Big 279: enable mixing types for comparisons, min, and max.

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>());
 }