DRAFT IEEE Standard for Binary Floating-Point Arithmetic - Sonic.net

DRAFT IEEE Standard for Floating-Point Arithmetic – 2003 August 12 10:20
[While NaN and infinity have multiple representations, they do not have cohorts
with the current definition. -JDD]
[Are +0.0 and -0.0 in the same cohort? Yes, if cohorts are based on extended
value values. -JDD]
[Note: Unlike 854, which would make no distinction among member of a cohort
(other than +0 and -0), 754R introduces operations for the express purpose of
distinguishing among the different elements in a cohort. This is a different
philosophy from 854; section 3.1 “The [854] standard allows an implementation
to encode some values redundantly provided that it does not distinguish redundant
encodings of nonzero values.” However, no 854 operation would return different
result based on which element of a 754R decimal cohort was used. -JDD]
Numbers in the decimal formats are encoded in the following four
fields as shown in Figure 1-10:
1. 1-bit sign S
2. 5-bit combination field G encoding classification, two leading exponent bits
whose value together is 0, 1, or 2, and one leading significand digit
3. w-bit following exponent field which, when combined with the two leading
exponent bits from the combination field, provides a w+2-bit biased exponent
E = e + bias
4. t-bit trailing significand field T = j 1 ... j J . There are J = t÷10
groups j i ; each these groups of ten bits is a declet encoding
three decimal digits. When the declets are combined with the
leading significand digit from the combination field, the format
has a total of p = 1 + 3× J decimal digits.
Figure 1-10 Basic Decimal Floating-Point Format
Copyright © 2003 by the Institute of Electrical and Electronics Engineers, Inc. This document is an unapproved
draft of a proposed IEEE-SA Standard - USE AT YOUR OWN RISK. See statement on page 1.
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