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@ -1,6 +1,7 @@
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#include <math.h>
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#include <stdio.h>
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#include <time.h>
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#include "chunk_array.h"
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/*fast fourier transform */
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/* THE COOLEY-TUKEY FAST FOURIER TRANSFORM */
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@ -90,7 +91,7 @@
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/* PROGRAM MODIFIED FROM A SUBROUTINE OF BRENNER */
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/* 10-06-2000, MLR */
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void fourt(double* datar, double* datai, int nn[3], int ndim, int ifrwd, int icplx, double* workr, double* worki, int cores) {
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void fourt(chunk_array_t* datar, chunk_array_t* datai, int nn[3], int ndim, int ifrwd, int icplx, double* workr, double* worki, int cores) {
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int ifact[21], ntot, idim, np1, n, np2, m, ntwo, iff, idiv, iquot, irem, inon2, non2p, np0, nprev, icase, ifmin, i, j, jmax, np2hf, i2, i1max, i3, j3, i1, ifp1, ifp2, i2max, i1rng, istep, imin, imax, mmax, mmin, mstep, j1, j2max, j2, jmin, j3max, nhalf;
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double theta, wstpr, wstpi, wminr, wmini, wr, wi, wtemp, thetm, wmstr, wmsti, twowr, sr, si, oldsr, oldsi, stmpr, stmpi, tempr, tempi, difi, difr, sumr, sumi, TWOPI = 6.283185307179586476925286766559;
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@ -99,6 +100,9 @@ void fourt(double* datar, double* datai, int nn[3], int ndim, int ifrwd, int icp
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ntot *= nn[idim];
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}
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chunk_array_read(datar);
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chunk_array_read(datai);
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/*main loop for each dimension*/
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np1 = 1;
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for (idim = 1; idim <= ndim; idim++) {
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@ -184,8 +188,11 @@ void fourt(double* datar, double* datai, int nn[3], int ndim, int ifrwd, int icp
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ntot /= 2;
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i = 1;
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for (j = 1; j <= ntot; j++) {
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datar[j] = datar[i];
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datai[j] = datar[i + 1];
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double valuei, valuei1;
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chunk_array_get(datar, i, &valuei);
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chunk_array_get(datar, i+1, &valuei1);
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chunk_array_save(datar, j, valuei);
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chunk_array_save(datai, j, valuei1);
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i += 2;
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}
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@ -202,12 +209,20 @@ void fourt(double* datar, double* datai, int nn[3], int ndim, int ifrwd, int icp
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for (i1 = i2; i1 <= i1max; i1++) {
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for (i3 = i1; i3 <= ntot; i3 += np2) {
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j3 = j + i3 - i2;
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tempr = datar[i3];
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tempi = datai[i3];
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datar[i3] = datar[j3];
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datai[i3] = datai[j3];
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datar[j3] = tempr;
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datai[j3] = tempi;
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double valueri3, valueii3, valuerj3, valueij3;
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chunk_array_get(datar, i3, &valueri3);
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chunk_array_get(datai, i3, &valueii3);
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chunk_array_get(datar, j3, &valuerj3);
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chunk_array_get(datai, j3, &valueij3);
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tempr = valueri3;
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tempi = valueii3;
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chunk_array_save(datar, i3, valuerj3);
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chunk_array_save(datai, i3, valueij3);
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chunk_array_save(datar, j3, tempr);
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chunk_array_save(datai, j3, tempi);
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}
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}
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@ -232,11 +247,14 @@ void fourt(double* datar, double* datai, int nn[3], int ndim, int ifrwd, int icp
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for (i3 = i1; i3 <= ntot; i3 += np2) {
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j = i3;
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for (i = 1; i <= n; i++) {
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double valuerj, valueij;
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chunk_array_get(datar, j, &valuerj);
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chunk_array_get(datai, j, &valueij);
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if (icase != 3) {
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workr[i] = datar[j];
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worki[i] = datai[j];
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workr[i] = valuerj;
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worki[i] = valueij;
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} else {
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workr[i] = datar[j];
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workr[i] = valuerj;
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worki[i] = 0.;
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}
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ifp2 = np2;
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@ -255,8 +273,8 @@ void fourt(double* datar, double* datai, int nn[3], int ndim, int ifrwd, int icp
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i2max = i3 + np2 - np1;
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i = 1;
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for (i2 = i3; i2 <= i2max; i2 += np1) {
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datar[i2] = workr[i];
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datai[i2] = worki[i];
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chunk_save(datar, i2, workr[i]);
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chunk_save(datai, i2, worki[i]);
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i++;
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}
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}
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@ -277,12 +295,16 @@ void fourt(double* datar, double* datai, int nn[3], int ndim, int ifrwd, int icp
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L310:
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j = i1;
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for (i = imin; i <= ntot; i += istep) {
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tempr = datar[i];
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tempi = datai[i];
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datar[i] = datar[j] - tempr;
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datai[i] = datai[j] - tempi;
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datar[j] = datar[j] + tempr;
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datai[j] = datai[j] + tempi;
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chunk_array_get(datar, i, &tempr);
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chunk_array_get(datai, i, &tempi);
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double valuerj, valueij;
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chunk_array_get(datar, j, &valuerj);
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chunk_array_get(datai, j, &valueij);
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chunk_array_save(datar, i, valuerj - tempr);
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chunk_array_save(datai, i, valueij - tempi);
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chunk_array_save(datar, j, valuerj + tempr);
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chunk_array_save(datai, j, valueij + tempi);
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j += istep;
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}
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imin = 2 * imin - i1;
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@ -301,16 +323,26 @@ void fourt(double* datar, double* datai, int nn[3], int ndim, int ifrwd, int icp
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j = imin - istep / 2;
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for (i = imin; i <= ntot; i += istep) {
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if (ifrwd != 0) {
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tempr = datai[i];
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tempi = -datar[i];
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chunk_array_get(datai, i, &tempr);
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chunk_array_get(datar, i, &tempi);
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tempi = -tempi;
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} else {
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tempr = -datai[i];
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tempi = datar[i];
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chunk_array_get(datai, i, &tempr);
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chunk_array_get(datar, i, &tempi);
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}
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datar[i] = datar[j] - tempr;
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datai[i] = datai[j] - tempi;
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datar[j] += tempr;
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datai[j] += tempi;
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double valuerj, valueij;
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chunk_array_get(datar, j, &valuerj);
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chunk_array_get(datai, j, &valueij);
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chunk_array_save(datar, i, valuerj - tempr);
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chunk_array_save(datai, i, valueij - tempi);
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chunk_array_get(datar, j, &valuerj);
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chunk_array_get(datai, j, &valueij);
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chunk_array_save(datar, j, valuerj + tempr);
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chunk_array_save(datai, j, valueij + tempi);
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j += istep;
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}
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@ -347,12 +379,18 @@ void fourt(double* datar, double* datai, int nn[3], int ndim, int ifrwd, int icp
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L510:
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j = imin - istep / 2;
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for (i = imin; i <= ntot; i += istep) {
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tempr = datar[i] * wr - datai[i] * wi;
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tempi = datar[i] * wi + datai[i] * wr;
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datar[i] = datar[j] - tempr;
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datai[i] = datai[j] - tempi;
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datar[j] += tempr;
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datai[j] += tempi;
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double valueri, valueii, valuerj, valueij;
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chunk_array_get(datar, i, &valueri);
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chunk_array_get(datar, j, &valuerj);
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chunk_array_get(datai, i, &valueii);
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chunk_array_get(datai, j, &valueij);
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tempr = valueri * wr - valueii * wi;
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tempi = valueri * wi + valueii * wr;
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chunk_data_save(datar, i, valuerj - tempr);
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chunk_data_save(datai, i, valueij - tempi);
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chunk_data_save(datar, j, valuerj + tempr);
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chunk_data_save(datai, j, valueij + tempi);
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j += istep;
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}
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imin = 2 * imin - i1;
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@ -405,23 +443,27 @@ void fourt(double* datar, double* datai, int nn[3], int ndim, int ifrwd, int icp
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j3max = j2 + np2 - ifp2;
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for (j3 = j2; j3 <= j3max; j3 += ifp2) {
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j = jmin + ifp2 - ifp1;
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sr = datar[j];
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si = datai[j];
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chunk_array_get(datar, j, &sr);
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chunk_array_get(datai, j, &si);
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oldsr = 0.;
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oldsi = 0.;
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j -= ifp1;
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L620:
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stmpr = sr;
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stmpi = si;
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sr = twowr * sr - oldsr + datar[j];
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si = twowr * si - oldsi + datai[j];
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double valuerj, valueij;
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chunk_array_get(datar, j, &valuerj);
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chunk_array_get(datai, j, &valueij);
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sr = twowr * sr - oldsr + valuerj;
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si = twowr * si - oldsi + valueij;
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oldsr = stmpr;
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oldsi = stmpi;
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j -= ifp1;
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if (j > jmin)
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goto L620;
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workr[i] = wr * sr - wi * si - oldsr + datar[j];
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worki[i] = wi * sr + wr * si - oldsi + datai[j];
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workr[i] = wr * sr - wi * si - oldsr + valuerj;
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worki[i] = wi * sr + wr * si - oldsi + valueij;
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jmin += ifp2;
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i++;
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}
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@ -433,8 +475,8 @@ void fourt(double* datar, double* datai, int nn[3], int ndim, int ifrwd, int icp
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for (j2 = i3; j2 <= j2max; j2 += ifp1) {
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j3max = j2 + np2 - ifp2;
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for (j3 = j2; j3 <= j3max; j3 += ifp2) {
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datar[j3] = workr[i];
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datai[j3] = worki[i];
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chunk_array_save(datar, j3, workr[i]);
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chunk_array_save(datai, j3, worki[i]);
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i++;
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}
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}
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@ -478,16 +520,22 @@ void fourt(double* datar, double* datai, int nn[3], int ndim, int ifrwd, int icp
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L710:
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j = jmin;
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for (i = imin; i <= ntot; i += np2) {
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sumr = (datar[i] + datar[j]) / 2.;
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sumi = (datai[i] + datai[j]) / 2.;
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difr = (datar[i] - datar[j]) / 2.;
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difi = (datai[i] - datai[j]) / 2.;
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double valueri, valueii, valuerj, valueij;
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chunk_array_get(datar, i, &valueri);
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chunk_array_get(datai, i, &valueii);
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chunk_array_get(datar, j, &valuerj);
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chunk_array_get(datai, j, &valueij);
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sumr = (valueri + valuerj) / 2.;
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sumi = (valueii + valueij) / 2.;
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difr = (valueri - valuerj) / 2.;
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difi = (valueii - valueij) / 2.;
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tempr = wr * sumi + wi * difr;
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tempi = wi * sumi - wr * difr;
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datar[i] = sumr + tempr;
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datai[i] = difi + tempi;
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datar[j] = sumr - tempr;
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datai[j] = tempi - difi;
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chunk_data_save(datar, i, sumr + tempr);
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chunk_data_save(datai, i, difi + tempi);
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chunk_data_save(datar, j, sumr - tempr);
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chunk_data_save(datai, j, tempi - difi);
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j += np2;
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}
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imin++;
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@ -504,7 +552,9 @@ void fourt(double* datar, double* datai, int nn[3], int ndim, int ifrwd, int icp
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if (ifrwd == 0)
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goto L740;
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for (i = imin; i <= ntot; i += np2) {
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datai[i] = -datai[i];
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double valueii;
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chunk_data_get(datai, i, &valueii);
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chunk_data_save(datai, i, -valueii);
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}
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L740:
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np2 *= 2;
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@ -515,36 +565,56 @@ void fourt(double* datar, double* datai, int nn[3], int ndim, int ifrwd, int icp
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imin = imax - nhalf;
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i = imin;
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goto L755;
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L750:
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datar[j] = datar[i];
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datai[j] = -datai[i];
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L750: ;
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|
|
|
double valueri, valueii;
|
|
|
|
|
chunk_data_get(datar, i, &valueri);
|
|
|
|
|
chunk_data_get(datai, i, &valueii);
|
|
|
|
|
chunk_data_save(datar, j, valueri);
|
|
|
|
|
chunk_data_save(datai, j, -valueii);
|
|
|
|
|
L755:
|
|
|
|
|
i++;
|
|
|
|
|
j--;
|
|
|
|
|
if (i < imax)
|
|
|
|
|
goto L750;
|
|
|
|
|
datar[j] = datar[imin] - datai[imin];
|
|
|
|
|
datai[j] = 0.;
|
|
|
|
|
double valuerimin, valueiimin;
|
|
|
|
|
chunk_data_get(datar, imin, &valuerimin);
|
|
|
|
|
chunk_data_get(datai, imin, &valueiimin);
|
|
|
|
|
|
|
|
|
|
chunk_data_save(datar, j, valuerimin - valueiimin);
|
|
|
|
|
chunk_data_save(datai, j, 0.);
|
|
|
|
|
if (i >= j) {
|
|
|
|
|
goto L780;
|
|
|
|
|
} else {
|
|
|
|
|
goto L770;
|
|
|
|
|
}
|
|
|
|
|
L765:
|
|
|
|
|
datar[j] = datar[i];
|
|
|
|
|
datai[j] = datai[i];
|
|
|
|
|
chunk_data_get(datar, i, &valueri);
|
|
|
|
|
chunk_data_get(datai, i, &valueii);
|
|
|
|
|
|
|
|
|
|
chunk_data_save(datar, j, valueri);
|
|
|
|
|
chunk_data_save(datai, j, valueii);
|
|
|
|
|
L770:
|
|
|
|
|
i--;
|
|
|
|
|
j--;
|
|
|
|
|
if (i > imin)
|
|
|
|
|
goto L765;
|
|
|
|
|
datar[j] = datar[imin] + datai[imin];
|
|
|
|
|
datai[j] = 0.;
|
|
|
|
|
|
|
|
|
|
chunk_data_get(datar, imin, &valuerimin);
|
|
|
|
|
chunk_data_get(datai, imin, &valueiimin);
|
|
|
|
|
|
|
|
|
|
chunk_data_save(datar, j, valuerimin + valueiimin);
|
|
|
|
|
chunk_data_save(datai, j, 0.);
|
|
|
|
|
|
|
|
|
|
imax = imin;
|
|
|
|
|
goto L745;
|
|
|
|
|
L780:
|
|
|
|
|
datar[1] += datai[1];
|
|
|
|
|
datai[1] = 0.;
|
|
|
|
|
L780: ;
|
|
|
|
|
double valuei1, valuer1;
|
|
|
|
|
chunk_data_get(datai, 1, &valuei1);
|
|
|
|
|
chunk_data_get(datar, 1, &valuer1);
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
chunk_data_save(datar, 1, valuei1 + valuer1);
|
|
|
|
|
chunk_data_save(datai, 1, 0.);
|
|
|
|
|
goto L900;
|
|
|
|
|
|
|
|
|
|
/*complete a real transform for the 2nd, 3rd, ... dimension by conjugate symmetries*/
|
|
|
|
@ -562,15 +632,24 @@ void fourt(double* datar, double* datai, int nn[3], int ndim, int ifrwd, int icp
|
|
|
|
|
if (idim > 2) {
|
|
|
|
|
j = jmax + np0;
|
|
|
|
|
for (i = imin; i <= imax; i++) {
|
|
|
|
|
datar[i] = datar[j];
|
|
|
|
|
datai[i] = -datai[j];
|
|
|
|
|
double valuerj, valueij;
|
|
|
|
|
chunk_data_get(datar, j, &valuerj);
|
|
|
|
|
chunk_data_get(datai, j, &valueij);
|
|
|
|
|
|
|
|
|
|
chunk_data_save(datar, i, valuerj);
|
|
|
|
|
chunk_data_save(datai, i, -valueij);
|
|
|
|
|
j--;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
j = jmax;
|
|
|
|
|
for (i = imin; i <= imax; i += np0) {
|
|
|
|
|
datar[i] = datar[j];
|
|
|
|
|
datai[i] = -datai[j];
|
|
|
|
|
double valuerj, valueij;
|
|
|
|
|
chunk_data_get(datar, j, &valuerj);
|
|
|
|
|
chunk_data_get(datai, j, &valueij);
|
|
|
|
|
|
|
|
|
|
chunk_data_save(datar, i, valuerj);
|
|
|
|
|
chunk_data_save(datai, i, -valueij);
|
|
|
|
|
|
|
|
|
|
j -= np0;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|