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Optimization of 32-bit Unsigned Division by Constants on 64-bit Targets

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arXiv:2604.07902 (cs)
[Submitted on 9 Apr 2026]

Title:Optimization of 32-bit Unsigned Division by Constants on 64-bit Targets

Authors:Shigeo Mitsunari, Takashi Hoshino
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Abstract:Granlund and Montgomery proposed an optimization method for unsigned integer division by constants [3]. Their method (called the GM method in this paper) was further improved in part by works such as [1] and [7], and is now adopted by major compilers including GCC, Clang, Microsoft Compiler, and Apple Clang. However, for example, for x/7, the generated code is designed for 32-bit CPUs and therefore does not fully exploit 64-bit capabilities. This paper proposes an optimization method for 32-bit unsigned division by constants targeting 64-bit CPUs. We implemented patches for LLVM/GCC and achieved speedups of 1.67x on Intel Xeon w9-3495X (Sapphire Rapids) and 1.98x on Apple M4 (Apple M-series SoC) in the microbenchmark described later. The LLVM patch has already been merged into llvm:main [6], demonstrating the practical applicability of the proposed method.
Subjects: Programming Languages (cs.PL); Hardware Architecture (cs.AR)
ACM classes: D.3.4
Cite as: arXiv:2604.07902 [cs.PL]
(or arXiv:2604.07902v1 [cs.PL] for this version)
https://doi.org/10.48550/arXiv.2604.07902

Submission history

From: Takashi Hoshino [view email]
[v1] Thu, 9 Apr 2026 07:18:31 UTC (9 KB)
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