diff --git a/Eigen/src/Core/GenericPacketMath.h b/Eigen/src/Core/GenericPacketMath.h
index f8950eaf7..fc5d7570c 100644
--- a/Eigen/src/Core/GenericPacketMath.h
+++ b/Eigen/src/Core/GenericPacketMath.h
@@ -135,7 +135,14 @@ template <typename T>
 struct unpacket_traits {
   typedef T type;
   typedef T half;
-  enum { size = 1, alignment = 1, vectorizable = false, masked_load_available = false, masked_store_available = false };
+  typedef typename numext::get_integer_by_size<sizeof(T)>::signed_type integer_packet;
+  enum {
+    size = 1,
+    alignment = alignof(T),
+    vectorizable = false,
+    masked_load_available = false,
+    masked_store_available = false
+  };
 };
 
 template <typename T>
diff --git a/Eigen/src/Core/arch/AltiVec/PacketMath.h b/Eigen/src/Core/arch/AltiVec/PacketMath.h
index 06901df1a..eed545c48 100644
--- a/Eigen/src/Core/arch/AltiVec/PacketMath.h
+++ b/Eigen/src/Core/arch/AltiVec/PacketMath.h
@@ -3178,8 +3178,8 @@ struct packet_traits<double> : default_packet_traits {
     HasMin = 1,
     HasMax = 1,
     HasAbs = 1,
-    HasSin = 0,
-    HasCos = 0,
+    HasSin = EIGEN_FAST_MATH,
+    HasCos = EIGEN_FAST_MATH,
     HasATan = 0,
     HasLog = 0,
     HasExp = 1,
@@ -3214,10 +3214,11 @@ struct unpacket_traits<Packet2d> {
 template <>
 struct unpacket_traits<Packet2l> {
   typedef int64_t type;
+  typedef Packet2l half;
   enum {
     size = 2,
     alignment = Aligned16,
-    vectorizable = true,
+    vectorizable = false,
     masked_load_available = false,
     masked_store_available = false
   };