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This algori thm consists of two logically distinct parts: (1) a package of six F O R T R A N subroutines to facilitate the use of a special form of computer floating-point ar i thmetic tha t we call extended-range arithmetic; and (2) a FORT R A N subroutine tha t computes values of normalized Legendre polynomials according to an algori thm tha t generates (for some inputs) floating-point numbers tha t are outside the range of any computer . Our desire to produce a robust F O R T R A N subroutine to compute these polynomials st imulated the development of the extended-range software package. This package may prove to be useful for many other computations. Normalized Legendre polynomials are defined by the formula

Algorithm 567: Extended-Range Arithmetic and Normalized Legendre Polynomials [A1], [C1]