diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
index e29733c13..7c67ffdf7 100644
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
@@ -476,31 +476,35 @@ inline NewType cast(const OldType& x)
 * Implementation of round                                                   *
 ****************************************************************************/
 
+template<typename Scalar>
+struct round_impl
+{
+  EIGEN_DEVICE_FUNC
+  static inline Scalar run(const Scalar& x)
+  {
+    EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL)
 #if EIGEN_HAS_CXX11_MATH
-  template<typename Scalar>
-  struct round_impl {
-    EIGEN_DEVICE_FUNC
-    static inline Scalar run(const Scalar& x)
-    {
-      EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL)
-      EIGEN_USING_STD(round);
+    EIGEN_USING_STD(round);
+    return Scalar(round(x));
+#elif EIGEN_HAS_C99_MATH
+    if (is_same<Scalar, float>::value) {
+      return Scalar(::roundf(x));
+    } else {
       return Scalar(round(x));
     }
-  };
 #else
-  template<typename Scalar>
-  struct round_impl
-  {
-    EIGEN_DEVICE_FUNC
-    static inline Scalar run(const Scalar& x)
-    {
-      EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL)
-      EIGEN_USING_STD(floor);
-      EIGEN_USING_STD(ceil);
-      return (x > Scalar(0)) ? floor(x + Scalar(0.5)) : ceil(x - Scalar(0.5));
+    EIGEN_USING_STD(floor);
+    EIGEN_USING_STD(ceil);
+    // If not enough precision to resolve a decimal at all, return the input.
+    // Otherwise, adding 0.5 can trigger an increment by 1.
+    const Scalar limit = Scalar(1ull << (NumTraits<Scalar>::digits() - 1));
+    if (x >= limit || x <= -limit) {
+      return x;
     }
-  };
+    return (x > Scalar(0)) ? Scalar(floor(x + Scalar(0.5))) : Scalar(ceil(x - Scalar(0.5)));
 #endif
+  }
+};
 
 template<typename Scalar>
 struct round_retval