diff --git a/Eigen/src/Cholesky/LDLT.h b/Eigen/src/Cholesky/LDLT.h
index 67e97ff..492cd5a 100644
--- a/Eigen/src/Cholesky/LDLT.h
+++ b/Eigen/src/Cholesky/LDLT.h
@@ -53,7 +53,7 @@
   * decomposition to determine whether a system of equations has a solution.
   *
   * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
-  * 
+  *
   * \sa MatrixBase::ldlt(), SelfAdjointView::ldlt(), class LLT
   */
 template<typename _MatrixType, int _UpLo> class LDLT
@@ -246,8 +246,8 @@
       */
     const LDLT& adjoint() const { return *this; };
 
-    inline Index rows() const { return m_matrix.rows(); }
-    inline Index cols() const { return m_matrix.cols(); }
+    EIGEN_DEVICE_FUNC inline Index rows() const { return m_matrix.rows(); }
+    EIGEN_DEVICE_FUNC inline Index cols() const { return m_matrix.cols(); }
 
     /** \brief Reports whether previous computation was successful.
       *
diff --git a/Eigen/src/Core/AssignEvaluator.h b/Eigen/src/Core/AssignEvaluator.h
index 229e258..47ccf62 100644
--- a/Eigen/src/Core/AssignEvaluator.h
+++ b/Eigen/src/Core/AssignEvaluator.h
@@ -17,7 +17,7 @@
 // This implementation is based on Assign.h
 
 namespace internal {
-  
+
 /***************************************************************************
 * Part 1 : the logic deciding a strategy for traversal and unrolling       *
 ***************************************************************************/
@@ -29,12 +29,12 @@
 {
   typedef typename DstEvaluator::XprType Dst;
   typedef typename Dst::Scalar DstScalar;
-  
+
   enum {
     DstFlags = DstEvaluator::Flags,
     SrcFlags = SrcEvaluator::Flags
   };
-  
+
 public:
   enum {
     DstAlignment = DstEvaluator::Alignment,
@@ -99,7 +99,8 @@
 
 public:
   enum {
-    Traversal = (int(MayLinearVectorize) && (LinearPacketSize>InnerPacketSize)) ? int(LinearVectorizedTraversal)
+    Traversal =  int(Dst::SizeAtCompileTime) == 0 ? int(AllAtOnceTraversal) // If compile-size is zero, traversing will fail at compile-time.
+              : (int(MayLinearVectorize) && (LinearPacketSize>InnerPacketSize)) ? int(LinearVectorizedTraversal)
               : int(MayInnerVectorize)   ? int(InnerVectorizedTraversal)
               : int(MayLinearVectorize)  ? int(LinearVectorizedTraversal)
               : int(MaySliceVectorize)   ? int(SliceVectorizedTraversal)
@@ -137,7 +138,7 @@
                           ? int(CompleteUnrolling)
                           : int(NoUnrolling) )
               : int(Traversal) == int(LinearTraversal)
-                ? ( bool(MayUnrollCompletely) ? int(CompleteUnrolling) 
+                ? ( bool(MayUnrollCompletely) ? int(CompleteUnrolling)
                                               : int(NoUnrolling) )
 #if EIGEN_UNALIGNED_VECTORIZE
               : int(Traversal) == int(SliceVectorizedTraversal)
@@ -199,7 +200,7 @@
   // FIXME: this is not very clean, perhaps this information should be provided by the kernel?
   typedef typename Kernel::DstEvaluatorType DstEvaluatorType;
   typedef typename DstEvaluatorType::XprType DstXprType;
-  
+
   enum {
     outer = Index / DstXprType::InnerSizeAtCompileTime,
     inner = Index % DstXprType::InnerSizeAtCompileTime
@@ -265,7 +266,7 @@
   typedef typename Kernel::DstEvaluatorType DstEvaluatorType;
   typedef typename DstEvaluatorType::XprType DstXprType;
   typedef typename Kernel::PacketType PacketType;
-  
+
   enum {
     outer = Index / DstXprType::InnerSizeAtCompileTime,
     inner = Index % DstXprType::InnerSizeAtCompileTime,
@@ -317,6 +318,22 @@
 struct dense_assignment_loop;
 
 /************************
+***** Special Cases *****
+************************/
+
+// Zero-sized assignment is a no-op.
+template<typename Kernel, int Unrolling>
+struct dense_assignment_loop<Kernel, AllAtOnceTraversal, Unrolling>
+{
+  EIGEN_DEVICE_FUNC static void EIGEN_STRONG_INLINE run(Kernel& /*kernel*/)
+  {
+    typedef typename Kernel::DstEvaluatorType::XprType DstXprType;
+    EIGEN_STATIC_ASSERT(int(DstXprType::SizeAtCompileTime) == 0,
+      EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT)
+  }
+};
+
+/************************
 *** Default traversal ***
 ************************/
 
@@ -430,7 +447,7 @@
   {
     typedef typename Kernel::DstEvaluatorType::XprType DstXprType;
     typedef typename Kernel::PacketType PacketType;
-    
+
     enum { size = DstXprType::SizeAtCompileTime,
            packetSize =unpacket_traits<PacketType>::size,
            alignedSize = (size/packetSize)*packetSize };
@@ -572,14 +589,15 @@
     typedef typename Kernel::DstEvaluatorType::XprType DstXprType;
     typedef typename Kernel::PacketType PacketType;
 
-    enum { size = DstXprType::InnerSizeAtCompileTime,
+    enum { innerSize = DstXprType::InnerSizeAtCompileTime,
            packetSize =unpacket_traits<PacketType>::size,
-           vectorizableSize = (size/packetSize)*packetSize };
+           vectorizableSize = (innerSize/packetSize)*packetSize,
+           size = DstXprType::SizeAtCompileTime };
 
     for(Index outer = 0; outer < kernel.outerSize(); ++outer)
     {
       copy_using_evaluator_innervec_InnerUnrolling<Kernel, 0, vectorizableSize, 0, 0>::run(kernel, outer);
-      copy_using_evaluator_DefaultTraversal_InnerUnrolling<Kernel, vectorizableSize, size>::run(kernel, outer);
+      copy_using_evaluator_DefaultTraversal_InnerUnrolling<Kernel, vectorizableSize, innerSize>::run(kernel, outer);
     }
   }
 };
@@ -603,14 +621,14 @@
   typedef typename DstEvaluatorTypeT::XprType DstXprType;
   typedef typename SrcEvaluatorTypeT::XprType SrcXprType;
 public:
-  
+
   typedef DstEvaluatorTypeT DstEvaluatorType;
   typedef SrcEvaluatorTypeT SrcEvaluatorType;
   typedef typename DstEvaluatorType::Scalar Scalar;
   typedef copy_using_evaluator_traits<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor> AssignmentTraits;
   typedef typename AssignmentTraits::PacketType PacketType;
-  
-  
+
+
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
   generic_dense_assignment_kernel(DstEvaluatorType &dst, const SrcEvaluatorType &src, const Functor &func, DstXprType& dstExpr)
     : m_dst(dst), m_src(src), m_functor(func), m_dstExpr(dstExpr)
@@ -619,58 +637,58 @@
     AssignmentTraits::debug();
     #endif
   }
-  
+
   EIGEN_DEVICE_FUNC Index size() const        { return m_dstExpr.size(); }
   EIGEN_DEVICE_FUNC Index innerSize() const   { return m_dstExpr.innerSize(); }
   EIGEN_DEVICE_FUNC Index outerSize() const   { return m_dstExpr.outerSize(); }
   EIGEN_DEVICE_FUNC Index rows() const        { return m_dstExpr.rows(); }
   EIGEN_DEVICE_FUNC Index cols() const        { return m_dstExpr.cols(); }
   EIGEN_DEVICE_FUNC Index outerStride() const { return m_dstExpr.outerStride(); }
-  
+
   EIGEN_DEVICE_FUNC DstEvaluatorType& dstEvaluator() { return m_dst; }
   EIGEN_DEVICE_FUNC const SrcEvaluatorType& srcEvaluator() const { return m_src; }
-  
+
   /// Assign src(row,col) to dst(row,col) through the assignment functor.
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(Index row, Index col)
   {
     m_functor.assignCoeff(m_dst.coeffRef(row,col), m_src.coeff(row,col));
   }
-  
+
   /// \sa assignCoeff(Index,Index)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(Index index)
   {
     m_functor.assignCoeff(m_dst.coeffRef(index), m_src.coeff(index));
   }
-  
+
   /// \sa assignCoeff(Index,Index)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeffByOuterInner(Index outer, Index inner)
   {
-    Index row = rowIndexByOuterInner(outer, inner); 
-    Index col = colIndexByOuterInner(outer, inner); 
+    Index row = rowIndexByOuterInner(outer, inner);
+    Index col = colIndexByOuterInner(outer, inner);
     assignCoeff(row, col);
   }
-  
-  
+
+
   template<int StoreMode, int LoadMode, typename PacketType>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignPacket(Index row, Index col)
   {
     m_functor.template assignPacket<StoreMode>(&m_dst.coeffRef(row,col), m_src.template packet<LoadMode,PacketType>(row,col));
   }
-  
+
   template<int StoreMode, int LoadMode, typename PacketType>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignPacket(Index index)
   {
     m_functor.template assignPacket<StoreMode>(&m_dst.coeffRef(index), m_src.template packet<LoadMode,PacketType>(index));
   }
-  
+
   template<int StoreMode, int LoadMode, typename PacketType>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignPacketByOuterInner(Index outer, Index inner)
   {
-    Index row = rowIndexByOuterInner(outer, inner); 
+    Index row = rowIndexByOuterInner(outer, inner);
     Index col = colIndexByOuterInner(outer, inner);
     assignPacket<StoreMode,LoadMode,PacketType>(row, col);
   }
-  
+
   EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Index rowIndexByOuterInner(Index outer, Index inner)
   {
     typedef typename DstEvaluatorType::ExpressionTraits Traits;
@@ -693,7 +711,7 @@
   {
     return m_dstExpr.data();
   }
-  
+
 protected:
   DstEvaluatorType& m_dst;
   const SrcEvaluatorType& m_src;
@@ -716,13 +734,13 @@
     typedef typename Base::DstXprType DstXprType;
     typedef copy_using_evaluator_traits<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, 4> AssignmentTraits;
     typedef typename AssignmentTraits::PacketType PacketType;
-    
+
     EIGEN_DEVICE_FUNC restricted_packet_dense_assignment_kernel(DstEvaluatorTypeT &dst, const SrcEvaluatorTypeT &src, const Functor &func, DstXprType& dstExpr)
     : Base(dst, src, func, dstExpr)
   {
   }
  };
- 
+
 /***************************************************************************
 * Part 5 : Entry point for dense rectangular assignment
 ***************************************************************************/
@@ -760,7 +778,7 @@
   resize_if_allowed(dst, src, func);
 
   DstEvaluatorType dstEvaluator(dst);
-    
+
   typedef generic_dense_assignment_kernel<DstEvaluatorType,SrcEvaluatorType,Functor> Kernel;
   Kernel kernel(dstEvaluator, srcEvaluator, func, dst.const_cast_derived());
 
@@ -788,7 +806,7 @@
 
 template<typename,typename> struct AssignmentKind { typedef EigenBase2EigenBase Kind; };
 template<> struct AssignmentKind<DenseShape,DenseShape> { typedef Dense2Dense Kind; };
-    
+
 // This is the main assignment class
 template< typename DstXprType, typename SrcXprType, typename Functor,
           typename Kind = typename AssignmentKind< typename evaluator_traits<DstXprType>::Shape , typename evaluator_traits<SrcXprType>::Shape >::Kind,
@@ -813,7 +831,7 @@
 {
   call_assignment(dst, src, internal::assign_op<typename Dst::Scalar,typename Src::Scalar>());
 }
-                     
+
 // Deal with "assume-aliasing"
 template<typename Dst, typename Src, typename Func>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
@@ -853,12 +871,12 @@
   typedef typename internal::conditional<NeedToTranspose, Transpose<Dst>, Dst>::type ActualDstTypeCleaned;
   typedef typename internal::conditional<NeedToTranspose, Transpose<Dst>, Dst&>::type ActualDstType;
   ActualDstType actualDst(dst);
-  
+
   // TODO check whether this is the right place to perform these checks:
   EIGEN_STATIC_ASSERT_LVALUE(Dst)
   EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(ActualDstTypeCleaned,Src)
   EIGEN_CHECK_BINARY_COMPATIBILIY(Func,typename ActualDstTypeCleaned::Scalar,typename Src::Scalar);
-  
+
   Assignment<ActualDstTypeCleaned,Src,Func>::run(actualDst, src, func);
 }
 
@@ -875,7 +893,7 @@
 
     SrcEvaluatorType srcEvaluator(src);
     resize_if_allowed(dst, src, func);
-    
+
     DstEvaluatorType dstEvaluator(dst);
     Kernel kernel(dstEvaluator, srcEvaluator, func, dst.const_cast_derived());
 
@@ -922,7 +940,7 @@
 #ifndef EIGEN_NO_DEBUG
     internal::check_for_aliasing(dst, src);
 #endif
-    
+
     call_dense_assignment_loop(dst, src, func);
   }
 };
diff --git a/Eigen/src/Core/GenericPacketMath.h b/Eigen/src/Core/GenericPacketMath.h
index e2fc700..671ed3c 100644
--- a/Eigen/src/Core/GenericPacketMath.h
+++ b/Eigen/src/Core/GenericPacketMath.h
@@ -539,6 +539,20 @@
 template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet
 plset(const typename unpacket_traits<Packet>::type& a) { return a; }
 
+/** \internal \returns a packet with constant coefficients \a a, e.g.: (x, 0, x, 0),
+     where x is the value of all 1-bits. */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+peven_mask(const Packet& /*a*/) {
+  typedef typename unpacket_traits<Packet>::type Scalar;
+  const size_t n = unpacket_traits<Packet>::size;
+  Scalar elements[n];
+  for(size_t i = 0; i < n; ++i) {
+    memset(elements+i, ((i & 1) == 0 ? 0xff : 0), sizeof(Scalar));
+  }
+  return ploadu<Packet>(elements);
+}
+
+
 /** \internal copy the packet \a from to \a *to, \a to must be 16 bytes aligned */
 template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pstore(Scalar* to, const Packet& from)
 { (*to) = from; }
@@ -568,7 +582,7 @@
 #if defined(EIGEN_HIP_DEVICE_COMPILE)
   // do nothing
 #elif defined(EIGEN_CUDA_ARCH)
-#if defined(__LP64__)
+#if defined(__LP64__) || EIGEN_OS_WIN64
   // 64-bit pointer operand constraint for inlined asm
   asm(" prefetch.L1 [ %1 ];" : "=l"(addr) : "l"(addr));
 #else
@@ -650,6 +664,13 @@
 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet plog10(const Packet& a) { EIGEN_USING_STD(log10); return log10(a); }
 
+/** \internal \returns the log10 of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog2(const Packet& a) {
+  typedef typename internal::unpacket_traits<Packet>::type Scalar;
+  return pmul(pset1<Packet>(Scalar(EIGEN_LOG2E)), plog(a)); 
+}
+
 /** \internal \returns the square-root of \a a (coeff-wise) */
 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet psqrt(const Packet& a) { EIGEN_USING_STD(sqrt); return sqrt(a); }
diff --git a/Eigen/src/Core/GlobalFunctions.h b/Eigen/src/Core/GlobalFunctions.h
index 0a539ed..629af94 100644
--- a/Eigen/src/Core/GlobalFunctions.h
+++ b/Eigen/src/Core/GlobalFunctions.h
@@ -81,7 +81,8 @@
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(expm1,scalar_expm1_op,exponential of a value minus 1,\sa ArrayBase::expm1)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log,scalar_log_op,natural logarithm,\sa Eigen::log10 DOXCOMMA ArrayBase::log)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log1p,scalar_log1p_op,natural logarithm of 1 plus the value,\sa ArrayBase::log1p)
-  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log10,scalar_log10_op,base 10 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log10,scalar_log10_op,base 10 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log10)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log2,scalar_log2_op,base 2 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log2)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs,scalar_abs_op,absolute value,\sa ArrayBase::abs DOXCOMMA MatrixBase::cwiseAbs)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs2,scalar_abs2_op,squared absolute value,\sa ArrayBase::abs2 DOXCOMMA MatrixBase::cwiseAbs2)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(arg,scalar_arg_op,complex argument,\sa ArrayBase::arg DOXCOMMA MatrixBase::cwiseArg)
diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
index e9da359..3cf91bd 100644
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
@@ -10,9 +10,11 @@
 #ifndef EIGEN_MATHFUNCTIONS_H
 #define EIGEN_MATHFUNCTIONS_H
 
-// source: http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html
 // TODO this should better be moved to NumTraits
-#define EIGEN_PI 3.141592653589793238462643383279502884197169399375105820974944592307816406L
+// Source: WolframAlpha
+#define EIGEN_PI    3.141592653589793238462643383279502884197169399375105820974944592307816406L
+#define EIGEN_LOG2E 1.442695040888963407359924681001892137426645954152985934135449406931109219L
+#define EIGEN_LN2   0.693147180559945309417232121458176568075500134360255254120680009493393621L
 
 namespace Eigen {
 
@@ -1374,6 +1376,11 @@
   return sqrt(x);
 }
 
+// Boolean specialization, avoids implicit float to bool conversion (-Wimplicit-conversion-floating-point-to-bool).
+template<>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_DEVICE_FUNC
+bool sqrt<bool>(const bool &x) { return x; }
+
 #if defined(SYCL_DEVICE_ONLY)
 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(sqrt, sqrt)
 #endif
diff --git a/Eigen/src/Core/ProductEvaluators.h b/Eigen/src/Core/ProductEvaluators.h
index 6e220d7..02b5843 100644
--- a/Eigen/src/Core/ProductEvaluators.h
+++ b/Eigen/src/Core/ProductEvaluators.h
@@ -14,7 +14,7 @@
 #define EIGEN_PRODUCTEVALUATORS_H
 
 namespace Eigen {
-  
+
 namespace internal {
 
 /** \internal
@@ -22,19 +22,19 @@
   * Since products require special treatments to handle all possible cases,
   * we simply defer the evaluation logic to a product_evaluator class
   * which offers more partial specialization possibilities.
-  * 
+  *
   * \sa class product_evaluator
   */
 template<typename Lhs, typename Rhs, int Options>
-struct evaluator<Product<Lhs, Rhs, Options> > 
+struct evaluator<Product<Lhs, Rhs, Options> >
  : public product_evaluator<Product<Lhs, Rhs, Options> >
 {
   typedef Product<Lhs, Rhs, Options> XprType;
   typedef product_evaluator<XprType> Base;
-  
+
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& xpr) : Base(xpr) {}
 };
- 
+
 // Catch "scalar * ( A * B )" and transform it to "(A*scalar) * B"
 // TODO we should apply that rule only if that's really helpful
 template<typename Lhs, typename Rhs, typename Scalar1, typename Scalar2, typename Plain1>
@@ -62,12 +62,12 @@
 
 
 template<typename Lhs, typename Rhs, int DiagIndex>
-struct evaluator<Diagonal<const Product<Lhs, Rhs, DefaultProduct>, DiagIndex> > 
+struct evaluator<Diagonal<const Product<Lhs, Rhs, DefaultProduct>, DiagIndex> >
  : public evaluator<Diagonal<const Product<Lhs, Rhs, LazyProduct>, DiagIndex> >
 {
   typedef Diagonal<const Product<Lhs, Rhs, DefaultProduct>, DiagIndex> XprType;
   typedef evaluator<Diagonal<const Product<Lhs, Rhs, LazyProduct>, DiagIndex> > Base;
-  
+
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& xpr)
     : Base(Diagonal<const Product<Lhs, Rhs, LazyProduct>, DiagIndex>(
         Product<Lhs, Rhs, LazyProduct>(xpr.nestedExpression().lhs(), xpr.nestedExpression().rhs()),
@@ -108,23 +108,23 @@
     : m_result(xpr.rows(), xpr.cols())
   {
     ::new (static_cast<Base*>(this)) Base(m_result);
-    
+
 // FIXME shall we handle nested_eval here?,
 // if so, then we must take care at removing the call to nested_eval in the specializations (e.g., in permutation_matrix_product, transposition_matrix_product, etc.)
 //     typedef typename internal::nested_eval<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
 //     typedef typename internal::nested_eval<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
 //     typedef typename internal::remove_all<LhsNested>::type LhsNestedCleaned;
 //     typedef typename internal::remove_all<RhsNested>::type RhsNestedCleaned;
-//     
+//
 //     const LhsNested lhs(xpr.lhs());
 //     const RhsNested rhs(xpr.rhs());
-//   
+//
 //     generic_product_impl<LhsNestedCleaned, RhsNestedCleaned>::evalTo(m_result, lhs, rhs);
 
     generic_product_impl<Lhs, Rhs, LhsShape, RhsShape, ProductTag>::evalTo(m_result, xpr.lhs(), xpr.rhs());
   }
-  
-protected:  
+
+protected:
   PlainObject m_result;
 };
 
@@ -250,7 +250,7 @@
   {
     dst.coeffRef(0,0) = (lhs.transpose().cwiseProduct(rhs)).sum();
   }
-  
+
   template<typename Dst>
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   {
@@ -298,7 +298,7 @@
 {
   template<typename T> struct is_row_major : internal::conditional<(int(T::Flags)&RowMajorBit), internal::true_type, internal::false_type>::type {};
   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
-  
+
   // TODO it would be nice to be able to exploit our *_assign_op functors for that purpose
   struct set  { template<typename Dst, typename Src> EIGEN_DEVICE_FUNC void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived()  = src; } };
   struct add  { template<typename Dst, typename Src> EIGEN_DEVICE_FUNC void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() += src; } };
@@ -310,31 +310,31 @@
       dst.const_cast_derived() += m_scale * src;
     }
   };
-  
+
   template<typename Dst>
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   {
     internal::outer_product_selector_run(dst, lhs, rhs, set(), is_row_major<Dst>());
   }
-  
+
   template<typename Dst>
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   {
     internal::outer_product_selector_run(dst, lhs, rhs, add(), is_row_major<Dst>());
   }
-  
+
   template<typename Dst>
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   {
     internal::outer_product_selector_run(dst, lhs, rhs, sub(), is_row_major<Dst>());
   }
-  
+
   template<typename Dst>
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
   {
     internal::outer_product_selector_run(dst, lhs, rhs, adds(alpha), is_row_major<Dst>());
   }
-  
+
 };
 
 
@@ -343,7 +343,7 @@
 struct generic_product_impl_base
 {
   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
-  
+
   template<typename Dst>
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   { dst.setZero(); scaleAndAddTo(dst, lhs, rhs, Scalar(1)); }
@@ -355,7 +355,7 @@
   template<typename Dst>
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   { scaleAndAddTo(dst, lhs, rhs, Scalar(-1)); }
-  
+
   template<typename Dst>
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
   { Derived::scaleAndAddTo(dst,lhs,rhs,alpha); }
@@ -379,7 +379,7 @@
     if (lhs.rows() == 1 && rhs.cols() == 1) {
       dst.coeffRef(0,0) += alpha * lhs.row(0).conjugate().dot(rhs.col(0));
       return;
-    } 
+    }
     LhsNested actual_lhs(lhs);
     RhsNested actual_rhs(rhs);
     internal::gemv_dense_selector<Side,
@@ -390,10 +390,10 @@
 };
 
 template<typename Lhs, typename Rhs>
-struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,CoeffBasedProductMode> 
+struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,CoeffBasedProductMode>
 {
   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
-  
+
   template<typename Dst>
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   {
@@ -408,7 +408,7 @@
     // dst.noalias() += lhs.lazyProduct(rhs);
     call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::add_assign_op<typename Dst::Scalar,Scalar>());
   }
-  
+
   template<typename Dst>
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   {
@@ -525,7 +525,7 @@
 
   typedef typename internal::nested_eval<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
   typedef typename internal::nested_eval<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
-  
+
   typedef typename internal::remove_all<LhsNested>::type LhsNestedCleaned;
   typedef typename internal::remove_all<RhsNested>::type RhsNestedCleaned;
 
@@ -544,7 +544,7 @@
   typedef typename find_best_packet<Scalar,ColsAtCompileTime>::type RhsVecPacketType;
 
   enum {
-      
+
     LhsCoeffReadCost = LhsEtorType::CoeffReadCost,
     RhsCoeffReadCost = RhsEtorType::CoeffReadCost,
     CoeffReadCost = InnerSize==0 ? NumTraits<Scalar>::ReadCost
@@ -553,10 +553,10 @@
                     + (InnerSize - 1) * NumTraits<Scalar>::AddCost,
 
     Unroll = CoeffReadCost <= EIGEN_UNROLLING_LIMIT,
-    
+
     LhsFlags = LhsEtorType::Flags,
     RhsFlags = RhsEtorType::Flags,
-    
+
     LhsRowMajor = LhsFlags & RowMajorBit,
     RhsRowMajor = RhsFlags & RowMajorBit,
 
@@ -566,7 +566,7 @@
     // Here, we don't care about alignment larger than the usable packet size.
     LhsAlignment = EIGEN_PLAIN_ENUM_MIN(LhsEtorType::Alignment,LhsVecPacketSize*int(sizeof(typename LhsNestedCleaned::Scalar))),
     RhsAlignment = EIGEN_PLAIN_ENUM_MIN(RhsEtorType::Alignment,RhsVecPacketSize*int(sizeof(typename RhsNestedCleaned::Scalar))),
-      
+
     SameType = is_same<typename LhsNestedCleaned::Scalar,typename RhsNestedCleaned::Scalar>::value,
 
     CanVectorizeRhs = bool(RhsRowMajor) && (RhsFlags & PacketAccessBit) && (ColsAtCompileTime!=1),
@@ -581,7 +581,7 @@
           // TODO enable vectorization for mixed types
           | (SameType && (CanVectorizeLhs || CanVectorizeRhs) ? PacketAccessBit : 0)
           | (XprType::IsVectorAtCompileTime ? LinearAccessBit : 0),
-          
+
     LhsOuterStrideBytes = int(LhsNestedCleaned::OuterStrideAtCompileTime) * int(sizeof(typename LhsNestedCleaned::Scalar)),
     RhsOuterStrideBytes = int(RhsNestedCleaned::OuterStrideAtCompileTime) * int(sizeof(typename RhsNestedCleaned::Scalar)),
 
@@ -600,7 +600,7 @@
                         && (LhsFlags & RhsFlags & ActualPacketAccessBit)
                         && (InnerSize % packet_traits<Scalar>::size == 0)
   };
-  
+
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index row, Index col) const
   {
     return (m_lhs.row(row).transpose().cwiseProduct( m_rhs.col(col) )).sum();
@@ -642,7 +642,7 @@
 protected:
   typename internal::add_const_on_value_type<LhsNested>::type m_lhs;
   typename internal::add_const_on_value_type<RhsNested>::type m_rhs;
-  
+
   LhsEtorType m_lhsImpl;
   RhsEtorType m_rhsImpl;
 
@@ -673,7 +673,7 @@
 template<int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>
 struct etor_product_packet_impl<RowMajor, UnrollingIndex, Lhs, Rhs, Packet, LoadMode>
 {
-  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet &res)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet &res)
   {
     etor_product_packet_impl<RowMajor, UnrollingIndex-1, Lhs, Rhs, Packet, LoadMode>::run(row, col, lhs, rhs, innerDim, res);
     res =  pmadd(pset1<Packet>(lhs.coeff(row, Index(UnrollingIndex-1))), rhs.template packet<LoadMode,Packet>(Index(UnrollingIndex-1), col), res);
@@ -683,7 +683,7 @@
 template<int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>
 struct etor_product_packet_impl<ColMajor, UnrollingIndex, Lhs, Rhs, Packet, LoadMode>
 {
-  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet &res)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet &res)
   {
     etor_product_packet_impl<ColMajor, UnrollingIndex-1, Lhs, Rhs, Packet, LoadMode>::run(row, col, lhs, rhs, innerDim, res);
     res =  pmadd(lhs.template packet<LoadMode,Packet>(row, Index(UnrollingIndex-1)), pset1<Packet>(rhs.coeff(Index(UnrollingIndex-1), col)), res);
@@ -693,7 +693,7 @@
 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
 struct etor_product_packet_impl<RowMajor, 1, Lhs, Rhs, Packet, LoadMode>
 {
-  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, Packet &res)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, Packet &res)
   {
     res = pmul(pset1<Packet>(lhs.coeff(row, Index(0))),rhs.template packet<LoadMode,Packet>(Index(0), col));
   }
@@ -702,7 +702,7 @@
 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
 struct etor_product_packet_impl<ColMajor, 1, Lhs, Rhs, Packet, LoadMode>
 {
-  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, Packet &res)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, Packet &res)
   {
     res = pmul(lhs.template packet<LoadMode,Packet>(row, Index(0)), pset1<Packet>(rhs.coeff(Index(0), col)));
   }
@@ -711,7 +711,7 @@
 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
 struct etor_product_packet_impl<RowMajor, 0, Lhs, Rhs, Packet, LoadMode>
 {
-  static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Index /*innerDim*/, Packet &res)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Index /*innerDim*/, Packet &res)
   {
     res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
   }
@@ -720,7 +720,7 @@
 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
 struct etor_product_packet_impl<ColMajor, 0, Lhs, Rhs, Packet, LoadMode>
 {
-  static EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Index /*innerDim*/, Packet &res)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Index /*innerDim*/, Packet &res)
   {
     res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
   }
@@ -729,7 +729,7 @@
 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
 struct etor_product_packet_impl<RowMajor, Dynamic, Lhs, Rhs, Packet, LoadMode>
 {
-  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet& res)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet& res)
   {
     res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
     for(Index i = 0; i < innerDim; ++i)
@@ -740,7 +740,7 @@
 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
 struct etor_product_packet_impl<ColMajor, Dynamic, Lhs, Rhs, Packet, LoadMode>
 {
-  static EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet& res)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet& res)
   {
     res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
     for(Index i = 0; i < innerDim; ++i)
@@ -762,7 +762,7 @@
   : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,TriangularShape,DenseShape,ProductTag> >
 {
   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
-  
+
   template<typename Dest>
   static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
   {
@@ -776,7 +776,7 @@
 : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,TriangularShape,ProductTag> >
 {
   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
-  
+
   template<typename Dest>
   static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
   {
@@ -797,7 +797,7 @@
   : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,SelfAdjointShape,DenseShape,ProductTag> >
 {
   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
-  
+
   template<typename Dest>
   static EIGEN_DEVICE_FUNC
   void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
@@ -811,7 +811,7 @@
 : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,SelfAdjointShape,ProductTag> >
 {
   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
-  
+
   template<typename Dest>
   static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
   {
@@ -823,7 +823,7 @@
 /***************************************************************************
 * Diagonal products
 ***************************************************************************/
-  
+
 template<typename MatrixType, typename DiagonalType, typename Derived, int ProductOrder>
 struct diagonal_product_evaluator_base
   : evaluator_base<Derived>
@@ -832,10 +832,10 @@
 public:
   enum {
     CoeffReadCost = NumTraits<Scalar>::MulCost + evaluator<MatrixType>::CoeffReadCost + evaluator<DiagonalType>::CoeffReadCost,
-    
+
     MatrixFlags = evaluator<MatrixType>::Flags,
     DiagFlags = evaluator<DiagonalType>::Flags,
-    
+
     _StorageOrder = (Derived::MaxRowsAtCompileTime==1 && Derived::MaxColsAtCompileTime!=1) ? RowMajor
                   : (Derived::MaxColsAtCompileTime==1 && Derived::MaxRowsAtCompileTime!=1) ? ColMajor
                   : MatrixFlags & RowMajorBit ? RowMajor : ColMajor,
@@ -858,14 +858,14 @@
                       ||  (DiagonalType::SizeAtCompileTime==Dynamic && MatrixType::RowsAtCompileTime==1 && ProductOrder==OnTheLeft)
                       ||  (DiagonalType::SizeAtCompileTime==Dynamic && MatrixType::ColsAtCompileTime==1 && ProductOrder==OnTheRight)
   };
-  
+
   EIGEN_DEVICE_FUNC diagonal_product_evaluator_base(const MatrixType &mat, const DiagonalType &diag)
     : m_diagImpl(diag), m_matImpl(mat)
   {
     EIGEN_INTERNAL_CHECK_COST_VALUE(NumTraits<Scalar>::MulCost);
     EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
   }
-  
+
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index idx) const
   {
     if(AsScalarProduct)
@@ -873,7 +873,7 @@
     else
       return m_diagImpl.coeff(idx) * m_matImpl.coeff(idx);
   }
-  
+
 protected:
   template<int LoadMode,typename PacketType>
   EIGEN_STRONG_INLINE PacketType packet_impl(Index row, Index col, Index id, internal::true_type) const
@@ -881,7 +881,7 @@
     return internal::pmul(m_matImpl.template packet<LoadMode,PacketType>(row, col),
                           internal::pset1<PacketType>(m_diagImpl.coeff(id)));
   }
-  
+
   template<int LoadMode,typename PacketType>
   EIGEN_STRONG_INLINE PacketType packet_impl(Index row, Index col, Index id, internal::false_type) const
   {
@@ -892,7 +892,7 @@
     return internal::pmul(m_matImpl.template packet<LoadMode,PacketType>(row, col),
                           m_diagImpl.template packet<DiagonalPacketLoadMode,PacketType>(id));
   }
-  
+
   evaluator<DiagonalType> m_diagImpl;
   evaluator<MatrixType>   m_matImpl;
 };
@@ -907,24 +907,24 @@
   using Base::m_matImpl;
   using Base::coeff;
   typedef typename Base::Scalar Scalar;
-  
+
   typedef Product<Lhs, Rhs, ProductKind> XprType;
   typedef typename XprType::PlainObject PlainObject;
   typedef typename Lhs::DiagonalVectorType DiagonalType;
 
-  
+
   enum { StorageOrder = Base::_StorageOrder };
 
   EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
     : Base(xpr.rhs(), xpr.lhs().diagonal())
   {
   }
-  
+
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const
   {
     return m_diagImpl.coeff(row) * m_matImpl.coeff(row, col);
   }
-  
+
 #ifndef EIGEN_GPUCC
   template<int LoadMode,typename PacketType>
   EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const
@@ -934,7 +934,7 @@
     return this->template packet_impl<LoadMode,PacketType>(row,col, row,
                                  typename internal::conditional<int(StorageOrder)==RowMajor, internal::true_type, internal::false_type>::type());
   }
-  
+
   template<int LoadMode,typename PacketType>
   EIGEN_STRONG_INLINE PacketType packet(Index idx) const
   {
@@ -953,22 +953,22 @@
   using Base::m_matImpl;
   using Base::coeff;
   typedef typename Base::Scalar Scalar;
-  
+
   typedef Product<Lhs, Rhs, ProductKind> XprType;
   typedef typename XprType::PlainObject PlainObject;
-  
+
   enum { StorageOrder = Base::_StorageOrder };
 
   EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
     : Base(xpr.lhs(), xpr.rhs().diagonal())
   {
   }
-  
+
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const
   {
     return m_matImpl.coeff(row, col) * m_diagImpl.coeff(col);
   }
-  
+
 #ifndef EIGEN_GPUCC
   template<int LoadMode,typename PacketType>
   EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const
@@ -976,7 +976,7 @@
     return this->template packet_impl<LoadMode,PacketType>(row,col, col,
                                  typename internal::conditional<int(StorageOrder)==ColMajor, internal::true_type, internal::false_type>::type());
   }
-  
+
   template<int LoadMode,typename PacketType>
   EIGEN_STRONG_INLINE PacketType packet(Index idx) const
   {
@@ -1004,7 +1004,7 @@
     typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;
 
     template<typename Dest, typename PermutationType>
-    static inline void run(Dest& dst, const PermutationType& perm, const ExpressionType& xpr)
+    static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Dest& dst, const PermutationType& perm, const ExpressionType& xpr)
     {
       MatrixType mat(xpr);
       const Index n = Side==OnTheLeft ? mat.rows() : mat.cols();
@@ -1058,7 +1058,7 @@
 struct generic_product_impl<Lhs, Rhs, PermutationShape, MatrixShape, ProductTag>
 {
   template<typename Dest>
-  static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
   {
     permutation_matrix_product<Rhs, OnTheLeft, false, MatrixShape>::run(dst, lhs, rhs);
   }
@@ -1068,7 +1068,7 @@
 struct generic_product_impl<Lhs, Rhs, MatrixShape, PermutationShape, ProductTag>
 {
   template<typename Dest>
-  static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
   {
     permutation_matrix_product<Lhs, OnTheRight, false, MatrixShape>::run(dst, rhs, lhs);
   }
@@ -1078,7 +1078,7 @@
 struct generic_product_impl<Inverse<Lhs>, Rhs, PermutationShape, MatrixShape, ProductTag>
 {
   template<typename Dest>
-  static void evalTo(Dest& dst, const Inverse<Lhs>& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Inverse<Lhs>& lhs, const Rhs& rhs)
   {
     permutation_matrix_product<Rhs, OnTheLeft, true, MatrixShape>::run(dst, lhs.nestedExpression(), rhs);
   }
@@ -1088,7 +1088,7 @@
 struct generic_product_impl<Lhs, Inverse<Rhs>, MatrixShape, PermutationShape, ProductTag>
 {
   template<typename Dest>
-  static void evalTo(Dest& dst, const Lhs& lhs, const Inverse<Rhs>& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Inverse<Rhs>& rhs)
   {
     permutation_matrix_product<Lhs, OnTheRight, true, MatrixShape>::run(dst, rhs.nestedExpression(), lhs);
   }
@@ -1110,9 +1110,9 @@
 {
   typedef typename nested_eval<ExpressionType, 1>::type MatrixType;
   typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;
-  
+
   template<typename Dest, typename TranspositionType>
-  static inline void run(Dest& dst, const TranspositionType& tr, const ExpressionType& xpr)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Dest& dst, const TranspositionType& tr, const ExpressionType& xpr)
   {
     MatrixType mat(xpr);
     typedef typename TranspositionType::StorageIndex StorageIndex;
@@ -1135,7 +1135,7 @@
 struct generic_product_impl<Lhs, Rhs, TranspositionsShape, MatrixShape, ProductTag>
 {
   template<typename Dest>
-  static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
   {
     transposition_matrix_product<Rhs, OnTheLeft, false, MatrixShape>::run(dst, lhs, rhs);
   }
@@ -1145,7 +1145,7 @@
 struct generic_product_impl<Lhs, Rhs, MatrixShape, TranspositionsShape, ProductTag>
 {
   template<typename Dest>
-  static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
   {
     transposition_matrix_product<Lhs, OnTheRight, false, MatrixShape>::run(dst, rhs, lhs);
   }
@@ -1156,7 +1156,7 @@
 struct generic_product_impl<Transpose<Lhs>, Rhs, TranspositionsShape, MatrixShape, ProductTag>
 {
   template<typename Dest>
-  static void evalTo(Dest& dst, const Transpose<Lhs>& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Transpose<Lhs>& lhs, const Rhs& rhs)
   {
     transposition_matrix_product<Rhs, OnTheLeft, true, MatrixShape>::run(dst, lhs.nestedExpression(), rhs);
   }
@@ -1166,7 +1166,7 @@
 struct generic_product_impl<Lhs, Transpose<Rhs>, MatrixShape, TranspositionsShape, ProductTag>
 {
   template<typename Dest>
-  static void evalTo(Dest& dst, const Lhs& lhs, const Transpose<Rhs>& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Transpose<Rhs>& rhs)
   {
     transposition_matrix_product<Lhs, OnTheRight, true, MatrixShape>::run(dst, rhs.nestedExpression(), lhs);
   }
diff --git a/Eigen/src/Core/Reshaped.h b/Eigen/src/Core/Reshaped.h
index a78fd88..36b4f41 100644
--- a/Eigen/src/Core/Reshaped.h
+++ b/Eigen/src/Core/Reshaped.h
@@ -12,7 +12,6 @@
 #define EIGEN_RESHAPED_H
 
 namespace Eigen {
-namespace internal {
 
 /** \class Reshaped
   * \ingroup Core_Module
@@ -44,6 +43,8 @@
   * \sa DenseBase::reshaped(NRowsType,NColsType)
   */
 
+namespace internal {
+
 template<typename XprType, int Rows, int Cols, int Order>
 struct traits<Reshaped<XprType, Rows, Cols, Order> > : traits<XprType>
 {
diff --git a/Eigen/src/Core/SolveTriangular.h b/Eigen/src/Core/SolveTriangular.h
index 813fef0d..dc53b5e 100644
--- a/Eigen/src/Core/SolveTriangular.h
+++ b/Eigen/src/Core/SolveTriangular.h
@@ -10,7 +10,7 @@
 #ifndef EIGEN_SOLVETRIANGULAR_H
 #define EIGEN_SOLVETRIANGULAR_H
 
-namespace Eigen { 
+namespace Eigen {
 
 namespace internal {
 
@@ -54,7 +54,7 @@
   typedef blas_traits<Lhs> LhsProductTraits;
   typedef typename LhsProductTraits::ExtractType ActualLhsType;
   typedef Map<Matrix<RhsScalar,Dynamic,1>, Aligned> MappedRhs;
-  static void run(const Lhs& lhs, Rhs& rhs)
+  static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs)
   {
     ActualLhsType actualLhs = LhsProductTraits::extract(lhs);
 
@@ -64,7 +64,7 @@
 
     ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhs,rhs.size(),
                                                   (useRhsDirectly ? rhs.data() : 0));
-                                                  
+
     if(!useRhsDirectly)
       MappedRhs(actualRhs,rhs.size()) = rhs;
 
@@ -85,7 +85,7 @@
   typedef blas_traits<Lhs> LhsProductTraits;
   typedef typename LhsProductTraits::DirectLinearAccessType ActualLhsType;
 
-  static void run(const Lhs& lhs, Rhs& rhs)
+  static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs)
   {
     typename internal::add_const_on_value_type<ActualLhsType>::type actualLhs = LhsProductTraits::extract(lhs);
 
@@ -118,7 +118,7 @@
     DiagIndex  = IsLower ? LoopIndex : Size - LoopIndex - 1,
     StartIndex = IsLower ? 0         : DiagIndex+1
   };
-  static void run(const Lhs& lhs, Rhs& rhs)
+  static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs)
   {
     if (LoopIndex>0)
       rhs.coeffRef(DiagIndex) -= lhs.row(DiagIndex).template segment<LoopIndex>(StartIndex).transpose()
@@ -133,22 +133,22 @@
 
 template<typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size>
 struct triangular_solver_unroller<Lhs,Rhs,Mode,LoopIndex,Size,true> {
-  static void run(const Lhs&, Rhs&) {}
+  static EIGEN_DEVICE_FUNC void run(const Lhs&, Rhs&) {}
 };
 
 template<typename Lhs, typename Rhs, int Mode>
 struct triangular_solver_selector<Lhs,Rhs,OnTheLeft,Mode,CompleteUnrolling,1> {
-  static void run(const Lhs& lhs, Rhs& rhs)
+  static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs)
   { triangular_solver_unroller<Lhs,Rhs,Mode,0,Rhs::SizeAtCompileTime>::run(lhs,rhs); }
 };
 
 template<typename Lhs, typename Rhs, int Mode>
 struct triangular_solver_selector<Lhs,Rhs,OnTheRight,Mode,CompleteUnrolling,1> {
-  static void run(const Lhs& lhs, Rhs& rhs)
+  static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs)
   {
     Transpose<const Lhs> trLhs(lhs);
     Transpose<Rhs> trRhs(rhs);
-    
+
     triangular_solver_unroller<Transpose<const Lhs>,Transpose<Rhs>,
                               ((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),
                               0,Rhs::SizeAtCompileTime>::run(trLhs,trRhs);
diff --git a/Eigen/src/Core/Transpositions.h b/Eigen/src/Core/Transpositions.h
index fcfe6f4..f323a2b 100644
--- a/Eigen/src/Core/Transpositions.h
+++ b/Eigen/src/Core/Transpositions.h
@@ -47,6 +47,7 @@
     Index cols() const { return indices().size(); }
 
     /** Direct access to the underlying index vector */
+    EIGEN_DEVICE_FUNC
     inline const StorageIndex& coeff(Index i) const { return indices().coeff(i); }
     /** Direct access to the underlying index vector */
     inline StorageIndex& coeffRef(Index i) { return indices().coeffRef(i); }
@@ -373,6 +374,7 @@
       return Product<Transpose, OtherDerived, AliasFreeProduct>(*this, matrix.derived());
     }
 
+    EIGEN_DEVICE_FUNC
     const TranspositionType& nestedExpression() const { return m_transpositions; }
 
   protected:
diff --git a/Eigen/src/Core/arch/AVX/Complex.h b/Eigen/src/Core/arch/AVX/Complex.h
index 23568ca..506ca0b 100644
--- a/Eigen/src/Core/arch/AVX/Complex.h
+++ b/Eigen/src/Core/arch/AVX/Complex.h
@@ -38,6 +38,7 @@
     HasMul    = 1,
     HasDiv    = 1,
     HasNegate = 1,
+    HasSqrt   = 1,
     HasAbs    = 0,
     HasAbs2   = 0,
     HasMin    = 0,
@@ -47,7 +48,18 @@
 };
 #endif
 
-template<> struct unpacket_traits<Packet4cf> { typedef std::complex<float> type; enum {size=4, alignment=Aligned32, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet2cf half; };
+template<> struct unpacket_traits<Packet4cf> {
+  typedef std::complex<float> type;
+  typedef Packet2cf half;
+  typedef Packet8f as_real;
+  enum {
+    size=4,
+    alignment=Aligned32,
+    vectorizable=true,
+    masked_load_available=false,
+    masked_store_available=false
+  };
+};
 
 template<> EIGEN_STRONG_INLINE Packet4cf padd<Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_add_ps(a.v,b.v)); }
 template<> EIGEN_STRONG_INLINE Packet4cf psub<Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_sub_ps(a.v,b.v)); }
@@ -228,6 +240,7 @@
     HasMul    = 1,
     HasDiv    = 1,
     HasNegate = 1,
+    HasSqrt   = 1,
     HasAbs    = 0,
     HasAbs2   = 0,
     HasMin    = 0,
@@ -237,7 +250,18 @@
 };
 #endif
 
-template<> struct unpacket_traits<Packet2cd> { typedef std::complex<double> type; enum {size=2, alignment=Aligned32, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet1cd half; };
+template<> struct unpacket_traits<Packet2cd> {
+  typedef std::complex<double> type;
+  typedef Packet1cd half;
+  typedef Packet4d as_real;
+  enum {
+    size=2,
+    alignment=Aligned32,
+    vectorizable=true,
+    masked_load_available=false,
+    masked_store_available=false
+  };
+};
 
 template<> EIGEN_STRONG_INLINE Packet2cd padd<Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_add_pd(a.v,b.v)); }
 template<> EIGEN_STRONG_INLINE Packet2cd psub<Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_sub_pd(a.v,b.v)); }
@@ -399,6 +423,14 @@
  kernel.packet[0].v = tmp;
 }
 
+template<> EIGEN_STRONG_INLINE Packet2cd psqrt<Packet2cd>(const Packet2cd& a) {
+  return psqrt_complex<Packet2cd>(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cf psqrt<Packet4cf>(const Packet4cf& a) {
+  return psqrt_complex<Packet4cf>(a);
+}
+
 } // end namespace internal
 
 } // end namespace Eigen
diff --git a/Eigen/src/Core/arch/AVX/MathFunctions.h b/Eigen/src/Core/arch/AVX/MathFunctions.h
index 9b123db..5fe2cff 100644
--- a/Eigen/src/Core/arch/AVX/MathFunctions.h
+++ b/Eigen/src/Core/arch/AVX/MathFunctions.h
@@ -42,6 +42,18 @@
   return plog_double(_x);
 }
 
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f
+plog2<Packet8f>(const Packet8f& _x) {
+  return plog2_float(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4d
+plog2<Packet4d>(const Packet4d& _x) {
+  return plog2_double(_x);
+}
+
 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
 Packet8f plog1p<Packet8f>(const Packet8f& _x) {
   return generic_plog1p(_x);
@@ -158,9 +170,21 @@
   return _mm256_div_pd(p4d_one, _mm256_sqrt_pd(_x));
 }
 
+F16_PACKET_FUNCTION(Packet8f, Packet8h, psin)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pcos)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, plog)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, plog2)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, plog1p)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pexpm1)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pexp)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, ptanh)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, psqrt)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, prsqrt)
+
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, psin)
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pcos)
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, plog)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, plog2)
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, plog1p)
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pexpm1)
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pexp)
diff --git a/Eigen/src/Core/arch/AVX/PacketMath.h b/Eigen/src/Core/arch/AVX/PacketMath.h
index ae111c6..3974935 100644
--- a/Eigen/src/Core/arch/AVX/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX/PacketMath.h
@@ -105,7 +105,8 @@
     HasBlend = 1,
     HasRound = 1,
     HasFloor = 1,
-    HasCeil = 1
+    HasCeil = 1,
+    HasRint = 1
   };
 };
 
@@ -119,22 +120,36 @@
     AlignedOnScalar = 1,
     size = 8,
     HasHalfPacket = 0,
+
+    HasCmp    = 1,
     HasAdd    = 1,
     HasSub    = 1,
     HasMul    = 1,
     HasDiv    = 1,
+    HasSin    = EIGEN_FAST_MATH,
+    HasCos    = EIGEN_FAST_MATH,
     HasNegate = 1,
-    HasAbs    = 0,
+    HasAbs    = 1,
     HasAbs2   = 0,
-    HasMin    = 0,
-    HasMax    = 0,
-    HasConj   = 0,
+    HasMin    = 1,
+    HasMax    = 1,
+    HasConj   = 1,
     HasSetLinear = 0,
-    HasSqrt = 0,
-    HasRsqrt = 0,
-    HasExp = 0,
-    HasLog = 0,
-    HasBlend = 0
+    HasLog    = 1,
+    HasLog1p  = 1,
+    HasExpm1  = 1,
+    HasExp    = 1,
+    HasSqrt   = 1,
+    HasRsqrt  = 1,
+    HasTanh   = EIGEN_FAST_MATH,
+    HasErf    = EIGEN_FAST_MATH,
+    HasBlend  = 0,
+    HasRound  = 1,
+    HasFloor  = 1,
+    HasCeil   = 1,
+    HasRint   = 1,
+    HasBessel = 1,
+    HasNdtri  = 1,
   };
 };
 
@@ -150,16 +165,24 @@
     size = 8,
     HasHalfPacket = 0,
 
-    HasCmp  = 1,
+    HasCmp = 1,
+    HasAdd = 1,
+    HasSub = 1,
+    HasMul = 1,
     HasDiv = 1,
     HasSin = EIGEN_FAST_MATH,
     HasCos = EIGEN_FAST_MATH,
+    HasNegate = 1,
+    HasAbs    = 1,
+    HasAbs2   = 0,
+    HasMin    = 1,
+    HasMax    = 1,
+    HasConj   = 1,
+    HasSetLinear = 0,
     HasLog = 1,
     HasLog1p  = 1,
     HasExpm1  = 1,
     HasExp = 1,
-    HasNdtri = 1,
-    HasBessel  = 1,
     HasSqrt = 1,
     HasRsqrt = 1,
     HasTanh = EIGEN_FAST_MATH,
@@ -168,7 +191,9 @@
     HasRound = 1,
     HasFloor = 1,
     HasCeil = 1,
-    HasRint = 1
+    HasRint = 1,
+    HasBessel = 1,
+    HasNdtri  = 1,
   };
 };
 #endif
@@ -211,6 +236,7 @@
                          _mm256_extractf128_si256(_mm256_castps_si256(rf), 1));
 }
 
+
 template<> EIGEN_STRONG_INLINE Packet8f pset1<Packet8f>(const float&  from) { return _mm256_set1_ps(from); }
 template<> EIGEN_STRONG_INLINE Packet4d pset1<Packet4d>(const double& from) { return _mm256_set1_pd(from); }
 template<> EIGEN_STRONG_INLINE Packet8i pset1<Packet8i>(const int&    from) { return _mm256_set1_epi32(from); }
@@ -222,6 +248,11 @@
 template<> EIGEN_STRONG_INLINE Packet4d pzero(const Packet4d& /*a*/) { return _mm256_setzero_pd(); }
 template<> EIGEN_STRONG_INLINE Packet8i pzero(const Packet8i& /*a*/) { return _mm256_setzero_si256(); }
 
+
+template<> EIGEN_STRONG_INLINE Packet8f peven_mask(const Packet8f& /*a*/) { return _mm256_castsi256_ps(_mm256_set_epi32(0, -1, 0, -1, 0, -1, 0, -1)); }
+template<> EIGEN_STRONG_INLINE Packet8i peven_mask(const Packet8i& /*a*/) { return _mm256_set_epi32(0, -1, 0, -1, 0, -1, 0, -1); }
+template<> EIGEN_STRONG_INLINE Packet4d peven_mask(const Packet4d& /*a*/) { return _mm256_castsi256_pd(_mm256_set_epi32(0, 0, -1, -1, 0, 0, -1, -1)); }
+
 template<> EIGEN_STRONG_INLINE Packet8f pload1<Packet8f>(const float*  from) { return _mm256_broadcast_ss(from); }
 template<> EIGEN_STRONG_INLINE Packet4d pload1<Packet4d>(const double* from) { return _mm256_broadcast_sd(from); }
 
@@ -258,7 +289,15 @@
 
 template<> EIGEN_STRONG_INLINE Packet8f pmul<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_mul_ps(a,b); }
 template<> EIGEN_STRONG_INLINE Packet4d pmul<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_mul_pd(a,b); }
-
+template<> EIGEN_STRONG_INLINE Packet8i pmul<Packet8i>(const Packet8i& a, const Packet8i& b) {
+#ifdef EIGEN_VECTORIZE_AVX2
+  return _mm256_mullo_epi32(a,b);
+#else
+  const __m128i lo = _mm_mullo_epi32(_mm256_extractf128_si256(a, 0), _mm256_extractf128_si256(b, 0));
+  const __m128i hi = _mm_mullo_epi32(_mm256_extractf128_si256(a, 1), _mm256_extractf128_si256(b, 1));
+  return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
 
 template<> EIGEN_STRONG_INLINE Packet8f pdiv<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_div_ps(a,b); }
 template<> EIGEN_STRONG_INLINE Packet4d pdiv<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_div_pd(a,b); }
@@ -479,14 +518,14 @@
 
 template<> EIGEN_STRONG_INLINE Packet8f pround<Packet8f>(const Packet8f& a)
 {
-  const Packet8f mask = pset1frombits<Packet8f>(0x80000000u);
-  const Packet8f prev0dot5 = pset1frombits<Packet8f>(0x3EFFFFFFu);
+  const Packet8f mask = pset1frombits<Packet8f>(static_cast<numext::uint32_t>(0x80000000u));
+  const Packet8f prev0dot5 = pset1frombits<Packet8f>(static_cast<numext::uint32_t>(0x3EFFFFFFu));
   return _mm256_round_ps(padd(por(pand(a, mask), prev0dot5), a), _MM_FROUND_TO_ZERO);
 }
 template<> EIGEN_STRONG_INLINE Packet4d pround<Packet4d>(const Packet4d& a)
 {
-  const Packet4d mask = _mm256_castsi256_pd(_mm256_set_epi64x(0x8000000000000000ull, 0x8000000000000000ull, 0x8000000000000000ull, 0x8000000000000000ull));
-  const Packet4d prev0dot5 = _mm256_castsi256_pd(_mm256_set_epi64x(0x3FDFFFFFFFFFFFFFull, 0x3FDFFFFFFFFFFFFFull, 0x3FDFFFFFFFFFFFFFull, 0x3FDFFFFFFFFFFFFFull));
+  const Packet4d mask = pset1frombits<Packet4d>(static_cast<numext::uint64_t>(0x8000000000000000ull));
+  const Packet4d prev0dot5 = pset1frombits<Packet4d>(static_cast<numext::uint64_t>(0x3FDFFFFFFFFFFFFFull));
   return _mm256_round_pd(padd(por(pand(a, mask), prev0dot5), a), _MM_FROUND_TO_ZERO);
 }
 
@@ -695,13 +734,11 @@
   __m256i a_expo = _mm256_castpd_si256(pand(a, cst_exp_mask));
 #ifdef EIGEN_VECTORIZE_AVX2
   a_expo = _mm256_srli_epi64(a_expo, 52);
-#endif
-#if defined(EIGEN_VECTORIZE_AVX2) && defined(EIGEN_VECTORIZE_AVX512DQ)
-  exponent =  _mm256_cvtepi64_pd(a_expo);
+  __m128i lo = _mm256_extractf128_si256(a_expo, 0);
+  __m128i hi = _mm256_extractf128_si256(a_expo, 1);
 #else
   __m128i lo = _mm256_extractf128_si256(a_expo, 0);
   __m128i hi = _mm256_extractf128_si256(a_expo, 1);
-#ifndef EIGEN_VECTORIZE_AVX2
   lo = _mm_srli_epi64(lo, 52);
   hi = _mm_srli_epi64(hi, 52);
 #endif
@@ -709,7 +746,6 @@
   Packet2d exponent_hi = _mm_cvtepi32_pd(vec4i_swizzle1(hi, 0, 2, 1, 3));
   exponent = _mm256_insertf128_pd(exponent, exponent_lo, 0);
   exponent = _mm256_insertf128_pd(exponent, exponent_hi, 1);
-#endif  // EIGEN_VECTORIZE_AVX512DQ
   exponent = psub(exponent, cst_1022d);
   const Packet4d cst_mant_mask  = pset1frombits<Packet4d>(static_cast<uint64_t>(~0x7ff0000000000000ull));
   return por(pand(a, cst_mant_mask), cst_half);
@@ -870,14 +906,15 @@
 }
 
 // Packet math for Eigen::half
+
 template<> struct unpacket_traits<Packet8h> { typedef Eigen::half type; enum {size=8, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet8h half; };
 
 template<> EIGEN_STRONG_INLINE Packet8h pset1<Packet8h>(const Eigen::half& from) {
-  return _mm_set1_epi16(from.x);
+  return _mm_set1_epi16(numext::bit_cast<numext::uint16_t>(from));
 }
 
 template<> EIGEN_STRONG_INLINE Eigen::half pfirst<Packet8h>(const Packet8h& from) {
-  return half_impl::raw_uint16_to_half(static_cast<unsigned short>(_mm_extract_epi16(from, 0)));
+  return numext::bit_cast<Eigen::half>(static_cast<numext::uint16_t>(_mm_extract_epi16(from, 0)));
 }
 
 template<> EIGEN_STRONG_INLINE Packet8h pload<Packet8h>(const Eigen::half* from) {
@@ -898,20 +935,30 @@
 
 template<> EIGEN_STRONG_INLINE Packet8h
 ploaddup<Packet8h>(const Eigen::half*  from) {
-  unsigned short a = from[0].x;
-  unsigned short b = from[1].x;
-  unsigned short c = from[2].x;
-  unsigned short d = from[3].x;
+  const numext::uint16_t a = numext::bit_cast<numext::uint16_t>(from[0]);
+  const numext::uint16_t b = numext::bit_cast<numext::uint16_t>(from[1]);
+  const numext::uint16_t c = numext::bit_cast<numext::uint16_t>(from[2]);
+  const numext::uint16_t d = numext::bit_cast<numext::uint16_t>(from[3]);
   return _mm_set_epi16(d, d, c, c, b, b, a, a);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8h
 ploadquad<Packet8h>(const Eigen::half* from) {
-  unsigned short a = from[0].x;
-  unsigned short b = from[1].x;
+  const numext::uint16_t a = numext::bit_cast<numext::uint16_t>(from[0]);
+  const numext::uint16_t b = numext::bit_cast<numext::uint16_t>(from[1]);
   return _mm_set_epi16(b, b, b, b, a, a, a, a);
 }
 
+template<> EIGEN_STRONG_INLINE Packet8h ptrue(const Packet8h& a) {
+ return _mm_cmpeq_epi32(a, a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pabs(const Packet8h& a) {
+  const __m128i sign_mask = _mm_set1_epi16(static_cast<numext::uint16_t>(0x8000));
+  return _mm_andnot_si128(sign_mask, a);
+}
+
 EIGEN_STRONG_INLINE Packet8f half2float(const Packet8h& a) {
 #ifdef EIGEN_HAS_FP16_C
   return _mm256_cvtph_ps(a);
@@ -937,21 +984,33 @@
 #else
   EIGEN_ALIGN32 float aux[8];
   pstore(aux, a);
-  Eigen::half h0(aux[0]);
-  Eigen::half h1(aux[1]);
-  Eigen::half h2(aux[2]);
-  Eigen::half h3(aux[3]);
-  Eigen::half h4(aux[4]);
-  Eigen::half h5(aux[5]);
-  Eigen::half h6(aux[6]);
-  Eigen::half h7(aux[7]);
-
-  return _mm_set_epi16(h7.x, h6.x, h5.x, h4.x, h3.x, h2.x, h1.x, h0.x);
+  const numext::uint16_t s0 = numext::bit_cast<numext::uint16_t>(Eigen::half(aux[0]));
+  const numext::uint16_t s1 = numext::bit_cast<numext::uint16_t>(Eigen::half(aux[1]));
+  const numext::uint16_t s2 = numext::bit_cast<numext::uint16_t>(Eigen::half(aux[2]));
+  const numext::uint16_t s3 = numext::bit_cast<numext::uint16_t>(Eigen::half(aux[3]));
+  const numext::uint16_t s4 = numext::bit_cast<numext::uint16_t>(Eigen::half(aux[4]));
+  const numext::uint16_t s5 = numext::bit_cast<numext::uint16_t>(Eigen::half(aux[5]));
+  const numext::uint16_t s6 = numext::bit_cast<numext::uint16_t>(Eigen::half(aux[6]));
+  const numext::uint16_t s7 = numext::bit_cast<numext::uint16_t>(Eigen::half(aux[7]));
+  return _mm_set_epi16(s7, s6, s5, s4, s3, s2, s1, s0);
 #endif
 }
 
-template<> EIGEN_STRONG_INLINE Packet8h ptrue(const Packet8h& a) {
- return _mm_cmpeq_epi32(a, a);
+template <>
+EIGEN_STRONG_INLINE Packet8h pmin<Packet8h>(const Packet8h& a,
+                                            const Packet8h& b) {
+  return float2half(pmin<Packet8f>(half2float(a), half2float(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pmax<Packet8h>(const Packet8h& a,
+                                            const Packet8h& b) {
+  return float2half(pmax<Packet8f>(half2float(a), half2float(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h plset<Packet8h>(const half& a) {
+  return float2half(plset<Packet8f>(static_cast<float>(a)));
 }
 
 template<> EIGEN_STRONG_INLINE Packet8h por(const Packet8h& a,const Packet8h& b) {
@@ -973,19 +1032,42 @@
   return _mm_blendv_epi8(b, a, mask);
 }
 
+template<> EIGEN_STRONG_INLINE Packet8h pround<Packet8h>(const Packet8h& a) {
+  return float2half(pround<Packet8f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h print<Packet8h>(const Packet8h& a) {
+  return float2half(print<Packet8f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pceil<Packet8h>(const Packet8h& a) {
+  return float2half(pceil<Packet8f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pfloor<Packet8h>(const Packet8h& a) {
+  return float2half(pfloor<Packet8f>(half2float(a)));
+}
+
 template<> EIGEN_STRONG_INLINE Packet8h pcmp_eq(const Packet8h& a,const Packet8h& b) {
-  Packet8f af = half2float(a);
-  Packet8f bf = half2float(b);
-  Packet8f rf = pcmp_eq(af, bf);
-  // Pack the 32-bit flags into 16-bits flags.
-  return _mm_packs_epi32(_mm256_extractf128_si256(_mm256_castps_si256(rf), 0),
-                         _mm256_extractf128_si256(_mm256_castps_si256(rf), 1));
+  return Pack16To8(pcmp_eq(half2float(a), half2float(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pcmp_le(const Packet8h& a,const Packet8h& b) {
+  return Pack16To8(pcmp_le(half2float(a), half2float(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pcmp_lt(const Packet8h& a,const Packet8h& b) {
+  return Pack16To8(pcmp_lt(half2float(a), half2float(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pcmp_lt_or_nan(const Packet8h& a,const Packet8h& b) {
+  return Pack16To8(pcmp_lt_or_nan(half2float(a), half2float(b)));
 }
 
 template<> EIGEN_STRONG_INLINE Packet8h pconj(const Packet8h& a) { return a; }
 
 template<> EIGEN_STRONG_INLINE Packet8h pnegate(const Packet8h& a) {
-  Packet8h sign_mask = _mm_set1_epi16(static_cast<unsigned short>(0x8000));
+  Packet8h sign_mask = _mm_set1_epi16(static_cast<numext::uint16_t>(0x8000));
   return _mm_xor_si128(a, sign_mask);
 }
 
@@ -1019,7 +1101,15 @@
 
 template<> EIGEN_STRONG_INLINE Packet8h pgather<Eigen::half, Packet8h>(const Eigen::half* from, Index stride)
 {
-  return _mm_set_epi16(from[7*stride].x, from[6*stride].x, from[5*stride].x, from[4*stride].x, from[3*stride].x, from[2*stride].x, from[1*stride].x, from[0*stride].x);
+  const numext::uint16_t s0 = numext::bit_cast<numext::uint16_t>(from[0*stride]);
+  const numext::uint16_t s1 = numext::bit_cast<numext::uint16_t>(from[1*stride]);
+  const numext::uint16_t s2 = numext::bit_cast<numext::uint16_t>(from[2*stride]);
+  const numext::uint16_t s3 = numext::bit_cast<numext::uint16_t>(from[3*stride]);
+  const numext::uint16_t s4 = numext::bit_cast<numext::uint16_t>(from[4*stride]);
+  const numext::uint16_t s5 = numext::bit_cast<numext::uint16_t>(from[5*stride]);
+  const numext::uint16_t s6 = numext::bit_cast<numext::uint16_t>(from[6*stride]);
+  const numext::uint16_t s7 = numext::bit_cast<numext::uint16_t>(from[7*stride]);
+  return _mm_set_epi16(s7, s6, s5, s4, s3, s2, s1, s0);
 }
 
 template<> EIGEN_STRONG_INLINE void pscatter<Eigen::half, Packet8h>(Eigen::half* to, const Packet8h& from, Index stride)
@@ -1139,6 +1229,8 @@
   kernel.packet[3] = pload<Packet8h>(out[3]);
 }
 
+// BFloat16 implementation.
+
 EIGEN_STRONG_INLINE Packet8f Bf16ToF32(const Packet8bf& a) {
 #ifdef EIGEN_VECTORIZE_AVX2
   __m256i extend = _mm256_cvtepu16_epi32(a);
@@ -1178,7 +1270,7 @@
   __m256 mask = _mm256_cmp_ps(flush, flush, _CMP_ORD_Q);
   __m256i nan = _mm256_set1_epi32(0x7fc0);
   t = _mm256_blendv_epi8(nan, t, _mm256_castps_si256(mask));
-  // output.value = static_cast<uint16_t>(input);
+  // output = numext::bit_cast<uint16_t>(input);
   return _mm_packus_epi32(_mm256_extractf128_si256(t, 0),
                          _mm256_extractf128_si256(t, 1));
 #else
@@ -1202,17 +1294,17 @@
   __m128i nan = _mm_set1_epi32(0x7fc0);
   lo = _mm_blendv_epi8(nan, lo, _mm_castps_si128(_mm256_castps256_ps128(mask)));
   hi = _mm_blendv_epi8(nan, hi, _mm_castps_si128(_mm256_extractf128_ps(mask, 1)));
-  // output.value = static_cast<uint16_t>(input);
+  // output = numext::bit_cast<uint16_t>(input);
   return _mm_packus_epi32(lo, hi);
 #endif
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf pset1<Packet8bf>(const bfloat16& from) {
-  return _mm_set1_epi16(from.value);
+  return _mm_set1_epi16(numext::bit_cast<numext::uint16_t>(from));
 }
 
 template<> EIGEN_STRONG_INLINE bfloat16 pfirst<Packet8bf>(const Packet8bf& from) {
-  return bfloat16_impl::raw_uint16_to_bfloat16(static_cast<unsigned short>(_mm_extract_epi16(from, 0)));
+  return numext::bit_cast<bfloat16>(static_cast<numext::uint16_t>(_mm_extract_epi16(from, 0)));
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf pload<Packet8bf>(const bfloat16* from) {
@@ -1233,17 +1325,17 @@
 
 template<> EIGEN_STRONG_INLINE Packet8bf
 ploaddup<Packet8bf>(const bfloat16* from) {
-  unsigned short a = from[0].value;
-  unsigned short b = from[1].value;
-  unsigned short c = from[2].value;
-  unsigned short d = from[3].value;
+  const numext::uint16_t a = numext::bit_cast<numext::uint16_t>(from[0]);
+  const numext::uint16_t b = numext::bit_cast<numext::uint16_t>(from[1]);
+  const numext::uint16_t c = numext::bit_cast<numext::uint16_t>(from[2]);
+  const numext::uint16_t d = numext::bit_cast<numext::uint16_t>(from[3]);
   return _mm_set_epi16(d, d, c, c, b, b, a, a);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf
 ploadquad<Packet8bf>(const bfloat16* from) {
-  unsigned short a = from[0].value;
-  unsigned short b = from[1].value;
+  const numext::uint16_t a = numext::bit_cast<numext::uint16_t>(from[0]);
+  const numext::uint16_t b = numext::bit_cast<numext::uint16_t>(from[1]);
   return _mm_set_epi16(b, b, b, b, a, a, a, a);
 }
 
@@ -1253,7 +1345,8 @@
 
 template <>
 EIGEN_STRONG_INLINE Packet8bf pabs(const Packet8bf& a) {
-  return F32ToBf16(pabs<Packet8f>(Bf16ToF32(a)));
+  const __m128i sign_mask = _mm_set1_epi16(static_cast<numext::uint16_t>(0x8000));
+  return _mm_andnot_si128(sign_mask, a);
 }
 
 template <>
@@ -1326,7 +1419,7 @@
 template<> EIGEN_STRONG_INLINE Packet8bf pconj(const Packet8bf& a) { return a; }
 
 template<> EIGEN_STRONG_INLINE Packet8bf pnegate(const Packet8bf& a) {
-  Packet8bf sign_mask = _mm_set1_epi16(static_cast<unsigned short>(0x8000));
+  Packet8bf sign_mask = _mm_set1_epi16(static_cast<numext::uint16_t>(0x8000));
   return _mm_xor_si128(a, sign_mask);
 }
 
@@ -1349,7 +1442,15 @@
 
 template<> EIGEN_STRONG_INLINE Packet8bf pgather<bfloat16, Packet8bf>(const bfloat16* from, Index stride)
 {
-  return _mm_set_epi16(from[7*stride].value, from[6*stride].value, from[5*stride].value, from[4*stride].value, from[3*stride].value, from[2*stride].value, from[1*stride].value, from[0*stride].value);
+  const numext::uint16_t s0 = numext::bit_cast<numext::uint16_t>(from[0*stride]);
+  const numext::uint16_t s1 = numext::bit_cast<numext::uint16_t>(from[1*stride]);
+  const numext::uint16_t s2 = numext::bit_cast<numext::uint16_t>(from[2*stride]);
+  const numext::uint16_t s3 = numext::bit_cast<numext::uint16_t>(from[3*stride]);
+  const numext::uint16_t s4 = numext::bit_cast<numext::uint16_t>(from[4*stride]);
+  const numext::uint16_t s5 = numext::bit_cast<numext::uint16_t>(from[5*stride]);
+  const numext::uint16_t s6 = numext::bit_cast<numext::uint16_t>(from[6*stride]);
+  const numext::uint16_t s7 = numext::bit_cast<numext::uint16_t>(from[7*stride]);
+  return _mm_set_epi16(s7, s6, s5, s4, s3, s2, s1, s0);
 }
 
 template<> EIGEN_STRONG_INLINE void pscatter<bfloat16, Packet8bf>(bfloat16* to, const Packet8bf& from, Index stride)
diff --git a/Eigen/src/Core/arch/AVX512/Complex.h b/Eigen/src/Core/arch/AVX512/Complex.h
index 53ee53d..45f22f4 100644
--- a/Eigen/src/Core/arch/AVX512/Complex.h
+++ b/Eigen/src/Core/arch/AVX512/Complex.h
@@ -37,6 +37,7 @@
     HasMul    = 1,
     HasDiv    = 1,
     HasNegate = 1,
+    HasSqrt   = 1,
     HasAbs    = 0,
     HasAbs2   = 0,
     HasMin    = 0,
@@ -47,6 +48,8 @@
 
 template<> struct unpacket_traits<Packet8cf> {
   typedef std::complex<float> type;
+  typedef Packet4cf half;
+  typedef Packet16f as_real;
   enum {
     size = 8,
     alignment=unpacket_traits<Packet16f>::alignment,
@@ -54,7 +57,6 @@
     masked_load_available=false,
     masked_store_available=false
   };
-  typedef Packet4cf half;
 };
 
 template<> EIGEN_STRONG_INLINE Packet8cf ptrue<Packet8cf>(const Packet8cf& a) { return Packet8cf(ptrue(Packet16f(a.v))); }
@@ -223,6 +225,7 @@
     HasMul    = 1,
     HasDiv    = 1,
     HasNegate = 1,
+    HasSqrt   = 1,
     HasAbs    = 0,
     HasAbs2   = 0,
     HasMin    = 0,
@@ -233,6 +236,8 @@
 
 template<> struct unpacket_traits<Packet4cd> {
   typedef std::complex<double> type;
+  typedef Packet2cd half;
+  typedef Packet8d as_real;
   enum {
     size = 4,
     alignment = unpacket_traits<Packet8d>::alignment,
@@ -240,7 +245,6 @@
     masked_load_available=false,
     masked_store_available=false
   };
-  typedef Packet2cd half;
 };
 
 template<> EIGEN_STRONG_INLINE Packet4cd padd<Packet4cd>(const Packet4cd& a, const Packet4cd& b) { return Packet4cd(_mm512_add_pd(a.v,b.v)); }
@@ -437,8 +441,15 @@
   kernel.packet[0] = Packet4cd(_mm512_shuffle_f64x2(T0, T2, (shuffle_mask<0,2,0,2>::mask))); // [a0 b0 c0 d0]
 }
 
-} // end namespace internal
+template<> EIGEN_STRONG_INLINE Packet4cd psqrt<Packet4cd>(const Packet4cd& a) {
+  return psqrt_complex<Packet4cd>(a);
+}
 
+template<> EIGEN_STRONG_INLINE Packet8cf psqrt<Packet8cf>(const Packet8cf& a) {
+  return psqrt_complex<Packet8cf>(a);
+}
+
+} // end namespace internal
 } // end namespace Eigen
 
 #endif // EIGEN_COMPLEX_AVX512_H
diff --git a/Eigen/src/Core/arch/AVX512/MathFunctions.h b/Eigen/src/Core/arch/AVX512/MathFunctions.h
index bfd30c0..66f3252 100644
--- a/Eigen/src/Core/arch/AVX512/MathFunctions.h
+++ b/Eigen/src/Core/arch/AVX512/MathFunctions.h
@@ -35,7 +35,6 @@
 #define _EIGEN_DECLARE_CONST_Packet16bf_FROM_INT(NAME, X) \
   const Packet16bf p16bf_##NAME =  preinterpret<Packet16bf,Packet16i>(pset1<Packet16i>(X))
 
-#if defined(EIGEN_VECTORIZE_AVX512DQ)
 template <>
 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f
 plog<Packet16f>(const Packet16f& _x) {
@@ -48,8 +47,23 @@
   return plog_double(_x);
 }
 
+F16_PACKET_FUNCTION(Packet16f, Packet16h, plog)
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog)
-#endif
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f
+plog2<Packet16f>(const Packet16f& _x) {
+  return plog2_float(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8d
+plog2<Packet8d>(const Packet8d& _x) {
+  return plog2_double(_x);
+}
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, plog2)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog2)
 
 // Exponential function. Works by writing "x = m*log(2) + r" where
 // "m = floor(x/log(2)+1/2)" and "r" is the remainder. The result is then
@@ -174,6 +188,7 @@
   return pmax(pmul(x, e), _x);
   }*/
 
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pexp)
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pexp)
 
 // Functions for sqrt.
@@ -232,6 +247,7 @@
 }
 #endif
 
+F16_PACKET_FUNCTION(Packet16f, Packet16h, psqrt)
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, psqrt)
 
 // prsqrt for float.
@@ -256,7 +272,7 @@
   __mmask16 inf_mask = _mm512_cmp_ps_mask(_x, p16f_inf, _CMP_EQ_OQ);
   __mmask16 not_pos_mask = _mm512_cmp_ps_mask(_x, _mm512_setzero_ps(), _CMP_LE_OQ);
   __mmask16 not_finite_pos_mask = not_pos_mask | inf_mask;
-  
+
   // Compute an approximate result using the rsqrt intrinsic, forcing +inf
   // for denormals for consistency with AVX and SSE implementations.
   Packet16f y_approx = _mm512_rsqrt14_ps(_x);
@@ -281,6 +297,7 @@
 }
 #endif
 
+F16_PACKET_FUNCTION(Packet16f, Packet16h, prsqrt)
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, prsqrt)
 
 // prsqrt for double.
@@ -330,12 +347,12 @@
 }
 #endif
 
-#if defined(EIGEN_VECTORIZE_AVX512DQ)
 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
 Packet16f plog1p<Packet16f>(const Packet16f& _x) {
   return generic_plog1p(_x);
 }
 
+F16_PACKET_FUNCTION(Packet16f, Packet16h, plog1p)
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog1p)
 
 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
@@ -343,8 +360,8 @@
   return generic_expm1(_x);
 }
 
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pexpm1)
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pexpm1)
-#endif
 
 #endif
 
@@ -367,6 +384,10 @@
   return internal::generic_fast_tanh_float(_x);
 }
 
+F16_PACKET_FUNCTION(Packet16f, Packet16h, psin)
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pcos)
+F16_PACKET_FUNCTION(Packet16f, Packet16h, ptanh)
+
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, psin)
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pcos)
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, ptanh)
diff --git a/Eigen/src/Core/arch/AVX512/PacketMath.h b/Eigen/src/Core/arch/AVX512/PacketMath.h
index bf7f0db..f838857 100644
--- a/Eigen/src/Core/arch/AVX512/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX512/PacketMath.h
@@ -58,23 +58,37 @@
     Vectorizable = 1,
     AlignedOnScalar = 1,
     size = 16,
-    HasHalfPacket = 0,
+    HasHalfPacket = 1,
+
+    HasCmp    = 1,
     HasAdd    = 1,
     HasSub    = 1,
     HasMul    = 1,
     HasDiv    = 1,
     HasNegate = 1,
-    HasAbs    = 0,
+    HasAbs    = 1,
     HasAbs2   = 0,
-    HasMin    = 0,
-    HasMax    = 0,
-    HasConj   = 0,
+    HasMin    = 1,
+    HasMax    = 1,
+    HasConj   = 1,
     HasSetLinear = 0,
-    HasSqrt = 0,
-    HasRsqrt = 0,
-    HasExp = 0,
-    HasLog = 0,
-    HasBlend = 0
+    HasLog    = 1,
+    HasLog1p  = 1,
+    HasExpm1  = 1,
+    HasExp    = 1,
+    HasSqrt   = 1,
+    HasRsqrt  = 1,
+    HasSin    = EIGEN_FAST_MATH,
+    HasCos    = EIGEN_FAST_MATH,
+    HasTanh   = EIGEN_FAST_MATH,
+    HasErf    = EIGEN_FAST_MATH,
+    HasBlend = 0,
+    HasRound  = 1,
+    HasFloor  = 1,
+    HasCeil   = 1,
+    HasRint   = 1,
+    HasBessel = 1,
+    HasNdtri  = 1,
   };
 };
 
@@ -87,17 +101,20 @@
     AlignedOnScalar = 1,
     size = 16,
     HasHalfPacket = 1,
+
+    HasAbs = 1,
+    HasMin    = 1,
+    HasMax    = 1,
+    HasConj   = 1,
     HasBlend = 0,
     HasSin = EIGEN_FAST_MATH,
     HasCos = EIGEN_FAST_MATH,
 #if EIGEN_GNUC_AT_LEAST(5, 3) || (!EIGEN_COMP_GNUC_STRICT)
-#ifdef EIGEN_VECTORIZE_AVX512DQ
     HasLog = 1,
     HasLog1p  = 1,
     HasExpm1  = 1,
     HasNdtri = 1,
     HasBessel  = 1,
-#endif
     HasExp = 1,
     HasSqrt = EIGEN_FAST_MATH,
     HasRsqrt = EIGEN_FAST_MATH,
@@ -105,7 +122,11 @@
     HasErf = EIGEN_FAST_MATH,
 #endif
     HasCmp  = 1,
-    HasDiv = 1
+    HasDiv = 1,
+    HasRound = 1,
+    HasFloor = 1,
+    HasCeil = 1,
+    HasRint = 1
   };
  };
 template<> struct packet_traits<double> : default_packet_traits
@@ -118,14 +139,16 @@
     size = 8,
     HasHalfPacket = 1,
 #if EIGEN_GNUC_AT_LEAST(5, 3) || (!EIGEN_COMP_GNUC_STRICT)
-#ifdef EIGEN_VECTORIZE_AVX512DQ
     HasLog  = 1,
-#endif
     HasSqrt = EIGEN_FAST_MATH,
     HasRsqrt = EIGEN_FAST_MATH,
 #endif
     HasCmp  = 1,
-    HasDiv = 1
+    HasDiv = 1,
+    HasRound = 1,
+    HasFloor = 1,
+    HasCeil = 1,
+    HasRint = 1
   };
 };
 
@@ -165,7 +188,7 @@
 template<>
 struct unpacket_traits<Packet16h> {
   typedef Eigen::half type;
-  typedef Packet16h half;
+  typedef Packet8h half;
   enum {size=16, alignment=Aligned32, vectorizable=true, masked_load_available=false, masked_store_available=false};
 };
 
@@ -188,10 +211,27 @@
 }
 
 template <>
-EIGEN_STRONG_INLINE Packet8d pset1frombits<Packet8d>(uint64_t from) {
+EIGEN_STRONG_INLINE Packet8d pset1frombits<Packet8d>(const numext::uint64_t from) {
   return _mm512_castsi512_pd(_mm512_set1_epi64(from));
 }
 
+template<> EIGEN_STRONG_INLINE Packet16f pzero(const Packet16f& /*a*/) { return _mm512_setzero_ps(); }
+template<> EIGEN_STRONG_INLINE Packet8d pzero(const Packet8d& /*a*/) { return _mm512_setzero_pd(); }
+template<> EIGEN_STRONG_INLINE Packet16i pzero(const Packet16i& /*a*/) { return _mm512_setzero_si512(); }
+
+template<> EIGEN_STRONG_INLINE Packet16f peven_mask(const Packet16f& /*a*/) {
+  return _mm512_castsi512_ps(_mm512_set_epi32(0, -1, 0, -1, 0, -1, 0, -1,
+                                              0, -1, 0, -1, 0, -1, 0, -1));
+}
+template<> EIGEN_STRONG_INLINE Packet16i peven_mask(const Packet16i& /*a*/) {
+  return _mm512_set_epi32(0, -1, 0, -1, 0, -1, 0, -1,
+                          0, -1, 0, -1, 0, -1, 0, -1);
+}
+template<> EIGEN_STRONG_INLINE Packet8d peven_mask(const Packet8d& /*a*/) {
+  return _mm512_castsi512_pd(_mm512_set_epi32(0, 0, -1, -1, 0, 0, -1, -1,
+                                              0, 0, -1, -1, 0, 0, -1, -1));
+}
+
 template <>
 EIGEN_STRONG_INLINE Packet16f pload1<Packet16f>(const float* from) {
   return _mm512_broadcastss_ps(_mm_load_ps1(from));
@@ -281,7 +321,7 @@
 template <>
 EIGEN_STRONG_INLINE Packet16i pmul<Packet16i>(const Packet16i& a,
                                               const Packet16i& b) {
-  return _mm512_mul_epi32(a, b);
+  return _mm512_mullo_epi32(a, b);
 }
 
 template <>
@@ -482,6 +522,15 @@
       _mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu));
 }
 
+template<> EIGEN_STRONG_INLINE Packet16f print<Packet16f>(const Packet16f& a) { return _mm512_roundscale_ps(a, _MM_FROUND_CUR_DIRECTION); }
+template<> EIGEN_STRONG_INLINE Packet8d print<Packet8d>(const Packet8d& a) { return _mm512_roundscale_pd(a, _MM_FROUND_CUR_DIRECTION); }
+
+template<> EIGEN_STRONG_INLINE Packet16f pceil<Packet16f>(const Packet16f& a) { return _mm512_roundscale_ps(a, _MM_FROUND_TO_POS_INF); }
+template<> EIGEN_STRONG_INLINE Packet8d pceil<Packet8d>(const Packet8d& a) { return _mm512_roundscale_pd(a, _MM_FROUND_TO_POS_INF); }
+
+template<> EIGEN_STRONG_INLINE Packet16f pfloor<Packet16f>(const Packet16f& a) { return _mm512_roundscale_ps(a, _MM_FROUND_TO_NEG_INF); }
+template<> EIGEN_STRONG_INLINE Packet8d pfloor<Packet8d>(const Packet8d& a) { return _mm512_roundscale_pd(a, _MM_FROUND_TO_NEG_INF); }
+
 template <>
 EIGEN_STRONG_INLINE Packet16i ptrue<Packet16i>(const Packet16i& /*a*/) {
   return _mm512_set1_epi32(0xffffffffu);
@@ -598,6 +647,21 @@
 #endif
 }
 
+template<> EIGEN_STRONG_INLINE Packet16f pround<Packet16f>(const Packet16f& a)
+{
+  // Work-around for default std::round rounding mode.
+  const Packet16f mask = pset1frombits<Packet16f>(static_cast<numext::uint32_t>(0x80000000u));
+  const Packet16f prev0dot5 = pset1frombits<Packet16f>(static_cast<numext::uint32_t>(0x3EFFFFFFu));
+  return _mm512_roundscale_ps(padd(por(pand(a, mask), prev0dot5), a), _MM_FROUND_TO_ZERO);
+}
+template<> EIGEN_STRONG_INLINE Packet8d pround<Packet8d>(const Packet8d& a)
+{
+  // Work-around for default std::round rounding mode.
+  const Packet8d mask = pset1frombits<Packet8d>(static_cast<numext::uint64_t>(0x8000000000000000ull));
+  const Packet8d prev0dot5 = pset1frombits<Packet8d>(static_cast<numext::uint64_t>(0x3FDFFFFFFFFFFFFFull));
+  return _mm512_roundscale_pd(padd(por(pand(a, mask), prev0dot5), a), _MM_FROUND_TO_ZERO);
+}
+
 template<int N> EIGEN_STRONG_INLINE Packet16i parithmetic_shift_right(Packet16i a) {
   return _mm512_srai_epi32(a, N);
 }
@@ -835,12 +899,34 @@
 }
 
 template<>
-EIGEN_STRONG_INLINE Packet8d pfrexp<Packet8d>(const Packet8d& a, Packet8d& exponent){
+EIGEN_STRONG_INLINE Packet8d pfrexp<Packet8d>(const Packet8d& a, Packet8d& exponent) {
   const Packet8d cst_1022d = pset1<Packet8d>(1022.0);
+#ifdef EIGEN_TEST_AVX512DQ
+  exponent = psub(_mm512_cvtepi64_pd(_mm512_srli_epi64(_mm512_castpd_si512(a), 52)), cst_1022d);
+#else
+  exponent = psub(_mm512_cvtepi32_pd(_mm512_cvtepi64_epi32(_mm512_srli_epi64(_mm512_castpd_si512(a), 52))),
+                                     cst_1022d);
+#endif
   const Packet8d cst_half = pset1<Packet8d>(0.5);
   const Packet8d cst_inv_mant_mask  = pset1frombits<Packet8d>(static_cast<uint64_t>(~0x7ff0000000000000ull));
-  exponent = psub(_mm512_cvtepi64_pd(_mm512_srli_epi64(_mm512_castpd_si512(a), 52)), cst_1022d);
-  return por(pand(a, cst_inv_mant_mask), cst_half);  
+  return por(pand(a, cst_inv_mant_mask), cst_half);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f pldexp<Packet16f>(const Packet16f& a, const Packet16f& exponent) {
+  return pldexp_float(a,exponent);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8d pldexp<Packet8d>(const Packet8d& a, const Packet8d& exponent) {
+  // Build e=2^n by constructing the exponents in a 256-bit vector and
+  // shifting them to where they belong in double-precision values.
+  Packet8i cst_1023 = pset1<Packet8i>(1023);
+  __m256i emm0 = _mm512_cvtpd_epi32(exponent);
+  emm0 = _mm256_add_epi32(emm0, cst_1023);
+  emm0 = _mm256_shuffle_epi32(emm0, _MM_SHUFFLE(3, 1, 2, 0));
+  __m256i lo = _mm256_slli_epi64(emm0, 52);
+  __m256i hi = _mm256_slli_epi64(_mm256_srli_epi64(emm0, 32), 52);
+  __m512d b = _mm512_castsi512_pd(_mm512_inserti64x4(_mm512_castsi256_si512(lo), hi, 1));
+  return pmul(a, b);
 }
 
 #ifdef EIGEN_VECTORIZE_AVX512DQ
@@ -1270,22 +1356,6 @@
   return _mm512_mask_blend_pd(m, elsePacket, thenPacket);
 }
 
-template<> EIGEN_STRONG_INLINE Packet16i pcast<Packet16f, Packet16i>(const Packet16f& a) {
-  return _mm512_cvttps_epi32(a);
-}
-
-template<> EIGEN_STRONG_INLINE Packet16f pcast<Packet16i, Packet16f>(const Packet16i& a) {
-  return _mm512_cvtepi32_ps(a);
-}
-
-template<> EIGEN_STRONG_INLINE Packet16i preinterpret<Packet16i,Packet16f>(const Packet16f& a) {
-  return _mm512_castps_si512(a);
-}
-
-template<> EIGEN_STRONG_INLINE Packet16f preinterpret<Packet16f,Packet16i>(const Packet16i& a) {
-  return _mm512_castsi512_ps(a);
-}
-
 // Packet math for Eigen::half
 template<> EIGEN_STRONG_INLINE Packet16h pset1<Packet16h>(const Eigen::half& from) {
   return _mm256_set1_epi16(from.x);
@@ -1398,6 +1468,29 @@
   return ptrue(Packet8i(a));
 }
 
+template <>
+EIGEN_STRONG_INLINE Packet16h pabs(const Packet16h& a) {
+  const __m256i sign_mask = _mm256_set1_epi16(static_cast<numext::uint16_t>(0x8000));
+  return _mm256_andnot_si256(sign_mask, a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pmin<Packet16h>(const Packet16h& a,
+                                              const Packet16h& b) {
+  return float2half(pmin<Packet16f>(half2float(a), half2float(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pmax<Packet16h>(const Packet16h& a,
+                                              const Packet16h& b) {
+  return float2half(pmax<Packet16f>(half2float(a), half2float(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h plset<Packet16h>(const half& a) {
+  return float2half(plset<Packet16f>(static_cast<float>(a)));
+}
+
 template<> EIGEN_STRONG_INLINE Packet16h por(const Packet16h& a,const Packet16h& b) {
   // in some cases Packet8i is a wrapper around __m256i, so we need to
   // cast to Packet8i to call the correct overload.
@@ -1417,12 +1510,42 @@
   return _mm256_blendv_epi8(b, a, mask);
 }
 
+template<> EIGEN_STRONG_INLINE Packet16h pround<Packet16h>(const Packet16h& a) {
+  return float2half(pround<Packet16f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h print<Packet16h>(const Packet16h& a) {
+  return float2half(print<Packet16f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pceil<Packet16h>(const Packet16h& a) {
+  return float2half(pceil<Packet16f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pfloor<Packet16h>(const Packet16h& a) {
+  return float2half(pfloor<Packet16f>(half2float(a)));
+}
+
 template<> EIGEN_STRONG_INLINE Packet16h pcmp_eq(const Packet16h& a,const Packet16h& b) {
   Packet16f af = half2float(a);
   Packet16f bf = half2float(b);
   return Pack32To16(pcmp_eq(af, bf));
 }
 
+template<> EIGEN_STRONG_INLINE Packet16h pcmp_le(const Packet16h& a,const Packet16h& b) {
+  return Pack32To16(pcmp_le(half2float(a), half2float(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pcmp_lt(const Packet16h& a,const Packet16h& b) {
+  return Pack32To16(pcmp_lt(half2float(a), half2float(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pcmp_lt_or_nan(const Packet16h& a,const Packet16h& b) {
+  return Pack32To16(pcmp_lt_or_nan(half2float(a), half2float(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pconj(const Packet16h& a) { return a; }
+
 template<> EIGEN_STRONG_INLINE Packet16h pnegate(const Packet16h& a) {
   Packet16h sign_mask = _mm256_set1_epi16(static_cast<unsigned short>(0x8000));
   return _mm256_xor_si256(a, sign_mask);
@@ -1461,6 +1584,25 @@
   return half(predux(from_float));
 }
 
+template <>
+EIGEN_STRONG_INLINE Packet8h predux_half_dowto4<Packet16h>(const Packet16h& a) {
+  Packet8h lane0 = _mm256_extractf128_si256(a, 0);
+  Packet8h lane1 = _mm256_extractf128_si256(a, 1);
+  return padd<Packet8h>(lane0, lane1);
+}
+
+template<> EIGEN_STRONG_INLINE Eigen::half predux_max<Packet16h>(const Packet16h& a) {
+  Packet16f af = half2float(a);
+  float reduced = predux_max<Packet16f>(af);
+  return Eigen::half(reduced);
+}
+
+template<> EIGEN_STRONG_INLINE Eigen::half predux_min<Packet16h>(const Packet16h& a) {
+  Packet16f af = half2float(a);
+  float reduced = predux_min<Packet16f>(af);
+  return Eigen::half(reduced);
+}
+
 template<> EIGEN_STRONG_INLINE half predux_mul<Packet16h>(const Packet16h& from) {
   Packet16f from_float = half2float(from);
   return half(predux_mul(from_float));
@@ -1487,22 +1629,22 @@
 {
   EIGEN_ALIGN64 half aux[16];
   pstore(aux, from);
-  to[stride*0].x = aux[0].x;
-  to[stride*1].x = aux[1].x;
-  to[stride*2].x = aux[2].x;
-  to[stride*3].x = aux[3].x;
-  to[stride*4].x = aux[4].x;
-  to[stride*5].x = aux[5].x;
-  to[stride*6].x = aux[6].x;
-  to[stride*7].x = aux[7].x;
-  to[stride*8].x = aux[8].x;
-  to[stride*9].x = aux[9].x;
-  to[stride*10].x = aux[10].x;
-  to[stride*11].x = aux[11].x;
-  to[stride*12].x = aux[12].x;
-  to[stride*13].x = aux[13].x;
-  to[stride*14].x = aux[14].x;
-  to[stride*15].x = aux[15].x;
+  to[stride*0] = aux[0];
+  to[stride*1] = aux[1];
+  to[stride*2] = aux[2];
+  to[stride*3] = aux[3];
+  to[stride*4] = aux[4];
+  to[stride*5] = aux[5];
+  to[stride*6] = aux[6];
+  to[stride*7] = aux[7];
+  to[stride*8] = aux[8];
+  to[stride*9] = aux[9];
+  to[stride*10] = aux[10];
+  to[stride*11] = aux[11];
+  to[stride*12] = aux[12];
+  to[stride*13] = aux[13];
+  to[stride*14] = aux[14];
+  to[stride*15] = aux[15];
 }
 
 EIGEN_STRONG_INLINE void
@@ -1694,7 +1836,7 @@
     HasCos = EIGEN_FAST_MATH,
 #if EIGEN_GNUC_AT_LEAST(5, 3) || (!EIGEN_COMP_GNUC_STRICT)
 #ifdef EIGEN_VECTORIZE_AVX512DQ
-    HasLog = 1,
+    HasLog = 1,  // Currently fails test with bad accuracy.
     HasLog1p  = 1,
     HasExpm1  = 1,
     HasNdtri = 1,
@@ -1859,6 +2001,23 @@
   return _mm256_blendv_epi8(b, a, mask);
 }
 
+template<> EIGEN_STRONG_INLINE Packet16bf pround<Packet16bf>(const Packet16bf& a)
+{
+  return F32ToBf16(pround<Packet16f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16bf print<Packet16bf>(const Packet16bf& a) {
+  return F32ToBf16(print<Packet16f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16bf pceil<Packet16bf>(const Packet16bf& a) {
+  return F32ToBf16(pceil<Packet16f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16bf pfloor<Packet16bf>(const Packet16bf& a) {
+  return F32ToBf16(pfloor<Packet16f>(Bf16ToF32(a)));
+}
+
 template <>
 EIGEN_STRONG_INLINE Packet16bf pcmp_eq(const Packet16bf& a,
                                        const Packet16bf& b) {
@@ -1885,9 +2044,7 @@
 
 template <>
 EIGEN_STRONG_INLINE Packet16bf pnegate(const Packet16bf& a) {
-  Packet16bf sign_mask;
-  sign_mask = _mm256_set1_epi16(static_cast<unsigned short>(0x8000));
-  Packet16bf result;
+  Packet16bf sign_mask = _mm256_set1_epi16(static_cast<unsigned short>(0x8000));
   return _mm256_xor_si256(a, sign_mask);
 }
 
@@ -1898,7 +2055,8 @@
 
 template <>
 EIGEN_STRONG_INLINE Packet16bf pabs(const Packet16bf& a) {
-  return F32ToBf16(pabs<Packet16f>(Bf16ToF32(a)));
+  const __m256i sign_mask = _mm256_set1_epi16(static_cast<numext::uint16_t>(0x8000));
+  return _mm256_andnot_si256(sign_mask, a);
 }
 
 template <>
@@ -1997,22 +2155,22 @@
                                                         Index stride) {
   EIGEN_ALIGN64 bfloat16 aux[16];
   pstore(aux, from);
-  to[stride*0].value = aux[0].value;
-  to[stride*1].value = aux[1].value;
-  to[stride*2].value = aux[2].value;
-  to[stride*3].value = aux[3].value;
-  to[stride*4].value = aux[4].value;
-  to[stride*5].value = aux[5].value;
-  to[stride*6].value = aux[6].value;
-  to[stride*7].value = aux[7].value;
-  to[stride*8].value = aux[8].value;
-  to[stride*9].value = aux[9].value;
-  to[stride*10].value = aux[10].value;
-  to[stride*11].value = aux[11].value;
-  to[stride*12].value = aux[12].value;
-  to[stride*13].value = aux[13].value;
-  to[stride*14].value = aux[14].value;
-  to[stride*15].value = aux[15].value;
+  to[stride*0] = aux[0];
+  to[stride*1] = aux[1];
+  to[stride*2] = aux[2];
+  to[stride*3] = aux[3];
+  to[stride*4] = aux[4];
+  to[stride*5] = aux[5];
+  to[stride*6] = aux[6];
+  to[stride*7] = aux[7];
+  to[stride*8] = aux[8];
+  to[stride*9] = aux[9];
+  to[stride*10] = aux[10];
+  to[stride*11] = aux[11];
+  to[stride*12] = aux[12];
+  to[stride*13] = aux[13];
+  to[stride*14] = aux[14];
+  to[stride*15] = aux[15];
 }
 
 EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16bf,16>& kernel) {
diff --git a/Eigen/src/Core/arch/AVX512/TypeCasting.h b/Eigen/src/Core/arch/AVX512/TypeCasting.h
index e643b18..3304127 100644
--- a/Eigen/src/Core/arch/AVX512/TypeCasting.h
+++ b/Eigen/src/Core/arch/AVX512/TypeCasting.h
@@ -14,6 +14,22 @@
 
 namespace internal {
 
+template<> EIGEN_STRONG_INLINE Packet16i pcast<Packet16f, Packet16i>(const Packet16f& a) {
+  return _mm512_cvttps_epi32(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f pcast<Packet16i, Packet16f>(const Packet16i& a) {
+  return _mm512_cvtepi32_ps(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16i preinterpret<Packet16i, Packet16f>(const Packet16f& a) {
+  return _mm512_castps_si512(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f preinterpret<Packet16f, Packet16i>(const Packet16i& a) {
+  return _mm512_castsi512_ps(a);
+}
+
 template <>
 struct type_casting_traits<half, float> {
   enum {
diff --git a/Eigen/src/Core/arch/Default/BFloat16.h b/Eigen/src/Core/arch/Default/BFloat16.h
index 351f451..72a489b 100644
--- a/Eigen/src/Core/arch/Default/BFloat16.h
+++ b/Eigen/src/Core/arch/Default/BFloat16.h
@@ -512,6 +512,9 @@
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 log10(const bfloat16& a) {
   return bfloat16(::log10f(float(a)));
 }
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 log2(const bfloat16& a) {
+  return bfloat16(static_cast<float>(EIGEN_LOG2E) * ::logf(float(a)));
+}
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 sqrt(const bfloat16& a) {
     return bfloat16(::sqrtf(float(a)));
 }
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 6d92d1c..a6d2de6 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -59,21 +59,21 @@
   return pmul(a, preinterpret<Packet>(plogical_shift_left<52>(ei)));
 }
 
-// Natural logarithm
+// Natural or base 2 logarithm.
 // Computes log(x) as log(2^e * m) = C*e + log(m), where the constant C =log(2)
 // and m is in the range [sqrt(1/2),sqrt(2)). In this range, the logarithm can
 // be easily approximated by a polynomial centered on m=1 for stability.
 // TODO(gonnet): Further reduce the interval allowing for lower-degree
 //               polynomial interpolants -> ... -> profit!
-template <typename Packet>
+template <typename Packet, bool base2>
 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 EIGEN_UNUSED
-Packet plog_float(const Packet _x)
+Packet plog_impl_float(const Packet _x)
 {
   Packet x = _x;
 
   const Packet cst_1              = pset1<Packet>(1.0f);
-  const Packet cst_half           = pset1<Packet>(0.5f);
+  const Packet cst_neg_half       = pset1<Packet>(-0.5f);
   // The smallest non denormalized float number.
   const Packet cst_min_norm_pos   = pset1frombits<Packet>( 0x00800000u);
   const Packet cst_minus_inf      = pset1frombits<Packet>( 0xff800000u);
@@ -90,8 +90,6 @@
   const Packet cst_cephes_log_p6 = pset1<Packet>(+2.0000714765E-1f);
   const Packet cst_cephes_log_p7 = pset1<Packet>(-2.4999993993E-1f);
   const Packet cst_cephes_log_p8 = pset1<Packet>(+3.3333331174E-1f);
-  const Packet cst_cephes_log_q1 = pset1<Packet>(-2.12194440e-4f);
-  const Packet cst_cephes_log_q2 = pset1<Packet>(0.693359375f);
 
   // Truncate input values to the minimum positive normal.
   x = pmax(x, cst_min_norm_pos);
@@ -129,14 +127,17 @@
   y  = pmadd(y, x3, y2);
   y  = pmul(y, x3);
 
+  y = pmadd(cst_neg_half, x2, y);
+  x = padd(x, y);
+
   // Add the logarithm of the exponent back to the result of the interpolation.
-  y1  = pmul(e, cst_cephes_log_q1);
-  tmp = pmul(x2, cst_half);
-  y   = padd(y, y1);
-  x   = psub(x, tmp);
-  y2  = pmul(e, cst_cephes_log_q2);
-  x   = padd(x, y);
-  x   = padd(x, y2);
+  if (base2) {
+    const Packet cst_log2e = pset1<Packet>(static_cast<float>(EIGEN_LOG2E));
+    x = pmadd(x, cst_log2e, e);
+  } else {
+    const Packet cst_ln2 = pset1<Packet>(static_cast<float>(EIGEN_LN2));
+    x = pmadd(e, cst_ln2, x);
+  }
 
   Packet invalid_mask = pcmp_lt_or_nan(_x, pzero(_x));
   Packet iszero_mask  = pcmp_eq(_x,pzero(_x));
@@ -149,33 +150,46 @@
                               por(pselect(pos_inf_mask,cst_pos_inf,x), invalid_mask));
 }
 
-
-/* Returns the base e (2.718...) logarithm of x.
- * The argument is separated into its exponent and fractional
- * parts.  If the exponent is between -1 and +1, the logarithm
- * of the fraction is approximated by
- *
- *     log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
- *
- * Otherwise, setting  z = 2(x-1)/x+1),
- *                     log(x) = z + z**3 P(z)/Q(z).
- * 
- * for more detail see: http://www.netlib.org/cephes/
- */
 template <typename Packet>
 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 EIGEN_UNUSED
-Packet plog_double(const Packet _x)
+Packet plog_float(const Packet _x)
+{
+  return plog_impl_float<Packet, /* base2 */ false>(_x);
+}
+
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+EIGEN_UNUSED
+Packet plog2_float(const Packet _x)
+{
+  return plog_impl_float<Packet, /* base2 */ true>(_x);
+}
+
+/* Returns the base e (2.718...) or base 2 logarithm of x.
+ * The argument is separated into its exponent and fractional parts.
+ * The logarithm of the fraction in the interval [sqrt(1/2), sqrt(2)],
+ * is approximated by
+ *
+ *     log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * for more detail see: http://www.netlib.org/cephes/
+ */
+template <typename Packet, bool base2>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+EIGEN_UNUSED
+Packet plog_impl_double(const Packet _x)
 {
   Packet x = _x;
 
   const Packet cst_1              = pset1<Packet>(1.0);
-  const Packet cst_half           = pset1<Packet>(0.5);
-  // The smallest non denormalized float number.
+  const Packet cst_neg_half       = pset1<Packet>(-0.5);
+  // The smallest non denormalized double.
   const Packet cst_min_norm_pos   = pset1frombits<Packet>( static_cast<uint64_t>(0x0010000000000000ull));
   const Packet cst_minus_inf      = pset1frombits<Packet>( static_cast<uint64_t>(0xfff0000000000000ull));
   const Packet cst_pos_inf        = pset1frombits<Packet>( static_cast<uint64_t>(0x7ff0000000000000ull));
 
+
  // Polynomial Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
  //                             1/sqrt(2) <= x < sqrt(2)
   const Packet cst_cephes_SQRTHF = pset1<Packet>(0.70710678118654752440E0);
@@ -186,15 +200,12 @@
   const Packet cst_cephes_log_p4 = pset1<Packet>(1.79368678507819816313E1);
   const Packet cst_cephes_log_p5 = pset1<Packet>(7.70838733755885391666E0);
 
-  const Packet cst_cephes_log_r0 = pset1<Packet>(1.0);
-  const Packet cst_cephes_log_r1 = pset1<Packet>(1.12873587189167450590E1);
-  const Packet cst_cephes_log_r2 = pset1<Packet>(4.52279145837532221105E1);
-  const Packet cst_cephes_log_r3 = pset1<Packet>(8.29875266912776603211E1);
-  const Packet cst_cephes_log_r4 = pset1<Packet>(7.11544750618563894466E1);
-  const Packet cst_cephes_log_r5 = pset1<Packet>(2.31251620126765340583E1);
-
-  const Packet cst_cephes_log_q1 = pset1<Packet>(-2.121944400546905827679e-4);
-  const Packet cst_cephes_log_q2 = pset1<Packet>(0.693359375);
+  const Packet cst_cephes_log_q0 = pset1<Packet>(1.0);
+  const Packet cst_cephes_log_q1 = pset1<Packet>(1.12873587189167450590E1);
+  const Packet cst_cephes_log_q2 = pset1<Packet>(4.52279145837532221105E1);
+  const Packet cst_cephes_log_q3 = pset1<Packet>(8.29875266912776603211E1);
+  const Packet cst_cephes_log_q4 = pset1<Packet>(7.11544750618563894466E1);
+  const Packet cst_cephes_log_q5 = pset1<Packet>(2.31251620126765340583E1);
 
   // Truncate input values to the minimum positive normal.
   x = pmax(x, cst_min_norm_pos);
@@ -220,31 +231,34 @@
   Packet x3 = pmul(x2, x);
 
   // Evaluate the polynomial approximant , probably to improve instruction-level parallelism.
-  // y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 5 ) );
-  Packet y, y1, y2,y_;
+  // y = x - 0.5*x^2 + x^3 * polevl( x, P, 5 ) / p1evl( x, Q, 5 ) );
+  Packet y, y1, y_;
   y  = pmadd(cst_cephes_log_p0, x, cst_cephes_log_p1);
   y1 = pmadd(cst_cephes_log_p3, x, cst_cephes_log_p4);
   y  = pmadd(y, x, cst_cephes_log_p2);
   y1 = pmadd(y1, x, cst_cephes_log_p5);
   y_ = pmadd(y, x3, y1);
 
-  y  = pmadd(cst_cephes_log_r0, x, cst_cephes_log_r1);
-  y1 = pmadd(cst_cephes_log_r3, x, cst_cephes_log_r4);
-  y  = pmadd(y, x, cst_cephes_log_r2);
-  y1 = pmadd(y1, x, cst_cephes_log_r5);
+  y  = pmadd(cst_cephes_log_q0, x, cst_cephes_log_q1);
+  y1 = pmadd(cst_cephes_log_q3, x, cst_cephes_log_q4);
+  y  = pmadd(y, x, cst_cephes_log_q2);
+  y1 = pmadd(y1, x, cst_cephes_log_q5);
   y  = pmadd(y, x3, y1);
 
   y_ = pmul(y_, x3);
   y  = pdiv(y_, y);
 
+  y = pmadd(cst_neg_half, x2, y);
+  x = padd(x, y);
+
   // Add the logarithm of the exponent back to the result of the interpolation.
-  y1  = pmul(e, cst_cephes_log_q1);
-  tmp = pmul(x2, cst_half);
-  y   = padd(y, y1);
-  x   = psub(x, tmp);
-  y2  = pmul(e, cst_cephes_log_q2);
-  x   = padd(x, y);
-  x   = padd(x, y2);
+  if (base2) {
+    const Packet cst_log2e = pset1<Packet>(static_cast<double>(EIGEN_LOG2E));
+    x = pmadd(x, cst_log2e, e);
+  } else {
+    const Packet cst_ln2 = pset1<Packet>(static_cast<double>(EIGEN_LN2));
+    x = pmadd(e, cst_ln2, x);
+  }
 
   Packet invalid_mask = pcmp_lt_or_nan(_x, pzero(_x));
   Packet iszero_mask  = pcmp_eq(_x,pzero(_x));
@@ -257,6 +271,22 @@
                               por(pselect(pos_inf_mask,cst_pos_inf,x), invalid_mask));
 }
 
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+EIGEN_UNUSED
+Packet plog_double(const Packet _x)
+{
+  return plog_impl_double<Packet, /* base2 */ false>(_x);
+}
+
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+EIGEN_UNUSED
+Packet plog2_double(const Packet _x)
+{
+  return plog_impl_double<Packet, /* base2 */ true>(_x);
+}
+
 /** \internal \returns log(1 + x) computed using W. Kahan's formula.
     See: http://www.plunk.org/~hatch/rightway.php
  */
@@ -643,6 +673,120 @@
   return psincos_float<false>(x);
 }
 
+
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+EIGEN_UNUSED
+Packet psqrt_complex(const Packet& a) {
+  typedef typename unpacket_traits<Packet>::type Scalar;
+  typedef typename Scalar::value_type RealScalar;
+  typedef typename unpacket_traits<Packet>::as_real RealPacket;
+
+  // Computes the principal sqrt of the complex numbers in the input.
+  //
+  // For example, for packets containing 2 complex numbers stored in interleaved format
+  //    a = [a0, a1] = [x0, y0, x1, y1],
+  // where x0 = real(a0), y0 = imag(a0) etc., this function returns
+  //    b = [b0, b1] = [u0, v0, u1, v1],
+  // such that b0^2 = a0, b1^2 = a1.
+  //
+  // To derive the formula for the complex square roots, let's consider the equation for
+  // a single complex square root of the number x + i*y. We want to find real numbers
+  // u and v such that
+  //    (u + i*v)^2 = x + i*y  <=>
+  //    u^2 - v^2 + i*2*u*v = x + i*v.
+  // By equating the real and imaginary parts we get:
+  //    u^2 - v^2 = x
+  //    2*u*v = y.
+  //
+  // For x >= 0, this has the numerically stable solution
+  //    u = sqrt(0.5 * (x + sqrt(x^2 + y^2)))
+  //    v = 0.5 * (y / u)
+  // and for x < 0,
+  //    v = sign(y) * sqrt(0.5 * (x + sqrt(x^2 + y^2)))
+  //    u = |0.5 * (y / v)|
+  //
+  //  To avoid unnecessary over- and underflow, we compute sqrt(x^2 + y^2) as
+  //     l = max(|x|, |y|) * sqrt(1 + (min(|x|, |y|) / max(|x|, |y|))^2) ,
+
+  // In the following, without lack of generality, we have annotated the code, assuming
+  // that the input is a packet of 2 complex numbers.
+  //
+  // Step 1. Compute l = [l0, l0, l1, l1], where
+  //    l0 = sqrt(x0^2 + y0^2),  l1 = sqrt(x1^2 + y1^2)
+  // To avoid over- and underflow, we use the stable formula for each hypotenuse
+  //    l0 = (min0 == 0 ? max0 : max0 * sqrt(1 + (min0/max0)**2)),
+  // where max0 = max(|x0|, |y0|), min0 = min(|x0|, |y0|), and similarly for l1.
+
+  Packet a_flip = pcplxflip(a);
+  RealPacket a_abs = pabs(a.v);           // [|x0|, |y0|, |x1|, |y1|]
+  RealPacket a_abs_flip = pabs(a_flip.v); // [|y0|, |x0|, |y1|, |x1|]
+  RealPacket a_max = pmax(a_abs, a_abs_flip);
+  RealPacket a_min = pmin(a_abs, a_abs_flip);
+  RealPacket a_min_zero_mask = pcmp_eq(a_min, pzero(a_min));
+  RealPacket a_max_zero_mask = pcmp_eq(a_max, pzero(a_max));
+  RealPacket r = pdiv(a_min, a_max);
+  const RealPacket cst_one  = pset1<RealPacket>(RealScalar(1));
+  RealPacket l = pmul(a_max, psqrt(padd(cst_one, pmul(r, r))));  // [l0, l0, l1, l1]
+  // Set l to a_max if a_min is zero.
+  l = pselect(a_min_zero_mask, a_max, l);
+
+  // Step 2. Compute [rho0, *, rho1, *], where
+  // rho0 = sqrt(0.5 * (l0 + |x0|)), rho1 =  sqrt(0.5 * (l1 + |x1|))
+  // We don't care about the imaginary parts computed here. They will be overwritten later.
+  const RealPacket cst_half = pset1<RealPacket>(RealScalar(0.5));
+  Packet rho;
+  rho.v = psqrt(pmul(cst_half, padd(a_abs, l)));
+
+  // Step 3. Compute [rho0, eta0, rho1, eta1], where
+  // eta0 = (y0 / l0) / 2, and eta1 = (y1 / l1) / 2.
+  // set eta = 0 of input is 0 + i0.
+  RealPacket eta = pandnot(pmul(cst_half, pdiv(a.v, pcplxflip(rho).v)), a_max_zero_mask);
+  RealPacket real_mask = peven_mask(a.v);
+  Packet positive_real_result;
+  // Compute result for inputs with positive real part.
+  positive_real_result.v = pselect(real_mask, rho.v, eta);
+
+  // Step 4. Compute solution for inputs with negative real part:
+  //         [|eta0|, sign(y0)*rho0, |eta1|, sign(y1)*rho1]
+  const RealPacket cst_imag_sign_mask = pset1<Packet>(Scalar(RealScalar(0.0), RealScalar(-0.0))).v;
+  RealPacket imag_signs = pand(a.v, cst_imag_sign_mask);
+  Packet negative_real_result;
+  // Notice that rho is positive, so taking it's absolute value is a noop.
+  negative_real_result.v = por(pabs(pcplxflip(positive_real_result).v), imag_signs);
+
+  // Step 5. Select solution branch based on the sign of the real parts.
+  Packet negative_real_mask;
+  negative_real_mask.v = pcmp_lt(pand(real_mask, a.v), pzero(a.v));
+  negative_real_mask.v = por(negative_real_mask.v, pcplxflip(negative_real_mask).v);
+  Packet result = pselect(negative_real_mask, negative_real_result, positive_real_result);
+
+  // Step 6. Handle special cases for infinities:
+  // * If z is (x,+∞), the result is (+∞,+∞) even if x is NaN
+  // * If z is (x,-∞), the result is (+∞,-∞) even if x is NaN
+  // * If z is (-∞,y), the result is (0*|y|,+∞) for finite or NaN y
+  // * If z is (+∞,y), the result is (+∞,0*|y|) for finite or NaN y
+  const RealPacket cst_pos_inf = pset1<RealPacket>(NumTraits<RealScalar>::infinity());
+  Packet is_inf;
+  is_inf.v = pcmp_eq(a_abs, cst_pos_inf);
+  Packet is_real_inf;
+  is_real_inf.v = pand(is_inf.v, real_mask);
+  is_real_inf = por(is_real_inf, pcplxflip(is_real_inf));
+  // prepare packet of (+∞,0*|y|) or (0*|y|,+∞), depending on the sign of the infinite real part.
+  Packet real_inf_result;
+  real_inf_result.v = pmul(a_abs, pset1<Packet>(Scalar(RealScalar(1.0), RealScalar(0.0))).v);
+  real_inf_result.v = pselect(negative_real_mask.v, pcplxflip(real_inf_result).v, real_inf_result.v);
+  // prepare packet of (+∞,+∞) or (+∞,-∞), depending on the sign of the infinite imaginary part.
+  Packet is_imag_inf;
+  is_imag_inf.v = pandnot(is_inf.v, real_mask);
+  is_imag_inf = por(is_imag_inf, pcplxflip(is_imag_inf));
+  Packet imag_inf_result;
+  imag_inf_result.v = por(pand(cst_pos_inf, real_mask), pandnot(a.v, real_mask));
+
+  return  pselect(is_imag_inf, imag_inf_result,
+                  pselect(is_real_inf, real_inf_result,result));
+}
+
 /* polevl (modified for Eigen)
  *
  *      Evaluate polynomial
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctionsFwd.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctionsFwd.h
index 0e02a1b..491f1c9 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctionsFwd.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctionsFwd.h
@@ -32,12 +32,24 @@
 EIGEN_UNUSED
 Packet plog_float(const Packet _x);
 
+/** \internal \returns log2(x) for single precision float */
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+EIGEN_UNUSED
+Packet plog2_float(const Packet _x);
+
 /** \internal \returns log(x) for single precision float */
 template <typename Packet>
 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 EIGEN_UNUSED
 Packet plog_double(const Packet _x);
 
+/** \internal \returns log2(x) for single precision float */
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+EIGEN_UNUSED
+Packet plog2_double(const Packet _x);
+
 /** \internal \returns log(1 + x) */
 template<typename Packet>
 Packet generic_plog1p(const Packet& x);
@@ -70,8 +82,15 @@
 EIGEN_UNUSED
 Packet pcos_float(const Packet& x);
 
+/** \internal \returns sqrt(x) for complex types */
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+EIGEN_UNUSED
+Packet psqrt_complex(const Packet& a);
+
 template <typename Packet, int N> struct ppolevl;
 
+
 } // end namespace internal
 } // end namespace Eigen
 
diff --git a/Eigen/src/Core/arch/Default/Half.h b/Eigen/src/Core/arch/Default/Half.h
index 4dde913..b273abe 100644
--- a/Eigen/src/Core/arch/Default/Half.h
+++ b/Eigen/src/Core/arch/Default/Half.h
@@ -36,12 +36,6 @@
 #ifndef EIGEN_HALF_H
 #define EIGEN_HALF_H
 
-#if EIGEN_HAS_CXX11
-#define EIGEN_EXPLICIT_CAST(tgt_type) explicit operator tgt_type()
-#else
-#define EIGEN_EXPLICIT_CAST(tgt_type) operator tgt_type()
-#endif
-
 #include <sstream>
 
 #if defined(EIGEN_HAS_GPU_FP16) || defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
@@ -56,6 +50,13 @@
   #define EIGEN_CONSTEXPR
 #endif
 
+#define F16_PACKET_FUNCTION(PACKET_F, PACKET_F16, METHOD)           \
+  template <>                                                       \
+  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_UNUSED                \
+  PACKET_F16 METHOD<PACKET_F16>(const PACKET_F16& _x) {             \
+    return float2half(METHOD<PACKET_F>(half2float(_x)));            \
+  }
+
 namespace Eigen {
 
 struct half;
@@ -80,14 +81,12 @@
   // Nothing to do here
   // HIP fp16 header file has a definition for __half_raw
 #elif defined(EIGEN_HAS_CUDA_FP16)
- #if defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER < 90000
-// In CUDA < 9.0, __half is the equivalent of CUDA 9's __half_raw
- typedef __half __half_raw;
- #endif // defined(EIGEN_HAS_CUDA_FP16)
-
+  #if EIGEN_CUDA_SDK_VER < 90000
+    // In CUDA < 9.0, __half is the equivalent of CUDA 9's __half_raw
+    typedef __half __half_raw;
+  #endif // defined(EIGEN_HAS_CUDA_FP16)
 #elif defined(SYCL_DEVICE_ONLY)
-typedef cl::sycl::half __half_raw;
-
+  typedef cl::sycl::half __half_raw;
 #endif
 
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw raw_uint16_to_half(numext::uint16_t x);
@@ -102,7 +101,7 @@
  #if defined(EIGEN_HAS_HIP_FP16)
   EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half_base(const __half& h) { x = __half_as_ushort(h); }
  #elif defined(EIGEN_HAS_CUDA_FP16)
-  #if (defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER >= 90000)
+  #if EIGEN_CUDA_SDK_VER >= 90000
   EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half_base(const __half& h) : __half_raw(*(__half_raw*)&h) {}
   #endif
  #endif
@@ -200,7 +199,7 @@
   static Eigen::half round_error() { return Eigen::half(0.5); }
   static Eigen::half infinity() { return Eigen::half_impl::raw_uint16_to_half(0x7c00); }
   static Eigen::half quiet_NaN() { return Eigen::half_impl::raw_uint16_to_half(0x7e00); }
-  static Eigen::half signaling_NaN() { return Eigen::half_impl::raw_uint16_to_half(0x7e00); }
+  static Eigen::half signaling_NaN() { return Eigen::half_impl::raw_uint16_to_half(0x7d00); }
   static Eigen::half denorm_min() { return Eigen::half_impl::raw_uint16_to_half(0x1); }
 };
 
@@ -448,7 +447,7 @@
 #endif
 }
 
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR numext::uint16_t raw_half_as_uint16(const __half_raw& h) {
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC numext::uint16_t raw_half_as_uint16(const __half_raw& h) {
   // HIP/CUDA/Default have a member 'x' of type uint16_t.
   // For ARM64 native half, the member 'x' is of type __fp16, so we need to bit-cast.
   // For SYCL, cl::sycl::half is _Float16, so cast directly.
@@ -617,6 +616,10 @@
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log10(const half& a) {
   return half(::log10f(float(a)));
 }
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log2(const half& a) {
+  return half(static_cast<float>(EIGEN_LOG2E) * ::logf(float(a)));
+}
+
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half sqrt(const half& a) {
 #if (EIGEN_CUDA_SDK_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 530) || \
   defined(EIGEN_HIP_DEVICE_COMPILE)
@@ -744,7 +747,7 @@
     return half_impl::raw_uint16_to_half(0x7c00);
   }
   EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::half quiet_NaN() {
-    return half_impl::raw_uint16_to_half(0x7c01);
+    return half_impl::raw_uint16_to_half(0x7e00);
   }
 };
 
@@ -767,27 +770,6 @@
 
 } // end namespace std
 
-// Add the missing shfl_xor intrinsic
-#if (defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
-  defined(EIGEN_HIPCC)
-
-__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_xor(Eigen::half var, int laneMask, int width=warpSize) {
-  #if (EIGEN_CUDA_SDK_VER < 90000) || \
-    defined(EIGEN_HAS_HIP_FP16)
-  return static_cast<Eigen::half>(__shfl_xor(static_cast<float>(var), laneMask, width));
-  #else
-  return static_cast<Eigen::half>(__shfl_xor_sync(0xFFFFFFFF, static_cast<float>(var), laneMask, width));
-  #endif
-}
-#endif
-
-// ldg() has an overload for __half_raw, but we also need one for Eigen::half.
-#if (defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 350) || defined(EIGEN_HIPCC)
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half __ldg(const Eigen::half* ptr) {
-  return Eigen::half_impl::raw_uint16_to_half(__ldg(reinterpret_cast<const Eigen::numext::uint16_t*>(ptr)));
-}
-#endif
-
 namespace Eigen {
 namespace numext {
 
@@ -823,4 +805,69 @@
 }  // namespace numext
 }  // namespace Eigen
 
+// Add the missing shfl* intrinsics.
+// The __shfl* functions are only valid on HIP or _CUDA_ARCH_ >= 300.
+//   CUDA defines them for (__CUDA_ARCH__ >= 300 || !defined(__CUDA_ARCH__))
+//
+// HIP and CUDA prior to SDK 9.0 define
+//    __shfl, __shfl_up, __shfl_down, __shfl_xor for int and float
+// CUDA since 9.0 deprecates those and instead defines
+//    __shfl_sync, __shfl_up_sync, __shfl_down_sync, __shfl_xor_sync,
+//    with native support for __half and __nv_bfloat16
+//
+// Note that the following are __device__ - only functions.
+#if (defined(EIGEN_CUDACC) && (!defined(EIGEN_CUDA_ARCH) || EIGEN_CUDA_ARCH >= 300)) \
+    || defined(EIGEN_HIPCC)
+
+#if defined(EIGEN_HAS_CUDA_FP16) && EIGEN_CUDA_SDK_VER >= 90000
+
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_sync(unsigned mask, Eigen::half var, int srcLane, int width=warpSize) {
+  return static_cast<Eigen::half>(__shfl_sync(mask, static_cast<__half>(var), srcLane, width));
+}
+
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_up_sync(unsigned mask, Eigen::half var, unsigned int delta, int width=warpSize) {
+  return static_cast<Eigen::half>(__shfl_up_sync(mask, static_cast<__half>(var), delta, width));
+}
+
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_down_sync(unsigned mask, Eigen::half var, unsigned int delta, int width=warpSize) {
+  return static_cast<Eigen::half>(__shfl_down_sync(mask, static_cast<__half>(var), delta, width));
+}
+
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_xor_sync(unsigned mask, Eigen::half var, int laneMask, int width=warpSize) {
+  return static_cast<Eigen::half>(__shfl_xor_sync(mask, static_cast<__half>(var), laneMask, width));
+}
+
+#else // HIP or CUDA SDK < 9.0
+
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl(Eigen::half var, int srcLane, int width=warpSize) {
+  const int ivar = static_cast<int>(Eigen::numext::bit_cast<Eigen::numext::uint16_t>(var));
+  return Eigen::numext::bit_cast<Eigen::half>(static_cast<Eigen::numext::uint16_t>(__shfl(ivar, srcLane, width)));
+}
+
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_up(Eigen::half var, unsigned int delta, int width=warpSize) {
+  const int ivar = static_cast<int>(Eigen::numext::bit_cast<Eigen::numext::uint16_t>(var));
+  return Eigen::numext::bit_cast<Eigen::half>(static_cast<Eigen::numext::uint16_t>(__shfl_up(ivar, delta, width)));
+}
+
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_down(Eigen::half var, unsigned int delta, int width=warpSize) {
+  const int ivar = static_cast<int>(Eigen::numext::bit_cast<Eigen::numext::uint16_t>(var));
+  return Eigen::numext::bit_cast<Eigen::half>(static_cast<Eigen::numext::uint16_t>(__shfl_down(ivar, delta, width)));
+}
+
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_xor(Eigen::half var, int laneMask, int width=warpSize) {
+  const int ivar = static_cast<int>(Eigen::numext::bit_cast<Eigen::numext::uint16_t>(var));
+  return Eigen::numext::bit_cast<Eigen::half>(static_cast<Eigen::numext::uint16_t>(__shfl_xor(ivar, laneMask, width)));
+}
+
+#endif // HIP vs CUDA
+#endif // __shfl*
+
+// ldg() has an overload for __half_raw, but we also need one for Eigen::half.
+#if (defined(EIGEN_CUDACC) && (!defined(EIGEN_CUDA_ARCH) || EIGEN_CUDA_ARCH >= 350)) \
+    || defined(EIGEN_HIPCC)
+EIGEN_STRONG_INLINE __device__ Eigen::half __ldg(const Eigen::half* ptr) {
+  return Eigen::half_impl::raw_uint16_to_half(__ldg(reinterpret_cast<const Eigen::numext::uint16_t*>(ptr)));
+}
+#endif // __ldg
+
 #endif // EIGEN_HALF_H
diff --git a/Eigen/src/Core/arch/GPU/PacketMath.h b/Eigen/src/Core/arch/GPU/PacketMath.h
index dd4e77d..c16f95e 100644
--- a/Eigen/src/Core/arch/GPU/PacketMath.h
+++ b/Eigen/src/Core/arch/GPU/PacketMath.h
@@ -14,10 +14,21 @@
 
 namespace internal {
 
+// Read-only data cached load available.
+#if defined(EIGEN_HIP_DEVICE_COMPILE) || EIGEN_CUDA_ARCH >= 350
+#define EIGEN_GPU_HAS_LDG 1
+#endif
+
+// FP16 math available.
+#if defined(EIGEN_HIP_DEVICE_COMPILE) || EIGEN_CUDA_ARCH >= 530
+#define EIGEN_GPU_HAS_FP16_ARITHMETIC 1
+#endif
+
 // Make sure this is only available when targeting a GPU: we don't want to
 // introduce conflicts between these packet_traits definitions and the ones
 // we'll use on the host side (SSE, AVX, ...)
 #if defined(EIGEN_GPUCC) && defined(EIGEN_USE_GPU)
+
 template<> struct is_arithmetic<float4>  { enum { value = true }; };
 template<> struct is_arithmetic<double2> { enum { value = true }; };
 
@@ -237,7 +248,7 @@
 pcmp_lt<double2>(const double2& a, const double2& b) {
   return make_double2(lt_mask(a.x, b.x), lt_mask(a.y, b.y));
 }
-#endif  // EIGEN_CUDA_ARCH || defined(EIGEN_HIP_DEVICE_COMPILE)
+#endif // defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIPCC) || (defined(EIGEN_CUDACC) && EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC)
 
 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 plset<float4>(const float& a) {
   return make_float4(a, a+1, a+2, a+3);
@@ -342,7 +353,7 @@
 
 template<>
 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float4 ploadt_ro<float4, Aligned>(const float* from) {
-#if defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 350
+#if defined(EIGEN_GPU_HAS_LDG)
   return __ldg((const float4*)from);
 #else
   return make_float4(from[0], from[1], from[2], from[3]);
@@ -350,7 +361,7 @@
 }
 template<>
 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double2 ploadt_ro<double2, Aligned>(const double* from) {
-#if defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 350
+#if defined(EIGEN_GPU_HAS_LDG)
   return __ldg((const double2*)from);
 #else
   return make_double2(from[0], from[1]);
@@ -359,7 +370,7 @@
 
 template<>
 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float4 ploadt_ro<float4, Unaligned>(const float* from) {
-#if defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 350
+#if defined(EIGEN_GPU_HAS_LDG)
   return make_float4(__ldg(from+0), __ldg(from+1), __ldg(from+2), __ldg(from+3));
 #else
   return make_float4(from[0], from[1], from[2], from[3]);
@@ -367,7 +378,7 @@
 }
 template<>
 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double2 ploadt_ro<double2, Unaligned>(const double* from) {
-#if defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 350
+#if defined(EIGEN_GPU_HAS_LDG)
   return make_double2(__ldg(from+0), __ldg(from+1));
 #else
   return make_double2(from[0], from[1]);
@@ -480,9 +491,7 @@
 
 // Packet4h2 must be defined in the macro without EIGEN_CUDA_ARCH, meaning
 // its corresponding packet_traits<Eigen::half> must be visible on host.
-#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDACC)) || \
-  (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIPCC)) || \
-  (defined(EIGEN_HAS_CUDA_FP16) && defined(__clang__) && defined(__CUDA__))
+#if defined(EIGEN_HAS_CUDA_FP16) || defined(EIGEN_HAS_HIP_FP16)
 
 typedef ulonglong2 Packet4h2;
 template<> struct unpacket_traits<Packet4h2> { typedef Eigen::half type; enum {size=8, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet4h2 half; };
@@ -513,17 +522,41 @@
   };
 };
 
+namespace {
+// This is equivalent to make_half2, which is undocumented and doesn't seem to always exist.
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 combine_half(const __half& a, const __half& b) {
+#if defined(EIGEN_GPU_COMPILE_PHASE)
+  return __halves2half2(a, b);
+#else
+  // Round-about way since __halves2half2 is a __device__ function.
+  return __floats2half2_rn(__half2float(a), __half2float(b));
+#endif
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE __half get_half2_low(const half2& a) {
+#if defined(EIGEN_GPU_COMPILE_PHASE)
+  return __low2half(a);
+#else
+  return __float2half(__low2float(a));
+#endif
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE __half get_half2_high(const half2& a) {
+#if defined(EIGEN_GPU_COMPILE_PHASE)
+  return __high2half(a);
+#else
+  return __float2half(__high2float(a));
+#endif
+}
+} // namespace
+
 template<>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pset1<half2>(const Eigen::half& from) {
-#if !defined(EIGEN_CUDA_ARCH) && !defined(EIGEN_HIPCC)
-  half2 r;
-  r.x = from;
-  r.y = from;
-  return r;
-#elif defined(EIGEN_HIPCC)
-  return __half2{from,from};
-#else
+#if defined(EIGEN_GPU_COMPILE_PHASE)
   return __half2half2(from);
+#else
+  const float f = __half2float(from);
+  return __floats2half2_rn(f, f);
 #endif
 }
 
@@ -539,7 +572,8 @@
   return r;
 }
 
-#if defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIPCC) || (defined(EIGEN_CUDACC) && EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC)
+// We now need this visible on both host and device.
+// #if defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIPCC) || (defined(EIGEN_CUDACC) && EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC)
 namespace {
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pload(const Eigen::half* from) {
@@ -547,11 +581,11 @@
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ploadu(const Eigen::half* from) {
-  return __halves2half2(from[0], from[1]);
+  return combine_half(from[0], from[1]);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ploaddup(const Eigen::half*  from) {
-  return __halves2half2(from[0], from[0]);
+  return combine_half(from[0], from[0]);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore(Eigen::half* to,
@@ -561,201 +595,164 @@
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu(Eigen::half* to,
                                                    const half2& from) {
-#if !defined(EIGEN_CUDA_ARCH) && !defined(EIGEN_HIPCC)
-  to[0] = from.x;
-  to[1] = from.y;
-#else
-  to[0] = __low2half(from);
-  to[1] = __high2half(from);
-#endif
+  to[0] = get_half2_low(from);
+  to[1] = get_half2_high(from);
 }
 
 
 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE half2 ploadt_ro_aligned(
     const Eigen::half* from) {
-
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
+#if defined(EIGEN_GPU_HAS_LDG)
   return __ldg((const half2*)from);
-
-#else  // EIGEN_CUDA_ARCH
-
-#if EIGEN_CUDA_ARCH >= 350
-   return __ldg((const half2*)from);
 #else
-  return __halves2half2(*(from+0), *(from+1));
-#endif
-
+  return combine_half(*(from+0), *(from+1));
 #endif
 }
 
 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE half2 ploadt_ro_unaligned(
     const Eigen::half* from) {
-
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
+#if defined(EIGEN_GPU_HAS_LDG)
   return __halves2half2(__ldg(from+0), __ldg(from+1));
-
-#else  // EIGEN_CUDA_ARCH
-
-#if EIGEN_CUDA_ARCH >= 350
-   return __halves2half2(__ldg(from+0), __ldg(from+1));
 #else
-  return __halves2half2(*(from+0), *(from+1));
-#endif
-
+  return combine_half(*(from+0), *(from+1));
 #endif
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pgather(const Eigen::half* from,
                                                     Index stride) {
-  return __halves2half2(from[0*stride], from[1*stride]);
+  return combine_half(from[0*stride], from[1*stride]);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter(
     Eigen::half* to, const half2& from, Index stride) {
-  to[stride*0] = __low2half(from);
-  to[stride*1] = __high2half(from);
+  to[stride*0] = get_half2_low(from);
+  to[stride*1] = get_half2_high(from);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half pfirst(const half2& a) {
-  return __low2half(a);
+  return get_half2_low(a);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pabs(const half2& a) {
-  half a1 = __low2half(a);
-  half a2 = __high2half(a);
+  half a1 = get_half2_low(a);
+  half a2 = get_half2_high(a);
   half result1 = half_impl::raw_uint16_to_half(a1.x & 0x7FFF);
   half result2 = half_impl::raw_uint16_to_half(a2.x & 0x7FFF);
-  return __halves2half2(result1, result2);
+  return combine_half(result1, result2);
 }
 
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ptrue(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ptrue(const half2& /*a*/) {
   half true_half = half_impl::raw_uint16_to_half(0xffffu);
   return pset1<half2>(true_half);
 }
 
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pzero(const half2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pzero(const half2& /*a*/) {
   half false_half = half_impl::raw_uint16_to_half(0x0000u);
   return pset1<half2>(false_half);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void
 ptranspose(PacketBlock<half2,2>& kernel) {
-  __half a1 = __low2half(kernel.packet[0]);
-  __half a2 = __high2half(kernel.packet[0]);
-  __half b1 = __low2half(kernel.packet[1]);
-  __half b2 = __high2half(kernel.packet[1]);
-  kernel.packet[0] = __halves2half2(a1, b1);
-  kernel.packet[1] = __halves2half2(a2, b2);
+  __half a1 = get_half2_low(kernel.packet[0]);
+  __half a2 = get_half2_high(kernel.packet[0]);
+  __half b1 = get_half2_low(kernel.packet[1]);
+  __half b2 = get_half2_high(kernel.packet[1]);
+  kernel.packet[0] = combine_half(a1, b1);
+  kernel.packet[1] = combine_half(a2, b2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plset(const Eigen::half& a) {
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
-  return __halves2half2(a, __hadd(a, __float2half(1.0f)));
-
-#else  // EIGEN_CUDA_ARCH
-
-#if EIGEN_CUDA_ARCH >= 530
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
   return __halves2half2(a, __hadd(a, __float2half(1.0f)));
 #else
   float f = __half2float(a) + 1.0f;
-  return __halves2half2(a, __float2half(f));
-#endif
-
+  return combine_half(a, __float2half(f));
 #endif
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pselect(const half2& mask,
                                                     const half2& a,
                                                     const half2& b) {
-  half mask_low = __low2half(mask);
-  half mask_high = __high2half(mask);
-  half result_low = mask_low == half(0) ? __low2half(b) : __low2half(a);
-  half result_high = mask_high == half(0) ? __high2half(b) : __high2half(a);
-  return __halves2half2(result_low, result_high);
+  half mask_low = get_half2_low(mask);
+  half mask_high = get_half2_high(mask);
+  half result_low = mask_low == half(0) ? get_half2_low(b) : get_half2_low(a);
+  half result_high = mask_high == half(0) ? get_half2_high(b) : get_half2_high(a);
+  return combine_half(result_low, result_high);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_eq(const half2& a,
                                                     const half2& b) {
   half true_half = half_impl::raw_uint16_to_half(0xffffu);
   half false_half = half_impl::raw_uint16_to_half(0x0000u);
-  half a1 = __low2half(a);
-  half a2 = __high2half(a);
-  half b1 = __low2half(b);
-  half b2 = __high2half(b);
+  half a1 = get_half2_low(a);
+  half a2 = get_half2_high(a);
+  half b1 = get_half2_low(b);
+  half b2 = get_half2_high(b);
   half eq1 = __half2float(a1) == __half2float(b1) ? true_half : false_half;
   half eq2 = __half2float(a2) == __half2float(b2) ? true_half : false_half;
-  return __halves2half2(eq1, eq2);
+  return combine_half(eq1, eq2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_lt(const half2& a,
                                                     const half2& b) {
   half true_half = half_impl::raw_uint16_to_half(0xffffu);
   half false_half = half_impl::raw_uint16_to_half(0x0000u);
-  half a1 = __low2half(a);
-  half a2 = __high2half(a);
-  half b1 = __low2half(b);
-  half b2 = __high2half(b);
+  half a1 = get_half2_low(a);
+  half a2 = get_half2_high(a);
+  half b1 = get_half2_low(b);
+  half b2 = get_half2_high(b);
   half eq1 = __half2float(a1) < __half2float(b1) ? true_half : false_half;
   half eq2 = __half2float(a2) < __half2float(b2) ? true_half : false_half;
-  return __halves2half2(eq1, eq2);
+  return combine_half(eq1, eq2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pand(const half2& a,
                                                  const half2& b) {
-  half a1 = __low2half(a);
-  half a2 = __high2half(a);
-  half b1 = __low2half(b);
-  half b2 = __high2half(b);
+  half a1 = get_half2_low(a);
+  half a2 = get_half2_high(a);
+  half b1 = get_half2_low(b);
+  half b2 = get_half2_high(b);
   half result1 = half_impl::raw_uint16_to_half(a1.x & b1.x);
   half result2 = half_impl::raw_uint16_to_half(a2.x & b2.x);
-  return __halves2half2(result1, result2);
+  return combine_half(result1, result2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 por(const half2& a,
                                                 const half2& b) {
-  half a1 = __low2half(a);
-  half a2 = __high2half(a);
-  half b1 = __low2half(b);
-  half b2 = __high2half(b);
+  half a1 = get_half2_low(a);
+  half a2 = get_half2_high(a);
+  half b1 = get_half2_low(b);
+  half b2 = get_half2_high(b);
   half result1 = half_impl::raw_uint16_to_half(a1.x | b1.x);
   half result2 = half_impl::raw_uint16_to_half(a2.x | b2.x);
-  return __halves2half2(result1, result2);
+  return combine_half(result1, result2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pxor(const half2& a,
                                                  const half2& b) {
-  half a1 = __low2half(a);
-  half a2 = __high2half(a);
-  half b1 = __low2half(b);
-  half b2 = __high2half(b);
+  half a1 = get_half2_low(a);
+  half a2 = get_half2_high(a);
+  half b1 = get_half2_low(b);
+  half b2 = get_half2_high(b);
   half result1 = half_impl::raw_uint16_to_half(a1.x ^ b1.x);
   half result2 = half_impl::raw_uint16_to_half(a2.x ^ b2.x);
-  return __halves2half2(result1, result2);
+  return combine_half(result1, result2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pandnot(const half2& a,
                                                     const half2& b) {
-  half a1 = __low2half(a);
-  half a2 = __high2half(a);
-  half b1 = __low2half(b);
-  half b2 = __high2half(b);
+  half a1 = get_half2_low(a);
+  half a2 = get_half2_high(a);
+  half b1 = get_half2_low(b);
+  half b2 = get_half2_high(b);
   half result1 = half_impl::raw_uint16_to_half(a1.x & ~b1.x);
   half result2 = half_impl::raw_uint16_to_half(a2.x & ~b2.x);
-  return __halves2half2(result1, result2);
+  return combine_half(result1, result2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 padd(const half2& a,
                                                  const half2& b) {
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
-  return __hadd2(a, b);
-
-#else  // EIGEN_CUDA_ARCH
-
-#if EIGEN_CUDA_ARCH >= 530
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
   return __hadd2(a, b);
 #else
   float a1 = __low2float(a);
@@ -766,19 +763,11 @@
   float r2 = a2 + b2;
   return __floats2half2_rn(r1, r2);
 #endif
-
-#endif
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 psub(const half2& a,
                                                  const half2& b) {
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
-  return __hsub2(a, b);
-
-#else  // EIGEN_CUDA_ARCH
-
-#if EIGEN_CUDA_ARCH >= 530
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
   return __hsub2(a, b);
 #else
   float a1 = __low2float(a);
@@ -789,39 +778,23 @@
   float r2 = a2 - b2;
   return __floats2half2_rn(r1, r2);
 #endif
-
-#endif
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pnegate(const half2& a) {
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
-  return __hneg2(a);
-
-#else  // EIGEN_CUDA_ARCH
-
-#if EIGEN_CUDA_ARCH >= 530
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
   return __hneg2(a);
 #else
   float a1 = __low2float(a);
   float a2 = __high2float(a);
   return __floats2half2_rn(-a1, -a2);
 #endif
-
-#endif
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pconj(const half2& a) { return a; }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmul(const half2& a,
                                                  const half2& b) {
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
-  return __hmul2(a, b);
-
-#else  // EIGEN_CUDA_ARCH
-
-#if EIGEN_CUDA_ARCH >= 530
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
   return __hmul2(a, b);
 #else
   float a1 = __low2float(a);
@@ -832,20 +805,12 @@
   float r2 = a2 * b2;
   return __floats2half2_rn(r1, r2);
 #endif
-
-#endif
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmadd(const half2& a,
                                                   const half2& b,
                                                   const half2& c) {
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
-   return __hfma2(a, b, c);
-
-#else  // EIGEN_CUDA_ARCH
-
-#if EIGEN_CUDA_ARCH >= 530
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
    return __hfma2(a, b, c);
 #else
   float a1 = __low2float(a);
@@ -858,18 +823,13 @@
   float r2 = a2 * b2 + c2;
   return __floats2half2_rn(r1, r2);
 #endif
-
-#endif
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pdiv(const half2& a,
                                                  const half2& b) {
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
   return __h2div(a, b);
-
-#else // EIGEN_CUDA_ARCH
-
+#else
   float a1 = __low2float(a);
   float a2 = __high2float(a);
   float b1 = __low2float(b);
@@ -877,7 +837,6 @@
   float r1 = a1 / b1;
   float r2 = a2 / b2;
   return __floats2half2_rn(r1, r2);
-
 #endif
 }
 
@@ -887,9 +846,9 @@
   float a2 = __high2float(a);
   float b1 = __low2float(b);
   float b2 = __high2float(b);
-  __half r1 = a1 < b1 ? __low2half(a) : __low2half(b);
-  __half r2 = a2 < b2 ? __high2half(a) : __high2half(b);
-  return __halves2half2(r1, r2);
+  __half r1 = a1 < b1 ? get_half2_low(a) : get_half2_low(b);
+  __half r2 = a2 < b2 ? get_half2_high(a) : get_half2_high(b);
+  return combine_half(r1, r2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmax(const half2& a,
@@ -898,89 +857,53 @@
   float a2 = __high2float(a);
   float b1 = __low2float(b);
   float b2 = __high2float(b);
-  __half r1 = a1 > b1 ? __low2half(a) : __low2half(b);
-  __half r2 = a2 > b2 ? __high2half(a) : __high2half(b);
-  return __halves2half2(r1, r2);
+  __half r1 = a1 > b1 ? get_half2_low(a) : get_half2_low(b);
+  __half r2 = a2 > b2 ? get_half2_high(a) : get_half2_high(b);
+  return combine_half(r1, r2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux(const half2& a) {
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
-  return __hadd(__low2half(a), __high2half(a));
-
-#else  // EIGEN_CUDA_ARCH
-
-#if EIGEN_CUDA_ARCH >= 530
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
   return __hadd(__low2half(a), __high2half(a));
 #else
   float a1 = __low2float(a);
   float a2 = __high2float(a);
   return Eigen::half(__float2half(a1 + a2));
 #endif
-
-#endif
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_max(const half2& a) {
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
-  __half first = __low2half(a);
-  __half second = __high2half(a);
-  return __hgt(first, second) ? first : second;
-
-#else  // EIGEN_CUDA_ARCH
-
-#if EIGEN_CUDA_ARCH >= 530
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
   __half first = __low2half(a);
   __half second = __high2half(a);
   return __hgt(first, second) ? first : second;
 #else
   float a1 = __low2float(a);
   float a2 = __high2float(a);
-  return a1 > a2 ? __low2half(a) : __high2half(a);
-#endif
-
+  return a1 > a2 ? get_half2_low(a) : get_half2_high(a);
 #endif
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_min(const half2& a) {
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
-  __half first = __low2half(a);
-  __half second = __high2half(a);
-  return __hlt(first, second) ? first : second;
-
-#else  // EIGEN_CUDA_ARCH
-
-#if EIGEN_CUDA_ARCH >= 530
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
   __half first = __low2half(a);
   __half second = __high2half(a);
   return __hlt(first, second) ? first : second;
 #else
   float a1 = __low2float(a);
   float a2 = __high2float(a);
-  return a1 < a2 ? __low2half(a) : __high2half(a);
-#endif
-
+  return a1 < a2 ? get_half2_low(a) : get_half2_high(a);
 #endif
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_mul(const half2& a) {
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
-  return __hmul(__low2half(a), __high2half(a));
-
-#else  // EIGEN_CUDA_ARCH
-
-#if EIGEN_CUDA_ARCH >= 530
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
   return __hmul(__low2half(a), __high2half(a));
 #else
   float a1 = __low2float(a);
   float a2 = __high2float(a);
   return Eigen::half(__float2half(a1 * a2));
 #endif
-
-#endif
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plog1p(const half2& a) {
@@ -1108,14 +1031,7 @@
 template <>
 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet4h2
 ploadt_ro<Packet4h2, Aligned>(const Eigen::half* from) {
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
-  Packet4h2 r;
-  r = __ldg((const Packet4h2*)from);
-  return r;
-#else  // EIGEN_CUDA_ARCH
-
-#if EIGEN_CUDA_ARCH >= 350
+#if defined(EIGEN_GPU_HAS_LDG)
   Packet4h2 r;
   r = __ldg((const Packet4h2*)from);
   return r;
@@ -1128,8 +1044,6 @@
   r_alias[3] = ploadt_ro_aligned(from + 6);
   return r;
 #endif
-
-#endif
 }
 
 template <>
@@ -1149,10 +1063,10 @@
 pgather<Eigen::half, Packet4h2>(const Eigen::half* from, Index stride) {
   Packet4h2 r;
   half2* p_alias = reinterpret_cast<half2*>(&r);
-  p_alias[0] = __halves2half2(from[0 * stride], from[1 * stride]);
-  p_alias[1] = __halves2half2(from[2 * stride], from[3 * stride]);
-  p_alias[2] = __halves2half2(from[4 * stride], from[5 * stride]);
-  p_alias[3] = __halves2half2(from[6 * stride], from[7 * stride]);
+  p_alias[0] = combine_half(from[0 * stride], from[1 * stride]);
+  p_alias[1] = combine_half(from[2 * stride], from[3 * stride]);
+  p_alias[2] = combine_half(from[4 * stride], from[5 * stride]);
+  p_alias[3] = combine_half(from[6 * stride], from[7 * stride]);
   return r;
 }
 
@@ -1187,13 +1101,13 @@
 
 template <>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 ptrue<Packet4h2>(
-    const Packet4h2& a) {
+    const Packet4h2& /*a*/) {
   half true_half = half_impl::raw_uint16_to_half(0xffffu);
   return pset1<Packet4h2>(true_half);
 }
 
 template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pzero<Packet4h2>(const Packet4h2& a) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pzero<Packet4h2>(const Packet4h2& /*a*/) {
   half false_half = half_impl::raw_uint16_to_half(0x0000u);
   return pset1<Packet4h2>(false_half);
 }
@@ -1233,12 +1147,12 @@
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void
 ptranspose_half(half2& f0, half2& f1) {
-  __half a1 = __low2half(f0);
-  __half a2 = __high2half(f0);
-  __half b1 = __low2half(f1);
-  __half b2 = __high2half(f1);
-  f0 = __halves2half2(a1, b1);
-  f1 = __halves2half2(a2, b2);
+  __half a1 = get_half2_low(f0);
+  __half a2 = get_half2_high(f0);
+  __half b1 = get_half2_low(f1);
+  __half b2 = get_half2_high(f1);
+  f0 = combine_half(a1, b1);
+  f1 = combine_half(a2, b2);
 }
 
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void
@@ -1294,7 +1208,7 @@
   ptranspose_half(f_row0[1], f_row1[1]);
   ptranspose_half(f_row2[0], f_row3[0]);
   ptranspose_half(f_row2[1], f_row3[1]);
-  
+
 }
 
 template <>
@@ -1312,9 +1226,7 @@
   p_alias[3] = __halves2half2(__hadd(a, __float2half(6.0f)),
                               __hadd(a, __float2half(7.0f)));
   return r;
-#else  // EIGEN_CUDA_ARCH
-
-#if EIGEN_CUDA_ARCH >= 530
+#elif EIGEN_CUDA_ARCH >= 530
   Packet4h2 r;
   half2* r_alias = reinterpret_cast<half2*>(&r);
 
@@ -1337,14 +1249,12 @@
   float f = __half2float(a);
   Packet4h2 r;
   half2* p_alias = reinterpret_cast<half2*>(&r);
-  p_alias[0] = __halves2half2(a, __float2half(f + 1.0f));
-  p_alias[1] = __halves2half2(__float2half(f + 2.0f), __float2half(f + 3.0f));
-  p_alias[2] = __halves2half2(__float2half(f + 4.0f), __float2half(f + 5.0f));
-  p_alias[3] = __halves2half2(__float2half(f + 6.0f), __float2half(f + 7.0f));
+  p_alias[0] = combine_half(a, __float2half(f + 1.0f));
+  p_alias[1] = combine_half(__float2half(f + 2.0f), __float2half(f + 3.0f));
+  p_alias[2] = combine_half(__float2half(f + 4.0f), __float2half(f + 5.0f));
+  p_alias[3] = combine_half(__float2half(f + 6.0f), __float2half(f + 7.0f));
   return r;
 #endif
-
-#endif
 }
 
 template <>
@@ -1562,9 +1472,9 @@
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_max<Packet4h2>(
     const Packet4h2& a) {
   const half2* a_alias = reinterpret_cast<const half2*>(&a);
-  half2 m0 = __halves2half2(predux_max(a_alias[0]),
+  half2 m0 = combine_half(predux_max(a_alias[0]),
                             predux_max(a_alias[1]));
-  half2 m1 = __halves2half2(predux_max(a_alias[2]),
+  half2 m1 = combine_half(predux_max(a_alias[2]),
                             predux_max(a_alias[3]));
   __half first  = predux_max(m0);
   __half second = predux_max(m1);
@@ -1581,9 +1491,9 @@
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_min<Packet4h2>(
     const Packet4h2& a) {
   const half2* a_alias = reinterpret_cast<const half2*>(&a);
-  half2 m0 = __halves2half2(predux_min(a_alias[0]),
+  half2 m0 = combine_half(predux_min(a_alias[0]),
                             predux_min(a_alias[1]));
-  half2 m1 = __halves2half2(predux_min(a_alias[2]),
+  half2 m1 = combine_half(predux_min(a_alias[2]),
                             predux_min(a_alias[3]));
   __half first  = predux_min(m0);
   __half second = predux_min(m1);
@@ -1685,13 +1595,7 @@
 template<>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 padd<half2>(const half2& a,
                                                         const half2& b) {
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
-  return __hadd2(a, b);
-
-#else  // EIGEN_CUDA_ARCH
-
-#if EIGEN_CUDA_ARCH >= 530
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
   return __hadd2(a, b);
 #else
   float a1 = __low2float(a);
@@ -1702,20 +1606,12 @@
   float r2 = a2 + b2;
   return __floats2half2_rn(r1, r2);
 #endif
-
-#endif
 }
 
 template<>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmul<half2>(const half2& a,
                                                         const half2& b) {
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
-  return __hmul2(a, b);
-
-#else  // EIGEN_CUDA_ARCH
-
-#if EIGEN_CUDA_ARCH >= 530
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
   return __hmul2(a, b);
 #else
   float a1 = __low2float(a);
@@ -1726,19 +1622,14 @@
   float r2 = a2 * b2;
   return __floats2half2_rn(r1, r2);
 #endif
-
-#endif
 }
 
 template<>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pdiv<half2>(const half2& a,
                                                         const half2& b) {
-#if defined(EIGEN_HIP_DEVICE_COMPILE)
-
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
   return __h2div(a, b);
-
-#else // EIGEN_CUDA_ARCH
-
+#else
   float a1 = __low2float(a);
   float a2 = __high2float(a);
   float b1 = __low2float(b);
@@ -1746,7 +1637,6 @@
   float r1 = a1 / b1;
   float r2 = a2 / b2;
   return __floats2half2_rn(r1, r2);
-
 #endif
 }
 
@@ -1757,9 +1647,9 @@
   float a2 = __high2float(a);
   float b1 = __low2float(b);
   float b2 = __high2float(b);
-  __half r1 = a1 < b1 ? __low2half(a) : __low2half(b);
-  __half r2 = a2 < b2 ? __high2half(a) : __high2half(b);
-  return __halves2half2(r1, r2);
+  __half r1 = a1 < b1 ? get_half2_low(a) : get_half2_low(b);
+  __half r2 = a2 < b2 ? get_half2_high(a) : get_half2_high(b);
+  return combine_half(r1, r2);
 }
 
 template<>
@@ -1769,14 +1659,17 @@
   float a2 = __high2float(a);
   float b1 = __low2float(b);
   float b2 = __high2float(b);
-  __half r1 = a1 > b1 ? __low2half(a) : __low2half(b);
-  __half r2 = a2 > b2 ? __high2half(a) : __high2half(b);
-  return __halves2half2(r1, r2);
+  __half r1 = a1 > b1 ? get_half2_low(a) : get_half2_low(b);
+  __half r2 = a2 > b2 ? get_half2_high(a) : get_half2_high(b);
+  return combine_half(r1, r2);
 }
 
-#endif // defined(EIGEN_CUDA_ARCH)
+// #endif // defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIPCC) || (defined(EIGEN_CUDACC) && EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC)
 
-#endif // defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDACC)
+#endif // defined(EIGEN_HAS_CUDA_FP16) || defined(EIGEN_HAS_HIP_FP16)
+
+#undef EIGEN_GPU_HAS_LDG
+#undef EIGEN_GPU_HAS_FP16_ARITHMETIC
 
 } // end namespace internal
 
diff --git a/Eigen/src/Core/arch/NEON/Complex.h b/Eigen/src/Core/arch/NEON/Complex.h
index 448600b..a889ab1 100644
--- a/Eigen/src/Core/arch/NEON/Complex.h
+++ b/Eigen/src/Core/arch/NEON/Complex.h
@@ -76,6 +76,7 @@
 {
   typedef std::complex<float> type;
   typedef Packet1cf half;
+  typedef Packet2f as_real;
   enum
   {
     size = 1,
@@ -89,6 +90,7 @@
 {
   typedef std::complex<float> type;
   typedef Packet1cf half;
+  typedef Packet4f as_real;
   enum
   {
     size = 2,
@@ -430,6 +432,14 @@
   kernel.packet[1].v = tmp;
 }
 
+template<> EIGEN_STRONG_INLINE Packet1cf psqrt<Packet1cf>(const Packet1cf& a) {
+  return psqrt_complex<Packet1cf>(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf psqrt<Packet2cf>(const Packet2cf& a) {
+  return psqrt_complex<Packet2cf>(a);
+}
+
 //---------- double ----------
 #if EIGEN_ARCH_ARM64 && !EIGEN_APPLE_DOUBLE_NEON_BUG
 
@@ -475,6 +485,8 @@
 template<> struct unpacket_traits<Packet1cd>
 {
   typedef std::complex<double> type;
+  typedef Packet1cd half;
+  typedef Packet2d as_real;
   enum
   {
     size=1,
@@ -483,7 +495,6 @@
     masked_load_available=false,
     masked_store_available=false
   };
-  typedef Packet1cd half;
 };
 
 template<> EIGEN_STRONG_INLINE Packet1cd pload<Packet1cd>(const std::complex<double>* from)
@@ -640,6 +651,11 @@
   kernel.packet[0].v = vcombine_f64(vget_low_f64(kernel.packet[0].v), vget_low_f64(kernel.packet[1].v));
   kernel.packet[1].v = tmp;
 }
+
+template<> EIGEN_STRONG_INLINE Packet1cd psqrt<Packet1cd>(const Packet1cd& a) {
+  return psqrt_complex<Packet1cd>(a);
+}
+
 #endif // EIGEN_ARCH_ARM64
 
 } // end namespace internal
diff --git a/Eigen/src/Core/arch/NEON/PacketMath.h b/Eigen/src/Core/arch/NEON/PacketMath.h
index 709cebe..90ffee7 100644
--- a/Eigen/src/Core/arch/NEON/PacketMath.h
+++ b/Eigen/src/Core/arch/NEON/PacketMath.h
@@ -192,7 +192,9 @@
     HasExp  = 1,
     HasSqrt = 1,
     HasTanh = EIGEN_FAST_MATH,
-    HasErf  = EIGEN_FAST_MATH
+    HasErf  = EIGEN_FAST_MATH,
+    HasBessel = 0,  // Issues with accuracy.
+    HasNdtri = 0
   };
 };
 
@@ -1157,6 +1159,17 @@
 
 template<> EIGEN_STRONG_INLINE Packet2f pmin<Packet2f>(const Packet2f& a, const Packet2f& b) { return vmin_f32(a,b); }
 template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return vminq_f32(a,b); }
+
+#ifdef __ARM_FEATURE_NUMERIC_MAXMIN
+// numeric max and min are only available if ARM_FEATURE_NUMERIC_MAXMIN is defined (which can only be the case for Armv8 systems).
+template<> EIGEN_STRONG_INLINE Packet4f pmin<PropagateNumbers, Packet4f>(const Packet4f& a, const Packet4f& b) { return vminnmq_f32(a, b); }
+template<> EIGEN_STRONG_INLINE Packet2f pmin<PropagateNumbers, Packet2f>(const Packet2f& a, const Packet2f& b) { return vminnm_f32(a, b); }
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4f pmin<PropagateNaN, Packet4f>(const Packet4f& a, const Packet4f& b) { return pmin<Packet4f>(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet2f pmin<PropagateNaN, Packet2f>(const Packet2f& a, const Packet2f& b) { return pmin<Packet2f>(a, b); }
+
 template<> EIGEN_STRONG_INLINE Packet4c pmin<Packet4c>(const Packet4c& a, const Packet4c& b)
 {
   return vget_lane_s32(vreinterpret_s32_s8(vmin_s8(
@@ -1194,6 +1207,17 @@
 
 template<> EIGEN_STRONG_INLINE Packet2f pmax<Packet2f>(const Packet2f& a, const Packet2f& b) { return vmax_f32(a,b); }
 template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return vmaxq_f32(a,b); }
+
+#ifdef __ARM_FEATURE_NUMERIC_MAXMIN
+// numeric max and min are only available if ARM_FEATURE_NUMERIC_MAXMIN is defined (which can only be the case for Armv8 systems).
+template<> EIGEN_STRONG_INLINE Packet4f pmax<PropagateNumbers, Packet4f>(const Packet4f& a, const Packet4f& b) { return vmaxnmq_f32(a, b); }
+template<> EIGEN_STRONG_INLINE Packet2f pmax<PropagateNumbers, Packet2f>(const Packet2f& a, const Packet2f& b) { return vmaxnm_f32(a, b); }
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4f pmax<PropagateNaN, Packet4f>(const Packet4f& a, const Packet4f& b) { return pmax<Packet4f>(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet2f pmax<PropagateNaN, Packet2f>(const Packet2f& a, const Packet2f& b) { return pmax<Packet2f>(a, b); }
+
 template<> EIGEN_STRONG_INLINE Packet4c pmax<Packet4c>(const Packet4c& a, const Packet4c& b)
 {
   return vget_lane_s32(vreinterpret_s32_s8(vmax_s8(
@@ -3321,7 +3345,9 @@
     HasExp  = 1,
     HasSqrt = 0,
     HasTanh = EIGEN_FAST_MATH,
-    HasErf  = EIGEN_FAST_MATH
+    HasErf  = EIGEN_FAST_MATH,
+    HasBessel = 0,  // Issues with accuracy.
+    HasNdtri = 0
   };
 };
 
@@ -3371,6 +3397,10 @@
   return reinterpret_cast<Packet4f>(vshlq_n_u32(vmovl_u16(p), 16));
 }
 
+EIGEN_STRONG_INLINE Packet4bf F32MaskToBf16Mask(const Packet4f& p) {
+  return vmovn_u32(vreinterpretq_u32_f32(p));
+}
+
 template<> EIGEN_STRONG_INLINE Packet4bf pset1<Packet4bf>(const bfloat16& from) {
   return pset1<Packet4us>(from.value);
 }
@@ -3408,12 +3438,34 @@
   return F32ToBf16(pabs<Packet4f>(Bf16ToF32(a)));
 }
 
+template <> EIGEN_STRONG_INLINE Packet4bf pmin<PropagateNumbers, Packet4bf>(const Packet4bf &a,
+                                                                            const Packet4bf &b)
+{
+  return F32ToBf16(pmin<PropagateNumbers, Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+template <> EIGEN_STRONG_INLINE Packet4bf pmin<PropagateNaN, Packet4bf>(const Packet4bf &a,
+                                                                        const Packet4bf &b)
+{
+  return F32ToBf16(pmin<PropagateNaN, Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
 template <> EIGEN_STRONG_INLINE Packet4bf pmin<Packet4bf>(const Packet4bf &a,
                                                           const Packet4bf &b)
 {
   return F32ToBf16(pmin<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
 }
 
+template <> EIGEN_STRONG_INLINE Packet4bf pmax<PropagateNumbers, Packet4bf>(const Packet4bf &a,
+                                                                            const Packet4bf &b)
+{
+  return F32ToBf16(pmax<PropagateNumbers, Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+template <> EIGEN_STRONG_INLINE Packet4bf pmax<PropagateNaN, Packet4bf>(const Packet4bf &a,
+                                                                        const Packet4bf &b)
+{
+  return F32ToBf16(pmax<PropagateNaN, Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
 template <> EIGEN_STRONG_INLINE Packet4bf pmax<Packet4bf>(const Packet4bf &a,
                                                           const Packet4bf &b)
 {
@@ -3528,17 +3580,17 @@
 
 template<> EIGEN_STRONG_INLINE Packet4bf pcmp_eq<Packet4bf>(const Packet4bf& a, const Packet4bf& b)
 {
-  return F32ToBf16(pcmp_eq<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+  return F32MaskToBf16Mask(pcmp_eq<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
 }
 
 template<> EIGEN_STRONG_INLINE Packet4bf pcmp_lt<Packet4bf>(const Packet4bf& a, const Packet4bf& b)
 {
-  return F32ToBf16(pcmp_lt<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+  return F32MaskToBf16Mask(pcmp_lt<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
 }
 
 template<> EIGEN_STRONG_INLINE Packet4bf pcmp_le<Packet4bf>(const Packet4bf& a, const Packet4bf& b)
 {
-  return F32ToBf16(pcmp_le<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+  return F32MaskToBf16Mask(pcmp_le<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
 }
 
 template<> EIGEN_STRONG_INLINE Packet4bf pnegate<Packet4bf>(const Packet4bf& a)
@@ -3684,8 +3736,20 @@
 
 template<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) { return vminq_f64(a,b); }
 
+#ifdef __ARM_FEATURE_NUMERIC_MAXMIN
+// numeric max and min are only available if ARM_FEATURE_NUMERIC_MAXMIN is defined (which can only be the case for Armv8 systems).
+template<> EIGEN_STRONG_INLINE Packet2d pmin<PropagateNumbers, Packet2d>(const Packet2d& a, const Packet2d& b) { return vminnmq_f64(a, b); }
+template<> EIGEN_STRONG_INLINE Packet2d pmax<PropagateNumbers, Packet2d>(const Packet2d& a, const Packet2d& b) { return vmaxnmq_f64(a, b); }
+
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet2d pmin<PropagateNaN, Packet2d>(const Packet2d& a, const Packet2d& b) { return pmin<Packet2d>(a, b); }
+
 template<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) { return vmaxq_f64(a,b); }
 
+
+template<> EIGEN_STRONG_INLINE Packet2d pmax<PropagateNaN, Packet2d>(const Packet2d& a, const Packet2d& b) { return pmax<Packet2d>(a, b); }
+
 // WARNING: this pfloor implementation makes sense for inputs that fit in
 // signed int64 integers (up to ~9.22e18), hence this is currently only used
 // by pexp and not exposed through HasFloor.
@@ -3883,7 +3947,10 @@
     HasCos = 0,
     HasLog = 0,
     HasExp = 0,
-    HasSqrt = 1
+    HasSqrt = 1,
+    HasErf = EIGEN_FAST_MATH,
+    HasBessel = 0,  // Issues with accuracy.
+    HasNdtri = 0,
   };
 };
 
@@ -4022,6 +4089,16 @@
   return vmin_f16(a, b);
 }
 
+#ifdef __ARM_FEATURE_NUMERIC_MAXMIN
+// numeric max and min are only available if ARM_FEATURE_NUMERIC_MAXMIN is defined (which can only be the case for Armv8 systems).
+template<> EIGEN_STRONG_INLINE Packet4hf pmin<PropagateNumbers, Packet4hf>(const Packet4hf& a, const Packet4hf& b) { return vminnm_f16(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8hf pmin<PropagateNumbers, Packet8hf>(const Packet8hf& a, const Packet8hf& b) { return vminnmq_f16(a, b); }
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4hf pmin<PropagateNaN, Packet4hf>(const Packet4hf& a, const Packet4hf& b) { return pmin<Packet4hf>(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet8hf pmin<PropagateNaN, Packet8hf>(const Packet8hf& a, const Packet8hf& b) { return pmin<Packet8hf>(a, b); }
+
 template <>
 EIGEN_STRONG_INLINE Packet8hf pmax<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
   return vmaxq_f16(a, b);
@@ -4032,6 +4109,16 @@
   return vmax_f16(a, b);
 }
 
+#ifdef __ARM_FEATURE_NUMERIC_MAXMIN
+// numeric max and min are only available if ARM_FEATURE_NUMERIC_MAXMIN is defined (which can only be the case for Armv8 systems).
+template<> EIGEN_STRONG_INLINE Packet4hf pmax<PropagateNumbers, Packet4hf>(const Packet4hf& a, const Packet4hf& b) { return vmaxnm_f16(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8hf pmax<PropagateNumbers, Packet8hf>(const Packet8hf& a, const Packet8hf& b) { return vmaxnmq_f16(a, b); }
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4hf pmax<PropagateNaN, Packet4hf>(const Packet4hf& a, const Packet4hf& b) { return pmax<Packet4hf>(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet8hf pmax<PropagateNaN, Packet8hf>(const Packet8hf& a, const Packet8hf& b) { return pmax<Packet8hf>(a, b); }
+
 #define EIGEN_MAKE_ARM_FP16_CMP_8(name)                                               \
   template <>                                                                         \
   EIGEN_STRONG_INLINE Packet8hf pcmp_##name(const Packet8hf& a, const Packet8hf& b) { \
diff --git a/Eigen/src/Core/arch/SSE/Complex.h b/Eigen/src/Core/arch/SSE/Complex.h
index 0d322a2..58cdb5d 100644
--- a/Eigen/src/Core/arch/SSE/Complex.h
+++ b/Eigen/src/Core/arch/SSE/Complex.h
@@ -40,6 +40,7 @@
     HasMul    = 1,
     HasDiv    = 1,
     HasNegate = 1,
+    HasSqrt   = 1,
     HasAbs    = 0,
     HasAbs2   = 0,
     HasMin    = 0,
@@ -50,7 +51,18 @@
 };
 #endif
 
-template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet2cf half; };
+template<> struct unpacket_traits<Packet2cf> {
+  typedef std::complex<float> type;
+  typedef Packet2cf half;
+  typedef Packet4f as_real;
+  enum {
+    size=2,
+    alignment=Aligned16,
+    vectorizable=true,
+    masked_load_available=false,
+    masked_store_available=false
+  };
+};
 
 template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_add_ps(a.v,b.v)); }
 template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_sub_ps(a.v,b.v)); }
@@ -83,7 +95,6 @@
 }
 
 template<> EIGEN_STRONG_INLINE Packet2cf ptrue  <Packet2cf>(const Packet2cf& a) { return Packet2cf(ptrue(Packet4f(a.v))); }
-
 template<> EIGEN_STRONG_INLINE Packet2cf pand   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_and_ps(a.v,b.v)); }
 template<> EIGEN_STRONG_INLINE Packet2cf por    <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_or_ps(a.v,b.v)); }
 template<> EIGEN_STRONG_INLINE Packet2cf pxor   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_xor_ps(a.v,b.v)); }
@@ -255,6 +266,7 @@
     HasMul    = 1,
     HasDiv    = 1,
     HasNegate = 1,
+    HasSqrt   = 1,
     HasAbs    = 0,
     HasAbs2   = 0,
     HasMin    = 0,
@@ -264,7 +276,18 @@
 };
 #endif
 
-template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet1cd half; };
+template<> struct unpacket_traits<Packet1cd> {
+  typedef std::complex<double> type;
+  typedef Packet1cd half;
+  typedef Packet2d as_real;
+  enum {
+    size=1,
+    alignment=Aligned16,
+    vectorizable=true,
+    masked_load_available=false,
+    masked_store_available=false
+  };
+};
 
 template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_add_pd(a.v,b.v)); }
 template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_sub_pd(a.v,b.v)); }
@@ -426,8 +449,15 @@
   return Packet2cf(_mm_castpd_ps(result));
 }
 
-} // end namespace internal
+template<> EIGEN_STRONG_INLINE Packet1cd psqrt<Packet1cd>(const Packet1cd& a) {
+  return psqrt_complex<Packet1cd>(a);
+}
 
+template<> EIGEN_STRONG_INLINE Packet2cf psqrt<Packet2cf>(const Packet2cf& a) {
+  return psqrt_complex<Packet2cf>(a);
+}
+
+} // end namespace internal
 } // end namespace Eigen
 
 #endif // EIGEN_COMPLEX_SSE_H
diff --git a/Eigen/src/Core/arch/SSE/MathFunctions.h b/Eigen/src/Core/arch/SSE/MathFunctions.h
index 71ec6f8..2d7df2f 100644
--- a/Eigen/src/Core/arch/SSE/MathFunctions.h
+++ b/Eigen/src/Core/arch/SSE/MathFunctions.h
@@ -30,6 +30,16 @@
 }
 
 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet4f plog2<Packet4f>(const Packet4f& _x) {
+  return plog2_float(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet2d plog2<Packet2d>(const Packet2d& _x) {
+  return plog2_double(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
 Packet4f plog1p<Packet4f>(const Packet4f& _x) {
   return generic_plog1p(_x);
 }
@@ -99,6 +109,9 @@
 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
 Packet2d psqrt<Packet2d>(const Packet2d& x) { return _mm_sqrt_pd(x); }
 
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet16b psqrt<Packet16b>(const Packet16b& x) { return x; }
+
 #if EIGEN_FAST_MATH
 
 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
diff --git a/Eigen/src/Core/arch/SSE/PacketMath.h b/Eigen/src/Core/arch/SSE/PacketMath.h
index 4db7014..4e733c7 100755
--- a/Eigen/src/Core/arch/SSE/PacketMath.h
+++ b/Eigen/src/Core/arch/SSE/PacketMath.h
@@ -218,7 +218,8 @@
     HasAbs2      = 0,
     HasMin       = 0,
     HasMax       = 0,
-    HasConj      = 0
+    HasConj      = 0,
+    HasSqrt      = 1
   };
 };
 
@@ -266,6 +267,10 @@
 template<> EIGEN_STRONG_INLINE Packet4f pset1frombits<Packet4f>(unsigned int from) { return _mm_castsi128_ps(pset1<Packet4i>(from)); }
 template<> EIGEN_STRONG_INLINE Packet2d pset1frombits<Packet2d>(uint64_t from) { return _mm_castsi128_pd(_mm_set1_epi64x(from)); }
 
+template<> EIGEN_STRONG_INLINE Packet4f peven_mask(const Packet4f& /*a*/) { return _mm_castsi128_ps(_mm_set_epi32(0, -1, 0, -1)); }
+template<> EIGEN_STRONG_INLINE Packet4i peven_mask(const Packet4i& /*a*/) { return _mm_set_epi32(0, -1, 0, -1); }
+template<> EIGEN_STRONG_INLINE Packet2d peven_mask(const Packet2d& /*a*/) { return _mm_castsi128_pd(_mm_set_epi32(0, 0, -1, -1)); }
+
 template<> EIGEN_STRONG_INLINE Packet4f pzero(const Packet4f& /*a*/) { return _mm_setzero_ps(); }
 template<> EIGEN_STRONG_INLINE Packet2d pzero(const Packet2d& /*a*/) { return _mm_setzero_pd(); }
 template<> EIGEN_STRONG_INLINE Packet4i pzero(const Packet4i& /*a*/) { return _mm_setzero_si128(); }
diff --git a/Eigen/src/Core/arch/ZVector/Complex.h b/Eigen/src/Core/arch/ZVector/Complex.h
index d3e41b4..ddf5a97 100644
--- a/Eigen/src/Core/arch/ZVector/Complex.h
+++ b/Eigen/src/Core/arch/ZVector/Complex.h
@@ -140,6 +140,11 @@
 template<> EIGEN_STRONG_INLINE Packet1cd pxor    <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_xor(a.v,b.v)); }
 template<> EIGEN_STRONG_INLINE Packet1cd pandnot <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_and(a.v, vec_nor(b.v,b.v))); }
 template<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>*     from) {  return pset1<Packet1cd>(*from); }
+template<> EIGEN_STRONG_INLINE Packet1cd pcmp_eq(const Packet1cd& a, const Packet1cd& b) {
+  Packet2d eq = vec_cmpeq (a.v, b.v);
+  Packet2d tmp = { eq[1], eq[0] };
+  return (Packet1cd)pand<Packet2d>(eq, tmp);
+}
 
 template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> *   addr) { EIGEN_ZVECTOR_PREFETCH(addr); }
 
@@ -281,6 +286,17 @@
 
 
 #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ < 12)
+
+template<> EIGEN_STRONG_INLINE Packet2cf pcmp_eq(const Packet2cf& a, const Packet2cf& b) {
+  Packet4f eq = pcmp_eq<Packet4f> (a.v, b.v);
+  Packet2cf res;
+  Packet2d tmp1 = { eq.v4f[0][1], eq.v4f[0][0] };
+  Packet2d tmp2 = { eq.v4f[1][1], eq.v4f[1][0] };
+  res.v.v4f[0] = pand<Packet2d>(eq.v4f[0], tmp1);
+  res.v.v4f[1] = pand<Packet2d>(eq.v4f[1], tmp2);
+  return res;
+}
+
 template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a)
 {
   Packet2cf res;
@@ -387,6 +403,11 @@
   return result;
 }
 #else
+template<> EIGEN_STRONG_INLINE Packet2cf pcmp_eq(const Packet2cf& a, const Packet2cf& b) {
+  Packet4f eq = vec_cmpeq (a.v, b.v);
+  Packet4f tmp = { eq[1], eq[0], eq[3], eq[2] };
+  return (Packet2cf)pand<Packet4f>(eq, tmp);
+}
 template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a) { return Packet2cf(pxor<Packet4f>(a.v, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR))); }
 template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
 {
diff --git a/Eigen/src/Core/arch/ZVector/MathFunctions.h b/Eigen/src/Core/arch/ZVector/MathFunctions.h
index 689ecc7..1635e12 100644
--- a/Eigen/src/Core/arch/ZVector/MathFunctions.h
+++ b/Eigen/src/Core/arch/ZVector/MathFunctions.h
@@ -140,7 +140,6 @@
 Packet4f pexp<Packet4f>(const Packet4f& _x)
 {
 #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
-/*
   Packet4f x = _x;
 
   Packet4f tmp, fx;
@@ -171,16 +170,11 @@
   y = padd(y, p4f_1);
 
   // build 2^n
-  emm0 = vec_cts(fx, 0);
+  emm0 = (Packet4i){ (int)fx[0], (int)fx[1], (int)fx[2], (int)fx[3] };
   emm0 = emm0 + p4i_0x7f;
   emm0 = emm0 << reinterpret_cast<Packet4i>(p4i_23);
 
-  // Altivec's max & min operators just drop silent NaNs. Check NaNs in 
-  // inputs and return them unmodified.
-  Packet4ui isnumber_mask = reinterpret_cast<Packet4ui>(vec_cmpeq(_x, _x));
-  return vec_sel(_x, pmax(pmul(y, reinterpret_cast<Packet4f>(emm0)), _x),
-                 isnumber_mask);*/
-  return _x;
+  return pmax(pmul(y, reinterpret_cast<Packet4f>(emm0)), _x);
 #else
   Packet4f res;
   res.v4f[0] = pexp<Packet2d>(_x.v4f[0]);
diff --git a/Eigen/src/Core/arch/ZVector/PacketMath.h b/Eigen/src/Core/arch/ZVector/PacketMath.h
index 3fb642a..eb378a1 100755
--- a/Eigen/src/Core/arch/ZVector/PacketMath.h
+++ b/Eigen/src/Core/arch/ZVector/PacketMath.h
@@ -193,11 +193,7 @@
     HasSin = 0,
     HasCos = 0,
     HasLog = 0,
-#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
-    HasExp = 0,
-#else
     HasExp = 1,
-#endif
     HasSqrt = 1,
     HasRsqrt = 1,
     HasTanh = 1,
@@ -741,16 +737,16 @@
 template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b)
 {
   Packet4f res;
-  res.v4f[0] = pand(a.v4f[0], b.v4f[0]);
-  res.v4f[1] = pand(a.v4f[1], b.v4f[1]);
+  res.v4f[0] = por(a.v4f[0], b.v4f[0]);
+  res.v4f[1] = por(a.v4f[1], b.v4f[1]);
   return res;
 }
 
 template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b)
 {
   Packet4f res;
-  res.v4f[0] = pand(a.v4f[0], b.v4f[0]);
-  res.v4f[1] = pand(a.v4f[1], b.v4f[1]);
+  res.v4f[0] = pxor(a.v4f[0], b.v4f[0]);
+  res.v4f[1] = pxor(a.v4f[1], b.v4f[1]);
   return res;
 }
 
@@ -890,6 +886,31 @@
   result.v4f[1] = vec_sel(elsePacket.v4f[1], thenPacket.v4f[1], mask_lo);
   return result;
 }
+
+template<> Packet4f EIGEN_STRONG_INLINE pcmp_le<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+  Packet4f res;
+  res.v4f[0] = pcmp_le(a.v4f[0], b.v4f[0]);
+  res.v4f[1] = pcmp_le(a.v4f[1], b.v4f[1]);
+  return res;
+}
+
+template<> Packet4f EIGEN_STRONG_INLINE pcmp_lt<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+  Packet4f res;
+  res.v4f[0] = pcmp_lt(a.v4f[0], b.v4f[0]);
+  res.v4f[1] = pcmp_lt(a.v4f[1], b.v4f[1]);
+  return res;
+}
+
+template<> Packet4f EIGEN_STRONG_INLINE pcmp_eq<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+  Packet4f res;
+  res.v4f[0] = pcmp_eq(a.v4f[0], b.v4f[0]);
+  res.v4f[1] = pcmp_eq(a.v4f[1], b.v4f[1]);
+  return res;
+}
+
 #else
 template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from)
 {
diff --git a/Eigen/src/Core/functors/UnaryFunctors.h b/Eigen/src/Core/functors/UnaryFunctors.h
index c7ed18c..eee6ae1 100644
--- a/Eigen/src/Core/functors/UnaryFunctors.h
+++ b/Eigen/src/Core/functors/UnaryFunctors.h
@@ -396,6 +396,22 @@
 { enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasLog10 }; };
 
 /** \internal
+  *
+  * \brief Template functor to compute the base-2 logarithm of a scalar
+  *
+  * \sa class CwiseUnaryOp, Cwise::log2()
+  */
+template<typename Scalar> struct scalar_log2_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_log2_op)
+  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return Scalar(EIGEN_LOG2E) * std::log(a); }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog2(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_log2_op<Scalar> >
+{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasLog }; };
+
+/** \internal
   * \brief Template functor to compute the square root of a scalar
   * \sa class CwiseUnaryOp, Cwise::sqrt()
   */
@@ -422,6 +438,18 @@
   };
 };
 
+// Boolean specialization to eliminate -Wimplicit-conversion-floating-point-to-bool warnings.
+template<> struct scalar_sqrt_op<bool> {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_sqrt_op)
+  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline bool operator() (const bool& a) const { return a; }
+  template <typename Packet>
+  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return a; }
+};
+template <>
+struct functor_traits<scalar_sqrt_op<bool> > {
+  enum { Cost = 1, PacketAccess = packet_traits<bool>::Vectorizable };
+};
+
 /** \internal
   * \brief Template functor to compute the reciprocal square root of a scalar
   * \sa class CwiseUnaryOp, Cwise::rsqrt()
@@ -719,6 +747,19 @@
 struct functor_traits<scalar_square_op<Scalar> >
 { enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
 
+// Boolean specialization to avoid -Wint-in-bool-context warnings on GCC.
+template<>
+struct scalar_square_op<bool> {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_square_op)
+  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline bool operator() (const bool& a) const { return a; }
+  template<typename Packet>
+  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
+  { return a; }
+};
+template<>
+struct functor_traits<scalar_square_op<bool> >
+{ enum { Cost = 0, PacketAccess = packet_traits<bool>::Vectorizable }; };
+
 /** \internal
   * \brief Template functor to compute the cube of a scalar
   * \sa class CwiseUnaryOp, Cwise::cube()
@@ -735,6 +776,19 @@
 struct functor_traits<scalar_cube_op<Scalar> >
 { enum { Cost = 2*NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
 
+// Boolean specialization to avoid -Wint-in-bool-context warnings on GCC.
+template<>
+struct scalar_cube_op<bool> {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_cube_op)
+  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline bool operator() (const bool& a) const { return a; }
+  template<typename Packet>
+  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
+  { return a; }
+};
+template<>
+struct functor_traits<scalar_cube_op<bool> >
+{ enum { Cost = 0, PacketAccess = packet_traits<bool>::Vectorizable }; };
+
 /** \internal
   * \brief Template functor to compute the rounded value of a scalar
   * \sa class CwiseUnaryOp, ArrayBase::round()
diff --git a/Eigen/src/Geometry/Scaling.h b/Eigen/src/Geometry/Scaling.h
old mode 100755
new mode 100644
index df650fd..d352f1f
--- a/Eigen/src/Geometry/Scaling.h
+++ b/Eigen/src/Geometry/Scaling.h
@@ -14,7 +14,7 @@
 
 /** \geometry_module \ingroup Geometry_Module
   *
-  * \class Scaling
+  * \class UniformScaling
   *
   * \brief Represents a generic uniform scaling transformation
   *
diff --git a/Eigen/src/SparseCore/SparseMatrix.h b/Eigen/src/SparseCore/SparseMatrix.h
index 4e639d1..6e6cab3 100644
--- a/Eigen/src/SparseCore/SparseMatrix.h
+++ b/Eigen/src/SparseCore/SparseMatrix.h
@@ -1086,7 +1086,7 @@
   * \code
     typedef Triplet<double> T;
     std::vector<T> tripletList;
-    triplets.reserve(estimation_of_entries);
+    tripletList.reserve(estimation_of_entries);
     for(...)
     {
       // ...
diff --git a/Eigen/src/StlSupport/StdDeque.h b/Eigen/src/StlSupport/StdDeque.h
index 006ac11..6d47e75 100644
--- a/Eigen/src/StlSupport/StdDeque.h
+++ b/Eigen/src/StlSupport/StdDeque.h
@@ -98,19 +98,7 @@
   { return deque_base::insert(position,x); }
   void insert(const_iterator position, size_type new_size, const value_type& x)
   { deque_base::insert(position, new_size, x); }
-#elif defined(_GLIBCXX_DEQUE) && EIGEN_GNUC_AT_LEAST(4,2) && !EIGEN_GNUC_AT_LEAST(10, 1)
-  // workaround GCC std::deque implementation
-  // GCC 10.1 doesn't let us access _Deque_impl _M_impl anymore and we have to
-  // fall-back to the default case
-  void resize(size_type new_size, const value_type& x)
-  {
-    if (new_size < deque_base::size())
-      deque_base::_M_erase_at_end(this->_M_impl._M_start + new_size);
-    else
-      deque_base::insert(deque_base::end(), new_size - deque_base::size(), x);
-  }
 #else
-  // either non-GCC or GCC between 4.1 and 10.1
   // default implementation which should always work.
   void resize(size_type new_size, const value_type& x)
   {
diff --git a/Eigen/src/plugins/ArrayCwiseUnaryOps.h b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
index 59a4ee6..b7ea22a 100644
--- a/Eigen/src/plugins/ArrayCwiseUnaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
@@ -14,6 +14,7 @@
 typedef CwiseUnaryOp<internal::scalar_log_op<Scalar>, const Derived> LogReturnType;
 typedef CwiseUnaryOp<internal::scalar_log1p_op<Scalar>, const Derived> Log1pReturnType;
 typedef CwiseUnaryOp<internal::scalar_log10_op<Scalar>, const Derived> Log10ReturnType;
+typedef CwiseUnaryOp<internal::scalar_log2_op<Scalar>, const Derived> Log2ReturnType;
 typedef CwiseUnaryOp<internal::scalar_cos_op<Scalar>, const Derived> CosReturnType;
 typedef CwiseUnaryOp<internal::scalar_sin_op<Scalar>, const Derived> SinReturnType;
 typedef CwiseUnaryOp<internal::scalar_tan_op<Scalar>, const Derived> TanReturnType;
@@ -159,6 +160,18 @@
   return Log10ReturnType(derived());
 }
 
+/** \returns an expression of the coefficient-wise base-2 logarithm of *this.
+  *
+  * This function computes the coefficient-wise base-2 logarithm.
+  *
+  */
+EIGEN_DEVICE_FUNC
+inline const Log2ReturnType
+log2() const
+{
+  return Log2ReturnType(derived());
+}
+
 /** \returns an expression of the coefficient-wise square root of *this.
   *
   * This function computes the coefficient-wise square root. The function MatrixBase::sqrt() in the
diff --git a/cmake/FindMetis.cmake b/cmake/FindMetis.cmake
index 5c9cbcb..747f882 100644
--- a/cmake/FindMetis.cmake
+++ b/cmake/FindMetis.cmake
@@ -258,7 +258,8 @@
 include(FindPackageHandleStandardArgs)
 find_package_handle_standard_args(METIS DEFAULT_MSG
   METIS_LIBRARIES
-  METIS_WORKS)
+  METIS_WORKS
+  METIS_INCLUDE_DIRS)
 #
 # TODO: Add possibility to check for specific functions in the library
 #
diff --git a/debug/msvc/eigen.natvis b/debug/msvc/eigen.natvis
index 22cf346..da89857 100644
--- a/debug/msvc/eigen.natvis
+++ b/debug/msvc/eigen.natvis
@@ -1,235 +1,235 @@
-<?xml version="1.0" encoding="utf-8"?>
-
-<AutoVisualizer xmlns="http://schemas.microsoft.com/vstudio/debugger/natvis/2010">
-
-  <!-- Fixed x Fixed Matrix -->
-  <Type Name="Eigen::Matrix&lt;*,*,*,*,*,*&gt;">      
-      <AlternativeType Name="Eigen::Array&lt;*,-1,-1,*,*,*&gt;"/>
-      <DisplayString>[{$T2}, {$T3}] (fixed matrix)</DisplayString>
-      <Expand>
-        <ArrayItems Condition="Flags%2"> <!-- row major layout -->
-          <Rank>2</Rank>
-          <Size>$i==0 ? $T2 : $T3</Size>
-          <ValuePointer>m_storage.m_data.array</ValuePointer>
-        </ArrayItems>
-        <ArrayItems Condition="!(Flags%2)"> <!-- column major layout -->
-          <Direction>Backward</Direction>
-          <Rank>2</Rank>
-          <Size>$i==0 ? $T2 : $T3</Size>
-          <ValuePointer>m_storage.m_data.array</ValuePointer>
-        </ArrayItems>
-      </Expand>
-  </Type>
-  
-  <!-- 2 x 2 Matrix -->
-  <Type Name="Eigen::Matrix&lt;*,2,2,*,*,*&gt;">      
-      <AlternativeType Name="Eigen::Array&lt;*,2,2,*,*,*&gt;"/>
-      <DisplayString>[2, 2] (fixed matrix)</DisplayString>
-      <Expand>
-        <Synthetic Name="[row 0]" Condition="Flags%2">
-          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]})</DisplayString>
-        </Synthetic>
-        <Synthetic Name="[row 0]" Condition="!(Flags%2)">
-          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[2]})</DisplayString>
-        </Synthetic>
-        <Synthetic Name="[row 1]" Condition="Flags%2">
-          <DisplayString>({m_storage.m_data.array[2]}, {m_storage.m_data.array[3]})</DisplayString>
-        </Synthetic>
-        <Synthetic Name="[row 1]" Condition="!(Flags%2)">
-          <DisplayString>({m_storage.m_data.array[1]}, {m_storage.m_data.array[3]})</DisplayString>
-        </Synthetic>        
-      </Expand>
-  </Type>
-  
-  <!-- 3 x 3 Matrix -->
-  <Type Name="Eigen::Matrix&lt;*,3,3,*,*,*&gt;">      
-      <AlternativeType Name="Eigen::Array&lt;*,3,3,*,*,*&gt;"/>
-      <DisplayString>[3, 3] (fixed matrix)</DisplayString>
-      <Expand>
-        <Synthetic Name="[row 0]" Condition="Flags%2">
-          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]}, {m_storage.m_data.array[2]})</DisplayString>
-        </Synthetic>
-        <Synthetic Name="[row 0]" Condition="!(Flags%2)">
-          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[3]}, {m_storage.m_data.array[6]})</DisplayString>
-        </Synthetic>
-        <Synthetic Name="[row 1]" Condition="Flags%2">
-          <DisplayString>({m_storage.m_data.array[3]}, {m_storage.m_data.array[4]}, {m_storage.m_data.array[5]})</DisplayString>
-        </Synthetic>
-        <Synthetic Name="[row 1]" Condition="!(Flags%2)">
-          <DisplayString>({m_storage.m_data.array[1]}, {m_storage.m_data.array[4]}, {m_storage.m_data.array[7]})</DisplayString>
-        </Synthetic>
-        <Synthetic Name="[row 2]" Condition="Flags%2">
-          <DisplayString>({m_storage.m_data.array[6]}, {m_storage.m_data.array[7]}, {m_storage.m_data.array[8]})</DisplayString>
-        </Synthetic>
-        <Synthetic Name="[row 2]" Condition="!(Flags%2)">
-          <DisplayString>({m_storage.m_data.array[2]}, {m_storage.m_data.array[5]}, {m_storage.m_data.array[8]})</DisplayString>
-        </Synthetic>        
-      </Expand>
-  </Type>
-  
-  <!-- 4 x 4 Matrix -->
-  <Type Name="Eigen::Matrix&lt;*,4,4,*,*,*&gt;">      
-      <AlternativeType Name="Eigen::Array&lt;*,4,4,*,*,*&gt;"/>
-      <DisplayString>[4, 4] (fixed matrix)</DisplayString>
-      <Expand>
-        <Synthetic Name="[row 0]" Condition="Flags%2">
-          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]}, {m_storage.m_data.array[2]}, {m_storage.m_data.array[3]})</DisplayString>
-        </Synthetic>
-        <Synthetic Name="[row 0]" Condition="!(Flags%2)">
-          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[4]}, {m_storage.m_data.array[8]}, {m_storage.m_data.array[12]})</DisplayString>
-        </Synthetic>
-        <Synthetic Name="[row 1]" Condition="Flags%2">
-          <DisplayString>({m_storage.m_data.array[4]}, {m_storage.m_data.array[5]}, {m_storage.m_data.array[6]}, {m_storage.m_data.array[7]})</DisplayString>
-        </Synthetic>
-        <Synthetic Name="[row 1]" Condition="!(Flags%2)">
-          <DisplayString>({m_storage.m_data.array[1]}, {m_storage.m_data.array[5]}, {m_storage.m_data.array[9]}, {m_storage.m_data.array[13]})</DisplayString>
-        </Synthetic>
-        <Synthetic Name="[row 2]" Condition="Flags%2">
-          <DisplayString>({m_storage.m_data.array[8]}, {m_storage.m_data.array[9]}, {m_storage.m_data.array[10]}, {m_storage.m_data.array[11]})</DisplayString>
-        </Synthetic>
-        <Synthetic Name="[row 2]" Condition="!(Flags%2)">
-          <DisplayString>({m_storage.m_data.array[2]}, {m_storage.m_data.array[6]}, {m_storage.m_data.array[10]}, {m_storage.m_data.array[14]})</DisplayString>
-        </Synthetic>
-        <Synthetic Name="[row 3]" Condition="Flags%2">
-          <DisplayString>({m_storage.m_data.array[12]}, {m_storage.m_data.array[13]}, {m_storage.m_data.array[14]}, {m_storage.m_data.array[15]})</DisplayString>
-        </Synthetic>
-        <Synthetic Name="[row 3]" Condition="!(Flags%2)">
-          <DisplayString>({m_storage.m_data.array[3]}, {m_storage.m_data.array[7]}, {m_storage.m_data.array[11]}, {m_storage.m_data.array[15]})</DisplayString>
-        </Synthetic>        
-      </Expand>
-  </Type>  
-  
-  <!-- Dynamic x Dynamic Matrix -->
-  <Type Name="Eigen::Matrix&lt;*,-1,-1,*,*,*&gt;">      
-      <AlternativeType Name="Eigen::Array&lt;*,-1,-1,*,*,*&gt;"/>
-      <DisplayString Condition="m_storage.m_data == 0">empty</DisplayString>
-      <DisplayString Condition="m_storage.m_data != 0">[{m_storage.m_rows}, {m_storage.m_cols}] (dynamic matrix)</DisplayString>
-      <Expand>
-        <ArrayItems Condition="Flags%2"> <!-- row major layout -->
-          <Rank>2</Rank>
-          <Size>$i==0 ? m_storage.m_rows : m_storage.m_cols</Size>
-          <ValuePointer>m_storage.m_data</ValuePointer>
-        </ArrayItems>
-        <ArrayItems Condition="!(Flags%2)"> <!-- column major layout -->
-          <Direction>Backward</Direction>
-          <Rank>2</Rank>
-          <Size>$i==0 ? m_storage.m_rows : m_storage.m_cols</Size>
-          <ValuePointer>m_storage.m_data</ValuePointer>
-        </ArrayItems>
-      </Expand>
-  </Type>
-  
-  <!-- Fixed x Dynamic Matrix -->
-  <Type Name="Eigen::Matrix&lt;*,*,-1,*,*,*&gt;">
-      <AlternativeType Name="Eigen::Array&lt;*,*,-1,*,*,*&gt;"/>
-      <DisplayString Condition="m_storage.m_data == 0">empty</DisplayString>
-      <DisplayString Condition="m_storage.m_data != 0">[{$T2}, {m_storage.m_cols}] (dynamic column matrix)</DisplayString>
-      <Expand>
-        <ArrayItems Condition="Flags%2"> <!-- row major layout -->
-          <Rank>2</Rank>
-          <Size>$i==0 ? $T2 : m_storage.m_cols</Size>
-          <ValuePointer>m_storage.m_data</ValuePointer>
-        </ArrayItems>
-        <ArrayItems Condition="!(Flags%2)"> <!-- column major layout -->
-          <Direction>Backward</Direction>
-          <Rank>2</Rank>
-          <Size>$i==0 ? $T2 : m_storage.m_cols</Size>
-          <ValuePointer>m_storage.m_data</ValuePointer>
-        </ArrayItems>
-      </Expand>
-  </Type>
-  
-  <!-- Dynamic x Fixed Matrix -->
-  <Type Name="Eigen::Matrix&lt;*,-1,*,*,*,*&gt;">
-      <AlternativeType Name="Eigen::Array&lt;*,-1,*,*,*,*&gt;"/>
-      <DisplayString Condition="m_storage.m_data == 0">empty</DisplayString>
-      <DisplayString Condition="m_storage.m_data != 0">[{m_storage.m_rows}, {$T2}] (dynamic row matrix)</DisplayString>
-      <Expand>
-        <ArrayItems Condition="Flags%2"> <!-- row major layout -->
-          <Rank>2</Rank>
-          <Size>$i==0 ? m_storage.m_rows : $T2</Size>
-          <ValuePointer>m_storage.m_data</ValuePointer>
-        </ArrayItems>
-        <ArrayItems Condition="!(Flags%2)"> <!-- column major layout -->
-          <Direction>Backward</Direction>
-          <Rank>2</Rank>
-          <Size>$i==0 ? m_storage.m_rows : $T2</Size>
-          <ValuePointer>m_storage.m_data</ValuePointer>
-        </ArrayItems>
-      </Expand>
-  </Type>
-  
-  <!-- Dynamic Column Vector -->
-  <Type Name="Eigen::Matrix&lt;*,1,-1,*,*,*&gt;">
-      <AlternativeType Name="Eigen::Array&lt;*,1,-1,*,*,*&gt;"/>
-      <DisplayString Condition="m_storage.m_data == 0">empty</DisplayString>
-      <DisplayString Condition="m_storage.m_data != 0">[{m_storage.m_cols}] (dynamic column vector)</DisplayString>
-      <Expand>
-        <Item Name="[size]">m_storage.m_cols</Item>
-        <ArrayItems>
-          <Size>m_storage.m_cols</Size>
-          <ValuePointer>m_storage.m_data</ValuePointer>
-        </ArrayItems>
-      </Expand>
-  </Type>
-  
-  <!-- Dynamic Row Vector -->
-  <Type Name="Eigen::Matrix&lt;*,-1,1,*,*,*&gt;">
-      <AlternativeType Name="Eigen::Array&lt;*,-1,1,*,*,*&gt;"/>
-      <DisplayString Condition="m_storage.m_data == 0">empty</DisplayString>
-      <DisplayString Condition="m_storage.m_data != 0">[{m_storage.m_rows}] (dynamic row vector)</DisplayString>
-      <Expand>
-        <Item Name="[size]">m_storage.m_rows</Item>
-        <ArrayItems>
-          <Size>m_storage.m_rows</Size>
-          <ValuePointer>m_storage.m_data</ValuePointer>
-        </ArrayItems>
-      </Expand>
-  </Type>
-  
-  <!-- Fixed Vector -->
-  <Type Name="Eigen::Matrix&lt;*,1,1,*,*,*&gt;">
-      <AlternativeType Name="Eigen::Array&lt;*,1,1,*,*,*&gt;"/>
-      <DisplayString>[1] ({m_storage.m_data.array[0]})</DisplayString>
-      <Expand>
-        <Item Name="[x]">m_storage.m_data.array[0]</Item>
-      </Expand>
-  </Type>
-  
-  <Type Name="Eigen::Matrix&lt;*,2,1,*,*,*&gt;">
-      <AlternativeType Name="Eigen::Matrix&lt;*,1,2,*,*,*&gt;"/>
-      <AlternativeType Name="Eigen::Array&lt;*,2,1,*,*,*&gt;"/>
-      <AlternativeType Name="Eigen::Array&lt;*,1,2,*,*,*&gt;"/>
-      <DisplayString>[2] ({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]})</DisplayString>
-      <Expand>
-        <Item Name="[x]">m_storage.m_data.array[0]</Item>
-        <Item Name="[y]">m_storage.m_data.array[1]</Item>
-      </Expand>
-  </Type>
-  
-  <Type Name="Eigen::Matrix&lt;*,3,1,*,*,*&gt;">
-      <AlternativeType Name="Eigen::Matrix&lt;*,1,3,*,*,*&gt;"/>
-      <AlternativeType Name="Eigen::Array&lt;*,3,1,*,*,*&gt;"/>
-      <AlternativeType Name="Eigen::Array&lt;*,1,3,*,*,*&gt;"/>
-      <DisplayString>[3] ({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]}, {m_storage.m_data.array[2]})</DisplayString>
-      <Expand>
-        <Item Name="[x]">m_storage.m_data.array[0]</Item>
-        <Item Name="[y]">m_storage.m_data.array[1]</Item>
-        <Item Name="[z]">m_storage.m_data.array[2]</Item>
-      </Expand>
-  </Type>
-  
-    <Type Name="Eigen::Matrix&lt;*,4,1,*,*,*&gt;">
-      <AlternativeType Name="Eigen::Matrix&lt;*,1,4,*,*,*&gt;"/>
-      <AlternativeType Name="Eigen::Array&lt;*,4,1,*,*,*&gt;"/>
-      <AlternativeType Name="Eigen::Array&lt;*,1,4,*,*,*&gt;"/>
-      <DisplayString>[4] ({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]}, {m_storage.m_data.array[2]}, {m_storage.m_data.array[3]})</DisplayString>
-      <Expand>
-        <Item Name="[x]">m_storage.m_data.array[0]</Item>
-        <Item Name="[y]">m_storage.m_data.array[1]</Item>
-        <Item Name="[z]">m_storage.m_data.array[2]</Item>
-        <Item Name="[w]">m_storage.m_data.array[3]</Item>
-      </Expand>
-  </Type>
-
-</AutoVisualizer>
+<?xml version="1.0" encoding="utf-8"?>
+
+<AutoVisualizer xmlns="http://schemas.microsoft.com/vstudio/debugger/natvis/2010">
+
+  <!-- Fixed x Fixed Matrix -->
+  <Type Name="Eigen::Matrix&lt;*,*,*,*,*,*&gt;">      
+      <AlternativeType Name="Eigen::Array&lt;*,-1,-1,*,*,*&gt;"/>
+      <DisplayString>[{$T2}, {$T3}] (fixed matrix)</DisplayString>
+      <Expand>
+        <ArrayItems Condition="Flags%2"> <!-- row major layout -->
+          <Rank>2</Rank>
+          <Size>$i==0 ? $T2 : $T3</Size>
+          <ValuePointer>m_storage.m_data.array</ValuePointer>
+        </ArrayItems>
+        <ArrayItems Condition="!(Flags%2)"> <!-- column major layout -->
+          <Direction>Backward</Direction>
+          <Rank>2</Rank>
+          <Size>$i==0 ? $T2 : $T3</Size>
+          <ValuePointer>m_storage.m_data.array</ValuePointer>
+        </ArrayItems>
+      </Expand>
+  </Type>
+  
+  <!-- 2 x 2 Matrix -->
+  <Type Name="Eigen::Matrix&lt;*,2,2,*,*,*&gt;">      
+      <AlternativeType Name="Eigen::Array&lt;*,2,2,*,*,*&gt;"/>
+      <DisplayString>[2, 2] (fixed matrix)</DisplayString>
+      <Expand>
+        <Synthetic Name="[row 0]" Condition="Flags%2">
+          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]})</DisplayString>
+        </Synthetic>
+        <Synthetic Name="[row 0]" Condition="!(Flags%2)">
+          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[2]})</DisplayString>
+        </Synthetic>
+        <Synthetic Name="[row 1]" Condition="Flags%2">
+          <DisplayString>({m_storage.m_data.array[2]}, {m_storage.m_data.array[3]})</DisplayString>
+        </Synthetic>
+        <Synthetic Name="[row 1]" Condition="!(Flags%2)">
+          <DisplayString>({m_storage.m_data.array[1]}, {m_storage.m_data.array[3]})</DisplayString>
+        </Synthetic>        
+      </Expand>
+  </Type>
+  
+  <!-- 3 x 3 Matrix -->
+  <Type Name="Eigen::Matrix&lt;*,3,3,*,*,*&gt;">      
+      <AlternativeType Name="Eigen::Array&lt;*,3,3,*,*,*&gt;"/>
+      <DisplayString>[3, 3] (fixed matrix)</DisplayString>
+      <Expand>
+        <Synthetic Name="[row 0]" Condition="Flags%2">
+          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]}, {m_storage.m_data.array[2]})</DisplayString>
+        </Synthetic>
+        <Synthetic Name="[row 0]" Condition="!(Flags%2)">
+          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[3]}, {m_storage.m_data.array[6]})</DisplayString>
+        </Synthetic>
+        <Synthetic Name="[row 1]" Condition="Flags%2">
+          <DisplayString>({m_storage.m_data.array[3]}, {m_storage.m_data.array[4]}, {m_storage.m_data.array[5]})</DisplayString>
+        </Synthetic>
+        <Synthetic Name="[row 1]" Condition="!(Flags%2)">
+          <DisplayString>({m_storage.m_data.array[1]}, {m_storage.m_data.array[4]}, {m_storage.m_data.array[7]})</DisplayString>
+        </Synthetic>
+        <Synthetic Name="[row 2]" Condition="Flags%2">
+          <DisplayString>({m_storage.m_data.array[6]}, {m_storage.m_data.array[7]}, {m_storage.m_data.array[8]})</DisplayString>
+        </Synthetic>
+        <Synthetic Name="[row 2]" Condition="!(Flags%2)">
+          <DisplayString>({m_storage.m_data.array[2]}, {m_storage.m_data.array[5]}, {m_storage.m_data.array[8]})</DisplayString>
+        </Synthetic>        
+      </Expand>
+  </Type>
+  
+  <!-- 4 x 4 Matrix -->
+  <Type Name="Eigen::Matrix&lt;*,4,4,*,*,*&gt;">      
+      <AlternativeType Name="Eigen::Array&lt;*,4,4,*,*,*&gt;"/>
+      <DisplayString>[4, 4] (fixed matrix)</DisplayString>
+      <Expand>
+        <Synthetic Name="[row 0]" Condition="Flags%2">
+          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]}, {m_storage.m_data.array[2]}, {m_storage.m_data.array[3]})</DisplayString>
+        </Synthetic>
+        <Synthetic Name="[row 0]" Condition="!(Flags%2)">
+          <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[4]}, {m_storage.m_data.array[8]}, {m_storage.m_data.array[12]})</DisplayString>
+        </Synthetic>
+        <Synthetic Name="[row 1]" Condition="Flags%2">
+          <DisplayString>({m_storage.m_data.array[4]}, {m_storage.m_data.array[5]}, {m_storage.m_data.array[6]}, {m_storage.m_data.array[7]})</DisplayString>
+        </Synthetic>
+        <Synthetic Name="[row 1]" Condition="!(Flags%2)">
+          <DisplayString>({m_storage.m_data.array[1]}, {m_storage.m_data.array[5]}, {m_storage.m_data.array[9]}, {m_storage.m_data.array[13]})</DisplayString>
+        </Synthetic>
+        <Synthetic Name="[row 2]" Condition="Flags%2">
+          <DisplayString>({m_storage.m_data.array[8]}, {m_storage.m_data.array[9]}, {m_storage.m_data.array[10]}, {m_storage.m_data.array[11]})</DisplayString>
+        </Synthetic>
+        <Synthetic Name="[row 2]" Condition="!(Flags%2)">
+          <DisplayString>({m_storage.m_data.array[2]}, {m_storage.m_data.array[6]}, {m_storage.m_data.array[10]}, {m_storage.m_data.array[14]})</DisplayString>
+        </Synthetic>
+        <Synthetic Name="[row 3]" Condition="Flags%2">
+          <DisplayString>({m_storage.m_data.array[12]}, {m_storage.m_data.array[13]}, {m_storage.m_data.array[14]}, {m_storage.m_data.array[15]})</DisplayString>
+        </Synthetic>
+        <Synthetic Name="[row 3]" Condition="!(Flags%2)">
+          <DisplayString>({m_storage.m_data.array[3]}, {m_storage.m_data.array[7]}, {m_storage.m_data.array[11]}, {m_storage.m_data.array[15]})</DisplayString>
+        </Synthetic>        
+      </Expand>
+  </Type>  
+  
+  <!-- Dynamic x Dynamic Matrix -->
+  <Type Name="Eigen::Matrix&lt;*,-1,-1,*,*,*&gt;">      
+      <AlternativeType Name="Eigen::Array&lt;*,-1,-1,*,*,*&gt;"/>
+      <DisplayString Condition="m_storage.m_data == 0">empty</DisplayString>
+      <DisplayString Condition="m_storage.m_data != 0">[{m_storage.m_rows}, {m_storage.m_cols}] (dynamic matrix)</DisplayString>
+      <Expand>
+        <ArrayItems Condition="Flags%2"> <!-- row major layout -->
+          <Rank>2</Rank>
+          <Size>$i==0 ? m_storage.m_rows : m_storage.m_cols</Size>
+          <ValuePointer>m_storage.m_data</ValuePointer>
+        </ArrayItems>
+        <ArrayItems Condition="!(Flags%2)"> <!-- column major layout -->
+          <Direction>Backward</Direction>
+          <Rank>2</Rank>
+          <Size>$i==0 ? m_storage.m_rows : m_storage.m_cols</Size>
+          <ValuePointer>m_storage.m_data</ValuePointer>
+        </ArrayItems>
+      </Expand>
+  </Type>
+  
+  <!-- Fixed x Dynamic Matrix -->
+  <Type Name="Eigen::Matrix&lt;*,*,-1,*,*,*&gt;">
+      <AlternativeType Name="Eigen::Array&lt;*,*,-1,*,*,*&gt;"/>
+      <DisplayString Condition="m_storage.m_data == 0">empty</DisplayString>
+      <DisplayString Condition="m_storage.m_data != 0">[{$T2}, {m_storage.m_cols}] (dynamic column matrix)</DisplayString>
+      <Expand>
+        <ArrayItems Condition="Flags%2"> <!-- row major layout -->
+          <Rank>2</Rank>
+          <Size>$i==0 ? $T2 : m_storage.m_cols</Size>
+          <ValuePointer>m_storage.m_data</ValuePointer>
+        </ArrayItems>
+        <ArrayItems Condition="!(Flags%2)"> <!-- column major layout -->
+          <Direction>Backward</Direction>
+          <Rank>2</Rank>
+          <Size>$i==0 ? $T2 : m_storage.m_cols</Size>
+          <ValuePointer>m_storage.m_data</ValuePointer>
+        </ArrayItems>
+      </Expand>
+  </Type>
+  
+  <!-- Dynamic x Fixed Matrix -->
+  <Type Name="Eigen::Matrix&lt;*,-1,*,*,*,*&gt;">
+      <AlternativeType Name="Eigen::Array&lt;*,-1,*,*,*,*&gt;"/>
+      <DisplayString Condition="m_storage.m_data == 0">empty</DisplayString>
+      <DisplayString Condition="m_storage.m_data != 0">[{m_storage.m_rows}, {$T2}] (dynamic row matrix)</DisplayString>
+      <Expand>
+        <ArrayItems Condition="Flags%2"> <!-- row major layout -->
+          <Rank>2</Rank>
+          <Size>$i==0 ? m_storage.m_rows : $T2</Size>
+          <ValuePointer>m_storage.m_data</ValuePointer>
+        </ArrayItems>
+        <ArrayItems Condition="!(Flags%2)"> <!-- column major layout -->
+          <Direction>Backward</Direction>
+          <Rank>2</Rank>
+          <Size>$i==0 ? m_storage.m_rows : $T2</Size>
+          <ValuePointer>m_storage.m_data</ValuePointer>
+        </ArrayItems>
+      </Expand>
+  </Type>
+  
+  <!-- Dynamic Column Vector -->
+  <Type Name="Eigen::Matrix&lt;*,1,-1,*,*,*&gt;">
+      <AlternativeType Name="Eigen::Array&lt;*,1,-1,*,*,*&gt;"/>
+      <DisplayString Condition="m_storage.m_data == 0">empty</DisplayString>
+      <DisplayString Condition="m_storage.m_data != 0">[{m_storage.m_cols}] (dynamic column vector)</DisplayString>
+      <Expand>
+        <Item Name="[size]">m_storage.m_cols</Item>
+        <ArrayItems>
+          <Size>m_storage.m_cols</Size>
+          <ValuePointer>m_storage.m_data</ValuePointer>
+        </ArrayItems>
+      </Expand>
+  </Type>
+  
+  <!-- Dynamic Row Vector -->
+  <Type Name="Eigen::Matrix&lt;*,-1,1,*,*,*&gt;">
+      <AlternativeType Name="Eigen::Array&lt;*,-1,1,*,*,*&gt;"/>
+      <DisplayString Condition="m_storage.m_data == 0">empty</DisplayString>
+      <DisplayString Condition="m_storage.m_data != 0">[{m_storage.m_rows}] (dynamic row vector)</DisplayString>
+      <Expand>
+        <Item Name="[size]">m_storage.m_rows</Item>
+        <ArrayItems>
+          <Size>m_storage.m_rows</Size>
+          <ValuePointer>m_storage.m_data</ValuePointer>
+        </ArrayItems>
+      </Expand>
+  </Type>
+  
+  <!-- Fixed Vector -->
+  <Type Name="Eigen::Matrix&lt;*,1,1,*,*,*&gt;">
+      <AlternativeType Name="Eigen::Array&lt;*,1,1,*,*,*&gt;"/>
+      <DisplayString>[1] ({m_storage.m_data.array[0]})</DisplayString>
+      <Expand>
+        <Item Name="[x]">m_storage.m_data.array[0]</Item>
+      </Expand>
+  </Type>
+  
+  <Type Name="Eigen::Matrix&lt;*,2,1,*,*,*&gt;">
+      <AlternativeType Name="Eigen::Matrix&lt;*,1,2,*,*,*&gt;"/>
+      <AlternativeType Name="Eigen::Array&lt;*,2,1,*,*,*&gt;"/>
+      <AlternativeType Name="Eigen::Array&lt;*,1,2,*,*,*&gt;"/>
+      <DisplayString>[2] ({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]})</DisplayString>
+      <Expand>
+        <Item Name="[x]">m_storage.m_data.array[0]</Item>
+        <Item Name="[y]">m_storage.m_data.array[1]</Item>
+      </Expand>
+  </Type>
+  
+  <Type Name="Eigen::Matrix&lt;*,3,1,*,*,*&gt;">
+      <AlternativeType Name="Eigen::Matrix&lt;*,1,3,*,*,*&gt;"/>
+      <AlternativeType Name="Eigen::Array&lt;*,3,1,*,*,*&gt;"/>
+      <AlternativeType Name="Eigen::Array&lt;*,1,3,*,*,*&gt;"/>
+      <DisplayString>[3] ({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]}, {m_storage.m_data.array[2]})</DisplayString>
+      <Expand>
+        <Item Name="[x]">m_storage.m_data.array[0]</Item>
+        <Item Name="[y]">m_storage.m_data.array[1]</Item>
+        <Item Name="[z]">m_storage.m_data.array[2]</Item>
+      </Expand>
+  </Type>
+  
+    <Type Name="Eigen::Matrix&lt;*,4,1,*,*,*&gt;">
+      <AlternativeType Name="Eigen::Matrix&lt;*,1,4,*,*,*&gt;"/>
+      <AlternativeType Name="Eigen::Array&lt;*,4,1,*,*,*&gt;"/>
+      <AlternativeType Name="Eigen::Array&lt;*,1,4,*,*,*&gt;"/>
+      <DisplayString>[4] ({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]}, {m_storage.m_data.array[2]}, {m_storage.m_data.array[3]})</DisplayString>
+      <Expand>
+        <Item Name="[x]">m_storage.m_data.array[0]</Item>
+        <Item Name="[y]">m_storage.m_data.array[1]</Item>
+        <Item Name="[z]">m_storage.m_data.array[2]</Item>
+        <Item Name="[w]">m_storage.m_data.array[3]</Item>
+      </Expand>
+  </Type>
+
+</AutoVisualizer>
diff --git a/debug/msvc/eigen_autoexp_part.dat b/debug/msvc/eigen_autoexp_part.dat
index 273c10d..35ef580 100644
--- a/debug/msvc/eigen_autoexp_part.dat
+++ b/debug/msvc/eigen_autoexp_part.dat
@@ -1,295 +1,295 @@
-; ***************************************************************
-; * Eigen Visualizer
-; *
-; * Author: Hauke Heibel <hauke.heibel@gmail.com>
-; *
-; * Support the enhanced debugging of the following Eigen
-; * types (*: any, +:fixed dimension) :
-; *
-; * - Eigen::Matrix<*,4,1,*,*,*> and Eigen::Matrix<*,1,4,*,*,*>
-; * - Eigen::Matrix<*,3,1,*,*,*> and Eigen::Matrix<*,1,3,*,*,*>
-; * - Eigen::Matrix<*,2,1,*,*,*> and Eigen::Matrix<*,1,2,*,*,*>
-; * - Eigen::Matrix<*,-1,-1,*,*,*>
-; * - Eigen::Matrix<*,+,-1,*,*,*>
-; * - Eigen::Matrix<*,-1,+,*,*,*>
-; * - Eigen::Matrix<*,+,+,*,*,*>
-; *
-; * Matrices are displayed properly independently of the memory
-; * alignment (RowMajor vs. ColMajor).
-; *
-; * This file is distributed WITHOUT ANY WARRANTY. Please ensure
-; * that your original autoexp.dat file is copied to a safe 
-; * place before proceeding with its modification.
-; ***************************************************************
-
-[Visualizer]
-
-; Fixed size 4-vectors
-Eigen::Matrix<*,4,1,*,*,*>|Eigen::Matrix<*,1,4,*,*,*>{
-   children
-   (
-      #(
-        [internals]: [$c,!],
-         x : ($c.m_storage.m_data.array)[0],
-         y : ($c.m_storage.m_data.array)[1],
-         z : ($c.m_storage.m_data.array)[2],
-         w : ($c.m_storage.m_data.array)[3]
-      )
-   )
-
-   preview
-   (
-      #(
-        "[",
-        4,
-        "](",
-        #array(expr: $e.m_storage.m_data.array[$i], size: 4),
-        ")"
-      )
-   )
-}
-
-; Fixed size 3-vectors
-Eigen::Matrix<*,3,1,*,*,*>|Eigen::Matrix<*,1,3,*,*,*>{
-   children
-   (
-      #(
-        [internals]: [$c,!],
-         x : ($c.m_storage.m_data.array)[0],
-         y : ($c.m_storage.m_data.array)[1],
-         z : ($c.m_storage.m_data.array)[2]
-      )
-   )
-
-   preview
-   (
-      #(
-        "[",
-        3,
-        "](",
-        #array(expr: $e.m_storage.m_data.array[$i], size: 3),
-        ")"
-      )
-   )
-}
-
-; Fixed size 2-vectors
-Eigen::Matrix<*,2,1,*,*,*>|Eigen::Matrix<*,1,2,*,*,*>{
-   children
-   (
-      #(
-        [internals]: [$c,!],
-         x : ($c.m_storage.m_data.array)[0],
-         y : ($c.m_storage.m_data.array)[1]
-      )
-   )
-
-   preview
-   (
-      #(
-        "[",
-        2,
-        "](",
-        #array(expr: $e.m_storage.m_data.array[$i], size: 2),
-        ")"
-      )
-   )
-}
-
-; Fixed size 1-vectors
-Eigen::Matrix<*,1,1,*,*,*>|Eigen::Matrix<*,1,1,*,*,*>{
-   children
-   (
-      #(
-        [internals]: [$c,!],
-         x : ($c.m_storage.m_data.array)[0]
-      )
-   )
-
-   preview
-   (
-      #(
-        "[",
-        1,
-        "](",
-        #array(expr: $e.m_storage.m_data.array[$i], size: 1),
-        ")"
-      )
-   )
-}
-
-; Dynamic matrices (ColMajor and RowMajor support)
-Eigen::Matrix<*,-1,-1,*,*,*>{
-  children
-   (
-      #(
-         [internals]: [$c,!],
-         rows: $c.m_storage.m_rows,
-         cols: $c.m_storage.m_cols,
-         ; Check for RowMajorBit
-         #if ($c.Flags & 0x1) (
-             #array(
-                rank: 2,
-                base: 0,
-                expr: ($c.m_storage.m_data)[($i % $c.m_storage.m_rows)*$c.m_storage.m_cols + (($i- $i % $c.m_storage.m_rows)/$c.m_storage.m_rows)], 
-                size: ($r==1)*$c.m_storage.m_rows+($r==0)*$c.m_storage.m_cols
-             )
-         ) #else (
-             #array(
-                rank: 2,
-                base: 0,
-                expr: ($c.m_storage.m_data)[$i],
-                size: ($r==1)*$c.m_storage.m_rows+($r==0)*$c.m_storage.m_cols
-             )
-         )
-      )
-   )
-
-   preview
-   (
-     #(
-         "[",
-           $c.m_storage.m_rows,
-         ",",
-           $c.m_storage.m_cols,
-         "](",
-           #array(
-            expr :    [($c.m_storage.m_data)[$i],g],
-            size :    $c.m_storage.m_rows*$c.m_storage.m_cols
-           ),
-         ")"
-      )
-   )
-}
-
-; Fixed rows, dynamic columns matrix (ColMajor and RowMajor support)
-Eigen::Matrix<*,*,-1,*,*,*>{
-  children
-   (
-      #(
-         [internals]: [$c,!],
-         rows: $c.RowsAtCompileTime,
-         cols: $c.m_storage.m_cols,
-         ; Check for RowMajorBit
-         #if ($c.Flags & 0x1) (
-             #array(
-                rank: 2,
-                base: 0,
-                expr: ($c.m_storage.m_data)[($i % $c.RowsAtCompileTime)*$c.m_storage.m_cols + (($i- $i % $c.RowsAtCompileTime)/$c.RowsAtCompileTime)],
-                size: ($r==1)*$c.RowsAtCompileTime+($r==0)*$c.m_storage.m_cols
-             )
-         ) #else (
-             #array(
-                rank: 2,
-                base: 0,
-                expr: ($c.m_storage.m_data)[$i],
-                size: ($r==1)*$c.RowsAtCompileTime+($r==0)*$c.m_storage.m_cols
-             )
-         )
-      )
-   )
-
-   preview
-   (
-     #(
-         "[",
-           $c.RowsAtCompileTime,
-         ",",
-           $c.m_storage.m_cols,
-         "](",
-           #array(
-            expr :    [($c.m_storage.m_data)[$i],g],
-            size :    $c.RowsAtCompileTime*$c.m_storage.m_cols
-           ),
-         ")"
-      )
-   )
-}
-
-; Dynamic rows, fixed columns matrix (ColMajor and RowMajor support)
-Eigen::Matrix<*,-1,*,*,*,*>{
-  children
-   (
-      #(
-         [internals]: [$c,!],
-         rows: $c.m_storage.m_rows,
-         cols: $c.ColsAtCompileTime,
-         ; Check for RowMajorBit
-         #if ($c.Flags & 0x1) (
-             #array(
-                rank: 2,
-                base: 0,
-                expr: ($c.m_storage.m_data)[($i % $c.m_storage.m_rows)*$c.ColsAtCompileTime + (($i- $i % $c.m_storage.m_rows)/$c.m_storage.m_rows)], 
-                size: ($r==1)*$c.m_storage.m_rows+($r==0)*$c.ColsAtCompileTime
-             )
-         ) #else (
-             #array(
-                rank: 2,
-                base: 0,
-                expr: ($c.m_storage.m_data)[$i],
-                size: ($r==1)*$c.m_storage.m_rows+($r==0)*$c.ColsAtCompileTime
-             )
-         )
-      )
-   )
-
-   preview
-   (
-     #(
-         "[",
-           $c.m_storage.m_rows,
-         ",",
-           $c.ColsAtCompileTime,
-         "](",
-           #array(
-            expr :    [($c.m_storage.m_data)[$i],g],
-            size :    $c.m_storage.m_rows*$c.ColsAtCompileTime
-           ),
-         ")"
-      )
-   )
-}
-
-; Fixed size matrix (ColMajor and RowMajor support)
-Eigen::Matrix<*,*,*,*,*,*>{
-  children
-   (
-      #(
-         [internals]: [$c,!],
-         rows: $c.RowsAtCompileTime,
-         cols: $c.ColsAtCompileTime,
-         ; Check for RowMajorBit
-         #if ($c.Flags & 0x1) (
-             #array(
-                rank: 2,
-                base: 0,
-                expr: ($c.m_storage.m_data.array)[($i % $c.RowsAtCompileTime)*$c.ColsAtCompileTime + (($i- $i % $c.RowsAtCompileTime)/$c.RowsAtCompileTime)], 
-                size: ($r==1)*$c.RowsAtCompileTime+($r==0)*$c.ColsAtCompileTime
-             )
-         ) #else (
-             #array(
-                rank: 2,
-                base: 0,
-                expr: ($c.m_storage.m_data.array)[$i],
-                size: ($r==1)*$c.RowsAtCompileTime+($r==0)*$c.ColsAtCompileTime
-             )
-         )
-      )
-   )
-
-   preview
-   (
-     #(
-         "[",
-           $c.RowsAtCompileTime,
-         ",",
-           $c.ColsAtCompileTime,
-         "](",
-           #array(
-            expr :    [($c.m_storage.m_data.array)[$i],g],
-            size :    $c.RowsAtCompileTime*$c.ColsAtCompileTime
-           ),
-         ")"
-      )
-   )
-}
+; ***************************************************************
+; * Eigen Visualizer
+; *
+; * Author: Hauke Heibel <hauke.heibel@gmail.com>
+; *
+; * Support the enhanced debugging of the following Eigen
+; * types (*: any, +:fixed dimension) :
+; *
+; * - Eigen::Matrix<*,4,1,*,*,*> and Eigen::Matrix<*,1,4,*,*,*>
+; * - Eigen::Matrix<*,3,1,*,*,*> and Eigen::Matrix<*,1,3,*,*,*>
+; * - Eigen::Matrix<*,2,1,*,*,*> and Eigen::Matrix<*,1,2,*,*,*>
+; * - Eigen::Matrix<*,-1,-1,*,*,*>
+; * - Eigen::Matrix<*,+,-1,*,*,*>
+; * - Eigen::Matrix<*,-1,+,*,*,*>
+; * - Eigen::Matrix<*,+,+,*,*,*>
+; *
+; * Matrices are displayed properly independently of the memory
+; * alignment (RowMajor vs. ColMajor).
+; *
+; * This file is distributed WITHOUT ANY WARRANTY. Please ensure
+; * that your original autoexp.dat file is copied to a safe 
+; * place before proceeding with its modification.
+; ***************************************************************
+
+[Visualizer]
+
+; Fixed size 4-vectors
+Eigen::Matrix<*,4,1,*,*,*>|Eigen::Matrix<*,1,4,*,*,*>{
+   children
+   (
+      #(
+        [internals]: [$c,!],
+         x : ($c.m_storage.m_data.array)[0],
+         y : ($c.m_storage.m_data.array)[1],
+         z : ($c.m_storage.m_data.array)[2],
+         w : ($c.m_storage.m_data.array)[3]
+      )
+   )
+
+   preview
+   (
+      #(
+        "[",
+        4,
+        "](",
+        #array(expr: $e.m_storage.m_data.array[$i], size: 4),
+        ")"
+      )
+   )
+}
+
+; Fixed size 3-vectors
+Eigen::Matrix<*,3,1,*,*,*>|Eigen::Matrix<*,1,3,*,*,*>{
+   children
+   (
+      #(
+        [internals]: [$c,!],
+         x : ($c.m_storage.m_data.array)[0],
+         y : ($c.m_storage.m_data.array)[1],
+         z : ($c.m_storage.m_data.array)[2]
+      )
+   )
+
+   preview
+   (
+      #(
+        "[",
+        3,
+        "](",
+        #array(expr: $e.m_storage.m_data.array[$i], size: 3),
+        ")"
+      )
+   )
+}
+
+; Fixed size 2-vectors
+Eigen::Matrix<*,2,1,*,*,*>|Eigen::Matrix<*,1,2,*,*,*>{
+   children
+   (
+      #(
+        [internals]: [$c,!],
+         x : ($c.m_storage.m_data.array)[0],
+         y : ($c.m_storage.m_data.array)[1]
+      )
+   )
+
+   preview
+   (
+      #(
+        "[",
+        2,
+        "](",
+        #array(expr: $e.m_storage.m_data.array[$i], size: 2),
+        ")"
+      )
+   )
+}
+
+; Fixed size 1-vectors
+Eigen::Matrix<*,1,1,*,*,*>|Eigen::Matrix<*,1,1,*,*,*>{
+   children
+   (
+      #(
+        [internals]: [$c,!],
+         x : ($c.m_storage.m_data.array)[0]
+      )
+   )
+
+   preview
+   (
+      #(
+        "[",
+        1,
+        "](",
+        #array(expr: $e.m_storage.m_data.array[$i], size: 1),
+        ")"
+      )
+   )
+}
+
+; Dynamic matrices (ColMajor and RowMajor support)
+Eigen::Matrix<*,-1,-1,*,*,*>{
+  children
+   (
+      #(
+         [internals]: [$c,!],
+         rows: $c.m_storage.m_rows,
+         cols: $c.m_storage.m_cols,
+         ; Check for RowMajorBit
+         #if ($c.Flags & 0x1) (
+             #array(
+                rank: 2,
+                base: 0,
+                expr: ($c.m_storage.m_data)[($i % $c.m_storage.m_rows)*$c.m_storage.m_cols + (($i- $i % $c.m_storage.m_rows)/$c.m_storage.m_rows)], 
+                size: ($r==1)*$c.m_storage.m_rows+($r==0)*$c.m_storage.m_cols
+             )
+         ) #else (
+             #array(
+                rank: 2,
+                base: 0,
+                expr: ($c.m_storage.m_data)[$i],
+                size: ($r==1)*$c.m_storage.m_rows+($r==0)*$c.m_storage.m_cols
+             )
+         )
+      )
+   )
+
+   preview
+   (
+     #(
+         "[",
+           $c.m_storage.m_rows,
+         ",",
+           $c.m_storage.m_cols,
+         "](",
+           #array(
+            expr :    [($c.m_storage.m_data)[$i],g],
+            size :    $c.m_storage.m_rows*$c.m_storage.m_cols
+           ),
+         ")"
+      )
+   )
+}
+
+; Fixed rows, dynamic columns matrix (ColMajor and RowMajor support)
+Eigen::Matrix<*,*,-1,*,*,*>{
+  children
+   (
+      #(
+         [internals]: [$c,!],
+         rows: $c.RowsAtCompileTime,
+         cols: $c.m_storage.m_cols,
+         ; Check for RowMajorBit
+         #if ($c.Flags & 0x1) (
+             #array(
+                rank: 2,
+                base: 0,
+                expr: ($c.m_storage.m_data)[($i % $c.RowsAtCompileTime)*$c.m_storage.m_cols + (($i- $i % $c.RowsAtCompileTime)/$c.RowsAtCompileTime)],
+                size: ($r==1)*$c.RowsAtCompileTime+($r==0)*$c.m_storage.m_cols
+             )
+         ) #else (
+             #array(
+                rank: 2,
+                base: 0,
+                expr: ($c.m_storage.m_data)[$i],
+                size: ($r==1)*$c.RowsAtCompileTime+($r==0)*$c.m_storage.m_cols
+             )
+         )
+      )
+   )
+
+   preview
+   (
+     #(
+         "[",
+           $c.RowsAtCompileTime,
+         ",",
+           $c.m_storage.m_cols,
+         "](",
+           #array(
+            expr :    [($c.m_storage.m_data)[$i],g],
+            size :    $c.RowsAtCompileTime*$c.m_storage.m_cols
+           ),
+         ")"
+      )
+   )
+}
+
+; Dynamic rows, fixed columns matrix (ColMajor and RowMajor support)
+Eigen::Matrix<*,-1,*,*,*,*>{
+  children
+   (
+      #(
+         [internals]: [$c,!],
+         rows: $c.m_storage.m_rows,
+         cols: $c.ColsAtCompileTime,
+         ; Check for RowMajorBit
+         #if ($c.Flags & 0x1) (
+             #array(
+                rank: 2,
+                base: 0,
+                expr: ($c.m_storage.m_data)[($i % $c.m_storage.m_rows)*$c.ColsAtCompileTime + (($i- $i % $c.m_storage.m_rows)/$c.m_storage.m_rows)], 
+                size: ($r==1)*$c.m_storage.m_rows+($r==0)*$c.ColsAtCompileTime
+             )
+         ) #else (
+             #array(
+                rank: 2,
+                base: 0,
+                expr: ($c.m_storage.m_data)[$i],
+                size: ($r==1)*$c.m_storage.m_rows+($r==0)*$c.ColsAtCompileTime
+             )
+         )
+      )
+   )
+
+   preview
+   (
+     #(
+         "[",
+           $c.m_storage.m_rows,
+         ",",
+           $c.ColsAtCompileTime,
+         "](",
+           #array(
+            expr :    [($c.m_storage.m_data)[$i],g],
+            size :    $c.m_storage.m_rows*$c.ColsAtCompileTime
+           ),
+         ")"
+      )
+   )
+}
+
+; Fixed size matrix (ColMajor and RowMajor support)
+Eigen::Matrix<*,*,*,*,*,*>{
+  children
+   (
+      #(
+         [internals]: [$c,!],
+         rows: $c.RowsAtCompileTime,
+         cols: $c.ColsAtCompileTime,
+         ; Check for RowMajorBit
+         #if ($c.Flags & 0x1) (
+             #array(
+                rank: 2,
+                base: 0,
+                expr: ($c.m_storage.m_data.array)[($i % $c.RowsAtCompileTime)*$c.ColsAtCompileTime + (($i- $i % $c.RowsAtCompileTime)/$c.RowsAtCompileTime)], 
+                size: ($r==1)*$c.RowsAtCompileTime+($r==0)*$c.ColsAtCompileTime
+             )
+         ) #else (
+             #array(
+                rank: 2,
+                base: 0,
+                expr: ($c.m_storage.m_data.array)[$i],
+                size: ($r==1)*$c.RowsAtCompileTime+($r==0)*$c.ColsAtCompileTime
+             )
+         )
+      )
+   )
+
+   preview
+   (
+     #(
+         "[",
+           $c.RowsAtCompileTime,
+         ",",
+           $c.ColsAtCompileTime,
+         "](",
+           #array(
+            expr :    [($c.m_storage.m_data.array)[$i],g],
+            size :    $c.RowsAtCompileTime*$c.ColsAtCompileTime
+           ),
+         ")"
+      )
+   )
+}
diff --git a/doc/Doxyfile.in b/doc/Doxyfile.in
index ddfd7e8..bc1e03c 100644
--- a/doc/Doxyfile.in
+++ b/doc/Doxyfile.in
@@ -737,6 +737,14 @@
                          "${Eigen_SOURCE_DIR}/unsupported/doc/examples" \
                          "${Eigen_SOURCE_DIR}/unsupported/doc/snippets"
 
+# Forward declarations of class templates cause the title of the main page for
+# the class template to not contain the template signature.  This only happens
+# when the \class command is used to document the class.  Possibly caused
+# by https://github.com/doxygen/doxygen/issues/7698.  Confirmed fixed by
+# doxygen release 1.8.19.
+
+EXCLUDE += "${Eigen_SOURCE_DIR}/Eigen/src/Core/util/ForwardDeclarations.h"
+
 # The EXCLUDE_SYMLINKS tag can be used to select whether or not files or
 # directories that are symbolic links (a Unix file system feature) are excluded
 # from the input.
diff --git a/doc/SparseQuickReference.dox b/doc/SparseQuickReference.dox
index 81a73ee..9779f3f 100644
--- a/doc/SparseQuickReference.dox
+++ b/doc/SparseQuickReference.dox
@@ -244,7 +244,7 @@
 <td>
 \code
 sm1.valuePtr();      // Pointer to the values
-sm1.innerIndextr();  // Pointer to the indices.
+sm1.innerIndexPtr();  // Pointer to the indices.
 sm1.outerIndexPtr(); // Pointer to the beginning of each inner vector
 \endcode
 </td>
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
index 59440cf..8eda8d2 100644
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -450,7 +450,7 @@
   endif()
 endif()
 
-option(EIGEN_TEST_BUILD_DOCUMENTATION "Test building the doxygen documentation" OFF)
+cmake_dependent_option(EIGEN_TEST_BUILD_DOCUMENTATION "Test building the doxygen documentation" OFF "EIGEN_BUILD_DOC" OFF)
 if(EIGEN_TEST_BUILD_DOCUMENTATION)
   add_dependencies(buildtests doc)
 endif()
diff --git a/test/array_cwise.cpp b/test/array_cwise.cpp
index 48c0935..6910f0e 100644
--- a/test/array_cwise.cpp
+++ b/test/array_cwise.cpp
@@ -319,6 +319,7 @@
   VERIFY_IS_APPROX(m3.log(), log(m3));
   VERIFY_IS_APPROX(m3.log1p(), log1p(m3));
   VERIFY_IS_APPROX(m3.log10(), log10(m3));
+  VERIFY_IS_APPROX(m3.log2(), log2(m3));
 
 
   VERIFY((!(m1>m2) == (m1<=m2)).all());
@@ -372,6 +373,7 @@
   VERIFY_IS_APPROX(pow(m3,RealScalar(-0.5)), m3.rsqrt());
 
   VERIFY_IS_APPROX(log10(m3), log(m3)/log(10));
+  VERIFY_IS_APPROX(log2(m3), log(m3)/log(2));
 
   // scalar by array division
   const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon());
@@ -423,6 +425,7 @@
   VERIFY_IS_APPROX(m1.inverse(), inverse(m1));
   VERIFY_IS_APPROX(m1.log(), log(m1));
   VERIFY_IS_APPROX(m1.log10(), log10(m1));
+  VERIFY_IS_APPROX(m1.log2(), log2(m1));
   VERIFY_IS_APPROX(m1.abs(), abs(m1));
   VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
   VERIFY_IS_APPROX(m1.sqrt(), sqrt(m1));
@@ -478,6 +481,7 @@
   VERIFY_IS_APPROX(abs(m1), sqrt(square(m1.real())+square(m1.imag())));
   VERIFY_IS_APPROX(abs(m1), sqrt(abs2(m1)));
   VERIFY_IS_APPROX(log10(m1), log(m1)/log(10));
+  VERIFY_IS_APPROX(log2(m1), log(m1)/log(2));
 
   VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() );
   VERIFY_IS_APPROX( m1.sign() * m1.abs(), m1);
diff --git a/test/bfloat16_float.cpp b/test/bfloat16_float.cpp
index fc648df..1df22f7 100644
--- a/test/bfloat16_float.cpp
+++ b/test/bfloat16_float.cpp
@@ -274,9 +274,23 @@
   VERIFY_IS_EQUAL(
     numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::infinity()),
     numext::bit_cast<numext::uint16_t>(bfloat16(std::numeric_limits<float>::infinity())) );
-  VERIFY_IS_EQUAL(
-    numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::quiet_NaN()),
-    numext::bit_cast<numext::uint16_t>(bfloat16(std::numeric_limits<float>::quiet_NaN())) );
+  // There is no guarantee that casting a 32-bit NaN to bfloat16 has a precise
+  // bit pattern.  We test that it is in fact a NaN, then test the signaling
+  // bit (msb of significand is 1 for quiet, 0 for signaling).
+  const numext::uint16_t BFLOAT16_QUIET_BIT = 0x0040;
+  VERIFY(
+    (numext::isnan)(std::numeric_limits<bfloat16>::quiet_NaN())
+    && (numext::isnan)(bfloat16(std::numeric_limits<float>::quiet_NaN()))
+    && ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::quiet_NaN()) & BFLOAT16_QUIET_BIT) > 0)
+    && ((numext::bit_cast<numext::uint16_t>(bfloat16(std::numeric_limits<float>::quiet_NaN())) & BFLOAT16_QUIET_BIT) > 0) );
+  // After a cast to bfloat16, a signaling NaN may become non-signaling. Thus,
+  // we check that both are NaN, and that only the `numeric_limits` version is
+  // signaling.
+  VERIFY(
+    (numext::isnan)(std::numeric_limits<bfloat16>::signaling_NaN())
+    && (numext::isnan)(bfloat16(std::numeric_limits<float>::signaling_NaN()))
+    && ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::signaling_NaN()) & BFLOAT16_QUIET_BIT) == 0) );
+
   VERIFY( (std::numeric_limits<bfloat16>::min)() > bfloat16(0.f) );
   VERIFY( (std::numeric_limits<bfloat16>::denorm_min)() > bfloat16(0.f) );
   VERIFY_IS_EQUAL( (std::numeric_limits<bfloat16>::denorm_min)()/bfloat16(2), bfloat16(0.f) );
diff --git a/test/half_float.cpp b/test/half_float.cpp
index cf6df54..b2c2219 100644
--- a/test/half_float.cpp
+++ b/test/half_float.cpp
@@ -136,12 +136,22 @@
   VERIFY_IS_EQUAL(
     numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::infinity()),
     numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::infinity())) );
-  VERIFY_IS_EQUAL(
-    numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::quiet_NaN()),
-    numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::quiet_NaN())) );
-  VERIFY_IS_EQUAL(
-    numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::signaling_NaN()),
-    numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::signaling_NaN())) );
+  // There is no guarantee that casting a 32-bit NaN to 16-bit has a precise
+  // bit pattern.  We test that it is in fact a NaN, then test the signaling
+  // bit (msb of significand is 1 for quiet, 0 for signaling).
+  const numext::uint16_t HALF_QUIET_BIT = 0x0200;
+  VERIFY(
+    (numext::isnan)(std::numeric_limits<half>::quiet_NaN())
+    && (numext::isnan)(half(std::numeric_limits<float>::quiet_NaN()))
+    && ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::quiet_NaN()) & HALF_QUIET_BIT) > 0)
+    && ((numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::quiet_NaN())) & HALF_QUIET_BIT) > 0) );
+  // After a cast to half, a signaling NaN may become non-signaling
+  // (e.g. in the case of casting float to native __fp16). Thus, we check that
+  // both are NaN, and that only the `numeric_limits` version is signaling.
+  VERIFY(
+    (numext::isnan)(std::numeric_limits<half>::signaling_NaN())
+    && (numext::isnan)(half(std::numeric_limits<float>::signaling_NaN()))
+    && ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::signaling_NaN()) & HALF_QUIET_BIT) == 0) );
 
   VERIFY( (std::numeric_limits<half>::min)() > half(0.f) );
   VERIFY( (std::numeric_limits<half>::denorm_min)() > half(0.f) );
diff --git a/test/main.h b/test/main.h
index e830d68..4f9887c 100644
--- a/test/main.h
+++ b/test/main.h
@@ -47,6 +47,7 @@
 #include <list>
 #if __cplusplus >= 201103L
 #include <random>
+#include <chrono>
 #ifdef EIGEN_USE_THREADS
 #include <future>
 #endif
diff --git a/test/packetmath.cpp b/test/packetmath.cpp
index afe36ea..f19d725 100644
--- a/test/packetmath.cpp
+++ b/test/packetmath.cpp
@@ -473,8 +473,6 @@
     CHECK_CWISE3_IF(true, internal::pselect, internal::pselect);
   }
 
-  CHECK_CWISE1_IF(PacketTraits::HasSqrt, numext::sqrt, internal::psqrt);
-
   for (int i = 0; i < size; ++i) {
     data1[i] = internal::random<Scalar>();
   }
@@ -486,6 +484,18 @@
   packetmath_boolean_mask_ops<Scalar, Packet>();
   packetmath_pcast_ops_runner<Scalar, Packet>::run();
   packetmath_minus_zero_add<Scalar, Packet>();
+
+  for (int i = 0; i < size; ++i) {
+    data1[i] = numext::abs(internal::random<Scalar>());
+  }
+  CHECK_CWISE1_IF(PacketTraits::HasSqrt, numext::sqrt, internal::psqrt);
+}
+
+// Notice that this definition works for complex types as well.
+// c++11 has std::log2 for real, but not for complex types.
+template <typename Scalar>
+Scalar log2(Scalar x) {
+  return Scalar(EIGEN_LOG2E) * std::log(x);
 }
 
 template <typename Scalar, typename Packet>
@@ -506,6 +516,7 @@
   if (internal::random<float>(0, 1) < 0.1f) data1[internal::random<int>(0, PacketSize)] = Scalar(0);
 
   CHECK_CWISE1_IF(PacketTraits::HasLog, std::log, internal::plog);
+  CHECK_CWISE1_IF(PacketTraits::HasLog, log2, internal::plog2);
   CHECK_CWISE1_IF(PacketTraits::HasRsqrt, 1 / std::sqrt, internal::prsqrt);
 
   for (int i = 0; i < size; ++i) {
@@ -556,7 +567,7 @@
     VERIFY((numext::isnan)(data2[0]));
     // TODO(rmlarsen): Re-enable for bfloat16.
     if (!internal::is_same<Scalar, bfloat16>::value) {
-      VERIFY_IS_EQUAL(std::exp(small), data2[1]);
+      VERIFY_IS_APPROX(std::exp(small), data2[1]);
     }
 
     data1[0] = -small;
@@ -564,21 +575,21 @@
     h.store(data2, internal::pexp(h.load(data1)));
     // TODO(rmlarsen): Re-enable for bfloat16.
     if (!internal::is_same<Scalar, bfloat16>::value) {
-      VERIFY_IS_EQUAL(std::exp(-small), data2[0]);
+      VERIFY_IS_APPROX(std::exp(-small), 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]);
+    VERIFY_IS_APPROX(std::exp((std::numeric_limits<Scalar>::min)()), data2[0]);
+    VERIFY_IS_APPROX(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]);
+    VERIFY_IS_APPROX(std::exp(std::numeric_limits<Scalar>::denorm_min()), data2[0]);
+    VERIFY_IS_APPROX(std::exp(-std::numeric_limits<Scalar>::denorm_min()), data2[1]);
   }
 
   if (PacketTraits::HasTanh) {
@@ -618,7 +629,10 @@
       test::packet_helper<PacketTraits::HasLog, Packet> h;
       h.store(data2, internal::plog(h.load(data1)));
       VERIFY((numext::isnan)(data2[0]));
-      VERIFY_IS_EQUAL(std::log(std::numeric_limits<Scalar>::epsilon()), data2[1]);
+      // TODO(cantonios): Re-enable for bfloat16.
+      if (!internal::is_same<Scalar, bfloat16>::value) {
+        VERIFY_IS_APPROX(std::log(data1[1]), data2[1]);
+      }
 
       data1[0] = -std::numeric_limits<Scalar>::epsilon();
       data1[1] = Scalar(0);
@@ -629,7 +643,10 @@
       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]);
+      // TODO(cantonios): Re-enable for bfloat16.
+      if (!internal::is_same<Scalar, bfloat16>::value) {
+        VERIFY_IS_APPROX(std::log((std::numeric_limits<Scalar>::min)()), data2[0]);
+      }
       VERIFY((numext::isnan)(data2[1]));
 
       // Note: 32-bit arm always flushes denorms to zero.
@@ -672,8 +689,10 @@
       VERIFY((numext::isnan)(data2[0]));
       VERIFY((numext::isnan)(data2[1]));
     }
-    // TODO(rmlarsen): Re-enable for bfloat16.
-    if (PacketTraits::HasCos && !internal::is_same<Scalar, bfloat16>::value) {
+    // TODO(rmlarsen): Re-enable for half and bfloat16.
+    if (PacketTraits::HasCos
+        && !internal::is_same<Scalar, half>::value
+        && !internal::is_same<Scalar, bfloat16>::value) {
       test::packet_helper<PacketTraits::HasCos, Packet> h;
       for (Scalar k = Scalar(1); k < Scalar(10000) / std::numeric_limits<Scalar>::epsilon(); k *= Scalar(2)) {
         for (int k1 = 0; k1 <= 1; ++k1) {
@@ -729,54 +748,6 @@
   VERIFY(test::areApprox(ref, data2, PacketSize) && #POP); \
 }
 
-template <>
-void packetmath_real<bfloat16, typename internal::packet_traits<bfloat16>::type>(){
-  typedef internal::packet_traits<bfloat16> PacketTraits;
-  typedef internal::packet_traits<bfloat16>::type Packet;
-
-  const int PacketSize = internal::unpacket_traits<Packet>::size;
-  const int size = PacketSize * 4;
-  EIGEN_ALIGN_MAX bfloat16 data1[PacketSize * 4];
-  EIGEN_ALIGN_MAX bfloat16 data2[PacketSize * 4];
-  EIGEN_ALIGN_MAX bfloat16 ref[PacketSize * 4];
-
-  for (int i = 0; i < size; ++i) {
-    data1[i] = bfloat16(internal::random<float>(0, 1) * std::pow(float(10), internal::random<float>(-6, 6)));
-    data2[i] = bfloat16(internal::random<float>(0, 1) * std::pow(float(10), internal::random<float>(-6, 6)));
-    data1[i] = bfloat16(0);
-  }
-
-  if (internal::random<float>(0, 1) < 0.1f) data1[internal::random<int>(0, PacketSize)] = bfloat16(0);
-
-  CAST_CHECK_CWISE1_IF(PacketTraits::HasLog, std::log, internal::plog, bfloat16, float);
-  CAST_CHECK_CWISE1_IF(PacketTraits::HasRsqrt, float(1) / std::sqrt, internal::prsqrt, bfloat16, float);
-
-  for (int i = 0; i < size; ++i) {
-    data1[i] = bfloat16(internal::random<float>(-1, 1) * std::pow(float(10), internal::random<float>(-3, 3)));
-    data2[i] = bfloat16(internal::random<float>(-1, 1) * std::pow(float(10), internal::random<float>(-3, 3)));
-  }
-  CAST_CHECK_CWISE1_IF(PacketTraits::HasSin, std::sin, internal::psin, bfloat16, float);
-  CAST_CHECK_CWISE1_IF(PacketTraits::HasCos, std::cos, internal::pcos, bfloat16, float);
-  CAST_CHECK_CWISE1_IF(PacketTraits::HasTan, std::tan, internal::ptan, bfloat16, float);
-
-  CAST_CHECK_CWISE1_IF(PacketTraits::HasRound, numext::round, internal::pround, bfloat16, float);
-  CAST_CHECK_CWISE1_IF(PacketTraits::HasCeil, numext::ceil, internal::pceil, bfloat16, float);
-  CAST_CHECK_CWISE1_IF(PacketTraits::HasFloor, numext::floor, internal::pfloor, bfloat16, float);
-
-  for (int i = 0; i < size; ++i) {
-    data1[i] = bfloat16(-1.5 + i);
-    data2[i] = bfloat16(-1.5 + i);
-  }
-  CAST_CHECK_CWISE1_IF(PacketTraits::HasRound, numext::round, internal::pround, bfloat16, float);
-
-  for (int i = 0; i < size; ++i) {
-    data1[i] = bfloat16(internal::random<float>(-87, 88));
-    data2[i] = bfloat16(internal::random<float>(-87, 88));
-  }
-  CAST_CHECK_CWISE1_IF(PacketTraits::HasExp, std::exp, internal::pexp, bfloat16, float);
-
-}
-
 template <typename Scalar>
 Scalar propagate_nan_max(const Scalar& a, const Scalar& b) {
   if ((numext::isnan)(a)) return a;
@@ -791,6 +762,20 @@
   return (numext::mini)(a,b);
 }
 
+template <typename Scalar>
+Scalar propagate_number_max(const Scalar& a, const Scalar& b) {
+  if ((numext::isnan)(a)) return b;
+  if ((numext::isnan)(b)) return a;
+  return (numext::maxi)(a,b);
+}
+
+template <typename Scalar>
+Scalar propagate_number_min(const Scalar& a, const Scalar& b) {
+  if ((numext::isnan)(a)) return b;
+  if ((numext::isnan)(b)) return a;
+  return (numext::mini)(a,b);
+}
+
 template <typename Scalar, typename Packet>
 void packetmath_notcomplex() {
   typedef internal::packet_traits<Scalar> PacketTraits;
@@ -807,15 +792,9 @@
 
   CHECK_CWISE2_IF(PacketTraits::HasMin, (std::min), internal::pmin);
   CHECK_CWISE2_IF(PacketTraits::HasMax, (std::max), internal::pmax);
-#if EIGEN_HAS_CXX11_MATH
-  using std::fmin;
-  using std::fmax;
-#else
-  using ::fmin;
-  using ::fmax;
-#endif
-  CHECK_CWISE2_IF(PacketTraits::HasMin, fmin, (internal::pmin<PropagateNumbers>));
-  CHECK_CWISE2_IF(PacketTraits::HasMax, fmax, internal::pmax<PropagateNumbers>);
+
+  CHECK_CWISE2_IF(PacketTraits::HasMin, propagate_number_min, internal::pmin<PropagateNumbers>);
+  CHECK_CWISE2_IF(PacketTraits::HasMax, propagate_number_max, internal::pmax<PropagateNumbers>);
   CHECK_CWISE1(numext::abs, internal::pabs);
   CHECK_CWISE2_IF(PacketTraits::HasAbsDiff, REF_ABS_DIFF, internal::pabsdiff);
 
@@ -888,54 +867,13 @@
       data1[i + PacketSize] = internal::random<bool>() ? std::numeric_limits<Scalar>::quiet_NaN() : Scalar(0);
     }
     // Note: NaN propagation is implementation defined for pmin/pmax, so we do not test it here.
-    CHECK_CWISE2_IF(PacketTraits::HasMin, fmin, (internal::pmin<PropagateNumbers>));
-    CHECK_CWISE2_IF(PacketTraits::HasMax, fmax, internal::pmax<PropagateNumbers>);
+    CHECK_CWISE2_IF(PacketTraits::HasMin, propagate_number_min, (internal::pmin<PropagateNumbers>));
+    CHECK_CWISE2_IF(PacketTraits::HasMax, propagate_number_max, internal::pmax<PropagateNumbers>);
     CHECK_CWISE2_IF(PacketTraits::HasMin, propagate_nan_min, (internal::pmin<PropagateNaN>));
     CHECK_CWISE2_IF(PacketTraits::HasMax, propagate_nan_max, internal::pmax<PropagateNaN>);
   }
 }
 
-template <>
-void packetmath_notcomplex<bfloat16, typename internal::packet_traits<bfloat16>::type>(){
-  typedef bfloat16 Scalar;
-  typedef internal::packet_traits<bfloat16>::type Packet;
-  typedef internal::packet_traits<Scalar> PacketTraits;
-  const int PacketSize = internal::unpacket_traits<Packet>::size;
-
-  EIGEN_ALIGN_MAX Scalar data1[PacketSize * 4];
-  EIGEN_ALIGN_MAX Scalar data2[PacketSize * 4];
-  EIGEN_ALIGN_MAX Scalar ref[PacketSize * 4];
-  Array<Scalar, Dynamic, 1>::Map(data1, PacketSize * 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");
-
-  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(numext::abs, internal::pabs);
-  CHECK_CWISE2_IF(PacketTraits::HasAbsDiff, REF_ABS_DIFF, internal::pabsdiff);
-
-  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");
-
-  {
-    unsigned char* data1_bits = reinterpret_cast<unsigned char*>(data1);
-    // predux_any
-    for (unsigned int i = 0; i < PacketSize * sizeof(Scalar); ++i) data1_bits[i] = 0x0;
-    VERIFY((!internal::predux_any(internal::pload<Packet>(data1))) && "internal::predux_any(0000)");
-    for (int k = 0; k < PacketSize; ++k) {
-      for (unsigned int i = 0; i < sizeof(Scalar); ++i) data1_bits[k * sizeof(Scalar) + i] = 0xff;
-      VERIFY(internal::predux_any(internal::pload<Packet>(data1)) && "internal::predux_any(0101)");
-      for (unsigned int i = 0; i < sizeof(Scalar); ++i) data1_bits[k * sizeof(Scalar) + i] = 0x00;
-    }
-  }
-}
-
 template <typename Scalar, typename Packet, bool ConjLhs, bool ConjRhs>
 void test_conj_helper(Scalar* data1, Scalar* data2, Scalar* ref, Scalar* pval) {
   const int PacketSize = internal::unpacket_traits<Packet>::size;
@@ -964,6 +902,8 @@
 
 template <typename Scalar, typename Packet>
 void packetmath_complex() {
+  typedef internal::packet_traits<Scalar> PacketTraits;
+  typedef typename Scalar::value_type RealScalar;
   const int PacketSize = internal::unpacket_traits<Packet>::size;
 
   const int size = PacketSize * 4;
@@ -982,11 +922,55 @@
   test_conj_helper<Scalar, Packet, true, false>(data1, data2, ref, pval);
   test_conj_helper<Scalar, Packet, true, true>(data1, data2, ref, pval);
 
+  // Test pcplxflip.
   {
     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(test::areApprox(ref, pval, PacketSize) && "pcplxflip");
   }
+
+  if (PacketTraits::HasSqrt) {
+    for (int i = 0; i < size; ++i) {
+      data1[i] = Scalar(internal::random<RealScalar>(), internal::random<RealScalar>());
+    }
+    CHECK_CWISE1(numext::sqrt, internal::psqrt);
+
+    // Test misc. corner cases.
+    const RealScalar zero = RealScalar(0);
+    const RealScalar one = RealScalar(1);
+    const RealScalar inf = std::numeric_limits<RealScalar>::infinity();
+    const RealScalar nan = std::numeric_limits<RealScalar>::quiet_NaN();
+    data1[0] = Scalar(zero, zero);
+    data1[1] = Scalar(-zero, zero);
+    data1[2] = Scalar(one, zero);
+    data1[3] = Scalar(zero, one);
+    CHECK_CWISE1(numext::sqrt, internal::psqrt);
+    data1[0] = Scalar(-one, zero);
+    data1[1] = Scalar(zero, -one);
+    data1[2] = Scalar(one, one);
+    data1[3] = Scalar(-one, -one);
+    CHECK_CWISE1(numext::sqrt, internal::psqrt);
+    data1[0] = Scalar(inf, zero);
+    data1[1] = Scalar(zero, inf);
+    data1[2] = Scalar(-inf, zero);
+    data1[3] = Scalar(zero, -inf);
+    CHECK_CWISE1(numext::sqrt, internal::psqrt);
+    data1[0] = Scalar(inf, inf);
+    data1[1] = Scalar(-inf, inf);
+    data1[2] = Scalar(inf, -inf);
+    data1[3] = Scalar(-inf, -inf);
+    CHECK_CWISE1(numext::sqrt, internal::psqrt);
+    data1[0] = Scalar(nan, zero);
+    data1[1] = Scalar(zero, nan);
+    data1[2] = Scalar(nan, one);
+    data1[3] = Scalar(one, nan);
+    CHECK_CWISE1(numext::sqrt, internal::psqrt);
+    data1[0] = Scalar(nan, nan);
+    data1[1] = Scalar(inf, nan);
+    data1[2] = Scalar(nan, inf);
+    data1[3] = Scalar(-inf, nan);
+    CHECK_CWISE1(numext::sqrt, internal::psqrt);
+  }
 }
 
 template <typename Scalar, typename Packet>
@@ -1001,8 +985,9 @@
 
   int stride = internal::random<int>(1, 20);
 
-  EIGEN_ALIGN_MAX Scalar buffer[PacketSize * 20];
-  memset(buffer, 0, 20 * PacketSize * sizeof(Scalar));
+  // Buffer of zeros.
+  EIGEN_ALIGN_MAX Scalar buffer[PacketSize * 20] = {};
+
   Packet packet = internal::pload<Packet>(data1);
   internal::pscatter<Scalar, Packet>(buffer, packet, stride);
 
@@ -1073,12 +1058,7 @@
     CALL_SUBTEST_10(test::runner<uint64_t>::run());
     CALL_SUBTEST_11(test::runner<std::complex<float> >::run());
     CALL_SUBTEST_12(test::runner<std::complex<double> >::run());
-#if defined(EIGEN_VECTORIZE_AVX)
-    // AVX half packets not fully implemented.
-    CALL_SUBTEST_13((packetmath<half, internal::packet_traits<half>::type>()));
-#else
     CALL_SUBTEST_13(test::runner<half>::run());
-#endif
     CALL_SUBTEST_14((packetmath<bool, internal::packet_traits<bool>::type>()));
     CALL_SUBTEST_15(test::runner<bfloat16>::run());
     g_first_pass = false;
diff --git a/unsupported/CMakeLists.txt b/unsupported/CMakeLists.txt
index 9a56661..34408c0 100644
--- a/unsupported/CMakeLists.txt
+++ b/unsupported/CMakeLists.txt
@@ -1,5 +1,7 @@
 add_subdirectory(Eigen)
-add_subdirectory(doc EXCLUDE_FROM_ALL)
+if(EIGEN_BUILD_DOC)
+  add_subdirectory(doc EXCLUDE_FROM_ALL)
+endif()
 if(BUILD_TESTING)
   if(EIGEN_LEAVE_TEST_IN_ALL_TARGET)
     add_subdirectory(test) # can't do EXCLUDE_FROM_ALL here, breaks CTest
diff --git a/unsupported/Eigen/CXX11/Tensor b/unsupported/Eigen/CXX11/Tensor
index 2640f95..beed230 100644
--- a/unsupported/Eigen/CXX11/Tensor
+++ b/unsupported/Eigen/CXX11/Tensor
@@ -33,10 +33,13 @@
   * Much of the documentation can be found \ref eigen_tensors "here".
   */
 
+#include <atomic>
+#include <chrono>
 #include <cmath>
 #include <cstddef>
 #include <cstring>
 #include <random>
+#include <thread>
 
 #ifdef _WIN32
 typedef __int16 int16_t;
@@ -48,7 +51,6 @@
 #include <windows.h>
 #else
 #include <stdint.h>
-#include <unistd.h>
 #endif
 
 #ifdef _WIN32
@@ -70,8 +72,6 @@
   #else
     #include <cuda_runtime.h>
   #endif
-  #include <atomic>
-  #include <unistd.h>
 #endif
 
 #include "src/Tensor/TensorMacros.h"
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceGpu.h b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceGpu.h
index 7f33944..9422dcd 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceGpu.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceGpu.h
@@ -83,7 +83,7 @@
       // Wait for the other thread to inititialize the properties.
       while (!m_devicePropInitialized) {
         std::atomic_thread_fence(std::memory_order_acquire);
-        EIGEN_SLEEP(1000);
+        std::this_thread::sleep_for(std::chrono::milliseconds(1000));
       }
     }
   }
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorMacros.h b/unsupported/Eigen/CXX11/src/Tensor/TensorMacros.h
index 76d15f1..73ff3d2 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorMacros.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorMacros.h
@@ -43,15 +43,6 @@
 #define EIGEN_SFINAE_ENABLE_IF( __condition__ ) \
     typename internal::enable_if< ( __condition__ ) , int >::type = 0
 
-
-#if EIGEN_OS_WIN || EIGEN_OS_WIN64
-#define EIGEN_SLEEP(n) Sleep(n)
-#elif EIGEN_OS_GNULINUX
-#define EIGEN_SLEEP(n) usleep(n * 1000);
-#else
-#define EIGEN_SLEEP(n) sleep(std::max<unsigned>(1, n/1000))
-#endif
-
 // Define a macro to use a reference on the host but a value on the device
 #if defined(SYCL_DEVICE_ONLY)
   #define EIGEN_DEVICE_REF
diff --git a/unsupported/Eigen/SpecialFunctions b/unsupported/Eigen/SpecialFunctions
index dda6618..f6a2460 100644
--- a/unsupported/Eigen/SpecialFunctions
+++ b/unsupported/Eigen/SpecialFunctions
@@ -61,23 +61,36 @@
 }
 
 #include "src/SpecialFunctions/BesselFunctionsImpl.h"
-#include "src/SpecialFunctions/BesselFunctionsPacketMath.h"
 #include "src/SpecialFunctions/BesselFunctionsBFloat16.h"
 #include "src/SpecialFunctions/BesselFunctionsHalf.h"
+#include "src/SpecialFunctions/BesselFunctionsPacketMath.h"
 #include "src/SpecialFunctions/BesselFunctionsFunctors.h"
 #include "src/SpecialFunctions/BesselFunctionsArrayAPI.h"
 #include "src/SpecialFunctions/SpecialFunctionsImpl.h"
 #if defined(EIGEN_HIPCC)
 #include "src/SpecialFunctions/HipVectorCompatibility.h"
 #endif
-#include "src/SpecialFunctions/SpecialFunctionsPacketMath.h"
 #include "src/SpecialFunctions/SpecialFunctionsBFloat16.h"
 #include "src/SpecialFunctions/SpecialFunctionsHalf.h"
+#include "src/SpecialFunctions/SpecialFunctionsPacketMath.h"
 #include "src/SpecialFunctions/SpecialFunctionsFunctors.h"
 #include "src/SpecialFunctions/SpecialFunctionsArrayAPI.h"
 
+#if defined EIGEN_VECTORIZE_AVX512
+  #include "src/SpecialFunctions/arch/AVX/BesselFunctions.h"
+  #include "src/SpecialFunctions/arch/AVX/SpecialFunctions.h"
+  #include "src/SpecialFunctions/arch/AVX512/BesselFunctions.h"
+  #include "src/SpecialFunctions/arch/AVX512/SpecialFunctions.h"
+#elif defined EIGEN_VECTORIZE_AVX
+  #include "src/SpecialFunctions/arch/AVX/BesselFunctions.h"
+  #include "src/SpecialFunctions/arch/AVX/SpecialFunctions.h"
+#elif defined EIGEN_VECTORIZE_NEON
+  #include "src/SpecialFunctions/arch/NEON/BesselFunctions.h"
+  #include "src/SpecialFunctions/arch/NEON/SpecialFunctions.h"
+#endif
+
 #if defined EIGEN_VECTORIZE_GPU
-  #include "src/SpecialFunctions/arch/GPU/GpuSpecialFunctions.h"
+  #include "src/SpecialFunctions/arch/GPU/SpecialFunctions.h"
 #endif
 
 namespace Eigen {
diff --git a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsImpl.h b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsImpl.h
index a9b6ad9..24812be 100644
--- a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsImpl.h
+++ b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsImpl.h
@@ -46,7 +46,7 @@
   typedef Scalar type;
 };
 
-template <typename T, typename ScalarType>
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
 struct generic_i0e {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE T run(const T&) {
@@ -201,11 +201,11 @@
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_i0e_impl {
   EIGEN_DEVICE_FUNC
-  static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
-    return generic_i0e<Scalar, Scalar>::run(x);
+  static EIGEN_STRONG_INLINE T run(const T x) {
+    return generic_i0e<T>::run(x);
   }
 };
 
@@ -214,7 +214,7 @@
   typedef Scalar type;
 };
 
-template <typename T, typename ScalarType>
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
 struct generic_i0 {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE T run(const T& x) {
@@ -224,11 +224,11 @@
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_i0_impl {
   EIGEN_DEVICE_FUNC
-  static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
-    return generic_i0<Scalar, Scalar>::run(x);
+  static EIGEN_STRONG_INLINE T run(const T x) {
+    return generic_i0<T>::run(x);
   }
 };
 
@@ -237,7 +237,7 @@
   typedef Scalar type;
 };
 
-template <typename T, typename ScalarType>
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type >
 struct generic_i1e {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE T run(const T&) {
@@ -396,20 +396,20 @@
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_i1e_impl {
   EIGEN_DEVICE_FUNC
-  static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
-    return generic_i1e<Scalar, Scalar>::run(x);
+  static EIGEN_STRONG_INLINE T run(const T x) {
+    return generic_i1e<T>::run(x);
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_i1_retval {
-  typedef Scalar type;
+  typedef T type;
 };
 
-template <typename T, typename ScalarType>
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
 struct generic_i1 {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE T run(const T& x) {
@@ -419,20 +419,20 @@
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_i1_impl {
   EIGEN_DEVICE_FUNC
-  static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
-    return generic_i1<Scalar, Scalar>::run(x);
+  static EIGEN_STRONG_INLINE T run(const T x) {
+    return generic_i1<T>::run(x);
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_k0e_retval {
-  typedef Scalar type;
+  typedef T type;
 };
 
-template <typename T, typename ScalarType>
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
 struct generic_k0e {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE T run(const T&) {
@@ -582,20 +582,20 @@
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_k0e_impl {
   EIGEN_DEVICE_FUNC
-  static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
-    return generic_k0e<Scalar, Scalar>::run(x);
+  static EIGEN_STRONG_INLINE T run(const T x) {
+    return generic_k0e<T>::run(x);
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_k0_retval {
-  typedef Scalar type;
+  typedef T type;
 };
 
-template <typename T, typename ScalarType>
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
 struct generic_k0 {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE T run(const T&) {
@@ -754,20 +754,20 @@
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_k0_impl {
   EIGEN_DEVICE_FUNC
-  static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
-    return generic_k0<Scalar, Scalar>::run(x);
+  static EIGEN_STRONG_INLINE T run(const T x) {
+    return generic_k0<T>::run(x);
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_k1e_retval {
-  typedef Scalar type;
+  typedef T type;
 };
 
-template <typename T, typename ScalarType>
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
 struct generic_k1e {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE T run(const T&) {
@@ -910,20 +910,20 @@
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_k1e_impl {
   EIGEN_DEVICE_FUNC
-  static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
-    return generic_k1e<Scalar, Scalar>::run(x);
+  static EIGEN_STRONG_INLINE T run(const T x) {
+    return generic_k1e<T>::run(x);
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_k1_retval {
-  typedef Scalar type;
+  typedef T type;
 };
 
-template <typename T, typename ScalarType>
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
 struct generic_k1 {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE T run(const T&) {
@@ -1076,20 +1076,20 @@
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_k1_impl {
   EIGEN_DEVICE_FUNC
-  static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
-    return generic_k1<Scalar, Scalar>::run(x);
+  static EIGEN_STRONG_INLINE T run(const T x) {
+    return generic_k1<T>::run(x);
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_j0_retval {
-  typedef Scalar type;
+  typedef T type;
 };
 
-template <typename T, typename ScalarType>
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
 struct generic_j0 {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE T run(const T&) {
@@ -1276,20 +1276,20 @@
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_j0_impl {
   EIGEN_DEVICE_FUNC
-  static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
-    return generic_j0<Scalar, Scalar>::run(x);
+  static EIGEN_STRONG_INLINE T run(const T x) {
+    return generic_j0<T>::run(x);
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_y0_retval {
-  typedef Scalar type;
+  typedef T type;
 };
 
-template <typename T, typename ScalarType>
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
 struct generic_y0 {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE T run(const T&) {
@@ -1474,20 +1474,20 @@
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_y0_impl {
   EIGEN_DEVICE_FUNC
-  static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
-    return generic_y0<Scalar, Scalar>::run(x);
+  static EIGEN_STRONG_INLINE T run(const T x) {
+    return generic_y0<T>::run(x);
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_j1_retval {
-  typedef Scalar type;
+  typedef T type;
 };
 
-template <typename T, typename ScalarType>
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
 struct generic_j1 {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE T run(const T&) {
@@ -1665,20 +1665,20 @@
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_j1_impl {
   EIGEN_DEVICE_FUNC
-  static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
-    return generic_j1<Scalar, Scalar>::run(x);
+  static EIGEN_STRONG_INLINE T run(const T x) {
+    return generic_j1<T>::run(x);
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_y1_retval {
-  typedef Scalar type;
+  typedef T type;
 };
 
-template <typename T, typename ScalarType>
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
 struct generic_y1 {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE T run(const T&) {
@@ -1868,11 +1868,11 @@
   }
 };
 
-template <typename Scalar>
+template <typename T>
 struct bessel_y1_impl {
   EIGEN_DEVICE_FUNC
-  static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
-    return generic_y1<Scalar, Scalar>::run(x);
+  static EIGEN_STRONG_INLINE T run(const T x) {
+    return generic_y1<T>::run(x);
   }
 };
 
diff --git a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsPacketMath.h b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsPacketMath.h
index efc6d9c..943d10f 100644
--- a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsPacketMath.h
+++ b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsPacketMath.h
@@ -19,8 +19,7 @@
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet pbessel_i0(const Packet& x) {
-  typedef typename unpacket_traits<Packet>::type ScalarType;
-  using internal::generic_i0; return generic_i0<Packet, ScalarType>::run(x);
+  return numext::bessel_i0(x);
 }
 
 /** \internal \returns the exponentially scaled modified Bessel function of
@@ -28,8 +27,7 @@
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet pbessel_i0e(const Packet& x) {
-  typedef typename unpacket_traits<Packet>::type ScalarType;
-  using internal::generic_i0e; return generic_i0e<Packet, ScalarType>::run(x);
+  return numext::bessel_i0e(x);
 }
 
 /** \internal \returns the exponentially scaled modified Bessel function of
@@ -37,8 +35,7 @@
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet pbessel_i1(const Packet& x) {
-  typedef typename unpacket_traits<Packet>::type ScalarType;
-  using internal::generic_i1; return generic_i1<Packet, ScalarType>::run(x);
+  return numext::bessel_i1(x);
 }
 
 /** \internal \returns the exponentially scaled modified Bessel function of
@@ -46,8 +43,7 @@
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet pbessel_i1e(const Packet& x) {
-  typedef typename unpacket_traits<Packet>::type ScalarType;
-  using internal::generic_i1e; return generic_i1e<Packet, ScalarType>::run(x);
+  return numext::bessel_i1e(x);
 }
 
 /** \internal \returns the exponentially scaled modified Bessel function of
@@ -55,8 +51,7 @@
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet pbessel_j0(const Packet& x) {
-  typedef typename unpacket_traits<Packet>::type ScalarType;
-  using internal::generic_j0; return generic_j0<Packet, ScalarType>::run(x);
+  return numext::bessel_j0(x);
 }
 
 /** \internal \returns the exponentially scaled modified Bessel function of
@@ -64,8 +59,7 @@
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet pbessel_j1(const Packet& x) {
-  typedef typename unpacket_traits<Packet>::type ScalarType;
-  using internal::generic_j1; return generic_j1<Packet, ScalarType>::run(x);
+  return numext::bessel_j1(x);
 }
 
 /** \internal \returns the exponentially scaled modified Bessel function of
@@ -73,8 +67,7 @@
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet pbessel_y0(const Packet& x) {
-  typedef typename unpacket_traits<Packet>::type ScalarType;
-  using internal::generic_y0; return generic_y0<Packet, ScalarType>::run(x);
+  return numext::bessel_y0(x);
 }
 
 /** \internal \returns the exponentially scaled modified Bessel function of
@@ -82,8 +75,7 @@
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet pbessel_y1(const Packet& x) {
-  typedef typename unpacket_traits<Packet>::type ScalarType;
-  using internal::generic_y1; return generic_y1<Packet, ScalarType>::run(x);
+  return numext::bessel_y1(x);
 }
 
 /** \internal \returns the exponentially scaled modified Bessel function of
@@ -91,8 +83,7 @@
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet pbessel_k0(const Packet& x) {
-  typedef typename unpacket_traits<Packet>::type ScalarType;
-  using internal::generic_k0; return generic_k0<Packet, ScalarType>::run(x);
+  return numext::bessel_k0(x);
 }
 
 /** \internal \returns the exponentially scaled modified Bessel function of
@@ -100,8 +91,7 @@
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet pbessel_k0e(const Packet& x) {
-  typedef typename unpacket_traits<Packet>::type ScalarType;
-  using internal::generic_k0e; return generic_k0e<Packet, ScalarType>::run(x);
+  return numext::bessel_k0e(x);
 }
 
 /** \internal \returns the exponentially scaled modified Bessel function of
@@ -109,8 +99,7 @@
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet pbessel_k1(const Packet& x) {
-  typedef typename unpacket_traits<Packet>::type ScalarType;
-  using internal::generic_k1; return generic_k1<Packet, ScalarType>::run(x);
+  return numext::bessel_k1(x);
 }
 
 /** \internal \returns the exponentially scaled modified Bessel function of
@@ -118,8 +107,7 @@
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet pbessel_k1e(const Packet& x) {
-  typedef typename unpacket_traits<Packet>::type ScalarType;
-  using internal::generic_k1e; return generic_k1e<Packet, ScalarType>::run(x);
+  return numext::bessel_k1e(x);
 }
 
 } // end namespace internal
diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h
index 648eb05..cfc13af 100644
--- a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h
+++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h
@@ -348,7 +348,7 @@
 template <typename T>
 struct erf_impl {
   EIGEN_DEVICE_FUNC
-  static EIGEN_STRONG_INLINE T run(const T x) {
+  static EIGEN_STRONG_INLINE T run(const T& x) {
     return generic_fast_erf_float(x);
   }
 };
@@ -490,7 +490,8 @@
 template<typename T>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T flipsign(
     const T& should_flipsign, const T& x) {
-  const T sign_mask = pset1<T>(-0.0);
+  typedef typename unpacket_traits<T>::type Scalar;
+  const T sign_mask = pset1<T>(Scalar(-0.0));
   T sign_bit = pand<T>(should_flipsign, sign_mask);
   return pxor<T>(sign_bit, x);
 }
diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/AVX/BesselFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/AVX/BesselFunctions.h
new file mode 100644
index 0000000..2d76692
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/arch/AVX/BesselFunctions.h
@@ -0,0 +1,46 @@
+#ifndef EIGEN_AVX_BESSELFUNCTIONS_H
+#define EIGEN_AVX_BESSELFUNCTIONS_H
+
+namespace Eigen {
+namespace internal {
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_i0)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_i0)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_i0e)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_i0e)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_i1)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_i1)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_i1e)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_i1e)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_j0)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_j0)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_j1)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_j1)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_k0)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_k0)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_k0e)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_k0e)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_k1)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_k1)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_k1e)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_k1e)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_y0)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_y0)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_y1)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_y1)
+
+}  // namespace internal
+}  // namespace Eigen
+
+#endif  // EIGEN_AVX_BESSELFUNCTIONS_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/AVX/SpecialFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/AVX/SpecialFunctions.h
new file mode 100644
index 0000000..35e62a8
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/arch/AVX/SpecialFunctions.h
@@ -0,0 +1,16 @@
+#ifndef EIGEN_AVX_SPECIALFUNCTIONS_H
+#define EIGEN_AVX_SPECIALFUNCTIONS_H
+
+namespace Eigen {
+namespace internal {
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, perf)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, perf)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pndtri)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pndtri)
+
+}  // namespace internal
+}  // namespace Eigen
+
+#endif  // EIGEN_AVX_SPECIAL_FUNCTIONS_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/AVX512/BesselFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/AVX512/BesselFunctions.h
new file mode 100644
index 0000000..7dd3c3e
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/arch/AVX512/BesselFunctions.h
@@ -0,0 +1,46 @@
+#ifndef EIGEN_AVX512_BESSELFUNCTIONS_H
+#define EIGEN_AVX512_BESSELFUNCTIONS_H
+
+namespace Eigen {
+namespace internal {
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_i0)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_i0)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_i0e)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_i0e)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_i1)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_i1)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_i1e)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_i1e)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_j0)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_j0)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_j1)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_j1)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_k0)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_k0)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_k0e)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_k0e)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_k1)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_k1)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_k1e)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_k1e)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_y0)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_y0)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_y1)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_y1)
+
+}  // namespace internal
+}  // namespace Eigen
+
+#endif  // EIGEN_AVX512_BESSELFUNCTIONS_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/AVX512/SpecialFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/AVX512/SpecialFunctions.h
new file mode 100644
index 0000000..79878f2
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/arch/AVX512/SpecialFunctions.h
@@ -0,0 +1,16 @@
+#ifndef EIGEN_AVX512_SPECIALFUNCTIONS_H
+#define EIGEN_AVX512_SPECIALFUNCTIONS_H
+
+namespace Eigen {
+namespace internal {
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, perf)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, perf)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pndtri)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pndtri)
+
+}  // namespace internal
+}  // namespace Eigen
+
+#endif  // EIGEN_AVX512_SPECIAL_FUNCTIONS_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/GPU/GpuSpecialFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/GPU/SpecialFunctions.h
similarity index 100%
rename from unsupported/Eigen/src/SpecialFunctions/arch/GPU/GpuSpecialFunctions.h
rename to unsupported/Eigen/src/SpecialFunctions/arch/GPU/SpecialFunctions.h
diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/NEON/BesselFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/NEON/BesselFunctions.h
new file mode 100644
index 0000000..67433b0
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/arch/NEON/BesselFunctions.h
@@ -0,0 +1,54 @@
+#ifndef EIGEN_NEON_BESSELFUNCTIONS_H
+#define EIGEN_NEON_BESSELFUNCTIONS_H
+
+namespace Eigen {
+namespace internal {
+
+#if EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
+
+#define NEON_HALF_TO_FLOAT_FUNCTIONS(METHOD)                            \
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                       \
+Packet8hf METHOD<Packet8hf>(const Packet8hf& x) {                       \
+  const Packet4f lo = METHOD<Packet4f>(vcvt_f32_f16(vget_low_f16(x)));  \
+  const Packet4f hi = METHOD<Packet4f>(vcvt_f32_f16(vget_high_f16(x))); \
+  return vcombine_f16(vcvt_f16_f32(lo), vcvt_f16_f32(hi));              \
+}                                                                       \
+                                                                        \
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                       \
+Packet4hf METHOD<Packet4hf>(const Packet4hf& x) {                       \
+  return vcvt_f16_f32(METHOD<Packet4f>(vcvt_f32_f16(x)));               \
+}
+
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_i0)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_i0e)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_i1)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_i1e)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_j0)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_j1)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_k0)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_k0e)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_k1)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_k1e)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_y0)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_y1)
+
+#undef NEON_HALF_TO_FLOAT_FUNCTIONS
+#endif
+
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_i0)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_i0e)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_i1)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_i1e)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_j0)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_j1)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_k0)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_k0e)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_k1)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_k1e)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_y0)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_y1)
+
+}  // namespace internal
+}  // namespace Eigen
+
+#endif  // EIGEN_NEON_BESSELFUNCTIONS_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/NEON/SpecialFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/NEON/SpecialFunctions.h
new file mode 100644
index 0000000..ec92951
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/arch/NEON/SpecialFunctions.h
@@ -0,0 +1,34 @@
+#ifndef EIGEN_NEON_SPECIALFUNCTIONS_H
+#define EIGEN_NEON_SPECIALFUNCTIONS_H
+
+namespace Eigen {
+namespace internal {
+
+#if EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
+
+#define NEON_HALF_TO_FLOAT_FUNCTIONS(METHOD)                            \
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                       \
+Packet8hf METHOD<Packet8hf>(const Packet8hf& x) {                       \
+  const Packet4f lo = METHOD<Packet4f>(vcvt_f32_f16(vget_low_f16(x)));  \
+  const Packet4f hi = METHOD<Packet4f>(vcvt_f32_f16(vget_high_f16(x))); \
+  return vcombine_f16(vcvt_f16_f32(lo), vcvt_f16_f32(hi));              \
+}                                                                       \
+                                                                        \
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE                       \
+Packet4hf METHOD<Packet4hf>(const Packet4hf& x) {                       \
+  return vcvt_f16_f32(METHOD<Packet4f>(vcvt_f32_f16(x)));               \
+}
+
+NEON_HALF_TO_FLOAT_FUNCTIONS(perf)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pndtri)
+
+#undef NEON_HALF_TO_FLOAT_FUNCTIONS
+#endif
+
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, perf)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pndtri)
+
+}  // namespace internal
+}  // namespace Eigen
+
+#endif  // EIGEN_NEON_SPECIALFUNCTIONS_H
diff --git a/unsupported/test/cxx11_non_blocking_thread_pool.cpp b/unsupported/test/cxx11_non_blocking_thread_pool.cpp
index 90b330f..993ee17 100644
--- a/unsupported/test/cxx11_non_blocking_thread_pool.cpp
+++ b/unsupported/test/cxx11_non_blocking_thread_pool.cpp
@@ -109,7 +109,9 @@
   // Schedule a large number of closure that each sleeps for one second. This
   // will keep the thread pool busy for much longer than the default test timeout.
   for (int i = 0; i < 1000; ++i) {
-    tp.Schedule([]() { EIGEN_SLEEP(2000); });
+    tp.Schedule([]() {
+      std::this_thread::sleep_for(std::chrono::milliseconds(2000));
+    });
   }
 
   // Cancel the processing of all the closures that are still pending.
diff --git a/unsupported/test/cxx11_tensor_block_eval.cpp b/unsupported/test/cxx11_tensor_block_eval.cpp
index a7a49fa..b2e26eb 100644
--- a/unsupported/test/cxx11_tensor_block_eval.cpp
+++ b/unsupported/test/cxx11_tensor_block_eval.cpp
@@ -222,7 +222,7 @@
   input.setRandom();
 
   VerifyBlockEvaluator<T, NumDims, Layout>(
-      input.square(), [&dims]() { return RandomBlock<Layout>(dims, 1, 10); });
+      input.abs(), [&dims]() { return RandomBlock<Layout>(dims, 1, 10); });
 }
 
 template <typename T, int NumDims, int Layout>
@@ -274,7 +274,7 @@
   // Check that desc.destination() memory is not shared between two broadcast
   // materializations.
   VerifyBlockEvaluator<T, NumDims, Layout>(
-      input.broadcast(bcast) * input.square().broadcast(bcast),
+      input.broadcast(bcast) * input.abs().broadcast(bcast),
       [&bcasted_dims]() { return SkewedInnerBlock<Layout>(bcasted_dims); });
 }
 
@@ -391,27 +391,46 @@
 
   // Block expression assignment.
   VerifyBlockEvaluator<T, NumDims - 1, Layout>(
-      input.square().chip(chip_offset, chip_dim),
+      input.abs().chip(chip_offset, chip_dim),
       [&chipped_dims]() { return FixedSizeBlock(chipped_dims); });
 
   VerifyBlockEvaluator<T, NumDims - 1, Layout>(
-      input.square().chip(chip_offset, chip_dim),
+      input.abs().chip(chip_offset, chip_dim),
       [&chipped_dims]() { return RandomBlock<Layout>(chipped_dims, 1, 10); });
 }
 
+
+template<typename T, int NumDims>
+struct SimpleTensorGenerator {
+  T operator()(const array<Index, NumDims>& coords) const {
+    T result = static_cast<T>(0);
+    for (int i = 0; i < NumDims; ++i) {
+      result += static_cast<T>((i + 1) * coords[i]);
+    }
+    return result;
+  }
+};
+
+// Boolean specialization to avoid -Wint-in-bool-context warnings on GCC.
+template<int NumDims>
+struct SimpleTensorGenerator<bool, NumDims> {
+  bool operator()(const array<Index, NumDims>& coords) const {
+    bool result = false;
+    for (int i = 0; i < NumDims; ++i) {
+      result ^= coords[i];
+    }
+    return result;
+  }
+};
+
+
 template <typename T, int NumDims, int Layout>
 static void test_eval_tensor_generator() {
   DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
   Tensor<T, NumDims, Layout> input(dims);
   input.setRandom();
 
-  auto generator = [](const array<Index, NumDims>& coords) -> T {
-    T result = static_cast<T>(0);
-    for (int i = 0; i < NumDims; ++i) {
-      result += static_cast<T>((i + 1) * coords[i]);
-    }
-    return result;
-  };
+  auto generator = SimpleTensorGenerator<T, NumDims>();
 
   VerifyBlockEvaluator<T, NumDims, Layout>(
       input.generate(generator), [&dims]() { return FixedSizeBlock(dims); });
diff --git a/unsupported/test/cxx11_tensor_notification.cpp b/unsupported/test/cxx11_tensor_notification.cpp
index 2bade8d..8e81653 100644
--- a/unsupported/test/cxx11_tensor_notification.cpp
+++ b/unsupported/test/cxx11_tensor_notification.cpp
@@ -23,7 +23,7 @@
   Eigen::Notification n;
   auto func = [&n, &counter](){ n.Wait(); ++counter;};
   thread_pool.Schedule(func);
-  EIGEN_SLEEP(1000);
+  std::this_thread::sleep_for(std::chrono::milliseconds(1000));
 
   // The thread should be waiting for the notification.
   VERIFY_IS_EQUAL(counter, 0);
@@ -31,7 +31,7 @@
   // Unblock the thread
   n.Notify();
 
-  EIGEN_SLEEP(1000);
+  std::this_thread::sleep_for(std::chrono::milliseconds(1000));
 
   // Verify the counter has been incremented
   VERIFY_IS_EQUAL(counter, 1);
@@ -50,10 +50,10 @@
   thread_pool.Schedule(func);
   thread_pool.Schedule(func);
   thread_pool.Schedule(func);
-  EIGEN_SLEEP(1000);
+  std::this_thread::sleep_for(std::chrono::milliseconds(1000));
   VERIFY_IS_EQUAL(counter, 0);
   n.Notify();
-  EIGEN_SLEEP(1000);
+  std::this_thread::sleep_for(std::chrono::milliseconds(1000));
   VERIFY_IS_EQUAL(counter, 4);
 }
 
diff --git a/unsupported/test/special_functions.cpp b/unsupported/test/special_functions.cpp
index 1027272..56848da 100644
--- a/unsupported/test/special_functions.cpp
+++ b/unsupported/test/special_functions.cpp
@@ -11,6 +11,17 @@
 #include "main.h"
 #include "../Eigen/SpecialFunctions"
 
+// Hack to allow "implicit" conversions from double to Scalar via comma-initialization.
+template<typename Derived>
+Eigen::CommaInitializer<Derived> operator<<(Eigen::DenseBase<Derived>& dense, double v) {
+  return (dense << static_cast<typename Derived::Scalar>(v));
+}
+
+template<typename XprType>
+Eigen::CommaInitializer<XprType>& operator,(Eigen::CommaInitializer<XprType>& ci, double v) {
+  return (ci, static_cast<typename XprType::Scalar>(v));
+}
+
 template<typename X, typename Y>
 void verify_component_wise(const X& x, const Y& y)
 {
@@ -65,8 +76,8 @@
       //   igamma(a, x) = gamma(a, x) / Gamma(a)
       // where Gamma and gamma are considered the standard unnormalized
       // upper and lower incomplete gamma functions, respectively.
-      ArrayType a = m1.abs() + 2;
-      ArrayType x = m2.abs() + 2;
+      ArrayType a = m1.abs() + Scalar(2);
+      ArrayType x = m2.abs() + Scalar(2);
       ArrayType zero = ArrayType::Zero(rows, cols);
       ArrayType one = ArrayType::Constant(rows, cols, Scalar(1.0));
       ArrayType a_m1 = a - one;
@@ -83,18 +94,18 @@
       VERIFY_IS_APPROX(Gamma_a_x + gamma_a_x, a.lgamma().exp());
 
       // Gamma(a, x) == (a - 1) * Gamma(a-1, x) + x^(a-1) * exp(-x)
-      VERIFY_IS_APPROX(Gamma_a_x, (a - 1) * Gamma_a_m1_x + x.pow(a-1) * (-x).exp());
+      VERIFY_IS_APPROX(Gamma_a_x, (a - Scalar(1)) * Gamma_a_m1_x + x.pow(a-Scalar(1)) * (-x).exp());
 
       // gamma(a, x) == (a - 1) * gamma(a-1, x) - x^(a-1) * exp(-x)
-      VERIFY_IS_APPROX(gamma_a_x, (a - 1) * gamma_a_m1_x - x.pow(a-1) * (-x).exp());
+      VERIFY_IS_APPROX(gamma_a_x, (a - Scalar(1)) * gamma_a_m1_x - x.pow(a-Scalar(1)) * (-x).exp());
     }
     {
       // Verify for large a and x that values are between 0 and 1.
       ArrayType m1 = ArrayType::Random(rows,cols);
       ArrayType m2 = ArrayType::Random(rows,cols);
-      Scalar max_exponent = std::numeric_limits<Scalar>::max_exponent10;
-      ArrayType a = m1.abs() *  pow(10., max_exponent - 1);
-      ArrayType x = m2.abs() *  pow(10., max_exponent - 1);
+      int max_exponent = std::numeric_limits<Scalar>::max_exponent10;
+      ArrayType a = m1.abs() *  Scalar(pow(10., max_exponent - 1));
+      ArrayType x = m2.abs() *  Scalar(pow(10., max_exponent - 1));
       for (int i = 0; i < a.size(); ++i) {
         Scalar igam = numext::igamma(a(i), x(i));
         VERIFY(0 <= igam);
@@ -108,27 +119,37 @@
       Scalar x_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};
 
       // location i*6+j corresponds to a_s[i], x_s[j].
-      Scalar igamma_s[][6] = {{0.0, nan, nan, nan, nan, nan},
-                              {0.0, 0.6321205588285578, 0.7768698398515702,
-                              0.9816843611112658, 9.999500016666262e-05, 1.0},
-                              {0.0, 0.4275932955291202, 0.608374823728911,
-                              0.9539882943107686, 7.522076445089201e-07, 1.0},
-                              {0.0, 0.01898815687615381, 0.06564245437845008,
-                              0.5665298796332909, 4.166333347221828e-18, 1.0},
-                              {0.0, 0.9999780593618628, 0.9999899967080838,
-                              0.9999996219837988, 0.9991370418689945, 1.0},
-                              {0.0, 0.0, 0.0, 0.0, 0.0, 0.5042041932513908}};
-      Scalar igammac_s[][6] = {{nan, nan, nan, nan, nan, nan},
-                              {1.0, 0.36787944117144233, 0.22313016014842982,
-                                0.018315638888734182, 0.9999000049998333, 0.0},
-                              {1.0, 0.5724067044708798, 0.3916251762710878,
-                                0.04601170568923136, 0.9999992477923555, 0.0},
-                              {1.0, 0.9810118431238462, 0.9343575456215499,
-                                0.4334701203667089, 1.0, 0.0},
-                              {1.0, 2.1940638138146658e-05, 1.0003291916285e-05,
-                                3.7801620118431334e-07, 0.0008629581310054535,
-                                0.0},
-                              {1.0, 1.0, 1.0, 1.0, 1.0, 0.49579580674813944}};
+      Scalar igamma_s[][6] = {
+          {Scalar(0.0), nan, nan, nan, nan, nan},
+          {Scalar(0.0), Scalar(0.6321205588285578), Scalar(0.7768698398515702),
+           Scalar(0.9816843611112658), Scalar(9.999500016666262e-05),
+           Scalar(1.0)},
+          {Scalar(0.0), Scalar(0.4275932955291202), Scalar(0.608374823728911),
+           Scalar(0.9539882943107686), Scalar(7.522076445089201e-07),
+           Scalar(1.0)},
+          {Scalar(0.0), Scalar(0.01898815687615381),
+           Scalar(0.06564245437845008), Scalar(0.5665298796332909),
+           Scalar(4.166333347221828e-18), Scalar(1.0)},
+          {Scalar(0.0), Scalar(0.9999780593618628), Scalar(0.9999899967080838),
+           Scalar(0.9999996219837988), Scalar(0.9991370418689945), Scalar(1.0)},
+          {Scalar(0.0), Scalar(0.0), Scalar(0.0), Scalar(0.0), Scalar(0.0),
+           Scalar(0.5042041932513908)}};
+      Scalar igammac_s[][6] = {
+          {nan, nan, nan, nan, nan, nan},
+          {Scalar(1.0), Scalar(0.36787944117144233),
+           Scalar(0.22313016014842982), Scalar(0.018315638888734182),
+           Scalar(0.9999000049998333), Scalar(0.0)},
+          {Scalar(1.0), Scalar(0.5724067044708798), Scalar(0.3916251762710878),
+           Scalar(0.04601170568923136), Scalar(0.9999992477923555),
+           Scalar(0.0)},
+          {Scalar(1.0), Scalar(0.9810118431238462), Scalar(0.9343575456215499),
+           Scalar(0.4334701203667089), Scalar(1.0), Scalar(0.0)},
+          {Scalar(1.0), Scalar(2.1940638138146658e-05),
+           Scalar(1.0003291916285e-05), Scalar(3.7801620118431334e-07),
+           Scalar(0.0008629581310054535), Scalar(0.0)},
+          {Scalar(1.0), Scalar(1.0), Scalar(1.0), Scalar(1.0), Scalar(1.0),
+           Scalar(0.49579580674813944)}};
+
       for (int i = 0; i < 6; ++i) {
         for (int j = 0; j < 6; ++j) {
           if ((std::isnan)(igamma_s[i][j])) {
@@ -162,8 +183,8 @@
         ArrayType m1 = ArrayType::Random(32);
         using std::sqrt;
 
-        ArrayType cdf_val = (m1 / sqrt(2.)).erf();
-        cdf_val = (cdf_val + 1.) / 2.;
+        ArrayType cdf_val = (m1 / Scalar(sqrt(2.))).erf();
+        cdf_val = (cdf_val + Scalar(1)) / Scalar(2);
         verify_component_wise(cdf_val.ndtri(), m1););
 
   }
@@ -190,7 +211,6 @@
     CALL_SUBTEST( res = digamma(x);  verify_component_wise(res, ref); );
   }
 
-
 #if EIGEN_HAS_C99_MATH
   {
     ArrayType n(11), x(11), res(11), ref(11);
@@ -323,8 +343,8 @@
     ArrayType m3 = ArrayType::Random(32);
     ArrayType one = ArrayType::Constant(32, Scalar(1.0));
     const Scalar eps = std::numeric_limits<Scalar>::epsilon();
-    ArrayType a = (m1 * 4.0).exp();
-    ArrayType b = (m2 * 4.0).exp();
+    ArrayType a = (m1 * Scalar(4)).exp();
+    ArrayType b = (m2 * Scalar(4)).exp();
     ArrayType x = m3.abs();
 
     // betainc(a, 1, x) == x**a
@@ -471,4 +491,7 @@
 {
   CALL_SUBTEST_1(array_special_functions<ArrayXf>());
   CALL_SUBTEST_2(array_special_functions<ArrayXd>());
+  // TODO(cantonios): half/bfloat16 don't have enough precision to reproduce results above.
+  // CALL_SUBTEST_3(array_special_functions<ArrayX<Eigen::half>>());
+  // CALL_SUBTEST_4(array_special_functions<ArrayX<Eigen::bfloat16>>());
 }
diff --git a/unsupported/test/special_packetmath.cpp b/unsupported/test/special_packetmath.cpp
index 87b8735..4f426eb 100644
--- a/unsupported/test/special_packetmath.cpp
+++ b/unsupported/test/special_packetmath.cpp
@@ -8,6 +8,7 @@
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
+#include <limits>
 #include "packetmath_test_shared.h"
 #include "../Eigen/SpecialFunctions"
 
@@ -43,42 +44,48 @@
   }
   {
     for (int i=0; i<size; ++i) {
-      data1[i] = internal::random<Scalar>(0,1);
+      data1[i] = internal::random<Scalar>(Scalar(0),Scalar(1));
     }
     CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasNdtri, numext::ndtri, internal::pndtri);
   }
 #endif  // EIGEN_HAS_C99_MATH
 
   // For bessel_i*e and bessel_j*, the valid range is negative reals.
-  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));
-  }
+    const int max_exponent = numext::mini(std::numeric_limits<Scalar>::max_exponent10-1, 6);
+    for (int i=0; i<size; ++i)
+    {
+      data1[i] = internal::random<Scalar>(Scalar(-1),Scalar(1)) * Scalar(std::pow(Scalar(10), internal::random<Scalar>(Scalar(-max_exponent),Scalar(max_exponent))));
+      data2[i] = internal::random<Scalar>(Scalar(-1),Scalar(1)) * Scalar(std::pow(Scalar(10), internal::random<Scalar>(Scalar(-max_exponent),Scalar(max_exponent))));
+    }
 
-  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_i0e, internal::pbessel_i0e);
-  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_i1e, internal::pbessel_i1e);
-  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_j0, internal::pbessel_j0);
-  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_j1, internal::pbessel_j1);
+    CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_i0e, internal::pbessel_i0e);
+    CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_i1e, internal::pbessel_i1e);
+    CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_j0, internal::pbessel_j0);
+    CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_j1, internal::pbessel_j1);
+  }
 
   // Use a smaller data range for the bessel_i* as these can become very large.
   // Following #1693, we also restrict this range further to avoid inf's due to
   // differences in pexp and exp.
   for (int i=0; i<size; ++i) {
-      data1[i] = internal::random<Scalar>(0.01,1) * std::pow(
-          Scalar(9), internal::random<Scalar>(-1,2));
-      data2[i] = internal::random<Scalar>(0.01,1) * std::pow(
-          Scalar(9), internal::random<Scalar>(-1,2));
+      data1[i] = internal::random<Scalar>(Scalar(0.01),Scalar(1)) *
+                  Scalar(std::pow(Scalar(9), internal::random<Scalar>(Scalar(-1),Scalar(2))));
+      data2[i] = internal::random<Scalar>(Scalar(0.01),Scalar(1)) *
+                  Scalar(std::pow(Scalar(9), internal::random<Scalar>(Scalar(-1),Scalar(2))));
   }
   CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_i0, internal::pbessel_i0);
   CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_i1, internal::pbessel_i1);
 
 
   // y_i, and k_i are valid for x > 0.
-  for (int i=0; i<size; ++i)
   {
-    data1[i] = internal::random<Scalar>(0.01,1) * std::pow(Scalar(10), internal::random<Scalar>(-2,5));
-    data2[i] = internal::random<Scalar>(0.01,1) * std::pow(Scalar(10), internal::random<Scalar>(-2,5));
+    const int max_exponent = numext::mini(std::numeric_limits<Scalar>::max_exponent10-1, 5);
+    for (int i=0; i<size; ++i)
+    {
+      data1[i] = internal::random<Scalar>(Scalar(0.01),Scalar(1)) * Scalar(std::pow(Scalar(10), internal::random<Scalar>(Scalar(-2),Scalar(max_exponent))));
+      data2[i] = internal::random<Scalar>(Scalar(0.01),Scalar(1)) * Scalar(std::pow(Scalar(10), internal::random<Scalar>(Scalar(-2),Scalar(max_exponent))));
+    }
   }
 
   // TODO(srvasude): Re-enable this test once properly investigated why the
@@ -91,20 +98,20 @@
   // Following #1693, we restrict the range for exp to avoid zeroing out too
   // fast.
   for (int i=0; i<size; ++i) {
-      data1[i] = internal::random<Scalar>(0.01,1) * std::pow(
-          Scalar(9), internal::random<Scalar>(-1,2));
-      data2[i] = internal::random<Scalar>(0.01,1) * std::pow(
-          Scalar(9), internal::random<Scalar>(-1,2));
+      data1[i] = internal::random<Scalar>(Scalar(0.01),Scalar(1)) *
+                  Scalar(std::pow(Scalar(9), internal::random<Scalar>(Scalar(-1),Scalar(2))));
+      data2[i] = internal::random<Scalar>(Scalar(0.01),Scalar(1)) *
+                  Scalar(std::pow(Scalar(9), internal::random<Scalar>(Scalar(-1),Scalar(2))));
   }
   CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_k0, internal::pbessel_k0);
   CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_k1, internal::pbessel_k1);
 
 
   for (int i=0; i<size; ++i) {
-      data1[i] = internal::random<Scalar>(0.01,1) * std::pow(
-          Scalar(10), internal::random<Scalar>(-1,2));
-      data2[i] = internal::random<Scalar>(0.01,1) * std::pow(
-          Scalar(10), internal::random<Scalar>(-1,2));
+      data1[i] = internal::random<Scalar>(Scalar(0.01),Scalar(1)) *
+                  Scalar(std::pow(Scalar(10), internal::random<Scalar>(Scalar(-1),Scalar(2))));
+      data2[i] = internal::random<Scalar>(Scalar(0.01),Scalar(1)) *
+                  Scalar(std::pow(Scalar(10), internal::random<Scalar>(Scalar(-1),Scalar(2))));
   }
 
 #if EIGEN_HAS_C99_MATH && (__cplusplus > 199711L)
@@ -135,6 +142,8 @@
 
     CALL_SUBTEST_1( test::runner<float>::run() );
     CALL_SUBTEST_2( test::runner<double>::run() );
+    CALL_SUBTEST_3( test::runner<Eigen::half>::run() );
+    CALL_SUBTEST_4( test::runner<Eigen::bfloat16>::run() );
     g_first_pass = false;
   }
 }