As with division by zero there were two standard

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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 non-over 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.

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