Parallel floating-point expansions for extended-precision GPU computations

Abstract : GPUs are an important hardware development platform for problems where massive parallel computations are needed. Many of these problems require a higher precision than the standard double floating-point (FP) available. One common way of extending the precision is the multiple-component approach, in which real numbers are represented as the unevaluated sum of several standard machine precision FP numbers. This representation is called a FP expansion and it offers the simplicity of using directly available and highly optimized FP operations. In this article we present new data-parallel algorithms for adding and multiplying FP expansions specially designed for extended precision computations on GPUs. These are generalized algorithms that can manipulate FP expansions of different sizes (from double-double up to a few tens of doubles) and ensure a certain worst case error bound on the results.