Automatic Controlled Precision Calculations

Authors:
Bruce A. Chartres
Affiliations:
Department of Applied Mathematics and Computer Science, University, of Virginia, Charlottesville, Va and Division of Applied Mathematics, Brown University, Providence, Rhode Island
Venue:
Journal of the ACM (JACM)
Year:
1966

Citing 6
Cited 3

Unnormalized Floating Point Arithmetic

Journal of the ACM (JACM)
Floating-Point Arithmetics

Journal of the ACM (JACM)
An example in “significant-digit” arithmetic

Communications of the ACM
Significance arithmetic on a digital computer

Communications of the ACM
Algorithm 61: procedures for range arithmetic

Communications of the ACM
Rounding Errors in Algebraic Processes

Rounding Errors in Algebraic Processes

Computing a Subinterval of the Image

Journal of the ACM (JACM)
A precise numerical analysis program

Communications of the ACM
Implementation of interval arithmetic using APL

ACM SIGAPL APL Quote Quad

Quantified Score

Hi-index	0.02

Visualization

Abstract

Recent developments in computer design and error analysis have made feasible the use of variable precision arithmetic and the preparation of programs that automatically determine their own precision requirements. Such programs enable the user to specify the accuracy he wants, and yield answers guaranteed to lie within the bounds prescribed. A class of such programs, called “contracting error programs,” is defined in which the precision is determined by prescribing error bounds on the data. A variant of interval arithmetic is defined which enables a limited class of algorithms to be programmed as contracting error programs. A contracting error program for the solution of simultaneous linear equations is described, demonstrating the application of the idea to a wider class of problems.