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

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 fe...

• Type: Conference
• Year: 2006
• Where: FCCM
• Authors: Robert Strzodka, Dominik Göddeke
• Keywords: Double Precision, Double Precision Solver, FCCM 2006, Hardware, Precision Scientific Computations