diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
index ecc6f3883..6b1bfacdd 100644
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
@@ -229,63 +229,6 @@ struct imag_ref_retval
   typedef typename NumTraits<Scalar>::Real & type;
 };
 
-
-/****************************************************************************
-* Implementation of sign                                                 *
-****************************************************************************/
-template<typename Scalar, bool IsComplex = (NumTraits<Scalar>::IsComplex!=0),
-    bool IsInteger = (NumTraits<Scalar>::IsInteger!=0)>
-struct sign_impl
-{
-  EIGEN_DEVICE_FUNC
-  static inline Scalar run(const Scalar& a)
-  {
-    return Scalar( (a>Scalar(0)) - (a<Scalar(0)) );
-  }
-};
-
-template<typename Scalar>
-struct sign_impl<Scalar, false, false>
-{
-  EIGEN_DEVICE_FUNC
-  static inline Scalar run(const Scalar& a)
-  {
-    return (std::isnan)(a) ? a : Scalar( (a>Scalar(0)) - (a<Scalar(0)) );
-  }
-};
-
-template<typename Scalar, bool IsInteger>
-struct sign_impl<Scalar, true, IsInteger>
-{
-  EIGEN_DEVICE_FUNC
-  static inline Scalar run(const Scalar& a)
-  {
-    using real_type = typename NumTraits<Scalar>::Real;
-    real_type aa = std::abs(a);
-    if (aa==real_type(0))
-      return Scalar(0);
-    aa = real_type(1)/aa;
-    return Scalar(a.real()*aa, a.imag()*aa );
-  }
-};
-
-// The sign function for bool is the identity.
-template<>
-struct sign_impl<bool, false, true>
-{
-  EIGEN_DEVICE_FUNC
-  static inline bool run(const bool& a)
-  {
-    return a;
-  }
-};
-
-template<typename Scalar>
-struct sign_retval
-{
-  typedef Scalar type;
-};
-
 /****************************************************************************
 * Implementation of conj                                                 *
 ****************************************************************************/
@@ -664,7 +607,7 @@ struct expm1_impl {
   EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x)
   {
     EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
-    using std::expm1;
+    EIGEN_USING_STD(expm1);
     return expm1(x);
   }
 };
@@ -725,7 +668,7 @@ struct log1p_impl {
 
   EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x)
   {
-    using std::log1p;
+    EIGEN_USING_STD(log1p);
     return log1p(x);
   }
 };
@@ -938,128 +881,114 @@ inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random()
 
 // Implementation of is* functions
 
-// std::is* do not work with fast-math and gcc, std::is* are available on MSVC 2013 and newer, as well as in clang.
-#if (!(EIGEN_COMP_GNUC_STRICT && __FINITE_MATH_ONLY__)) || (EIGEN_COMP_MSVC) || (EIGEN_COMP_CLANG)
-#define EIGEN_USE_STD_FPCLASSIFY 1
-#else
-#define EIGEN_USE_STD_FPCLASSIFY 0
-#endif
-
-template<typename T>
-EIGEN_DEVICE_FUNC
-std::enable_if_t<internal::is_integral<T>::value,bool>
-isnan_impl(const T&) { return false; }
-
-template<typename T>
-EIGEN_DEVICE_FUNC
-std::enable_if_t<internal::is_integral<T>::value,bool>
-isinf_impl(const T&) { return false; }
-
-template<typename T>
-EIGEN_DEVICE_FUNC
-std::enable_if_t<internal::is_integral<T>::value,bool>
-isfinite_impl(const T&) { return true; }
-
-template<typename T>
-EIGEN_DEVICE_FUNC
-std::enable_if_t<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>
-isfinite_impl(const T& x)
-{
-  #if defined(EIGEN_GPU_COMPILE_PHASE)
-    return (::isfinite)(x);
-  #elif EIGEN_USE_STD_FPCLASSIFY
-    using std::isfinite;
-    return isfinite EIGEN_NOT_A_MACRO (x);
-  #else
-    return x<=NumTraits<T>::highest() && x>=NumTraits<T>::lowest();
-  #endif
+template <typename T>
+EIGEN_DEVICE_FUNC std::enable_if_t<!(std::numeric_limits<T>::has_infinity ||
+                                     std::numeric_limits<T>::has_quiet_NaN ||
+                                     std::numeric_limits<T>::has_signaling_NaN),
+                                   bool>
+isfinite_impl(const T&) {
+  return true;
 }
 
-template<typename T>
+template <typename T>
+EIGEN_DEVICE_FUNC std::enable_if_t<(std::numeric_limits<T>::has_infinity || std::numeric_limits<T>::has_quiet_NaN ||
+                                    std::numeric_limits<T>::has_signaling_NaN) &&
+                                       (!NumTraits<T>::IsComplex),
+                                   bool>
+isfinite_impl(const T& x) {
+  EIGEN_USING_STD(isfinite);
+  return (isfinite)(x);
+}
+
+template <typename T>
+EIGEN_DEVICE_FUNC std::enable_if_t<!std::numeric_limits<T>::has_infinity, bool>
+isinf_impl(const T&) {
+  return false;
+}
+
+template <typename T>
+EIGEN_DEVICE_FUNC std::enable_if_t<
+    (std::numeric_limits<T>::has_infinity && !NumTraits<T>::IsComplex), bool>
+isinf_impl(const T& x) {
+  EIGEN_USING_STD(isinf);
+  return (isinf)(x);
+}
+
+template <typename T>
+EIGEN_DEVICE_FUNC std::enable_if_t<!(std::numeric_limits<T>::has_quiet_NaN ||
+                                     std::numeric_limits<T>::has_signaling_NaN),
+                                   bool>
+isnan_impl(const T&) {
+  return false;
+}
+
+template <typename T>
 EIGEN_DEVICE_FUNC
-std::enable_if_t<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>
-isinf_impl(const T& x)
-{
-  #if defined(EIGEN_GPU_COMPILE_PHASE)
-    return (::isinf)(x);
-  #elif EIGEN_USE_STD_FPCLASSIFY
-    using std::isinf;
-    return isinf EIGEN_NOT_A_MACRO (x);
-  #else
-    return x>NumTraits<T>::highest() || x<NumTraits<T>::lowest();
-  #endif
+    std::enable_if_t<(std::numeric_limits<T>::has_quiet_NaN ||
+                      std::numeric_limits<T>::has_signaling_NaN) &&
+                         (!NumTraits<T>::IsComplex),
+                     bool>
+    isnan_impl(const T& x) {
+  EIGEN_USING_STD(isnan);
+  return (isnan)(x);
 }
 
-template<typename T>
-EIGEN_DEVICE_FUNC
-std::enable_if_t<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>
-isnan_impl(const T& x)
-{
-  #if defined(EIGEN_GPU_COMPILE_PHASE)
-    return (::isnan)(x);
-  #elif EIGEN_USE_STD_FPCLASSIFY
-    using std::isnan;
-    return isnan EIGEN_NOT_A_MACRO (x);
-  #else
-    return x != x;
-  #endif
-}
-
-#if (!EIGEN_USE_STD_FPCLASSIFY)
-
-#if EIGEN_COMP_MSVC
-
-template<typename T> EIGEN_DEVICE_FUNC bool isinf_msvc_helper(T x)
-{
-  return _fpclass(x)==_FPCLASS_NINF || _fpclass(x)==_FPCLASS_PINF;
-}
-
-//MSVC defines a _isnan builtin function, but for double only
-#ifndef EIGEN_GPU_COMPILE_PHASE
-EIGEN_DEVICE_FUNC inline bool isnan_impl(const long double& x) { return _isnan(x)!=0; }
-#endif
-EIGEN_DEVICE_FUNC inline bool isnan_impl(const double& x)      { return _isnan(x)!=0; }
-EIGEN_DEVICE_FUNC inline bool isnan_impl(const float& x)       { return _isnan(x)!=0; }
-
-#ifndef EIGEN_GPU_COMPILE_PHASE
-EIGEN_DEVICE_FUNC inline bool isinf_impl(const long double& x) { return isinf_msvc_helper(x); }
-#endif
-EIGEN_DEVICE_FUNC inline bool isinf_impl(const double& x)      { return isinf_msvc_helper(x); }
-EIGEN_DEVICE_FUNC inline bool isinf_impl(const float& x)       { return isinf_msvc_helper(x); }
-
-#elif (defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ && EIGEN_COMP_GNUC)
-
-#if EIGEN_COMP_GNUC
-  #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((optimize("no-finite-math-only")))
-#else
-  // NOTE the inline qualifier and noinline attribute are both needed: the former is to avoid linking issue (duplicate symbol),
-  //      while the second prevent too aggressive optimizations in fast-math mode:
-  #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((noinline,optimize("no-finite-math-only")))
-#endif
-
-#ifndef EIGEN_GPU_COMPILE_PHASE
-template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const long double& x) { return __builtin_isnan(x); }
-#endif
-template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const double& x)      { return __builtin_isnan(x); }
-template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const float& x)       { return __builtin_isnan(x); }
-template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const double& x)      { return __builtin_isinf(x); }
-template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const float& x)       { return __builtin_isinf(x); }
-#ifndef EIGEN_GPU_COMPILE_PHASE
-template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const long double& x) { return __builtin_isinf(x); }
-#endif
-
-#undef EIGEN_TMP_NOOPT_ATTRIB
-
-#endif
-
-#endif
-
 // The following overload are defined at the end of this file
-template<typename T> EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x);
-template<typename T> EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x);
-template<typename T> EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x);
+template <typename T>
+EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x);
+template <typename T>
+EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x);
+template <typename T>
+EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x);
+template <typename T>
+T generic_fast_tanh_float(const T& a_x);
+
+/****************************************************************************
+ * Implementation of sign                                                 *
+ ****************************************************************************/
+template <typename Scalar, bool IsComplex = (NumTraits<Scalar>::IsComplex != 0),
+          bool IsInteger = (NumTraits<Scalar>::IsInteger != 0)>
+struct sign_impl {
+  EIGEN_DEVICE_FUNC
+  static inline Scalar run(const Scalar& a) {
+    return Scalar((a > Scalar(0)) - (a < Scalar(0)));
+  }
+};
+
+template <typename Scalar>
+struct sign_impl<Scalar, false, false> {
+  EIGEN_DEVICE_FUNC
+  static inline Scalar run(const Scalar& a) {
+    return (isnan_impl<Scalar>)(a) ? a
+                                   : Scalar((a > Scalar(0)) - (a < Scalar(0)));
+  }
+};
+
+template <typename Scalar, bool IsInteger>
+struct sign_impl<Scalar, true, IsInteger> {
+  EIGEN_DEVICE_FUNC
+  static inline Scalar run(const Scalar& a) {
+    using real_type = typename NumTraits<Scalar>::Real;
+    EIGEN_USING_STD(abs);
+    real_type aa = abs(a);
+    if (aa == real_type(0)) return Scalar(0);
+    aa = real_type(1) / aa;
+    return Scalar(a.real() * aa, a.imag() * aa);
+  }
+};
+
+// The sign function for bool is the identity.
+template <>
+struct sign_impl<bool, false, true> {
+  EIGEN_DEVICE_FUNC
+  static inline bool run(const bool& a) { return a; }
+};
+
+template <typename Scalar>
+struct sign_retval {
+  typedef Scalar type;
+};
 
-template<typename T> T generic_fast_tanh_float(const T& a_x);
 } // end namespace internal
 
 /****************************************************************************
diff --git a/test/AnnoyingScalar.h b/test/AnnoyingScalar.h
index dc20d43a7..94b513c41 100644
--- a/test/AnnoyingScalar.h
+++ b/test/AnnoyingScalar.h
@@ -65,7 +65,7 @@ class AnnoyingScalar
 
     AnnoyingScalar operator-() const
     { return AnnoyingScalar(-*v); }
-    
+
     AnnoyingScalar operator-(const AnnoyingScalar& other) const
     { return AnnoyingScalar(*v-*other.v); }
     
@@ -140,11 +140,6 @@ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
 bool (isfinite)(const AnnoyingScalar& x) {
   return (numext::isfinite)(*x.v);
 }
-template<>
-EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
-bool (isnan)(const AnnoyingScalar& x) {
-  return (numext::isnan)(*x.v);
-}
 }
 
 namespace internal {