Extended-Range Arithmetic and Normalized Legendre Polynomials

Abstract

An algorithm is presented for the computation of normalrzed Legendre polynomials. In order to permit wide ranges of argument, degree, and order of these functions, an "extended-range" arithmetic is introduced whereby a separate storage location is allocated to the exponent of a floatmg-pomt number. Since this device may have other applications, separate subroutines are developed for addition of extended-range numbers and also for conversion to and from ordinary floating-point form.