`hypergeometric_1F1(a, b, x)` with large enough x hangs.

[WarrenWeckesser]

With the develop branch, the call hypergeometric_1F1(2.0, 3.0, 1e30) never returns. With smaller (but still "large") values of x, e.g. hypergeometric_1F1(2.0, 3.0, 1e10), the expected overflow_error exception is thrown.

(I originally found this problem when calling boost/math from SciPy, and verified that a C++ program that used the develop branch also has the problem.)

[WarrenWeckesser]

I think the problem is in the implementation of hypergeometric_1F1_imp(const T& a, const T& b, const T& z, const Policy& pol) where it processes the result of hypergeometric_1F1_imp(a, b, z, pol, log_scaling). As the comment there says, "Actual result will be result * e^log_scaling". There are two loops that iteratively update result and log_scaling, but they don't consider the possibility of result becoming inf.

I don't know if this would be the best (or even correct) fix, but a quick fix is to change this line:

math/include/boost/math/special_functions/hypergeometric_1F1.hpp

Line 640 in 3698582

while (log_scaling > max_scaling)

to

      while (!isinf(result) && log_scaling > max_scaling)

EDIT: The above "quick fix" was checked with a few examples with the default double promotion policy. More work is needed to handle the very large arguments when double promotion is disabled.

[jzmaddock]

Thanks for the report: I'll look into this, but I have a hunch this is caused by a "feature".