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2 <html>
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3 <!-- This manual is for FFTW
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4 (version 3.3.5, 30 July 2016).
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5
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6 Copyright (C) 2003 Matteo Frigo.
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7
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8 Copyright (C) 2003 Massachusetts Institute of Technology.
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9
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10 Permission is granted to make and distribute verbatim copies of this
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12 preserved on all copies.
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13
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14 Permission is granted to copy and distribute modified versions of this
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15 manual under the conditions for verbatim copying, provided that the
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16 entire resulting derived work is distributed under the terms of a
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17 permission notice identical to this one.
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18
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19 Permission is granted to copy and distribute translations of this manual
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22 approved by the Free Software Foundation. -->
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23 <!-- Created by GNU Texinfo 5.2, http://www.gnu.org/software/texinfo/ -->
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24 <head>
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25 <title>FFTW 3.3.5: Load balancing</title>
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26
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27 <meta name="description" content="FFTW 3.3.5: Load balancing">
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34 <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
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35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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36 <link href="MPI-Data-Distribution.html#MPI-Data-Distribution" rel="up" title="MPI Data Distribution">
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37 <link href="Transposed-distributions.html#Transposed-distributions" rel="next" title="Transposed distributions">
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65 -->
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66 </style>
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68
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69 </head>
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70
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71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
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72 <a name="Load-balancing"></a>
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73 <div class="header">
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74 <p>
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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> [<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>
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76 </div>
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77 <hr>
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78 <a name="Load-balancing-1"></a>
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79 <h4 class="subsection">6.4.2 Load balancing</h4>
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80 <a name="index-load-balancing"></a>
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81
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82 <p>Ideally, when you parallelize a transform over some <em>P</em>
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83 processes, each process should end up with work that takes equal time.
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84 Otherwise, all of the processes end up waiting on whichever process is
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85 slowest. This goal is known as “load balancing.” In this section,
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86 we describe the circumstances under which FFTW is able to load-balance
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87 well, and in particular how you should choose your transform size in
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88 order to load balance.
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89 </p>
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90 <p>Load balancing is especially difficult when you are parallelizing over
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91 heterogeneous machines; for example, if one of your processors is a
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92 old 486 and another is a Pentium IV, obviously you should give the
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93 Pentium more work to do than the 486 since the latter is much slower.
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94 FFTW does not deal with this problem, however—it assumes that your
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95 processes run on hardware of comparable speed, and that the goal is
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96 therefore to divide the problem as equally as possible.
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97 </p>
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98 <p>For a multi-dimensional complex DFT, FFTW can divide the problem
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99 equally among the processes if: (i) the <em>first</em> dimension
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100 <code>n0</code> is divisible by <em>P</em>; and (ii), the <em>product</em> of
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101 the subsequent dimensions is divisible by <em>P</em>. (For the advanced
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102 interface, where you can specify multiple simultaneous transforms via
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103 some “vector” length <code>howmany</code>, a factor of <code>howmany</code> is
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104 included in the product of the subsequent dimensions.)
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105 </p>
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106 <p>For a one-dimensional complex DFT, the length <code>N</code> of the data
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107 should be divisible by <em>P</em> <em>squared</em> to be able to divide
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108 the problem equally among the processes.
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109 </p>
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110
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111
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112
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113 </body>
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114 </html>
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