Construction and Performance Evaluation of an Arbitrary-Precision Floating-Point Arithmetic Environment on CUDA

Abstract

Arbitrary-precision floating-point arithmetic is used to solve ill-conditioned problems in scientific computing, and MPFR and MPC have become the de facto standard libraries for CPU-based computations. However, no publicly available environment provides MPFR/MPC functionality on GPUs. In this study, we developed mpc\_cuda, an arbitrary-precision arithmetic environment for GPUs, by leveraging generative AI (Claude Code) and rerunnable conversion scripts to faithfully port the mini-GMP-based MPFR/MPC libraries to CUDA kernels while reserving a per-thread temporary storage region (a bump arena). This approach accelerates real and complex elementary functions and basic linear algebra on GPUs by approximately 40--105$\times$, while remaining bit-identical to the host. In addition, we implemented compile-time fixed-precision types cu\_freal/cu\_fcomplex, and demonstrate, through benchmark tests involving the GMRES($m$) method and algebraic equation solving on GB10 and H100 GPUs, that the proposed implementation outperforms the existing GPU libraries CUMP and CAMPARY at low-to-medium precision.