diff --git a/Eigen/src/Core/functors/UnaryFunctors.h b/Eigen/src/Core/functors/UnaryFunctors.h
index 72d485814..1092fee50 100644
--- a/Eigen/src/Core/functors/UnaryFunctors.h
+++ b/Eigen/src/Core/functors/UnaryFunctors.h
@@ -1026,8 +1026,10 @@ struct scalar_logistic_op {
   template <typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
   Packet packetOp(const Packet& x) const {
     const Packet one = pset1<Packet>(T(1));
+    const Packet inf = pset1<Packet>(NumTraits<T>::infinity());
     const Packet e = pexp(x);
-    return pdiv(e, padd(one, e));
+    const Packet inf_mask = pcmp_eq(e, inf);
+    return pselect(inf_mask, one, pdiv(e, padd(one, e)));
   }
 };
 
@@ -1052,7 +1054,9 @@ template <>
 struct scalar_logistic_op<float> {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_logistic_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float operator()(const float& x) const {
-    const float e = numext::exp(x);
+    // Truncate at the first point where the interpolant is exactly one.
+    const float cst_exp_hi = 16.6355324f;
+    const float e = numext::exp(numext::mini(x, cst_exp_hi));
     return e / (1.0f + e);
   }
 
@@ -1062,7 +1066,8 @@ struct scalar_logistic_op<float> {
     const Packet cst_zero = pset1<Packet>(0.0f);
     const Packet cst_one = pset1<Packet>(1.0f);
     const Packet cst_half = pset1<Packet>(0.5f);
-    const Packet cst_exp_hi = pset1<Packet>(16.f);
+    // Truncate at the first point where the interpolant is exactly one.
+    const Packet cst_exp_hi = pset1<Packet>(16.6355324f);
     const Packet cst_exp_lo = pset1<Packet>(-104.f);
 
     // Clamp x to the non-trivial range where S(x). Outside this
@@ -1117,6 +1122,7 @@ struct scalar_logistic_op<float> {
 };
 #endif  // #ifndef EIGEN_GPU_COMPILE_PHASE
 
+
 template <typename T>
 struct functor_traits<scalar_logistic_op<T> > {
   enum {