Semi-Automatic Floating-Point Implementation of Special Functions

Abstract—This work introduces an approach to the computerassisted implementation of mathematical functions geared toward special functions such as those occurring in mathematical physics. The general idea is to start with an exact symbolic representation of a function and automate as much as possible of the process of implementing it. In order to deal with a large class of special functions, our symbolic representation is an implicit one: the input is a linear differential equation with polynomial coefficients along with initial values. The output is a C program to evaluate the solution of the equation using domain splitting, argument reduction and polynomial approximations in double-precision arithmetic, in the usual style of mathematical libraries. Our generation method combines symbolic-numeric manipulations of linear ODEs with interval-based tools for the floatingpoint implementation of “black-box” functions. We describe a prototype code generator that can automatically pro...

• Type: Journal
• Year: 2015
• Where: ARITH
• Authors: Christoph Quirin Lauter, Marc Mezzarobba
• Keywords: Applied Computing, ARITH 2015