diff --git a/include/boost/math/ccmath/floor.hpp b/include/boost/math/ccmath/floor.hpp
index fa071e24ba..fb1dea34db 100644
--- a/include/boost/math/ccmath/floor.hpp
+++ b/include/boost/math/ccmath/floor.hpp
@@ -15,6 +15,7 @@
 #include <boost/math/ccmath/abs.hpp>
 #include <boost/math/ccmath/isinf.hpp>
 #include <boost/math/ccmath/isnan.hpp>
+#include <limits>
 
 namespace boost::math::ccmath {
 
@@ -23,6 +24,13 @@ namespace detail {
 template <typename T>
 inline constexpr T floor_pos_impl(T arg) noexcept
 {
+    constexpr auto max_comp_val = T(1) / std::numeric_limits<T>::epsilon();
+
+    if (arg >= max_comp_val)
+    {
+        return arg;
+    }
+
     T result = 1;
 
     if(result < arg)
diff --git a/test/ccmath_ceil_test.cpp b/test/ccmath_ceil_test.cpp
index 9540ea99d6..79c92bffd8 100644
--- a/test/ccmath_ceil_test.cpp
+++ b/test/ccmath_ceil_test.cpp
@@ -37,6 +37,20 @@ constexpr void test()
     static_assert(boost::math::ccmath::ceil(T(2.9)) == T(3));
     static_assert(boost::math::ccmath::ceil(T(-2.7)) == T(-2));
     static_assert(boost::math::ccmath::ceil(T(-2)) == T(-2));
+
+    using std::ceil;
+
+    constexpr T half_max_ceil = boost::math::ccmath::ceil(T((std::numeric_limits<T>::max)() / 2));
+    static_assert(half_max_ceil == (std::numeric_limits<T>::max)() / 2);
+    BOOST_MATH_ASSERT(half_max_ceil == ceil((std::numeric_limits<T>::max)() / 2));
+
+    constexpr T third_max_ceil = boost::math::ccmath::ceil(T((std::numeric_limits<T>::max)() / 3));
+    static_assert(third_max_ceil == (std::numeric_limits<T>::max)() / 3);
+    BOOST_MATH_ASSERT(third_max_ceil == ceil((std::numeric_limits<T>::max)() / 3));
+
+    constexpr T one_over_eps = boost::math::ccmath::ceil(1 / T(std::numeric_limits<T>::epsilon()));
+    static_assert(one_over_eps == 1 / T(std::numeric_limits<T>::epsilon()));
+    BOOST_MATH_ASSERT(one_over_eps == ceil(1 / T(std::numeric_limits<T>::epsilon())));
 }
 
 #if !defined(BOOST_MATH_NO_CONSTEXPR_DETECTION) && !defined(BOOST_MATH_USING_BUILTIN_CONSTANT_P)
diff --git a/test/ccmath_floor_test.cpp b/test/ccmath_floor_test.cpp
index aa907fab11..ddd0a53e9d 100644
--- a/test/ccmath_floor_test.cpp
+++ b/test/ccmath_floor_test.cpp
@@ -37,6 +37,20 @@ constexpr void test()
     static_assert(boost::math::ccmath::floor(T(2.9)) == T(2));
     static_assert(boost::math::ccmath::floor(T(-2.7)) == T(-3));
     static_assert(boost::math::ccmath::floor(T(-2)) == T(-2));
+
+    using std::floor;
+
+    constexpr T half_max_floor = boost::math::ccmath::floor(T((std::numeric_limits<T>::max)() / 2));
+    static_assert(half_max_floor == (std::numeric_limits<T>::max)() / 2);
+    BOOST_MATH_ASSERT(half_max_floor == floor((std::numeric_limits<T>::max)() / 2));
+
+    constexpr T third_max_floor = boost::math::ccmath::floor(T((std::numeric_limits<T>::max)() / 3));
+    static_assert(third_max_floor == (std::numeric_limits<T>::max)() / 3);
+    BOOST_MATH_ASSERT(third_max_floor == floor((std::numeric_limits<T>::max)() / 3));
+
+    constexpr T one_over_eps = boost::math::ccmath::floor(1 / T(std::numeric_limits<T>::epsilon()));
+    static_assert(one_over_eps == 1 / T(std::numeric_limits<T>::epsilon()));
+    BOOST_MATH_ASSERT(one_over_eps == floor(1 / T(std::numeric_limits<T>::epsilon())));
 }
 
 #if !defined(BOOST_MATH_NO_CONSTEXPR_DETECTION) && !defined(BOOST_MATH_USING_BUILTIN_CONSTANT_P)