Pipelined mixed precision algorithms on FPGAs for fast and accurate PDE solvers from low precision components

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Pipelined mixed precision algorithms on FPGAs for fast and accurate PDE solvers from low precision components (2006)

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by Robert Strzodka , Dominik Göddeke

Venue:	In IEEE Proceedings on Field–Programmable Custom Computing Machines (FCCM
Citations:	16 - 2 self

BibTeX

@INPROCEEDINGS{Strzodka06pipelinedmixed,
    author = {Robert Strzodka and Dominik Göddeke},
    title = {Pipelined mixed precision algorithms on FPGAs for fast and accurate PDE solvers from low precision components},
    booktitle = {In IEEE Proceedings on Field–Programmable Custom Computing Machines (FCCM},
    year = {2006}
}

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Abstract

FPGAs are becoming more and more attractive for high precision scientific computations. One of the main problems in efficient resource utilization is the quadratically growing resource usage of multipliers depending on the operand size. Many research efforts have been devoted to the optimization of individual arithmetic and linear algebra operations. In this paper we take a higher level approach and seek to reduce the intermediate computational precision on the algorithmic level by optimizing the accuracy towards the final result of an algorithm. In our case this is the accurate solution of partial differential equations (PDEs). Using the Poisson Problem as a typical PDE example we show that most intermediate operations can be computed with floats or even smaller formats and only very few operations (e.g. 1%) must be performed in double precision to obtain the same accuracy as a full double precision solver. Thus the FPGA can be configured with many parallel float rather than few resource hungry double operations. To achieve this, we adapt the general concept of mixed precision iterative refinement methods to FPGAs and develop a fully pipelined version of the Conjugate Gradient solver. We combine this solver with different iterative refinement schemes and precision combinations to obtain resource efficient mappings of the pipelined algorithm core onto the FPGA. 1.

Keyphrases

accurate pde solver mixed precision algorithm low precision component operand size partial differential equation poisson problem main problem algorithmic level intermediate computational precision resource usage general concept precision combination final result resource efficient mapping mixed precision iterative refinement method resource hungry double operation level approach different iterative refinement scheme typical pde example many parallel float intermediate operation conjugate gradient full double precision solver efficient resource utilization many research effort high precision scientific computation accurate solution double precision pipelined algorithm core linear algebra operation

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