On Local Roundoff Errors in Floating-Point Arithmetic

Authors:
Toyohisa Kaneko;Bede Liu
Affiliations:
IBM Thomas J Watson Research Center, Yorktown Heights, NY and Princeton University, Princeton, New Jersey;Department of Electrical Engineering, Brackett Hall, Engineering Quadrangle, Princeton University, Princeton, New Jersey
Venue:
Journal of the ACM (JACM)
Year:
1973

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Abstract

A bound on the relative error in floating-point addition using a single-precision accumulator with guard digits is derived. It is shown that even with a single guard digit, the accuracy can be almost as good as that using a double-precision accumulator. A statistical model for the roundoff error in double-precision multiplication and addition is also derived. The model is confirmed by experimental measurements.