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This paper addresses the challenges of performing multiple double arithmetic on NVIDIA tensor cores, which are optimized for 64-bit floating-point operations but struggle with the necessary renormalization process. By adapting a solution akin to the Ozaki scheme, the authors enable efficient handling of multiple double operations without the performance penalties typically associated with branching. The resulting software, available under the GPU GPL license, enhances computational capabilities for applications requiring high precision arithmetic on tensor cores.
Achieving efficient multiple double arithmetic on NVIDIA tensor cores could significantly boost performance in high-precision applications.
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.
