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

DRAFT IEEE Standard for Floating-Point Arithmetic – 2003 August 12 10:20
3. (Previous draft) Formats
This standard defines four floating-point formats in two groups, basic and
extended, each having two widths, single and double. The standard levels of
implementation are distinguished by the combinations of formats supported.
3.1. Sets of Values
This section concerns only the numerical values representable within a format, not
the encodings. The only values representable in a chosen format are those
specified by way of the following three integer parameters:
• p = the number of significant bits (precision)
• E max = the maximum exponent
• E min = the minimum exponent .
Each format's parameters are given in Table 1. Within each format only the
following entities shall be provided:
• Numbers of the form (–1) s 2 E ( b 0 . b 1 b 2 ... b p–1 ), where
• s = 0 or 1
• E = any integer between E min and E max , inclusive
• b i = 0 or 1
• Two infinities, +¥ and –¥
• At least one signaling NaN
• At least one quiet NaN
The foregoing description enumerates some values redundantly, for example, 2 0
(1.0) = 2 1 (0.1) = 2 2 (0.0 1) = ... . However, the encodings of such nonzero
values may be redundant only in extended formats (3.3). The nonzero values of
the form ± 2 E min (0 . b 1 b 2 ... b p–1 ) are called denormalized. Reserved exponents
may be used to encode NaNs, ±¥ , ±0, and denormalized numbers. For any
variable that has the value zero, the sign bit s provides an extra bit of information.
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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