Multiple Double Arithmetic on NVIDIA Tensor Cores

Abstract

A multiple double is an unevaluated sum of doubles. An NVIDIA tensor core is a specialized high performance compute core for matrix multiplication. The Ampere A100, released in 2020, introduced tensor cores capable of 64-bit floating-point arithmetic. Every multiple double arithmetical operation requires renormalization, which involves branching, for which tensor cores are unsuited. To solve this problem caused by renormalization, we apply a solution similar to the Ozaki scheme [Ozaki et al, Numerical Algorithms, 2012]. Our software is available under the GPU GPL license on github.