FloatingPointRepresentation

When the operation just illustrated modi ed to re ect

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Unformatted text preview: illustrated, modi ed to re ect the Cray's longer wordlength, is performed on a Cray XMP, the result generated is wrong by a factor of two since a one is shifted past the end of the second operand's signi cand and discarded. In this example, instead of having x y = (x ; y)(1 + ) where (3) we have x y = 2(x ; y ). On a Cray YMP, on the other hand, the second operand is rounded before the operation takes place. This converts the second operand to the value 1.0 and causes a nal result of 0.0 to be computed, i.e. x y = 0. Evidently, Cray supercomputers do not use correctly rounded arithmetic. 19 Machines supporting the IEEE standard do, however, have correctly rounded arithmetic, so that (3), for example, always holds. Exactly how this is implemented depends on the machine, but typically oating point operations are carried out using extended precision registers, e.g. 80-bit registers, even if the values loaded from and stored to memory are only single or double precision. This e ectively provides many...
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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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