diff --git a/libcxx/include/__math/traits.h b/libcxx/include/__math/traits.h
index 35c283cc9e21c..2ca231e0428fb 100644
--- a/libcxx/include/__math/traits.h
+++ b/libcxx/include/__math/traits.h
@@ -127,14 +127,21 @@ _LIBCPP_NODISCARD inline _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI boo
 
 // isnormal
 
-template <class _A1, __enable_if_t<is_floating_point<_A1>::value, int> = 0>
+template <class _A1, __enable_if_t<is_integral<_A1>::value, int> = 0>
 _LIBCPP_NODISCARD _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI bool isnormal(_A1 __x) _NOEXCEPT {
+  return __x != 0;
+}
+
+_LIBCPP_NODISCARD inline _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI bool isnormal(float __x) _NOEXCEPT {
   return __builtin_isnormal(__x);
 }
 
-template <class _A1, __enable_if_t<is_integral<_A1>::value, int> = 0>
-_LIBCPP_NODISCARD _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI bool isnormal(_A1 __x) _NOEXCEPT {
-  return __x != 0;
+_LIBCPP_NODISCARD inline _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI bool isnormal(double __x) _NOEXCEPT {
+  return __builtin_isnormal(__x);
+}
+
+_LIBCPP_NODISCARD inline _LIBCPP_CONSTEXPR_SINCE_CXX23 _LIBCPP_HIDE_FROM_ABI bool isnormal(long double __x) _NOEXCEPT {
+  return __builtin_isnormal(__x);
 }
 
 // isgreater
diff --git a/libcxx/test/std/numerics/c.math/isnormal.pass.cpp b/libcxx/test/std/numerics/c.math/isnormal.pass.cpp
index c3b8f31359f98..76c3d13520d99 100644
--- a/libcxx/test/std/numerics/c.math/isnormal.pass.cpp
+++ b/libcxx/test/std/numerics/c.math/isnormal.pass.cpp
@@ -62,9 +62,23 @@ struct TestInt {
   }
 };
 
+template <typename T>
+struct ConvertibleTo {
+  operator T() const { return T(1); }
+};
+
 int main(int, char**) {
   types::for_each(types::floating_point_types(), TestFloat());
   types::for_each(types::integral_types(), TestInt());
 
+  // Make sure we can call `std::isnormal` with convertible types. This checks
+  // whether overloads for all cv-unqualified floating-point types are working
+  // as expected.
+  {
+    assert(std::isnormal(ConvertibleTo<float>()));
+    assert(std::isnormal(ConvertibleTo<double>()));
+    assert(std::isnormal(ConvertibleTo<long double>()));
+  }
+
   return 0;
 }