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  Tutorial: 3D Fast Fourier Transform Library for Blue Gene/L

A C++ library for computing distributed complex-to-complex, three-dimensional Fast Fourier Transforms on the Blue Gene/L supercomputer.

Tutorial Details:

At the core of many real-world scientific and engineering applications is the necessity for computing three-dimensional Fast Fourier Transforms (FFT). Although there are many available FFT libraries, 3D Fast Fourier Transform Library for Blue Gene/L (BGL3DFFT) is specifically designed to take advantage of the IBM Blue Gene architecture by enabling applications that use three-dimensional FFTs to scale to thousands of Blue Gene/L processors. Most of the alternative parallel libraries compute three-dimensional FFTs by using a technique called slab decomposition. However, the scalability of the slab-based methods is limited by the number of the data elements along a single dimension of the three-dimensional FFT. For instance, a 1283 sized three-dimensional FFT can scale only up to 128 processors. In BGL3DFFT, the three-dimensional FFT implementation is based on a full distribution of the n2 1D FFTs required for each phase of the row-column method for computation of a three-dimensional FFT. This approach enables scalability for up to 1282=16,384 processors for computing the same 1283 FFT.

BGL3DFFT is a scalable C++ library for computing distributed, three-dimensional Fast Fourier Transforms on the Blue Gene/L platform. The library can be used to perform transforms on 3D arrays of complex data where each dimension is a power-of-two on Blue Gene/L processor partitions where each dimension (of the 3D partition) is a power-of-two.

This FFT library is a three-dimensional, torus architecture-specific library. The torus is one of the five major interconnection networks of the Blue Gene/L and it is used for both point-to-point messaging and collective communications. The 3D FFT algorithm is designed to scale effectively to thousands of processors by its fine-tuned decomposition and effective use of the three-dimensional torus topology of the Blue Gene/L supercomputer. Performance measurements indicate that the algorithm scales well up to 8192 processors for a 1283 FFT using the MPI (message-passing interface) communication layer. BGL3DFFT can be used to enable the scaling of large-scale scientific or engineering codes.


 

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