Accession Number : ADA210429

Title :   On the Monotonicity of Some Computed Functions,

Corporate Author : CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS

Personal Author(s) : Kahan, W.

Report Date : JAN 1985

Pagination or Media Count : 12

Abstract : Techniques are introduced to help decide whether roundoff errors will abrogate the monotonicity properties of a function when it is computed. Those techniques are applied to several expressions, among them z/(1+a), z+z/(1+z), 2y - y square, W + 1/w, t - t/(1+4)/'t squared), ..., that have turned up during the calculation of certain elementary transcendental functions. Within appropriate ranges of their variables, the expressions are shown to remain monotonic when computed in binary arithmetic rounded as specified in proposed IEEE standards P754 and p854. Because these standards are IEEE standards p754 and p854. Because these standards are being adopted so widely, the conclusions from this error-analysis will be appreciated widely enough to justify its propagation. (jes)

Descriptors :   *BINARY ARITHMETIC, *TRANSCENDENTAL FUNCTIONS, FUNCTIONS.

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE