only solve problems if have enough precision (#1004)

include/boost/math/special_functions/detail/ibeta_inverse.hpp

@@ -25,23 +25,16 @@ namespace boost{ namespace math{ namespace detail{
 template <class T>
 struct temme_root_finder
 {
- temme_root_finder(const T t_, const T a_) : t(t_), a(a_) {}
+ temme_root_finder(const T t_, const T a_) : t(t_), a(a_) {
+ const T x_extrema = 1 / (1 + a);
+ BOOST_MATH_ASSERT(0 < x_extrema && x_extrema < 1);
+ }
 
  boost::math::tuple<T, T> operator()(T x)
  {
  BOOST_MATH_STD_USING // ADL of std names
 
  T y = 1 - x;
- if(y == 0)
- {
- T big = tools::max_value<T>() / 4;
- return boost::math::make_tuple(static_cast<T>(-big), static_cast<T>(-big));
- }
- if(x == 0)
- {
- T big = tools::max_value<T>() / 4;
- return boost::math::make_tuple(static_cast<T>(-big), big);
- }
  T f = log(x) + a * log(y) + t;
  T f1 = (1 / x) - (a / (y));
  return boost::math::make_tuple(f, f1);
@@ -410,6 +403,10 @@ T temme_method_3_ibeta_inverse(T a, T b, T p, T q, const Policy& pol)
  T lower = eta < mu ? cross : 0;
  T upper = eta < mu ? 1 : cross;
  T x = (lower + upper) / 2;
+
+ // Early exit for cases with numerical precision issues.
+ if (cross == 0 || cross == 1) { return cross; }
+
  x = tools::newton_raphson_iterate(
  temme_root_finder<T>(u, mu), x, lower, upper, policies::digits<T, Policy>() / 2);
 #ifdef BOOST_INSTRUMENT