Unformatted text preview: , there were two
standard treatments before IEEE arithmetic: either set the result to (plus
or minus) the largest oating point number, or interrupt the program with
an error message. In IEEE arithmetic, the standard response depends on the
rounding mode. Suppose that the over owed value is positive. Then round up
gives the result 1, while round down and round towards zero set the result to
the largest oating point number. In the case of round to nearest, the result
is 1. From a strictly mathematical point of view, this is not consistent with
the de nition for nonover owed values, since a nite over ow value cannot
be said to be closer to 1 than to some other nite number. From a practical
point of view, however, the choice 1 is important, since round to nearest is
the default rounding mode and any other choice may lead to very misleading
nal computational results.
Under ow is said to occur when the true result of an arithmetic operation
is smaller in magnitude than the smallest normalized oating point number
which can be stored. Historically, the respon...
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This note was uploaded on 02/12/2014 for the course MATH 4800 taught by Professor Lie during the Spring '09 term at Rensselaer Polytechnic Institute.
 Spring '09
 LIE

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