comparison src/fftw-3.3.5/libbench2/verify-lib.c @ 42:2cd0e3b3e1fd

Current fftw source

+/*
+ * Copyright (c) 2003, 2007-14 Matteo Frigo
+ * Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
+ *
+ */
+
+
+#include "verify.h"
+#include <math.h>
+#include <stdlib.h>
+#include <stdio.h>
+
+/*
+ * Utility functions:
+ */
+static double dabs(double x) { return (x < 0.0) ? -x : x; }
+static double dmin(double x, double y) { return (x < y) ? x : y; }
+static double norm2(double x, double y) { return dmax(dabs(x), dabs(y)); }
+
+double dmax(double x, double y) { return (x > y) ? x : y; }
+
+static double aerror(C *a, C *b, int n)
+{
+     if (n > 0) {
+	  /* compute the relative Linf error */
+	  double e = 0.0, mag = 0.0;
+	  int i;
+
+	  for (i = 0; i < n; ++i) {
+	       e = dmax(e, norm2(c_re(a[i]) - c_re(b[i]),
+				 c_im(a[i]) - c_im(b[i])));
+	       mag = dmax(mag, 
+			  dmin(norm2(c_re(a[i]), c_im(a[i])),
+			       norm2(c_re(b[i]), c_im(b[i]))));
+	  }
+	  e /= mag;
+
+#ifdef HAVE_ISNAN
+	  BENCH_ASSERT(!isnan(e));
+#endif
+	  return e;
+     } else
+	  return 0.0;
+}
+
+#ifdef HAVE_DRAND48
+#  if defined(HAVE_DECL_DRAND48) && !HAVE_DECL_DRAND48
+extern double drand48(void);
+#  endif
+double mydrand(void)
+{
+     return drand48() - 0.5;
+}
+#else
+double mydrand(void)
+{
+     double d = rand();
+     return (d / (double) RAND_MAX) - 0.5;
+}
+#endif
+
+void arand(C *a, int n)
+{
+     int i;
+
+     /* generate random inputs */
+     for (i = 0; i < n; ++i) {
+	  c_re(a[i]) = mydrand();
+	  c_im(a[i]) = mydrand();
+     }
+}
+
+/* make array real */
+void mkreal(C *A, int n)
+{
+     int i;
+
+     for (i = 0; i < n; ++i) {
+          c_im(A[i]) = 0.0;
+     }
+}
+
+static void assign_conj(C *Ac, C *A, int rank, const bench_iodim *dim, int stride)
+{
+     if (rank == 0) {
+          c_re(*Ac) = c_re(*A);
+          c_im(*Ac) = -c_im(*A);
+     }
+     else {
+          int i, n0 = dim[rank - 1].n, s = stride;
+          rank -= 1;
+	  stride *= n0;
+          assign_conj(Ac, A, rank, dim, stride);
+          for (i = 1; i < n0; ++i)
+               assign_conj(Ac + (n0 - i) * s, A + i * s, rank, dim, stride);
+     }
+}
+
+/* make array hermitian */
+void mkhermitian(C *A, int rank, const bench_iodim *dim, int stride)
+{
+     if (rank == 0)
+          c_im(*A) = 0.0;
+     else {
+          int i, n0 = dim[rank - 1].n, s = stride;
+          rank -= 1;
+	  stride *= n0;
+          mkhermitian(A, rank, dim, stride);
+          for (i = 1; 2*i < n0; ++i)
+               assign_conj(A + (n0 - i) * s, A + i * s, rank, dim, stride);
+          if (2*i == n0)
+               mkhermitian(A + i * s, rank, dim, stride);
+     }
+}
+
+void mkhermitian1(C *a, int n)
+{
+     bench_iodim d;
+
+     d.n = n;
+     d.is = d.os = 1;
+     mkhermitian(a, 1, &d, 1);
+}
+
+/* C = A */
+void acopy(C *c, C *a, int n)
+{
+     int i;
+
+     for (i = 0; i < n; ++i) {
+	  c_re(c[i]) = c_re(a[i]);
+	  c_im(c[i]) = c_im(a[i]);
+     }
+}
+
+/* C = A + B */
+void aadd(C *c, C *a, C *b, int n)
+{
+     int i;
+
+     for (i = 0; i < n; ++i) {
+	  c_re(c[i]) = c_re(a[i]) + c_re(b[i]);
+	  c_im(c[i]) = c_im(a[i]) + c_im(b[i]);
+     }
+}
+
+/* C = A - B */
+void asub(C *c, C *a, C *b, int n)
+{
+     int i;
+
+     for (i = 0; i < n; ++i) {
+	  c_re(c[i]) = c_re(a[i]) - c_re(b[i]);
+	  c_im(c[i]) = c_im(a[i]) - c_im(b[i]);
+     }
+}
+
+/* B = rotate left A (complex) */
+void arol(C *b, C *a, int n, int nb, int na)
+{
+     int i, ib, ia;
+
+     for (ib = 0; ib < nb; ++ib) {
+	  for (i = 0; i < n - 1; ++i)
+	       for (ia = 0; ia < na; ++ia) {
+		    C *pb = b + (ib * n + i) * na + ia;
+		    C *pa = a + (ib * n + i + 1) * na + ia;
+		    c_re(*pb) = c_re(*pa);
+		    c_im(*pb) = c_im(*pa);
+	       }
+
+	  for (ia = 0; ia < na; ++ia) {
+	       C *pb = b + (ib * n + n - 1) * na + ia;
+	       C *pa = a + ib * n * na + ia;
+	       c_re(*pb) = c_re(*pa);
+	       c_im(*pb) = c_im(*pa);
+	  }
+     }
+}
+
+void aphase_shift(C *b, C *a, int n, int nb, int na, double sign)
+{
+     int j, jb, ja;
+     trigreal twopin;
+     twopin = K2PI / n;
+
+     for (jb = 0; jb < nb; ++jb)
+	  for (j = 0; j < n; ++j) {
+	       trigreal s = sign * SIN(j * twopin);
+	       trigreal c = COS(j * twopin);
+
+	       for (ja = 0; ja < na; ++ja) {
+		    int k = (jb * n + j) * na + ja;
+		    c_re(b[k]) = c_re(a[k]) * c - c_im(a[k]) * s;
+		    c_im(b[k]) = c_re(a[k]) * s + c_im(a[k]) * c;
+	       }
+	  }
+}
+
+/* A = alpha * A  (complex, in place) */
+void ascale(C *a, C alpha, int n)
+{
+     int i;
+
+     for (i = 0; i < n; ++i) {
+	  R xr = c_re(a[i]), xi = c_im(a[i]);
+	  c_re(a[i]) = xr * c_re(alpha) - xi * c_im(alpha);
+	  c_im(a[i]) = xr * c_im(alpha) + xi * c_re(alpha);
+     }
+}
+
+
+double acmp(C *a, C *b, int n, const char *test, double tol)
+{
+     double d = aerror(a, b, n);
+     if (d > tol) {
+	  ovtpvt_err("Found relative error %e (%s)\n", d, test);
+
+	  {
+	       int i, N;
+	       N = n > 300 && verbose <= 2 ? 300 : n;
+	       for (i = 0; i < N; ++i) 
+		    ovtpvt_err("%8d %16.12f %16.12f   %16.12f %16.12f\n", i, 
+			       (double) c_re(a[i]), (double) c_im(a[i]),
+			       (double) c_re(b[i]), (double) c_im(b[i]));
+	  }
+
+	  bench_exit(EXIT_FAILURE);
+     }
+     return d;
+}
+
+
+/*
+ * Implementation of the FFT tester described in
+ *
+ * Funda Ergün. Testing multivariate linear functions: Overcoming the
+ * generator bottleneck. In Proceedings of the Twenty-Seventh Annual
+ * ACM Symposium on the Theory of Computing, pages 407-416, Las Vegas,
+ * Nevada, 29 May--1 June 1995.
+ *
+ * Also: F. Ergun, S. R. Kumar, and D. Sivakumar, "Self-testing without
+ * the generator bottleneck," SIAM J. on Computing 29 (5), 1630-51 (2000).
+ */
+
+static double impulse0(dofft_closure *k,
+		       int n, int vecn, 
+		       C *inA, C *inB, C *inC,
+		       C *outA, C *outB, C *outC,
+		       C *tmp, int rounds, double tol)
+{
+     int N = n * vecn;
+     double e = 0.0;
+     int j;
+
+     k->apply(k, inA, tmp);
+     e = dmax(e, acmp(tmp, outA, N, "impulse 1", tol));
+
+     for (j = 0; j < rounds; ++j) {
+	  arand(inB, N);
+	  asub(inC, inA, inB, N);
+	  k->apply(k, inB, outB);
+	  k->apply(k, inC, outC);
+	  aadd(tmp, outB, outC, N);
+	  e = dmax(e, acmp(tmp, outA, N, "impulse", tol));
+     }
+     return e;
+}
+
+double impulse(dofft_closure *k,
+	       int n, int vecn, 
+	       C *inA, C *inB, C *inC,
+	       C *outA, C *outB, C *outC,
+	       C *tmp, int rounds, double tol)
+{
+     int i, j;
+     double e = 0.0;
+
+     /* check impulsive input */
+     for (i = 0; i < vecn; ++i) {
+	  R x = (sqrt(n)*(i+1)) / (double)(vecn+1);
+	  for (j = 0; j < n; ++j) {
+	       c_re(inA[j + i * n]) = 0;
+	       c_im(inA[j + i * n]) = 0;
+	       c_re(outA[j + i * n]) = x;
+	       c_im(outA[j + i * n]) = 0;
+	  }
+	  c_re(inA[i * n]) = x;
+	  c_im(inA[i * n]) = 0;
+     }
+
+     e = dmax(e, impulse0(k, n, vecn, inA, inB, inC, outA, outB, outC,
+			  tmp, rounds, tol));
+
+     /* check constant input */
+     for (i = 0; i < vecn; ++i) {
+	  R x = (i+1) / ((double)(vecn+1) * sqrt(n));
+	  for (j = 0; j < n; ++j) {
+	       c_re(inA[j + i * n]) = x;
+	       c_im(inA[j + i * n]) = 0;
+	       c_re(outA[j + i * n]) = 0;
+	       c_im(outA[j + i * n]) = 0;
+	  }
+	  c_re(outA[i * n]) = n * x;
+	  c_im(outA[i * n]) = 0;
+     }
+
+     e = dmax(e, impulse0(k, n, vecn, inA, inB, inC, outA, outB, outC,
+			  tmp, rounds, tol));
+     return e;
+}
+
+double linear(dofft_closure *k, int realp,
+	      int n, C *inA, C *inB, C *inC, C *outA,
+	      C *outB, C *outC, C *tmp, int rounds, double tol)
+{
+     int j;
+     double e = 0.0;
+
+     for (j = 0; j < rounds; ++j) {
+	  C alpha, beta;
+	  c_re(alpha) = mydrand();
+	  c_im(alpha) = realp ? 0.0 : mydrand();
+	  c_re(beta) = mydrand();
+	  c_im(beta) = realp ? 0.0 : mydrand();
+	  arand(inA, n);
+	  arand(inB, n);
+	  k->apply(k, inA, outA);
+	  k->apply(k, inB, outB);
+
+	  ascale(outA, alpha, n);
+	  ascale(outB, beta, n);
+	  aadd(tmp, outA, outB, n);
+	  ascale(inA, alpha, n);
+	  ascale(inB, beta, n);
+	  aadd(inC, inA, inB, n);
+	  k->apply(k, inC, outC);
+
+	  e = dmax(e, acmp(outC, tmp, n, "linear", tol));
+     }
+     return e;
+}
+
+
+
+double tf_shift(dofft_closure *k,
+		int realp, const bench_tensor *sz,
+		int n, int vecn, double sign,
+		C *inA, C *inB, C *outA, C *outB, C *tmp,
+		int rounds, double tol, int which_shift)
+{
+     int nb, na, dim, N = n * vecn;
+     int i, j;
+     double e = 0.0;
+
+     /* test 3: check the time-shift property */
+     /* the paper performs more tests, but this code should be fine too */
+
+     nb = 1;
+     na = n;
+
+     /* check shifts across all SZ dimensions */
+     for (dim = 0; dim < sz->rnk; ++dim) {
+	  int ncur = sz->dims[dim].n;
+
+	  na /= ncur;
+
+	  for (j = 0; j < rounds; ++j) {
+	       arand(inA, N);
+
+	       if (which_shift == TIME_SHIFT) {
+		    for (i = 0; i < vecn; ++i) {
+			 if (realp) mkreal(inA + i * n, n);
+			 arol(inB + i * n, inA + i * n, ncur, nb, na);
+		    }
+		    k->apply(k, inA, outA);
+		    k->apply(k, inB, outB);
+		    for (i = 0; i < vecn; ++i) 
+			 aphase_shift(tmp + i * n, outB + i * n, ncur, 
+				      nb, na, sign);
+		    e = dmax(e, acmp(tmp, outA, N, "time shift", tol));
+	       } else {
+		    for (i = 0; i < vecn; ++i) {
+			 if (realp) 
+			      mkhermitian(inA + i * n, sz->rnk, sz->dims, 1);
+			 aphase_shift(inB + i * n, inA + i * n, ncur,
+				      nb, na, -sign);
+		    }
+		    k->apply(k, inA, outA);
+		    k->apply(k, inB, outB);
+		    for (i = 0; i < vecn; ++i) 
+			 arol(tmp + i * n, outB + i * n, ncur, nb, na);
+		    e = dmax(e, acmp(tmp, outA, N, "freq shift", tol));
+	       }
+	  }
+
+	  nb *= ncur;
+     }
+     return e;
+}
+
+
+void preserves_input(dofft_closure *k, aconstrain constrain,
+		     int n, C *inA, C *inB, C *outB, int rounds)
+{
+     int j;
+     int recopy_input = k->recopy_input;
+
+     k->recopy_input = 1;
+     for (j = 0; j < rounds; ++j) {
+	  arand(inA, n);
+	  if (constrain)
+	       constrain(inA, n);
+	  
+	  acopy(inB, inA, n);
+	  k->apply(k, inB, outB);
+	  acmp(inB, inA, n, "preserves_input", 0.0);
+     }
+     k->recopy_input = recopy_input;
+}
+
+
+/* Make a copy of the size tensor, with the same dimensions, but with
+   the strides corresponding to a "packed" row-major array with the
+   given stride. */
+bench_tensor *verify_pack(const bench_tensor *sz, int s)
+{
+     bench_tensor *x = tensor_copy(sz);
+     if (BENCH_FINITE_RNK(x->rnk) && x->rnk > 0) {
+	  int i;
+	  x->dims[x->rnk - 1].is = s;
+	  x->dims[x->rnk - 1].os = s;
+	  for (i = x->rnk - 1; i > 0; --i) {
+	       x->dims[i - 1].is = x->dims[i].is * x->dims[i].n;
+	       x->dims[i - 1].os = x->dims[i].os * x->dims[i].n;
+	  }
+     }
+     return x;
+}
+
+static int all_zero(C *a, int n)
+{
+     int i;
+     for (i = 0; i < n; ++i)
+	  if (c_re(a[i]) != 0.0 || c_im(a[i]) != 0.0)
+	       return 0;
+     return 1;
+}
+
+static int one_accuracy_test(dofft_closure *k, aconstrain constrain,
+			     int sign, int n, C *a, C *b, 
+			     double t[6])
+{
+     double err[6];
+
+     if (constrain)
+	  constrain(a, n);
+     
+     if (all_zero(a, n))
+	  return 0;
+     
+     k->apply(k, a, b);
+     fftaccuracy(n, a, b, sign, err);
+     
+     t[0] += err[0];
+     t[1] += err[1] * err[1];
+     t[2] = dmax(t[2], err[2]);
+     t[3] += err[3];
+     t[4] += err[4] * err[4];
+     t[5] = dmax(t[5], err[5]);
+
+     return 1;
+}
+
+void accuracy_test(dofft_closure *k, aconstrain constrain,
+		   int sign, int n, C *a, C *b, int rounds, int impulse_rounds,
+		   double t[6])
+{
+     int r, i;
+     int ntests = 0;
+     bench_complex czero = {0, 0};
+
+     for (i = 0; i < 6; ++i) t[i] = 0.0;
+
+     for (r = 0; r < rounds; ++r) {
+	  arand(a, n);
+	  if (one_accuracy_test(k, constrain, sign, n, a, b, t))
+	       ++ntests;
+     }
+
+     /* impulses at beginning of array */
+     for (r = 0; r < impulse_rounds; ++r) {
+	  if (r > n - r - 1)
+	       continue;
+	  
+	  caset(a, n, czero);
+	  c_re(a[r]) = c_im(a[r]) = 1.0;
+	  
+	  if (one_accuracy_test(k, constrain, sign, n, a, b, t))
+	       ++ntests;
+     }
+     
+     /* impulses at end of array */
+     for (r = 0; r < impulse_rounds; ++r) {
+	  if (r <= n - r - 1)
+	       continue;
+	  
+	  caset(a, n, czero);
+	  c_re(a[n - r - 1]) = c_im(a[n - r - 1]) = 1.0;
+	  
+	  if (one_accuracy_test(k, constrain, sign, n, a, b, t))
+	       ++ntests;
+     }
+     
+     /* randomly-located impulses */
+     for (r = 0; r < impulse_rounds; ++r) {
+	  caset(a, n, czero);
+	  i = rand() % n;
+	  c_re(a[i]) = c_im(a[i]) = 1.0;
+	  
+	  if (one_accuracy_test(k, constrain, sign, n, a, b, t))
+	       ++ntests;
+     }
+
+     t[0] /= ntests;
+     t[1] = sqrt(t[1] / ntests);
+     t[3] /= ntests;
+     t[4] = sqrt(t[4] / ntests);
+
+     fftaccuracy_done();
+}