diff --git a/include/boost/math/special_functions/round.hpp b/include/boost/math/special_functions/round.hpp
index e6602908c6..7fe78d6c85 100644
--- a/include/boost/math/special_functions/round.hpp
+++ b/include/boost/math/special_functions/round.hpp
@@ -18,39 +18,17 @@
 #include <limits>
 #include <cmath>
 
+#if __cplusplus >= 201703L || _MSVC_LANG >= 201703L
+#include <boost/math/ccmath/ldexp.hpp>
+#  ifndef BOOST_MATH_NO_CONSTEXPR_DETECTION
+#    define BOOST_MATH_HAS_CONSTEXPR_LDEXP
+#  endif
+#endif
+
 namespace boost{ namespace math{
 
 namespace detail{
 
-// https://stackoverflow.com/questions/8905246/how-to-check-if-float-can-be-exactly-represented-as-an-integer/17822304#17822304
-template <typename T, typename ResultType>
-inline ResultType float_to_int(T x)
-{
-   BOOST_MATH_STD_USING
-
-   constexpr int sign = std::is_signed<ResultType>::value ? -1 : 0;
-
-   T y = floor(x);
-   if (y < static_cast<T>(0.0L))
-   {
-      return 0;
-   }
-   
-   if (y >= ldexp(static_cast<T>(1.0L), (sizeof(ResultType) * CHAR_BIT) + sign) + sign)
-   {
-      return (std::numeric_limits<ResultType>::max)();
-   }
-
-   return static_cast<ResultType>(y);
-}
-
-template <typename T, typename TargetType>
-inline bool is_representable(T x)
-{
-   BOOST_MATH_STD_USING
-   return (floor(x) == x && x >= static_cast<T>(0.0L) && x < ldexp(static_cast<T>(1.0L), sizeof(TargetType) * CHAR_BIT));
-}
-
 template <class T, class Policy>
 inline tools::promote_args_t<T> round(const T& v, const Policy& pol, const std::false_type&)
 {
@@ -158,25 +136,21 @@ template <class T, class Policy>
 inline long long llround(const T& v, const Policy& pol)
 {
    BOOST_MATH_STD_USING
-   using result_type = tools::promote_args_t<T>;
+   using result_type = boost::math::tools::promote_args_t<T>;
 
-   T r = boost::math::round(v, pol);
-   long long return_val = boost::math::detail::float_to_int<result_type, long long>(r);
-   bool representable = boost::math::detail::is_representable<result_type, long long>(r);
+   result_type r = boost::math::round(v, pol);
 
-   if ((return_val == (std::numeric_limits<long long>::max)() && !representable) ||
-       r < static_cast<result_type>((std::numeric_limits<long long>::min)()) ||
-       r > static_cast<result_type>((std::numeric_limits<long long>::max)()))
-   {
-      return static_cast<long long>(policies::raise_rounding_error("boost::math::llround<%1%>(%1%)", nullptr, v, static_cast<long long>(0), pol));
-   }
+   #ifdef BOOST_MATH_HAS_CONSTEXPR_LDEXP
+   constexpr result_type max_val = boost::math::ccmath::ldexp(static_cast<result_type>(1), std::numeric_limits<long long>::digits);
+   #else
+   static const result_type max_val = std::ldexp(static_cast<result_type>(1), std::numeric_limits<long long>::digits);
+   #endif
 
-   if (r < 0)
+   if (r >= max_val || r < -max_val)
    {
-      return_val = static_cast<long long>(r);
+      return static_cast<long long>(boost::math::policies::raise_rounding_error("boost::math::llround<%1%>(%1%)", nullptr, v, static_cast<long long>(0), pol));
    }
-
-   return return_val;
+   return static_cast<long long>(r);
 }
 template <class T>
 inline long long llround(const T& v)
diff --git a/test/git_issue_430.cpp b/test/git_issue_430.cpp
index fd6bc89a93..907bc9ed5d 100644
--- a/test/git_issue_430.cpp
+++ b/test/git_issue_430.cpp
@@ -1,4 +1,5 @@
-// Copyright Matt Borland, 2023
+// Copyright Matt Borland 2023
+// 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)
@@ -6,14 +7,40 @@
 // See: https://godbolt.org/z/Ev4ManrsW
 
 #include <boost/math/special_functions/round.hpp>
+#define BOOST_TEST_MAIN
+#include <boost/test/unit_test.hpp>
 #include <cstdint>
-#include "math_unit_test.hpp"
 
-double x = 9223372036854775807.0;  // can't be represented as double, will have a different value at runtime. 
-int main()
+template <typename Real>
+void test_llround_near_boundary()
 {
-    int64_t result = boost::math::llround(x);
-    CHECK_EQUAL(result, INT64_C(9223372036854775807));
+   using std::ldexp;
+   Real boundary = ldexp(static_cast<Real>(1), std::numeric_limits<long long>::digits);
 
-    return boost::math::test::report_errors();
+   Real value;
+   int i;
+
+   for (value = boundary, i = 0; i < 100; value = boost::math::float_next(value), ++i)
+   {
+      BOOST_CHECK_THROW(boost::math::llround(value), boost::math::rounding_error);
+   }
+   for (value = boost::math::float_prior(boundary), i = 0; i < 1000; value = boost::math::float_prior(value), ++i)
+   {
+      BOOST_CHECK_EQUAL(static_cast<Real>(boost::math::llround(value)), boost::math::round(value));
+   }
+   for (value = boost::math::float_prior(-boundary), i = 0; i < 100; value = boost::math::float_prior(value), ++i)
+   {
+      BOOST_CHECK_THROW(boost::math::llround(value), boost::math::rounding_error);
+   }
+   for (value = -boundary, i = 0; i < 1000; value = boost::math::float_next(value), ++i)
+   {
+      BOOST_CHECK_EQUAL(static_cast<Real>(boost::math::llround(value)), boost::math::round(value));
+   }
+}
+
+BOOST_AUTO_TEST_CASE( test_main )
+{
+    test_llround_near_boundary<float>();
+    test_llround_near_boundary<double>();
+    test_llround_near_boundary<long double>();
 }