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Add FFTW3
author Chris Cannam <cannam@all-day-breakfast.com>
date Wed, 20 Mar 2013 15:35:50 +0000
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3 <title>Load balancing - FFTW 3.3.3</title>
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49 <a name="Load-balancing"></a>
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56
57 <h4 class="subsection">6.4.2 Load balancing</h4>
58
59 <p><a name="index-load-balancing-378"></a>
60 Ideally, when you parallelize a transform over some P
61 processes, each process should end up with work that takes equal time.
62 Otherwise, all of the processes end up waiting on whichever process is
63 slowest. This goal is known as &ldquo;load balancing.&rdquo; In this section,
64 we describe the circumstances under which FFTW is able to load-balance
65 well, and in particular how you should choose your transform size in
66 order to load balance.
67
68 <p>Load balancing is especially difficult when you are parallelizing over
69 heterogeneous machines; for example, if one of your processors is a
70 old 486 and another is a Pentium IV, obviously you should give the
71 Pentium more work to do than the 486 since the latter is much slower.
72 FFTW does not deal with this problem, however&mdash;it assumes that your
73 processes run on hardware of comparable speed, and that the goal is
74 therefore to divide the problem as equally as possible.
75
76 <p>For a multi-dimensional complex DFT, FFTW can divide the problem
77 equally among the processes if: (i) the <em>first</em> dimension
78 <code>n0</code> is divisible by P; and (ii), the <em>product</em> of
79 the subsequent dimensions is divisible by P. (For the advanced
80 interface, where you can specify multiple simultaneous transforms via
81 some &ldquo;vector&rdquo; length <code>howmany</code>, a factor of <code>howmany</code> is
82 included in the product of the subsequent dimensions.)
83
84 <p>For a one-dimensional complex DFT, the length <code>N</code> of the data
85 should be divisible by P <em>squared</em> to be able to divide
86 the problem equally among the processes.
87
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89