Inconsistent behavior of ibeta_inv(a, b, x) with nan input

[WarrenWeckesser]

I don't know if this qualifies as a bug, or is undefined behavior as far as boost/math is concerned, but I get three different behaviors from ibeta_inv(nan, 2, 0.5), ibeta_inv(2, nan, 0.5) and ibeta_inv(2, 2, nan):

• ibeta_inv(nan, 2, 0.5) does not raise an exception; nan is returned.

• ibeta_inv(2, nan, 0.5) raises:

  ibeta_inv: /home/warren/repos/git/forks/boost/math/include/boost/math/special_functions/beta.hpp:723:
  T boost::math::detail::ibeta_fraction2(T, T, T, T, const Policy&, bool, T*)
  [with T = long double; Policy = boost::math::policies::policy<boost::math::policies::promote_float<false>, boost::math::policies::promote_double<false>, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy, boost::math::policies::default_policy>]:
  Assertion `*p_derivative >= 0' failed.
  

• ibeta_inv(2, 2, nan) raises:

  terminate called after throwing an instance of 'boost::wrapexcept<boost::math::rounding_error>'
  what():  Error in function boost::math::trunc<long double>(long double):
  Value nan can not be represented in the target integer type.
  

[jzmaddock]

I would say it's a bug, and should probably raise a domain error in all 3 cases. Will investigate.