[Cfp-interest] AI about exp10m1 range error

[Jim Thomas]

> Action Item: exp10m1: Look at exp10m1 difference between the TS and 754 in more detail.



David H asked if exp10m1 shouldn’t allow a range error if the magnitude of x is too small, like expm1 does. I believe Fred raised the same question some time back. 

It’s true that exp10m1 (and expm1) can underflow in the 754 sense.

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.

The C definition of underflow is based on “denormalization loss” as in 754-1985, which was removed in 754-2008.

I think C footnote 232 should be changed.

Jim Thomas