From d6d39c7ddb127d91ebfa4ea62e93ea51036f1760 Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Tue, 7 Jun 2016 14:35:08 -0700
Subject: [PATCH 01/86] Added missing EIGEN_DEVICE_FUNC

---
 unsupported/Eigen/CXX11/src/Tensor/TensorMorphing.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorMorphing.h b/unsupported/Eigen/CXX11/src/Tensor/TensorMorphing.h
index 52cfc2824..d34f1e328 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorMorphing.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorMorphing.h
@@ -148,7 +148,7 @@ struct TensorEvaluator<const TensorReshapingOp<NewDimensions, ArgType>, Device>
 
   EIGEN_DEVICE_FUNC Scalar* data() const { return const_cast<Scalar*>(m_impl.data()); }
 
-  const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }
+  EIGEN_DEVICE_FUNC const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }
 
  protected:
   TensorEvaluator<ArgType, Device> m_impl;

From 8fd57a97f203edac3f7e8681eafe752294386a24 Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Tue, 7 Jun 2016 18:22:18 -0700
Subject: [PATCH 02/86] Enable the vectorization of adds and mults of fp16

---
 Eigen/src/Core/arch/CUDA/PacketMathHalf.h | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Eigen/src/Core/arch/CUDA/PacketMathHalf.h b/Eigen/src/Core/arch/CUDA/PacketMathHalf.h
index 51386506f..959dff886 100644
--- a/Eigen/src/Core/arch/CUDA/PacketMathHalf.h
+++ b/Eigen/src/Core/arch/CUDA/PacketMathHalf.h
@@ -28,6 +28,8 @@ template<> struct packet_traits<Eigen::half> : default_packet_traits
     AlignedOnScalar = 1,
     size=2,
     HasHalfPacket = 0,
+    HasAdd    = 1,
+    HasMul    = 1,
     HasDiv    = 1,
     HasSqrt   = 1,
     HasRsqrt  = 1,

From 9dd9d58273362d643eaa0b8f4f16f8aa3d5ef6cd Mon Sep 17 00:00:00 2001
From: Christoph Hertzberg <chtz@informatik.uni-bremen.de>
Date: Wed, 8 Jun 2016 15:36:42 +0200
Subject: [PATCH 03/86] Copied a regression test from 3.2 branch.

---
 test/geo_homogeneous.cpp | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/test/geo_homogeneous.cpp b/test/geo_homogeneous.cpp
index bf63c69ec..305794cdf 100644
--- a/test/geo_homogeneous.cpp
+++ b/test/geo_homogeneous.cpp
@@ -58,6 +58,8 @@ template<typename Scalar,int Size> void homogeneous(void)
   T2MatrixType t2 = T2MatrixType::Random();
   VERIFY_IS_APPROX(t2 * (v0.homogeneous().eval()), t2 * v0.homogeneous());
   VERIFY_IS_APPROX(t2 * (m0.colwise().homogeneous().eval()), t2 * m0.colwise().homogeneous());
+  VERIFY_IS_APPROX(t2 * (v0.homogeneous().asDiagonal()), t2 * hv0.asDiagonal());
+  VERIFY_IS_APPROX((v0.homogeneous().asDiagonal()) * t2, hv0.asDiagonal() * t2);
 
   VERIFY_IS_APPROX((v0.transpose().rowwise().homogeneous().eval()) * t2,
                     v0.transpose().rowwise().homogeneous() * t2);

From 9fc8379328dad5fb74249003f56fb608c304ae4d Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Wed, 8 Jun 2016 16:39:11 +0200
Subject: [PATCH 04/86] Fix extraction of complex eigenvalue pairs in real
 generalized eigenvalue problems.

---
 .../src/Eigenvalues/GeneralizedEigenSolver.h  | 32 +++++++++++++++----
 1 file changed, 26 insertions(+), 6 deletions(-)

diff --git a/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h b/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
index a9d6790d5..07a9ccf46 100644
--- a/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
+++ b/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
@@ -327,13 +327,33 @@ GeneralizedEigenSolver<MatrixType>::compute(const MatrixType& A, const MatrixTyp
       }
       else
       {
-        Scalar p = Scalar(0.5) * (m_matS.coeff(i, i) - m_matS.coeff(i+1, i+1));
-        Scalar z = sqrt(abs(p * p + m_matS.coeff(i+1, i) * m_matS.coeff(i, i+1)));
-        m_alphas.coeffRef(i)   = ComplexScalar(m_matS.coeff(i+1, i+1) + p, z);
-        m_alphas.coeffRef(i+1) = ComplexScalar(m_matS.coeff(i+1, i+1) + p, -z);
+        // We need to extract the generalized eigenvalues of the pair of a general 2x2 block S and a triangular 2x2 block T
+        // From the eigen decomposition of T = U * E * U^-1,
+        // we can extract the eigenvalues of (U^-1 * S * U) / E
+        // Here, we can take advantage that E = diag(T), and U = [ 1 T_01 ; 0 T_11-T_00], and U^-1 = [1 -T_11/(T_11-T_00) ; 0 1/(T_11-T_00)].
+        // Then taking beta=T_00*T_11*(T_11-T_00), we can avoid any division, and alpha is the eigenvalues of A = (U^-1 * S * U) * diag(T_11,T_00) * (T_11-T_00):
+
+        // T =  [a b ; 0 c]
+        // S =  [e f ; g h]
+        RealScalar a = m_realQZ.matrixT().coeff(i, i), b = m_realQZ.matrixT().coeff(i, i+1), c = m_realQZ.matrixT().coeff(i+1, i+1);
+        RealScalar e = m_matS.coeff(i, i), f = m_matS.coeff(i, i+1), g = m_matS.coeff(i+1, i), h = m_matS.coeff(i+1, i+1);
+        RealScalar d = c-a;
+        RealScalar gb = g*b;
+        Matrix<RealScalar,2,2> A;
+        A <<  (e*d-gb)*c,  ((e*b+f*d-h*b)*d-gb*b)*a,
+              g*c       ,  (gb+h*d)*a;
+
+        // NOTE, we could also compute the SVD of T's block during the QZ factorization so that the respective T block is guaranteed to be diagonal,
+        // and then we could directly apply the formula below (while taking care of scaling S columns by T11,T00):
+
+        Scalar p = Scalar(0.5) * (A.coeff(i, i) - A.coeff(i+1, i+1));
+        Scalar z = sqrt(abs(p * p + A.coeff(i+1, i) * A.coeff(i, i+1)));
+        m_alphas.coeffRef(i)   = ComplexScalar(A.coeff(i+1, i+1) + p, z);
+        m_alphas.coeffRef(i+1) = ComplexScalar(A.coeff(i+1, i+1) + p, -z);
+
+        m_betas.coeffRef(i)   =
+        m_betas.coeffRef(i+1) = a*c*d;
 
-        m_betas.coeffRef(i)   = m_realQZ.matrixT().coeff(i,i);
-        m_betas.coeffRef(i+1) = m_realQZ.matrixT().coeff(i,i);
         i += 2;
       }
     }

From df095cab104550a8179c28e93d477406dfab6849 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Wed, 8 Jun 2016 18:31:19 +0200
Subject: [PATCH 05/86] Fixes for PARDISO: warnings, and defaults to metis+
 in-core mode.

---
 Eigen/src/PardisoSupport/PardisoSupport.h | 35 ++++++++++++++---------
 1 file changed, 22 insertions(+), 13 deletions(-)

diff --git a/Eigen/src/PardisoSupport/PardisoSupport.h b/Eigen/src/PardisoSupport/PardisoSupport.h
index 80d914f25..091c3970e 100644
--- a/Eigen/src/PardisoSupport/PardisoSupport.h
+++ b/Eigen/src/PardisoSupport/PardisoSupport.h
@@ -183,7 +183,7 @@ class PardisoImpl : public SparseSolverBase<Derived>
     {
       if(m_isInitialized) // Factorization ran at least once
       {
-        internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, -1, m_size,0, 0, 0, m_perm.data(), 0,
+        internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, -1, internal::convert_index<StorageIndex>(m_size),0, 0, 0, m_perm.data(), 0,
                                                           m_iparm.data(), m_msglvl, NULL, NULL);
         m_isInitialized = false;
       }
@@ -194,11 +194,11 @@ class PardisoImpl : public SparseSolverBase<Derived>
       m_type = type;
       bool symmetric = std::abs(m_type) < 10;
       m_iparm[0] = 1;   // No solver default
-      m_iparm[1] = 3;   // use Metis for the ordering
-      m_iparm[2] = 1;   // Numbers of processors, value of OMP_NUM_THREADS
+      m_iparm[1] = 2;   // use Metis for the ordering
+      m_iparm[2] = 0;   // Reserved. Set to zero. (??Numbers of processors, value of OMP_NUM_THREADS??)
       m_iparm[3] = 0;   // No iterative-direct algorithm
       m_iparm[4] = 0;   // No user fill-in reducing permutation
-      m_iparm[5] = 0;   // Write solution into x
+      m_iparm[5] = 0;   // Write solution into x, b is left unchanged
       m_iparm[6] = 0;   // Not in use
       m_iparm[7] = 2;   // Max numbers of iterative refinement steps
       m_iparm[8] = 0;   // Not in use
@@ -219,7 +219,8 @@ class PardisoImpl : public SparseSolverBase<Derived>
       m_iparm[26] = 0;  // No matrix checker
       m_iparm[27] = (sizeof(RealScalar) == 4) ? 1 : 0;
       m_iparm[34] = 1;  // C indexing
-      m_iparm[59] = 1;  // Automatic switch between In-Core and Out-of-Core modes
+      m_iparm[36] = 0;  // CSR
+      m_iparm[59] = 0;  // 0 - In-Core ; 1 - Automatic switch between In-Core and Out-of-Core modes ; 2 - Out-of-Core
       
       memset(m_pt, 0, sizeof(m_pt));
     }
@@ -246,7 +247,7 @@ class PardisoImpl : public SparseSolverBase<Derived>
     mutable SparseMatrixType m_matrix;
     mutable ComputationInfo m_info;
     bool m_analysisIsOk, m_factorizationIsOk;
-    Index m_type, m_msglvl;
+    StorageIndex m_type, m_msglvl;
     mutable void *m_pt[64];
     mutable ParameterType m_iparm;
     mutable IntColVectorType m_perm;
@@ -265,10 +266,9 @@ Derived& PardisoImpl<Derived>::compute(const MatrixType& a)
   derived().getMatrix(a);
   
   Index error;
-  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 12, m_size,
+  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 12, internal::convert_index<StorageIndex>(m_size),
                                                             m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
                                                             m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
-
   manageErrorCode(error);
   m_analysisIsOk = true;
   m_factorizationIsOk = true;
@@ -287,7 +287,7 @@ Derived& PardisoImpl<Derived>::analyzePattern(const MatrixType& a)
   derived().getMatrix(a);
   
   Index error;
-  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 11, m_size,
+  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 11, internal::convert_index<StorageIndex>(m_size),
                                                             m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
                                                             m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
   
@@ -306,8 +306,8 @@ Derived& PardisoImpl<Derived>::factorize(const MatrixType& a)
   
   derived().getMatrix(a);
 
-  Index error;  
-  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 22, m_size,
+  Index error;
+  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 22, internal::convert_index<StorageIndex>(m_size),
                                                             m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
                                                             m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
   
@@ -354,9 +354,9 @@ void PardisoImpl<Derived>::_solve_impl(const MatrixBase<BDerived> &b, MatrixBase
   }
   
   Index error;
-  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 33, m_size,
+  error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 33, internal::convert_index<StorageIndex>(m_size),
                                                             m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
-                                                            m_perm.data(), nrhs, m_iparm.data(), m_msglvl,
+                                                            m_perm.data(), internal::convert_index<StorageIndex>(nrhs), m_iparm.data(), m_msglvl,
                                                             rhs_ptr, x.derived().data());
 
   manageErrorCode(error);
@@ -371,6 +371,9 @@ void PardisoImpl<Derived>::_solve_impl(const MatrixBase<BDerived> &b, MatrixBase
   * using the Intel MKL PARDISO library. The sparse matrix A must be squared and invertible.
   * The vectors or matrices X and B can be either dense or sparse.
   *
+  * By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:
+  * \code solver.pardisoParameterArray()[59] = 1; \endcode
+  *
   * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
   *
   * \implsparsesolverconcept
@@ -421,6 +424,9 @@ class PardisoLU : public PardisoImpl< PardisoLU<MatrixType> >
   * using the Intel MKL PARDISO library. The sparse matrix A must be selfajoint and positive definite.
   * The vectors or matrices X and B can be either dense or sparse.
   *
+  * By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:
+  * \code solver.pardisoParameterArray()[59] = 1; \endcode
+  *
   * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
   * \tparam UpLo can be any bitwise combination of Upper, Lower. The default is Upper, meaning only the upper triangular part has to be used.
   *         Upper|Lower can be used to tell both triangular parts can be used as input.
@@ -480,6 +486,9 @@ class PardisoLLT : public PardisoImpl< PardisoLLT<MatrixType,_UpLo> >
   * For complex matrices, A can also be symmetric only, see the \a Options template parameter.
   * The vectors or matrices X and B can be either dense or sparse.
   *
+  * By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:
+  * \code solver.pardisoParameterArray()[59] = 1; \endcode
+  *
   * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
   * \tparam Options can be any bitwise combination of Upper, Lower, and Symmetric. The default is Upper, meaning only the upper triangular part has to be used.
   *         Symmetric can be used for symmetric, non-selfadjoint complex matrices, the default being to assume a selfadjoint matrix.

From 0beabb4776b887c25977186b5af6811eb49aaa23 Mon Sep 17 00:00:00 2001
From: Abhijit Kundu <abhijit.dgp@gmail.com>
Date: Wed, 8 Jun 2016 16:12:04 -0400
Subject: [PATCH 06/86] Fixed type conversion from int

---
 Eigen/src/Geometry/Transform.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Eigen/src/Geometry/Transform.h b/Eigen/src/Geometry/Transform.h
index 1a06c1e35..073f4dcd1 100644
--- a/Eigen/src/Geometry/Transform.h
+++ b/Eigen/src/Geometry/Transform.h
@@ -1367,7 +1367,7 @@ struct transform_right_product_impl< TransformType, MatrixType, 2, 1> // rhs is
     EIGEN_STATIC_ASSERT(OtherRows==Dim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);
 
     Matrix<typename ResultType::Scalar, Dim+1, 1> rhs;
-    rhs.template head<Dim>() = other; rhs[Dim] = 1;
+    rhs.template head<Dim>() = other; rhs[Dim] = typename ResultType::Scalar(1);
     Matrix<typename ResultType::Scalar, WorkingRows, 1> res(T.matrix() * rhs);
     return res.template head<Dim>();
   }

From a20d2ec1c02d2629cbfa8871898b64cd22445595 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Thu, 9 Jun 2016 16:16:22 +0200
Subject: [PATCH 07/86] Fix shadow variable, and indexing.

---
 Eigen/src/Eigenvalues/GeneralizedEigenSolver.h | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h b/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
index 07a9ccf46..08caed281 100644
--- a/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
+++ b/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
@@ -339,17 +339,17 @@ GeneralizedEigenSolver<MatrixType>::compute(const MatrixType& A, const MatrixTyp
         RealScalar e = m_matS.coeff(i, i), f = m_matS.coeff(i, i+1), g = m_matS.coeff(i+1, i), h = m_matS.coeff(i+1, i+1);
         RealScalar d = c-a;
         RealScalar gb = g*b;
-        Matrix<RealScalar,2,2> A;
-        A <<  (e*d-gb)*c,  ((e*b+f*d-h*b)*d-gb*b)*a,
-              g*c       ,  (gb+h*d)*a;
+        Matrix<RealScalar,2,2> S2;
+        S2 <<  (e*d-gb)*c,  ((e*b+f*d-h*b)*d-gb*b)*a,
+               g*c       ,  (gb+h*d)*a;
 
         // NOTE, we could also compute the SVD of T's block during the QZ factorization so that the respective T block is guaranteed to be diagonal,
         // and then we could directly apply the formula below (while taking care of scaling S columns by T11,T00):
 
-        Scalar p = Scalar(0.5) * (A.coeff(i, i) - A.coeff(i+1, i+1));
-        Scalar z = sqrt(abs(p * p + A.coeff(i+1, i) * A.coeff(i, i+1)));
-        m_alphas.coeffRef(i)   = ComplexScalar(A.coeff(i+1, i+1) + p, z);
-        m_alphas.coeffRef(i+1) = ComplexScalar(A.coeff(i+1, i+1) + p, -z);
+        Scalar p = Scalar(0.5) * (S2.coeff(0,0) - S2.coeff(1,1));
+        Scalar z = sqrt(abs(p * p + S2.coeff(1,0) * S2.coeff(0,1)));
+        m_alphas.coeffRef(i)   = ComplexScalar(S2.coeff(1,1) + p,  z);
+        m_alphas.coeffRef(i+1) = ComplexScalar(S2.coeff(1,1) + p, -z);
 
         m_betas.coeffRef(i)   =
         m_betas.coeffRef(i+1) = a*c*d;

From 15890c304edbccedc8a989468ed3fc475f428059 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Thu, 9 Jun 2016 16:17:27 +0200
Subject: [PATCH 08/86] Add unit test for non symmetric generalized eigenvalues

---
 test/eigensolver_generalized_real.cpp | 32 ++++++++++++++++++++-------
 1 file changed, 24 insertions(+), 8 deletions(-)

diff --git a/test/eigensolver_generalized_real.cpp b/test/eigensolver_generalized_real.cpp
index a46a2e50e..da14482de 100644
--- a/test/eigensolver_generalized_real.cpp
+++ b/test/eigensolver_generalized_real.cpp
@@ -1,7 +1,7 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
-// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2012-2016 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
@@ -10,6 +10,7 @@
 #include "main.h"
 #include <limits>
 #include <Eigen/Eigenvalues>
+#include <Eigen/LU>
 
 template<typename MatrixType> void generalized_eigensolver_real(const MatrixType& m)
 {
@@ -21,6 +22,7 @@ template<typename MatrixType> void generalized_eigensolver_real(const MatrixType
   Index cols = m.cols();
 
   typedef typename MatrixType::Scalar Scalar;
+  typedef std::complex<Scalar> ComplexScalar;
   typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
 
   MatrixType a = MatrixType::Random(rows,cols);
@@ -31,14 +33,28 @@ template<typename MatrixType> void generalized_eigensolver_real(const MatrixType
   MatrixType spdB =  b.adjoint() * b + b1.adjoint() * b1;
 
   // lets compare to GeneralizedSelfAdjointEigenSolver
-  GeneralizedSelfAdjointEigenSolver<MatrixType> symmEig(spdA, spdB);
-  GeneralizedEigenSolver<MatrixType> eig(spdA, spdB);
+  {
+    GeneralizedSelfAdjointEigenSolver<MatrixType> symmEig(spdA, spdB);
+    GeneralizedEigenSolver<MatrixType> eig(spdA, spdB);
 
-  VERIFY_IS_EQUAL(eig.eigenvalues().imag().cwiseAbs().maxCoeff(), 0);
+    VERIFY_IS_EQUAL(eig.eigenvalues().imag().cwiseAbs().maxCoeff(), 0);
 
-  VectorType realEigenvalues = eig.eigenvalues().real();
-  std::sort(realEigenvalues.data(), realEigenvalues.data()+realEigenvalues.size());
-  VERIFY_IS_APPROX(realEigenvalues, symmEig.eigenvalues());
+    VectorType realEigenvalues = eig.eigenvalues().real();
+    std::sort(realEigenvalues.data(), realEigenvalues.data()+realEigenvalues.size());
+    VERIFY_IS_APPROX(realEigenvalues, symmEig.eigenvalues());
+  }
+
+  // non symmetric case:
+  {
+    GeneralizedEigenSolver<MatrixType> eig(a,b);
+    for(Index k=0; k<cols; ++k)
+    {
+      Matrix<ComplexScalar,Dynamic,Dynamic> tmp = (eig.betas()(k)*a).template cast<ComplexScalar>() - eig.alphas()(k)*b;
+      if(tmp.norm()>(std::numeric_limits<Scalar>::min)())
+        tmp /= tmp.norm();
+      VERIFY_IS_MUCH_SMALLER_THAN( std::abs(tmp.determinant()), Scalar(1) );
+    }
+  }
 
   // regression test for bug 1098
   {
@@ -57,7 +73,7 @@ void test_eigensolver_generalized_real()
     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
     CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(s,s)) );
 
-    // some trivial but implementation-wise tricky cases
+    // some trivial but implementation-wise special cases
     CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(1,1)) );
     CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(2,2)) );
     CALL_SUBTEST_3( generalized_eigensolver_real(Matrix<double,1,1>()) );

From c1f9ca925405c8fad126f327b4bdca7f983fc96e Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Thu, 9 Jun 2016 17:11:03 +0200
Subject: [PATCH 09/86] Update RealQZ to reduce 2x2 diagonal block of T
 corresponding to non reduced diagonal block of S to positive diagonal form.
 This step involve a real 2x2 SVD problem. The respective routine is thus in
 src/misc/ to be shared by both EVD and AVD modules.

---
 Eigen/Eigenvalues              |  1 +
 Eigen/SVD                      |  1 +
 Eigen/src/Eigenvalues/RealQZ.h | 32 +++++++++++++++++++-
 Eigen/src/SVD/JacobiSVD.h      | 32 --------------------
 Eigen/src/misc/RealSvd2x2.h    | 54 ++++++++++++++++++++++++++++++++++
 5 files changed, 87 insertions(+), 33 deletions(-)
 create mode 100644 Eigen/src/misc/RealSvd2x2.h

diff --git a/Eigen/Eigenvalues b/Eigen/Eigenvalues
index ea93eb303..216a6d51d 100644
--- a/Eigen/Eigenvalues
+++ b/Eigen/Eigenvalues
@@ -32,6 +32,7 @@
   * \endcode
   */
 
+#include "src/misc/RealSvd2x2.h"
 #include "src/Eigenvalues/Tridiagonalization.h"
 #include "src/Eigenvalues/RealSchur.h"
 #include "src/Eigenvalues/EigenSolver.h"
diff --git a/Eigen/SVD b/Eigen/SVD
index b353f3f54..565d9c90d 100644
--- a/Eigen/SVD
+++ b/Eigen/SVD
@@ -31,6 +31,7 @@
   * \endcode
   */
 
+#include "src/misc/RealSvd2x2.h"
 #include "src/SVD/UpperBidiagonalization.h"
 #include "src/SVD/SVDBase.h"
 #include "src/SVD/JacobiSVD.h"
diff --git a/Eigen/src/Eigenvalues/RealQZ.h b/Eigen/src/Eigenvalues/RealQZ.h
index a62071d42..c4715b954 100644
--- a/Eigen/src/Eigenvalues/RealQZ.h
+++ b/Eigen/src/Eigenvalues/RealQZ.h
@@ -552,7 +552,6 @@ namespace Eigen {
       m_T.coeffRef(l,l-1) = Scalar(0.0);
     }
 
-
   template<typename MatrixType>
     RealQZ<MatrixType>& RealQZ<MatrixType>::compute(const MatrixType& A_in, const MatrixType& B_in, bool computeQZ)
     {
@@ -616,6 +615,37 @@ namespace Eigen {
       }
       // check if we converged before reaching iterations limit
       m_info = (local_iter<m_maxIters) ? Success : NoConvergence;
+
+      // For each non triangular 2x2 diagonal block of S,
+      //    reduce the respective 2x2 diagonal block of T to positive diagonal form using 2x2 SVD.
+      // This step is not mandatory for QZ, but it does help further extraction of eigenvalues/eigenvectors,
+      // and is in par with Lapack/Matlab QZ.
+      if(m_info==Success)
+      {
+        for(Index i=0; i<dim-1; ++i)
+        {
+          if(m_S.coeff(i+1, i) != Scalar(0))
+          {
+            JacobiRotation<Scalar> j_left, j_right;
+            internal::real_2x2_jacobi_svd(m_T, i, i+1, &j_left, &j_right);
+
+            // Apply resulting Jacobi rotations
+            m_T.applyOnTheLeft(i,i+1,j_left);
+            m_T.applyOnTheRight(i,i+1,j_right);
+            m_S.applyOnTheLeft(i,i+1,j_left);
+            m_S.applyOnTheRight(i,i+1,j_right);
+            m_T(i,i+1) = Scalar(0);
+
+            if(m_computeQZ) {
+              m_Q.applyOnTheRight(i,i+1,j_left.transpose());
+              m_Z.applyOnTheLeft(i,i+1,j_right.transpose());
+            }
+
+            i++;
+          }
+        }
+      }
+
       return *this;
     } // end compute
 
diff --git a/Eigen/src/SVD/JacobiSVD.h b/Eigen/src/SVD/JacobiSVD.h
index 1940c8294..b83fd7a4d 100644
--- a/Eigen/src/SVD/JacobiSVD.h
+++ b/Eigen/src/SVD/JacobiSVD.h
@@ -419,38 +419,6 @@ struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
   }
 };
 
-template<typename MatrixType, typename RealScalar, typename Index>
-void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
-                         JacobiRotation<RealScalar> *j_left,
-                         JacobiRotation<RealScalar> *j_right)
-{
-  using std::sqrt;
-  using std::abs;
-  Matrix<RealScalar,2,2> m;
-  m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),
-       numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,q));
-  JacobiRotation<RealScalar> rot1;
-  RealScalar t = m.coeff(0,0) + m.coeff(1,1);
-  RealScalar d = m.coeff(1,0) - m.coeff(0,1);
-  if(d == RealScalar(0))
-  {
-    rot1.s() = RealScalar(0);
-    rot1.c() = RealScalar(1);
-  }
-  else
-  {
-    // If d!=0, then t/d cannot overflow because the magnitude of the
-    // entries forming d are not too small compared to the ones forming t.
-    RealScalar u = t / d;
-    RealScalar tmp = sqrt(RealScalar(1) + numext::abs2(u));
-    rot1.s() = RealScalar(1) / tmp;
-    rot1.c() = u / tmp;
-  }
-  m.applyOnTheLeft(0,1,rot1);
-  j_right->makeJacobi(m,0,1);
-  *j_left = rot1 * j_right->transpose();
-}
-
 template<typename _MatrixType, int QRPreconditioner> 
 struct traits<JacobiSVD<_MatrixType,QRPreconditioner> >
 {
diff --git a/Eigen/src/misc/RealSvd2x2.h b/Eigen/src/misc/RealSvd2x2.h
new file mode 100644
index 000000000..cdd7777d2
--- /dev/null
+++ b/Eigen/src/misc/RealSvd2x2.h
@@ -0,0 +1,54 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2013-2016 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_REALSVD2X2_H
+#define EIGEN_REALSVD2X2_H
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename MatrixType, typename RealScalar, typename Index>
+void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
+                         JacobiRotation<RealScalar> *j_left,
+                         JacobiRotation<RealScalar> *j_right)
+{
+  using std::sqrt;
+  using std::abs;
+  Matrix<RealScalar,2,2> m;
+  m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),
+       numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,q));
+  JacobiRotation<RealScalar> rot1;
+  RealScalar t = m.coeff(0,0) + m.coeff(1,1);
+  RealScalar d = m.coeff(1,0) - m.coeff(0,1);
+  if(d == RealScalar(0))
+  {
+    rot1.s() = RealScalar(0);
+    rot1.c() = RealScalar(1);
+  }
+  else
+  {
+    // If d!=0, then t/d cannot overflow because the magnitude of the
+    // entries forming d are not too small compared to the ones forming t.
+    RealScalar u = t / d;
+    RealScalar tmp = sqrt(RealScalar(1) + numext::abs2(u));
+    rot1.s() = RealScalar(1) / tmp;
+    rot1.c() = u / tmp;
+  }
+  m.applyOnTheLeft(0,1,rot1);
+  j_right->makeJacobi(m,0,1);
+  *j_left = rot1 * j_right->transpose();
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_REALSVD2X2_H
\ No newline at end of file

From 2bd59b0e0d667dcdcb6b070596a1bf023e3e88f1 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Thu, 9 Jun 2016 17:12:03 +0200
Subject: [PATCH 10/86] Take advantage that T is already diagonal in the
 extraction of generalized complex eigenvalues.

---
 .../src/Eigenvalues/GeneralizedEigenSolver.h  | 25 ++++++-------------
 1 file changed, 7 insertions(+), 18 deletions(-)

diff --git a/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h b/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
index 08caed281..9f43fd544 100644
--- a/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
+++ b/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
@@ -327,24 +327,13 @@ GeneralizedEigenSolver<MatrixType>::compute(const MatrixType& A, const MatrixTyp
       }
       else
       {
-        // We need to extract the generalized eigenvalues of the pair of a general 2x2 block S and a triangular 2x2 block T
-        // From the eigen decomposition of T = U * E * U^-1,
-        // we can extract the eigenvalues of (U^-1 * S * U) / E
-        // Here, we can take advantage that E = diag(T), and U = [ 1 T_01 ; 0 T_11-T_00], and U^-1 = [1 -T_11/(T_11-T_00) ; 0 1/(T_11-T_00)].
-        // Then taking beta=T_00*T_11*(T_11-T_00), we can avoid any division, and alpha is the eigenvalues of A = (U^-1 * S * U) * diag(T_11,T_00) * (T_11-T_00):
+        // We need to extract the generalized eigenvalues of the pair of a general 2x2 block S and a positive diagonal 2x2 block T
+        // Then taking beta=T_00*T_11, we can avoid any division, and alpha is the eigenvalues of A = (U^-1 * S * U) * diag(T_11,T_00):
 
-        // T =  [a b ; 0 c]
-        // S =  [e f ; g h]
-        RealScalar a = m_realQZ.matrixT().coeff(i, i), b = m_realQZ.matrixT().coeff(i, i+1), c = m_realQZ.matrixT().coeff(i+1, i+1);
-        RealScalar e = m_matS.coeff(i, i), f = m_matS.coeff(i, i+1), g = m_matS.coeff(i+1, i), h = m_matS.coeff(i+1, i+1);
-        RealScalar d = c-a;
-        RealScalar gb = g*b;
-        Matrix<RealScalar,2,2> S2;
-        S2 <<  (e*d-gb)*c,  ((e*b+f*d-h*b)*d-gb*b)*a,
-               g*c       ,  (gb+h*d)*a;
-
-        // NOTE, we could also compute the SVD of T's block during the QZ factorization so that the respective T block is guaranteed to be diagonal,
-        // and then we could directly apply the formula below (while taking care of scaling S columns by T11,T00):
+        // T =  [a 0]
+        //      [0 b]
+        RealScalar a = m_realQZ.matrixT().coeff(i, i), b = m_realQZ.matrixT().coeff(i+1, i+1);
+        Matrix<RealScalar,2,2> S2 = m_matS.template block<2,2>(i,i) * Matrix<Scalar,2,1>(b,a).asDiagonal();
 
         Scalar p = Scalar(0.5) * (S2.coeff(0,0) - S2.coeff(1,1));
         Scalar z = sqrt(abs(p * p + S2.coeff(1,0) * S2.coeff(0,1)));
@@ -352,7 +341,7 @@ GeneralizedEigenSolver<MatrixType>::compute(const MatrixType& A, const MatrixTyp
         m_alphas.coeffRef(i+1) = ComplexScalar(S2.coeff(1,1) + p, -z);
 
         m_betas.coeffRef(i)   =
-        m_betas.coeffRef(i+1) = a*c*d;
+        m_betas.coeffRef(i+1) = a*b;
 
         i += 2;
       }

From e2b383632699684d06ae180b3ad85cfb0189973a Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Thu, 9 Jun 2016 17:13:33 +0200
Subject: [PATCH 11/86] Include recent changesets that played with product's
 kernel

---
 bench/perf_monitoring/gemm/changesets.txt | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/bench/perf_monitoring/gemm/changesets.txt b/bench/perf_monitoring/gemm/changesets.txt
index fb3e48e99..d00b4603a 100644
--- a/bench/perf_monitoring/gemm/changesets.txt
+++ b/bench/perf_monitoring/gemm/changesets.txt
@@ -44,4 +44,8 @@ before-evaluators
 7013:f875e75f07e5   # organize a little our default cache sizes, and use a saner default L1 outside of x86 (10% faster on Nexus 5)
 7591:09a8e2186610   # 3.3-alpha1
 7650:b0f3c8f43025   # help clang inlining
+8744:74b789ada92a   # Improved the matrix multiplication blocking in the case where mr is not a power of 2 (e.g on Haswell CPUs)
+8789:efcb912e4356   # Made the index type a template parameter to evaluateProductBlockingSizes. Use numext::mini and numext::maxi instead of std::min/std::max to compute blocking sizes
+8972:81d53c711775   # Don't optimize the processing of the last rows of a matrix matrix product in cases that violate the assumptions made by the optimized code path
+8985:d935df21a082   # Remove the rotating kernel.
 

From aa33446dace833fbf06632e586c80119b3d8ac11 Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Thu, 9 Jun 2016 08:22:27 -0700
Subject: [PATCH 12/86] Improved support for vectorization of 16-bit floats

---
 .../Eigen/CXX11/src/Tensor/TensorFunctors.h   | 86 +++++++++++++++++++
 .../Eigen/CXX11/src/Tensor/TensorMeta.h       |  5 ++
 .../CXX11/src/Tensor/TensorReductionCuda.h    |  8 +-
 3 files changed, 95 insertions(+), 4 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h b/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h
index 3dd32e9d1..bf52e490f 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h
@@ -84,6 +84,14 @@ struct functor_traits<scalar_sigmoid_op<T> > {
 };
 
 
+template<typename Reducer, typename Device>
+struct reducer_traits {
+  enum {
+    Cost = 1,
+    PacketAccess = false
+  };
+};
+
 // Standard reduction functors
 template <typename T> struct SumReducer
 {
@@ -119,6 +127,15 @@ template <typename T> struct SumReducer
   }
 };
 
+template <typename T, typename Device>
+struct reducer_traits<SumReducer<T>, Device> {
+  enum {
+    Cost = NumTraits<T>::AddCost,
+    PacketAccess = PacketType<T, Device>::type::HasAdd
+  };
+};
+
+
 template <typename T> struct MeanReducer
 {
   static const bool PacketAccess = packet_traits<T>::HasAdd && !NumTraits<T>::IsInteger;
@@ -162,6 +179,15 @@ template <typename T> struct MeanReducer
     DenseIndex packetCount_;
 };
 
+template <typename T, typename Device>
+struct reducer_traits<MeanReducer<T>, Device> {
+  enum {
+    Cost = NumTraits<T>::AddCost,
+    PacketAccess = PacketType<T, Device>::type::HasAdd
+  };
+};
+
+
 template <typename T> struct MaxReducer
 {
   static const bool PacketAccess = packet_traits<T>::HasMax;
@@ -195,6 +221,15 @@ template <typename T> struct MaxReducer
   }
 };
 
+template <typename T, typename Device>
+struct reducer_traits<MaxReducer<T>, Device> {
+  enum {
+    Cost = NumTraits<T>::AddCost,
+    PacketAccess = PacketType<T, Device>::type::HasMax
+  };
+};
+
+
 template <typename T> struct MinReducer
 {
   static const bool PacketAccess = packet_traits<T>::HasMin;
@@ -228,6 +263,14 @@ template <typename T> struct MinReducer
   }
 };
 
+template <typename T, typename Device>
+struct reducer_traits<MinReducer<T>, Device> {
+  enum {
+    Cost = NumTraits<T>::AddCost,
+    PacketAccess = PacketType<T, Device>::type::HasMin
+  };
+};
+
 
 template <typename T> struct ProdReducer
 {
@@ -263,6 +306,14 @@ template <typename T> struct ProdReducer
   }
 };
 
+template <typename T, typename Device>
+struct reducer_traits<ProdReducer<T>, Device> {
+  enum {
+    Cost = NumTraits<T>::MulCost,
+    PacketAccess = PacketType<T, Device>::type::HasMul
+  };
+};
+
 
 struct AndReducer
 {
@@ -280,6 +331,15 @@ struct AndReducer
   }
 };
 
+template <typename Device>
+struct reducer_traits<AndReducer, Device> {
+  enum {
+    Cost = 1,
+    PacketAccess = false
+  };
+};
+
+
 struct OrReducer {
   static const bool PacketAccess = false;
   static const bool IsStateful = false;
@@ -295,6 +355,15 @@ struct OrReducer {
   }
 };
 
+template <typename Device>
+struct reducer_traits<OrReducer, Device> {
+  enum {
+    Cost = 1,
+    PacketAccess = false
+  };
+};
+
+
 // Argmin/Argmax reducers
 template <typename T> struct ArgMaxTupleReducer
 {
@@ -312,6 +381,15 @@ template <typename T> struct ArgMaxTupleReducer
   }
 };
 
+template <typename T, typename Device>
+struct reducer_traits<ArgMaxTupleReducer<T>, Device> {
+  enum {
+    Cost = NumTraits<T>::AddCost,
+    PacketAccess = false
+  };
+};
+
+
 template <typename T> struct ArgMinTupleReducer
 {
   static const bool PacketAccess = false;
@@ -328,6 +406,14 @@ template <typename T> struct ArgMinTupleReducer
   }
 };
 
+template <typename T, typename Device>
+struct reducer_traits<ArgMinTupleReducer<T>, Device> {
+  enum {
+    Cost = NumTraits<T>::AddCost,
+    PacketAccess = false
+  };
+};
+
 
 // Random number generation
 namespace {
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h b/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h
index b1645d56f..82a905a65 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h
@@ -54,6 +54,11 @@ struct PacketType {
 
 // For CUDA packet types when using a GpuDevice
 #if defined(EIGEN_USE_GPU) && defined(__CUDACC__)
+template <>
+  struct PacketType<half, GpuDevice> {
+  typedef half2 type;
+  static const int size = 2;
+ };
 template <>
 struct PacketType<float, GpuDevice> {
   typedef float4 type;
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h
index e82530955..1b4fdd03f 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h
@@ -331,7 +331,7 @@ struct FullReducer<Self, Op, GpuDevice, Vectorizable> {
   #ifdef EIGEN_HAS_CUDA_FP16
   static const bool HasOptimizedImplementation = !Op::IsStateful &&
       (internal::is_same<typename Self::CoeffReturnType, float>::value ||
-       (internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value && Op::PacketAccess));
+       (internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value && reducer_traits<Op, GpuDevice>::PacketAccess));
 #else
   static const bool HasOptimizedImplementation = !Op::IsStateful &&
                                                  internal::is_same<typename Self::CoeffReturnType, float>::value;
@@ -346,7 +346,7 @@ struct FullReducer<Self, Op, GpuDevice, Vectorizable> {
       return;
     }
 
-    FullReductionLauncher<Self, Op, OutputType, Op::PacketAccess>::run(self, reducer, device, output, num_coeffs);
+    FullReductionLauncher<Self, Op, OutputType, reducer_traits<Op, GpuDevice>::PacketAccess>::run(self, reducer, device, output, num_coeffs);
   }
 };
 
@@ -608,7 +608,7 @@ struct InnerReducer<Self, Op, GpuDevice> {
 #ifdef EIGEN_HAS_CUDA_FP16
   static const bool HasOptimizedImplementation = !Op::IsStateful &&
       (internal::is_same<typename Self::CoeffReturnType, float>::value ||
-       (internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value && Op::PacketAccess));
+       (internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value && reducer_traits<Op, GpuDevice>::PacketAccess));
 #else
   static const bool HasOptimizedImplementation = !Op::IsStateful &&
                                                  internal::is_same<typename Self::CoeffReturnType, float>::value;
@@ -627,7 +627,7 @@ struct InnerReducer<Self, Op, GpuDevice> {
       return true;
     }
 
-    return InnerReductionLauncher<Self, Op, OutputType, Op::PacketAccess>::run(self, reducer, device, output, num_coeffs_to_reduce, num_preserved_vals);
+    return InnerReductionLauncher<Self, Op, OutputType, reducer_traits<Op, GpuDevice>::PacketAccess>::run(self, reducer, device, output, num_coeffs_to_reduce, num_preserved_vals);
   }
 };
 

From 8f92c26319a6e06cce6d0ba2a252521c8096a2c0 Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Thu, 9 Jun 2016 08:23:42 -0700
Subject: [PATCH 13/86] Improved code formatting

---
 unsupported/Eigen/CXX11/src/Tensor/TensorScan.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h b/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h
index 61df8032d..0d084141d 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h
@@ -122,7 +122,7 @@ struct TensorEvaluator<const TensorScanOp<Op, ArgType>, Device> {
   }
 
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const {
-      return m_dimensions;
+    return m_dimensions;
   }
 
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* data) {

From 14a112ee153f7d8554c3a8848e8a0461c7b82f13 Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Thu, 9 Jun 2016 08:25:22 -0700
Subject: [PATCH 14/86] Use signed integers more consistently to encode the
 number of threads to use to evaluate a tensor expression.

---
 .../CXX11/src/Tensor/TensorContractionThreadPool.h   | 12 ++++++------
 .../Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h  | 10 +++++-----
 2 files changed, 11 insertions(+), 11 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionThreadPool.h b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionThreadPool.h
index a60a17049..ee16cde9b 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionThreadPool.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionThreadPool.h
@@ -202,7 +202,7 @@ struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgT
     // across k dimension.
     const TensorOpCost cost =
         contractionCost(m, n, bm, bn, bk, shard_by_col, false);
-    Index num_threads = TensorCostModel<ThreadPoolDevice>::numThreads(
+    int num_threads = TensorCostModel<ThreadPoolDevice>::numThreads(
         static_cast<double>(n) * m, cost, this->m_device.numThreads());
 
     // TODO(dvyukov): this is a stop-gap to prevent regressions while the cost
@@ -301,7 +301,7 @@ struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgT
   class Context {
    public:
     Context(const Device& device, int num_threads, LhsMapper& lhs,
-            RhsMapper& rhs, Scalar* buffer, Index m, Index n, Index k, Index bm,
+            RhsMapper& rhs, Scalar* buffer, Index tm, Index tn, Index tk, Index bm,
             Index bn, Index bk, Index nm, Index nn, Index nk, Index gm,
             Index gn, Index nm0, Index nn0, bool shard_by_col,
             bool parallel_pack)
@@ -309,13 +309,13 @@ struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgT
           lhs_(lhs),
           rhs_(rhs),
           buffer_(buffer),
-          output_(buffer, m),
+          output_(buffer, tm),
           num_threads_(num_threads),
           shard_by_col_(shard_by_col),
           parallel_pack_(parallel_pack),
-          m_(m),
-          n_(n),
-          k_(k),
+          m_(tm),
+          n_(tn),
+          k_(tk),
           bm_(bm),
           bn_(bn),
           bk_(bk),
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h
index d31b0ad38..c770d024f 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h
@@ -106,7 +106,7 @@ static EIGEN_STRONG_INLINE void wait_until_ready(SyncType* n) {
 // Build a thread pool device on top the an existing pool of threads.
 struct ThreadPoolDevice {
   // The ownership of the thread pool remains with the caller.
-  ThreadPoolDevice(ThreadPoolInterface* pool, size_t num_cores) : pool_(pool), num_threads_(num_cores) { }
+  ThreadPoolDevice(ThreadPoolInterface* pool, int num_cores) : pool_(pool), num_threads_(num_cores) { }
 
   EIGEN_STRONG_INLINE void* allocate(size_t num_bytes) const {
     return internal::aligned_malloc(num_bytes);
@@ -130,7 +130,7 @@ struct ThreadPoolDevice {
     ::memset(buffer, c, n);
   }
 
-  EIGEN_STRONG_INLINE size_t numThreads() const {
+  EIGEN_STRONG_INLINE int numThreads() const {
     return num_threads_;
   }
 
@@ -182,7 +182,7 @@ struct ThreadPoolDevice {
                    std::function<void(Index, Index)> f) const {
     typedef TensorCostModel<ThreadPoolDevice> CostModel;
     if (n <= 1 || numThreads() == 1 ||
-        CostModel::numThreads(n, cost, numThreads()) == 1) {
+        CostModel::numThreads(n, cost, static_cast<int>(numThreads())) == 1) {
       f(0, n);
       return;
     }
@@ -242,7 +242,7 @@ struct ThreadPoolDevice {
     // Recursively divide size into halves until we reach block_size.
     // Division code rounds mid to block_size, so we are guaranteed to get
     // block_count leaves that do actual computations.
-    Barrier barrier(block_count);
+    Barrier barrier(static_cast<unsigned int>(block_count));
     std::function<void(Index, Index)> handleRange;
     handleRange = [=, &handleRange, &barrier, &f](Index first, Index last) {
       if (last - first <= block_size) {
@@ -268,7 +268,7 @@ struct ThreadPoolDevice {
 
  private:
   ThreadPoolInterface* pool_;
-  size_t num_threads_;
+  int num_threads_;
 };
 
 

From 66796e843df723eeac04d6dc725f6a8b27a574ba Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Thu, 9 Jun 2016 08:50:01 -0700
Subject: [PATCH 15/86] Fixed definition of some of the reducer_traits

---
 unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h b/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h
index bf52e490f..e6ff70460 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h
@@ -131,7 +131,7 @@ template <typename T, typename Device>
 struct reducer_traits<SumReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::AddCost,
-    PacketAccess = PacketType<T, Device>::type::HasAdd
+    PacketAccess = packet_traits<typename PacketType<T, Device>::type>::HasAdd
   };
 };
 
@@ -183,7 +183,7 @@ template <typename T, typename Device>
 struct reducer_traits<MeanReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::AddCost,
-    PacketAccess = PacketType<T, Device>::type::HasAdd
+    PacketAccess = packet_traits<typename PacketType<T, Device>::type>::HasAdd
   };
 };
 
@@ -225,7 +225,7 @@ template <typename T, typename Device>
 struct reducer_traits<MaxReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::AddCost,
-    PacketAccess = PacketType<T, Device>::type::HasMax
+    PacketAccess = packet_traits<typename PacketType<T, Device>::type>::HasMax
   };
 };
 
@@ -267,7 +267,7 @@ template <typename T, typename Device>
 struct reducer_traits<MinReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::AddCost,
-    PacketAccess = PacketType<T, Device>::type::HasMin
+    PacketAccess = packet_traits<typename PacketType<T, Device>::type>::HasMin
   };
 };
 
@@ -310,7 +310,7 @@ template <typename T, typename Device>
 struct reducer_traits<ProdReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::MulCost,
-    PacketAccess = PacketType<T, Device>::type::HasMul
+    PacketAccess = packet_traits<typename PacketType<T, Device>::type>::HasMul
   };
 };
 

From 37638dafd71e39407d22d4269b32d1c73b84feb8 Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Thu, 9 Jun 2016 10:29:52 -0700
Subject: [PATCH 16/86] Simplified the code that dispatches vectorized
 reductions on GPU

---
 .../Eigen/CXX11/src/Tensor/TensorFunctors.h   | 10 ++---
 .../Eigen/CXX11/src/Tensor/TensorMeta.h       | 38 ++++++++++++-------
 .../CXX11/src/Tensor/TensorReductionCuda.h    |  2 +-
 3 files changed, 31 insertions(+), 19 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h b/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h
index e6ff70460..a8e48fced 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h
@@ -131,7 +131,7 @@ template <typename T, typename Device>
 struct reducer_traits<SumReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::AddCost,
-    PacketAccess = packet_traits<typename PacketType<T, Device>::type>::HasAdd
+    PacketAccess = PacketType<T, Device>::HasAdd
   };
 };
 
@@ -183,7 +183,7 @@ template <typename T, typename Device>
 struct reducer_traits<MeanReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::AddCost,
-    PacketAccess = packet_traits<typename PacketType<T, Device>::type>::HasAdd
+    PacketAccess = PacketType<T, Device>::HasAdd
   };
 };
 
@@ -225,7 +225,7 @@ template <typename T, typename Device>
 struct reducer_traits<MaxReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::AddCost,
-    PacketAccess = packet_traits<typename PacketType<T, Device>::type>::HasMax
+    PacketAccess = PacketType<T, Device>::HasMax
   };
 };
 
@@ -267,7 +267,7 @@ template <typename T, typename Device>
 struct reducer_traits<MinReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::AddCost,
-    PacketAccess = packet_traits<typename PacketType<T, Device>::type>::HasMin
+    PacketAccess = PacketType<T, Device>::HasMin
   };
 };
 
@@ -310,7 +310,7 @@ template <typename T, typename Device>
 struct reducer_traits<ProdReducer<T>, Device> {
   enum {
     Cost = NumTraits<T>::MulCost,
-    PacketAccess = packet_traits<typename PacketType<T, Device>::type>::HasMul
+    PacketAccess = PacketType<T, Device>::HasMul
   };
 };
 
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h b/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h
index 82a905a65..0f3778e6e 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h
@@ -47,27 +47,39 @@ template <> struct max_n_1<0> {
 
 // Default packet types
 template <typename Scalar, typename Device>
-struct PacketType {
+struct PacketType : internal::packet_traits<Scalar> {
   typedef typename internal::packet_traits<Scalar>::type type;
-  enum { size = internal::unpacket_traits<type>::size };
 };
 
 // For CUDA packet types when using a GpuDevice
 #if defined(EIGEN_USE_GPU) && defined(__CUDACC__)
 template <>
-  struct PacketType<half, GpuDevice> {
+struct PacketType<half, GpuDevice> {
   typedef half2 type;
   static const int size = 2;
- };
-template <>
-struct PacketType<float, GpuDevice> {
-  typedef float4 type;
-  static const int size = 4;
-};
-template <>
-struct PacketType<double, GpuDevice> {
-  typedef double2 type;
-  static const int size = 2;
+  enum {
+    HasAdd    = 1,
+    HasSub    = 1,
+    HasMul    = 1,
+    HasNegate = 1,
+    HasAbs    = 1,
+    HasArg    = 0,
+    HasAbs2   = 0,
+    HasMin    = 1,
+    HasMax    = 1,
+    HasConj   = 0,
+    HasSetLinear = 0,
+    HasBlend  = 0,
+
+    HasDiv    = 1,
+    HasSqrt   = 1,
+    HasRsqrt  = 1,
+    HasExp    = 1,
+    HasLog    = 1,
+    HasLog1p  = 0,
+    HasLog10  = 0,
+    HasPow    = 1,
+  };
 };
 #endif
 
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h
index 1b4fdd03f..d9bbcd858 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h
@@ -328,7 +328,7 @@ struct FullReducer<Self, Op, GpuDevice, Vectorizable> {
   // Unfortunately nvidia doesn't support well exotic types such as complex,
   // so reduce the scope of the optimized version of the code to the simple case
   // of floats and half floats.
-  #ifdef EIGEN_HAS_CUDA_FP16
+#ifdef EIGEN_HAS_CUDA_FP16
   static const bool HasOptimizedImplementation = !Op::IsStateful &&
       (internal::is_same<typename Self::CoeffReturnType, float>::value ||
        (internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value && reducer_traits<Op, GpuDevice>::PacketAccess));

From 1fc2746417c8b4bf1645c703b1f99b1871c8d16e Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Thu, 9 Jun 2016 22:52:37 +0200
Subject: [PATCH 17/86] Make Arrays's ctor/assignment noexcept

---
 Eigen/src/Core/Array.h | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Eigen/src/Core/Array.h b/Eigen/src/Core/Array.h
index c0af4aa9d..7c2e0de16 100644
--- a/Eigen/src/Core/Array.h
+++ b/Eigen/src/Core/Array.h
@@ -149,7 +149,7 @@ class Array
 
 #if EIGEN_HAS_RVALUE_REFERENCES
     EIGEN_DEVICE_FUNC
-    Array(Array&& other)
+    Array(Array&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_constructible<Scalar>::value)
       : Base(std::move(other))
     {
       Base::_check_template_params();
@@ -157,7 +157,7 @@ class Array
         Base::_set_noalias(other);
     }
     EIGEN_DEVICE_FUNC
-    Array& operator=(Array&& other)
+    Array& operator=(Array&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable<Scalar>::value)
     {
       other.swap(*this);
       return *this;

From bd212438217dc3e169a35052f78e2e41a7ce3a3d Mon Sep 17 00:00:00 2001
From: Sean Templeton <seantempleton@outlook.com>
Date: Fri, 3 Jun 2016 10:51:35 -0500
Subject: [PATCH 18/86] Fix compile errors initializing packets on ARM DS-5
 5.20

The ARM DS-5 5.20 compiler fails compiling with the following errors:

"src/Core/arch/NEON/PacketMath.h", line 113: Error:  #146: too many initializer values
    Packet4f countdown = EIGEN_INIT_NEON_PACKET4(0, 1, 2, 3);
                         ^
"src/Core/arch/NEON/PacketMath.h", line 118: Error:  #146: too many initializer values
    Packet4i countdown = EIGEN_INIT_NEON_PACKET4(0, 1, 2, 3);
                         ^
"src/Core/arch/NEON/Complex.h", line 30: Error:  #146: too many initializer values
  static uint32x4_t p4ui_CONJ_XOR = EIGEN_INIT_NEON_PACKET4(0x00000000, 0x80000000, 0x00000000, 0x80000000);
                                    ^
"src/Core/arch/NEON/Complex.h", line 31: Error:  #146: too many initializer values
  static uint32x2_t p2ui_CONJ_XOR = EIGEN_INIT_NEON_PACKET2(0x00000000, 0x80000000);
                                    ^

The vectors are implemented as two doubles, hence the too many initializer values error.
Changed the code to use intrinsic load functions which all compilers
implementing NEON should have.
---
 Eigen/src/Core/arch/NEON/Complex.h    |  5 +++--
 Eigen/src/Core/arch/NEON/PacketMath.h | 15 +++++++--------
 2 files changed, 10 insertions(+), 10 deletions(-)

diff --git a/Eigen/src/Core/arch/NEON/Complex.h b/Eigen/src/Core/arch/NEON/Complex.h
index d2d467936..234f29b80 100644
--- a/Eigen/src/Core/arch/NEON/Complex.h
+++ b/Eigen/src/Core/arch/NEON/Complex.h
@@ -14,8 +14,9 @@ namespace Eigen {
 
 namespace internal {
 
-static uint32x4_t p4ui_CONJ_XOR = EIGEN_INIT_NEON_PACKET4(0x00000000, 0x80000000, 0x00000000, 0x80000000);
-static uint32x2_t p2ui_CONJ_XOR = EIGEN_INIT_NEON_PACKET2(0x00000000, 0x80000000);
+const uint32_t  conj_XOR_DATA[] = { 0x00000000, 0x80000000, 0x00000000, 0x80000000 };
+static uint32x4_t p4ui_CONJ_XOR = vld1q_u32( conj_XOR_DATA );
+static uint32x2_t p2ui_CONJ_XOR = vld1_u32( conj_XOR_DATA );
 
 //---------- float ----------
 struct Packet2cf
diff --git a/Eigen/src/Core/arch/NEON/PacketMath.h b/Eigen/src/Core/arch/NEON/PacketMath.h
index deb2d7e42..fa16bc9c8 100644
--- a/Eigen/src/Core/arch/NEON/PacketMath.h
+++ b/Eigen/src/Core/arch/NEON/PacketMath.h
@@ -51,15 +51,12 @@ typedef uint32x4_t  Packet4ui;
 
 #if EIGEN_COMP_LLVM && !EIGEN_COMP_CLANG
   //Special treatment for Apple's llvm-gcc, its NEON packet types are unions
-  #define EIGEN_INIT_NEON_PACKET2(X, Y)       {{X, Y}}
-  #define EIGEN_INIT_NEON_PACKET4(X, Y, Z, W) {{X, Y, Z, W}}
+  #define EIGEN_INIT_NEON_PACKET2D(X, Y)       {{X, Y}}
 #else
   //Default initializer for packets
-  #define EIGEN_INIT_NEON_PACKET2(X, Y)       {X, Y}
-  #define EIGEN_INIT_NEON_PACKET4(X, Y, Z, W) {X, Y, Z, W}
+  #define EIGEN_INIT_NEON_PACKET2D(X, Y)       {X, Y}
 #endif
 
-
 // arm64 does have the pld instruction. If available, let's trust the __builtin_prefetch built-in function
 // which available on LLVM and GCC (at least)
 #if EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC
@@ -122,12 +119,14 @@ template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from)   {
 
 template<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a)
 {
-  Packet4f countdown = EIGEN_INIT_NEON_PACKET4(0, 1, 2, 3);
+  const float32_t f[] = {0, 1, 2, 3};
+  Packet4f countdown = vld1q_f32(f);
   return vaddq_f32(pset1<Packet4f>(a), countdown);
 }
 template<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a)
 {
-  Packet4i countdown = EIGEN_INIT_NEON_PACKET4(0, 1, 2, 3);
+  const int32_t i[] = {0, 1, 2, 3};
+  Packet4i countdown = vld1q_s32(i);
   return vaddq_s32(pset1<Packet4i>(a), countdown);
 }
 
@@ -585,7 +584,7 @@ template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double&  from) { r
 
 template<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a)
 {
-  Packet2d countdown = EIGEN_INIT_NEON_PACKET2(0, 1);
+  Packet2d countdown = EIGEN_INIT_NEON_PACKET2D(0, 1);
   return vaddq_f64(pset1<Packet2d>(a), countdown);
 }
 template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return vaddq_f64(a,b); }

From 76308e7fd277ad962a87724040670da827a27db4 Mon Sep 17 00:00:00 2001
From: Rasmus Munk Larsen <rmlarsen@google.com>
Date: Fri, 3 Jun 2016 16:28:58 -0700
Subject: [PATCH 19/86] Add CurrentThreadId and NumThreads methods to Eigen
 threadpools and TensorDeviceThreadPool.

---
 .../CXX11/src/Tensor/TensorDeviceThreadPool.h |  4 +++
 .../src/ThreadPool/NonBlockingThreadPool.h    | 26 +++++++++++----
 .../CXX11/src/ThreadPool/SimpleThreadPool.h   | 32 +++++++++++++++++--
 .../src/ThreadPool/ThreadPoolInterface.h      |  7 ++++
 .../test/cxx11_non_blocking_thread_pool.cpp   |  5 +++
 5 files changed, 65 insertions(+), 9 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h
index d31b0ad38..90fded8ad 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h
@@ -172,6 +172,10 @@ struct ThreadPoolDevice {
     pool_->Schedule(func);
   }
 
+  EIGEN_STRONG_INLINE size_t currentThreadId() const {
+    return pool_->CurrentThreadId();
+  }
+
   // parallelFor executes f with [0, n) arguments in parallel and waits for
   // completion. F accepts a half-open interval [first, last).
   // Block size is choosen based on the iteration cost and resulting parallel
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h b/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
index c094563b7..1465878b7 100644
--- a/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
@@ -74,7 +74,7 @@ class NonBlockingThreadPoolTempl : public Eigen::ThreadPoolInterface {
     PerThread* pt = GetPerThread();
     if (pt->pool == this) {
       // Worker thread of this pool, push onto the thread's queue.
-      Queue* q = queues_[pt->index];
+      Queue* q = queues_[pt->thread_id];
       t = q->PushFront(std::move(t));
     } else {
       // A free-standing thread (or worker of another pool), push onto a random
@@ -95,13 +95,27 @@ class NonBlockingThreadPoolTempl : public Eigen::ThreadPoolInterface {
       env_.ExecuteTask(t);  // Push failed, execute directly.
   }
 
+  size_t NumThreads() const final {
+    return threads_.size();
+  }
+
+  size_t CurrentThreadId() const {
+    const PerThread* pt =
+        const_cast<NonBlockingThreadPoolTempl*>(this)->GetPerThread();
+    if (pt->pool == this) {
+      return static_cast<size_t>(pt->thread_id);
+    } else {
+      return threads_.size();
+    }
+  }
+
  private:
   typedef typename Environment::EnvThread Thread;
 
   struct PerThread {
     bool inited;
     NonBlockingThreadPoolTempl* pool;  // Parent pool, or null for normal threads.
-    unsigned index;         // Worker thread index in pool.
+    unsigned thread_id;         // Worker thread index in pool.
     unsigned rand;          // Random generator state.
   };
 
@@ -116,12 +130,12 @@ class NonBlockingThreadPoolTempl : public Eigen::ThreadPoolInterface {
   EventCount ec_;
 
   // Main worker thread loop.
-  void WorkerLoop(unsigned index) {
+  void WorkerLoop(unsigned thread_id) {
     PerThread* pt = GetPerThread();
     pt->pool = this;
-    pt->index = index;
-    Queue* q = queues_[index];
-    EventCount::Waiter* waiter = &waiters_[index];
+    pt->thread_id = thread_id;
+    Queue* q = queues_[thread_id];
+    EventCount::Waiter* waiter = &waiters_[thread_id];
     for (;;) {
       Task t = q->PopFront();
       if (!t.f) {
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/SimpleThreadPool.h b/unsupported/Eigen/CXX11/src/ThreadPool/SimpleThreadPool.h
index 17fd1658b..fde80afdf 100644
--- a/unsupported/Eigen/CXX11/src/ThreadPool/SimpleThreadPool.h
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/SimpleThreadPool.h
@@ -24,7 +24,7 @@ class SimpleThreadPoolTempl : public ThreadPoolInterface {
   explicit SimpleThreadPoolTempl(int num_threads, Environment env = Environment())
       : env_(env), threads_(num_threads), waiters_(num_threads) {
     for (int i = 0; i < num_threads; i++) {
-      threads_.push_back(env.CreateThread([this]() { WorkerLoop(); }));
+      threads_.push_back(env.CreateThread([this, i]() { WorkerLoop(i); }));
     }
   }
 
@@ -55,7 +55,7 @@ class SimpleThreadPoolTempl : public ThreadPoolInterface {
 
   // Schedule fn() for execution in the pool of threads. The functions are
   // executed in the order in which they are scheduled.
-  void Schedule(std::function<void()> fn) {
+  void Schedule(std::function<void()> fn) final {
     Task t = env_.CreateTask(std::move(fn));
     std::unique_lock<std::mutex> l(mu_);
     if (waiters_.empty()) {
@@ -69,9 +69,25 @@ class SimpleThreadPoolTempl : public ThreadPoolInterface {
     }
   }
 
+  size_t NumThreads() const final {
+    return threads_.size();
+  }
+
+  size_t CurrentThreadId() const final {
+    const PerThread* pt = this->GetPerThread();
+    if (pt->pool == this) {
+      return pt->thread_id;
+    } else {
+      return threads_.size();
+    }
+  }
+
  protected:
-  void WorkerLoop() {
+  void WorkerLoop(size_t thread_id) {
     std::unique_lock<std::mutex> l(mu_);
+    PerThread* pt = GetPerThread();
+    pt->pool = this;
+    pt->thread_id = thread_id;
     Waiter w;
     Task t;
     while (!exiting_) {
@@ -111,6 +127,11 @@ class SimpleThreadPoolTempl : public ThreadPoolInterface {
     bool ready;
   };
 
+  struct PerThread {
+    ThreadPoolTempl* pool;  // Parent pool, or null for normal threads.
+    size_t thread_id;       // Worker thread index in pool.
+  };
+
   Environment env_;
   std::mutex mu_;
   MaxSizeVector<Thread*> threads_;  // All threads
@@ -118,6 +139,11 @@ class SimpleThreadPoolTempl : public ThreadPoolInterface {
   std::deque<Task> pending_;          // Queue of pending work
   std::condition_variable empty_;          // Signaled on pending_.empty()
   bool exiting_ = false;
+
+  PerThread* GetPerThread() const {
+    static EIGEN_THREAD_LOCAL PerThread per_thread;
+    return &per_thread;
+  }
 };
 
 typedef SimpleThreadPoolTempl<StlThreadEnvironment> SimpleThreadPool;
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h
index 38b40aceb..b1beccdde 100644
--- a/unsupported/Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h
@@ -18,6 +18,13 @@ class ThreadPoolInterface {
  public:
   virtual void Schedule(std::function<void()> fn) = 0;
 
+  // Returns the number of threads in the pool.
+  virtual size_t NumThreads() const = 0;
+
+  // Returns a logical thread index between 0 and NumThreads() - 1 if called
+  // from one of the threads in the pool. Returns NumThreads() otherwise.
+  virtual size_t CurrentThreadId() const = 0;
+
   virtual ~ThreadPoolInterface() {}
 };
 
diff --git a/unsupported/test/cxx11_non_blocking_thread_pool.cpp b/unsupported/test/cxx11_non_blocking_thread_pool.cpp
index 6569218c4..844a1fbf4 100644
--- a/unsupported/test/cxx11_non_blocking_thread_pool.cpp
+++ b/unsupported/test/cxx11_non_blocking_thread_pool.cpp
@@ -27,6 +27,8 @@ static void test_parallelism()
   // Test we never-ever fail to match available tasks with idle threads.
   const int kThreads = 16;  // code below expects that this is a multiple of 4
   NonBlockingThreadPool tp(kThreads);
+  VERIFY_IS_EQUAL(tp.NumThreads(), kThreads);
+  VERIFY_IS_EQUAL(tp.CurrentThreadId(), kThreads);
   for (int iter = 0; iter < 100; ++iter) {
     std::atomic<int> running(0);
     std::atomic<int> done(0);
@@ -34,6 +36,9 @@ static void test_parallelism()
     // Schedule kThreads tasks and ensure that they all are running.
     for (int i = 0; i < kThreads; ++i) {
       tp.Schedule([&]() {
+        const size_t thread_id = tp.CurrentThreadId();
+        VERIFY_GE(thread_id, 0);
+        VERIFY_LE(thread_id, kThreads - 1);
         running++;
         while (phase < 1) {
         }

From f1f2ff8208f82680aabd9e191810d0cd10be9048 Mon Sep 17 00:00:00 2001
From: Rasmus Munk Larsen <rmlarsen@google.com>
Date: Fri, 3 Jun 2016 18:06:37 -0700
Subject: [PATCH 20/86] size_t -> int

---
 .../CXX11/src/Tensor/TensorDeviceThreadPool.h  |  2 +-
 .../src/ThreadPool/NonBlockingThreadPool.h     | 18 +++++++++---------
 .../CXX11/src/ThreadPool/SimpleThreadPool.h    | 16 ++++++++--------
 .../CXX11/src/ThreadPool/ThreadPoolInterface.h |  4 ++--
 .../test/cxx11_non_blocking_thread_pool.cpp    |  2 +-
 5 files changed, 21 insertions(+), 21 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h
index 90fded8ad..9073c611a 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h
@@ -172,7 +172,7 @@ struct ThreadPoolDevice {
     pool_->Schedule(func);
   }
 
-  EIGEN_STRONG_INLINE size_t currentThreadId() const {
+  EIGEN_STRONG_INLINE int currentThreadId() const {
     return pool_->CurrentThreadId();
   }
 
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h b/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
index 1465878b7..8bc986c84 100644
--- a/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
@@ -95,17 +95,17 @@ class NonBlockingThreadPoolTempl : public Eigen::ThreadPoolInterface {
       env_.ExecuteTask(t);  // Push failed, execute directly.
   }
 
-  size_t NumThreads() const final {
-    return threads_.size();
+  int NumThreads() const final {
+    return static_cast<int>(threads_.size());
   }
 
-  size_t CurrentThreadId() const {
+  int CurrentThreadId() const {
     const PerThread* pt =
         const_cast<NonBlockingThreadPoolTempl*>(this)->GetPerThread();
     if (pt->pool == this) {
-      return static_cast<size_t>(pt->thread_id);
+      return pt->thread_id;
     } else {
-      return threads_.size();
+      return NumThreads();
     }
   }
 
@@ -114,9 +114,9 @@ class NonBlockingThreadPoolTempl : public Eigen::ThreadPoolInterface {
 
   struct PerThread {
     bool inited;
-    NonBlockingThreadPoolTempl* pool;  // Parent pool, or null for normal threads.
-    unsigned thread_id;         // Worker thread index in pool.
-    unsigned rand;          // Random generator state.
+    NonBlockingThreadPoolTempl*  pool;  // Parent pool, or null for normal threads.
+    int thread_id;  // Worker thread index in pool.
+    unsigned rand;  // Random generator state.
   };
 
   Environment env_;
@@ -130,7 +130,7 @@ class NonBlockingThreadPoolTempl : public Eigen::ThreadPoolInterface {
   EventCount ec_;
 
   // Main worker thread loop.
-  void WorkerLoop(unsigned thread_id) {
+  void WorkerLoop(int thread_id) {
     PerThread* pt = GetPerThread();
     pt->pool = this;
     pt->thread_id = thread_id;
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/SimpleThreadPool.h b/unsupported/Eigen/CXX11/src/ThreadPool/SimpleThreadPool.h
index fde80afdf..36eb6950f 100644
--- a/unsupported/Eigen/CXX11/src/ThreadPool/SimpleThreadPool.h
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/SimpleThreadPool.h
@@ -69,21 +69,21 @@ class SimpleThreadPoolTempl : public ThreadPoolInterface {
     }
   }
 
-  size_t NumThreads() const final {
-    return threads_.size();
+  int NumThreads() const final {
+    return static_cast<int>(threads_.size());
   }
 
-  size_t CurrentThreadId() const final {
+  int CurrentThreadId() const final {
     const PerThread* pt = this->GetPerThread();
     if (pt->pool == this) {
       return pt->thread_id;
     } else {
-      return threads_.size();
+      return NumThreads();
     }
   }
 
  protected:
-  void WorkerLoop(size_t thread_id) {
+  void WorkerLoop(int thread_id) {
     std::unique_lock<std::mutex> l(mu_);
     PerThread* pt = GetPerThread();
     pt->pool = this;
@@ -129,15 +129,15 @@ class SimpleThreadPoolTempl : public ThreadPoolInterface {
 
   struct PerThread {
     ThreadPoolTempl* pool;  // Parent pool, or null for normal threads.
-    size_t thread_id;       // Worker thread index in pool.
+    int thread_id;          // Worker thread index in pool.
   };
 
   Environment env_;
   std::mutex mu_;
   MaxSizeVector<Thread*> threads_;  // All threads
   MaxSizeVector<Waiter*> waiters_;  // Stack of waiting threads.
-  std::deque<Task> pending_;          // Queue of pending work
-  std::condition_variable empty_;          // Signaled on pending_.empty()
+  std::deque<Task> pending_;        // Queue of pending work
+  std::condition_variable empty_;   // Signaled on pending_.empty()
   bool exiting_ = false;
 
   PerThread* GetPerThread() const {
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h
index b1beccdde..569cd4bc8 100644
--- a/unsupported/Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h
@@ -19,11 +19,11 @@ class ThreadPoolInterface {
   virtual void Schedule(std::function<void()> fn) = 0;
 
   // Returns the number of threads in the pool.
-  virtual size_t NumThreads() const = 0;
+  virtual int NumThreads() const = 0;
 
   // Returns a logical thread index between 0 and NumThreads() - 1 if called
   // from one of the threads in the pool. Returns NumThreads() otherwise.
-  virtual size_t CurrentThreadId() const = 0;
+  virtual int CurrentThreadId() const = 0;
 
   virtual ~ThreadPoolInterface() {}
 };
diff --git a/unsupported/test/cxx11_non_blocking_thread_pool.cpp b/unsupported/test/cxx11_non_blocking_thread_pool.cpp
index 844a1fbf4..6e4e5cbab 100644
--- a/unsupported/test/cxx11_non_blocking_thread_pool.cpp
+++ b/unsupported/test/cxx11_non_blocking_thread_pool.cpp
@@ -36,7 +36,7 @@ static void test_parallelism()
     // Schedule kThreads tasks and ensure that they all are running.
     for (int i = 0; i < kThreads; ++i) {
       tp.Schedule([&]() {
-        const size_t thread_id = tp.CurrentThreadId();
+        const int thread_id = tp.CurrentThreadId();
         VERIFY_GE(thread_id, 0);
         VERIFY_LE(thread_id, kThreads - 1);
         running++;

From 5b95b4daf9933063c57c24c2338b043ec257d461 Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Sun, 5 Jun 2016 12:57:48 -0700
Subject: [PATCH 21/86] Moved static assertions into the class constructor to
 make the code more portable

---
 Eigen/src/Core/CwiseTernaryOp.h | 41 +++++++++++----------------------
 1 file changed, 13 insertions(+), 28 deletions(-)

diff --git a/Eigen/src/Core/CwiseTernaryOp.h b/Eigen/src/Core/CwiseTernaryOp.h
index fe71c07cf..9f3576fec 100644
--- a/Eigen/src/Core/CwiseTernaryOp.h
+++ b/Eigen/src/Core/CwiseTernaryOp.h
@@ -34,22 +34,6 @@ struct traits<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> > {
   typedef typename result_of<TernaryOp(
       const typename Arg1::Scalar&, const typename Arg2::Scalar&,
       const typename Arg3::Scalar&)>::type Scalar;
-  EIGEN_STATIC_ASSERT(
-      (internal::is_same<typename internal::traits<Arg1>::StorageKind,
-                         typename internal::traits<Arg2>::StorageKind>::value),
-      STORAGE_KIND_MUST_MATCH)
-  EIGEN_STATIC_ASSERT(
-      (internal::is_same<typename internal::traits<Arg1>::StorageKind,
-                         typename internal::traits<Arg3>::StorageKind>::value),
-      STORAGE_KIND_MUST_MATCH)
-  EIGEN_STATIC_ASSERT(
-      (internal::is_same<typename internal::traits<Arg1>::StorageIndex,
-                         typename internal::traits<Arg3>::StorageIndex>::value),
-      STORAGE_INDEX_MUST_MATCH)
-  EIGEN_STATIC_ASSERT(
-      (internal::is_same<typename internal::traits<Arg1>::StorageIndex,
-                         typename internal::traits<Arg3>::StorageIndex>::value),
-      STORAGE_INDEX_MUST_MATCH)
 
   typedef typename internal::traits<Arg1>::StorageKind StorageKind;
   typedef typename internal::traits<Arg1>::StorageIndex StorageIndex;
@@ -100,18 +84,8 @@ template <typename TernaryOp, typename Arg1Type, typename Arg2Type,
 class CwiseTernaryOp : public CwiseTernaryOpImpl<
                            TernaryOp, Arg1Type, Arg2Type, Arg3Type,
                            typename internal::traits<Arg1Type>::StorageKind>,
-                       internal::no_assignment_operator {
-  EIGEN_STATIC_ASSERT(
-      (internal::is_same<
-          typename internal::traits<Arg1Type>::StorageKind,
-          typename internal::traits<Arg2Type>::StorageKind>::value),
-      STORAGE_KIND_MUST_MATCH)
-  EIGEN_STATIC_ASSERT(
-      (internal::is_same<
-          typename internal::traits<Arg1Type>::StorageKind,
-          typename internal::traits<Arg3Type>::StorageKind>::value),
-      STORAGE_KIND_MUST_MATCH)
-
+                       internal::no_assignment_operator
+{
  public:
   typedef typename internal::remove_all<Arg1Type>::type Arg1;
   typedef typename internal::remove_all<Arg2Type>::type Arg2;
@@ -137,6 +111,17 @@ class CwiseTernaryOp : public CwiseTernaryOpImpl<
     // require the sizes to match
     EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Arg1, Arg2)
     EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Arg1, Arg3)
+
+    // The index types should match
+    EIGEN_STATIC_ASSERT((internal::is_same<
+                         typename internal::traits<Arg1Type>::StorageKind,
+                         typename internal::traits<Arg2Type>::StorageKind>::value),
+                        STORAGE_KIND_MUST_MATCH)
+    EIGEN_STATIC_ASSERT((internal::is_same<
+                         typename internal::traits<Arg1Type>::StorageKind,
+                         typename internal::traits<Arg3Type>::StorageKind>::value),
+                        STORAGE_KIND_MUST_MATCH)
+
     eigen_assert(a1.rows() == a2.rows() && a1.cols() == a2.cols() &&
                  a1.rows() == a3.rows() && a1.cols() == a3.cols());
   }

From 1f1e0b9e30a175c7a3197ffc87898404dda7c45e Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Sun, 5 Jun 2016 12:59:11 -0700
Subject: [PATCH 22/86] Silenced compilation warning

---
 Eigen/src/Core/SpecialFunctions.h | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Eigen/src/Core/SpecialFunctions.h b/Eigen/src/Core/SpecialFunctions.h
index 0dd9a1dc3..a657cb854 100644
--- a/Eigen/src/Core/SpecialFunctions.h
+++ b/Eigen/src/Core/SpecialFunctions.h
@@ -1050,8 +1050,8 @@ struct betainc_impl {
 template <typename Scalar>
 struct betainc_impl {
   EIGEN_DEVICE_FUNC
-  static EIGEN_STRONG_INLINE Scalar run(Scalar a, Scalar b, Scalar x) {
-    /*							betaincf.c
+  static EIGEN_STRONG_INLINE Scalar run(Scalar, Scalar, Scalar) {
+    /*	betaincf.c
      *
      *	Incomplete beta integral
      *

From 66e99ab6a1444d8e3d47211e4540837e6b982a3a Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Mon, 6 Jun 2016 15:11:41 +0200
Subject: [PATCH 23/86] Relax mixing-type constraints for binary
 coefficient-wise operators: - Replace internal::scalar_product_traits<A,B> by
 Eigen::ScalarBinaryOpTraits<A,B,OP> - Remove the "functor_is_product_like"
 helper (was pretty ugly) - Currently, OP is not used, but it is available to
 the user for fine grained tuning - Currently, only the following operators
 have been generalized: *,/,+,-,=,*=,/=,+=,-= - TODO: generalize all other
 binray operators (comparisons,pow,etc.) - TODO: handle "scalar op array"
 operators (currently only * is handled) - TODO: move the handling of the
 "void" scalar type to ScalarBinaryOpTraits

---
 Eigen/src/Core/ArrayBase.h                    |  4 +-
 Eigen/src/Core/AssignEvaluator.h              | 12 ++--
 Eigen/src/Core/CwiseBinaryOp.h                |  4 +-
 Eigen/src/Core/DiagonalMatrix.h               |  6 +-
 Eigen/src/Core/Dot.h                          | 12 ++--
 Eigen/src/Core/EigenBase.h                    |  4 +-
 Eigen/src/Core/MatrixBase.h                   |  4 +-
 Eigen/src/Core/NoAlias.h                      |  6 +-
 Eigen/src/Core/PlainObjectBase.h              |  2 +-
 Eigen/src/Core/Product.h                      |  3 +-
 Eigen/src/Core/ProductEvaluators.h            | 55 ++++++++--------
 Eigen/src/Core/Redux.h                        |  4 +-
 Eigen/src/Core/Ref.h                          |  2 +-
 Eigen/src/Core/SelfCwiseBinaryOp.h            | 10 +--
 Eigen/src/Core/Solve.h                        | 13 ++--
 Eigen/src/Core/TriangularMatrix.h             | 20 +++---
 Eigen/src/Core/VectorwiseOp.h                 |  4 +-
 Eigen/src/Core/functors/AssignmentFunctors.h  | 54 ++++++++--------
 Eigen/src/Core/functors/BinaryFunctors.h      | 64 ++++++++-----------
 .../Core/products/GeneralBlockPanelKernel.h   |  4 +-
 Eigen/src/Core/products/GeneralMatrixMatrix.h |  4 +-
 .../products/GeneralMatrixMatrixTriangular.h  |  4 +-
 Eigen/src/Core/products/GeneralMatrixVector.h |  4 +-
 .../Core/products/TriangularMatrixVector.h    |  4 +-
 Eigen/src/Core/util/ForwardDeclarations.h     |  5 +-
 Eigen/src/Core/util/Macros.h                  |  4 +-
 Eigen/src/Core/util/Meta.h                    | 64 +++++++++++--------
 Eigen/src/Core/util/XprHelper.h               | 10 +--
 Eigen/src/Geometry/AlignedBox.h               |  6 +-
 Eigen/src/Geometry/Homogeneous.h              | 12 ++--
 Eigen/src/Householder/HouseholderSequence.h   |  2 +-
 .../IterativeLinearSolvers/SolveWithGuess.h   |  4 +-
 Eigen/src/LU/FullPivLU.h                      |  6 +-
 Eigen/src/LU/InverseImpl.h                    |  6 +-
 Eigen/src/LU/PartialPivLU.h                   |  6 +-
 Eigen/src/QR/ColPivHouseholderQR.h            |  4 +-
 .../src/QR/CompleteOrthogonalDecomposition.h  |  4 +-
 Eigen/src/QR/FullPivHouseholderQR.h           |  4 +-
 Eigen/src/SparseCore/SparseAssign.h           | 20 +++---
 Eigen/src/SparseCore/SparseCwiseBinaryOp.h    | 20 +++---
 Eigen/src/SparseCore/SparseDenseProduct.h     |  4 +-
 Eigen/src/SparseCore/SparseMatrix.h           |  4 +-
 Eigen/src/SparseCore/SparseMatrixBase.h       |  2 +-
 Eigen/src/SparseCore/SparseProduct.h          | 12 ++--
 Eigen/src/SparseCore/SparseSelfAdjointView.h  | 10 +--
 Eigen/src/SparseQR/SparseQR.h                 |  8 +--
 Eigen/src/plugins/ArrayCwiseBinaryOps.h       |  4 +-
 Eigen/src/plugins/CommonCwiseBinaryOps.h      | 18 +++++-
 Eigen/src/plugins/CommonCwiseUnaryOps.h       |  6 +-
 Eigen/src/plugins/MatrixCwiseBinaryOps.h      |  4 +-
 blas/PackedTriangularMatrixVector.h           |  4 +-
 test/array.cpp                                |  2 +-
 test/array_for_matrix.cpp                     |  2 +-
 test/mixingtypes.cpp                          | 32 +++++++---
 test/vectorization_logic.cpp                  |  7 +-
 .../Eigen/src/AutoDiff/AutoDiffScalar.h       | 56 ++++++++--------
 .../KroneckerProduct/KroneckerTensorProduct.h |  4 +-
 57 files changed, 345 insertions(+), 314 deletions(-)

diff --git a/Eigen/src/Core/ArrayBase.h b/Eigen/src/Core/ArrayBase.h
index 3d9c37bf6..62851a0c2 100644
--- a/Eigen/src/Core/ArrayBase.h
+++ b/Eigen/src/Core/ArrayBase.h
@@ -176,7 +176,7 @@ template<typename OtherDerived>
 EIGEN_STRONG_INLINE Derived &
 ArrayBase<Derived>::operator-=(const ArrayBase<OtherDerived> &other)
 {
-  call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar>());
+  call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
   return derived();
 }
 
@@ -189,7 +189,7 @@ template<typename OtherDerived>
 EIGEN_STRONG_INLINE Derived &
 ArrayBase<Derived>::operator+=(const ArrayBase<OtherDerived>& other)
 {
-  call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar>());
+  call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
   return derived();
 }
 
diff --git a/Eigen/src/Core/AssignEvaluator.h b/Eigen/src/Core/AssignEvaluator.h
index 4b914ac0c..f966724cc 100644
--- a/Eigen/src/Core/AssignEvaluator.h
+++ b/Eigen/src/Core/AssignEvaluator.h
@@ -687,7 +687,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void call_dense_assignment_loop(const DstX
 template<typename DstXprType, typename SrcXprType>
 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>());
+  call_dense_assignment_loop(dst, src, internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());
 }
 
 /***************************************************************************
@@ -722,13 +722,13 @@ template<typename Dst, typename 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>());
+  call_assignment(dst, src, internal::assign_op<typename Dst::Scalar,typename Src::Scalar>());
 }
 template<typename Dst, typename 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>());
+  call_assignment(dst, src, internal::assign_op<typename Dst::Scalar,typename Src::Scalar>());
 }
                      
 // Deal with "assume-aliasing"
@@ -787,7 +787,7 @@ template<typename Dst, typename 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>());
+  call_assignment_no_alias(dst, src, internal::assign_op<typename Dst::Scalar,typename Src::Scalar>());
 }
 
 template<typename Dst, typename Src, typename Func>
@@ -809,7 +809,7 @@ template<typename Dst, typename 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>());
+  call_assignment_no_alias_no_transpose(dst, src, internal::assign_op<typename Dst::Scalar,typename Src::Scalar>());
 }
 
 // forward declaration
@@ -838,7 +838,7 @@ template< typename DstXprType, typename SrcXprType, typename Functor, typename S
 struct Assignment<DstXprType, SrcXprType, Functor, EigenBase2EigenBase, Scalar>
 {
   EIGEN_DEVICE_FUNC
-  static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar> &/*func*/)
+  static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
   {
     eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
     src.evalTo(dst);
diff --git a/Eigen/src/Core/CwiseBinaryOp.h b/Eigen/src/Core/CwiseBinaryOp.h
index 39820fd7d..aa3297354 100644
--- a/Eigen/src/Core/CwiseBinaryOp.h
+++ b/Eigen/src/Core/CwiseBinaryOp.h
@@ -160,7 +160,7 @@ template<typename OtherDerived>
 EIGEN_STRONG_INLINE Derived &
 MatrixBase<Derived>::operator-=(const MatrixBase<OtherDerived> &other)
 {
-  call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar>());
+  call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
   return derived();
 }
 
@@ -173,7 +173,7 @@ template<typename OtherDerived>
 EIGEN_STRONG_INLINE Derived &
 MatrixBase<Derived>::operator+=(const MatrixBase<OtherDerived>& other)
 {
-  call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar>());
+  call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
   return derived();
 }
 
diff --git a/Eigen/src/Core/DiagonalMatrix.h b/Eigen/src/Core/DiagonalMatrix.h
index 5a9e3abd4..aa619dd5c 100644
--- a/Eigen/src/Core/DiagonalMatrix.h
+++ b/Eigen/src/Core/DiagonalMatrix.h
@@ -320,16 +320,16 @@ template<> struct AssignmentKind<DenseShape,DiagonalShape> { typedef Diagonal2De
 template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar>
 struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Dense, Scalar>
 {
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar> &/*func*/)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
   {
     dst.setZero();
     dst.diagonal() = src.diagonal();
   }
   
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar> &/*func*/)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
   { dst.diagonal() += src.diagonal(); }
   
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar> &/*func*/)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
   { dst.diagonal() -= src.diagonal(); }
 };
 
diff --git a/Eigen/src/Core/Dot.h b/Eigen/src/Core/Dot.h
index f3c869635..1d7f2262e 100644
--- a/Eigen/src/Core/Dot.h
+++ b/Eigen/src/Core/Dot.h
@@ -28,22 +28,24 @@ template<typename T, typename U,
 >
 struct dot_nocheck
 {
-  typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar;
+  typedef scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> conj_prod;
+  typedef typename conj_prod::result_type ResScalar;
   EIGEN_DEVICE_FUNC
   static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
   {
-    return a.template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum();
+    return a.template binaryExpr<conj_prod>(b).sum();
   }
 };
 
 template<typename T, typename U>
 struct dot_nocheck<T, U, true>
 {
-  typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar;
+  typedef scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> conj_prod;
+  typedef typename conj_prod::result_type ResScalar;
   EIGEN_DEVICE_FUNC
   static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
   {
-    return a.transpose().template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum();
+    return a.transpose().template binaryExpr<conj_prod>(b).sum();
   }
 };
 
@@ -62,7 +64,7 @@ struct dot_nocheck<T, U, true>
 template<typename Derived>
 template<typename OtherDerived>
 EIGEN_DEVICE_FUNC
-typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
+typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
 MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const
 {
   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
diff --git a/Eigen/src/Core/EigenBase.h b/Eigen/src/Core/EigenBase.h
index ba8e09674..f76995af9 100644
--- a/Eigen/src/Core/EigenBase.h
+++ b/Eigen/src/Core/EigenBase.h
@@ -138,7 +138,7 @@ template<typename Derived>
 template<typename OtherDerived>
 Derived& DenseBase<Derived>::operator+=(const EigenBase<OtherDerived> &other)
 {
-  call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar>());
+  call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
   return derived();
 }
 
@@ -146,7 +146,7 @@ template<typename Derived>
 template<typename OtherDerived>
 Derived& DenseBase<Derived>::operator-=(const EigenBase<OtherDerived> &other)
 {
-  call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar>());
+  call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
   return derived();
 }
 
diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h
index b8b7f458f..f63505fef 100644
--- a/Eigen/src/Core/MatrixBase.h
+++ b/Eigen/src/Core/MatrixBase.h
@@ -193,7 +193,7 @@ template<typename Derived> class MatrixBase
 
     template<typename OtherDerived>
     EIGEN_DEVICE_FUNC
-    typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
+    typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
     dot(const MatrixBase<OtherDerived>& other) const;
 
     EIGEN_DEVICE_FUNC RealScalar squaredNorm() const;
@@ -381,7 +381,7 @@ template<typename Derived> class MatrixBase
     #ifndef EIGEN_PARSED_BY_DOXYGEN
     /// \internal helper struct to form the return type of the cross product
     template<typename OtherDerived> struct cross_product_return_type {
-      typedef typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
+      typedef typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
       typedef Matrix<Scalar,MatrixBase::RowsAtCompileTime,MatrixBase::ColsAtCompileTime> type;
     };
     #endif // EIGEN_PARSED_BY_DOXYGEN
diff --git a/Eigen/src/Core/NoAlias.h b/Eigen/src/Core/NoAlias.h
index ffb673cee..33908010b 100644
--- a/Eigen/src/Core/NoAlias.h
+++ b/Eigen/src/Core/NoAlias.h
@@ -39,7 +39,7 @@ class NoAlias
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE ExpressionType& operator=(const StorageBase<OtherDerived>& other)
     {
-      call_assignment_no_alias(m_expression, other.derived(), internal::assign_op<Scalar>());
+      call_assignment_no_alias(m_expression, other.derived(), internal::assign_op<Scalar,typename OtherDerived::Scalar>());
       return m_expression;
     }
     
@@ -47,7 +47,7 @@ class NoAlias
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE ExpressionType& operator+=(const StorageBase<OtherDerived>& other)
     {
-      call_assignment_no_alias(m_expression, other.derived(), internal::add_assign_op<Scalar>());
+      call_assignment_no_alias(m_expression, other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
       return m_expression;
     }
     
@@ -55,7 +55,7 @@ class NoAlias
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE ExpressionType& operator-=(const StorageBase<OtherDerived>& other)
     {
-      call_assignment_no_alias(m_expression, other.derived(), internal::sub_assign_op<Scalar>());
+      call_assignment_no_alias(m_expression, other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
       return m_expression;
     }
 
diff --git a/Eigen/src/Core/PlainObjectBase.h b/Eigen/src/Core/PlainObjectBase.h
index 570dbd53b..64f5eb052 100644
--- a/Eigen/src/Core/PlainObjectBase.h
+++ b/Eigen/src/Core/PlainObjectBase.h
@@ -718,7 +718,7 @@ class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
       //_resize_to_match(other);
       // the 'false' below means to enforce lazy evaluation. We don't use lazyAssign() because
       // it wouldn't allow to copy a row-vector into a column-vector.
-      internal::call_assignment_no_alias(this->derived(), other.derived(), internal::assign_op<Scalar>());
+      internal::call_assignment_no_alias(this->derived(), other.derived(), internal::assign_op<Scalar,typename OtherDerived::Scalar>());
       return this->derived();
     }
 
diff --git a/Eigen/src/Core/Product.h b/Eigen/src/Core/Product.h
index 8aa1de081..bad289761 100644
--- a/Eigen/src/Core/Product.h
+++ b/Eigen/src/Core/Product.h
@@ -18,11 +18,12 @@ namespace internal {
 
 // Determine the scalar of Product<Lhs, Rhs>. This is normally the same as Lhs::Scalar times
 // Rhs::Scalar, but product with permutation matrices inherit the scalar of the other factor.
+// TODO: this could be removed once ScalarBinaryOpTraits handles void.
 template<typename Lhs, typename Rhs, typename LhsShape = typename evaluator_traits<Lhs>::Shape, 
          typename RhsShape = typename evaluator_traits<Rhs>::Shape >
 struct product_result_scalar
 {
-  typedef typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
+  typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
 };
 
 template<typename Lhs, typename Rhs, typename RhsShape>
diff --git a/Eigen/src/Core/ProductEvaluators.h b/Eigen/src/Core/ProductEvaluators.h
index cc7166062..7f041e5dd 100644
--- a/Eigen/src/Core/ProductEvaluators.h
+++ b/Eigen/src/Core/ProductEvaluators.h
@@ -124,12 +124,12 @@ protected:
 
 // Dense = Product
 template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar>
-struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::assign_op<Scalar>, Dense2Dense,
+struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::assign_op<Scalar,typename Product<Lhs,Rhs,Options>::Scalar>, Dense2Dense,
   typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct),Scalar>::type>
 {
   typedef Product<Lhs,Rhs,Options> SrcXprType;
   static EIGEN_STRONG_INLINE
-  void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename SrcXprType::Scalar> &)
   {
     // FIXME shall we handle nested_eval here?
     generic_product_impl<Lhs, Rhs>::evalTo(dst, src.lhs(), src.rhs());
@@ -138,12 +138,12 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::assign_op<Scal
 
 // Dense += Product
 template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar>
-struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::add_assign_op<Scalar>, Dense2Dense,
+struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::add_assign_op<Scalar,typename Product<Lhs,Rhs,Options>::Scalar>, Dense2Dense,
   typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct),Scalar>::type>
 {
   typedef Product<Lhs,Rhs,Options> SrcXprType;
   static EIGEN_STRONG_INLINE
-  void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<Scalar> &)
+  void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<Scalar,typename SrcXprType::Scalar> &)
   {
     // FIXME shall we handle nested_eval here?
     generic_product_impl<Lhs, Rhs>::addTo(dst, src.lhs(), src.rhs());
@@ -152,12 +152,12 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::add_assign_op<
 
 // Dense -= Product
 template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar>
-struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::sub_assign_op<Scalar>, Dense2Dense,
+struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::sub_assign_op<Scalar,typename Product<Lhs,Rhs,Options>::Scalar>, Dense2Dense,
   typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct),Scalar>::type>
 {
   typedef Product<Lhs,Rhs,Options> SrcXprType;
   static EIGEN_STRONG_INLINE
-  void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<Scalar> &)
+  void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<Scalar,typename SrcXprType::Scalar> &)
   {
     // FIXME shall we handle nested_eval here?
     generic_product_impl<Lhs, Rhs>::subTo(dst, src.lhs(), src.rhs());
@@ -187,37 +187,38 @@ struct Assignment<DstXprType, CwiseUnaryOp<internal::scalar_multiple_op<ScalarBi
 // 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,
+struct evaluator_assume_aliasing<CwiseBinaryOp<internal::scalar_sum_op<typename OtherXpr::Scalar,typename Product<Lhs,Rhs,DefaultProduct>::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>
+template<typename DstXprType, typename OtherXpr, typename ProductType, typename Func1, typename Func2>
 struct assignment_from_xpr_plus_product
 {
-  typedef CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const OtherXpr, const ProductType> SrcXprType;
+  typedef CwiseBinaryOp<internal::scalar_sum_op<typename OtherXpr::Scalar,typename ProductType::Scalar>, const OtherXpr, const ProductType> SrcXprType;
+  template<typename InitialFunc>
   static EIGEN_STRONG_INLINE
-  void run(DstXprType &dst, const SrcXprType &src, const Func1& func)
+  void run(DstXprType &dst, const SrcXprType &src, const InitialFunc& /*func*/)
   {
-    call_assignment_no_alias(dst, src.lhs(), func);
+    call_assignment_no_alias(dst, src.lhs(), Func1());
     call_assignment_no_alias(dst, src.rhs(), Func2());
   }
 };
 
-template< typename DstXprType, typename OtherXpr, typename Lhs, typename Rhs, typename Scalar>
-struct Assignment<DstXprType, CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const OtherXpr,
-                                           const Product<Lhs,Rhs,DefaultProduct> >, internal::assign_op<Scalar>, Dense2Dense>
-  : assignment_from_xpr_plus_product<DstXprType, OtherXpr, Product<Lhs,Rhs,DefaultProduct>, Scalar, internal::assign_op<Scalar>, internal::add_assign_op<Scalar> >
+template< typename DstXprType, typename OtherXpr, typename Lhs, typename Rhs, typename DstScalar, typename SrcScalar, typename OtherScalar,typename ProdScalar>
+struct Assignment<DstXprType, CwiseBinaryOp<internal::scalar_sum_op<OtherScalar,ProdScalar>, const OtherXpr,
+                                           const Product<Lhs,Rhs,DefaultProduct> >, internal::assign_op<DstScalar,SrcScalar>, Dense2Dense>
+  : assignment_from_xpr_plus_product<DstXprType, OtherXpr, Product<Lhs,Rhs,DefaultProduct>, internal::assign_op<DstScalar,OtherScalar>, internal::add_assign_op<DstScalar,ProdScalar> >
 {};
-template< typename DstXprType, typename OtherXpr, typename Lhs, typename Rhs, typename Scalar>
-struct Assignment<DstXprType, CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const OtherXpr,
-                                           const Product<Lhs,Rhs,DefaultProduct> >, internal::add_assign_op<Scalar>, Dense2Dense>
-  : assignment_from_xpr_plus_product<DstXprType, OtherXpr, Product<Lhs,Rhs,DefaultProduct>, Scalar, internal::add_assign_op<Scalar>, internal::add_assign_op<Scalar> >
+template< typename DstXprType, typename OtherXpr, typename Lhs, typename Rhs, typename DstScalar, typename SrcScalar, typename OtherScalar,typename ProdScalar>
+struct Assignment<DstXprType, CwiseBinaryOp<internal::scalar_sum_op<OtherScalar,ProdScalar>, const OtherXpr,
+                                           const Product<Lhs,Rhs,DefaultProduct> >, internal::add_assign_op<DstScalar,SrcScalar>, Dense2Dense>
+  : assignment_from_xpr_plus_product<DstXprType, OtherXpr, Product<Lhs,Rhs,DefaultProduct>, internal::add_assign_op<DstScalar,OtherScalar>, internal::add_assign_op<DstScalar,ProdScalar> >
 {};
-template< typename DstXprType, typename OtherXpr, typename Lhs, typename Rhs, typename Scalar>
-struct Assignment<DstXprType, CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const OtherXpr,
-                                           const Product<Lhs,Rhs,DefaultProduct> >, internal::sub_assign_op<Scalar>, Dense2Dense>
-  : assignment_from_xpr_plus_product<DstXprType, OtherXpr, Product<Lhs,Rhs,DefaultProduct>, Scalar, internal::sub_assign_op<Scalar>, internal::sub_assign_op<Scalar> >
+template< typename DstXprType, typename OtherXpr, typename Lhs, typename Rhs, typename DstScalar, typename SrcScalar, typename OtherScalar,typename ProdScalar>
+struct Assignment<DstXprType, CwiseBinaryOp<internal::scalar_sum_op<OtherScalar,ProdScalar>, const OtherXpr,
+                                           const Product<Lhs,Rhs,DefaultProduct> >, internal::sub_assign_op<DstScalar,SrcScalar>, Dense2Dense>
+  : assignment_from_xpr_plus_product<DstXprType, OtherXpr, Product<Lhs,Rhs,DefaultProduct>, internal::sub_assign_op<DstScalar,OtherScalar>, internal::sub_assign_op<DstScalar,ProdScalar> >
 {};
 //----------------------------------------
 
@@ -369,21 +370,21 @@ struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,CoeffBasedProductMode>
   {
     // Same as: dst.noalias() = lhs.lazyProduct(rhs);
     // but easier on the compiler side
-    call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::assign_op<Scalar>());
+    call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::assign_op<typename Dst::Scalar,Scalar>());
   }
   
   template<typename Dst>
   static EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   {
     // dst.noalias() += lhs.lazyProduct(rhs);
-    call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::add_assign_op<Scalar>());
+    call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::add_assign_op<typename Dst::Scalar,Scalar>());
   }
   
   template<typename Dst>
   static EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   {
     // dst.noalias() -= lhs.lazyProduct(rhs);
-    call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::sub_assign_op<Scalar>());
+    call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::sub_assign_op<typename Dst::Scalar,Scalar>());
   }
   
 //   template<typename Dst>
@@ -735,7 +736,7 @@ template<typename MatrixType, typename DiagonalType, typename Derived, int Produ
 struct diagonal_product_evaluator_base
   : evaluator_base<Derived>
 {
-   typedef typename scalar_product_traits<typename MatrixType::Scalar, typename DiagonalType::Scalar>::ReturnType Scalar;
+   typedef typename ScalarBinaryOpTraits<typename MatrixType::Scalar, typename DiagonalType::Scalar>::ReturnType Scalar;
 public:
   enum {
     CoeffReadCost = NumTraits<Scalar>::MulCost + evaluator<MatrixType>::CoeffReadCost + evaluator<DiagonalType>::CoeffReadCost,
diff --git a/Eigen/src/Core/Redux.h b/Eigen/src/Core/Redux.h
index 7984cd6e1..ec969d9b9 100644
--- a/Eigen/src/Core/Redux.h
+++ b/Eigen/src/Core/Redux.h
@@ -450,7 +450,7 @@ DenseBase<Derived>::sum() const
 {
   if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
     return Scalar(0);
-  return derived().redux(Eigen::internal::scalar_sum_op<Scalar>());
+  return derived().redux(Eigen::internal::scalar_sum_op<Scalar,Scalar>());
 }
 
 /** \returns the mean of all coefficients of *this
@@ -465,7 +465,7 @@ DenseBase<Derived>::mean() const
   #pragma warning push
   #pragma warning ( disable : 2259 )
 #endif
-  return Scalar(derived().redux(Eigen::internal::scalar_sum_op<Scalar>())) / Scalar(this->size());
+  return Scalar(derived().redux(Eigen::internal::scalar_sum_op<Scalar,Scalar>())) / Scalar(this->size());
 #ifdef __INTEL_COMPILER
   #pragma warning pop
 #endif
diff --git a/Eigen/src/Core/Ref.h b/Eigen/src/Core/Ref.h
index 6e94181f3..17065fdd5 100644
--- a/Eigen/src/Core/Ref.h
+++ b/Eigen/src/Core/Ref.h
@@ -262,7 +262,7 @@ template<typename TPlainObjectType, int Options, typename StrideType> class Ref<
     template<typename Expression>
     EIGEN_DEVICE_FUNC void construct(const Expression& expr, internal::false_type)
     {
-      internal::call_assignment_no_alias(m_object,expr,internal::assign_op<Scalar>());
+      internal::call_assignment_no_alias(m_object,expr,internal::assign_op<Scalar,Scalar>());
       Base::construct(m_object);
     }
 
diff --git a/Eigen/src/Core/SelfCwiseBinaryOp.h b/Eigen/src/Core/SelfCwiseBinaryOp.h
index 78fff1549..719ed72a5 100644
--- a/Eigen/src/Core/SelfCwiseBinaryOp.h
+++ b/Eigen/src/Core/SelfCwiseBinaryOp.h
@@ -12,11 +12,13 @@
 
 namespace Eigen { 
 
+// TODO generalize the scalar type of 'other'
+
 template<typename Derived>
 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>());
+  internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::mul_assign_op<Scalar,Scalar>());
   return derived();
 }
 
@@ -24,7 +26,7 @@ template<typename Derived>
 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>());
+  internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::add_assign_op<Scalar,Scalar>());
   return derived();
 }
 
@@ -32,7 +34,7 @@ template<typename Derived>
 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>());
+  internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::sub_assign_op<Scalar,Scalar>());
   return derived();
 }
 
@@ -40,7 +42,7 @@ template<typename Derived>
 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>());
+  internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::div_assign_op<Scalar,Scalar>());
   return derived();
 }
 
diff --git a/Eigen/src/Core/Solve.h b/Eigen/src/Core/Solve.h
index ba2ee53b8..038ad5b11 100644
--- a/Eigen/src/Core/Solve.h
+++ b/Eigen/src/Core/Solve.h
@@ -134,10 +134,10 @@ protected:
 // Specialization for "dst = dec.solve(rhs)"
 // NOTE we need to specialize it for Dense2Dense to avoid ambiguous specialization error and a Sparse2Sparse specialization must exist somewhere
 template<typename DstXprType, typename DecType, typename RhsType, typename Scalar>
-struct Assignment<DstXprType, Solve<DecType,RhsType>, internal::assign_op<Scalar>, Dense2Dense, Scalar>
+struct Assignment<DstXprType, Solve<DecType,RhsType>, internal::assign_op<Scalar,Scalar>, Dense2Dense, Scalar>
 {
   typedef Solve<DecType,RhsType> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
   {
     // FIXME shall we resize dst here?
     src.dec()._solve_impl(src.rhs(), dst);
@@ -146,10 +146,10 @@ struct Assignment<DstXprType, Solve<DecType,RhsType>, internal::assign_op<Scalar
 
 // Specialization for "dst = dec.transpose().solve(rhs)"
 template<typename DstXprType, typename DecType, typename RhsType, typename Scalar>
-struct Assignment<DstXprType, Solve<Transpose<const DecType>,RhsType>, internal::assign_op<Scalar>, Dense2Dense, Scalar>
+struct Assignment<DstXprType, Solve<Transpose<const DecType>,RhsType>, internal::assign_op<Scalar,Scalar>, Dense2Dense, Scalar>
 {
   typedef Solve<Transpose<const DecType>,RhsType> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
   {
     src.dec().nestedExpression().template _solve_impl_transposed<false>(src.rhs(), dst);
   }
@@ -157,10 +157,11 @@ struct Assignment<DstXprType, Solve<Transpose<const DecType>,RhsType>, internal:
 
 // Specialization for "dst = dec.adjoint().solve(rhs)"
 template<typename DstXprType, typename DecType, typename RhsType, typename Scalar>
-struct Assignment<DstXprType, Solve<CwiseUnaryOp<internal::scalar_conjugate_op<typename DecType::Scalar>, const Transpose<const DecType> >,RhsType>, internal::assign_op<Scalar>, Dense2Dense, Scalar>
+struct Assignment<DstXprType, Solve<CwiseUnaryOp<internal::scalar_conjugate_op<typename DecType::Scalar>, const Transpose<const DecType> >,RhsType>,
+                  internal::assign_op<Scalar,Scalar>, Dense2Dense, Scalar>
 {
   typedef Solve<CwiseUnaryOp<internal::scalar_conjugate_op<typename DecType::Scalar>, const Transpose<const DecType> >,RhsType> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
   {
     src.dec().nestedExpression().nestedExpression().template _solve_impl_transposed<true>(src.rhs(), dst);
   }
diff --git a/Eigen/src/Core/TriangularMatrix.h b/Eigen/src/Core/TriangularMatrix.h
index 5c5e5028e..8731e9127 100644
--- a/Eigen/src/Core/TriangularMatrix.h
+++ b/Eigen/src/Core/TriangularMatrix.h
@@ -367,14 +367,14 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularViewImpl<_Mat
     template<typename Other>
     EIGEN_DEVICE_FUNC
     TriangularViewType&  operator+=(const DenseBase<Other>& other) {
-      internal::call_assignment_no_alias(derived(), other.derived(), internal::add_assign_op<Scalar>());
+      internal::call_assignment_no_alias(derived(), other.derived(), internal::add_assign_op<Scalar,typename Other::Scalar>());
       return derived();
     }
     /** \sa MatrixBase::operator-=() */
     template<typename Other>
     EIGEN_DEVICE_FUNC
     TriangularViewType&  operator-=(const DenseBase<Other>& other) {
-      internal::call_assignment_no_alias(derived(), other.derived(), internal::sub_assign_op<Scalar>());
+      internal::call_assignment_no_alias(derived(), other.derived(), internal::sub_assign_op<Scalar,typename Other::Scalar>());
       return derived();
     }
     
@@ -552,7 +552,7 @@ template<typename OtherDerived>
 inline TriangularView<MatrixType, Mode>&
 TriangularViewImpl<MatrixType, Mode, Dense>::operator=(const MatrixBase<OtherDerived>& other)
 {
-  internal::call_assignment_no_alias(derived(), other.derived(), internal::assign_op<Scalar>());
+  internal::call_assignment_no_alias(derived(), other.derived(), internal::assign_op<Scalar,typename OtherDerived::Scalar>());
   return derived();
 }
 
@@ -804,7 +804,7 @@ template<int Mode, bool SetOpposite, typename DstXprType, typename SrcXprType>
 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>());
+  call_triangular_assignment_loop<Mode,SetOpposite>(dst, src, internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());
 }
 
 template<> struct AssignmentKind<TriangularShape,TriangularShape> { typedef Triangular2Triangular Kind; };
@@ -933,10 +933,10 @@ namespace internal {
   
 // Triangular = Product
 template< typename DstXprType, typename Lhs, typename Rhs, typename Scalar>
-struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::assign_op<Scalar>, Dense2Triangular, Scalar>
+struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular, Scalar>
 {
   typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename SrcXprType::Scalar> &)
   {
     dst.setZero();
     dst._assignProduct(src, 1);
@@ -945,10 +945,10 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::assign_
 
 // Triangular += Product
 template< typename DstXprType, typename Lhs, typename Rhs, typename Scalar>
-struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::add_assign_op<Scalar>, Dense2Triangular, Scalar>
+struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::add_assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular, Scalar>
 {
   typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<Scalar,typename SrcXprType::Scalar> &)
   {
     dst._assignProduct(src, 1);
   }
@@ -956,10 +956,10 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::add_ass
 
 // Triangular -= Product
 template< typename DstXprType, typename Lhs, typename Rhs, typename Scalar>
-struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::sub_assign_op<Scalar>, Dense2Triangular, Scalar>
+struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::sub_assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular, Scalar>
 {
   typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<Scalar,typename SrcXprType::Scalar> &)
   {
     dst._assignProduct(src, -1);
   }
diff --git a/Eigen/src/Core/VectorwiseOp.h b/Eigen/src/Core/VectorwiseOp.h
index 193891189..00a4a8c39 100644
--- a/Eigen/src/Core/VectorwiseOp.h
+++ b/Eigen/src/Core/VectorwiseOp.h
@@ -540,7 +540,7 @@ template<typename ExpressionType, int Direction> class VectorwiseOp
 
     /** Returns the expression of the sum of the vector \a other to each subvector of \c *this */
     template<typename OtherDerived> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
-    CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
+    CwiseBinaryOp<internal::scalar_sum_op<Scalar,typename OtherDerived::Scalar>,
                   const ExpressionTypeNestedCleaned,
                   const typename ExtendedType<OtherDerived>::Type>
     operator+(const DenseBase<OtherDerived>& other) const
@@ -553,7 +553,7 @@ template<typename ExpressionType, int Direction> class VectorwiseOp
     /** Returns the expression of the difference between each subvector of \c *this and the vector \a other */
     template<typename OtherDerived>
     EIGEN_DEVICE_FUNC
-    CwiseBinaryOp<internal::scalar_difference_op<Scalar>,
+    CwiseBinaryOp<internal::scalar_difference_op<Scalar,typename OtherDerived::Scalar>,
                   const ExpressionTypeNestedCleaned,
                   const typename ExtendedType<OtherDerived>::Type>
     operator-(const DenseBase<OtherDerived>& other) const
diff --git a/Eigen/src/Core/functors/AssignmentFunctors.h b/Eigen/src/Core/functors/AssignmentFunctors.h
index 51fef50e8..9b373c783 100644
--- a/Eigen/src/Core/functors/AssignmentFunctors.h
+++ b/Eigen/src/Core/functors/AssignmentFunctors.h
@@ -18,20 +18,24 @@ namespace internal {
   * \brief Template functor for scalar/packet assignment
   *
   */
-template<typename Scalar> struct assign_op {
+template<typename DstScalar,typename SrcScalar> struct assign_op {
 
   EIGEN_EMPTY_STRUCT_CTOR(assign_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(Scalar& a, const Scalar& b) const { a = b; }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(DstScalar& a, const SrcScalar& b) const { a = b; }
   
   template<int Alignment, typename Packet>
-  EIGEN_STRONG_INLINE void assignPacket(Scalar* a, const Packet& b) const
-  { internal::pstoret<Scalar,Packet,Alignment>(a,b); }
+  EIGEN_STRONG_INLINE void assignPacket(DstScalar* a, const Packet& b) const
+  { internal::pstoret<DstScalar,Packet,Alignment>(a,b); }
 };
-template<typename Scalar>
-struct functor_traits<assign_op<Scalar> > {
+
+// Empty overload for void type (used by PermutationMatrix
+template<typename DstScalar> struct assign_op<DstScalar,void> {};
+
+template<typename DstScalar,typename SrcScalar>
+struct functor_traits<assign_op<DstScalar,SrcScalar> > {
   enum {
-    Cost = NumTraits<Scalar>::ReadCost,
-    PacketAccess = packet_traits<Scalar>::Vectorizable
+    Cost = NumTraits<DstScalar>::ReadCost,
+    PacketAccess = is_same<DstScalar,SrcScalar>::value && packet_traits<DstScalar>::Vectorizable && packet_traits<SrcScalar>::Vectorizable
   };
 };
 
@@ -39,20 +43,20 @@ struct functor_traits<assign_op<Scalar> > {
   * \brief Template functor for scalar/packet assignment with addition
   *
   */
-template<typename Scalar> struct add_assign_op {
+template<typename DstScalar,typename SrcScalar> struct add_assign_op {
 
   EIGEN_EMPTY_STRUCT_CTOR(add_assign_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(Scalar& a, const Scalar& b) const { a += b; }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(DstScalar& a, const SrcScalar& b) const { a += b; }
   
   template<int Alignment, typename Packet>
-  EIGEN_STRONG_INLINE void assignPacket(Scalar* a, const Packet& b) const
-  { internal::pstoret<Scalar,Packet,Alignment>(a,internal::padd(internal::ploadt<Packet,Alignment>(a),b)); }
+  EIGEN_STRONG_INLINE void assignPacket(DstScalar* a, const Packet& b) const
+  { internal::pstoret<DstScalar,Packet,Alignment>(a,internal::padd(internal::ploadt<Packet,Alignment>(a),b)); }
 };
-template<typename Scalar>
-struct functor_traits<add_assign_op<Scalar> > {
+template<typename DstScalar,typename SrcScalar>
+struct functor_traits<add_assign_op<DstScalar,SrcScalar> > {
   enum {
-    Cost = NumTraits<Scalar>::ReadCost + NumTraits<Scalar>::AddCost,
-    PacketAccess = packet_traits<Scalar>::HasAdd
+    Cost = NumTraits<DstScalar>::ReadCost + NumTraits<DstScalar>::AddCost,
+    PacketAccess = is_same<DstScalar,SrcScalar>::value && packet_traits<DstScalar>::HasAdd
   };
 };
 
@@ -60,20 +64,20 @@ struct functor_traits<add_assign_op<Scalar> > {
   * \brief Template functor for scalar/packet assignment with subtraction
   *
   */
-template<typename Scalar> struct sub_assign_op {
+template<typename DstScalar,typename SrcScalar> struct sub_assign_op {
 
   EIGEN_EMPTY_STRUCT_CTOR(sub_assign_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(Scalar& a, const Scalar& b) const { a -= b; }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(DstScalar& a, const SrcScalar& b) const { a -= b; }
   
   template<int Alignment, typename Packet>
-  EIGEN_STRONG_INLINE void assignPacket(Scalar* a, const Packet& b) const
-  { internal::pstoret<Scalar,Packet,Alignment>(a,internal::psub(internal::ploadt<Packet,Alignment>(a),b)); }
+  EIGEN_STRONG_INLINE void assignPacket(DstScalar* a, const Packet& b) const
+  { internal::pstoret<DstScalar,Packet,Alignment>(a,internal::psub(internal::ploadt<Packet,Alignment>(a),b)); }
 };
-template<typename Scalar>
-struct functor_traits<sub_assign_op<Scalar> > {
+template<typename DstScalar,typename SrcScalar>
+struct functor_traits<sub_assign_op<DstScalar,SrcScalar> > {
   enum {
-    Cost = NumTraits<Scalar>::ReadCost + NumTraits<Scalar>::AddCost,
-    PacketAccess = packet_traits<Scalar>::HasSub
+    Cost = NumTraits<DstScalar>::ReadCost + NumTraits<DstScalar>::AddCost,
+    PacketAccess = is_same<DstScalar,SrcScalar>::value && packet_traits<DstScalar>::HasSub
   };
 };
 
@@ -98,7 +102,6 @@ struct functor_traits<mul_assign_op<DstScalar,SrcScalar> > {
     PacketAccess = is_same<DstScalar,SrcScalar>::value && packet_traits<DstScalar>::HasMul
   };
 };
-template<typename DstScalar,typename SrcScalar> struct functor_is_product_like<mul_assign_op<DstScalar,SrcScalar> > { enum { ret = 1 }; };
 
 /** \internal
   * \brief Template functor for scalar/packet assignment with diviving
@@ -120,7 +123,6 @@ struct functor_traits<div_assign_op<DstScalar,SrcScalar> > {
     PacketAccess = is_same<DstScalar,SrcScalar>::value && packet_traits<DstScalar>::HasDiv
   };
 };
-template<typename DstScalar,typename SrcScalar> struct functor_is_product_like<div_assign_op<DstScalar,SrcScalar> > { enum { ret = 1 }; };
 
 /** \internal
   * \brief Template functor for scalar/packet assignment with swapping
diff --git a/Eigen/src/Core/functors/BinaryFunctors.h b/Eigen/src/Core/functors/BinaryFunctors.h
index 6eb5b91ce..98fcebae5 100644
--- a/Eigen/src/Core/functors/BinaryFunctors.h
+++ b/Eigen/src/Core/functors/BinaryFunctors.h
@@ -21,22 +21,23 @@ namespace internal {
   *
   * \sa class CwiseBinaryOp, MatrixBase::operator+, class VectorwiseOp, DenseBase::sum()
   */
-template<typename Scalar> struct scalar_sum_op {
-//   typedef Scalar result_type;
+template<typename LhsScalar,typename RhsScalar> struct scalar_sum_op {
+  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_sum_op>::ReturnType result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_sum_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a + b; }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a + b; }
   template<typename Packet>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
   { return internal::padd(a,b); }
   template<typename Packet>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar predux(const Packet& a) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type predux(const Packet& a) const
   { return internal::predux(a); }
 };
-template<typename Scalar>
-struct functor_traits<scalar_sum_op<Scalar> > {
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_sum_op<LhsScalar,RhsScalar> > {
   enum {
-    Cost = NumTraits<Scalar>::AddCost,
-    PacketAccess = packet_traits<Scalar>::HasAdd
+    Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2, // rough estimate!
+    PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasAdd && packet_traits<RhsScalar>::HasAdd
+    // TODO vectorize mixed sum
   };
 };
 
@@ -45,7 +46,7 @@ struct functor_traits<scalar_sum_op<Scalar> > {
   * This is required to solve Bug 426.
   * \sa DenseBase::count(), DenseBase::any(), ArrayBase::cast(), MatrixBase::cast()
   */
-template<> struct scalar_sum_op<bool> : scalar_sum_op<int> {
+template<> struct scalar_sum_op<bool,bool> : scalar_sum_op<int,int> {
   EIGEN_DEPRECATED
   scalar_sum_op() {}
 };
@@ -57,11 +58,7 @@ template<> struct scalar_sum_op<bool> : scalar_sum_op<int> {
   * \sa class CwiseBinaryOp, Cwise::operator*(), class VectorwiseOp, MatrixBase::redux()
   */
 template<typename LhsScalar,typename RhsScalar> struct scalar_product_op {
-  enum {
-    // TODO vectorize mixed product
-    Vectorizable = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasMul && packet_traits<RhsScalar>::HasMul
-  };
-  typedef typename scalar_product_traits<LhsScalar,RhsScalar>::ReturnType result_type;
+  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_product_op>::ReturnType result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_product_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a * b; }
   template<typename Packet>
@@ -75,7 +72,8 @@ template<typename LhsScalar,typename RhsScalar>
 struct functor_traits<scalar_product_op<LhsScalar,RhsScalar> > {
   enum {
     Cost = (NumTraits<LhsScalar>::MulCost + NumTraits<RhsScalar>::MulCost)/2, // rough estimate!
-    PacketAccess = scalar_product_op<LhsScalar,RhsScalar>::Vectorizable
+    PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasMul && packet_traits<RhsScalar>::HasMul
+    // TODO vectorize mixed product
   };
 };
 
@@ -90,7 +88,7 @@ template<typename LhsScalar,typename RhsScalar> struct scalar_conj_product_op {
     Conj = NumTraits<LhsScalar>::IsComplex
   };
   
-  typedef typename scalar_product_traits<LhsScalar,RhsScalar>::ReturnType result_type;
+  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_conj_product_op>::ReturnType result_type;
   
   EIGEN_EMPTY_STRUCT_CTOR(scalar_conj_product_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const
@@ -269,18 +267,19 @@ struct functor_traits<scalar_binary_pow_op<Scalar,OtherScalar> > {
   *
   * \sa class CwiseBinaryOp, MatrixBase::operator-
   */
-template<typename Scalar> struct scalar_difference_op {
+template<typename LhsScalar,typename RhsScalar> struct scalar_difference_op {
+  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_difference_op>::ReturnType result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_difference_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a - b; }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a - b; }
   template<typename Packet>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
   { return internal::psub(a,b); }
 };
-template<typename Scalar>
-struct functor_traits<scalar_difference_op<Scalar> > {
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_difference_op<LhsScalar,RhsScalar> > {
   enum {
-    Cost = NumTraits<Scalar>::AddCost,
-    PacketAccess = packet_traits<Scalar>::HasSub
+    Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,
+    PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasSub && packet_traits<RhsScalar>::HasSub
   };
 };
 
@@ -290,11 +289,7 @@ struct functor_traits<scalar_difference_op<Scalar> > {
   * \sa class CwiseBinaryOp, Cwise::operator/()
   */
 template<typename LhsScalar,typename RhsScalar> struct scalar_quotient_op {
-  enum {
-    // TODO vectorize mixed product
-    Vectorizable = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasDiv && packet_traits<RhsScalar>::HasDiv
-  };
-  typedef typename scalar_product_traits<LhsScalar,RhsScalar>::ReturnType result_type;
+  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_quotient_op>::ReturnType result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_quotient_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a / b; }
   template<typename Packet>
@@ -305,7 +300,7 @@ 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 {
-    PacketAccess = scalar_quotient_op<LhsScalar,RhsScalar>::Vectorizable,
+    PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasDiv && packet_traits<RhsScalar>::HasDiv,
     Cost = NumTraits<result_type>::template Div<PacketAccess>::Cost
   };
 };
@@ -446,7 +441,7 @@ struct functor_traits<scalar_multiple_op<Scalar> >
 
 template<typename Scalar1, typename Scalar2>
 struct scalar_multiple2_op {
-  typedef typename scalar_product_traits<Scalar1,Scalar2>::ReturnType result_type;
+  typedef typename ScalarBinaryOpTraits<Scalar1,Scalar2>::ReturnType result_type;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_multiple2_op(const scalar_multiple2_op& other) : m_other(other.m_other) { }
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_multiple2_op(const Scalar2& other) : m_other(other) { }
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const Scalar1& a) const { return a * m_other; }
@@ -481,7 +476,7 @@ struct functor_traits<scalar_quotient1_op<Scalar> >
 
 template<typename Scalar1, typename Scalar2>
 struct scalar_quotient2_op {
-  typedef typename scalar_product_traits<Scalar1,Scalar2>::ReturnType result_type;
+  typedef typename ScalarBinaryOpTraits<Scalar1,Scalar2>::ReturnType result_type;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_quotient2_op(const scalar_quotient2_op& other) : m_other(other.m_other) { }
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_quotient2_op(const Scalar2& other) : m_other(other) { }
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const Scalar1& a) const { return a / m_other; }
@@ -491,15 +486,6 @@ template<typename Scalar1,typename Scalar2>
 struct functor_traits<scalar_quotient2_op<Scalar1,Scalar2> >
 { enum { Cost = 2 * NumTraits<Scalar1>::MulCost, PacketAccess = false }; };
 
-// In Eigen, any binary op (Product, CwiseBinaryOp) require the Lhs and Rhs to have the same scalar type, except for multiplication
-// where the mixing of different types is handled by scalar_product_traits
-// In particular, real * complex<real> is allowed.
-// FIXME move this to functor_traits adding a functor_default
-template<typename Functor> struct functor_is_product_like { enum { ret = 0 }; };
-template<typename LhsScalar,typename RhsScalar> struct functor_is_product_like<scalar_product_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
-template<typename LhsScalar,typename RhsScalar> struct functor_is_product_like<scalar_conj_product_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
-template<typename LhsScalar,typename RhsScalar> struct functor_is_product_like<scalar_quotient_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
-
 
 /** \internal
   * \brief Template functor to add a scalar to a fixed other one
diff --git a/Eigen/src/Core/products/GeneralBlockPanelKernel.h b/Eigen/src/Core/products/GeneralBlockPanelKernel.h
index 253c03462..63a9fc462 100644
--- a/Eigen/src/Core/products/GeneralBlockPanelKernel.h
+++ b/Eigen/src/Core/products/GeneralBlockPanelKernel.h
@@ -363,7 +363,7 @@ class gebp_traits
 public:
   typedef _LhsScalar LhsScalar;
   typedef _RhsScalar RhsScalar;
-  typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
 
   enum {
     ConjLhs = _ConjLhs,
@@ -478,7 +478,7 @@ class gebp_traits<std::complex<RealScalar>, RealScalar, _ConjLhs, false>
 public:
   typedef std::complex<RealScalar> LhsScalar;
   typedef RealScalar RhsScalar;
-  typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
 
   enum {
     ConjLhs = _ConjLhs,
diff --git a/Eigen/src/Core/products/GeneralMatrixMatrix.h b/Eigen/src/Core/products/GeneralMatrixMatrix.h
index 7528fef24..b1465c3b5 100644
--- a/Eigen/src/Core/products/GeneralMatrixMatrix.h
+++ b/Eigen/src/Core/products/GeneralMatrixMatrix.h
@@ -25,7 +25,7 @@ struct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLh
 {
   typedef gebp_traits<RhsScalar,LhsScalar> Traits;
   
-  typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
   static EIGEN_STRONG_INLINE void run(
     Index rows, Index cols, Index depth,
     const LhsScalar* lhs, Index lhsStride,
@@ -55,7 +55,7 @@ struct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLh
 
 typedef gebp_traits<LhsScalar,RhsScalar> Traits;
   
-typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
 static void run(Index rows, Index cols, Index depth,
   const LhsScalar* _lhs, Index lhsStride,
   const RhsScalar* _rhs, Index rhsStride,
diff --git a/Eigen/src/Core/products/GeneralMatrixMatrixTriangular.h b/Eigen/src/Core/products/GeneralMatrixMatrixTriangular.h
index 80ba89465..29d6dc721 100644
--- a/Eigen/src/Core/products/GeneralMatrixMatrixTriangular.h
+++ b/Eigen/src/Core/products/GeneralMatrixMatrixTriangular.h
@@ -40,7 +40,7 @@ template <typename Index, typename LhsScalar, int LhsStorageOrder, bool Conjugat
                           typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int  UpLo, int Version>
 struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,UpLo,Version>
 {
-  typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+  typedef typename ScalarBinaryOpTraits<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, level3_blocking<RhsScalar,LhsScalar>& blocking)
@@ -57,7 +57,7 @@ template <typename Index, typename LhsScalar, int LhsStorageOrder, bool Conjugat
                           typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int  UpLo, int Version>
 struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Version>
 {
-  typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+  typedef typename ScalarBinaryOpTraits<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, level3_blocking<LhsScalar,RhsScalar>& blocking)
diff --git a/Eigen/src/Core/products/GeneralMatrixVector.h b/Eigen/src/Core/products/GeneralMatrixVector.h
index fc8886511..4a5cf3fb6 100644
--- a/Eigen/src/Core/products/GeneralMatrixVector.h
+++ b/Eigen/src/Core/products/GeneralMatrixVector.h
@@ -58,7 +58,7 @@ namespace internal {
 template<typename Index, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version>
 struct general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,ConjugateLhs,RhsScalar,RhsMapper,ConjugateRhs,Version>
 {
-  typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
 
 enum {
   Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable
@@ -334,7 +334,7 @@ EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,LhsMapper,C
 template<typename Index, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version>
 struct general_matrix_vector_product<Index,LhsScalar,LhsMapper,RowMajor,ConjugateLhs,RhsScalar,RhsMapper,ConjugateRhs,Version>
 {
-typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
 
 enum {
   Vectorizable = packet_traits<LhsScalar>::Vectorizable && packet_traits<RhsScalar>::Vectorizable
diff --git a/Eigen/src/Core/products/TriangularMatrixVector.h b/Eigen/src/Core/products/TriangularMatrixVector.h
index f79840aa7..c11a983c7 100644
--- a/Eigen/src/Core/products/TriangularMatrixVector.h
+++ b/Eigen/src/Core/products/TriangularMatrixVector.h
@@ -20,7 +20,7 @@ struct triangular_matrix_vector_product;
 template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int Version>
 struct triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,ColMajor,Version>
 {
-  typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
   enum {
     IsLower = ((Mode&Lower)==Lower),
     HasUnitDiag = (Mode & UnitDiag)==UnitDiag,
@@ -91,7 +91,7 @@ EIGEN_DONT_INLINE void triangular_matrix_vector_product<Index,Mode,LhsScalar,Con
 template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs,int Version>
 struct triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,RowMajor,Version>
 {
-  typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
   enum {
     IsLower = ((Mode&Lower)==Lower),
     HasUnitDiag = (Mode & UnitDiag)==UnitDiag,
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index 42e2e75b9..045e22658 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -131,6 +131,7 @@ template<typename ExpressionType> class ArrayWrapper;
 template<typename ExpressionType> class MatrixWrapper;
 template<typename Derived> class SolverBase;
 template<typename XprType> class InnerIterator;
+template<typename ScalarA, typename ScalarB, typename BinaryOp=void> struct ScalarBinaryOpTraits;
 
 namespace internal {
 template<typename DecompositionType> struct kernel_retval_base;
@@ -175,8 +176,8 @@ namespace internal {
 // with optional conjugation of the arguments.
 template<typename LhsScalar, typename RhsScalar, bool ConjLhs=false, bool ConjRhs=false> struct conj_helper;
 
-template<typename Scalar> struct scalar_sum_op;
-template<typename Scalar> struct scalar_difference_op;
+template<typename LhsScalar,typename RhsScalar> struct scalar_sum_op;
+template<typename LhsScalar,typename RhsScalar> struct scalar_difference_op;
 template<typename LhsScalar,typename RhsScalar> struct scalar_conj_product_op;
 template<typename Scalar> struct scalar_opposite_op;
 template<typename Scalar> struct scalar_conjugate_op;
diff --git a/Eigen/src/Core/util/Macros.h b/Eigen/src/Core/util/Macros.h
index c9a0b9893..35547fdda 100644
--- a/Eigen/src/Core/util/Macros.h
+++ b/Eigen/src/Core/util/Macros.h
@@ -885,9 +885,9 @@ namespace Eigen {
   }
 
 // the expression type of a cwise product
-#define EIGEN_CWISE_PRODUCT_RETURN_TYPE(LHS,RHS) \
+#define EIGEN_CWISE_BINARY_RETURN_TYPE(LHS,RHS,OPNAME) \
     CwiseBinaryOp< \
-      internal::scalar_product_op< \
+      EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)< \
           typename internal::traits<LHS>::Scalar, \
           typename internal::traits<RHS>::Scalar \
       >, \
diff --git a/Eigen/src/Core/util/Meta.h b/Eigen/src/Core/util/Meta.h
index 7ecd59add..af661c313 100644
--- a/Eigen/src/Core/util/Meta.h
+++ b/Eigen/src/Core/util/Meta.h
@@ -375,33 +375,6 @@ template<typename T, typename U> struct scalar_product_traits
   enum { Defined = 0 };
 };
 
-template<typename T> struct scalar_product_traits<T,T>
-{
-  enum {
-    // Cost = NumTraits<T>::MulCost,
-    Defined = 1
-  };
-  typedef T ReturnType;
-};
-
-template<typename T> struct scalar_product_traits<T,std::complex<T> >
-{
-  enum {
-    // Cost = 2*NumTraits<T>::MulCost,
-    Defined = 1
-  };
-  typedef std::complex<T> ReturnType;
-};
-
-template<typename T> struct scalar_product_traits<std::complex<T>, T>
-{
-  enum {
-    // Cost = 2*NumTraits<T>::MulCost,
-    Defined = 1
-  };
-  typedef std::complex<T> ReturnType;
-};
-
 // FIXME quick workaround around current limitation of result_of
 // template<typename Scalar, typename ArgType0, typename ArgType1>
 // struct result_of<scalar_product_op<Scalar>(ArgType0,ArgType1)> {
@@ -434,6 +407,43 @@ T div_ceil(const T &a, const T &b)
 
 } // end namespace numext
 
+
+/** \class ScalarBinaryOpTraits
+  * \ingroup Core_Module
+  *
+  * \brief Determines whether the given binary operation of two numeric types is allowed and what the scalar return type is.
+  *
+  * \sa CwiseBinaryOp
+  */
+template<typename ScalarA, typename ScalarB, typename BinaryOp>
+struct ScalarBinaryOpTraits
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+  // for backward compatibility, use the hints given by the (deprecated) internal::scalar_product_traits class.
+  : internal::scalar_product_traits<ScalarA,ScalarB>
+#endif // EIGEN_PARSED_BY_DOXYGEN
+{};
+
+template<typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<T,T,BinaryOp>
+{
+  enum { Defined = 1 };
+  typedef T ReturnType;
+};
+
+template<typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<T,std::complex<T>,BinaryOp>
+{
+  enum { Defined = 1 };
+  typedef std::complex<T> ReturnType;
+};
+
+template<typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<std::complex<T>, T,BinaryOp>
+{
+  enum { Defined = 1 };
+  typedef std::complex<T> ReturnType;
+};
+
 } // end namespace Eigen
 
 #endif // EIGEN_META_H
diff --git a/Eigen/src/Core/util/XprHelper.h b/Eigen/src/Core/util/XprHelper.h
index 3605de6fd..4fd4a9b0d 100644
--- a/Eigen/src/Core/util/XprHelper.h
+++ b/Eigen/src/Core/util/XprHelper.h
@@ -649,17 +649,13 @@ std::string demangle_flags(int f)
 
 } // end namespace internal
 
-// we require Lhs and Rhs to have the same scalar type. Currently there is no example of a binary functor
-// that would take two operands of different types. If there were such an example, then this check should be
-// moved to the BinaryOp functors, on a per-case basis. This would however require a change in the BinaryOp functors, as
-// currently they take only one typename Scalar template parameter.
+// We require Lhs and Rhs to have "compatible" scalar types.
 // It is tempting to always allow mixing different types but remember that this is often impossible in the vectorized paths.
 // So allowing mixing different types gives very unexpected errors when enabling vectorization, when the user tries to
 // add together a float matrix and a double matrix.
+// Treat "void" as a special case. Needed for permutation products. TODO: this should be handled by ScalarBinaryOpTraits
 #define EIGEN_CHECK_BINARY_COMPATIBILIY(BINOP,LHS,RHS) \
-  EIGEN_STATIC_ASSERT((internal::functor_is_product_like<BINOP>::ret \
-                        ? int(internal::scalar_product_traits<LHS, RHS>::Defined) \
-                        : int(internal::is_same_or_void<LHS, RHS>::value)), \
+  EIGEN_STATIC_ASSERT(int(internal::is_same_or_void<LHS, RHS>::value) || int(ScalarBinaryOpTraits<LHS, RHS,BINOP>::Defined), \
     YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
     
 } // end namespace Eigen
diff --git a/Eigen/src/Geometry/AlignedBox.h b/Eigen/src/Geometry/AlignedBox.h
index 03f1a11f8..aeb043a6c 100644
--- a/Eigen/src/Geometry/AlignedBox.h
+++ b/Eigen/src/Geometry/AlignedBox.h
@@ -112,7 +112,7 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
 
   /** \returns the center of the box */
   inline const CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>,
-                            const CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> >
+                            const CwiseBinaryOp<internal::scalar_sum_op<Scalar,Scalar>, const VectorType, const VectorType> >
   center() const
   { return (m_min+m_max)/2; }
 
@@ -120,7 +120,7 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
     * Note that this function does not get the same
     * result for integral or floating scalar types: see
     */
-  inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> sizes() const
+  inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar,Scalar>, const VectorType, const VectorType> sizes() const
   { return m_max - m_min; }
 
   /** \returns the volume of the bounding box */
@@ -131,7 +131,7 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
     * if the length of the diagonal is needed: diagonal().norm()
     * will provide it.
     */
-  inline CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> diagonal() const
+  inline CwiseBinaryOp< internal::scalar_difference_op<Scalar,Scalar>, const VectorType, const VectorType> diagonal() const
   { return sizes(); }
 
   /** \returns the vertex of the bounding box at the corner defined by
diff --git a/Eigen/src/Geometry/Homogeneous.h b/Eigen/src/Geometry/Homogeneous.h
index cd52b5470..1c35ca486 100644
--- a/Eigen/src/Geometry/Homogeneous.h
+++ b/Eigen/src/Geometry/Homogeneous.h
@@ -329,10 +329,10 @@ protected:
 
 // dense = homogeneous
 template< typename DstXprType, typename ArgType, typename Scalar>
-struct Assignment<DstXprType, Homogeneous<ArgType,Vertical>, internal::assign_op<Scalar>, Dense2Dense, Scalar>
+struct Assignment<DstXprType, Homogeneous<ArgType,Vertical>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense, Scalar>
 {
   typedef Homogeneous<ArgType,Vertical> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)
   {
     dst.template topRows<ArgType::RowsAtCompileTime>(src.nestedExpression().rows()) = src.nestedExpression();
     dst.row(dst.rows()-1).setOnes();
@@ -341,10 +341,10 @@ struct Assignment<DstXprType, Homogeneous<ArgType,Vertical>, internal::assign_op
 
 // dense = homogeneous
 template< typename DstXprType, typename ArgType, typename Scalar>
-struct Assignment<DstXprType, Homogeneous<ArgType,Horizontal>, internal::assign_op<Scalar>, Dense2Dense, Scalar>
+struct Assignment<DstXprType, Homogeneous<ArgType,Horizontal>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense, Scalar>
 {
   typedef Homogeneous<ArgType,Horizontal> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)
   {
     dst.template leftCols<ArgType::ColsAtCompileTime>(src.nestedExpression().cols()) = src.nestedExpression();
     dst.col(dst.cols()-1).setOnes();
@@ -373,7 +373,7 @@ struct homogeneous_right_product_refactoring_helper
   typedef typename Rhs::ConstRowXpr                                     ConstantColumn;
   typedef Replicate<const ConstantColumn,Rows,1>                        ConstantBlock;
   typedef Product<Lhs,LinearBlock,LazyProduct>                          LinearProduct;
-  typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
+  typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
 };
 
 template<typename Lhs, typename Rhs, int ProductTag>
@@ -414,7 +414,7 @@ struct homogeneous_left_product_refactoring_helper
   typedef typename Lhs::ConstColXpr                                     ConstantColumn;
   typedef Replicate<const ConstantColumn,1,Cols>                        ConstantBlock;
   typedef Product<LinearBlock,Rhs,LazyProduct>                          LinearProduct;
-  typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
+  typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
 };
 
 template<typename Lhs, typename Rhs, int ProductTag>
diff --git a/Eigen/src/Householder/HouseholderSequence.h b/Eigen/src/Householder/HouseholderSequence.h
index a57f81764..3ce0a693d 100644
--- a/Eigen/src/Householder/HouseholderSequence.h
+++ b/Eigen/src/Householder/HouseholderSequence.h
@@ -108,7 +108,7 @@ struct hseq_side_dependent_impl<VectorsType, CoeffsType, OnTheRight>
 
 template<typename OtherScalarType, typename MatrixType> struct matrix_type_times_scalar_type
 {
-  typedef typename scalar_product_traits<OtherScalarType, typename MatrixType::Scalar>::ReturnType
+  typedef typename ScalarBinaryOpTraits<OtherScalarType, typename MatrixType::Scalar>::ReturnType
     ResultScalar;
   typedef Matrix<ResultScalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime,
                  0, MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime> Type;
diff --git a/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h b/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h
index 35923be3d..7d67d3ce2 100644
--- a/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h
+++ b/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h
@@ -91,10 +91,10 @@ protected:
 // Specialization for "dst = dec.solveWithGuess(rhs)"
 // NOTE we need to specialize it for Dense2Dense to avoid ambiguous specialization error and a Sparse2Sparse specialization must exist somewhere
 template<typename DstXprType, typename DecType, typename RhsType, typename GuessType, typename Scalar>
-struct Assignment<DstXprType, SolveWithGuess<DecType,RhsType,GuessType>, internal::assign_op<Scalar>, Dense2Dense, Scalar>
+struct Assignment<DstXprType, SolveWithGuess<DecType,RhsType,GuessType>, internal::assign_op<Scalar,Scalar>, Dense2Dense, Scalar>
 {
   typedef SolveWithGuess<DecType,RhsType,GuessType> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
   {
     // FIXME shall we resize dst here?
     dst = src.guess();
diff --git a/Eigen/src/LU/FullPivLU.h b/Eigen/src/LU/FullPivLU.h
index c39f8e3d5..2d01b18c6 100644
--- a/Eigen/src/LU/FullPivLU.h
+++ b/Eigen/src/LU/FullPivLU.h
@@ -839,12 +839,12 @@ namespace internal {
 
 
 /***** Implementation of inverse() *****************************************************/
-template<typename DstXprType, typename MatrixType, typename Scalar>
-struct Assignment<DstXprType, Inverse<FullPivLU<MatrixType> >, internal::assign_op<Scalar>, Dense2Dense, Scalar>
+template<typename DstXprType, typename MatrixType>
+struct Assignment<DstXprType, Inverse<FullPivLU<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename FullPivLU<MatrixType>::Scalar>, Dense2Dense>
 {
   typedef FullPivLU<MatrixType> LuType;
   typedef Inverse<LuType> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename MatrixType::Scalar> &)
   {
     dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols()));
   }
diff --git a/Eigen/src/LU/InverseImpl.h b/Eigen/src/LU/InverseImpl.h
index e202a55cb..3134632e1 100644
--- a/Eigen/src/LU/InverseImpl.h
+++ b/Eigen/src/LU/InverseImpl.h
@@ -286,11 +286,11 @@ struct compute_inverse_and_det_with_check<MatrixType, ResultType, 4>
 namespace internal {
 
 // Specialization for "dense = dense_xpr.inverse()"
-template<typename DstXprType, typename XprType, typename Scalar>
-struct Assignment<DstXprType, Inverse<XprType>, internal::assign_op<Scalar>, Dense2Dense, Scalar>
+template<typename DstXprType, typename XprType>
+struct Assignment<DstXprType, Inverse<XprType>, internal::assign_op<typename DstXprType::Scalar,typename XprType::Scalar>, Dense2Dense>
 {
   typedef Inverse<XprType> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename XprType::Scalar> &)
   {
     // FIXME shall we resize dst here?
     const int Size = EIGEN_PLAIN_ENUM_MIN(XprType::ColsAtCompileTime,DstXprType::ColsAtCompileTime);
diff --git a/Eigen/src/LU/PartialPivLU.h b/Eigen/src/LU/PartialPivLU.h
index b68916287..ac2902261 100644
--- a/Eigen/src/LU/PartialPivLU.h
+++ b/Eigen/src/LU/PartialPivLU.h
@@ -525,12 +525,12 @@ MatrixType PartialPivLU<MatrixType>::reconstructedMatrix() const
 namespace internal {
 
 /***** Implementation of inverse() *****************************************************/
-template<typename DstXprType, typename MatrixType, typename Scalar>
-struct Assignment<DstXprType, Inverse<PartialPivLU<MatrixType> >, internal::assign_op<Scalar>, Dense2Dense, Scalar>
+template<typename DstXprType, typename MatrixType>
+struct Assignment<DstXprType, Inverse<PartialPivLU<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename PartialPivLU<MatrixType>::Scalar>, Dense2Dense>
 {
   typedef PartialPivLU<MatrixType> LuType;
   typedef Inverse<LuType> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename LuType::Scalar> &)
   {
     dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols()));
   }
diff --git a/Eigen/src/QR/ColPivHouseholderQR.h b/Eigen/src/QR/ColPivHouseholderQR.h
index 7c559f952..525ee8c18 100644
--- a/Eigen/src/QR/ColPivHouseholderQR.h
+++ b/Eigen/src/QR/ColPivHouseholderQR.h
@@ -598,11 +598,11 @@ void ColPivHouseholderQR<_MatrixType>::_solve_impl(const RhsType &rhs, DstType &
 namespace internal {
 
 template<typename DstXprType, typename MatrixType, typename Scalar>
-struct Assignment<DstXprType, Inverse<ColPivHouseholderQR<MatrixType> >, internal::assign_op<Scalar>, Dense2Dense, Scalar>
+struct Assignment<DstXprType, Inverse<ColPivHouseholderQR<MatrixType> >, internal::assign_op<Scalar,Scalar>, Dense2Dense, Scalar>
 {
   typedef ColPivHouseholderQR<MatrixType> QrType;
   typedef Inverse<QrType> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
   {
     dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols()));
   }
diff --git a/Eigen/src/QR/CompleteOrthogonalDecomposition.h b/Eigen/src/QR/CompleteOrthogonalDecomposition.h
index 230d0d23c..52bcc2173 100644
--- a/Eigen/src/QR/CompleteOrthogonalDecomposition.h
+++ b/Eigen/src/QR/CompleteOrthogonalDecomposition.h
@@ -510,11 +510,11 @@ void CompleteOrthogonalDecomposition<_MatrixType>::_solve_impl(
 namespace internal {
 
 template<typename DstXprType, typename MatrixType, typename Scalar>
-struct Assignment<DstXprType, Inverse<CompleteOrthogonalDecomposition<MatrixType> >, internal::assign_op<Scalar>, Dense2Dense, Scalar>
+struct Assignment<DstXprType, Inverse<CompleteOrthogonalDecomposition<MatrixType> >, internal::assign_op<Scalar,Scalar>, Dense2Dense, Scalar>
 {
   typedef CompleteOrthogonalDecomposition<MatrixType> CodType;
   typedef Inverse<CodType> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
   {
     dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.rows()));
   }
diff --git a/Eigen/src/QR/FullPivHouseholderQR.h b/Eigen/src/QR/FullPivHouseholderQR.h
index 32a10f3fe..4f55d52a5 100644
--- a/Eigen/src/QR/FullPivHouseholderQR.h
+++ b/Eigen/src/QR/FullPivHouseholderQR.h
@@ -560,11 +560,11 @@ void FullPivHouseholderQR<_MatrixType>::_solve_impl(const RhsType &rhs, DstType
 namespace internal {
   
 template<typename DstXprType, typename MatrixType, typename Scalar>
-struct Assignment<DstXprType, Inverse<FullPivHouseholderQR<MatrixType> >, internal::assign_op<Scalar>, Dense2Dense, Scalar>
+struct Assignment<DstXprType, Inverse<FullPivHouseholderQR<MatrixType> >, internal::assign_op<Scalar,Scalar>, Dense2Dense, Scalar>
 {
   typedef FullPivHouseholderQR<MatrixType> QrType;
   typedef Inverse<QrType> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
   {    
     dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols()));
   }
diff --git a/Eigen/src/SparseCore/SparseAssign.h b/Eigen/src/SparseCore/SparseAssign.h
index 4a8dd12e4..b284fa9e4 100644
--- a/Eigen/src/SparseCore/SparseAssign.h
+++ b/Eigen/src/SparseCore/SparseAssign.h
@@ -34,8 +34,8 @@ template<typename OtherDerived>
 inline Derived& SparseMatrixBase<Derived>::operator=(const SparseMatrixBase<OtherDerived>& other)
 {
   // by default sparse evaluation do not alias, so we can safely bypass the generic call_assignment routine
-  internal::Assignment<Derived,OtherDerived,internal::assign_op<Scalar> >
-          ::run(derived(), other.derived(), internal::assign_op<Scalar>());
+  internal::Assignment<Derived,OtherDerived,internal::assign_op<Scalar,typename OtherDerived::Scalar> >
+          ::run(derived(), other.derived(), internal::assign_op<Scalar,typename OtherDerived::Scalar>());
   return derived();
 }
 
@@ -127,7 +127,7 @@ void assign_sparse_to_sparse(DstXprType &dst, const SrcXprType &src)
 template< typename DstXprType, typename SrcXprType, typename Functor, typename Scalar>
 struct Assignment<DstXprType, SrcXprType, Functor, Sparse2Sparse, Scalar>
 {
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar> &/*func*/)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
   {
     assign_sparse_to_sparse(dst.derived(), src.derived());
   }
@@ -141,7 +141,7 @@ struct Assignment<DstXprType, SrcXprType, Functor, Sparse2Dense, Scalar>
   {
     eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
 
-    if(internal::is_same<Functor,internal::assign_op<Scalar> >::value)
+    if(internal::is_same<Functor,internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> >::value)
       dst.setZero();
     
     internal::evaluator<SrcXprType> srcEval(src);
@@ -156,10 +156,10 @@ struct Assignment<DstXprType, SrcXprType, Functor, Sparse2Dense, Scalar>
 // Specialization for "dst = dec.solve(rhs)"
 // NOTE we need to specialize it for Sparse2Sparse to avoid ambiguous specialization error
 template<typename DstXprType, typename DecType, typename RhsType, typename Scalar>
-struct Assignment<DstXprType, Solve<DecType,RhsType>, internal::assign_op<Scalar>, Sparse2Sparse, Scalar>
+struct Assignment<DstXprType, Solve<DecType,RhsType>, internal::assign_op<Scalar,Scalar>, Sparse2Sparse, Scalar>
 {
   typedef Solve<DecType,RhsType> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
   {
     src.dec()._solve_impl(src.rhs(), dst);
   }
@@ -176,7 +176,7 @@ struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Sparse, Scalar>
   typedef Array<StorageIndex,Dynamic,1> ArrayXI;
   typedef Array<Scalar,Dynamic,1> ArrayXS;
   template<int Options>
-  static void run(SparseMatrix<Scalar,Options,StorageIndex> &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar> &/*func*/)
+  static void run(SparseMatrix<Scalar,Options,StorageIndex> &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
   {
     Index size = src.diagonal().size();
     dst.makeCompressed();
@@ -187,15 +187,15 @@ struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Sparse, Scalar>
   }
   
   template<typename DstDerived>
-  static void run(SparseMatrixBase<DstDerived> &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar> &/*func*/)
+  static void run(SparseMatrixBase<DstDerived> &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
   {
     dst.diagonal() = src.diagonal();
   }
   
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar> &/*func*/)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
   { dst.diagonal() += src.diagonal(); }
   
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar> &/*func*/)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
   { dst.diagonal() -= src.diagonal(); }
 };
 } // end namespace internal
diff --git a/Eigen/src/SparseCore/SparseCwiseBinaryOp.h b/Eigen/src/SparseCore/SparseCwiseBinaryOp.h
index d422f3cbe..dd21eb8c5 100644
--- a/Eigen/src/SparseCore/SparseCwiseBinaryOp.h
+++ b/Eigen/src/SparseCore/SparseCwiseBinaryOp.h
@@ -579,7 +579,7 @@ template<typename Derived>
 template<typename OtherDerived>
 Derived& SparseMatrixBase<Derived>::operator+=(const DiagonalBase<OtherDerived>& other)
 {
-  call_assignment_no_alias(derived(), other.derived(), internal::add_assign_op<Scalar>());
+  call_assignment_no_alias(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
   return derived();
 }
 
@@ -587,7 +587,7 @@ template<typename Derived>
 template<typename OtherDerived>
 Derived& SparseMatrixBase<Derived>::operator-=(const DiagonalBase<OtherDerived>& other)
 {
-  call_assignment_no_alias(derived(), other.derived(), internal::sub_assign_op<Scalar>());
+  call_assignment_no_alias(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
   return derived();
 }
     
@@ -600,31 +600,31 @@ SparseMatrixBase<Derived>::cwiseProduct(const MatrixBase<OtherDerived> &other) c
 }
 
 template<typename DenseDerived, typename SparseDerived>
-EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_sum_op<typename DenseDerived::Scalar>, const DenseDerived, const SparseDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_sum_op<typename DenseDerived::Scalar,typename SparseDerived::Scalar>, const DenseDerived, const SparseDerived>
 operator+(const MatrixBase<DenseDerived> &a, const SparseMatrixBase<SparseDerived> &b)
 {
-  return CwiseBinaryOp<internal::scalar_sum_op<typename DenseDerived::Scalar>, const DenseDerived, const SparseDerived>(a.derived(), b.derived());
+  return CwiseBinaryOp<internal::scalar_sum_op<typename DenseDerived::Scalar,typename SparseDerived::Scalar>, const DenseDerived, const SparseDerived>(a.derived(), b.derived());
 }
 
 template<typename SparseDerived, typename DenseDerived>
-EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_sum_op<typename DenseDerived::Scalar>, const SparseDerived, const DenseDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_sum_op<typename SparseDerived::Scalar,typename DenseDerived::Scalar>, const SparseDerived, const DenseDerived>
 operator+(const SparseMatrixBase<SparseDerived> &a, const MatrixBase<DenseDerived> &b)
 {
-  return CwiseBinaryOp<internal::scalar_sum_op<typename DenseDerived::Scalar>, const SparseDerived, const DenseDerived>(a.derived(), b.derived());
+  return CwiseBinaryOp<internal::scalar_sum_op<typename SparseDerived::Scalar,typename DenseDerived::Scalar>, const SparseDerived, const DenseDerived>(a.derived(), b.derived());
 }
 
 template<typename DenseDerived, typename SparseDerived>
-EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_difference_op<typename DenseDerived::Scalar>, const DenseDerived, const SparseDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_difference_op<typename DenseDerived::Scalar,typename SparseDerived::Scalar>, const DenseDerived, const SparseDerived>
 operator-(const MatrixBase<DenseDerived> &a, const SparseMatrixBase<SparseDerived> &b)
 {
-  return CwiseBinaryOp<internal::scalar_difference_op<typename DenseDerived::Scalar>, const DenseDerived, const SparseDerived>(a.derived(), b.derived());
+  return CwiseBinaryOp<internal::scalar_difference_op<typename DenseDerived::Scalar,typename SparseDerived::Scalar>, const DenseDerived, const SparseDerived>(a.derived(), b.derived());
 }
 
 template<typename SparseDerived, typename DenseDerived>
-EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_difference_op<typename DenseDerived::Scalar>, const SparseDerived, const DenseDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_difference_op<typename SparseDerived::Scalar,typename DenseDerived::Scalar>, const SparseDerived, const DenseDerived>
 operator-(const SparseMatrixBase<SparseDerived> &a, const MatrixBase<DenseDerived> &b)
 {
-  return CwiseBinaryOp<internal::scalar_difference_op<typename DenseDerived::Scalar>, const SparseDerived, const DenseDerived>(a.derived(), b.derived());
+  return CwiseBinaryOp<internal::scalar_difference_op<typename SparseDerived::Scalar,typename DenseDerived::Scalar>, const SparseDerived, const DenseDerived>(a.derived(), b.derived());
 }
 
 } // end namespace Eigen
diff --git a/Eigen/src/SparseCore/SparseDenseProduct.h b/Eigen/src/SparseCore/SparseDenseProduct.h
index 476796dd7..0547db596 100644
--- a/Eigen/src/SparseCore/SparseDenseProduct.h
+++ b/Eigen/src/SparseCore/SparseDenseProduct.h
@@ -74,7 +74,7 @@ struct sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, t
 // FIXME: what is the purpose of the following specialization? Is it for the BlockedSparse format?
 // -> let's disable it for now as it is conflicting with generic scalar*matrix and matrix*scalar operators
 // template<typename T1, typename T2/*, int _Options, typename _StrideType*/>
-// struct scalar_product_traits<T1, Ref<T2/*, _Options, _StrideType*/> >
+// struct ScalarBinaryOpTraits<T1, Ref<T2/*, _Options, _StrideType*/> >
 // {
 //   enum {
 //     Defined = 1
@@ -97,7 +97,7 @@ struct sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, A
       for(Index j=0; j<lhs.outerSize(); ++j)
       {
 //        typename Res::Scalar rhs_j = alpha * rhs.coeff(j,c);
-        typename internal::scalar_product_traits<AlphaType, typename Rhs::Scalar>::ReturnType rhs_j(alpha * rhs.coeff(j,c));
+        typename ScalarBinaryOpTraits<AlphaType, typename Rhs::Scalar>::ReturnType rhs_j(alpha * rhs.coeff(j,c));
         for(LhsInnerIterator it(lhsEval,j); it ;++it)
           res.coeffRef(it.index(),c) += it.value() * rhs_j;
       }
diff --git a/Eigen/src/SparseCore/SparseMatrix.h b/Eigen/src/SparseCore/SparseMatrix.h
index a78bd57c3..531fea399 100644
--- a/Eigen/src/SparseCore/SparseMatrix.h
+++ b/Eigen/src/SparseCore/SparseMatrix.h
@@ -440,7 +440,7 @@ class SparseMatrix
     template<typename InputIterators,typename DupFunctor>
     void setFromTriplets(const InputIterators& begin, const InputIterators& end, DupFunctor dup_func);
 
-    void sumupDuplicates() { collapseDuplicates(internal::scalar_sum_op<Scalar>()); }
+    void sumupDuplicates() { collapseDuplicates(internal::scalar_sum_op<Scalar,Scalar>()); }
 
     template<typename DupFunctor>
     void collapseDuplicates(DupFunctor dup_func = DupFunctor());
@@ -979,7 +979,7 @@ template<typename Scalar, int _Options, typename _Index>
 template<typename InputIterators>
 void SparseMatrix<Scalar,_Options,_Index>::setFromTriplets(const InputIterators& begin, const InputIterators& end)
 {
-  internal::set_from_triplets<InputIterators, SparseMatrix<Scalar,_Options,_Index> >(begin, end, *this, internal::scalar_sum_op<Scalar>());
+  internal::set_from_triplets<InputIterators, SparseMatrix<Scalar,_Options,_Index> >(begin, end, *this, internal::scalar_sum_op<Scalar,Scalar>());
 }
 
 /** The same as setFromTriplets but when duplicates are met the functor \a dup_func is applied:
diff --git a/Eigen/src/SparseCore/SparseMatrixBase.h b/Eigen/src/SparseCore/SparseMatrixBase.h
index 24df36884..45f64e7f2 100644
--- a/Eigen/src/SparseCore/SparseMatrixBase.h
+++ b/Eigen/src/SparseCore/SparseMatrixBase.h
@@ -256,7 +256,7 @@ template<typename Derived> class SparseMatrixBase
     Derived& operator/=(const Scalar& other);
 
     template<typename OtherDerived> struct CwiseProductDenseReturnType {
-      typedef CwiseBinaryOp<internal::scalar_product_op<typename internal::scalar_product_traits<
+      typedef CwiseBinaryOp<internal::scalar_product_op<typename ScalarBinaryOpTraits<
                                                           typename internal::traits<Derived>::Scalar,
                                                           typename internal::traits<OtherDerived>::Scalar
                                                         >::ReturnType>,
diff --git a/Eigen/src/SparseCore/SparseProduct.h b/Eigen/src/SparseCore/SparseProduct.h
index b23003bb1..84e69903b 100644
--- a/Eigen/src/SparseCore/SparseProduct.h
+++ b/Eigen/src/SparseCore/SparseProduct.h
@@ -99,10 +99,10 @@ struct generic_product_impl<Lhs, Rhs, SparseTriangularShape, SparseShape, Produc
 
 // dense = sparse-product (can be sparse*sparse, sparse*perm, etc.)
 template< typename DstXprType, typename Lhs, typename Rhs>
-struct Assignment<DstXprType, Product<Lhs,Rhs,AliasFreeProduct>, internal::assign_op<typename DstXprType::Scalar>, Sparse2Dense>
+struct Assignment<DstXprType, Product<Lhs,Rhs,AliasFreeProduct>, internal::assign_op<typename DstXprType::Scalar,typename Product<Lhs,Rhs,AliasFreeProduct>::Scalar>, Sparse2Dense>
 {
   typedef Product<Lhs,Rhs,AliasFreeProduct> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &)
   {
     generic_product_impl<Lhs, Rhs>::evalTo(dst,src.lhs(),src.rhs());
   }
@@ -110,10 +110,10 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,AliasFreeProduct>, internal::assig
 
 // dense += sparse-product (can be sparse*sparse, sparse*perm, etc.)
 template< typename DstXprType, typename Lhs, typename Rhs>
-struct Assignment<DstXprType, Product<Lhs,Rhs,AliasFreeProduct>, internal::add_assign_op<typename DstXprType::Scalar>, Sparse2Dense>
+struct Assignment<DstXprType, Product<Lhs,Rhs,AliasFreeProduct>, internal::add_assign_op<typename DstXprType::Scalar,typename Product<Lhs,Rhs,AliasFreeProduct>::Scalar>, Sparse2Dense>
 {
   typedef Product<Lhs,Rhs,AliasFreeProduct> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &)
   {
     generic_product_impl<Lhs, Rhs>::addTo(dst,src.lhs(),src.rhs());
   }
@@ -121,10 +121,10 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,AliasFreeProduct>, internal::add_a
 
 // dense -= sparse-product (can be sparse*sparse, sparse*perm, etc.)
 template< typename DstXprType, typename Lhs, typename Rhs>
-struct Assignment<DstXprType, Product<Lhs,Rhs,AliasFreeProduct>, internal::sub_assign_op<typename DstXprType::Scalar>, Sparse2Dense>
+struct Assignment<DstXprType, Product<Lhs,Rhs,AliasFreeProduct>, internal::sub_assign_op<typename DstXprType::Scalar,typename Product<Lhs,Rhs,AliasFreeProduct>::Scalar>, Sparse2Dense>
 {
   typedef Product<Lhs,Rhs,AliasFreeProduct> SrcXprType;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar> &)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &)
   {
     generic_product_impl<Lhs, Rhs>::subTo(dst,src.lhs(),src.rhs());
   }
diff --git a/Eigen/src/SparseCore/SparseSelfAdjointView.h b/Eigen/src/SparseCore/SparseSelfAdjointView.h
index b92bb17e2..4f0c84d88 100644
--- a/Eigen/src/SparseCore/SparseSelfAdjointView.h
+++ b/Eigen/src/SparseCore/SparseSelfAdjointView.h
@@ -223,13 +223,13 @@ struct Assignment<DstXprType, SrcXprType, Functor, SparseSelfAdjoint2Sparse, Sca
 {
   typedef typename DstXprType::StorageIndex StorageIndex;
   template<typename DestScalar,int StorageOrder>
-  static void run(SparseMatrix<DestScalar,StorageOrder,StorageIndex> &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar> &/*func*/)
+  static void run(SparseMatrix<DestScalar,StorageOrder,StorageIndex> &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
   {
     internal::permute_symm_to_fullsymm<SrcXprType::Mode>(src.matrix(), dst);
   }
   
   template<typename DestScalar>
-  static void run(DynamicSparseMatrix<DestScalar,ColMajor,StorageIndex>& dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar> &/*func*/)
+  static void run(DynamicSparseMatrix<DestScalar,ColMajor,StorageIndex>& dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
   {
     // TODO directly evaluate into dst;
     SparseMatrix<DestScalar,ColMajor,StorageIndex> tmp(dst.rows(),dst.cols());
@@ -586,12 +586,12 @@ class SparseSymmetricPermutationProduct
 namespace internal {
   
 template<typename DstXprType, typename MatrixType, int Mode, typename Scalar>
-struct Assignment<DstXprType, SparseSymmetricPermutationProduct<MatrixType,Mode>, internal::assign_op<Scalar>, Sparse2Sparse>
+struct Assignment<DstXprType, SparseSymmetricPermutationProduct<MatrixType,Mode>, internal::assign_op<Scalar,typename MatrixType::Scalar>, Sparse2Sparse>
 {
   typedef SparseSymmetricPermutationProduct<MatrixType,Mode> SrcXprType;
   typedef typename DstXprType::StorageIndex DstIndex;
   template<int Options>
-  static void run(SparseMatrix<Scalar,Options,DstIndex> &dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  static void run(SparseMatrix<Scalar,Options,DstIndex> &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename MatrixType::Scalar> &)
   {
     // internal::permute_symm_to_fullsymm<Mode>(m_matrix,_dest,m_perm.indices().data());
     SparseMatrix<Scalar,(Options&RowMajor)==RowMajor ? ColMajor : RowMajor, DstIndex> tmp;
@@ -600,7 +600,7 @@ struct Assignment<DstXprType, SparseSymmetricPermutationProduct<MatrixType,Mode>
   }
   
   template<typename DestType,unsigned int DestMode>
-  static void run(SparseSelfAdjointView<DestType,DestMode>& dst, const SrcXprType &src, const internal::assign_op<Scalar> &)
+  static void run(SparseSelfAdjointView<DestType,DestMode>& dst, const SrcXprType &src, const internal::assign_op<Scalar,typename MatrixType::Scalar> &)
   {
     internal::permute_symm_to_symm<Mode,DestMode>(src.matrix(),dst.matrix(),src.perm().indices().data());
   }
diff --git a/Eigen/src/SparseQR/SparseQR.h b/Eigen/src/SparseQR/SparseQR.h
index acd7f7e10..2d4498b03 100644
--- a/Eigen/src/SparseQR/SparseQR.h
+++ b/Eigen/src/SparseQR/SparseQR.h
@@ -705,12 +705,12 @@ struct evaluator_traits<SparseQRMatrixQReturnType<SparseQRType> >
 };
 
 template< typename DstXprType, typename SparseQRType>
-struct Assignment<DstXprType, SparseQRMatrixQReturnType<SparseQRType>, internal::assign_op<typename DstXprType::Scalar>, Sparse2Sparse>
+struct Assignment<DstXprType, SparseQRMatrixQReturnType<SparseQRType>, internal::assign_op<typename DstXprType::Scalar,typename DstXprType::Scalar>, Sparse2Sparse>
 {
   typedef SparseQRMatrixQReturnType<SparseQRType> SrcXprType;
   typedef typename DstXprType::Scalar Scalar;
   typedef typename DstXprType::StorageIndex StorageIndex;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &/*func*/)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &/*func*/)
   {
     typename DstXprType::PlainObject idMat(src.m_qr.rows(), src.m_qr.rows());
     idMat.setIdentity();
@@ -721,12 +721,12 @@ struct Assignment<DstXprType, SparseQRMatrixQReturnType<SparseQRType>, internal:
 };
 
 template< typename DstXprType, typename SparseQRType>
-struct Assignment<DstXprType, SparseQRMatrixQReturnType<SparseQRType>, internal::assign_op<typename DstXprType::Scalar>, Sparse2Dense>
+struct Assignment<DstXprType, SparseQRMatrixQReturnType<SparseQRType>, internal::assign_op<typename DstXprType::Scalar,typename DstXprType::Scalar>, Sparse2Dense>
 {
   typedef SparseQRMatrixQReturnType<SparseQRType> SrcXprType;
   typedef typename DstXprType::Scalar Scalar;
   typedef typename DstXprType::StorageIndex StorageIndex;
-  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &/*func*/)
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &/*func*/)
   {
     dst = src.m_qr.matrixQ() * DstXprType::Identity(src.m_qr.rows(), src.m_qr.rows());
   }
diff --git a/Eigen/src/plugins/ArrayCwiseBinaryOps.h b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
index c3f8c2575..c6ea12c90 100644
--- a/Eigen/src/plugins/ArrayCwiseBinaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
@@ -4,10 +4,10 @@
   */
 template<typename OtherDerived>
 EIGEN_DEVICE_FUNC
-EIGEN_STRONG_INLINE const EIGEN_CWISE_PRODUCT_RETURN_TYPE(Derived,OtherDerived)
+EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,product)
 operator*(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
 {
-  return EIGEN_CWISE_PRODUCT_RETURN_TYPE(Derived,OtherDerived)(derived(), other.derived());
+  return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,product)(derived(), other.derived());
 }
 
 /** \returns an expression of the coefficient wise quotient of \c *this and \a other
diff --git a/Eigen/src/plugins/CommonCwiseBinaryOps.h b/Eigen/src/plugins/CommonCwiseBinaryOps.h
index a8fa287c9..3c13b7f06 100644
--- a/Eigen/src/plugins/CommonCwiseBinaryOps.h
+++ b/Eigen/src/plugins/CommonCwiseBinaryOps.h
@@ -1,7 +1,7 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
-// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
 //
 // This Source Code Form is subject to the terms of the Mozilla
@@ -16,7 +16,13 @@
   *
   * \sa class CwiseBinaryOp, operator-=()
   */
-EIGEN_MAKE_CWISE_BINARY_OP(operator-,internal::scalar_difference_op)
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,difference)
+operator-(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+  return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,difference)(derived(), other.derived());
+}
 
 /** \returns an expression of the sum of \c *this and \a other
   *
@@ -24,7 +30,13 @@ EIGEN_MAKE_CWISE_BINARY_OP(operator-,internal::scalar_difference_op)
   *
   * \sa class CwiseBinaryOp, operator+=()
   */
-EIGEN_MAKE_CWISE_BINARY_OP(operator+,internal::scalar_sum_op)
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,sum)
+operator+(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+  return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,sum)(derived(), other.derived());
+}
 
 /** \returns an expression of a custom coefficient-wise operator \a func of *this and \a other
   *
diff --git a/Eigen/src/plugins/CommonCwiseUnaryOps.h b/Eigen/src/plugins/CommonCwiseUnaryOps.h
index 67ec601b9..927167aff 100644
--- a/Eigen/src/plugins/CommonCwiseUnaryOps.h
+++ b/Eigen/src/plugins/CommonCwiseUnaryOps.h
@@ -73,7 +73,7 @@ operator/(const Scalar& scalar) const
 /** Overloaded for efficiently multipling with compatible scalar types */
 template <typename T>
 EIGEN_DEVICE_FUNC inline
-typename internal::enable_if<internal::scalar_product_traits<T,Scalar>::Defined,
+typename internal::enable_if<ScalarBinaryOpTraits<T,Scalar>::Defined,
                              const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,T>, const Derived> >::type
 operator*(const T& scalar) const
 {
@@ -91,7 +91,7 @@ operator*(const Scalar& scalar, const StorageBaseType& matrix)
 
 template <typename T>
 EIGEN_DEVICE_FUNC inline friend
-typename internal::enable_if<internal::scalar_product_traits<Scalar,T>::Defined,
+typename internal::enable_if<ScalarBinaryOpTraits<Scalar,T>::Defined,
                              const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,T>, const Derived> >::type
 operator*(const T& scalar, const StorageBaseType& matrix)
 {
@@ -104,7 +104,7 @@ operator*(const T& scalar, const StorageBaseType& matrix)
 
 template <typename T>
 EIGEN_DEVICE_FUNC inline
-typename internal::enable_if<internal::scalar_product_traits<Scalar,T>::Defined,
+typename internal::enable_if<ScalarBinaryOpTraits<Scalar,T>::Defined,
                              const CwiseUnaryOp<internal::scalar_quotient2_op<Scalar,T>, const Derived> >::type
 operator/(const T& scalar) const
 {
diff --git a/Eigen/src/plugins/MatrixCwiseBinaryOps.h b/Eigen/src/plugins/MatrixCwiseBinaryOps.h
index 6dd2e1192..59581e618 100644
--- a/Eigen/src/plugins/MatrixCwiseBinaryOps.h
+++ b/Eigen/src/plugins/MatrixCwiseBinaryOps.h
@@ -19,10 +19,10 @@
   */
 template<typename OtherDerived>
 EIGEN_DEVICE_FUNC
-EIGEN_STRONG_INLINE const EIGEN_CWISE_PRODUCT_RETURN_TYPE(Derived,OtherDerived)
+EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,product)
 cwiseProduct(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
 {
-  return EIGEN_CWISE_PRODUCT_RETURN_TYPE(Derived,OtherDerived)(derived(), other.derived());
+  return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,product)(derived(), other.derived());
 }
 
 /** \returns an expression of the coefficient-wise == operator of *this and \a other
diff --git a/blas/PackedTriangularMatrixVector.h b/blas/PackedTriangularMatrixVector.h
index e9886d56f..0039536a8 100644
--- a/blas/PackedTriangularMatrixVector.h
+++ b/blas/PackedTriangularMatrixVector.h
@@ -18,7 +18,7 @@ struct packed_triangular_matrix_vector_product;
 template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs>
 struct packed_triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,ColMajor>
 {
-  typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
   enum {
     IsLower     = (Mode & Lower)   ==Lower,
     HasUnitDiag = (Mode & UnitDiag)==UnitDiag,
@@ -47,7 +47,7 @@ struct packed_triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsS
 template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs>
 struct packed_triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,RowMajor>
 {
-  typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+  typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
   enum {
     IsLower     = (Mode & Lower)   ==Lower,
     HasUnitDiag = (Mode & UnitDiag)==UnitDiag,
diff --git a/test/array.cpp b/test/array.cpp
index 4cd4f262b..bd470d5f7 100644
--- a/test/array.cpp
+++ b/test/array.cpp
@@ -72,7 +72,7 @@ template<typename ArrayType> void array(const ArrayType& m)
   VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()), m1.abs().sum());
   if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1+m2).sum()), m1.abs().sum(), test_precision<Scalar>()))
       VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum());
-  VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar>()));
+  VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar,Scalar>()));
 
   // vector-wise ops
   m3 = m1;
diff --git a/test/array_for_matrix.cpp b/test/array_for_matrix.cpp
index 75e6a778f..97e03be83 100644
--- a/test/array_for_matrix.cpp
+++ b/test/array_for_matrix.cpp
@@ -45,7 +45,7 @@ template<typename MatrixType> void array_for_matrix(const MatrixType& m)
   VERIFY_IS_MUCH_SMALLER_THAN(m1.rowwise().sum().sum() - m1.sum(), m1.squaredNorm());
   VERIFY_IS_MUCH_SMALLER_THAN(m1.colwise().sum() + m2.colwise().sum() - (m1+m2).colwise().sum(), (m1+m2).squaredNorm());
   VERIFY_IS_MUCH_SMALLER_THAN(m1.rowwise().sum() - m2.rowwise().sum() - (m1-m2).rowwise().sum(), (m1-m2).squaredNorm());
-  VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar>()));
+  VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar,Scalar>()));
 
   // vector-wise ops
   m3 = m1;
diff --git a/test/mixingtypes.cpp b/test/mixingtypes.cpp
index dbcf468ea..66d9b777a 100644
--- a/test/mixingtypes.cpp
+++ b/test/mixingtypes.cpp
@@ -42,6 +42,7 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
 
   Mat_f mf    = Mat_f::Random(size,size);
   Mat_d md    = mf.template cast<double>();
+  //Mat_d rd    = md;
   Mat_cf mcf  = Mat_cf::Random(size,size);
   Mat_cd mcd  = mcf.template cast<complex<double> >();
   Mat_cd rcd = mcd;
@@ -56,16 +57,12 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
 
 
   mf+mf;
-  VERIFY_RAISES_ASSERT(mf+md);
-#if !EIGEN_HAS_STD_RESULT_OF
-  // this one does not even compile with C++11
-  VERIFY_RAISES_ASSERT(mf+mcf);
-#endif
+
+//   VERIFY_RAISES_ASSERT(mf+md); // does not even compile
 
 #ifdef EIGEN_DONT_VECTORIZE
   VERIFY_RAISES_ASSERT(vf=vd);
   VERIFY_RAISES_ASSERT(vf+=vd);
-  VERIFY_RAISES_ASSERT(mcd=md);
 #endif
   
   // check scalar products
@@ -186,16 +183,35 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
                    Mat_cd((scd * md.template cast<CD>().eval() * mcd).template triangularView<Upper>()));
 
 
-  VERIFY_IS_APPROX( md.array() * mcd.array(), md.template cast<CD>().eval().array() * mcd.array() );
-  VERIFY_IS_APPROX( mcd.array() * md.array(), mcd.array() * md.template cast<CD>().eval().array() );
+
+  VERIFY_IS_APPROX( md.array()  * mcd.array(), md.template cast<CD>().eval().array() * mcd.array() );
+  VERIFY_IS_APPROX( mcd.array() * md.array(),  mcd.array() * md.template cast<CD>().eval().array() );
+
+  VERIFY_IS_APPROX( md.array()  + mcd.array(), md.template cast<CD>().eval().array() + mcd.array() );
+  VERIFY_IS_APPROX( mcd.array() + md.array(),  mcd.array() + md.template cast<CD>().eval().array() );
+
+  VERIFY_IS_APPROX( md.array()  - mcd.array(), md.template cast<CD>().eval().array() - mcd.array() );
+  VERIFY_IS_APPROX( mcd.array() - md.array(),  mcd.array() - md.template cast<CD>().eval().array() );
 
 //   VERIFY_IS_APPROX( md.array() / mcd.array(), md.template cast<CD>().eval().array() / mcd.array() );
   VERIFY_IS_APPROX( mcd.array() / md.array(), mcd.array() / md.template cast<CD>().eval().array() );
 
+  rcd = mcd;
+  VERIFY_IS_APPROX( rcd = md, md.template cast<CD>().eval() );
+  rcd = mcd;
+  VERIFY_IS_APPROX( rcd += md, mcd + md.template cast<CD>().eval() );
+  rcd = mcd;
+  VERIFY_IS_APPROX( rcd -= md, mcd - md.template cast<CD>().eval() );
   rcd = mcd;
   VERIFY_IS_APPROX( rcd.array() *= md.array(), mcd.array() * md.template cast<CD>().eval().array() );
   rcd = mcd;
   VERIFY_IS_APPROX( rcd.array() /= md.array(), mcd.array() / md.template cast<CD>().eval().array() );
+
+  rcd = mcd;
+  VERIFY_IS_APPROX( rcd += md + mcd*md, mcd + (md.template cast<CD>().eval()) + mcd*(md.template cast<CD>().eval()));
+
+  rcd = mcd;
+  VERIFY_IS_APPROX( rcd += mcd + md*md, mcd + mcd + ((md*md).template cast<CD>().eval()) );
 }
 
 void test_mixingtypes()
diff --git a/test/vectorization_logic.cpp b/test/vectorization_logic.cpp
index 24a7641ff..b7c2df64b 100644
--- a/test/vectorization_logic.cpp
+++ b/test/vectorization_logic.cpp
@@ -29,7 +29,7 @@ using internal::demangle_unrolling;
 template<typename Dst, typename Src>
 bool test_assign(const Dst&, const Src&, int traversal, int unrolling)
 {
-  typedef internal::copy_using_evaluator_traits<internal::evaluator<Dst>,internal::evaluator<Src>, internal::assign_op<typename Dst::Scalar> > traits;
+  typedef internal::copy_using_evaluator_traits<internal::evaluator<Dst>,internal::evaluator<Src>, internal::assign_op<typename Dst::Scalar,typename Src::Scalar> > traits;
   bool res = traits::Traversal==traversal;
   if(unrolling==InnerUnrolling+CompleteUnrolling)
     res = res && (int(traits::Unrolling)==InnerUnrolling || int(traits::Unrolling)==CompleteUnrolling);
@@ -53,7 +53,7 @@ bool test_assign(const Dst&, const Src&, int traversal, int unrolling)
 template<typename Dst, typename Src>
 bool test_assign(int traversal, int unrolling)
 {
-  typedef internal::copy_using_evaluator_traits<internal::evaluator<Dst>,internal::evaluator<Src>, internal::assign_op<typename Dst::Scalar> > traits;
+  typedef internal::copy_using_evaluator_traits<internal::evaluator<Dst>,internal::evaluator<Src>, internal::assign_op<typename Dst::Scalar,typename Src::Scalar> > traits;
   bool res = traits::Traversal==traversal && traits::Unrolling==unrolling;
   if(!res)
   {
@@ -73,7 +73,8 @@ bool test_assign(int traversal, int unrolling)
 template<typename Xpr>
 bool test_redux(const Xpr&, int traversal, int unrolling)
 {
-  typedef internal::redux_traits<internal::scalar_sum_op<typename Xpr::Scalar>,internal::redux_evaluator<Xpr> > traits;
+  typedef typename Xpr::Scalar Scalar;
+  typedef internal::redux_traits<internal::scalar_sum_op<Scalar,Scalar>,internal::redux_evaluator<Xpr> > traits;
   
   bool res = traits::Traversal==traversal && traits::Unrolling==unrolling;
   if(!res)
diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
index 089042751..ba61288a3 100755
--- a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
+++ b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
@@ -501,36 +501,36 @@ struct make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows,
   }
 };
 
-template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols>
-struct scalar_product_traits<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>,A_Scalar>
-{
-  enum { Defined = 1 };
-  typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> ReturnType;
-};
-
-template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols>
-struct scalar_product_traits<A_Scalar, Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> >
-{
-  enum { Defined = 1 };
-  typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> ReturnType;
-};
-
-template<typename DerType>
-struct scalar_product_traits<AutoDiffScalar<DerType>,typename DerType::Scalar>
-{
-  enum { Defined = 1 };
-  typedef AutoDiffScalar<DerType> ReturnType;
-};
-
-template<typename DerType>
-struct scalar_product_traits<typename DerType::Scalar,AutoDiffScalar<DerType> >
-{
-  enum { Defined = 1 };
-  typedef AutoDiffScalar<DerType> ReturnType;
-};
-
 } // end namespace internal
 
+template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols>
+struct ScalarBinaryOpTraits<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>,A_Scalar>
+{
+  enum { Defined = 1 };
+  typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> ReturnType;
+};
+
+template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols>
+struct ScalarBinaryOpTraits<A_Scalar, Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> >
+{
+  enum { Defined = 1 };
+  typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> ReturnType;
+};
+
+template<typename DerType>
+struct ScalarBinaryOpTraits<AutoDiffScalar<DerType>,typename DerType::Scalar>
+{
+  enum { Defined = 1 };
+  typedef AutoDiffScalar<DerType> ReturnType;
+};
+
+template<typename DerType>
+struct ScalarBinaryOpTraits<typename DerType::Scalar,AutoDiffScalar<DerType> >
+{
+  enum { Defined = 1 };
+  typedef AutoDiffScalar<DerType> ReturnType;
+};
+
 #define EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(FUNC,CODE) \
   template<typename DerType> \
   inline const Eigen::AutoDiffScalar<Eigen::CwiseUnaryOp<Eigen::internal::scalar_multiple_op<typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar>, const typename Eigen::internal::remove_all<DerType>::type> > \
diff --git a/unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h b/unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h
index bf9727c21..582fa8512 100644
--- a/unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h
+++ b/unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h
@@ -203,7 +203,7 @@ struct traits<KroneckerProduct<_Lhs,_Rhs> >
 {
   typedef typename remove_all<_Lhs>::type Lhs;
   typedef typename remove_all<_Rhs>::type Rhs;
-  typedef typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
+  typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
   typedef typename promote_index_type<typename Lhs::StorageIndex, typename Rhs::StorageIndex>::type StorageIndex;
 
   enum {
@@ -222,7 +222,7 @@ struct traits<KroneckerProductSparse<_Lhs,_Rhs> >
   typedef MatrixXpr XprKind;
   typedef typename remove_all<_Lhs>::type Lhs;
   typedef typename remove_all<_Rhs>::type Rhs;
-  typedef typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
+  typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
   typedef typename cwise_promote_storage_type<typename traits<Lhs>::StorageKind, typename traits<Rhs>::StorageKind, scalar_product_op<typename Lhs::Scalar, typename Rhs::Scalar> >::ret StorageKind;
   typedef typename promote_index_type<typename Lhs::StorageIndex, typename Rhs::StorageIndex>::type StorageIndex;
 

From 9137f560f0c84470c7859a6db704bf5f18ae999d Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Mon, 6 Jun 2016 07:26:48 -0700
Subject: [PATCH 24/86] Moved assertions to the constructor to make the code
 more portable

---
 .../Eigen/CXX11/src/Tensor/TensorEvaluator.h     | 14 ++++++++++++++
 unsupported/Eigen/CXX11/src/Tensor/TensorExpr.h  | 16 ----------------
 2 files changed, 14 insertions(+), 16 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorEvaluator.h b/unsupported/Eigen/CXX11/src/Tensor/TensorEvaluator.h
index 4e873011e..a48cb1daa 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorEvaluator.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorEvaluator.h
@@ -426,6 +426,20 @@ struct TensorEvaluator<const TensorCwiseTernaryOp<TernaryOp, Arg1Type, Arg2Type,
       m_arg3Impl(op.arg3Expression(), device)
   {
     EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<Arg1Type, Device>::Layout) == static_cast<int>(TensorEvaluator<Arg3Type, Device>::Layout) || internal::traits<XprType>::NumDimensions <= 1), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+    EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Arg1Type>::StorageKind,
+                         typename internal::traits<Arg2Type>::StorageKind>::value),
+                        STORAGE_KIND_MUST_MATCH)
+    EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Arg1Type>::StorageKind,
+                         typename internal::traits<Arg3Type>::StorageKind>::value),
+                        STORAGE_KIND_MUST_MATCH)
+    EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Arg1Type>::Index,
+                         typename internal::traits<Arg2Type>::Index>::value),
+                        STORAGE_INDEX_MUST_MATCH)
+    EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Arg1Type>::Index,
+                         typename internal::traits<Arg3Type>::Index>::value),
+                        STORAGE_INDEX_MUST_MATCH)
+
     eigen_assert(dimensions_match(m_arg1Impl.dimensions(), m_arg2Impl.dimensions()) && dimensions_match(m_arg1Impl.dimensions(), m_arg3Impl.dimensions()));
   }
 
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorExpr.h b/unsupported/Eigen/CXX11/src/Tensor/TensorExpr.h
index 9509f8002..5f2e329f2 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorExpr.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorExpr.h
@@ -227,22 +227,6 @@ struct traits<TensorCwiseTernaryOp<TernaryOp, Arg1XprType, Arg2XprType, Arg3XprT
       TernaryOp(typename Arg1XprType::Scalar,
                 typename Arg2XprType::Scalar,
                 typename Arg3XprType::Scalar)>::type Scalar;
-  EIGEN_STATIC_ASSERT(
-      (internal::is_same<typename traits<Arg1XprType>::StorageKind,
-                         typename traits<Arg2XprType>::StorageKind>::value),
-      STORAGE_KIND_MUST_MATCH)
-  EIGEN_STATIC_ASSERT(
-      (internal::is_same<typename traits<Arg1XprType>::StorageKind,
-                         typename traits<Arg3XprType>::StorageKind>::value),
-      STORAGE_KIND_MUST_MATCH)
-  EIGEN_STATIC_ASSERT(
-      (internal::is_same<typename traits<Arg1XprType>::Index,
-                         typename traits<Arg2XprType>::Index>::value),
-      STORAGE_INDEX_MUST_MATCH)
-  EIGEN_STATIC_ASSERT(
-      (internal::is_same<typename traits<Arg1XprType>::Index,
-                         typename traits<Arg3XprType>::Index>::value),
-      STORAGE_INDEX_MUST_MATCH)
   typedef traits<Arg1XprType> XprTraits;
   typedef typename traits<Arg1XprType>::StorageKind StorageKind;
   typedef typename traits<Arg1XprType>::Index Index;

From df24f4a01d762b0ae7dee8a1a0c769c96e4da835 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Mon, 6 Jun 2016 16:46:46 +0200
Subject: [PATCH 25/86] bug #1201: improve code generation of affine*vec with
 MSVC

---
 Eigen/src/Geometry/Transform.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Eigen/src/Geometry/Transform.h b/Eigen/src/Geometry/Transform.h
index 4fc876bcf..1a06c1e35 100644
--- a/Eigen/src/Geometry/Transform.h
+++ b/Eigen/src/Geometry/Transform.h
@@ -1367,7 +1367,7 @@ struct transform_right_product_impl< TransformType, MatrixType, 2, 1> // rhs is
     EIGEN_STATIC_ASSERT(OtherRows==Dim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);
 
     Matrix<typename ResultType::Scalar, Dim+1, 1> rhs;
-    rhs << other,1;
+    rhs.template head<Dim>() = other; rhs[Dim] = 1;
     Matrix<typename ResultType::Scalar, WorkingRows, 1> res(T.matrix() * rhs);
     return res.template head<Dim>();
   }

From 33f0340188eb309dfa3b16c0758a878c3ea114d9 Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Mon, 6 Jun 2016 12:06:42 -0700
Subject: [PATCH 26/86] Implement result_of for the new ternary functors

---
 Eigen/src/Core/util/Meta.h | 24 ++++++++++++++++++++++++
 1 file changed, 24 insertions(+)

diff --git a/Eigen/src/Core/util/Meta.h b/Eigen/src/Core/util/Meta.h
index 7ecd59add..bd3a0aa5d 100644
--- a/Eigen/src/Core/util/Meta.h
+++ b/Eigen/src/Core/util/Meta.h
@@ -328,6 +328,30 @@ struct result_of<Func(ArgType0,ArgType1)> {
     enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
     typedef typename binary_result_of_select<Func, ArgType0, ArgType1, FunctorType>::type type;
 };
+
+template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2, int SizeOf=sizeof(has_none)>
+struct ternary_result_of_select {typedef typename internal::remove_all<ArgType0>::type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>
+struct ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, sizeof(has_std_result_type)>
+{typedef typename Func::result_type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>
+struct ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, sizeof(has_tr1_result)>
+{typedef typename Func::template result<Func(ArgType0,ArgType1,ArgType2)>::type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>
+struct result_of<Func(ArgType0,ArgType1,ArgType2)> {
+    template<typename T>
+    static has_std_result_type    testFunctor(T const *, typename T::result_type const * = 0);
+    template<typename T>
+    static has_tr1_result         testFunctor(T const *, typename T::template result<T(ArgType0,ArgType1,ArgType2)>::type const * = 0);
+    static has_none               testFunctor(...);
+
+    // note that the following indirection is needed for gcc-3.3
+    enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
+    typedef typename ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, FunctorType>::type type;
+};
 #endif
 
 /** \internal In short, it computes int(sqrt(\a Y)) with \a Y an integer.

From ea75dba2014ffa58acfcd160b5e59975c453f8da Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Mon, 6 Jun 2016 13:32:28 -0700
Subject: [PATCH 27/86] Added missing EIGEN_DEVICE_FUNC qualifiers to the unary
 array ops

---
 Eigen/src/plugins/ArrayCwiseUnaryOps.h | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/Eigen/src/plugins/ArrayCwiseUnaryOps.h b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
index 775fa6ee0..9e35dc571 100644
--- a/Eigen/src/plugins/ArrayCwiseUnaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
@@ -248,6 +248,7 @@ tan() const
   *
   * \sa tan(), asin(), acos()
   */
+EIGEN_DEVICE_FUNC
 inline const AtanReturnType
 atan() const
 {
@@ -289,6 +290,7 @@ asin() const
   *
   * \sa tan(), sinh(), cosh()
   */
+EIGEN_DEVICE_FUNC
 inline const TanhReturnType
 tanh() const
 {
@@ -302,6 +304,7 @@ tanh() const
   *
   * \sa sin(), tanh(), cosh()
   */
+EIGEN_DEVICE_FUNC
 inline const SinhReturnType
 sinh() const
 {
@@ -315,6 +318,7 @@ sinh() const
   *
   * \sa tan(), sinh(), cosh()
   */
+EIGEN_DEVICE_FUNC
 inline const CoshReturnType
 cosh() const
 {
@@ -332,6 +336,7 @@ cosh() const
   *
   * \sa digamma()
   */
+EIGEN_DEVICE_FUNC
 inline const LgammaReturnType
 lgamma() const
 {
@@ -346,6 +351,7 @@ lgamma() const
   *
   * \sa Eigen::digamma(), Eigen::polygamma(), lgamma()
   */
+EIGEN_DEVICE_FUNC
 inline const DigammaReturnType
 digamma() const
 {
@@ -364,6 +370,7 @@ digamma() const
   *
   * \sa erfc()
   */
+EIGEN_DEVICE_FUNC
 inline const ErfReturnType
 erf() const
 {
@@ -382,6 +389,7 @@ erf() const
   *
   * \sa erf()
   */
+EIGEN_DEVICE_FUNC
 inline const ErfcReturnType
 erfc() const
 {
@@ -455,6 +463,7 @@ cube() const
   *
   * \sa ceil(), floor()
   */
+EIGEN_DEVICE_FUNC
 inline const RoundReturnType
 round() const
 {
@@ -468,6 +477,7 @@ round() const
   *
   * \sa ceil(), round()
   */
+EIGEN_DEVICE_FUNC
 inline const FloorReturnType
 floor() const
 {
@@ -481,6 +491,7 @@ floor() const
   *
   * \sa floor(), round()
   */
+EIGEN_DEVICE_FUNC
 inline const CeilReturnType
 ceil() const
 {
@@ -494,6 +505,7 @@ ceil() const
   *
   * \sa isfinite(), isinf()
   */
+EIGEN_DEVICE_FUNC
 inline const IsNaNReturnType
 isNaN() const
 {
@@ -507,6 +519,7 @@ isNaN() const
   *
   * \sa isnan(), isfinite()
   */
+EIGEN_DEVICE_FUNC
 inline const IsInfReturnType
 isInf() const
 {
@@ -520,6 +533,7 @@ isInf() const
   *
   * \sa isnan(), isinf()
   */
+EIGEN_DEVICE_FUNC
 inline const IsFiniteReturnType
 isFinite() const
 {

From 7ef9f47b5874c33d15649a3312d463ecbd290365 Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Mon, 6 Jun 2016 14:09:46 -0700
Subject: [PATCH 28/86] Misc small improvements to the reduction code.

---
 .../CXX11/src/Tensor/TensorReductionCuda.h     | 18 ++++++++----------
 1 file changed, 8 insertions(+), 10 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h
index 0d1a098b7..e82530955 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionCuda.h
@@ -130,15 +130,17 @@ __global__ void FullReductionKernel(Reducer reducer, const Self input, Index num
       if (block == 0) {
         // We're the first block to run, initialize the output value
         atomicExch(output, reducer.initialize());
-        unsigned int old = atomicExch(semaphore, 2u);
-        assert(old == 1u);
+        __threadfence();
+        atomicExch(semaphore, 2u);
       }
       else {
+        // Wait for the first block to initialize the output value.
         // Use atomicCAS here to ensure that the reads aren't cached
-        unsigned int val = atomicCAS(semaphore, 2u, 2u);
-        while (val < 2u) {
+        unsigned int val;
+        do {
           val = atomicCAS(semaphore, 2u, 2u);
         }
+        while (val < 2u);
       }
     }
   }
@@ -166,12 +168,8 @@ __global__ void FullReductionKernel(Reducer reducer, const Self input, Index num
   }
 
   if (gridDim.x > 1 && threadIdx.x == 0) {
-    unsigned int ticket = atomicInc(semaphore, UINT_MAX);
-    assert(ticket >= 2u);
-    if (ticket == gridDim.x + 1) {
-      // We're the last block, reset the semaphore
-      *semaphore = 0;
-    }
+    // Let the last block reset the semaphore
+    atomicInc(semaphore, gridDim.x + 1);
   }
 }
 

From 3d71d3918e750be81739f24cdc0687648fb7f5c5 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Mon, 6 Jun 2016 23:10:55 +0200
Subject: [PATCH 29/86] Disable shortcuts for res ?= prod when the scalar types
 do not match exactly.

---
 Eigen/src/Core/ProductEvaluators.h | 15 +++++++++------
 test/mixingtypes.cpp               | 13 +++++++++++--
 2 files changed, 20 insertions(+), 8 deletions(-)

diff --git a/Eigen/src/Core/ProductEvaluators.h b/Eigen/src/Core/ProductEvaluators.h
index 7f041e5dd..71ae6e54c 100644
--- a/Eigen/src/Core/ProductEvaluators.h
+++ b/Eigen/src/Core/ProductEvaluators.h
@@ -122,14 +122,17 @@ protected:
   PlainObject m_result;
 };
 
+// The following three shortcuts are enabled only if the scalar types match excatly.
+// TODO: we could enable them for different scalar types when the product is not vectorized.
+
 // Dense = Product
 template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar>
-struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::assign_op<Scalar,typename Product<Lhs,Rhs,Options>::Scalar>, Dense2Dense,
+struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::assign_op<Scalar,Scalar>, Dense2Dense,
   typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct),Scalar>::type>
 {
   typedef Product<Lhs,Rhs,Options> SrcXprType;
   static EIGEN_STRONG_INLINE
-  void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename SrcXprType::Scalar> &)
+  void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
   {
     // FIXME shall we handle nested_eval here?
     generic_product_impl<Lhs, Rhs>::evalTo(dst, src.lhs(), src.rhs());
@@ -138,12 +141,12 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::assign_op<Scal
 
 // Dense += Product
 template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar>
-struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::add_assign_op<Scalar,typename Product<Lhs,Rhs,Options>::Scalar>, Dense2Dense,
+struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::add_assign_op<Scalar,Scalar>, Dense2Dense,
   typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct),Scalar>::type>
 {
   typedef Product<Lhs,Rhs,Options> SrcXprType;
   static EIGEN_STRONG_INLINE
-  void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<Scalar,typename SrcXprType::Scalar> &)
+  void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<Scalar,Scalar> &)
   {
     // FIXME shall we handle nested_eval here?
     generic_product_impl<Lhs, Rhs>::addTo(dst, src.lhs(), src.rhs());
@@ -152,12 +155,12 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::add_assign_op<
 
 // Dense -= Product
 template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar>
-struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::sub_assign_op<Scalar,typename Product<Lhs,Rhs,Options>::Scalar>, Dense2Dense,
+struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::sub_assign_op<Scalar,Scalar>, Dense2Dense,
   typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct),Scalar>::type>
 {
   typedef Product<Lhs,Rhs,Options> SrcXprType;
   static EIGEN_STRONG_INLINE
-  void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<Scalar,typename SrcXprType::Scalar> &)
+  void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<Scalar,Scalar> &)
   {
     // FIXME shall we handle nested_eval here?
     generic_product_impl<Lhs, Rhs>::subTo(dst, src.lhs(), src.rhs());
diff --git a/test/mixingtypes.cpp b/test/mixingtypes.cpp
index 66d9b777a..2af188b25 100644
--- a/test/mixingtypes.cpp
+++ b/test/mixingtypes.cpp
@@ -208,10 +208,19 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
   VERIFY_IS_APPROX( rcd.array() /= md.array(), mcd.array() / md.template cast<CD>().eval().array() );
 
   rcd = mcd;
-  VERIFY_IS_APPROX( rcd += md + mcd*md, mcd + (md.template cast<CD>().eval()) + mcd*(md.template cast<CD>().eval()));
+  VERIFY_IS_APPROX( rcd.noalias() += md + mcd*md, mcd + (md.template cast<CD>().eval()) + mcd*(md.template cast<CD>().eval()));
 
+  VERIFY_IS_APPROX( rcd.noalias()  = md*md,       ((md*md).eval().template cast<CD>()) );
   rcd = mcd;
-  VERIFY_IS_APPROX( rcd += mcd + md*md, mcd + mcd + ((md*md).template cast<CD>().eval()) );
+  VERIFY_IS_APPROX( rcd.noalias() += md*md, mcd + ((md*md).eval().template cast<CD>()) );
+  rcd = mcd;
+  VERIFY_IS_APPROX( rcd.noalias() -= md*md, mcd - ((md*md).eval().template cast<CD>()) );
+
+  VERIFY_IS_APPROX( rcd.noalias()  = mcd + md*md,       mcd + ((md*md).eval().template cast<CD>()) );
+  rcd = mcd;
+  VERIFY_IS_APPROX( rcd.noalias() += mcd + md*md, mcd + mcd + ((md*md).eval().template cast<CD>()) );
+  rcd = mcd;
+  VERIFY_IS_APPROX( rcd.noalias() -= mcd + md*md,           - ((md*md).eval().template cast<CD>()) );
 }
 
 void test_mixingtypes()

From 2c462f4201365d1ac4872245e81066746f09ac47 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Mon, 6 Jun 2016 23:11:38 +0200
Subject: [PATCH 30/86] Clean handling for void type in
 EIGEN_CHECK_BINARY_COMPATIBILIY

---
 Eigen/src/Core/util/Meta.h      | 24 ++++++++++++++++++++++++
 Eigen/src/Core/util/XprHelper.h |  8 +-------
 2 files changed, 25 insertions(+), 7 deletions(-)

diff --git a/Eigen/src/Core/util/Meta.h b/Eigen/src/Core/util/Meta.h
index af661c313..efb9961ce 100644
--- a/Eigen/src/Core/util/Meta.h
+++ b/Eigen/src/Core/util/Meta.h
@@ -430,6 +430,30 @@ struct ScalarBinaryOpTraits<T,T,BinaryOp>
   typedef T ReturnType;
 };
 
+// For Matrix * Permutation
+template<typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<T,void,BinaryOp>
+{
+  enum { Defined = 1 };
+  typedef T ReturnType;
+};
+
+// For Permutation * Matrix
+template<typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<void,T,BinaryOp>
+{
+  enum { Defined = 1 };
+  typedef T ReturnType;
+};
+
+// for Permutation*Permutation
+template<typename BinaryOp>
+struct ScalarBinaryOpTraits<void,void,BinaryOp>
+{
+  enum { Defined = 1 };
+  typedef void ReturnType;
+};
+
 template<typename T, typename BinaryOp>
 struct ScalarBinaryOpTraits<T,std::complex<T>,BinaryOp>
 {
diff --git a/Eigen/src/Core/util/XprHelper.h b/Eigen/src/Core/util/XprHelper.h
index 4fd4a9b0d..828813161 100644
--- a/Eigen/src/Core/util/XprHelper.h
+++ b/Eigen/src/Core/util/XprHelper.h
@@ -610,11 +610,6 @@ bool is_same_dense(const T1 &, const T2 &, typename enable_if<!(has_direct_acces
   return false;
 }
 
-template<typename T, typename U> struct is_same_or_void { enum { value = is_same<T,U>::value }; };
-template<typename T> struct is_same_or_void<void,T>     { enum { value = 1 }; };
-template<typename T> struct is_same_or_void<T,void>     { enum { value = 1 }; };
-template<>           struct is_same_or_void<void,void>  { enum { value = 1 }; };
-
 #ifdef EIGEN_DEBUG_ASSIGN
 std::string demangle_traversal(int t)
 {
@@ -653,9 +648,8 @@ std::string demangle_flags(int f)
 // It is tempting to always allow mixing different types but remember that this is often impossible in the vectorized paths.
 // So allowing mixing different types gives very unexpected errors when enabling vectorization, when the user tries to
 // add together a float matrix and a double matrix.
-// Treat "void" as a special case. Needed for permutation products. TODO: this should be handled by ScalarBinaryOpTraits
 #define EIGEN_CHECK_BINARY_COMPATIBILIY(BINOP,LHS,RHS) \
-  EIGEN_STATIC_ASSERT(int(internal::is_same_or_void<LHS, RHS>::value) || int(ScalarBinaryOpTraits<LHS, RHS,BINOP>::Defined), \
+  EIGEN_STATIC_ASSERT(int(ScalarBinaryOpTraits<LHS, RHS,BINOP>::Defined), \
     YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
     
 } // end namespace Eigen

From 84b2060a9e3e57e49bad6208873e52c327ad135b Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Mon, 6 Jun 2016 17:16:19 -0700
Subject: [PATCH 31/86] Fixed compilation error with gcc 4.4

---
 unsupported/Eigen/CXX11/src/Tensor/TensorScan.h | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h b/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h
index 031dbf6f2..61df8032d 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h
@@ -106,7 +106,7 @@ struct TensorEvaluator<const TensorScanOp<Op, ArgType>, Device> {
         m_output(NULL) {
 
     // Accumulating a scalar isn't supported.
-    EIGEN_STATIC_ASSERT(NumDims > 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
+    EIGEN_STATIC_ASSERT((NumDims > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
     eigen_assert(m_axis >= 0 && m_axis < NumDims);
 
     // Compute stride of scan axis
@@ -136,7 +136,7 @@ struct TensorEvaluator<const TensorScanOp<Op, ArgType>, Device> {
       return true;
     }
   }
-  
+
   template<int LoadMode>
   EIGEN_DEVICE_FUNC PacketReturnType packet(Index index) const {
     return internal::ploadt<PacketReturnType, LoadMode>(m_output + index);

From db0118342c2480ba0da7e8e4fbdd6aebaac687a4 Mon Sep 17 00:00:00 2001
From: Christoph Hertzberg <chtz@informatik.uni-bremen.de>
Date: Tue, 7 Jun 2016 19:17:18 +0200
Subject: [PATCH 32/86] Fixed compilation of BVH_Example (required for make
 doc)

---
 unsupported/doc/examples/BVH_Example.cpp | 2 --
 1 file changed, 2 deletions(-)

diff --git a/unsupported/doc/examples/BVH_Example.cpp b/unsupported/doc/examples/BVH_Example.cpp
index 6b6fac075..4315fb440 100644
--- a/unsupported/doc/examples/BVH_Example.cpp
+++ b/unsupported/doc/examples/BVH_Example.cpp
@@ -6,9 +6,7 @@ using namespace Eigen;
 typedef AlignedBox<double, 2> Box2d;
 
 namespace Eigen {
-    namespace internal {
         Box2d bounding_box(const Vector2d &v) { return Box2d(v, v); } //compute the bounding box of a single point
-    }
 }
 
 struct PointPointMinimizer //how to compute squared distances between points and rectangles

From 86aedc9282f85966461544c40403979b861d3e19 Mon Sep 17 00:00:00 2001
From: Igor Babuschkin <igor@babuschk.in>
Date: Tue, 7 Jun 2016 20:06:38 +0100
Subject: [PATCH 33/86] Add small fixes to TensorScanOp

---
 unsupported/Eigen/CXX11/src/Tensor/TensorScan.h | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h b/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h
index 61df8032d..66fcacd8e 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h
@@ -81,7 +81,7 @@ struct TensorEvaluator<const TensorScanOp<Op, ArgType>, Device> {
   typedef typename XprType::Index Index;
   static const int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
   typedef DSizes<Index, NumDims> Dimensions;
-  typedef typename XprType::Scalar Scalar;
+  typedef typename internal::remove_const<typename XprType::Scalar>::type Scalar;
   typedef typename XprType::CoeffReturnType CoeffReturnType;
   typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
 
@@ -152,6 +152,10 @@ struct TensorEvaluator<const TensorScanOp<Op, ArgType>, Device> {
     return m_output[index];
   }
 
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool) const {
+    return TensorOpCost(sizeof(CoeffReturnType), 0, 0);
+  }
+
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {
     if (m_output != NULL) {
       m_device.deallocate(m_output);

From 002804938087acc829941c7500a5230fa5cf28b0 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Thu, 9 Jun 2016 23:08:11 +0200
Subject: [PATCH 34/86] bug #1240: Remove any assumption on NEON vector types.

---
 Eigen/src/Core/arch/NEON/Complex.h    |  3 ++-
 Eigen/src/Core/arch/NEON/PacketMath.h | 11 ++---------
 2 files changed, 4 insertions(+), 10 deletions(-)

diff --git a/Eigen/src/Core/arch/NEON/Complex.h b/Eigen/src/Core/arch/NEON/Complex.h
index 234f29b80..ccc00e5a6 100644
--- a/Eigen/src/Core/arch/NEON/Complex.h
+++ b/Eigen/src/Core/arch/NEON/Complex.h
@@ -275,7 +275,8 @@ ptranspose(PacketBlock<Packet2cf,2>& kernel) {
 //---------- double ----------
 #if EIGEN_ARCH_ARM64 && !EIGEN_APPLE_DOUBLE_NEON_BUG
 
-static uint64x2_t p2ul_CONJ_XOR = EIGEN_INIT_NEON_PACKET2(0x0, 0x8000000000000000);
+const uint64_t  p2ul_conj_XOR_DATA[] = { 0x0, 0x8000000000000000 };
+static uint64x2_t p2ul_CONJ_XOR = vld1q_u64( p2ul_conj_XOR_DATA );
 
 struct Packet1cd
 {
diff --git a/Eigen/src/Core/arch/NEON/PacketMath.h b/Eigen/src/Core/arch/NEON/PacketMath.h
index fa16bc9c8..e1247696d 100644
--- a/Eigen/src/Core/arch/NEON/PacketMath.h
+++ b/Eigen/src/Core/arch/NEON/PacketMath.h
@@ -49,14 +49,6 @@ typedef uint32x4_t  Packet4ui;
 #define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
   const Packet4i p4i_##NAME = pset1<Packet4i>(X)
 
-#if EIGEN_COMP_LLVM && !EIGEN_COMP_CLANG
-  //Special treatment for Apple's llvm-gcc, its NEON packet types are unions
-  #define EIGEN_INIT_NEON_PACKET2D(X, Y)       {{X, Y}}
-#else
-  //Default initializer for packets
-  #define EIGEN_INIT_NEON_PACKET2D(X, Y)       {X, Y}
-#endif
-
 // arm64 does have the pld instruction. If available, let's trust the __builtin_prefetch built-in function
 // which available on LLVM and GCC (at least)
 #if EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC
@@ -584,7 +576,8 @@ template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double&  from) { r
 
 template<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a)
 {
-  Packet2d countdown = EIGEN_INIT_NEON_PACKET2D(0, 1);
+  const double countdown_raw[] = {0.0,1.0};
+  const Packet2d countdown = vld1q_f64(countdown_raw);
   return vaddq_f64(pset1<Packet2d>(a), countdown);
 }
 template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return vaddq_f64(a,b); }

From 2e238bafb69ab0ee2ab2e682d5ac1a43376f9496 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Fri, 10 Jun 2016 15:05:43 +0200
Subject: [PATCH 35/86] Big 279: enable mixing types for comparisons, min, and
 max.

---
 Eigen/src/Core/Redux.h                        |  4 +-
 Eigen/src/Core/functors/BinaryFunctors.h      | 74 ++++++++++---------
 Eigen/src/Core/util/ForwardDeclarations.h     |  7 +-
 Eigen/src/Core/util/Macros.h                  | 18 ++---
 .../src/Eigenvalues/GeneralizedEigenSolver.h  | 32 ++++++--
 Eigen/src/plugins/ArrayCwiseBinaryOps.h       | 20 ++---
 Eigen/src/plugins/CommonCwiseBinaryOps.h      | 30 ++++----
 Eigen/src/plugins/MatrixCwiseBinaryOps.h      | 16 ++--
 8 files changed, 113 insertions(+), 88 deletions(-)

diff --git a/Eigen/src/Core/Redux.h b/Eigen/src/Core/Redux.h
index ec969d9b9..b6e8f8887 100644
--- a/Eigen/src/Core/Redux.h
+++ b/Eigen/src/Core/Redux.h
@@ -425,7 +425,7 @@ template<typename Derived>
 EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
 DenseBase<Derived>::minCoeff() const
 {
-  return derived().redux(Eigen::internal::scalar_min_op<Scalar>());
+  return derived().redux(Eigen::internal::scalar_min_op<Scalar,Scalar>());
 }
 
 /** \returns the maximum of all coefficients of \c *this.
@@ -435,7 +435,7 @@ template<typename Derived>
 EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
 DenseBase<Derived>::maxCoeff() const
 {
-  return derived().redux(Eigen::internal::scalar_max_op<Scalar>());
+  return derived().redux(Eigen::internal::scalar_max_op<Scalar,Scalar>());
 }
 
 /** \returns the sum of all coefficients of \c *this
diff --git a/Eigen/src/Core/functors/BinaryFunctors.h b/Eigen/src/Core/functors/BinaryFunctors.h
index 98fcebae5..c59147db4 100644
--- a/Eigen/src/Core/functors/BinaryFunctors.h
+++ b/Eigen/src/Core/functors/BinaryFunctors.h
@@ -111,21 +111,22 @@ struct functor_traits<scalar_conj_product_op<LhsScalar,RhsScalar> > {
   *
   * \sa class CwiseBinaryOp, MatrixBase::cwiseMin, class VectorwiseOp, MatrixBase::minCoeff()
   */
-template<typename Scalar> struct scalar_min_op {
+template<typename LhsScalar,typename RhsScalar> struct scalar_min_op {
+  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_min_op>::ReturnType result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_min_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return numext::mini(a, b); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return numext::mini(a, b); }
   template<typename Packet>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
   { return internal::pmin(a,b); }
   template<typename Packet>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar predux(const Packet& a) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type predux(const Packet& a) const
   { return internal::predux_min(a); }
 };
-template<typename Scalar>
-struct functor_traits<scalar_min_op<Scalar> > {
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_min_op<LhsScalar,RhsScalar> > {
   enum {
-    Cost = NumTraits<Scalar>::AddCost,
-    PacketAccess = packet_traits<Scalar>::HasMin
+    Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,
+    PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMin
   };
 };
 
@@ -134,21 +135,22 @@ struct functor_traits<scalar_min_op<Scalar> > {
   *
   * \sa class CwiseBinaryOp, MatrixBase::cwiseMax, class VectorwiseOp, MatrixBase::maxCoeff()
   */
-template<typename Scalar> struct scalar_max_op {
+template<typename LhsScalar,typename RhsScalar> struct scalar_max_op {
+  typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_max_op>::ReturnType result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_max_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return numext::maxi(a, b); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return numext::maxi(a, b); }
   template<typename Packet>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
   { return internal::pmax(a,b); }
   template<typename Packet>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar predux(const Packet& a) const
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type predux(const Packet& a) const
   { return internal::predux_max(a); }
 };
-template<typename Scalar>
-struct functor_traits<scalar_max_op<Scalar> > {
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_max_op<LhsScalar,RhsScalar> > {
   enum {
-    Cost = NumTraits<Scalar>::AddCost,
-    PacketAccess = packet_traits<Scalar>::HasMax
+    Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,
+    PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMax
   };
 };
 
@@ -156,56 +158,56 @@ struct functor_traits<scalar_max_op<Scalar> > {
   * \brief Template functors for comparison of two scalars
   * \todo Implement packet-comparisons
   */
-template<typename Scalar, ComparisonName cmp> struct scalar_cmp_op;
+template<typename LhsScalar, typename RhsScalar, ComparisonName cmp> struct scalar_cmp_op;
 
-template<typename Scalar, ComparisonName cmp>
-struct functor_traits<scalar_cmp_op<Scalar, cmp> > {
+template<typename LhsScalar, typename RhsScalar, ComparisonName cmp>
+struct functor_traits<scalar_cmp_op<LhsScalar,RhsScalar, cmp> > {
   enum {
-    Cost = NumTraits<Scalar>::AddCost,
+    Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,
     PacketAccess = false
   };
 };
 
-template<ComparisonName Cmp, typename Scalar>
-struct result_of<scalar_cmp_op<Scalar, Cmp>(Scalar,Scalar)> {
+template<ComparisonName Cmp, typename LhsScalar, typename RhsScalar>
+struct result_of<scalar_cmp_op<LhsScalar, RhsScalar, Cmp>(LhsScalar,RhsScalar)> {
   typedef bool type;
 };
 
 
-template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_EQ> {
+template<typename LhsScalar, typename RhsScalar> struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_EQ> {
   typedef bool result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return a==b;}
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a==b;}
 };
-template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_LT> {
+template<typename LhsScalar, typename RhsScalar> struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_LT> {
   typedef bool result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return a<b;}
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a<b;}
 };
-template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_LE> {
+template<typename LhsScalar, typename RhsScalar> struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_LE> {
   typedef bool result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return a<=b;}
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a<=b;}
 };
-template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_GT> {
+template<typename LhsScalar, typename RhsScalar> struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_GT> {
   typedef bool result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return a>b;}
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a>b;}
 };
-template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_GE> {
+template<typename LhsScalar, typename RhsScalar> struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_GE> {
   typedef bool result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return a>=b;}
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a>=b;}
 };
-template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_UNORD> {
+template<typename LhsScalar, typename RhsScalar> struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_UNORD> {
   typedef bool result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return !(a<=b || b<=a);}
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return !(a<=b || b<=a);}
 };
-template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_NEQ> {
+template<typename LhsScalar, typename RhsScalar> struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_NEQ> {
   typedef bool result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const Scalar& a, const Scalar& b) const {return a!=b;}
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a!=b;}
 };
 
 
@@ -214,7 +216,7 @@ template<typename Scalar> struct scalar_cmp_op<Scalar, cmp_NEQ> {
   *
   * \sa MatrixBase::stableNorm(), class Redux
   */
-template<typename Scalar> struct scalar_hypot_op {
+template<typename Scalar> struct scalar_hypot_op<Scalar,Scalar> {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_hypot_op)
 //   typedef typename NumTraits<Scalar>::Real result_type;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& _x, const Scalar& _y) const
@@ -235,7 +237,7 @@ template<typename Scalar> struct scalar_hypot_op {
   }
 };
 template<typename Scalar>
-struct functor_traits<scalar_hypot_op<Scalar> > {
+struct functor_traits<scalar_hypot_op<Scalar,Scalar> > {
   enum
   {
     Cost = 3 * NumTraits<Scalar>::AddCost +
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index 045e22658..340d1f3a5 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -179,6 +179,8 @@ template<typename LhsScalar, typename RhsScalar, bool ConjLhs=false, bool ConjRh
 template<typename LhsScalar,typename RhsScalar> struct scalar_sum_op;
 template<typename LhsScalar,typename RhsScalar> struct scalar_difference_op;
 template<typename LhsScalar,typename RhsScalar> struct scalar_conj_product_op;
+template<typename LhsScalar,typename RhsScalar> struct scalar_min_op;
+template<typename LhsScalar,typename RhsScalar> struct scalar_max_op;
 template<typename Scalar> struct scalar_opposite_op;
 template<typename Scalar> struct scalar_conjugate_op;
 template<typename Scalar> struct scalar_real_op;
@@ -201,8 +203,6 @@ template<typename Scalar> struct scalar_cube_op;
 template<typename Scalar, typename NewType> struct scalar_cast_op;
 template<typename Scalar> struct scalar_multiple_op;
 template<typename Scalar> struct scalar_quotient1_op;
-template<typename Scalar> struct scalar_min_op;
-template<typename Scalar> struct scalar_max_op;
 template<typename Scalar> struct scalar_random_op;
 template<typename Scalar> struct scalar_add_op;
 template<typename Scalar> struct scalar_constant_op;
@@ -212,9 +212,10 @@ template<typename Scalar> struct scalar_igamma_op;
 template<typename Scalar> struct scalar_igammac_op;
 template<typename Scalar> struct scalar_betainc_op;
 
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_hypot_op;
 template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_product_op;
-template<typename LhsScalar,typename RhsScalar> struct scalar_multiple2_op;
 template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_quotient_op;
+template<typename LhsScalar,typename RhsScalar> struct scalar_multiple2_op;
 template<typename LhsScalar,typename RhsScalar> struct scalar_quotient2_op;
 
 } // end namespace internal
diff --git a/Eigen/src/Core/util/Macros.h b/Eigen/src/Core/util/Macros.h
index 35547fdda..a51572463 100644
--- a/Eigen/src/Core/util/Macros.h
+++ b/Eigen/src/Core/util/Macros.h
@@ -876,15 +876,7 @@ namespace Eigen {
 
 #define EIGEN_IMPLIES(a,b) (!(a) || (b))
 
-#define EIGEN_MAKE_CWISE_BINARY_OP(METHOD,FUNCTOR) \
-  template<typename OtherDerived> \
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<FUNCTOR<Scalar>, const Derived, const OtherDerived> \
-  (METHOD)(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
-  { \
-    return CwiseBinaryOp<FUNCTOR<Scalar>, const Derived, const OtherDerived>(derived(), other.derived()); \
-  }
-
-// the expression type of a cwise product
+// the expression type of a standard coefficient wise binary operation
 #define EIGEN_CWISE_BINARY_RETURN_TYPE(LHS,RHS,OPNAME) \
     CwiseBinaryOp< \
       EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)< \
@@ -895,6 +887,14 @@ namespace Eigen {
       const RHS \
     >
 
+#define EIGEN_MAKE_CWISE_BINARY_OP(METHOD,OPNAME) \
+  template<typename OtherDerived> \
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME) \
+  (METHOD)(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
+  { \
+    return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME)(derived(), other.derived()); \
+  }
+
 #ifdef EIGEN_EXCEPTIONS
 #  define EIGEN_THROW_X(X) throw X
 #  define EIGEN_THROW throw
diff --git a/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h b/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
index a9d6790d5..07a9ccf46 100644
--- a/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
+++ b/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
@@ -327,13 +327,33 @@ GeneralizedEigenSolver<MatrixType>::compute(const MatrixType& A, const MatrixTyp
       }
       else
       {
-        Scalar p = Scalar(0.5) * (m_matS.coeff(i, i) - m_matS.coeff(i+1, i+1));
-        Scalar z = sqrt(abs(p * p + m_matS.coeff(i+1, i) * m_matS.coeff(i, i+1)));
-        m_alphas.coeffRef(i)   = ComplexScalar(m_matS.coeff(i+1, i+1) + p, z);
-        m_alphas.coeffRef(i+1) = ComplexScalar(m_matS.coeff(i+1, i+1) + p, -z);
+        // We need to extract the generalized eigenvalues of the pair of a general 2x2 block S and a triangular 2x2 block T
+        // From the eigen decomposition of T = U * E * U^-1,
+        // we can extract the eigenvalues of (U^-1 * S * U) / E
+        // Here, we can take advantage that E = diag(T), and U = [ 1 T_01 ; 0 T_11-T_00], and U^-1 = [1 -T_11/(T_11-T_00) ; 0 1/(T_11-T_00)].
+        // Then taking beta=T_00*T_11*(T_11-T_00), we can avoid any division, and alpha is the eigenvalues of A = (U^-1 * S * U) * diag(T_11,T_00) * (T_11-T_00):
+
+        // T =  [a b ; 0 c]
+        // S =  [e f ; g h]
+        RealScalar a = m_realQZ.matrixT().coeff(i, i), b = m_realQZ.matrixT().coeff(i, i+1), c = m_realQZ.matrixT().coeff(i+1, i+1);
+        RealScalar e = m_matS.coeff(i, i), f = m_matS.coeff(i, i+1), g = m_matS.coeff(i+1, i), h = m_matS.coeff(i+1, i+1);
+        RealScalar d = c-a;
+        RealScalar gb = g*b;
+        Matrix<RealScalar,2,2> A;
+        A <<  (e*d-gb)*c,  ((e*b+f*d-h*b)*d-gb*b)*a,
+              g*c       ,  (gb+h*d)*a;
+
+        // NOTE, we could also compute the SVD of T's block during the QZ factorization so that the respective T block is guaranteed to be diagonal,
+        // and then we could directly apply the formula below (while taking care of scaling S columns by T11,T00):
+
+        Scalar p = Scalar(0.5) * (A.coeff(i, i) - A.coeff(i+1, i+1));
+        Scalar z = sqrt(abs(p * p + A.coeff(i+1, i) * A.coeff(i, i+1)));
+        m_alphas.coeffRef(i)   = ComplexScalar(A.coeff(i+1, i+1) + p, z);
+        m_alphas.coeffRef(i+1) = ComplexScalar(A.coeff(i+1, i+1) + p, -z);
+
+        m_betas.coeffRef(i)   =
+        m_betas.coeffRef(i+1) = a*c*d;
 
-        m_betas.coeffRef(i)   = m_realQZ.matrixT().coeff(i,i);
-        m_betas.coeffRef(i+1) = m_realQZ.matrixT().coeff(i,i);
         i += 2;
       }
     }
diff --git a/Eigen/src/plugins/ArrayCwiseBinaryOps.h b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
index c6ea12c90..da47a7ed7 100644
--- a/Eigen/src/plugins/ArrayCwiseBinaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
@@ -29,14 +29,14 @@ operator/(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
   *
   * \sa max()
   */
-EIGEN_MAKE_CWISE_BINARY_OP(min,internal::scalar_min_op)
+EIGEN_MAKE_CWISE_BINARY_OP(min,min)
 
 /** \returns an expression of the coefficient-wise min of \c *this and scalar \a other
   *
   * \sa max()
   */
 EIGEN_DEVICE_FUNC
-EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived,
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar>, const Derived,
                                         const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> >
 #ifdef EIGEN_PARSED_BY_DOXYGEN
 min
@@ -55,14 +55,14 @@ min
   *
   * \sa min()
   */
-EIGEN_MAKE_CWISE_BINARY_OP(max,internal::scalar_max_op)
+EIGEN_MAKE_CWISE_BINARY_OP(max,max)
 
 /** \returns an expression of the coefficient-wise max of \c *this and scalar \a other
   *
   * \sa min()
   */
 EIGEN_DEVICE_FUNC
-EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived,
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived,
                                         const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> >
 #ifdef EIGEN_PARSED_BY_DOXYGEN
 max
@@ -95,13 +95,13 @@ pow(const ArrayBase<ExponentDerived>& exponents) const
 // TODO code generating macros could be moved to Macros.h and could include generation of documentation
 #define EIGEN_MAKE_CWISE_COMP_OP(OP, COMPARATOR) \
 template<typename OtherDerived> \
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const OtherDerived> \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_cmp_op<Scalar, typename OtherDerived::Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const OtherDerived> \
 OP(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
 { \
-  return CwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const OtherDerived>(derived(), other.derived()); \
+  return CwiseBinaryOp<internal::scalar_cmp_op<Scalar, typename OtherDerived::Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const OtherDerived>(derived(), other.derived()); \
 }\
-typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> > Cmp ## COMPARATOR ## ReturnType; \
-typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_ ## COMPARATOR>, const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject>, const Derived > RCmp ## COMPARATOR ## ReturnType; \
+typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar,Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> > Cmp ## COMPARATOR ## ReturnType; \
+typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar,Scalar, internal::cmp_ ## COMPARATOR>, const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject>, const Derived > RCmp ## COMPARATOR ## ReturnType; \
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Cmp ## COMPARATOR ## ReturnType \
 OP(const Scalar& s) const { \
   return this->OP(Derived::PlainObject::Constant(rows(), cols(), s)); \
@@ -113,10 +113,10 @@ OP(const Scalar& s, const Derived& d) { \
 
 #define EIGEN_MAKE_CWISE_COMP_R_OP(OP, R_OP, RCOMPARATOR) \
 template<typename OtherDerived> \
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_##RCOMPARATOR>, const OtherDerived, const Derived> \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_cmp_op<typename OtherDerived::Scalar, Scalar, internal::cmp_##RCOMPARATOR>, const OtherDerived, const Derived> \
 OP(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
 { \
-  return CwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_##RCOMPARATOR>, const OtherDerived, const Derived>(other.derived(), derived()); \
+  return CwiseBinaryOp<internal::scalar_cmp_op<typename OtherDerived::Scalar, Scalar, internal::cmp_##RCOMPARATOR>, const OtherDerived, const Derived>(other.derived(), derived()); \
 } \
 EIGEN_DEVICE_FUNC \
 inline const RCmp ## RCOMPARATOR ## ReturnType \
diff --git a/Eigen/src/plugins/CommonCwiseBinaryOps.h b/Eigen/src/plugins/CommonCwiseBinaryOps.h
index 3c13b7f06..6a5ccc1aa 100644
--- a/Eigen/src/plugins/CommonCwiseBinaryOps.h
+++ b/Eigen/src/plugins/CommonCwiseBinaryOps.h
@@ -16,13 +16,14 @@
   *
   * \sa class CwiseBinaryOp, operator-=()
   */
-template<typename OtherDerived>
-EIGEN_DEVICE_FUNC
-EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,difference)
-operator-(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
-{
-  return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,difference)(derived(), other.derived());
-}
+EIGEN_MAKE_CWISE_BINARY_OP(operator-,difference)
+// template<typename OtherDerived>
+// EIGEN_DEVICE_FUNC
+// EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,difference)
+// operator-(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+// {
+//   return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,difference)(derived(), other.derived());
+// }
 
 /** \returns an expression of the sum of \c *this and \a other
   *
@@ -30,13 +31,14 @@ operator-(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
   *
   * \sa class CwiseBinaryOp, operator+=()
   */
-template<typename OtherDerived>
-EIGEN_DEVICE_FUNC
-EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,sum)
-operator+(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
-{
-  return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,sum)(derived(), other.derived());
-}
+EIGEN_MAKE_CWISE_BINARY_OP(operator+,sum)
+// template<typename OtherDerived>
+// EIGEN_DEVICE_FUNC
+// EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,sum)
+// operator+(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+// {
+//   return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,sum)(derived(), other.derived());
+// }
 
 /** \returns an expression of a custom coefficient-wise operator \a func of *this and \a other
   *
diff --git a/Eigen/src/plugins/MatrixCwiseBinaryOps.h b/Eigen/src/plugins/MatrixCwiseBinaryOps.h
index 59581e618..f1084abef 100644
--- a/Eigen/src/plugins/MatrixCwiseBinaryOps.h
+++ b/Eigen/src/plugins/MatrixCwiseBinaryOps.h
@@ -74,10 +74,10 @@ cwiseNotEqual(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
   */
 template<typename OtherDerived>
 EIGEN_DEVICE_FUNC
-EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const OtherDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar>, const Derived, const OtherDerived>
 cwiseMin(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
 {
-  return CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
+  return CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
 }
 
 /** \returns an expression of the coefficient-wise min of *this and scalar \a other
@@ -85,7 +85,7 @@ cwiseMin(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
   * \sa class CwiseBinaryOp, min()
   */
 EIGEN_DEVICE_FUNC
-EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const ConstantReturnType>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar>, const Derived, const ConstantReturnType>
 cwiseMin(const Scalar &other) const
 {
   return cwiseMin(Derived::Constant(rows(), cols(), other));
@@ -100,10 +100,10 @@ cwiseMin(const Scalar &other) const
   */
 template<typename OtherDerived>
 EIGEN_DEVICE_FUNC
-EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const OtherDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived, const OtherDerived>
 cwiseMax(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
 {
-  return CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
+  return CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
 }
 
 /** \returns an expression of the coefficient-wise max of *this and scalar \a other
@@ -111,7 +111,7 @@ cwiseMax(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
   * \sa class CwiseBinaryOp, min()
   */
 EIGEN_DEVICE_FUNC
-EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const ConstantReturnType>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived, const ConstantReturnType>
 cwiseMax(const Scalar &other) const
 {
   return cwiseMax(Derived::Constant(rows(), cols(), other));
@@ -133,7 +133,7 @@ cwiseQuotient(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
   return CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
 }
 
-typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar,internal::cmp_EQ>, const Derived, const ConstantReturnType> CwiseScalarEqualReturnType;
+typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar,Scalar,internal::cmp_EQ>, const Derived, const ConstantReturnType> CwiseScalarEqualReturnType;
 
 /** \returns an expression of the coefficient-wise == operator of \c *this and a scalar \a s
   *
@@ -148,5 +148,5 @@ EIGEN_DEVICE_FUNC
 inline const CwiseScalarEqualReturnType
 cwiseEqual(const Scalar& s) const
 {
-  return CwiseScalarEqualReturnType(derived(), Derived::Constant(rows(), cols(), s), internal::scalar_cmp_op<Scalar,internal::cmp_EQ>());
+  return CwiseScalarEqualReturnType(derived(), Derived::Constant(rows(), cols(), s), internal::scalar_cmp_op<Scalar,Scalar,internal::cmp_EQ>());
 }

From 5fdd7036293aef88e5bdfe30acc74206486d82af Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Fri, 10 Jun 2016 15:58:04 +0200
Subject: [PATCH 36/86] Enable mixing types in numext::pow

---
 Eigen/src/Core/MathFunctions.h            | 35 +++++++++--------------
 Eigen/src/Core/functors/BinaryFunctors.h  |  3 +-
 Eigen/src/Core/util/ForwardDeclarations.h |  1 +
 3 files changed, 17 insertions(+), 22 deletions(-)

diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
index ece04b754..2a05ae12d 100644
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
@@ -494,24 +494,26 @@ struct log1p_retval
 * Implementation of pow                                                  *
 ****************************************************************************/
 
-template<typename Scalar, bool IsInteger>
-struct pow_default_impl
+template<typename ScalarX,typename ScalarY, bool IsInteger = NumTraits<ScalarX>::IsInteger&&NumTraits<ScalarY>::IsInteger>
+struct pow_impl
 {
-  typedef Scalar retval;
-  static EIGEN_DEVICE_FUNC inline Scalar run(const Scalar& x, const Scalar& y)
+  //typedef Scalar retval;
+  typedef typename ScalarBinaryOpTraits<ScalarX,ScalarY,internal::scalar_binary_pow_op<ScalarX,ScalarY> >::ReturnType result_type;
+  static EIGEN_DEVICE_FUNC inline result_type run(const ScalarX& x, const ScalarY& y)
   {
     EIGEN_USING_STD_MATH(pow);
     return pow(x, y);
   }
 };
 
-template<typename Scalar>
-struct pow_default_impl<Scalar, true>
+template<typename ScalarX,typename ScalarY>
+struct pow_impl<ScalarX,ScalarY, true>
 {
-  static EIGEN_DEVICE_FUNC inline Scalar run(Scalar x, Scalar y)
+  typedef ScalarX result_type;
+  static EIGEN_DEVICE_FUNC inline ScalarX run(const ScalarX &x, const ScalarY &y)
   {
-    Scalar res(1);
-    eigen_assert(!NumTraits<Scalar>::IsSigned || y >= 0);
+    ScalarX res(1);
+    eigen_assert(!NumTraits<ScalarY>::IsSigned || y >= 0);
     if(y & 1) res *= x;
     y >>= 1;
     while(y)
@@ -524,15 +526,6 @@ struct pow_default_impl<Scalar, true>
   }
 };
 
-template<typename Scalar>
-struct pow_impl : pow_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
-
-template<typename Scalar>
-struct pow_retval
-{
-  typedef Scalar type;
-};
-
 /****************************************************************************
 * Implementation of random                                               *
 ****************************************************************************/
@@ -928,11 +921,11 @@ inline EIGEN_MATHFUNC_RETVAL(log1p, Scalar) log1p(const Scalar& x)
   return EIGEN_MATHFUNC_IMPL(log1p, Scalar)::run(x);
 }
 
-template<typename Scalar>
+template<typename ScalarX,typename ScalarY>
 EIGEN_DEVICE_FUNC
-inline EIGEN_MATHFUNC_RETVAL(pow, Scalar) pow(const Scalar& x, const Scalar& y)
+inline typename internal::pow_impl<ScalarX,ScalarY>::result_type pow(const ScalarX& x, const ScalarY& y)
 {
-  return EIGEN_MATHFUNC_IMPL(pow, Scalar)::run(x, y);
+  return internal::pow_impl<ScalarX,ScalarY>::run(x, y);
 }
 
 template<typename T> EIGEN_DEVICE_FUNC bool (isnan)   (const T &x) { return internal::isnan_impl(x); }
diff --git a/Eigen/src/Core/functors/BinaryFunctors.h b/Eigen/src/Core/functors/BinaryFunctors.h
index c59147db4..ec06499a0 100644
--- a/Eigen/src/Core/functors/BinaryFunctors.h
+++ b/Eigen/src/Core/functors/BinaryFunctors.h
@@ -251,9 +251,10 @@ struct functor_traits<scalar_hypot_op<Scalar,Scalar> > {
   * \brief Template functor to compute the pow of two scalars
   */
 template<typename Scalar, typename OtherScalar> struct scalar_binary_pow_op {
+  typedef typename ScalarBinaryOpTraits<Scalar,OtherScalar,scalar_binary_pow_op>::ReturnType result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_binary_pow_op)
   EIGEN_DEVICE_FUNC
-  inline Scalar operator() (const Scalar& a, const OtherScalar& b) const { return numext::pow(a, b); }
+  inline result_type operator() (const Scalar& a, const OtherScalar& b) const { return numext::pow(a, b); }
 };
 template<typename Scalar, typename OtherScalar>
 struct functor_traits<scalar_binary_pow_op<Scalar,OtherScalar> > {
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index 340d1f3a5..760d6bcf6 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -217,6 +217,7 @@ template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_product_
 template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_quotient_op;
 template<typename LhsScalar,typename RhsScalar> struct scalar_multiple2_op;
 template<typename LhsScalar,typename RhsScalar> struct scalar_quotient2_op;
+template<typename ScalarX, typename ScalarY> struct scalar_binary_pow_op;
 
 } // end namespace internal
 

From 5de8d7036b8b48bc4986d96f677c77eb466ce02b Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Fri, 10 Jun 2016 15:58:22 +0200
Subject: [PATCH 37/86] Add real.pow(complex), complex.pow(real) unit tests.

---
 test/mixingtypes.cpp | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/test/mixingtypes.cpp b/test/mixingtypes.cpp
index 2af188b25..d719a3c53 100644
--- a/test/mixingtypes.cpp
+++ b/test/mixingtypes.cpp
@@ -196,6 +196,9 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
 //   VERIFY_IS_APPROX( md.array() / mcd.array(), md.template cast<CD>().eval().array() / mcd.array() );
   VERIFY_IS_APPROX( mcd.array() / md.array(), mcd.array() / md.template cast<CD>().eval().array() );
 
+  VERIFY_IS_APPROX( md.array().pow(mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()) );
+  VERIFY_IS_APPROX( mcd.array().pow(md.array()),  mcd.array().pow(md.template cast<CD>().eval().array()) );
+
   rcd = mcd;
   VERIFY_IS_APPROX( rcd = md, md.template cast<CD>().eval() );
   rcd = mcd;

From fabae6c9a180669f6afbd732ee6973311a36476c Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Fri, 10 Jun 2016 15:58:33 +0200
Subject: [PATCH 38/86] Cleanup

---
 Eigen/src/plugins/ArrayCwiseBinaryOps.h  | 12 ++----------
 Eigen/src/plugins/CommonCwiseBinaryOps.h | 14 --------------
 2 files changed, 2 insertions(+), 24 deletions(-)

diff --git a/Eigen/src/plugins/ArrayCwiseBinaryOps.h b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
index da47a7ed7..7f7d0dbf4 100644
--- a/Eigen/src/plugins/ArrayCwiseBinaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
@@ -81,16 +81,8 @@ max
   * Example: \include Cwise_array_power_array.cpp
   * Output: \verbinclude Cwise_array_power_array.out
   */
-template<typename ExponentDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-const CwiseBinaryOp<internal::scalar_binary_pow_op<Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>
-pow(const ArrayBase<ExponentDerived>& exponents) const
-{
-  return CwiseBinaryOp<internal::scalar_binary_pow_op<Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>(
-    this->derived(),
-    exponents.derived()
-  );
-}
+EIGEN_MAKE_CWISE_BINARY_OP(pow,binary_pow)
+
 
 // TODO code generating macros could be moved to Macros.h and could include generation of documentation
 #define EIGEN_MAKE_CWISE_COMP_OP(OP, COMPARATOR) \
diff --git a/Eigen/src/plugins/CommonCwiseBinaryOps.h b/Eigen/src/plugins/CommonCwiseBinaryOps.h
index 6a5ccc1aa..f16be7bea 100644
--- a/Eigen/src/plugins/CommonCwiseBinaryOps.h
+++ b/Eigen/src/plugins/CommonCwiseBinaryOps.h
@@ -17,13 +17,6 @@
   * \sa class CwiseBinaryOp, operator-=()
   */
 EIGEN_MAKE_CWISE_BINARY_OP(operator-,difference)
-// template<typename OtherDerived>
-// EIGEN_DEVICE_FUNC
-// EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,difference)
-// operator-(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
-// {
-//   return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,difference)(derived(), other.derived());
-// }
 
 /** \returns an expression of the sum of \c *this and \a other
   *
@@ -32,13 +25,6 @@ EIGEN_MAKE_CWISE_BINARY_OP(operator-,difference)
   * \sa class CwiseBinaryOp, operator+=()
   */
 EIGEN_MAKE_CWISE_BINARY_OP(operator+,sum)
-// template<typename OtherDerived>
-// EIGEN_DEVICE_FUNC
-// EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,sum)
-// operator+(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
-// {
-//   return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,sum)(derived(), other.derived());
-// }
 
 /** \returns an expression of a custom coefficient-wise operator \a func of *this and \a other
   *

From a05607875a57129821f81e6aae1727357f4db5e6 Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Fri, 10 Jun 2016 11:53:56 -0700
Subject: [PATCH 39/86] Don't refer to the half2 type unless it's been defined

---
 unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h b/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h
index 0f3778e6e..fdb5ee6b8 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h
@@ -52,7 +52,7 @@ struct PacketType : internal::packet_traits<Scalar> {
 };
 
 // For CUDA packet types when using a GpuDevice
-#if defined(EIGEN_USE_GPU) && defined(__CUDACC__)
+#if defined(EIGEN_USE_GPU) && defined(__CUDACC__) && defined(EIGEN_HAS_CUDA_FP16)
 template <>
 struct PacketType<half, GpuDevice> {
   typedef half2 type;

From 83904a21c11ffdb88f3ad8a65ded7bf46c1a068a Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Sat, 11 Jun 2016 14:41:36 +0200
Subject: [PATCH 40/86] Make sure T(i+1,i)==0 when diagonalizing T(i:i+1,i:i+1)

---
 Eigen/src/Eigenvalues/RealQZ.h | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Eigen/src/Eigenvalues/RealQZ.h b/Eigen/src/Eigenvalues/RealQZ.h
index c4715b954..b3a910dd9 100644
--- a/Eigen/src/Eigenvalues/RealQZ.h
+++ b/Eigen/src/Eigenvalues/RealQZ.h
@@ -630,11 +630,11 @@ namespace Eigen {
             internal::real_2x2_jacobi_svd(m_T, i, i+1, &j_left, &j_right);
 
             // Apply resulting Jacobi rotations
-            m_T.applyOnTheLeft(i,i+1,j_left);
-            m_T.applyOnTheRight(i,i+1,j_right);
             m_S.applyOnTheLeft(i,i+1,j_left);
             m_S.applyOnTheRight(i,i+1,j_right);
-            m_T(i,i+1) = Scalar(0);
+            m_T.applyOnTheLeft(i,i+1,j_left);
+            m_T.applyOnTheRight(i,i+1,j_right);
+            m_T(i+1,i) = m_T(i,i+1) = Scalar(0);
 
             if(m_computeQZ) {
               m_Q.applyOnTheRight(i,i+1,j_left.transpose());

From a3a4714abac02ba48a683c3c3967cebee2833188 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Sat, 11 Jun 2016 14:41:53 +0200
Subject: [PATCH 41/86] Add debug output.

---
 test/real_qz.cpp | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/test/real_qz.cpp b/test/real_qz.cpp
index a1766c6d9..45ae8d763 100644
--- a/test/real_qz.cpp
+++ b/test/real_qz.cpp
@@ -49,11 +49,20 @@ template<typename MatrixType> void real_qz(const MatrixType& m)
   for (Index i=0; i<A.cols(); i++)
     for (Index j=0; j<i; j++) {
       if (abs(qz.matrixT()(i,j))!=Scalar(0.0))
+      {
+        std::cerr << "Error: T(" << i << "," << j << ") = " << qz.matrixT()(i,j) << std::endl;
         all_zeros = false;
+      }
       if (j<i-1 && abs(qz.matrixS()(i,j))!=Scalar(0.0))
+      {
+        std::cerr << "Error: S(" << i << "," << j << ") = " << qz.matrixS()(i,j) << std::endl;
         all_zeros = false;
+      }
       if (j==i-1 && j>0 && abs(qz.matrixS()(i,j))!=Scalar(0.0) && abs(qz.matrixS()(i-1,j-1))!=Scalar(0.0))
+      {
+        std::cerr << "Error: S(" << i << "," << j << ") = " << qz.matrixS()(i,j)  << " && S(" << i-1 << "," << j-1 << ") = " << qz.matrixS()(i-1,j-1) << std::endl;
         all_zeros = false;
+      }
     }
   VERIFY_IS_EQUAL(all_zeros, true);
   VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixS()*qz.matrixZ(), A);

From 4c61f00838202889045ec9e5ad0d60b79f00fec5 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Sun, 12 Jun 2016 22:42:13 +0200
Subject: [PATCH 42/86] Add missing explicit scalar conversion

---
 Eigen/src/Eigenvalues/Tridiagonalization.h | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Eigen/src/Eigenvalues/Tridiagonalization.h b/Eigen/src/Eigenvalues/Tridiagonalization.h
index 2030b5be1..1d102c17b 100644
--- a/Eigen/src/Eigenvalues/Tridiagonalization.h
+++ b/Eigen/src/Eigenvalues/Tridiagonalization.h
@@ -367,10 +367,10 @@ void tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs)
     hCoeffs.tail(n-i-1).noalias() = (matA.bottomRightCorner(remainingSize,remainingSize).template selfadjointView<Lower>()
                                   * (conj(h) * matA.col(i).tail(remainingSize)));
 
-    hCoeffs.tail(n-i-1) += (conj(h)*Scalar(-0.5)*(hCoeffs.tail(remainingSize).dot(matA.col(i).tail(remainingSize)))) * matA.col(i).tail(n-i-1);
+    hCoeffs.tail(n-i-1) += (conj(h)*RealScalar(-0.5)*(hCoeffs.tail(remainingSize).dot(matA.col(i).tail(remainingSize)))) * matA.col(i).tail(n-i-1);
 
     matA.bottomRightCorner(remainingSize, remainingSize).template selfadjointView<Lower>()
-      .rankUpdate(matA.col(i).tail(remainingSize), hCoeffs.tail(remainingSize), -1);
+      .rankUpdate(matA.col(i).tail(remainingSize), hCoeffs.tail(remainingSize), Scalar(-1));
 
     matA.col(i).coeffRef(i+1) = beta;
     hCoeffs.coeffRef(i) = h;

From 2ca2ffb65e10af6310382bd6efb294efb4f74588 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Mon, 13 Jun 2016 16:15:32 +0200
Subject: [PATCH 43/86] check for mixing types in "array / scalar" expressions

---
 test/mixingtypes.cpp | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/test/mixingtypes.cpp b/test/mixingtypes.cpp
index d719a3c53..dee4f35df 100644
--- a/test/mixingtypes.cpp
+++ b/test/mixingtypes.cpp
@@ -67,9 +67,13 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
   
   // check scalar products
   VERIFY_IS_APPROX(vcf * sf , vcf * complex<float>(sf));
-  VERIFY_IS_APPROX(sd * vcd, complex<double>(sd) * vcd);
+  VERIFY_IS_APPROX(sd * vcd , complex<double>(sd) * vcd);
   VERIFY_IS_APPROX(vf * scf , vf.template cast<complex<float> >() * scf);
-  VERIFY_IS_APPROX(scd * vd, scd * vd.template cast<complex<double> >());
+  VERIFY_IS_APPROX(scd * vd , scd * vd.template cast<complex<double> >());
+
+  // check scalar quotients
+  VERIFY_IS_APPROX(vcf / sf , vcf / complex<float>(sf));
+  VERIFY_IS_APPROX(vf / scf , vf.template cast<complex<float> >() / scf);
 
   // check dot product
   vf.dot(vf);

From 7a9ef7bbb4d71e9ea5150a244238e62d350a8896 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Mon, 13 Jun 2016 16:17:23 +0200
Subject: [PATCH 44/86] Add default template parameters for the second scalar
 type of binary functors. This enhences backward compatibility.

---
 Eigen/src/Core/util/ForwardDeclarations.h | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index 760d6bcf6..af3dce21b 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -176,11 +176,11 @@ namespace internal {
 // with optional conjugation of the arguments.
 template<typename LhsScalar, typename RhsScalar, bool ConjLhs=false, bool ConjRhs=false> struct conj_helper;
 
-template<typename LhsScalar,typename RhsScalar> struct scalar_sum_op;
-template<typename LhsScalar,typename RhsScalar> struct scalar_difference_op;
-template<typename LhsScalar,typename RhsScalar> struct scalar_conj_product_op;
-template<typename LhsScalar,typename RhsScalar> struct scalar_min_op;
-template<typename LhsScalar,typename RhsScalar> struct scalar_max_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_sum_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_difference_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_conj_product_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_min_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_max_op;
 template<typename Scalar> struct scalar_opposite_op;
 template<typename Scalar> struct scalar_conjugate_op;
 template<typename Scalar> struct scalar_real_op;

From 3c12e241643ebea97706c9ed7412e9a7c1bf16d0 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Mon, 13 Jun 2016 16:18:59 +0200
Subject: [PATCH 45/86] Add bind1st_op and bind2nd_op helpers to turn binary
 functors into unary ones, and implement scalar_multiple2 and scalar_quotient2
 on top of them.

---
 Eigen/src/Core/functors/BinaryFunctors.h      | 140 +++++++++++++-----
 Eigen/src/Core/util/ForwardDeclarations.h     |   2 -
 Eigen/src/plugins/CommonCwiseUnaryOps.h       |  23 ++-
 .../Eigen/src/AutoDiff/AutoDiffScalar.h       |   8 +-
 4 files changed, 115 insertions(+), 58 deletions(-)

diff --git a/Eigen/src/Core/functors/BinaryFunctors.h b/Eigen/src/Core/functors/BinaryFunctors.h
index ec06499a0..637514a20 100644
--- a/Eigen/src/Core/functors/BinaryFunctors.h
+++ b/Eigen/src/Core/functors/BinaryFunctors.h
@@ -16,12 +16,21 @@ namespace internal {
 
 //---------- associative binary functors ----------
 
+template<typename Arg1, typename Arg2>
+struct binary_op_base
+{
+  typedef Arg1 first_argument_type;
+  typedef Arg2 second_argument_type;
+};
+
 /** \internal
   * \brief Template functor to compute the sum of two scalars
   *
   * \sa class CwiseBinaryOp, MatrixBase::operator+, class VectorwiseOp, DenseBase::sum()
   */
-template<typename LhsScalar,typename RhsScalar> struct scalar_sum_op {
+template<typename LhsScalar,typename RhsScalar>
+struct scalar_sum_op : binary_op_base<LhsScalar,RhsScalar>
+{
   typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_sum_op>::ReturnType result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_sum_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a + b; }
@@ -57,7 +66,9 @@ template<> struct scalar_sum_op<bool,bool> : scalar_sum_op<int,int> {
   *
   * \sa class CwiseBinaryOp, Cwise::operator*(), class VectorwiseOp, MatrixBase::redux()
   */
-template<typename LhsScalar,typename RhsScalar> struct scalar_product_op {
+template<typename LhsScalar,typename RhsScalar>
+struct scalar_product_op  : binary_op_base<LhsScalar,RhsScalar>
+{
   typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_product_op>::ReturnType result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_product_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a * b; }
@@ -82,7 +93,9 @@ struct functor_traits<scalar_product_op<LhsScalar,RhsScalar> > {
   *
   * This is a short cut for conj(x) * y which is needed for optimization purpose; in Eigen2 support mode, this becomes x * conj(y)
   */
-template<typename LhsScalar,typename RhsScalar> struct scalar_conj_product_op {
+template<typename LhsScalar,typename RhsScalar>
+struct scalar_conj_product_op  : binary_op_base<LhsScalar,RhsScalar>
+{
 
   enum {
     Conj = NumTraits<LhsScalar>::IsComplex
@@ -111,7 +124,9 @@ struct functor_traits<scalar_conj_product_op<LhsScalar,RhsScalar> > {
   *
   * \sa class CwiseBinaryOp, MatrixBase::cwiseMin, class VectorwiseOp, MatrixBase::minCoeff()
   */
-template<typename LhsScalar,typename RhsScalar> struct scalar_min_op {
+template<typename LhsScalar,typename RhsScalar>
+struct scalar_min_op : binary_op_base<LhsScalar,RhsScalar>
+{
   typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_min_op>::ReturnType result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_min_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return numext::mini(a, b); }
@@ -135,7 +150,9 @@ struct functor_traits<scalar_min_op<LhsScalar,RhsScalar> > {
   *
   * \sa class CwiseBinaryOp, MatrixBase::cwiseMax, class VectorwiseOp, MatrixBase::maxCoeff()
   */
-template<typename LhsScalar,typename RhsScalar> struct scalar_max_op {
+template<typename LhsScalar,typename RhsScalar>
+struct scalar_max_op  : binary_op_base<LhsScalar,RhsScalar>
+{
   typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_max_op>::ReturnType result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_max_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return numext::maxi(a, b); }
@@ -174,37 +191,51 @@ struct result_of<scalar_cmp_op<LhsScalar, RhsScalar, Cmp>(LhsScalar,RhsScalar)>
 };
 
 
-template<typename LhsScalar, typename RhsScalar> struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_EQ> {
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_EQ> : binary_op_base<LhsScalar,RhsScalar>
+{
   typedef bool result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a==b;}
 };
-template<typename LhsScalar, typename RhsScalar> struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_LT> {
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_LT> : binary_op_base<LhsScalar,RhsScalar>
+{
   typedef bool result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a<b;}
 };
-template<typename LhsScalar, typename RhsScalar> struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_LE> {
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_LE> : binary_op_base<LhsScalar,RhsScalar>
+{
   typedef bool result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a<=b;}
 };
-template<typename LhsScalar, typename RhsScalar> struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_GT> {
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_GT> : binary_op_base<LhsScalar,RhsScalar>
+{
   typedef bool result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a>b;}
 };
-template<typename LhsScalar, typename RhsScalar> struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_GE> {
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_GE> : binary_op_base<LhsScalar,RhsScalar>
+{
   typedef bool result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a>=b;}
 };
-template<typename LhsScalar, typename RhsScalar> struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_UNORD> {
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_UNORD> : binary_op_base<LhsScalar,RhsScalar>
+{
   typedef bool result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return !(a<=b || b<=a);}
 };
-template<typename LhsScalar, typename RhsScalar> struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_NEQ> {
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_NEQ> : binary_op_base<LhsScalar,RhsScalar>
+{
   typedef bool result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_cmp_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a!=b;}
@@ -216,7 +247,9 @@ template<typename LhsScalar, typename RhsScalar> struct scalar_cmp_op<LhsScalar,
   *
   * \sa MatrixBase::stableNorm(), class Redux
   */
-template<typename Scalar> struct scalar_hypot_op<Scalar,Scalar> {
+template<typename Scalar>
+struct scalar_hypot_op<Scalar,Scalar> : binary_op_base<Scalar,Scalar>
+{
   EIGEN_EMPTY_STRUCT_CTOR(scalar_hypot_op)
 //   typedef typename NumTraits<Scalar>::Real result_type;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& _x, const Scalar& _y) const
@@ -250,7 +283,9 @@ struct functor_traits<scalar_hypot_op<Scalar,Scalar> > {
 /** \internal
   * \brief Template functor to compute the pow of two scalars
   */
-template<typename Scalar, typename OtherScalar> struct scalar_binary_pow_op {
+template<typename Scalar, typename OtherScalar>
+struct scalar_binary_pow_op  : binary_op_base<Scalar,OtherScalar>
+{
   typedef typename ScalarBinaryOpTraits<Scalar,OtherScalar,scalar_binary_pow_op>::ReturnType result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_binary_pow_op)
   EIGEN_DEVICE_FUNC
@@ -270,7 +305,9 @@ struct functor_traits<scalar_binary_pow_op<Scalar,OtherScalar> > {
   *
   * \sa class CwiseBinaryOp, MatrixBase::operator-
   */
-template<typename LhsScalar,typename RhsScalar> struct scalar_difference_op {
+template<typename LhsScalar,typename RhsScalar>
+struct scalar_difference_op : binary_op_base<LhsScalar,RhsScalar>
+{
   typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_difference_op>::ReturnType result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_difference_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a - b; }
@@ -291,7 +328,9 @@ struct functor_traits<scalar_difference_op<LhsScalar,RhsScalar> > {
   *
   * \sa class CwiseBinaryOp, Cwise::operator/()
   */
-template<typename LhsScalar,typename RhsScalar> struct scalar_quotient_op {
+template<typename LhsScalar,typename RhsScalar>
+struct scalar_quotient_op  : binary_op_base<LhsScalar,RhsScalar>
+{
   typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_quotient_op>::ReturnType result_type;
   EIGEN_EMPTY_STRUCT_CTOR(scalar_quotient_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a / b; }
@@ -363,7 +402,8 @@ template<> struct functor_traits<scalar_boolean_xor_op> {
   *
   * \sa class CwiseBinaryOp, Cwise::igamma
   */
-template<typename Scalar> struct scalar_igamma_op {
+template<typename Scalar> struct scalar_igamma_op : binary_op_base<Scalar,Scalar>
+{
   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);
@@ -388,7 +428,8 @@ struct functor_traits<scalar_igamma_op<Scalar> > {
   *
   * \sa class CwiseBinaryOp, Cwise::igammac
   */
-template<typename Scalar> struct scalar_igammac_op {
+template<typename Scalar> struct scalar_igammac_op : binary_op_base<Scalar,Scalar>
+{
   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);
@@ -411,6 +452,47 @@ struct functor_traits<scalar_igammac_op<Scalar> > {
 
 //---------- binary functors bound to a constant, thus appearing as a unary functor ----------
 
+// The following two classes permits to turn any binary functor into a unary one with one argument bound to a constant value.
+// They are analogues to std::binder1st/binder2nd but with the following differences:
+//  - they are compatible with packetOp
+//  - they are portable across C++ versions (the std::binder* are deprecated in C++11)
+template<typename BinaryOp> struct bind1st_op : BinaryOp {
+
+  typedef typename BinaryOp::first_argument_type  first_argument_type;
+  typedef typename BinaryOp::second_argument_type second_argument_type;
+  typedef typename BinaryOp::result_type          result_type;
+
+  bind1st_op(const first_argument_type &val) : m_value(val) {}
+
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const second_argument_type& b) const { return BinaryOp::operator()(m_value,b); }
+
+  template<typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& b) const
+  { return BinaryOp::packetOp(internal::pset1<Packet>(m_value), b); }
+
+  first_argument_type m_value;
+};
+template<typename BinaryOp> struct functor_traits<bind1st_op<BinaryOp> > : functor_traits<BinaryOp> {};
+
+
+template<typename BinaryOp> struct bind2nd_op : BinaryOp {
+
+  typedef typename BinaryOp::first_argument_type  first_argument_type;
+  typedef typename BinaryOp::second_argument_type second_argument_type;
+  typedef typename BinaryOp::result_type          result_type;
+
+  bind2nd_op(const second_argument_type &val) : m_value(val) {}
+
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const first_argument_type& a) const { return BinaryOp::operator()(a,m_value); }
+
+  template<typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+  { return BinaryOp::packetOp(a,internal::pset1<Packet>(m_value)); }
+
+  second_argument_type m_value;
+};
+template<typename BinaryOp> struct functor_traits<bind2nd_op<BinaryOp> > : functor_traits<BinaryOp> {};
+
 /** \internal
   * \brief Template functor to multiply a scalar by a fixed other one
   *
@@ -442,17 +524,6 @@ template<typename Scalar>
 struct functor_traits<scalar_multiple_op<Scalar> >
 { enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
 
-template<typename Scalar1, typename Scalar2>
-struct scalar_multiple2_op {
-  typedef typename ScalarBinaryOpTraits<Scalar1,Scalar2>::ReturnType result_type;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_multiple2_op(const scalar_multiple2_op& other) : m_other(other.m_other) { }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_multiple2_op(const Scalar2& other) : m_other(other) { }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const Scalar1& a) const { return a * m_other; }
-  typename add_const_on_value_type<typename NumTraits<Scalar2>::Nested>::type m_other;
-};
-template<typename Scalar1,typename Scalar2>
-struct functor_traits<scalar_multiple2_op<Scalar1,Scalar2> >
-{ enum { Cost = NumTraits<Scalar1>::MulCost, PacketAccess = false }; };
 
 /** \internal
   * \brief Template functor to divide a scalar by a fixed other one
@@ -477,17 +548,6 @@ template<typename Scalar>
 struct functor_traits<scalar_quotient1_op<Scalar> >
 { enum { Cost = 2 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasDiv }; };
 
-template<typename Scalar1, typename Scalar2>
-struct scalar_quotient2_op {
-  typedef typename ScalarBinaryOpTraits<Scalar1,Scalar2>::ReturnType result_type;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_quotient2_op(const scalar_quotient2_op& other) : m_other(other.m_other) { }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_quotient2_op(const Scalar2& other) : m_other(other) { }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const Scalar1& a) const { return a / m_other; }
-  typename add_const_on_value_type<typename NumTraits<Scalar2>::Nested>::type m_other;
-};
-template<typename Scalar1,typename Scalar2>
-struct functor_traits<scalar_quotient2_op<Scalar1,Scalar2> >
-{ enum { Cost = 2 * NumTraits<Scalar1>::MulCost, PacketAccess = false }; };
 
 
 /** \internal
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index af3dce21b..84d505d4a 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -215,8 +215,6 @@ template<typename Scalar> struct scalar_betainc_op;
 template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_hypot_op;
 template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_product_op;
 template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_quotient_op;
-template<typename LhsScalar,typename RhsScalar> struct scalar_multiple2_op;
-template<typename LhsScalar,typename RhsScalar> struct scalar_quotient2_op;
 template<typename ScalarX, typename ScalarY> struct scalar_binary_pow_op;
 
 } // end namespace internal
diff --git a/Eigen/src/plugins/CommonCwiseUnaryOps.h b/Eigen/src/plugins/CommonCwiseUnaryOps.h
index 927167aff..80dc46cd4 100644
--- a/Eigen/src/plugins/CommonCwiseUnaryOps.h
+++ b/Eigen/src/plugins/CommonCwiseUnaryOps.h
@@ -14,7 +14,6 @@
 
 /** \internal Represents a scalar multiple of an expression */
 typedef CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const Derived> ScalarMultipleReturnType;
-typedef CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, const Derived> ScalarComplexMultipleReturnType;
 
 /** \internal Represents a quotient of an expression by a scalar*/
 typedef CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>, const Derived> ScalarQuotient1ReturnType;
@@ -73,15 +72,15 @@ operator/(const Scalar& scalar) const
 /** Overloaded for efficiently multipling with compatible scalar types */
 template <typename T>
 EIGEN_DEVICE_FUNC inline
-typename internal::enable_if<ScalarBinaryOpTraits<T,Scalar>::Defined,
-                             const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,T>, const Derived> >::type
+typename internal::enable_if<ScalarBinaryOpTraits<Scalar,T>::Defined,
+                             const CwiseUnaryOp<internal::bind2nd_op<internal::scalar_product_op<Scalar,T> >, const Derived> >::type
 operator*(const T& scalar) const
 {
 #ifdef EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN
   EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN
 #endif
-  return CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,T>, const Derived>(
-            derived(), internal::scalar_multiple2_op<Scalar,T>(scalar) );
+  typedef internal::bind2nd_op<internal::scalar_product_op<Scalar,T> > op;
+  return CwiseUnaryOp<op, const Derived>(derived(), op(scalar) );
 }
 
 EIGEN_DEVICE_FUNC
@@ -91,28 +90,28 @@ operator*(const Scalar& scalar, const StorageBaseType& matrix)
 
 template <typename T>
 EIGEN_DEVICE_FUNC inline friend
-typename internal::enable_if<ScalarBinaryOpTraits<Scalar,T>::Defined,
-                             const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,T>, const Derived> >::type
+typename internal::enable_if<ScalarBinaryOpTraits<T,Scalar>::Defined,
+                             const CwiseUnaryOp<internal::bind1st_op<internal::scalar_product_op<T,Scalar> >, const Derived> >::type
 operator*(const T& scalar, const StorageBaseType& matrix)
 {
 #ifdef EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN
   EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN
 #endif
-  return CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,T>, const Derived>(
-            matrix.derived(), internal::scalar_multiple2_op<Scalar,T>(scalar) );
+  typedef internal::bind1st_op<internal::scalar_product_op<T,Scalar> > op;
+  return CwiseUnaryOp<op, const Derived>(matrix.derived(), op(scalar) );
 }
 
 template <typename T>
 EIGEN_DEVICE_FUNC inline
 typename internal::enable_if<ScalarBinaryOpTraits<Scalar,T>::Defined,
-                             const CwiseUnaryOp<internal::scalar_quotient2_op<Scalar,T>, const Derived> >::type
+                             const CwiseUnaryOp<internal::bind2nd_op<internal::scalar_quotient_op<Scalar,T> >, const Derived> >::type
 operator/(const T& scalar) const
 {
 #ifdef EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN
   EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN
 #endif
-  return CwiseUnaryOp<internal::scalar_quotient2_op<Scalar,T>, const Derived>(
-            derived(), internal::scalar_quotient2_op<Scalar,T>(scalar) );
+  typedef internal::bind2nd_op<internal::scalar_quotient_op<Scalar,T> > op;
+  return CwiseUnaryOp<op, const Derived>(derived(), op(scalar) );
 }
 
 template<class NewType> struct CastXpr { typedef typename internal::cast_return_type<Derived,const CwiseUnaryOp<internal::scalar_cast_op<Scalar, NewType>, const Derived> >::type Type; };
diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
index ba61288a3..0ed91fdb7 100755
--- a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
+++ b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
@@ -426,18 +426,18 @@ struct auto_diff_special_op<_DerType, true>
   }
 
 
-  inline const AutoDiffScalar<typename CwiseUnaryOp<scalar_multiple2_op<Scalar,Real>, DerType>::Type >
+  inline const AutoDiffScalar<typename CwiseUnaryOp<bind2nd_op<scalar_product_op<Scalar,Real> >, DerType>::Type >
   operator*(const Real& other) const
   {
-    return AutoDiffScalar<typename CwiseUnaryOp<scalar_multiple2_op<Scalar,Real>, DerType>::Type >(
+    return AutoDiffScalar<typename CwiseUnaryOp<bind2nd_op<scalar_product_op<Scalar,Real> >, DerType>::Type >(
       derived().value() * other,
       derived().derivatives() * other);
   }
 
-  friend inline const AutoDiffScalar<typename CwiseUnaryOp<scalar_multiple2_op<Scalar,Real>, DerType>::Type >
+  friend inline const AutoDiffScalar<typename CwiseUnaryOp<bind1st_op<scalar_product_op<Real,Scalar> >, DerType>::Type >
   operator*(const Real& other, const AutoDiffScalar<_DerType>& a)
   {
-    return AutoDiffScalar<typename CwiseUnaryOp<scalar_multiple2_op<Scalar,Real>, DerType>::Type >(
+    return AutoDiffScalar<typename CwiseUnaryOp<bind1st_op<scalar_product_op<Real,Scalar> >, DerType>::Type >(
       a.value() * other,
       a.derivatives() * other);
   }

From 39781dc1e230a2ece36b484dbef76f66d2136f86 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 14 Jun 2016 11:03:26 +0200
Subject: [PATCH 46/86] Fix compilation of evaluator unit test

---
 test/evaluators.cpp | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/test/evaluators.cpp b/test/evaluators.cpp
index 876dffe22..aed5a05a7 100644
--- a/test/evaluators.cpp
+++ b/test/evaluators.cpp
@@ -21,7 +21,7 @@ namespace Eigen {
   EIGEN_STRONG_INLINE
   DstXprType& copy_using_evaluator(const EigenBase<DstXprType> &dst, const SrcXprType &src)
   {
-    call_assignment(dst.const_cast_derived(), src.derived(), internal::assign_op<typename DstXprType::Scalar>());
+    call_assignment(dst.const_cast_derived(), src.derived(), internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());
     return dst.const_cast_derived();
   }
   
@@ -29,7 +29,7 @@ namespace Eigen {
   EIGEN_STRONG_INLINE
   const DstXprType& copy_using_evaluator(const NoAlias<DstXprType, StorageBase>& dst, const SrcXprType &src)
   {
-    call_assignment(dst, src.derived(), internal::assign_op<typename DstXprType::Scalar>());
+    call_assignment(dst, src.derived(), internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());
     return dst.expression();
   }
   
@@ -45,7 +45,7 @@ namespace Eigen {
     dst.const_cast_derived().resizeLike(src.derived());
   #endif
     
-    call_assignment(dst.const_cast_derived(), src.derived(), internal::assign_op<typename DstXprType::Scalar>());
+    call_assignment(dst.const_cast_derived(), src.derived(), internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());
     return dst.const_cast_derived();
   }
 
@@ -53,28 +53,28 @@ namespace Eigen {
   void add_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src)
   {
     typedef typename DstXprType::Scalar Scalar;
-    call_assignment(const_cast<DstXprType&>(dst), src.derived(), internal::add_assign_op<Scalar>());
+    call_assignment(const_cast<DstXprType&>(dst), src.derived(), internal::add_assign_op<Scalar,typename SrcXprType::Scalar>());
   }
 
   template<typename DstXprType, typename SrcXprType>
   void subtract_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src)
   {
     typedef typename DstXprType::Scalar Scalar;
-    call_assignment(const_cast<DstXprType&>(dst), src.derived(), internal::sub_assign_op<Scalar>());
+    call_assignment(const_cast<DstXprType&>(dst), src.derived(), internal::sub_assign_op<Scalar,typename SrcXprType::Scalar>());
   }
 
   template<typename DstXprType, typename SrcXprType>
   void multiply_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src)
   {
     typedef typename DstXprType::Scalar Scalar;
-    call_assignment(dst.const_cast_derived(), src.derived(), internal::mul_assign_op<Scalar>());
+    call_assignment(dst.const_cast_derived(), src.derived(), internal::mul_assign_op<Scalar,typename SrcXprType::Scalar>());
   }
 
   template<typename DstXprType, typename SrcXprType>
   void divide_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src)
   {
     typedef typename DstXprType::Scalar Scalar;
-    call_assignment(dst.const_cast_derived(), src.derived(), internal::div_assign_op<Scalar>());
+    call_assignment(dst.const_cast_derived(), src.derived(), internal::div_assign_op<Scalar,typename SrcXprType::Scalar>());
   }
   
   template<typename DstXprType, typename SrcXprType>

From 64fcfd314f594bbc358aa8e2b8dc8def9b288b66 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 14 Jun 2016 11:26:57 +0200
Subject: [PATCH 47/86] Implement scalar multiples and division by a scalar as
 a binary-expression with a constant expression. This slightly complexifies
 the type of the expressions and implies that we now have to distinguish
 between scalar*expr and expr*scalar to catch scalar-multiple expression
 (e.g., see BlasUtil.h), but this brings several advantages: - it makes it
 clear on each side the scalar is applied, - it clearly reflects that we are
 dealing with a binary-expression, - the complexity of the type is hidden
 through macros defined at the end of Macros.h, - distinguishing between
 "scalar op expr" and "expr op scalar" is important to support non commutative
 fields (like quaternions) - "scalar op expr" is now fully equivalent to
 "ConstantExpr(scalar) op expr" - scalar_multiple_op, scalar_quotient1_op and
 scalar_quotient2_op are not used anymore in officially supported modules
 (still used in Tensor)

---
 Eigen/src/Core/DiagonalMatrix.h           |  9 ++-
 Eigen/src/Core/ProductEvaluators.h        | 37 +++++++-----
 Eigen/src/Core/SelfAdjointView.h          |  2 +-
 Eigen/src/Core/util/BlasUtil.h            | 24 ++++++++
 Eigen/src/Core/util/ForwardDeclarations.h |  2 -
 Eigen/src/Core/util/Macros.h              | 45 ++++++++++++++
 Eigen/src/Core/util/XprHelper.h           | 14 +++++
 Eigen/src/Geometry/AlignedBox.h           |  8 +--
 Eigen/src/plugins/ArrayCwiseBinaryOps.h   |  1 +
 Eigen/src/plugins/CommonCwiseBinaryOps.h  | 30 ++++++++++
 Eigen/src/plugins/CommonCwiseUnaryOps.h   | 71 -----------------------
 test/array.cpp                            |  2 +-
 12 files changed, 146 insertions(+), 99 deletions(-)

diff --git a/Eigen/src/Core/DiagonalMatrix.h b/Eigen/src/Core/DiagonalMatrix.h
index aa619dd5c..d6f89bced 100644
--- a/Eigen/src/Core/DiagonalMatrix.h
+++ b/Eigen/src/Core/DiagonalMatrix.h
@@ -71,18 +71,17 @@ class DiagonalBase : public EigenBase<Derived>
       return InverseReturnType(diagonal().cwiseInverse());
     }
     
-    typedef DiagonalWrapper<const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DiagonalVectorType> > ScalarMultipleReturnType;
     EIGEN_DEVICE_FUNC
-    inline const ScalarMultipleReturnType
+    inline const DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType,Scalar,product) >
     operator*(const Scalar& scalar) const
     {
-      return ScalarMultipleReturnType(diagonal() * scalar);
+      return DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType,Scalar,product) >(diagonal() * scalar);
     }
     EIGEN_DEVICE_FUNC
-    friend inline const ScalarMultipleReturnType
+    friend inline const DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,DiagonalVectorType,product) >
     operator*(const Scalar& scalar, const DiagonalBase& other)
     {
-      return ScalarMultipleReturnType(other.diagonal() * scalar);
+      return DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,DiagonalVectorType,product) >(scalar * other.diagonal());
     }
 };
 
diff --git a/Eigen/src/Core/ProductEvaluators.h b/Eigen/src/Core/ProductEvaluators.h
index 71ae6e54c..77549e709 100644
--- a/Eigen/src/Core/ProductEvaluators.h
+++ b/Eigen/src/Core/ProductEvaluators.h
@@ -35,22 +35,28 @@ struct evaluator<Product<Lhs, Rhs, Options> >
   EIGEN_DEVICE_FUNC explicit evaluator(const XprType& xpr) : Base(xpr) {}
 };
  
-// Catch scalar * ( A * B ) and transform it to (A*scalar) * B
+// 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_assume_aliasing<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>,  const Product<Lhs, Rhs, DefaultProduct>  > >
+template<typename Lhs, typename Rhs, typename Scalar1, typename Scalar2, typename Plain1>
+struct evaluator_assume_aliasing<CwiseBinaryOp<internal::scalar_product_op<Scalar1,Scalar2>,
+                                               const CwiseNullaryOp<internal::scalar_constant_op<Scalar1>, Plain1>,
+                                               const Product<Lhs, Rhs, DefaultProduct> > >
 {
   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>  > > 
- : public evaluator<Product<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>,const Lhs>, Rhs, DefaultProduct> >
+template<typename Lhs, typename Rhs, typename Scalar1, typename Scalar2, typename Plain1>
+struct evaluator<CwiseBinaryOp<internal::scalar_product_op<Scalar1,Scalar2>,
+                               const CwiseNullaryOp<internal::scalar_constant_op<Scalar1>, Plain1>,
+                               const Product<Lhs, Rhs, DefaultProduct> > >
+ : public evaluator<Product<EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar1,Lhs,product), Rhs, DefaultProduct> >
 {
-  typedef CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const Product<Lhs, Rhs, DefaultProduct> > XprType;
-  typedef evaluator<Product<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>,const Lhs>, Rhs, DefaultProduct> > Base;
-  
+  typedef CwiseBinaryOp<internal::scalar_product_op<Scalar1,Scalar2>,
+                               const CwiseNullaryOp<internal::scalar_constant_op<Scalar1>, Plain1>,
+                               const Product<Lhs, Rhs, DefaultProduct> > XprType;
+  typedef evaluator<Product<EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar1,Lhs,product), Rhs, DefaultProduct> > Base;
+
   EIGEN_DEVICE_FUNC explicit evaluator(const XprType& xpr)
-    : Base(xpr.functor().m_other * xpr.nestedExpression().lhs() * xpr.nestedExpression().rhs())
+    : Base(xpr.lhs().functor().m_other * xpr.rhs().lhs() * xpr.rhs().rhs())
   {}
 };
 
@@ -171,16 +177,17 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::sub_assign_op<
 // Dense ?= scalar * Product
 // TODO we should apply that rule if that's really helpful
 // for instance, this is not good for inner products
-template< typename DstXprType, typename Lhs, typename Rhs, typename AssignFunc, typename Scalar, typename ScalarBis>
-struct Assignment<DstXprType, CwiseUnaryOp<internal::scalar_multiple_op<ScalarBis>,
+template< typename DstXprType, typename Lhs, typename Rhs, typename AssignFunc, typename Scalar, typename ScalarBis, typename Plain>
+struct Assignment<DstXprType, CwiseBinaryOp<internal::scalar_product_op<ScalarBis,Scalar>, const CwiseNullaryOp<internal::scalar_constant_op<ScalarBis>,Plain>,
                                            const Product<Lhs,Rhs,DefaultProduct> >, AssignFunc, Dense2Dense, Scalar>
 {
-  typedef CwiseUnaryOp<internal::scalar_multiple_op<ScalarBis>,
-                       const Product<Lhs,Rhs,DefaultProduct> > SrcXprType;
+  typedef CwiseBinaryOp<internal::scalar_product_op<ScalarBis,Scalar>,
+                        const CwiseNullaryOp<internal::scalar_constant_op<ScalarBis>,Plain>,
+                        const Product<Lhs,Rhs,DefaultProduct> > SrcXprType;
   static EIGEN_STRONG_INLINE
   void run(DstXprType &dst, const SrcXprType &src, const AssignFunc& func)
   {
-    call_assignment_no_alias(dst, (src.functor().m_other * src.nestedExpression().lhs())*src.nestedExpression().rhs(), func);
+    call_assignment_no_alias(dst, (src.lhs().functor().m_other * src.rhs().lhs())*src.rhs().rhs(), func);
   }
 };
 
diff --git a/Eigen/src/Core/SelfAdjointView.h b/Eigen/src/Core/SelfAdjointView.h
index 92c541f08..62d4180da 100644
--- a/Eigen/src/Core/SelfAdjointView.h
+++ b/Eigen/src/Core/SelfAdjointView.h
@@ -129,7 +129,7 @@ template<typename _MatrixType, unsigned int UpLo> class SelfAdjointView
     }
     
     friend EIGEN_DEVICE_FUNC
-    const SelfAdjointView<const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>,MatrixType>,UpLo>
+    const SelfAdjointView<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,MatrixType,product),UpLo>
     operator*(const Scalar& s, const SelfAdjointView& mat)
     {
       return (s*mat.nestedExpression()).template selfadjointView<UpLo>();
diff --git a/Eigen/src/Core/util/BlasUtil.h b/Eigen/src/Core/util/BlasUtil.h
index c163f1458..7e8f90d88 100755
--- a/Eigen/src/Core/util/BlasUtil.h
+++ b/Eigen/src/Core/util/BlasUtil.h
@@ -293,6 +293,30 @@ struct blas_traits<CwiseUnaryOp<scalar_conjugate_op<Scalar>, NestedXpr> >
 };
 
 // pop scalar multiple
+template<typename Scalar, typename NestedXpr, typename Plain>
+struct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain>, NestedXpr> >
+ : blas_traits<NestedXpr>
+{
+  typedef blas_traits<NestedXpr> Base;
+  typedef CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain>, NestedXpr> XprType;
+  typedef typename Base::ExtractType ExtractType;
+  static inline ExtractType extract(const XprType& x) { return Base::extract(x.rhs()); }
+  static inline Scalar extractScalarFactor(const XprType& x)
+  { return x.lhs().functor().m_other * Base::extractScalarFactor(x.rhs()); }
+};
+template<typename Scalar, typename NestedXpr, typename Plain>
+struct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, NestedXpr, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain> > >
+ : blas_traits<NestedXpr>
+{
+  typedef blas_traits<NestedXpr> Base;
+  typedef CwiseBinaryOp<scalar_product_op<Scalar>, NestedXpr, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain> > XprType;
+  typedef typename Base::ExtractType ExtractType;
+  static inline ExtractType extract(const XprType& x) { return Base::extract(x.lhs()); }
+  static inline Scalar extractScalarFactor(const XprType& x)
+  { return Base::extractScalarFactor(x.lhs()) * x.rhs().functor().m_other; }
+};
+
+// pop scalar multiple (using deprecated scalar_multiple_op)
 template<typename Scalar, typename NestedXpr>
 struct blas_traits<CwiseUnaryOp<scalar_multiple_op<Scalar>, NestedXpr> >
  : blas_traits<NestedXpr>
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index 84d505d4a..8334446d6 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -201,8 +201,6 @@ template<typename Scalar> struct scalar_inverse_op;
 template<typename Scalar> struct scalar_square_op;
 template<typename Scalar> struct scalar_cube_op;
 template<typename Scalar, typename NewType> struct scalar_cast_op;
-template<typename Scalar> struct scalar_multiple_op;
-template<typename Scalar> struct scalar_quotient1_op;
 template<typename Scalar> struct scalar_random_op;
 template<typename Scalar> struct scalar_add_op;
 template<typename Scalar> struct scalar_constant_op;
diff --git a/Eigen/src/Core/util/Macros.h b/Eigen/src/Core/util/Macros.h
index a51572463..f3c6512c9 100644
--- a/Eigen/src/Core/util/Macros.h
+++ b/Eigen/src/Core/util/Macros.h
@@ -895,6 +895,51 @@ namespace Eigen {
     return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME)(derived(), other.derived()); \
   }
 
+#define EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(EXPR,SCALAR,OPNAME) \
+  CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<typename internal::traits<EXPR>::Scalar,SCALAR>, const EXPR, \
+                const typename internal::plain_constant_type<EXPR,SCALAR>::type>
+
+#define EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(SCALAR,EXPR,OPNAME) \
+  CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<SCALAR,typename internal::traits<EXPR>::Scalar>, \
+                const typename internal::plain_constant_type<EXPR,SCALAR>::type, const EXPR>
+
+#define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME) \
+  EIGEN_DEVICE_FUNC inline \
+  const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,Scalar,OPNAME) \
+  (METHOD)(const Scalar& scalar) const { \
+    return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,Scalar,OPNAME)(derived(), \
+           typename internal::plain_constant_type<Derived,Scalar>::type(derived().rows(), derived().cols(), scalar)); \
+  } \
+  \
+  template <typename T> EIGEN_DEVICE_FUNC inline \
+  typename internal::enable_if<ScalarBinaryOpTraits<Scalar,T>::Defined, \
+                               const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,T,OPNAME) >::type \
+  (METHOD)(const T& scalar) const { \
+    return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,T,OPNAME)(derived(), \
+           typename internal::plain_constant_type<Derived,T>::type(derived().rows(), derived().cols(), scalar)); \
+  }
+
+#define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
+  EIGEN_DEVICE_FUNC inline friend \
+  const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,OPNAME) \
+  (METHOD)(const Scalar& scalar, const StorageBaseType& matrix) { \
+    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,OPNAME)( \
+           typename internal::plain_constant_type<Derived,Scalar>::type(matrix.derived().rows(), matrix.derived().cols(), scalar), matrix.derived()); \
+  } \
+  \
+  template <typename T> EIGEN_DEVICE_FUNC inline friend \
+  typename internal::enable_if<ScalarBinaryOpTraits<T,Scalar>::Defined, \
+                               const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(T,Derived,OPNAME) >::type \
+  (METHOD)(const T& scalar, const StorageBaseType& matrix) { \
+    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(T,Derived,OPNAME)( \
+           typename internal::plain_constant_type<Derived,T>::type(matrix.derived().rows(), matrix.derived().cols(), scalar), matrix.derived()); \
+  }
+
+#define EIGEN_MAKE_SCALAR_BINARY_OP(METHOD,OPNAME) \
+  EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
+  EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME)
+
+
 #ifdef EIGEN_EXCEPTIONS
 #  define EIGEN_THROW_X(X) throw X
 #  define EIGEN_THROW throw
diff --git a/Eigen/src/Core/util/XprHelper.h b/Eigen/src/Core/util/XprHelper.h
index 828813161..c41c408b0 100644
--- a/Eigen/src/Core/util/XprHelper.h
+++ b/Eigen/src/Core/util/XprHelper.h
@@ -576,6 +576,20 @@ struct plain_diag_type
   >::type type;
 };
 
+template<typename Expr,typename Scalar = typename Expr::Scalar>
+struct plain_constant_type
+{
+  enum { Options = (traits<Expr>::Flags&RowMajorBit)?RowMajor:0 };
+
+  typedef Array<Scalar,  traits<Expr>::RowsAtCompileTime,   traits<Expr>::ColsAtCompileTime,
+                Options, traits<Expr>::MaxRowsAtCompileTime,traits<Expr>::MaxColsAtCompileTime> array_type;
+
+  typedef Matrix<Scalar,  traits<Expr>::RowsAtCompileTime,   traits<Expr>::ColsAtCompileTime,
+                 Options, traits<Expr>::MaxRowsAtCompileTime,traits<Expr>::MaxColsAtCompileTime> matrix_type;
+
+  typedef CwiseNullaryOp<scalar_constant_op<Scalar>, const typename conditional<is_same< typename traits<Expr>::XprKind, MatrixXpr >::value, matrix_type, array_type>::type > type;
+};
+
 template<typename ExpressionType>
 struct is_lvalue
 {
diff --git a/Eigen/src/Geometry/AlignedBox.h b/Eigen/src/Geometry/AlignedBox.h
index aeb043a6c..d20d17492 100644
--- a/Eigen/src/Geometry/AlignedBox.h
+++ b/Eigen/src/Geometry/AlignedBox.h
@@ -36,8 +36,9 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
   typedef NumTraits<Scalar>                         ScalarTraits;
   typedef Eigen::Index                              Index; ///< \deprecated since Eigen 3.3
   typedef typename ScalarTraits::Real               RealScalar;
-  typedef typename ScalarTraits::NonInteger      NonInteger;
+  typedef typename ScalarTraits::NonInteger         NonInteger;
   typedef Matrix<Scalar,AmbientDimAtCompileTime,1>  VectorType;
+  typedef CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> VectorTypeSum;
 
   /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */
   enum CornerType
@@ -111,10 +112,9 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
   inline VectorType& (max)() { return m_max; }
 
   /** \returns the center of the box */
-  inline const CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>,
-                            const CwiseBinaryOp<internal::scalar_sum_op<Scalar,Scalar>, const VectorType, const VectorType> >
+  inline const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(VectorTypeSum, RealScalar, quotient)
   center() const
-  { return (m_min+m_max)/2; }
+  { return (m_min+m_max)/RealScalar(2); }
 
   /** \returns the lengths of the sides of the bounding box.
     * Note that this function does not get the same
diff --git a/Eigen/src/plugins/ArrayCwiseBinaryOps.h b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
index 7f7d0dbf4..351762e82 100644
--- a/Eigen/src/plugins/ArrayCwiseBinaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
@@ -1,3 +1,4 @@
+
 /** \returns an expression of the coefficient wise product of \c *this and \a other
   *
   * \sa MatrixBase::cwiseProduct
diff --git a/Eigen/src/plugins/CommonCwiseBinaryOps.h b/Eigen/src/plugins/CommonCwiseBinaryOps.h
index f16be7bea..c5eaea16d 100644
--- a/Eigen/src/plugins/CommonCwiseBinaryOps.h
+++ b/Eigen/src/plugins/CommonCwiseBinaryOps.h
@@ -45,3 +45,33 @@ binaryExpr(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other, const Cu
   return CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived>(derived(), other.derived(), func);
 }
 
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+EIGEN_MAKE_SCALAR_BINARY_OP(operator*,product);
+#else
+/** \returns an expression of \c *this scaled by the scalar factor \a scalar
+  *
+  * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
+  */
+template<typename T>
+const CwiseBinaryOp<internal::scalar_product_op<Scalar,T>,Derived,Constant<Scalar> > operator*(const T& scalar) const;
+/** \returns an expression of \c *this scaled by the scalar factor \a scalar
+  *
+  * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
+  */
+template<typename T> friend
+const CwiseBinaryOp<internal::scalar_product_op<T,Scalar>,Constant<Scalar>,Derived> operator*(const T& scalar, const StorageBaseType& expr);
+#endif
+
+
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(operator/,quotient);
+#else
+/** \returns an expression of \c *this divided by the scalar value \a scalar
+  *
+  * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
+  */
+template<typename T>
+const CwiseBinaryOp<internal::scalar_quotient_op<Scalar,T>,Derived,Constant<Scalar> > operator/(const T& scalar) const;
+#endif
diff --git a/Eigen/src/plugins/CommonCwiseUnaryOps.h b/Eigen/src/plugins/CommonCwiseUnaryOps.h
index 80dc46cd4..6cd5479a0 100644
--- a/Eigen/src/plugins/CommonCwiseUnaryOps.h
+++ b/Eigen/src/plugins/CommonCwiseUnaryOps.h
@@ -12,11 +12,6 @@
 
 #ifndef EIGEN_PARSED_BY_DOXYGEN
 
-/** \internal Represents a scalar multiple of an expression */
-typedef CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const Derived> ScalarMultipleReturnType;
-
-/** \internal Represents a quotient of an expression by a scalar*/
-typedef CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>, const Derived> ScalarQuotient1ReturnType;
 /** \internal the return type of conjugate() */
 typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
                     const CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, const Derived>,
@@ -38,7 +33,6 @@ typedef CwiseUnaryOp<internal::scalar_imag_op<Scalar>, const Derived> ImagReturn
 typedef CwiseUnaryView<internal::scalar_imag_ref_op<Scalar>, Derived> NonConstImagReturnType;
 
 typedef CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const Derived> NegativeReturnType;
-//typedef CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>, const Derived>
 
 #endif // not EIGEN_PARSED_BY_DOXYGEN
 
@@ -49,71 +43,6 @@ inline const NegativeReturnType
 operator-() const { return NegativeReturnType(derived()); }
 
 
-/** \returns an expression of \c *this scaled by the scalar factor \a scalar */
-EIGEN_DEVICE_FUNC
-inline const ScalarMultipleReturnType
-operator*(const Scalar& scalar) const
-{
-  return ScalarMultipleReturnType(derived(), internal::scalar_multiple_op<Scalar>(scalar));
-}
-
-#ifdef EIGEN_PARSED_BY_DOXYGEN
-const ScalarMultipleReturnType operator*(const RealScalar& scalar) const;
-#endif
-
-/** \returns an expression of \c *this divided by the scalar value \a scalar */
-EIGEN_DEVICE_FUNC
-inline const ScalarQuotient1ReturnType
-operator/(const Scalar& scalar) const
-{
-  return ScalarQuotient1ReturnType(derived(), internal::scalar_quotient1_op<Scalar>(scalar));
-}
-
-/** Overloaded for efficiently multipling with compatible scalar types */
-template <typename T>
-EIGEN_DEVICE_FUNC inline
-typename internal::enable_if<ScalarBinaryOpTraits<Scalar,T>::Defined,
-                             const CwiseUnaryOp<internal::bind2nd_op<internal::scalar_product_op<Scalar,T> >, const Derived> >::type
-operator*(const T& scalar) const
-{
-#ifdef EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN
-  EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN
-#endif
-  typedef internal::bind2nd_op<internal::scalar_product_op<Scalar,T> > op;
-  return CwiseUnaryOp<op, const Derived>(derived(), op(scalar) );
-}
-
-EIGEN_DEVICE_FUNC
-inline friend const ScalarMultipleReturnType
-operator*(const Scalar& scalar, const StorageBaseType& matrix)
-{ return matrix*scalar; }
-
-template <typename T>
-EIGEN_DEVICE_FUNC inline friend
-typename internal::enable_if<ScalarBinaryOpTraits<T,Scalar>::Defined,
-                             const CwiseUnaryOp<internal::bind1st_op<internal::scalar_product_op<T,Scalar> >, const Derived> >::type
-operator*(const T& scalar, const StorageBaseType& matrix)
-{
-#ifdef EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN
-  EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN
-#endif
-  typedef internal::bind1st_op<internal::scalar_product_op<T,Scalar> > op;
-  return CwiseUnaryOp<op, const Derived>(matrix.derived(), op(scalar) );
-}
-
-template <typename T>
-EIGEN_DEVICE_FUNC inline
-typename internal::enable_if<ScalarBinaryOpTraits<Scalar,T>::Defined,
-                             const CwiseUnaryOp<internal::bind2nd_op<internal::scalar_quotient_op<Scalar,T> >, const Derived> >::type
-operator/(const T& scalar) const
-{
-#ifdef EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN
-  EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN
-#endif
-  typedef internal::bind2nd_op<internal::scalar_quotient_op<Scalar,T> > op;
-  return CwiseUnaryOp<op, const Derived>(derived(), op(scalar) );
-}
-
 template<class NewType> struct CastXpr { typedef typename internal::cast_return_type<Derived,const CwiseUnaryOp<internal::scalar_cast_op<Scalar, NewType>, const Derived> >::type Type; };
 
 /** \returns an expression of *this with the \a Scalar type casted to
diff --git a/test/array.cpp b/test/array.cpp
index bd470d5f7..0416ec5d2 100644
--- a/test/array.cpp
+++ b/test/array.cpp
@@ -807,7 +807,7 @@ void test_array()
   VERIFY((internal::is_same< internal::global_math_functions_filtering_base<int>::type, int >::value));
   VERIFY((internal::is_same< internal::global_math_functions_filtering_base<float>::type, float >::value));
   VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Array2i>::type, ArrayBase<Array2i> >::value));
-  typedef CwiseUnaryOp<internal::scalar_multiple_op<double>, ArrayXd > Xpr;
+  typedef CwiseUnaryOp<internal::scalar_abs_op<double>, ArrayXd > Xpr;
   VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type,
                            ArrayBase<Xpr>
                          >::value));

From deb8306e60c53f052d1df16dce38a4b6c6c98aab Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 14 Jun 2016 11:28:03 +0200
Subject: [PATCH 48/86] Move MatrixBase::operaotr*(UniformScaling) as a free
 function in Scaling.h, and fix return type.

---
 Eigen/src/Core/MatrixBase.h  |  4 +---
 Eigen/src/Geometry/Scaling.h | 11 +++++++----
 2 files changed, 8 insertions(+), 7 deletions(-)

diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h
index f63505fef..d9d2426ad 100644
--- a/Eigen/src/Core/MatrixBase.h
+++ b/Eigen/src/Core/MatrixBase.h
@@ -403,7 +403,6 @@ template<typename Derived> class MatrixBase
 
     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 };
@@ -416,8 +415,7 @@ template<typename Derived> class MatrixBase
     typedef Block<const Derived,
                   internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1,
                   internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne;
-    typedef CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>,
-                const ConstStartMinusOne > HNormalizedReturnType;
+    typedef EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(ConstStartMinusOne,Scalar,quotient) HNormalizedReturnType;
 
     inline const HNormalizedReturnType hnormalized() const;
 
diff --git a/Eigen/src/Geometry/Scaling.h b/Eigen/src/Geometry/Scaling.h
index 643138199..3e12681b0 100644
--- a/Eigen/src/Geometry/Scaling.h
+++ b/Eigen/src/Geometry/Scaling.h
@@ -107,12 +107,15 @@ public:
 /** \addtogroup Geometry_Module */
 //@{
 
-/** Concatenates a linear transformation matrix and a uniform scaling */
+/** Concatenates a linear transformation matrix and a uniform scaling
+  * \relates UniformScaling
+  */
 // NOTE this operator is defiend in MatrixBase and not as a friend function
 // of UniformScaling to fix an internal crash of Intel's ICC
-template<typename Derived> typename MatrixBase<Derived>::ScalarMultipleReturnType
-MatrixBase<Derived>::operator*(const UniformScaling<Scalar>& s) const
-{ return derived() * s.factor(); }
+template<typename Derived,typename Scalar>
+EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,Scalar,product)
+operator*(const MatrixBase<Derived>& matrix, const UniformScaling<Scalar>& s)
+{ return matrix.derived() * s.factor(); }
 
 /** Constructs a uniform scaling from scale factor \a s */
 static inline UniformScaling<float> Scaling(float s) { return UniformScaling<float>(s); }

From f5b1c7394537cc74978617383628c3b6b9399e57 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 14 Jun 2016 11:29:06 +0200
Subject: [PATCH 49/86] Set cost of constant expression to 0 (the cost should
 be amortized through the expression)

---
 Eigen/src/Core/functors/NullaryFunctors.h | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Eigen/src/Core/functors/NullaryFunctors.h b/Eigen/src/Core/functors/NullaryFunctors.h
index 78cc22277..eaa582f23 100644
--- a/Eigen/src/Core/functors/NullaryFunctors.h
+++ b/Eigen/src/Core/functors/NullaryFunctors.h
@@ -26,7 +26,8 @@ struct scalar_constant_op {
 };
 template<typename Scalar>
 struct functor_traits<scalar_constant_op<Scalar> >
-{ enum { Cost = 1, PacketAccess = packet_traits<Scalar>::Vectorizable, IsRepeatable = true }; };
+{ enum { Cost = 0 /* as the constant value should be loaded in register only once for the whole expression */,
+         PacketAccess = packet_traits<Scalar>::Vectorizable, IsRepeatable = true }; };
 
 template<typename Scalar> struct scalar_identity_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_identity_op)

From f57fd78e308c80d25b1f8c92ae8db2bdc5045a29 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 14 Jun 2016 11:29:54 +0200
Subject: [PATCH 50/86] Generalize coeff-wise sparse products to support
 different scalar types

---
 Eigen/src/SparseCore/SparseCwiseBinaryOp.h | 27 ++++++++++++----------
 1 file changed, 15 insertions(+), 12 deletions(-)

diff --git a/Eigen/src/SparseCore/SparseCwiseBinaryOp.h b/Eigen/src/SparseCore/SparseCwiseBinaryOp.h
index dd21eb8c5..aad7b7d79 100644
--- a/Eigen/src/SparseCore/SparseCwiseBinaryOp.h
+++ b/Eigen/src/SparseCore/SparseCwiseBinaryOp.h
@@ -28,6 +28,9 @@ namespace Eigen {
 //                         generic      sparse
 //  4 - dense op dense     product      dense
 //                         generic      dense
+//
+// TODO to ease compiler job, we could specialize product/quotient with a scalar
+//      and fallback to cwise-unary evaluator using bind1st_op and bind2nd_op.
 
 template<typename BinaryOp, typename Lhs, typename Rhs>
 class CwiseBinaryOpImpl<BinaryOp, Lhs, Rhs, Sparse>
@@ -323,12 +326,12 @@ protected:
 };
 
 // "sparse .* sparse"
-template<typename T, typename Lhs, typename Rhs>
-struct binary_evaluator<CwiseBinaryOp<scalar_product_op<T>, Lhs, Rhs>, IteratorBased, IteratorBased>
-  : evaluator_base<CwiseBinaryOp<scalar_product_op<T>, Lhs, Rhs> >
+template<typename T1, typename T2, typename Lhs, typename Rhs>
+struct binary_evaluator<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs>, IteratorBased, IteratorBased>
+  : evaluator_base<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs> >
 {
 protected:
-  typedef scalar_product_op<T> BinaryOp;
+  typedef scalar_product_op<T1,T2> BinaryOp;
   typedef typename evaluator<Lhs>::InnerIterator  LhsIterator;
   typedef typename evaluator<Rhs>::InnerIterator  RhsIterator;
   typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> XprType;
@@ -407,12 +410,12 @@ protected:
 };
 
 // "dense .* sparse"
-template<typename T, typename Lhs, typename Rhs>
-struct binary_evaluator<CwiseBinaryOp<scalar_product_op<T>, Lhs, Rhs>, IndexBased, IteratorBased>
-  : evaluator_base<CwiseBinaryOp<scalar_product_op<T>, Lhs, Rhs> >
+template<typename T1, typename T2, typename Lhs, typename Rhs>
+struct binary_evaluator<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs>, IndexBased, IteratorBased>
+  : evaluator_base<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs> >
 {
 protected:
-  typedef scalar_product_op<T> BinaryOp;
+  typedef scalar_product_op<T1,T2> BinaryOp;
   typedef evaluator<Lhs>  LhsEvaluator;
   typedef typename evaluator<Rhs>::InnerIterator  RhsIterator;
   typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> XprType;
@@ -480,12 +483,12 @@ protected:
 };
 
 // "sparse .* dense"
-template<typename T, typename Lhs, typename Rhs>
-struct binary_evaluator<CwiseBinaryOp<scalar_product_op<T>, Lhs, Rhs>, IteratorBased, IndexBased>
-  : evaluator_base<CwiseBinaryOp<scalar_product_op<T>, Lhs, Rhs> >
+template<typename T1, typename T2, typename Lhs, typename Rhs>
+struct binary_evaluator<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs>, IteratorBased, IndexBased>
+  : evaluator_base<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs> >
 {
 protected:
-  typedef scalar_product_op<T> BinaryOp;
+  typedef scalar_product_op<T1,T2> BinaryOp;
   typedef typename evaluator<Lhs>::InnerIterator  LhsIterator;
   typedef evaluator<Rhs>  RhsEvaluator;
   typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> XprType;

From bcc0f38f981f8efadeba314fb41e58f911c60ccc Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 14 Jun 2016 11:31:27 +0200
Subject: [PATCH 51/86] Add unittesting plugins to scalar_product_op and
 scalar_quotient_op to help chaking that types are properly propagated.

---
 Eigen/src/Core/functors/BinaryFunctors.h | 12 ++++++++++++
 test/linearstructure.cpp                 |  2 +-
 2 files changed, 13 insertions(+), 1 deletion(-)

diff --git a/Eigen/src/Core/functors/BinaryFunctors.h b/Eigen/src/Core/functors/BinaryFunctors.h
index 637514a20..77e9e6e93 100644
--- a/Eigen/src/Core/functors/BinaryFunctors.h
+++ b/Eigen/src/Core/functors/BinaryFunctors.h
@@ -70,7 +70,13 @@ template<typename LhsScalar,typename RhsScalar>
 struct scalar_product_op  : binary_op_base<LhsScalar,RhsScalar>
 {
   typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_product_op>::ReturnType result_type;
+#ifndef EIGEN_SCALAR_BINARY_OP_PLUGIN
   EIGEN_EMPTY_STRUCT_CTOR(scalar_product_op)
+#else
+  scalar_product_op() {
+    EIGEN_SCALAR_BINARY_OP_PLUGIN
+  }
+#endif
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a * b; }
   template<typename Packet>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
@@ -332,7 +338,13 @@ template<typename LhsScalar,typename RhsScalar>
 struct scalar_quotient_op  : binary_op_base<LhsScalar,RhsScalar>
 {
   typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_quotient_op>::ReturnType result_type;
+#ifndef EIGEN_SCALAR_BINARY_OP_PLUGIN
   EIGEN_EMPTY_STRUCT_CTOR(scalar_quotient_op)
+#else
+  scalar_quotient_op() {
+    EIGEN_SCALAR_BINARY_OP_PLUGIN
+  }
+#endif
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a / b; }
   template<typename Packet>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
diff --git a/test/linearstructure.cpp b/test/linearstructure.cpp
index e7f4b3dc5..7eef976d2 100644
--- a/test/linearstructure.cpp
+++ b/test/linearstructure.cpp
@@ -9,7 +9,7 @@
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
 static bool g_called;
-#define EIGEN_SPECIAL_SCALAR_MULTIPLE_PLUGIN { g_called = true; }
+#define EIGEN_SCALAR_BINARY_OP_PLUGIN { g_called |= (!internal::is_same<LhsScalar,RhsScalar>::value); }
 
 #include "main.h"
 

From 12350d3ac7a1192407b0f920bd937d4f753ec118 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 14 Jun 2016 11:31:52 +0200
Subject: [PATCH 52/86] Add unit test for AlignedBox::center

---
 test/geo_alignedbox.cpp | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/test/geo_alignedbox.cpp b/test/geo_alignedbox.cpp
index 2bdb4b7f2..ba3378aab 100644
--- a/test/geo_alignedbox.cpp
+++ b/test/geo_alignedbox.cpp
@@ -48,6 +48,8 @@ template<typename BoxType> void alignedbox(const BoxType& _box)
   b0.extend(p0);
   b0.extend(p1);
   VERIFY(b0.contains(p0*s1+(Scalar(1)-s1)*p1));
+  VERIFY(b0.contains(b0.center()));
+  VERIFY(b0.center()==(p0+p1)/Scalar(2));
 
   (b2 = b0).extend(b1);
   VERIFY(b2.contains(b0));

From f925dba3d981829fce7b383bec4d52fe41a023a4 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 14 Jun 2016 11:32:09 +0200
Subject: [PATCH 53/86] Fix compilation of BVH example

---
 unsupported/doc/examples/BVH_Example.cpp | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/unsupported/doc/examples/BVH_Example.cpp b/unsupported/doc/examples/BVH_Example.cpp
index 6b6fac075..afb0c94c2 100644
--- a/unsupported/doc/examples/BVH_Example.cpp
+++ b/unsupported/doc/examples/BVH_Example.cpp
@@ -6,9 +6,7 @@ using namespace Eigen;
 typedef AlignedBox<double, 2> Box2d;
 
 namespace Eigen {
-    namespace internal {
-        Box2d bounding_box(const Vector2d &v) { return Box2d(v, v); } //compute the bounding box of a single point
-    }
+  Box2d bounding_box(const Vector2d &v) { return Box2d(v, v); } //compute the bounding box of a single point
 }
 
 struct PointPointMinimizer //how to compute squared distances between points and rectangles

From 756ac4a93dea57bf61079c4867e712a8c26d77f6 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 14 Jun 2016 12:03:39 +0200
Subject: [PATCH 54/86] Fix doc.

---
 Eigen/src/plugins/CommonCwiseBinaryOps.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Eigen/src/plugins/CommonCwiseBinaryOps.h b/Eigen/src/plugins/CommonCwiseBinaryOps.h
index c5eaea16d..03c4aac94 100644
--- a/Eigen/src/plugins/CommonCwiseBinaryOps.h
+++ b/Eigen/src/plugins/CommonCwiseBinaryOps.h
@@ -55,7 +55,7 @@ EIGEN_MAKE_SCALAR_BINARY_OP(operator*,product);
   */
 template<typename T>
 const CwiseBinaryOp<internal::scalar_product_op<Scalar,T>,Derived,Constant<Scalar> > operator*(const T& scalar) const;
-/** \returns an expression of \c *this scaled by the scalar factor \a scalar
+/** \returns an expression of \a expr scaled by the scalar factor \a scalar
   *
   * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
   */

From a8c08e8b8e8bdd486a5a27b9f1e92c48ef4361cd Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 14 Jun 2016 12:06:10 +0200
Subject: [PATCH 55/86] Implement expr+scalar, scalar+expr, expr-scalar, and
 scalar-expr as binary expressions, and generalize supported scalar types. The
 following functors are now deprecated: scalar_add_op, scalar_sub_op, and
 scalar_rsub_op.

---
 Eigen/src/Core/functors/BinaryFunctors.h  | 31 ++++++------
 Eigen/src/Core/util/ForwardDeclarations.h |  1 -
 Eigen/src/plugins/ArrayCwiseBinaryOps.h   | 57 ++++++++++++-----------
 test/linearstructure.cpp                  | 16 +++++++
 test/mixingtypes.cpp                      | 12 +++++
 5 files changed, 70 insertions(+), 47 deletions(-)

diff --git a/Eigen/src/Core/functors/BinaryFunctors.h b/Eigen/src/Core/functors/BinaryFunctors.h
index 77e9e6e93..fd7b5f8b4 100644
--- a/Eigen/src/Core/functors/BinaryFunctors.h
+++ b/Eigen/src/Core/functors/BinaryFunctors.h
@@ -32,7 +32,13 @@ template<typename LhsScalar,typename RhsScalar>
 struct scalar_sum_op : binary_op_base<LhsScalar,RhsScalar>
 {
   typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_sum_op>::ReturnType result_type;
+#ifndef EIGEN_SCALAR_BINARY_OP_PLUGIN
   EIGEN_EMPTY_STRUCT_CTOR(scalar_sum_op)
+#else
+  scalar_sum_op() {
+    EIGEN_SCALAR_BINARY_OP_PLUGIN
+  }
+#endif
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a + b; }
   template<typename Packet>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
@@ -315,7 +321,13 @@ template<typename LhsScalar,typename RhsScalar>
 struct scalar_difference_op : binary_op_base<LhsScalar,RhsScalar>
 {
   typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_difference_op>::ReturnType result_type;
+#ifndef EIGEN_SCALAR_BINARY_OP_PLUGIN
   EIGEN_EMPTY_STRUCT_CTOR(scalar_difference_op)
+#else
+  scalar_difference_op() {
+    EIGEN_SCALAR_BINARY_OP_PLUGIN
+  }
+#endif
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a - b; }
   template<typename Packet>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
@@ -584,7 +596,7 @@ struct functor_traits<scalar_add_op<Scalar> >
 
 /** \internal
   * \brief Template functor to subtract a fixed scalar to another one
-  * \sa class CwiseUnaryOp, Array::operator-, struct scalar_add_op, struct scalar_rsub_op
+  * \sa class CwiseUnaryOp, Array::operator-, struct scalar_add_op
   */
 template<typename Scalar>
 struct scalar_sub_op {
@@ -600,23 +612,6 @@ template<typename Scalar>
 struct functor_traits<scalar_sub_op<Scalar> >
 { enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = packet_traits<Scalar>::HasAdd }; };
 
-/** \internal
-  * \brief Template functor to subtract a scalar to fixed another one
-  * \sa class CwiseUnaryOp, Array::operator-, struct scalar_add_op, struct scalar_sub_op
-  */
-template<typename Scalar>
-struct scalar_rsub_op {
-  EIGEN_DEVICE_FUNC inline scalar_rsub_op(const scalar_rsub_op& other) : m_other(other.m_other) { }
-  EIGEN_DEVICE_FUNC inline scalar_rsub_op(const Scalar& other) : m_other(other) { }
-  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return m_other - a; }
-  template <typename Packet>
-  EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
-  { return internal::psub(pset1<Packet>(m_other), a); }
-  const Scalar m_other;
-};
-template<typename Scalar>
-struct functor_traits<scalar_rsub_op<Scalar> >
-{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = packet_traits<Scalar>::HasAdd }; };
 
 /** \internal
   * \brief Template functor to raise a scalar to a power
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index 8334446d6..c1295dc5f 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -202,7 +202,6 @@ template<typename Scalar> struct scalar_square_op;
 template<typename Scalar> struct scalar_cube_op;
 template<typename Scalar, typename NewType> struct scalar_cast_op;
 template<typename Scalar> struct scalar_random_op;
-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;
diff --git a/Eigen/src/plugins/ArrayCwiseBinaryOps.h b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
index 351762e82..8bf4e9b18 100644
--- a/Eigen/src/plugins/ArrayCwiseBinaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
@@ -192,48 +192,49 @@ EIGEN_MAKE_CWISE_COMP_OP(operator!=, NEQ)
 #undef EIGEN_MAKE_CWISE_COMP_R_OP
 
 // scalar addition
-
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+EIGEN_MAKE_SCALAR_BINARY_OP(operator+,sum);
+#else
 /** \returns an expression of \c *this with each coeff incremented by the constant \a scalar
+  *
+  * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
   *
   * Example: \include Cwise_plus.cpp
   * Output: \verbinclude Cwise_plus.out
   *
   * \sa operator+=(), operator-()
   */
-EIGEN_DEVICE_FUNC
-inline const CwiseUnaryOp<internal::scalar_add_op<Scalar>, const Derived>
-operator+(const Scalar& scalar) const
-{
-  return CwiseUnaryOp<internal::scalar_add_op<Scalar>, const Derived>(derived(), internal::scalar_add_op<Scalar>(scalar));
-}
-
-EIGEN_DEVICE_FUNC
-friend inline const CwiseUnaryOp<internal::scalar_add_op<Scalar>, const Derived>
-operator+(const Scalar& scalar,const EIGEN_CURRENT_STORAGE_BASE_CLASS<Derived>& other)
-{
-  return other + scalar;
-}
+template<typename T>
+const CwiseBinaryOp<internal::scalar_sum_op<Scalar,T>,Derived,Constant<Scalar> > operator+(const T& scalar) const;
+/** \returns an expression of \a expr with each coeff incremented by the constant \a scalar
+  *
+  * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
+  */
+template<typename T> friend
+const CwiseBinaryOp<internal::scalar_sum_op<T,Scalar>,Constant<Scalar>,Derived> operator+(const T& scalar, const StorageBaseType& expr);
+#endif
 
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+EIGEN_MAKE_SCALAR_BINARY_OP(operator-,difference);
+#else
 /** \returns an expression of \c *this with each coeff decremented by the constant \a scalar
+  *
+  * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
   *
   * Example: \include Cwise_minus.cpp
   * Output: \verbinclude Cwise_minus.out
   *
-  * \sa operator+(), operator-=()
+  * \sa operator+=(), operator-()
   */
-EIGEN_DEVICE_FUNC
-inline const CwiseUnaryOp<internal::scalar_sub_op<Scalar>, const Derived>
-operator-(const Scalar& scalar) const
-{
-  return CwiseUnaryOp<internal::scalar_sub_op<Scalar>, const Derived>(derived(), internal::scalar_sub_op<Scalar>(scalar));;
-}
-
-EIGEN_DEVICE_FUNC
-friend inline const CwiseUnaryOp<internal::scalar_rsub_op<Scalar>, const Derived>
-operator-(const Scalar& scalar,const EIGEN_CURRENT_STORAGE_BASE_CLASS<Derived>& other)
-{
-  return CwiseUnaryOp<internal::scalar_rsub_op<Scalar>, const Derived>(other.derived(), internal::scalar_rsub_op<Scalar>(scalar));;
-}
+template<typename T>
+const CwiseBinaryOp<internal::scalar_difference_op<Scalar,T>,Derived,Constant<Scalar> > operator-(const T& scalar) const;
+/** \returns an expression of the constant matrix of value \a scalar decremented by the coefficients of \a expr
+  *
+  * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
+  */
+template<typename T> friend
+const CwiseBinaryOp<internal::scalar_difference_op<T,Scalar>,Constant<Scalar>,Derived> operator-(const T& scalar, const StorageBaseType& expr);
+#endif
 
 /** \returns an expression of the coefficient-wise && operator of *this and \a other
   *
diff --git a/test/linearstructure.cpp b/test/linearstructure.cpp
index 7eef976d2..17474af10 100644
--- a/test/linearstructure.cpp
+++ b/test/linearstructure.cpp
@@ -93,6 +93,22 @@ template<typename MatrixType> void real_complex(DenseIndex rows = MatrixType::Ro
   g_called = false;
   VERIFY_IS_APPROX(m1/s, m1/Scalar(s));
   VERIFY(g_called && "matrix<complex> / real not properly optimized");
+
+  g_called = false;
+  VERIFY_IS_APPROX(s+m1.array(), Scalar(s)+m1.array());
+  VERIFY(g_called && "real + matrix<complex> not properly optimized");
+
+  g_called = false;
+  VERIFY_IS_APPROX(m1.array()+s, m1.array()+Scalar(s));
+  VERIFY(g_called && "matrix<complex> + real not properly optimized");
+
+  g_called = false;
+  VERIFY_IS_APPROX(s-m1.array(), Scalar(s)-m1.array());
+  VERIFY(g_called && "real - matrix<complex> not properly optimized");
+
+  g_called = false;
+  VERIFY_IS_APPROX(m1.array()-s, m1.array()-Scalar(s));
+  VERIFY(g_called && "matrix<complex> - real not properly optimized");
 }
 
 void test_linearstructure()
diff --git a/test/mixingtypes.cpp b/test/mixingtypes.cpp
index dee4f35df..cf2207114 100644
--- a/test/mixingtypes.cpp
+++ b/test/mixingtypes.cpp
@@ -75,6 +75,18 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
   VERIFY_IS_APPROX(vcf / sf , vcf / complex<float>(sf));
   VERIFY_IS_APPROX(vf / scf , vf.template cast<complex<float> >() / scf);
 
+  // check scalar increment
+  VERIFY_IS_APPROX(vcf.array() + sf , vcf.array() + complex<float>(sf));
+  VERIFY_IS_APPROX(sd  + vcd.array(), complex<double>(sd) + vcd.array());
+  VERIFY_IS_APPROX(vf.array()  + scf, vf.template cast<complex<float> >().array() + scf);
+  VERIFY_IS_APPROX(scd + vd.array() , scd + vd.template cast<complex<double> >().array());
+
+  // check scalar subtractions
+  VERIFY_IS_APPROX(vcf.array() - sf , vcf.array() - complex<float>(sf));
+  VERIFY_IS_APPROX(sd  - vcd.array(), complex<double>(sd) - vcd.array());
+  VERIFY_IS_APPROX(vf.array()  - scf, vf.template cast<complex<float> >().array() - scf);
+  VERIFY_IS_APPROX(scd - vd.array() , scd - vd.template cast<complex<double> >().array());
+
   // check dot product
   vf.dot(vf);
 #if 0 // we get other compilation errors here than just static asserts

From a9bb653a684b55fca1c9f58089f94871484ae50c Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 14 Jun 2016 12:07:00 +0200
Subject: [PATCH 56/86] Update doc (scalar_add_op is now deprecated)

---
 doc/CustomizingEigen.dox | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/doc/CustomizingEigen.dox b/doc/CustomizingEigen.dox
index cb25f4ec9..607f86658 100644
--- a/doc/CustomizingEigen.dox
+++ b/doc/CustomizingEigen.dox
@@ -56,13 +56,13 @@ void makeFloor(const MatrixBase<OtherDerived>& other) { derived() = derived().cw
 template<typename OtherDerived>
 void makeCeil(const MatrixBase<OtherDerived>& other) { derived() = derived().cwiseMax(other.derived()); }
 
-const CwiseUnaryOp<internal::scalar_add_op<Scalar>, Derived>
+const CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const Derived, const ConstantReturnType>
 operator+(const Scalar& scalar) const
-{ return CwiseUnaryOp<internal::scalar_add_op<Scalar>, Derived>(derived(), internal::scalar_add_op<Scalar>(scalar)); }
+{ return CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const Derived, const ConstantReturnType>(derived(), Constant(rows(),cols(),scalar)); }
 
-friend const CwiseUnaryOp<internal::scalar_add_op<Scalar>, Derived>
+friend const CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const ConstantReturnType, Derived>
 operator+(const Scalar& scalar, const MatrixBase<Derived>& mat)
-{ return CwiseUnaryOp<internal::scalar_add_op<Scalar>, Derived>(mat.derived(), internal::scalar_add_op<Scalar>(scalar)); }
+{ return CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const ConstantReturnType, Derived>(Constant(rows(),cols(),scalar), mat.derived()); }
 \endcode
 
 Then one can the following declaration in the config.h or whatever prerequisites header file of his project:

From 396d9cfb6eaa62ecafc6f2d02851f0d2f8d6b4ef Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 14 Jun 2016 14:10:07 +0200
Subject: [PATCH 57/86] Generalize expr.pow(scalar), pow(expr,scalar) and
 pow(scalar,expr). Internal: scalar_pow_op (unary) is removed, and
 scalar_binary_pow_op is renamed scalar_pow_op.

---
 Eigen/src/Core/GlobalFunctions.h          | 60 ++++++++++++++++++-----
 Eigen/src/Core/MathFunctions.h            |  2 +-
 Eigen/src/Core/functors/BinaryFunctors.h  | 39 ++++++---------
 Eigen/src/Core/util/ForwardDeclarations.h |  3 +-
 Eigen/src/plugins/ArrayCwiseBinaryOps.h   | 21 +++++++-
 Eigen/src/plugins/ArrayCwiseUnaryOps.h    | 19 -------
 test/mixingtypes.cpp                      | 47 ++++++++++++------
 7 files changed, 118 insertions(+), 73 deletions(-)

diff --git a/Eigen/src/Core/GlobalFunctions.h b/Eigen/src/Core/GlobalFunctions.h
index e489cefec..60e2ccfed 100644
--- a/Eigen/src/Core/GlobalFunctions.h
+++ b/Eigen/src/Core/GlobalFunctions.h
@@ -89,14 +89,32 @@ namespace Eigen
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sign,scalar_sign_op,sign (or 0),\sa ArrayBase::sign)
   
   /** \returns an expression of the coefficient-wise power of \a x to the given constant \a exponent.
+    *
+    * \tparam ScalarExponent is the scalar type of \a exponent. It must be compatible with the scalar type of the given expression (\c Derived::Scalar).
     *
     * \sa ArrayBase::pow()
+    *
+    * \relates ArrayBase
     */
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+  template<typename Derived,typename ScalarExponent>
+  inline const CwiseBinaryOp<internal::scalar_pow_op<Derived::Scalar,ScalarExponent>,Derived,Constant<ScalarExponent> >
+  pow(const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent);
+#else
+  template<typename Derived,typename ScalarExponent>
+  inline typename internal::enable_if<   !(internal::is_same<typename Derived::Scalar,ScalarExponent>::value)
+                                      && ScalarBinaryOpTraits<typename Derived::Scalar,ScalarExponent>::Defined,
+          const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,ScalarExponent,pow) >::type
+  pow(const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent) {
+    return x.derived().pow(exponent);
+  }
+
   template<typename Derived>
-  inline const Eigen::CwiseUnaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar>, const Derived>
+  inline const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,typename Derived::Scalar,pow)
   pow(const Eigen::ArrayBase<Derived>& x, const typename Derived::Scalar& exponent) {
     return x.derived().pow(exponent);
   }
+#endif
 
   /** \returns an expression of the coefficient-wise power of \a x to the given array of \a exponents.
     *
@@ -106,12 +124,14 @@ namespace Eigen
     * Output: \verbinclude Cwise_array_power_array.out
     * 
     * \sa ArrayBase::pow()
+    *
+    * \relates ArrayBase
     */
   template<typename Derived,typename ExponentDerived>
-  inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_binary_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>
+  inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>
   pow(const Eigen::ArrayBase<Derived>& x, const Eigen::ArrayBase<ExponentDerived>& exponents) 
   {
-    return Eigen::CwiseBinaryOp<Eigen::internal::scalar_binary_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>(
+    return Eigen::CwiseBinaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>(
       x.derived(),
       exponents.derived()
     );
@@ -120,23 +140,39 @@ namespace Eigen
   /** \returns an expression of the coefficient-wise power of the scalar \a x to the given array of \a exponents.
     *
     * This function computes the coefficient-wise power between a scalar and an array of exponents.
-    * Beaware that the scalar type of the input scalar \a x and the exponents \a exponents must be the same.
+    *
+    * \tparam Scalar is the scalar type of \a x. It must be compatible with the scalar type of the given array expression (\c Derived::Scalar).
     *
     * Example: \include Cwise_scalar_power_array.cpp
     * Output: \verbinclude Cwise_scalar_power_array.out
     * 
     * \sa ArrayBase::pow()
+    *
+    * \relates ArrayBase
     */
-  template<typename Derived>
-  inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_binary_pow_op<typename Derived::Scalar, typename Derived::Scalar>, const typename Derived::ConstantReturnType, const Derived>
-  pow(const typename Derived::Scalar& x, const Eigen::ArrayBase<Derived>& exponents) 
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+  template<typename Scalar,typename Derived>
+  inline const CwiseBinaryOp<internal::scalar_pow_op<Scalar,Derived::Scalar>,Constant<Scalar>,Derived>
+  pow(const Scalar& x,const Eigen::ArrayBase<Derived>& x);
+#else
+  template<typename Scalar, typename Derived>
+  inline typename internal::enable_if<   !(internal::is_same<typename Derived::Scalar,Scalar>::value)
+                                      && ScalarBinaryOpTraits<Scalar,typename Derived::Scalar>::Defined,
+          const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,pow) >::type
+  pow(const Scalar& x, const Eigen::ArrayBase<Derived>& exponents)
   {
-    typename Derived::ConstantReturnType constant_x(exponents.rows(), exponents.cols(), x);
-    return Eigen::CwiseBinaryOp<Eigen::internal::scalar_binary_pow_op<typename Derived::Scalar, typename Derived::Scalar>, const typename Derived::ConstantReturnType, const Derived>(
-      constant_x,
-      exponents.derived()
-    );
+    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,pow)(
+            typename internal::plain_constant_type<Derived,Scalar>::type(exponents.rows(), exponents.cols(), x), exponents.derived() );
   }
+
+  template<typename Derived>
+  inline const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename Derived::Scalar,Derived,pow)
+  pow(const typename Derived::Scalar& x, const Eigen::ArrayBase<Derived>& exponents)
+  {
+    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename Derived::Scalar,Derived,pow)(
+      typename internal::plain_constant_type<Derived,typename Derived::Scalar>::type(exponents.rows(), exponents.cols(), x), exponents.derived() );
+  }
+#endif
   
   /**
     * \brief Component-wise division of a scalar by array elements.
diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
index 2a05ae12d..b683effab 100644
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
@@ -498,7 +498,7 @@ template<typename ScalarX,typename ScalarY, bool IsInteger = NumTraits<ScalarX>:
 struct pow_impl
 {
   //typedef Scalar retval;
-  typedef typename ScalarBinaryOpTraits<ScalarX,ScalarY,internal::scalar_binary_pow_op<ScalarX,ScalarY> >::ReturnType result_type;
+  typedef typename ScalarBinaryOpTraits<ScalarX,ScalarY,internal::scalar_pow_op<ScalarX,ScalarY> >::ReturnType result_type;
   static EIGEN_DEVICE_FUNC inline result_type run(const ScalarX& x, const ScalarY& y)
   {
     EIGEN_USING_STD_MATH(pow);
diff --git a/Eigen/src/Core/functors/BinaryFunctors.h b/Eigen/src/Core/functors/BinaryFunctors.h
index fd7b5f8b4..9e40303be 100644
--- a/Eigen/src/Core/functors/BinaryFunctors.h
+++ b/Eigen/src/Core/functors/BinaryFunctors.h
@@ -295,16 +295,24 @@ struct functor_traits<scalar_hypot_op<Scalar,Scalar> > {
 /** \internal
   * \brief Template functor to compute the pow of two scalars
   */
-template<typename Scalar, typename OtherScalar>
-struct scalar_binary_pow_op  : binary_op_base<Scalar,OtherScalar>
+template<typename Scalar, typename Exponent>
+struct scalar_pow_op  : binary_op_base<Scalar,Exponent>
 {
-  typedef typename ScalarBinaryOpTraits<Scalar,OtherScalar,scalar_binary_pow_op>::ReturnType result_type;
-  EIGEN_EMPTY_STRUCT_CTOR(scalar_binary_pow_op)
+  typedef typename ScalarBinaryOpTraits<Scalar,Exponent,scalar_pow_op>::ReturnType result_type;
+#ifndef EIGEN_SCALAR_BINARY_OP_PLUGIN
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_pow_op)
+#else
+  scalar_pow_op() {
+    typedef Scalar LhsScalar;
+    typedef Exponent RhsScalar;
+    EIGEN_SCALAR_BINARY_OP_PLUGIN
+  }
+#endif
   EIGEN_DEVICE_FUNC
-  inline result_type operator() (const Scalar& a, const OtherScalar& b) const { return numext::pow(a, b); }
+  inline result_type operator() (const Scalar& a, const Exponent& b) const { return numext::pow(a, b); }
 };
-template<typename Scalar, typename OtherScalar>
-struct functor_traits<scalar_binary_pow_op<Scalar,OtherScalar> > {
+template<typename Scalar, typename Exponent>
+struct functor_traits<scalar_pow_op<Scalar,Exponent> > {
   enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false };
 };
 
@@ -613,23 +621,6 @@ struct functor_traits<scalar_sub_op<Scalar> >
 { enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = packet_traits<Scalar>::HasAdd }; };
 
 
-/** \internal
-  * \brief Template functor to raise a scalar to a power
-  * \sa class CwiseUnaryOp, Cwise::pow
-  */
-template<typename Scalar>
-struct scalar_pow_op {
-  // FIXME default copy constructors seems bugged with std::complex<>
-  EIGEN_DEVICE_FUNC inline scalar_pow_op(const scalar_pow_op& other) : m_exponent(other.m_exponent) { }
-  EIGEN_DEVICE_FUNC inline scalar_pow_op(const Scalar& exponent) : m_exponent(exponent) {}
-  EIGEN_DEVICE_FUNC
-  inline Scalar operator() (const Scalar& a) const { return numext::pow(a, m_exponent); }
-  const Scalar m_exponent;
-};
-template<typename Scalar>
-struct functor_traits<scalar_pow_op<Scalar> >
-{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false }; };
-
 /** \internal
   * \brief Template functor to compute the quotient between a scalar and array entries.
   * \sa class CwiseUnaryOp, Cwise::inverse()
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index c1295dc5f..830f20f90 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -196,7 +196,6 @@ template<typename Scalar> struct scalar_sin_op;
 template<typename Scalar> struct scalar_acos_op;
 template<typename Scalar> struct scalar_asin_op;
 template<typename Scalar> struct scalar_tan_op;
-template<typename Scalar> struct scalar_pow_op;
 template<typename Scalar> struct scalar_inverse_op;
 template<typename Scalar> struct scalar_square_op;
 template<typename Scalar> struct scalar_cube_op;
@@ -209,10 +208,10 @@ template<typename Scalar> struct scalar_igamma_op;
 template<typename Scalar> struct scalar_igammac_op;
 template<typename Scalar> struct scalar_betainc_op;
 
+template<typename Scalar,typename ScalarExponent> struct scalar_pow_op;
 template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_hypot_op;
 template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_product_op;
 template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_quotient_op;
-template<typename ScalarX, typename ScalarY> struct scalar_binary_pow_op;
 
 } // end namespace internal
 
diff --git a/Eigen/src/plugins/ArrayCwiseBinaryOps.h b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
index 8bf4e9b18..1e20e35d7 100644
--- a/Eigen/src/plugins/ArrayCwiseBinaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
@@ -82,7 +82,26 @@ max
   * Example: \include Cwise_array_power_array.cpp
   * Output: \verbinclude Cwise_array_power_array.out
   */
-EIGEN_MAKE_CWISE_BINARY_OP(pow,binary_pow)
+EIGEN_MAKE_CWISE_BINARY_OP(pow,pow)
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(pow,pow);
+#else
+/** \returns an expression of the coefficients of \c *this rasied to the constant power \a exponent
+  *
+  * \tparam T is the scalar type of \a exponent. It must be compatible with the scalar type of the given expression.
+  *
+  * This function computes the coefficient-wise power. The function MatrixBase::pow() in the
+  * unsupported module MatrixFunctions computes the matrix power.
+  *
+  * Example: \include Cwise_pow.cpp
+  * Output: \verbinclude Cwise_pow.out
+  *
+  * \sa ArrayBase::pow(ArrayBase), square(), cube(), exp(), log()
+  */
+template<typename T>
+const CwiseBinaryOp<internal::scalar_pow_op<Scalar,T>,Derived,Constant<Scalar> > pow(const T& exponent) const;
+#endif
 
 
 // TODO code generating macros could be moved to Macros.h and could include generation of documentation
diff --git a/Eigen/src/plugins/ArrayCwiseUnaryOps.h b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
index 775fa6ee0..4a6361d8a 100644
--- a/Eigen/src/plugins/ArrayCwiseUnaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
@@ -26,7 +26,6 @@ typedef CwiseUnaryOp<internal::scalar_lgamma_op<Scalar>, const Derived> LgammaRe
 typedef CwiseUnaryOp<internal::scalar_digamma_op<Scalar>, const Derived> DigammaReturnType;
 typedef CwiseUnaryOp<internal::scalar_erf_op<Scalar>, const Derived> ErfReturnType;
 typedef CwiseUnaryOp<internal::scalar_erfc_op<Scalar>, const Derived> ErfcReturnType;
-typedef CwiseUnaryOp<internal::scalar_pow_op<Scalar>, const Derived> PowReturnType;
 typedef CwiseUnaryOp<internal::scalar_square_op<Scalar>, const Derived> SquareReturnType;
 typedef CwiseUnaryOp<internal::scalar_cube_op<Scalar>, const Derived> CubeReturnType;
 typedef CwiseUnaryOp<internal::scalar_round_op<Scalar>, const Derived> RoundReturnType;
@@ -388,24 +387,6 @@ erfc() const
   return ErfcReturnType(derived());
 }
 
-/** \returns an expression of the coefficient-wise power of *this to the given exponent.
-  *
-  * This function computes the coefficient-wise power. The function MatrixBase::pow() in the
-  * unsupported module MatrixFunctions computes the matrix power.
-  *
-  * Example: \include Cwise_pow.cpp
-  * Output: \verbinclude Cwise_pow.out
-  *
-  * \sa exp(), log()
-  */
-EIGEN_DEVICE_FUNC
-inline const PowReturnType
-pow(const Scalar& exponent) const
-{
-  return PowReturnType(derived(), internal::scalar_pow_op<Scalar>(exponent));
-}
-
-
 /** \returns an expression of the coefficient-wise inverse of *this.
   *
   * Example: \include Cwise_inverse.cpp
diff --git a/test/mixingtypes.cpp b/test/mixingtypes.cpp
index cf2207114..b38271a17 100644
--- a/test/mixingtypes.cpp
+++ b/test/mixingtypes.cpp
@@ -23,10 +23,18 @@
 
 #endif
 
+static bool g_called;
+#define EIGEN_SCALAR_BINARY_OP_PLUGIN { g_called |= (!internal::is_same<LhsScalar,RhsScalar>::value); }
+
 #include "main.h"
 
 using namespace std;
 
+#define VERIFY_MIX_SCALAR(XPR,REF) \
+  g_called = false; \
+  VERIFY_IS_APPROX(XPR,REF); \
+  VERIFY( g_called && #XPR" not properly optimized");
+
 template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
 {
   typedef std::complex<float>   CF;
@@ -66,26 +74,34 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
 #endif
   
   // check scalar products
-  VERIFY_IS_APPROX(vcf * sf , vcf * complex<float>(sf));
-  VERIFY_IS_APPROX(sd * vcd , complex<double>(sd) * vcd);
-  VERIFY_IS_APPROX(vf * scf , vf.template cast<complex<float> >() * scf);
-  VERIFY_IS_APPROX(scd * vd , scd * vd.template cast<complex<double> >());
+  VERIFY_MIX_SCALAR(vcf * sf , vcf * complex<float>(sf));
+  VERIFY_MIX_SCALAR(sd * vcd , complex<double>(sd) * vcd);
+  VERIFY_MIX_SCALAR(vf * scf , vf.template cast<complex<float> >() * scf);
+  VERIFY_MIX_SCALAR(scd * vd , scd * vd.template cast<complex<double> >());
 
   // check scalar quotients
-  VERIFY_IS_APPROX(vcf / sf , vcf / complex<float>(sf));
-  VERIFY_IS_APPROX(vf / scf , vf.template cast<complex<float> >() / scf);
+  VERIFY_MIX_SCALAR(vcf / sf , vcf / complex<float>(sf));
+  VERIFY_MIX_SCALAR(vf / scf , vf.template cast<complex<float> >() / scf);
 
   // check scalar increment
-  VERIFY_IS_APPROX(vcf.array() + sf , vcf.array() + complex<float>(sf));
-  VERIFY_IS_APPROX(sd  + vcd.array(), complex<double>(sd) + vcd.array());
-  VERIFY_IS_APPROX(vf.array()  + scf, vf.template cast<complex<float> >().array() + scf);
-  VERIFY_IS_APPROX(scd + vd.array() , scd + vd.template cast<complex<double> >().array());
+  VERIFY_MIX_SCALAR(vcf.array() + sf , vcf.array() + complex<float>(sf));
+  VERIFY_MIX_SCALAR(sd  + vcd.array(), complex<double>(sd) + vcd.array());
+  VERIFY_MIX_SCALAR(vf.array()  + scf, vf.template cast<complex<float> >().array() + scf);
+  VERIFY_MIX_SCALAR(scd + vd.array() , scd + vd.template cast<complex<double> >().array());
 
   // check scalar subtractions
-  VERIFY_IS_APPROX(vcf.array() - sf , vcf.array() - complex<float>(sf));
-  VERIFY_IS_APPROX(sd  - vcd.array(), complex<double>(sd) - vcd.array());
-  VERIFY_IS_APPROX(vf.array()  - scf, vf.template cast<complex<float> >().array() - scf);
-  VERIFY_IS_APPROX(scd - vd.array() , scd - vd.template cast<complex<double> >().array());
+  VERIFY_MIX_SCALAR(vcf.array() - sf , vcf.array() - complex<float>(sf));
+  VERIFY_MIX_SCALAR(sd  - vcd.array(), complex<double>(sd) - vcd.array());
+  VERIFY_MIX_SCALAR(vf.array()  - scf, vf.template cast<complex<float> >().array() - scf);
+  VERIFY_MIX_SCALAR(scd - vd.array() , scd - vd.template cast<complex<double> >().array());
+
+  // check scalar powers
+  VERIFY_MIX_SCALAR( pow(vcf.array(), sf), pow(vcf.array(), complex<float>(sf)) );
+  VERIFY_MIX_SCALAR( vcf.array().pow(sf) , pow(vcf.array(), complex<float>(sf)) );
+  VERIFY_MIX_SCALAR( pow(sd, vcd.array()), pow(complex<double>(sd), vcd.array()) );
+  VERIFY_MIX_SCALAR( pow(vf.array(), scf), pow(vf.template cast<complex<float> >().array(), scf) );
+  VERIFY_MIX_SCALAR( vf.array().pow(scf) , pow(vf.template cast<complex<float> >().array(), scf) );
+  VERIFY_MIX_SCALAR( pow(scd, vd.array()), pow(scd, vd.template cast<complex<double> >().array()) );
 
   // check dot product
   vf.dot(vf);
@@ -215,6 +231,9 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
   VERIFY_IS_APPROX( md.array().pow(mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()) );
   VERIFY_IS_APPROX( mcd.array().pow(md.array()),  mcd.array().pow(md.template cast<CD>().eval().array()) );
 
+  VERIFY_IS_APPROX( pow(md.array(),mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()) );
+  VERIFY_IS_APPROX( pow(mcd.array(),md.array()),  mcd.array().pow(md.template cast<CD>().eval().array()) );
+
   rcd = mcd;
   VERIFY_IS_APPROX( rcd = md, md.template cast<CD>().eval() );
   rcd = mcd;

From 5d3820373513c950fbd238b0d8fd73bf3cd3e7fb Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 14 Jun 2016 15:06:03 +0200
Subject: [PATCH 58/86] Update Tensor module to use bind1st_op and bind2nd_op

---
 .../Eigen/CXX11/src/Tensor/TensorBase.h       | 74 +++++++++----------
 1 file changed, 36 insertions(+), 38 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h b/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h
index 8f3580ba7..aeaa9dea9 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h
@@ -204,64 +204,62 @@ class TensorBase<Derived, ReadOnlyAccessors>
     }
 
     EIGEN_DEVICE_FUNC
-    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_pow_op<Scalar>, const Derived>
+    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::bind2nd_op<internal::scalar_pow_op<Scalar,Scalar> >, const Derived>
     pow(Scalar exponent) const {
-      return unaryExpr(internal::scalar_pow_op<Scalar>(exponent));
+      return unaryExpr(internal::bind2nd_op<internal::scalar_pow_op<Scalar,Scalar> >(exponent));
     }
 
     EIGEN_DEVICE_FUNC
-    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_add_op<Scalar>, const Derived>
+    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::bind2nd_op<internal::scalar_sum_op<Scalar,Scalar> >, const Derived>
     operator+ (Scalar rhs) const {
-      return unaryExpr(internal::scalar_add_op<Scalar>(rhs));
+      return unaryExpr(internal::bind2nd_op<internal::scalar_sum_op<Scalar,Scalar> >(rhs));
     }
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE friend
-    const TensorCwiseUnaryOp<internal::scalar_add_op<Scalar>, const Derived>
+    const TensorCwiseUnaryOp<internal::bind1st_op<internal::scalar_sum_op<Scalar> >, const Derived>
     operator+ (Scalar lhs, const Derived& rhs) {
-      return rhs + lhs;
+      return rhs.unaryExpr(internal::bind1st_op<internal::scalar_sum_op<Scalar> >(lhs));
     }
 
     EIGEN_DEVICE_FUNC
-    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_sub_op<Scalar>, const Derived>
+    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::bind2nd_op<internal::scalar_difference_op<Scalar,Scalar> >, const Derived>
     operator- (Scalar rhs) const {
       EIGEN_STATIC_ASSERT((NumTraits<Scalar>::IsSigned || internal::is_same<Scalar, const std::complex<float> >::value), YOU_MADE_A_PROGRAMMING_MISTAKE);
-      return unaryExpr(internal::scalar_sub_op<Scalar>(rhs));
+      return unaryExpr(internal::bind2nd_op<internal::scalar_difference_op<Scalar,Scalar> >(rhs));
     }
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE friend
-    const TensorCwiseUnaryOp<internal::scalar_add_op<Scalar>,
-                             const TensorCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const Derived> >
+    const TensorCwiseUnaryOp<internal::bind1st_op<internal::scalar_difference_op<Scalar> >, const Derived>
     operator- (Scalar lhs, const Derived& rhs) {
-      return -rhs + lhs;
+      return rhs.unaryExpr(internal::bind1st_op<internal::scalar_difference_op<Scalar> >(lhs));
     }
 
     EIGEN_DEVICE_FUNC
-    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const Derived>
+    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::bind2nd_op<internal::scalar_product_op<Scalar,Scalar> >, const Derived>
     operator* (Scalar rhs) const {
-      return unaryExpr(internal::scalar_multiple_op<Scalar>(rhs));
+      return unaryExpr(internal::bind2nd_op<internal::scalar_product_op<Scalar,Scalar> >(rhs));
     }
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE friend
-    const TensorCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const Derived>
+    const TensorCwiseUnaryOp<internal::bind1st_op<internal::scalar_product_op<Scalar> >, const Derived>
     operator* (Scalar lhs, const Derived& rhs) {
-      return rhs * lhs;
+      return rhs.unaryExpr(internal::bind1st_op<internal::scalar_product_op<Scalar> >(lhs));
     }
 
     EIGEN_DEVICE_FUNC
-    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_quotient1_op<Scalar>, const Derived>
+    EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::bind2nd_op<internal::scalar_quotient_op<Scalar,Scalar> >, const Derived>
     operator/ (Scalar rhs) const {
-      return unaryExpr(internal::scalar_quotient1_op<Scalar>(rhs));
+      return unaryExpr(internal::bind2nd_op<internal::scalar_quotient_op<Scalar,Scalar> >(rhs));
     }
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE friend
-    const TensorCwiseUnaryOp<internal::scalar_multiple_op<Scalar>,
-                             const TensorCwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived> >
+    const TensorCwiseUnaryOp<internal::bind1st_op<internal::scalar_quotient_op<Scalar> >, const Derived>
     operator/ (Scalar lhs, const Derived& rhs) {
-      return rhs.inverse() * lhs;
+      return rhs.unaryExpr(internal::bind1st_op<internal::scalar_quotient_op<Scalar> >(lhs));
     }
 
     EIGEN_DEVICE_FUNC
@@ -371,66 +369,66 @@ class TensorBase<Derived, ReadOnlyAccessors>
 
     // Comparisons and tests.
     template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_LT>, const Derived, const OtherDerived>
+    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LT>, const Derived, const OtherDerived>
     operator<(const OtherDerived& other) const {
-      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, internal::cmp_LT>());
+      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LT>());
     }
     template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_LE>, const Derived, const OtherDerived>
+    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LE>, const Derived, const OtherDerived>
     operator<=(const OtherDerived& other) const {
-      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, internal::cmp_LE>());
+      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LE>());
     }
     template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_GT>, const Derived, const OtherDerived>
+    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GT>, const Derived, const OtherDerived>
     operator>(const OtherDerived& other) const {
-      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, internal::cmp_GT>());
+      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GT>());
     }
     template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_GE>, const Derived, const OtherDerived>
+    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GE>, const Derived, const OtherDerived>
     operator>=(const OtherDerived& other) const {
-      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, internal::cmp_GE>());
+      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GE>());
     }
 
     template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_EQ>, const Derived, const OtherDerived>
+    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_EQ>, const Derived, const OtherDerived>
     operator==(const OtherDerived& other) const {
-      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, internal::cmp_EQ>());
+      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_EQ>());
     }
 
     template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_NEQ>, const Derived, const OtherDerived>
+    const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_NEQ>, const Derived, const OtherDerived>
     operator!=(const OtherDerived& other) const {
-      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, internal::cmp_NEQ>());
+      return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_NEQ>());
     }
 
     // comparisons and tests for Scalars
     EIGEN_DEVICE_FUNC
-    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_LT>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
+    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LT>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
     operator<(Scalar threshold) const {
       return operator<(constant(threshold));
     }
     EIGEN_DEVICE_FUNC
-    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_LE>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
+    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LE>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
     operator<=(Scalar threshold) const {
       return operator<=(constant(threshold));
     }
     EIGEN_DEVICE_FUNC
-    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_GT>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
+    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GT>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
     operator>(Scalar threshold) const {
       return operator>(constant(threshold));
     }
     EIGEN_DEVICE_FUNC
-    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_GE>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
+    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GE>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
     operator>=(Scalar threshold) const {
       return operator>=(constant(threshold));
     }
     EIGEN_DEVICE_FUNC
-    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_EQ>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
+    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_EQ>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
     operator==(Scalar threshold) const {
       return operator==(constant(threshold));
     }
     EIGEN_DEVICE_FUNC
-    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, internal::cmp_NEQ>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
+    EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_NEQ>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
     operator!=(Scalar threshold) const {
       return operator!=(constant(threshold));
     }

From 62134082aa0dd33cb7328f9f9a86491d21a52444 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 14 Jun 2016 15:06:35 +0200
Subject: [PATCH 59/86] Update AutoDiffScalar wrt to scalar-multiple.

---
 Eigen/src/Core/util/Macros.h                  |  2 +
 .../Eigen/src/AutoDiff/AutoDiffScalar.h       | 89 +++++++++----------
 2 files changed, 43 insertions(+), 48 deletions(-)

diff --git a/Eigen/src/Core/util/Macros.h b/Eigen/src/Core/util/Macros.h
index f3c6512c9..031e0892e 100644
--- a/Eigen/src/Core/util/Macros.h
+++ b/Eigen/src/Core/util/Macros.h
@@ -462,6 +462,8 @@
 #define EIGEN_CAT2(a,b) a ## b
 #define EIGEN_CAT(a,b) EIGEN_CAT2(a,b)
 
+#define EIGEN_COMMA ,
+
 // convert a token to a string
 #define EIGEN_MAKESTRING2(a) #a
 #define EIGEN_MAKESTRING(a) EIGEN_MAKESTRING2(a)
diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
index 0ed91fdb7..feaeeaf5a 100755
--- a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
+++ b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
@@ -30,6 +30,13 @@ template<typename _DerType, bool Enable> struct auto_diff_special_op;
 
 } // end namespace internal
 
+template<typename _DerType> class AutoDiffScalar;
+
+template<typename NewDerType>
+inline AutoDiffScalar<NewDerType> MakeAutoDiffScalar(const typename NewDerType::Scalar& value, const NewDerType &der) {
+  return AutoDiffScalar<NewDerType>(value,der);
+}
+
 /** \class AutoDiffScalar
   * \brief A scalar type replacement with automatic differentation capability
   *
@@ -257,20 +264,16 @@ class AutoDiffScalar
         -m_derivatives);
     }
 
-    inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >
+    inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >
     operator*(const Scalar& other) const
     {
-      return AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >(
-        m_value * other,
-        (m_derivatives * other));
+      return MakeAutoDiffScalar(m_value * other, m_derivatives * other);
     }
 
-    friend inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >
+    friend inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >
     operator*(const Scalar& other, const AutoDiffScalar& a)
     {
-      return AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >(
-        a.value() * other,
-        a.derivatives() * other);
+      return MakeAutoDiffScalar(a.value() * other, a.derivatives() * other);
     }
 
 //     inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >
@@ -289,20 +292,16 @@ class AutoDiffScalar
 //         a.derivatives() * other);
 //     }
 
-    inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >
+    inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >
     operator/(const Scalar& other) const
     {
-      return AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >(
-        m_value / other,
-        (m_derivatives * (Scalar(1)/other)));
+      return MakeAutoDiffScalar(m_value / other, (m_derivatives * (Scalar(1)/other)));
     }
 
-    friend inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >
+    friend inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >
     operator/(const Scalar& other, const AutoDiffScalar& a)
     {
-      return AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >(
-        other / a.value(),
-        a.derivatives() * (Scalar(-other) / (a.value()*a.value())));
+      return MakeAutoDiffScalar(other / a.value(), a.derivatives() * (Scalar(-other) / (a.value()*a.value())));
     }
 
 //     inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >
@@ -322,34 +321,29 @@ class AutoDiffScalar
 //     }
 
     template<typename OtherDerType>
-    inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>,
-        const CwiseBinaryOp<internal::scalar_difference_op<Scalar>,
-          const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType>,
-          const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const typename internal::remove_all<OtherDerType>::type > > > >
+    inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(
+        CwiseBinaryOp<internal::scalar_difference_op<Scalar> EIGEN_COMMA
+          const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) EIGEN_COMMA
+          const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename internal::remove_all<OtherDerType>::type,Scalar,product) >,Scalar,product) >
     operator/(const AutoDiffScalar<OtherDerType>& other) const
     {
       internal::make_coherent(m_derivatives, other.derivatives());
-      return AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>,
-        const CwiseBinaryOp<internal::scalar_difference_op<Scalar>,
-          const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType>,
-          const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const typename internal::remove_all<OtherDerType>::type > > > >(
+      return MakeAutoDiffScalar(
         m_value / other.value(),
-          ((m_derivatives * other.value()) - (m_value * other.derivatives()))
+          ((m_derivatives * other.value()) - (other.derivatives() * m_value))
         * (Scalar(1)/(other.value()*other.value())));
     }
 
     template<typename OtherDerType>
     inline const AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
-        const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType>,
-        const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const typename internal::remove_all<OtherDerType>::type> > >
+        const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product),
+        const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename internal::remove_all<OtherDerType>::type,Scalar,product) > >
     operator*(const AutoDiffScalar<OtherDerType>& other) const
     {
       internal::make_coherent(m_derivatives, other.derivatives());
-      return AutoDiffScalar<const CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
-        const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType>,
-        const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const typename internal::remove_all<OtherDerType>::type > > >(
+      return MakeAutoDiffScalar(
         m_value * other.value(),
-        (m_derivatives * other.value()) + (m_value * other.derivatives()));
+        (m_derivatives * other.value()) + (other.derivatives() * m_value));
     }
 
     inline AutoDiffScalar& operator*=(const Scalar& other)
@@ -533,11 +527,11 @@ struct ScalarBinaryOpTraits<typename DerType::Scalar,AutoDiffScalar<DerType> >
 
 #define EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(FUNC,CODE) \
   template<typename DerType> \
-  inline const Eigen::AutoDiffScalar<Eigen::CwiseUnaryOp<Eigen::internal::scalar_multiple_op<typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar>, const typename Eigen::internal::remove_all<DerType>::type> > \
+  inline const Eigen::AutoDiffScalar< \
+  EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename Eigen::internal::remove_all<DerType>::type, typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar, product) > \
   FUNC(const Eigen::AutoDiffScalar<DerType>& x) { \
     using namespace Eigen; \
     typedef typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar Scalar; \
-    typedef AutoDiffScalar<CwiseUnaryOp<Eigen::internal::scalar_multiple_op<Scalar>, const typename Eigen::internal::remove_all<DerType>::type> > ReturnType; \
     CODE; \
   }
 
@@ -570,46 +564,45 @@ inline AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::Plain
 
 EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs,
   using std::abs;
-  return ReturnType(abs(x.value()), x.derivatives() * (x.value()<0 ? -1 : 1) );)
+  return Eigen::MakeAutoDiffScalar(abs(x.value()), x.derivatives() * (x.value()<0 ? -1 : 1) );)
 
 EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs2,
   using numext::abs2;
-  return ReturnType(abs2(x.value()), x.derivatives() * (Scalar(2)*x.value()));)
+  return Eigen::MakeAutoDiffScalar(abs2(x.value()), x.derivatives() * (Scalar(2)*x.value()));)
 
 EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sqrt,
   using std::sqrt;
   Scalar sqrtx = sqrt(x.value());
-  return ReturnType(sqrtx,x.derivatives() * (Scalar(0.5) / sqrtx));)
+  return Eigen::MakeAutoDiffScalar(sqrtx,x.derivatives() * (Scalar(0.5) / sqrtx));)
 
 EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(cos,
   using std::cos;
   using std::sin;
-  return ReturnType(cos(x.value()), x.derivatives() * (-sin(x.value())));)
+  return Eigen::MakeAutoDiffScalar(cos(x.value()), x.derivatives() * (-sin(x.value())));)
 
 EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sin,
   using std::sin;
   using std::cos;
-  return ReturnType(sin(x.value()),x.derivatives() * cos(x.value()));)
+  return Eigen::MakeAutoDiffScalar(sin(x.value()),x.derivatives() * cos(x.value()));)
 
 EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(exp,
   using std::exp;
   Scalar expx = exp(x.value());
-  return ReturnType(expx,x.derivatives() * expx);)
+  return Eigen::MakeAutoDiffScalar(expx,x.derivatives() * expx);)
 
 EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(log,
   using std::log;
-  return ReturnType(log(x.value()),x.derivatives() * (Scalar(1)/x.value()));)
+  return Eigen::MakeAutoDiffScalar(log(x.value()),x.derivatives() * (Scalar(1)/x.value()));)
 
 template<typename DerType>
-inline const Eigen::AutoDiffScalar<Eigen::CwiseUnaryOp<Eigen::internal::scalar_multiple_op<typename internal::traits<typename internal::remove_all<DerType>::type>::Scalar>, const typename internal::remove_all<DerType>::type> >
-pow(const Eigen::AutoDiffScalar<DerType>& x, const typename internal::traits<typename internal::remove_all<DerType>::type>::Scalar &y)
+inline const Eigen::AutoDiffScalar<
+EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename internal::remove_all<DerType>::type,typename internal::traits<typename internal::remove_all<DerType>::type>::Scalar,product) >
+pow(const Eigen::AutoDiffScalar<DerType> &x, const typename internal::traits<typename internal::remove_all<DerType>::type>::Scalar &y)
 {
   using namespace Eigen;
   typedef typename internal::remove_all<DerType>::type DerTypeCleaned;
   typedef typename Eigen::internal::traits<DerTypeCleaned>::Scalar Scalar;
-  return AutoDiffScalar<CwiseUnaryOp<Eigen::internal::scalar_multiple_op<Scalar>, const DerTypeCleaned> >(
-    std::pow(x.value(),y),
-    x.derivatives() * (y * std::pow(x.value(),y-1)));
+  return Eigen::MakeAutoDiffScalar(std::pow(x.value(),y), x.derivatives() * (y * std::pow(x.value(),y-1)));
 }
 
 
@@ -634,17 +627,17 @@ atan2(const AutoDiffScalar<DerTypeA>& a, const AutoDiffScalar<DerTypeB>& b)
 EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(tan,
   using std::tan;
   using std::cos;
-  return ReturnType(tan(x.value()),x.derivatives() * (Scalar(1)/numext::abs2(cos(x.value()))));)
+  return Eigen::MakeAutoDiffScalar(tan(x.value()),x.derivatives() * (Scalar(1)/numext::abs2(cos(x.value()))));)
 
 EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(asin,
   using std::sqrt;
   using std::asin;
-  return ReturnType(asin(x.value()),x.derivatives() * (Scalar(1)/sqrt(1-numext::abs2(x.value()))));)
+  return Eigen::MakeAutoDiffScalar(asin(x.value()),x.derivatives() * (Scalar(1)/sqrt(1-numext::abs2(x.value()))));)
   
 EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(acos,
   using std::sqrt;
   using std::acos;
-  return ReturnType(acos(x.value()),x.derivatives() * (Scalar(-1)/sqrt(1-numext::abs2(x.value()))));)
+  return Eigen::MakeAutoDiffScalar(acos(x.value()),x.derivatives() * (Scalar(-1)/sqrt(1-numext::abs2(x.value()))));)
 
 #undef EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY
 

From 70dad84b737374e97319733ebff6f36e86ac384d Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 14 Jun 2016 15:26:37 +0200
Subject: [PATCH 60/86] Generalize expr/expr and scalar/expr wrt scalar types.

---
 Eigen/src/Core/GlobalFunctions.h        | 34 +++++++++++++++++++------
 Eigen/src/plugins/ArrayCwiseBinaryOps.h |  4 +--
 test/mixingtypes.cpp                    |  4 ++-
 3 files changed, 31 insertions(+), 11 deletions(-)

diff --git a/Eigen/src/Core/GlobalFunctions.h b/Eigen/src/Core/GlobalFunctions.h
index 60e2ccfed..5ffa6c694 100644
--- a/Eigen/src/Core/GlobalFunctions.h
+++ b/Eigen/src/Core/GlobalFunctions.h
@@ -175,18 +175,36 @@ namespace Eigen
 #endif
   
   /**
-    * \brief Component-wise division of a scalar by array elements.
+    * \brief Component-wise division of the scalar \a s by array elements of \a a.
+    *
+    * \tparam Scalar is the scalar type of \a x. It must be compatible with the scalar type of the given array expression (\c Derived::Scalar).
+    *
+    * \relates ArrayBase
     **/
-  template <typename Derived>
-  inline const Eigen::CwiseUnaryOp<Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>, const Derived>
-    operator/(const typename Derived::Scalar& s, const Eigen::ArrayBase<Derived>& a)
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+  template<typename Scalar,typename Derived>
+  inline const CwiseBinaryOp<internal::scalar_quotient_op<Scalar,Derived::Scalar>,Constant<Scalar>,Derived>
+  operator/(const Scalar& s,const Eigen::ArrayBase<Derived>& a);
+#else
+  template<typename Scalar, typename Derived>
+  inline typename internal::enable_if<   !(internal::is_same<typename Derived::Scalar,Scalar>::value)
+                                      && ScalarBinaryOpTraits<Scalar,typename Derived::Scalar>::Defined,
+          const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,quotient) >::type
+  operator/(const Scalar& s, const Eigen::ArrayBase<Derived>& a)
   {
-    return Eigen::CwiseUnaryOp<Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>, const Derived>(
-      a.derived(),
-      Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>(s)  
-    );
+    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,quotient)(
+            typename internal::plain_constant_type<Derived,Scalar>::type(a.rows(), a.cols(), s), a.derived() );
   }
 
+  template<typename Derived>
+  inline const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename Derived::Scalar,Derived,quotient)
+  operator/(const typename Derived::Scalar& s, const Eigen::ArrayBase<Derived>& a)
+  {
+    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename Derived::Scalar,Derived,quotient)(
+      typename internal::plain_constant_type<Derived,typename Derived::Scalar>::type(a.rows(), a.cols(), s), a.derived() );
+  }
+#endif
+
   /** \cpp11 \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.
diff --git a/Eigen/src/plugins/ArrayCwiseBinaryOps.h b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
index 1e20e35d7..0c1429c75 100644
--- a/Eigen/src/plugins/ArrayCwiseBinaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
@@ -17,10 +17,10 @@ operator*(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
   */
 template<typename OtherDerived>
 EIGEN_DEVICE_FUNC
-EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_quotient_op<Scalar,typename OtherDerived::Scalar>, const Derived, const OtherDerived>
 operator/(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
 {
-  return CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
+  return CwiseBinaryOp<internal::scalar_quotient_op<Scalar,typename OtherDerived::Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
 }
 
 /** \returns an expression of the coefficient-wise min of \c *this and \a other
diff --git a/test/mixingtypes.cpp b/test/mixingtypes.cpp
index b38271a17..fe8c16470 100644
--- a/test/mixingtypes.cpp
+++ b/test/mixingtypes.cpp
@@ -82,6 +82,8 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
   // check scalar quotients
   VERIFY_MIX_SCALAR(vcf / sf , vcf / complex<float>(sf));
   VERIFY_MIX_SCALAR(vf / scf , vf.template cast<complex<float> >() / scf);
+  VERIFY_MIX_SCALAR(vf.array()  / scf, vf.template cast<complex<float> >().array() / scf);
+  VERIFY_MIX_SCALAR(scd / vd.array() , scd / vd.template cast<complex<double> >().array());
 
   // check scalar increment
   VERIFY_MIX_SCALAR(vcf.array() + sf , vcf.array() + complex<float>(sf));
@@ -225,7 +227,7 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
   VERIFY_IS_APPROX( md.array()  - mcd.array(), md.template cast<CD>().eval().array() - mcd.array() );
   VERIFY_IS_APPROX( mcd.array() - md.array(),  mcd.array() - md.template cast<CD>().eval().array() );
 
-//   VERIFY_IS_APPROX( md.array() / mcd.array(), md.template cast<CD>().eval().array() / mcd.array() );
+  VERIFY_IS_APPROX( md.array() / mcd.array(), md.template cast<CD>().eval().array() / mcd.array() );
   VERIFY_IS_APPROX( mcd.array() / md.array(), mcd.array() / md.template cast<CD>().eval().array() );
 
   VERIFY_IS_APPROX( md.array().pow(mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()) );

From 1004c4df99a3e4a019f05b83badb06f4e2df5ee6 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 14 Jun 2016 15:27:28 +0200
Subject: [PATCH 61/86] Cleanup unused functors.

---
 Eigen/src/Core/functors/BinaryFunctors.h | 113 -----------------------
 Eigen/src/Core/util/BlasUtil.h           |  13 ---
 2 files changed, 126 deletions(-)

diff --git a/Eigen/src/Core/functors/BinaryFunctors.h b/Eigen/src/Core/functors/BinaryFunctors.h
index 9e40303be..2c1331208 100644
--- a/Eigen/src/Core/functors/BinaryFunctors.h
+++ b/Eigen/src/Core/functors/BinaryFunctors.h
@@ -525,119 +525,6 @@ template<typename BinaryOp> struct bind2nd_op : BinaryOp {
 };
 template<typename BinaryOp> struct functor_traits<bind2nd_op<BinaryOp> > : functor_traits<BinaryOp> {};
 
-/** \internal
-  * \brief Template functor to multiply a scalar by a fixed other one
-  *
-  * \sa class CwiseUnaryOp, MatrixBase::operator*, MatrixBase::operator/
-  */
-/* NOTE why doing the pset1() in packetOp *is* an optimization ?
- * indeed it seems better to declare m_other as a Packet and do the pset1() once
- * in the constructor. However, in practice:
- *  - GCC does not like m_other as a Packet and generate a load every time it needs it
- *  - on the other hand GCC is able to moves the pset1() outside the loop :)
- *  - simpler code ;)
- * (ICC and gcc 4.4 seems to perform well in both cases, the issue is visible with y = a*x + b*y)
- */
-template<typename Scalar>
-struct scalar_multiple_op {
-  // FIXME default copy constructors seems bugged with std::complex<>
-  EIGEN_DEVICE_FUNC
-  EIGEN_STRONG_INLINE scalar_multiple_op(const scalar_multiple_op& other) : m_other(other.m_other) { }
-  EIGEN_DEVICE_FUNC
-  EIGEN_STRONG_INLINE scalar_multiple_op(const Scalar& other) : m_other(other) { }
-  EIGEN_DEVICE_FUNC
-  EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a * m_other; }
-  template <typename Packet>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
-  { return internal::pmul(a, pset1<Packet>(m_other)); }
-  typename add_const_on_value_type<typename NumTraits<Scalar>::Nested>::type m_other;
-};
-template<typename Scalar>
-struct functor_traits<scalar_multiple_op<Scalar> >
-{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
-
-
-/** \internal
-  * \brief Template functor to divide a scalar by a fixed other one
-  *
-  * This functor is used to implement the quotient of a matrix by
-  * a scalar where the scalar type is not necessarily a floating point type.
-  *
-  * \sa class CwiseUnaryOp, MatrixBase::operator/
-  */
-template<typename Scalar>
-struct scalar_quotient1_op {
-  // FIXME default copy constructors seems bugged with std::complex<>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_quotient1_op(const scalar_quotient1_op& other) : m_other(other.m_other) { }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_quotient1_op(const Scalar& other) : m_other(other) {}
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a / m_other; }
-  template <typename Packet>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
-  { return internal::pdiv(a, pset1<Packet>(m_other)); }
-  typename add_const_on_value_type<typename NumTraits<Scalar>::Nested>::type m_other;
-};
-template<typename Scalar>
-struct functor_traits<scalar_quotient1_op<Scalar> >
-{ enum { Cost = 2 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasDiv }; };
-
-
-
-/** \internal
-  * \brief Template functor to add a scalar to a fixed other one
-  * \sa class CwiseUnaryOp, Array::operator+
-  */
-/* If you wonder why doing the pset1() in packetOp() is an optimization check scalar_multiple_op */
-template<typename Scalar>
-struct scalar_add_op {
-  // FIXME default copy constructors seems bugged with std::complex<>
-  EIGEN_DEVICE_FUNC inline scalar_add_op(const scalar_add_op& other) : m_other(other.m_other) { }
-  EIGEN_DEVICE_FUNC inline scalar_add_op(const Scalar& other) : m_other(other) { }
-  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return a + m_other; }
-  template <typename Packet>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
-  { return internal::padd(a, pset1<Packet>(m_other)); }
-  const Scalar m_other;
-};
-template<typename Scalar>
-struct functor_traits<scalar_add_op<Scalar> >
-{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = packet_traits<Scalar>::HasAdd }; };
-
-/** \internal
-  * \brief Template functor to subtract a fixed scalar to another one
-  * \sa class CwiseUnaryOp, Array::operator-, struct scalar_add_op
-  */
-template<typename Scalar>
-struct scalar_sub_op {
-  EIGEN_DEVICE_FUNC inline scalar_sub_op(const scalar_sub_op& other) : m_other(other.m_other) { }
-  EIGEN_DEVICE_FUNC inline scalar_sub_op(const Scalar& other) : m_other(other) { }
-  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return a - m_other; }
-  template <typename Packet>
-  EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
-  { return internal::psub(a, pset1<Packet>(m_other)); }
-  const Scalar m_other;
-};
-template<typename Scalar>
-struct functor_traits<scalar_sub_op<Scalar> >
-{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = packet_traits<Scalar>::HasAdd }; };
-
-
-/** \internal
-  * \brief Template functor to compute the quotient between a scalar and array entries.
-  * \sa class CwiseUnaryOp, Cwise::inverse()
-  */
-template<typename Scalar>
-struct scalar_inverse_mult_op {
-  EIGEN_DEVICE_FUNC scalar_inverse_mult_op(const Scalar& other) : m_other(other) {}
-  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return m_other / a; }
-  template<typename Packet>
-  EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
-  { 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
 
diff --git a/Eigen/src/Core/util/BlasUtil.h b/Eigen/src/Core/util/BlasUtil.h
index 7e8f90d88..a85ad558f 100755
--- a/Eigen/src/Core/util/BlasUtil.h
+++ b/Eigen/src/Core/util/BlasUtil.h
@@ -316,19 +316,6 @@ struct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, NestedXpr, const Cwi
   { return Base::extractScalarFactor(x.lhs()) * x.rhs().functor().m_other; }
 };
 
-// pop scalar multiple (using deprecated scalar_multiple_op)
-template<typename Scalar, typename NestedXpr>
-struct blas_traits<CwiseUnaryOp<scalar_multiple_op<Scalar>, NestedXpr> >
- : blas_traits<NestedXpr>
-{
-  typedef blas_traits<NestedXpr> Base;
-  typedef CwiseUnaryOp<scalar_multiple_op<Scalar>, NestedXpr> XprType;
-  typedef typename Base::ExtractType ExtractType;
-  static inline ExtractType extract(const XprType& x) { return Base::extract(x.nestedExpression()); }
-  static inline Scalar extractScalarFactor(const XprType& x)
-  { return x.functor().m_other * Base::extractScalarFactor(x.nestedExpression()); }
-};
-
 // pop opposite
 template<typename Scalar, typename NestedXpr>
 struct blas_traits<CwiseUnaryOp<scalar_opposite_op<Scalar>, NestedXpr> >

From c4d10e921f02409d771e960647beae0b6d26dc88 Mon Sep 17 00:00:00 2001
From: Igor Babuschkin <igor@babuschk.in>
Date: Tue, 14 Jun 2016 19:44:07 +0100
Subject: [PATCH 62/86] Implement exclusive scan option

---
 .../Eigen/CXX11/src/Tensor/TensorBase.h       | 12 +++++-----
 .../Eigen/CXX11/src/Tensor/TensorScan.h       | 22 ++++++++++++-----
 unsupported/test/cxx11_tensor_scan.cpp        | 24 +++++++++++++++++++
 3 files changed, 46 insertions(+), 12 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h b/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h
index 8f3580ba7..87fa672f4 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h
@@ -486,22 +486,22 @@ class TensorBase<Derived, ReadOnlyAccessors>
     typedef TensorScanOp<internal::SumReducer<CoeffReturnType>, const Derived> TensorScanSumOp;
     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     const TensorScanSumOp
-    cumsum(const Index& axis) const {
-      return TensorScanSumOp(derived(), axis);
+    cumsum(const Index& axis, bool exclusive = false) const {
+      return TensorScanSumOp(derived(), axis, exclusive);
     }
 
     typedef TensorScanOp<internal::ProdReducer<CoeffReturnType>, const Derived> TensorScanProdOp;
     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     const TensorScanProdOp
-    cumprod(const Index& axis) const {
-      return TensorScanProdOp(derived(), axis);
+    cumprod(const Index& axis, bool exclusive = false) const {
+      return TensorScanProdOp(derived(), axis, exclusive);
     }
 
     template <typename Reducer>
     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     const TensorScanOp<Reducer, const Derived>
-    scan(const Index& axis, const Reducer& reducer) const {
-      return TensorScanOp<Reducer, const Derived>(derived(), axis, reducer);
+    scan(const Index& axis, const Reducer& reducer, bool exclusive = false) const {
+      return TensorScanOp<Reducer, const Derived>(derived(), axis, exclusive, reducer);
     }
 
     // Reductions.
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h b/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h
index 5207f6a8d..1aa196b84 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h
@@ -57,8 +57,8 @@ public:
   typedef typename Eigen::internal::traits<TensorScanOp>::Index Index;
 
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorScanOp(
-      const XprType& expr, const Index& axis, const Op& op = Op())
-      : m_expr(expr), m_axis(axis), m_accumulator(op) {}
+      const XprType& expr, const Index& axis, bool exclusive = false, const Op& op = Op())
+      : m_expr(expr), m_axis(axis), m_accumulator(op), m_exclusive(exclusive) {}
 
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
   const Index axis() const { return m_axis; }
@@ -66,11 +66,14 @@ public:
   const XprType& expression() const { return m_expr; }
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
   const Op accumulator() const { return m_accumulator; }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  bool exclusive() const { return m_exclusive; }
 
 protected:
   typename XprType::Nested m_expr;
   const Index m_axis;
   const Op m_accumulator;
+  const bool m_exclusive;
 };
 
 // Eval as rvalue
@@ -99,6 +102,7 @@ struct TensorEvaluator<const TensorScanOp<Op, ArgType>, Device> {
       : m_impl(op.expression(), device),
         m_device(device),
         m_axis(op.axis()),
+        m_exclusive(op.exclusive()),
         m_accumulator(op.accumulator()),
         m_dimensions(m_impl.dimensions()),
         m_size(m_dimensions[m_axis]),
@@ -168,6 +172,7 @@ protected:
   TensorEvaluator<ArgType, Device> m_impl;
   const Device& m_device;
   const Index m_axis;
+  const bool m_exclusive;
   Op m_accumulator;
   const Dimensions& m_dimensions;
   const Index& m_size;
@@ -176,7 +181,7 @@ protected:
 
   // TODO(ibab) Parallelize this single-threaded implementation if desired
   EIGEN_DEVICE_FUNC void accumulateTo(Scalar* data) {
-    // We fix the index along the scan axis to 0 and perform an
+    // We fix the index along the scan axis to 0 and perform a
     // scan per remaining entry. The iteration is split into two nested
     // loops to avoid an integer division by keeping track of each idx1 and idx2.
     for (Index idx1 = 0; idx1 < dimensions().TotalSize() / m_size; idx1 += m_stride) {
@@ -184,12 +189,17 @@ protected:
           // Calculate the starting offset for the scan
           Index offset = idx1 * m_size + idx2;
 
-          // Compute the prefix sum along the axis, starting at the calculated offset
+          // Compute the scan along the axis, starting at the calculated offset
           CoeffReturnType accum = m_accumulator.initialize();
           for (Index idx3 = 0; idx3 < m_size; idx3++) {
             Index curr = offset + idx3 * m_stride;
-            m_accumulator.reduce(m_impl.coeff(curr), &accum);
-            data[curr] = m_accumulator.finalize(accum);
+            if (m_exclusive) {
+              data[curr] = m_accumulator.finalize(accum);
+              m_accumulator.reduce(m_impl.coeff(curr), &accum);
+            } else {
+              m_accumulator.reduce(m_impl.coeff(curr), &accum);
+              data[curr] = m_accumulator.finalize(accum);
+            }
           }
        }
     }
diff --git a/unsupported/test/cxx11_tensor_scan.cpp b/unsupported/test/cxx11_tensor_scan.cpp
index dbd3023d7..bafa6c96e 100644
--- a/unsupported/test/cxx11_tensor_scan.cpp
+++ b/unsupported/test/cxx11_tensor_scan.cpp
@@ -38,6 +38,30 @@ static void test_1d_scan()
     }
 }
 
+template <int DataLayout, typename Type=float>
+static void test_1d_inclusive_scan()
+{
+    int size = 50;
+    Tensor<Type, 1, DataLayout> tensor(size);
+    tensor.setRandom();
+    Tensor<Type, 1, DataLayout> result = tensor.cumsum(0, true);
+
+    VERIFY_IS_EQUAL(tensor.dimension(0), result.dimension(0));
+
+    float accum = 0;
+    for (int i = 0; i < size; i++) {
+      VERIFY_IS_EQUAL(result(i), accum);
+      accum += tensor(i);
+    }
+
+    accum = 1;
+    result = tensor.cumprod(0, true);
+    for (int i = 0; i < size; i++) {
+      VERIFY_IS_EQUAL(result(i), accum);
+      accum *= tensor(i);
+    }
+}
+
 template <int DataLayout, typename Type=float>
 static void test_4d_scan()
 {

From 101ea26f5e18919972b321b5f7e3ef4e07be3fd6 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Wed, 15 Jun 2016 00:01:16 +0200
Subject: [PATCH 63/86] Include the cost of stores in unrolling (also fix
 infinite unrolling with expression costing 0 like Constant)

---
 Eigen/src/Core/AssignEvaluator.h | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Eigen/src/Core/AssignEvaluator.h b/Eigen/src/Core/AssignEvaluator.h
index f966724cc..1df717bac 100644
--- a/Eigen/src/Core/AssignEvaluator.h
+++ b/Eigen/src/Core/AssignEvaluator.h
@@ -116,9 +116,9 @@ private:
                         : 1,
     UnrollingLimit      = EIGEN_UNROLLING_LIMIT * ActualPacketSize,
     MayUnrollCompletely = int(Dst::SizeAtCompileTime) != Dynamic
-                       && int(Dst::SizeAtCompileTime) * int(SrcEvaluator::CoeffReadCost) <= int(UnrollingLimit),
+                       && int(Dst::SizeAtCompileTime) * (int(DstEvaluator::CoeffReadCost)+int(SrcEvaluator::CoeffReadCost)) <= int(UnrollingLimit),
     MayUnrollInner      = int(InnerSize) != Dynamic
-                       && int(InnerSize) * int(SrcEvaluator::CoeffReadCost) <= int(UnrollingLimit)
+                       && int(InnerSize) * (int(DstEvaluator::CoeffReadCost)+int(SrcEvaluator::CoeffReadCost)) <= int(UnrollingLimit)
   };
 
 public:

From 4e7c3af874e9e1273b5bf3acdc4b53e8c6bdf086 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Wed, 15 Jun 2016 00:04:10 +0200
Subject: [PATCH 64/86] Cleanup useless helper: internal::product_result_scalar

---
 Eigen/src/Core/Product.h | 36 +-----------------------------------
 1 file changed, 1 insertion(+), 35 deletions(-)

diff --git a/Eigen/src/Core/Product.h b/Eigen/src/Core/Product.h
index bad289761..ae0c94b38 100644
--- a/Eigen/src/Core/Product.h
+++ b/Eigen/src/Core/Product.h
@@ -16,40 +16,6 @@ template<typename Lhs, typename Rhs, int Option, typename StorageKind> class Pro
 
 namespace internal {
 
-// Determine the scalar of Product<Lhs, Rhs>. This is normally the same as Lhs::Scalar times
-// Rhs::Scalar, but product with permutation matrices inherit the scalar of the other factor.
-// TODO: this could be removed once ScalarBinaryOpTraits handles void.
-template<typename Lhs, typename Rhs, typename LhsShape = typename evaluator_traits<Lhs>::Shape, 
-         typename RhsShape = typename evaluator_traits<Rhs>::Shape >
-struct product_result_scalar
-{
-  typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
-};
-
-template<typename Lhs, typename Rhs, typename RhsShape>
-struct product_result_scalar<Lhs, Rhs, PermutationShape, RhsShape>
-{
-  typedef typename Rhs::Scalar Scalar;
-};
-
-template<typename Lhs, typename Rhs, typename LhsShape>
-  struct product_result_scalar<Lhs, Rhs, LhsShape, PermutationShape>
-{
-  typedef typename Lhs::Scalar Scalar;
-};
-
-template<typename Lhs, typename Rhs, typename RhsShape>
-struct product_result_scalar<Lhs, Rhs, TranspositionsShape, RhsShape>
-{
-  typedef typename Rhs::Scalar Scalar;
-};
-
-template<typename Lhs, typename Rhs, typename LhsShape>
-  struct product_result_scalar<Lhs, Rhs, LhsShape, TranspositionsShape>
-{
-  typedef typename Lhs::Scalar Scalar;
-};
-
 template<typename Lhs, typename Rhs, int Option>
 struct traits<Product<Lhs, Rhs, Option> >
 {
@@ -60,7 +26,7 @@ struct traits<Product<Lhs, Rhs, Option> >
   
   typedef MatrixXpr XprKind;
   
-  typedef typename product_result_scalar<LhsCleaned,RhsCleaned>::Scalar Scalar;
+  typedef typename ScalarBinaryOpTraits<typename traits<LhsCleaned>::Scalar, typename traits<RhsCleaned>::Scalar>::ReturnType Scalar;
   typedef typename product_promote_storage_type<typename LhsTraits::StorageKind,
                                                 typename RhsTraits::StorageKind,
                                                 internal::product_type<Lhs,Rhs>::ret>::ret StorageKind;

From aedc5be1d6b6b42f5037c4005b437f3e552ac101 Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Tue, 14 Jun 2016 17:51:47 -0700
Subject: [PATCH 65/86] Avoid generating pseudo random numbers that are
 multiple of 5: this helps spread the load over multiple cpus without havind
 to rely on work stealing.

---
 .../src/ThreadPool/NonBlockingThreadPool.h    | 19 +++++++++++--------
 1 file changed, 11 insertions(+), 8 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h b/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
index c094563b7..30b292352 100644
--- a/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
@@ -99,10 +99,12 @@ class NonBlockingThreadPoolTempl : public Eigen::ThreadPoolInterface {
   typedef typename Environment::EnvThread Thread;
 
   struct PerThread {
-    bool inited;
+    PerThread() : pool(NULL), index(-1) {
+      rand = std::hash<std::thread::id>()(std::this_thread::get_id());
+    }
     NonBlockingThreadPoolTempl* pool;  // Parent pool, or null for normal threads.
     unsigned index;         // Worker thread index in pool.
-    unsigned rand;          // Random generator state.
+    uint64_t rand;          // Random generator state.
   };
 
   Environment env_;
@@ -235,17 +237,18 @@ class NonBlockingThreadPoolTempl : public Eigen::ThreadPoolInterface {
     return -1;
   }
 
-  PerThread* GetPerThread() {
+  static EIGEN_STRONG_INLINE PerThread* GetPerThread() {
     EIGEN_THREAD_LOCAL PerThread per_thread_;
     PerThread* pt = &per_thread_;
-    if (pt->inited) return pt;
-    pt->inited = true;
-    pt->rand = static_cast<unsigned>(std::hash<std::thread::id>()(std::this_thread::get_id()));
     return pt;
   }
 
-  static unsigned Rand(unsigned* state) {
-    return *state = *state * 1103515245 + 12345;
+  static EIGEN_STRONG_INLINE unsigned Rand(uint64_t* state) {
+    uint64_t current = *state;
+    // Update the internal state
+    *state = current * 6364136223846793005ULL + 0xda3e39cb94b95bdbULL;
+    // Generate the random output (using the PCG-XSH-RS scheme)
+    return (current ^ (current >> 22)) >> (22 + (current >> 61));
   }
 };
 

From c55035b9c0c894551850d122ac8b0cf1a053c28e Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Wed, 15 Jun 2016 09:57:33 +0200
Subject: [PATCH 66/86] Include the cost of stores in unrolling of triangular
 expressions.

---
 Eigen/src/Core/TriangularMatrix.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Eigen/src/Core/TriangularMatrix.h b/Eigen/src/Core/TriangularMatrix.h
index 8731e9127..c599e0b32 100644
--- a/Eigen/src/Core/TriangularMatrix.h
+++ b/Eigen/src/Core/TriangularMatrix.h
@@ -794,7 +794,7 @@ void call_triangular_assignment_loop(const DstXprType& dst, const SrcXprType& sr
   enum {
       unroll = DstXprType::SizeAtCompileTime != Dynamic
             && SrcEvaluatorType::CoeffReadCost < HugeCost
-            && DstXprType::SizeAtCompileTime * SrcEvaluatorType::CoeffReadCost / 2 <= EIGEN_UNROLLING_LIMIT
+            && DstXprType::SizeAtCompileTime * (DstEvaluatorType::CoeffReadCost+SrcEvaluatorType::CoeffReadCost) / 2 <= EIGEN_UNROLLING_LIMIT
     };
   
   triangular_assignment_loop<Kernel, Mode, unroll ? int(DstXprType::SizeAtCompileTime) : Dynamic, SetOpposite>::run(kernel);

From 4794834397aa0e2a6570a2f736b65b72b7db1aad Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Wed, 15 Jun 2016 09:58:49 +0200
Subject: [PATCH 67/86] Propagate functor to ScalarBinaryOpTraits

---
 Eigen/src/Core/GlobalFunctions.h | 6 +++---
 Eigen/src/Core/util/Macros.h     | 4 ++--
 2 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/Eigen/src/Core/GlobalFunctions.h b/Eigen/src/Core/GlobalFunctions.h
index 5ffa6c694..0361b40ad 100644
--- a/Eigen/src/Core/GlobalFunctions.h
+++ b/Eigen/src/Core/GlobalFunctions.h
@@ -103,7 +103,7 @@ namespace Eigen
 #else
   template<typename Derived,typename ScalarExponent>
   inline typename internal::enable_if<   !(internal::is_same<typename Derived::Scalar,ScalarExponent>::value)
-                                      && ScalarBinaryOpTraits<typename Derived::Scalar,ScalarExponent>::Defined,
+                                      && ScalarBinaryOpTraits<typename Derived::Scalar,ScalarExponent,internal::scalar_pow_op<typename Derived::Scalar,ScalarExponent> >::Defined,
           const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,ScalarExponent,pow) >::type
   pow(const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent) {
     return x.derived().pow(exponent);
@@ -157,7 +157,7 @@ namespace Eigen
 #else
   template<typename Scalar, typename Derived>
   inline typename internal::enable_if<   !(internal::is_same<typename Derived::Scalar,Scalar>::value)
-                                      && ScalarBinaryOpTraits<Scalar,typename Derived::Scalar>::Defined,
+                                      && ScalarBinaryOpTraits<Scalar,typename Derived::Scalar,internal::scalar_pow_op<Scalar,typename Derived::Scalar> >::Defined,
           const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,pow) >::type
   pow(const Scalar& x, const Eigen::ArrayBase<Derived>& exponents)
   {
@@ -188,7 +188,7 @@ namespace Eigen
 #else
   template<typename Scalar, typename Derived>
   inline typename internal::enable_if<   !(internal::is_same<typename Derived::Scalar,Scalar>::value)
-                                      && ScalarBinaryOpTraits<Scalar,typename Derived::Scalar>::Defined,
+                                      && ScalarBinaryOpTraits<Scalar,typename Derived::Scalar,internal::scalar_pow_op<Scalar,typename Derived::Scalar> >::Defined,
           const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,quotient) >::type
   operator/(const Scalar& s, const Eigen::ArrayBase<Derived>& a)
   {
diff --git a/Eigen/src/Core/util/Macros.h b/Eigen/src/Core/util/Macros.h
index 031e0892e..87cc44657 100644
--- a/Eigen/src/Core/util/Macros.h
+++ b/Eigen/src/Core/util/Macros.h
@@ -914,7 +914,7 @@ namespace Eigen {
   } \
   \
   template <typename T> EIGEN_DEVICE_FUNC inline \
-  typename internal::enable_if<ScalarBinaryOpTraits<Scalar,T>::Defined, \
+  typename internal::enable_if<ScalarBinaryOpTraits<Scalar,T,EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<Scalar,T> >::Defined, \
                                const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,T,OPNAME) >::type \
   (METHOD)(const T& scalar) const { \
     return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,T,OPNAME)(derived(), \
@@ -930,7 +930,7 @@ namespace Eigen {
   } \
   \
   template <typename T> EIGEN_DEVICE_FUNC inline friend \
-  typename internal::enable_if<ScalarBinaryOpTraits<T,Scalar>::Defined, \
+  typename internal::enable_if<ScalarBinaryOpTraits<T,Scalar,EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<T,Scalar> >::Defined, \
                                const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(T,Derived,OPNAME) >::type \
   (METHOD)(const T& scalar, const StorageBaseType& matrix) { \
     return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(T,Derived,OPNAME)( \

From eb91345d641cc1aa7a62af1bf6db3e38a6d7225a Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Wed, 15 Jun 2016 15:22:03 +0200
Subject: [PATCH 68/86] Move scalar/expr to ArrayBase and fix documentation

---
 Eigen/src/Core/GlobalFunctions.h         | 31 ------------------------
 Eigen/src/plugins/ArrayCwiseBinaryOps.h  | 24 ++++++++++++++----
 Eigen/src/plugins/CommonCwiseBinaryOps.h |  6 ++---
 3 files changed, 22 insertions(+), 39 deletions(-)

diff --git a/Eigen/src/Core/GlobalFunctions.h b/Eigen/src/Core/GlobalFunctions.h
index 0361b40ad..b9c3ec25b 100644
--- a/Eigen/src/Core/GlobalFunctions.h
+++ b/Eigen/src/Core/GlobalFunctions.h
@@ -173,37 +173,6 @@ namespace Eigen
       typename internal::plain_constant_type<Derived,typename Derived::Scalar>::type(exponents.rows(), exponents.cols(), x), exponents.derived() );
   }
 #endif
-  
-  /**
-    * \brief Component-wise division of the scalar \a s by array elements of \a a.
-    *
-    * \tparam Scalar is the scalar type of \a x. It must be compatible with the scalar type of the given array expression (\c Derived::Scalar).
-    *
-    * \relates ArrayBase
-    **/
-#ifdef EIGEN_PARSED_BY_DOXYGEN
-  template<typename Scalar,typename Derived>
-  inline const CwiseBinaryOp<internal::scalar_quotient_op<Scalar,Derived::Scalar>,Constant<Scalar>,Derived>
-  operator/(const Scalar& s,const Eigen::ArrayBase<Derived>& a);
-#else
-  template<typename Scalar, typename Derived>
-  inline typename internal::enable_if<   !(internal::is_same<typename Derived::Scalar,Scalar>::value)
-                                      && ScalarBinaryOpTraits<Scalar,typename Derived::Scalar,internal::scalar_pow_op<Scalar,typename Derived::Scalar> >::Defined,
-          const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,quotient) >::type
-  operator/(const Scalar& s, const Eigen::ArrayBase<Derived>& a)
-  {
-    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,quotient)(
-            typename internal::plain_constant_type<Derived,Scalar>::type(a.rows(), a.cols(), s), a.derived() );
-  }
-
-  template<typename Derived>
-  inline const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename Derived::Scalar,Derived,quotient)
-  operator/(const typename Derived::Scalar& s, const Eigen::ArrayBase<Derived>& a)
-  {
-    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename Derived::Scalar,Derived,quotient)(
-      typename internal::plain_constant_type<Derived,typename Derived::Scalar>::type(a.rows(), a.cols(), s), a.derived() );
-  }
-#endif
 
   /** \cpp11 \returns an expression of the coefficient-wise igamma(\a a, \a x) to the given arrays.
     *
diff --git a/Eigen/src/plugins/ArrayCwiseBinaryOps.h b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
index 0c1429c75..6cb609604 100644
--- a/Eigen/src/plugins/ArrayCwiseBinaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
@@ -100,7 +100,7 @@ EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(pow,pow);
   * \sa ArrayBase::pow(ArrayBase), square(), cube(), exp(), log()
   */
 template<typename T>
-const CwiseBinaryOp<internal::scalar_pow_op<Scalar,T>,Derived,Constant<Scalar> > pow(const T& exponent) const;
+const CwiseBinaryOp<internal::scalar_pow_op<Scalar,T>,Derived,Constant<T> > pow(const T& exponent) const;
 #endif
 
 
@@ -224,13 +224,13 @@ EIGEN_MAKE_SCALAR_BINARY_OP(operator+,sum);
   * \sa operator+=(), operator-()
   */
 template<typename T>
-const CwiseBinaryOp<internal::scalar_sum_op<Scalar,T>,Derived,Constant<Scalar> > operator+(const T& scalar) const;
+const CwiseBinaryOp<internal::scalar_sum_op<Scalar,T>,Derived,Constant<T> > operator+(const T& scalar) const;
 /** \returns an expression of \a expr with each coeff incremented by the constant \a scalar
   *
   * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
   */
 template<typename T> friend
-const CwiseBinaryOp<internal::scalar_sum_op<T,Scalar>,Constant<Scalar>,Derived> operator+(const T& scalar, const StorageBaseType& expr);
+const CwiseBinaryOp<internal::scalar_sum_op<T,Scalar>,Constant<T>,Derived> operator+(const T& scalar, const StorageBaseType& expr);
 #endif
 
 #ifndef EIGEN_PARSED_BY_DOXYGEN
@@ -246,13 +246,27 @@ EIGEN_MAKE_SCALAR_BINARY_OP(operator-,difference);
   * \sa operator+=(), operator-()
   */
 template<typename T>
-const CwiseBinaryOp<internal::scalar_difference_op<Scalar,T>,Derived,Constant<Scalar> > operator-(const T& scalar) const;
+const CwiseBinaryOp<internal::scalar_difference_op<Scalar,T>,Derived,Constant<T> > operator-(const T& scalar) const;
 /** \returns an expression of the constant matrix of value \a scalar decremented by the coefficients of \a expr
   *
   * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
   */
 template<typename T> friend
-const CwiseBinaryOp<internal::scalar_difference_op<T,Scalar>,Constant<Scalar>,Derived> operator-(const T& scalar, const StorageBaseType& expr);
+const CwiseBinaryOp<internal::scalar_difference_op<T,Scalar>,Constant<T>,Derived> operator-(const T& scalar, const StorageBaseType& expr);
+#endif
+
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+  EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(operator/,quotient)
+#else
+  /**
+    * \brief Component-wise division of the scalar \a s by array elements of \a a.
+    *
+    * \tparam Scalar is the scalar type of \a x. It must be compatible with the scalar type of the given array expression (\c Derived::Scalar).
+    */
+  template<typename T> friend
+  inline const CwiseBinaryOp<internal::scalar_quotient_op<T,Scalar>,Constant<T>,Derived>
+  operator/(const T& s,const StorageBaseType& a);
 #endif
 
 /** \returns an expression of the coefficient-wise && operator of *this and \a other
diff --git a/Eigen/src/plugins/CommonCwiseBinaryOps.h b/Eigen/src/plugins/CommonCwiseBinaryOps.h
index 03c4aac94..afac08a3f 100644
--- a/Eigen/src/plugins/CommonCwiseBinaryOps.h
+++ b/Eigen/src/plugins/CommonCwiseBinaryOps.h
@@ -54,13 +54,13 @@ EIGEN_MAKE_SCALAR_BINARY_OP(operator*,product);
   * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
   */
 template<typename T>
-const CwiseBinaryOp<internal::scalar_product_op<Scalar,T>,Derived,Constant<Scalar> > operator*(const T& scalar) const;
+const CwiseBinaryOp<internal::scalar_product_op<Scalar,T>,Derived,Constant<T> > operator*(const T& scalar) const;
 /** \returns an expression of \a expr scaled by the scalar factor \a scalar
   *
   * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
   */
 template<typename T> friend
-const CwiseBinaryOp<internal::scalar_product_op<T,Scalar>,Constant<Scalar>,Derived> operator*(const T& scalar, const StorageBaseType& expr);
+const CwiseBinaryOp<internal::scalar_product_op<T,Scalar>,Constant<T>,Derived> operator*(const T& scalar, const StorageBaseType& expr);
 #endif
 
 
@@ -73,5 +73,5 @@ EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(operator/,quotient);
   * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
   */
 template<typename T>
-const CwiseBinaryOp<internal::scalar_quotient_op<Scalar,T>,Derived,Constant<Scalar> > operator/(const T& scalar) const;
+const CwiseBinaryOp<internal::scalar_quotient_op<Scalar,T>,Derived,Constant<T> > operator/(const T& scalar) const;
 #endif

From 67c12531e567629e84713fbb3150560c916bd08c Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Wed, 15 Jun 2016 18:11:33 +0200
Subject: [PATCH 69/86] Fix warnings with gcc

---
 Eigen/src/plugins/ArrayCwiseBinaryOps.h  | 6 +++---
 Eigen/src/plugins/CommonCwiseBinaryOps.h | 4 ++--
 2 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/Eigen/src/plugins/ArrayCwiseBinaryOps.h b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
index 6cb609604..19e25ab62 100644
--- a/Eigen/src/plugins/ArrayCwiseBinaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
@@ -85,7 +85,7 @@ max
 EIGEN_MAKE_CWISE_BINARY_OP(pow,pow)
 
 #ifndef EIGEN_PARSED_BY_DOXYGEN
-EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(pow,pow);
+EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(pow,pow)
 #else
 /** \returns an expression of the coefficients of \c *this rasied to the constant power \a exponent
   *
@@ -212,7 +212,7 @@ EIGEN_MAKE_CWISE_COMP_OP(operator!=, NEQ)
 
 // scalar addition
 #ifndef EIGEN_PARSED_BY_DOXYGEN
-EIGEN_MAKE_SCALAR_BINARY_OP(operator+,sum);
+EIGEN_MAKE_SCALAR_BINARY_OP(operator+,sum)
 #else
 /** \returns an expression of \c *this with each coeff incremented by the constant \a scalar
   *
@@ -234,7 +234,7 @@ const CwiseBinaryOp<internal::scalar_sum_op<T,Scalar>,Constant<T>,Derived> opera
 #endif
 
 #ifndef EIGEN_PARSED_BY_DOXYGEN
-EIGEN_MAKE_SCALAR_BINARY_OP(operator-,difference);
+EIGEN_MAKE_SCALAR_BINARY_OP(operator-,difference)
 #else
 /** \returns an expression of \c *this with each coeff decremented by the constant \a scalar
   *
diff --git a/Eigen/src/plugins/CommonCwiseBinaryOps.h b/Eigen/src/plugins/CommonCwiseBinaryOps.h
index afac08a3f..b51ee9e4c 100644
--- a/Eigen/src/plugins/CommonCwiseBinaryOps.h
+++ b/Eigen/src/plugins/CommonCwiseBinaryOps.h
@@ -47,7 +47,7 @@ binaryExpr(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other, const Cu
 
 
 #ifndef EIGEN_PARSED_BY_DOXYGEN
-EIGEN_MAKE_SCALAR_BINARY_OP(operator*,product);
+EIGEN_MAKE_SCALAR_BINARY_OP(operator*,product)
 #else
 /** \returns an expression of \c *this scaled by the scalar factor \a scalar
   *
@@ -66,7 +66,7 @@ const CwiseBinaryOp<internal::scalar_product_op<T,Scalar>,Constant<T>,Derived> o
 
 
 #ifndef EIGEN_PARSED_BY_DOXYGEN
-EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(operator/,quotient);
+EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(operator/,quotient)
 #else
 /** \returns an expression of \c *this divided by the scalar value \a scalar
   *

From b055590e9135ffe762775ec919e490513b6974fa Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Thu, 16 Jun 2016 11:37:40 -0700
Subject: [PATCH 70/86] Made log1p_impl usable inside a GPU kernel

---
 Eigen/src/Core/MathFunctions.h | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
index ece04b754..342b47ced 100644
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
@@ -462,7 +462,7 @@ struct arg_retval
 template<typename Scalar, bool isComplex = NumTraits<Scalar>::IsComplex >
 struct log1p_impl
 {
-  static inline Scalar run(const Scalar& x)
+  static EIGEN_DEVICE_FUNC inline Scalar run(const Scalar& x)
   {
     EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
     typedef typename NumTraits<Scalar>::Real RealScalar;
@@ -472,7 +472,7 @@ struct log1p_impl
   }
 };
 
-#if EIGEN_HAS_CXX11_MATH
+#if EIGEN_HAS_CXX11_MATH && !defined(__CUDACC__)
 template<typename Scalar>
 struct log1p_impl<Scalar, false> {
   static inline Scalar run(const Scalar& x)

From de32f8d656c3ea7855ced77457ea661e43d417b7 Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Mon, 20 Jun 2016 10:46:45 -0700
Subject: [PATCH 71/86] Fixed the printing of rank-0 tensors

---
 unsupported/Eigen/CXX11/src/Tensor/TensorIO.h | 68 +++++++++++++------
 unsupported/test/cxx11_tensor_io.cpp          | 16 +++++
 2 files changed, 62 insertions(+), 22 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h b/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h
index 38a833f82..3db692ac6 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h
@@ -17,34 +17,58 @@ template<>
 struct significant_decimals_impl<std::string>
     : significant_decimals_default_impl<std::string, true>
 {};
-}
 
 
-template <typename T>
-std::ostream& operator << (std::ostream& os, const TensorBase<T, ReadOnlyAccessors>& expr) {
-  // Evaluate the expression if needed
-  TensorForcedEvalOp<const T> eval = expr.eval();
-  TensorEvaluator<const TensorForcedEvalOp<const T>, DefaultDevice> tensor(eval, DefaultDevice());
-  tensor.evalSubExprsIfNeeded(NULL);
-
-  typedef typename internal::remove_const<typename T::Scalar>::type Scalar;
-  typedef typename T::Index Index;
-  typedef typename TensorEvaluator<const TensorForcedEvalOp<const T>, DefaultDevice>::Dimensions Dimensions;
-  const Index total_size = internal::array_prod(tensor.dimensions());
-
-  // Print the tensor as a 1d vector or a 2d matrix.
-  static const int rank = internal::array_size<Dimensions>::value;
-  if (rank == 0) {
-    os << tensor.coeff(0);
-  } else if (rank == 1) {
-    Map<const Array<Scalar, Dynamic, 1> > array(const_cast<Scalar*>(tensor.data()), total_size);
-    os << array;
-  } else {
+// Print the tensor as a 2d matrix
+template <typename Tensor, int Rank>
+struct TensorPrinter {
+  static void run (std::ostream& os, const Tensor& tensor) {
+    typedef typename internal::remove_const<typename Tensor::Scalar>::type Scalar;
+    typedef typename Tensor::Index Index;
+    const Index total_size = internal::array_prod(tensor.dimensions());
     const Index first_dim = Eigen::internal::array_get<0>(tensor.dimensions());
-    static const int layout = TensorEvaluator<const TensorForcedEvalOp<const T>, DefaultDevice>::Layout;
+    static const int layout = Tensor::Layout;
     Map<const Array<Scalar, Dynamic, Dynamic, layout> > matrix(const_cast<Scalar*>(tensor.data()), first_dim, total_size/first_dim);
     os << matrix;
   }
+};
+
+
+// Print the tensor as a vector
+template <typename Tensor>
+struct TensorPrinter<Tensor, 1> {
+  static void run (std::ostream& os, const Tensor& tensor) {
+    typedef typename internal::remove_const<typename Tensor::Scalar>::type Scalar;
+    typedef typename Tensor::Index Index;
+    const Index total_size = internal::array_prod(tensor.dimensions());
+    Map<const Array<Scalar, Dynamic, 1> > array(const_cast<Scalar*>(tensor.data()), total_size);
+    os << array;
+  }
+};
+
+
+// Print the tensor as a scalar
+template <typename Tensor>
+struct TensorPrinter<Tensor, 0> {
+  static void run (std::ostream& os, const Tensor& tensor) {
+    os << tensor.coeff(0);
+  }
+};
+}
+
+template <typename T>
+std::ostream& operator << (std::ostream& os, const TensorBase<T, ReadOnlyAccessors>& expr) {
+  typedef TensorEvaluator<const TensorForcedEvalOp<const T>, DefaultDevice> Evaluator;
+  typedef typename Evaluator::Dimensions Dimensions;
+
+  // Evaluate the expression if needed
+  TensorForcedEvalOp<const T> eval = expr.eval();
+  Evaluator tensor(eval, DefaultDevice());
+  tensor.evalSubExprsIfNeeded(NULL);
+
+  // Print the result
+  static const int rank = internal::array_size<Dimensions>::value;
+  internal::TensorPrinter<Evaluator, rank>::run(os, tensor);
 
   // Cleanup.
   tensor.cleanup();
diff --git a/unsupported/test/cxx11_tensor_io.cpp b/unsupported/test/cxx11_tensor_io.cpp
index 8bbcf7089..8267dcadd 100644
--- a/unsupported/test/cxx11_tensor_io.cpp
+++ b/unsupported/test/cxx11_tensor_io.cpp
@@ -13,6 +13,20 @@
 #include <Eigen/CXX11/Tensor>
 
 
+template<int DataLayout>
+static void test_output_0d()
+{
+  Tensor<int, 0, DataLayout> tensor;
+  tensor() = 123;
+
+  std::stringstream os;
+  os << tensor;
+
+  std::string expected("123");
+  VERIFY_IS_EQUAL(std::string(os.str()), expected);
+}
+
+
 template<int DataLayout>
 static void test_output_1d()
 {
@@ -101,6 +115,8 @@ static void test_output_const()
 
 void test_cxx11_tensor_io()
 {
+  CALL_SUBTEST(test_output_0d<ColMajor>());
+  CALL_SUBTEST(test_output_0d<RowMajor>());
   CALL_SUBTEST(test_output_1d<ColMajor>());
   CALL_SUBTEST(test_output_1d<RowMajor>());
   CALL_SUBTEST(test_output_2d<ColMajor>());

From c58df317473277b297dd018a2dc3d8fe85b00c92 Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Tue, 21 Jun 2016 09:22:43 -0700
Subject: [PATCH 72/86] Handle empty tensors in the print functions

---
 unsupported/Eigen/CXX11/src/Tensor/TensorIO.h | 22 ++++++++++++++-----
 1 file changed, 16 insertions(+), 6 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h b/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h
index 3db692ac6..58ffaefab 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h
@@ -26,10 +26,15 @@ struct TensorPrinter {
     typedef typename internal::remove_const<typename Tensor::Scalar>::type Scalar;
     typedef typename Tensor::Index Index;
     const Index total_size = internal::array_prod(tensor.dimensions());
-    const Index first_dim = Eigen::internal::array_get<0>(tensor.dimensions());
-    static const int layout = Tensor::Layout;
-    Map<const Array<Scalar, Dynamic, Dynamic, layout> > matrix(const_cast<Scalar*>(tensor.data()), first_dim, total_size/first_dim);
-    os << matrix;
+    if (total_size == 0) {
+      os << "Empty tensor of rank " << Rank;
+    }
+    else {
+      const Index first_dim = Eigen::internal::array_get<0>(tensor.dimensions());
+      static const int layout = Tensor::Layout;
+      Map<const Array<Scalar, Dynamic, Dynamic, layout> > matrix(const_cast<Scalar*>(tensor.data()), first_dim, total_size/first_dim);
+      os << matrix;
+    }
   }
 };
 
@@ -41,8 +46,13 @@ struct TensorPrinter<Tensor, 1> {
     typedef typename internal::remove_const<typename Tensor::Scalar>::type Scalar;
     typedef typename Tensor::Index Index;
     const Index total_size = internal::array_prod(tensor.dimensions());
-    Map<const Array<Scalar, Dynamic, 1> > array(const_cast<Scalar*>(tensor.data()), total_size);
-    os << array;
+    if (total_size == 0) {
+      os << "Empty tensor of rank 1";
+    }
+    else {
+      Map<const Array<Scalar, Dynamic, 1> > array(const_cast<Scalar*>(tensor.data()), total_size);
+      os << array;
+    }
   }
 };
 

From f8fcd6b32d6b1a3613330e553bb3bc52a0007192 Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Wed, 22 Jun 2016 16:03:11 -0700
Subject: [PATCH 73/86] Turned the constructor of the PerThread struct into
 what is effectively a constant expression to make the code compatible with a
 wider range of compilers

---
 .../Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h       | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h b/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
index 30b292352..8d4973ded 100644
--- a/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
@@ -99,9 +99,7 @@ class NonBlockingThreadPoolTempl : public Eigen::ThreadPoolInterface {
   typedef typename Environment::EnvThread Thread;
 
   struct PerThread {
-    PerThread() : pool(NULL), index(-1) {
-      rand = std::hash<std::thread::id>()(std::this_thread::get_id());
-    }
+    PerThread() : pool(NULL), index(-1), rand(0) { }
     NonBlockingThreadPoolTempl* pool;  // Parent pool, or null for normal threads.
     unsigned index;         // Worker thread index in pool.
     uint64_t rand;          // Random generator state.
@@ -122,6 +120,7 @@ class NonBlockingThreadPoolTempl : public Eigen::ThreadPoolInterface {
     PerThread* pt = GetPerThread();
     pt->pool = this;
     pt->index = index;
+    pt->rand = std::hash<std::thread::id>()(std::this_thread::get_id());
     Queue* q = queues_[index];
     EventCount::Waiter* waiter = &waiters_[index];
     for (;;) {

From a29a2cb4ff4eb153d8e725f126f178371cc0468c Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Wed, 22 Jun 2016 16:43:02 -0700
Subject: [PATCH 74/86] Silenced a couple of compilation warnings generated by
 xcode

---
 .../Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h        | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h b/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
index 8d4973ded..c6db01a6b 100644
--- a/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
@@ -99,7 +99,7 @@ class NonBlockingThreadPoolTempl : public Eigen::ThreadPoolInterface {
   typedef typename Environment::EnvThread Thread;
 
   struct PerThread {
-    PerThread() : pool(NULL), index(-1), rand(0) { }
+    constexpr PerThread() : pool(NULL), index(-1), rand(0) { }
     NonBlockingThreadPoolTempl* pool;  // Parent pool, or null for normal threads.
     unsigned index;         // Worker thread index in pool.
     uint64_t rand;          // Random generator state.
@@ -247,7 +247,7 @@ class NonBlockingThreadPoolTempl : public Eigen::ThreadPoolInterface {
     // Update the internal state
     *state = current * 6364136223846793005ULL + 0xda3e39cb94b95bdbULL;
     // Generate the random output (using the PCG-XSH-RS scheme)
-    return (current ^ (current >> 22)) >> (22 + (current >> 61));
+    return static_cast<unsigned>((current ^ (current >> 22)) >> (22 + (current >> 61)));
   }
 };
 

From a3f7edf7e7672094190e04a0b4417de1abfa3de5 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Thu, 23 Jun 2016 10:25:04 +0200
Subject: [PATCH 75/86] Biug 1242: fix comma init with empty matrices.

---
 Eigen/src/Core/CommaInitializer.h |  7 +++++--
 test/commainitializer.cpp         | 23 +++++++++++++++++++++++
 2 files changed, 28 insertions(+), 2 deletions(-)

diff --git a/Eigen/src/Core/CommaInitializer.h b/Eigen/src/Core/CommaInitializer.h
index 2abc6605c..38b1112ff 100644
--- a/Eigen/src/Core/CommaInitializer.h
+++ b/Eigen/src/Core/CommaInitializer.h
@@ -80,8 +80,11 @@ struct CommaInitializer
   EIGEN_DEVICE_FUNC
   CommaInitializer& operator,(const DenseBase<OtherDerived>& other)
   {
-    if(other.cols()==0 || other.rows()==0)
+    if(other.rows()==0)
+    {
+      m_col += other.cols();
       return *this;
+    }
     if (m_col==m_xpr.cols())
     {
       m_row+=m_currentBlockRows;
@@ -90,7 +93,7 @@ struct CommaInitializer
       eigen_assert(m_row+m_currentBlockRows<=m_xpr.rows()
         && "Too many rows passed to comma initializer (operator<<)");
     }
-    eigen_assert(m_col<m_xpr.cols()
+    eigen_assert(m_col<m_xpr.cols() || (m_xpr.cols()==0 && m_col==0)
       && "Too many coefficients passed to comma initializer (operator<<)");
     eigen_assert(m_currentBlockRows==other.rows());
     if (OtherDerived::SizeAtCompileTime != Dynamic)
diff --git a/test/commainitializer.cpp b/test/commainitializer.cpp
index 99102b966..86bdb040e 100644
--- a/test/commainitializer.cpp
+++ b/test/commainitializer.cpp
@@ -43,4 +43,27 @@ void test_commainitializer()
         4, 5, 6,
         vec[2].transpose();
   VERIFY_IS_APPROX(m3, ref);
+
+
+  // Check with empty matrices (bug #1242)
+  {
+    int const M = 0;
+    int const N1 = 2;
+    int const N2 = 1;
+
+    {
+      Matrix<double, M, N1> A1;
+      Matrix<double, M, N2> A2;
+      Matrix<double, M, N1 + N2> B;
+      B << A1, A2;
+    }
+    {
+      Matrix<double, N1, M> A1;
+      Matrix<double, N2, M> A2;
+      Matrix<double, N1 + N2, M> B;
+      B << A1,
+           A2;
+    }
+  }
+
 }

From 76faf4a9657efeed089aeedc98a769410c32d3d7 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Thu, 23 Jun 2016 14:27:20 +0200
Subject: [PATCH 76/86] Introduce a NumTraits<T>::Literal type to be used for
 literals, and improve mixing type support in operations between arrays and
 scalars:  - 2 * ArrayXcf is now optimized in the sense that the integer 2 is
 properly promoted to a float instead of a complex<float> (fix a regression) 
 - 2.1 * ArrayXi is now forbiden (previously, 2.1 was converted to 2)  - This
 mechanism should be applicable to any custom scalar type, assuming
 NumTraits<T>::Literal is properly defined (it defaults to T)

---
 Eigen/src/Core/NumTraits.h      | 11 ++++++++---
 Eigen/src/Core/util/Macros.h    | 30 ++++++++----------------------
 Eigen/src/Core/util/XprHelper.h | 28 ++++++++++++++++++++++++++++
 test/mixingtypes.cpp            |  5 +++++
 test/nesting_ops.cpp            |  4 ++--
 5 files changed, 51 insertions(+), 27 deletions(-)

diff --git a/Eigen/src/Core/NumTraits.h b/Eigen/src/Core/NumTraits.h
index e065fa714..03f64a8e9 100644
--- a/Eigen/src/Core/NumTraits.h
+++ b/Eigen/src/Core/NumTraits.h
@@ -22,14 +22,16 @@ namespace Eigen {
   * This class stores enums, typedefs and static methods giving information about a numeric type.
   *
   * The provided data consists of:
-  * \li A typedef \a Real, giving the "real part" type of \a T. If \a T is already real,
-  *     then \a Real is just a typedef to \a T. If \a T is \c std::complex<U> then \a Real
+  * \li A typedef \c Real, giving the "real part" type of \a T. If \a T is already real,
+  *     then \c Real is just a typedef to \a T. If \a T is \c std::complex<U> then \c Real
   *     is a typedef to \a U.
-  * \li A typedef \a NonInteger, giving the type that should be used for operations producing non-integral values,
+  * \li A typedef \c NonInteger, giving the type that should be used for operations producing non-integral values,
   *     such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives
   *     \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to
   *     take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is
   *     only intended as a helper for code that needs to explicitly promote types.
+  * \li A typedef \c Literal giving the type to use for numeric literals such as "2" or "0.5". For instance, for \c std::complex<U>, Literal is defined as \c U.
+  *     Of course, this type must be fully compatible with \a T. In doubt, just use \a T here.
   * \li A typedef \a Nested giving the type to use to nest a value inside of the expression tree. If you don't know what
   *     this means, just use \a T here.
   * \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c std::complex
@@ -84,6 +86,7 @@ template<typename T> struct GenericNumTraits
                      T
                    >::type NonInteger;
   typedef T Nested;
+  typedef T Literal;
 
   EIGEN_DEVICE_FUNC
   static inline Real epsilon()
@@ -145,6 +148,7 @@ template<typename _Real> struct NumTraits<std::complex<_Real> >
   : GenericNumTraits<std::complex<_Real> >
 {
   typedef _Real Real;
+  typedef typename NumTraits<_Real>::Literal Literal;
   enum {
     IsComplex = 1,
     RequireInitialization = NumTraits<_Real>::RequireInitialization,
@@ -168,6 +172,7 @@ 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;
+  typedef typename NumTraits<Scalar>::Literal Literal;
 
   enum {
     IsComplex = NumTraits<Scalar>::IsComplex,
diff --git a/Eigen/src/Core/util/Macros.h b/Eigen/src/Core/util/Macros.h
index 87cc44657..6de21d2bb 100644
--- a/Eigen/src/Core/util/Macros.h
+++ b/Eigen/src/Core/util/Macros.h
@@ -906,35 +906,21 @@ namespace Eigen {
                 const typename internal::plain_constant_type<EXPR,SCALAR>::type, const EXPR>
 
 #define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME) \
-  EIGEN_DEVICE_FUNC inline \
-  const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,Scalar,OPNAME) \
-  (METHOD)(const Scalar& scalar) const { \
-    return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,Scalar,OPNAME)(derived(), \
-           typename internal::plain_constant_type<Derived,Scalar>::type(derived().rows(), derived().cols(), scalar)); \
-  } \
-  \
   template <typename T> EIGEN_DEVICE_FUNC inline \
-  typename internal::enable_if<ScalarBinaryOpTraits<Scalar,T,EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<Scalar,T> >::Defined, \
-                               const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,T,OPNAME) >::type \
+  const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,typename internal::promote_scalar_arg<Scalar EIGEN_COMMA T EIGEN_COMMA ScalarBinaryOpTraits<Scalar EIGEN_COMMA T EIGEN_COMMA EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<Scalar EIGEN_COMMA T> >::Defined>::type,OPNAME) \
   (METHOD)(const T& scalar) const { \
-    return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,T,OPNAME)(derived(), \
-           typename internal::plain_constant_type<Derived,T>::type(derived().rows(), derived().cols(), scalar)); \
+    typedef typename internal::promote_scalar_arg<Scalar,T,ScalarBinaryOpTraits<Scalar,T,EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<Scalar,T> >::Defined>::type PromotedT; \
+    return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,PromotedT,OPNAME)(derived(), \
+           typename internal::plain_constant_type<Derived,PromotedT>::type(derived().rows(), derived().cols(), internal::scalar_constant_op<PromotedT>(scalar))); \
   }
 
 #define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
-  EIGEN_DEVICE_FUNC inline friend \
-  const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,OPNAME) \
-  (METHOD)(const Scalar& scalar, const StorageBaseType& matrix) { \
-    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,Derived,OPNAME)( \
-           typename internal::plain_constant_type<Derived,Scalar>::type(matrix.derived().rows(), matrix.derived().cols(), scalar), matrix.derived()); \
-  } \
-  \
   template <typename T> EIGEN_DEVICE_FUNC inline friend \
-  typename internal::enable_if<ScalarBinaryOpTraits<T,Scalar,EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<T,Scalar> >::Defined, \
-                               const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(T,Derived,OPNAME) >::type \
+  const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename internal::promote_scalar_arg<Scalar EIGEN_COMMA T EIGEN_COMMA ScalarBinaryOpTraits<T EIGEN_COMMA Scalar EIGEN_COMMA EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<T EIGEN_COMMA Scalar> >::Defined>::type,Derived,OPNAME) \
   (METHOD)(const T& scalar, const StorageBaseType& matrix) { \
-    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(T,Derived,OPNAME)( \
-           typename internal::plain_constant_type<Derived,T>::type(matrix.derived().rows(), matrix.derived().cols(), scalar), matrix.derived()); \
+    typedef typename internal::promote_scalar_arg<Scalar,T,ScalarBinaryOpTraits<T,Scalar,EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<T,Scalar> >::Defined>::type PromotedT; \
+    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedT,Derived,OPNAME)( \
+           typename internal::plain_constant_type<Derived,PromotedT>::type(matrix.derived().rows(), matrix.derived().cols(), internal::scalar_constant_op<PromotedT>(scalar)), matrix.derived()); \
   }
 
 #define EIGEN_MAKE_SCALAR_BINARY_OP(METHOD,OPNAME) \
diff --git a/Eigen/src/Core/util/XprHelper.h b/Eigen/src/Core/util/XprHelper.h
index c41c408b0..b372ac1ad 100644
--- a/Eigen/src/Core/util/XprHelper.h
+++ b/Eigen/src/Core/util/XprHelper.h
@@ -45,6 +45,34 @@ inline IndexDest convert_index(const IndexSrc& idx) {
 }
 
 
+// promote_scalar_arg is an helper used in operation between an expression and a scalar, like:
+//    expression * scalar
+// Its role is to determine how the type T of the scalar operand should be promoted given the scalar type ExprScalar of the given expression.
+// The IsSupported template parameter must be provided by the caller as: ScalarBinaryOpTraits<ExprScalar,T,op>::Defined using the proper order for ExprScalar and T.
+// Then the logic is as follows:
+//  - if the operation is natively supported as defined by IsSupported, then the scalar type is not promoted, and T is returned.
+//  - otherwise, NumTraits<T>::Literal is returned if T is implicitly convertible to NumTraits<T>::Literal AND that this does not imply a float to integer conversion.
+//  - In all other cases, the promoted type is not defined, and the respective operation is thus invalid and not available (SFINAE).
+template<typename ExprScalar,typename T,
+  bool IsSupported,
+  bool ConvertibleToLiteral = internal::is_convertible<T,typename NumTraits<ExprScalar>::Literal>::value,
+  bool IsSafe = NumTraits<T>::IsInteger || !NumTraits<typename NumTraits<ExprScalar>::Literal>::IsInteger>
+struct promote_scalar_arg
+{
+};
+
+template<typename S,typename T, bool ConvertibleToLiteral, bool IsSafe>
+struct promote_scalar_arg<S,T,true,ConvertibleToLiteral,IsSafe>
+{
+  typedef T type;
+};
+
+template<typename S,typename T>
+struct promote_scalar_arg<S,T,false,true,true>
+{
+  typedef typename NumTraits<S>::Literal type;
+};
+
 //classes inheriting no_assignment_operator don't generate a default operator=.
 class no_assignment_operator
 {
diff --git a/test/mixingtypes.cpp b/test/mixingtypes.cpp
index fe8c16470..57ef85c32 100644
--- a/test/mixingtypes.cpp
+++ b/test/mixingtypes.cpp
@@ -79,6 +79,11 @@ template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
   VERIFY_MIX_SCALAR(vf * scf , vf.template cast<complex<float> >() * scf);
   VERIFY_MIX_SCALAR(scd * vd , scd * vd.template cast<complex<double> >());
 
+  VERIFY_MIX_SCALAR(vcf * 2 , vcf * complex<float>(2));
+  VERIFY_MIX_SCALAR(vcf * 2.1 , vcf * complex<float>(2.1));
+  VERIFY_MIX_SCALAR(2 * vcf, vcf * complex<float>(2));
+  VERIFY_MIX_SCALAR(2.1 * vcf , vcf * complex<float>(2.1));
+
   // check scalar quotients
   VERIFY_MIX_SCALAR(vcf / sf , vcf / complex<float>(sf));
   VERIFY_MIX_SCALAR(vf / scf , vf.template cast<complex<float> >() / scf);
diff --git a/test/nesting_ops.cpp b/test/nesting_ops.cpp
index 2f5025305..a419b0e44 100644
--- a/test/nesting_ops.cpp
+++ b/test/nesting_ops.cpp
@@ -75,8 +75,8 @@ template <typename MatrixType> void run_nesting_ops_2(const MatrixType& _m)
     }
     else
     {
-      VERIFY( verify_eval_type<1>(2*m1, 2*m1) );
-      VERIFY( verify_eval_type<2>(2*m1, m1) );
+      VERIFY( verify_eval_type<2>(2*m1, 2*m1) );
+      VERIFY( verify_eval_type<3>(2*m1, m1) );
     }
     VERIFY( verify_eval_type<2>(m1+m1, m1+m1) );
     VERIFY( verify_eval_type<3>(m1+m1, m1) );

From bf2d5edecc46808b42baeaf3eaced816b34f3364 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Thu, 23 Jun 2016 15:35:17 +0200
Subject: [PATCH 77/86] Fix warning.

---
 Eigen/src/misc/RealSvd2x2.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Eigen/src/misc/RealSvd2x2.h b/Eigen/src/misc/RealSvd2x2.h
index cdd7777d2..dfaaa0b17 100644
--- a/Eigen/src/misc/RealSvd2x2.h
+++ b/Eigen/src/misc/RealSvd2x2.h
@@ -51,4 +51,4 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
 
 } // end namespace Eigen
 
-#endif // EIGEN_REALSVD2X2_H
\ No newline at end of file
+#endif // EIGEN_REALSVD2X2_H

From 55fc04e8b5d9f3bf3b82bc4203a1562f0c7637dd Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Thu, 23 Jun 2016 15:36:42 +0200
Subject: [PATCH 78/86] Fix operator priority

---
 Eigen/src/Core/CommaInitializer.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Eigen/src/Core/CommaInitializer.h b/Eigen/src/Core/CommaInitializer.h
index 38b1112ff..787743b8f 100644
--- a/Eigen/src/Core/CommaInitializer.h
+++ b/Eigen/src/Core/CommaInitializer.h
@@ -93,7 +93,7 @@ struct CommaInitializer
       eigen_assert(m_row+m_currentBlockRows<=m_xpr.rows()
         && "Too many rows passed to comma initializer (operator<<)");
     }
-    eigen_assert(m_col<m_xpr.cols() || (m_xpr.cols()==0 && m_col==0)
+    eigen_assert((m_col<m_xpr.cols() || (m_xpr.cols()==0 && m_col==0))
       && "Too many coefficients passed to comma initializer (operator<<)");
     eigen_assert(m_currentBlockRows==other.rows());
     if (OtherDerived::SizeAtCompileTime != Dynamic)

From 360a743a10392e0b82fd4acaae60e4114cfb7806 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Thu, 23 Jun 2016 18:47:31 +0200
Subject: [PATCH 79/86] bug #1241: does not emmit anything for empty tensors

---
 unsupported/Eigen/CXX11/src/Tensor/TensorIO.h | 10 ++--------
 1 file changed, 2 insertions(+), 8 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h b/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h
index 58ffaefab..f3a3a1b88 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h
@@ -26,10 +26,7 @@ struct TensorPrinter {
     typedef typename internal::remove_const<typename Tensor::Scalar>::type Scalar;
     typedef typename Tensor::Index Index;
     const Index total_size = internal::array_prod(tensor.dimensions());
-    if (total_size == 0) {
-      os << "Empty tensor of rank " << Rank;
-    }
-    else {
+    if (total_size > 0) {
       const Index first_dim = Eigen::internal::array_get<0>(tensor.dimensions());
       static const int layout = Tensor::Layout;
       Map<const Array<Scalar, Dynamic, Dynamic, layout> > matrix(const_cast<Scalar*>(tensor.data()), first_dim, total_size/first_dim);
@@ -46,10 +43,7 @@ struct TensorPrinter<Tensor, 1> {
     typedef typename internal::remove_const<typename Tensor::Scalar>::type Scalar;
     typedef typename Tensor::Index Index;
     const Index total_size = internal::array_prod(tensor.dimensions());
-    if (total_size == 0) {
-      os << "Empty tensor of rank 1";
-    }
-    else {
+    if (total_size > 0) {
       Map<const Array<Scalar, Dynamic, 1> > array(const_cast<Scalar*>(tensor.data()), total_size);
       os << array;
     }

From 361dbd246d0b0f0ceff8d6dea6991807cffde821 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Thu, 23 Jun 2016 18:54:30 +0200
Subject: [PATCH 80/86] Add unit test for printing empty tensors

---
 unsupported/test/cxx11_tensor_io.cpp | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/unsupported/test/cxx11_tensor_io.cpp b/unsupported/test/cxx11_tensor_io.cpp
index 8267dcadd..489960529 100644
--- a/unsupported/test/cxx11_tensor_io.cpp
+++ b/unsupported/test/cxx11_tensor_io.cpp
@@ -40,6 +40,12 @@ static void test_output_1d()
 
   std::string expected("0\n1\n2\n3\n4");
   VERIFY_IS_EQUAL(std::string(os.str()), expected);
+
+  Eigen::Tensor<double,1,DataLayout> empty_tensor(0);
+  std::stringstream empty_os;
+  empty_os << empty_tensor;
+  std::string empty_string;
+  VERIFY_IS_EQUAL(std::string(empty_os.str()), empty_string);
 }
 
 

From a9c1e4d7b7ce7c9dc5310cee1ed13fdef08e506e Mon Sep 17 00:00:00 2001
From: Rasmus Munk Larsen <rmlarsen@google.com>
Date: Thu, 23 Jun 2016 16:40:07 -0700
Subject: [PATCH 81/86] Return -1 from CurrentThreadId when called by thread
 outside the pool.

---
 .../Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h    |  2 ++
 .../Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h | 10 +++++-----
 .../Eigen/CXX11/src/ThreadPool/SimpleThreadPool.h      |  9 +++++----
 .../Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h   |  2 +-
 unsupported/test/cxx11_non_blocking_thread_pool.cpp    |  2 +-
 5 files changed, 14 insertions(+), 11 deletions(-)

diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h
index 0af91fe64..34270730b 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h
@@ -172,6 +172,8 @@ struct ThreadPoolDevice {
     pool_->Schedule(func);
   }
 
+  // Returns a logical thread index between 0 and pool_->NumThreads() - 1 if
+  // called from one of the threads in pool_. Returns -1 otherwise.
   EIGEN_STRONG_INLINE int currentThreadId() const {
     return pool_->CurrentThreadId();
   }
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h b/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
index 1369ca183..33ae45131 100644
--- a/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
@@ -99,13 +99,13 @@ class NonBlockingThreadPoolTempl : public Eigen::ThreadPoolInterface {
     return static_cast<int>(threads_.size());
   }
 
-  int CurrentThreadId() const {
+  int CurrentThreadId() const final {
     const PerThread* pt =
         const_cast<NonBlockingThreadPoolTempl*>(this)->GetPerThread();
     if (pt->pool == this) {
       return pt->thread_id;
     } else {
-      return NumThreads();
+      return -1;
     }
   }
 
@@ -113,10 +113,10 @@ class NonBlockingThreadPoolTempl : public Eigen::ThreadPoolInterface {
   typedef typename Environment::EnvThread Thread;
 
   struct PerThread {
-    constexpr PerThread() : pool(NULL), index(-1), rand(0) { }
+    constexpr PerThread() : pool(NULL), rand(0), thread_id(-1) { }
     NonBlockingThreadPoolTempl* pool;  // Parent pool, or null for normal threads.
-    int thread_id;         // Worker thread index in pool.
-    uint64_t rand;          // Random generator state.
+    uint64_t rand;  // Random generator state.
+    int thread_id;  // Worker thread index in pool.
   };
 
   Environment env_;
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/SimpleThreadPool.h b/unsupported/Eigen/CXX11/src/ThreadPool/SimpleThreadPool.h
index 36eb6950f..e75d0f467 100644
--- a/unsupported/Eigen/CXX11/src/ThreadPool/SimpleThreadPool.h
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/SimpleThreadPool.h
@@ -78,7 +78,7 @@ class SimpleThreadPoolTempl : public ThreadPoolInterface {
     if (pt->pool == this) {
       return pt->thread_id;
     } else {
-      return NumThreads();
+      return -1;
     }
   }
 
@@ -128,8 +128,9 @@ class SimpleThreadPoolTempl : public ThreadPoolInterface {
   };
 
   struct PerThread {
-    ThreadPoolTempl* pool;  // Parent pool, or null for normal threads.
-    int thread_id;          // Worker thread index in pool.
+    constexpr PerThread() : pool(NULL), thread_id(-1) { }
+    SimpleThreadPoolTempl* pool;  // Parent pool, or null for normal threads.
+    int thread_id;                // Worker thread index in pool.
   };
 
   Environment env_;
@@ -141,7 +142,7 @@ class SimpleThreadPoolTempl : public ThreadPoolInterface {
   bool exiting_ = false;
 
   PerThread* GetPerThread() const {
-    static EIGEN_THREAD_LOCAL PerThread per_thread;
+    EIGEN_THREAD_LOCAL PerThread per_thread;
     return &per_thread;
   }
 };
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h
index 569cd4bc8..a65ee97c9 100644
--- a/unsupported/Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h
@@ -22,7 +22,7 @@ class ThreadPoolInterface {
   virtual int NumThreads() const = 0;
 
   // Returns a logical thread index between 0 and NumThreads() - 1 if called
-  // from one of the threads in the pool. Returns NumThreads() otherwise.
+  // from one of the threads in the pool. Returns -1 otherwise.
   virtual int CurrentThreadId() const = 0;
 
   virtual ~ThreadPoolInterface() {}
diff --git a/unsupported/test/cxx11_non_blocking_thread_pool.cpp b/unsupported/test/cxx11_non_blocking_thread_pool.cpp
index 6e4e5cbab..5f9bb938b 100644
--- a/unsupported/test/cxx11_non_blocking_thread_pool.cpp
+++ b/unsupported/test/cxx11_non_blocking_thread_pool.cpp
@@ -28,7 +28,7 @@ static void test_parallelism()
   const int kThreads = 16;  // code below expects that this is a multiple of 4
   NonBlockingThreadPool tp(kThreads);
   VERIFY_IS_EQUAL(tp.NumThreads(), kThreads);
-  VERIFY_IS_EQUAL(tp.CurrentThreadId(), kThreads);
+  VERIFY_IS_EQUAL(tp.CurrentThreadId(), -1);
   for (int iter = 0; iter < 100; ++iter) {
     std::atomic<int> running(0);
     std::atomic<int> done(0);

From deb45ad4bc5542b7c66cfb3b465ac106294c3ddd Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Fri, 24 Jun 2016 09:52:25 +0200
Subject: [PATCH 82/86] bug #1245: fix compilation with msvc

---
 Eigen/src/Core/util/ForwardDeclarations.h | 1 -
 Eigen/src/Core/util/Meta.h                | 2 +-
 2 files changed, 1 insertion(+), 2 deletions(-)

diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index 830f20f90..1c90c0e2b 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -131,7 +131,6 @@ template<typename ExpressionType> class ArrayWrapper;
 template<typename ExpressionType> class MatrixWrapper;
 template<typename Derived> class SolverBase;
 template<typename XprType> class InnerIterator;
-template<typename ScalarA, typename ScalarB, typename BinaryOp=void> struct ScalarBinaryOpTraits;
 
 namespace internal {
 template<typename DecompositionType> struct kernel_retval_base;
diff --git a/Eigen/src/Core/util/Meta.h b/Eigen/src/Core/util/Meta.h
index a4a491ff8..02b3d961a 100644
--- a/Eigen/src/Core/util/Meta.h
+++ b/Eigen/src/Core/util/Meta.h
@@ -439,7 +439,7 @@ T div_ceil(const T &a, const T &b)
   *
   * \sa CwiseBinaryOp
   */
-template<typename ScalarA, typename ScalarB, typename BinaryOp>
+template<typename ScalarA, typename ScalarB, typename BinaryOp=void>
 struct ScalarBinaryOpTraits
 #ifndef EIGEN_PARSED_BY_DOXYGEN
   // for backward compatibility, use the hints given by the (deprecated) internal::scalar_product_traits class.

From cd577a275c3420d743a044e37484ab8fd1e17e37 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Fri, 24 Jun 2016 11:28:54 +0200
Subject: [PATCH 83/86] Relax promote_scalar_arg logic to enable promotion to
 Expr::Scalar if conversion to Expr::Literal fails. This is useful to cancel
 expression template at the scalar level, e.g. with AutoDiff<AutoDiff<>>. This
 patch also defers calls to NumTraits in cases for which types are not
 directly compatible.

---
 Eigen/src/Core/util/XprHelper.h | 46 ++++++++++++++++++++++++---------
 1 file changed, 34 insertions(+), 12 deletions(-)

diff --git a/Eigen/src/Core/util/XprHelper.h b/Eigen/src/Core/util/XprHelper.h
index b372ac1ad..3e8048d27 100644
--- a/Eigen/src/Core/util/XprHelper.h
+++ b/Eigen/src/Core/util/XprHelper.h
@@ -51,28 +51,50 @@ inline IndexDest convert_index(const IndexSrc& idx) {
 // The IsSupported template parameter must be provided by the caller as: ScalarBinaryOpTraits<ExprScalar,T,op>::Defined using the proper order for ExprScalar and T.
 // Then the logic is as follows:
 //  - if the operation is natively supported as defined by IsSupported, then the scalar type is not promoted, and T is returned.
-//  - otherwise, NumTraits<T>::Literal is returned if T is implicitly convertible to NumTraits<T>::Literal AND that this does not imply a float to integer conversion.
+//  - otherwise, NumTraits<ExprScalar>::Literal is returned if T is implicitly convertible to NumTraits<ExprScalar>::Literal AND that this does not imply a float to integer conversion.
+//  - otherwise, ExprScalar is returned if T is implicitly convertible to ExprScalar AND that this does not imply a float to integer conversion.
 //  - In all other cases, the promoted type is not defined, and the respective operation is thus invalid and not available (SFINAE).
-template<typename ExprScalar,typename T,
-  bool IsSupported,
-  bool ConvertibleToLiteral = internal::is_convertible<T,typename NumTraits<ExprScalar>::Literal>::value,
-  bool IsSafe = NumTraits<T>::IsInteger || !NumTraits<typename NumTraits<ExprScalar>::Literal>::IsInteger>
-struct promote_scalar_arg
-{
-};
+template<typename ExprScalar,typename T, bool IsSupported>
+struct promote_scalar_arg;
 
-template<typename S,typename T, bool ConvertibleToLiteral, bool IsSafe>
-struct promote_scalar_arg<S,T,true,ConvertibleToLiteral,IsSafe>
+template<typename S,typename T>
+struct promote_scalar_arg<S,T,true>
 {
   typedef T type;
 };
 
+// Recursively check safe conversion to PromotedType, and then ExprScalar if they are different.
+template<typename ExprScalar,typename T,typename PromotedType,
+  bool ConvertibleToLiteral = internal::is_convertible<T,PromotedType>::value,
+  bool IsSafe = NumTraits<T>::IsInteger || !NumTraits<PromotedType>::IsInteger>
+struct promote_scalar_arg_unsupported;
+
+// Start recursion with NumTraits<ExprScalar>::Literal
 template<typename S,typename T>
-struct promote_scalar_arg<S,T,false,true,true>
+struct promote_scalar_arg<S,T,false> : promote_scalar_arg_unsupported<S,T,typename NumTraits<S>::Literal> {};
+
+// We found a match!
+template<typename S,typename T, typename PromotedType>
+struct promote_scalar_arg_unsupported<S,T,PromotedType,true,true>
 {
-  typedef typename NumTraits<S>::Literal type;
+  typedef PromotedType type;
 };
 
+// No match, but no real-to-integer issues, and ExprScalar and current PromotedType are different,
+// so let's try to promote to ExprScalar
+template<typename ExprScalar,typename T, typename PromotedType>
+struct promote_scalar_arg_unsupported<ExprScalar,T,PromotedType,false,true>
+   : promote_scalar_arg_unsupported<ExprScalar,T,ExprScalar>
+{};
+
+// Unsafe real-to-integer, let's stop.
+template<typename S,typename T, typename PromotedType>
+struct promote_scalar_arg_unsupported<S,T,PromotedType,false,false> {};
+
+// T is not even convertible to ExprScalar, let's stop.
+template<typename S,typename T>
+struct promote_scalar_arg_unsupported<S,T,S,false,true> {};
+
 //classes inheriting no_assignment_operator don't generate a default operator=.
 class no_assignment_operator
 {

From fa39f81b48b4fb20410e788e39459ed448dc461d Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Fri, 24 Jun 2016 11:33:30 +0200
Subject: [PATCH 84/86] Fix instantiation of ScalarBinaryOpTraits for AutoDiff.

---
 .../Eigen/src/AutoDiff/AutoDiffScalar.h        | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
index feaeeaf5a..0abd12210 100755
--- a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
+++ b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
@@ -67,7 +67,7 @@ template<typename _DerType>
 class AutoDiffScalar
   : public internal::auto_diff_special_op
             <_DerType, !internal::is_same<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar,
-                                        typename NumTraits<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar>::Real>::value>
+                                          typename NumTraits<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar>::Real>::value>
 {
   public:
     typedef internal::auto_diff_special_op
@@ -497,29 +497,29 @@ struct make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows,
 
 } // end namespace internal
 
-template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols>
-struct ScalarBinaryOpTraits<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>,A_Scalar>
+template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols, typename BinOp>
+struct ScalarBinaryOpTraits<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>,A_Scalar,BinOp>
 {
   enum { Defined = 1 };
   typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> ReturnType;
 };
 
-template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols>
-struct ScalarBinaryOpTraits<A_Scalar, Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> >
+template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols, typename BinOp>
+struct ScalarBinaryOpTraits<A_Scalar, Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>, BinOp>
 {
   enum { Defined = 1 };
   typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> ReturnType;
 };
 
-template<typename DerType>
-struct ScalarBinaryOpTraits<AutoDiffScalar<DerType>,typename DerType::Scalar>
+template<typename DerType, typename BinOp>
+struct ScalarBinaryOpTraits<AutoDiffScalar<DerType>,typename DerType::Scalar,BinOp>
 {
   enum { Defined = 1 };
   typedef AutoDiffScalar<DerType> ReturnType;
 };
 
-template<typename DerType>
-struct ScalarBinaryOpTraits<typename DerType::Scalar,AutoDiffScalar<DerType> >
+template<typename DerType, typename BinOp>
+struct ScalarBinaryOpTraits<typename DerType::Scalar,AutoDiffScalar<DerType>, BinOp>
 {
   enum { Defined = 1 };
   typedef AutoDiffScalar<DerType> ReturnType;

From ce90647fa58cd81c3561170947e2a507571b2e43 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Fri, 24 Jun 2016 11:34:02 +0200
Subject: [PATCH 85/86] Fix NumTraits<AutoDiff>

---
 .../Eigen/src/AutoDiff/AutoDiffScalar.h       | 20 ++++++++++++++++++-
 1 file changed, 19 insertions(+), 1 deletion(-)

diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
index 0abd12210..8e40569c1 100755
--- a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
+++ b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
@@ -525,6 +525,23 @@ struct ScalarBinaryOpTraits<typename DerType::Scalar,AutoDiffScalar<DerType>, Bi
   typedef AutoDiffScalar<DerType> ReturnType;
 };
 
+
+// The following is an attempt to let Eigen's known about expression template, but that's more tricky!
+
+// template<typename DerType, typename BinOp>
+// struct ScalarBinaryOpTraits<AutoDiffScalar<DerType>,AutoDiffScalar<DerType>, BinOp>
+// {
+//   enum { Defined = 1 };
+//   typedef AutoDiffScalar<typename DerType::PlainObject> ReturnType;
+// };
+//
+// template<typename DerType1,typename DerType2, typename BinOp>
+// struct ScalarBinaryOpTraits<AutoDiffScalar<DerType1>,AutoDiffScalar<DerType2>, BinOp>
+// {
+//   enum { Defined = 1 };//internal::is_same<typename DerType1::Scalar,typename DerType2::Scalar>::value };
+//   typedef AutoDiffScalar<typename DerType1::PlainObject> ReturnType;
+// };
+
 #define EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(FUNC,CODE) \
   template<typename DerType> \
   inline const Eigen::AutoDiffScalar< \
@@ -645,9 +662,10 @@ template<typename DerType> struct NumTraits<AutoDiffScalar<DerType> >
   : NumTraits< typename NumTraits<typename DerType::Scalar>::Real >
 {
   typedef AutoDiffScalar<Matrix<typename NumTraits<typename DerType::Scalar>::Real,DerType::RowsAtCompileTime,DerType::ColsAtCompileTime,
-                                DerType::Options, DerType::MaxRowsAtCompileTime, DerType::MaxColsAtCompileTime> > Real;
+                                0, DerType::MaxRowsAtCompileTime, DerType::MaxColsAtCompileTime> > Real;
   typedef AutoDiffScalar<DerType> NonInteger;
   typedef AutoDiffScalar<DerType> Nested;
+  typedef typename NumTraits<typename DerType::Scalar>::Literal Literal;
   enum{
     RequireInitialization = 1
   };

From 6dd9077070d8c9f09101b0b050ab32a7c660c3a0 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Fri, 24 Jun 2016 11:34:21 +0200
Subject: [PATCH 86/86] Fix some unused typedef warnings.

---
 unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
index 8e40569c1..ee7a92274 100755
--- a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
+++ b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
@@ -548,7 +548,7 @@ struct ScalarBinaryOpTraits<typename DerType::Scalar,AutoDiffScalar<DerType>, Bi
   EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename Eigen::internal::remove_all<DerType>::type, typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar, product) > \
   FUNC(const Eigen::AutoDiffScalar<DerType>& x) { \
     using namespace Eigen; \
-    typedef typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar Scalar; \
+    EIGEN_UNUSED typedef typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar Scalar; \
     CODE; \
   }
 
@@ -617,8 +617,6 @@ EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename internal::remove_all<DerType>::t
 pow(const Eigen::AutoDiffScalar<DerType> &x, const typename internal::traits<typename internal::remove_all<DerType>::type>::Scalar &y)
 {
   using namespace Eigen;
-  typedef typename internal::remove_all<DerType>::type DerTypeCleaned;
-  typedef typename Eigen::internal::traits<DerTypeCleaned>::Scalar Scalar;
   return Eigen::MakeAutoDiffScalar(std::pow(x.value(),y), x.derivatives() * (y * std::pow(x.value(),y-1)));
 }