A Machine-Independent ALGOL Procedure for Accurate Floating-Point Summation

Abstract

The paper describes all ALGOL 60 procedure which is an implementation of the floating-point summation technique described in Malcolm (1971). This implementation is machine-independent in the sense that it will work on nay computer having a floating-point number system F characterized as follows: Each number x which belongs to F has a radix-beta t-digit fraction where t > or = 1. The radix beta can be any positive integer greater than 1. The number 0 is contained in F , but no assumption is made about its representation. All floating-point operations (e.g., addition and multiplication) are assumed to result in either 0 or a normalized floating-point number contained in F . The machine may do either proper rounding or chopping (truncation). (Note that this definition of F excludes machines using extra-length accumulators for intermediate arithmetic. However, this algorithm is seldom needed on such machines).

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1973
Accession Number
AD0764275

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  • Michael A. Malcolm

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  • Stanford University

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DTIC Thesaurus Topics

  • Accumulators
  • Accuracy
  • Algorithms
  • Arithmetic
  • Commerce
  • Computer Science
  • Computers
  • Contracts
  • Equations
  • Errors
  • Floating Point Operations
  • Humanities
  • Mathematics
  • Military Research
  • Notation
  • Precision
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