Multiple Double Arithmetic on NVIDIA Tensor Cores
Mathematical Software
2026-07-08 v1 Distributed, Parallel, and Cluster Computing
Numerical Analysis
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.
Cite
@article{arxiv.2607.06881,
title = {Multiple Double Arithmetic on NVIDIA Tensor Cores},
author = {Howard Chen and Jan Verschelde},
journal= {arXiv preprint arXiv:2607.06881},
year = {2026}
}
Comments
accepted for inclusion in the proceedings of ICMS 2026, the International Conference on Mathematical Software