[Cfp-interest 2063] Re: Underflow

[Jim Thomas]

> So, I am in favor of something like:
> 
>   The result underflows (unless specified otherwise) if the magnitude
>   (absolute value) of the mathematical result is nonzero and less than
>   the minimum normal number in the type and not equal to the result in
>   the type.249)

This seems to require the implementation to determine whether the magnitude of the mathematical result is less than the minimum normal number. How would this be a reasonable requirement given that implementations are not required to meet any error bounds? For most functions, the input value could be tested against a predetermined underflow threshold, but that might yield a surprising determination of underflow given the value returned. For example, a returned result might be zero but underflow disallowed because the mathematical function value is in the normal range. Does underflow (or overflow) occur because the implementation's approximation is out of range or because the mathematical function is out of range? If the implementation is correctly rounded, the two are the same. Otherwise, the former is more practical and arguably more useful.
- Jim Thomas
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