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<h4 class="subsection">6.7.3 An improved replacement for MPI_Alltoall</h4>

<p>We close this section by noting that FFTW's MPI transpose routines can
be thought of as a generalization for the <code>MPI_Alltoall</code> function
(albeit only for floating-point types), and in some circumstances can
function as an improved replacement.
<a name="index-MPI_005fAlltoall-406"></a>

   <p><code>MPI_Alltoall</code> is defined by the MPI standard as:

<pre class="example">     int MPI_Alltoall(void *sendbuf, int sendcount, MPI_Datatype sendtype,
                      void *recvbuf, int recvcnt, MPI_Datatype recvtype,
                      MPI_Comm comm);
</pre>
   <p>In particular, for <code>double*</code> arrays <code>in</code> and <code>out</code>,
consider the call:

<pre class="example">     MPI_Alltoall(in, howmany, MPI_DOUBLE, out, howmany MPI_DOUBLE, comm);
</pre>
   <p>This is completely equivalent to:

<pre class="example">     MPI_Comm_size(comm, &amp;P);
     plan = fftw_mpi_plan_many_transpose(P, P, howmany, 1, 1, in, out, comm, FFTW_ESTIMATE);
     fftw_execute(plan);
     fftw_destroy_plan(plan);
</pre>
   <p>That is, computing a P&nbsp;&times;&nbsp;P transpose on <code>P</code> processes,
with a block size of 1, is just a standard all-to-all communication.

   <p>However, using the FFTW routine instead of <code>MPI_Alltoall</code> may
have certain advantages.  First of all, FFTW's routine can operate
in-place (<code>in == out</code>) whereas <code>MPI_Alltoall</code> can only
operate out-of-place.
<a name="index-in_002dplace-407"></a>

   <p>Second, even for out-of-place plans, FFTW's routine may be faster,
especially if you need to perform the all-to-all communication many
times and can afford to use <code>FFTW_MEASURE</code> or
<code>FFTW_PATIENT</code>.  It should certainly be no slower, not including
the time to create the plan, since one of the possible algorithms that
FFTW uses for an out-of-place transpose <em>is</em> simply to call
<code>MPI_Alltoall</code>.  However, FFTW also considers several other
possible algorithms that, depending on your MPI implementation and
your hardware, may be faster.
<a name="index-FFTW_005fMEASURE-408"></a><a name="index-FFTW_005fPATIENT-409"></a>
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author	Chris Cannam
date	Wed, 20 Mar 2013 15:35:50 +0000
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