Chris@42: /*
Chris@42:  * Copyright (c) 2003, 2007-14 Matteo Frigo
Chris@42:  * Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
Chris@42:  *
Chris@42:  * This program is free software; you can redistribute it and/or modify
Chris@42:  * it under the terms of the GNU General Public License as published by
Chris@42:  * the Free Software Foundation; either version 2 of the License, or
Chris@42:  * (at your option) any later version.
Chris@42:  *
Chris@42:  * This program is distributed in the hope that it will be useful,
Chris@42:  * but WITHOUT ANY WARRANTY; without even the implied warranty of
Chris@42:  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
Chris@42:  * GNU General Public License for more details.
Chris@42:  *
Chris@42:  * You should have received a copy of the GNU General Public License
Chris@42:  * along with this program; if not, write to the Free Software
Chris@42:  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
Chris@42:  *
Chris@42:  */
Chris@42: 
Chris@42: #include "ifftw-mpi.h"
Chris@42: 
Chris@42: /* Return the radix r for a 1d MPI transform of a distributed dimension d,
Chris@42:    with the given flags and transform size.   That is, decomposes d.n
Chris@42:    as r * m, Cooley-Tukey style.  Also computes the block sizes rblock
Chris@42:    and mblock.  Returns 0 if such a decomposition is not feasible.
Chris@42:    This is unfortunately somewhat complicated.
Chris@42: 
Chris@42:    A distributed Cooley-Tukey algorithm works as follows (see dft-rank1.c):
Chris@42: 
Chris@42:    d.n is initially distributed as an m x r array with block size mblock[IB].
Chris@42:    Then it is internally transposed to an r x m array with block size
Chris@42:    rblock[IB].  Then it is internally transposed to m x r again with block
Chris@42:    size mblock[OB].  Finally, it is transposed to r x m with block size
Chris@42:    rblock[IB].
Chris@42: 
Chris@42:    If flags & SCRAMBLED_IN, then the first transpose is skipped (the array
Chris@42:    starts out as r x m).  If flags & SCRAMBLED_OUT, then the last transpose
Chris@42:    is skipped (the array ends up as m x r).  To make sure the forward
Chris@42:    and backward transforms use the same "scrambling" format, we swap r
Chris@42:    and m when sign != FFT_SIGN.
Chris@42: 
Chris@42:    There are some downsides to this, especially in the case where
Chris@42:    either m or r is not divisible by n_pes.  For one thing, it means
Chris@42:    that in general we can't use the same block size for the input and
Chris@42:    output.  For another thing, it means that we can't in general honor
Chris@42:    a user's "requested" block sizes in d.b[].  Therefore, for simplicity,
Chris@42:    we simply ignore d.b[] for now.
Chris@42: */
Chris@42: INT XM(choose_radix)(ddim d, int n_pes, unsigned flags, int sign,
Chris@42: 		     INT rblock[2], INT mblock[2])
Chris@42: {
Chris@42:      INT r, m;
Chris@42: 
Chris@42:      UNUSED(flags); /* we would need this if we paid attention to d.b[*] */
Chris@42: 
Chris@42:      /* If n_pes is a factor of d.n, then choose r to be d.n / n_pes.
Chris@42:         This not only ensures that the input (the m dimension) is
Chris@42:         equally distributed if possible, and at the r dimension is
Chris@42:         maximally equally distributed (if d.n/n_pes >= n_pes), it also
Chris@42:         makes one of the local transpositions in the algorithm
Chris@42:         trivial. */
Chris@42:      if (d.n % n_pes == 0 /* it's good if n_pes divides d.n ...*/
Chris@42: 	 && d.n / n_pes >= n_pes /* .. unless we can't use n_pes processes */)
Chris@42: 	  r = d.n / n_pes;
Chris@42:      else {  /* n_pes does not divide d.n, pick a factor close to sqrt(d.n) */
Chris@42: 	  for (r = X(isqrt)(d.n); d.n % r != 0; ++r)
Chris@42: 	       ;
Chris@42:      }
Chris@42:      if (r == 1 || r == d.n) return 0; /* punt if we can't reduce size */
Chris@42: 
Chris@42:      if (sign != FFT_SIGN) { /* swap {m,r} so that scrambling is reversible */
Chris@42: 	  m = r;
Chris@42: 	  r = d.n / m;
Chris@42:      }
Chris@42:      else
Chris@42: 	  m = d.n / r;
Chris@42: 
Chris@42:      rblock[IB] = rblock[OB] = XM(default_block)(r, n_pes);
Chris@42:      mblock[IB] = mblock[OB] = XM(default_block)(m, n_pes);
Chris@42: 
Chris@42:      return r;
Chris@42: }