Add manual promotion to arcsine, beta, and Bernoulli distributions

[mborland]

This is an extension to #1294 since it looks like most of the distributions have functions where manual promotion needs to be applied to follow what the policy says. I tried to reduce the ugliness as much as possible, but the result is that the code is generally less readable than it is without this PR. Thoughts @jzmaddock and @WarrenWeckesser. If there's no real opposition I can continue plugging along with this.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 94.47%. Comparing base (483f36c) to head (2852b4b).
⚠️ Report is 275 commits behind head on develop.

Additional details and impacted files

@@             Coverage Diff             @@
##           develop    #1299      +/-   ##
===========================================
- Coverage    95.07%   94.47%   -0.60%     
===========================================
  Files          796      686     -110     
  Lines        67020    49438   -17582     
===========================================
- Hits         63717    46705   -17012     
+ Misses        3303     2733     -570     

Files with missing lines	Coverage Δ
include/boost/math/distributions/beta.hpp	77.27% <ø> (-8.16%)	⬇️
include/boost/math/policies/policy.hpp	95.83% <ø> (ø)

... and 138 files with indirect coverage changes

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[JacobHass8]

I tried to reduce the ugliness as much as possible, but the result is that the code is generally less readable than it is without this PR. Thoughts @jzmaddock and @WarrenWeckesser. If there's no real opposition I can continue plugging along with this.

Would it be a little prettier if all the computations were done in a separate function. This is seems to be how type promotion is done with special functions. It seems a little more human readable to me since all the promotions are handled in one function and the computations in another. For example, the mean of the arcsin function would be something like this

template <class RealType, class Policy>
BOOST_MATH_GPU_ENABLED inline RealType mean(const arcsine_distribution<RealType, Policy>& dist)
{ // Mean of arcsine distribution .
  RealType result;
  RealType x_min = dist.x_min();
  RealType x_max = dist.x_max();

  if (false == arcsine_detail::check_dist(
    "boost::math::mean(arcsine_distribution<%1%> const&, %1% )",
    x_min,
    x_max,
    &result, Policy())
    )
  {
    return result;
  }

  using policy_promoted_type = policies::evaluation_t<RealType, Policy>;

  return static_cast<RealType>(arcsine_mean(static_cast<policy_promoted_type>(x_min), static_cast<policy_promoted_type>(x_max)));
}

template <class RealType>
inline RealType arcsine_mean(const RealType x_min, const RealType x_max)
{
  return (x_max + x_min) / 2;
}

For the arcsine distribution, this isn't that big of a change. However, it might make things prettier for more complicated functions.

If this seems reasonable, I can take a hack at it.

[mborland]

That does seem like a more elegant solution to me. If you'd like to take a stab at it, be my guest.

[JacobHass8]

That does seem like a more elegant solution to me. If you'd like to take a stab at it, be my guest.

Great! Should I make a new PR? I don't think I have write access to this PR.

[mborland]

That does seem like a more elegant solution to me. If you'd like to take a stab at it, be my guest.

Great! Should I make a new PR? I don't think I have write access to this PR.

Yes. I will close this one.