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

DRAFT IEEE Standard for Floating-Point Arithmetic – 2003 August 12 10:20
3.3. Basic Decimal Format Encodings
Unlike basic binary floating-point formats, a representable numerical value may
have multiple representations in a basic decimal format; the set of all the distinct
representations of the name numerical value form that value’s cohort. For
example, in terms of the parameters in section 3.1, the values
{e+1-p = 0, m = 100},
{e+1-p = 1, m = 10}, and
{e+1-p = 2, m = 1}
are three distinct and distinguishable representations from the cohort of one
hundred. Consequently, unlike basic binary formats, basic decimal formats do not
require values to have a normalized representation. While numerically equal,
different members of a cohort can be distinguished by the decimal-specific
operations discussed in section 5.11. The cohorts of different values may have
different numbers of elements. If a nonzero value has v decimal digits from its
most significant nonzero digit to its least significant nonzero digit, the value’s
cohort will have at most (p-v)+1 elements where p is the number of digits of
precision in the format. For example, a 1-digit value can have up to p different
representations while a p-digit value only has one representation. (A v digit value
may have fewer than (p-v)+1 elements in its cohort if the value is near the
extremes of the format’s exponent range.) Zero has a much larger cohort; +0 and
-0 have a representation for each exponent. For decimal arithmetic, besides
specifying a numerical result, the arithmetic operands also specify which member
of the cohort to return; see section 5.12 for a discussion of this determination.
Traditional decimal applications make use of the additional exponent encoding
information cohorts allow.
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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