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3 <title>Load balancing - FFTW 3.2alpha3</title>
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9 <link rel="prev" href="Basic-and-advanced-distribution-interfaces.html#Basic-and-advanced-distribution-interfaces" title="Basic and advanced distribution interfaces">
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12 <!--
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13 This manual is for FFTW
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14 (version 3.2alpha3, 14 August 2007).
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15
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16 Copyright (C) 2003 Matteo Frigo.
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17
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18 Copyright (C) 2003 Massachusetts Institute of Technology.
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19
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20 Permission is granted to make and distribute verbatim copies of
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24 Permission is granted to copy and distribute modified versions of
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25 this manual under the conditions for verbatim copying, provided
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26 that the entire resulting derived work is distributed under the
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27 terms of a permission notice identical to this one.
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28
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29 Permission is granted to copy and distribute translations of this
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30 manual into another language, under the above conditions for
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31 modified versions, except that this permission notice may be
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32 stated in a translation approved by the Free Software Foundation.
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45 --></style>
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46 </head>
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47 <body>
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48 <div class="node">
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49 <p>
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50 <a name="Load-balancing"></a>
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51 Next: <a rel="next" accesskey="n" href="Transposed-distributions.html#Transposed-distributions">Transposed distributions</a>,
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52 Previous: <a rel="previous" accesskey="p" href="Basic-and-advanced-distribution-interfaces.html#Basic-and-advanced-distribution-interfaces">Basic and advanced distribution interfaces</a>,
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53 Up: <a rel="up" accesskey="u" href="MPI-data-distribution.html#MPI-data-distribution">MPI data distribution</a>
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54 <hr>
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55 </div>
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56
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57 <h4 class="subsection">6.4.2 Load balancing</h4>
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58
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59 <p><a name="index-load-balancing-358"></a>
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60 Ideally, when you parallelize a transform over some P
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61 processes, each process should end up with work that takes equal time.
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62 Otherwise, all of the processes end up waiting on whichever process is
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63 slowest. This goal is known as “load balancing.” In this section,
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64 we describe the circumstances under which FFTW is able to load-balance
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65 well, and in particular how you should choose your transform size in
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66 order to load balance.
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67
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68 <p>Load balancing is especially difficult when you are parallelizing over
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69 heterogeneous machines; for example, if one of your processors is a
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70 old 486 and another is a Pentium IV, obviously you should give the
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71 Pentium more work to do than the 486 since the latter is much slower.
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72 FFTW does not deal with this problem, however—it assumes that your
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73 processes run on hardware of comparable speed, and that the goal is
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74 therefore to divide the problem as equally as possible.
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75
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76 <p>For a multi-dimensional complex DFT, FFTW can divide the problem
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77 equally among the processes if: (i) the <em>first</em> dimension
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78 <code>n0</code> is divisible by P; and (ii), the <em>product</em> of
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79 the subsequent dimensions is divisible by P. (For the advanced
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80 interface, where you can specify multiple simultaneous transforms via
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81 some “vector” length <code>howmany</code>, a factor of <code>howmany</code> is
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82 included in the product of the subsequent dimensions.)
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83
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84 <p>For a one-dimensional complex DFT, the length <code>N</code> of the data
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85 should be divisible by P <em>squared</em> to be able to divide
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86 the problem equally among the processes.
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87
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88 </body></html>
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89
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