Environment Parameters and Basic Functions for Floating-Point Computation
Warren S. Brown, Stuart I. Feldman · ACM Transactions on Mathematical Software · 1980
This paper presents a language-independent proposal for envtronment parameters and basic functions for floating-point computation, and suggests a speofic representation m terms of generic functions for Fortran 77 The enwronment parameters were introduced m 1967 by Forsythe and Moler, who attributed the essentmls of their theory to Wilkinson These parameters are also used m the PORT mathemaucal subroutine library, with precise definitions in terms of a more recent model of floatingpoint computatmn, and a similar set has been proposed by the IFIP Working Group on Numerical Software.Three of the basra functmns are taken from another proposal by this group, but redefined m terms of the parameters and the model to provide a firm theoretical foundation The other three basic functmns can be expressed in tetras of these, but we feel they should be provided separately for convenienceThe proposed parameters specify the base of the floating-point number system, the maximum precision consistent with the representational and operatmnal accuracy of the machine, and the maxnnum exponent range within whmh one can compute without fear of overflow, underflow, or unexpected loss of accuracy The proposed functions separate a floating-point number into its constituents, reconstruct a number from those constituents, scale a number by a power of the base, and determine the absolute or relatwe spacing (in the sense of the model) between numbers in the vmmlty of a given number.Key Words and Phrases' environment parameters,