comparison src/fftw-3.3.3/mpi/choose-radix.c @ 10:37bf6b4a2645

Add FFTW3

+/*
+ * Copyright (c) 2003, 2007-11 Matteo Frigo
+ * Copyright (c) 2003, 2007-11 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 "ifftw-mpi.h"
+
+/* Return the radix r for a 1d MPI transform of a distributed dimension d,
+   with the given flags and transform size.   That is, decomposes d.n
+   as r * m, Cooley-Tukey style.  Also computes the block sizes rblock
+   and mblock.  Returns 0 if such a decomposition is not feasible.
+   This is unfortunately somewhat complicated.
+
+   A distributed Cooley-Tukey algorithm works as follows (see dft-rank1.c):
+
+   d.n is initially distributed as an m x r array with block size mblock[IB].
+   Then it is internally transposed to an r x m array with block size
+   rblock[IB].  Then it is internally transposed to m x r again with block
+   size mblock[OB].  Finally, it is transposed to r x m with block size
+   rblock[IB].
+
+   If flags & SCRAMBLED_IN, then the first transpose is skipped (the array
+   starts out as r x m).  If flags & SCRAMBLED_OUT, then the last transpose
+   is skipped (the array ends up as m x r).  To make sure the forward
+   and backward transforms use the same "scrambling" format, we swap r
+   and m when sign != FFT_SIGN.
+
+   There are some downsides to this, especially in the case where
+   either m or r is not divisible by n_pes.  For one thing, it means
+   that in general we can't use the same block size for the input and
+   output.  For another thing, it means that we can't in general honor
+   a user's "requested" block sizes in d.b[].  Therefore, for simplicity,
+   we simply ignore d.b[] for now.
+*/
+INT XM(choose_radix)(ddim d, int n_pes, unsigned flags, int sign,
+		     INT rblock[2], INT mblock[2])
+{
+     INT r, m;
+
+     UNUSED(flags); /* we would need this if we paid attention to d.b[*] */
+
+     /* If n_pes is a factor of d.n, then choose r to be d.n / n_pes.
+        This not only ensures that the input (the m dimension) is
+        equally distributed if possible, and at the r dimension is
+        maximally equally distributed (if d.n/n_pes >= n_pes), it also
+        makes one of the local transpositions in the algorithm
+        trivial. */
+     if (d.n % n_pes == 0 /* it's good if n_pes divides d.n ...*/
+	 && d.n / n_pes >= n_pes /* .. unless we can't use n_pes processes */)
+	  r = d.n / n_pes;
+     else {  /* n_pes does not divide d.n, pick a factor close to sqrt(d.n) */
+	  for (r = X(isqrt)(d.n); d.n % r != 0; ++r)
+	       ;
+     }
+     if (r == 1 || r == d.n) return 0; /* punt if we can't reduce size */
+
+     if (sign != FFT_SIGN) { /* swap {m,r} so that scrambling is reversible */
+	  m = r;
+	  r = d.n / m;
+     }
+     else
+	  m = d.n / r;
+
+     rblock[IB] = rblock[OB] = XM(default_block)(r, n_pes);
+     mblock[IB] = mblock[OB] = XM(default_block)(m, n_pes);
+
+     return r;
+}