Pull latest updates from upstream

CMakeLists.txt

@@ -246,7 +246,7 @@ if(NOT MSVC)
     else()
       set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfpu=neon")
     endif()
-    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfloat-abi=softfp")
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfloat-abi=hard")
     message(STATUS "Enabling NEON in tests/examples")
   endif()
 
@@ -256,7 +256,11 @@ if(NOT MSVC)
     message(STATUS "Enabling NEON in tests/examples")
   endif()
 
-
+  option(EIGEN_TEST_ZVECTOR "Enable/Disable S390X(zEC13) ZVECTOR in tests/examples" OFF)
+  if(EIGEN_TEST_ZVECTOR)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -march=z13 -mzvector")
+    message(STATUS "Enabling S390X(zEC13) ZVECTOR in tests/examples")
+  endif()
 
   check_cxx_compiler_flag("-fopenmp" COMPILER_SUPPORT_OPENMP)
   if(COMPILER_SUPPORT_OPENMP)
@@ -342,6 +346,8 @@ endif()
 
 option(EIGEN_TEST_CXX11 "Enable testing with C++11 and C++11 features (e.g. Tensor module)." OFF)
 
+set(EIGEN_CUDA_COMPUTE_ARCH 30 CACHE STRING "The CUDA compute architecture level to target when compiling CUDA code")
+
 include_directories(${CMAKE_CURRENT_SOURCE_DIR} ${CMAKE_CURRENT_BINARY_DIR})
 
 # Backward compatibility support for EIGEN_INCLUDE_INSTALL_DIR

Eigen/CholmodSupport

@@ -19,7 +19,7 @@ extern "C" {
 /** \ingroup Support_modules
   * \defgroup CholmodSupport_Module CholmodSupport module
   *
-  * This module provides an interface to the Cholmod library which is part of the <a href="http://www.cise.ufl.edu/research/sparse/SuiteSparse/">suitesparse</a> package.
+  * This module provides an interface to the Cholmod library which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
   * It provides the two following main factorization classes:
   * - class CholmodSupernodalLLT: a supernodal LLT Cholesky factorization.
   * - class CholmodDecomposiiton: a general L(D)LT Cholesky factorization with automatic or explicit runtime selection of the underlying factorization method (supernodal or simplicial).

Eigen/Core

@@ -42,7 +42,10 @@
   
 #endif
 
-#if defined(__CUDA_ARCH__)
+// When compiling CUDA device code with NVCC, pull in math functions from the
+// global namespace.  In host mode, and when device doee with clang, use the
+// std versions.
+#if defined(__CUDA_ARCH__) && defined(__NVCC__)
   #define EIGEN_USING_STD_MATH(FUNC) using ::FUNC;
 #else
   #define EIGEN_USING_STD_MATH(FUNC) using std::FUNC;
@@ -202,12 +205,25 @@
     #define EIGEN_VECTORIZE
     #define EIGEN_VECTORIZE_NEON
     #include <arm_neon.h>
+  #elif (defined __s390x__ && defined __VEC__)
+    #define EIGEN_VECTORIZE
+    #define EIGEN_VECTORIZE_ZVECTOR
+    #include <vecintrin.h>
   #endif
 #endif
 
+#if defined(__F16C__)
+  // We can use the optimized fp16 to float and float to fp16 conversion routines
+  #define EIGEN_HAS_FP16_C
+#endif
+
 #if defined __CUDACC__
   #define EIGEN_VECTORIZE_CUDA
   #include <vector_types.h>
+  #if defined __CUDACC_VER__ && __CUDACC_VER__ >= 70500
+    #define EIGEN_HAS_CUDA_FP16
+    #include <cuda_fp16.h>
+  #endif
 #endif
 
 #if (defined _OPENMP) && (!defined EIGEN_DONT_PARALLELIZE)
@@ -273,6 +289,8 @@ inline static const char *SimdInstructionSetsInUse(void) {
   return "VSX";
 #elif defined(EIGEN_VECTORIZE_NEON)
   return "ARM NEON";
+#elif defined(EIGEN_VECTORIZE_ZVECTOR)
+  return "S390X ZVECTOR";
 #else
   return "None";
 #endif
@@ -310,6 +328,7 @@ using std::ptrdiff_t;
 
 #include "src/Core/NumTraits.h"
 #include "src/Core/MathFunctions.h"
+#include "src/Core/SpecialFunctions.h"
 #include "src/Core/GenericPacketMath.h"
 
 #if defined EIGEN_VECTORIZE_AVX512
@@ -339,11 +358,19 @@ using std::ptrdiff_t;
   #include "src/Core/arch/NEON/PacketMath.h"
   #include "src/Core/arch/NEON/MathFunctions.h"
   #include "src/Core/arch/NEON/Complex.h"
+#elif defined EIGEN_VECTORIZE_ZVECTOR
+  #include "src/Core/arch/ZVector/PacketMath.h"
+  #include "src/Core/arch/ZVector/MathFunctions.h"
+  #include "src/Core/arch/ZVector/Complex.h"
 #endif
 
+#include "src/Core/arch/CUDA/Half.h"
+
 #if defined EIGEN_VECTORIZE_CUDA
   #include "src/Core/arch/CUDA/PacketMath.h"
+  #include "src/Core/arch/CUDA/PacketMathHalf.h"
   #include "src/Core/arch/CUDA/MathFunctions.h"
+  #include "src/Core/arch/CUDA/TypeCasting.h"
 #endif
 
 #include "src/Core/arch/Default/Settings.h"
@@ -438,14 +465,14 @@ using std::ptrdiff_t;
 #include "src/Core/ArrayWrapper.h"
 
 #ifdef EIGEN_USE_BLAS
-#include "src/Core/products/GeneralMatrixMatrix_MKL.h"
+#include "src/Core/products/GeneralMatrixMatrix_BLAS.h"
-#include "src/Core/products/GeneralMatrixVector_MKL.h"
+#include "src/Core/products/GeneralMatrixVector_BLAS.h"
-#include "src/Core/products/GeneralMatrixMatrixTriangular_MKL.h"
+#include "src/Core/products/GeneralMatrixMatrixTriangular_BLAS.h"
-#include "src/Core/products/SelfadjointMatrixMatrix_MKL.h"
+#include "src/Core/products/SelfadjointMatrixMatrix_BLAS.h"
-#include "src/Core/products/SelfadjointMatrixVector_MKL.h"
+#include "src/Core/products/SelfadjointMatrixVector_BLAS.h"
-#include "src/Core/products/TriangularMatrixMatrix_MKL.h"
+#include "src/Core/products/TriangularMatrixMatrix_BLAS.h"
-#include "src/Core/products/TriangularMatrixVector_MKL.h"
+#include "src/Core/products/TriangularMatrixVector_BLAS.h"
-#include "src/Core/products/TriangularSolverMatrix_MKL.h"
+#include "src/Core/products/TriangularSolverMatrix_BLAS.h"
 #endif // EIGEN_USE_BLAS
 
 #ifdef EIGEN_USE_MKL_VML

Eigen/Geometry

@@ -17,16 +17,16 @@
 #include <limits>
 
 /** \defgroup Geometry_Module Geometry module
-  *
-  *
   *
   * This module provides support for:
   *  - fixed-size homogeneous transformations
   *  - translation, scaling, 2D and 3D rotations
-  *  - quaternions
+  *  - \link Quaternion quaternions \endlink
-  *  - \ref MatrixBase::cross() "cross product"
+  *  - cross products (\ref MatrixBase::cross, \ref MatrixBase::cross3)
-  *  - \ref MatrixBase::unitOrthogonal() "orthognal vector generation"
+  *  - orthognal vector generation (\ref MatrixBase::unitOrthogonal)
-  *  - some linear components: parametrized-lines and hyperplanes
+  *  - some linear components: \link ParametrizedLine parametrized-lines \endlink and \link Hyperplane hyperplanes \endlink
+  *  - \link AlignedBox axis aligned bounding boxes \endlink
+  *  - \link umeyama least-square transformation fitting \endlink
   *
   * \code
   * #include <Eigen/Geometry>

Eigen/PaStiXSupport

@@ -12,7 +12,6 @@
 
 #include "src/Core/util/DisableStupidWarnings.h"
 
-#include <complex.h>
 extern "C" {
 #include <pastix_nompi.h>
 #include <pastix.h>

Eigen/PardisoSupport

@@ -14,8 +14,6 @@
 
 #include <mkl_pardiso.h>
 
-#include <unsupported/Eigen/SparseExtra>
-
 /** \ingroup Support_modules
   * \defgroup PardisoSupport_Module PardisoSupport module
   *

Eigen/QR

@@ -34,6 +34,7 @@
 #include "src/QR/HouseholderQR.h"
 #include "src/QR/FullPivHouseholderQR.h"
 #include "src/QR/ColPivHouseholderQR.h"
+#include "src/QR/CompleteOrthogonalDecomposition.h"
 #ifdef EIGEN_USE_LAPACKE
 #include "src/QR/HouseholderQR_MKL.h"
 #include "src/QR/ColPivHouseholderQR_MKL.h"

Eigen/SPQRSupport

@@ -17,7 +17,7 @@
 /** \ingroup Support_modules
   * \defgroup SPQRSupport_Module SuiteSparseQR module
   * 
-  * This module provides an interface to the SPQR library, which is part of the <a href="http://www.cise.ufl.edu/research/sparse/SuiteSparse/">suitesparse</a> package.
+  * This module provides an interface to the SPQR library, which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
   *
   * \code
   * #include <Eigen/SPQRSupport>

Eigen/SuperLUSupport

@@ -43,6 +43,8 @@ namespace Eigen { struct SluMatrix; }
   * - class SuperLU: a supernodal sequential LU factorization.
   * - class SuperILU: a supernodal sequential incomplete LU factorization (to be used as a preconditioner for iterative methods).
   *
+  * \warning This wrapper is only for the 4.x versions of SuperLU. The 3.x and 5.x versions are not supported.
+  *
   * \warning When including this module, you have to use SUPERLU_EMPTY instead of EMPTY which is no longer defined because it is too polluting.
   *
   * \code

Eigen/UmfPackSupport

@@ -19,7 +19,7 @@ extern "C" {
 /** \ingroup Support_modules
   * \defgroup UmfPackSupport_Module UmfPackSupport module
   *
-  * This module provides an interface to the UmfPack library which is part of the <a href="http://www.cise.ufl.edu/research/sparse/SuiteSparse/">suitesparse</a> package.
+  * This module provides an interface to the UmfPack library which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
   * It provides the following factorization class:
   * - class UmfPackLU: a multifrontal sequential LU factorization.
   *

Eigen/src/Cholesky/LDLT.h

@@ -28,8 +28,8 @@ namespace internal {
   *
   * \brief Robust Cholesky decomposition of a matrix with pivoting
   *
-  * \param MatrixType the type of the matrix of which to compute the LDL^T Cholesky decomposition
+  * \tparam _MatrixType the type of the matrix of which to compute the LDL^T Cholesky decomposition
-  * \param UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper.
+  * \tparam _UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper.
   *             The other triangular part won't be read.
   *
   * Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite
@@ -266,8 +266,8 @@ template<> struct ldlt_inplace<Lower>
     if (size <= 1)
     {
       transpositions.setIdentity();
-      if (numext::real(mat.coeff(0,0)) > 0) sign = PositiveSemiDef;
+      if (numext::real(mat.coeff(0,0)) > static_cast<RealScalar>(0) ) sign = PositiveSemiDef;
-      else if (numext::real(mat.coeff(0,0)) < 0) sign = NegativeSemiDef;
+      else if (numext::real(mat.coeff(0,0)) < static_cast<RealScalar>(0)) sign = NegativeSemiDef;
       else sign = ZeroSign;
       return true;
     }
@@ -324,12 +324,12 @@ template<> struct ldlt_inplace<Lower>
         A21 /= realAkk;
 
       if (sign == PositiveSemiDef) {
-        if (realAkk < 0) sign = Indefinite;
+        if (realAkk < static_cast<RealScalar>(0)) sign = Indefinite;
       } else if (sign == NegativeSemiDef) {
-        if (realAkk > 0) sign = Indefinite;
+        if (realAkk > static_cast<RealScalar>(0)) sign = Indefinite;
       } else if (sign == ZeroSign) {
-        if (realAkk > 0) sign = PositiveSemiDef;
+        if (realAkk > static_cast<RealScalar>(0)) sign = PositiveSemiDef;
-        else if (realAkk < 0) sign = NegativeSemiDef;
+        else if (realAkk < static_cast<RealScalar>(0)) sign = NegativeSemiDef;
       }
     }
 

Eigen/src/Cholesky/LLT.h

@@ -22,8 +22,8 @@ template<typename MatrixType, int UpLo> struct LLT_Traits;
   *
   * \brief Standard Cholesky decomposition (LL^T) of a matrix and associated features
   *
-  * \param MatrixType the type of the matrix of which we are computing the LL^T Cholesky decomposition
+  * \tparam _MatrixType the type of the matrix of which we are computing the LL^T Cholesky decomposition
-  * \param UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper.
+  * \tparam _UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper.
   *             The other triangular part won't be read.
   *
   * This class performs a LL^T Cholesky decomposition of a symmetric, positive definite
@@ -436,10 +436,7 @@ void LLT<_MatrixType,_UpLo>::_solve_impl(const RhsType &rhs, DstType &dst) const
   *
   * \param bAndX represents both the right-hand side matrix b and result x.
   *
-  * \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
+  * This version avoids a copy when the right hand side matrix b is not needed anymore.
-  *
-  * This version avoids a copy when the right hand side matrix b is not
-  * needed anymore.
   *
   * \sa LLT::solve(), MatrixBase::llt()
   */

Eigen/src/CholmodSupport/CholmodSupport.h

@@ -78,7 +78,7 @@ cholmod_sparse viewAsCholmod(SparseMatrix<_Scalar,_Options,_StorageIndex>& mat)
   {
     res.itype = CHOLMOD_INT;
   }
-  else if (internal::is_same<_StorageIndex,SuiteSparse_long>::value)
+  else if (internal::is_same<_StorageIndex,long>::value)
   {
     res.itype = CHOLMOD_LONG;
   }
@@ -178,14 +178,14 @@ class CholmodBase : public SparseSolverBase<Derived>
   public:
 
     CholmodBase()
-      : m_cholmodFactor(0), m_info(Success)
+      : m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false)
     {
       m_shiftOffset[0] = m_shiftOffset[1] = RealScalar(0.0);
       cholmod_start(&m_cholmod);
     }
 
     explicit CholmodBase(const MatrixType& matrix)
-      : m_cholmodFactor(0), m_info(Success)
+      : m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false)
     {
       m_shiftOffset[0] = m_shiftOffset[1] = RealScalar(0.0);
       cholmod_start(&m_cholmod);
@@ -273,9 +273,10 @@ class CholmodBase : public SparseSolverBase<Derived>
       const Index size = m_cholmodFactor->n;
       EIGEN_UNUSED_VARIABLE(size);
       eigen_assert(size==b.rows());
+      
+      // Cholmod needs column-major stoarge without inner-stride, which corresponds to the default behavior of Ref.
+      Ref<const Matrix<typename Rhs::Scalar,Dynamic,Dynamic,ColMajor> > b_ref(b.derived());
 
-      // note: cd stands for Cholmod Dense
-      Rhs& b_ref(b.const_cast_derived());
       cholmod_dense b_cd = viewAsCholmod(b_ref);
       cholmod_dense* x_cd = cholmod_solve(CHOLMOD_A, m_cholmodFactor, &b_cd, &m_cholmod);
       if(!x_cd)
@@ -327,6 +328,57 @@ class CholmodBase : public SparseSolverBase<Derived>
       return derived();
     }
     
+    /** \returns the determinant of the underlying matrix from the current factorization */
+    Scalar determinant() const
+    {
+      using std::exp;
+      return exp(logDeterminant());
+    }
+
+    /** \returns the log determinant of the underlying matrix from the current factorization */
+    Scalar logDeterminant() const
+    {
+      using std::log;
+      using numext::real;
+      eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
+
+      RealScalar logDet = 0;
+      Scalar *x = static_cast<Scalar*>(m_cholmodFactor->x);
+      if (m_cholmodFactor->is_super)
+      {
+        // Supernodal factorization stored as a packed list of dense column-major blocs,
+        // as described by the following structure:
+
+        // super[k] == index of the first column of the j-th super node
+        StorageIndex *super = static_cast<StorageIndex*>(m_cholmodFactor->super);
+        // pi[k] == offset to the description of row indices
+        StorageIndex *pi = static_cast<StorageIndex*>(m_cholmodFactor->pi);
+        // px[k] == offset to the respective dense block
+        StorageIndex *px = static_cast<StorageIndex*>(m_cholmodFactor->px);
+
+        Index nb_super_nodes = m_cholmodFactor->nsuper;
+        for (Index k=0; k < nb_super_nodes; ++k)
+        {
+          StorageIndex ncols = super[k + 1] - super[k];
+          StorageIndex nrows = pi[k + 1] - pi[k];
+
+          Map<const Array<Scalar,1,Dynamic>, 0, InnerStride<> > sk(x + px[k], ncols, InnerStride<>(nrows+1));
+          logDet += sk.real().log().sum();
+        }
+      }
+      else
+      {
+        // Simplicial factorization stored as standard CSC matrix.
+        StorageIndex *p = static_cast<StorageIndex*>(m_cholmodFactor->p);
+        Index size = m_cholmodFactor->n;
+        for (Index k=0; k<size; ++k)
+          logDet += log(real( x[p[k]] ));
+      }
+      if (m_cholmodFactor->is_ll)
+        logDet *= 2.0;
+      return logDet;
+    };
+
     template<typename Stream>
     void dumpMemory(Stream& /*s*/)
     {}
@@ -358,7 +410,7 @@ class CholmodBase : public SparseSolverBase<Derived>
   *
   * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
   *
-  * \sa \ref TutorialSparseDirectSolvers, class CholmodSupernodalLLT, class SimplicialLLT
+  * \sa \ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLLT
   */
 template<typename _MatrixType, int _UpLo = Lower>
 class CholmodSimplicialLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT<_MatrixType, _UpLo> >
@@ -407,7 +459,7 @@ class CholmodSimplicialLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimpl
   *
   * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
   *
-  * \sa \ref TutorialSparseDirectSolvers, class CholmodSupernodalLLT, class SimplicialLDLT
+  * \sa \ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLDLT
   */
 template<typename _MatrixType, int _UpLo = Lower>
 class CholmodSimplicialLDLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT<_MatrixType, _UpLo> >
@@ -454,7 +506,7 @@ class CholmodSimplicialLDLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimp
   *
   * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
   *
-  * \sa \ref TutorialSparseDirectSolvers
+  * \sa \ref TutorialSparseSolverConcept
   */
 template<typename _MatrixType, int _UpLo = Lower>
 class CholmodSupernodalLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT<_MatrixType, _UpLo> >
@@ -503,7 +555,7 @@ class CholmodSupernodalLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSuper
   *
   * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
   *
-  * \sa \ref TutorialSparseDirectSolvers
+  * \sa \ref TutorialSparseSolverConcept
   */
 template<typename _MatrixType, int _UpLo = Lower>
 class CholmodDecomposition : public CholmodBase<_MatrixType, _UpLo, CholmodDecomposition<_MatrixType, _UpLo> >

Eigen/src/Core/Array.h

@@ -12,7 +12,16 @@
 
 namespace Eigen {
 
-/** \class Array 
+namespace internal {
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+struct traits<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > : traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
+{
+  typedef ArrayXpr XprKind;
+  typedef ArrayBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > XprBase;
+};
+}
+
+/** \class Array
   * \ingroup Core_Module
   *
   * \brief General-purpose arrays with easy API for coefficient-wise operations
@@ -26,21 +35,12 @@ namespace Eigen {
   *
   * See documentation of class Matrix for detailed information on the template parameters
   * storage layout.
-  * 
+  *
   * This class can be extended with the help of the plugin mechanism described on the page
   * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_ARRAY_PLUGIN.
   *
-  * \sa \ref TutorialArrayClass, \ref TopicClassHierarchy
+  * \sa \blank \ref TutorialArrayClass, \ref TopicClassHierarchy
   */
-namespace internal {
-template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
-struct traits<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > : traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
-{
-  typedef ArrayXpr XprKind;
-  typedef ArrayBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> > XprBase;
-};
-}
-
 template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
 class Array
   : public PlainObjectBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >

Eigen/src/Core/ArrayBase.h

@@ -103,7 +103,7 @@ template<typename Derived> class ArrayBase
     /** Special case of the template operator=, in order to prevent the compiler
       * from generating a default operator= (issue hit with g++ 4.1)
       */
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     Derived& operator=(const ArrayBase& other)
     {
       internal::call_assignment(derived(), other.derived());
@@ -112,28 +112,28 @@ template<typename Derived> class ArrayBase
     
     /** Set all the entries to \a value.
       * \sa DenseBase::setConstant(), DenseBase::fill() */
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     Derived& operator=(const Scalar &value)
     { Base::setConstant(value); return derived(); }
 
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     Derived& operator+=(const Scalar& scalar);
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     Derived& operator-=(const Scalar& scalar);
 
     template<typename OtherDerived>
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     Derived& operator+=(const ArrayBase<OtherDerived>& other);
     template<typename OtherDerived>
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     Derived& operator-=(const ArrayBase<OtherDerived>& other);
 
     template<typename OtherDerived>
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     Derived& operator*=(const ArrayBase<OtherDerived>& other);
 
     template<typename OtherDerived>
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     Derived& operator/=(const ArrayBase<OtherDerived>& other);
 
   public:

Eigen/src/Core/ArrayWrapper.h

@@ -52,7 +52,7 @@ class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> >
                        const Scalar
                      >::type ScalarWithConstIfNotLvalue;
 
-    typedef typename internal::ref_selector<ExpressionType>::type NestedExpressionType;
+    typedef typename internal::ref_selector<ExpressionType>::non_const_type NestedExpressionType;
 
     EIGEN_DEVICE_FUNC
     explicit EIGEN_STRONG_INLINE ArrayWrapper(ExpressionType& matrix) : m_expression(matrix) {}
@@ -67,7 +67,7 @@ class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> >
     inline Index innerStride() const { return m_expression.innerStride(); }
 
     EIGEN_DEVICE_FUNC
-    inline ScalarWithConstIfNotLvalue* data() { return m_expression.const_cast_derived().data(); }
+    inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
     EIGEN_DEVICE_FUNC
     inline const Scalar* data() const { return m_expression.data(); }
 
@@ -80,13 +80,13 @@ class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> >
     EIGEN_DEVICE_FUNC
     inline Scalar& coeffRef(Index rowId, Index colId)
     {
-      return m_expression.const_cast_derived().coeffRef(rowId, colId);
+      return m_expression.coeffRef(rowId, colId);
     }
 
     EIGEN_DEVICE_FUNC
     inline const Scalar& coeffRef(Index rowId, Index colId) const
     {
-      return m_expression.const_cast_derived().coeffRef(rowId, colId);
+      return m_expression.coeffRef(rowId, colId);
     }
 
     EIGEN_DEVICE_FUNC
@@ -98,13 +98,13 @@ class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> >
     EIGEN_DEVICE_FUNC
     inline Scalar& coeffRef(Index index)
     {
-      return m_expression.const_cast_derived().coeffRef(index);
+      return m_expression.coeffRef(index);
     }
 
     EIGEN_DEVICE_FUNC
     inline const Scalar& coeffRef(Index index) const
     {
-      return m_expression.const_cast_derived().coeffRef(index);
+      return m_expression.coeffRef(index);
     }
 
     template<int LoadMode>
@@ -116,7 +116,7 @@ class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> >
     template<int LoadMode>
     inline void writePacket(Index rowId, Index colId, const PacketScalar& val)
     {
-      m_expression.const_cast_derived().template writePacket<LoadMode>(rowId, colId, val);
+      m_expression.template writePacket<LoadMode>(rowId, colId, val);
     }
 
     template<int LoadMode>
@@ -128,7 +128,7 @@ class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> >
     template<int LoadMode>
     inline void writePacket(Index index, const PacketScalar& val)
     {
-      m_expression.const_cast_derived().template writePacket<LoadMode>(index, val);
+      m_expression.template writePacket<LoadMode>(index, val);
     }
 
     template<typename Dest>
@@ -145,11 +145,11 @@ class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> >
     /** Forwards the resizing request to the nested expression
       * \sa DenseBase::resize(Index)  */
     EIGEN_DEVICE_FUNC
-    void resize(Index newSize) { m_expression.const_cast_derived().resize(newSize); }
+    void resize(Index newSize) { m_expression.resize(newSize); }
     /** Forwards the resizing request to the nested expression
       * \sa DenseBase::resize(Index,Index)*/
     EIGEN_DEVICE_FUNC
-    void resize(Index rows, Index cols) { m_expression.const_cast_derived().resize(rows,cols); }
+    void resize(Index rows, Index cols) { m_expression.resize(rows,cols); }
 
   protected:
     NestedExpressionType m_expression;
@@ -195,7 +195,7 @@ class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> >
                        const Scalar
                      >::type ScalarWithConstIfNotLvalue;
 
-    typedef typename internal::ref_selector<ExpressionType>::type NestedExpressionType;
+    typedef typename internal::ref_selector<ExpressionType>::non_const_type NestedExpressionType;
 
     EIGEN_DEVICE_FUNC
     explicit inline MatrixWrapper(ExpressionType& matrix) : m_expression(matrix) {}
@@ -210,7 +210,7 @@ class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> >
     inline Index innerStride() const { return m_expression.innerStride(); }
 
     EIGEN_DEVICE_FUNC
-    inline ScalarWithConstIfNotLvalue* data() { return m_expression.const_cast_derived().data(); }
+    inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
     EIGEN_DEVICE_FUNC
     inline const Scalar* data() const { return m_expression.data(); }
 
@@ -223,7 +223,7 @@ class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> >
     EIGEN_DEVICE_FUNC
     inline Scalar& coeffRef(Index rowId, Index colId)
     {
-      return m_expression.const_cast_derived().coeffRef(rowId, colId);
+      return m_expression.coeffRef(rowId, colId);
     }
 
     EIGEN_DEVICE_FUNC
@@ -241,13 +241,13 @@ class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> >
     EIGEN_DEVICE_FUNC
     inline Scalar& coeffRef(Index index)
     {
-      return m_expression.const_cast_derived().coeffRef(index);
+      return m_expression.coeffRef(index);
     }
 
     EIGEN_DEVICE_FUNC
     inline const Scalar& coeffRef(Index index) const
     {
-      return m_expression.const_cast_derived().coeffRef(index);
+      return m_expression.coeffRef(index);
     }
 
     template<int LoadMode>
@@ -259,7 +259,7 @@ class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> >
     template<int LoadMode>
     inline void writePacket(Index rowId, Index colId, const PacketScalar& val)
     {
-      m_expression.const_cast_derived().template writePacket<LoadMode>(rowId, colId, val);
+      m_expression.template writePacket<LoadMode>(rowId, colId, val);
     }
 
     template<int LoadMode>
@@ -271,7 +271,7 @@ class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> >
     template<int LoadMode>
     inline void writePacket(Index index, const PacketScalar& val)
     {
-      m_expression.const_cast_derived().template writePacket<LoadMode>(index, val);
+      m_expression.template writePacket<LoadMode>(index, val);
     }
 
     EIGEN_DEVICE_FUNC
@@ -284,11 +284,11 @@ class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> >
     /** Forwards the resizing request to the nested expression
       * \sa DenseBase::resize(Index)  */
     EIGEN_DEVICE_FUNC
-    void resize(Index newSize) { m_expression.const_cast_derived().resize(newSize); }
+    void resize(Index newSize) { m_expression.resize(newSize); }
     /** Forwards the resizing request to the nested expression
       * \sa DenseBase::resize(Index,Index)*/
     EIGEN_DEVICE_FUNC
-    void resize(Index rows, Index cols) { m_expression.const_cast_derived().resize(rows,cols); }
+    void resize(Index rows, Index cols) { m_expression.resize(rows,cols); }
 
   protected:
     NestedExpressionType m_expression;

Eigen/src/Core/AssignEvaluator.h

@@ -606,7 +606,7 @@ public:
     assignPacket<StoreMode,LoadMode,PacketType>(row, col);
   }
   
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static Index rowIndexByOuterInner(Index outer, Index inner)
+  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Index rowIndexByOuterInner(Index outer, Index inner)
   {
     typedef typename DstEvaluatorType::ExpressionTraits Traits;
     return int(Traits::RowsAtCompileTime) == 1 ? 0
@@ -615,7 +615,7 @@ public:
       : inner;
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static Index colIndexByOuterInner(Index outer, Index inner)
+  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Index colIndexByOuterInner(Index outer, Index inner)
   {
     typedef typename DstEvaluatorType::ExpressionTraits Traits;
     return int(Traits::ColsAtCompileTime) == 1 ? 0
@@ -637,7 +637,7 @@ protected:
 ***************************************************************************/
 
 template<typename DstXprType, typename SrcXprType, typename Functor>
-EIGEN_DEVICE_FUNC void call_dense_assignment_loop(const DstXprType& dst, const SrcXprType& src, const Functor &func)
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void call_dense_assignment_loop(const DstXprType& dst, const SrcXprType& src, const Functor &func)
 {
   eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
   
@@ -654,7 +654,7 @@ EIGEN_DEVICE_FUNC void call_dense_assignment_loop(const DstXprType& dst, const S
 }
 
 template<typename DstXprType, typename SrcXprType>
-EIGEN_DEVICE_FUNC void call_dense_assignment_loop(const DstXprType& dst, const SrcXprType& src)
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void call_dense_assignment_loop(const DstXprType& dst, const SrcXprType& src)
 {
   call_dense_assignment_loop(dst, src, internal::assign_op<typename DstXprType::Scalar>());
 }
@@ -682,47 +682,53 @@ template< typename DstXprType, typename SrcXprType, typename Functor,
 struct Assignment;
 
 
-// The only purpose of this call_assignment() function is to deal with noalias() / AssumeAliasing and automatic transposition.
+// The only purpose of this call_assignment() function is to deal with noalias() / "assume-aliasing" and automatic transposition.
-// Indeed, I (Gael) think that this concept of AssumeAliasing was a mistake, and it makes thing quite complicated.
+// Indeed, I (Gael) think that this concept of "assume-aliasing" was a mistake, and it makes thing quite complicated.
-// So this intermediate function removes everything related to AssumeAliasing such that Assignment
+// So this intermediate function removes everything related to "assume-aliasing" such that Assignment
 // does not has to bother about these annoying details.
 
 template<typename Dst, typename Src>
-EIGEN_DEVICE_FUNC void call_assignment(Dst& dst, const Src& src)
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_assignment(Dst& dst, const Src& src)
 {
   call_assignment(dst, src, internal::assign_op<typename Dst::Scalar>());
 }
 template<typename Dst, typename Src>
-EIGEN_DEVICE_FUNC void call_assignment(const Dst& dst, const Src& src)
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_assignment(const Dst& dst, const Src& src)
 {
   call_assignment(dst, src, internal::assign_op<typename Dst::Scalar>());
 }
                      
-// Deal with AssumeAliasing
+// Deal with "assume-aliasing"
 template<typename Dst, typename Src, typename Func>
-EIGEN_DEVICE_FUNC void call_assignment(Dst& dst, const Src& src, const Func& func, typename enable_if<evaluator_traits<Src>::AssumeAliasing==1, void*>::type = 0)
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_assignment(Dst& dst, const Src& src, const Func& func, typename enable_if< evaluator_assume_aliasing<Src>::value, void*>::type = 0)
 {
   typename plain_matrix_type<Src>::type tmp(src);
   call_assignment_no_alias(dst, tmp, func);
 }
 
 template<typename Dst, typename Src, typename Func>
-EIGEN_DEVICE_FUNC void call_assignment(Dst& dst, const Src& src, const Func& func, typename enable_if<evaluator_traits<Src>::AssumeAliasing==0, void*>::type = 0)
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_assignment(Dst& dst, const Src& src, const Func& func, typename enable_if<!evaluator_assume_aliasing<Src>::value, void*>::type = 0)
 {
   call_assignment_no_alias(dst, src, func);
 }
 
-// by-pass AssumeAliasing
+// by-pass "assume-aliasing"
 // When there is no aliasing, we require that 'dst' has been properly resized
 template<typename Dst, template <typename> class StorageBase, typename Src, typename Func>
-EIGEN_DEVICE_FUNC void call_assignment(NoAlias<Dst,StorageBase>& dst, const Src& src, const Func& func)
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_assignment(NoAlias<Dst,StorageBase>& dst, const Src& src, const Func& func)
 {
   call_assignment_no_alias(dst.expression(), src, func);
 }
 
 
 template<typename Dst, typename Src, typename Func>
-EIGEN_DEVICE_FUNC void call_assignment_no_alias(Dst& dst, const Src& src, const Func& func)
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_assignment_no_alias(Dst& dst, const Src& src, const Func& func)
 {
   enum {
     NeedToTranspose = (    (int(Dst::RowsAtCompileTime) == 1 && int(Src::ColsAtCompileTime) == 1)
@@ -747,13 +753,15 @@ EIGEN_DEVICE_FUNC void call_assignment_no_alias(Dst& dst, const Src& src, const
   Assignment<ActualDstTypeCleaned,Src,Func>::run(actualDst, src, func);
 }
 template<typename Dst, typename Src>
-EIGEN_DEVICE_FUNC void call_assignment_no_alias(Dst& dst, const Src& src)
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_assignment_no_alias(Dst& dst, const Src& src)
 {
   call_assignment_no_alias(dst, src, internal::assign_op<typename Dst::Scalar>());
 }
 
 template<typename Dst, typename Src, typename Func>
-EIGEN_DEVICE_FUNC void call_assignment_no_alias_no_transpose(Dst& dst, const Src& src, const Func& func)
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_assignment_no_alias_no_transpose(Dst& dst, const Src& src, const Func& func)
 {
   Index dstRows = src.rows();
   Index dstCols = src.cols();
@@ -767,7 +775,8 @@ EIGEN_DEVICE_FUNC void call_assignment_no_alias_no_transpose(Dst& dst, const Src
   Assignment<Dst,Src,Func>::run(dst, src, func);
 }
 template<typename Dst, typename Src>
-EIGEN_DEVICE_FUNC void call_assignment_no_alias_no_transpose(Dst& dst, const Src& src)
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_assignment_no_alias_no_transpose(Dst& dst, const Src& src)
 {
   call_assignment_no_alias_no_transpose(dst, src, internal::assign_op<typename Dst::Scalar>());
 }
@@ -779,7 +788,8 @@ template<typename Dst, typename Src> void check_for_aliasing(const Dst &dst, con
 template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar>
 struct Assignment<DstXprType, SrcXprType, Functor, Dense2Dense, Scalar>
 {
-  EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const Functor &func)
+  EIGEN_DEVICE_FUNC
+  static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const Functor &func)
   {
     eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
     
@@ -796,7 +806,8 @@ struct Assignment<DstXprType, SrcXprType, Functor, Dense2Dense, Scalar>
 template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar>
 struct Assignment<DstXprType, SrcXprType, Functor, EigenBase2EigenBase, Scalar>
 {
-  EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar> &/*func*/)
+  EIGEN_DEVICE_FUNC
+  static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar> &/*func*/)
   {
     eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
     src.evalTo(dst);

Eigen/src/Core/BandMatrix.h

@@ -161,15 +161,15 @@ class BandMatrixBase : public EigenBase<Derived>
   *
   * \brief Represents a rectangular matrix with a banded storage
   *
-  * \param _Scalar Numeric type, i.e. float, double, int
+  * \tparam _Scalar Numeric type, i.e. float, double, int
-  * \param Rows Number of rows, or \b Dynamic
+  * \tparam _Rows Number of rows, or \b Dynamic
-  * \param Cols Number of columns, or \b Dynamic
+  * \tparam _Cols Number of columns, or \b Dynamic
-  * \param Supers Number of super diagonal
+  * \tparam _Supers Number of super diagonal
-  * \param Subs Number of sub diagonal
+  * \tparam _Subs Number of sub diagonal
-  * \param _Options A combination of either \b #RowMajor or \b #ColMajor, and of \b #SelfAdjoint
+  * \tparam _Options A combination of either \b #RowMajor or \b #ColMajor, and of \b #SelfAdjoint
-  *                 The former controls \ref TopicStorageOrders "storage order", and defaults to
+  *                  The former controls \ref TopicStorageOrders "storage order", and defaults to
-  *                 column-major. The latter controls whether the matrix represents a selfadjoint 
+  *                  column-major. The latter controls whether the matrix represents a selfadjoint
-  *                 matrix in which case either Supers of Subs have to be null.
+  *                  matrix in which case either Supers of Subs have to be null.
   *
   * \sa class TridiagonalMatrix
   */
@@ -302,9 +302,9 @@ class BandMatrixWrapper : public BandMatrixBase<BandMatrixWrapper<_CoefficientsT
   *
   * \brief Represents a tridiagonal matrix with a compact banded storage
   *
-  * \param _Scalar Numeric type, i.e. float, double, int
+  * \tparam Scalar Numeric type, i.e. float, double, int
-  * \param Size Number of rows and cols, or \b Dynamic
+  * \tparam Size Number of rows and cols, or \b Dynamic
-  * \param _Options Can be 0 or \b SelfAdjoint
+  * \tparam Options Can be 0 or \b SelfAdjoint
   *
   * \sa class BandMatrix
   */

Eigen/src/Core/Block.h

@@ -13,41 +13,6 @@
 
 namespace Eigen { 
 
-/** \class Block
-  * \ingroup Core_Module
-  *
-  * \brief Expression of a fixed-size or dynamic-size block
-  *
-  * \param XprType the type of the expression in which we are taking a block
-  * \param BlockRows the number of rows of the block we are taking at compile time (optional)
-  * \param BlockCols the number of columns of the block we are taking at compile time (optional)
-  * \param InnerPanel is true, if the block maps to a set of rows of a row major matrix or
-  *        to set of columns of a column major matrix (optional). The parameter allows to determine
-  *        at compile time whether aligned access is possible on the block expression.
-  *
-  * This class represents an expression of either a fixed-size or dynamic-size block. It is the return
-  * type of DenseBase::block(Index,Index,Index,Index) and DenseBase::block<int,int>(Index,Index) and
-  * most of the time this is the only way it is used.
-  *
-  * However, if you want to directly maniputate block expressions,
-  * for instance if you want to write a function returning such an expression, you
-  * will need to use this class.
-  *
-  * Here is an example illustrating the dynamic case:
-  * \include class_Block.cpp
-  * Output: \verbinclude class_Block.out
-  *
-  * \note Even though this expression has dynamic size, in the case where \a XprType
-  * has fixed size, this expression inherits a fixed maximal size which means that evaluating
-  * it does not cause a dynamic memory allocation.
-  *
-  * Here is an example illustrating the fixed-size case:
-  * \include class_FixedBlock.cpp
-  * Output: \verbinclude class_FixedBlock.out
-  *
-  * \sa DenseBase::block(Index,Index,Index,Index), DenseBase::block(Index,Index), class VectorBlock
-  */
-
 namespace internal {
 template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
 struct traits<Block<XprType, BlockRows, BlockCols, InnerPanel> > : traits<XprType>
@@ -101,6 +66,40 @@ template<typename XprType, int BlockRows=Dynamic, int BlockCols=Dynamic, bool In
 
 template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, typename StorageKind> class BlockImpl;
 
+/** \class Block
+  * \ingroup Core_Module
+  *
+  * \brief Expression of a fixed-size or dynamic-size block
+  *
+  * \tparam XprType the type of the expression in which we are taking a block
+  * \tparam BlockRows the number of rows of the block we are taking at compile time (optional)
+  * \tparam BlockCols the number of columns of the block we are taking at compile time (optional)
+  * \tparam InnerPanel is true, if the block maps to a set of rows of a row major matrix or
+  *         to set of columns of a column major matrix (optional). The parameter allows to determine
+  *         at compile time whether aligned access is possible on the block expression.
+  *
+  * This class represents an expression of either a fixed-size or dynamic-size block. It is the return
+  * type of DenseBase::block(Index,Index,Index,Index) and DenseBase::block<int,int>(Index,Index) and
+  * most of the time this is the only way it is used.
+  *
+  * However, if you want to directly maniputate block expressions,
+  * for instance if you want to write a function returning such an expression, you
+  * will need to use this class.
+  *
+  * Here is an example illustrating the dynamic case:
+  * \include class_Block.cpp
+  * Output: \verbinclude class_Block.out
+  *
+  * \note Even though this expression has dynamic size, in the case where \a XprType
+  * has fixed size, this expression inherits a fixed maximal size which means that evaluating
+  * it does not cause a dynamic memory allocation.
+  *
+  * Here is an example illustrating the fixed-size case:
+  * \include class_FixedBlock.cpp
+  * Output: \verbinclude class_FixedBlock.out
+  *
+  * \sa DenseBase::block(Index,Index,Index,Index), DenseBase::block(Index,Index), class VectorBlock
+  */
 template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel> class Block
   : public BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, typename internal::traits<XprType>::StorageKind>
 {
@@ -130,8 +129,8 @@ template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel> class
       : Impl(xpr, startRow, startCol)
     {
       EIGEN_STATIC_ASSERT(RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic,THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE)
-      eigen_assert(startRow >= 0 && BlockRows >= 1 && startRow + BlockRows <= xpr.rows()
+      eigen_assert(startRow >= 0 && BlockRows >= 0 && startRow + BlockRows <= xpr.rows()
-             && startCol >= 0 && BlockCols >= 1 && startCol + BlockCols <= xpr.cols());
+             && startCol >= 0 && BlockCols >= 0 && startCol + BlockCols <= xpr.cols());
     }
 
     /** Dynamic-size constructor
@@ -174,6 +173,7 @@ template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool H
   : public internal::dense_xpr_base<Block<XprType, BlockRows, BlockCols, InnerPanel> >::type
 {
     typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;
+    typedef typename internal::ref_selector<XprType>::non_const_type XprTypeNested;
   public:
 
     typedef typename internal::dense_xpr_base<BlockType>::type Base;
@@ -222,15 +222,13 @@ template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool H
     inline Scalar& coeffRef(Index rowId, Index colId)
     {
       EIGEN_STATIC_ASSERT_LVALUE(XprType)
-      return m_xpr.const_cast_derived()
+      return m_xpr.coeffRef(rowId + m_startRow.value(), colId + m_startCol.value());
-               .coeffRef(rowId + m_startRow.value(), colId + m_startCol.value());
     }
 
     EIGEN_DEVICE_FUNC
     inline const Scalar& coeffRef(Index rowId, Index colId) const
     {
-      return m_xpr.derived()
+      return m_xpr.derived().coeffRef(rowId + m_startRow.value(), colId + m_startCol.value());
-               .coeffRef(rowId + m_startRow.value(), colId + m_startCol.value());
     }
 
     EIGEN_DEVICE_FUNC
@@ -243,39 +241,34 @@ template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool H
     inline Scalar& coeffRef(Index index)
     {
       EIGEN_STATIC_ASSERT_LVALUE(XprType)
-      return m_xpr.const_cast_derived()
+      return m_xpr.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
-             .coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+                            m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
-                       m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
     }
 
     EIGEN_DEVICE_FUNC
     inline const Scalar& coeffRef(Index index) const
     {
-      return m_xpr.const_cast_derived()
+      return m_xpr.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
-             .coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+                            m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
-                       m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
     }
 
     EIGEN_DEVICE_FUNC
     inline const CoeffReturnType coeff(Index index) const
     {
-      return m_xpr
+      return m_xpr.coeff(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
-             .coeff(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+                         m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
-                    m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
     }
 
     template<int LoadMode>
     inline PacketScalar packet(Index rowId, Index colId) const
     {
-      return m_xpr.template packet<Unaligned>
+      return m_xpr.template packet<Unaligned>(rowId + m_startRow.value(), colId + m_startCol.value());
-              (rowId + m_startRow.value(), colId + m_startCol.value());
     }
 
     template<int LoadMode>
     inline void writePacket(Index rowId, Index colId, const PacketScalar& val)
     {
-      m_xpr.const_cast_derived().template writePacket<Unaligned>
+      m_xpr.template writePacket<Unaligned>(rowId + m_startRow.value(), colId + m_startCol.value(), val);
-              (rowId + m_startRow.value(), colId + m_startCol.value(), val);
     }
 
     template<int LoadMode>
@@ -289,7 +282,7 @@ template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool H
     template<int LoadMode>
     inline void writePacket(Index index, const PacketScalar& val)
     {
-      m_xpr.const_cast_derived().template writePacket<Unaligned>
+      m_xpr.template writePacket<Unaligned>
          (m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
           m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0), val);
     }
@@ -302,10 +295,13 @@ template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool H
     #endif
 
     EIGEN_DEVICE_FUNC
-    const typename internal::remove_all<typename XprType::Nested>::type& nestedExpression() const
+    const typename internal::remove_all<XprTypeNested>::type& nestedExpression() const
     { 
       return m_xpr; 
     }
+
+    EIGEN_DEVICE_FUNC
+    XprType& nestedExpression() { return m_xpr; }
       
     EIGEN_DEVICE_FUNC
     StorageIndex startRow() const
@@ -321,9 +317,9 @@ template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool H
 
   protected:
 
-    const typename XprType::Nested m_xpr;
+    XprTypeNested m_xpr;
-    const internal::variable_if_dynamic<StorageIndex, XprType::RowsAtCompileTime == 1 ? 0 : Dynamic> m_startRow;
+    const internal::variable_if_dynamic<StorageIndex, (XprType::RowsAtCompileTime == 1 && BlockRows==1) ? 0 : Dynamic> m_startRow;
-    const internal::variable_if_dynamic<StorageIndex, XprType::ColsAtCompileTime == 1 ? 0 : Dynamic> m_startCol;
+    const internal::variable_if_dynamic<StorageIndex, (XprType::ColsAtCompileTime == 1 && BlockCols==1) ? 0 : Dynamic> m_startCol;
     const internal::variable_if_dynamic<StorageIndex, RowsAtCompileTime> m_blockRows;
     const internal::variable_if_dynamic<StorageIndex, ColsAtCompileTime> m_blockCols;
 };
@@ -334,6 +330,7 @@ class BlockImpl_dense<XprType,BlockRows,BlockCols, InnerPanel,true>
   : public MapBase<Block<XprType, BlockRows, BlockCols, InnerPanel> >
 {
     typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;
+    typedef typename internal::ref_selector<XprType>::non_const_type XprTypeNested;
     enum {
       XprTypeIsRowMajor = (int(traits<XprType>::Flags)&RowMajorBit) != 0
     };
@@ -351,7 +348,9 @@ class BlockImpl_dense<XprType,BlockRows,BlockCols, InnerPanel,true>
                                 || ((BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) && ( XprTypeIsRowMajor)) ? xpr.innerStride() : xpr.outerStride()),
              BlockRows==1 ? 1 : xpr.rows(),
              BlockCols==1 ? 1 : xpr.cols()),
-        m_xpr(xpr)
+        m_xpr(xpr),
+        m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0),
+        m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0)
     {
       init();
     }
@@ -361,7 +360,7 @@ class BlockImpl_dense<XprType,BlockRows,BlockCols, InnerPanel,true>
     EIGEN_DEVICE_FUNC
     inline BlockImpl_dense(XprType& xpr, Index startRow, Index startCol)
       : Base(xpr.data()+xpr.innerStride()*(XprTypeIsRowMajor?startCol:startRow) + xpr.outerStride()*(XprTypeIsRowMajor?startRow:startCol)),
-        m_xpr(xpr)
+        m_xpr(xpr), m_startRow(startRow), m_startCol(startCol)
     {
       init();
     }
@@ -373,16 +372,19 @@ class BlockImpl_dense<XprType,BlockRows,BlockCols, InnerPanel,true>
           Index startRow, Index startCol,
           Index blockRows, Index blockCols)
       : Base(xpr.data()+xpr.innerStride()*(XprTypeIsRowMajor?startCol:startRow) + xpr.outerStride()*(XprTypeIsRowMajor?startRow:startCol), blockRows, blockCols),
-        m_xpr(xpr)
+        m_xpr(xpr), m_startRow(startRow), m_startCol(startCol)
     {
       init();
     }
 
     EIGEN_DEVICE_FUNC
-    const typename internal::remove_all<typename XprType::Nested>::type& nestedExpression() const
+    const typename internal::remove_all<XprTypeNested>::type& nestedExpression() const
     { 
       return m_xpr; 
     }
+
+    EIGEN_DEVICE_FUNC
+    XprType& nestedExpression() { return m_xpr; }
       
     /** \sa MapBase::innerStride() */
     EIGEN_DEVICE_FUNC
@@ -400,6 +402,18 @@ class BlockImpl_dense<XprType,BlockRows,BlockCols, InnerPanel,true>
       return m_outerStride;
     }
 
+    EIGEN_DEVICE_FUNC
+    StorageIndex startRow() const
+    {
+      return m_startRow.value();
+    }
+
+    EIGEN_DEVICE_FUNC
+    StorageIndex startCol() const
+    {
+      return m_startCol.value();
+    }
+
   #ifndef __SUNPRO_CC
   // FIXME sunstudio is not friendly with the above friend...
   // META-FIXME there is no 'friend' keyword around here. Is this obsolete?
@@ -425,7 +439,9 @@ class BlockImpl_dense<XprType,BlockRows,BlockCols, InnerPanel,true>
                     : m_xpr.innerStride();
     }
 
-    typename XprType::Nested m_xpr;
+    XprTypeNested m_xpr;
+    const internal::variable_if_dynamic<StorageIndex, (XprType::RowsAtCompileTime == 1 && BlockRows==1) ? 0 : Dynamic> m_startRow;
+    const internal::variable_if_dynamic<StorageIndex, (XprType::ColsAtCompileTime == 1 && BlockCols==1) ? 0 : Dynamic> m_startCol;
     Index m_outerStride;
 };
 

Eigen/src/Core/CommaInitializer.h

@@ -22,7 +22,7 @@ namespace Eigen {
   * the return type of MatrixBase::operator<<, and most of the time this is the only
   * way it is used.
   *
-  * \sa \ref MatrixBaseCommaInitRef "MatrixBase::operator<<", CommaInitializer::finished()
+  * \sa \blank \ref MatrixBaseCommaInitRef "MatrixBase::operator<<", CommaInitializer::finished()
   */
 template<typename XprType>
 struct CommaInitializer

Eigen/src/Core/CoreEvaluators.h

@@ -63,10 +63,6 @@ struct evaluator_traits_base
   // by default, get evaluator kind and shape from storage
   typedef typename storage_kind_to_evaluator_kind<typename traits<T>::StorageKind>::Kind Kind;
   typedef typename storage_kind_to_shape<typename traits<T>::StorageKind>::Shape Shape;
-  
-  // 1 if assignment A = B assumes aliasing when B is of type T and thus B needs to be evaluated into a
-  // temporary; 0 if not.
-  static const int AssumeAliasing = 0;
 };
 
 // Default evaluator traits
@@ -75,6 +71,10 @@ struct evaluator_traits : public evaluator_traits_base<T>
 {
 };
 
+template<typename T, typename Shape = typename evaluator_traits<T>::Shape >
+struct evaluator_assume_aliasing {
+  static const bool value = false;
+};
 
 // By default, we assume a unary expression:
 template<typename T>
@@ -148,7 +148,8 @@ struct evaluator<PlainObjectBase<Derived> >
     EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
   }
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index row, Index col) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index row, Index col) const
   {
     if (IsRowMajor)
       return m_data[row * m_outerStride.value() + col];
@@ -156,12 +157,14 @@ struct evaluator<PlainObjectBase<Derived> >
       return m_data[row + col * m_outerStride.value()];
   }
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index index) const
   {
     return m_data[index];
   }
 
-  EIGEN_DEVICE_FUNC Scalar& coeffRef(Index row, Index col)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  Scalar& coeffRef(Index row, Index col)
   {
     if (IsRowMajor)
       return const_cast<Scalar*>(m_data)[row * m_outerStride.value() + col];
@@ -169,12 +172,14 @@ struct evaluator<PlainObjectBase<Derived> >
       return const_cast<Scalar*>(m_data)[row + col * m_outerStride.value()];
   }
 
-  EIGEN_DEVICE_FUNC Scalar& coeffRef(Index index)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  Scalar& coeffRef(Index index)
   {
     return const_cast<Scalar*>(m_data)[index];
   }
 
   template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index row, Index col) const
   {
     if (IsRowMajor)
@@ -184,12 +189,14 @@ struct evaluator<PlainObjectBase<Derived> >
   }
 
   template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index index) const
   {
     return ploadt<PacketType, LoadMode>(m_data + index);
   }
 
   template<int StoreMode,typename PacketType>
+  EIGEN_STRONG_INLINE
   void writePacket(Index row, Index col, const PacketType& x)
   {
     if (IsRowMajor)
@@ -201,6 +208,7 @@ struct evaluator<PlainObjectBase<Derived> >
   }
 
   template<int StoreMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   void writePacket(Index index, const PacketType& x)
   {
     return pstoret<Scalar, PacketType, StoreMode>(const_cast<Scalar*>(m_data) + index, x);
@@ -260,45 +268,53 @@ struct unary_evaluator<Transpose<ArgType>, IndexBased>
   typedef typename XprType::Scalar Scalar;
   typedef typename XprType::CoeffReturnType CoeffReturnType;
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index row, Index col) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index row, Index col) const
   {
     return m_argImpl.coeff(col, row);
   }
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index index) const
   {
     return m_argImpl.coeff(index);
   }
 
-  EIGEN_DEVICE_FUNC Scalar& coeffRef(Index row, Index col)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  Scalar& coeffRef(Index row, Index col)
   {
     return m_argImpl.coeffRef(col, row);
   }
 
-  EIGEN_DEVICE_FUNC typename XprType::Scalar& coeffRef(Index index)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  typename XprType::Scalar& coeffRef(Index index)
   {
     return m_argImpl.coeffRef(index);
   }
 
   template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index row, Index col) const
   {
     return m_argImpl.template packet<LoadMode,PacketType>(col, row);
   }
 
   template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index index) const
   {
     return m_argImpl.template packet<LoadMode,PacketType>(index);
   }
 
-  template<int StoreMode, typename PacketType> 
+  template<int StoreMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   void writePacket(Index row, Index col, const PacketType& x)
   {
     m_argImpl.template writePacket<StoreMode,PacketType>(col, row, x);
   }
 
-  template<int StoreMode, typename PacketType> 
+  template<int StoreMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   void writePacket(Index index, const PacketType& x)
   {
     m_argImpl.template writePacket<StoreMode,PacketType>(index, x);
@@ -338,23 +354,27 @@ struct evaluator<CwiseNullaryOp<NullaryOp,PlainObjectType> >
 
   typedef typename XprType::CoeffReturnType CoeffReturnType;
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index row, Index col) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index row, Index col) const
   {
     return m_functor(row, col);
   }
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index index) const
   {
     return m_functor(index);
   }
 
   template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index row, Index col) const
   {
     return m_functor.template packetOp<Index,PacketType>(row, col);
   }
 
   template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index index) const
   {
     return m_functor.template packetOp<Index,PacketType>(index);
@@ -380,7 +400,8 @@ struct unary_evaluator<CwiseUnaryOp<UnaryOp, ArgType>, IndexBased >
     Alignment = evaluator<ArgType>::Alignment
   };
 
-  EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& op)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  explicit unary_evaluator(const XprType& op)
     : m_functor(op.functor()), 
       m_argImpl(op.nestedExpression()) 
   {
@@ -390,23 +411,27 @@ struct unary_evaluator<CwiseUnaryOp<UnaryOp, ArgType>, IndexBased >
 
   typedef typename XprType::CoeffReturnType CoeffReturnType;
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index row, Index col) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index row, Index col) const
   {
     return m_functor(m_argImpl.coeff(row, col));
   }
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index index) const
   {
     return m_functor(m_argImpl.coeff(index));
   }
 
   template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index row, Index col) const
   {
     return m_functor.packetOp(m_argImpl.template packet<LoadMode, PacketType>(row, col));
   }
 
   template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index index) const
   {
     return m_functor.packetOp(m_argImpl.template packet<LoadMode, PacketType>(index));
@@ -466,17 +491,20 @@ struct binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs>, IndexBased, IndexBase
 
   typedef typename XprType::CoeffReturnType CoeffReturnType;
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index row, Index col) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index row, Index col) const
   {
     return m_functor(m_lhsImpl.coeff(row, col), m_rhsImpl.coeff(row, col));
   }
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index index) const
   {
     return m_functor(m_lhsImpl.coeff(index), m_rhsImpl.coeff(index));
   }
 
   template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index row, Index col) const
   {
     return m_functor.packetOp(m_lhsImpl.template packet<LoadMode,PacketType>(row, col),
@@ -484,6 +512,7 @@ struct binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs>, IndexBased, IndexBase
   }
 
   template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index index) const
   {
     return m_functor.packetOp(m_lhsImpl.template packet<LoadMode,PacketType>(index),
@@ -523,22 +552,26 @@ struct unary_evaluator<CwiseUnaryView<UnaryOp, ArgType>, IndexBased>
   typedef typename XprType::Scalar Scalar;
   typedef typename XprType::CoeffReturnType CoeffReturnType;
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index row, Index col) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index row, Index col) const
   {
     return m_unaryOp(m_argImpl.coeff(row, col));
   }
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index index) const
   {
     return m_unaryOp(m_argImpl.coeff(index));
   }
 
-  EIGEN_DEVICE_FUNC Scalar& coeffRef(Index row, Index col)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  Scalar& coeffRef(Index row, Index col)
   {
     return m_unaryOp(m_argImpl.coeffRef(row, col));
   }
 
-  EIGEN_DEVICE_FUNC Scalar& coeffRef(Index index)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  Scalar& coeffRef(Index index)
   {
     return m_unaryOp(m_argImpl.coeffRef(index));
   }
@@ -578,47 +611,55 @@ struct mapbase_evaluator : evaluator_base<Derived>
     EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
   }
  
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index row, Index col) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index row, Index col) const
   {
     return m_data[col * m_xpr.colStride() + row * m_xpr.rowStride()];
   }
   
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index index) const
   {
     return m_data[index * m_xpr.innerStride()];
   }
 
-  EIGEN_DEVICE_FUNC Scalar& coeffRef(Index row, Index col)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  Scalar& coeffRef(Index row, Index col)
   {
     return m_data[col * m_xpr.colStride() + row * m_xpr.rowStride()];
   }
   
-  EIGEN_DEVICE_FUNC Scalar& coeffRef(Index index)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  Scalar& coeffRef(Index index)
   {
     return m_data[index * m_xpr.innerStride()];
   }
  
-  template<int LoadMode, typename PacketType> 
+  template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index row, Index col) const 
   {
     PointerType ptr = m_data + row * m_xpr.rowStride() + col * m_xpr.colStride();
     return internal::ploadt<PacketType, LoadMode>(ptr);
   }
 
-  template<int LoadMode, typename PacketType> 
+  template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index index) const 
   {
     return internal::ploadt<PacketType, LoadMode>(m_data + index * m_xpr.innerStride());
   }
   
-  template<int StoreMode, typename PacketType> 
+  template<int StoreMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   void writePacket(Index row, Index col, const PacketType& x) 
   {
     PointerType ptr = m_data + row * m_xpr.rowStride() + col * m_xpr.colStride();
     return internal::pstoret<Scalar, PacketType, StoreMode>(ptr, x);
   }
   
-  template<int StoreMode, typename PacketType> 
+  template<int StoreMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   void writePacket(Index index, const PacketType& x) 
   {
     internal::pstoret<Scalar, PacketType, StoreMode>(m_data + index * m_xpr.innerStride(), x);
@@ -767,46 +808,54 @@ struct unary_evaluator<Block<ArgType, BlockRows, BlockCols, InnerPanel>, IndexBa
     RowsAtCompileTime = XprType::RowsAtCompileTime
   };
  
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index row, Index col) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index row, Index col) const
   { 
     return m_argImpl.coeff(m_startRow.value() + row, m_startCol.value() + col); 
   }
   
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index index) const
   { 
     return coeff(RowsAtCompileTime == 1 ? 0 : index, RowsAtCompileTime == 1 ? index : 0);
   }
 
-  EIGEN_DEVICE_FUNC Scalar& coeffRef(Index row, Index col)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  Scalar& coeffRef(Index row, Index col)
   { 
     return m_argImpl.coeffRef(m_startRow.value() + row, m_startCol.value() + col); 
   }
   
-  EIGEN_DEVICE_FUNC Scalar& coeffRef(Index index)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  Scalar& coeffRef(Index index)
   { 
     return coeffRef(RowsAtCompileTime == 1 ? 0 : index, RowsAtCompileTime == 1 ? index : 0);
   }
  
-  template<int LoadMode, typename PacketType> 
+  template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index row, Index col) const 
   { 
     return m_argImpl.template packet<LoadMode,PacketType>(m_startRow.value() + row, m_startCol.value() + col); 
   }
 
-  template<int LoadMode, typename PacketType> 
+  template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index index) const 
   { 
     return packet<LoadMode,PacketType>(RowsAtCompileTime == 1 ? 0 : index,
                                        RowsAtCompileTime == 1 ? index : 0);
   }
   
-  template<int StoreMode, typename PacketType> 
+  template<int StoreMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   void writePacket(Index row, Index col, const PacketType& x) 
   { 
     return m_argImpl.template writePacket<StoreMode,PacketType>(m_startRow.value() + row, m_startCol.value() + col, x); 
   }
   
-  template<int StoreMode, typename PacketType> 
+  template<int StoreMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   void writePacket(Index index, const PacketType& x) 
   { 
     return writePacket<StoreMode,PacketType>(RowsAtCompileTime == 1 ? 0 : index,
@@ -816,8 +865,8 @@ struct unary_evaluator<Block<ArgType, BlockRows, BlockCols, InnerPanel>, IndexBa
  
 protected:
   evaluator<ArgType> m_argImpl;
-  const variable_if_dynamic<Index, ArgType::RowsAtCompileTime == 1 ? 0 : Dynamic> m_startRow;
+  const variable_if_dynamic<Index, (ArgType::RowsAtCompileTime == 1 && BlockRows==1) ? 0 : Dynamic> m_startRow;
-  const variable_if_dynamic<Index, ArgType::ColsAtCompileTime == 1 ? 0 : Dynamic> m_startCol;
+  const variable_if_dynamic<Index, (ArgType::ColsAtCompileTime == 1 && BlockCols==1) ? 0 : Dynamic> m_startCol;
 };
 
 // TODO: This evaluator does not actually use the child evaluator; 
@@ -859,7 +908,7 @@ struct evaluator<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >
     Alignment = EIGEN_PLAIN_ENUM_MIN(evaluator<ThenMatrixType>::Alignment, evaluator<ElseMatrixType>::Alignment)
   };
 
-  inline EIGEN_DEVICE_FUNC  explicit evaluator(const XprType& select)
+  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& select)
     : m_conditionImpl(select.conditionMatrix()),
       m_thenImpl(select.thenMatrix()),
       m_elseImpl(select.elseMatrix())
@@ -869,7 +918,8 @@ struct evaluator<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >
  
   typedef typename XprType::CoeffReturnType CoeffReturnType;
 
-  inline EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index row, Index col) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index row, Index col) const
   {
     if (m_conditionImpl.coeff(row, col))
       return m_thenImpl.coeff(row, col);
@@ -877,7 +927,8 @@ struct evaluator<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >
       return m_elseImpl.coeff(row, col);
   }
 
-  inline EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index index) const
   {
     if (m_conditionImpl.coeff(index))
       return m_thenImpl.coeff(index);
@@ -921,7 +972,8 @@ struct unary_evaluator<Replicate<ArgType, RowFactor, ColFactor> >
       m_cols(replicate.nestedExpression().cols())
   {}
  
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index row, Index col) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index row, Index col) const
   {
     // try to avoid using modulo; this is a pure optimization strategy
     const Index actual_row = internal::traits<XprType>::RowsAtCompileTime==1 ? 0
@@ -934,7 +986,8 @@ struct unary_evaluator<Replicate<ArgType, RowFactor, ColFactor> >
     return m_argImpl.coeff(actual_row, actual_col);
   }
   
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index index) const
   {
     // try to avoid using modulo; this is a pure optimization strategy
     const Index actual_index = internal::traits<XprType>::RowsAtCompileTime==1
@@ -945,6 +998,7 @@ struct unary_evaluator<Replicate<ArgType, RowFactor, ColFactor> >
   }
 
   template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index row, Index col) const
   {
     const Index actual_row = internal::traits<XprType>::RowsAtCompileTime==1 ? 0
@@ -958,6 +1012,7 @@ struct unary_evaluator<Replicate<ArgType, RowFactor, ColFactor> >
   }
   
   template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index index) const
   {
     const Index actual_index = internal::traits<XprType>::RowsAtCompileTime==1
@@ -994,7 +1049,7 @@ struct evaluator<PartialReduxExpr<ArgType, MemberOp, Direction> >
     CoeffReadCost = TraversalSize==Dynamic ? HugeCost
                   : TraversalSize * evaluator<ArgType>::CoeffReadCost + int(CostOpType::value),
     
-    Flags = (traits<XprType>::Flags&RowMajorBit) | (evaluator<ArgType>::Flags&HereditaryBits),
+    Flags = (traits<XprType>::Flags&RowMajorBit) | (evaluator<ArgType>::Flags&(HereditaryBits&(~RowMajorBit))) | LinearAccessBit,
     
     Alignment = 0 // FIXME this will need to be improved once PartialReduxExpr is vectorized
   };
@@ -1008,7 +1063,8 @@ struct evaluator<PartialReduxExpr<ArgType, MemberOp, Direction> >
 
   typedef typename XprType::CoeffReturnType CoeffReturnType;
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index i, Index j) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  const Scalar coeff(Index i, Index j) const
   {
     if (Direction==Vertical)
       return m_functor(m_arg.col(j));
@@ -1016,7 +1072,8 @@ struct evaluator<PartialReduxExpr<ArgType, MemberOp, Direction> >
       return m_functor(m_arg.row(i));
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index index) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  const Scalar coeff(Index index) const
   {
     if (Direction==Vertical)
       return m_functor(m_arg.col(index));
@@ -1051,45 +1108,53 @@ struct evaluator_wrapper_base
   typedef typename ArgType::Scalar Scalar;
   typedef typename ArgType::CoeffReturnType CoeffReturnType;
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index row, Index col) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index row, Index col) const
   {
     return m_argImpl.coeff(row, col);
   }
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index index) const
   {
     return m_argImpl.coeff(index);
   }
 
-  EIGEN_DEVICE_FUNC Scalar& coeffRef(Index row, Index col)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  Scalar& coeffRef(Index row, Index col)
   {
     return m_argImpl.coeffRef(row, col);
   }
 
-  EIGEN_DEVICE_FUNC Scalar& coeffRef(Index index)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  Scalar& coeffRef(Index index)
   {
     return m_argImpl.coeffRef(index);
   }
 
-  template<int LoadMode, typename PacketType> 
+  template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index row, Index col) const
   {
     return m_argImpl.template packet<LoadMode,PacketType>(row, col);
   }
 
-  template<int LoadMode, typename PacketType> 
+  template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index index) const
   {
     return m_argImpl.template packet<LoadMode,PacketType>(index);
   }
 
-  template<int StoreMode, typename PacketType> 
+  template<int StoreMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   void writePacket(Index row, Index col, const PacketType& x)
   {
     m_argImpl.template writePacket<StoreMode>(row, col, x);
   }
 
-  template<int StoreMode, typename PacketType> 
+  template<int StoreMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   void writePacket(Index index, const PacketType& x)
   {
     m_argImpl.template writePacket<StoreMode>(index, x);
@@ -1164,29 +1229,34 @@ struct unary_evaluator<Reverse<ArgType, Direction> >
       m_cols(ReverseCol ? reverse.nestedExpression().cols() : 1)
   { }
  
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index row, Index col) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index row, Index col) const
   {
     return m_argImpl.coeff(ReverseRow ? m_rows.value() - row - 1 : row,
                            ReverseCol ? m_cols.value() - col - 1 : col);
   }
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index index) const
   {
     return m_argImpl.coeff(m_rows.value() * m_cols.value() - index - 1);
   }
 
-  EIGEN_DEVICE_FUNC Scalar& coeffRef(Index row, Index col)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  Scalar& coeffRef(Index row, Index col)
   {
     return m_argImpl.coeffRef(ReverseRow ? m_rows.value() - row - 1 : row,
                               ReverseCol ? m_cols.value() - col - 1 : col);
   }
 
-  EIGEN_DEVICE_FUNC Scalar& coeffRef(Index index)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  Scalar& coeffRef(Index index)
   {
     return m_argImpl.coeffRef(m_rows.value() * m_cols.value() - index - 1);
   }
 
   template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index row, Index col) const
   {
     enum {
@@ -1201,6 +1271,7 @@ struct unary_evaluator<Reverse<ArgType, Direction> >
   }
 
   template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   PacketType packet(Index index) const
   {
     enum { PacketSize = unpacket_traits<PacketType>::size };
@@ -1208,6 +1279,7 @@ struct unary_evaluator<Reverse<ArgType, Direction> >
   }
 
   template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   void writePacket(Index row, Index col, const PacketType& x)
   {
     // FIXME we could factorize some code with packet(i,j)
@@ -1224,6 +1296,7 @@ struct unary_evaluator<Reverse<ArgType, Direction> >
   }
 
   template<int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE
   void writePacket(Index index, const PacketType& x)
   {
     enum { PacketSize = unpacket_traits<PacketType>::size };
@@ -1267,22 +1340,26 @@ struct evaluator<Diagonal<ArgType, DiagIndex> >
   typedef typename internal::conditional<!internal::is_same<typename ArgType::StorageKind,Sparse>::value,
                                          typename XprType::CoeffReturnType,Scalar>::type CoeffReturnType;
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index row, Index) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index row, Index) const
   {
     return m_argImpl.coeff(row + rowOffset(), row + colOffset());
   }
 
-  EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  CoeffReturnType coeff(Index index) const
   {
     return m_argImpl.coeff(index + rowOffset(), index + colOffset());
   }
 
-  EIGEN_DEVICE_FUNC Scalar& coeffRef(Index row, Index)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  Scalar& coeffRef(Index row, Index)
   {
     return m_argImpl.coeffRef(row + rowOffset(), row + colOffset());
   }
 
-  EIGEN_DEVICE_FUNC Scalar& coeffRef(Index index)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  Scalar& coeffRef(Index index)
   {
     return m_argImpl.coeffRef(index + rowOffset(), index + colOffset());
   }

Eigen/src/Core/CwiseBinaryOp.h

@@ -13,26 +13,6 @@
 
 namespace Eigen {
 
-/** \class CwiseBinaryOp
-  * \ingroup Core_Module
-  *
-  * \brief Generic expression where a coefficient-wise binary operator is applied to two expressions
-  *
-  * \param BinaryOp template functor implementing the operator
-  * \param Lhs the type of the left-hand side
-  * \param Rhs the type of the right-hand side
-  *
-  * This class represents an expression  where a coefficient-wise binary operator is applied to two expressions.
-  * It is the return type of binary operators, by which we mean only those binary operators where
-  * both the left-hand side and the right-hand side are Eigen expressions.
-  * For example, the return type of matrix1+matrix2 is a CwiseBinaryOp.
-  *
-  * Most of the time, this is the only way that it is used, so you typically don't have to name
-  * CwiseBinaryOp types explicitly.
-  *
-  * \sa MatrixBase::binaryExpr(const MatrixBase<OtherDerived> &,const CustomBinaryOp &) const, class CwiseUnaryOp, class CwiseNullaryOp
-  */
-
 namespace internal {
 template<typename BinaryOp, typename Lhs, typename Rhs>
 struct traits<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
@@ -52,8 +32,8 @@ struct traits<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
   // we still want to handle the case when the result type is different.
   typedef typename result_of<
                      BinaryOp(
-                       typename Lhs::Scalar,
+                       const typename Lhs::Scalar&,
-                       typename Rhs::Scalar
+                       const typename Rhs::Scalar&
                      )
                    >::type Scalar;
   typedef typename cwise_promote_storage_type<typename traits<Lhs>::StorageKind,
@@ -74,6 +54,25 @@ struct traits<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
 template<typename BinaryOp, typename Lhs, typename Rhs, typename StorageKind>
 class CwiseBinaryOpImpl;
 
+/** \class CwiseBinaryOp
+  * \ingroup Core_Module
+  *
+  * \brief Generic expression where a coefficient-wise binary operator is applied to two expressions
+  *
+  * \tparam BinaryOp template functor implementing the operator
+  * \tparam LhsType the type of the left-hand side
+  * \tparam RhsType the type of the right-hand side
+  *
+  * This class represents an expression  where a coefficient-wise binary operator is applied to two expressions.
+  * It is the return type of binary operators, by which we mean only those binary operators where
+  * both the left-hand side and the right-hand side are Eigen expressions.
+  * For example, the return type of matrix1+matrix2 is a CwiseBinaryOp.
+  *
+  * Most of the time, this is the only way that it is used, so you typically don't have to name
+  * CwiseBinaryOp types explicitly.
+  *
+  * \sa MatrixBase::binaryExpr(const MatrixBase<OtherDerived> &,const CustomBinaryOp &) const, class CwiseUnaryOp, class CwiseNullaryOp
+  */
 template<typename BinaryOp, typename LhsType, typename RhsType>
 class CwiseBinaryOp : 
   public CwiseBinaryOpImpl<

Eigen/src/Core/CwiseNullaryOp.h

@@ -12,24 +12,6 @@
 
 namespace Eigen {
 
-/** \class CwiseNullaryOp
-  * \ingroup Core_Module
-  *
-  * \brief Generic expression of a matrix where all coefficients are defined by a functor
-  *
-  * \param NullaryOp template functor implementing the operator
-  * \param PlainObjectType the underlying plain matrix/array type
-  *
-  * This class represents an expression of a generic nullary operator.
-  * It is the return type of the Ones(), Zero(), Constant(), Identity() and Random() methods,
-  * and most of the time this is the only way it is used.
-  *
-  * However, if you want to write a function returning such an expression, you
-  * will need to use this class.
-  *
-  * \sa class CwiseUnaryOp, class CwiseBinaryOp, DenseBase::NullaryExpr()
-  */
-
 namespace internal {
 template<typename NullaryOp, typename PlainObjectType>
 struct traits<CwiseNullaryOp<NullaryOp, PlainObjectType> > : traits<PlainObjectType>
@@ -40,6 +22,23 @@ struct traits<CwiseNullaryOp<NullaryOp, PlainObjectType> > : traits<PlainObjectT
 };
 }
 
+/** \class CwiseNullaryOp
+  * \ingroup Core_Module
+  *
+  * \brief Generic expression of a matrix where all coefficients are defined by a functor
+  *
+  * \tparam NullaryOp template functor implementing the operator
+  * \tparam PlainObjectType the underlying plain matrix/array type
+  *
+  * This class represents an expression of a generic nullary operator.
+  * It is the return type of the Ones(), Zero(), Constant(), Identity() and Random() methods,
+  * and most of the time this is the only way it is used.
+  *
+  * However, if you want to write a function returning such an expression, you
+  * will need to use this class.
+  *
+  * \sa class CwiseUnaryOp, class CwiseBinaryOp, DenseBase::NullaryExpr()
+  */
 template<typename NullaryOp, typename PlainObjectType>
 class CwiseNullaryOp : public internal::dense_xpr_base< CwiseNullaryOp<NullaryOp, PlainObjectType> >::type, internal::no_assignment_operator
 {
@@ -224,7 +223,7 @@ DenseBase<Derived>::Constant(const Scalar& value)
 }
 
 /**
-  * \brief Sets a linearly space vector.
+  * \brief Sets a linearly spaced vector.
   *
   * The function generates 'size' equally spaced values in the closed interval [low,high].
   * This particular version of LinSpaced() uses sequential access, i.e. vector access is
@@ -262,7 +261,7 @@ DenseBase<Derived>::LinSpaced(Sequential_t, const Scalar& low, const Scalar& hig
 }
 
 /**
-  * \brief Sets a linearly space vector.
+  * \brief Sets a linearly spaced vector.
   *
   * The function generates 'size' equally spaced values in the closed interval [low,high].
   * When size is set to 1, a vector of length 1 containing 'high' is returned.
@@ -328,7 +327,7 @@ EIGEN_STRONG_INLINE void DenseBase<Derived>::fill(const Scalar& val)
   setConstant(val);
 }
 
-/** Sets all coefficients in this expression to \a value.
+/** Sets all coefficients in this expression to value \a val.
   *
   * \sa fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes()
   */
@@ -338,7 +337,7 @@ EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setConstant(const Scalar& val)
   return derived() = Constant(rows(), cols(), val);
 }
 
-/** Resizes to the given \a size, and sets all coefficients in this expression to the given \a value.
+/** Resizes to the given \a size, and sets all coefficients in this expression to the given value \a val.
   *
   * \only_for_vectors
   *
@@ -355,7 +354,7 @@ PlainObjectBase<Derived>::setConstant(Index size, const Scalar& val)
   return setConstant(val);
 }
 
-/** Resizes to the given size, and sets all coefficients in this expression to the given \a value.
+/** Resizes to the given size, and sets all coefficients in this expression to the given value \a val.
   *
   * \param rows the new number of rows
   * \param cols the new number of columns
@@ -375,7 +374,7 @@ PlainObjectBase<Derived>::setConstant(Index rows, Index cols, const Scalar& val)
 }
 
 /**
-  * \brief Sets a linearly space vector.
+  * \brief Sets a linearly spaced vector.
   *
   * The function generates 'size' equally spaced values in the closed interval [low,high].
   * When size is set to 1, a vector of length 1 containing 'high' is returned.
@@ -395,7 +394,7 @@ EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(Index newSize, con
 }
 
 /**
-  * \brief Sets a linearly space vector.
+  * \brief Sets a linearly spaced vector.
   *
   * The function fill *this with equally spaced values in the closed interval [low,high].
   * When size is set to 1, a vector of length 1 containing 'high' is returned.

Eigen/src/Core/CwiseUnaryOp.h

@@ -13,33 +13,13 @@
 
 namespace Eigen { 
 
-/** \class CwiseUnaryOp
-  * \ingroup Core_Module
-  *
-  * \brief Generic expression where a coefficient-wise unary operator is applied to an expression
-  *
-  * \param UnaryOp template functor implementing the operator
-  * \param XprType the type of the expression to which we are applying the unary operator
-  *
-  * This class represents an expression where a unary operator is applied to an expression.
-  * It is the return type of all operations taking exactly 1 input expression, regardless of the
-  * presence of other inputs such as scalars. For example, the operator* in the expression 3*matrix
-  * is considered unary, because only the right-hand side is an expression, and its
-  * return type is a specialization of CwiseUnaryOp.
-  *
-  * Most of the time, this is the only way that it is used, so you typically don't have to name
-  * CwiseUnaryOp types explicitly.
-  *
-  * \sa MatrixBase::unaryExpr(const CustomUnaryOp &) const, class CwiseBinaryOp, class CwiseNullaryOp
-  */
-
 namespace internal {
 template<typename UnaryOp, typename XprType>
 struct traits<CwiseUnaryOp<UnaryOp, XprType> >
  : traits<XprType>
 {
   typedef typename result_of<
-                     UnaryOp(typename XprType::Scalar)
+                     UnaryOp(const typename XprType::Scalar&)
                    >::type Scalar;
   typedef typename XprType::Nested XprTypeNested;
   typedef typename remove_reference<XprTypeNested>::type _XprTypeNested;
@@ -52,6 +32,25 @@ struct traits<CwiseUnaryOp<UnaryOp, XprType> >
 template<typename UnaryOp, typename XprType, typename StorageKind>
 class CwiseUnaryOpImpl;
 
+/** \class CwiseUnaryOp
+  * \ingroup Core_Module
+  *
+  * \brief Generic expression where a coefficient-wise unary operator is applied to an expression
+  *
+  * \tparam UnaryOp template functor implementing the operator
+  * \tparam XprType the type of the expression to which we are applying the unary operator
+  *
+  * This class represents an expression where a unary operator is applied to an expression.
+  * It is the return type of all operations taking exactly 1 input expression, regardless of the
+  * presence of other inputs such as scalars. For example, the operator* in the expression 3*matrix
+  * is considered unary, because only the right-hand side is an expression, and its
+  * return type is a specialization of CwiseUnaryOp.
+  *
+  * Most of the time, this is the only way that it is used, so you typically don't have to name
+  * CwiseUnaryOp types explicitly.
+  *
+  * \sa MatrixBase::unaryExpr(const CustomUnaryOp &) const, class CwiseBinaryOp, class CwiseNullaryOp
+  */
 template<typename UnaryOp, typename XprType>
 class CwiseUnaryOp : public CwiseUnaryOpImpl<UnaryOp, XprType, typename internal::traits<XprType>::StorageKind>, internal::no_assignment_operator
 {
@@ -59,33 +58,34 @@ class CwiseUnaryOp : public CwiseUnaryOpImpl<UnaryOp, XprType, typename internal
 
     typedef typename CwiseUnaryOpImpl<UnaryOp, XprType,typename internal::traits<XprType>::StorageKind>::Base Base;
     EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryOp)
+    typedef typename internal::ref_selector<XprType>::type XprTypeNested;
     typedef typename internal::remove_all<XprType>::type NestedExpression;
 
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    explicit inline CwiseUnaryOp(const XprType& xpr, const UnaryOp& func = UnaryOp())
+    explicit CwiseUnaryOp(const XprType& xpr, const UnaryOp& func = UnaryOp())
       : m_xpr(xpr), m_functor(func) {}
 
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    EIGEN_STRONG_INLINE Index rows() const { return m_xpr.rows(); }
+    Index rows() const { return m_xpr.rows(); }
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    EIGEN_STRONG_INLINE Index cols() const { return m_xpr.cols(); }
+    Index cols() const { return m_xpr.cols(); }
 
     /** \returns the functor representing the unary operation */
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     const UnaryOp& functor() const { return m_functor; }
 
     /** \returns the nested expression */
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    const typename internal::remove_all<typename XprType::Nested>::type&
+    const typename internal::remove_all<XprTypeNested>::type&
     nestedExpression() const { return m_xpr; }
 
     /** \returns the nested expression */
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    typename internal::remove_all<typename XprType::Nested>::type&
+    typename internal::remove_all<XprTypeNested>::type&
-    nestedExpression() { return m_xpr.const_cast_derived(); }
+    nestedExpression() { return m_xpr; }
 
   protected:
-    typename XprType::Nested m_xpr;
+    XprTypeNested m_xpr;
     const UnaryOp m_functor;
 };
 

Eigen/src/Core/CwiseUnaryView.h

@@ -12,27 +12,13 @@
 
 namespace Eigen {
 
-/** \class CwiseUnaryView
-  * \ingroup Core_Module
-  *
-  * \brief Generic lvalue expression of a coefficient-wise unary operator of a matrix or a vector
-  *
-  * \param ViewOp template functor implementing the view
-  * \param MatrixType the type of the matrix we are applying the unary operator
-  *
-  * This class represents a lvalue expression of a generic unary view operator of a matrix or a vector.
-  * It is the return type of real() and imag(), and most of the time this is the only way it is used.
-  *
-  * \sa MatrixBase::unaryViewExpr(const CustomUnaryOp &) const, class CwiseUnaryOp
-  */
-
 namespace internal {
 template<typename ViewOp, typename MatrixType>
 struct traits<CwiseUnaryView<ViewOp, MatrixType> >
  : traits<MatrixType>
 {
   typedef typename result_of<
-                     ViewOp(typename traits<MatrixType>::Scalar)
+                     ViewOp(const typename traits<MatrixType>::Scalar&)
                    >::type Scalar;
   typedef typename MatrixType::Nested MatrixTypeNested;
   typedef typename remove_all<MatrixTypeNested>::type _MatrixTypeNested;
@@ -55,6 +41,19 @@ struct traits<CwiseUnaryView<ViewOp, MatrixType> >
 template<typename ViewOp, typename MatrixType, typename StorageKind>
 class CwiseUnaryViewImpl;
 
+/** \class CwiseUnaryView
+  * \ingroup Core_Module
+  *
+  * \brief Generic lvalue expression of a coefficient-wise unary operator of a matrix or a vector
+  *
+  * \tparam ViewOp template functor implementing the view
+  * \tparam MatrixType the type of the matrix we are applying the unary operator
+  *
+  * This class represents a lvalue expression of a generic unary view operator of a matrix or a vector.
+  * It is the return type of real() and imag(), and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::unaryViewExpr(const CustomUnaryOp &) const, class CwiseUnaryOp
+  */
 template<typename ViewOp, typename MatrixType>
 class CwiseUnaryView : public CwiseUnaryViewImpl<ViewOp, MatrixType, typename internal::traits<MatrixType>::StorageKind>
 {
@@ -62,6 +61,7 @@ class CwiseUnaryView : public CwiseUnaryViewImpl<ViewOp, MatrixType, typename in
 
     typedef typename CwiseUnaryViewImpl<ViewOp, MatrixType,typename internal::traits<MatrixType>::StorageKind>::Base Base;
     EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryView)
+    typedef typename internal::ref_selector<MatrixType>::non_const_type MatrixTypeNested;
     typedef typename internal::remove_all<MatrixType>::type NestedExpression;
 
     explicit inline CwiseUnaryView(MatrixType& mat, const ViewOp& func = ViewOp())
@@ -76,15 +76,15 @@ class CwiseUnaryView : public CwiseUnaryViewImpl<ViewOp, MatrixType, typename in
     const ViewOp& functor() const { return m_functor; }
 
     /** \returns the nested expression */
-    const typename internal::remove_all<typename MatrixType::Nested>::type&
+    const typename internal::remove_all<MatrixTypeNested>::type&
     nestedExpression() const { return m_matrix; }
 
     /** \returns the nested expression */
-    typename internal::remove_all<typename MatrixType::Nested>::type&
+    typename internal::remove_reference<MatrixTypeNested>::type&
     nestedExpression() { return m_matrix.const_cast_derived(); }
 
   protected:
-    typename internal::ref_selector<MatrixType>::type m_matrix;
+    MatrixTypeNested m_matrix;
     ViewOp m_functor;
 };
 

Eigen/src/Core/DenseBase.h

@@ -36,7 +36,7 @@ static inline void check_DenseIndex_is_signed() {
   * This class can be extended with the help of the plugin mechanism described on the page
   * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_DENSEBASE_PLUGIN.
   *
-  * \sa \ref TopicClassHierarchy
+  * \sa \blank \ref TopicClassHierarchy
   */
 template<typename Derived> class DenseBase
 #ifndef EIGEN_PARSED_BY_DOXYGEN
@@ -60,7 +60,7 @@ template<typename Derived> class DenseBase
       * \brief The type used to store indices
       * \details This typedef is relevant for types that store multiple indices such as
       *          PermutationMatrix or Transpositions, otherwise it defaults to Eigen::Index
-      * \sa \ref TopicPreprocessorDirectives, Eigen::Index, SparseMatrixBase.
+      * \sa \blank \ref TopicPreprocessorDirectives, Eigen::Index, SparseMatrixBase.
      */
     typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
 
@@ -275,13 +275,13 @@ template<typename Derived> class DenseBase
 
     /** Copies \a other into *this. \returns a reference to *this. */
     template<typename OtherDerived>
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     Derived& operator=(const DenseBase<OtherDerived>& other);
 
     /** Special case of the template operator=, in order to prevent the compiler
       * from generating a default operator= (issue hit with g++ 4.1)
       */
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     Derived& operator=(const DenseBase& other);
 
     template<typename OtherDerived>
@@ -388,10 +388,10 @@ template<typename Derived> class DenseBase
     inline bool hasNaN() const;
     inline bool allFinite() const;
 
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    inline Derived& operator*=(const Scalar& other);
+    Derived& operator*=(const Scalar& other);
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    inline Derived& operator/=(const Scalar& other);
+    Derived& operator/=(const Scalar& other);
 
     typedef typename internal::add_const_on_value_type<typename internal::eval<Derived>::type>::type EvalReturnType;
     /** \returns the matrix or vector obtained by evaluating this expression.

Eigen/src/Core/DenseCoeffsBase.h

@@ -191,19 +191,31 @@ class DenseCoeffsBase<Derived,ReadOnlyAccessors> : public EigenBase<Derived>
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE CoeffReturnType
-    y() const { return (*this)[1]; }
+    y() const
+    {
+      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=2, OUT_OF_RANGE_ACCESS);
+      return (*this)[1];
+    }
 
     /** equivalent to operator[](2).  */
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE CoeffReturnType
-    z() const { return (*this)[2]; }
+    z() const
+    {
+      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=3, OUT_OF_RANGE_ACCESS);
+      return (*this)[2];
+    }
 
     /** equivalent to operator[](3).  */
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE CoeffReturnType
-    w() const { return (*this)[3]; }
+    w() const
+    {
+      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=4, OUT_OF_RANGE_ACCESS);
+      return (*this)[3];
+    }
 
     /** \internal
       * \returns the packet of coefficients starting at the given row and column. It is your responsibility
@@ -424,19 +436,31 @@ class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived,
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE Scalar&
-    y() { return (*this)[1]; }
+    y()
+    {
+      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=2, OUT_OF_RANGE_ACCESS);
+      return (*this)[1];
+    }
 
     /** equivalent to operator[](2).  */
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE Scalar&
-    z() { return (*this)[2]; }
+    z()
+    {
+      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=3, OUT_OF_RANGE_ACCESS);
+      return (*this)[2];
+    }
 
     /** equivalent to operator[](3).  */
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE Scalar&
-    w() { return (*this)[3]; }
+    w()
+    {
+      EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=4, OUT_OF_RANGE_ACCESS);
+      return (*this)[3];
+    }
 };
 
 /** \brief Base class providing direct read-only coefficient access to matrices and arrays.
@@ -448,7 +472,7 @@ class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived,
   * inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which defines functions to access entries read-only using
   * \c operator() .
   *
-  * \sa \ref TopicClassHierarchy
+  * \sa \blank \ref TopicClassHierarchy
   */
 template<typename Derived>
 class DenseCoeffsBase<Derived, DirectAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>
@@ -521,7 +545,7 @@ class DenseCoeffsBase<Derived, DirectAccessors> : public DenseCoeffsBase<Derived
   * inherits DenseCoeffsBase<Derived, WriteAccessors> which defines functions to access entries read/write using
   * \c operator().
   *
-  * \sa \ref TopicClassHierarchy
+  * \sa \blank \ref TopicClassHierarchy
   */
 template<typename Derived>
 class DenseCoeffsBase<Derived, DirectWriteAccessors>

Eigen/src/Core/Diagonal.h

@@ -103,21 +103,21 @@ template<typename MatrixType, int _DiagIndex> class Diagonal
                      >::type ScalarWithConstIfNotLvalue;
 
     EIGEN_DEVICE_FUNC
-    inline ScalarWithConstIfNotLvalue* data() { return &(m_matrix.const_cast_derived().coeffRef(rowOffset(), colOffset())); }
+    inline ScalarWithConstIfNotLvalue* data() { return &(m_matrix.coeffRef(rowOffset(), colOffset())); }
     EIGEN_DEVICE_FUNC
-    inline const Scalar* data() const { return &(m_matrix.const_cast_derived().coeffRef(rowOffset(), colOffset())); }
+    inline const Scalar* data() const { return &(m_matrix.coeffRef(rowOffset(), colOffset())); }
 
     EIGEN_DEVICE_FUNC
     inline Scalar& coeffRef(Index row, Index)
     {
       EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
-      return m_matrix.const_cast_derived().coeffRef(row+rowOffset(), row+colOffset());
+      return m_matrix.coeffRef(row+rowOffset(), row+colOffset());
     }
 
     EIGEN_DEVICE_FUNC
     inline const Scalar& coeffRef(Index row, Index) const
     {
-      return m_matrix.const_cast_derived().coeffRef(row+rowOffset(), row+colOffset());
+      return m_matrix.coeffRef(row+rowOffset(), row+colOffset());
     }
 
     EIGEN_DEVICE_FUNC
@@ -130,13 +130,13 @@ template<typename MatrixType, int _DiagIndex> class Diagonal
     inline Scalar& coeffRef(Index idx)
     {
       EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
-      return m_matrix.const_cast_derived().coeffRef(idx+rowOffset(), idx+colOffset());
+      return m_matrix.coeffRef(idx+rowOffset(), idx+colOffset());
     }
 
     EIGEN_DEVICE_FUNC
     inline const Scalar& coeffRef(Index idx) const
     {
-      return m_matrix.const_cast_derived().coeffRef(idx+rowOffset(), idx+colOffset());
+      return m_matrix.coeffRef(idx+rowOffset(), idx+colOffset());
     }
 
     EIGEN_DEVICE_FUNC
@@ -159,7 +159,7 @@ template<typename MatrixType, int _DiagIndex> class Diagonal
     }
 
   protected:
-    typename MatrixType::Nested m_matrix;
+    typename internal::ref_selector<MatrixType>::non_const_type m_matrix;
     const internal::variable_if_dynamicindex<Index, DiagIndex> m_index;
 
   private:

Eigen/src/Core/Dot.h

@@ -82,7 +82,7 @@ MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const
   * In both cases, it consists in the sum of the square of all the matrix entries.
   * For vectors, this is also equals to the dot product of \c *this with itself.
   *
-  * \sa dot(), norm()
+  * \sa dot(), norm(), lpNorm()
   */
 template<typename Derived>
 EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::squaredNorm() const
@@ -94,16 +94,18 @@ EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scala
   * In both cases, it consists in the square root of the sum of the square of all the matrix entries.
   * For vectors, this is also equals to the square root of the dot product of \c *this with itself.
   *
-  * \sa dot(), squaredNorm()
+  * \sa lpNorm(), dot(), squaredNorm()
   */
 template<typename Derived>
 inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm() const
 {
-  EIGEN_USING_STD_MATH(sqrt)
+  return numext::sqrt(squaredNorm());
-  return sqrt(squaredNorm());
 }
 
-/** \returns an expression of the quotient of *this by its own norm.
+/** \returns an expression of the quotient of \c *this by its own norm.
+  *
+  * \warning If the input vector is too small (i.e., this->norm()==0),
+  *          then this function returns a copy of the input.
   *
   * \only_for_vectors
   *
@@ -115,19 +117,75 @@ MatrixBase<Derived>::normalized() const
 {
   typedef typename internal::nested_eval<Derived,2>::type _Nested;
   _Nested n(derived());
-  return n / n.norm();
+  RealScalar z = n.squaredNorm();
+  // NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU
+  if(z>RealScalar(0))
+    return n / numext::sqrt(z);
+  else
+    return n;
 }
 
 /** Normalizes the vector, i.e. divides it by its own norm.
   *
   * \only_for_vectors
   *
+  * \warning If the input vector is too small (i.e., this->norm()==0), then \c *this is left unchanged.
+  *
   * \sa norm(), normalized()
   */
 template<typename Derived>
 inline void MatrixBase<Derived>::normalize()
 {
-  *this /= norm();
+  RealScalar z = squaredNorm();
+  // NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU
+  if(z>RealScalar(0))
+    derived() /= numext::sqrt(z);
+}
+
+/** \returns an expression of the quotient of \c *this by its own norm while avoiding underflow and overflow.
+  *
+  * \only_for_vectors
+  *
+  * This method is analogue to the normalized() method, but it reduces the risk of
+  * underflow and overflow when computing the norm.
+  *
+  * \warning If the input vector is too small (i.e., this->norm()==0),
+  *          then this function returns a copy of the input.
+  *
+  * \sa stableNorm(), stableNormalize(), normalized()
+  */
+template<typename Derived>
+inline const typename MatrixBase<Derived>::PlainObject
+MatrixBase<Derived>::stableNormalized() const
+{
+  typedef typename internal::nested_eval<Derived,3>::type _Nested;
+  _Nested n(derived());
+  RealScalar w = n.cwiseAbs().maxCoeff();
+  RealScalar z = (n/w).squaredNorm();
+  if(z>RealScalar(0))
+    return n / (numext::sqrt(z)*w);
+  else
+    return n;
+}
+
+/** Normalizes the vector while avoid underflow and overflow
+  *
+  * \only_for_vectors
+  *
+  * This method is analogue to the normalize() method, but it reduces the risk of
+  * underflow and overflow when computing the norm.
+  *
+  * \warning If the input vector is too small (i.e., this->norm()==0), then \c *this is left unchanged.
+  *
+  * \sa stableNorm(), stableNormalized(), normalize()
+  */
+template<typename Derived>
+inline void MatrixBase<Derived>::stableNormalize()
+{
+  RealScalar w = cwiseAbs().maxCoeff();
+  RealScalar z = (derived()/w).squaredNorm();
+  if(z>RealScalar(0))
+    derived() /= numext::sqrt(z)*w;
 }
 
 //---------- implementation of other norms ----------
@@ -188,7 +246,11 @@ struct lpNorm_selector<Derived, Infinity>
   */
 template<typename Derived>
 template<int p>
+#ifndef EIGEN_PARSED_BY_DOXYGEN
 inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+#else
+MatrixBase<Derived>::RealScalar
+#endif
 MatrixBase<Derived>::lpNorm() const
 {
   return internal::lpNorm_selector<Derived, p>::run(*this);

Eigen/src/Core/EigenBase.h

@@ -23,7 +23,7 @@ namespace Eigen {
   *
   * Notice that this class is trivial, it is only used to disambiguate overloaded functions.
   *
-  * \sa \ref TopicClassHierarchy
+  * \sa \blank \ref TopicClassHierarchy
   */
 template<typename Derived> struct EigenBase
 {

Eigen/src/Core/GeneralProduct.h

@@ -76,32 +76,6 @@ public:
 #endif
 };
 
-// template<typename Lhs, typename Rhs> struct product_tag
-// {
-// private:
-//   
-//   typedef typename remove_all<Lhs>::type _Lhs;
-//   typedef typename remove_all<Rhs>::type _Rhs;
-//   enum {
-//     Rows  = _Lhs::RowsAtCompileTime,
-//     Cols  = _Rhs::ColsAtCompileTime,
-//     Depth = EIGEN_SIZE_MIN_PREFER_FIXED(_Lhs::ColsAtCompileTime, _Rhs::RowsAtCompileTime)
-//   };
-// 
-//   enum {
-//     rows_select = Rows==1 ? int(Rows) : int(Large),
-//     cols_select = Cols==1 ? int(Cols) : int(Large),
-//     depth_select = Depth==1 ? int(Depth) : int(Large)
-//   };
-//   typedef product_type_selector<rows_select, cols_select, depth_select> selector;
-// 
-// public:
-//   enum {
-//     ret = selector::ret
-//   };
-// 
-// };
-
 /* The following allows to select the kind of product at compile time
  * based on the three dimensions of the product.
  * This is a compile time mapping from {1,Small,Large}^3 -> {product types} */
@@ -125,8 +99,8 @@ template<>              struct product_type_selector<Small,Small,Large>  { enum
 template<>              struct product_type_selector<Large,Small,Large>  { enum { ret = GemmProduct }; };
 template<>              struct product_type_selector<Small,Large,Large>  { enum { ret = GemmProduct }; };
 template<>              struct product_type_selector<Large,Large,Large>  { enum { ret = GemmProduct }; };
-template<>              struct product_type_selector<Large,Small,Small>  { enum { ret = GemmProduct }; };
+template<>              struct product_type_selector<Large,Small,Small>  { enum { ret = CoeffBasedProductMode }; };
-template<>              struct product_type_selector<Small,Large,Small>  { enum { ret = GemmProduct }; };
+template<>              struct product_type_selector<Small,Large,Small>  { enum { ret = CoeffBasedProductMode }; };
 template<>              struct product_type_selector<Large,Large,Small>  { enum { ret = GemmProduct }; };
 
 } // end namespace internal
@@ -239,15 +213,18 @@ template<> struct gemv_dense_selector<OnTheRight,ColMajor,true>
     ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(lhs)
                                   * RhsBlasTraits::extractScalarFactor(rhs);
 
+    // make sure Dest is a compile-time vector type (bug 1166)
+    typedef typename conditional<Dest::IsVectorAtCompileTime, Dest, typename Dest::ColXpr>::type ActualDest;
+
     enum {
       // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
       // on, the other hand it is good for the cache to pack the vector anyways...
-      EvalToDestAtCompileTime = Dest::InnerStrideAtCompileTime==1,
+      EvalToDestAtCompileTime = (ActualDest::InnerStrideAtCompileTime==1),
       ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
-      MightCannotUseDest = (Dest::InnerStrideAtCompileTime!=1) || ComplexByReal
+      MightCannotUseDest = (ActualDest::InnerStrideAtCompileTime!=1) || ComplexByReal
     };
 
-    gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
+    gemv_static_vector_if<ResScalar,ActualDest::SizeAtCompileTime,ActualDest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
 
     const bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));
     const bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
@@ -340,7 +317,7 @@ template<> struct gemv_dense_selector<OnTheRight,RowMajor,true>
         actualLhs.rows(), actualLhs.cols(),
         LhsMapper(actualLhs.data(), actualLhs.outerStride()),
         RhsMapper(actualRhsPtr, 1),
-        dest.data(), dest.innerStride(),
+        dest.data(), dest.col(0).innerStride(), //NOTE  if dest is not a vector at compile-time, then dest.innerStride() might be wrong. (bug 1166)
         actualAlpha);
   }
 };

Eigen/src/Core/GenericPacketMath.h

@@ -43,7 +43,7 @@ struct default_packet_traits
 {
   enum {
     HasHalfPacket = 0,
-    
+
     HasAdd    = 1,
     HasSub    = 1,
     HasMul    = 1,
@@ -62,7 +62,7 @@ struct default_packet_traits
     HasRsqrt  = 0,
     HasExp    = 0,
     HasLog    = 0,
-    HasLog10    = 0,
+    HasLog10  = 0,
     HasPow    = 0,
 
     HasSin    = 0,
@@ -71,9 +71,17 @@ struct default_packet_traits
     HasASin   = 0,
     HasACos   = 0,
     HasATan   = 0,
-    HasSinh    = 0,
+    HasSinh   = 0,
-    HasCosh    = 0,
+    HasCosh   = 0,
-    HasTanh    = 0,
+    HasTanh   = 0,
+    HasLGamma = 0,
+    HasDiGamma = 0,
+    HasZeta = 0,
+    HasPolygamma = 0,
+    HasErf = 0,
+    HasErfc = 0,
+    HasIGamma = 0,
+    HasIGammac = 0,
 
     HasRound  = 0,
     HasFloor  = 0,
@@ -130,6 +138,11 @@ pcast(const SrcPacket& a, const SrcPacket& /*b*/) {
   return static_cast<TgtPacket>(a);
 }
 
+template <typename SrcPacket, typename TgtPacket>
+EIGEN_DEVICE_FUNC inline TgtPacket
+pcast(const SrcPacket& a, const SrcPacket& /*b*/, const SrcPacket& /*c*/, const SrcPacket& /*d*/) {
+  return static_cast<TgtPacket>(a);
+}
 
 /** \internal \returns a + b (coeff-wise) */
 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
@@ -281,7 +294,7 @@ template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pstoreu
  { pstore(to, from); }
 
 /** \internal tries to do cache prefetching of \a addr */
-template<typename Scalar> inline void prefetch(const Scalar* addr)
+template<typename Scalar> EIGEN_DEVICE_FUNC inline void prefetch(const Scalar* addr)
 {
 #ifdef __CUDA_ARCH__
 #if defined(__LP64__)
@@ -432,6 +445,38 @@ Packet pfloor(const Packet& a) { using numext::floor; return floor(a); }
 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet pceil(const Packet& a) { using numext::ceil; return ceil(a); }
 
+/** \internal \returns the ln(|gamma(\a a)|) (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plgamma(const Packet& a) { using numext::lgamma; return lgamma(a); }
+
+/** \internal \returns the derivative of lgamma, psi(\a a) (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pdigamma(const Packet& a) { using numext::digamma; return digamma(a); }
+    
+/** \internal \returns the zeta function of two arguments (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pzeta(const Packet& x, const Packet& q) { using numext::zeta; return zeta(x, q); }
+
+/** \internal \returns the polygamma function (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet ppolygamma(const Packet& n, const Packet& x) { using numext::polygamma; return polygamma(n, x); }
+
+/** \internal \returns the erf(\a a) (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet perf(const Packet& a) { using numext::erf; return erf(a); }
+
+/** \internal \returns the erfc(\a a) (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet perfc(const Packet& a) { using numext::erfc; return erfc(a); }
+
+/** \internal \returns the incomplete gamma function igamma(\a a, \a x) */
+template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+Packet pigamma(const Packet& a, const Packet& x) { using numext::igamma; return igamma(a, x); }
+
+/** \internal \returns the complementary incomplete gamma function igammac(\a a, \a x) */
+template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+Packet pigammac(const Packet& a, const Packet& x) { using numext::igammac; return igammac(a, x); }
+
 /***************************************************************************
 * The following functions might not have to be overwritten for vectorized types
 ***************************************************************************/

Eigen/src/Core/GlobalFunctions.h

@@ -49,6 +49,12 @@ namespace Eigen
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sinh,scalar_sinh_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cosh,scalar_cosh_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tanh,scalar_tanh_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(lgamma,scalar_lgamma_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(digamma,scalar_digamma_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(zeta,scalar_zeta_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(polygamma,scalar_polygamma_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erf,scalar_erf_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erfc,scalar_erfc_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp,scalar_exp_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log,scalar_log_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log10,scalar_log10_op)
@@ -125,6 +131,36 @@ namespace Eigen
     );
   }
 
+  /** \returns an expression of the coefficient-wise igamma(\a a, \a x) to the given arrays.
+    *
+    * This function computes the coefficient-wise incomplete gamma function.
+    *
+    */
+  template<typename Derived,typename ExponentDerived>
+  inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
+  igamma(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x) 
+  {
+    return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
+      a.derived(),
+      x.derived()
+    );
+  }
+
+  /** \returns an expression of the coefficient-wise igammac(\a a, \a x) to the given arrays.
+    *
+    * This function computes the coefficient-wise complementary incomplete gamma function.
+    *
+    */
+  template<typename Derived,typename ExponentDerived>
+  inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
+  igammac(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x) 
+  {
+    return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
+      a.derived(),
+      x.derived()
+    );
+  }
+
   namespace internal
   {
     EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(real,scalar_real_op)

Eigen/src/Core/IO.h

@@ -80,7 +80,7 @@ struct IOFormat
   *
   * \brief Pseudo expression providing matrix output with given format
   *
-  * \param ExpressionType the type of the object on which IO stream operations are performed
+  * \tparam ExpressionType the type of the object on which IO stream operations are performed
   *
   * This class represents an expression with stream operators controlled by a given IOFormat.
   * It is the return type of DenseBase::format()

Eigen/src/Core/Map.h

@@ -13,6 +13,28 @@
 
 namespace Eigen { 
 
+namespace internal {
+template<typename PlainObjectType, int MapOptions, typename StrideType>
+struct traits<Map<PlainObjectType, MapOptions, StrideType> >
+  : public traits<PlainObjectType>
+{
+  typedef traits<PlainObjectType> TraitsBase;
+  enum {
+    InnerStrideAtCompileTime = StrideType::InnerStrideAtCompileTime == 0
+                             ? int(PlainObjectType::InnerStrideAtCompileTime)
+                             : int(StrideType::InnerStrideAtCompileTime),
+    OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0
+                             ? int(PlainObjectType::OuterStrideAtCompileTime)
+                             : int(StrideType::OuterStrideAtCompileTime),
+    Alignment = int(MapOptions)&int(AlignedMask),
+    Flags0 = TraitsBase::Flags & (~NestByRefBit),
+    Flags = is_lvalue<PlainObjectType>::value ? int(Flags0) : (int(Flags0) & ~LvalueBit)
+  };
+private:
+  enum { Options }; // Expressions don't have Options
+};
+}
+
 /** \class Map
   * \ingroup Core_Module
   *
@@ -63,29 +85,6 @@ namespace Eigen {
   *
   * \sa PlainObjectBase::Map(), \ref TopicStorageOrders
   */
-
-namespace internal {
-template<typename PlainObjectType, int MapOptions, typename StrideType>
-struct traits<Map<PlainObjectType, MapOptions, StrideType> >
-  : public traits<PlainObjectType>
-{
-  typedef traits<PlainObjectType> TraitsBase;
-  enum {
-    InnerStrideAtCompileTime = StrideType::InnerStrideAtCompileTime == 0
-                             ? int(PlainObjectType::InnerStrideAtCompileTime)
-                             : int(StrideType::InnerStrideAtCompileTime),
-    OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0
-                             ? int(PlainObjectType::OuterStrideAtCompileTime)
-                             : int(StrideType::OuterStrideAtCompileTime),
-    Alignment = int(MapOptions)&int(AlignedMask),
-    Flags0 = TraitsBase::Flags & (~NestByRefBit),
-    Flags = is_lvalue<PlainObjectType>::value ? int(Flags0) : (int(Flags0) & ~LvalueBit)
-  };
-private:
-  enum { Options }; // Expressions don't have Options
-};
-}
-
 template<typename PlainObjectType, int MapOptions, typename StrideType> class Map
   : public MapBase<Map<PlainObjectType, MapOptions, StrideType> >
 {

Eigen/src/Core/MapBase.h

@@ -130,7 +130,7 @@ template<typename Derived> class MapBase<Derived, ReadOnlyAccessors>
     explicit inline MapBase(PointerType dataPtr) : m_data(dataPtr), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime)
     {
       EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
-      checkSanity();
+      checkSanity<Derived>();
     }
 
     EIGEN_DEVICE_FUNC
@@ -142,7 +142,7 @@ template<typename Derived> class MapBase<Derived, ReadOnlyAccessors>
       EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
       eigen_assert(vecSize >= 0);
       eigen_assert(dataPtr == 0 || SizeAtCompileTime == Dynamic || SizeAtCompileTime == vecSize);
-      checkSanity();
+      checkSanity<Derived>();
     }
 
     EIGEN_DEVICE_FUNC
@@ -152,19 +152,30 @@ template<typename Derived> class MapBase<Derived, ReadOnlyAccessors>
       eigen_assert( (dataPtr == 0)
               || (   rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
                   && cols >= 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols)));
-      checkSanity();
+      checkSanity<Derived>();
     }
 
+    #ifdef EIGEN_MAPBASE_PLUGIN
+    #include EIGEN_MAPBASE_PLUGIN
+    #endif
+
   protected:
 
+    template<typename T>
     EIGEN_DEVICE_FUNC
-    void checkSanity() const
+    void checkSanity(typename internal::enable_if<(internal::traits<T>::Alignment>0),void*>::type = 0) const
     {
 #if EIGEN_MAX_ALIGN_BYTES>0
-      eigen_assert(((size_t(m_data) % EIGEN_PLAIN_ENUM_MAX(1,internal::traits<Derived>::Alignment)) == 0) && "data is not aligned");
+      eigen_assert((   ((size_t(m_data) % internal::traits<Derived>::Alignment) == 0)
+                    || (cols() * rows() * innerStride() * sizeof(Scalar)) < internal::traits<Derived>::Alignment ) && "data is not aligned");
 #endif
     }
 
+    template<typename T>
+    EIGEN_DEVICE_FUNC
+    void checkSanity(typename internal::enable_if<internal::traits<T>::Alignment==0,void*>::type = 0) const
+    {}
+
     PointerType m_data;
     const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
     const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;

Eigen/src/Core/MathFunctions.h

@@ -23,10 +23,10 @@ double      abs(double      x) { return (fabs(x));  }
 float       abs(float       x) { return (fabsf(x)); }
 long double abs(long double x) { return (fabsl(x)); }
 #endif
-  
+
 namespace internal {
 
-/** \internal \struct global_math_functions_filtering_base
+/** \internal \class global_math_functions_filtering_base
   *
   * What it does:
   * Defines a typedef 'type' as follows:
@@ -496,7 +496,7 @@ template<typename Scalar, bool IsInteger>
 struct pow_default_impl
 {
   typedef Scalar retval;
-  static inline Scalar run(const Scalar& x, const Scalar& y)
+  static EIGEN_DEVICE_FUNC inline Scalar run(const Scalar& x, const Scalar& y)
   {
     EIGEN_USING_STD_MATH(pow);
     return pow(x, y);
@@ -506,7 +506,7 @@ struct pow_default_impl
 template<typename Scalar>
 struct pow_default_impl<Scalar, true>
 {
-  static inline Scalar run(Scalar x, Scalar y)
+  static EIGEN_DEVICE_FUNC inline Scalar run(Scalar x, Scalar y)
   {
     Scalar res(1);
     eigen_assert(!NumTraits<Scalar>::IsSigned || y >= 0);
@@ -704,11 +704,13 @@ EIGEN_DEVICE_FUNC
 typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type
 isfinite_impl(const T& x)
 {
-  #if EIGEN_USE_STD_FPCLASSIFY
+  #ifdef __CUDA_ARCH__
+    return (::isfinite)(x);
+  #elif EIGEN_USE_STD_FPCLASSIFY
     using std::isfinite;
     return isfinite EIGEN_NOT_A_MACRO (x);
   #else
-    return x<NumTraits<T>::highest() && x>NumTraits<T>::lowest();
+    return x<=NumTraits<T>::highest() && x>=NumTraits<T>::lowest();
   #endif
 }
 
@@ -717,7 +719,9 @@ EIGEN_DEVICE_FUNC
 typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type
 isinf_impl(const T& x)
 {
-  #if EIGEN_USE_STD_FPCLASSIFY
+  #ifdef __CUDA_ARCH__
+    return (::isinf)(x);
+  #elif EIGEN_USE_STD_FPCLASSIFY
     using std::isinf;
     return isinf EIGEN_NOT_A_MACRO (x);
   #else
@@ -730,7 +734,9 @@ EIGEN_DEVICE_FUNC
 typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type
 isnan_impl(const T& x)
 {
-  #if EIGEN_USE_STD_FPCLASSIFY
+  #ifdef __CUDA_ARCH__
+    return (::isnan)(x);
+  #elif EIGEN_USE_STD_FPCLASSIFY
     using std::isnan;
     return isnan EIGEN_NOT_A_MACRO (x);
   #else
@@ -748,9 +754,9 @@ template<typename T> EIGEN_DEVICE_FUNC bool isinf_msvc_helper(T x)
 }
 
 //MSVC defines a _isnan builtin function, but for double only
-EIGEN_DEVICE_FUNC inline bool isnan_impl(const long double& x) { return _isnan(x); }
+EIGEN_DEVICE_FUNC inline bool isnan_impl(const long double& x) { return _isnan(x)!=0; }
-EIGEN_DEVICE_FUNC inline bool isnan_impl(const double& x)      { return _isnan(x); }
+EIGEN_DEVICE_FUNC inline bool isnan_impl(const double& x)      { return _isnan(x)!=0; }
-EIGEN_DEVICE_FUNC inline bool isnan_impl(const float& x)       { return _isnan(x); }
+EIGEN_DEVICE_FUNC inline bool isnan_impl(const float& x)       { return _isnan(x)!=0; }
 
 EIGEN_DEVICE_FUNC inline bool isinf_impl(const long double& x) { return isinf_msvc_helper(x); }
 EIGEN_DEVICE_FUNC inline bool isinf_impl(const double& x)      { return isinf_msvc_helper(x); }
@@ -780,9 +786,9 @@ template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const long double& x) { return
 #endif
 
 // The following overload are defined at the end of this file
-template<typename T> bool isfinite_impl(const std::complex<T>& x);
+template<typename T> EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x);
-template<typename T> bool isnan_impl(const std::complex<T>& x);
+template<typename T> EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x);
-template<typename T> bool isinf_impl(const std::complex<T>& x);
+template<typename T> EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x);
 
 } // end namespace internal
 
@@ -946,6 +952,14 @@ T (floor)(const T& x)
   return floor(x);
 }
 
+#ifdef __CUDACC__
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float floor(const float &x) { return ::floorf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double floor(const double &x) { return ::floor(x); }
+#endif
+
 template<typename T>
 EIGEN_DEVICE_FUNC
 T (ceil)(const T& x)
@@ -954,8 +968,17 @@ T (ceil)(const T& x)
   return ceil(x);
 }
 
-// Log base 2 for 32 bits positive integers.
+#ifdef __CUDACC__
-// Conveniently returns 0 for x==0.
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float ceil(const float &x) { return ::ceilf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double ceil(const double &x) { return ::ceil(x); }
+#endif
+
+
+/** Log base 2 for 32 bits positive integers.
+  * Conveniently returns 0 for x==0. */
 inline int log2(int x)
 {
   eigen_assert(x>=0);
@@ -969,24 +992,122 @@ inline int log2(int x)
   return table[(v * 0x07C4ACDDU) >> 27];
 }
 
+/** \returns the square root of \a x.
+  *
+  * It is essentially equivalent to \code using std::sqrt; return sqrt(x); \endcode,
+  * but slightly faster for float/double and some compilers (e.g., gcc), thanks to
+  * specializations when SSE is enabled.
+  *
+  * It's usage is justified in performance critical functions, like norm/normalize.
+  */
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T sqrt(const T &x)
+{
+  EIGEN_USING_STD_MATH(sqrt);
+  return sqrt(x);
+}
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T log(const T &x) {
+  EIGEN_USING_STD_MATH(log);
+  return log(x);
+}
+
+#ifdef __CUDACC__
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float log(const float &x) { return ::logf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double log(const double &x) { return ::log(x); }
+#endif
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T tan(const T &x) {
+  EIGEN_USING_STD_MATH(tan);
+  return tan(x);
+}
+
+#ifdef __CUDACC__
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float tan(const float &x) { return ::tanf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double tan(const double &x) { return ::tan(x); }
+#endif
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+typename NumTraits<T>::Real abs(const T &x) {
+  EIGEN_USING_STD_MATH(abs);
+  return abs(x);
+}
+
+#ifdef __CUDACC__
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float abs(const float &x) { return ::fabsf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double abs(const double &x) { return ::fabs(x); }
+#endif
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T exp(const T &x) {
+  EIGEN_USING_STD_MATH(exp);
+  return exp(x);
+}
+
+#ifdef __CUDACC__
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float exp(const float &x) { return ::expf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double exp(const double &x) { return ::exp(x); }
+#endif
+
+
+template <typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T fmod(const T& a, const T& b) {
+  EIGEN_USING_STD_MATH(floor);
+  return fmod(a, b);
+}
+
+#ifdef __CUDACC__
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float fmod(const float& a, const float& b) {
+  return ::fmodf(a, b);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double fmod(const double& a, const double& b) {
+  return ::fmod(a, b);
+}
+#endif
+
 } // end namespace numext
 
 namespace internal {
 
 template<typename T>
-bool isfinite_impl(const std::complex<T>& x)
+EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x)
 {
   return (numext::isfinite)(numext::real(x)) && (numext::isfinite)(numext::imag(x));
 }
 
 template<typename T>
-bool isnan_impl(const std::complex<T>& x)
+EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x)
 {
   return (numext::isnan)(numext::real(x)) || (numext::isnan)(numext::imag(x));
 }
 
 template<typename T>
-bool isinf_impl(const std::complex<T>& x)
+EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x)
 {
   return ((numext::isinf)(numext::real(x)) || (numext::isinf)(numext::imag(x))) && (!(numext::isnan)(x));
 }
@@ -1007,14 +1128,12 @@ struct scalar_fuzzy_default_impl<Scalar, false, false>
   template<typename OtherScalar> EIGEN_DEVICE_FUNC
   static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
   {
-    EIGEN_USING_STD_MATH(abs);
+    return numext::abs(x) <= numext::abs(y) * prec;
-    return abs(x) <= abs(y) * prec;
   }
   EIGEN_DEVICE_FUNC
   static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
   {
-    EIGEN_USING_STD_MATH(abs);
+    return numext::abs(x - y) <= numext::mini(numext::abs(x), numext::abs(y)) * prec;
-    return abs(x - y) <= numext::mini(abs(x), abs(y)) * prec;
   }
   EIGEN_DEVICE_FUNC
   static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar& prec)
@@ -1064,21 +1183,21 @@ struct scalar_fuzzy_impl : scalar_fuzzy_default_impl<Scalar, NumTraits<Scalar>::
 
 template<typename Scalar, typename OtherScalar> EIGEN_DEVICE_FUNC
 inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y,
-                                   typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
+                              const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
 {
   return scalar_fuzzy_impl<Scalar>::template isMuchSmallerThan<OtherScalar>(x, y, precision);
 }
 
 template<typename Scalar> EIGEN_DEVICE_FUNC
 inline bool isApprox(const Scalar& x, const Scalar& y,
-                          typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
+                     const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
 {
   return scalar_fuzzy_impl<Scalar>::isApprox(x, y, precision);
 }
 
 template<typename Scalar> EIGEN_DEVICE_FUNC
 inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y,
-                                    typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision())
+                               const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
 {
   return scalar_fuzzy_impl<Scalar>::isApproxOrLessThan(x, y, precision);
 }

Eigen/src/Core/Matrix.h

@@ -13,6 +13,45 @@
 
 namespace Eigen {
 
+namespace internal {
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+struct traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
+{
+private:
+  enum { size = internal::size_at_compile_time<_Rows,_Cols>::ret };
+  typedef typename find_best_packet<_Scalar,size>::type PacketScalar;
+  enum {
+      row_major_bit = _Options&RowMajor ? RowMajorBit : 0,
+      is_dynamic_size_storage = _MaxRows==Dynamic || _MaxCols==Dynamic,
+      max_size = is_dynamic_size_storage ? Dynamic : _MaxRows*_MaxCols,
+      default_alignment = compute_default_alignment<_Scalar,max_size>::value,
+      actual_alignment = ((_Options&DontAlign)==0) ? default_alignment : 0,
+      required_alignment = unpacket_traits<PacketScalar>::alignment,
+      packet_access_bit = packet_traits<_Scalar>::Vectorizable && (actual_alignment>=required_alignment) ? PacketAccessBit : 0
+    };
+    
+public:
+  typedef _Scalar Scalar;
+  typedef Dense StorageKind;
+  typedef Eigen::Index StorageIndex;
+  typedef MatrixXpr XprKind;
+  enum {
+    RowsAtCompileTime = _Rows,
+    ColsAtCompileTime = _Cols,
+    MaxRowsAtCompileTime = _MaxRows,
+    MaxColsAtCompileTime = _MaxCols,
+    Flags = compute_matrix_flags<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::ret,
+    Options = _Options,
+    InnerStrideAtCompileTime = 1,
+    OuterStrideAtCompileTime = (Options&RowMajor) ? ColsAtCompileTime : RowsAtCompileTime,
+    
+    // FIXME, the following flag in only used to define NeedsToAlign in PlainObjectBase
+    EvaluatorFlags = LinearAccessBit | DirectAccessBit | packet_access_bit | row_major_bit,
+    Alignment = actual_alignment
+  };
+};
+}
+
 /** \class Matrix
   * \ingroup Core_Module
   *
@@ -98,7 +137,7 @@ namespace Eigen {
   * </dl>
   *
   * <i><b>ABI and storage layout</b></i>
-  * 
+  *
   * The table below summarizes the ABI of some possible Matrix instances which is fixed thorough the lifetime of Eigen 3.
   * <table  class="manual">
   * <tr><th>Matrix type</th><th>Equivalent C structure</th></tr>
@@ -130,50 +169,11 @@ namespace Eigen {
   * </table>
   * Note that in this table Rows, Cols, MaxRows and MaxCols are all positive integers. A(S) is defined to the largest possible power-of-two
   * smaller to EIGEN_MAX_STATIC_ALIGN_BYTES.
-  * 
+  *
-  * \see MatrixBase for the majority of the API methods for matrices, \ref TopicClassHierarchy, 
+  * \see MatrixBase for the majority of the API methods for matrices, \ref TopicClassHierarchy,
-  * \ref TopicStorageOrders 
+  * \ref TopicStorageOrders
   */
 
-namespace internal {
-template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
-struct traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
-{
-private:
-  enum { size = internal::size_at_compile_time<_Rows,_Cols>::ret };
-  typedef typename find_best_packet<_Scalar,size>::type PacketScalar;
-  enum {
-      row_major_bit = _Options&RowMajor ? RowMajorBit : 0,
-      is_dynamic_size_storage = _MaxRows==Dynamic || _MaxCols==Dynamic,
-      max_size = is_dynamic_size_storage ? Dynamic : _MaxRows*_MaxCols,
-      default_alignment = compute_default_alignment<_Scalar,max_size>::value,
-      actual_alignment = ((_Options&DontAlign)==0) ? default_alignment : 0,
-      required_alignment = unpacket_traits<PacketScalar>::alignment,
-      packet_access_bit = packet_traits<_Scalar>::Vectorizable && (actual_alignment>=required_alignment) ? PacketAccessBit : 0
-    };
-    
-public:
-  typedef _Scalar Scalar;
-  typedef Dense StorageKind;
-  typedef Eigen::Index StorageIndex;
-  typedef MatrixXpr XprKind;
-  enum {
-    RowsAtCompileTime = _Rows,
-    ColsAtCompileTime = _Cols,
-    MaxRowsAtCompileTime = _MaxRows,
-    MaxColsAtCompileTime = _MaxCols,
-    Flags = compute_matrix_flags<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::ret,
-    Options = _Options,
-    InnerStrideAtCompileTime = 1,
-    OuterStrideAtCompileTime = (Options&RowMajor) ? ColsAtCompileTime : RowsAtCompileTime,
-    
-    // FIXME, the following flag in only used to define NeedsToAlign in PlainObjectBase
-    EvaluatorFlags = LinearAccessBit | DirectAccessBit | packet_access_bit | row_major_bit,
-    Alignment = actual_alignment
-  };
-};
-}
-
 template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
 class Matrix
   : public PlainObjectBase<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >

Eigen/src/Core/MatrixBase.h

@@ -43,7 +43,7 @@ namespace Eigen {
   * This class can be extended with the help of the plugin mechanism described on the page
   * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_MATRIXBASE_PLUGIN.
   *
-  * \sa \ref TopicClassHierarchy
+  * \sa \blank \ref TopicClassHierarchy
   */
 template<typename Derived> class MatrixBase
   : public DenseBase<Derived>
@@ -66,7 +66,7 @@ template<typename Derived> class MatrixBase
     using Base::MaxSizeAtCompileTime;
     using Base::IsVectorAtCompileTime;
     using Base::Flags;
-    
+
     using Base::derived;
     using Base::const_cast_derived;
     using Base::rows;
@@ -135,14 +135,14 @@ template<typename Derived> class MatrixBase
     /** Special case of the template operator=, in order to prevent the compiler
       * from generating a default operator= (issue hit with g++ 4.1)
       */
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     Derived& operator=(const MatrixBase& other);
 
     // We cannot inherit here via Base::operator= since it is causing
     // trouble with MSVC.
 
     template <typename OtherDerived>
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     Derived& operator=(const DenseBase<OtherDerived>& other);
 
     template <typename OtherDerived>
@@ -154,10 +154,10 @@ template<typename Derived> class MatrixBase
     Derived& operator=(const ReturnByValue<OtherDerived>& other);
 
     template<typename OtherDerived>
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     Derived& operator+=(const MatrixBase<OtherDerived>& other);
     template<typename OtherDerived>
-    EIGEN_DEVICE_FUNC
+    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     Derived& operator-=(const MatrixBase<OtherDerived>& other);
 
 #ifdef __CUDACC__
@@ -175,7 +175,7 @@ template<typename Derived> class MatrixBase
 #endif
 
     template<typename OtherDerived>
-    EIGEN_DEVICE_FUNC 
+    EIGEN_DEVICE_FUNC
     const Product<Derived,OtherDerived,LazyProduct>
     lazyProduct(const MatrixBase<OtherDerived> &other) const;
 
@@ -204,7 +204,9 @@ template<typename Derived> class MatrixBase
     RealScalar blueNorm() const;
     RealScalar hypotNorm() const;
     EIGEN_DEVICE_FUNC const PlainObject normalized() const;
+    EIGEN_DEVICE_FUNC const PlainObject stableNormalized() const;
     EIGEN_DEVICE_FUNC void normalize();
+    EIGEN_DEVICE_FUNC void stableNormalize();
 
     EIGEN_DEVICE_FUNC const AdjointReturnType adjoint() const;
     EIGEN_DEVICE_FUNC void adjointInPlace();
@@ -212,7 +214,7 @@ template<typename Derived> class MatrixBase
     typedef Diagonal<Derived> DiagonalReturnType;
     EIGEN_DEVICE_FUNC
     DiagonalReturnType diagonal();
-    
+
     typedef typename internal::add_const<Diagonal<const Derived> >::type ConstDiagonalReturnType;
     EIGEN_DEVICE_FUNC
     ConstDiagonalReturnType diagonal() const;
@@ -220,14 +222,14 @@ template<typename Derived> class MatrixBase
     template<int Index> struct DiagonalIndexReturnType { typedef Diagonal<Derived,Index> Type; };
     template<int Index> struct ConstDiagonalIndexReturnType { typedef const Diagonal<const Derived,Index> Type; };
 
-    template<int Index> 
+    template<int Index>
     EIGEN_DEVICE_FUNC
     typename DiagonalIndexReturnType<Index>::Type diagonal();
 
     template<int Index>
     EIGEN_DEVICE_FUNC
     typename ConstDiagonalIndexReturnType<Index>::Type diagonal() const;
-    
+
     typedef Diagonal<Derived,DynamicIndex> DiagonalDynamicIndexReturnType;
     typedef typename internal::add_const<Diagonal<const Derived,DynamicIndex> >::type ConstDiagonalDynamicIndexReturnType;
 
@@ -249,7 +251,7 @@ template<typename Derived> class MatrixBase
     template<unsigned int UpLo> struct SelfAdjointViewReturnType { typedef SelfAdjointView<Derived, UpLo> Type; };
     template<unsigned int UpLo> struct ConstSelfAdjointViewReturnType { typedef const SelfAdjointView<const Derived, UpLo> Type; };
 
-    template<unsigned int UpLo> 
+    template<unsigned int UpLo>
     EIGEN_DEVICE_FUNC
     typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();
     template<unsigned int UpLo>
@@ -338,7 +340,7 @@ template<typename Derived> class MatrixBase
 
     EIGEN_DEVICE_FUNC
     inline const Inverse<Derived> inverse() const;
-    
+
     template<typename ResultType>
     inline void computeInverseAndDetWithCheck(
       ResultType& inverse,
@@ -364,6 +366,7 @@ template<typename Derived> class MatrixBase
     inline const HouseholderQR<PlainObject> householderQr() const;
     inline const ColPivHouseholderQR<PlainObject> colPivHouseholderQr() const;
     inline const FullPivHouseholderQR<PlainObject> fullPivHouseholderQr() const;
+    inline const CompleteOrthogonalDecomposition<PlainObject> completeOrthogonalDecomposition() const;
 
 /////////// Eigenvalues module ///////////
 
@@ -386,25 +389,29 @@ template<typename Derived> class MatrixBase
     #endif // EIGEN_PARSED_BY_DOXYGEN
     template<typename OtherDerived>
     EIGEN_DEVICE_FUNC
+#ifndef EIGEN_PARSED_BY_DOXYGEN
     inline typename cross_product_return_type<OtherDerived>::type
+#else
+    inline PlainObject
+#endif
     cross(const MatrixBase<OtherDerived>& other) const;
-    
+
     template<typename OtherDerived>
     EIGEN_DEVICE_FUNC
     inline PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
-    
+
     EIGEN_DEVICE_FUNC
     inline PlainObject unitOrthogonal(void) const;
-    
+
     inline Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const;
-    
+
     inline ScalarMultipleReturnType operator*(const UniformScaling<Scalar>& s) const;
     // put this as separate enum value to work around possible GCC 4.3 bug (?)
     enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1&&RowsAtCompileTime==1 ? ((internal::traits<Derived>::Flags&RowMajorBit)==RowMajorBit ? Horizontal : Vertical)
                                           : ColsAtCompileTime==1 ? Vertical : Horizontal };
     typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType;
     inline HomogeneousReturnType homogeneous() const;
-    
+
     enum {
       SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1
     };

Eigen/src/Core/NestByValue.h

@@ -13,25 +13,24 @@
 
 namespace Eigen {
 
-/** \class NestByValue
-  * \ingroup Core_Module
-  *
-  * \brief Expression which must be nested by value
-  *
-  * \param ExpressionType the type of the object of which we are requiring nesting-by-value
-  *
-  * This class is the return type of MatrixBase::nestByValue()
-  * and most of the time this is the only way it is used.
-  *
-  * \sa MatrixBase::nestByValue()
-  */
-
 namespace internal {
 template<typename ExpressionType>
 struct traits<NestByValue<ExpressionType> > : public traits<ExpressionType>
 {};
 }
 
+/** \class NestByValue
+  * \ingroup Core_Module
+  *
+  * \brief Expression which must be nested by value
+  *
+  * \tparam ExpressionType the type of the object of which we are requiring nesting-by-value
+  *
+  * This class is the return type of MatrixBase::nestByValue()
+  * and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::nestByValue()
+  */
 template<typename ExpressionType> class NestByValue
   : public internal::dense_xpr_base< NestByValue<ExpressionType> >::type
 {

Eigen/src/Core/NoAlias.h

@@ -17,7 +17,7 @@ namespace Eigen {
   *
   * \brief Pseudo expression providing an operator = assuming no aliasing
   *
-  * \param ExpressionType the type of the object on which to do the lazy assignment
+  * \tparam ExpressionType the type of the object on which to do the lazy assignment
   *
   * This class represents an expression with special assignment operators
   * assuming no aliasing between the target expression and the source expression.

Eigen/src/Core/NumTraits.h

@@ -17,7 +17,7 @@ namespace Eigen {
   *
   * \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
   *
-  * \param T the numeric type at hand
+  * \tparam T the numeric type at hand
   *
   * This class stores enums, typedefs and static methods giving information about a numeric type.
   *
@@ -60,6 +60,23 @@ template<typename T> struct GenericNumTraits
     MulCost = 1
   };
 
+  // Division is messy but important, because it is expensive and throughput
+  // varies significantly. The following numbers are based on min division
+  // throughput on Haswell.
+  template<bool Vectorized>
+  struct Div {
+    enum {
+#ifdef EIGEN_VECTORIZE_AVX
+      AVX = true,
+#else
+      AVX = false,
+#endif
+      Cost = IsInteger ? (sizeof(T) == 8 ? (IsSigned ? 24 : 21) : (IsSigned ? 8 : 9)):
+          Vectorized ? (sizeof(T) == 8 ? (AVX ? 16 : 8) : (AVX ? 14 : 7)) : 8
+    };
+  };
+
+
   typedef T Real;
   typedef typename internal::conditional<
                      IsInteger,
@@ -71,11 +88,7 @@ template<typename T> struct GenericNumTraits
   EIGEN_DEVICE_FUNC
   static inline Real epsilon()
   {
-    #if defined(__CUDA_ARCH__)
+    return numext::numeric_limits<T>::epsilon();
-    return internal::device::numeric_limits<T>::epsilon();
-    #else
-    return std::numeric_limits<T>::epsilon();
-    #endif
   }
   EIGEN_DEVICE_FUNC
   static inline Real dummy_precision()
@@ -87,20 +100,22 @@ template<typename T> struct GenericNumTraits
 
   EIGEN_DEVICE_FUNC
   static inline T highest() {
-#if defined(__CUDA_ARCH__)
+    return (numext::numeric_limits<T>::max)();
-    return (internal::device::numeric_limits<T>::max)();
-#else
-    return (std::numeric_limits<T>::max)();
-#endif
   }
 
   EIGEN_DEVICE_FUNC
   static inline T lowest()  {
-#if defined(__CUDA_ARCH__)
+    return IsInteger ? (numext::numeric_limits<T>::min)() : (-(numext::numeric_limits<T>::max)());
-    return IsInteger ? (internal::device::numeric_limits<T>::min)() : (-(internal::device::numeric_limits<T>::max)());
+  }
-#else
+
-    return IsInteger ? (std::numeric_limits<T>::min)() : (-(std::numeric_limits<T>::max)());
+  EIGEN_DEVICE_FUNC
-#endif
+  static inline T infinity() {
+    return numext::numeric_limits<T>::infinity();
+  }
+
+  EIGEN_DEVICE_FUNC
+  static inline T quiet_NaN() {
+    return numext::numeric_limits<T>::quiet_NaN();
   }
 };
 
@@ -138,7 +153,9 @@ template<typename _Real> struct NumTraits<std::complex<_Real> >
     MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
   };
 
+  EIGEN_DEVICE_FUNC
   static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
+  EIGEN_DEVICE_FUNC
   static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
 };
 
@@ -151,7 +168,7 @@ struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >
   typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar;
   typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger;
   typedef ArrayType & Nested;
-  
+
   enum {
     IsComplex = NumTraits<Scalar>::IsComplex,
     IsInteger = NumTraits<Scalar>::IsInteger,
@@ -161,8 +178,10 @@ struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >
     AddCost  = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::AddCost,
     MulCost  = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::MulCost
   };
-  
+
+  EIGEN_DEVICE_FUNC
   static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
+  EIGEN_DEVICE_FUNC
   static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }
 };
 

Eigen/src/Core/PermutationMatrix.h

@@ -13,12 +13,18 @@
 
 namespace Eigen { 
 
+namespace internal {
+
+enum PermPermProduct_t {PermPermProduct};
+
+} // end namespace internal
+
 /** \class PermutationBase
   * \ingroup Core_Module
   *
   * \brief Base class for permutations
   *
-  * \param Derived the derived class
+  * \tparam Derived the derived class
   *
   * This class is the base class for all expressions representing a permutation matrix,
   * internally stored as a vector of integers.
@@ -36,13 +42,6 @@ namespace Eigen {
   *
   * \sa class PermutationMatrix, class PermutationWrapper
   */
-
-namespace internal {
-
-enum PermPermProduct_t {PermPermProduct};
-
-} // end namespace internal
-
 template<typename Derived>
 class PermutationBase : public EigenBase<Derived>
 {
@@ -192,13 +191,13 @@ class PermutationBase : public EigenBase<Derived>
 
     /** \returns the inverse permutation matrix.
       *
-      * \note \note_try_to_help_rvo
+      * \note \blank \note_try_to_help_rvo
       */
     inline InverseReturnType inverse() const
     { return InverseReturnType(derived()); }
     /** \returns the tranpose permutation matrix.
       *
-      * \note \note_try_to_help_rvo
+      * \note \blank \note_try_to_help_rvo
       */
     inline InverseReturnType transpose() const
     { return InverseReturnType(derived()); }
@@ -225,7 +224,7 @@ class PermutationBase : public EigenBase<Derived>
 
     /** \returns the product permutation matrix.
       *
-      * \note \note_try_to_help_rvo
+      * \note \blank \note_try_to_help_rvo
       */
     template<typename Other>
     inline PlainPermutationType operator*(const PermutationBase<Other>& other) const
@@ -233,7 +232,7 @@ class PermutationBase : public EigenBase<Derived>
 
     /** \returns the product of a permutation with another inverse permutation.
       *
-      * \note \note_try_to_help_rvo
+      * \note \blank \note_try_to_help_rvo
       */
     template<typename Other>
     inline PlainPermutationType operator*(const InverseImpl<Other,PermutationStorage>& other) const
@@ -241,7 +240,7 @@ class PermutationBase : public EigenBase<Derived>
 
     /** \returns the product of an inverse permutation with another permutation.
       *
-      * \note \note_try_to_help_rvo
+      * \note \blank \note_try_to_help_rvo
       */
     template<typename Other> friend
     inline PlainPermutationType operator*(const InverseImpl<Other, PermutationStorage>& other, const PermutationBase& perm)
@@ -280,20 +279,6 @@ class PermutationBase : public EigenBase<Derived>
 
 };
 
-/** \class PermutationMatrix
-  * \ingroup Core_Module
-  *
-  * \brief Permutation matrix
-  *
-  * \param SizeAtCompileTime the number of rows/cols, or Dynamic
-  * \param MaxSizeAtCompileTime the maximum number of rows/cols, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
-  * \param StorageIndex the integer type of the indices
-  *
-  * This class represents a permutation matrix, internally stored as a vector of integers.
-  *
-  * \sa class PermutationBase, class PermutationWrapper, class DiagonalMatrix
-  */
-
 namespace internal {
 template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex>
 struct traits<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex> >
@@ -306,6 +291,19 @@ struct traits<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, _Storag
 };
 }
 
+/** \class PermutationMatrix
+  * \ingroup Core_Module
+  *
+  * \brief Permutation matrix
+  *
+  * \tparam SizeAtCompileTime the number of rows/cols, or Dynamic
+  * \tparam MaxSizeAtCompileTime the maximum number of rows/cols, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
+  * \tparam _StorageIndex the integer type of the indices
+  *
+  * This class represents a permutation matrix, internally stored as a vector of integers.
+  *
+  * \sa class PermutationBase, class PermutationWrapper, class DiagonalMatrix
+  */
 template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex>
 class PermutationMatrix : public PermutationBase<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex> >
 {
@@ -482,18 +480,6 @@ class Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, _StorageInd
     IndicesType m_indices;
 };
 
-/** \class PermutationWrapper
-  * \ingroup Core_Module
-  *
-  * \brief Class to view a vector of integers as a permutation matrix
-  *
-  * \param _IndicesType the type of the vector of integer (can be any compatible expression)
-  *
-  * This class allows to view any vector expression of integers as a permutation matrix.
-  *
-  * \sa class PermutationBase, class PermutationMatrix
-  */
-
 template<typename _IndicesType> class TranspositionsWrapper;
 namespace internal {
 template<typename _IndicesType>
@@ -513,6 +499,17 @@ struct traits<PermutationWrapper<_IndicesType> >
 };
 }
 
+/** \class PermutationWrapper
+  * \ingroup Core_Module
+  *
+  * \brief Class to view a vector of integers as a permutation matrix
+  *
+  * \tparam _IndicesType the type of the vector of integer (can be any compatible expression)
+  *
+  * This class allows to view any vector expression of integers as a permutation matrix.
+  *
+  * \sa class PermutationBase, class PermutationMatrix
+  */
 template<typename _IndicesType>
 class PermutationWrapper : public PermutationBase<PermutationWrapper<_IndicesType> >
 {

Eigen/src/Core/PlainObjectBase.h

@@ -533,7 +533,7 @@ class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
 
   public:
 
-    /** \copydoc MatrixBase::operator=(const EigenBase<OtherDerived>&)
+    /** \copydoc DenseBase::operator=(const EigenBase<OtherDerived>&)
       */
     template<typename OtherDerived>
     EIGEN_DEVICE_FUNC 
@@ -618,8 +618,8 @@ class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
     //@}
 
     using Base::setConstant;
-    EIGEN_DEVICE_FUNC Derived& setConstant(Index size, const Scalar& value);
+    EIGEN_DEVICE_FUNC Derived& setConstant(Index size, const Scalar& val);
-    EIGEN_DEVICE_FUNC Derived& setConstant(Index rows, Index cols, const Scalar& value);
+    EIGEN_DEVICE_FUNC Derived& setConstant(Index rows, Index cols, const Scalar& val);
 
     using Base::setZero;
     EIGEN_DEVICE_FUNC Derived& setZero(Index size);

Eigen/src/Core/Product.h

@@ -14,22 +14,6 @@ namespace Eigen {
 
 template<typename Lhs, typename Rhs, int Option, typename StorageKind> class ProductImpl;
 
-/** \class Product
-  * \ingroup Core_Module
-  *
-  * \brief Expression of the product of two arbitrary matrices or vectors
-  *
-  * \param Lhs the type of the left-hand side expression
-  * \param Rhs the type of the right-hand side expression
-  *
-  * This class represents an expression of the product of two arbitrary matrices.
-  * 
-  * The other template parameters are:
-  * \tparam Option     can be DefaultProduct, AliasFreeProduct, or LazyProduct
-  *
-  */
-
-
 namespace internal {
 
 // Determine the scalar of Product<Lhs, Rhs>. This is normally the same as Lhs::Scalar times
@@ -102,7 +86,20 @@ struct traits<Product<Lhs, Rhs, Option> >
 
 } // end namespace internal
 
-
+/** \class Product
+  * \ingroup Core_Module
+  *
+  * \brief Expression of the product of two arbitrary matrices or vectors
+  *
+  * \tparam _Lhs the type of the left-hand side expression
+  * \tparam _Rhs the type of the right-hand side expression
+  *
+  * This class represents an expression of the product of two arbitrary matrices.
+  *
+  * The other template parameters are:
+  * \tparam Option     can be DefaultProduct, AliasFreeProduct, or LazyProduct
+  *
+  */
 template<typename _Lhs, typename _Rhs, int Option>
 class Product : public ProductImpl<_Lhs,_Rhs,Option,
                                    typename internal::product_promote_storage_type<typename internal::traits<_Lhs>::StorageKind,

Eigen/src/Core/ProductEvaluators.h

@@ -38,10 +38,9 @@ struct evaluator<Product<Lhs, Rhs, Options> >
 // 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 Scalar>
-struct evaluator_traits<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>,  const Product<Lhs, Rhs, DefaultProduct>  > >
+struct evaluator_assume_aliasing<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>,  const Product<Lhs, Rhs, DefaultProduct>  > >
- : evaluator_traits_base<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>,  const Product<Lhs, Rhs, DefaultProduct>  > >
 {
-  enum { AssumeAliasing = 1 };
+  static const bool value = true;
 };
 template<typename Lhs, typename Rhs, typename Scalar>
 struct evaluator<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>,  const Product<Lhs, Rhs, DefaultProduct>  > > 
@@ -81,17 +80,8 @@ template< typename Lhs, typename Rhs,
 struct generic_product_impl;
 
 template<typename Lhs, typename Rhs>
-struct evaluator_traits<Product<Lhs, Rhs, DefaultProduct> > 
+struct evaluator_assume_aliasing<Product<Lhs, Rhs, DefaultProduct> > {
- : evaluator_traits_base<Product<Lhs, Rhs, DefaultProduct> >
+  static const bool value = true;
-{
-  enum { AssumeAliasing = 1 };
-};
-
-template<typename Lhs, typename Rhs>
-struct evaluator_traits<Product<Lhs, Rhs, AliasFreeProduct> > 
- : evaluator_traits_base<Product<Lhs, Rhs, AliasFreeProduct> >
-{
-  enum { AssumeAliasing = 0 };
 };
 
 // This is the default evaluator implementation for products:
@@ -107,7 +97,8 @@ struct product_evaluator<Product<Lhs, Rhs, Options>, ProductTag, LhsShape, RhsSh
     Flags = Base::Flags | EvalBeforeNestingBit
   };
 
-  EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  explicit product_evaluator(const XprType& xpr)
     : m_result(xpr.rows(), xpr.cols())
   {
     ::new (static_cast<Base*>(this)) Base(m_result);
@@ -189,6 +180,13 @@ struct Assignment<DstXprType, CwiseUnaryOp<internal::scalar_multiple_op<ScalarBi
 //----------------------------------------
 // Catch "Dense ?= xpr + Product<>" expression to save one temporary
 // FIXME we could probably enable these rules for any product, i.e., not only Dense and DefaultProduct
+// TODO enable it for "Dense ?= xpr - Product<>" as well.
+
+template<typename OtherXpr, typename Lhs, typename Rhs>
+struct evaluator_assume_aliasing<CwiseBinaryOp<internal::scalar_sum_op<typename OtherXpr::Scalar>, const OtherXpr,
+                                               const Product<Lhs,Rhs,DefaultProduct> >, DenseShape > {
+  static const bool value = true;
+};
 
 template<typename DstXprType, typename OtherXpr, typename ProductType, typename Scalar, typename Func1, typename Func2>
 struct assignment_from_xpr_plus_product
@@ -415,7 +413,8 @@ struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, DenseShape,
   typedef typename XprType::PacketScalar PacketScalar;
   typedef typename XprType::PacketReturnType PacketReturnType;
 
-  EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  explicit product_evaluator(const XprType& xpr)
     : m_lhs(xpr.lhs()),
       m_rhs(xpr.rhs()),
       m_lhsImpl(m_lhs),     // FIXME the creation of the evaluator objects should result in a no-op, but check that!

Eigen/src/Core/Ref.h

@@ -12,76 +12,6 @@
 
 namespace Eigen { 
 
-/** \class Ref
-  * \ingroup Core_Module
-  *
-  * \brief A matrix or vector expression mapping an existing expression
-  *
-  * \tparam PlainObjectType the equivalent matrix type of the mapped data
-  * \tparam MapOptions specifies the pointer alignment in bytes. It can be: \c #Aligned128, , \c #Aligned64, \c #Aligned32, \c #Aligned16, \c #Aligned8 or \c #Unaligned.
-  *                The default is \c #Unaligned.
-  * \tparam StrideType optionally specifies strides. By default, Ref implies a contiguous storage along the inner dimension (inner stride==1),
-  *                   but accepts a variable outer stride (leading dimension).
-  *                   This can be overridden by specifying strides.
-  *                   The type passed here must be a specialization of the Stride template, see examples below.
-  *
-  * This class provides a way to write non-template functions taking Eigen objects as parameters while limiting the number of copies.
-  * A Ref<> object can represent either a const expression or a l-value:
-  * \code
-  * // in-out argument:
-  * void foo1(Ref<VectorXf> x);
-  *
-  * // read-only const argument:
-  * void foo2(const Ref<const VectorXf>& x);
-  * \endcode
-  *
-  * In the in-out case, the input argument must satisfy the constraints of the actual Ref<> type, otherwise a compilation issue will be triggered.
-  * By default, a Ref<VectorXf> can reference any dense vector expression of float having a contiguous memory layout.
-  * Likewise, a Ref<MatrixXf> can reference any column-major dense matrix expression of float whose column's elements are contiguously stored with
-  * the possibility to have a constant space in-between each column, i.e. the inner stride must be equal to 1, but the outer stride (or leading dimension)
-  * can be greater than the number of rows.
-  *
-  * In the const case, if the input expression does not match the above requirement, then it is evaluated into a temporary before being passed to the function.
-  * Here are some examples:
-  * \code
-  * MatrixXf A;
-  * VectorXf a;
-  * foo1(a.head());             // OK
-  * foo1(A.col());              // OK
-  * foo1(A.row());              // Compilation error because here innerstride!=1
-  * foo2(A.row());              // Compilation error because A.row() is a 1xN object while foo2 is expecting a Nx1 object
-  * foo2(A.row().transpose());  // The row is copied into a contiguous temporary
-  * foo2(2*a);                  // The expression is evaluated into a temporary
-  * foo2(A.col().segment(2,4)); // No temporary
-  * \endcode
-  *
-  * The range of inputs that can be referenced without temporary can be enlarged using the last two template parameters.
-  * Here is an example accepting an innerstride!=1:
-  * \code
-  * // in-out argument:
-  * void foo3(Ref<VectorXf,0,InnerStride<> > x);
-  * foo3(A.row());              // OK
-  * \endcode
-  * The downside here is that the function foo3 might be significantly slower than foo1 because it won't be able to exploit vectorization, and will involve more
-  * expensive address computations even if the input is contiguously stored in memory. To overcome this issue, one might propose to overload internally calling a
-  * template function, e.g.:
-  * \code
-  * // in the .h:
-  * void foo(const Ref<MatrixXf>& A);
-  * void foo(const Ref<MatrixXf,0,Stride<> >& A);
-  *
-  * // in the .cpp:
-  * template<typename TypeOfA> void foo_impl(const TypeOfA& A) {
-  *     ... // crazy code goes here
-  * }
-  * void foo(const Ref<MatrixXf>& A) { foo_impl(A); }
-  * void foo(const Ref<MatrixXf,0,Stride<> >& A) { foo_impl(A); }
-  * \endcode
-  *
-  *
-  * \sa PlainObjectBase::Map(), \ref TopicStorageOrders
-  */
-
 namespace internal {
 
 template<typename _PlainObjectType, int _Options, typename _StrideType>
@@ -182,7 +112,75 @@ protected:
   StrideBase m_stride;
 };
 
-
+/** \class Ref
+  * \ingroup Core_Module
+  *
+  * \brief A matrix or vector expression mapping an existing expression
+  *
+  * \tparam PlainObjectType the equivalent matrix type of the mapped data
+  * \tparam Options specifies the pointer alignment in bytes. It can be: \c #Aligned128, , \c #Aligned64, \c #Aligned32, \c #Aligned16, \c #Aligned8 or \c #Unaligned.
+  *                 The default is \c #Unaligned.
+  * \tparam StrideType optionally specifies strides. By default, Ref implies a contiguous storage along the inner dimension (inner stride==1),
+  *                   but accepts a variable outer stride (leading dimension).
+  *                   This can be overridden by specifying strides.
+  *                   The type passed here must be a specialization of the Stride template, see examples below.
+  *
+  * This class provides a way to write non-template functions taking Eigen objects as parameters while limiting the number of copies.
+  * A Ref<> object can represent either a const expression or a l-value:
+  * \code
+  * // in-out argument:
+  * void foo1(Ref<VectorXf> x);
+  *
+  * // read-only const argument:
+  * void foo2(const Ref<const VectorXf>& x);
+  * \endcode
+  *
+  * In the in-out case, the input argument must satisfy the constraints of the actual Ref<> type, otherwise a compilation issue will be triggered.
+  * By default, a Ref<VectorXf> can reference any dense vector expression of float having a contiguous memory layout.
+  * Likewise, a Ref<MatrixXf> can reference any column-major dense matrix expression of float whose column's elements are contiguously stored with
+  * the possibility to have a constant space in-between each column, i.e. the inner stride must be equal to 1, but the outer stride (or leading dimension)
+  * can be greater than the number of rows.
+  *
+  * In the const case, if the input expression does not match the above requirement, then it is evaluated into a temporary before being passed to the function.
+  * Here are some examples:
+  * \code
+  * MatrixXf A;
+  * VectorXf a;
+  * foo1(a.head());             // OK
+  * foo1(A.col());              // OK
+  * foo1(A.row());              // Compilation error because here innerstride!=1
+  * foo2(A.row());              // Compilation error because A.row() is a 1xN object while foo2 is expecting a Nx1 object
+  * foo2(A.row().transpose());  // The row is copied into a contiguous temporary
+  * foo2(2*a);                  // The expression is evaluated into a temporary
+  * foo2(A.col().segment(2,4)); // No temporary
+  * \endcode
+  *
+  * The range of inputs that can be referenced without temporary can be enlarged using the last two template parameters.
+  * Here is an example accepting an innerstride!=1:
+  * \code
+  * // in-out argument:
+  * void foo3(Ref<VectorXf,0,InnerStride<> > x);
+  * foo3(A.row());              // OK
+  * \endcode
+  * The downside here is that the function foo3 might be significantly slower than foo1 because it won't be able to exploit vectorization, and will involve more
+  * expensive address computations even if the input is contiguously stored in memory. To overcome this issue, one might propose to overload internally calling a
+  * template function, e.g.:
+  * \code
+  * // in the .h:
+  * void foo(const Ref<MatrixXf>& A);
+  * void foo(const Ref<MatrixXf,0,Stride<> >& A);
+  *
+  * // in the .cpp:
+  * template<typename TypeOfA> void foo_impl(const TypeOfA& A) {
+  *     ... // crazy code goes here
+  * }
+  * void foo(const Ref<MatrixXf>& A) { foo_impl(A); }
+  * void foo(const Ref<MatrixXf,0,Stride<> >& A) { foo_impl(A); }
+  * \endcode
+  *
+  *
+  * \sa PlainObjectBase::Map(), \ref TopicStorageOrders
+  */
 template<typename PlainObjectType, int Options, typename StrideType> class Ref
   : public RefBase<Ref<PlainObjectType, Options, StrideType> >
 {
@@ -209,6 +207,7 @@ template<typename PlainObjectType, int Options, typename StrideType> class Ref
     EIGEN_DEVICE_FUNC inline Ref(const DenseBase<Derived>& expr,
                                  typename internal::enable_if<bool(Traits::template match<Derived>::MatchAtCompileTime),Derived>::type* = 0)
     #else
+    /** Implicit constructor from any dense expression */
     template<typename Derived>
     inline Ref(DenseBase<Derived>& expr)
     #endif

Eigen/src/Core/Replicate.h

@@ -12,21 +12,6 @@
 
 namespace Eigen { 
 
-/**
-  * \class Replicate
-  * \ingroup Core_Module
-  *
-  * \brief Expression of the multiple replication of a matrix or vector
-  *
-  * \param MatrixType the type of the object we are replicating
-  *
-  * This class represents an expression of the multiple replication of a matrix or vector.
-  * It is the return type of DenseBase::replicate() and most of the time
-  * this is the only way it is used.
-  *
-  * \sa DenseBase::replicate()
-  */
-
 namespace internal {
 template<typename MatrixType,int RowFactor,int ColFactor>
 struct traits<Replicate<MatrixType,RowFactor,ColFactor> >
@@ -57,6 +42,22 @@ struct traits<Replicate<MatrixType,RowFactor,ColFactor> >
 };
 }
 
+/**
+  * \class Replicate
+  * \ingroup Core_Module
+  *
+  * \brief Expression of the multiple replication of a matrix or vector
+  *
+  * \tparam MatrixType the type of the object we are replicating
+  * \tparam RowFactor number of repetitions at compile time along the vertical direction, can be Dynamic.
+  * \tparam ColFactor number of repetitions at compile time along the horizontal direction, can be Dynamic.
+  *
+  * This class represents an expression of the multiple replication of a matrix or vector.
+  * It is the return type of DenseBase::replicate() and most of the time
+  * this is the only way it is used.
+  *
+  * \sa DenseBase::replicate()
+  */
 template<typename MatrixType,int RowFactor,int ColFactor> class Replicate
   : public internal::dense_xpr_base< Replicate<MatrixType,RowFactor,ColFactor> >::type
 {

Eigen/src/Core/ReturnByValue.h

@@ -13,11 +13,6 @@
 
 namespace Eigen {
 
-/** \class ReturnByValue
-  * \ingroup Core_Module
-  *
-  */
-
 namespace internal {
 
 template<typename Derived>
@@ -48,6 +43,10 @@ struct nested_eval<ReturnByValue<Derived>, n, PlainObject>
 
 } // end namespace internal
 
+/** \class ReturnByValue
+  * \ingroup Core_Module
+  *
+  */
 template<typename Derived> class ReturnByValue
   : public internal::dense_xpr_base< ReturnByValue<Derived> >::type, internal::no_assignment_operator
 {

Eigen/src/Core/Reverse.h

@@ -14,20 +14,6 @@
 
 namespace Eigen { 
 
-/** \class Reverse
-  * \ingroup Core_Module
-  *
-  * \brief Expression of the reverse of a vector or matrix
-  *
-  * \param MatrixType the type of the object of which we are taking the reverse
-  *
-  * This class represents an expression of the reverse of a vector.
-  * It is the return type of MatrixBase::reverse() and VectorwiseOp::reverse()
-  * and most of the time this is the only way it is used.
-  *
-  * \sa MatrixBase::reverse(), VectorwiseOp::reverse()
-  */
-
 namespace internal {
 
 template<typename MatrixType, int Direction>
@@ -60,6 +46,20 @@ template<typename PacketType> struct reverse_packet_cond<PacketType,false>
 
 } // end namespace internal 
 
+/** \class Reverse
+  * \ingroup Core_Module
+  *
+  * \brief Expression of the reverse of a vector or matrix
+  *
+  * \tparam MatrixType the type of the object of which we are taking the reverse
+  * \tparam Direction defines the direction of the reverse operation, can be Vertical, Horizontal, or BothDirections
+  *
+  * This class represents an expression of the reverse of a vector.
+  * It is the return type of MatrixBase::reverse() and VectorwiseOp::reverse()
+  * and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::reverse(), VectorwiseOp::reverse()
+  */
 template<typename MatrixType, int Direction> class Reverse
   : public internal::dense_xpr_base< Reverse<MatrixType, Direction> >::type
 {

Eigen/src/Core/SelfAdjointView.h

@@ -32,7 +32,7 @@ namespace internal {
 template<typename MatrixType, unsigned int UpLo>
 struct traits<SelfAdjointView<MatrixType, UpLo> > : traits<MatrixType>
 {
-  typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
+  typedef typename ref_selector<MatrixType>::non_const_type MatrixTypeNested;
   typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;
   typedef MatrixType ExpressionType;
   typedef typename MatrixType::PlainObject FullMatrixType;
@@ -97,7 +97,7 @@ template<typename _MatrixType, unsigned int UpLo> class SelfAdjointView
     {
       EIGEN_STATIC_ASSERT_LVALUE(SelfAdjointView);
       Base::check_coordinates_internal(row, col);
-      return m_matrix.const_cast_derived().coeffRef(row, col);
+      return m_matrix.coeffRef(row, col);
     }
 
     /** \internal */
@@ -107,7 +107,7 @@ template<typename _MatrixType, unsigned int UpLo> class SelfAdjointView
     EIGEN_DEVICE_FUNC
     const MatrixTypeNestedCleaned& nestedExpression() const { return m_matrix; }
     EIGEN_DEVICE_FUNC
-    MatrixTypeNestedCleaned& nestedExpression() { return *const_cast<MatrixTypeNestedCleaned*>(&m_matrix); }
+    MatrixTypeNestedCleaned& nestedExpression() { return m_matrix; }
 
     /** Efficient triangular matrix times vector/matrix product */
     template<typename OtherDerived>
@@ -203,8 +203,6 @@ struct evaluator_traits<SelfAdjointView<MatrixType,Mode> >
 {
   typedef typename storage_kind_to_evaluator_kind<typename MatrixType::StorageKind>::Kind Kind;
   typedef SelfAdjointShape Shape;
-  
-  static const int AssumeAliasing = 0;
 };
 
 template<int UpLo, int SetOpposite, typename DstEvaluatorTypeT, typename SrcEvaluatorTypeT, typename Functor, int Version>

Eigen/src/Core/SelfCwiseBinaryOp.h

@@ -13,7 +13,7 @@
 namespace Eigen { 
 
 template<typename Derived>
-inline Derived& DenseBase<Derived>::operator*=(const Scalar& other)
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator*=(const Scalar& other)
 {
   typedef typename Derived::PlainObject PlainObject;
   internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::mul_assign_op<Scalar>());
@@ -21,7 +21,7 @@ inline Derived& DenseBase<Derived>::operator*=(const Scalar& other)
 }
 
 template<typename Derived>
-inline Derived& ArrayBase<Derived>::operator+=(const Scalar& other)
+EIGEN_STRONG_INLINE Derived& ArrayBase<Derived>::operator+=(const Scalar& other)
 {
   typedef typename Derived::PlainObject PlainObject;
   internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::add_assign_op<Scalar>());
@@ -29,7 +29,7 @@ inline Derived& ArrayBase<Derived>::operator+=(const Scalar& other)
 }
 
 template<typename Derived>
-inline Derived& ArrayBase<Derived>::operator-=(const Scalar& other)
+EIGEN_STRONG_INLINE Derived& ArrayBase<Derived>::operator-=(const Scalar& other)
 {
   typedef typename Derived::PlainObject PlainObject;
   internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::sub_assign_op<Scalar>());
@@ -37,7 +37,7 @@ inline Derived& ArrayBase<Derived>::operator-=(const Scalar& other)
 }
 
 template<typename Derived>
-inline Derived& DenseBase<Derived>::operator/=(const Scalar& other)
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator/=(const Scalar& other)
 {
   typedef typename Derived::PlainObject PlainObject;
   internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::div_assign_op<Scalar>());

Eigen/src/Core/Stride.h

@@ -31,8 +31,8 @@ namespace Eigen {
   * arguments to the constructor.
   *
   * Indeed, this class takes two template parameters:
-  *  \param _OuterStrideAtCompileTime the outer stride, or Dynamic if you want to specify it at runtime.
+  *  \tparam _OuterStrideAtCompileTime the outer stride, or Dynamic if you want to specify it at runtime.
-  *  \param _InnerStrideAtCompileTime the inner stride, or Dynamic if you want to specify it at runtime.
+  *  \tparam _InnerStrideAtCompileTime the inner stride, or Dynamic if you want to specify it at runtime.
   *
   * Here is an example:
   * \include Map_general_stride.cpp

Eigen/src/Core/Transpose.h

@@ -13,20 +13,6 @@
 
 namespace Eigen { 
 
-/** \class Transpose
-  * \ingroup Core_Module
-  *
-  * \brief Expression of the transpose of a matrix
-  *
-  * \param MatrixType the type of the object of which we are taking the transpose
-  *
-  * This class represents an expression of the transpose of a matrix.
-  * It is the return type of MatrixBase::transpose() and MatrixBase::adjoint()
-  * and most of the time this is the only way it is used.
-  *
-  * \sa MatrixBase::transpose(), MatrixBase::adjoint()
-  */
-
 namespace internal {
 template<typename MatrixType>
 struct traits<Transpose<MatrixType> > : public traits<MatrixType>
@@ -50,11 +36,26 @@ struct traits<Transpose<MatrixType> > : public traits<MatrixType>
 
 template<typename MatrixType, typename StorageKind> class TransposeImpl;
 
+/** \class Transpose
+  * \ingroup Core_Module
+  *
+  * \brief Expression of the transpose of a matrix
+  *
+  * \tparam MatrixType the type of the object of which we are taking the transpose
+  *
+  * This class represents an expression of the transpose of a matrix.
+  * It is the return type of MatrixBase::transpose() and MatrixBase::adjoint()
+  * and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::transpose(), MatrixBase::adjoint()
+  */
 template<typename MatrixType> class Transpose
   : public TransposeImpl<MatrixType,typename internal::traits<MatrixType>::StorageKind>
 {
   public:
 
+    typedef typename internal::ref_selector<MatrixType>::non_const_type MatrixTypeNested;
+
     typedef typename TransposeImpl<MatrixType,typename internal::traits<MatrixType>::StorageKind>::Base Base;
     EIGEN_GENERIC_PUBLIC_INTERFACE(Transpose)
     typedef typename internal::remove_all<MatrixType>::type NestedExpression;
@@ -69,16 +70,16 @@ template<typename MatrixType> class Transpose
 
     /** \returns the nested expression */
     EIGEN_DEVICE_FUNC
-    const typename internal::remove_all<typename MatrixType::Nested>::type&
+    const typename internal::remove_all<MatrixTypeNested>::type&
     nestedExpression() const { return m_matrix; }
 
     /** \returns the nested expression */
     EIGEN_DEVICE_FUNC
-    typename internal::remove_all<typename MatrixType::Nested>::type&
+    typename internal::remove_reference<MatrixTypeNested>::type&
-    nestedExpression() { return m_matrix.const_cast_derived(); }
+    nestedExpression() { return m_matrix; }
 
   protected:
-    typename MatrixType::Nested m_matrix;
+    typename internal::ref_selector<MatrixType>::non_const_type m_matrix;
 };
 
 namespace internal {

Eigen/src/Core/Transpositions.h

@@ -12,35 +12,6 @@
 
 namespace Eigen { 
 
-/** \class Transpositions
-  * \ingroup Core_Module
-  *
-  * \brief Represents a sequence of transpositions (row/column interchange)
-  *
-  * \param SizeAtCompileTime the number of transpositions, or Dynamic
-  * \param MaxSizeAtCompileTime the maximum number of transpositions, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
-  *
-  * This class represents a permutation transformation as a sequence of \em n transpositions
-  * \f$[T_{n-1} \ldots T_{i} \ldots T_{0}]\f$. It is internally stored as a vector of integers \c indices.
-  * Each transposition \f$ T_{i} \f$ applied on the left of a matrix (\f$ T_{i} M\f$) interchanges
-  * the rows \c i and \c indices[i] of the matrix \c M.
-  * A transposition applied on the right (e.g., \f$ M T_{i}\f$) yields a column interchange.
-  *
-  * Compared to the class PermutationMatrix, such a sequence of transpositions is what is
-  * computed during a decomposition with pivoting, and it is faster when applying the permutation in-place.
-  * 
-  * To apply a sequence of transpositions to a matrix, simply use the operator * as in the following example:
-  * \code
-  * Transpositions tr;
-  * MatrixXf mat;
-  * mat = tr * mat;
-  * \endcode
-  * In this example, we detect that the matrix appears on both side, and so the transpositions
-  * are applied in-place without any temporary or extra copy.
-  *
-  * \sa class PermutationMatrix
-  */
-
 template<typename Derived>
 class TranspositionsBase
 {
@@ -154,6 +125,35 @@ struct traits<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageInde
 };
 }
 
+/** \class Transpositions
+  * \ingroup Core_Module
+  *
+  * \brief Represents a sequence of transpositions (row/column interchange)
+  *
+  * \tparam SizeAtCompileTime the number of transpositions, or Dynamic
+  * \tparam MaxSizeAtCompileTime the maximum number of transpositions, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
+  *
+  * This class represents a permutation transformation as a sequence of \em n transpositions
+  * \f$[T_{n-1} \ldots T_{i} \ldots T_{0}]\f$. It is internally stored as a vector of integers \c indices.
+  * Each transposition \f$ T_{i} \f$ applied on the left of a matrix (\f$ T_{i} M\f$) interchanges
+  * the rows \c i and \c indices[i] of the matrix \c M.
+  * A transposition applied on the right (e.g., \f$ M T_{i}\f$) yields a column interchange.
+  *
+  * Compared to the class PermutationMatrix, such a sequence of transpositions is what is
+  * computed during a decomposition with pivoting, and it is faster when applying the permutation in-place.
+  *
+  * To apply a sequence of transpositions to a matrix, simply use the operator * as in the following example:
+  * \code
+  * Transpositions tr;
+  * MatrixXf mat;
+  * mat = tr * mat;
+  * \endcode
+  * In this example, we detect that the matrix appears on both side, and so the transpositions
+  * are applied in-place without any temporary or extra copy.
+  *
+  * \sa class PermutationMatrix
+  */
+
 template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex>
 class Transpositions : public TranspositionsBase<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex> >
 {
@@ -325,7 +325,7 @@ class TranspositionsWrapper
 
   protected:
 
-    const typename IndicesType::Nested m_indices;
+    typename IndicesType::Nested m_indices;
 };
 
 

Eigen/src/Core/TriangularMatrix.h

@@ -168,7 +168,7 @@ namespace internal {
 template<typename MatrixType, unsigned int _Mode>
 struct traits<TriangularView<MatrixType, _Mode> > : traits<MatrixType>
 {
-  typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
+  typedef typename ref_selector<MatrixType>::non_const_type MatrixTypeNested;
   typedef typename remove_reference<MatrixTypeNested>::type MatrixTypeNestedNonRef;
   typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;
   typedef typename MatrixType::PlainObject FullMatrixType;
@@ -213,7 +213,6 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView
       IsVectorAtCompileTime = false
     };
 
-    // FIXME This, combined with const_cast_derived in transpose() leads to a const-correctness loophole
     EIGEN_DEVICE_FUNC
     explicit inline TriangularView(MatrixType& matrix) : m_matrix(matrix)
     {}
@@ -235,7 +234,7 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView
 
     /** \returns a reference to the nested expression */
     EIGEN_DEVICE_FUNC
-    NestedExpression& nestedExpression() { return *const_cast<NestedExpression*>(&m_matrix); }
+    NestedExpression& nestedExpression() { return m_matrix; }
     
     typedef TriangularView<const MatrixConjugateReturnType,Mode> ConjugateReturnType;
     /** \sa MatrixBase::conjugate() const */
@@ -255,7 +254,7 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView
     inline TransposeReturnType transpose()
     {
       EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
-      typename MatrixType::TransposeReturnType tmp(m_matrix.const_cast_derived());
+      typename MatrixType::TransposeReturnType tmp(m_matrix);
       return TransposeReturnType(tmp);
     }
     
@@ -418,7 +417,7 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularViewImpl<_Mat
     {
       EIGEN_STATIC_ASSERT_LVALUE(TriangularViewType);
       Base::check_coordinates_internal(row, col);
-      return derived().nestedExpression().const_cast_derived().coeffRef(row, col);
+      return derived().nestedExpression().coeffRef(row, col);
     }
 
     /** Assigns a triangular matrix to a triangular part of a dense matrix */
@@ -595,14 +594,7 @@ template<typename Derived>
 template<typename DenseDerived>
 void TriangularBase<Derived>::evalTo(MatrixBase<DenseDerived> &other) const
 {
-  if(internal::traits<Derived>::Flags & EvalBeforeAssigningBit)
+  evalToLazy(other.derived());
-  {
-    typename internal::plain_matrix_type<Derived>::type other_evaluated(rows(), cols());
-    evalToLazy(other_evaluated);
-    other.derived().swap(other_evaluated);
-  }
-  else
-    evalToLazy(other.derived());
 }
 
 /***************************************************************************
@@ -711,10 +703,6 @@ struct evaluator_traits<TriangularView<MatrixType,Mode> >
 {
   typedef typename storage_kind_to_evaluator_kind<typename MatrixType::StorageKind>::Kind Kind;
   typedef typename glue_shapes<typename evaluator_traits<MatrixType>::Shape, TriangularShape>::type Shape;
-  
-  // 1 if assignment A = B assumes aliasing when B is of type T and thus B needs to be evaluated into a
-  // temporary; 0 if not.
-  static const int AssumeAliasing = 0;
 };
 
 template<typename MatrixType, unsigned int Mode>
@@ -788,7 +776,8 @@ public:
 };
 
 template<int Mode, bool SetOpposite, typename DstXprType, typename SrcXprType, typename Functor>
-EIGEN_DEVICE_FUNC void call_triangular_assignment_loop(const DstXprType& dst, const SrcXprType& src, const Functor &func)
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_triangular_assignment_loop(const DstXprType& dst, const SrcXprType& src, const Functor &func)
 {
   eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
   
@@ -812,7 +801,8 @@ EIGEN_DEVICE_FUNC void call_triangular_assignment_loop(const DstXprType& dst, co
 }
 
 template<int Mode, bool SetOpposite, typename DstXprType, typename SrcXprType>
-EIGEN_DEVICE_FUNC void call_triangular_assignment_loop(const DstXprType& dst, const SrcXprType& src)
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_triangular_assignment_loop(const DstXprType& dst, const SrcXprType& src)
 {
   call_triangular_assignment_loop<Mode,SetOpposite>(dst, src, internal::assign_op<typename DstXprType::Scalar>());
 }

Eigen/src/Core/VectorBlock.h

@@ -13,13 +13,23 @@
 
 namespace Eigen { 
 
+namespace internal {
+template<typename VectorType, int Size>
+struct traits<VectorBlock<VectorType, Size> >
+  : public traits<Block<VectorType,
+                     traits<VectorType>::Flags & RowMajorBit ? 1 : Size,
+                     traits<VectorType>::Flags & RowMajorBit ? Size : 1> >
+{
+};
+}
+
 /** \class VectorBlock
   * \ingroup Core_Module
   *
   * \brief Expression of a fixed-size or dynamic-size sub-vector
   *
-  * \param VectorType the type of the object in which we are taking a sub-vector
+  * \tparam VectorType the type of the object in which we are taking a sub-vector
-  * \param Size size of the sub-vector we are taking at compile time (optional)
+  * \tparam Size size of the sub-vector we are taking at compile time (optional)
   *
   * This class represents an expression of either a fixed-size or dynamic-size sub-vector.
   * It is the return type of DenseBase::segment(Index,Index) and DenseBase::segment<int>(Index) and
@@ -43,17 +53,6 @@ namespace Eigen {
   *
   * \sa class Block, DenseBase::segment(Index,Index,Index,Index), DenseBase::segment(Index,Index)
   */
-
-namespace internal {
-template<typename VectorType, int Size>
-struct traits<VectorBlock<VectorType, Size> >
-  : public traits<Block<VectorType,
-                     traits<VectorType>::Flags & RowMajorBit ? 1 : Size,
-                     traits<VectorType>::Flags & RowMajorBit ? Size : 1> >
-{
-};
-}
-
 template<typename VectorType, int Size> class VectorBlock
   : public Block<VectorType,
                      internal::traits<VectorType>::Flags & RowMajorBit ? 1 : Size,

Eigen/src/Core/VectorwiseOp.h

@@ -115,7 +115,7 @@ struct member_lpnorm {
   typedef ResultType result_type;
   template<typename Scalar, int Size> struct Cost
   { enum { value = (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost }; };
-  EIGEN_DEVICE_FUNC explicit member_lpnorm() {}
+  EIGEN_DEVICE_FUNC member_lpnorm() {}
   template<typename XprType>
   EIGEN_DEVICE_FUNC inline ResultType operator()(const XprType& mat) const
   { return mat.template lpNorm<p>(); }
@@ -124,7 +124,7 @@ struct member_lpnorm {
 template <typename BinaryOp, typename Scalar>
 struct member_redux {
   typedef typename result_of<
-                     BinaryOp(Scalar,Scalar)
+                     BinaryOp(const Scalar&,const Scalar&)
                    >::type  result_type;
   template<typename _Scalar, int Size> struct Cost
   { enum { value = (Size-1) * functor_traits<BinaryOp>::Cost }; };
@@ -141,8 +141,8 @@ struct member_redux {
   *
   * \brief Pseudo expression providing partial reduction operations
   *
-  * \param ExpressionType the type of the object on which to do partial reductions
+  * \tparam ExpressionType the type of the object on which to do partial reductions
-  * \param Direction indicates the direction of the redux (#Vertical or #Horizontal)
+  * \tparam Direction indicates the direction of the redux (#Vertical or #Horizontal)
   *
   * This class represents a pseudo expression with partial reduction features.
   * It is the return type of DenseBase::colwise() and DenseBase::rowwise()
@@ -187,11 +187,11 @@ template<typename ExpressionType, int Direction> class VectorwiseOp
 
   protected:
 
-    /** \internal
-      * \returns the i-th subvector according to the \c Direction */
     typedef typename internal::conditional<isVertical,
                                typename ExpressionType::ColXpr,
                                typename ExpressionType::RowXpr>::type SubVector;
+    /** \internal
+      * \returns the i-th subvector according to the \c Direction */
     EIGEN_DEVICE_FUNC
     SubVector subVector(Index i)
     {

Eigen/src/Core/Visitor.h

@@ -197,7 +197,7 @@ struct functor_traits<max_coeff_visitor<Scalar> > {
 /** \returns the minimum of all coefficients of *this and puts in *row and *col its location.
   * \warning the result is undefined if \c *this contains NaN.
   *
-  * \sa DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visitor(), DenseBase::minCoeff()
+  * \sa DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visit(), DenseBase::minCoeff()
   */
 template<typename Derived>
 template<typename IndexType>
@@ -215,7 +215,7 @@ DenseBase<Derived>::minCoeff(IndexType* rowId, IndexType* colId) const
 /** \returns the minimum of all coefficients of *this and puts in *index its location.
   * \warning the result is undefined if \c *this contains NaN. 
   *
-  * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::minCoeff()
+  * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visit(), DenseBase::minCoeff()
   */
 template<typename Derived>
 template<typename IndexType>
@@ -233,7 +233,7 @@ DenseBase<Derived>::minCoeff(IndexType* index) const
 /** \returns the maximum of all coefficients of *this and puts in *row and *col its location.
   * \warning the result is undefined if \c *this contains NaN. 
   *
-  * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()
+  * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visit(), DenseBase::maxCoeff()
   */
 template<typename Derived>
 template<typename IndexType>

Eigen/src/Core/arch/AVX/MathFunctions.h

@@ -10,11 +10,6 @@
 #ifndef EIGEN_MATH_FUNCTIONS_AVX_H
 #define EIGEN_MATH_FUNCTIONS_AVX_H
 
-// For some reason, this function didn't make it into the avxintirn.h
-// used by the compiler, so we'll just wrap it.
-#define _mm256_setr_m128(lo, hi) \
-  _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1)
-
 /* The sin, cos, exp, and log functions of this file are loosely derived from
  * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
  */
@@ -23,6 +18,28 @@ namespace Eigen {
 
 namespace internal {
 
+inline Packet8i pshiftleft(Packet8i v, int n)
+{
+#ifdef EIGEN_VECTORIZE_AVX2
+  return _mm256_slli_epi32(v, n);
+#else
+  __m128i lo = _mm_slli_epi32(_mm256_extractf128_si256(v, 0), n);
+  __m128i hi = _mm_slli_epi32(_mm256_extractf128_si256(v, 1), n);
+  return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
+
+inline Packet8f pshiftright(Packet8f v, int n)
+{
+#ifdef EIGEN_VECTORIZE_AVX2
+  return _mm256_cvtepi32_ps(_mm256_srli_epi32(_mm256_castps_si256(v), n));
+#else
+  __m128i lo = _mm_srli_epi32(_mm256_extractf128_si256(_mm256_castps_si256(v), 0), n);
+  __m128i hi = _mm_srli_epi32(_mm256_extractf128_si256(_mm256_castps_si256(v), 1), n);
+  return _mm256_cvtepi32_ps(_mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1));
+#endif
+}
+
 // Sine function
 // Computes sin(x) by wrapping x to the interval [-Pi/4,3*Pi/4] and
 // evaluating interpolants in [-Pi/4,Pi/4] or [Pi/4,3*Pi/4]. The interpolants
@@ -54,17 +71,8 @@ psin<Packet8f>(const Packet8f& _x) {
   // Make a mask for the entries that need flipping, i.e. wherever the shift
   // is odd.
   Packet8i shift_ints = _mm256_cvtps_epi32(shift);
-  Packet8i shift_isodd =
+  Packet8i shift_isodd = _mm256_castps_si256(_mm256_and_ps(_mm256_castsi256_ps(shift_ints), _mm256_castsi256_ps(p8i_one)));
-      _mm256_castps_si256(_mm256_and_ps(_mm256_castsi256_ps(shift_ints), _mm256_castsi256_ps(p8i_one)));
+  Packet8i sign_flip_mask = pshiftleft(shift_isodd, 31);
-#ifdef EIGEN_VECTORIZE_AVX2
-  Packet8i sign_flip_mask = _mm256_slli_epi32(shift_isodd, 31);
-#else
-  __m128i lo =
-      _mm_slli_epi32(_mm256_extractf128_si256(shift_isodd, 0), 31);
-  __m128i hi =
-      _mm_slli_epi32(_mm256_extractf128_si256(shift_isodd, 1), 31);
-  Packet8i sign_flip_mask = _mm256_setr_m128(lo, hi);
-#endif
 
   // Create a mask for which interpolant to use, i.e. if z > 1, then the mask
   // is set to ones for that entry.
@@ -142,15 +150,7 @@ plog<Packet8f>(const Packet8f& _x) {
   // Truncate input values to the minimum positive normal.
   x = pmax(x, p8f_min_norm_pos);
 
-// Extract the shifted exponents (No bitwise shifting in regular AVX, so
+  Packet8f emm0 = pshiftright(x,23);
-// convert to SSE and do it there).
-#ifdef EIGEN_VECTORIZE_AVX2
-  Packet8f emm0 = _mm256_cvtepi32_ps(_mm256_srli_epi32(_mm256_castps_si256(x), 23));
-#else
-  __m128i lo = _mm_srli_epi32(_mm256_extractf128_si256(_mm256_castps_si256(x), 0), 23);
-  __m128i hi = _mm_srli_epi32(_mm256_extractf128_si256(_mm256_castps_si256(x), 1), 23);
-  Packet8f emm0 = _mm256_cvtepi32_ps(_mm256_setr_m128(lo, hi));
-#endif
   Packet8f e = _mm256_sub_ps(emm0, p8f_126f);
 
   // Set the exponents to -1, i.e. x are in the range [0.5,1).
@@ -259,18 +259,61 @@ pexp<Packet8f>(const Packet8f& _x) {
 
   // Build emm0 = 2^m.
   Packet8i emm0 = _mm256_cvttps_epi32(padd(m, p8f_127));
-#ifdef EIGEN_VECTORIZE_AVX2
+  emm0 = pshiftleft(emm0, 23);
-  emm0 = _mm256_slli_epi32(emm0, 23);
-#else
-  __m128i lo = _mm_slli_epi32(_mm256_extractf128_si256(emm0, 0), 23);
-  __m128i hi = _mm_slli_epi32(_mm256_extractf128_si256(emm0, 1), 23);
-  emm0 = _mm256_setr_m128(lo, hi);
-#endif
 
   // Return 2^m * exp(r).
   return pmax(pmul(y, _mm256_castsi256_ps(emm0)), _x);
 }
 
+// Hyperbolic Tangent function.
+// Doesn't do anything fancy, just a 13/6-degree rational interpolant which
+// is accurate up to a couple of ulp in the range [-9, 9], outside of which the
+// fl(tanh(x)) = +/-1.
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f
+ptanh<Packet8f>(const Packet8f& _x) {
+  // Clamp the inputs to the range [-9, 9] since anything outside
+  // this range is +/-1.0f in single-precision.
+  _EIGEN_DECLARE_CONST_Packet8f(plus_9, 9.0f);
+  _EIGEN_DECLARE_CONST_Packet8f(minus_9, -9.0f);
+  const Packet8f x = pmax(p8f_minus_9, pmin(p8f_plus_9, _x));
+
+  // The monomial coefficients of the numerator polynomial (odd).
+  _EIGEN_DECLARE_CONST_Packet8f(alpha_1, 4.89352455891786e-03f);
+  _EIGEN_DECLARE_CONST_Packet8f(alpha_3, 6.37261928875436e-04f);
+  _EIGEN_DECLARE_CONST_Packet8f(alpha_5, 1.48572235717979e-05f);
+  _EIGEN_DECLARE_CONST_Packet8f(alpha_7, 5.12229709037114e-08f);
+  _EIGEN_DECLARE_CONST_Packet8f(alpha_9, -8.60467152213735e-11f);
+  _EIGEN_DECLARE_CONST_Packet8f(alpha_11, 2.00018790482477e-13f);
+  _EIGEN_DECLARE_CONST_Packet8f(alpha_13, -2.76076847742355e-16f);
+
+  // The monomial coefficients of the denominator polynomial (even).
+  _EIGEN_DECLARE_CONST_Packet8f(beta_0, 4.89352518554385e-03f);
+  _EIGEN_DECLARE_CONST_Packet8f(beta_2, 2.26843463243900e-03f);
+  _EIGEN_DECLARE_CONST_Packet8f(beta_4, 1.18534705686654e-04f);
+  _EIGEN_DECLARE_CONST_Packet8f(beta_6, 1.19825839466702e-06f);
+
+  // Since the polynomials are odd/even, we need x^2.
+  const Packet8f x2 = pmul(x, x);
+
+  // Evaluate the numerator polynomial p.
+  Packet8f p = pmadd(x2, p8f_alpha_13, p8f_alpha_11);
+  p = pmadd(x2, p, p8f_alpha_9);
+  p = pmadd(x2, p, p8f_alpha_7);
+  p = pmadd(x2, p, p8f_alpha_5);
+  p = pmadd(x2, p, p8f_alpha_3);
+  p = pmadd(x2, p, p8f_alpha_1);
+  p = pmul(x, p);
+
+  // Evaluate the denominator polynomial p.
+  Packet8f q = pmadd(x2, p8f_beta_6, p8f_beta_4);
+  q = pmadd(x2, q, p8f_beta_2);
+  q = pmadd(x2, q, p8f_beta_0);
+
+  // Divide the numerator by the denominator.
+  return pdiv(p, q);
+}
+
 template <>
 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4d
 pexp<Packet4d>(const Packet4d& _x) {

Eigen/src/Core/arch/AVX/PacketMath.h

@@ -68,6 +68,7 @@ template<> struct packet_traits<float>  : default_packet_traits
     HasExp  = 1,
     HasSqrt = 1,
     HasRsqrt = 1,
+    HasTanh  = EIGEN_FAST_MATH,
     HasBlend = 1,
     HasRound = 1,
     HasFloor = 1,

Eigen/src/Core/arch/CUDA/Half.h

@@ -0,0 +1,497 @@
+// Standard 16-bit float type, mostly useful for GPUs. Defines a new
+// class Eigen::half (inheriting from CUDA's __half struct) with
+// operator overloads such that it behaves basically as an arithmetic
+// type. It will be quite slow on CPUs (so it is recommended to stay
+// in fp32 for CPUs, except for simple parameter conversions, I/O
+// to disk and the likes), but fast on GPUs.
+//
+//
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// 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/.
+//
+// The conversion routines are Copyright (c) Fabian Giesen, 2016.
+// The original license follows:
+//
+// Copyright (c) Fabian Giesen, 2016
+// All rights reserved.
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted.
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+#ifndef EIGEN_HALF_CUDA_H
+#define EIGEN_HALF_CUDA_H
+
+#if __cplusplus > 199711L
+#define EIGEN_EXPLICIT_CAST(tgt_type) explicit operator tgt_type()
+#else
+#define EIGEN_EXPLICIT_CAST(tgt_type) operator tgt_type()
+#endif
+
+
+#if !defined(EIGEN_HAS_CUDA_FP16)
+
+// Make our own __half definition that is similar to CUDA's.
+struct __half {
+  unsigned short x;
+};
+
+#endif
+
+namespace Eigen {
+
+namespace internal {
+
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half raw_uint16_to_half(unsigned short x);
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half float_to_half_rtne(float ff);
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float half_to_float(__half h);
+
+} // end namespace internal
+
+// Class definition.
+struct half : public __half {
+  EIGEN_DEVICE_FUNC half() {}
+
+  EIGEN_DEVICE_FUNC half(const __half& h) : __half(h) {}
+  EIGEN_DEVICE_FUNC half(const half& h) : __half(h) {}
+
+  explicit EIGEN_DEVICE_FUNC half(bool b)
+      : __half(internal::raw_uint16_to_half(b ? 0x3c00 : 0)) {}
+  explicit EIGEN_DEVICE_FUNC half(int i)
+      : __half(internal::float_to_half_rtne(static_cast<float>(i))) {}
+  explicit EIGEN_DEVICE_FUNC half(long l)
+      : __half(internal::float_to_half_rtne(static_cast<float>(l))) {}
+  explicit EIGEN_DEVICE_FUNC half(long long ll)
+      : __half(internal::float_to_half_rtne(static_cast<float>(ll))) {}
+  explicit EIGEN_DEVICE_FUNC half(float f)
+      : __half(internal::float_to_half_rtne(f)) {}
+  explicit EIGEN_DEVICE_FUNC half(double d)
+      : __half(internal::float_to_half_rtne(static_cast<float>(d))) {}
+
+  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(bool) const {
+    // +0.0 and -0.0 become false, everything else becomes true.
+    return (x & 0x7fff) != 0;
+  }
+  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(signed char) const {
+    return static_cast<signed char>(internal::half_to_float(*this));
+  }
+  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned char) const {
+    return static_cast<unsigned char>(internal::half_to_float(*this));
+  }
+  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(short) const {
+    return static_cast<short>(internal::half_to_float(*this));
+  }
+  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned short) const {
+    return static_cast<unsigned short>(internal::half_to_float(*this));
+  }
+  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(int) const {
+    return static_cast<int>(internal::half_to_float(*this));
+  }
+  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned int) const {
+    return static_cast<unsigned int>(internal::half_to_float(*this));
+  }
+  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(long) const {
+    return static_cast<long>(internal::half_to_float(*this));
+  }
+  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned long) const {
+    return static_cast<unsigned long>(internal::half_to_float(*this));
+  }
+  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(long long) const {
+    return static_cast<long long>(internal::half_to_float(*this));
+  }
+  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(unsigned long long) const {
+    return static_cast<unsigned long long>(internal::half_to_float(*this));
+  }
+  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(float) const {
+    return internal::half_to_float(*this);
+  }
+  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(double) const {
+    return static_cast<double>(internal::half_to_float(*this));
+  }
+
+  EIGEN_DEVICE_FUNC half& operator=(const half& other) {
+    x = other.x;
+    return *this;
+  }
+};
+
+#if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530
+
+// Intrinsics for native fp16 support. Note that on current hardware,
+// these are no faster than fp32 arithmetic (you need to use the half2
+// versions to get the ALU speed increased), but you do save the
+// conversion steps back and forth.
+
+__device__ half operator + (const half& a, const half& b) {
+  return __hadd(a, b);
+}
+__device__ half operator * (const half& a, const half& b) {
+  return __hmul(a, b);
+}
+__device__ half operator - (const half& a, const half& b) {
+  return __hsub(a, b);
+}
+__device__ half operator / (const half& a, const half& b) {
+  float num = __half2float(a);
+  float denom = __half2float(b);
+  return __float2half(num / denom);
+}
+__device__ half operator - (const half& a) {
+  return __hneg(a);
+}
+__device__ half& operator += (half& a, const half& b) {
+  a = a + b;
+  return a;
+}
+__device__ half& operator *= (half& a, const half& b) {
+  a = a * b;
+  return a;
+}
+__device__ half& operator -= (half& a, const half& b) {
+  a = a - b;
+  return a;
+}
+__device__ half& operator /= (half& a, const half& b) {
+  a = a / b;
+  return a;
+}
+__device__ bool operator == (const half& a, const half& b) {
+  return __heq(a, b);
+}
+__device__ bool operator != (const half& a, const half& b) {
+  return __hne(a, b);
+}
+__device__ bool operator < (const half& a, const half& b) {
+  return __hlt(a, b);
+}
+__device__ bool operator <= (const half& a, const half& b) {
+  return __hle(a, b);
+}
+__device__ bool operator > (const half& a, const half& b) {
+  return __hgt(a, b);
+}
+__device__ bool operator >= (const half& a, const half& b) {
+  return __hge(a, b);
+}
+
+#else  // Emulate support for half floats
+
+// Definitions for CPUs and older CUDA, mostly working through conversion
+// to/from fp32.
+
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator + (const half& a, const half& b) {
+  return half(float(a) + float(b));
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator * (const half& a, const half& b) {
+  return half(float(a) * float(b));
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (const half& a, const half& b) {
+  return half(float(a) - float(b));
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (const half& a, const half& b) {
+  return half(float(a) / float(b));
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (const half& a) {
+  half result;
+  result.x = a.x ^ 0x8000;
+  return result;
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator += (half& a, const half& b) {
+  a = half(float(a) + float(b));
+  return a;
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator *= (half& a, const half& b) {
+  a = half(float(a) * float(b));
+  return a;
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator -= (half& a, const half& b) {
+  a = half(float(a) - float(b));
+  return a;
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator /= (half& a, const half& b) {
+  a = half(float(a) / float(b));
+  return a;
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator == (const half& a, const half& b) {
+  return float(a) == float(b);
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator != (const half& a, const half& b) {
+  return float(a) != float(b);
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator < (const half& a, const half& b) {
+  return float(a) < float(b);
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator <= (const half& a, const half& b) {
+  return float(a) <= float(b);
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator > (const half& a, const half& b) {
+  return float(a) > float(b);
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator >= (const half& a, const half& b) {
+  return float(a) >= float(b);
+}
+
+#endif  // Emulate support for half floats
+
+// Division by an index. Do it in full float precision to avoid accuracy
+// issues in converting the denominator to half.
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (const half& a, Index b) {
+  return Eigen::half(static_cast<float>(a) / static_cast<float>(b));
+}
+
+// Conversion routines, including fallbacks for the host or older CUDA.
+// Note that newer Intel CPUs (Haswell or newer) have vectorized versions of
+// these in hardware. If we need more performance on older/other CPUs, they are
+// also possible to vectorize directly.
+
+namespace internal {
+
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half raw_uint16_to_half(unsigned short x) {
+  __half h;
+  h.x = x;
+  return h;
+}
+
+union FP32 {
+  unsigned int u;
+  float f;
+};
+
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half float_to_half_rtne(float ff) {
+#if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300
+  return __float2half(ff);
+
+#elif defined(EIGEN_HAS_FP16_C)
+  __half h;
+  h.x = _cvtss_sh(ff, 0);
+  return h;
+
+#else
+  FP32 f; f.f = ff;
+
+  const FP32 f32infty = { 255 << 23 };
+  const FP32 f16max = { (127 + 16) << 23 };
+  const FP32 denorm_magic = { ((127 - 15) + (23 - 10) + 1) << 23 };
+  unsigned int sign_mask = 0x80000000u;
+  __half o = { 0 };
+
+  unsigned int sign = f.u & sign_mask;
+  f.u ^= sign;
+
+  // NOTE all the integer compares in this function can be safely
+  // compiled into signed compares since all operands are below
+  // 0x80000000. Important if you want fast straight SSE2 code
+  // (since there's no unsigned PCMPGTD).
+
+  if (f.u >= f16max.u) {  // result is Inf or NaN (all exponent bits set)
+    o.x = (f.u > f32infty.u) ? 0x7e00 : 0x7c00; // NaN->qNaN and Inf->Inf
+  } else {  // (De)normalized number or zero
+    if (f.u < (113 << 23)) {  // resulting FP16 is subnormal or zero
+      // use a magic value to align our 10 mantissa bits at the bottom of
+      // the float. as long as FP addition is round-to-nearest-even this
+      // just works.
+      f.f += denorm_magic.f;
+
+      // and one integer subtract of the bias later, we have our final float!
+      o.x = static_cast<unsigned short>(f.u - denorm_magic.u);
+    } else {
+      unsigned int mant_odd = (f.u >> 13) & 1; // resulting mantissa is odd
+
+      // update exponent, rounding bias part 1
+      f.u += ((unsigned int)(15 - 127) << 23) + 0xfff;
+      // rounding bias part 2
+      f.u += mant_odd;
+      // take the bits!
+      o.x = static_cast<unsigned short>(f.u >> 13);
+    }
+  }
+
+  o.x |= static_cast<unsigned short>(sign >> 16);
+  return o;
+#endif
+}
+
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float half_to_float(__half h) {
+#if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300
+  return __half2float(h);
+
+#elif defined(EIGEN_HAS_FP16_C)
+  return _cvtsh_ss(h.x);
+
+#else
+  const FP32 magic = { 113 << 23 };
+  const unsigned int shifted_exp = 0x7c00 << 13; // exponent mask after shift
+  FP32 o;
+
+  o.u = (h.x & 0x7fff) << 13;             // exponent/mantissa bits
+  unsigned int exp = shifted_exp & o.u;   // just the exponent
+  o.u += (127 - 15) << 23;                // exponent adjust
+
+  // handle exponent special cases
+  if (exp == shifted_exp) {     // Inf/NaN?
+    o.u += (128 - 16) << 23;    // extra exp adjust
+  } else if (exp == 0) {        // Zero/Denormal?
+    o.u += 1 << 23;             // extra exp adjust
+    o.f -= magic.f;             // renormalize
+  }
+
+  o.u |= (h.x & 0x8000) << 16;    // sign bit
+  return o.f;
+#endif
+}
+
+} // end namespace internal
+
+// Traits.
+
+namespace internal {
+
+template<> struct is_arithmetic<half> { enum { value = true }; };
+
+} // end namespace internal
+
+template<> struct NumTraits<Eigen::half>
+    : GenericNumTraits<Eigen::half>
+{
+  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half epsilon() {
+    return internal::raw_uint16_to_half(0x0800);
+  }
+  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half dummy_precision() { return half(1e-3f); }
+  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half highest() {
+    return internal::raw_uint16_to_half(0x7bff);
+  }
+  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half lowest() {
+    return internal::raw_uint16_to_half(0xfbff);
+  }
+  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half infinity() {
+    return internal::raw_uint16_to_half(0x7c00);
+  }
+  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Eigen::half quiet_NaN() {
+    return internal::raw_uint16_to_half(0x7c01);
+  }
+};
+
+// Infinity/NaN checks.
+
+namespace numext {
+
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isinf)(const Eigen::half& a) {
+  return (a.x & 0x7fff) == 0x7c00;
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isnan)(const Eigen::half& a) {
+#if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530
+  return __hisnan(a);
+#else
+  return (a.x & 0x7fff) > 0x7c00;
+#endif
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isfinite)(const Eigen::half& a) {
+  return !(Eigen::numext::isinf)(a) && !(Eigen::numext::isnan)(a);
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half abs(const Eigen::half& a) {
+  Eigen::half result;
+  result.x = a.x & 0x7FFF;
+  return result;
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half exp(const Eigen::half& a) {
+  return Eigen::half(::expf(float(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half log(const Eigen::half& a) {
+  return Eigen::half(::logf(float(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half sqrt(const Eigen::half& a) {
+  return Eigen::half(::sqrtf(float(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half pow(const Eigen::half& a, const Eigen::half& b) {
+  return Eigen::half(::powf(float(a), float(b)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half floor(const Eigen::half& a) {
+  return Eigen::half(::floorf(float(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half ceil(const Eigen::half& a) {
+  return Eigen::half(::ceilf(float(a)));
+}
+
+} // end namespace numext
+
+} // end namespace Eigen
+
+// Standard mathematical functions and trancendentals.
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half fabsh(const Eigen::half& a) {
+  Eigen::half result;
+  result.x = a.x & 0x7FFF;
+  return result;
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half exph(const Eigen::half& a) {
+  return Eigen::half(::expf(float(a)));
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half logh(const Eigen::half& a) {
+  return Eigen::half(::logf(float(a)));
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half sqrth(const Eigen::half& a) {
+  return Eigen::half(::sqrtf(float(a)));
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half powh(const Eigen::half& a, const Eigen::half& b) {
+  return Eigen::half(::powf(float(a), float(b)));
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half floorh(const Eigen::half& a) {
+  return Eigen::half(::floorf(float(a)));
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half ceilh(const Eigen::half& a) {
+  return Eigen::half(::ceilf(float(a)));
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC int (isnan)(const Eigen::half& a) {
+  return (Eigen::numext::isnan)(a);
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC int (isinf)(const Eigen::half& a) {
+  return (Eigen::numext::isinf)(a);
+}
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC int (isfinite)(const Eigen::half& a) {
+  return !(Eigen::numext::isinf)(a) && !(Eigen::numext::isnan)(a);
+}
+
+
+namespace std {
+
+#if __cplusplus > 199711L
+template <>
+struct hash<Eigen::half> {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::size_t operator()(const Eigen::half& a) const {
+    return static_cast<std::size_t>(a.x);
+  }
+};
+#endif
+
+} // end namespace std
+
+
+// Add the missing shfl_xor intrinsic
+#if defined(EIGEN_HAS_CUDA_FP16) && defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_xor(Eigen::half var, int laneMask, int width=warpSize) {
+  return static_cast<Eigen::half>(__shfl_xor(static_cast<float>(var), laneMask, width));
+}
+#endif
+
+// ldg() has an overload for __half, but we also need one for Eigen::half.
+#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 320
+static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half __ldg(const Eigen::half* ptr) {
+  return Eigen::internal::raw_uint16_to_half(
+      __ldg(reinterpret_cast<const unsigned short*>(ptr)));
+}
+#endif
+
+
+#endif // EIGEN_HALF_CUDA_H

Eigen/src/Core/arch/CUDA/MathFunctions.h

@@ -66,6 +66,121 @@ double2 prsqrt<double2>(const double2& a)
   return make_double2(rsqrt(a.x), rsqrt(a.y));
 }
 
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 plgamma<float4>(const float4& a)
+{
+  return make_float4(lgammaf(a.x), lgammaf(a.y), lgammaf(a.z), lgammaf(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 plgamma<double2>(const double2& a)
+{
+  return make_double2(lgamma(a.x), lgamma(a.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 pdigamma<float4>(const float4& a)
+{
+  using numext::digamma;
+  return make_float4(digamma(a.x), digamma(a.y), digamma(a.z), digamma(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 pdigamma<double2>(const double2& a)
+{
+  using numext::digamma;
+  return make_double2(digamma(a.x), digamma(a.y));
+}
+    
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 pzeta<float4>(const float4& x, const float4& q)
+{
+    using numext::zeta;
+    return make_float4(zeta(x.x, q.x), zeta(x.y, q.y), zeta(x.z, q.z), zeta(x.w, q.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 pzeta<double2>(const double2& x, const double2& q)
+{
+    using numext::zeta;
+    return make_double2(zeta(x.x, q.x), zeta(x.y, q.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 ppolygamma<float4>(const float4& n, const float4& x)
+{
+    using numext::polygamma;
+    return make_float4(polygamma(n.x, x.x), polygamma(n.y, x.y), polygamma(n.z, x.z), polygamma(n.w, x.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 ppolygamma<double2>(const double2& n, const double2& x)
+{
+    using numext::polygamma;
+    return make_double2(polygamma(n.x, x.x), polygamma(n.y, x.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 perf<float4>(const float4& a)
+{
+  return make_float4(erf(a.x), erf(a.y), erf(a.z), erf(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 perf<double2>(const double2& a)
+{
+  return make_double2(erf(a.x), erf(a.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 perfc<float4>(const float4& a)
+{
+  return make_float4(erfc(a.x), erfc(a.y), erfc(a.z), erfc(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 perfc<double2>(const double2& a)
+{
+  return make_double2(erfc(a.x), erfc(a.y));
+}
+
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 pigamma<float4>(const float4& a, const float4& x)
+{
+  using numext::igamma;
+  return make_float4(
+      igamma(a.x, x.x),
+      igamma(a.y, x.y),
+      igamma(a.z, x.z),
+      igamma(a.w, x.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 pigamma<double2>(const double2& a, const double2& x)
+{
+  using numext::igamma;
+  return make_double2(igamma(a.x, x.x), igamma(a.y, x.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 pigammac<float4>(const float4& a, const float4& x)
+{
+  using numext::igammac;
+  return make_float4(
+      igammac(a.x, x.x),
+      igammac(a.y, x.y),
+      igammac(a.z, x.z),
+      igammac(a.w, x.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 pigammac<double2>(const double2& a, const double2& x)
+{
+  using numext::igammac;
+  return make_double2(igammac(a.x, x.x), igammac(a.y, x.y));
+}
+
 #endif
 
 } // end namespace internal

Eigen/src/Core/arch/CUDA/PacketMath.h

@@ -21,7 +21,6 @@ namespace internal {
 template<> struct is_arithmetic<float4>  { enum { value = true }; };
 template<> struct is_arithmetic<double2> { enum { value = true }; };
 
-
 template<> struct packet_traits<float> : default_packet_traits
 {
   typedef float4 type;
@@ -39,6 +38,14 @@ template<> struct packet_traits<float> : default_packet_traits
     HasExp  = 1,
     HasSqrt = 1,
     HasRsqrt = 1,
+    HasLGamma = 1,
+    HasDiGamma = 1,
+    HasZeta = 1,
+    HasPolygamma = 1,
+    HasErf = 1,
+    HasErfc = 1,
+    HasIgamma = 1,
+    HasIGammac = 1,
 
     HasBlend = 0,
   };
@@ -59,6 +66,12 @@ template<> struct packet_traits<double> : default_packet_traits
     HasExp  = 1,
     HasSqrt = 1,
     HasRsqrt = 1,
+    HasLGamma = 1,
+    HasDiGamma = 1,
+    HasErf = 1,
+    HasErfc = 1,
+    HasIGamma = 1,
+    HasIGammac = 1,
 
     HasBlend = 0,
   };
@@ -177,25 +190,39 @@ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu<double>(double* to
   to[1] = from.y;
 }
 
-#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 350
 template<>
 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float4 ploadt_ro<float4, Aligned>(const float* from) {
+#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 350
   return __ldg((const float4*)from);
+#else
+  return make_float4(from[0], from[1], from[2], from[3]);
+#endif
 }
 template<>
 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double2 ploadt_ro<double2, Aligned>(const double* from) {
+#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 350
   return __ldg((const double2*)from);
+#else
+  return make_double2(from[0], from[1]);
+#endif
 }
 
 template<>
 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float4 ploadt_ro<float4, Unaligned>(const float* from) {
+#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 350
   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]);
+#endif
 }
 template<>
 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double2 ploadt_ro<double2, Unaligned>(const double* from) {
+#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 350
   return make_double2(__ldg(from+0), __ldg(from+1));
-}
+#else
+  return make_double2(from[0], from[1]);
 #endif
+}
 
 template<> EIGEN_DEVICE_FUNC inline float4 pgather<float, float4>(const float* from, Index stride) {
   return make_float4(from[0*stride], from[1*stride], from[2*stride], from[3*stride]);
@@ -251,6 +278,35 @@ template<> EIGEN_DEVICE_FUNC inline double predux_mul<double2>(const double2& a)
   return a.x * a.y;
 }
 
+template<size_t offset>
+struct protate_impl<offset, float4>
+{
+  static float4 run(const float4& a) {
+    if (offset == 0) {
+      return make_float4(a.x, a.y, a.z, a.w);
+    }
+    if (offset == 1) {
+      return make_float4(a.w, a.x, a.y, a.z);
+    }
+    if (offset == 2) {
+      return make_float4(a.z, a.w, a.x, a.y);
+    }
+    return make_float4(a.y, a.z, a.w, a.x);
+  }
+};
+
+template<size_t offset>
+struct protate_impl<offset, double2>
+{
+  static double2 run(const double2& a) {
+    if (offset == 0) {
+      return make_double2(a.x, a.y);
+    }
+    return make_double2(a.y, a.x);
+  }
+};
+
+
 template<> EIGEN_DEVICE_FUNC inline float4  pabs<float4>(const float4& a) {
   return make_float4(fabsf(a.x), fabsf(a.y), fabsf(a.z), fabsf(a.w));
 }
@@ -258,7 +314,6 @@ template<> EIGEN_DEVICE_FUNC inline double2 pabs<double2>(const double2& a) {
   return make_double2(fabs(a.x), fabs(a.y));
 }
 
-
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<float4,4>& kernel) {
   double tmp = kernel.packet[0].y;

Eigen/src/Core/arch/CUDA/PacketMathHalf.h

@@ -0,0 +1,192 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// 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/.
+
+#ifndef EIGEN_PACKET_MATH_HALF_CUDA_H
+#define EIGEN_PACKET_MATH_HALF_CUDA_H
+
+#if defined(EIGEN_HAS_CUDA_FP16)
+
+// 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(__CUDACC__) && defined(EIGEN_USE_GPU)
+
+// Most of the following operations require arch >= 5.3
+#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530
+
+namespace Eigen {
+namespace internal {
+
+template<> struct is_arithmetic<half2> { enum { value = true }; };
+
+template<> struct packet_traits<half> : default_packet_traits
+{
+  typedef half2 type;
+  typedef half2 half;
+  enum {
+    Vectorizable = 1,
+    AlignedOnScalar = 1,
+    size=2,
+    HasHalfPacket = 0,
+    HasDiv  = 1
+  };
+};
+
+
+template<> struct unpacket_traits<half2> { typedef half type; enum {size=2, alignment=Aligned16}; typedef half2 half; };
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pset1<half2>(const half& from) {
+  return __half2half2(from);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pload<half2>(const half* from) {
+  return *reinterpret_cast<const half2*>(from);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ploadu<half2>(const half* from) {
+  return __halves2half2(from[0], from[1]);
+}
+
+template<> EIGEN_STRONG_INLINE half2 ploaddup<half2>(const half*  from) {
+  return __halves2half2(from[0], from[0]);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore<half>(half* to, const half2& from) {
+  *reinterpret_cast<half2*>(to) = from;
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu<half>(half* to, const half2& from) {
+  to[0] = __low2half(from);
+  to[1] = __high2half(from);
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE half2 ploadt_ro<half2, Aligned>(const half* from) {
+  return __ldg((const half2*)from);
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE half2 ploadt_ro<half2, Unaligned>(const half* from) {
+  return __halves2half2(__ldg(from+0), __ldg(from+1));
+}
+
+template<> EIGEN_DEVICE_FUNC inline half2 pgather<half, half2>(const half* from, Index stride) {
+  return __halves2half2(from[0*stride], from[1*stride]);
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<half, half2>(half* to, const half2& from, Index stride) {
+  to[stride*0] = __low2half(from);
+  to[stride*1] = __high2half(from);
+}
+
+template<> EIGEN_DEVICE_FUNC inline half pfirst<half2>(const half2& a) {
+  return __low2half(a);
+}
+
+template<> EIGEN_DEVICE_FUNC inline half2 pabs<half2>(const half2& a) {
+  half2 result;
+  result.x = a.x & 0x7FFF7FFF;
+  return result;
+}
+
+
+EIGEN_DEVICE_FUNC 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);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plset<half2>(const half& a) {
+  return __halves2half2(a, __hadd(a, __float2half(1.0f)));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 padd<half2>(const half2& a, const half2& b) {
+  return __hadd2(a, b);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 psub<half2>(const half2& a, const half2& b) {
+  return __hsub2(a, b);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pnegate(const half2& a) {
+  return __hneg2(a);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pconj(const half2& a) { return a; }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmul<half2>(const half2& a, const half2& b) {
+  return __hmul2(a, b);
+}
+
+ template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmadd<half2>(const half2& a, const half2& b, const half2& c) {
+   return __hfma2(a, b, c);
+ }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pdiv<half2>(const half2& a, const half2& b) {
+  float a1 = __low2float(a);
+  float a2 = __high2float(a);
+  float b1 = __low2float(b);
+  float b2 = __high2float(b);
+  float r1 = a1 / b1;
+  float r2 = a2 / b2;
+  return __floats2half2_rn(r1, r2);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmin<half2>(const half2& a, const half2& b) {
+  float a1 = __low2float(a);
+  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);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmax<half2>(const half2& a, const half2& b) {
+  float a1 = __low2float(a);
+  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);
+}
+
+template<> EIGEN_DEVICE_FUNC inline half predux<half2>(const half2& a) {
+  return __hadd(__low2half(a), __high2half(a));
+}
+
+template<> EIGEN_DEVICE_FUNC inline half predux_max<half2>(const half2& a) {
+  half first = __low2half(a);
+  half second = __high2half(a);
+  return __hgt(first, second) ? first : second;
+}
+
+template<> EIGEN_DEVICE_FUNC inline half predux_min<half2>(const half2& a) {
+  half first = __low2half(a);
+  half second = __high2half(a);
+  return __hlt(first, second) ? first : second;
+}
+
+template<> EIGEN_DEVICE_FUNC inline half predux_mul<half2>(const half2& a) {
+  return __hmul(__low2half(a), __high2half(a));
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif
+#endif
+#endif
+#endif // EIGEN_PACKET_MATH_HALF_CUDA_H

Eigen/src/Core/arch/CUDA/TypeCasting.h

@@ -0,0 +1,112 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// 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/.
+
+#ifndef EIGEN_TYPE_CASTING_CUDA_H
+#define EIGEN_TYPE_CASTING_CUDA_H
+
+namespace Eigen {
+
+namespace internal {
+
+#if defined(EIGEN_HAS_CUDA_FP16)
+
+template<>
+struct scalar_cast_op<float, half> {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_cast_op)
+  typedef half result_type;
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half operator() (const float& a) const {
+    #if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300
+      return __float2half(a);
+    #else
+      return half(a);
+    #endif
+  }
+};
+
+template<>
+struct functor_traits<scalar_cast_op<float, half> >
+{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };
+
+
+template<>
+struct scalar_cast_op<int, half> {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_cast_op)
+  typedef half result_type;
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half operator() (const int& a) const {
+    #if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300
+      return __float2half(static_cast<float>(a));
+    #else
+      return half(static_cast<float>(a));
+    #endif
+  }
+};
+
+template<>
+struct functor_traits<scalar_cast_op<int, half> >
+{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };
+
+
+template<>
+struct scalar_cast_op<half, float> {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_cast_op)
+  typedef float result_type;
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float operator() (const half& a) const {
+    #if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 300
+      return __half2float(a);
+    #else
+      return static_cast<float>(a);
+    #endif
+  }
+};
+
+template<>
+struct functor_traits<scalar_cast_op<half, float> >
+{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };
+
+
+
+#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 530
+
+template <>
+struct type_casting_traits<half, float> {
+  enum {
+    VectorizedCast = 1,
+    SrcCoeffRatio = 2,
+    TgtCoeffRatio = 1
+  };
+};
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pcast<half2, float4>(const half2& a, const half2& b) {
+  float2 r1 = __half22float2(a);
+  float2 r2 = __half22float2(b);
+  return make_float4(r1.x, r1.y, r2.x, r2.y);
+}
+
+template <>
+struct type_casting_traits<float, half> {
+  enum {
+    VectorizedCast = 1,
+    SrcCoeffRatio = 1,
+    TgtCoeffRatio = 2
+  };
+};
+
+template<> EIGEN_STRONG_INLINE half2 pcast<float4, half2>(const float4& a) {
+  // Simply discard the second half of the input
+  return __float22half2_rn(make_float2(a.x, a.y));
+}
+
+#endif
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TYPE_CASTING_CUDA_H

Eigen/src/Core/arch/NEON/PacketMath.h

@@ -177,7 +177,11 @@ template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, co
   return pset1<Packet4i>(0);
 }
 
-#ifdef __ARM_FEATURE_FMA
+// Clang/ARM wrongly advertises __ARM_FEATURE_FMA even when it's not available,
+// then implements a slow software scalar fallback calling fmaf()!
+// Filed LLVM bug:
+//     https://llvm.org/bugs/show_bug.cgi?id=27216
+#if (defined __ARM_FEATURE_FMA) && !(EIGEN_COMP_CLANG && EIGEN_ARCH_ARM)
 // See bug 936.
 // FMA is available on VFPv4 i.e. when compiling with -mfpu=neon-vfpv4.
 // FMA is a true fused multiply-add i.e. only 1 rounding at the end, no intermediate rounding.
@@ -186,7 +190,27 @@ template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, co
 // MLA: 10 GFlop/s ; FMA: 12 GFlops/s.
 template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vfmaq_f32(c,a,b); }
 #else
-template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vmlaq_f32(c,a,b); }
+template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) {
+#if EIGEN_COMP_CLANG && EIGEN_ARCH_ARM
+  // Clang/ARM will replace VMLA by VMUL+VADD at least for some values of -mcpu,
+  // at least -mcpu=cortex-a8 and -mcpu=cortex-a7. Since the former is the default on
+  // -march=armv7-a, that is a very common case.
+  // See e.g. this thread:
+  //     http://lists.llvm.org/pipermail/llvm-dev/2013-December/068806.html
+  // Filed LLVM bug:
+  //     https://llvm.org/bugs/show_bug.cgi?id=27219
+  Packet4f r = c;
+  asm volatile(
+    "vmla.f32 %q[r], %q[a], %q[b]"
+    : [r] "+w" (r)
+    : [a] "w" (a),
+      [b] "w" (b)
+    : );
+  return r;
+#else
+  return vmlaq_f32(c,a,b);
+#endif
+}
 #endif
 
 // No FMA instruction for int, so use MLA unconditionally.
@@ -532,20 +556,21 @@ ptranspose(PacketBlock<Packet4i,4>& kernel) {
 
 #if EIGEN_ARCH_ARM64 && !EIGEN_APPLE_DOUBLE_NEON_BUG
 
-#if (EIGEN_COMP_GNUC_STRICT && defined(__ANDROID__)) || defined(__apple_build_version__)
 // Bug 907: workaround missing declarations of the following two functions in the ADK
-__extension__ static __inline uint64x2_t __attribute__ ((__always_inline__))
+// Defining these functions as templates ensures that if these intrinsics are
-vreinterpretq_u64_f64 (float64x2_t __a)
+// already defined in arm_neon.h, then our workaround doesn't cause a conflict
+// and has lower priority in overload resolution.
+template <typename T>
+uint64x2_t vreinterpretq_u64_f64(T a)
 {
-  return (uint64x2_t) __a;
+  return (uint64x2_t) a;
 }
 
-__extension__ static __inline float64x2_t __attribute__ ((__always_inline__))
+template <typename T>
-vreinterpretq_f64_u64 (uint64x2_t __a)
+float64x2_t vreinterpretq_f64_u64(T a)
 {
-  return (float64x2_t) __a;
+  return (float64x2_t) a;
 }
-#endif
 
 typedef float64x2_t Packet2d;
 typedef float64x1_t Packet1d;

Eigen/src/Core/arch/SSE/Complex.h

@@ -255,7 +255,7 @@ template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, con
   return Packet2cf(_mm_div_ps(res.v,_mm_add_ps(s,_mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(s), 0xb1)))));
 }
 
-EIGEN_STRONG_INLINE Packet2cf pcplxflip/*<Packet2cf>*/(const Packet2cf& x)
+EIGEN_STRONG_INLINE Packet2cf pcplxflip/* <Packet2cf> */(const Packet2cf& x)
 {
   return Packet2cf(vec4f_swizzle1(x.v, 1, 0, 3, 2));
 }
@@ -456,7 +456,7 @@ template<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, con
   return Packet1cd(_mm_div_pd(res.v, _mm_add_pd(s,_mm_shuffle_pd(s, s, 0x1))));
 }
 
-EIGEN_STRONG_INLINE Packet1cd pcplxflip/*<Packet1cd>*/(const Packet1cd& x)
+EIGEN_STRONG_INLINE Packet1cd pcplxflip/* <Packet1cd> */(const Packet1cd& x)
 {
   return Packet1cd(preverse(Packet2d(x.v)));
 }

Eigen/src/Core/arch/SSE/MathFunctions.h

@@ -516,8 +516,81 @@ Packet2d prsqrt<Packet2d>(const Packet2d& x) {
   return _mm_div_pd(pset1<Packet2d>(1.0), _mm_sqrt_pd(x));
 }
 
+// Hyperbolic Tangent function.
+// Doesn't do anything fancy, just a 13/6-degree rational interpolant which
+// is accurate up to a couple of ulp in the range [-9, 9], outside of which the
+// fl(tanh(x)) = +/-1.
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
+ptanh<Packet4f>(const Packet4f& _x) {
+  // Clamp the inputs to the range [-9, 9] since anything outside
+  // this range is +/-1.0f in single-precision.
+  _EIGEN_DECLARE_CONST_Packet4f(plus_9, 9.0f);
+  _EIGEN_DECLARE_CONST_Packet4f(minus_9, -9.0f);
+  const Packet4f x = pmax(p4f_minus_9, pmin(p4f_plus_9, _x));
+
+  // The monomial coefficients of the numerator polynomial (odd).
+  _EIGEN_DECLARE_CONST_Packet4f(alpha_1, 4.89352455891786e-03f);
+  _EIGEN_DECLARE_CONST_Packet4f(alpha_3, 6.37261928875436e-04f);
+  _EIGEN_DECLARE_CONST_Packet4f(alpha_5, 1.48572235717979e-05f);
+  _EIGEN_DECLARE_CONST_Packet4f(alpha_7, 5.12229709037114e-08f);
+  _EIGEN_DECLARE_CONST_Packet4f(alpha_9, -8.60467152213735e-11f);
+  _EIGEN_DECLARE_CONST_Packet4f(alpha_11, 2.00018790482477e-13f);
+  _EIGEN_DECLARE_CONST_Packet4f(alpha_13, -2.76076847742355e-16f);
+
+  // The monomial coefficients of the denominator polynomial (even).
+  _EIGEN_DECLARE_CONST_Packet4f(beta_0, 4.89352518554385e-03f);
+  _EIGEN_DECLARE_CONST_Packet4f(beta_2, 2.26843463243900e-03f);
+  _EIGEN_DECLARE_CONST_Packet4f(beta_4, 1.18534705686654e-04f);
+  _EIGEN_DECLARE_CONST_Packet4f(beta_6, 1.19825839466702e-06f);
+
+  // Since the polynomials are odd/even, we need x^2.
+  const Packet4f x2 = pmul(x, x);
+
+  // Evaluate the numerator polynomial p.
+  Packet4f p = pmadd(x2, p4f_alpha_13, p4f_alpha_11);
+  p = pmadd(x2, p, p4f_alpha_9);
+  p = pmadd(x2, p, p4f_alpha_7);
+  p = pmadd(x2, p, p4f_alpha_5);
+  p = pmadd(x2, p, p4f_alpha_3);
+  p = pmadd(x2, p, p4f_alpha_1);
+  p = pmul(x, p);
+
+  // Evaluate the denominator polynomial p.
+  Packet4f q = pmadd(x2, p4f_beta_6, p4f_beta_4);
+  q = pmadd(x2, q, p4f_beta_2);
+  q = pmadd(x2, q, p4f_beta_0);
+
+  // Divide the numerator by the denominator.
+  return pdiv(p, q);
+}
+
 } // end namespace internal
 
+namespace numext {
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float sqrt(const float &x)
+{
+  return internal::pfirst(internal::Packet4f(_mm_sqrt_ss(_mm_set_ss(x))));
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double sqrt(const double &x)
+{
+#if EIGEN_COMP_GNUC_STRICT
+  // This works around a GCC bug generating poor code for _mm_sqrt_pd
+  // See https://bitbucket.org/eigen/eigen/commits/14f468dba4d350d7c19c9b93072e19f7b3df563b
+  return internal::pfirst(internal::Packet2d(__builtin_ia32_sqrtsd(_mm_set_sd(x))));
+#else
+  return internal::pfirst(internal::Packet2d(_mm_sqrt_pd(_mm_set_sd(x))));
+#endif
+}
+
+} // end namespace numex
+
 } // end namespace Eigen
 
 #endif // EIGEN_MATH_FUNCTIONS_SSE_H

Eigen/src/Core/arch/SSE/PacketMath.h

@@ -109,6 +109,7 @@ template<> struct packet_traits<float>  : default_packet_traits
     HasExp  = 1,
     HasSqrt = 1,
     HasRsqrt = 1,
+    HasTanh  = EIGEN_FAST_MATH,
     HasBlend = 1
 
 #ifdef EIGEN_VECTORIZE_SSE4_1
@@ -314,58 +315,27 @@ template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int*     from) { E
     return _mm_loadu_ps(from);
     #endif
   }
-  template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm_loadu_pd(from); }
-  template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int*    from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm_loadu_si128(reinterpret_cast<const __m128i*>(from)); }
 #else
 // NOTE: with the code below, MSVC's compiler crashes!
 
-#if EIGEN_COMP_GNUC && (EIGEN_ARCH_i386 || (EIGEN_ARCH_x86_64 && EIGEN_GNUC_AT_LEAST(4, 8)))
-  // bug 195: gcc/i386 emits weird x87 fldl/fstpl instructions for _mm_load_sd
-  #define EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS 1
-#elif EIGEN_COMP_CLANG
-  // bug 201: Segfaults in __mm_loadh_pd with clang 2.8
-  #define EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS 1
-#else
-  #define EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS 0
-#endif
-
 template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
 {
   EIGEN_DEBUG_UNALIGNED_LOAD
-#if EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS
   return _mm_loadu_ps(from);
-#else
-  __m128d res;
-  res =  _mm_load_sd((const double*)(from)) ;
-  res =  _mm_loadh_pd(res, (const double*)(from+2)) ;
-  return _mm_castpd_ps(res);
-#endif
 }
+#endif
+
 template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from)
 {
   EIGEN_DEBUG_UNALIGNED_LOAD
-#if EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS
   return _mm_loadu_pd(from);
-#else
-  __m128d res;
-  res = _mm_load_sd(from) ;
-  res = _mm_loadh_pd(res,from+1);
-  return res;
-#endif
 }
 template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
 {
   EIGEN_DEBUG_UNALIGNED_LOAD
-#if EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS
   return _mm_loadu_si128(reinterpret_cast<const __m128i*>(from));
-#else
-  __m128d res;
-  res =  _mm_load_sd((const double*)(from)) ;
-  res =  _mm_loadh_pd(res, (const double*)(from+2)) ;
-  return _mm_castpd_si128(res);
-#endif
 }
-#endif
+
 
 template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float*   from)
 {

Eigen/src/Core/arch/ZVector/CMakeLists.txt

@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Core_arch_ZVector_SRCS "*.h")
+
+INSTALL(FILES
+  ${Eigen_Core_arch_ZVector_SRCS}
+  DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Core/arch/ZVector COMPONENT Devel
+)

Eigen/src/Core/arch/ZVector/Complex.h

@@ -0,0 +1,201 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// 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/.
+
+#ifndef EIGEN_COMPLEX32_ALTIVEC_H
+#define EIGEN_COMPLEX32_ALTIVEC_H
+
+namespace Eigen {
+
+namespace internal {
+
+static Packet2ul  p2ul_CONJ_XOR1 = (Packet2ul) vec_sld((Packet4ui) p2d_ZERO_, (Packet4ui) p2l_ZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };
+static Packet2ul  p2ul_CONJ_XOR2 = (Packet2ul) vec_sld((Packet4ui) p2l_ZERO,  (Packet4ui) p2d_ZERO_, 8);//{ 0x8000000000000000, 0x0000000000000000 };
+
+struct Packet1cd
+{
+  EIGEN_STRONG_INLINE Packet1cd() {}
+  EIGEN_STRONG_INLINE explicit Packet1cd(const Packet2d& a) : v(a) {}
+  Packet2d v;
+};
+
+template<> struct packet_traits<std::complex<double> >  : default_packet_traits
+{
+  typedef Packet1cd type;
+  typedef Packet1cd half;
+  enum {
+    Vectorizable = 1,
+    AlignedOnScalar = 0,
+    size = 1,
+    HasHalfPacket = 0,
+
+    HasAdd    = 1,
+    HasSub    = 1,
+    HasMul    = 1,
+    HasDiv    = 1,
+    HasNegate = 1,
+    HasAbs    = 0,
+    HasAbs2   = 0,
+    HasMin    = 0,
+    HasMax    = 0,
+    HasSetLinear = 0
+  };
+};
+
+template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16}; typedef Packet1cd half; };
+
+template<> EIGEN_STRONG_INLINE Packet1cd pload <Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(pload<Packet2d>((const double*)from)); }
+template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(ploadu<Packet2d>((const double*)from)); }
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, from.v); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>&  from)
+{ /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); }
+
+template<> EIGEN_DEVICE_FUNC inline Packet1cd pgather<std::complex<double>, Packet1cd>(const std::complex<double>* from, Index stride)
+{
+  std::complex<double> EIGEN_ALIGN16 af[2];
+  af[0] = from[0*stride];
+  af[1] = from[1*stride];
+  return pload<Packet1cd>(af);
+}
+template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet1cd>(std::complex<double>* to, const Packet1cd& from, Index stride)
+{
+  std::complex<double> EIGEN_ALIGN16 af[2];
+  pstore<std::complex<double> >(af, from);
+  to[0*stride] = af[0];
+  to[1*stride] = af[1];
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v + b.v); }
+template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v - b.v); }
+template<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate(Packet2d(a.v))); }
+template<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a) { return Packet1cd((Packet2d)vec_xor((Packet2d)a.v, (Packet2d)p2ul_CONJ_XOR2)); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{
+  Packet2d a_re, a_im, v1, v2;
+
+  // Permute and multiply the real parts of a and b
+  a_re = vec_perm(a.v, a.v, p16uc_PSET64_HI);
+  // Get the imaginary parts of a
+  a_im = vec_perm(a.v, a.v, p16uc_PSET64_LO);
+  // multiply a_re * b
+  v1 = vec_madd(a_re, b.v, p2d_ZERO);
+  // multiply a_im * b and get the conjugate result
+  v2 = vec_madd(a_im, b.v, p2d_ZERO);
+  v2 = (Packet2d) vec_sld((Packet4ui)v2, (Packet4ui)v2, 8);
+  v2 = (Packet2d) vec_xor((Packet2d)v2, (Packet2d) p2ul_CONJ_XOR1);
+
+  return Packet1cd(v1 + v2);
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd pand   <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_and(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd por    <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_or(a.v,b.v)); }
+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 void prefetch<std::complex<double> >(const std::complex<double> *   addr) { EIGEN_ZVECTOR_PREFETCH(addr); }
+
+template<> EIGEN_STRONG_INLINE std::complex<double>  pfirst<Packet1cd>(const Packet1cd& a)
+{
+  std::complex<double> EIGEN_ALIGN16 res[2];
+  pstore<std::complex<double> >(res, a);
+
+  return res[0];
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a)
+{
+  return pfirst(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd preduxp<Packet1cd>(const Packet1cd* vecs)
+{
+  return vecs[0];
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a)
+{
+  return pfirst(a);
+}
+
+template<int Offset>
+struct palign_impl<Offset,Packet1cd>
+{
+  static EIGEN_STRONG_INLINE void run(Packet1cd& /*first*/, const Packet1cd& /*second*/)
+  {
+    // FIXME is it sure we never have to align a Packet1cd?
+    // Even though a std::complex<double> has 16 bytes, it is not necessarily aligned on a 16 bytes boundary...
+  }
+};
+
+template<> struct conj_helper<Packet1cd, Packet1cd, false,true>
+{
+  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const
+  { return padd(pmul(x,y),c); }
+
+  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const
+  {
+    return internal::pmul(a, pconj(b));
+  }
+};
+
+template<> struct conj_helper<Packet1cd, Packet1cd, true,false>
+{
+  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const
+  { return padd(pmul(x,y),c); }
+
+  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const
+  {
+    return internal::pmul(pconj(a), b);
+  }
+};
+
+template<> struct conj_helper<Packet1cd, Packet1cd, true,true>
+{
+  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const
+  { return padd(pmul(x,y),c); }
+
+  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const
+  {
+    return pconj(internal::pmul(a, b));
+  }
+};
+
+template<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{
+  // TODO optimize it for AltiVec
+  Packet1cd res = conj_helper<Packet1cd,Packet1cd,false,true>().pmul(a,b);
+  Packet2d s = vec_madd(b.v, b.v, p2d_ZERO_);
+  return Packet1cd(pdiv(res.v, s + vec_perm(s, s, p16uc_REVERSE64)));
+}
+
+EIGEN_STRONG_INLINE Packet1cd pcplxflip/*<Packet1cd>*/(const Packet1cd& x)
+{
+  return Packet1cd(preverse(Packet2d(x.v)));
+}
+
+EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet1cd,2>& kernel)
+{
+  Packet2d tmp = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_HI);
+  kernel.packet[1].v = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_LO);
+  kernel.packet[0].v = tmp;
+}
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX32_ALTIVEC_H

Eigen/src/Core/arch/ZVector/MathFunctions.h

@@ -0,0 +1,110 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007 Julien Pommier
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// 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/.
+
+/* The sin, cos, exp, and log functions of this file come from
+ * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
+ */
+
+#ifndef EIGEN_MATH_FUNCTIONS_ALTIVEC_H
+#define EIGEN_MATH_FUNCTIONS_ALTIVEC_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet2d pexp<Packet2d>(const Packet2d& _x)
+{
+  Packet2d x = _x;
+
+  _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);
+  _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);
+  _EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
+
+  _EIGEN_DECLARE_CONST_Packet2d(exp_hi,  709.437);
+  _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);
+
+  _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
+
+  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
+  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
+  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
+
+  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
+  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
+  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
+  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
+
+  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
+  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
+
+  Packet2d tmp, fx;
+  Packet2l emm0;
+
+  // clamp x
+  x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);
+  /* express exp(x) as exp(g + n*log(2)) */
+  fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);
+
+  fx = vec_floor(fx);
+
+  tmp = pmul(fx, p2d_cephes_exp_C1);
+  Packet2d z = pmul(fx, p2d_cephes_exp_C2);
+  x = psub(x, tmp);
+  x = psub(x, z);
+
+  Packet2d x2 = pmul(x,x);
+
+  Packet2d px = p2d_cephes_exp_p0;
+  px = pmadd(px, x2, p2d_cephes_exp_p1);
+  px = pmadd(px, x2, p2d_cephes_exp_p2);
+  px = pmul (px, x);
+
+  Packet2d qx = p2d_cephes_exp_q0;
+  qx = pmadd(qx, x2, p2d_cephes_exp_q1);
+  qx = pmadd(qx, x2, p2d_cephes_exp_q2);
+  qx = pmadd(qx, x2, p2d_cephes_exp_q3);
+
+  x = pdiv(px,psub(qx,px));
+  x = pmadd(p2d_2,x,p2d_1);
+
+  // build 2^n
+  emm0 = vec_ctsl(fx, 0);
+
+  static const Packet2l p2l_1023 = { 1023, 1023 };
+  static const Packet2ul p2ul_52 = { 52, 52 };
+
+  emm0 = emm0 + p2l_1023;
+  emm0 = emm0 << reinterpret_cast<Packet2l>(p2ul_52);
+
+  // Altivec's max & min operators just drop silent NaNs. Check NaNs in 
+  // inputs and return them unmodified.
+  Packet2ul isnumber_mask = reinterpret_cast<Packet2ul>(vec_cmpeq(_x, _x));
+  return vec_sel(_x, pmax(pmul(x, reinterpret_cast<Packet2d>(emm0)), _x),
+                 isnumber_mask);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet2d psqrt<Packet2d>(const Packet2d& x)
+{
+  return  __builtin_s390_vfsqdb(x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet2d prsqrt<Packet2d>(const Packet2d& x) {
+  // Unfortunately we can't use the much faster mm_rqsrt_pd since it only provides an approximation.
+  return pset1<Packet2d>(1.0) / psqrt<Packet2d>(x);
+}
+
+}  // end namespace internal
+
+}  // end namespace Eigen
+
+#endif  // EIGEN_MATH_FUNCTIONS_ALTIVEC_H

Eigen/src/Core/arch/ZVector/PacketMath.h

@@ -0,0 +1,575 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// 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/.
+
+#ifndef EIGEN_PACKET_MATH_ZVECTOR_H
+#define EIGEN_PACKET_MATH_ZVECTOR_H
+
+#include <stdint.h>
+
+namespace Eigen {
+
+namespace internal {
+
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 4
+#endif
+
+#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#endif
+
+#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_CJMADD
+#define EIGEN_HAS_SINGLE_INSTRUCTION_CJMADD
+#endif
+
+// NOTE Altivec has 32 registers, but Eigen only accepts a value of 8 or 16
+#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS  32
+#endif
+
+typedef __vector int                 Packet4i;
+typedef __vector unsigned int        Packet4ui;
+typedef __vector __bool int          Packet4bi;
+typedef __vector short int           Packet8i;
+typedef __vector unsigned char       Packet16uc;
+typedef __vector double              Packet2d;
+typedef __vector unsigned long long  Packet2ul;
+typedef __vector long long           Packet2l;
+
+typedef union {
+  int32_t   i[4];
+  uint32_t ui[4];
+  int64_t   l[2];
+  uint64_t ul[2];
+  double    d[2];
+  Packet4i  v4i;
+  Packet4ui v4ui;
+  Packet2l  v2l;
+  Packet2ul v2ul;
+  Packet2d  v2d;
+} Packet;
+
+// We don't want to write the same code all the time, but we need to reuse the constants
+// and it doesn't really work to declare them global, so we define macros instead
+
+#define _EIGEN_DECLARE_CONST_FAST_Packet4i(NAME,X) \
+  Packet4i p4i_##NAME = reinterpret_cast<Packet4i>(vec_splat_s32(X))
+
+#define _EIGEN_DECLARE_CONST_FAST_Packet2d(NAME,X) \
+  Packet2d p2d_##NAME = reinterpret_cast<Packet2d>(vec_splat_s64(X))
+
+#define _EIGEN_DECLARE_CONST_FAST_Packet2l(NAME,X) \
+  Packet2l p2l_##NAME = reinterpret_cast<Packet2l>(vec_splat_s64(X))
+
+#define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
+  Packet4i p4i_##NAME = pset1<Packet4i>(X)
+
+#define _EIGEN_DECLARE_CONST_Packet2d(NAME,X) \
+  Packet2d p2d_##NAME = pset1<Packet2d>(X)
+
+#define _EIGEN_DECLARE_CONST_Packet2l(NAME,X) \
+  Packet2l p2l_##NAME = pset1<Packet2l>(X)
+
+// These constants are endian-agnostic
+//static _EIGEN_DECLARE_CONST_FAST_Packet4i(ZERO, 0); //{ 0, 0, 0, 0,}
+static _EIGEN_DECLARE_CONST_FAST_Packet4i(ONE, 1); //{ 1, 1, 1, 1}
+
+static _EIGEN_DECLARE_CONST_FAST_Packet2d(ZERO, 0);
+static _EIGEN_DECLARE_CONST_FAST_Packet2l(ZERO, 0);
+static _EIGEN_DECLARE_CONST_FAST_Packet2l(ONE, 1);
+
+static Packet2d p2d_ONE = { 1.0, 1.0 }; 
+static Packet2d p2d_ZERO_ = { -0.0, -0.0 };
+
+static Packet4i p4i_COUNTDOWN = { 0, 1, 2, 3 };
+static Packet2d p2d_COUNTDOWN = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet16uc>(p2d_ZERO), reinterpret_cast<Packet16uc>(p2d_ONE), 8));
+
+static Packet16uc p16uc_PSET64_HI = { 0,1,2,3, 4,5,6,7, 0,1,2,3, 4,5,6,7 };
+static Packet16uc p16uc_DUPLICATE32_HI = { 0,1,2,3, 0,1,2,3, 4,5,6,7, 4,5,6,7 };
+
+// Mask alignment
+#define _EIGEN_MASK_ALIGNMENT	0xfffffffffffffff0
+
+#define _EIGEN_ALIGNED_PTR(x)	((ptrdiff_t)(x) & _EIGEN_MASK_ALIGNMENT)
+
+// Handle endianness properly while loading constants
+// Define global static constants:
+
+static Packet16uc p16uc_FORWARD =   { 0,1,2,3, 4,5,6,7, 8,9,10,11, 12,13,14,15 };
+static Packet16uc p16uc_REVERSE32 = { 12,13,14,15, 8,9,10,11, 4,5,6,7, 0,1,2,3 };
+static Packet16uc p16uc_REVERSE64 = { 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };
+
+static Packet16uc p16uc_PSET32_WODD   = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 0), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 2), 8);//{ 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 };
+static Packet16uc p16uc_PSET32_WEVEN  = vec_sld(p16uc_DUPLICATE32_HI, (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 3), 8);//{ 4,5,6,7, 4,5,6,7, 12,13,14,15, 12,13,14,15 };
+/*static Packet16uc p16uc_HALF64_0_16 = vec_sld((Packet16uc)p4i_ZERO, vec_splat((Packet16uc) vec_abs(p4i_MINUS16), 3), 8);      //{ 0,0,0,0, 0,0,0,0, 16,16,16,16, 16,16,16,16};
+
+static Packet16uc p16uc_PSET64_HI = (Packet16uc) vec_mergeh((Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN);     //{ 0,1,2,3, 4,5,6,7, 0,1,2,3, 4,5,6,7 };*/
+static Packet16uc p16uc_PSET64_LO = (Packet16uc) vec_mergel((Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN);     //{ 8,9,10,11, 12,13,14,15, 8,9,10,11, 12,13,14,15 };
+/*static Packet16uc p16uc_TRANSPOSE64_HI = vec_add(p16uc_PSET64_HI, p16uc_HALF64_0_16);                                         //{ 0,1,2,3, 4,5,6,7, 16,17,18,19, 20,21,22,23};
+static Packet16uc p16uc_TRANSPOSE64_LO = vec_add(p16uc_PSET64_LO, p16uc_HALF64_0_16);                                         //{ 8,9,10,11, 12,13,14,15, 24,25,26,27, 28,29,30,31};*/
+static Packet16uc p16uc_TRANSPOSE64_HI = { 0,1,2,3, 4,5,6,7, 16,17,18,19, 20,21,22,23};
+static Packet16uc p16uc_TRANSPOSE64_LO = { 8,9,10,11, 12,13,14,15, 24,25,26,27, 28,29,30,31};
+
+//static Packet16uc p16uc_COMPLEX32_REV = vec_sld(p16uc_REVERSE32, p16uc_REVERSE32, 8);                                         //{ 4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11 };
+
+//static Packet16uc p16uc_COMPLEX32_REV2 = vec_sld(p16uc_FORWARD, p16uc_FORWARD, 8);                                            //{ 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };
+
+
+#if EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC
+  #define EIGEN_ZVECTOR_PREFETCH(ADDR) __builtin_prefetch(ADDR);
+#else
+  #define EIGEN_ZVECTOR_PREFETCH(ADDR) asm( "   pfd [%[addr]]\n" :: [addr] "r" (ADDR) : "cc" );
+#endif
+
+template<> struct packet_traits<int>    : default_packet_traits
+{
+  typedef Packet4i type;
+  typedef Packet4i half;
+  enum {
+    // FIXME check the Has*
+    Vectorizable = 1,
+    AlignedOnScalar = 1,
+    size = 4,
+    HasHalfPacket = 0,
+
+    // FIXME check the Has*
+    HasAdd  = 1,
+    HasSub  = 1,
+    HasMul  = 1,
+    HasDiv  = 1,
+    HasBlend = 1
+  };
+};
+
+template<> struct packet_traits<double> : default_packet_traits
+{
+  typedef Packet2d type;
+  typedef Packet2d half;
+  enum {
+    Vectorizable = 1,
+    AlignedOnScalar = 1,
+    size=2,
+    HasHalfPacket = 1,
+
+    // FIXME check the Has*
+    HasAdd  = 1,
+    HasSub  = 1,
+    HasMul  = 1,
+    HasDiv  = 1,
+    HasMin  = 1,
+    HasMax  = 1,
+    HasAbs  = 1,
+    HasSin  = 0,
+    HasCos  = 0,
+    HasLog  = 0,
+    HasExp  = 1,
+    HasSqrt = 1,
+    HasRsqrt = 1,
+    HasRound = 1,
+    HasFloor = 1,
+    HasCeil = 1,
+    HasNegate = 1,
+    HasBlend = 1
+  };
+};
+
+template<> struct unpacket_traits<Packet4i> { typedef int    type; enum {size=4, alignment=Aligned16}; typedef Packet4i half; };
+template<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2, alignment=Aligned16}; typedef Packet2d half; };
+
+inline std::ostream & operator <<(std::ostream & s, const Packet4i & v)
+{
+  Packet vt;
+  vt.v4i = v;
+  s << vt.i[0] << ", " << vt.i[1] << ", " << vt.i[2] << ", " << vt.i[3];
+  return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet4ui & v)
+{
+  Packet vt;
+  vt.v4ui = v;
+  s << vt.ui[0] << ", " << vt.ui[1] << ", " << vt.ui[2] << ", " << vt.ui[3];
+  return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet2l & v)
+{
+  Packet vt;
+  vt.v2l = v;
+  s << vt.l[0] << ", " << vt.l[1];
+  return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet2ul & v)
+{
+  Packet vt;
+  vt.v2ul = v;
+  s << vt.ul[0] << ", " << vt.ul[1] ;
+  return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet2d & v)
+{
+  Packet vt;
+  vt.v2d = v;
+  s << vt.d[0] << ", " << vt.d[1];
+  return s;
+}
+
+template<int Offset>
+struct palign_impl<Offset,Packet4i>
+{
+  static EIGEN_STRONG_INLINE void run(Packet4i& first, const Packet4i& second)
+  {
+    switch (Offset % 4) {
+    case 1:
+      first = vec_sld(first, second, 4); break;
+    case 2:
+      first = vec_sld(first, second, 8); break;
+    case 3:
+      first = vec_sld(first, second, 12); break;
+    }
+  }
+};
+
+template<int Offset>
+struct palign_impl<Offset,Packet2d>
+{
+  static EIGEN_STRONG_INLINE void run(Packet2d& first, const Packet2d& second)
+  {
+    if (Offset == 1)
+      first = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(first), reinterpret_cast<Packet4i>(second), 8));
+  }
+};
+
+template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int*     from)
+{
+  // FIXME: No intrinsic yet
+  EIGEN_DEBUG_ALIGNED_LOAD
+  Packet *vfrom;
+  vfrom = (Packet *) from;
+  return vfrom->v4i;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from)
+{
+  // FIXME: No intrinsic yet
+  EIGEN_DEBUG_ALIGNED_LOAD
+  Packet *vfrom;
+  vfrom = (Packet *) from;
+  return vfrom->v2d;
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet4i& from)
+{
+  // FIXME: No intrinsic yet
+  EIGEN_DEBUG_ALIGNED_STORE
+  Packet *vto;
+  vto = (Packet *) to;
+  vto->v4i = from;
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<double>(double*   to, const Packet2d& from)
+{
+  // FIXME: No intrinsic yet
+  EIGEN_DEBUG_ALIGNED_STORE
+  Packet *vto;
+  vto = (Packet *) to;
+  vto->v2d = from;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from)
+{
+  return vec_splats(from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) {
+  return vec_splats(from);
+}
+
+template<> EIGEN_STRONG_INLINE void
+pbroadcast4<Packet4i>(const int *a,
+                      Packet4i& a0, Packet4i& a1, Packet4i& a2, Packet4i& a3)
+{
+  a3 = pload<Packet4i>(a);
+  a0 = vec_splat(a3, 0);
+  a1 = vec_splat(a3, 1);
+  a2 = vec_splat(a3, 2);
+  a3 = vec_splat(a3, 3);
+}
+
+template<> EIGEN_STRONG_INLINE void
+pbroadcast4<Packet2d>(const double *a,
+                      Packet2d& a0, Packet2d& a1, Packet2d& a2, Packet2d& a3)
+{
+  a1 = pload<Packet2d>(a);
+  a0 = vec_splat(a1, 0);
+  a1 = vec_splat(a1, 1);
+  a3 = pload<Packet2d>(a+2);
+  a2 = vec_splat(a3, 0);
+  a3 = vec_splat(a3, 1);
+}
+
+template<> EIGEN_DEVICE_FUNC inline Packet4i pgather<int, Packet4i>(const int* from, Index stride)
+{
+  int EIGEN_ALIGN16 ai[4];
+  ai[0] = from[0*stride];
+  ai[1] = from[1*stride];
+  ai[2] = from[2*stride];
+  ai[3] = from[3*stride];
+ return pload<Packet4i>(ai);
+}
+
+template<> EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride)
+{
+  double EIGEN_ALIGN16 af[2];
+  af[0] = from[0*stride];
+  af[1] = from[1*stride];
+ return pload<Packet2d>(af);
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<int, Packet4i>(int* to, const Packet4i& from, Index stride)
+{
+  int EIGEN_ALIGN16 ai[4];
+  pstore<int>((int *)ai, from);
+  to[0*stride] = ai[0];
+  to[1*stride] = ai[1];
+  to[2*stride] = ai[2];
+  to[3*stride] = ai[3];
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride)
+{
+  double EIGEN_ALIGN16 af[2];
+  pstore<double>(af, from);
+  to[0*stride] = af[0];
+  to[1*stride] = af[1];
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return (a + b); }
+template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return (a + b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return (a - b); }
+template<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return (a - b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) { return (a * b); }
+template<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return (a * b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& a, const Packet4i& b) { return (a / b); }
+template<> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return (a / b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return (-a); }
+template<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) { return (-a); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return padd<Packet4i>(pmul<Packet4i>(a, b), c); }
+template<> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return vec_madd(a, b, c); }
+
+template<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a)    { return padd<Packet4i>(pset1<Packet4i>(a), p4i_COUNTDOWN); }
+template<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) { return padd<Packet2d>(pset1<Packet2d>(a), p2d_COUNTDOWN); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_min(a, b); }
+template<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_min(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_max(a, b); }
+template<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_max(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, b); }
+template<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_or(a, b); }
+template<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_or(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_xor(a, b); }
+template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_xor(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return pand<Packet4i>(a, vec_nor(b, b)); }
+template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, vec_nor(b, b)); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pround<Packet2d>(const Packet2d& a) { return vec_round(a); }
+template<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const  Packet2d& a) { return vec_ceil(a); }
+template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) { return vec_floor(a); }
+
+template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int*       from) { return pload<Packet4i>(from); }
+template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double*    from) { return pload<Packet2d>(from); }
+
+
+template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int*     from)
+{
+  Packet4i p = pload<Packet4i>(from);
+  return vec_perm(p, p, p16uc_DUPLICATE32_HI);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double*   from)
+{
+  Packet2d p = pload<Packet2d>(from);
+  return vec_perm(p, p, p16uc_PSET64_HI);
+}
+
+template<> EIGEN_STRONG_INLINE void pstoreu<int>(int*        to, const Packet4i& from) { pstore<int>(to, from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<double>(double*  to, const Packet2d& from) { pstore<double>(to, from); }
+
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*       addr) { EIGEN_ZVECTOR_PREFETCH(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { EIGEN_ZVECTOR_PREFETCH(addr); }
+
+template<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { int    EIGEN_ALIGN16 x[4]; pstore(x, a); return x[0]; }
+template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { double EIGEN_ALIGN16 x[2]; pstore(x, a); return x[0]; }
+
+template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a)
+{
+  return reinterpret_cast<Packet4i>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a)
+{
+  return reinterpret_cast<Packet2d>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE64));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vec_abs(a); }
+template<> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a) { return vec_abs(a); }
+
+template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
+{
+  Packet4i b, sum;
+  b   = vec_sld(a, a, 8);
+  sum = padd<Packet4i>(a, b);
+  b   = vec_sld(sum, sum, 4);
+  sum = padd<Packet4i>(sum, b);
+  return pfirst(sum);
+}
+
+template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)
+{
+  Packet2d b, sum;
+  b   = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(a), 8));
+  sum = padd<Packet2d>(a, b);
+  return pfirst(sum);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)
+{
+  Packet4i v[4], sum[4];
+
+  // It's easier and faster to transpose then add as columns
+  // Check: http://www.freevec.org/function/matrix_4x4_transpose_floats for explanation
+  // Do the transpose, first set of moves
+  v[0] = vec_mergeh(vecs[0], vecs[2]);
+  v[1] = vec_mergel(vecs[0], vecs[2]);
+  v[2] = vec_mergeh(vecs[1], vecs[3]);
+  v[3] = vec_mergel(vecs[1], vecs[3]);
+  // Get the resulting vectors
+  sum[0] = vec_mergeh(v[0], v[2]);
+  sum[1] = vec_mergel(v[0], v[2]);
+  sum[2] = vec_mergeh(v[1], v[3]);
+  sum[3] = vec_mergel(v[1], v[3]);
+
+  // Now do the summation:
+  // Lines 0+1
+  sum[0] = padd<Packet4i>(sum[0], sum[1]);
+  // Lines 2+3
+  sum[1] = padd<Packet4i>(sum[2], sum[3]);
+  // Add the results
+  sum[0] = padd<Packet4i>(sum[0], sum[1]);
+
+  return sum[0];
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)
+{
+  Packet2d v[2], sum;
+  v[0] = padd<Packet2d>(vecs[0], reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(vecs[0]), reinterpret_cast<Packet4ui>(vecs[0]), 8)));
+  v[1] = padd<Packet2d>(vecs[1], reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(vecs[1]), reinterpret_cast<Packet4ui>(vecs[1]), 8)));
+ 
+  sum = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(v[0]), reinterpret_cast<Packet4ui>(v[1]), 8));
+
+  return sum;
+}
+
+// Other reduction functions:
+// mul
+template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
+{
+  EIGEN_ALIGN16 int aux[4];
+  pstore(aux, a);
+  return aux[0] * aux[1] * aux[2] * aux[3];
+}
+
+template<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)
+{
+  return pfirst(pmul(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(a), 8))));
+}
+
+// min
+template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
+{
+  Packet4i b, res;
+  b   = pmin<Packet4i>(a, vec_sld(a, a, 8));
+  res = pmin<Packet4i>(b, vec_sld(b, b, 4));
+  return pfirst(res);
+}
+
+template<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a)
+{
+  return pfirst(pmin<Packet2d>(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(a), 8))));
+}
+
+// max
+template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
+{
+  Packet4i b, res;
+  b = pmax<Packet4i>(a, vec_sld(a, a, 8));
+  res = pmax<Packet4i>(b, vec_sld(b, b, 4));
+  return pfirst(res);
+}
+
+// max
+template<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a)
+{
+  return pfirst(pmax<Packet2d>(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(a), 8))));
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet4i,4>& kernel) {
+  Packet4i t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
+  Packet4i t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
+  Packet4i t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
+  Packet4i t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
+  kernel.packet[0] = vec_mergeh(t0, t2);
+  kernel.packet[1] = vec_mergel(t0, t2);
+  kernel.packet[2] = vec_mergeh(t1, t3);
+  kernel.packet[3] = vec_mergel(t1, t3);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet2d,2>& kernel) {
+  Packet2d t0 = vec_perm(kernel.packet[0], kernel.packet[1], p16uc_TRANSPOSE64_HI);
+  Packet2d t1 = vec_perm(kernel.packet[0], kernel.packet[1], p16uc_TRANSPOSE64_LO);
+  kernel.packet[0] = t0;
+  kernel.packet[1] = t1;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i pblend(const Selector<4>& ifPacket, const Packet4i& thenPacket, const Packet4i& elsePacket) {
+  Packet4ui select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3] };
+  Packet4ui mask = vec_cmpeq(select, reinterpret_cast<Packet4ui>(p4i_ONE));
+  return vec_sel(elsePacket, thenPacket, mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pblend(const Selector<2>& ifPacket, const Packet2d& thenPacket, const Packet2d& elsePacket) {
+  Packet2ul select = { ifPacket.select[0], ifPacket.select[1] };
+  Packet2ul mask = vec_cmpeq(select, reinterpret_cast<Packet2ul>(p2l_ONE));
+  return vec_sel(elsePacket, thenPacket, mask);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PACKET_MATH_ZVECTOR_H

Eigen/src/Core/functors/BinaryFunctors.h

@@ -238,7 +238,13 @@ template<typename Scalar> struct scalar_hypot_op {
 };
 template<typename Scalar>
 struct functor_traits<scalar_hypot_op<Scalar> > {
-  enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess=0 };
+  enum
+  {
+    Cost = 3 * NumTraits<Scalar>::AddCost +
+           2 * NumTraits<Scalar>::MulCost +
+           2 * NumTraits<Scalar>::template Div<false>::Cost,
+    PacketAccess = false
+  };
 };
 
 /** \internal
@@ -297,9 +303,10 @@ template<typename LhsScalar,typename RhsScalar> struct scalar_quotient_op {
 };
 template<typename LhsScalar,typename RhsScalar>
 struct functor_traits<scalar_quotient_op<LhsScalar,RhsScalar> > {
+  typedef typename scalar_quotient_op<LhsScalar,RhsScalar>::result_type result_type;
   enum {
-    Cost = (NumTraits<LhsScalar>::MulCost + NumTraits<RhsScalar>::MulCost), // rough estimate!
+    PacketAccess = scalar_quotient_op<LhsScalar,RhsScalar>::Vectorizable,
-    PacketAccess = scalar_quotient_op<LhsScalar,RhsScalar>::Vectorizable
+    Cost = NumTraits<result_type>::template Div<PacketAccess>::Cost
   };
 };
 
@@ -337,6 +344,55 @@ template<> struct functor_traits<scalar_boolean_or_op> {
   };
 };
 
+/** \internal
+  * \brief Template functor to compute the incomplete gamma function igamma(a, x)
+  *
+  * \sa class CwiseBinaryOp, Cwise::igamma
+  */
+template<typename Scalar> struct scalar_igamma_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_igamma_op)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& x) const {
+    using numext::igamma; return igamma(a, x);
+  }
+  template<typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const {
+    return internal::pigammac(a, x);
+  }
+};
+template<typename Scalar>
+struct functor_traits<scalar_igamma_op<Scalar> > {
+  enum {
+    // Guesstimate
+    Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasIGamma
+  };
+};
+
+
+/** \internal
+  * \brief Template functor to compute the complementary incomplete gamma function igammac(a, x)
+  *
+  * \sa class CwiseBinaryOp, Cwise::igammac
+  */
+template<typename Scalar> struct scalar_igammac_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_igammac_op)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& x) const {
+    using numext::igammac; return igammac(a, x);
+  }
+  template<typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const
+  {
+    return internal::pigammac(a, x);
+  }
+};
+template<typename Scalar>
+struct functor_traits<scalar_igammac_op<Scalar> > {
+  enum {
+    // Guesstimate
+    Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasIGammac
+  };
+};
 
 
 //---------- binary functors bound to a constant, thus appearing as a unary functor ----------
@@ -515,6 +571,10 @@ struct scalar_inverse_mult_op {
   { return internal::pdiv(pset1<Packet>(m_other),a); }
   Scalar m_other;
 };
+template<typename Scalar>
+struct functor_traits<scalar_inverse_mult_op<Scalar> >
+{ enum { PacketAccess = packet_traits<Scalar>::HasDiv, Cost = NumTraits<Scalar>::template Div<PacketAccess>::Cost }; };
+
 
 } // end namespace internal
 

Eigen/src/Core/functors/NullaryFunctors.h

@@ -37,7 +37,7 @@ template<typename Scalar>
 struct functor_traits<scalar_identity_op<Scalar> >
 { enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = false, IsRepeatable = true }; };
 
-template <typename Scalar, typename Packet, bool RandomAccess> struct linspaced_op_impl;
+template <typename Scalar, typename Packet, bool RandomAccess, bool IsInteger> struct linspaced_op_impl;
 
 // linear access for packet ops:
 // 1) initialization
@@ -48,12 +48,12 @@ template <typename Scalar, typename Packet, bool RandomAccess> struct linspaced_
 // TODO: Perhaps it's better to initialize lazily (so not in the constructor but in packetOp)
 //       in order to avoid the padd() in operator() ?
 template <typename Scalar, typename Packet>
-struct linspaced_op_impl<Scalar,Packet,false>
+struct linspaced_op_impl<Scalar,Packet,/*RandomAccess*/false,/*IsInteger*/false>
 {
-  linspaced_op_impl(const Scalar& low, const Scalar& step) :
+  linspaced_op_impl(const Scalar& low, const Scalar& high, Index num_steps) :
-  m_low(low), m_step(step),
+    m_low(low), m_step(num_steps==1 ? Scalar() : (high-low)/Scalar(num_steps-1)),
-  m_packetStep(pset1<Packet>(unpacket_traits<Packet>::size*step)),
+    m_packetStep(pset1<Packet>(unpacket_traits<Packet>::size*m_step)),
-  m_base(padd(pset1<Packet>(low), pmul(pset1<Packet>(step),plset<Packet>(-unpacket_traits<Packet>::size)))) {}
+    m_base(padd(pset1<Packet>(low), pmul(pset1<Packet>(m_step),plset<Packet>(-unpacket_traits<Packet>::size)))) {}
 
   template<typename Index>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (Index i) const 
@@ -75,11 +75,11 @@ struct linspaced_op_impl<Scalar,Packet,false>
 // 1) each step
 //   [low, ..., low] + ( [step, ..., step] * ( [i, ..., i] + [0, ..., size] ) )
 template <typename Scalar, typename Packet>
-struct linspaced_op_impl<Scalar,Packet,true>
+struct linspaced_op_impl<Scalar,Packet,/*RandomAccess*/true,/*IsInteger*/false>
 {
-  linspaced_op_impl(const Scalar& low, const Scalar& step) :
+  linspaced_op_impl(const Scalar& low, const Scalar& high, Index num_steps) :
-  m_low(low), m_step(step),
+    m_low(low), m_step(num_steps==1 ? Scalar() : (high-low)/Scalar(num_steps-1)),
-  m_lowPacket(pset1<Packet>(m_low)), m_stepPacket(pset1<Packet>(m_step)), m_interPacket(plset<Packet>(0)) {}
+    m_lowPacket(pset1<Packet>(m_low)), m_stepPacket(pset1<Packet>(m_step)), m_interPacket(plset<Packet>(0)) {}
 
   template<typename Index>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (Index i) const { return m_low+i*m_step; }
@@ -95,6 +95,31 @@ struct linspaced_op_impl<Scalar,Packet,true>
   const Packet m_interPacket;
 };
 
+template <typename Scalar, typename Packet>
+struct linspaced_op_impl<Scalar,Packet,/*RandomAccess*/true,/*IsInteger*/true>
+{
+  linspaced_op_impl(const Scalar& low, const Scalar& high, Index num_steps) :
+    m_low(low), m_length(high-low), m_divisor(num_steps==1?1:num_steps-1), m_interPacket(plset<Packet>(0))
+  {}
+
+  template<typename Index>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  const Scalar operator() (Index i) const {
+    return m_low + (m_length*Scalar(i))/m_divisor;
+  }
+
+  template<typename Index>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  const Packet packetOp(Index i) const {
+    return internal::padd(pset1<Packet>(m_low), pdiv(pmul(pset1<Packet>(m_length), padd(pset1<Packet>(Scalar(i)),m_interPacket)),
+                                                     pset1<Packet>(m_divisor))); }
+
+  const Scalar m_low;
+  const Scalar m_length;
+  const Index  m_divisor;
+  const Packet m_interPacket;
+};
+
 // ----- Linspace functor ----------------------------------------------------------------
 
 // Forward declaration (we default to random access which does not really give
@@ -102,10 +127,20 @@ struct linspaced_op_impl<Scalar,Packet,true>
 // nested expressions).
 template <typename Scalar, typename PacketType, bool RandomAccess = true> struct linspaced_op;
 template <typename Scalar, typename PacketType, bool RandomAccess> struct functor_traits< linspaced_op<Scalar,PacketType,RandomAccess> >
-{ enum { Cost = 1, PacketAccess = packet_traits<Scalar>::HasSetLinear, IsRepeatable = true }; };
+{
+  enum
+  {
+    Cost = 1,
+    PacketAccess =   packet_traits<Scalar>::HasSetLinear
+                  && ((!NumTraits<Scalar>::IsInteger) || packet_traits<Scalar>::HasDiv),
+    IsRepeatable = true
+  };
+};
 template <typename Scalar, typename PacketType, bool RandomAccess> struct linspaced_op
 {
-  linspaced_op(const Scalar& low, const Scalar& high, Index num_steps) : impl((num_steps==1 ? high : low), (num_steps==1 ? Scalar() : (high-low)/Scalar(num_steps-1))) {}
+  linspaced_op(const Scalar& low, const Scalar& high, Index num_steps)
+    : impl((num_steps==1 ? high : low),high,num_steps)
+  {}
 
   template<typename Index>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (Index i) const { return impl(i); }
@@ -134,7 +169,9 @@ template <typename Scalar, typename PacketType, bool RandomAccess> struct linspa
   // This proxy object handles the actual required temporaries, the different
   // implementations (random vs. sequential access) as well as the
   // correct piping to size 2/4 packet operations.
-  const linspaced_op_impl<Scalar,PacketType,RandomAccess> impl;
+  // As long as we don't have a Bresenham-like implementation for linear-access and integer types,
+  // we have to by-pass RandomAccess for integer types. See bug 698.
+  const linspaced_op_impl<Scalar,PacketType,(NumTraits<Scalar>::IsInteger?true:RandomAccess),NumTraits<Scalar>::IsInteger> impl;
 };
 
 // all functors allow linear access, except scalar_identity_op. So we fix here a quick meta

Eigen/src/Core/functors/UnaryFunctors.h

@@ -41,7 +41,7 @@ struct functor_traits<scalar_opposite_op<Scalar> >
 template<typename Scalar> struct scalar_abs_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_abs_op)
   typedef typename NumTraits<Scalar>::Real result_type;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { using std::abs; return abs(a); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return numext::abs(a); }
   template<typename Packet>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
   { return internal::pabs(a); }
@@ -73,7 +73,7 @@ template<typename Scalar, typename=void> struct abs_knowing_score
   EIGEN_EMPTY_STRUCT_CTOR(abs_knowing_score)
   typedef typename NumTraits<Scalar>::Real result_type;
   template<typename Score>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a, const Score&) const { using std::abs; return abs(a); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a, const Score&) const { return numext::abs(a); }
 };
 template<typename Scalar> struct abs_knowing_score<Scalar, typename scalar_score_coeff_op<Scalar>::Score_is_abs>
 {
@@ -230,7 +230,7 @@ struct functor_traits<scalar_imag_ref_op<Scalar> >
   */
 template<typename Scalar> struct scalar_exp_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_exp_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { using std::exp; return exp(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::exp(a); }
   template <typename Packet>
   EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pexp(a); }
 };
@@ -246,7 +246,7 @@ struct functor_traits<scalar_exp_op<Scalar> >
   */
 template<typename Scalar> struct scalar_log_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_log_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { using std::log; return log(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::log(a); }
   template <typename Packet>
   EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog(a); }
 };
@@ -276,7 +276,7 @@ struct functor_traits<scalar_log10_op<Scalar> >
   */
 template<typename Scalar> struct scalar_sqrt_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_sqrt_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { using std::sqrt; return sqrt(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::sqrt(a); }
   template <typename Packet>
   EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psqrt(a); }
 };
@@ -294,7 +294,7 @@ struct functor_traits<scalar_sqrt_op<Scalar> >
   */
 template<typename Scalar> struct scalar_rsqrt_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_rsqrt_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { using std::sqrt; return Scalar(1)/sqrt(a); }
+  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return Scalar(1)/numext::sqrt(a); }
   template <typename Packet>
   EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::prsqrt(a); }
 };
@@ -403,6 +403,143 @@ struct functor_traits<scalar_asin_op<Scalar> >
   };
 };
 
+
+/** \internal
+ * \brief Template functor to compute the natural log of the absolute
+ * value of Gamma of a scalar
+ * \sa class CwiseUnaryOp, Cwise::lgamma()
+ */
+template<typename Scalar> struct scalar_lgamma_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_lgamma_op)
+  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const {
+    using numext::lgamma; return lgamma(a);
+  }
+  typedef typename packet_traits<Scalar>::type Packet;
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plgamma(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_lgamma_op<Scalar> >
+{
+  enum {
+    // Guesstimate
+    Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasLGamma
+  };
+};
+
+/** \internal
+ * \brief Template functor to compute psi, the derivative of lgamma of a scalar.
+ * \sa class CwiseUnaryOp, Cwise::digamma()
+ */
+template<typename Scalar> struct scalar_digamma_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_digamma_op)
+  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const {
+    using numext::digamma; return digamma(a);
+  }
+  typedef typename packet_traits<Scalar>::type Packet;
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pdigamma(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_digamma_op<Scalar> >
+{
+  enum {
+    // Guesstimate
+    Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasDiGamma
+  };
+};
+    
+/** \internal
+ * \brief Template functor to compute the Riemann Zeta function of two arguments.
+ * \sa class CwiseUnaryOp, Cwise::zeta()
+ */
+template<typename Scalar> struct scalar_zeta_op {
+    EIGEN_EMPTY_STRUCT_CTOR(scalar_zeta_op)
+    EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& x, const Scalar& q) const {
+        using numext::zeta; return zeta(x, q);
+    }
+    typedef typename packet_traits<Scalar>::type Packet;
+    EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& x, const Packet& q) const { return internal::pzeta(x, q); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_zeta_op<Scalar> >
+{
+    enum {
+        // Guesstimate
+        Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
+        PacketAccess = packet_traits<Scalar>::HasZeta
+    };
+};
+
+/** \internal
+ * \brief Template functor to compute the polygamma function.
+ * \sa class CwiseUnaryOp, Cwise::polygamma()
+ */
+template<typename Scalar> struct scalar_polygamma_op {
+    EIGEN_EMPTY_STRUCT_CTOR(scalar_polygamma_op)
+    EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& n, const Scalar& x) const {
+        using numext::polygamma; return polygamma(n, x);
+    }
+    typedef typename packet_traits<Scalar>::type Packet;
+    EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& n, const Packet& x) const { return internal::ppolygamma(n, x); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_polygamma_op<Scalar> >
+{
+    enum {
+        // Guesstimate
+        Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
+        PacketAccess = packet_traits<Scalar>::HasPolygamma
+    };
+};
+
+/** \internal
+ * \brief Template functor to compute the Gauss error function of a
+ * scalar
+ * \sa class CwiseUnaryOp, Cwise::erf()
+ */
+template<typename Scalar> struct scalar_erf_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_erf_op)
+  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const {
+    using numext::erf; return erf(a);
+  }
+  typedef typename packet_traits<Scalar>::type Packet;
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::perf(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_erf_op<Scalar> >
+{
+  enum {
+    // Guesstimate
+    Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasErf
+  };
+};
+
+/** \internal
+ * \brief Template functor to compute the Complementary Error Function
+ * of a scalar
+ * \sa class CwiseUnaryOp, Cwise::erfc()
+ */
+template<typename Scalar> struct scalar_erfc_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_erfc_op)
+  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const {
+    using numext::erfc; return erfc(a);
+  }
+  typedef typename packet_traits<Scalar>::type Packet;
+  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::perfc(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_erfc_op<Scalar> >
+{
+  enum {
+    // Guesstimate
+    Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasErfc
+  };
+};
+
+
 /** \internal
   * \brief Template functor to compute the atan of a scalar
   * \sa class CwiseUnaryOp, ArrayBase::atan()
@@ -422,6 +559,7 @@ struct functor_traits<scalar_atan_op<Scalar> >
   };
 };
 
+
 /** \internal
   * \brief Template functor to compute the tanh of a scalar
   * \sa class CwiseUnaryOp, ArrayBase::tanh()
@@ -572,7 +710,7 @@ struct functor_traits<scalar_floor_op<Scalar> >
 template<typename Scalar> struct scalar_ceil_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_ceil_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::ceil(a); }
-  typedef typename packet_traits<Scalar>::type Packet;
+  template <typename Packet>
   EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pceil(a); }
 };
 template<typename Scalar>
@@ -660,10 +798,10 @@ struct functor_traits<scalar_boolean_not_op<Scalar> > {
   * \sa class CwiseUnaryOp, Cwise::sign()
   */
 template<typename Scalar,bool iscpx=(NumTraits<Scalar>::IsComplex!=0) > struct scalar_sign_op;
-template<typename Scalar> 
+template<typename Scalar>
 struct scalar_sign_op<Scalar,false> {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_sign_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const 
+  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const
   {
       return Scalar( (a>Scalar(0)) - (a<Scalar(0)) );
   }
@@ -671,17 +809,16 @@ struct scalar_sign_op<Scalar,false> {
   //template <typename Packet>
   //EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psign(a); }
 };
-template<typename Scalar> 
+template<typename Scalar>
 struct scalar_sign_op<Scalar,true> {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_sign_op)
-  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const 
+  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const
   {
-    using std::abs;
     typedef typename NumTraits<Scalar>::Real real_type;
-    real_type aa = abs(a);
+    real_type aa = numext::abs(a);
     if (aa==0)
-      return Scalar(0); 
+      return Scalar(0);
-    aa = 1./aa; 
+    aa = 1./aa;
     return Scalar(real(a)*aa, imag(a)*aa );
   }
   //TODO

Eigen/src/Core/products/GeneralBlockPanelKernel.h

@@ -178,7 +178,7 @@ void evaluateProductBlockingSizesHeuristic(Index& k, Index& m, Index& n, Index n
     // We also include a register-level block of the result (mx x nr).
     // (In an ideal world only the lhs panel would stay in L1)
     // Moreover, kc has to be a multiple of 8 to be compatible with loop peeling, leading to a maximum blocking size of:
-    const Index max_kc = ((l1-k_sub)/k_div) & (~(k_peeling-1));
+    const Index max_kc = std::max<Index>(((l1-k_sub)/k_div) & (~(k_peeling-1)),1);
     const Index old_k = k;
     if(k>max_kc)
     {
@@ -252,7 +252,7 @@ void evaluateProductBlockingSizesHeuristic(Index& k, Index& m, Index& n, Index n
         // we have both L2 and L3, and problem is small enough to be kept in L2
         // Let's choose m such that lhs's block fit in 1/3 of L2
         actual_lm = l2;
-        max_mc = 576;
+        max_mc = (std::min<Index>)(576,max_mc);
       }
       Index mc = (std::min<Index>)(actual_lm/(3*k*sizeof(LhsScalar)), max_mc);
       if (mc > Traits::mr) mc -= mc % Traits::mr;

Eigen/src/Core/products/GeneralMatrixMatrix.h

@@ -145,12 +145,9 @@ static void run(Index rows, Index cols, Index depth,
 
       // Release all the sub blocks A'_i of A' for the current thread,
       // i.e., we simply decrement the number of users by 1
-      #pragma omp critical
-      {
       for(Index i=0; i<threads; ++i)
         #pragma omp atomic
         info[i].users -= 1;
-      }
     }
   }
   else
@@ -355,9 +352,8 @@ class gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, M
       }
       else  // no l3 blocking
       {
-        Index m = this->m_mc;
         Index n = this->m_nc;
-        computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, m, n, num_threads);
+        computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, this->m_mc, n, num_threads);
       }
 
       m_sizeA = this->m_mc * this->m_kc;

Eigen/src/Core/products/GeneralMatrixMatrixTriangular.h

@@ -42,13 +42,14 @@ struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,
 {
   typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
   static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* lhs, Index lhsStride,
-                                      const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resStride, const ResScalar& alpha)
+                                      const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resStride,
+                                      const ResScalar& alpha, level3_blocking<LhsScalar,RhsScalar>& blocking)
   {
     general_matrix_matrix_triangular_product<Index,
         RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,
         LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,
         ColMajor, UpLo==Lower?Upper:Lower>
-      ::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha);
+      ::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha,blocking);
   }
 };
 
@@ -58,7 +59,8 @@ struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,
 {
   typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
   static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* _lhs, Index lhsStride,
-                                      const RhsScalar* _rhs, Index rhsStride, ResScalar* _res, Index resStride, const ResScalar& alpha)
+                                      const RhsScalar* _rhs, Index rhsStride, ResScalar* _res, Index resStride,
+                                      const ResScalar& alpha, level3_blocking<LhsScalar,RhsScalar>& blocking)
   {
     typedef gebp_traits<LhsScalar,RhsScalar> Traits;
 
@@ -69,16 +71,18 @@ struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,
     RhsMapper rhs(_rhs,rhsStride);
     ResMapper res(_res, resStride);
 
-    Index kc = depth; // cache block size along the K direction
+    Index kc = blocking.kc();
-    Index mc = size;  // cache block size along the M direction
+    Index mc = (std::min)(size,blocking.mc());
-    Index nc = size;  // cache block size along the N direction
+
-    computeProductBlockingSizes<LhsScalar,RhsScalar>(kc, mc, nc, 1);
     // !!! mc must be a multiple of nr:
     if(mc > Traits::nr)
       mc = (mc/Traits::nr)*Traits::nr;
 
-    ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, kc*mc, 0);
+    std::size_t sizeA = kc*mc;
-    ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, kc*size, 0);
+    std::size_t sizeB = kc*size;
+
+    ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA());
+    ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB());
 
     gemm_pack_lhs<LhsScalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
     gemm_pack_rhs<RhsScalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs;
@@ -136,7 +140,7 @@ struct tribb_kernel
   typedef typename Traits::ResScalar ResScalar;
 
   enum {
-    BlockSize  = EIGEN_PLAIN_ENUM_MAX(mr,nr)
+    BlockSize  = meta_least_common_multiple<EIGEN_PLAIN_ENUM_MAX(mr,nr),EIGEN_PLAIN_ENUM_MIN(mr,nr)>::ret
   };
   void operator()(ResScalar* _res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, const ResScalar& alpha)
   {
@@ -256,13 +260,27 @@ struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,false>
 
     typename ProductType::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
 
+    enum {
+      IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0,
+      LhsIsRowMajor = _ActualLhs::Flags&RowMajorBit ? 1 : 0,
+      RhsIsRowMajor = _ActualRhs::Flags&RowMajorBit ? 1 : 0
+    };
+
+    Index size = mat.cols();
+    Index depth = actualLhs.cols();
+
+    typedef internal::gemm_blocking_space<IsRowMajor ? RowMajor : ColMajor,typename Lhs::Scalar,typename Rhs::Scalar,
+          MatrixType::MaxColsAtCompileTime, MatrixType::MaxColsAtCompileTime, _ActualRhs::MaxColsAtCompileTime> BlockingType;
+
+    BlockingType blocking(size, size, depth, 1, false);
+
     internal::general_matrix_matrix_triangular_product<Index,
-      typename Lhs::Scalar, _ActualLhs::Flags&RowMajorBit ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
+      typename Lhs::Scalar, LhsIsRowMajor ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
-      typename Rhs::Scalar, _ActualRhs::Flags&RowMajorBit ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
+      typename Rhs::Scalar, RhsIsRowMajor ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
-      MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor, UpLo>
+      IsRowMajor ? RowMajor : ColMajor, UpLo>
-      ::run(mat.cols(), actualLhs.cols(),
+      ::run(size, depth,
             &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &actualRhs.coeffRef(0,0), actualRhs.outerStride(),
-            mat.data(), mat.outerStride(), actualAlpha);
+            mat.data(), mat.outerStride(), actualAlpha, blocking);
   }
 };
 

Eigen/src/Core/products/GeneralMatrixMatrixTriangular_BLAS.h

@@ -25,13 +25,13 @@
  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 
  ********************************************************************************
- *   Content : Eigen bindings to Intel(R) MKL
+ *   Content : Eigen bindings to BLAS F77
  *   Level 3 BLAS SYRK/HERK implementation.
  ********************************************************************************
 */
 
-#ifndef EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_MKL_H
+#ifndef EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_BLAS_H
-#define EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_MKL_H
+#define EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_BLAS_H
 
 namespace Eigen { 
 
@@ -44,34 +44,35 @@ struct general_matrix_matrix_rankupdate :
 
 
 // try to go to BLAS specialization
-#define EIGEN_MKL_RANKUPDATE_SPECIALIZE(Scalar) \
+#define EIGEN_BLAS_RANKUPDATE_SPECIALIZE(Scalar) \
 template <typename Index, int LhsStorageOrder, bool ConjugateLhs, \
                           int RhsStorageOrder, bool ConjugateRhs, int  UpLo> \
 struct general_matrix_matrix_triangular_product<Index,Scalar,LhsStorageOrder,ConjugateLhs, \
                Scalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Specialized> { \
   static EIGEN_STRONG_INLINE void run(Index size, Index depth,const Scalar* lhs, Index lhsStride, \
-                          const Scalar* rhs, Index rhsStride, Scalar* res, Index resStride, Scalar alpha) \
+                          const Scalar* rhs, Index rhsStride, Scalar* res, Index resStride, Scalar alpha, level3_blocking<Scalar, Scalar>& blocking) \
   { \
     if (lhs==rhs) { \
       general_matrix_matrix_rankupdate<Index,Scalar,LhsStorageOrder,ConjugateLhs,ColMajor,UpLo> \
-      ::run(size,depth,lhs,lhsStride,rhs,rhsStride,res,resStride,alpha); \
+      ::run(size,depth,lhs,lhsStride,rhs,rhsStride,res,resStride,alpha,blocking); \
     } else { \
       general_matrix_matrix_triangular_product<Index, \
         Scalar, LhsStorageOrder, ConjugateLhs, \
         Scalar, RhsStorageOrder, ConjugateRhs, \
         ColMajor, UpLo, BuiltIn> \
-      ::run(size,depth,lhs,lhsStride,rhs,rhsStride,res,resStride,alpha); \
+      ::run(size,depth,lhs,lhsStride,rhs,rhsStride,res,resStride,alpha,blocking); \
     } \
   } \
 };
 
-EIGEN_MKL_RANKUPDATE_SPECIALIZE(double)
+EIGEN_BLAS_RANKUPDATE_SPECIALIZE(double)
-//EIGEN_MKL_RANKUPDATE_SPECIALIZE(dcomplex)
+EIGEN_BLAS_RANKUPDATE_SPECIALIZE(float)
-EIGEN_MKL_RANKUPDATE_SPECIALIZE(float)
+// TODO handle complex cases
-//EIGEN_MKL_RANKUPDATE_SPECIALIZE(scomplex)
+// EIGEN_BLAS_RANKUPDATE_SPECIALIZE(dcomplex)
+// EIGEN_BLAS_RANKUPDATE_SPECIALIZE(scomplex)
 
 // SYRK for float/double
-#define EIGEN_MKL_RANKUPDATE_R(EIGTYPE, MKLTYPE, MKLFUNC) \
+#define EIGEN_BLAS_RANKUPDATE_R(EIGTYPE, BLASTYPE, BLASFUNC) \
 template <typename Index, int AStorageOrder, bool ConjugateA, int  UpLo> \
 struct general_matrix_matrix_rankupdate<Index,EIGTYPE,AStorageOrder,ConjugateA,ColMajor,UpLo> { \
   enum { \
@@ -80,23 +81,19 @@ struct general_matrix_matrix_rankupdate<Index,EIGTYPE,AStorageOrder,ConjugateA,C
     conjA = ((AStorageOrder==ColMajor) && ConjugateA) ? 1 : 0 \
   }; \
   static EIGEN_STRONG_INLINE void run(Index size, Index depth,const EIGTYPE* lhs, Index lhsStride, \
-                          const EIGTYPE* rhs, Index rhsStride, EIGTYPE* res, Index resStride, EIGTYPE alpha) \
+                          const EIGTYPE* /*rhs*/, Index /*rhsStride*/, EIGTYPE* res, Index resStride, EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \
   { \
   /* typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs;*/ \
 \
-   MKL_INT lda=lhsStride, ldc=resStride, n=size, k=depth; \
+   BlasIndex lda=convert_index<BlasIndex>(lhsStride), ldc=convert_index<BlasIndex>(resStride), n=convert_index<BlasIndex>(size), k=convert_index<BlasIndex>(depth); \
    char uplo=(IsLower) ? 'L' : 'U', trans=(AStorageOrder==RowMajor) ? 'T':'N'; \
-   MKLTYPE alpha_, beta_; \
+   EIGTYPE beta; \
-\
+   BLASFUNC(&uplo, &trans, &n, &k, &numext::real_ref(alpha), lhs, &lda, &numext::real_ref(beta), res, &ldc); \
-/* Set alpha_ & beta_ */ \
-   assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); \
-   assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(beta_, EIGTYPE(1)); \
-   MKLFUNC(&uplo, &trans, &n, &k, &alpha_, lhs, &lda, &beta_, res, &ldc); \
   } \
 };
 
 // HERK for complex data
-#define EIGEN_MKL_RANKUPDATE_C(EIGTYPE, MKLTYPE, RTYPE, MKLFUNC) \
+#define EIGEN_BLAS_RANKUPDATE_C(EIGTYPE, BLASTYPE, RTYPE, BLASFUNC) \
 template <typename Index, int AStorageOrder, bool ConjugateA, int  UpLo> \
 struct general_matrix_matrix_rankupdate<Index,EIGTYPE,AStorageOrder,ConjugateA,ColMajor,UpLo> { \
   enum { \
@@ -105,18 +102,15 @@ struct general_matrix_matrix_rankupdate<Index,EIGTYPE,AStorageOrder,ConjugateA,C
     conjA = (((AStorageOrder==ColMajor) && ConjugateA) || ((AStorageOrder==RowMajor) && !ConjugateA)) ? 1 : 0 \
   }; \
   static EIGEN_STRONG_INLINE void run(Index size, Index depth,const EIGTYPE* lhs, Index lhsStride, \
-                          const EIGTYPE* rhs, Index rhsStride, EIGTYPE* res, Index resStride, EIGTYPE alpha) \
+                          const EIGTYPE* /*rhs*/, Index /*rhsStride*/, EIGTYPE* res, Index resStride, EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \
   { \
    typedef Matrix<EIGTYPE, Dynamic, Dynamic, AStorageOrder> MatrixType; \
 \
-   MKL_INT lda=lhsStride, ldc=resStride, n=size, k=depth; \
+   BlasIndex lda=convert_index<BlasIndex>(lhsStride), ldc=convert_index<BlasIndex>(resStride), n=convert_index<BlasIndex>(size), k=convert_index<BlasIndex>(depth); \
    char uplo=(IsLower) ? 'L' : 'U', trans=(AStorageOrder==RowMajor) ? 'C':'N'; \
    RTYPE alpha_, beta_; \
    const EIGTYPE* a_ptr; \
 \
-/* Set alpha_ & beta_ */ \
-/*   assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); */\
-/*   assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(beta_, EIGTYPE(1));*/ \
    alpha_ = alpha.real(); \
    beta_ = 1.0; \
 /* Copy with conjugation in some cases*/ \
@@ -127,20 +121,21 @@ struct general_matrix_matrix_rankupdate<Index,EIGTYPE,AStorageOrder,ConjugateA,C
      lda = a.outerStride(); \
      a_ptr = a.data(); \
    } else a_ptr=lhs; \
-   MKLFUNC(&uplo, &trans, &n, &k, &alpha_, (MKLTYPE*)a_ptr, &lda, &beta_, (MKLTYPE*)res, &ldc); \
+   BLASFUNC(&uplo, &trans, &n, &k, &alpha_, (BLASTYPE*)a_ptr, &lda, &beta_, (BLASTYPE*)res, &ldc); \
   } \
 };
 
 
-EIGEN_MKL_RANKUPDATE_R(double, double, dsyrk)
+EIGEN_BLAS_RANKUPDATE_R(double, double, dsyrk_)
-EIGEN_MKL_RANKUPDATE_R(float,  float,  ssyrk)
+EIGEN_BLAS_RANKUPDATE_R(float,  float,  ssyrk_)
 
-//EIGEN_MKL_RANKUPDATE_C(dcomplex, MKL_Complex16, double, zherk)
+// TODO hanlde complex cases
-//EIGEN_MKL_RANKUPDATE_C(scomplex, MKL_Complex8,  double, cherk)
+// EIGEN_BLAS_RANKUPDATE_C(dcomplex, double, double, zherk_)
+// EIGEN_BLAS_RANKUPDATE_C(scomplex, float,  float, cherk_)
 
 
 } // end namespace internal
 
 } // end namespace Eigen
 
-#endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_MKL_H
+#endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_BLAS_H

Eigen/src/Core/products/GeneralMatrixMatrix_BLAS.h

@@ -25,13 +25,13 @@
  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 
  ********************************************************************************
- *   Content : Eigen bindings to Intel(R) MKL
+ *   Content : Eigen bindings to BLAS F77
  *   General matrix-matrix product functionality based on ?GEMM.
  ********************************************************************************
 */
 
-#ifndef EIGEN_GENERAL_MATRIX_MATRIX_MKL_H
+#ifndef EIGEN_GENERAL_MATRIX_MATRIX_BLAS_H
-#define EIGEN_GENERAL_MATRIX_MATRIX_MKL_H
+#define EIGEN_GENERAL_MATRIX_MATRIX_BLAS_H
 
 namespace Eigen { 
 
@@ -46,7 +46,7 @@ namespace internal {
 
 // gemm specialization
 
-#define GEMM_SPECIALIZATION(EIGTYPE, EIGPREFIX, MKLTYPE, MKLPREFIX) \
+#define GEMM_SPECIALIZATION(EIGTYPE, EIGPREFIX, BLASTYPE, BLASPREFIX) \
 template< \
   typename Index, \
   int LhsStorageOrder, bool ConjugateLhs, \
@@ -66,55 +66,50 @@ static void run(Index rows, Index cols, Index depth, \
   using std::conj; \
 \
   char transa, transb; \
-  MKL_INT m, n, k, lda, ldb, ldc; \
+  BlasIndex m, n, k, lda, ldb, ldc; \
   const EIGTYPE *a, *b; \
-  MKLTYPE alpha_, beta_; \
+  EIGTYPE beta(1); \
   MatrixX##EIGPREFIX a_tmp, b_tmp; \
-  EIGTYPE myone(1);\
 \
 /* Set transpose options */ \
   transa = (LhsStorageOrder==RowMajor) ? ((ConjugateLhs) ? 'C' : 'T') : 'N'; \
   transb = (RhsStorageOrder==RowMajor) ? ((ConjugateRhs) ? 'C' : 'T') : 'N'; \
 \
 /* Set m, n, k */ \
-  m = (MKL_INT)rows;  \
+  m = convert_index<BlasIndex>(rows);  \
-  n = (MKL_INT)cols;  \
+  n = convert_index<BlasIndex>(cols);  \
-  k = (MKL_INT)depth; \
+  k = convert_index<BlasIndex>(depth); \
-\
-/* Set alpha_ & beta_ */ \
-  assign_scalar_eig2mkl(alpha_, alpha); \
-  assign_scalar_eig2mkl(beta_, myone); \
 \
 /* Set lda, ldb, ldc */ \
-  lda = (MKL_INT)lhsStride; \
+  lda = convert_index<BlasIndex>(lhsStride); \
-  ldb = (MKL_INT)rhsStride; \
+  ldb = convert_index<BlasIndex>(rhsStride); \
-  ldc = (MKL_INT)resStride; \
+  ldc = convert_index<BlasIndex>(resStride); \
 \
 /* Set a, b, c */ \
   if ((LhsStorageOrder==ColMajor) && (ConjugateLhs)) { \
     Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,m,k,OuterStride<>(lhsStride)); \
     a_tmp = lhs.conjugate(); \
     a = a_tmp.data(); \
-    lda = a_tmp.outerStride(); \
+    lda = convert_index<BlasIndex>(a_tmp.outerStride()); \
   } else a = _lhs; \
 \
   if ((RhsStorageOrder==ColMajor) && (ConjugateRhs)) { \
     Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,k,n,OuterStride<>(rhsStride)); \
     b_tmp = rhs.conjugate(); \
     b = b_tmp.data(); \
-    ldb = b_tmp.outerStride(); \
+    ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \
   } else b = _rhs; \
 \
-  MKLPREFIX##gemm(&transa, &transb, &m, &n, &k, &alpha_, (const MKLTYPE*)a, &lda, (const MKLTYPE*)b, &ldb, &beta_, (MKLTYPE*)res, &ldc); \
+  BLASPREFIX##gemm_(&transa, &transb, &m, &n, &k, &numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)b, &ldb, &numext::real_ref(beta), (BLASTYPE*)res, &ldc); \
 }};
 
-GEMM_SPECIALIZATION(double,   d,  double,        d)
+GEMM_SPECIALIZATION(double,   d,  double, d)
-GEMM_SPECIALIZATION(float,    f,  float,         s)
+GEMM_SPECIALIZATION(float,    f,  float,  s)
-GEMM_SPECIALIZATION(dcomplex, cd, MKL_Complex16, z)
+GEMM_SPECIALIZATION(dcomplex, cd, double, z)
-GEMM_SPECIALIZATION(scomplex, cf, MKL_Complex8,  c)
+GEMM_SPECIALIZATION(scomplex, cf, float,  c)
 
 } // end namespase internal
 
 } // end namespace Eigen
 
-#endif // EIGEN_GENERAL_MATRIX_MATRIX_MKL_H
+#endif // EIGEN_GENERAL_MATRIX_MATRIX_BLAS_H

Eigen/src/Core/products/GeneralMatrixVector_BLAS.h

@@ -25,13 +25,13 @@
  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 
  ********************************************************************************
- *   Content : Eigen bindings to Intel(R) MKL
+ *   Content : Eigen bindings to BLAS F77
  *   General matrix-vector product functionality based on ?GEMV.
  ********************************************************************************
 */
 
-#ifndef EIGEN_GENERAL_MATRIX_VECTOR_MKL_H
+#ifndef EIGEN_GENERAL_MATRIX_VECTOR_BLAS_H
-#define EIGEN_GENERAL_MATRIX_VECTOR_MKL_H
+#define EIGEN_GENERAL_MATRIX_VECTOR_BLAS_H
 
 namespace Eigen { 
 
@@ -49,7 +49,7 @@ namespace internal {
 template<typename Index, typename LhsScalar, int StorageOrder, bool ConjugateLhs, typename RhsScalar, bool ConjugateRhs>
 struct general_matrix_vector_product_gemv;
 
-#define EIGEN_MKL_GEMV_SPECIALIZE(Scalar) \
+#define EIGEN_BLAS_GEMV_SPECIALIZE(Scalar) \
 template<typename Index, bool ConjugateLhs, bool ConjugateRhs> \
 struct general_matrix_vector_product<Index,Scalar,const_blas_data_mapper<Scalar,Index,ColMajor>,ColMajor,ConjugateLhs,Scalar,const_blas_data_mapper<Scalar,Index,RowMajor>,ConjugateRhs,Specialized> { \
 static void run( \
@@ -80,12 +80,12 @@ static void run( \
 } \
 }; \
 
-EIGEN_MKL_GEMV_SPECIALIZE(double)
+EIGEN_BLAS_GEMV_SPECIALIZE(double)
-EIGEN_MKL_GEMV_SPECIALIZE(float)
+EIGEN_BLAS_GEMV_SPECIALIZE(float)
-EIGEN_MKL_GEMV_SPECIALIZE(dcomplex)
+EIGEN_BLAS_GEMV_SPECIALIZE(dcomplex)
-EIGEN_MKL_GEMV_SPECIALIZE(scomplex)
+EIGEN_BLAS_GEMV_SPECIALIZE(scomplex)
 
-#define EIGEN_MKL_GEMV_SPECIALIZATION(EIGTYPE,MKLTYPE,MKLPREFIX) \
+#define EIGEN_BLAS_GEMV_SPECIALIZATION(EIGTYPE,BLASTYPE,BLASPREFIX) \
 template<typename Index, int LhsStorageOrder, bool ConjugateLhs, bool ConjugateRhs> \
 struct general_matrix_vector_product_gemv<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,ConjugateRhs> \
 { \
@@ -97,16 +97,15 @@ static void run( \
   const EIGTYPE* rhs, Index rhsIncr, \
   EIGTYPE* res, Index resIncr, EIGTYPE alpha) \
 { \
-  MKL_INT m=rows, n=cols, lda=lhsStride, incx=rhsIncr, incy=resIncr; \
+  BlasIndex m=convert_index<BlasIndex>(rows), n=convert_index<BlasIndex>(cols), \
-  MKLTYPE alpha_, beta_; \
+            lda=convert_index<BlasIndex>(lhsStride), incx=convert_index<BlasIndex>(rhsIncr), incy=convert_index<BlasIndex>(resIncr); \
-  const EIGTYPE *x_ptr, myone(1); \
+  const EIGTYPE beta(1); \
+  const EIGTYPE *x_ptr; \
   char trans=(LhsStorageOrder==ColMajor) ? 'N' : (ConjugateLhs) ? 'C' : 'T'; \
   if (LhsStorageOrder==RowMajor) { \
-    m=cols; \
+    m = convert_index<BlasIndex>(cols); \
-    n=rows; \
+    n = convert_index<BlasIndex>(rows); \
   }\
-  assign_scalar_eig2mkl(alpha_, alpha); \
-  assign_scalar_eig2mkl(beta_, myone); \
   GEMVVector x_tmp; \
   if (ConjugateRhs) { \
     Map<const GEMVVector, 0, InnerStride<> > map_x(rhs,cols,1,InnerStride<>(incx)); \
@@ -114,17 +113,17 @@ static void run( \
     x_ptr=x_tmp.data(); \
     incx=1; \
   } else x_ptr=rhs; \
-  MKLPREFIX##gemv(&trans, &m, &n, &alpha_, (const MKLTYPE*)lhs, &lda, (const MKLTYPE*)x_ptr, &incx, &beta_, (MKLTYPE*)res, &incy); \
+  BLASPREFIX##gemv_(&trans, &m, &n, &numext::real_ref(alpha), (const BLASTYPE*)lhs, &lda, (const BLASTYPE*)x_ptr, &incx, &numext::real_ref(beta), (BLASTYPE*)res, &incy); \
 }\
 };
 
-EIGEN_MKL_GEMV_SPECIALIZATION(double,   double,        d)
+EIGEN_BLAS_GEMV_SPECIALIZATION(double,   double, d)
-EIGEN_MKL_GEMV_SPECIALIZATION(float,    float,         s)
+EIGEN_BLAS_GEMV_SPECIALIZATION(float,    float,  s)
-EIGEN_MKL_GEMV_SPECIALIZATION(dcomplex, MKL_Complex16, z)
+EIGEN_BLAS_GEMV_SPECIALIZATION(dcomplex, double, z)
-EIGEN_MKL_GEMV_SPECIALIZATION(scomplex, MKL_Complex8,  c)
+EIGEN_BLAS_GEMV_SPECIALIZATION(scomplex, float,  c)
 
 } // end namespase internal
 
 } // end namespace Eigen
 
-#endif // EIGEN_GENERAL_MATRIX_VECTOR_MKL_H
+#endif // EIGEN_GENERAL_MATRIX_VECTOR_BLAS_H

Eigen/src/Core/products/SelfadjointMatrixMatrix.h

@@ -291,7 +291,7 @@ struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,LhsSelfAdjoint,Co
     const Scalar* lhs, Index lhsStride,
     const Scalar* rhs, Index rhsStride,
     Scalar* res,       Index resStride,
-    const Scalar& alpha)
+    const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
   {
     product_selfadjoint_matrix<Scalar, Index,
       EIGEN_LOGICAL_XOR(RhsSelfAdjoint,RhsStorageOrder==RowMajor) ? ColMajor : RowMajor,
@@ -299,7 +299,7 @@ struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,LhsSelfAdjoint,Co
       EIGEN_LOGICAL_XOR(LhsSelfAdjoint,LhsStorageOrder==RowMajor) ? ColMajor : RowMajor,
       LhsSelfAdjoint, NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(LhsSelfAdjoint,ConjugateLhs),
       ColMajor>
-      ::run(cols, rows,  rhs, rhsStride,  lhs, lhsStride,  res, resStride,  alpha);
+      ::run(cols, rows,  rhs, rhsStride,  lhs, lhsStride,  res, resStride,  alpha, blocking);
   }
 };
 
@@ -314,7 +314,7 @@ struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,true,ConjugateLhs
     const Scalar* _lhs, Index lhsStride,
     const Scalar* _rhs, Index rhsStride,
     Scalar* res,        Index resStride,
-    const Scalar& alpha);
+    const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);
 };
 
 template <typename Scalar, typename Index,
@@ -325,7 +325,7 @@ EIGEN_DONT_INLINE void product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,t
     const Scalar* _lhs, Index lhsStride,
     const Scalar* _rhs, Index rhsStride,
     Scalar* _res,        Index resStride,
-    const Scalar& alpha)
+    const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
   {
     Index size = rows;
 
@@ -340,17 +340,14 @@ EIGEN_DONT_INLINE void product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,t
     RhsMapper rhs(_rhs,rhsStride);
     ResMapper res(_res, resStride);
 
-    Index kc = size;  // cache block size along the K direction
+    Index kc = blocking.kc();                   // cache block size along the K direction
-    Index mc = rows;  // cache block size along the M direction
+    Index mc = (std::min)(rows,blocking.mc());  // cache block size along the M direction
-    Index nc = cols;  // cache block size along the N direction
+    // kc must be smaller than mc
-    computeProductBlockingSizes<Scalar,Scalar>(kc, mc, nc, 1);
-    // kc must smaller than mc
     kc = (std::min)(kc,mc);
-
+    std::size_t sizeA = kc*mc;
     std::size_t sizeB = kc*cols;
-    ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0);
+    ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
-    ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0);
+    ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
-    Scalar* blockB = allocatedBlockB;
 
     gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
     symm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
@@ -410,7 +407,7 @@ struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,false,ConjugateLh
     const Scalar* _lhs, Index lhsStride,
     const Scalar* _rhs, Index rhsStride,
     Scalar* res,        Index resStride,
-    const Scalar& alpha);
+    const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);
 };
 
 template <typename Scalar, typename Index,
@@ -421,7 +418,7 @@ EIGEN_DONT_INLINE void product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,f
     const Scalar* _lhs, Index lhsStride,
     const Scalar* _rhs, Index rhsStride,
     Scalar* _res,        Index resStride,
-    const Scalar& alpha)
+    const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
   {
     Index size = cols;
 
@@ -432,14 +429,12 @@ EIGEN_DONT_INLINE void product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,f
     LhsMapper lhs(_lhs,lhsStride);
     ResMapper res(_res,resStride);
 
-    Index kc = size;  // cache block size along the K direction
+    Index kc = blocking.kc();                   // cache block size along the K direction
-    Index mc = rows;  // cache block size along the M direction
+    Index mc = (std::min)(rows,blocking.mc());  // cache block size along the M direction
-    Index nc = cols;  // cache block size along the N direction
+    std::size_t sizeA = kc*mc;
-    computeProductBlockingSizes<Scalar,Scalar>(kc, mc, nc, 1);
     std::size_t sizeB = kc*cols;
-    ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0);
+    ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
-    ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0);
+    ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
-    Scalar* blockB = allocatedBlockB;
 
     gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
     gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
@@ -498,6 +493,11 @@ struct selfadjoint_product_impl<Lhs,LhsMode,false,Rhs,RhsMode,false>
     Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(a_lhs)
                                * RhsBlasTraits::extractScalarFactor(a_rhs);
 
+    typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
+              Lhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxColsAtCompileTime,1> BlockingType;
+
+    BlockingType blocking(lhs.rows(), rhs.cols(), lhs.cols(), 1, false);
+
     internal::product_selfadjoint_matrix<Scalar, Index,
       EIGEN_LOGICAL_XOR(LhsIsUpper,internal::traits<Lhs>::Flags &RowMajorBit) ? RowMajor : ColMajor, LhsIsSelfAdjoint,
       NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(LhsIsUpper,bool(LhsBlasTraits::NeedToConjugate)),
@@ -509,7 +509,7 @@ struct selfadjoint_product_impl<Lhs,LhsMode,false,Rhs,RhsMode,false>
         &lhs.coeffRef(0,0), lhs.outerStride(),  // lhs info
         &rhs.coeffRef(0,0), rhs.outerStride(),  // rhs info
         &dst.coeffRef(0,0), dst.outerStride(),  // result info
-        actualAlpha                             // alpha
+        actualAlpha, blocking                   // alpha
       );
   }
 };

Eigen/src/Core/products/SelfadjointMatrixMatrix_BLAS.h

@@ -25,13 +25,13 @@
  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 //
  ********************************************************************************
- *   Content : Eigen bindings to Intel(R) MKL
+ *   Content : Eigen bindings to BLAS F77
  *   Self adjoint matrix * matrix product functionality based on ?SYMM/?HEMM.
  ********************************************************************************
 */
 
-#ifndef EIGEN_SELFADJOINT_MATRIX_MATRIX_MKL_H
+#ifndef EIGEN_SELFADJOINT_MATRIX_MATRIX_BLAS_H
-#define EIGEN_SELFADJOINT_MATRIX_MATRIX_MKL_H
+#define EIGEN_SELFADJOINT_MATRIX_MATRIX_BLAS_H
 
 namespace Eigen { 
 
@@ -40,7 +40,7 @@ namespace internal {
 
 /* Optimized selfadjoint matrix * matrix (?SYMM/?HEMM) product */
 
-#define EIGEN_MKL_SYMM_L(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
+#define EIGEN_BLAS_SYMM_L(EIGTYPE, BLASTYPE, EIGPREFIX, BLASPREFIX) \
 template <typename Index, \
           int LhsStorageOrder, bool ConjugateLhs, \
           int RhsStorageOrder, bool ConjugateRhs> \
@@ -52,28 +52,23 @@ struct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,true,ConjugateLh
     const EIGTYPE* _lhs, Index lhsStride, \
     const EIGTYPE* _rhs, Index rhsStride, \
     EIGTYPE* res,        Index resStride, \
-    EIGTYPE alpha) \
+    EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \
   { \
     char side='L', uplo='L'; \
-    MKL_INT m, n, lda, ldb, ldc; \
+    BlasIndex m, n, lda, ldb, ldc; \
     const EIGTYPE *a, *b; \
-    MKLTYPE alpha_, beta_; \
+    EIGTYPE beta(1); \
     MatrixX##EIGPREFIX b_tmp; \
-    EIGTYPE myone(1);\
 \
 /* Set transpose options */ \
 /* Set m, n, k */ \
-    m = (MKL_INT)rows;  \
+    m = convert_index<BlasIndex>(rows);  \
-    n = (MKL_INT)cols;  \
+    n = convert_index<BlasIndex>(cols);  \
-\
-/* Set alpha_ & beta_ */ \
-    assign_scalar_eig2mkl(alpha_, alpha); \
-    assign_scalar_eig2mkl(beta_, myone); \
 \
 /* Set lda, ldb, ldc */ \
-    lda = (MKL_INT)lhsStride; \
+    lda = convert_index<BlasIndex>(lhsStride); \
-    ldb = (MKL_INT)rhsStride; \
+    ldb = convert_index<BlasIndex>(rhsStride); \
-    ldc = (MKL_INT)resStride; \
+    ldc = convert_index<BlasIndex>(resStride); \
 \
 /* Set a, b, c */ \
     if (LhsStorageOrder==RowMajor) uplo='U'; \
@@ -83,16 +78,16 @@ struct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,true,ConjugateLh
       Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,n,m,OuterStride<>(rhsStride)); \
       b_tmp = rhs.adjoint(); \
       b = b_tmp.data(); \
-      ldb = b_tmp.outerStride(); \
+      ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \
     } else b = _rhs; \
 \
-    MKLPREFIX##symm(&side, &uplo, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (const MKLTYPE*)b, &ldb, &beta_, (MKLTYPE*)res, &ldc); \
+    BLASPREFIX##symm_(&side, &uplo, &m, &n, &numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)b, &ldb, &numext::real_ref(beta), (BLASTYPE*)res, &ldc); \
 \
   } \
 };
 
 
-#define EIGEN_MKL_HEMM_L(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
+#define EIGEN_BLAS_HEMM_L(EIGTYPE, BLASTYPE, EIGPREFIX, BLASPREFIX) \
 template <typename Index, \
           int LhsStorageOrder, bool ConjugateLhs, \
           int RhsStorageOrder, bool ConjugateRhs> \
@@ -103,29 +98,24 @@ struct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,true,ConjugateLh
     const EIGTYPE* _lhs, Index lhsStride, \
     const EIGTYPE* _rhs, Index rhsStride, \
     EIGTYPE* res,        Index resStride, \
-    EIGTYPE alpha) \
+    EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \
   { \
     char side='L', uplo='L'; \
-    MKL_INT m, n, lda, ldb, ldc; \
+    BlasIndex m, n, lda, ldb, ldc; \
     const EIGTYPE *a, *b; \
-    MKLTYPE alpha_, beta_; \
+    EIGTYPE beta(1); \
     MatrixX##EIGPREFIX b_tmp; \
     Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> a_tmp; \
-    EIGTYPE myone(1); \
 \
 /* Set transpose options */ \
 /* Set m, n, k */ \
-    m = (MKL_INT)rows; \
+    m = convert_index<BlasIndex>(rows); \
-    n = (MKL_INT)cols; \
+    n = convert_index<BlasIndex>(cols); \
-\
-/* Set alpha_ & beta_ */ \
-    assign_scalar_eig2mkl(alpha_, alpha); \
-    assign_scalar_eig2mkl(beta_, myone); \
 \
 /* Set lda, ldb, ldc */ \
-    lda = (MKL_INT)lhsStride; \
+    lda = convert_index<BlasIndex>(lhsStride); \
-    ldb = (MKL_INT)rhsStride; \
+    ldb = convert_index<BlasIndex>(rhsStride); \
-    ldc = (MKL_INT)resStride; \
+    ldc = convert_index<BlasIndex>(resStride); \
 \
 /* Set a, b, c */ \
     if (((LhsStorageOrder==ColMajor) && ConjugateLhs) || ((LhsStorageOrder==RowMajor) && (!ConjugateLhs))) { \
@@ -151,23 +141,23 @@ struct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,true,ConjugateLh
         b_tmp = rhs.transpose(); \
       } \
       b = b_tmp.data(); \
-      ldb = b_tmp.outerStride(); \
+      ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \
     } \
 \
-    MKLPREFIX##hemm(&side, &uplo, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (const MKLTYPE*)b, &ldb, &beta_, (MKLTYPE*)res, &ldc); \
+    BLASPREFIX##hemm_(&side, &uplo, &m, &n, &numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)b, &ldb, &numext::real_ref(beta), (BLASTYPE*)res, &ldc); \
 \
   } \
 };
 
-EIGEN_MKL_SYMM_L(double, double, d, d)
+EIGEN_BLAS_SYMM_L(double, double, d, d)
-EIGEN_MKL_SYMM_L(float, float, f, s)
+EIGEN_BLAS_SYMM_L(float, float, f, s)
-EIGEN_MKL_HEMM_L(dcomplex, MKL_Complex16, cd, z)
+EIGEN_BLAS_HEMM_L(dcomplex, double, cd, z)
-EIGEN_MKL_HEMM_L(scomplex, MKL_Complex8, cf, c)
+EIGEN_BLAS_HEMM_L(scomplex, float, cf, c)
 
 
 /* Optimized matrix * selfadjoint matrix (?SYMM/?HEMM) product */
 
-#define EIGEN_MKL_SYMM_R(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
+#define EIGEN_BLAS_SYMM_R(EIGTYPE, BLASTYPE, EIGPREFIX, BLASPREFIX) \
 template <typename Index, \
           int LhsStorageOrder, bool ConjugateLhs, \
           int RhsStorageOrder, bool ConjugateRhs> \
@@ -179,27 +169,22 @@ struct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,false,ConjugateL
     const EIGTYPE* _lhs, Index lhsStride, \
     const EIGTYPE* _rhs, Index rhsStride, \
     EIGTYPE* res,        Index resStride, \
-    EIGTYPE alpha) \
+    EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \
   { \
     char side='R', uplo='L'; \
-    MKL_INT m, n, lda, ldb, ldc; \
+    BlasIndex m, n, lda, ldb, ldc; \
     const EIGTYPE *a, *b; \
-    MKLTYPE alpha_, beta_; \
+    EIGTYPE beta(1); \
     MatrixX##EIGPREFIX b_tmp; \
-    EIGTYPE myone(1);\
 \
 /* Set m, n, k */ \
-    m = (MKL_INT)rows;  \
+    m = convert_index<BlasIndex>(rows);  \
-    n = (MKL_INT)cols;  \
+    n = convert_index<BlasIndex>(cols);  \
-\
-/* Set alpha_ & beta_ */ \
-    assign_scalar_eig2mkl(alpha_, alpha); \
-    assign_scalar_eig2mkl(beta_, myone); \
 \
 /* Set lda, ldb, ldc */ \
-    lda = (MKL_INT)rhsStride; \
+    lda = convert_index<BlasIndex>(rhsStride); \
-    ldb = (MKL_INT)lhsStride; \
+    ldb = convert_index<BlasIndex>(lhsStride); \
-    ldc = (MKL_INT)resStride; \
+    ldc = convert_index<BlasIndex>(resStride); \
 \
 /* Set a, b, c */ \
     if (RhsStorageOrder==RowMajor) uplo='U'; \
@@ -209,16 +194,16 @@ struct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,false,ConjugateL
       Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,n,m,OuterStride<>(rhsStride)); \
       b_tmp = lhs.adjoint(); \
       b = b_tmp.data(); \
-      ldb = b_tmp.outerStride(); \
+      ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \
     } else b = _lhs; \
 \
-    MKLPREFIX##symm(&side, &uplo, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (const MKLTYPE*)b, &ldb, &beta_, (MKLTYPE*)res, &ldc); \
+    BLASPREFIX##symm_(&side, &uplo, &m, &n, &numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)b, &ldb, &numext::real_ref(beta), (BLASTYPE*)res, &ldc); \
 \
   } \
 };
 
 
-#define EIGEN_MKL_HEMM_R(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
+#define EIGEN_BLAS_HEMM_R(EIGTYPE, BLASTYPE, EIGPREFIX, BLASPREFIX) \
 template <typename Index, \
           int LhsStorageOrder, bool ConjugateLhs, \
           int RhsStorageOrder, bool ConjugateRhs> \
@@ -229,35 +214,30 @@ struct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,false,ConjugateL
     const EIGTYPE* _lhs, Index lhsStride, \
     const EIGTYPE* _rhs, Index rhsStride, \
     EIGTYPE* res,        Index resStride, \
-    EIGTYPE alpha) \
+    EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \
   { \
     char side='R', uplo='L'; \
-    MKL_INT m, n, lda, ldb, ldc; \
+    BlasIndex m, n, lda, ldb, ldc; \
     const EIGTYPE *a, *b; \
-    MKLTYPE alpha_, beta_; \
+    EIGTYPE beta(1); \
     MatrixX##EIGPREFIX b_tmp; \
     Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> a_tmp; \
-    EIGTYPE myone(1); \
 \
 /* Set m, n, k */ \
-    m = (MKL_INT)rows; \
+    m = convert_index<BlasIndex>(rows); \
-    n = (MKL_INT)cols; \
+    n = convert_index<BlasIndex>(cols); \
-\
-/* Set alpha_ & beta_ */ \
-    assign_scalar_eig2mkl(alpha_, alpha); \
-    assign_scalar_eig2mkl(beta_, myone); \
 \
 /* Set lda, ldb, ldc */ \
-    lda = (MKL_INT)rhsStride; \
+    lda = convert_index<BlasIndex>(rhsStride); \
-    ldb = (MKL_INT)lhsStride; \
+    ldb = convert_index<BlasIndex>(lhsStride); \
-    ldc = (MKL_INT)resStride; \
+    ldc = convert_index<BlasIndex>(resStride); \
 \
 /* Set a, b, c */ \
     if (((RhsStorageOrder==ColMajor) && ConjugateRhs) || ((RhsStorageOrder==RowMajor) && (!ConjugateRhs))) { \
       Map<const Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder>, 0, OuterStride<> > rhs(_rhs,n,n,OuterStride<>(rhsStride)); \
       a_tmp = rhs.conjugate(); \
       a = a_tmp.data(); \
-      lda = a_tmp.outerStride(); \
+      lda = convert_index<BlasIndex>(a_tmp.outerStride()); \
     } else a = _rhs; \
     if (RhsStorageOrder==RowMajor) uplo='U'; \
 \
@@ -279,17 +259,17 @@ struct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,false,ConjugateL
       ldb = b_tmp.outerStride(); \
     } \
 \
-    MKLPREFIX##hemm(&side, &uplo, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (const MKLTYPE*)b, &ldb, &beta_, (MKLTYPE*)res, &ldc); \
+    BLASPREFIX##hemm_(&side, &uplo, &m, &n, &numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)b, &ldb, &numext::real_ref(beta), (BLASTYPE*)res, &ldc); \
   } \
 };
 
-EIGEN_MKL_SYMM_R(double, double, d, d)
+EIGEN_BLAS_SYMM_R(double, double, d, d)
-EIGEN_MKL_SYMM_R(float, float, f, s)
+EIGEN_BLAS_SYMM_R(float, float, f, s)
-EIGEN_MKL_HEMM_R(dcomplex, MKL_Complex16, cd, z)
+EIGEN_BLAS_HEMM_R(dcomplex, double, cd, z)
-EIGEN_MKL_HEMM_R(scomplex, MKL_Complex8, cf, c)
+EIGEN_BLAS_HEMM_R(scomplex, float, cf, c)
 
 } // end namespace internal
 
 } // end namespace Eigen
 
-#endif // EIGEN_SELFADJOINT_MATRIX_MATRIX_MKL_H
+#endif // EIGEN_SELFADJOINT_MATRIX_MATRIX_BLAS_H

Eigen/src/Core/products/SelfadjointMatrixVector_BLAS.h

@@ -25,13 +25,13 @@
  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 
  ********************************************************************************
- *   Content : Eigen bindings to Intel(R) MKL
+ *   Content : Eigen bindings to BLAS F77
  *   Selfadjoint matrix-vector product functionality based on ?SYMV/HEMV.
  ********************************************************************************
 */
 
-#ifndef EIGEN_SELFADJOINT_MATRIX_VECTOR_MKL_H
+#ifndef EIGEN_SELFADJOINT_MATRIX_VECTOR_BLAS_H
-#define EIGEN_SELFADJOINT_MATRIX_VECTOR_MKL_H
+#define EIGEN_SELFADJOINT_MATRIX_VECTOR_BLAS_H
 
 namespace Eigen { 
 
@@ -47,31 +47,31 @@ template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool Conju
 struct selfadjoint_matrix_vector_product_symv :
   selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,BuiltIn> {};
 
-#define EIGEN_MKL_SYMV_SPECIALIZE(Scalar) \
+#define EIGEN_BLAS_SYMV_SPECIALIZE(Scalar) \
 template<typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs> \
 struct selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,Specialized> { \
 static void run( \
   Index size, const Scalar*  lhs, Index lhsStride, \
-  const Scalar* _rhs, Index rhsIncr, Scalar* res, Scalar alpha) { \
+  const Scalar* _rhs, Scalar* res, Scalar alpha) { \
     enum {\
       IsColMajor = StorageOrder==ColMajor \
     }; \
     if (IsColMajor == ConjugateLhs) {\
       selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,BuiltIn>::run( \
-        size, lhs, lhsStride, _rhs, rhsIncr, res, alpha);  \
+        size, lhs, lhsStride, _rhs, res, alpha);  \
     } else {\
       selfadjoint_matrix_vector_product_symv<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs>::run( \
-        size, lhs, lhsStride, _rhs, rhsIncr, res, alpha);  \
+        size, lhs, lhsStride, _rhs, res, alpha);  \
     }\
   } \
 }; \
 
-EIGEN_MKL_SYMV_SPECIALIZE(double)
+EIGEN_BLAS_SYMV_SPECIALIZE(double)
-EIGEN_MKL_SYMV_SPECIALIZE(float)
+EIGEN_BLAS_SYMV_SPECIALIZE(float)
-EIGEN_MKL_SYMV_SPECIALIZE(dcomplex)
+EIGEN_BLAS_SYMV_SPECIALIZE(dcomplex)
-EIGEN_MKL_SYMV_SPECIALIZE(scomplex)
+EIGEN_BLAS_SYMV_SPECIALIZE(scomplex)
 
-#define EIGEN_MKL_SYMV_SPECIALIZATION(EIGTYPE,MKLTYPE,MKLFUNC) \
+#define EIGEN_BLAS_SYMV_SPECIALIZATION(EIGTYPE,BLASTYPE,BLASFUNC) \
 template<typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs> \
 struct selfadjoint_matrix_vector_product_symv<EIGTYPE,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs> \
 { \
@@ -79,36 +79,33 @@ typedef Matrix<EIGTYPE,Dynamic,1,ColMajor> SYMVVector;\
 \
 static void run( \
 Index size, const EIGTYPE*  lhs, Index lhsStride, \
-const EIGTYPE* _rhs, Index rhsIncr, EIGTYPE* res, EIGTYPE alpha) \
+const EIGTYPE* _rhs, EIGTYPE* res, EIGTYPE alpha) \
 { \
   enum {\
     IsRowMajor = StorageOrder==RowMajor ? 1 : 0, \
     IsLower = UpLo == Lower ? 1 : 0 \
   }; \
-  MKL_INT n=size, lda=lhsStride, incx=rhsIncr, incy=1; \
+  BlasIndex n=convert_index<BlasIndex>(size), lda=convert_index<BlasIndex>(lhsStride), incx=1, incy=1; \
-  MKLTYPE alpha_, beta_; \
+  EIGTYPE beta(1); \
-  const EIGTYPE *x_ptr, myone(1); \
+  const EIGTYPE *x_ptr; \
   char uplo=(IsRowMajor) ? (IsLower ? 'U' : 'L') : (IsLower ? 'L' : 'U'); \
-  assign_scalar_eig2mkl(alpha_, alpha); \
-  assign_scalar_eig2mkl(beta_, myone); \
   SYMVVector x_tmp; \
   if (ConjugateRhs) { \
-    Map<const SYMVVector, 0, InnerStride<> > map_x(_rhs,size,1,InnerStride<>(incx)); \
+    Map<const SYMVVector, 0 > map_x(_rhs,size,1); \
     x_tmp=map_x.conjugate(); \
     x_ptr=x_tmp.data(); \
-    incx=1; \
   } else x_ptr=_rhs; \
-  MKLFUNC(&uplo, &n, &alpha_, (const MKLTYPE*)lhs, &lda, (const MKLTYPE*)x_ptr, &incx, &beta_, (MKLTYPE*)res, &incy); \
+  BLASFUNC(&uplo, &n, &numext::real_ref(alpha), (const BLASTYPE*)lhs, &lda, (const BLASTYPE*)x_ptr, &incx, &numext::real_ref(beta), (BLASTYPE*)res, &incy); \
 }\
 };
 
-EIGEN_MKL_SYMV_SPECIALIZATION(double,   double,        dsymv)
+EIGEN_BLAS_SYMV_SPECIALIZATION(double,   double, dsymv_)
-EIGEN_MKL_SYMV_SPECIALIZATION(float,    float,         ssymv)
+EIGEN_BLAS_SYMV_SPECIALIZATION(float,    float,  ssymv_)
-EIGEN_MKL_SYMV_SPECIALIZATION(dcomplex, MKL_Complex16, zhemv)
+EIGEN_BLAS_SYMV_SPECIALIZATION(dcomplex, double, zhemv_)
-EIGEN_MKL_SYMV_SPECIALIZATION(scomplex, MKL_Complex8,  chemv)
+EIGEN_BLAS_SYMV_SPECIALIZATION(scomplex, float,  chemv_)
 
 } // end namespace internal
 
 } // end namespace Eigen
 
-#endif // EIGEN_SELFADJOINT_MATRIX_VECTOR_MKL_H
+#endif // EIGEN_SELFADJOINT_MATRIX_VECTOR_BLAS_H

Eigen/src/Core/products/SelfadjointProduct.h

@@ -92,15 +92,27 @@ struct selfadjoint_product_selector<MatrixType,OtherType,UpLo,false>
 
     Scalar actualAlpha = alpha * OtherBlasTraits::extractScalarFactor(other.derived());
 
-    enum { IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0 };
+    enum {
+      IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0,
+      OtherIsRowMajor = _ActualOtherType::Flags&RowMajorBit ? 1 : 0
+    };
+
+    Index size = mat.cols();
+    Index depth = actualOther.cols();
+
+    typedef internal::gemm_blocking_space<IsRowMajor ? RowMajor : ColMajor,Scalar,Scalar,
+              MatrixType::MaxColsAtCompileTime, MatrixType::MaxColsAtCompileTime, _ActualOtherType::MaxColsAtCompileTime> BlockingType;
+
+    BlockingType blocking(size, size, depth, 1, false);
+
 
     internal::general_matrix_matrix_triangular_product<Index,
-      Scalar, _ActualOtherType::Flags&RowMajorBit ? RowMajor : ColMajor,   OtherBlasTraits::NeedToConjugate  && NumTraits<Scalar>::IsComplex,
+      Scalar, OtherIsRowMajor ? RowMajor : ColMajor,   OtherBlasTraits::NeedToConjugate  && NumTraits<Scalar>::IsComplex,
-      Scalar, _ActualOtherType::Flags&RowMajorBit ? ColMajor : RowMajor, (!OtherBlasTraits::NeedToConjugate) && NumTraits<Scalar>::IsComplex,
+      Scalar, OtherIsRowMajor ? ColMajor : RowMajor, (!OtherBlasTraits::NeedToConjugate) && NumTraits<Scalar>::IsComplex,
-      MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor, UpLo>
+      IsRowMajor ? RowMajor : ColMajor, UpLo>
-      ::run(mat.cols(), actualOther.cols(),
+      ::run(size, depth,
             &actualOther.coeffRef(0,0), actualOther.outerStride(), &actualOther.coeffRef(0,0), actualOther.outerStride(),
-            mat.data(), mat.outerStride(), actualAlpha);
+            mat.data(), mat.outerStride(), actualAlpha, blocking);
   }
 };
 

Eigen/src/Core/products/TriangularMatrixMatrix.h

@@ -126,6 +126,10 @@ EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,true,
 
     Index kc = blocking.kc();                   // cache block size along the K direction
     Index mc = (std::min)(rows,blocking.mc());  // cache block size along the M direction
+    // The small panel size must not be larger than blocking size.
+    // Usually this should never be the case because SmallPanelWidth^2 is very small
+    // compared to L2 cache size, but let's be safe:
+    Index panelWidth = (std::min)(Index(SmallPanelWidth),(std::min)(kc,mc));
 
     std::size_t sizeA = kc*mc;
     std::size_t sizeB = kc*cols;
@@ -169,9 +173,9 @@ EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,true,
       if(IsLower || actual_k2<rows)
       {
         // for each small vertical panels of lhs
-        for (Index k1=0; k1<actual_kc; k1+=SmallPanelWidth)
+        for (Index k1=0; k1<actual_kc; k1+=panelWidth)
         {
-          Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth);
+          Index actualPanelWidth = std::min<Index>(actual_kc-k1, panelWidth);
           Index lengthTarget = IsLower ? actual_kc-k1-actualPanelWidth : k1;
           Index startBlock   = actual_k2+k1;
           Index blockBOffset = k1;

Eigen/src/Core/products/TriangularMatrixMatrix_BLAS.h

@@ -25,13 +25,13 @@
  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 
  ********************************************************************************
- *   Content : Eigen bindings to Intel(R) MKL
+ *   Content : Eigen bindings to BLAS F77
  *   Triangular matrix * matrix product functionality based on ?TRMM.
  ********************************************************************************
 */
 
-#ifndef EIGEN_TRIANGULAR_MATRIX_MATRIX_MKL_H
+#ifndef EIGEN_TRIANGULAR_MATRIX_MATRIX_BLAS_H
-#define EIGEN_TRIANGULAR_MATRIX_MATRIX_MKL_H
+#define EIGEN_TRIANGULAR_MATRIX_MATRIX_BLAS_H
 
 namespace Eigen { 
 
@@ -50,7 +50,7 @@ struct product_triangular_matrix_matrix_trmm :
 
 
 // try to go to BLAS specialization
-#define EIGEN_MKL_TRMM_SPECIALIZE(Scalar, LhsIsTriangular) \
+#define EIGEN_BLAS_TRMM_SPECIALIZE(Scalar, LhsIsTriangular) \
 template <typename Index, int Mode, \
           int LhsStorageOrder, bool ConjugateLhs, \
           int RhsStorageOrder, bool ConjugateRhs> \
@@ -65,17 +65,17 @@ struct product_triangular_matrix_matrix<Scalar,Index, Mode, LhsIsTriangular, \
   } \
 };
 
-EIGEN_MKL_TRMM_SPECIALIZE(double, true)
+EIGEN_BLAS_TRMM_SPECIALIZE(double, true)
-EIGEN_MKL_TRMM_SPECIALIZE(double, false)
+EIGEN_BLAS_TRMM_SPECIALIZE(double, false)
-EIGEN_MKL_TRMM_SPECIALIZE(dcomplex, true)
+EIGEN_BLAS_TRMM_SPECIALIZE(dcomplex, true)
-EIGEN_MKL_TRMM_SPECIALIZE(dcomplex, false)
+EIGEN_BLAS_TRMM_SPECIALIZE(dcomplex, false)
-EIGEN_MKL_TRMM_SPECIALIZE(float, true)
+EIGEN_BLAS_TRMM_SPECIALIZE(float, true)
-EIGEN_MKL_TRMM_SPECIALIZE(float, false)
+EIGEN_BLAS_TRMM_SPECIALIZE(float, false)
-EIGEN_MKL_TRMM_SPECIALIZE(scomplex, true)
+EIGEN_BLAS_TRMM_SPECIALIZE(scomplex, true)
-EIGEN_MKL_TRMM_SPECIALIZE(scomplex, false)
+EIGEN_BLAS_TRMM_SPECIALIZE(scomplex, false)
 
 // implements col-major += alpha * op(triangular) * op(general)
-#define EIGEN_MKL_TRMM_L(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
+#define EIGEN_BLAS_TRMM_L(EIGTYPE, BLASTYPE, EIGPREFIX, BLASPREFIX) \
 template <typename Index, int Mode, \
           int LhsStorageOrder, bool ConjugateLhs, \
           int RhsStorageOrder, bool ConjugateRhs> \
@@ -106,13 +106,14 @@ struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,true, \
    typedef Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> MatrixLhs; \
    typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs; \
 \
-/* Non-square case - doesn't fit to MKL ?TRMM. Fall to default triangular product or call MKL ?GEMM*/ \
+/* Non-square case - doesn't fit to BLAS ?TRMM. Fall to default triangular product or call BLAS ?GEMM*/ \
    if (rows != depth) { \
 \
-     int nthr = mkl_domain_get_max_threads(EIGEN_MKL_DOMAIN_BLAS); \
+     /* FIXME handle mkl_domain_get_max_threads */ \
+     /*int nthr = mkl_domain_get_max_threads(EIGEN_BLAS_DOMAIN_BLAS);*/ int nthr = 1;\
 \
      if (((nthr==1) && (((std::max)(rows,depth)-diagSize)/(double)diagSize < 0.5))) { \
-     /* Most likely no benefit to call TRMM or GEMM from MKL*/ \
+     /* Most likely no benefit to call TRMM or GEMM from BLAS */ \
        product_triangular_matrix_matrix<EIGTYPE,Index,Mode,true, \
        LhsStorageOrder,ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, BuiltIn>::run( \
            _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha, blocking); \
@@ -121,27 +122,23 @@ struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,true, \
      /* Make sense to call GEMM */ \
        Map<const MatrixLhs, 0, OuterStride<> > lhsMap(_lhs,rows,depth,OuterStride<>(lhsStride)); \
        MatrixLhs aa_tmp=lhsMap.template triangularView<Mode>(); \
-       MKL_INT aStride = aa_tmp.outerStride(); \
+       BlasIndex aStride = convert_index<BlasIndex>(aa_tmp.outerStride()); \
        gemm_blocking_space<ColMajor,EIGTYPE,EIGTYPE,Dynamic,Dynamic,Dynamic> gemm_blocking(_rows,_cols,_depth, 1, true); \
        general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor>::run( \
        rows, cols, depth, aa_tmp.data(), aStride, _rhs, rhsStride, res, resStride, alpha, gemm_blocking, 0); \
 \
-     /*std::cout << "TRMM_L: A is not square! Go to MKL GEMM implementation! " << nthr<<" \n";*/ \
+     /*std::cout << "TRMM_L: A is not square! Go to BLAS GEMM implementation! " << nthr<<" \n";*/ \
      } \
      return; \
    } \
    char side = 'L', transa, uplo, diag = 'N'; \
    EIGTYPE *b; \
    const EIGTYPE *a; \
-   MKL_INT m, n, lda, ldb; \
+   BlasIndex m, n, lda, ldb; \
-   MKLTYPE alpha_; \
-\
-/* Set alpha_*/ \
-   assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); \
 \
 /* Set m, n */ \
-   m = (MKL_INT)diagSize; \
+   m = convert_index<BlasIndex>(diagSize); \
-   n = (MKL_INT)cols; \
+   n = convert_index<BlasIndex>(cols); \
 \
 /* Set trans */ \
    transa = (LhsStorageOrder==RowMajor) ? ((ConjugateLhs) ? 'C' : 'T') : 'N'; \
@@ -152,7 +149,7 @@ struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,true, \
 \
    if (ConjugateRhs) b_tmp = rhs.conjugate(); else b_tmp = rhs; \
    b = b_tmp.data(); \
-   ldb = b_tmp.outerStride(); \
+   ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \
 \
 /* Set uplo */ \
    uplo = IsLower ? 'L' : 'U'; \
@@ -168,14 +165,14 @@ struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,true, \
      else if (IsUnitDiag) \
        a_tmp.diagonal().setOnes();\
      a = a_tmp.data(); \
-     lda = a_tmp.outerStride(); \
+     lda = convert_index<BlasIndex>(a_tmp.outerStride()); \
    } else { \
      a = _lhs; \
-     lda = lhsStride; \
+     lda = convert_index<BlasIndex>(lhsStride); \
    } \
-   /*std::cout << "TRMM_L: A is square! Go to MKL TRMM implementation! \n";*/ \
+   /*std::cout << "TRMM_L: A is square! Go to BLAS TRMM implementation! \n";*/ \
 /* call ?trmm*/ \
-   MKLPREFIX##trmm(&side, &uplo, &transa, &diag, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (MKLTYPE*)b, &ldb); \
+   BLASPREFIX##trmm_(&side, &uplo, &transa, &diag, &m, &n, &numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (BLASTYPE*)b, &ldb); \
 \
 /* Add op(a_triangular)*b into res*/ \
    Map<MatrixX##EIGPREFIX, 0, OuterStride<> > res_tmp(res,rows,cols,OuterStride<>(resStride)); \
@@ -183,13 +180,13 @@ struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,true, \
   } \
 };
 
-EIGEN_MKL_TRMM_L(double, double, d, d)
+EIGEN_BLAS_TRMM_L(double, double, d, d)
-EIGEN_MKL_TRMM_L(dcomplex, MKL_Complex16, cd, z)
+EIGEN_BLAS_TRMM_L(dcomplex, double, cd, z)
-EIGEN_MKL_TRMM_L(float, float, f, s)
+EIGEN_BLAS_TRMM_L(float, float, f, s)
-EIGEN_MKL_TRMM_L(scomplex, MKL_Complex8, cf, c)
+EIGEN_BLAS_TRMM_L(scomplex, float, cf, c)
 
 // implements col-major += alpha * op(general) * op(triangular)
-#define EIGEN_MKL_TRMM_R(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
+#define EIGEN_BLAS_TRMM_R(EIGTYPE, BLASTYPE, EIGPREFIX, BLASPREFIX) \
 template <typename Index, int Mode, \
           int LhsStorageOrder, bool ConjugateLhs, \
           int RhsStorageOrder, bool ConjugateRhs> \
@@ -220,13 +217,13 @@ struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,false, \
    typedef Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> MatrixLhs; \
    typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs; \
 \
-/* Non-square case - doesn't fit to MKL ?TRMM. Fall to default triangular product or call MKL ?GEMM*/ \
+/* Non-square case - doesn't fit to BLAS ?TRMM. Fall to default triangular product or call BLAS ?GEMM*/ \
    if (cols != depth) { \
 \
-     int nthr = mkl_domain_get_max_threads(EIGEN_MKL_DOMAIN_BLAS); \
+     int nthr = 1 /*mkl_domain_get_max_threads(EIGEN_BLAS_DOMAIN_BLAS)*/; \
 \
      if ((nthr==1) && (((std::max)(cols,depth)-diagSize)/(double)diagSize < 0.5)) { \
-     /* Most likely no benefit to call TRMM or GEMM from MKL*/ \
+     /* Most likely no benefit to call TRMM or GEMM from BLAS*/ \
        product_triangular_matrix_matrix<EIGTYPE,Index,Mode,false, \
        LhsStorageOrder,ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, BuiltIn>::run( \
            _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha, blocking); \
@@ -235,27 +232,23 @@ struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,false, \
      /* Make sense to call GEMM */ \
        Map<const MatrixRhs, 0, OuterStride<> > rhsMap(_rhs,depth,cols, OuterStride<>(rhsStride)); \
        MatrixRhs aa_tmp=rhsMap.template triangularView<Mode>(); \
-       MKL_INT aStride = aa_tmp.outerStride(); \
+       BlasIndex aStride = convert_index<BlasIndex>(aa_tmp.outerStride()); \
        gemm_blocking_space<ColMajor,EIGTYPE,EIGTYPE,Dynamic,Dynamic,Dynamic> gemm_blocking(_rows,_cols,_depth, 1, true); \
        general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor>::run( \
        rows, cols, depth, _lhs, lhsStride, aa_tmp.data(), aStride, res, resStride, alpha, gemm_blocking, 0); \
 \
-     /*std::cout << "TRMM_R: A is not square! Go to MKL GEMM implementation! " << nthr<<" \n";*/ \
+     /*std::cout << "TRMM_R: A is not square! Go to BLAS GEMM implementation! " << nthr<<" \n";*/ \
      } \
      return; \
    } \
    char side = 'R', transa, uplo, diag = 'N'; \
    EIGTYPE *b; \
    const EIGTYPE *a; \
-   MKL_INT m, n, lda, ldb; \
+   BlasIndex m, n, lda, ldb; \
-   MKLTYPE alpha_; \
-\
-/* Set alpha_*/ \
-   assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); \
 \
 /* Set m, n */ \
-   m = (MKL_INT)rows; \
+   m = convert_index<BlasIndex>(rows); \
-   n = (MKL_INT)diagSize; \
+   n = convert_index<BlasIndex>(diagSize); \
 \
 /* Set trans */ \
    transa = (RhsStorageOrder==RowMajor) ? ((ConjugateRhs) ? 'C' : 'T') : 'N'; \
@@ -266,7 +259,7 @@ struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,false, \
 \
    if (ConjugateLhs) b_tmp = lhs.conjugate(); else b_tmp = lhs; \
    b = b_tmp.data(); \
-   ldb = b_tmp.outerStride(); \
+   ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \
 \
 /* Set uplo */ \
    uplo = IsLower ? 'L' : 'U'; \
@@ -282,14 +275,14 @@ struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,false, \
      else if (IsUnitDiag) \
        a_tmp.diagonal().setOnes();\
      a = a_tmp.data(); \
-     lda = a_tmp.outerStride(); \
+     lda = convert_index<BlasIndex>(a_tmp.outerStride()); \
    } else { \
      a = _rhs; \
-     lda = rhsStride; \
+     lda = convert_index<BlasIndex>(rhsStride); \
    } \
-   /*std::cout << "TRMM_R: A is square! Go to MKL TRMM implementation! \n";*/ \
+   /*std::cout << "TRMM_R: A is square! Go to BLAS TRMM implementation! \n";*/ \
 /* call ?trmm*/ \
-   MKLPREFIX##trmm(&side, &uplo, &transa, &diag, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (MKLTYPE*)b, &ldb); \
+   BLASPREFIX##trmm_(&side, &uplo, &transa, &diag, &m, &n, &numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (BLASTYPE*)b, &ldb); \
 \
 /* Add op(a_triangular)*b into res*/ \
    Map<MatrixX##EIGPREFIX, 0, OuterStride<> > res_tmp(res,rows,cols,OuterStride<>(resStride)); \
@@ -297,13 +290,13 @@ struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,false, \
   } \
 };
 
-EIGEN_MKL_TRMM_R(double, double, d, d)
+EIGEN_BLAS_TRMM_R(double, double, d, d)
-EIGEN_MKL_TRMM_R(dcomplex, MKL_Complex16, cd, z)
+EIGEN_BLAS_TRMM_R(dcomplex, double, cd, z)
-EIGEN_MKL_TRMM_R(float, float, f, s)
+EIGEN_BLAS_TRMM_R(float, float, f, s)
-EIGEN_MKL_TRMM_R(scomplex, MKL_Complex8, cf, c)
+EIGEN_BLAS_TRMM_R(scomplex, float, cf, c)
 
 } // end namespace internal
 
 } // end namespace Eigen
 
-#endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_MKL_H
+#endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_BLAS_H

Eigen/src/Core/products/TriangularMatrixVector_BLAS.h

@@ -25,13 +25,13 @@
  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 
  ********************************************************************************
- *   Content : Eigen bindings to Intel(R) MKL
+ *   Content : Eigen bindings to BLAS F77
  *   Triangular matrix-vector product functionality based on ?TRMV.
  ********************************************************************************
 */
 
-#ifndef EIGEN_TRIANGULAR_MATRIX_VECTOR_MKL_H
+#ifndef EIGEN_TRIANGULAR_MATRIX_VECTOR_BLAS_H
-#define EIGEN_TRIANGULAR_MATRIX_VECTOR_MKL_H
+#define EIGEN_TRIANGULAR_MATRIX_VECTOR_BLAS_H
 
 namespace Eigen { 
 
@@ -47,7 +47,7 @@ template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename Rh
 struct triangular_matrix_vector_product_trmv :
   triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,StorageOrder,BuiltIn> {};
 
-#define EIGEN_MKL_TRMV_SPECIALIZE(Scalar) \
+#define EIGEN_BLAS_TRMV_SPECIALIZE(Scalar) \
 template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \
 struct triangular_matrix_vector_product<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,ColMajor,Specialized> { \
  static void run(Index _rows, Index _cols, const Scalar* _lhs, Index lhsStride, \
@@ -65,13 +65,13 @@ struct triangular_matrix_vector_product<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs
   } \
 };
 
-EIGEN_MKL_TRMV_SPECIALIZE(double)
+EIGEN_BLAS_TRMV_SPECIALIZE(double)
-EIGEN_MKL_TRMV_SPECIALIZE(float)
+EIGEN_BLAS_TRMV_SPECIALIZE(float)
-EIGEN_MKL_TRMV_SPECIALIZE(dcomplex)
+EIGEN_BLAS_TRMV_SPECIALIZE(dcomplex)
-EIGEN_MKL_TRMV_SPECIALIZE(scomplex)
+EIGEN_BLAS_TRMV_SPECIALIZE(scomplex)
 
 // implements col-major: res += alpha * op(triangular) * vector
-#define EIGEN_MKL_TRMV_CM(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
+#define EIGEN_BLAS_TRMV_CM(EIGTYPE, BLASTYPE, EIGPREFIX, BLASPREFIX) \
 template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \
 struct triangular_matrix_vector_product_trmv<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,ColMajor> { \
   enum { \
@@ -105,17 +105,15 @@ struct triangular_matrix_vector_product_trmv<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,
 /* Square part handling */\
 \
    char trans, uplo, diag; \
-   MKL_INT m, n, lda, incx, incy; \
+   BlasIndex m, n, lda, incx, incy; \
    EIGTYPE const *a; \
-   MKLTYPE alpha_, beta_; \
+   EIGTYPE beta(1); \
-   assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); \
-   assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(beta_, EIGTYPE(1)); \
 \
 /* Set m, n */ \
-   n = (MKL_INT)size; \
+   n = convert_index<BlasIndex>(size); \
-   lda = lhsStride; \
+   lda = convert_index<BlasIndex>(lhsStride); \
    incx = 1; \
-   incy = resIncr; \
+   incy = convert_index<BlasIndex>(resIncr); \
 \
 /* Set uplo, trans and diag*/ \
    trans = 'N'; \
@@ -123,39 +121,39 @@ struct triangular_matrix_vector_product_trmv<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,
    diag = IsUnitDiag ? 'U' : 'N'; \
 \
 /* call ?TRMV*/ \
-   MKLPREFIX##trmv(&uplo, &trans, &diag, &n, (const MKLTYPE*)_lhs, &lda, (MKLTYPE*)x, &incx); \
+   BLASPREFIX##trmv_(&uplo, &trans, &diag, &n, (const BLASTYPE*)_lhs, &lda, (BLASTYPE*)x, &incx); \
 \
 /* Add op(a_tr)rhs into res*/ \
-   MKLPREFIX##axpy(&n, &alpha_,(const MKLTYPE*)x, &incx, (MKLTYPE*)_res, &incy); \
+   BLASPREFIX##axpy_(&n, &numext::real_ref(alpha),(const BLASTYPE*)x, &incx, (BLASTYPE*)_res, &incy); \
-/* Non-square case - doesn't fit to MKL ?TRMV. Fall to default triangular product*/ \
+/* Non-square case - doesn't fit to BLAS ?TRMV. Fall to default triangular product*/ \
    if (size<(std::max)(rows,cols)) { \
      if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \
      x = x_tmp.data(); \
      if (size<rows) { \
        y = _res + size*resIncr; \
        a = _lhs + size; \
-       m = rows-size; \
+       m = convert_index<BlasIndex>(rows-size); \
-       n = size; \
+       n = convert_index<BlasIndex>(size); \
      } \
      else { \
        x += size; \
        y = _res; \
        a = _lhs + size*lda; \
-       m = size; \
+       m = convert_index<BlasIndex>(size); \
-       n = cols-size; \
+       n = convert_index<BlasIndex>(cols-size); \
      } \
-     MKLPREFIX##gemv(&trans, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (const MKLTYPE*)x, &incx, &beta_, (MKLTYPE*)y, &incy); \
+     BLASPREFIX##gemv_(&trans, &m, &n, &numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)x, &incx, &numext::real_ref(beta), (BLASTYPE*)y, &incy); \
    } \
   } \
 };
 
-EIGEN_MKL_TRMV_CM(double, double, d, d)
+EIGEN_BLAS_TRMV_CM(double,   double, d,  d)
-EIGEN_MKL_TRMV_CM(dcomplex, MKL_Complex16, cd, z)
+EIGEN_BLAS_TRMV_CM(dcomplex, double, cd, z)
-EIGEN_MKL_TRMV_CM(float, float, f, s)
+EIGEN_BLAS_TRMV_CM(float,    float,  f,  s)
-EIGEN_MKL_TRMV_CM(scomplex, MKL_Complex8, cf, c)
+EIGEN_BLAS_TRMV_CM(scomplex, float,  cf, c)
 
 // implements row-major: res += alpha * op(triangular) * vector
-#define EIGEN_MKL_TRMV_RM(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
+#define EIGEN_BLAS_TRMV_RM(EIGTYPE, BLASTYPE, EIGPREFIX, BLASPREFIX) \
 template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \
 struct triangular_matrix_vector_product_trmv<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,RowMajor> { \
   enum { \
@@ -189,17 +187,15 @@ struct triangular_matrix_vector_product_trmv<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,
 /* Square part handling */\
 \
    char trans, uplo, diag; \
-   MKL_INT m, n, lda, incx, incy; \
+   BlasIndex m, n, lda, incx, incy; \
    EIGTYPE const *a; \
-   MKLTYPE alpha_, beta_; \
+   EIGTYPE beta(1); \
-   assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); \
-   assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(beta_, EIGTYPE(1)); \
 \
 /* Set m, n */ \
-   n = (MKL_INT)size; \
+   n = convert_index<BlasIndex>(size); \
-   lda = lhsStride; \
+   lda = convert_index<BlasIndex>(lhsStride); \
    incx = 1; \
-   incy = resIncr; \
+   incy = convert_index<BlasIndex>(resIncr); \
 \
 /* Set uplo, trans and diag*/ \
    trans = ConjLhs ? 'C' : 'T'; \
@@ -207,39 +203,39 @@ struct triangular_matrix_vector_product_trmv<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,
    diag = IsUnitDiag ? 'U' : 'N'; \
 \
 /* call ?TRMV*/ \
-   MKLPREFIX##trmv(&uplo, &trans, &diag, &n, (const MKLTYPE*)_lhs, &lda, (MKLTYPE*)x, &incx); \
+   BLASPREFIX##trmv_(&uplo, &trans, &diag, &n, (const BLASTYPE*)_lhs, &lda, (BLASTYPE*)x, &incx); \
 \
 /* Add op(a_tr)rhs into res*/ \
-   MKLPREFIX##axpy(&n, &alpha_,(const MKLTYPE*)x, &incx, (MKLTYPE*)_res, &incy); \
+   BLASPREFIX##axpy_(&n, &numext::real_ref(alpha),(const BLASTYPE*)x, &incx, (BLASTYPE*)_res, &incy); \
-/* Non-square case - doesn't fit to MKL ?TRMV. Fall to default triangular product*/ \
+/* Non-square case - doesn't fit to BLAS ?TRMV. Fall to default triangular product*/ \
    if (size<(std::max)(rows,cols)) { \
      if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \
      x = x_tmp.data(); \
      if (size<rows) { \
        y = _res + size*resIncr; \
        a = _lhs + size*lda; \
-       m = rows-size; \
+       m = convert_index<BlasIndex>(rows-size); \
-       n = size; \
+       n = convert_index<BlasIndex>(size); \
      } \
      else { \
        x += size; \
        y = _res; \
        a = _lhs + size; \
-       m = size; \
+       m = convert_index<BlasIndex>(size); \
-       n = cols-size; \
+       n = convert_index<BlasIndex>(cols-size); \
      } \
-     MKLPREFIX##gemv(&trans, &n, &m, &alpha_, (const MKLTYPE*)a, &lda, (const MKLTYPE*)x, &incx, &beta_, (MKLTYPE*)y, &incy); \
+     BLASPREFIX##gemv_(&trans, &n, &m, &numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)x, &incx, &numext::real_ref(beta), (BLASTYPE*)y, &incy); \
    } \
   } \
 };
 
-EIGEN_MKL_TRMV_RM(double, double, d, d)
+EIGEN_BLAS_TRMV_RM(double,   double, d,  d)
-EIGEN_MKL_TRMV_RM(dcomplex, MKL_Complex16, cd, z)
+EIGEN_BLAS_TRMV_RM(dcomplex, double, cd, z)
-EIGEN_MKL_TRMV_RM(float, float, f, s)
+EIGEN_BLAS_TRMV_RM(float,    float,  f,  s)
-EIGEN_MKL_TRMV_RM(scomplex, MKL_Complex8, cf, c)
+EIGEN_BLAS_TRMV_RM(scomplex, float,  cf, c)
 
 } // end namespase internal
 
 } // end namespace Eigen
 
-#endif // EIGEN_TRIANGULAR_MATRIX_VECTOR_MKL_H
+#endif // EIGEN_TRIANGULAR_MATRIX_VECTOR_BLAS_H

Eigen/src/Core/products/TriangularSolverMatrix_BLAS.h

@@ -25,20 +25,20 @@
  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 
  ********************************************************************************
- *   Content : Eigen bindings to Intel(R) MKL
+ *   Content : Eigen bindings to BLAS F77
  *   Triangular matrix * matrix product functionality based on ?TRMM.
  ********************************************************************************
 */
 
-#ifndef EIGEN_TRIANGULAR_SOLVER_MATRIX_MKL_H
+#ifndef EIGEN_TRIANGULAR_SOLVER_MATRIX_BLAS_H
-#define EIGEN_TRIANGULAR_SOLVER_MATRIX_MKL_H
+#define EIGEN_TRIANGULAR_SOLVER_MATRIX_BLAS_H
 
 namespace Eigen {
 
 namespace internal {
 
 // implements LeftSide op(triangular)^-1 * general
-#define EIGEN_MKL_TRSM_L(EIGTYPE, MKLTYPE, MKLPREFIX) \
+#define EIGEN_BLAS_TRSM_L(EIGTYPE, BLASTYPE, BLASPREFIX) \
 template <typename Index, int Mode, bool Conjugate, int TriStorageOrder> \
 struct triangular_solve_matrix<EIGTYPE,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor> \
 { \
@@ -53,13 +53,11 @@ struct triangular_solve_matrix<EIGTYPE,Index,OnTheLeft,Mode,Conjugate,TriStorage
       const EIGTYPE* _tri, Index triStride, \
       EIGTYPE* _other, Index otherStride, level3_blocking<EIGTYPE,EIGTYPE>& /*blocking*/) \
   { \
-   MKL_INT m = size, n = otherSize, lda, ldb; \
+   BlasIndex m = convert_index<BlasIndex>(size), n = convert_index<BlasIndex>(otherSize), lda, ldb; \
    char side = 'L', uplo, diag='N', transa; \
    /* Set alpha_ */ \
-   MKLTYPE alpha; \
+   EIGTYPE alpha(1); \
-   EIGTYPE myone(1); \
+   ldb = convert_index<BlasIndex>(otherStride);\
-   assign_scalar_eig2mkl(alpha, myone); \
-   ldb = otherStride;\
 \
    const EIGTYPE *a; \
 /* Set trans */ \
@@ -75,25 +73,25 @@ struct triangular_solve_matrix<EIGTYPE,Index,OnTheLeft,Mode,Conjugate,TriStorage
    if (conjA) { \
      a_tmp = tri.conjugate(); \
      a = a_tmp.data(); \
-     lda = a_tmp.outerStride(); \
+     lda = convert_index<BlasIndex>(a_tmp.outerStride()); \
    } else { \
      a = _tri; \
-     lda = triStride; \
+     lda = convert_index<BlasIndex>(triStride); \
    } \
    if (IsUnitDiag) diag='U'; \
 /* call ?trsm*/ \
-   MKLPREFIX##trsm(&side, &uplo, &transa, &diag, &m, &n, &alpha, (const MKLTYPE*)a, &lda, (MKLTYPE*)_other, &ldb); \
+   BLASPREFIX##trsm_(&side, &uplo, &transa, &diag, &m, &n, &numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (BLASTYPE*)_other, &ldb); \
  } \
 };
 
-EIGEN_MKL_TRSM_L(double, double, d)
+EIGEN_BLAS_TRSM_L(double,   double, d)
-EIGEN_MKL_TRSM_L(dcomplex, MKL_Complex16, z)
+EIGEN_BLAS_TRSM_L(dcomplex, double, z)
-EIGEN_MKL_TRSM_L(float, float, s)
+EIGEN_BLAS_TRSM_L(float,    float,  s)
-EIGEN_MKL_TRSM_L(scomplex, MKL_Complex8, c)
+EIGEN_BLAS_TRSM_L(scomplex, float,  c)
 
 
 // implements RightSide general * op(triangular)^-1
-#define EIGEN_MKL_TRSM_R(EIGTYPE, MKLTYPE, MKLPREFIX) \
+#define EIGEN_BLAS_TRSM_R(EIGTYPE, BLASTYPE, BLASPREFIX) \
 template <typename Index, int Mode, bool Conjugate, int TriStorageOrder> \
 struct triangular_solve_matrix<EIGTYPE,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor> \
 { \
@@ -108,13 +106,11 @@ struct triangular_solve_matrix<EIGTYPE,Index,OnTheRight,Mode,Conjugate,TriStorag
       const EIGTYPE* _tri, Index triStride, \
       EIGTYPE* _other, Index otherStride, level3_blocking<EIGTYPE,EIGTYPE>& /*blocking*/) \
   { \
-   MKL_INT m = otherSize, n = size, lda, ldb; \
+   BlasIndex m = convert_index<BlasIndex>(otherSize), n = convert_index<BlasIndex>(size), lda, ldb; \
    char side = 'R', uplo, diag='N', transa; \
    /* Set alpha_ */ \
-   MKLTYPE alpha; \
+   EIGTYPE alpha(1); \
-   EIGTYPE myone(1); \
+   ldb = convert_index<BlasIndex>(otherStride);\
-   assign_scalar_eig2mkl(alpha, myone); \
-   ldb = otherStride;\
 \
    const EIGTYPE *a; \
 /* Set trans */ \
@@ -130,26 +126,26 @@ struct triangular_solve_matrix<EIGTYPE,Index,OnTheRight,Mode,Conjugate,TriStorag
    if (conjA) { \
      a_tmp = tri.conjugate(); \
      a = a_tmp.data(); \
-     lda = a_tmp.outerStride(); \
+     lda = convert_index<BlasIndex>(a_tmp.outerStride()); \
    } else { \
      a = _tri; \
-     lda = triStride; \
+     lda = convert_index<BlasIndex>(triStride); \
    } \
    if (IsUnitDiag) diag='U'; \
 /* call ?trsm*/ \
-   MKLPREFIX##trsm(&side, &uplo, &transa, &diag, &m, &n, &alpha, (const MKLTYPE*)a, &lda, (MKLTYPE*)_other, &ldb); \
+   BLASPREFIX##trsm_(&side, &uplo, &transa, &diag, &m, &n, &numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (BLASTYPE*)_other, &ldb); \
    /*std::cout << "TRMS_L specialization!\n";*/ \
  } \
 };
 
-EIGEN_MKL_TRSM_R(double, double, d)
+EIGEN_BLAS_TRSM_R(double,   double, d)
-EIGEN_MKL_TRSM_R(dcomplex, MKL_Complex16, z)
+EIGEN_BLAS_TRSM_R(dcomplex, double, z)
-EIGEN_MKL_TRSM_R(float, float, s)
+EIGEN_BLAS_TRSM_R(float,    float,  s)
-EIGEN_MKL_TRSM_R(scomplex, MKL_Complex8, c)
+EIGEN_BLAS_TRSM_R(scomplex, float,  c)
 
 
 } // end namespace internal
 
 } // end namespace Eigen
 
-#endif // EIGEN_TRIANGULAR_SOLVER_MATRIX_MKL_H
+#endif // EIGEN_TRIANGULAR_SOLVER_MATRIX_BLAS_H

Eigen/src/Core/util/BlasUtil.h

@@ -123,18 +123,18 @@ template<typename Scalar> struct get_factor<Scalar,typename NumTraits<Scalar>::R
 template<typename Scalar, typename Index>
 class BlasVectorMapper {
   public:
-  EIGEN_ALWAYS_INLINE BlasVectorMapper(Scalar *data) : m_data(data) {}
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE BlasVectorMapper(Scalar *data) : m_data(data) {}
 
-  EIGEN_ALWAYS_INLINE Scalar operator()(Index i) const {
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar operator()(Index i) const {
     return m_data[i];
   }
   template <typename Packet, int AlignmentType>
-  EIGEN_ALWAYS_INLINE Packet load(Index i) const {
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet load(Index i) const {
     return ploadt<Packet, AlignmentType>(m_data + i);
   }
 
   template <typename Packet>
-  bool aligned(Index i) const {
+  EIGEN_DEVICE_FUNC bool aligned(Index i) const {
     return (size_t(m_data+i)%sizeof(Packet))==0;
   }
 
@@ -148,25 +148,25 @@ class BlasLinearMapper {
   typedef typename packet_traits<Scalar>::type Packet;
   typedef typename packet_traits<Scalar>::half HalfPacket;
 
-  EIGEN_ALWAYS_INLINE BlasLinearMapper(Scalar *data) : m_data(data) {}
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE BlasLinearMapper(Scalar *data) : m_data(data) {}
 
-  EIGEN_ALWAYS_INLINE void prefetch(int i) const {
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void prefetch(int i) const {
     internal::prefetch(&operator()(i));
   }
 
-  EIGEN_ALWAYS_INLINE Scalar& operator()(Index i) const {
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar& operator()(Index i) const {
     return m_data[i];
   }
 
-  EIGEN_ALWAYS_INLINE Packet loadPacket(Index i) const {
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet loadPacket(Index i) const {
     return ploadt<Packet, AlignmentType>(m_data + i);
   }
 
-  EIGEN_ALWAYS_INLINE HalfPacket loadHalfPacket(Index i) const {
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE HalfPacket loadHalfPacket(Index i) const {
     return ploadt<HalfPacket, AlignmentType>(m_data + i);
   }
 
-  EIGEN_ALWAYS_INLINE void storePacket(Index i, const Packet &p) const {
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacket(Index i, const Packet &p) const {
     pstoret<Scalar, Packet, AlignmentType>(m_data + i, p);
   }
 
@@ -184,18 +184,18 @@ class blas_data_mapper {
   typedef BlasLinearMapper<Scalar, Index, AlignmentType> LinearMapper;
   typedef BlasVectorMapper<Scalar, Index> VectorMapper;
 
-  EIGEN_ALWAYS_INLINE blas_data_mapper(Scalar* data, Index stride) : m_data(data), m_stride(stride) {}
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE blas_data_mapper(Scalar* data, Index stride) : m_data(data), m_stride(stride) {}
 
-  EIGEN_ALWAYS_INLINE blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType>
+  EIGEN_DEVICE_FUNC  EIGEN_ALWAYS_INLINE blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType>
   getSubMapper(Index i, Index j) const {
     return blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType>(&operator()(i, j), m_stride);
   }
 
-  EIGEN_ALWAYS_INLINE LinearMapper getLinearMapper(Index i, Index j) const {
+  EIGEN_DEVICE_FUNC  EIGEN_ALWAYS_INLINE LinearMapper getLinearMapper(Index i, Index j) const {
     return LinearMapper(&operator()(i, j));
   }
 
-  EIGEN_ALWAYS_INLINE VectorMapper getVectorMapper(Index i, Index j) const {
+  EIGEN_DEVICE_FUNC  EIGEN_ALWAYS_INLINE VectorMapper getVectorMapper(Index i, Index j) const {
     return VectorMapper(&operator()(i, j));
   }
 
@@ -205,28 +205,28 @@ class blas_data_mapper {
     return m_data[StorageOrder==RowMajor ? j + i*m_stride : i + j*m_stride];
   }
 
-  EIGEN_ALWAYS_INLINE Packet loadPacket(Index i, Index j) const {
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet loadPacket(Index i, Index j) const {
     return ploadt<Packet, AlignmentType>(&operator()(i, j));
   }
 
-  EIGEN_ALWAYS_INLINE HalfPacket loadHalfPacket(Index i, Index j) const {
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE HalfPacket loadHalfPacket(Index i, Index j) const {
     return ploadt<HalfPacket, AlignmentType>(&operator()(i, j));
   }
 
   template<typename SubPacket>
-  EIGEN_ALWAYS_INLINE void scatterPacket(Index i, Index j, const SubPacket &p) const {
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void scatterPacket(Index i, Index j, const SubPacket &p) const {
     pscatter<Scalar, SubPacket>(&operator()(i, j), p, m_stride);
   }
 
   template<typename SubPacket>
-  EIGEN_ALWAYS_INLINE SubPacket gatherPacket(Index i, Index j) const {
+  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE SubPacket gatherPacket(Index i, Index j) const {
     return pgather<Scalar, SubPacket>(&operator()(i, j), m_stride);
   }
 
-  const Index stride() const { return m_stride; }
+  EIGEN_DEVICE_FUNC const Index stride() const { return m_stride; }
-  const Scalar* data() const { return m_data; }
+  EIGEN_DEVICE_FUNC const Scalar* data() const { return m_data; }
 
-  Index firstAligned(Index size) const {
+  EIGEN_DEVICE_FUNC Index firstAligned(Index size) const {
     if (size_t(m_data)%sizeof(Scalar)) {
       return -1;
     }

Eigen/src/Core/util/Constants.h

@@ -56,8 +56,8 @@ const int HugeCost = 10000;
   * for a matrix, this means that the storage order is row-major.
   * If this bit is not set, the storage order is column-major.
   * For an expression, this determines the storage order of
-  * the matrix created by evaluation of that expression. 
+  * the matrix created by evaluation of that expression.
-  * \sa \ref TopicStorageOrders */
+  * \sa \blank  \ref TopicStorageOrders */
 const unsigned int RowMajorBit = 0x1;
 
 /** \ingroup flags
@@ -67,6 +67,7 @@ const unsigned int EvalBeforeNestingBit = 0x2;
 /** \ingroup flags
   * \deprecated
   * means the expression should be evaluated before any assignment */
+EIGEN_DEPRECATED
 const unsigned int EvalBeforeAssigningBit = 0x4; // FIXME deprecated
 
 /** \ingroup flags
@@ -158,7 +159,7 @@ const unsigned int DirectAccessBit = 0x40;
   * expression.packet<Aligned>(0);
   * \endcode
   */
-const unsigned int AlignedBit = 0x80;
+EIGEN_DEPRECATED const unsigned int AlignedBit = 0x80;
 
 const unsigned int NestByRefBit = 0x100;
 
@@ -168,7 +169,7 @@ const unsigned int NestByRefBit = 0x100;
   * can be either row-major or column-major.
   * The precise choice will be decided at evaluation time or when
   * combined with other expressions.
-  * \sa \ref RowMajorBit, \ref TopicStorageOrders */
+  * \sa \blank  \ref RowMajorBit, \ref TopicStorageOrders */
 const unsigned int NoPreferredStorageOrderBit = 0x200;
 
 /** \ingroup flags
@@ -187,8 +188,7 @@ const unsigned int CompressedAccessBit = 0x400;
 
 // list of flags that are inherited by default
 const unsigned int HereditaryBits = RowMajorBit
-                                  | EvalBeforeNestingBit
+                                  | EvalBeforeNestingBit;
-                                  | EvalBeforeAssigningBit;
 
 /** \defgroup enums Enumerations
   * \ingroup Core_Module
@@ -224,7 +224,7 @@ enum {
 
 /** \ingroup enums
   * Enum for indicating whether a buffer is aligned or not. */
-enum { 
+enum {
   Unaligned=0,        /**< Data pointer has no specific alignment. */
   Aligned8=8,         /**< Data pointer is aligned on a 8 bytes boundary. */
   Aligned16=16,       /**< Data pointer is aligned on a 16 bytes boundary. */

Eigen/src/Core/util/DisableStupidWarnings.h

@@ -15,20 +15,25 @@
   // 4522 - 'class' : multiple assignment operators specified
   // 4700 - uninitialized local variable 'xyz' used
   // 4717 - 'function' : recursive on all control paths, function will cause runtime stack overflow
+  // 4800 - 'type' : forcing value to bool 'true' or 'false' (performance warning)
   #ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS
     #pragma warning( push )
   #endif
-  #pragma warning( disable : 4100 4101 4127 4181 4211 4244 4273 4324 4503 4512 4522 4700 4717 )
+  #pragma warning( disable : 4100 4101 4127 4181 4211 4244 4273 4324 4503 4512 4522 4700 4717 4800)
+
 #elif defined __INTEL_COMPILER
   // 2196 - routine is both "inline" and "noinline" ("noinline" assumed)
   //        ICC 12 generates this warning even without any inline keyword, when defining class methods 'inline' i.e. inside of class body
   //        typedef that may be a reference type.
   // 279  - controlling expression is constant
   //        ICC 12 generates this warning on assert(constant_expression_depending_on_template_params) and frankly this is a legitimate use case.
+  // 1684 - conversion from pointer to same-sized integral type (potential portability problem)
+  // 2259 - non-pointer conversion from "Eigen::Index={ptrdiff_t={long}}" to "int" may lose significant bits
   #ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS
     #pragma warning push
   #endif
-  #pragma warning disable 2196 279
+  #pragma warning disable 2196 279 1684 2259
+
 #elif defined __clang__
   // -Wconstant-logical-operand - warning: use of logical && with constant operand; switch to bitwise & or remove constant
   //     this is really a stupid warning as it warns on compile-time expressions involving enums
@@ -38,4 +43,16 @@
   #pragma clang diagnostic ignored "-Wconstant-logical-operand"
 #endif
 
+#if defined __NVCC__
+  // Disable the "statement is unreachable" message
+  #pragma diag_suppress code_is_unreachable
+  // Disable the "dynamic initialization in unreachable code" message
+  #pragma diag_suppress initialization_not_reachable
+  // Disable the "calling a __host__ function from a __host__ __device__ function is not allowed" messages (yes, there are 4 of them)
+  #pragma diag_suppress 2651
+  #pragma diag_suppress 2653
+  #pragma diag_suppress 2668
+  #pragma diag_suppress 2670
+#endif
+
 #endif // not EIGEN_WARNINGS_DISABLED

Eigen/src/Core/util/ForwardDeclarations.h

@@ -94,12 +94,8 @@ template<typename BinaryOp,  typename Lhs, typename Rhs>  class CwiseBinaryOp;
 template<typename Decomposition, typename Rhstype>        class Solve;
 template<typename XprType>                                class Inverse;
 
-namespace internal {
-  template<typename Lhs, typename Rhs> struct product_tag;
-}
-
 template<typename Lhs, typename Rhs, int Option = DefaultProduct> class Product;
-         
+
 template<typename Derived> class DiagonalBase;
 template<typename _DiagonalVectorType> class DiagonalWrapper;
 template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime=SizeAtCompileTime> class DiagonalMatrix;
@@ -210,6 +206,8 @@ template<typename Scalar> struct scalar_add_op;
 template<typename Scalar> struct scalar_constant_op;
 template<typename Scalar> struct scalar_identity_op;
 template<typename Scalar,bool iscpx> struct scalar_sign_op;
+template<typename Scalar> struct scalar_igamma_op;
+template<typename Scalar> struct scalar_igammac_op;
 
 template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_product_op;
 template<typename LhsScalar,typename RhsScalar> struct scalar_multiple2_op;
@@ -252,6 +250,7 @@ template<typename MatrixType> struct inverse_impl;
 template<typename MatrixType> class HouseholderQR;
 template<typename MatrixType> class ColPivHouseholderQR;
 template<typename MatrixType> class FullPivHouseholderQR;
+template<typename MatrixType> class CompleteOrthogonalDecomposition;
 template<typename MatrixType, int QRPreconditioner = ColPivHouseholderQRPreconditioner> class JacobiSVD;
 template<typename MatrixType> class BDCSVD;
 template<typename MatrixType, int UpLo = Lower> class LLT;

Eigen/src/Core/util/MKL_support.h

@@ -49,7 +49,7 @@
   #define EIGEN_USE_LAPACKE
 #endif
 
-#if defined(EIGEN_USE_BLAS) || defined(EIGEN_USE_LAPACKE) || defined(EIGEN_USE_MKL_VML)
+#if defined(EIGEN_USE_LAPACKE) || defined(EIGEN_USE_MKL_VML)
   #define EIGEN_USE_MKL
 #endif
 
@@ -64,7 +64,6 @@
 #   ifndef EIGEN_USE_MKL
     /*If the MKL version is too old, undef everything*/
 #       undef   EIGEN_USE_MKL_ALL
-#       undef   EIGEN_USE_BLAS
 #       undef   EIGEN_USE_LAPACKE
 #       undef   EIGEN_USE_MKL_VML
 #       undef   EIGEN_USE_LAPACKE_STRICT
@@ -107,52 +106,23 @@
 #else
 #define EIGEN_MKL_DOMAIN_PARDISO MKL_PARDISO
 #endif
+#endif
 
 namespace Eigen {
 
 typedef std::complex<double> dcomplex;
 typedef std::complex<float>  scomplex;
 
-namespace internal {
+#if defined(EIGEN_USE_MKL)
-
+typedef MKL_INT BlasIndex;
-template<typename MKLType, typename EigenType>
+#else
-static inline void assign_scalar_eig2mkl(MKLType& mklScalar, const EigenType& eigenScalar) {
+typedef int BlasIndex;
-  mklScalar=eigenScalar;
+#endif
-}
-
-template<typename MKLType, typename EigenType>
-static inline void assign_conj_scalar_eig2mkl(MKLType& mklScalar, const EigenType& eigenScalar) {
-  mklScalar=eigenScalar;
-}
-
-template <>
-inline void assign_scalar_eig2mkl<MKL_Complex16,dcomplex>(MKL_Complex16& mklScalar, const dcomplex& eigenScalar) {
-  mklScalar.real=eigenScalar.real();
-  mklScalar.imag=eigenScalar.imag();
-}
-
-template <>
-inline void assign_scalar_eig2mkl<MKL_Complex8,scomplex>(MKL_Complex8& mklScalar, const scomplex& eigenScalar) {
-  mklScalar.real=eigenScalar.real();
-  mklScalar.imag=eigenScalar.imag();
-}
-
-template <>
-inline void assign_conj_scalar_eig2mkl<MKL_Complex16,dcomplex>(MKL_Complex16& mklScalar, const dcomplex& eigenScalar) {
-  mklScalar.real=eigenScalar.real();
-  mklScalar.imag=-eigenScalar.imag();
-}
-
-template <>
-inline void assign_conj_scalar_eig2mkl<MKL_Complex8,scomplex>(MKL_Complex8& mklScalar, const scomplex& eigenScalar) {
-  mklScalar.real=eigenScalar.real();
-  mklScalar.imag=-eigenScalar.imag();
-}
-
-} // end namespace internal
 
 } // end namespace Eigen
 
+#if defined(EIGEN_USE_BLAS)
+#include "../../misc/blas.h"
 #endif
 
 #endif // EIGEN_MKL_SUPPORT_H

Eigen/src/Core/util/Macros.h

@@ -13,7 +13,7 @@
 
 #define EIGEN_WORLD_VERSION 3
 #define EIGEN_MAJOR_VERSION 2
-#define EIGEN_MINOR_VERSION 91
+#define EIGEN_MINOR_VERSION 92
 
 #define EIGEN_VERSION_AT_LEAST(x,y,z) (EIGEN_WORLD_VERSION>x || (EIGEN_WORLD_VERSION>=x && \
                                       (EIGEN_MAJOR_VERSION>y || (EIGEN_MAJOR_VERSION>=y && \
@@ -99,9 +99,16 @@
   #define EIGEN_COMP_ARM 0
 #endif
 
+/// \internal EIGEN_COMP_ARM set to 1 if the compiler is ARM Compiler
+#if defined(__EMSCRIPTEN__)
+  #define EIGEN_COMP_EMSCRIPTEN 1
+#else
+  #define EIGEN_COMP_EMSCRIPTEN 0
+#endif
+
 
 /// \internal EIGEN_GNUC_STRICT set to 1 if the compiler is really GCC and not a compatible compiler (e.g., ICC, clang, mingw, etc.)
-#if EIGEN_COMP_GNUC && !(EIGEN_COMP_CLANG || EIGEN_COMP_ICC || EIGEN_COMP_MINGW || EIGEN_COMP_PGI || EIGEN_COMP_IBM || EIGEN_COMP_ARM )
+#if EIGEN_COMP_GNUC && !(EIGEN_COMP_CLANG || EIGEN_COMP_ICC || EIGEN_COMP_MINGW || EIGEN_COMP_PGI || EIGEN_COMP_IBM || EIGEN_COMP_ARM || EIGEN_COMP_EMSCRIPTEN)
   #define EIGEN_COMP_GNUC_STRICT 1
 #else
   #define EIGEN_COMP_GNUC_STRICT 0
@@ -336,25 +343,35 @@
 // Do we support r-value references?
 #if (__has_feature(cxx_rvalue_references) || \
     (defined(__cplusplus) && __cplusplus >= 201103L) || \
-     defined(__GXX_EXPERIMENTAL_CXX0X__) || \
     (EIGEN_COMP_MSVC >= 1600))
   #define EIGEN_HAVE_RVALUE_REFERENCES
 #endif
 
+// Does the compiler support C99?
+#if (defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901))       \
+  || (defined(__GNUC__) && defined(_GLIBCXX_USE_C99)) \
+  || (defined(_LIBCPP_VERSION) && !defined(_MSC_VER))
+#define EIGEN_HAS_C99_MATH 1
+#endif
+
 // Does the compiler support result_of?
 #if (__has_feature(cxx_lambdas) || (defined(__cplusplus) && __cplusplus >= 201103L))
 #define EIGEN_HAS_STD_RESULT_OF 1
 #endif
 
 // Does the compiler support variadic templates?
-#if __cplusplus > 199711L
+#if __cplusplus > 199711L || EIGEN_COMP_MSVC >= 1900
+// Disable the use of variadic templates when compiling with nvcc on ARM devices:
+// this prevents nvcc from crashing when compiling Eigen on Tegra X1
+#if !defined(__NVCC__) || !EIGEN_ARCH_ARM_OR_ARM64
 #define EIGEN_HAS_VARIADIC_TEMPLATES 1
 #endif
+#endif
 
 // Does the compiler support const expressions?
 #ifdef __CUDACC__
-// Const expressions are supported provided that c++11 is enabled and we're using nvcc 7.5 or above
+// Const expressions are supported provided that c++11 is enabled and we're using either clang or nvcc 7.5 or above
-#if defined(__CUDACC_VER__) &&  __CUDACC_VER__ >= 70500 && __cplusplus > 199711L
+#if __cplusplus > 199711L && defined(__CUDACC_VER__) && (defined(__clang__) || __CUDACC_VER__ >= 70500)
   #define EIGEN_HAS_CONSTEXPR 1
 #endif
 #elif (defined(__cplusplus) && __cplusplus >= 201402L) || \

Eigen/src/Core/util/Memory.h

@@ -59,28 +59,6 @@
 
 #endif
 
-#ifndef EIGEN_HAS_POSIX_MEMALIGN
-  // See bug 554 (http://eigen.tuxfamily.org/bz/show_bug.cgi?id=554)
-  // It seems to be unsafe to check _POSIX_ADVISORY_INFO without including unistd.h first.
-  // Currently, let's include it only on unix systems:
-  #if EIGEN_OS_UNIX && !(EIGEN_OS_SUN || EIGEN_OS_SOLARIS)
-    #include <unistd.h>
-    #if (EIGEN_OS_QNX || (defined _GNU_SOURCE) || EIGEN_COMP_PGI || ((defined _XOPEN_SOURCE) && (_XOPEN_SOURCE >= 600))) && (defined _POSIX_ADVISORY_INFO) && (_POSIX_ADVISORY_INFO > 0)
-      #define EIGEN_HAS_POSIX_MEMALIGN 1
-    #endif
-  #endif
-
-  #ifndef EIGEN_HAS_POSIX_MEMALIGN
-    #define EIGEN_HAS_POSIX_MEMALIGN 0
-  #endif
-#endif
-
-#if defined EIGEN_VECTORIZE_SSE || defined EIGEN_VECTORIZE_AVX || defined EIGEN_VECTORIZE_AVX512
-  #define EIGEN_HAS_MM_MALLOC 1
-#else
-  #define EIGEN_HAS_MM_MALLOC 0
-#endif
-
 namespace Eigen {
 
 namespace internal {
@@ -122,7 +100,7 @@ inline void handmade_aligned_free(void *ptr)
 
 /** \internal
   * \brief Reallocates aligned memory.
-  * Since we know that our handmade version is based on std::realloc
+  * Since we know that our handmade version is based on std::malloc
   * we can use std::realloc to implement efficient reallocation.
   */
 inline void* handmade_aligned_realloc(void* ptr, std::size_t size, std::size_t = 0)
@@ -141,47 +119,6 @@ inline void* handmade_aligned_realloc(void* ptr, std::size_t size, std::size_t =
   return aligned;
 }
 
-/*****************************************************************************
-*** Implementation of generic aligned realloc (when no realloc can be used)***
-*****************************************************************************/
-
-EIGEN_DEVICE_FUNC void* aligned_malloc(std::size_t size);
-EIGEN_DEVICE_FUNC void  aligned_free(void *ptr);
-
-/** \internal
-  * \brief Reallocates aligned memory.
-  * Allows reallocation with aligned ptr types. This implementation will
-  * always create a new memory chunk and copy the old data.
-  */
-inline void* generic_aligned_realloc(void* ptr, size_t size, size_t old_size)
-{
-  if (ptr==0)
-    return aligned_malloc(size);
-
-  if (size==0)
-  {
-    aligned_free(ptr);
-    return 0;
-  }
-
-  void* newptr = aligned_malloc(size);
-  if (newptr == 0)
-  {
-    #ifdef EIGEN_HAS_ERRNO
-    errno = ENOMEM; // according to the standard
-    #endif
-    return 0;
-  }
-
-  if (ptr != 0)
-  {
-    std::memcpy(newptr, ptr, (std::min)(size,old_size));
-    aligned_free(ptr);
-  }
-
-  return newptr;
-}
-
 /*****************************************************************************
 *** Implementation of portable aligned versions of malloc/free/realloc     ***
 *****************************************************************************/
@@ -218,16 +155,11 @@ EIGEN_DEVICE_FUNC inline void* aligned_malloc(size_t size)
   check_that_malloc_is_allowed();
 
   void *result;
-  #if EIGEN_DEFAULT_ALIGN_BYTES==0
+  #if (EIGEN_DEFAULT_ALIGN_BYTES==0) || EIGEN_MALLOC_ALREADY_ALIGNED
     result = std::malloc(size);
-  #elif EIGEN_MALLOC_ALREADY_ALIGNED
+    #if EIGEN_DEFAULT_ALIGN_BYTES==16
-    result = std::malloc(size);
+    eigen_assert((size<16 || (std::size_t(result)%16)==0) && "System's malloc returned an unaligned pointer. Compile with EIGEN_MALLOC_ALREADY_ALIGNED=0 to fallback to handmade alignd memory allocator.");
-  #elif EIGEN_HAS_POSIX_MEMALIGN
+    #endif
-    if(posix_memalign(&result, EIGEN_DEFAULT_ALIGN_BYTES, size)) result = 0;
-  #elif EIGEN_HAS_MM_MALLOC
-    result = _mm_malloc(size, EIGEN_DEFAULT_ALIGN_BYTES);
-  #elif EIGEN_OS_WIN_STRICT
-    result = _aligned_malloc(size, EIGEN_DEFAULT_ALIGN_BYTES);
   #else
     result = handmade_aligned_malloc(size);
   #endif
@@ -241,48 +173,25 @@ EIGEN_DEVICE_FUNC inline void* aligned_malloc(size_t size)
 /** \internal Frees memory allocated with aligned_malloc. */
 EIGEN_DEVICE_FUNC inline void aligned_free(void *ptr)
 {
-  #if EIGEN_DEFAULT_ALIGN_BYTES==0
+  #if (EIGEN_DEFAULT_ALIGN_BYTES==0) || EIGEN_MALLOC_ALREADY_ALIGNED
     std::free(ptr);
-  #elif EIGEN_MALLOC_ALREADY_ALIGNED
-    std::free(ptr);
-  #elif EIGEN_HAS_POSIX_MEMALIGN
-    free(ptr);
-  #elif EIGEN_HAS_MM_MALLOC
-    _mm_free(ptr);
-  #elif EIGEN_OS_WIN_STRICT
-    _aligned_free(ptr);
   #else
     handmade_aligned_free(ptr);
   #endif
 }
 
 /**
-* \internal
+  * \internal
-* \brief Reallocates an aligned block of memory.
+  * \brief Reallocates an aligned block of memory.
-* \throws std::bad_alloc on allocation failure
+  * \throws std::bad_alloc on allocation failure
-**/
+  */
 inline void* aligned_realloc(void *ptr, size_t new_size, size_t old_size)
 {
   EIGEN_UNUSED_VARIABLE(old_size);
 
   void *result;
-#if EIGEN_DEFAULT_ALIGN_BYTES==0
+#if (EIGEN_DEFAULT_ALIGN_BYTES==0) || EIGEN_MALLOC_ALREADY_ALIGNED
   result = std::realloc(ptr,new_size);
-#elif EIGEN_MALLOC_ALREADY_ALIGNED
-  result = std::realloc(ptr,new_size);
-#elif EIGEN_HAS_POSIX_MEMALIGN
-  result = generic_aligned_realloc(ptr,new_size,old_size);
-#elif EIGEN_HAS_MM_MALLOC
-  // The defined(_mm_free) is just here to verify that this MSVC version
-  // implements _mm_malloc/_mm_free based on the corresponding _aligned_
-  // functions. This may not always be the case and we just try to be safe.
-  #if EIGEN_OS_WIN_STRICT && defined(_mm_free)
-    result = _aligned_realloc(ptr,new_size,EIGEN_DEFAULT_ALIGN_BYTES);
-  #else
-    result = generic_aligned_realloc(ptr,new_size,old_size);
-  #endif
-#elif EIGEN_OS_WIN_STRICT
-  result = _aligned_realloc(ptr,new_size,EIGEN_DEFAULT_ALIGN_BYTES);
 #else
   result = handmade_aligned_realloc(ptr,new_size,old_size);
 #endif
@@ -524,11 +433,11 @@ template<typename T, bool Align> EIGEN_DEVICE_FUNC inline void conditional_align
   * \sa first_default_aligned()
   */
 template<int Alignment, typename Scalar, typename Index>
-inline Index first_aligned(const Scalar* array, Index size)
+EIGEN_DEVICE_FUNC inline Index first_aligned(const Scalar* array, Index size)
 {
-  static const Index ScalarSize = sizeof(Scalar);
+  const Index ScalarSize = sizeof(Scalar);
-  static const Index AlignmentSize = Alignment / ScalarSize;
+  const Index AlignmentSize = Alignment / ScalarSize;
-  static const Index AlignmentMask = AlignmentSize-1;
+  const Index AlignmentMask = AlignmentSize-1;
 
   if(AlignmentSize<=1)
   {
@@ -544,14 +453,15 @@ inline Index first_aligned(const Scalar* array, Index size)
   }
   else
   {
-    return std::min<Index>( (AlignmentSize - (Index((std::size_t(array)/sizeof(Scalar))) & AlignmentMask)) & AlignmentMask, size);
+    Index first = (AlignmentSize - (Index((std::size_t(array)/sizeof(Scalar))) & AlignmentMask)) & AlignmentMask;
+    return (first < size) ? first : size;
   }
 }
 
 /** \internal Returns the index of the first element of the array that is well aligned with respect the largest packet requirement.
    * \sa first_aligned(Scalar*,Index) and first_default_aligned(DenseBase<Derived>) */
 template<typename Scalar, typename Index>
-inline Index first_default_aligned(const Scalar* array, Index size)
+EIGEN_DEVICE_FUNC inline Index first_default_aligned(const Scalar* array, Index size)
 {
   typedef typename packet_traits<Scalar>::type DefaultPacketType;
   return first_aligned<unpacket_traits<DefaultPacketType>::alignment>(array, size);
@@ -576,7 +486,12 @@ template<typename T> EIGEN_DEVICE_FUNC void smart_copy(const T* start, const T*
 
 template<typename T> struct smart_copy_helper<T,true> {
   EIGEN_DEVICE_FUNC static inline void run(const T* start, const T* end, T* target)
-  { memcpy(target, start, std::ptrdiff_t(end)-std::ptrdiff_t(start)); }
+  {
+    std::ptrdiff_t size = std::ptrdiff_t(end)-std::ptrdiff_t(start);
+    if(size==0) return;
+    eigen_internal_assert(start!=0 && end!=0 && target!=0);
+    memcpy(target, start, size);
+  }
 };
 
 template<typename T> struct smart_copy_helper<T,false> {
@@ -594,7 +509,12 @@ template<typename T> void smart_memmove(const T* start, const T* end, T* target)
 
 template<typename T> struct smart_memmove_helper<T,true> {
   static inline void run(const T* start, const T* end, T* target)
-  { std::memmove(target, start, std::ptrdiff_t(end)-std::ptrdiff_t(start)); }
+  {
+    std::ptrdiff_t size = std::ptrdiff_t(end)-std::ptrdiff_t(start);
+    if(size==0) return;
+    eigen_internal_assert(start!=0 && end!=0 && target!=0);
+    std::memmove(target, start, size);
+  }
 };
 
 template<typename T> struct smart_memmove_helper<T,false> {
@@ -784,7 +704,7 @@ template<typename T> void swap(scoped_array<T> &a,scoped_array<T> &b)
 * std::map< int, Vector3f > my_map_vec3;
 * \endcode
 *
-* \sa \ref TopicStlContainers.
+* \sa \blank \ref TopicStlContainers.
 */
 template<class T>
 class aligned_allocator : public std::allocator<T>