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Add FFTW 3.3.8 source, and a Linux build
author Chris Cannam
date Tue, 19 Nov 2019 14:52:55 +0000
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3 <!-- This manual is for FFTW
4 (version 3.3.8, 24 May 2018).
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6 Copyright (C) 2003 Matteo Frigo.
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8 Copyright (C) 2003 Massachusetts Institute of Technology.
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25 <title>FFTW 3.3.8: Load balancing</title>
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71 <a name="Load-balancing"></a>
72 <div class="header">
73 <p>
74 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>
75 </div>
76 <hr>
77 <a name="Load-balancing-1"></a>
78 <h4 class="subsection">6.4.2 Load balancing</h4>
79 <a name="index-load-balancing"></a>
80
81 <p>Ideally, when you parallelize a transform over some <em>P</em>
82 processes, each process should end up with work that takes equal time.
83 Otherwise, all of the processes end up waiting on whichever process is
84 slowest. This goal is known as &ldquo;load balancing.&rdquo; In this section,
85 we describe the circumstances under which FFTW is able to load-balance
86 well, and in particular how you should choose your transform size in
87 order to load balance.
88 </p>
89 <p>Load balancing is especially difficult when you are parallelizing over
90 heterogeneous machines; for example, if one of your processors is a
91 old 486 and another is a Pentium IV, obviously you should give the
92 Pentium more work to do than the 486 since the latter is much slower.
93 FFTW does not deal with this problem, however&mdash;it assumes that your
94 processes run on hardware of comparable speed, and that the goal is
95 therefore to divide the problem as equally as possible.
96 </p>
97 <p>For a multi-dimensional complex DFT, FFTW can divide the problem
98 equally among the processes if: (i) the <em>first</em> dimension
99 <code>n0</code> is divisible by <em>P</em>; and (ii), the <em>product</em> of
100 the subsequent dimensions is divisible by <em>P</em>. (For the advanced
101 interface, where you can specify multiple simultaneous transforms via
102 some &ldquo;vector&rdquo; length <code>howmany</code>, a factor of <code>howmany</code> is
103 included in the product of the subsequent dimensions.)
104 </p>
105 <p>For a one-dimensional complex DFT, the length <code>N</code> of the data
106 should be divisible by <em>P</em> <em>squared</em> to be able to divide
107 the problem equally among the processes.
108 </p>
109
110
111
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