Multistep gradual rounding

1 April 1989

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Computers

Vol. 38 (4) , 595-600
https://doi.org/10.1109/12.21152

Abstract

A value V is to be rounded to an arbitrary precision resulting in the value V". Conventional rounding technique uses one step to accomplish this. Multistep rounding uses several steps to round the value V to successively shorter precisions with the final rounding step producing the desired value V". This alternate rounding method is one way to implement with the minimum of hardware, the denormalization process that the IEEE Floating-Point Standard 754 requires when underflow occurs. There are certain cases for which multistep rounding produces a different result than single-step rounding. To prevent such a step error, the author introduces a rounding procedure called gradual rounding that is very similar to conventional rounding with the addition of two tag bits associated with each floating-point register.

Keywords

This publication has 2 references indexed in Scilit:

Numerical Turing
ACM SIGNUM Newsletter, 1985
A Proposed Radix- and Word-length-independent Standard for Floating-point Arithmetic
IEEE Micro, 1984