[llvm-commits] [test-suite] r44223 - /test-suite/trunk/SingleSource/Benchmarks/Misc/oourafft.c
Anton Korobeynikov
asl at math.spbu.ru
Sun Nov 18 16:33:48 PST 2007
Author: asl
Date: Sun Nov 18 18:33:47 2007
New Revision: 44223
URL: http://llvm.org/viewvc/llvm-project?rev=44223&view=rev
Log:
Add new number-crunching code. LLVM seems to be 20% slower on it compared to gcc.
Added:
test-suite/trunk/SingleSource/Benchmarks/Misc/oourafft.c
Added: test-suite/trunk/SingleSource/Benchmarks/Misc/oourafft.c
URL: http://llvm.org/viewvc/llvm-project/test-suite/trunk/SingleSource/Benchmarks/Misc/oourafft.c?rev=44223&view=auto
==============================================================================
--- test-suite/trunk/SingleSource/Benchmarks/Misc/oourafft.c (added)
+++ test-suite/trunk/SingleSource/Benchmarks/Misc/oourafft.c Sun Nov 18 18:33:47 2007
@@ -0,0 +1,747 @@
+#include <math.h>
+#include <malloc.h>
+#include <memory.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+/* random number generator, 0 <= RND < 1 */
+#define RND(p) ((*(p) = (*(p) * 7141 + 54773) % 259200) * (1.0 / 259200.0))
+#define MAX(x,y) ((x) > (y) ? (x) : (y))
+
+void makewt(int nw, int *ip, double *w);
+void cdft(int, int, double *, int *, double *);
+void putdata(int nini, int nend, double *a);
+double errorcheck(int nini, int nend, double scale, double *a);
+
+double get_time(void);
+
+#define N 1024
+#ifdef SMALL_PROBLEM_SIZE
+#define TRIES 15000
+#else
+#define TRIES 150000
+#endif
+
+int main()
+{
+ int i, j;
+ int *ip;
+ double *ref, *cmp, *src, *w;
+ double t_start, t_end, t_overhead, t_total = 0, err_val;
+
+ /* Measure overhead of get_time() call */
+ t_start = get_time();
+ t_end = get_time();
+ t_overhead = t_end - t_start;
+
+ /* Prepare aux data */
+ ip = memalign(16, sqrt(N)*sizeof(int));
+ w = memalign(16, 2*N*5/4*sizeof(double));
+ makewt(N >> 1, ip, w);
+
+ /* Allocate buffers */
+ ref = memalign(16, 2*N*sizeof(double));
+ cmp = memalign(16, 2*N*sizeof(double));
+ src = memalign(16, 2*N*sizeof(double));
+
+ /* Perform sanity check of FFT */
+ putdata(0, 2*N - 1, ref);
+ cdft(2*N, 1, ref, ip, w);
+ cdft(2*N, -1, ref, ip, w);
+ err_val = errorcheck(0, 2*N - 1, 1.0/N, ref);
+ if (fabs(err_val) > 1e-10) {
+ printf("FFT sanity check failed! Difference is: %le\n", err_val);
+ abort();
+ }
+
+ /* Prepare reference sequence */
+ memset(ref, 0, 2*N*sizeof(double));
+ putdata(0, N-1, ref);
+ cdft(2*N, 1, ref, ip, w);
+ for (j=0; j<N; ++j)
+ ref[2*j+1] = -ref[2*j+1];
+
+ /*printf("Doing %d correlations (%d FFTs of size %d)\n", TRIES, 2*TRIES, N);*/
+ memset(src, 0, 2*N*sizeof(double));
+ putdata(0, N-1, src);
+
+ t_start = get_time();
+ for (i=0; i<TRIES; ++i) {
+ int k;
+
+ memcpy(cmp, src, 2*N*sizeof(double));
+ cdft(2*N, 1, cmp, ip, w);
+
+ for (k=0; k<N; ++k) {
+ double re1 = cmp[2*k];
+ double re2 = ref[2*k];
+ double im1 = cmp[2*k+1];
+ double im2 = ref[2*k+1];
+ cmp[2*k] = re1*re2 - im1*im2;
+ cmp[2*k+1] = re1*im2 + im1*re2;
+ }
+
+ cdft(2*N, -1, cmp, ip, w);
+ }
+ t_end = get_time();
+ t_total += t_end - t_start - t_overhead;
+
+ for (j=0; j<N; ++j) {
+ printf("%e %e\n",
+ (fabs(cmp[2*j]) > 1e-9 ? cmp[2*j] : 0),
+ (fabs(cmp[2*j+1]) > 1e-9 ? cmp[2*j+1] : 0));
+ }
+ /*printf("Overall time: %le, for single correlation: %le\n", t_total, t_total/TRIES);*/
+
+ free(ref);
+ free(w);
+ free(ip);
+
+ free(cmp);
+ free(src);
+
+ return 0;
+}
+
+void putdata(int nini, int nend, double *a)
+{
+ int j, seed = 0;
+
+ for (j = nini; j <= nend; j++)
+ a[j] = RND(&seed);
+}
+
+double errorcheck(int nini, int nend, double scale, double *a)
+{
+ int j, seed = 0;
+ double err = 0, e;
+
+ for (j = nini; j <= nend; j++) {
+ e = RND(&seed) - a[j] * scale;
+ err = MAX(err, fabs(e));
+ }
+ return err;
+}
+
+#ifdef WIN32
+#include <windows.h>
+
+static LARGE_INTEGER t = {0, 0};
+
+double get_time(void)
+{
+ LARGE_INTEGER l;
+ if (t.QuadPart == 0)
+ QueryPerformanceFrequency(&t);
+ QueryPerformanceCounter(&l);
+ return (double)l.QuadPart / (double)t.QuadPart;
+}
+
+#else
+#include <sys/time.h>
+
+double get_time(void)
+{
+ struct timeval tv;
+
+ gettimeofday(&tv, NULL);
+ return (double)tv.tv_sec + (double)tv.tv_usec * 0.000001;
+}
+
+#endif
+
+void makewt(int nw, int *ip, double *w);
+static void bitrv2(int n, int *ip, double *a);
+static void bitrv2conj(int n, int *ip, double *a);
+static void cftfsub(int n, double *a, double *w);
+static void cftbsub(int n, double *a, double *w);
+static inline void cft1st(int n, double *a, double *w);
+static inline void cftmdl(int n, int l, double *a, double *w);
+
+void cdft(int n, int isgn, double *a, int *ip, double *w)
+{
+ if (n > 4) {
+ if (isgn >= 0) {
+ bitrv2(n, ip, a);
+ cftfsub(n, a, w);
+ } else {
+ bitrv2conj(n, ip, a);
+ cftbsub(n, a, w);
+ }
+ } else if (n == 4) {
+ cftfsub(n, a, w);
+ }
+}
+
+/* -------- initializing routines -------- */
+
+#include <math.h>
+
+void makewt(int nw, int *ip, double *w)
+{
+ int j, nwh;
+ double delta, x, y;
+
+ if (nw > 2) {
+ nwh = nw >> 1;
+ delta = atan(1.0) / nwh;
+ w[0] = 1;
+ w[1] = 0;
+ w[nwh] = cos(delta * nwh);
+ w[nwh + 1] = w[nwh];
+ if (nwh > 2) {
+ for (j = 2; j < nwh; j += 2) {
+ x = cos(delta * j);
+ y = sin(delta * j);
+ w[j] = x;
+ w[j + 1] = y;
+ w[nw - j] = y;
+ w[nw - j + 1] = x;
+ }
+ bitrv2(nw, ip, w);
+ }
+ }
+}
+
+/* -------- child routines -------- */
+
+void bitrv2(int n, int *ip, double *a)
+{
+ int j, j1, k, k1, l, m, m2;
+ double xr, xi, yr, yi;
+
+ ip[0] = 0;
+ l = n;
+ m = 1;
+ while ((m << 3) < l) {
+ l >>= 1;
+ for (j = 0; j < m; j++) {
+ ip[m + j] = ip[j] + l;
+ }
+ m <<= 1;
+ }
+ m2 = 2 * m;
+ if ((m << 3) == l) {
+ for (k = 0; k < m; k++) {
+ for (j = 0; j < k; j++) {
+ j1 = 2 * j + ip[k];
+ k1 = 2 * k + ip[j];
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += 2 * m2;
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 -= m2;
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += 2 * m2;
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ }
+ j1 = 2 * k + m2 + ip[k];
+ k1 = j1 + m2;
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ }
+ } else {
+ for (k = 1; k < m; k++) {
+ for (j = 0; j < k; j++) {
+ j1 = 2 * j + ip[k];
+ k1 = 2 * k + ip[j];
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += m2;
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ }
+ }
+ }
+}
+
+
+static void bitrv2conj(int n, int *ip, double *a)
+{
+ int j, j1, k, k1, l, m, m2;
+ double xr, xi, yr, yi;
+
+ ip[0] = 0;
+ l = n;
+ m = 1;
+ while ((m << 3) < l) {
+ l >>= 1;
+ for (j = 0; j < m; j++) {
+ ip[m + j] = ip[j] + l;
+ }
+ m <<= 1;
+ }
+ m2 = 2 * m;
+ if ((m << 3) == l) {
+ for (k = 0; k < m; k++) {
+ for (j = 0; j < k; j++) {
+ j1 = 2 * j + ip[k];
+ k1 = 2 * k + ip[j];
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += 2 * m2;
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 -= m2;
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += 2 * m2;
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ }
+ k1 = 2 * k + ip[k];
+ a[k1 + 1] = -a[k1 + 1];
+ j1 = k1 + m2;
+ k1 = j1 + m2;
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ k1 += m2;
+ a[k1 + 1] = -a[k1 + 1];
+ }
+ } else {
+ a[1] = -a[1];
+ a[m2 + 1] = -a[m2 + 1];
+ for (k = 1; k < m; k++) {
+ for (j = 0; j < k; j++) {
+ j1 = 2 * j + ip[k];
+ k1 = 2 * k + ip[j];
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += m2;
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ }
+ k1 = 2 * k + ip[k];
+ a[k1 + 1] = -a[k1 + 1];
+ a[k1 + m2 + 1] = -a[k1 + m2 + 1];
+ }
+ }
+}
+
+
+void cftfsub(int n, double *a, double *w)
+{
+ int j, j1, j2, j3, l;
+ double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
+
+ l = 2;
+ if (n > 8) {
+ cft1st(n, a, w);
+ l = 8;
+ while ((l << 2) < n) {
+ cftmdl(n, l, a, w);
+ l <<= 2;
+ }
+ }
+ if ((l << 2) == n) {
+ for (j = 0; j < l; j += 2) {
+ j1 = j + l;
+ j2 = j1 + l;
+ j3 = j2 + l;
+ x0r = a[j] + a[j1];
+ x0i = a[j + 1] + a[j1 + 1];
+ x1r = a[j] - a[j1];
+ x1i = a[j + 1] - a[j1 + 1];
+ x2r = a[j2] + a[j3];
+ x2i = a[j2 + 1] + a[j3 + 1];
+ x3r = a[j2] - a[j3];
+ x3i = a[j2 + 1] - a[j3 + 1];
+ a[j] = x0r + x2r;
+ a[j + 1] = x0i + x2i;
+ a[j2] = x0r - x2r;
+ a[j2 + 1] = x0i - x2i;
+ a[j1] = x1r - x3i;
+ a[j1 + 1] = x1i + x3r;
+ a[j3] = x1r + x3i;
+ a[j3 + 1] = x1i - x3r;
+ }
+ } else {
+ for (j = 0; j < l; j += 2) {
+ j1 = j + l;
+ x0r = a[j] - a[j1];
+ x0i = a[j + 1] - a[j1 + 1];
+ a[j] += a[j1];
+ a[j + 1] += a[j1 + 1];
+ a[j1] = x0r;
+ a[j1 + 1] = x0i;
+ }
+ }
+}
+
+
+void cftbsub(int n, double *a, double *w)
+{
+ int j, j1, j2, j3, l;
+ double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
+
+ l = 2;
+ if (n > 8) {
+ cft1st(n, a, w);
+ l = 8;
+ while ((l << 2) < n) {
+ cftmdl(n, l, a, w);
+ l <<= 2;
+ }
+ }
+ if ((l << 2) == n) {
+ for (j = 0; j < l; j += 2) {
+ j1 = j + l;
+ j2 = j1 + l;
+ j3 = j2 + l;
+ x0r = a[j] + a[j1];
+ x0i = -a[j + 1] - a[j1 + 1];
+ x1r = a[j] - a[j1];
+ x1i = -a[j + 1] + a[j1 + 1];
+ x2r = a[j2] + a[j3];
+ x2i = a[j2 + 1] + a[j3 + 1];
+ x3r = a[j2] - a[j3];
+ x3i = a[j2 + 1] - a[j3 + 1];
+ a[j] = x0r + x2r;
+ a[j + 1] = x0i - x2i;
+ a[j2] = x0r - x2r;
+ a[j2 + 1] = x0i + x2i;
+ a[j1] = x1r - x3i;
+ a[j1 + 1] = x1i - x3r;
+ a[j3] = x1r + x3i;
+ a[j3 + 1] = x1i + x3r;
+ }
+ } else {
+ for (j = 0; j < l; j += 2) {
+ j1 = j + l;
+ x0r = a[j] - a[j1];
+ x0i = -a[j + 1] + a[j1 + 1];
+ a[j] += a[j1];
+ a[j + 1] = -a[j + 1] - a[j1 + 1];
+ a[j1] = x0r;
+ a[j1 + 1] = x0i;
+ }
+ }
+}
+
+
+void cft1st(int n, double *a, double *w)
+{
+ int j, k1, k2;
+ double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
+ double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
+
+ x0r = a[0] + a[2];
+ x0i = a[1] + a[3];
+ x1r = a[0] - a[2];
+ x1i = a[1] - a[3];
+ x2r = a[4] + a[6];
+ x2i = a[5] + a[7];
+ x3r = a[4] - a[6];
+ x3i = a[5] - a[7];
+ a[0] = x0r + x2r;
+ a[1] = x0i + x2i;
+ a[4] = x0r - x2r;
+ a[5] = x0i - x2i;
+ a[2] = x1r - x3i;
+ a[3] = x1i + x3r;
+ a[6] = x1r + x3i;
+ a[7] = x1i - x3r;
+ wk1r = w[2];
+ x0r = a[8] + a[10];
+ x0i = a[9] + a[11];
+ x1r = a[8] - a[10];
+ x1i = a[9] - a[11];
+ x2r = a[12] + a[14];
+ x2i = a[13] + a[15];
+ x3r = a[12] - a[14];
+ x3i = a[13] - a[15];
+ a[8] = x0r + x2r;
+ a[9] = x0i + x2i;
+ a[12] = x2i - x0i;
+ a[13] = x0r - x2r;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[10] = wk1r * (x0r - x0i);
+ a[11] = wk1r * (x0r + x0i);
+ x0r = x3i + x1r;
+ x0i = x3r - x1i;
+ a[14] = wk1r * (x0i - x0r);
+ a[15] = wk1r * (x0i + x0r);
+ k1 = 0;
+ for (j = 16; j < n; j += 16) {
+ k1 += 2;
+ k2 = 2 * k1;
+ wk2r = w[k1];
+ wk2i = w[k1 + 1];
+ wk1r = w[k2];
+ wk1i = w[k2 + 1];
+ wk3r = wk1r - 2 * wk2i * wk1i;
+ wk3i = 2 * wk2i * wk1r - wk1i;
+ x0r = a[j] + a[j + 2];
+ x0i = a[j + 1] + a[j + 3];
+ x1r = a[j] - a[j + 2];
+ x1i = a[j + 1] - a[j + 3];
+ x2r = a[j + 4] + a[j + 6];
+ x2i = a[j + 5] + a[j + 7];
+ x3r = a[j + 4] - a[j + 6];
+ x3i = a[j + 5] - a[j + 7];
+ a[j] = x0r + x2r;
+ a[j + 1] = x0i + x2i;
+ x0r -= x2r;
+ x0i -= x2i;
+ a[j + 4] = wk2r * x0r - wk2i * x0i;
+ a[j + 5] = wk2r * x0i + wk2i * x0r;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[j + 2] = wk1r * x0r - wk1i * x0i;
+ a[j + 3] = wk1r * x0i + wk1i * x0r;
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j + 6] = wk3r * x0r - wk3i * x0i;
+ a[j + 7] = wk3r * x0i + wk3i * x0r;
+ wk1r = w[k2 + 2];
+ wk1i = w[k2 + 3];
+ wk3r = wk1r - 2 * wk2r * wk1i;
+ wk3i = 2 * wk2r * wk1r - wk1i;
+ x0r = a[j + 8] + a[j + 10];
+ x0i = a[j + 9] + a[j + 11];
+ x1r = a[j + 8] - a[j + 10];
+ x1i = a[j + 9] - a[j + 11];
+ x2r = a[j + 12] + a[j + 14];
+ x2i = a[j + 13] + a[j + 15];
+ x3r = a[j + 12] - a[j + 14];
+ x3i = a[j + 13] - a[j + 15];
+ a[j + 8] = x0r + x2r;
+ a[j + 9] = x0i + x2i;
+ x0r -= x2r;
+ x0i -= x2i;
+ a[j + 12] = -wk2i * x0r - wk2r * x0i;
+ a[j + 13] = -wk2i * x0i + wk2r * x0r;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[j + 10] = wk1r * x0r - wk1i * x0i;
+ a[j + 11] = wk1r * x0i + wk1i * x0r;
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j + 14] = wk3r * x0r - wk3i * x0i;
+ a[j + 15] = wk3r * x0i + wk3i * x0r;
+ }
+}
+
+
+void cftmdl(int n, int l, double *a, double *w)
+{
+ int j, j1, j2, j3, k, k1, k2, m, m2;
+ double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
+ double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
+
+ m = l << 2;
+ for (j = 0; j < l; j += 2) {
+ j1 = j + l;
+ j2 = j1 + l;
+ j3 = j2 + l;
+ x0r = a[j] + a[j1];
+ x0i = a[j + 1] + a[j1 + 1];
+ x1r = a[j] - a[j1];
+ x1i = a[j + 1] - a[j1 + 1];
+ x2r = a[j2] + a[j3];
+ x2i = a[j2 + 1] + a[j3 + 1];
+ x3r = a[j2] - a[j3];
+ x3i = a[j2 + 1] - a[j3 + 1];
+ a[j] = x0r + x2r;
+ a[j + 1] = x0i + x2i;
+ a[j2] = x0r - x2r;
+ a[j2 + 1] = x0i - x2i;
+ a[j1] = x1r - x3i;
+ a[j1 + 1] = x1i + x3r;
+ a[j3] = x1r + x3i;
+ a[j3 + 1] = x1i - x3r;
+ }
+ wk1r = w[2];
+ for (j = m; j < l + m; j += 2) {
+ j1 = j + l;
+ j2 = j1 + l;
+ j3 = j2 + l;
+ x0r = a[j] + a[j1];
+ x0i = a[j + 1] + a[j1 + 1];
+ x1r = a[j] - a[j1];
+ x1i = a[j + 1] - a[j1 + 1];
+ x2r = a[j2] + a[j3];
+ x2i = a[j2 + 1] + a[j3 + 1];
+ x3r = a[j2] - a[j3];
+ x3i = a[j2 + 1] - a[j3 + 1];
+ a[j] = x0r + x2r;
+ a[j + 1] = x0i + x2i;
+ a[j2] = x2i - x0i;
+ a[j2 + 1] = x0r - x2r;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[j1] = wk1r * (x0r - x0i);
+ a[j1 + 1] = wk1r * (x0r + x0i);
+ x0r = x3i + x1r;
+ x0i = x3r - x1i;
+ a[j3] = wk1r * (x0i - x0r);
+ a[j3 + 1] = wk1r * (x0i + x0r);
+ }
+ k1 = 0;
+ m2 = 2 * m;
+ for (k = m2; k < n; k += m2) {
+ k1 += 2;
+ k2 = 2 * k1;
+ wk2r = w[k1];
+ wk2i = w[k1 + 1];
+ wk1r = w[k2];
+ wk1i = w[k2 + 1];
+ wk3r = wk1r - 2 * wk2i * wk1i;
+ wk3i = 2 * wk2i * wk1r - wk1i;
+ for (j = k; j < l + k; j += 2) {
+ j1 = j + l;
+ j2 = j1 + l;
+ j3 = j2 + l;
+ x0r = a[j] + a[j1];
+ x0i = a[j + 1] + a[j1 + 1];
+ x1r = a[j] - a[j1];
+ x1i = a[j + 1] - a[j1 + 1];
+ x2r = a[j2] + a[j3];
+ x2i = a[j2 + 1] + a[j3 + 1];
+ x3r = a[j2] - a[j3];
+ x3i = a[j2 + 1] - a[j3 + 1];
+ a[j] = x0r + x2r;
+ a[j + 1] = x0i + x2i;
+ x0r -= x2r;
+ x0i -= x2i;
+ a[j2] = wk2r * x0r - wk2i * x0i;
+ a[j2 + 1] = wk2r * x0i + wk2i * x0r;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[j1] = wk1r * x0r - wk1i * x0i;
+ a[j1 + 1] = wk1r * x0i + wk1i * x0r;
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j3] = wk3r * x0r - wk3i * x0i;
+ a[j3 + 1] = wk3r * x0i + wk3i * x0r;
+ }
+ wk1r = w[k2 + 2];
+ wk1i = w[k2 + 3];
+ wk3r = wk1r - 2 * wk2r * wk1i;
+ wk3i = 2 * wk2r * wk1r - wk1i;
+ for (j = k + m; j < l + (k + m); j += 2) {
+ j1 = j + l;
+ j2 = j1 + l;
+ j3 = j2 + l;
+ x0r = a[j] + a[j1];
+ x0i = a[j + 1] + a[j1 + 1];
+ x1r = a[j] - a[j1];
+ x1i = a[j + 1] - a[j1 + 1];
+ x2r = a[j2] + a[j3];
+ x2i = a[j2 + 1] + a[j3 + 1];
+ x3r = a[j2] - a[j3];
+ x3i = a[j2 + 1] - a[j3 + 1];
+ a[j] = x0r + x2r;
+ a[j + 1] = x0i + x2i;
+ x0r -= x2r;
+ x0i -= x2i;
+ a[j2] = -wk2i * x0r - wk2r * x0i;
+ a[j2 + 1] = -wk2i * x0i + wk2r * x0r;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[j1] = wk1r * x0r - wk1i * x0i;
+ a[j1 + 1] = wk1r * x0i + wk1i * x0r;
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j3] = wk3r * x0r - wk3i * x0i;
+ a[j3 + 1] = wk3r * x0i + wk3i * x0r;
+ }
+ }
+}
+
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