diff --git a/test/packetmath.cpp b/test/packetmath.cpp
index 38aa256..7821a17 100644
--- a/test/packetmath.cpp
+++ b/test/packetmath.cpp
@@ -9,16 +9,28 @@
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
 #include "main.h"
+#include "unsupported/Eigen/SpecialFunctions"
 
+#if defined __GNUC__ && __GNUC__>=6
+  #pragma GCC diagnostic ignored "-Wignored-attributes"
+#endif
 // using namespace Eigen;
 
+#ifdef EIGEN_VECTORIZE_SSE
+const bool g_vectorize_sse = true;
+#else
+const bool g_vectorize_sse = false;
+#endif
+
 namespace Eigen {
 namespace internal {
 template<typename T> T negate(const T& x) { return -x; }
 }
 }
 
-template<typename Scalar> bool isApproxAbs(const Scalar& a, const Scalar& b, const typename NumTraits<Scalar>::Real& refvalue)
+// NOTE: we disbale inlining for this function to workaround a GCC issue when using -O3 and the i387 FPU.
+template<typename Scalar> EIGEN_DONT_INLINE
+bool isApproxAbs(const Scalar& a, const Scalar& b, const typename NumTraits<Scalar>::Real& refvalue)
 {
   return internal::isMuchSmallerThan(a-b, refvalue);
 }
@@ -29,7 +41,7 @@
   {
     if (!isApproxAbs(a[i],b[i],refvalue))
     {
-      std::cout << "[" << Map<const Matrix<Scalar,1,Dynamic> >(a,size) << "]" << " != " << Map<const Matrix<Scalar,1,Dynamic> >(b,size) << "\n";
+      std::cout << "ref: [" << Map<const Matrix<Scalar,1,Dynamic> >(a,size) << "]" << " != vec: [" << Map<const Matrix<Scalar,1,Dynamic> >(b,size) << "]\n";
       return false;
     }
   }
@@ -42,21 +54,13 @@
   {
     if (a[i]!=b[i] && !internal::isApprox(a[i],b[i]))
     {
-      std::cout << "[" << Map<const Matrix<Scalar,1,Dynamic> >(a,size) << "]" << " != " << Map<const Matrix<Scalar,1,Dynamic> >(b,size) << "\n";
+      std::cout << "ref: [" << Map<const Matrix<Scalar,1,Dynamic> >(a,size) << "]" << " != vec: [" << Map<const Matrix<Scalar,1,Dynamic> >(b,size) << "]\n";
       return false;
     }
   }
   return true;
 }
 
-
-#define CHECK_CWISE2(REFOP, POP) { \
-  for (int i=0; i<PacketSize; ++i) \
-    ref[i] = REFOP(data1[i], data1[i+PacketSize]); \
-  internal::pstore(data2, POP(internal::pload<Packet>(data1), internal::pload<Packet>(data1+PacketSize))); \
-  VERIFY(areApprox(ref, data2, PacketSize) && #POP); \
-}
-
 #define CHECK_CWISE1(REFOP, POP) { \
   for (int i=0; i<PacketSize; ++i) \
     ref[i] = REFOP(data1[i]); \
@@ -92,6 +96,14 @@
   VERIFY(areApprox(ref, data2, PacketSize) && #POP); \
 }
 
+#define CHECK_CWISE2_IF(COND, REFOP, POP) if(COND) { \
+  packet_helper<COND,Packet> h; \
+  for (int i=0; i<PacketSize; ++i) \
+    ref[i] = REFOP(data1[i], data1[i+PacketSize]); \
+  h.store(data2, POP(h.load(data1),h.load(data1+PacketSize))); \
+  VERIFY(areApprox(ref, data2, PacketSize) && #POP); \
+}
+
 #define REF_ADD(a,b) ((a)+(b))
 #define REF_SUB(a,b) ((a)-(b))
 #define REF_MUL(a,b) ((a)*(b))
@@ -100,15 +112,17 @@
 template<typename Scalar> void packetmath()
 {
   using std::abs;
-  typedef typename internal::packet_traits<Scalar>::type Packet;
-  const int PacketSize = internal::packet_traits<Scalar>::size;
+  typedef internal::packet_traits<Scalar> PacketTraits;
+  typedef typename PacketTraits::type Packet;
+  const int PacketSize = PacketTraits::size;
   typedef typename NumTraits<Scalar>::Real RealScalar;
 
-  const int size = PacketSize*4;
-  EIGEN_ALIGN16 Scalar data1[internal::packet_traits<Scalar>::size*4];
-  EIGEN_ALIGN16 Scalar data2[internal::packet_traits<Scalar>::size*4];
-  EIGEN_ALIGN16 Packet packets[PacketSize*2];
-  EIGEN_ALIGN16 Scalar ref[internal::packet_traits<Scalar>::size*4];
+  const int max_size = PacketSize > 4 ? PacketSize : 4;
+  const int size = PacketSize*max_size;
+  EIGEN_ALIGN_MAX Scalar data1[size];
+  EIGEN_ALIGN_MAX Scalar data2[size];
+  EIGEN_ALIGN_MAX Packet packets[PacketSize*2];
+  EIGEN_ALIGN_MAX Scalar ref[size];
   RealScalar refvalue = 0;
   for (int i=0; i<size; ++i)
   {
@@ -140,6 +154,18 @@
     else if (offset==1) internal::palign<1>(packets[0], packets[1]);
     else if (offset==2) internal::palign<2>(packets[0], packets[1]);
     else if (offset==3) internal::palign<3>(packets[0], packets[1]);
+    else if (offset==4) internal::palign<4>(packets[0], packets[1]);
+    else if (offset==5) internal::palign<5>(packets[0], packets[1]);
+    else if (offset==6) internal::palign<6>(packets[0], packets[1]);
+    else if (offset==7) internal::palign<7>(packets[0], packets[1]);
+    else if (offset==8) internal::palign<8>(packets[0], packets[1]);
+    else if (offset==9) internal::palign<9>(packets[0], packets[1]);
+    else if (offset==10) internal::palign<10>(packets[0], packets[1]);
+    else if (offset==11) internal::palign<11>(packets[0], packets[1]);
+    else if (offset==12) internal::palign<12>(packets[0], packets[1]);
+    else if (offset==13) internal::palign<13>(packets[0], packets[1]);
+    else if (offset==14) internal::palign<14>(packets[0], packets[1]);
+    else if (offset==15) internal::palign<15>(packets[0], packets[1]);
     internal::pstore(data2, packets[0]);
 
     for (int i=0; i<PacketSize; ++i)
@@ -148,13 +174,17 @@
     VERIFY(areApprox(ref, data2, PacketSize) && "internal::palign");
   }
 
-  CHECK_CWISE2(REF_ADD,  internal::padd);
-  CHECK_CWISE2(REF_SUB,  internal::psub);
-  CHECK_CWISE2(REF_MUL,  internal::pmul);
-  #ifndef EIGEN_VECTORIZE_ALTIVEC
-  if (!internal::is_same<Scalar,int>::value)
-    CHECK_CWISE2(REF_DIV,  internal::pdiv);
-  #endif
+  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasAdd);
+  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasSub);
+  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasMul);
+  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasNegate);
+  VERIFY((internal::is_same<Scalar,int>::value) || (!PacketTraits::Vectorizable) || PacketTraits::HasDiv);
+
+  CHECK_CWISE2_IF(PacketTraits::HasAdd, REF_ADD,  internal::padd);
+  CHECK_CWISE2_IF(PacketTraits::HasSub, REF_SUB,  internal::psub);
+  CHECK_CWISE2_IF(PacketTraits::HasMul, REF_MUL,  internal::pmul);
+  CHECK_CWISE2_IF(PacketTraits::HasDiv, REF_DIV, internal::pdiv);
+
   CHECK_CWISE1(internal::negate, internal::pnegate);
   CHECK_CWISE1(numext::conj, internal::pconj);
 
@@ -165,9 +195,31 @@
     internal::pstore(data2, internal::pset1<Packet>(data1[offset]));
     VERIFY(areApprox(ref, data2, PacketSize) && "internal::pset1");
   }
-  
+
+  {
+    for (int i=0; i<PacketSize*4; ++i)
+      ref[i] = data1[i/PacketSize];
+    Packet A0, A1, A2, A3;
+    internal::pbroadcast4<Packet>(data1, A0, A1, A2, A3);
+    internal::pstore(data2+0*PacketSize, A0);
+    internal::pstore(data2+1*PacketSize, A1);
+    internal::pstore(data2+2*PacketSize, A2);
+    internal::pstore(data2+3*PacketSize, A3);
+    VERIFY(areApprox(ref, data2, 4*PacketSize) && "internal::pbroadcast4");
+  }
+
+  {
+    for (int i=0; i<PacketSize*2; ++i)
+      ref[i] = data1[i/PacketSize];
+    Packet A0, A1;
+    internal::pbroadcast2<Packet>(data1, A0, A1);
+    internal::pstore(data2+0*PacketSize, A0);
+    internal::pstore(data2+1*PacketSize, A1);
+    VERIFY(areApprox(ref, data2, 2*PacketSize) && "internal::pbroadcast2");
+  }
+
   VERIFY(internal::isApprox(data1[0], internal::pfirst(internal::pload<Packet>(data1))) && "internal::pfirst");
-  
+
   if(PacketSize>1)
   {
     for(int offset=0;offset<4;++offset)
@@ -179,11 +231,31 @@
     }
   }
 
+  if(PacketSize>2)
+  {
+    for(int offset=0;offset<4;++offset)
+    {
+      for(int i=0;i<PacketSize/4;++i)
+        ref[4*i+0] = ref[4*i+1] = ref[4*i+2] = ref[4*i+3] = data1[offset+i];
+      internal::pstore(data2,internal::ploadquad<Packet>(data1+offset));
+      VERIFY(areApprox(ref, data2, PacketSize) && "ploadquad");
+    }
+  }
+
   ref[0] = 0;
   for (int i=0; i<PacketSize; ++i)
     ref[0] += data1[i];
   VERIFY(isApproxAbs(ref[0], internal::predux(internal::pload<Packet>(data1)), refvalue) && "internal::predux");
 
+  {
+    for (int i=0; i<4; ++i)
+      ref[i] = 0;
+    for (int i=0; i<PacketSize; ++i)
+      ref[i%4] += data1[i];
+    internal::pstore(data2, internal::predux_downto4(internal::pload<Packet>(data1)));
+    VERIFY(areApprox(ref, data2, PacketSize>4?PacketSize/2:PacketSize) && "internal::predux_downto4");
+  }
+
   ref[0] = 1;
   for (int i=0; i<PacketSize; ++i)
     ref[0] *= data1[i];
@@ -203,116 +275,258 @@
     ref[i] = data1[PacketSize-i-1];
   internal::pstore(data2, internal::preverse(internal::pload<Packet>(data1)));
   VERIFY(areApprox(ref, data2, PacketSize) && "internal::preverse");
+
+  internal::PacketBlock<Packet> kernel;
+  for (int i=0; i<PacketSize; ++i) {
+    kernel.packet[i] = internal::pload<Packet>(data1+i*PacketSize);
+  }
+  ptranspose(kernel);
+  for (int i=0; i<PacketSize; ++i) {
+    internal::pstore(data2, kernel.packet[i]);
+    for (int j = 0; j < PacketSize; ++j) {
+      VERIFY(isApproxAbs(data2[j], data1[i+j*PacketSize], refvalue) && "ptranspose");
+    }
+  }
+
+  if (PacketTraits::HasBlend) {
+    Packet thenPacket = internal::pload<Packet>(data1);
+    Packet elsePacket = internal::pload<Packet>(data2);
+    EIGEN_ALIGN_MAX internal::Selector<PacketSize> selector;
+    for (int i = 0; i < PacketSize; ++i) {
+      selector.select[i] = i;
+    }
+
+    Packet blend = internal::pblend(selector, thenPacket, elsePacket);
+    EIGEN_ALIGN_MAX Scalar result[size];
+    internal::pstore(result, blend);
+    for (int i = 0; i < PacketSize; ++i) {
+      VERIFY(isApproxAbs(result[i], (selector.select[i] ? data1[i] : data2[i]), refvalue));
+    }
+  }
+
+  if (PacketTraits::HasBlend || g_vectorize_sse) {
+    // pinsertfirst
+    for (int i=0; i<PacketSize; ++i)
+      ref[i] = data1[i];
+    Scalar s = internal::random<Scalar>();
+    ref[0] = s;
+    internal::pstore(data2, internal::pinsertfirst(internal::pload<Packet>(data1),s));
+    VERIFY(areApprox(ref, data2, PacketSize) && "internal::pinsertfirst");
+  }
+
+  if (PacketTraits::HasBlend || g_vectorize_sse) {
+    // pinsertlast
+    for (int i=0; i<PacketSize; ++i)
+      ref[i] = data1[i];
+    Scalar s = internal::random<Scalar>();
+    ref[PacketSize-1] = s;
+    internal::pstore(data2, internal::pinsertlast(internal::pload<Packet>(data1),s));
+    VERIFY(areApprox(ref, data2, PacketSize) && "internal::pinsertlast");
+  }
 }
 
 template<typename Scalar> void packetmath_real()
 {
   using std::abs;
-  typedef typename internal::packet_traits<Scalar>::type Packet;
-  const int PacketSize = internal::packet_traits<Scalar>::size;
+  typedef internal::packet_traits<Scalar> PacketTraits;
+  typedef typename PacketTraits::type Packet;
+  const int PacketSize = PacketTraits::size;
 
   const int size = PacketSize*4;
-  EIGEN_ALIGN16 Scalar data1[internal::packet_traits<Scalar>::size*4];
-  EIGEN_ALIGN16 Scalar data2[internal::packet_traits<Scalar>::size*4];
-  EIGEN_ALIGN16 Scalar ref[internal::packet_traits<Scalar>::size*4];
+  EIGEN_ALIGN_MAX Scalar data1[PacketTraits::size*4];
+  EIGEN_ALIGN_MAX Scalar data2[PacketTraits::size*4];
+  EIGEN_ALIGN_MAX Scalar ref[PacketTraits::size*4];
 
   for (int i=0; i<size; ++i)
   {
     data1[i] = internal::random<Scalar>(-1,1) * std::pow(Scalar(10), internal::random<Scalar>(-3,3));
     data2[i] = internal::random<Scalar>(-1,1) * std::pow(Scalar(10), internal::random<Scalar>(-3,3));
   }
-  CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasSin, std::sin, internal::psin);
-  CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasCos, std::cos, internal::pcos);
-  CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasTan, std::tan, internal::ptan);
-  
+  CHECK_CWISE1_IF(PacketTraits::HasSin, std::sin, internal::psin);
+  CHECK_CWISE1_IF(PacketTraits::HasCos, std::cos, internal::pcos);
+  CHECK_CWISE1_IF(PacketTraits::HasTan, std::tan, internal::ptan);
+
+  CHECK_CWISE1_IF(PacketTraits::HasRound, numext::round, internal::pround);
+  CHECK_CWISE1_IF(PacketTraits::HasCeil, numext::ceil, internal::pceil);
+  CHECK_CWISE1_IF(PacketTraits::HasFloor, numext::floor, internal::pfloor);
+
   for (int i=0; i<size; ++i)
   {
     data1[i] = internal::random<Scalar>(-1,1);
     data2[i] = internal::random<Scalar>(-1,1);
   }
-  CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasASin, std::asin, internal::pasin);
-  CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasACos, std::acos, internal::pacos);
+  CHECK_CWISE1_IF(PacketTraits::HasASin, std::asin, internal::pasin);
+  CHECK_CWISE1_IF(PacketTraits::HasACos, std::acos, internal::pacos);
 
   for (int i=0; i<size; ++i)
   {
     data1[i] = internal::random<Scalar>(-87,88);
     data2[i] = internal::random<Scalar>(-87,88);
   }
-  CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasExp, std::exp, internal::pexp);
+  CHECK_CWISE1_IF(PacketTraits::HasExp, std::exp, internal::pexp);
+  for (int i=0; i<size; ++i)
+  {
+    data1[i] = internal::random<Scalar>(-1,1) * std::pow(Scalar(10), internal::random<Scalar>(-6,6));
+    data2[i] = internal::random<Scalar>(-1,1) * std::pow(Scalar(10), internal::random<Scalar>(-6,6));
+  }
+  CHECK_CWISE1_IF(PacketTraits::HasTanh, std::tanh, internal::ptanh);
+  if(PacketTraits::HasExp && PacketTraits::size>=2)
   {
     data1[0] = std::numeric_limits<Scalar>::quiet_NaN();
-    packet_helper<internal::packet_traits<Scalar>::HasExp,Packet> h;
-    h.store(data2, internal::pexp(h.load(data1))); 
-    VERIFY(isNaN(data2[0]));
+    data1[1] = std::numeric_limits<Scalar>::epsilon();
+    packet_helper<PacketTraits::HasExp,Packet> h;
+    h.store(data2, internal::pexp(h.load(data1)));
+    VERIFY((numext::isnan)(data2[0]));
+    VERIFY_IS_EQUAL(std::exp(std::numeric_limits<Scalar>::epsilon()), data2[1]);
+
+    data1[0] = -std::numeric_limits<Scalar>::epsilon();
+    data1[1] = 0;
+    h.store(data2, internal::pexp(h.load(data1)));
+    VERIFY_IS_EQUAL(std::exp(-std::numeric_limits<Scalar>::epsilon()), data2[0]);
+    VERIFY_IS_EQUAL(std::exp(Scalar(0)), data2[1]);
+
+    data1[0] = (std::numeric_limits<Scalar>::min)();
+    data1[1] = -(std::numeric_limits<Scalar>::min)();
+    h.store(data2, internal::pexp(h.load(data1)));
+    VERIFY_IS_EQUAL(std::exp((std::numeric_limits<Scalar>::min)()), data2[0]);
+    VERIFY_IS_EQUAL(std::exp(-(std::numeric_limits<Scalar>::min)()), data2[1]);
+
+    data1[0] = std::numeric_limits<Scalar>::denorm_min();
+    data1[1] = -std::numeric_limits<Scalar>::denorm_min();
+    h.store(data2, internal::pexp(h.load(data1)));
+    VERIFY_IS_EQUAL(std::exp(std::numeric_limits<Scalar>::denorm_min()), data2[0]);
+    VERIFY_IS_EQUAL(std::exp(-std::numeric_limits<Scalar>::denorm_min()), data2[1]);
   }
 
+  if (PacketTraits::HasTanh) {
+    // NOTE this test migh fail with GCC prior to 6.3, see MathFunctionsImpl.h for details.
+    data1[0] = std::numeric_limits<Scalar>::quiet_NaN();
+    packet_helper<internal::packet_traits<Scalar>::HasTanh,Packet> h;
+    h.store(data2, internal::ptanh(h.load(data1)));
+    VERIFY((numext::isnan)(data2[0]));
+  }
+
+#if EIGEN_HAS_C99_MATH
+  {
+    data1[0] = std::numeric_limits<Scalar>::quiet_NaN();
+    packet_helper<internal::packet_traits<Scalar>::HasLGamma,Packet> h;
+    h.store(data2, internal::plgamma(h.load(data1)));
+    VERIFY((numext::isnan)(data2[0]));
+  }
+  {
+    data1[0] = std::numeric_limits<Scalar>::quiet_NaN();
+    packet_helper<internal::packet_traits<Scalar>::HasErf,Packet> h;
+    h.store(data2, internal::perf(h.load(data1)));
+    VERIFY((numext::isnan)(data2[0]));
+  }
+  {
+    data1[0] = std::numeric_limits<Scalar>::quiet_NaN();
+    packet_helper<internal::packet_traits<Scalar>::HasErfc,Packet> h;
+    h.store(data2, internal::perfc(h.load(data1)));
+    VERIFY((numext::isnan)(data2[0]));
+  }
+#endif  // EIGEN_HAS_C99_MATH
+
   for (int i=0; i<size; ++i)
   {
     data1[i] = internal::random<Scalar>(0,1) * std::pow(Scalar(10), internal::random<Scalar>(-6,6));
     data2[i] = internal::random<Scalar>(0,1) * std::pow(Scalar(10), internal::random<Scalar>(-6,6));
   }
-  if(internal::random<float>(0,1)<0.1)
+
+  if(internal::random<float>(0,1)<0.1f)
     data1[internal::random<int>(0, PacketSize)] = 0;
-  CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasSqrt, std::sqrt, internal::psqrt);
-  CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasLog, std::log, internal::plog);
+  CHECK_CWISE1_IF(PacketTraits::HasSqrt, std::sqrt, internal::psqrt);
+  CHECK_CWISE1_IF(PacketTraits::HasLog, std::log, internal::plog);
+#if EIGEN_HAS_C99_MATH && (__cplusplus > 199711L)
+  CHECK_CWISE1_IF(PacketTraits::HasLog1p, std::log1p, internal::plog1p);
+  CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasLGamma, std::lgamma, internal::plgamma);
+  CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasErf, std::erf, internal::perf);
+  CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasErfc, std::erfc, internal::perfc);
+#endif
+
+  if(PacketTraits::HasLog && PacketTraits::size>=2)
   {
     data1[0] = std::numeric_limits<Scalar>::quiet_NaN();
-    packet_helper<internal::packet_traits<Scalar>::HasLog,Packet> h;
+    data1[1] = std::numeric_limits<Scalar>::epsilon();
+    packet_helper<PacketTraits::HasLog,Packet> h;
     h.store(data2, internal::plog(h.load(data1)));
-    VERIFY(isNaN(data2[0]));
-    data1[0] = -1.0f;
+    VERIFY((numext::isnan)(data2[0]));
+    VERIFY_IS_EQUAL(std::log(std::numeric_limits<Scalar>::epsilon()), data2[1]);
+
+    data1[0] = -std::numeric_limits<Scalar>::epsilon();
+    data1[1] = 0;
     h.store(data2, internal::plog(h.load(data1)));
-    VERIFY(isNaN(data2[0]));
-#if !EIGEN_FAST_MATH
+    VERIFY((numext::isnan)(data2[0]));
+    VERIFY_IS_EQUAL(std::log(Scalar(0)), data2[1]);
+
+    data1[0] = (std::numeric_limits<Scalar>::min)();
+    data1[1] = -(std::numeric_limits<Scalar>::min)();
+    h.store(data2, internal::plog(h.load(data1)));
+    VERIFY_IS_EQUAL(std::log((std::numeric_limits<Scalar>::min)()), data2[0]);
+    VERIFY((numext::isnan)(data2[1]));
+
+    data1[0] = std::numeric_limits<Scalar>::denorm_min();
+    data1[1] = -std::numeric_limits<Scalar>::denorm_min();
+    h.store(data2, internal::plog(h.load(data1)));
+    // VERIFY_IS_EQUAL(std::log(std::numeric_limits<Scalar>::denorm_min()), data2[0]);
+    VERIFY((numext::isnan)(data2[1]));
+
+    data1[0] = Scalar(-1.0f);
+    h.store(data2, internal::plog(h.load(data1)));
+    VERIFY((numext::isnan)(data2[0]));
     h.store(data2, internal::psqrt(h.load(data1)));
-    VERIFY(isNaN(data2[0]));
-    VERIFY(isNaN(data2[1]));
-#endif
+    VERIFY((numext::isnan)(data2[0]));
+    VERIFY((numext::isnan)(data2[1]));
   }
 }
 
 template<typename Scalar> void packetmath_notcomplex()
 {
   using std::abs;
-  typedef typename internal::packet_traits<Scalar>::type Packet;
-  const int PacketSize = internal::packet_traits<Scalar>::size;
+  typedef internal::packet_traits<Scalar> PacketTraits;
+  typedef typename PacketTraits::type Packet;
+  const int PacketSize = PacketTraits::size;
 
-  EIGEN_ALIGN16 Scalar data1[internal::packet_traits<Scalar>::size*4];
-  EIGEN_ALIGN16 Scalar data2[internal::packet_traits<Scalar>::size*4];
-  EIGEN_ALIGN16 Scalar ref[internal::packet_traits<Scalar>::size*4];
-  
-  Array<Scalar,Dynamic,1>::Map(data1, internal::packet_traits<Scalar>::size*4).setRandom();
+  EIGEN_ALIGN_MAX Scalar data1[PacketTraits::size*4];
+  EIGEN_ALIGN_MAX Scalar data2[PacketTraits::size*4];
+  EIGEN_ALIGN_MAX Scalar ref[PacketTraits::size*4];
+
+  Array<Scalar,Dynamic,1>::Map(data1, PacketTraits::size*4).setRandom();
 
   ref[0] = data1[0];
   for (int i=0; i<PacketSize; ++i)
     ref[0] = (std::min)(ref[0],data1[i]);
   VERIFY(internal::isApprox(ref[0], internal::predux_min(internal::pload<Packet>(data1))) && "internal::predux_min");
 
-  CHECK_CWISE2((std::min), internal::pmin);
-  CHECK_CWISE2((std::max), internal::pmax);
+  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasMin);
+  VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasMax);
+
+  CHECK_CWISE2_IF(PacketTraits::HasMin, (std::min), internal::pmin);
+  CHECK_CWISE2_IF(PacketTraits::HasMax, (std::max), internal::pmax);
   CHECK_CWISE1(abs, internal::pabs);
 
   ref[0] = data1[0];
   for (int i=0; i<PacketSize; ++i)
     ref[0] = (std::max)(ref[0],data1[i]);
   VERIFY(internal::isApprox(ref[0], internal::predux_max(internal::pload<Packet>(data1))) && "internal::predux_max");
-  
+
   for (int i=0; i<PacketSize; ++i)
     ref[i] = data1[0]+Scalar(i);
-  internal::pstore(data2, internal::plset(data1[0]));
+  internal::pstore(data2, internal::plset<Packet>(data1[0]));
   VERIFY(areApprox(ref, data2, PacketSize) && "internal::plset");
 }
 
 template<typename Scalar,bool ConjLhs,bool ConjRhs> void test_conj_helper(Scalar* data1, Scalar* data2, Scalar* ref, Scalar* pval)
 {
-  typedef typename internal::packet_traits<Scalar>::type Packet;
-  const int PacketSize = internal::packet_traits<Scalar>::size;
-  
+  typedef internal::packet_traits<Scalar> PacketTraits;
+  typedef typename PacketTraits::type Packet;
+  const int PacketSize = PacketTraits::size;
+
   internal::conj_if<ConjLhs> cj0;
   internal::conj_if<ConjRhs> cj1;
   internal::conj_helper<Scalar,Scalar,ConjLhs,ConjRhs> cj;
   internal::conj_helper<Packet,Packet,ConjLhs,ConjRhs> pcj;
-  
+
   for(int i=0;i<PacketSize;++i)
   {
     ref[i] = cj0(data1[i]) * cj1(data2[i]);
@@ -320,7 +534,7 @@
   }
   internal::pstore(pval,pcj.pmul(internal::pload<Packet>(data1),internal::pload<Packet>(data2)));
   VERIFY(areApprox(ref, pval, PacketSize) && "conj_helper pmul");
-  
+
   for(int i=0;i<PacketSize;++i)
   {
     Scalar tmp = ref[i];
@@ -333,34 +547,70 @@
 
 template<typename Scalar> void packetmath_complex()
 {
-  typedef typename internal::packet_traits<Scalar>::type Packet;
-  const int PacketSize = internal::packet_traits<Scalar>::size;
+  typedef internal::packet_traits<Scalar> PacketTraits;
+  typedef typename PacketTraits::type Packet;
+  const int PacketSize = PacketTraits::size;
 
   const int size = PacketSize*4;
-  EIGEN_ALIGN16 Scalar data1[PacketSize*4];
-  EIGEN_ALIGN16 Scalar data2[PacketSize*4];
-  EIGEN_ALIGN16 Scalar ref[PacketSize*4];
-  EIGEN_ALIGN16 Scalar pval[PacketSize*4];
+  EIGEN_ALIGN_MAX Scalar data1[PacketSize*4];
+  EIGEN_ALIGN_MAX Scalar data2[PacketSize*4];
+  EIGEN_ALIGN_MAX Scalar ref[PacketSize*4];
+  EIGEN_ALIGN_MAX Scalar pval[PacketSize*4];
 
   for (int i=0; i<size; ++i)
   {
     data1[i] = internal::random<Scalar>() * Scalar(1e2);
     data2[i] = internal::random<Scalar>() * Scalar(1e2);
   }
-  
+
   test_conj_helper<Scalar,false,false> (data1,data2,ref,pval);
   test_conj_helper<Scalar,false,true>  (data1,data2,ref,pval);
   test_conj_helper<Scalar,true,false>  (data1,data2,ref,pval);
   test_conj_helper<Scalar,true,true>   (data1,data2,ref,pval);
-  
+
   {
     for(int i=0;i<PacketSize;++i)
       ref[i] = Scalar(std::imag(data1[i]),std::real(data1[i]));
     internal::pstore(pval,internal::pcplxflip(internal::pload<Packet>(data1)));
     VERIFY(areApprox(ref, pval, PacketSize) && "pcplxflip");
   }
-  
-  
+}
+
+template<typename Scalar> void packetmath_scatter_gather()
+{
+  typedef internal::packet_traits<Scalar> PacketTraits;
+  typedef typename PacketTraits::type Packet;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  const int PacketSize = PacketTraits::size;
+  EIGEN_ALIGN_MAX Scalar data1[PacketSize];
+  RealScalar refvalue = 0;
+  for (int i=0; i<PacketSize; ++i) {
+    data1[i] = internal::random<Scalar>()/RealScalar(PacketSize);
+  }
+
+  int stride = internal::random<int>(1,20);
+
+  EIGEN_ALIGN_MAX Scalar buffer[PacketSize*20];
+  memset(buffer, 0, 20*PacketSize*sizeof(Scalar));
+  Packet packet = internal::pload<Packet>(data1);
+  internal::pscatter<Scalar, Packet>(buffer, packet, stride);
+
+  for (int i = 0; i < PacketSize*20; ++i) {
+    if ((i%stride) == 0 && i<stride*PacketSize) {
+      VERIFY(isApproxAbs(buffer[i], data1[i/stride], refvalue) && "pscatter");
+    } else {
+      VERIFY(isApproxAbs(buffer[i], Scalar(0), refvalue) && "pscatter");
+    }
+  }
+
+  for (int i=0; i<PacketSize*7; ++i) {
+    buffer[i] = internal::random<Scalar>()/RealScalar(PacketSize);
+  }
+  packet = internal::pgather<Scalar, Packet>(buffer, 7);
+  internal::pstore(data1, packet);
+  for (int i = 0; i < PacketSize; ++i) {
+    VERIFY(isApproxAbs(data1[i], buffer[i*7], refvalue) && "pgather");
+  }
 }
 
 void test_packetmath()
@@ -369,17 +619,23 @@
     CALL_SUBTEST_1( packetmath<float>() );
     CALL_SUBTEST_2( packetmath<double>() );
     CALL_SUBTEST_3( packetmath<int>() );
-    CALL_SUBTEST_1( packetmath<std::complex<float> >() );
-    CALL_SUBTEST_2( packetmath<std::complex<double> >() );
+    CALL_SUBTEST_4( packetmath<std::complex<float> >() );
+    CALL_SUBTEST_5( packetmath<std::complex<double> >() );
 
     CALL_SUBTEST_1( packetmath_notcomplex<float>() );
     CALL_SUBTEST_2( packetmath_notcomplex<double>() );
     CALL_SUBTEST_3( packetmath_notcomplex<int>() );
-    
+
     CALL_SUBTEST_1( packetmath_real<float>() );
     CALL_SUBTEST_2( packetmath_real<double>() );
 
-    CALL_SUBTEST_1( packetmath_complex<std::complex<float> >() );
-    CALL_SUBTEST_2( packetmath_complex<std::complex<double> >() );
+    CALL_SUBTEST_4( packetmath_complex<std::complex<float> >() );
+    CALL_SUBTEST_5( packetmath_complex<std::complex<double> >() );
+
+    CALL_SUBTEST_1( packetmath_scatter_gather<float>() );
+    CALL_SUBTEST_2( packetmath_scatter_gather<double>() );
+    CALL_SUBTEST_3( packetmath_scatter_gather<int>() );
+    CALL_SUBTEST_4( packetmath_scatter_gather<std::complex<float> >() );
+    CALL_SUBTEST_5( packetmath_scatter_gather<std::complex<double> >() );
   }
 }