FloatingPointRepresentation

P number under ow set result to zero or subnormal

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Unformatted text preview: to zero or subnormal number Precision Set result to correctly rounded value normalized numbers? 5 . Exercise 24 Consider the computation of the previous exercise again. Is it possible that d and e could have many less digits of accuracy than a and b, even though a and b are normalized numbers? Altogether, the IEEE standard de nes ve kinds of exceptions: invalid operation, division by zero, over ow, under ow and precision, together with a standard response for each of these. All of these have just been described except the last. The last exception is, in fact, not exceptional at all because it occurs every time the result of an arithmetic operation is not a oating point number and therefore requires rounding. Table 4 summarizes the standard response for the ve exceptions. The IEEE standard speci es that when an exception occurs it must be signaled by setting an associated status ag, and that the programmer should have the option of either trapping the exception, providing special code to be executed when the exception occurs, or masking the exception, in which case the program continues executing with the standard response shown in the table. If the user is not programming...
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