NDLI: Pipelined Mixed Precision Algorithms on FPGAs for Fast and Accurate PDE Solvers from Low Precision Components

Content Provider	IEEE Xplore Digital Library
Author	Strzodka, R. Goddeke, D.
Copyright Year	2006
Description	Author affiliation: Max Planck Center, Stanford Univ., CA (Strzodka, R.)
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 the authors 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 the authors 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, the authors adapt the general concept of mixed precision iterative refinement methods to FPGAs and develop a fully pipelined version of the conjugate gradient solver. The authors combine this solver with different iterative refinement schemes and precision combinations to obtain resource efficient mappings of the pipelined algorithm core onto the FPGA
Starting Page	259
Ending Page	270
File Size	219837
Page Count	12
File Format	PDF
ISBN	0769526616
DOI	10.1109/FCCM.2006.57
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-04-24
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Field programmable gate arrays Arithmetic Character generation Iterative algorithms Logic Partial differential equations Sparse matrices Resource management Linear algebra Iterative methods
Content Type	Text
Resource Type	Article

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