Add 3-arg hypot impl

include/boost/math/special_functions/hypot.hpp

@@ -16,6 +16,7 @@
 #include <boost/math/tools/type_traits.hpp>
 #include <boost/math/policies/error_handling.hpp>
 #include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/math/tools/utility.hpp>
 
 namespace boost{ namespace math{ namespace detail{
 
@@ -53,6 +54,42 @@ BOOST_MATH_GPU_ENABLED T hypot_imp(T x, T y, const Policy& pol)
    return x * sqrt(1 + rat*rat);
 } // template <class T> T hypot(T x, T y)
 
+template <class T, class Policy>
+BOOST_MATH_GPU_ENABLED T hypot_impl(T x, T y, T z, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+
+   x = fabs(x);
+   y = fabs(y);
+   z = fabs(z);
+
+   #ifdef _MSC_VER
+   #pragma warning(push)
+   #pragma warning(disable: 4127)
+   #endif
+   // special case, see C99 Annex F:
+   BOOST_MATH_IF_CONSTEXPR (boost::math::numeric_limits<T>::has_infinity)
+   {
+      if(((x == boost::math::numeric_limits<T>::infinity())
+         || (y == boost::math::numeric_limits<T>::infinity())
+         || (z == boost::math::numeric_limits<T>::infinity())))
+         return policies::raise_overflow_error<T>("boost::math::hypot<%1%>(%1%,%1%,%1%)", nullptr, pol);
+   }
+   #ifdef _MSC_VER
+   #pragma warning(pop)
+   #endif
+
+   const T a {(max)((max)(x, y), z)};
+   const T x_div_a {x / a};
+   const T y_div_a {y / a};
+   const T z_div_a {z / a};
+
+   return a * sqrt(x_div_a * x_div_a
+                 + y_div_a * y_div_a
+                 + z_div_a * z_div_a);
+
+}
+
 }
 
 template <class T1, class T2>
@@ -73,6 +110,28 @@ BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T1, T2>::type
       static_cast<result_type>(x), static_cast<result_type>(y), pol);
 }
 
+template <class T1, class T2, class T3, boost::math::enable_if_t<!policies::is_policy<T3>::value, bool> = true>
+BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2, T3>
+   hypot(T1 x, T2 y, T3 z)
+{
+   using result_type = tools::promote_args_t<T1, T2, T3>;
+   return detail::hypot_imp(static_cast<result_type>(x),
+                            static_cast<result_type>(y),
+                            static_cast<result_type>(z),
+                            policies::policy<>());
+}
+
+template <class T1, class T2, class T3, class Policy>
+BOOST_MATH_GPU_ENABLED tools::promote_args_t<T1, T2, T3>
+   hypot(T1 x, T2 y, T3 z, const Policy& pol)
+{
+   using result_type = tools::promote_args_t<T1, T2, T3>;
+   return detail::hypot_imp(static_cast<result_type>(x),
+                            static_cast<result_type>(y),
+                            static_cast<result_type>(z),
+                            pol);
+}
+
 } // namespace math
 } // namespace boost