What to do with underflows when constituent would otherwise not underflow

[ckormanyos]

This curiously named issue relates to some of the discussions raised in #140.

In that issue we identified a test case:

// N[BesselK[-1000, 700], 51]
// 6.515619791447358189035538526063833129844093619841284E-31

At one point in the calculation of BesselK[-1000, 700], the value of exp(-700) is computed, which is approximately $9.86{\times}10^{-305}$. An exponent of $-305$ is out-of-range for cpp_double_fp< eight-byte-double >, hence eval_exp() returns $0$ which cascades to the final output being $0$ as well.

The result of the modified Bessel function is not an extreme edge-case, but getting to this result relies on edge-case (or near edge-case) multiplication.

What's the strategy on such calculations?

• Take the result of $0$ which is actually correct for the intermediate steps?
• Modify the scaling of the calculation? This seems like an overly-curated approach to handling the special functions calculations in Math.
• Eliminate the test point from the test suite for this particular backend type?

I'm curious what John (@jzmaddock) might think.

Cc: @sinandredemption and @cosurgi