Function Evaluation in Unnormalized Arithmetic
Journal of the ACM (JACM)
Number Base Conversion in a Significant Digit Arithmetic
Journal of the ACM (JACM)
Computable Error Bounds for Direct Solution of Linear Equations
Journal of the ACM (JACM)
Iterative Refinement in Floating Point
Journal of the ACM (JACM)
On the Compatibility of a Given Solution With the Data of a Linear System
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
Communications of the ACM
Error analysis in floating point arithmetic
Communications of the ACM
Approximations for Digital Computers
Approximations for Digital Computers
Normalized floating-point arithmetic with an index of significance
IRE-AIEE-ACM '59 (Eastern) Papers presented at the December 1-3, 1959, eastern joint IRE-AIEE-ACM computer conference
The Maniac III arithmetic system
AIEE-IRE '62 (Spring) Proceedings of the May 1-3, 1962, spring joint computer conference
The influence of machine design on numerical algorithms
AFIPS '67 (Spring) Proceedings of the April 18-20, 1967, spring joint computer conference
AFIPS '67 (Spring) Proceedings of the April 18-20, 1967, spring joint computer conference
Accurate solution of linear algebraic systems: a survey
AFIPS '67 (Spring) Proceedings of the April 18-20, 1967, spring joint computer conference
Statistical validation of mathematical computer routines
AFIPS '67 (Spring) Proceedings of the April 18-20, 1967, spring joint computer conference
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A scheme is proposed for permitting a user of conventional procedural programming languages (initially, Standard FORTRAN) to test actual error propagation in numerical calculations. The process is to be fully mechanistic so that, with no human resequencing required or permitted, a "numerical procedure debugging" tool is made available. Other goals include a quantification of the order-of-precision decision for specified accuracy, provision of an observational tool for determining word length requirements, and an automatic facility for utilizing other kinds of arithmetic interpretively in executing existing programs and program segments. The experimental package consists, in effect, of a compiler from FORTRAN source language into an artificial machine language in which arithmetic operations produce, in addition to numerical results, a measure of the current accuracy of each result operand.