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

DRAFT IEEE Standard for Floating-Point Arithmetic – 2003 August 12 10:20
[In addition to the IEEE 754 rounding modes, the Java BigDecimal class provides
a number of other rounding modes:
• round to nearest with ties rounding away from zero
• round to nearest with ties rounding toward zero
• round away from zero
• round unnecessary (throw exception for inexact)
-JDD]
4.3. Rounding Precision
Normally, a result is rounded to the precision of its destination. However, some
systems deliver arithmetic results only to destinations wider than their operands.
On such a system the user, which may be a high-level language compiler, shall be
able to specify that a result be rounded instead to any supported narrower
precision with only one rounding, though it may be stored in a wider format with
its wider exponent range. §Q
Normally, a result is rounded to the precision of its destination. However, some
systems deliver results only to double or extended destinations. On such a system
the user, which may be a high-level language compiler, shall be able to specify that
a result be rounded instead to single precision, though it may be stored in the
double or extended format with its wider exponent range. §Q
[FOOTNOTE 4: Control of rounding precision is intended to allow systems
whose destinations are always 64-bit or wider to mimic, in the absence of
over/underflow, the precisions of systems with only narrower destinations. But an
implementation should not provide operations that combine wider operands to
produce a narrower result, with only one rounding.] §Q
[FOOTNOTE 4: Control of rounding precision is intended to allow systems
whose destinations are always double or extended to mimic, in the absence of
over/underflow, the precisions of systems with single and double destinations. An
implementation should not provide operations that combine double or extended
operands to produce a single result, nor operations that combine double extended
operands to produce a double result, with only one rounding.] §Q
However, while it is permissible to provide only rounding to narrower precision
with wider exponent range, on such a system it should also be possible to round
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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