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# Second Order Statistical Round

IP.com Disclosure Number: IPCOM000092449D
Original Publication Date: 1966-Nov-01
Included in the Prior Art Database: 2005-Mar-05
Document File: 1 page(s) / 11K

IBM

## Related People

Freiman, CV: AUTHOR [+2]

## Abstract

In order to avoid either the time or hardware cost or both of a true rounding procedure, computers have employed a first-order statistical round. In this first-order procedure the lowest retained bit is set to 1 independent of the quantity deleted. Two serious disadvantages exist with this method. First, a true zero becomes nonzero when rounded. Secondly, in repeated roundings of positive intermediate results in normalized form, a systematic error is introduced.

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Second Order Statistical Round

In order to avoid either the time or hardware cost or both of a true rounding procedure, computers have employed a first-order statistical round. In this first- order procedure the lowest retained bit is set to 1 independent of the quantity deleted. Two serious disadvantages exist with this method. First, a true zero becomes nonzero when rounded. Secondly, in repeated roundings of positive intermediate results in normalized form, a systematic error is introduced.

The second-order method eliminates these problems and maintains the unbiased nature of the basic statistical round at extremely small hardware cost. The rounding rules are shown in tabular form where B and A are the original values of the two lowest retained bits and B' and A' are the rounded values of these bits. B A B' A'

0 0 0 0

0 1 1 0

1 0 1 1

1 1 1 1. Clearly, A' = B and B' = A v B.

Thus the requirement of second-order rounding over first-order rounding is one additional Or at worst.

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