Send exact -infinity in log functions to the overflow policy

[NAThompson]

Drop exact_infinity; fix logcdf at infinite x, students_t logcdf at huge |x|,
and polynomial_roots for variable precision (tools::). Part of #1569.

🤖 Generated with Claude Code

[ckormanyos]

Hi Nick (@NAThompson) I think it was in this PR, but I'm not quite sure. One of my independent projects fails the nightly now due to errors in policy. It is the second nightly run in a row failing, so it must have happened about 2 days ago.

run benchmarks with clang++ and language standard c++20

In file included from ./src/app/benchmark/app_benchmark_boost_math_cbrt_tgamma.cpp:39:
In file included from ../../boost-root/boost/math/constants/constants.hpp:16:
../../boost-root/boost/math/policies/policy.hpp:497:8: error: redefinition of 'policy<>'
  497 | struct policy<detail::forwarding_arg1, detail::forwarding_arg2, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy>
      |        ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
../../boost-root/boost/math/policies/policy.hpp:472:7: note: previous definition is here
  472 | class policy<default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy>
      |       ^
../../boost-root/boost/math/policies/policy.hpp:654:8: error: redefinition of 'normalise<boost::math::policies::policy<default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy>, boost::math::policies::promote_float<>, boost::math::policies::promote_double<>, boost::math::policies::discrete_quantile<>, boost::math::policies::assert_undefined<>>'
  654 | struct normalise<policy<detail::forwarding_arg1, detail::forwarding_arg2>,
      |        ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  655 |           promote_float<false>,
      |           ~~~~~~~~~~~~~~~~~~~~~
  656 |           promote_double<false>,
      |           ~~~~~~~~~~~~~~~~~~~~~~
  657 |           discrete_quantile<>,
      |           ~~~~~~~~~~~~~~~~~~~~
  658 |           assert_undefined<>,
      |           ~~~~~~~~~~~~~~~~~~~
  659 |           default_policy,
      |           ~~~~~~~~~~~~~~~
  660 |           default_policy,
      |           ~~~~~~~~~~~~~~~
  661 |           default_policy,
      |           ~~~~~~~~~~~~~~~
  662 |           default_policy,
      |           ~~~~~~~~~~~~~~~
  663 |           default_policy,
      |           ~~~~~~~~~~~~~~~
  664 |           default_policy,
      |           ~~~~~~~~~~~~~~~
  665 |           default_policy>
      |           ~~~~~~~~~~~~~~~
../../boost-root/boost/math/policies/policy.hpp:637:8: note: previous definition is here
  637 | struct normalise<policy<>,
      |        ^
2 errors generated.
In file included from ./src/app/benchmark/app_benchmark_boost_math_cyl_bessel_j.cpp:71:
In file included from ../../boost-root/boost/math/special_functions/bessel.hpp:22:
In file included from ../../boost-root/boost/math/tools/roots.hpp:20:
In file included from ../../boost-root/boost/math/special_functions/sign.hpp:20:
In file included from ../../boost-root/boost/math/special_functions/math_fwd.hpp:31:
../../boost-root/boost/math/policies/policy.hpp:497:8: error: redefinition of 'policy<>'
  497 | struct policy<detail::forwarding_arg1, detail::forwarding_arg2, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy>
      |        ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
../../boost-root/boost/math/policies/policy.hpp:472:7: note: previous definition is here
  472 | class policy<default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy>
      |       ^
../../boost-root/boost/math/policies/policy.hpp:654:8: error: redefinition of 'normalise<boost::math::policies::policy<default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy, default_policy>, boost::math::policies::promote_float<>, boost::math::policies::promote_double<>, boost::math::policies::discrete_quantile<>, boost::math::policies::assert_undefined<>>'
  654 | struct normalise<policy<detail::forwarding_arg1, detail::forwarding_arg2>,
      |        ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  655 |           promote_float<false>,
      |           ~~~~~~~~~~~~~~~~~~~~~
  656 |           promote_double<false>,
      |           ~~~~~~~~~~~~~~~~~~~~~~
  657 |           discrete_quantile<>,
      |           ~~~~~~~~~~~~~~~~~~~~
  658 |           assert_undefined<>,
      |           ~~~~~~~~~~~~~~~~~~~
  659 |           default_policy,
      |           ~~~~~~~~~~~~~~~
  660 |           default_policy,
      |           ~~~~~~~~~~~~~~~
  661 |           default_policy,
      |           ~~~~~~~~~~~~~~~
  662 |           default_policy,
      |           ~~~~~~~~~~~~~~~
  663 |           default_policy,
      |           ~~~~~~~~~~~~~~~
  664 |           default_policy,
      |           ~~~~~~~~~~~~~~~
  665 |           default_policy>
      |           ~~~~~~~~~~~~~~~
../../boost-root/boost/math/policies/policy.hpp:637:8: note: previous definition is here
  637 | struct normalise<policy<>,
      |        ^
2 errors generated.

[NAThompson]

@ckormanyos : Thanks for testing! New PR incoming.