Multiple Double Arithmetic on NVIDIA Tensor Cores
This work provides a method for high-precision arithmetic on specialized hardware, benefiting scientific computing applications that require accuracy beyond double precision.
The paper addresses the challenge of performing multiple double arithmetic on NVIDIA tensor cores, which are unsuited for the branching required in renormalization. By adapting the Ozaki scheme, they enable such arithmetic on Ampere A100 tensor cores, with software available under GPU GPL license.
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.