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Current fftw source
author Chris Cannam <cannam@all-day-breakfast.com>
date Tue, 18 Oct 2016 13:40:26 +0100
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cannam@127 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
cannam@127 2 <html>
cannam@127 3 <!-- This manual is for FFTW
cannam@127 4 (version 3.3.5, 30 July 2016).
cannam@127 5
cannam@127 6 Copyright (C) 2003 Matteo Frigo.
cannam@127 7
cannam@127 8 Copyright (C) 2003 Massachusetts Institute of Technology.
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cannam@127 24 <head>
cannam@127 25 <title>FFTW 3.3.5: Load balancing</title>
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cannam@127 69 </head>
cannam@127 70
cannam@127 71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
cannam@127 72 <a name="Load-balancing"></a>
cannam@127 73 <div class="header">
cannam@127 74 <p>
cannam@127 75 Next: <a href="Transposed-distributions.html#Transposed-distributions" accesskey="n" rel="next">Transposed distributions</a>, Previous: <a href="Basic-and-advanced-distribution-interfaces.html#Basic-and-advanced-distribution-interfaces" accesskey="p" rel="prev">Basic and advanced distribution interfaces</a>, Up: <a href="MPI-Data-Distribution.html#MPI-Data-Distribution" accesskey="u" rel="up">MPI Data Distribution</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
cannam@127 76 </div>
cannam@127 77 <hr>
cannam@127 78 <a name="Load-balancing-1"></a>
cannam@127 79 <h4 class="subsection">6.4.2 Load balancing</h4>
cannam@127 80 <a name="index-load-balancing"></a>
cannam@127 81
cannam@127 82 <p>Ideally, when you parallelize a transform over some <em>P</em>
cannam@127 83 processes, each process should end up with work that takes equal time.
cannam@127 84 Otherwise, all of the processes end up waiting on whichever process is
cannam@127 85 slowest. This goal is known as &ldquo;load balancing.&rdquo; In this section,
cannam@127 86 we describe the circumstances under which FFTW is able to load-balance
cannam@127 87 well, and in particular how you should choose your transform size in
cannam@127 88 order to load balance.
cannam@127 89 </p>
cannam@127 90 <p>Load balancing is especially difficult when you are parallelizing over
cannam@127 91 heterogeneous machines; for example, if one of your processors is a
cannam@127 92 old 486 and another is a Pentium IV, obviously you should give the
cannam@127 93 Pentium more work to do than the 486 since the latter is much slower.
cannam@127 94 FFTW does not deal with this problem, however&mdash;it assumes that your
cannam@127 95 processes run on hardware of comparable speed, and that the goal is
cannam@127 96 therefore to divide the problem as equally as possible.
cannam@127 97 </p>
cannam@127 98 <p>For a multi-dimensional complex DFT, FFTW can divide the problem
cannam@127 99 equally among the processes if: (i) the <em>first</em> dimension
cannam@127 100 <code>n0</code> is divisible by <em>P</em>; and (ii), the <em>product</em> of
cannam@127 101 the subsequent dimensions is divisible by <em>P</em>. (For the advanced
cannam@127 102 interface, where you can specify multiple simultaneous transforms via
cannam@127 103 some &ldquo;vector&rdquo; length <code>howmany</code>, a factor of <code>howmany</code> is
cannam@127 104 included in the product of the subsequent dimensions.)
cannam@127 105 </p>
cannam@127 106 <p>For a one-dimensional complex DFT, the length <code>N</code> of the data
cannam@127 107 should be divisible by <em>P</em> <em>squared</em> to be able to divide
cannam@127 108 the problem equally among the processes.
cannam@127 109 </p>
cannam@127 110
cannam@127 111
cannam@127 112
cannam@127 113 </body>
cannam@127 114 </html>