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d@0: Ideally, when you parallelize a transform over some P d@0: processes, each process should end up with work that takes equal time. d@0: Otherwise, all of the processes end up waiting on whichever process is d@0: slowest. This goal is known as “load balancing.” In this section, d@0: we describe the circumstances under which FFTW is able to load-balance d@0: well, and in particular how you should choose your transform size in d@0: order to load balance. d@0: d@0:
Load balancing is especially difficult when you are parallelizing over d@0: heterogeneous machines; for example, if one of your processors is a d@0: old 486 and another is a Pentium IV, obviously you should give the d@0: Pentium more work to do than the 486 since the latter is much slower. d@0: FFTW does not deal with this problem, however—it assumes that your d@0: processes run on hardware of comparable speed, and that the goal is d@0: therefore to divide the problem as equally as possible. d@0: d@0:
For a multi-dimensional complex DFT, FFTW can divide the problem
d@0: equally among the processes if: (i) the first dimension
d@0: n0 is divisible by P; and (ii), the product of
d@0: the subsequent dimensions is divisible by P. (For the advanced
d@0: interface, where you can specify multiple simultaneous transforms via
d@0: some “vector” length howmany, a factor of howmany is
d@0: included in the product of the subsequent dimensions.)
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For a one-dimensional complex DFT, the length N of the data
d@0: should be divisible by P squared to be able to divide
d@0: the problem equally among the processes.
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