On the Monotonicity of Some Computed Functions,

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)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1985
Accession Number
ADA210429

Entities

People

  • W. Kahan

Organizations

  • University of California, Berkeley

Tags

DTIC Thesaurus Topics

  • Arithmetic
  • Binary Arithmetic
  • Error Analysis
  • Errors
  • Mathematics
  • Standards
  • Transcendental Functions

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