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arXiv · 2606.06386

On GPU Implementation for Multi-Precision Integer Division

Martin B. Marchioro·Aske N. Raahauge·Marc I. Løvenskjold·Cosmin E. Oancea·Stephen M. Watt
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Abstract

This paper presents the issues arising in implementing a fast integer division algorithm on general purpose GPUs. The algorithm uses a Newton iteration based on the shifted inverse operation, keeping all arithmetic in the integer domain and relying on data-parallel operators. The principal contribution is an efficient GPU/CUDA implementation for integer precisions from $2^{15}$ to $2^{18}$ -- sizes not supported by \cgbn{} division. We propose algorithmic refinements, define a cost model in terms of multiplications, build on prefix sums and previous work on multi-precision multiplication, and present an evaluation showing near-optimal performance relative to the model for the target precision.

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Martin B. Marchioro, Aske N. Raahauge, Marc I. Løvenskjold, Cosmin E. Oancea, Stephen M. Watt. 2026-07-11. On GPU Implementation for Multi-Precision Integer Division. https://arxiv.org/abs/2606.06386

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