Efficient Boys function evaluation using minimax approximation.

Area of Science:

• Computational Physics
• Numerical Analysis

Background:

• Boys functions are crucial in computational quantum chemistry and physics.
• Efficient evaluation is needed for modern high-throughput computing architectures, especially GPUs.
• Existing methods can be inefficient due to data movement costs.

Purpose of the Study:

• To present a novel algorithm for efficient Boys function evaluation.
• To tailor the algorithm for modern computing architectures like GPUs.
• To achieve high accuracy with optimized computational performance.

Main Methods:

• Combining rational minimax approximations with upward and downward recurrence relations.
• Partitioning the non-negative real axis into three regions for distinct approximation strategies.
• Utilizing the rational Remez algorithm for generating minimax coefficients.
• Avoiding lookup tables and irregular memory access patterns.

Main Results:

• The algorithm is well-suited for hardware with high throughput and low latency.
• Achieved a target maximum absolute error of \( \epsilon_{tol} = 5 \times 10^{-14} \).
• Provided approximation regions and coefficients for Boys functions F0 to F32 in Appendix D.

Conclusions:

• The proposed algorithm offers an efficient and accurate method for Boys function evaluation.
• The approach is optimized for modern parallel computing architectures, reducing data movement overhead.
• This work facilitates faster and more reliable computations in fields relying on Boys functions.