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From: dgh%dgh@Sun.COM (David Hough)
Newsgroups: comp.arch
Subject: Re: IEEE floating point modes (and Interval Arithmetic)
Message-ID: <22601@sun.uucp>
Date: Thu, 2-Jul-87 14:41:37 EDT
Article-I.D.: sun.22601
Posted: Thu Jul  2 14:41:37 1987
Date-Received: Sat, 4-Jul-87 08:09:58 EDT
References: <93900007@hcx1>
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Summary: All IEEE rounding modes are useful.

An implementation of IEEE 754 or 854 floating point must provide
all four specified rounding modes with round-to-nearest as
default.  

As to why all are specified, round-to-nearest is most likely 
to provide the best results on most problems.  The directed
roundings toward zero, negative infinity, and positive infinity
are useful for special purposes.  Round toward zero is used
a lot for converting floating-point numbers to integers,
and for Fortran functions like AINT.  Likewise ceil(3m) and
floor(3m) are most easily implemented using the directed
rounding modes.

However the most important reason for requiring directed rounding
modes is to facilitate efficient implementation of interval arithmetic.
Interval arithmetic is a systematic approach to
bounding all the errors in a computation.  It has its limitations
but has been usefully applied in a great many situations.  
A group at Karlsruhe
led by Nickel has been studying applications for many years,
although handicapped by hardware that lacked directable rounding.  
And interval arithmetic has
even received a half-baked commercialization in the form of the
ACRITH hardware for some IBM mainframes.

Another interval arithmetic pioneer, Ramon Moore, has organized
a conference on the subject for September 8-11 at Ohio State.

David Hough

ARPA: dhough@sun.com
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