Not-Quite-Transcendental Functions For Logarithmic Interpolation of Tabulated Data

TL;DR

This paper introduces a novel, efficient interpolation method for large-range tabulated data in astrophysics, providing a faster alternative to traditional linear interpolation on logarithmic grids.

Contribution

The authors present a new interpolation strategy that improves accuracy and speed for large dynamic range tabulated data, applicable as a drop-in replacement for existing methods.

Findings

Faster interpolation compared to linear methods

Effective for nuclear and terrestrial equations of state

Handles large dynamic ranges accurately

Abstract

From tabulated nuclear and degenerate equations of state to photon and neutrino opacities, to nuclear reaction rates: tabulated data is ubiquitous in computational astrophysics. The dynamic range that must be covered by these tables typically spans many orders of magnitude. Here we present a novel strategy for accurately and performantly interpolating tabulated data that spans these large dynamic ranges. We demonstrate the efficacy of this strategy in tabulated lookups for nuclear and terrestrial equations of state. We show that this strategy is a faster \textit{drop-in} replacement for linear interpolation of logarithmic grids.