[Cfp-interest] AI about exp10m1 range error

[Fred J. Tydeman]

On Tue, 6 Feb 2018 10:20:45 -0800 Jim Thomas wrote:
>
>However, the C definition of underflow, in the specification of range errors, is: "The result underflows if the magnitude of the mathematical result is so small that the mathematical result cannot be represented, without extraordinary roundoff error, in an object of the specified type." For exp10m1(tiny) the result is accurate to the full precision of the type, so there is no extraordinary roundoff error (which is not the case for expm1). So I think our current specification is ok, albeit subtle.
>

I disagree.  To a first approximation, exp10m1(x) is x*ln(10) = 2.3*x
So, for subnormal numbers, it is not accurate to the full precision.


---
Fred J. Tydeman        Tydeman Consulting
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