Work

Efficient Boys function evaluation using minimax approximation

Year: 2026

Type: article

Abstract: We present an algorithm for efficient evaluation of Boys functions F0,…,Fkmax tailored to modern computing architectures, in particular graphical processing units, where maximum throughput is high and data movement is costly. The method combines rational minimax approximations with upward and downward recurrence relations. The non-negative real axis is partitioned into three regions, [0, ∞⟩ = A ∪ B ∪ C, where regions A and B are treated using rational minimax approximations and region C by an asymptotic approximation. This formulation avoids lookup tables and irregular memory access, making it well-suited for hardware with high maximum throughput and low latency. The rational minimax coefficients are generated using the rational Remez algorithm. For a target maximum absolute error of ɛtol = 5 × 10-14, the corresponding approximation regions and coefficients for Boys functions F0, …, F32 are provided in Appendix D.

Source: The Journal of Chemical Physics

DOI: 10.1063/5.0316073

Authors: Rasmus Vikhamar-Sandberg, Michal Repisky

Institutions: Comenius University Bratislava, UiT The Arctic University of Norway

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,500

Funders: Agentúra na Podporu Výskumu a Vývoja, Norges Forskningsråd, Vedecká Grantová Agentúra MŠVVaŠ SR a SAV, NextGenerationEU