AI 中文总结
本研究开发了适用于GPU的任意精度运算环境mpc_cuda，将MPFR/MPC库移植到CUDA内核，运算速度提升约40至105倍，在低至中等精度下优于现有GPU库CUMP和CAMPARY。
AI 中文摘要
任意精度浮点运算用于解决科学计算中的病态问题，MPFR和MPC已成为基于CPU计算的事实上的标准库。然而，目前没有公开可用的环境在GPU上提供MPFR/MPC功能。本研究利用生成式AI（Claude Code）和可重运行转换脚本，开发了适用于GPU的任意精度运算环境mpc_cuda，将基于mini-GMP的MPFR/MPC库忠实地移植到CUDA内核，同时保留每线程临时存储区域（ bump arena）。该方法在GPU上的实型和复型初等函数及基础线性代数运算速度提升约40至105倍，且与主机结果位一致。此外，我们实现了编译时固定精度类型cu_freal/cu_fcomplex，通过在GB10和H100 GPU上进行的GMRES(m)方法及代数方程求解的基准测试表明，所提实现在低至中等精度下优于现有GPU库CUMP和CAMPARY。
英文摘要
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.
