Fix ibeta_inv for very small p. (#962)

* Fix ibeta_inv for very small p.
Change assert's in temme_method_1_ibeta_inverse to corrections when guess goes out of range.
Change handling of non-convergence in second_order_root_finder to use bracketing when the end points are many orders of magnitude apart.
Fixes: https://github.com/boostorg/math/issues/961.

* Add missing copyright.
[CI SKIP]

test/Jamfile.v2

@@ -168,6 +168,7 @@ test-suite special_fun :
    [ run git_issue_705.cpp ../../test/build//boost_unit_test_framework  ]
    [ run git_issue_810.cpp ../../test/build//boost_unit_test_framework  ]
    [ run git_issue_826.cpp ../../test/build//boost_unit_test_framework  ]
+   [ run git_issue_961.cpp ]
    [ run special_functions_test.cpp ../../test/build//boost_unit_test_framework  ]
    [ run test_airy.cpp test_instances//test_instances pch_light ../../test/build//boost_unit_test_framework  ]
    [ run test_bessel_j.cpp test_instances//test_instances pch_light ../../test/build//boost_unit_test_framework  ]

test/git_issue_961.cpp

@@ -0,0 +1,76 @@
+//  (C) Copyright John Maddock 2023.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include <iostream>
+#include <iomanip>
+#include <cfenv>
+#include <boost/math/special_functions/beta.hpp>
+
+using namespace std;
+using namespace boost::math;
+
+void show_fp_exception_flags()
+{
+   if (std::fetestexcept(FE_DIVBYZERO)) {
+      cout << " FE_DIVBYZERO";
+   }
+   // FE_INEXACT is common and not interesting.
+   // if (std::fetestexcept(FE_INEXACT)) {
+   //     cout << " FE_INEXACT";
+   // }
+   if (std::fetestexcept(FE_INVALID)) {
+      cout << " FE_INVALID";
+   }
+   if (std::fetestexcept(FE_OVERFLOW)) {
+      cout << " FE_OVERFLOW";
+   }
+   if (std::fetestexcept(FE_UNDERFLOW)) {
+      cout << " FE_UNDERFLOW";
+   }
+   cout << endl;
+}
+
+template <class Policy>
+int test()
+{
+   double a = 14.208308325339239;
+   double b = a;
+
+   double p = 6.4898872103239473e-300;  // Throws exception: Assertion `x >= 0' failed.
+   // double p = 7.8e-307;  // No flags set, returns 8.57354094063444939e-23
+   // double p = 7.7e-307;  // FE_UNDERFLOW set, returns 0.0
+
+   while (p > (std::numeric_limits<double>::min)())
+   {
+      std::feclearexcept(FE_ALL_EXCEPT);
+
+      try {
+
+         double x = ibeta_inv(a, b, p, Policy());
+
+         show_fp_exception_flags();
+
+         std::cout << std::scientific << std::setw(24)
+            << std::setprecision(17) << x << std::endl;
+      }
+      catch (const std::exception& e)
+      {
+         std::cout << e.what() << std::endl;
+         return 1;
+      }
+
+      p /= 1.25;
+   }
+
+   return 0;
+}
+
+int main(int argc, char* argv[])
+{
+   using namespace boost::math::policies;
+   if (test<policy<>>())
+      return 1;
+   return test<policy<promote_double<false>>>();
+}