk1r * x0r - wk1i * x0i;
|
|
y0i = wk1r * x0i + wk1i * x0r;
|
|
y2r = wd1r * x2r - wd1i * x2i;
|
|
y2i = wd1r * x2i + wd1i * x2r;
|
|
a[j] = y0r + y2r;
|
|
a[j + 1] = y0i + y2i;
|
|
a[j1] = y0r - y2r;
|
|
a[j1 + 1] = y0i - y2i;
|
|
y0r = wk3r * x1r + wk3i * x1i;
|
|
y0i = wk3r * x1i - wk3i * x1r;
|
|
y2r = wd3r * x3r + wd3i * x3i;
|
|
y2i = wd3r * x3i - wd3i * x3r;
|
|
a[j2] = y0r + y2r;
|
|
a[j2 + 1] = y0i + y2i;
|
|
a[j3] = y0r - y2r;
|
|
a[j3 + 1] = y0i - y2i;
|
|
x0r = a[j + 2] - a[j2 + 3];
|
|
x0i = a[j + 3] + a[j2 + 2];
|
|
x1r = a[j + 2] + a[j2 + 3];
|
|
x1i = a[j + 3] - a[j2 + 2];
|
|
x2r = a[j1 + 2] - a[j3 + 3];
|
|
x2i = a[j1 + 3] + a[j3 + 2];
|
|
x3r = a[j1 + 2] + a[j3 + 3];
|
|
x3i = a[j1 + 3] - a[j3 + 2];
|
|
y0r = wl1r * x0r - wl1i * x0i;
|
|
y0i = wl1r * x0i + wl1i * x0r;
|
|
y2r = we1r * x2r - we1i * x2i;
|
|
y2i = we1r * x2i + we1i * x2r;
|
|
a[j + 2] = y0r + y2r;
|
|
a[j + 3] = y0i + y2i;
|
|
a[j1 + 2] = y0r - y2r;
|
|
a[j1 + 3] = y0i - y2i;
|
|
y0r = wl3r * x1r + wl3i * x1i;
|
|
y0i = wl3r * x1i - wl3i * x1r;
|
|
y2r = we3r * x3r + we3i * x3i;
|
|
y2i = we3r * x3i - we3i * x3r;
|
|
a[j2 + 2] = y0r + y2r;
|
|
a[j2 + 3] = y0i + y2i;
|
|
a[j3 + 2] = y0r - y2r;
|
|
a[j3 + 3] = y0i - y2i;
|
|
j0 = m - j;
|
|
j1 = j0 + m;
|
|
j2 = j1 + m;
|
|
j3 = j2 + m;
|
|
x0r = a[j0] - a[j2 + 1];
|
|
x0i = a[j0 + 1] + a[j2];
|
|
x1r = a[j0] + a[j2 + 1];
|
|
x1i = a[j0 + 1] - a[j2];
|
|
x2r = a[j1] - a[j3 + 1];
|
|
x2i = a[j1 + 1] + a[j3];
|
|
x3r = a[j1] + a[j3 + 1];
|
|
x3i = a[j1 + 1] - a[j3];
|
|
y0r = wd1i * x0r - wd1r * x0i;
|
|
y0i = wd1i * x0i + wd1r * x0r;
|
|
y2r = wk1i * x2r - wk1r * x2i;
|
|
y2i = wk1i * x2i + wk1r * x2r;
|
|
a[j0] = y0r + y2r;
|
|
a[j0 + 1] = y0i + y2i;
|
|
a[j1] = y0r - y2r;
|
|
a[j1 + 1] = y0i - y2i;
|
|
y0r = wd3i * x1r + wd3r * x1i;
|
|
y0i = wd3i * x1i - wd3r * x1r;
|
|
y2r = wk3i * x3r + wk3r * x3i;
|
|
y2i = wk3i * x3i - wk3r * x3r;
|
|
a[j2] = y0r + y2r;
|
|
a[j2 + 1] = y0i + y2i;
|
|
a[j3] = y0r - y2r;
|
|
a[j3 + 1] = y0i - y2i;
|
|
x0r = a[j0 - 2] - a[j2 - 1];
|
|
x0i = a[j0 - 1] + a[j2 - 2];
|
|
x1r = a[j0 - 2] + a[j2 - 1];
|
|
x1i = a[j0 - 1] - a[j2 - 2];
|
|
x2r = a[j1 - 2] - a[j3 - 1];
|
|
x2i = a[j1 - 1] + a[j3 - 2];
|
|
x3r = a[j1 - 2] + a[j3 - 1];
|
|
x3i = a[j1 - 1] - a[j3 - 2];
|
|
y0r = we1i * x0r - we1r * x0i;
|
|
y0i = we1i * x0i + we1r * x0r;
|
|
y2r = wl1i * x2r - wl1r * x2i;
|
|
y2i = wl1i * x2i + wl1r * x2r;
|
|
a[j0 - 2] = y0r + y2r;
|
|
a[j0 - 1] = y0i + y2i;
|
|
a[j1 - 2] = y0r - y2r;
|
|
a[j1 - 1] = y0i - y2i;
|
|
y0r = we3i * x1r + we3r * x1i;
|
|
y0i = we3i * x1i - we3r * x1r;
|
|
y2r = wl3i * x3r + wl3r * x3i;
|
|
y2i = wl3i * x3i - wl3r * x3r;
|
|
a[j2 - 2] = y0r + y2r;
|
|
a[j2 - 1] = y0i + y2i;
|
|
a[j3 - 2] = y0r - y2r;
|
|
a[j3 - 1] = y0i - y2i;
|
|
wk1r -= ss1 * wl1i;
|
|
wk1i += ss1 * wl1r;
|
|
wk3r -= ss3 * wl3i;
|
|
wk3i += ss3 * wl3r;
|
|
wd1r -= ss1 * we1i;
|
|
wd1i += ss1 * we1r;
|
|
wd3r -= ss3 * we3i;
|
|
wd3i += ss3 * we3r;
|
|
}
|
|
if (i0 == mh - 4) {
|
|
break;
|
|
}
|
|
wl1r = cos(ew * i0);
|
|
wl1i = sin(ew * i0);
|
|
wl3i = 4 * wl1i * wl1r;
|
|
wl3r = wl1r - wl3i * wl1i;
|
|
wl3i = wl1i - wl3i * wl1r;
|
|
we1r = wn4r * (wl1r - wl1i);
|
|
we1i = wn4r * (wl1i + wl1r);
|
|
we3r = -wn4r * (wl3r - wl3i);
|
|
we3i = -wn4r * (wl3i + wl3r);
|
|
wk1r = w1r * wl1r - w1i * wl1i;
|
|
wk1i = w1r * wl1i + w1i * wl1r;
|
|
wk3i = 4 * wk1i * wk1r;
|
|
wk3r = wk1r - wk3i * wk1i;
|
|
wk3i = wk1i - wk3i * wk1r;
|
|
wd1r = wn4r * (wk1r - wk1i);
|
|
wd1i = wn4r * (wk1i + wk1r);
|
|
wd3r = -wn4r * (wk3r - wk3i);
|
|
wd3i = -wn4r * (wk3i + wk3r);
|
|
i = i0;
|
|
}
|
|
wl1r -= ss1 * wk1i;
|
|
wl1i += ss1 * wk1r;
|
|
j0 = mh;
|
|
j1 = j0 + m;
|
|
j2 = j1 + m;
|
|
j3 = j2 + m;
|
|
x0r = a[j0 - 2] - a[j2 - 1];
|
|
x0i = a[j0 - 1] + a[j2 - 2];
|
|
x1r = a[j0 - 2] + a[j2 - 1];
|
|
x1i = a[j0 - 1] - a[j2 - 2];
|
|
x2r = a[j1 - 2] - a[j3 - 1];
|
|
x2i = a[j1 - 1] + a[j3 - 2];
|
|
x3r = a[j1 - 2] + a[j3 - 1];
|
|
x3i = a[j1 - 1] - a[j3 - 2];
|
|
y0r = wk1r * x0r - wk1i * x0i;
|
|
y0i = wk1r * x0i + wk1i * x0r;
|
|
y2r = wd1r * x2r - wd1i * x2i;
|
|
y2i = wd1r * x2i + wd1i * x2r;
|
|
a[j0 - 2] = y0r + y2r;
|
|
a[j0 - 1] = y0i + y2i;
|
|
a[j1 - 2] = y0r - y2r;
|
|
a[j1 - 1] = y0i - y2i;
|
|
y0r = wk3r * x1r + wk3i * x1i;
|
|
y0i = wk3r * x1i - wk3i * x1r;
|
|
y2r = wd3r * x3r + wd3i * x3i;
|
|
y2i = wd3r * x3i - wd3i * x3r;
|
|
a[j2 - 2] = y0r + y2r;
|
|
a[j2 - 1] = y0i + y2i;
|
|
a[j3 - 2] = y0r - y2r;
|
|
a[j3 - 1] = y0i - y2i;
|
|
x0r = a[j0] - a[j2 + 1];
|
|
x0i = a[j0 + 1] + a[j2];
|
|
x1r = a[j0] + a[j2 + 1];
|
|
x1i = a[j0 + 1] - a[j2];
|
|
x2r = a[j1] - a[j3 + 1];
|
|
x2i = a[j1 + 1] + a[j3];
|
|
x3r = a[j1] + a[j3 + 1];
|
|
x3i = a[j1 + 1] - a[j3];
|
|
y0r = wl1r * x0r - wl1i * x0i;
|
|
y0i = wl1r * x0i + wl1i * x0r;
|
|
y2r = wl1i * x2r - wl1r * x2i;
|
|
y2i = wl1i * x2i + wl1r * x2r;
|
|
a[j0] = y0r + y2r;
|
|
a[j0 + 1] = y0i + y2i;
|
|
a[j1] = y0r - y2r;
|
|
a[j1 + 1] = y0i - y2i;
|
|
y0r = wl1i * x1r - wl1r * x1i;
|
|
y0i = wl1i * x1i + wl1r * x1r;
|
|
y2r = wl1r * x3r - wl1i * x3i;
|
|
y2i = wl1r * x3i + wl1i * x3r;
|
|
a[j2] = y0r - y2r;
|
|
a[j2 + 1] = y0i - y2i;
|
|
a[j3] = y0r + y2r;
|
|
a[j3 + 1] = y0i + y2i;
|
|
x0r = a[j0 + 2] - a[j2 + 3];
|
|
x0i = a[j0 + 3] + a[j2 + 2];
|
|
x1r = a[j0 + 2] + a[j2 + 3];
|
|
x1i = a[j0 + 3] - a[j2 + 2];
|
|
x2r = a[j1 + 2] - a[j3 + 3];
|
|
x2i = a[j1 + 3] + a[j3 + 2];
|
|
x3r = a[j1 + 2] + a[j3 + 3];
|
|
x3i = a[j1 + 3] - a[j3 + 2];
|
|
y0r = wd1i * x0r - wd1r * x0i;
|
|
y0i = wd1i * x0i + wd1r * x0r;
|
|
y2r = wk1i * x2r - wk1r * x2i;
|
|
y2i = wk1i * x2i + wk1r * x2r;
|
|
a[j0 + 2] = y0r + y2r;
|
|
a[j0 + 3] = y0i + y2i;
|
|
a[j1 + 2] = y0r - y2r;
|
|
a[j1 + 3] = y0i - y2i;
|
|
y0r = wd3i * x1r + wd3r * x1i;
|
|
y0i = wd3i * x1i - wd3r * x1r;
|
|
y2r = wk3i * x3r + wk3r * x3i;
|
|
y2i = wk3i * x3i - wk3r * x3r;
|
|
a[j2 + 2] = y0r + y2r;
|
|
a[j2 + 3] = y0i + y2i;
|
|
a[j3 + 2] = y0r - y2r;
|
|
a[j3 + 3] = y0i - y2i;
|
|
}
|
|
|
|
void cftfx41(int n, double *a) {
|
|
if (n == 128) {
|
|
cftf161(a);
|
|
cftf162(&a[32]);
|
|
cftf161(&a[64]);
|
|
cftf161(&a[96]);
|
|
} else {
|
|
cftf081(a);
|
|
cftf082(&a[16]);
|
|
cftf081(&a[32]);
|
|
cftf081(&a[48]);
|
|
}
|
|
}
|
|
|
|
void cftfx42(int n, double *a) {
|
|
if (n == 128) {
|
|
cftf161(a);
|
|
cftf162(&a[32]);
|
|
cftf161(&a[64]);
|
|
cftf162(&a[96]);
|
|
} else {
|
|
cftf081(a);
|
|
cftf082(&a[16]);
|
|
cftf081(&a[32]);
|
|
cftf082(&a[48]);
|
|
}
|
|
}
|
|
|
|
void cftf161(double *a) {
|
|
double wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i, y8r, y8i,
|
|
y9r, y9i, y10r, y10i, y11r, y11i, y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;
|
|
|
|
wn4r = WR5000;
|
|
wk1r = WR2500;
|
|
wk1i = WI2500;
|
|
x0r = a[0] + a[16];
|
|
x0i = a[1] + a[17];
|
|
x1r = a[0] - a[16];
|
|
x1i = a[1] - a[17];
|
|
x2r = a[8] + a[24];
|
|
x2i = a[9] + a[25];
|
|
x3r = a[8] - a[24];
|
|
x3i = a[9] - a[25];
|
|
y0r = x0r + x2r;
|
|
y0i = x0i + x2i;
|
|
y4r = x0r - x2r;
|
|
y4i = x0i - x2i;
|
|
y8r = x1r - x3i;
|
|
y8i = x1i + x3r;
|
|
y12r = x1r + x3i;
|
|
y12i = x1i - x3r;
|
|
x0r = a[2] + a[18];
|
|
x0i = a[3] + a[19];
|
|
x1r = a[2] - a[18];
|
|
x1i = a[3] - a[19];
|
|
x2r = a[10] + a[26];
|
|
x2i = a[11] + a[27];
|
|
x3r = a[10] - a[26];
|
|
x3i = a[11] - a[27];
|
|
y1r = x0r + x2r;
|
|
y1i = x0i + x2i;
|
|
y5r = x0r - x2r;
|
|
y5i = x0i - x2i;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
y9r = wk1r * x0r - wk1i * x0i;
|
|
y9i = wk1r * x0i + wk1i * x0r;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
y13r = wk1i * x0r - wk1r * x0i;
|
|
y13i = wk1i * x0i + wk1r * x0r;
|
|
x0r = a[4] + a[20];
|
|
x0i = a[5] + a[21];
|
|
x1r = a[4] - a[20];
|
|
x1i = a[5] - a[21];
|
|
x2r = a[12] + a[28];
|
|
x2i = a[13] + a[29];
|
|
x3r = a[12] - a[28];
|
|
x3i = a[13] - a[29];
|
|
y2r = x0r + x2r;
|
|
y2i = x0i + x2i;
|
|
y6r = x0r - x2r;
|
|
y6i = x0i - x2i;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
y10r = wn4r * (x0r - x0i);
|
|
y10i = wn4r * (x0i + x0r);
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
y14r = wn4r * (x0r + x0i);
|
|
y14i = wn4r * (x0i - x0r);
|
|
x0r = a[6] + a[22];
|
|
x0i = a[7] + a[23];
|
|
x1r = a[6] - a[22];
|
|
x1i = a[7] - a[23];
|
|
x2r = a[14] + a[30];
|
|
x2i = a[15] + a[31];
|
|
x3r = a[14] - a[30];
|
|
x3i = a[15] - a[31];
|
|
y3r = x0r + x2r;
|
|
y3i = x0i + x2i;
|
|
y7r = x0r - x2r;
|
|
y7i = x0i - x2i;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
y11r = wk1i * x0r - wk1r * x0i;
|
|
y11i = wk1i * x0i + wk1r * x0r;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
y15r = wk1r * x0r - wk1i * x0i;
|
|
y15i = wk1r * x0i + wk1i * x0r;
|
|
x0r = y12r - y14r;
|
|
x0i = y12i - y14i;
|
|
x1r = y12r + y14r;
|
|
x1i = y12i + y14i;
|
|
x2r = y13r - y15r;
|
|
x2i = y13i - y15i;
|
|
x3r = y13r + y15r;
|
|
x3i = y13i + y15i;
|
|
a[24] = x0r + x2r;
|
|
a[25] = x0i + x2i;
|
|
a[26] = x0r - x2r;
|
|
a[27] = x0i - x2i;
|
|
a[28] = x1r - x3i;
|
|
a[29] = x1i + x3r;
|
|
a[30] = x1r + x3i;
|
|
a[31] = x1i - x3r;
|
|
x0r = y8r + y10r;
|
|
x0i = y8i + y10i;
|
|
x1r = y8r - y10r;
|
|
x1i = y8i - y10i;
|
|
x2r = y9r + y11r;
|
|
x2i = y9i + y11i;
|
|
x3r = y9r - y11r;
|
|
x3i = y9i - y11i;
|
|
a[16] = x0r + x2r;
|
|
a[17] = x0i + x2i;
|
|
a[18] = x0r - x2r;
|
|
a[19] = x0i - x2i;
|
|
a[20] = x1r - x3i;
|
|
a[21] = x1i + x3r;
|
|
a[22] = x1r + x3i;
|
|
a[23] = x1i - x3r;
|
|
x0r = y5r - y7i;
|
|
x0i = y5i + y7r;
|
|
x2r = wn4r * (x0r - x0i);
|
|
x2i = wn4r * (x0i + x0r);
|
|
x0r = y5r + y7i;
|
|
x0i = y5i - y7r;
|
|
x3r = wn4r * (x0r - x0i);
|
|
x3i = wn4r * (x0i + x0r);
|
|
x0r = y4r - y6i;
|
|
x0i = y4i + y6r;
|
|
x1r = y4r + y6i;
|
|
x1i = y4i - y6r;
|
|
a[8] = x0r + x2r;
|
|
a[9] = x0i + x2i;
|
|
a[10] = x0r - x2r;
|
|
a[11] = x0i - x2i;
|
|
a[12] = x1r - x3i;
|
|
a[13] = x1i + x3r;
|
|
a[14] = x1r + x3i;
|
|
a[15] = x1i - x3r;
|
|
x0r = y0r + y2r;
|
|
x0i = y0i + y2i;
|
|
x1r = y0r - y2r;
|
|
x1i = y0i - y2i;
|
|
x2r = y1r + y3r;
|
|
x2i = y1i + y3i;
|
|
x3r = y1r - y3r;
|
|
x3i = y1i - y3i;
|
|
a[0] = x0r + x2r;
|
|
a[1] = x0i + x2i;
|
|
a[2] = x0r - x2r;
|
|
a[3] = x0i - x2i;
|
|
a[4] = x1r - x3i;
|
|
a[5] = x1i + x3r;
|
|
a[6] = x1r + x3i;
|
|
a[7] = x1i - x3r;
|
|
}
|
|
|
|
void cftf162(double *a) {
|
|
double wn4r, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i, x0r, x0i, x1r, x1i, x2r, x2i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i,
|
|
y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i, y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;
|
|
|
|
wn4r = WR5000;
|
|
wk1r = WR1250;
|
|
wk1i = WI1250;
|
|
wk2r = WR2500;
|
|
wk2i = WI2500;
|
|
wk3r = WR3750;
|
|
wk3i = WI3750;
|
|
x1r = a[0] - a[17];
|
|
x1i = a[1] + a[16];
|
|
x0r = a[8] - a[25];
|
|
x0i = a[9] + a[24];
|
|
x2r = wn4r * (x0r - x0i);
|
|
x2i = wn4r * (x0i + x0r);
|
|
y0r = x1r + x2r;
|
|
y0i = x1i + x2i;
|
|
y4r = x1r - x2r;
|
|
y4i = x1i - x2i;
|
|
x1r = a[0] + a[17];
|
|
x1i = a[1] - a[16];
|
|
x0r = a[8] + a[25];
|
|
x0i = a[9] - a[24];
|
|
x2r = wn4r * (x0r - x0i);
|
|
x2i = wn4r * (x0i + x0r);
|
|
y8r = x1r - x2i;
|
|
y8i = x1i + x2r;
|
|
y12r = x1r + x2i;
|
|
y12i = x1i - x2r;
|
|
x0r = a[2] - a[19];
|
|
x0i = a[3] + a[18];
|
|
x1r = wk1r * x0r - wk1i * x0i;
|
|
x1i = wk1r * x0i + wk1i * x0r;
|
|
x0r = a[10] - a[27];
|
|
x0i = a[11] + a[26];
|
|
x2r = wk3i * x0r - wk3r * x0i;
|
|
x2i = wk3i * x0i + wk3r * x0r;
|
|
y1r = x1r + x2r;
|
|
y1i = x1i + x2i;
|
|
y5r = x1r - x2r;
|
|
y5i = x1i - x2i;
|
|
x0r = a[2] + a[19];
|
|
x0i = a[3] - a[18];
|
|
x1r = wk3r * x0r - wk3i * x0i;
|
|
x1i = wk3r * x0i + wk3i * x0r;
|
|
x0r = a[10] + a[27];
|
|
x0i = a[11] - a[26];
|
|
x2r = wk1r * x0r + wk1i * x0i;
|
|
x2i = wk1r * x0i - wk1i * x0r;
|
|
y9r = x1r - x2r;
|
|
y9i = x1i - x2i;
|
|
y13r = x1r + x2r;
|
|
y13i = x1i + x2i;
|
|
x0r = a[4] - a[21];
|
|
x0i = a[5] + a[20];
|
|
x1r = wk2r * x0r - wk2i * x0i;
|
|
x1i = wk2r * x0i + wk2i * x0r;
|
|
x0r = a[12] - a[29];
|
|
x0i = a[13] + a[28];
|
|
x2r = wk2i * x0r - wk2r * x0i;
|
|
x2i = wk2i * x0i + wk2r * x0r;
|
|
y2r = x1r + x2r;
|
|
y2i = x1i + x2i;
|
|
y6r = x1r - x2r;
|
|
y6i = x1i - x2i;
|
|
x0r = a[4] + a[21];
|
|
x0i = a[5] - a[20];
|
|
x1r = wk2i * x0r - wk2r * x0i;
|
|
x1i = wk2i * x0i + wk2r * x0r;
|
|
x0r = a[12] + a[29];
|
|
x0i = a[13] - a[28];
|
|
x2r = wk2r * x0r - wk2i * x0i;
|
|
x2i = wk2r * x0i + wk2i * x0r;
|
|
y10r = x1r - x2r;
|
|
y10i = x1i - x2i;
|
|
y14r = x1r + x2r;
|
|
y14i = x1i + x2i;
|
|
x0r = a[6] - a[23];
|
|
x0i = a[7] + a[22];
|
|
x1r = wk3r * x0r - wk3i * x0i;
|
|
x1i = wk3r * x0i + wk3i * x0r;
|
|
x0r = a[14] - a[31];
|
|
x0i = a[15] + a[30];
|
|
x2r = wk1i * x0r - wk1r * x0i;
|
|
x2i = wk1i * x0i + wk1r * x0r;
|
|
y3r = x1r + x2r;
|
|
y3i = x1i + x2i;
|
|
y7r = x1r - x2r;
|
|
y7i = x1i - x2i;
|
|
x0r = a[6] + a[23];
|
|
x0i = a[7] - a[22];
|
|
x1r = wk1i * x0r + wk1r * x0i;
|
|
x1i = wk1i * x0i - wk1r * x0r;
|
|
x0r = a[14] + a[31];
|
|
x0i = a[15] - a[30];
|
|
x2r = wk3i * x0r - wk3r * x0i;
|
|
x2i = wk3i * x0i + wk3r * x0r;
|
|
y11r = x1r + x2r;
|
|
y11i = x1i + x2i;
|
|
y15r = x1r - x2r;
|
|
y15i = x1i - x2i;
|
|
x1r = y0r + y2r;
|
|
x1i = y0i + y2i;
|
|
x2r = y1r + y3r;
|
|
x2i = y1i + y3i;
|
|
a[0] = x1r + x2r;
|
|
a[1] = x1i + x2i;
|
|
a[2] = x1r - x2r;
|
|
a[3] = x1i - x2i;
|
|
x1r = y0r - y2r;
|
|
x1i = y0i - y2i;
|
|
x2r = y1r - y3r;
|
|
x2i = y1i - y3i;
|
|
a[4] = x1r - x2i;
|
|
a[5] = x1i + x2r;
|
|
a[6] = x1r + x2i;
|
|
a[7] = x1i - x2r;
|
|
x1r = y4r - y6i;
|
|
x1i = y4i + y6r;
|
|
x0r = y5r - y7i;
|
|
x0i = y5i + y7r;
|
|
x2r = wn4r * (x0r - x0i);
|
|
x2i = wn4r * (x0i + x0r);
|
|
a[8] = x1r + x2r;
|
|
a[9] = x1i + x2i;
|
|
a[10] = x1r - x2r;
|
|
a[11] = x1i - x2i;
|
|
x1r = y4r + y6i;
|
|
x1i = y4i - y6r;
|
|
x0r = y5r + y7i;
|
|
x0i = y5i - y7r;
|
|
x2r = wn4r * (x0r - x0i);
|
|
x2i = wn4r * (x0i + x0r);
|
|
a[12] = x1r - x2i;
|
|
a[13] = x1i + x2r;
|
|
a[14] = x1r + x2i;
|
|
a[15] = x1i - x2r;
|
|
x1r = y8r + y10r;
|
|
x1i = y8i + y10i;
|
|
x2r = y9r - y11r;
|
|
x2i = y9i - y11i;
|
|
a[16] = x1r + x2r;
|
|
a[17] = x1i + x2i;
|
|
a[18] = x1r - x2r;
|
|
a[19] = x1i - x2i;
|
|
x1r = y8r - y10r;
|
|
x1i = y8i - y10i;
|
|
x2r = y9r + y11r;
|
|
x2i = y9i + y11i;
|
|
a[20] = x1r - x2i;
|
|
a[21] = x1i + x2r;
|
|
a[22] = x1r + x2i;
|
|
a[23] = x1i - x2r;
|
|
x1r = y12r - y14i;
|
|
x1i = y12i + y14r;
|
|
x0r = y13r + y15i;
|
|
x0i = y13i - y15r;
|
|
x2r = wn4r * (x0r - x0i);
|
|
x2i = wn4r * (x0i + x0r);
|
|
a[24] = x1r + x2r;
|
|
a[25] = x1i + x2i;
|
|
a[26] = x1r - x2r;
|
|
a[27] = x1i - x2i;
|
|
x1r = y12r + y14i;
|
|
x1i = y12i - y14r;
|
|
x0r = y13r - y15i;
|
|
x0i = y13i + y15r;
|
|
x2r = wn4r * (x0r - x0i);
|
|
x2i = wn4r * (x0i + x0r);
|
|
a[28] = x1r - x2i;
|
|
a[29] = x1i + x2r;
|
|
a[30] = x1r + x2i;
|
|
a[31] = x1i - x2r;
|
|
}
|
|
|
|
void cftf081(double *a) {
|
|
double wn4r, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;
|
|
|
|
wn4r = WR5000;
|
|
x0r = a[0] + a[8];
|
|
x0i = a[1] + a[9];
|
|
x1r = a[0] - a[8];
|
|
x1i = a[1] - a[9];
|
|
x2r = a[4] + a[12];
|
|
x2i = a[5] + a[13];
|
|
x3r = a[4] - a[12];
|
|
x3i = a[5] - a[13];
|
|
y0r = x0r + x2r;
|
|
y0i = x0i + x2i;
|
|
y2r = x0r - x2r;
|
|
y2i = x0i - x2i;
|
|
y1r = x1r - x3i;
|
|
y1i = x1i + x3r;
|
|
y3r = x1r + x3i;
|
|
y3i = x1i - x3r;
|
|
x0r = a[2] + a[10];
|
|
x0i = a[3] + a[11];
|
|
x1r = a[2] - a[10];
|
|
x1i = a[3] - a[11];
|
|
x2r = a[6] + a[14];
|
|
x2i = a[7] + a[15];
|
|
x3r = a[6] - a[14];
|
|
x3i = a[7] - a[15];
|
|
y4r = x0r + x2r;
|
|
y4i = x0i + x2i;
|
|
y6r = x0r - x2r;
|
|
y6i = x0i - x2i;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
x2r = x1r + x3i;
|
|
x2i = x1i - x3r;
|
|
y5r = wn4r * (x0r - x0i);
|
|
y5i = wn4r * (x0r + x0i);
|
|
y7r = wn4r * (x2r - x2i);
|
|
y7i = wn4r * (x2r + x2i);
|
|
a[8] = y1r + y5r;
|
|
a[9] = y1i + y5i;
|
|
a[10] = y1r - y5r;
|
|
a[11] = y1i - y5i;
|
|
a[12] = y3r - y7i;
|
|
a[13] = y3i + y7r;
|
|
a[14] = y3r + y7i;
|
|
a[15] = y3i - y7r;
|
|
a[0] = y0r + y4r;
|
|
a[1] = y0i + y4i;
|
|
a[2] = y0r - y4r;
|
|
a[3] = y0i - y4i;
|
|
a[4] = y2r - y6i;
|
|
a[5] = y2i + y6r;
|
|
a[6] = y2r + y6i;
|
|
a[7] = y2i - y6r;
|
|
}
|
|
|
|
void cftf082(double *a) {
|
|
double wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;
|
|
|
|
wn4r = WR5000;
|
|
wk1r = WR2500;
|
|
wk1i = WI2500;
|
|
y0r = a[0] - a[9];
|
|
y0i = a[1] + a[8];
|
|
y1r = a[0] + a[9];
|
|
y1i = a[1] - a[8];
|
|
x0r = a[4] - a[13];
|
|
x0i = a[5] + a[12];
|
|
y2r = wn4r * (x0r - x0i);
|
|
y2i = wn4r * (x0i + x0r);
|
|
x0r = a[4] + a[13];
|
|
x0i = a[5] - a[12];
|
|
y3r = wn4r * (x0r - x0i);
|
|
y3i = wn4r * (x0i + x0r);
|
|
x0r = a[2] - a[11];
|
|
x0i = a[3] + a[10];
|
|
y4r = wk1r * x0r - wk1i * x0i;
|
|
y4i = wk1r * x0i + wk1i * x0r;
|
|
x0r = a[2] + a[11];
|
|
x0i = a[3] - a[10];
|
|
y5r = wk1i * x0r - wk1r * x0i;
|
|
y5i = wk1i * x0i + wk1r * x0r;
|
|
x0r = a[6] - a[15];
|
|
x0i = a[7] + a[14];
|
|
y6r = wk1i * x0r - wk1r * x0i;
|
|
y6i = wk1i * x0i + wk1r * x0r;
|
|
x0r = a[6] + a[15];
|
|
x0i = a[7] - a[14];
|
|
y7r = wk1r * x0r - wk1i * x0i;
|
|
y7i = wk1r * x0i + wk1i * x0r;
|
|
x0r = y0r + y2r;
|
|
x0i = y0i + y2i;
|
|
x1r = y4r + y6r;
|
|
x1i = y4i + y6i;
|
|
a[0] = x0r + x1r;
|
|
a[1] = x0i + x1i;
|
|
a[2] = x0r - x1r;
|
|
a[3] = x0i - x1i;
|
|
x0r = y0r - y2r;
|
|
x0i = y0i - y2i;
|
|
x1r = y4r - y6r;
|
|
x1i = y4i - y6i;
|
|
a[4] = x0r - x1i;
|
|
a[5] = x0i + x1r;
|
|
a[6] = x0r + x1i;
|
|
a[7] = x0i - x1r;
|
|
x0r = y1r - y3i;
|
|
x0i = y1i + y3r;
|
|
x1r = y5r - y7r;
|
|
x1i = y5i - y7i;
|
|
a[8] = x0r + x1r;
|
|
a[9] = x0i + x1i;
|
|
a[10] = x0r - x1r;
|
|
a[11] = x0i - x1i;
|
|
x0r = y1r + y3i;
|
|
x0i = y1i - y3r;
|
|
x1r = y5r + y7r;
|
|
x1i = y5i + y7i;
|
|
a[12] = x0r - x1i;
|
|
a[13] = x0i + x1r;
|
|
a[14] = x0r + x1i;
|
|
a[15] = x0i - x1r;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
void rftfsub(int n, double *a) {
|
|
int i, i0, j, k;
|
|
double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi;
|
|
|
|
ec = 2 * M_PI_2 / n;
|
|
wkr = 0;
|
|
wki = 0;
|
|
wdi = cos(ec);
|
|
wdr = sin(ec);
|
|
wdi *= wdr;
|
|
wdr *= wdr;
|
|
w1r = 1 - 2 * wdr;
|
|
w1i = 2 * wdi;
|
|
ss = 2 * w1i;
|
|
i = n >> 1;
|
|
for (;;) {
|
|
i0 = i - 4 * RDFT_LOOP_DIV;
|
|
if (i0 < 4) {
|
|
i0 = 4;
|
|
}
|
|
for (j = i - 4; j >= i0; j -= 4) {
|
|
k = n - j;
|
|
xr = a[j + 2] - a[k - 2];
|
|
xi = a[j + 3] + a[k - 1];
|
|
yr = wdr * xr - wdi * xi;
|
|
yi = wdr * xi + wdi * xr;
|
|
a[j + 2] -= yr;
|
|
a[j + 3] -= yi;
|
|
a[k - 2] += yr;
|
|
a[k - 1] -= yi;
|
|
wkr += ss * wdi;
|
|
wki += ss * (0.5 - wdr);
|
|
xr = a[j] - a[k];
|
|
xi = a[j + 1] + a[k + 1];
|
|
yr = wkr * xr - wki * xi;
|
|
yi = wkr * xi + wki * xr;
|
|
a[j] -= yr;
|
|
a[j + 1] -= yi;
|
|
a[k] += yr;
|
|
a[k + 1] -= yi;
|
|
wdr += ss * wki;
|
|
wdi += ss * (0.5 - wkr);
|
|
}
|
|
if (i0 == 4) {
|
|
break;
|
|
}
|
|
wkr = 0.5 * sin(ec * i0);
|
|
wki = 0.5 * cos(ec * i0);
|
|
wdr = 0.5 - (wkr * w1r - wki * w1i);
|
|
wdi = wkr * w1i + wki * w1r;
|
|
wkr = 0.5 - wkr;
|
|
i = i0;
|
|
}
|
|
xr = a[2] - a[n - 2];
|
|
xi = a[3] + a[n - 1];
|
|
yr = wdr * xr - wdi * xi;
|
|
yi = wdr * xi + wdi * xr;
|
|
a[2] -= yr;
|
|
a[3] -= yi;
|
|
a[n - 2] += yr;
|
|
a[n - 1] -= yi;
|
|
}
|
|
|
|
void rftbsub(int n, double *a) {
|
|
int i, i0, j, k;
|
|
double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi;
|
|
|
|
ec = 2 * M_PI_2 / n;
|
|
wkr = 0;
|
|
wki = 0;
|
|
wdi = cos(ec);
|
|
wdr = sin(ec);
|
|
wdi *= wdr;
|
|
wdr *= wdr;
|
|
w1r = 1 - 2 * wdr;
|
|
w1i = 2 * wdi;
|
|
ss = 2 * w1i;
|
|
i = n >> 1;
|
|
for (;;) {
|
|
i0 = i - 4 * RDFT_LOOP_DIV;
|
|
if (i0 < 4) {
|
|
i0 = 4;
|
|
}
|
|
for (j = i - 4; j >= i0; j -= 4) {
|
|
k = n - j;
|
|
xr = a[j + 2] - a[k - 2];
|
|
xi = a[j + 3] + a[k - 1];
|
|
yr = wdr * xr + wdi * xi;
|
|
yi = wdr * xi - wdi * xr;
|
|
a[j + 2] -= yr;
|
|
a[j + 3] -= yi;
|
|
a[k - 2] += yr;
|
|
a[k - 1] -= yi;
|
|
wkr += ss * wdi;
|
|
wki += ss * (0.5 - wdr);
|
|
xr = a[j] - a[k];
|
|
xi = a[j + 1] + a[k + 1];
|
|
yr = wkr * xr + wki * xi;
|
|
yi = wkr * xi - wki * xr;
|
|
a[j] -= yr;
|
|
a[j + 1] -= yi;
|
|
a[k] += yr;
|
|
a[k + 1] -= yi;
|
|
wdr += ss * wki;
|
|
wdi += ss * (0.5 - wkr);
|
|
}
|
|
if (i0 == 4) {
|
|
break;
|
|
}
|
|
wkr = 0.5 * sin(ec * i0);
|
|
wki = 0.5 * cos(ec * i0);
|
|
wdr = 0.5 - (wkr * w1r - wki * w1i);
|
|
wdi = wkr * w1i + wki * w1r;
|
|
wkr = 0.5 - wkr;
|
|
i = i0;
|
|
}
|
|
xr = a[2] - a[n - 2];
|
|
xi = a[3] + a[n - 1];
|
|
yr = wdr * xr + wdi * xi;
|
|
yi = wdr * xi - wdi * xr;
|
|
a[2] -= yr;
|
|
a[3] -= yi;
|
|
a[n - 2] += yr;
|
|
a[n - 1] -= yi;
|
|
}
|
|
|
|
void dctsub(int n, double *a) {
|
|
int i, i0, j, k, m;
|
|
double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi;
|
|
|
|
ec = M_PI_2 / n;
|
|
wkr = 0.5;
|
|
wki = 0.5;
|
|
w1r = cos(ec);
|
|
w1i = sin(ec);
|
|
wdr = 0.5 * (w1r - w1i);
|
|
wdi = 0.5 * (w1r + w1i);
|
|
ss = 2 * w1i;
|
|
m = n >> 1;
|
|
i = 0;
|
|
for (;;) {
|
|
i0 = i + 2 * DCST_LOOP_DIV;
|
|
if (i0 > m - 2) {
|
|
i0 = m - 2;
|
|
}
|
|
for (j = i + 2; j <= i0; j += 2) {
|
|
k = n - j;
|
|
xr = wdi * a[j - 1] - wdr * a[k + 1];
|
|
xi = wdr * a[j - 1] + wdi * a[k + 1];
|
|
wkr -= ss * wdi;
|
|
wki += ss * wdr;
|
|
yr = wki * a[j] - wkr * a[k];
|
|
yi = wkr * a[j] + wki * a[k];
|
|
wdr -= ss * wki;
|
|
wdi += ss * wkr;
|
|
a[k + 1] = xr;
|
|
a[k] = yr;
|
|
a[j - 1] = xi;
|
|
a[j] = yi;
|
|
}
|
|
if (i0 == m - 2) {
|
|
break;
|
|
}
|
|
wdr = cos(ec * i0);
|
|
wdi = sin(ec * i0);
|
|
wkr = 0.5 * (wdr - wdi);
|
|
wki = 0.5 * (wdr + wdi);
|
|
wdr = wkr * w1r - wki * w1i;
|
|
wdi = wkr * w1i + wki * w1r;
|
|
i = i0;
|
|
}
|
|
xr = wdi * a[m - 1] - wdr * a[m + 1];
|
|
a[m - 1] = wdr * a[m - 1] + wdi * a[m + 1];
|
|
a[m + 1] = xr;
|
|
a[m] *= wki + ss * wdr;
|
|
}
|
|
|
|
void dstsub(int n, double *a) {
|
|
int i, i0, j, k, m;
|
|
double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi;
|
|
|
|
ec = M_PI_2 / n;
|
|
wkr = 0.5;
|
|
wki = 0.5;
|
|
w1r = cos(ec);
|
|
w1i = sin(ec);
|
|
wdr = 0.5 * (w1r - w1i);
|
|
wdi = 0.5 * (w1r + w1i);
|
|
ss = 2 * w1i;
|
|
m = n >> 1;
|
|
i = 0;
|
|
for (;;) {
|
|
i0 = i + 2 * DCST_LOOP_DIV;
|
|
if (i0 > m - 2) {
|
|
i0 = m - 2;
|
|
}
|
|
for (j = i + 2; j <= i0; j += 2) {
|
|
k = n - j;
|
|
xr = wdi * a[k + 1] - wdr * a[j - 1];
|
|
xi = wdr * a[k + 1] + wdi * a[j - 1];
|
|
wkr -= ss * wdi;
|
|
wki += ss * wdr;
|
|
yr = wki * a[k] - wkr * a[j];
|
|
yi = wkr * a[k] + wki * a[j];
|
|
wdr -= ss * wki;
|
|
wdi += ss * wkr;
|
|
a[j - 1] = xr;
|
|
a[j] = yr;
|
|
a[k + 1] = xi;
|
|
a[k] = yi;
|
|
}
|
|
if (i0 == m - 2) {
|
|
break;
|
|
}
|
|
wdr = cos(ec * i0);
|
|
wdi = sin(ec * i0);
|
|
wkr = 0.5 * (wdr - wdi);
|
|
wki = 0.5 * (wdr + wdi);
|
|
wdr = wkr * w1r - wki * w1i;
|
|
wdi = wkr * w1i + wki * w1r;
|
|
i = i0;
|
|
}
|
|
xr = wdi * a[m + 1] - wdr * a[m - 1];
|
|
a[m + 1] = wdr * a[m + 1] + wdi * a[m - 1];
|
|
a[m - 1] = xr;
|
|
a[m] *= wki + ss * wdr;
|
|
}
|
|
|
|
void dctsub4(int n, double *a) {
|
|
int m;
|
|
double wki, wdr, wdi, xr;
|
|
|
|
wki = WR5000;
|
|
m = n >> 1;
|
|
if (m == 2) {
|
|
wdr = wki * WI2500;
|
|
wdi = wki * WR2500;
|
|
xr = wdi * a[1] - wdr * a[3];
|
|
a[1] = wdr * a[1] + wdi * a[3];
|
|
a[3] = xr;
|
|
}
|
|
a[m] *= wki;
|
|
}
|
|
|
|
void dstsub4(int n, double *a) {
|
|
int m;
|
|
double wki, wdr, wdi, xr;
|
|
|
|
wki = WR5000;
|
|
m = n >> 1;
|
|
if (m == 2) {
|
|
wdr = wki * WI2500;
|
|
wdi = wki * WR2500;
|
|
xr = wdi * a[3] - wdr * a[1];
|
|
a[3] = wdr * a[3] + wdi * a[1];
|
|
a[1] = xr;
|
|
}
|
|
a[m] *= wki;
|
|
}
|