Automatic Generation of Complete Polynomial Interpolation Hardware Design Space

TL;DR

This paper explores the full range of polynomial approximation options for hardware design, enabling optimized, accurate implementations that are adaptable across different hardware technologies.

Contribution

It introduces a method to determine the complete design space of polynomial approximations meeting accuracy requirements, aiding in hardware optimization.

Findings

Identifies the minimal number of regions needed for accurate approximation

Provides a decision procedure adaptable to various hardware technologies

Enables generation of optimized hardware implementations

Abstract

Hardware implementations of complex functions regularly deploy piecewise polynomial approximations. This work determines the complete design space of piecewise polynomial approximations meeting a given accuracy specification. Knowledge of this design space determines the minimum number of regions required to approximate the function accurately enough and facilitates the generation of optimized hardware which is competitive against the state of the art. Targeting alternative hardware technologies simply requires a modified decision procedure to explore the space.