First commit - moving from LuaForge to SourceForge

1 files changed, 806 insertions, 0 deletions

diff --git a/src/fftw/fftwnd.c b/src/fftw/fftwnd.c
new file mode 100644
index 0000000..57354b0
--- /dev/null
+++ b/src/fftw/fftwnd.c
@@ -0,0 +1,806 @@
+/*
+ * Copyright (c) 1997-1999, 2003 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+ *
+ */
+
+/* $Id: fftwnd.c,v 1.1 2008/10/17 06:13:18 scuri Exp $ */
+
+#include "fftw-int.h"
+
+/* the number of buffers to use for buffered transforms: */
+#define FFTWND_NBUFFERS 8
+
+/* the default number of buffers to use: */
+#define FFTWND_DEFAULT_NBUFFERS 0
+
+/* the number of "padding" elements between consecutive buffer lines */
+#define FFTWND_BUFFER_PADDING 8
+
+static void destroy_plan_array(int rank, fftw_plan *plans);
+
+static void init_test_array(fftw_complex *arr, int stride, int n)
+{
+     int j;
+
+     for (j = 0; j < n; ++j) {
+	  c_re(arr[stride * j]) = 0.0;
+	  c_im(arr[stride * j]) = 0.0;
+     }
+}
+
+/*
+ * Same as fftw_measure_runtime, except for fftwnd plan.
+ */
+double fftwnd_measure_runtime(fftwnd_plan plan,
+			      fftw_complex *in, int istride,
+			      fftw_complex *out, int ostride)
+{
+     fftw_time begin, end, start;
+     double t, tmax, tmin;
+     int i, iter;
+     int n;
+     int repeat;
+
+     if (plan->rank == 0)
+	  return 0.0;
+
+     n = 1;
+     for (i = 0; i < plan->rank; ++i)
+	  n *= plan->n[i];
+
+     iter = 1;
+
+     for (;;) {
+	  tmin = 1.0E10;
+	  tmax = -1.0E10;
+	  init_test_array(in, istride, n);
+
+	  start = fftw_get_time();
+	  /* repeat the measurement FFTW_TIME_REPEAT times */
+	  for (repeat = 0; repeat < FFTW_TIME_REPEAT; ++repeat) {
+	       begin = fftw_get_time();
+	       for (i = 0; i < iter; ++i) {
+		    fftwnd(plan, 1, in, istride, 0, out, ostride, 0);
+	       }
+	       end = fftw_get_time();
+
+	       t = fftw_time_to_sec(fftw_time_diff(end, begin));
+	       if (t < tmin)
+		    tmin = t;
+	       if (t > tmax)
+		    tmax = t;
+
+	       /* do not run for too long */
+	       t = fftw_time_to_sec(fftw_time_diff(end, start));
+	       if (t > FFTW_TIME_LIMIT)
+		    break;
+	  }
+
+	  if (tmin >= FFTW_TIME_MIN)
+	       break;
+
+	  iter *= 2;
+     }
+
+     tmin /= (double) iter;
+     tmax /= (double) iter;
+
+     return tmin;
+}
+
+/********************** Initializing the FFTWND Plan ***********************/
+
+/* Initialize everything except for the 1D plans and the work array: */
+fftwnd_plan fftwnd_create_plan_aux(int rank, const int *n,
+				   fftw_direction dir, int flags)
+{
+     int i;
+     fftwnd_plan p;
+
+     if (rank < 0)
+	  return 0;
+
+     for (i = 0; i < rank; ++i)
+	  if (n[i] <= 0)
+	       return 0;
+
+     p = (fftwnd_plan) fftw_malloc(sizeof(fftwnd_data));
+     p->n = 0;
+     p->n_before = 0;
+     p->n_after = 0;
+     p->plans = 0;
+     p->work = 0;
+     p->dir = dir;
+
+     p->rank = rank;
+     p->is_in_place = flags & FFTW_IN_PLACE;
+
+     p->nwork = 0;
+     p->nbuffers = 0;
+
+     if (rank == 0)
+	  return 0;
+
+     p->n = (int *) fftw_malloc(sizeof(int) * rank);
+     p->n_before = (int *) fftw_malloc(sizeof(int) * rank);
+     p->n_after = (int *) fftw_malloc(sizeof(int) * rank);
+     p->n_before[0] = 1;
+     p->n_after[rank - 1] = 1;
+
+     for (i = 0; i < rank; ++i) {
+	  p->n[i] = n[i];
+
+	  if (i) {
+	       p->n_before[i] = p->n_before[i - 1] * n[i - 1];
+	       p->n_after[rank - 1 - i] = p->n_after[rank - i] * n[rank - i];
+	  }
+     }
+
+     return p;
+}
+
+/* create an empty new array of rank 1d plans */
+fftw_plan *fftwnd_new_plan_array(int rank)
+{
+     fftw_plan *plans;
+     int i;
+
+     plans = (fftw_plan *) fftw_malloc(rank * sizeof(fftw_plan));
+     if (!plans)
+	  return 0;
+     for (i = 0; i < rank; ++i)
+	  plans[i] = 0;
+     return plans;
+}
+
+/* 
+ * create an array of plans using the ordinary 1d fftw_create_plan,
+ * which allocates its own array and creates plans optimized for
+ * contiguous data. 
+ */
+fftw_plan *fftwnd_create_plans_generic(fftw_plan *plans,
+				       int rank, const int *n,
+				       fftw_direction dir, int flags)
+{
+     if (rank <= 0)
+	  return 0;
+
+     if (plans) {
+	  int i, j;
+	  int cur_flags;
+
+	  for (i = 0; i < rank; ++i) {
+	       if (i < rank - 1 || (flags & FFTW_IN_PLACE)) {
+		    /* 
+		     * fft's except the last dimension are always in-place 
+		     */
+		    cur_flags = flags | FFTW_IN_PLACE;
+		    for (j = i - 1; j >= 0 && n[i] != n[j]; --j);
+	       } else {
+		    cur_flags = flags;
+		    /* 
+		     * we must create a separate plan for the last
+		     * dimension 
+		     */
+		    j = -1;
+	       }
+
+	       if (j >= 0) {
+		    /* 
+		     * If a plan already exists for this size
+		     * array, reuse it: 
+		     */
+		    plans[i] = plans[j];
+	       } else {
+		    /* generate a new plan: */
+		    plans[i] = fftw_create_plan(n[i], dir, cur_flags);
+		    if (!plans[i]) {
+			 destroy_plan_array(rank, plans);
+			 return 0;
+		    }
+	       }
+	  }
+     }
+     return plans;
+}
+
+static int get_maxdim(int rank, const int *n, int flags)
+{
+     int i;
+     int maxdim = 0;
+
+     for (i = 0; i < rank - 1; ++i)
+	  if (n[i] > maxdim)
+	       maxdim = n[i];
+     if (rank > 0 && flags & FFTW_IN_PLACE && n[rank - 1] > maxdim)
+	  maxdim = n[rank - 1];
+
+     return maxdim;
+}
+
+/* compute number of elements required for work array (has to
+   be big enough to hold ncopies of the largest dimension in
+   n that will need an in-place transform. */
+int fftwnd_work_size(int rank, const int *n, int flags, int ncopies)
+{
+     return (ncopies * get_maxdim(rank, n, flags)
+	     + (ncopies - 1) * FFTWND_BUFFER_PADDING);
+}
+
+/*
+ * create plans using the fftw_create_plan_specific planner, which
+ * allows us to create plans for each dimension that are specialized
+ * for the strides that we are going to use. 
+ */
+fftw_plan *fftwnd_create_plans_specific(fftw_plan *plans,
+					int rank, const int *n,
+					const int *n_after,
+					fftw_direction dir, int flags,
+					fftw_complex *in, int istride,
+					fftw_complex *out, int ostride)
+{
+     if (rank <= 0)
+	  return 0;
+
+     if (plans) {
+	  int i, stride, cur_flags;
+	  fftw_complex *work = 0;
+	  int nwork;
+
+	  nwork = fftwnd_work_size(rank, n, flags, 1);
+	  if (nwork)
+	       work = (fftw_complex*)fftw_malloc(nwork * sizeof(fftw_complex));
+
+	  for (i = 0; i < rank; ++i) {
+	       /* fft's except the last dimension are always in-place */
+	       if (i < rank - 1)
+		    cur_flags = flags | FFTW_IN_PLACE;
+	       else
+		    cur_flags = flags;
+
+	       /* stride for transforming ith dimension */
+	       stride = n_after[i];
+
+	       if (cur_flags & FFTW_IN_PLACE)
+		    plans[i] = fftw_create_plan_specific(n[i], dir, cur_flags,
+						    in, istride * stride,
+							 work, 1);
+	       else
+		    plans[i] = fftw_create_plan_specific(n[i], dir, cur_flags,
+						    in, istride * stride,
+						  out, ostride * stride);
+	       if (!plans[i]) {
+		    destroy_plan_array(rank, plans);
+		    fftw_free(work);
+		    return 0;
+	       }
+	  }
+
+	  if (work)
+	       fftw_free(work);
+     }
+     return plans;
+}
+
+/*
+ * Create an fftwnd_plan specialized for specific arrays.  (These
+ * arrays are ignored, however, if they are NULL or if the flags do
+ * not include FFTW_MEASURE.)  The main advantage of being provided
+ * arrays like this is that we can do runtime timing measurements of
+ * our options, without worrying about allocating excessive scratch
+ * space.
+ */
+fftwnd_plan fftwnd_create_plan_specific(int rank, const int *n,
+					fftw_direction dir, int flags,
+					fftw_complex *in, int istride,
+					fftw_complex *out, int ostride)
+{
+     fftwnd_plan p;
+
+     if (!(p = fftwnd_create_plan_aux(rank, n, dir, flags)))
+	  return 0;
+
+     if (!(flags & FFTW_MEASURE) || in == 0
+	 || (!p->is_in_place && out == 0)) {
+
+/**** use default plan ****/
+
+	  p->plans = fftwnd_create_plans_generic(fftwnd_new_plan_array(rank),
+						 rank, n, dir, flags);
+	  if (!p->plans) {
+	       fftwnd_destroy_plan(p);
+	       return 0;
+	  }
+	  if (flags & FFTWND_FORCE_BUFFERED)
+	       p->nbuffers = FFTWND_NBUFFERS;
+	  else
+	       p->nbuffers = FFTWND_DEFAULT_NBUFFERS;
+
+	  p->nwork = fftwnd_work_size(rank, n, flags, p->nbuffers + 1);
+	  if (p->nwork && !(flags & FFTW_THREADSAFE)) {
+	       p->work = (fftw_complex*) fftw_malloc(p->nwork 
+						     * sizeof(fftw_complex));
+	       if (!p->work) {
+		    fftwnd_destroy_plan(p);
+		    return 0;
+	       }
+	  }
+     } else {
+/**** use runtime measurements to pick plan ****/
+
+	  fftw_plan *plans_buf, *plans_nobuf;
+	  double t_buf, t_nobuf;
+
+	  p->nwork = fftwnd_work_size(rank, n, flags, FFTWND_NBUFFERS + 1);
+	  if (p->nwork && !(flags & FFTW_THREADSAFE)) {
+	       p->work = (fftw_complex*) fftw_malloc(p->nwork 
+						     * sizeof(fftw_complex));
+	       if (!p->work) {
+		    fftwnd_destroy_plan(p);
+		    return 0;
+	       }
+	  }
+	  else
+	       p->work = (fftw_complex*) NULL;
+
+	  /* two possible sets of 1D plans: */
+	  plans_buf = fftwnd_create_plans_generic(fftwnd_new_plan_array(rank),
+						  rank, n, dir, flags);
+	  plans_nobuf = 
+	       fftwnd_create_plans_specific(fftwnd_new_plan_array(rank),
+					    rank, n, p->n_after, dir,
+					    flags, in, istride,
+					    out, ostride);
+	  if (!plans_buf || !plans_nobuf) {
+	       destroy_plan_array(rank, plans_nobuf);
+	       destroy_plan_array(rank, plans_buf);
+	       fftwnd_destroy_plan(p);
+	       return 0;
+	  }
+	  /* time the two possible plans */
+	  p->plans = plans_nobuf;
+	  p->nbuffers = 0;
+	  p->nwork = fftwnd_work_size(rank, n, flags, p->nbuffers + 1);
+	  t_nobuf = fftwnd_measure_runtime(p, in, istride, out, ostride);
+	  p->plans = plans_buf;
+	  p->nbuffers = FFTWND_NBUFFERS;
+	  p->nwork = fftwnd_work_size(rank, n, flags, p->nbuffers + 1);
+	  t_buf = fftwnd_measure_runtime(p, in, istride, out, ostride);
+
+	  /* pick the better one: */
+	  if (t_nobuf < t_buf) {	/* use unbuffered transform */
+	       p->plans = plans_nobuf;
+	       p->nbuffers = 0;
+
+	       /* work array is unnecessarily large */
+	       if (p->work)
+		    fftw_free(p->work);
+	       p->work = 0;
+
+	       destroy_plan_array(rank, plans_buf);
+
+	       /* allocate a work array of the correct size: */
+	       p->nwork = fftwnd_work_size(rank, n, flags, p->nbuffers + 1);
+	       if (p->nwork && !(flags & FFTW_THREADSAFE)) {
+		    p->work = (fftw_complex*) fftw_malloc(p->nwork 
+						       * sizeof(fftw_complex));
+		    if (!p->work) {
+			 fftwnd_destroy_plan(p);
+			 return 0;
+		    }
+	       }
+	  } else {		/* use buffered transform */
+	       destroy_plan_array(rank, plans_nobuf);
+	  }
+     }
+
+     return p;
+}
+
+fftwnd_plan fftw2d_create_plan_specific(int nx, int ny,
+					fftw_direction dir, int flags,
+					fftw_complex *in, int istride,
+					fftw_complex *out, int ostride)
+{
+     int n[2];
+
+     n[0] = nx;
+     n[1] = ny;
+
+     return fftwnd_create_plan_specific(2, n, dir, flags,
+					in, istride, out, ostride);
+}
+
+fftwnd_plan fftw3d_create_plan_specific(int nx, int ny, int nz,
+					fftw_direction dir, int flags,
+					fftw_complex *in, int istride,
+					fftw_complex *out, int ostride)
+{
+     int n[3];
+
+     n[0] = nx;
+     n[1] = ny;
+     n[2] = nz;
+
+     return fftwnd_create_plan_specific(3, n, dir, flags,
+					in, istride, out, ostride);
+}
+
+/* Create a generic fftwnd plan: */
+
+fftwnd_plan fftwnd_create_plan(int rank, const int *n,
+			       fftw_direction dir, int flags)
+{
+     return fftwnd_create_plan_specific(rank, n, dir, flags, 0, 1, 0, 1);
+}
+
+fftwnd_plan fftw2d_create_plan(int nx, int ny,
+			       fftw_direction dir, int flags)
+{
+     return fftw2d_create_plan_specific(nx, ny, dir, flags, 0, 1, 0, 1);
+}
+
+fftwnd_plan fftw3d_create_plan(int nx, int ny, int nz,
+			       fftw_direction dir, int flags)
+{
+     return fftw3d_create_plan_specific(nx, ny, nz, dir, flags, 0, 1, 0, 1);
+}
+
+/************************ Freeing the FFTWND Plan ************************/
+
+static void destroy_plan_array(int rank, fftw_plan *plans)
+{
+     if (plans) {
+	  int i, j;
+
+	  for (i = 0; i < rank; ++i) {
+	       for (j = i - 1;
+		    j >= 0 && plans[i] != plans[j];
+		    --j);
+	       if (j < 0 && plans[i])
+		    fftw_destroy_plan(plans[i]);
+	  }
+	  fftw_free(plans);
+     }
+}
+
+void fftwnd_destroy_plan(fftwnd_plan plan)
+{
+     if (plan) {
+	  destroy_plan_array(plan->rank, plan->plans);
+
+	  if (plan->n)
+	       fftw_free(plan->n);
+
+	  if (plan->n_before)
+	       fftw_free(plan->n_before);
+
+	  if (plan->n_after)
+	       fftw_free(plan->n_after);
+
+	  if (plan->work)
+	       fftw_free(plan->work);
+
+	  fftw_free(plan);
+     }
+}
+
+/************************ Printing the FFTWND Plan ************************/
+
+void fftwnd_fprint_plan(FILE *f, fftwnd_plan plan)
+{
+     if (plan) {
+	  int i, j;
+
+	  if (plan->rank == 0) {
+	       fprintf(f, "plan for rank 0 (null) transform.\n");
+	       return;
+	  }
+	  fprintf(f, "plan for ");
+	  for (i = 0; i < plan->rank; ++i)
+	       fprintf(f, "%s%d", i ? "x" : "", plan->n[i]);
+	  fprintf(f, " transform:\n");
+
+	  if (plan->nbuffers > 0)
+	       fprintf(f, "  -- using buffered transforms (%d buffers)\n",
+		       plan->nbuffers);
+	  else
+	       fprintf(f, "  -- using unbuffered transform\n");
+
+	  for (i = 0; i < plan->rank; ++i) {
+	       fprintf(f, "* dimension %d (size %d) ", i, plan->n[i]);
+
+	       for (j = i - 1; j >= 0; --j)
+		    if (plan->plans[j] == plan->plans[i])
+			 break;
+
+	       if (j < 0)
+		    fftw_fprint_plan(f, plan->plans[i]);
+	       else
+		    fprintf(f, "plan is same as dimension %d plan.\n", j);
+	  }
+     }
+}
+
+void fftwnd_print_plan(fftwnd_plan plan)
+{
+     fftwnd_fprint_plan(stdout, plan);
+}
+
+/********************* Buffered FFTW (in-place) *********************/
+
+void fftw_buffered(fftw_plan p, int howmany,
+		   fftw_complex *in, int istride, int idist,
+		   fftw_complex *work,
+		   int nbuffers, fftw_complex *buffers)
+{
+     int i = 0, n, nb;
+
+     n = p->n;
+     nb = n + FFTWND_BUFFER_PADDING;
+
+     do {
+	  for (; i <= howmany - nbuffers; i += nbuffers) {
+	       fftw_complex *cur_in = in + i * idist;
+	       int j, buf;
+
+	       /* 
+	        * First, copy nbuffers strided arrays to the
+	        * contiguous buffer arrays (reading consecutive
+	        * locations, assuming that idist is 1):
+	        */
+	       for (j = 0; j < n; ++j) {
+		    fftw_complex *cur_in2 = cur_in + j * istride;
+		    fftw_complex *cur_buffers = buffers + j;
+
+		    for (buf = 0; buf <= nbuffers - 4; buf += 4) {
+			 fftw_real r0, i0, r1, i1, r2, i2, r3, i3;
+			 r0 = c_re(cur_in2[0]);
+			 i0 = c_im(cur_in2[0]);
+			 r1 = c_re(cur_in2[idist]);
+			 i1 = c_im(cur_in2[idist]);
+			 r2 = c_re(cur_in2[2 * idist]);
+			 i2 = c_im(cur_in2[2 * idist]);
+			 r3 = c_re(cur_in2[3 * idist]);
+			 i3 = c_im(cur_in2[3 * idist]);
+			 c_re(cur_buffers[0]) = r0;
+			 c_im(cur_buffers[0]) = i0;
+			 c_re(cur_buffers[nb]) = r1;
+			 c_im(cur_buffers[nb]) = i1;
+			 c_re(cur_buffers[2 * nb]) = r2;
+			 c_im(cur_buffers[2 * nb]) = i2;
+			 c_re(cur_buffers[3 * nb]) = r3;
+			 c_im(cur_buffers[3 * nb]) = i3;
+			 cur_buffers += 4 * nb;
+			 cur_in2 += 4 * idist;
+		    }
+		    for (; buf < nbuffers; ++buf) {
+			 *cur_buffers = *cur_in2;
+			 cur_buffers += nb;
+			 cur_in2 += idist;
+		    }
+	       }
+
+	       /* 
+	        * Now, compute the FFTs in the buffers (in-place
+	        * using work): 
+	        */
+	       fftw(p, nbuffers, buffers, 1, nb, work, 1, 0);
+
+	       /* 
+	        * Finally, copy the results back from the contiguous
+	        * buffers to the strided arrays (writing consecutive
+	        * locations):
+	        */
+	       for (j = 0; j < n; ++j) {
+		    fftw_complex *cur_in2 = cur_in + j * istride;
+		    fftw_complex *cur_buffers = buffers + j;
+
+		    for (buf = 0; buf <= nbuffers - 4; buf += 4) {
+			 fftw_real r0, i0, r1, i1, r2, i2, r3, i3;
+			 r0 = c_re(cur_buffers[0]);
+			 i0 = c_im(cur_buffers[0]);
+			 r1 = c_re(cur_buffers[nb]);
+			 i1 = c_im(cur_buffers[nb]);
+			 r2 = c_re(cur_buffers[2 * nb]);
+			 i2 = c_im(cur_buffers[2 * nb]);
+			 r3 = c_re(cur_buffers[3 * nb]);
+			 i3 = c_im(cur_buffers[3 * nb]);
+			 c_re(cur_in2[0]) = r0;
+			 c_im(cur_in2[0]) = i0;
+			 c_re(cur_in2[idist]) = r1;
+			 c_im(cur_in2[idist]) = i1;
+			 c_re(cur_in2[2 * idist]) = r2;
+			 c_im(cur_in2[2 * idist]) = i2;
+			 c_re(cur_in2[3 * idist]) = r3;
+			 c_im(cur_in2[3 * idist]) = i3;
+			 cur_buffers += 4 * nb;
+			 cur_in2 += 4 * idist;
+		    }
+		    for (; buf < nbuffers; ++buf) {
+			 *cur_in2 = *cur_buffers;
+			 cur_buffers += nb;
+			 cur_in2 += idist;
+		    }
+	       }
+	  }
+
+	  /* 
+	   * we skip howmany % nbuffers ffts at the end of the loop,
+	   * so we have to go back and do them: 
+	   */
+	  nbuffers = howmany - i;
+     } while (i < howmany);
+}
+
+/********************* Computing the N-Dimensional FFT *********************/
+
+void fftwnd_aux(fftwnd_plan p, int cur_dim,
+		fftw_complex *in, int istride,
+		fftw_complex *out, int ostride,
+		fftw_complex *work)
+{
+     int n_after = p->n_after[cur_dim], n = p->n[cur_dim];
+
+     if (cur_dim == p->rank - 2) {
+	  /* just do the last dimension directly: */
+	  if (p->is_in_place)
+	       fftw(p->plans[p->rank - 1], n,
+		    in, istride, n_after * istride,
+		    work, 1, 0);
+	  else
+	       fftw(p->plans[p->rank - 1], n,
+		    in, istride, n_after * istride,
+		    out, ostride, n_after * ostride);
+     } else {			/* we have at least two dimensions to go */
+	  int i;
+
+	  /* 
+	   * process the subsequent dimensions recursively, in hyperslabs,
+	   * to get maximum locality: 
+	   */
+	  for (i = 0; i < n; ++i)
+	       fftwnd_aux(p, cur_dim + 1,
+			  in + i * n_after * istride, istride,
+			  out + i * n_after * ostride, ostride, work);
+     }
+
+     /* do the current dimension (in-place): */
+     if (p->nbuffers == 0) {
+	  fftw(p->plans[cur_dim], n_after,
+	       out, n_after * ostride, ostride,
+	       work, 1, 0);
+     } else			/* using contiguous copy buffers: */
+	  fftw_buffered(p->plans[cur_dim], n_after,
+			out, n_after * ostride, ostride,
+			work, p->nbuffers, work + n);
+}
+
+/*
+ * alternate version of fftwnd_aux -- this version pushes the howmany
+ * loop down to the leaves of the computation, for greater locality in
+ * cases where dist < stride
+ */
+void fftwnd_aux_howmany(fftwnd_plan p, int cur_dim,
+			int howmany,
+			fftw_complex *in, int istride, int idist,
+			fftw_complex *out, int ostride, int odist,
+			fftw_complex *work)
+{
+     int n_after = p->n_after[cur_dim], n = p->n[cur_dim];
+     int k;
+
+     if (cur_dim == p->rank - 2) {
+	  /* just do the last dimension directly: */
+	  if (p->is_in_place)
+	       for (k = 0; k < n; ++k)
+		    fftw(p->plans[p->rank - 1], howmany,
+			 in + k * n_after * istride, istride, idist,
+			 work, 1, 0);
+	  else
+	       for (k = 0; k < n; ++k)
+		    fftw(p->plans[p->rank - 1], howmany,
+			 in + k * n_after * istride, istride, idist,
+			 out + k * n_after * ostride, ostride, odist);
+     } else {			/* we have at least two dimensions to go */
+	  int i;
+
+	  /* 
+	   * process the subsequent dimensions recursively, in
+	   * hyperslabs, to get maximum locality:
+	   */
+	  for (i = 0; i < n; ++i)
+	       fftwnd_aux_howmany(p, cur_dim + 1, howmany,
+			      in + i * n_after * istride, istride, idist,
+				  out + i * n_after * ostride, ostride, odist,
+				  work);
+     }
+
+     /* do the current dimension (in-place): */
+     if (p->nbuffers == 0)
+	  for (k = 0; k < n_after; ++k)
+	       fftw(p->plans[cur_dim], howmany,
+		    out + k * ostride, n_after * ostride, odist,
+		    work, 1, 0);
+     else			/* using contiguous copy buffers: */
+	  for (k = 0; k < n_after; ++k)
+	       fftw_buffered(p->plans[cur_dim], howmany,
+			     out + k * ostride, n_after * ostride, odist,
+			     work, p->nbuffers, work + n);
+}
+
+void fftwnd(fftwnd_plan p, int howmany,
+	    fftw_complex *in, int istride, int idist,
+	    fftw_complex *out, int ostride, int odist)
+{
+     fftw_complex *work;
+
+#ifdef FFTW_DEBUG
+     if (p->rank > 0 && (p->plans[0]->flags & FFTW_THREADSAFE)
+	 && p->nwork && p->work)
+	  fftw_die("bug with FFTW_THREADSAFE flag\n");
+#endif
+
+     if (p->nwork && !p->work)
+	  work = (fftw_complex *) fftw_malloc(p->nwork * sizeof(fftw_complex));
+     else
+	  work = p->work;
+
+     switch (p->rank) {
+	 case 0:
+	      break;
+	 case 1:
+	      if (p->is_in_place)	/* fft is in-place */
+		   fftw(p->plans[0], howmany, in, istride, idist,
+			work, 1, 0);
+	      else
+		   fftw(p->plans[0], howmany, in, istride, idist,
+			out, ostride, odist);
+	      break;
+	 default:		/* rank >= 2 */
+	      {
+		   if (p->is_in_place) {
+			out = in;
+			ostride = istride;
+			odist = idist;
+		   }
+		   if (howmany > 1 && odist < ostride)
+			fftwnd_aux_howmany(p, 0, howmany,
+					   in, istride, idist,
+					   out, ostride, odist,
+					   work);
+		   else {
+			int i;
+
+			for (i = 0; i < howmany; ++i)
+			     fftwnd_aux(p, 0,
+					in + i * idist, istride,
+					out + i * odist, ostride,
+					work);
+		   }
+	      }
+     }
+
+     if (p->nwork && !p->work)
+	  fftw_free(work);
+
+}
+
+void fftwnd_one(fftwnd_plan p, fftw_complex *in, fftw_complex *out)
+{
+     fftwnd(p, 1, in, 1, 1, out, 1, 1);
+}