Fix bug #314: move remaining math functions from internal to numext namespace

43 files changed, 323 insertions, 303 deletions

diff --git a/Eigen/Core b/Eigen/Core
index 8197c944f..7e068cbbd 100644
--- a/Eigen/Core
+++ b/Eigen/Core
@@ -245,8 +245,8 @@ using std::ptrdiff_t;
 #include "src/Core/util/Constants.h"
 #include "src/Core/util/ForwardDeclarations.h"
 #include "src/Core/util/Meta.h"
-#include "src/Core/util/XprHelper.h"
 #include "src/Core/util/StaticAssert.h"
+#include "src/Core/util/XprHelper.h"
 #include "src/Core/util/Memory.h"
 
 #include "src/Core/NumTraits.h"
diff --git a/Eigen/src/Cholesky/LDLT.h b/Eigen/src/Cholesky/LDLT.h
index d933b10d4..d19cb3968 100644
--- a/Eigen/src/Cholesky/LDLT.h
+++ b/Eigen/src/Cholesky/LDLT.h
@@ -259,7 +259,7 @@ template<> struct ldlt_inplace<Lower>
     {
       transpositions.setIdentity();
       if(sign)
-        *sign = real(mat.coeff(0,0))>0 ? 1:-1;
+        *sign = numext::real(mat.coeff(0,0))>0 ? 1:-1;
       return true;
     }
 
@@ -300,11 +300,11 @@ template<> struct ldlt_inplace<Lower>
         for(int i=k+1;i<index_of_biggest_in_corner;++i)
         {
           Scalar tmp = mat.coeffRef(i,k);
-          mat.coeffRef(i,k) = conj(mat.coeffRef(index_of_biggest_in_corner,i));
-          mat.coeffRef(index_of_biggest_in_corner,i) = conj(tmp);
+          mat.coeffRef(i,k) = numext::conj(mat.coeffRef(index_of_biggest_in_corner,i));
+          mat.coeffRef(index_of_biggest_in_corner,i) = numext::conj(tmp);
         }
         if(NumTraits<Scalar>::IsComplex)
-          mat.coeffRef(index_of_biggest_in_corner,k) = conj(mat.coeff(index_of_biggest_in_corner,k));
+          mat.coeffRef(index_of_biggest_in_corner,k) = numext::conj(mat.coeff(index_of_biggest_in_corner,k));
       }
 
       // partition the matrix:
@@ -329,7 +329,7 @@ template<> struct ldlt_inplace<Lower>
       if(sign)
       {
         // LDLT is not guaranteed to work for indefinite matrices, but let's try to get the sign right
-        int newSign = real(mat.diagonal().coeff(index_of_biggest_in_corner)) > 0;
+        int newSign = numext::real(mat.diagonal().coeff(index_of_biggest_in_corner)) > 0;
         if(k == 0)
           *sign = newSign;
         else if(*sign != newSign)
@@ -350,7 +350,7 @@ template<> struct ldlt_inplace<Lower>
   template<typename MatrixType, typename WDerived>
   static bool updateInPlace(MatrixType& mat, MatrixBase<WDerived>& w, const typename MatrixType::RealScalar& sigma=1)
   {
-    using internal::isfinite;
+    using numext::isfinite;
     typedef typename MatrixType::Scalar Scalar;
     typedef typename MatrixType::RealScalar RealScalar;
     typedef typename MatrixType::Index Index;
@@ -368,9 +368,9 @@ template<> struct ldlt_inplace<Lower>
         break;
 
       // Update the diagonal terms
-      RealScalar dj = real(mat.coeff(j,j));
+      RealScalar dj = numext::real(mat.coeff(j,j));
       Scalar wj = w.coeff(j);
-      RealScalar swj2 = sigma*abs2(wj);
+      RealScalar swj2 = sigma*numext::abs2(wj);
       RealScalar gamma = dj*alpha + swj2;
 
       mat.coeffRef(j,j) += swj2/alpha;
@@ -381,7 +381,7 @@ template<> struct ldlt_inplace<Lower>
       Index rs = size-j-1;
       w.tail(rs) -= wj * mat.col(j).tail(rs);
       if(gamma != 0)
-        mat.col(j).tail(rs) += (sigma*conj(wj)/gamma)*w.tail(rs);
+        mat.col(j).tail(rs) += (sigma*numext::conj(wj)/gamma)*w.tail(rs);
     }
     return true;
   }
diff --git a/Eigen/src/Cholesky/LLT.h b/Eigen/src/Cholesky/LLT.h
index db22a2f85..2e6189f7d 100644
--- a/Eigen/src/Cholesky/LLT.h
+++ b/Eigen/src/Cholesky/LLT.h
@@ -232,10 +232,10 @@ static typename MatrixType::Index llt_rank_update_lower(MatrixType& mat, const V
     RealScalar beta = 1;
     for(Index j=0; j<n; ++j)
     {
-      RealScalar Ljj = real(mat.coeff(j,j));
-      RealScalar dj = abs2(Ljj);
+      RealScalar Ljj = numext::real(mat.coeff(j,j));
+      RealScalar dj = numext::abs2(Ljj);
       Scalar wj = temp.coeff(j);
-      RealScalar swj2 = sigma*abs2(wj);
+      RealScalar swj2 = sigma*numext::abs2(wj);
       RealScalar gamma = dj*beta + swj2;
 
       RealScalar x = dj + swj2/beta;
@@ -251,7 +251,7 @@ static typename MatrixType::Index llt_rank_update_lower(MatrixType& mat, const V
       {
         temp.tail(rs) -= (wj/Ljj) * mat.col(j).tail(rs);
         if(gamma != 0)
-          mat.col(j).tail(rs) = (nLjj/Ljj) * mat.col(j).tail(rs) + (nLjj * sigma*conj(wj)/gamma)*temp.tail(rs);
+          mat.col(j).tail(rs) = (nLjj/Ljj) * mat.col(j).tail(rs) + (nLjj * sigma*numext::conj(wj)/gamma)*temp.tail(rs);
       }
     }
   }
@@ -277,7 +277,7 @@ template<typename Scalar> struct llt_inplace<Scalar, Lower>
       Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
       Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
 
-      RealScalar x = real(mat.coeff(k,k));
+      RealScalar x = numext::real(mat.coeff(k,k));
       if (k>0) x -= A10.squaredNorm();
       if (x<=RealScalar(0))
         return k;
diff --git a/Eigen/src/Core/Dot.h b/Eigen/src/Core/Dot.h
index 9d513d699..e4107a1ac 100644
--- a/Eigen/src/Core/Dot.h
+++ b/Eigen/src/Core/Dot.h
@@ -112,7 +112,7 @@ MatrixBase<Derived>::eigen2_dot(const MatrixBase<OtherDerived>& other) const
 template<typename Derived>
 EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::squaredNorm() const
 {
-  return internal::real((*this).cwiseAbs2().sum());
+  return numext::real((*this).cwiseAbs2().sum());
 }
 
 /** \returns, for vectors, the \em l2 norm of \c *this, and for matrices the Frobenius norm.
@@ -228,7 +228,7 @@ bool MatrixBase<Derived>::isOrthogonal
 {
   typename internal::nested<Derived,2>::type nested(derived());
   typename internal::nested<OtherDerived,2>::type otherNested(other.derived());
-  return internal::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
+  return numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
 }
 
 /** \returns true if *this is approximately an unitary matrix,
diff --git a/Eigen/src/Core/Functors.h b/Eigen/src/Core/Functors.h
index 9a84e8f26..04fb21732 100644
--- a/Eigen/src/Core/Functors.h
+++ b/Eigen/src/Core/Functors.h
@@ -171,7 +171,7 @@ struct functor_traits<scalar_hypot_op<Scalar> > {
   */
 template<typename Scalar, typename OtherScalar> struct scalar_binary_pow_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_binary_pow_op)
-  inline Scalar operator() (const Scalar& a, const OtherScalar& b) const { return internal::pow(a, b); }
+  inline Scalar 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> > {
@@ -310,7 +310,7 @@ struct functor_traits<scalar_abs_op<Scalar> >
 template<typename Scalar> struct scalar_abs2_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_abs2_op)
   typedef typename NumTraits<Scalar>::Real result_type;
-  EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return internal::abs2(a); }
+  EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return numext::abs2(a); }
   template<typename Packet>
   EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
   { return internal::pmul(a,a); }
@@ -326,7 +326,7 @@ struct functor_traits<scalar_abs2_op<Scalar> >
   */
 template<typename Scalar> struct scalar_conjugate_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_conjugate_op)
-  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { using internal::conj; return conj(a); }
+  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { using numext::conj; return conj(a); }
   template<typename Packet>
   EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const { return internal::pconj(a); }
 };
@@ -363,7 +363,7 @@ template<typename Scalar>
 struct scalar_real_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_real_op)
   typedef typename NumTraits<Scalar>::Real result_type;
-  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return internal::real(a); }
+  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return numext::real(a); }
 };
 template<typename Scalar>
 struct functor_traits<scalar_real_op<Scalar> >
@@ -378,7 +378,7 @@ template<typename Scalar>
 struct scalar_imag_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_imag_op)
   typedef typename NumTraits<Scalar>::Real result_type;
-  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return internal::imag(a); }
+  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return numext::imag(a); }
 };
 template<typename Scalar>
 struct functor_traits<scalar_imag_op<Scalar> >
@@ -393,7 +393,7 @@ template<typename Scalar>
 struct scalar_real_ref_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_real_ref_op)
   typedef typename NumTraits<Scalar>::Real result_type;
-  EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return internal::real_ref(*const_cast<Scalar*>(&a)); }
+  EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return numext::real_ref(*const_cast<Scalar*>(&a)); }
 };
 template<typename Scalar>
 struct functor_traits<scalar_real_ref_op<Scalar> >
@@ -408,7 +408,7 @@ template<typename Scalar>
 struct scalar_imag_ref_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_imag_ref_op)
   typedef typename NumTraits<Scalar>::Real result_type;
-  EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return internal::imag_ref(*const_cast<Scalar*>(&a)); }
+  EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return numext::imag_ref(*const_cast<Scalar*>(&a)); }
 };
 template<typename Scalar>
 struct functor_traits<scalar_imag_ref_op<Scalar> >
@@ -801,7 +801,7 @@ struct scalar_pow_op {
   // FIXME default copy constructors seems bugged with std::complex<>
   inline scalar_pow_op(const scalar_pow_op& other) : m_exponent(other.m_exponent) { }
   inline scalar_pow_op(const Scalar& exponent) : m_exponent(exponent) {}
-  inline Scalar operator() (const Scalar& a) const { return internal::pow(a, m_exponent); }
+  inline Scalar operator() (const Scalar& a) const { return numext::pow(a, m_exponent); }
   const Scalar m_exponent;
 };
 template<typename Scalar>
diff --git a/Eigen/src/Core/Fuzzy.h b/Eigen/src/Core/Fuzzy.h
index 8fb9a01dd..fe63bd298 100644
--- a/Eigen/src/Core/Fuzzy.h
+++ b/Eigen/src/Core/Fuzzy.h
@@ -42,7 +42,7 @@ struct isMuchSmallerThan_object_selector
 {
   static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)
   {
-    return x.cwiseAbs2().sum() <= abs2(prec) * y.cwiseAbs2().sum();
+    return x.cwiseAbs2().sum() <= numext::abs2(prec) * y.cwiseAbs2().sum();
   }
 };
 
@@ -60,7 +60,7 @@ struct isMuchSmallerThan_scalar_selector
 {
   static bool run(const Derived& x, const typename Derived::RealScalar& y, const typename Derived::RealScalar& prec)
   {
-    return x.cwiseAbs2().sum() <= abs2(prec * y);
+    return x.cwiseAbs2().sum() <= numext::abs2(prec * y);
   }
 };
 
diff --git a/Eigen/src/Core/GeneralProduct.h b/Eigen/src/Core/GeneralProduct.h
index 4e6448353..2a59d9464 100644
--- a/Eigen/src/Core/GeneralProduct.h
+++ b/Eigen/src/Core/GeneralProduct.h
@@ -435,7 +435,7 @@ template<> struct gemv_selector<OnTheRight,ColMajor,true>
 
     gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
 
-    bool alphaIsCompatible = (!ComplexByReal) || (imag(actualAlpha)==RealScalar(0));
+    bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));
     bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
     
     RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
diff --git a/Eigen/src/Core/GlobalFunctions.h b/Eigen/src/Core/GlobalFunctions.h
index 02cae552e..2acf97723 100644
--- a/Eigen/src/Core/GlobalFunctions.h
+++ b/Eigen/src/Core/GlobalFunctions.h
@@ -39,6 +39,7 @@ namespace Eigen
 {
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(real,scalar_real_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(imag,scalar_imag_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(conj,scalar_conjugate_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sin,scalar_sin_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cos,scalar_cos_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asin,scalar_asin_op)
@@ -86,6 +87,6 @@ namespace Eigen
   }
 }
 
-// TODO: cleanly disable those functions that are not supported on Array (internal::real_ref, internal::random, internal::isApprox...)
+// TODO: cleanly disable those functions that are not supported on Array (numext::real_ref, internal::random, internal::isApprox...)
 
 #endif // EIGEN_GLOBAL_FUNCTIONS_H
diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
index a2c55f255..5df2d8bca 100644
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
@@ -51,16 +51,15 @@ struct global_math_functions_filtering_base
   typedef typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl type;
 };
 
-#define EIGEN_MATHFUNC_IMPL(func, scalar) func##_impl<typename global_math_functions_filtering_base<scalar>::type>
-#define EIGEN_MATHFUNC_RETVAL(func, scalar) typename func##_retval<typename global_math_functions_filtering_base<scalar>::type>::type
-
+#define EIGEN_MATHFUNC_IMPL(func, scalar) Eigen::internal::func##_impl<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>
+#define EIGEN_MATHFUNC_RETVAL(func, scalar) typename Eigen::internal::func##_retval<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>::type
 
 /****************************************************************************
 * Implementation of real                                                 *
 ****************************************************************************/
 
-template<typename Scalar>
-struct real_impl
+template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
+struct real_default_impl
 {
   typedef typename NumTraits<Scalar>::Real RealScalar;
   static inline RealScalar run(const Scalar& x)
@@ -69,34 +68,32 @@ struct real_impl
   }
 };
 
-template<typename RealScalar>
-struct real_impl<std::complex<RealScalar> >
+template<typename Scalar>
+struct real_default_impl<Scalar,true>
 {
-  static inline RealScalar run(const std::complex<RealScalar>& x)
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  static inline RealScalar run(const Scalar& x)
   {
     using std::real;
     return real(x);
   }
 };
 
+template<typename Scalar> struct real_impl : real_default_impl<Scalar> {};
+
 template<typename Scalar>
 struct real_retval
 {
   typedef typename NumTraits<Scalar>::Real type;
 };
 
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x)
-{
-  return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);
-}
 
 /****************************************************************************
 * Implementation of imag                                                 *
 ****************************************************************************/
 
-template<typename Scalar>
-struct imag_impl
+template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
+struct imag_default_impl
 {
   typedef typename NumTraits<Scalar>::Real RealScalar;
   static inline RealScalar run(const Scalar&)
@@ -105,28 +102,25 @@ struct imag_impl
   }
 };
 
-template<typename RealScalar>
-struct imag_impl<std::complex<RealScalar> >
+template<typename Scalar>
+struct imag_default_impl<Scalar,true>
 {
-  static inline RealScalar run(const std::complex<RealScalar>& x)
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  static inline RealScalar run(const Scalar& x)
   {
     using std::imag;
     return imag(x);
   }
 };
 
+template<typename Scalar> struct imag_impl : imag_default_impl<Scalar> {};
+
 template<typename Scalar>
 struct imag_retval
 {
   typedef typename NumTraits<Scalar>::Real type;
 };
 
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x)
-{
-  return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);
-}
-
 /****************************************************************************
 * Implementation of real_ref                                             *
 ****************************************************************************/
@@ -151,18 +145,6 @@ struct real_ref_retval
   typedef typename NumTraits<Scalar>::Real & type;
 };
 
-template<typename Scalar>
-inline typename add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(const Scalar& x)
-{
-  return real_ref_impl<Scalar>::run(x);
-}
-
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x)
-{
-  return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);
-}
-
 /****************************************************************************
 * Implementation of imag_ref                                             *
 ****************************************************************************/
@@ -203,23 +185,11 @@ struct imag_ref_retval
   typedef typename NumTraits<Scalar>::Real & type;
 };
 
-template<typename Scalar>
-inline typename add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(const Scalar& x)
-{
-  return imag_ref_impl<Scalar>::run(x);
-}
-
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x)
-{
-  return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x);
-}
-
 /****************************************************************************
 * Implementation of conj                                                 *
 ****************************************************************************/
 
-template<typename Scalar>
+template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
 struct conj_impl
 {
   static inline Scalar run(const Scalar& x)
@@ -228,10 +198,10 @@ struct conj_impl
   }
 };
 
-template<typename RealScalar>
-struct conj_impl<std::complex<RealScalar> >
+template<typename Scalar>
+struct conj_impl<Scalar,true>
 {
-  static inline std::complex<RealScalar> run(const std::complex<RealScalar>& x)
+  static inline Scalar run(const Scalar& x)
   {
     using std::conj;
     return conj(x);
@@ -244,12 +214,6 @@ struct conj_retval
   typedef Scalar type;
 };
 
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x)
-{
-  return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);
-}
-
 /****************************************************************************
 * Implementation of abs2                                                 *
 ****************************************************************************/
@@ -279,12 +243,6 @@ struct abs2_retval
   typedef typename NumTraits<Scalar>::Real type;
 };
 
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x)
-{
-  return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x);
-}
-
 /****************************************************************************
 * Implementation of norm1                                                *
 ****************************************************************************/
@@ -319,12 +277,6 @@ struct norm1_retval
   typedef typename NumTraits<Scalar>::Real type;
 };
 
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x)
-{
-  return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);
-}
-
 /****************************************************************************
 * Implementation of hypot                                                *
 ****************************************************************************/
@@ -342,6 +294,7 @@ struct hypot_impl
     RealScalar _x = abs(x);
     RealScalar _y = abs(y);
     RealScalar p = (max)(_x, _y);
+    if(p==RealScalar(0)) return 0;
     RealScalar q = (min)(_x, _y);
     RealScalar qp = q/p;
     return p * sqrt(RealScalar(1) + qp*qp);
@@ -354,12 +307,6 @@ struct hypot_retval
   typedef typename NumTraits<Scalar>::Real type;
 };
 
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y)
-{
-  return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);
-}
-
 /****************************************************************************
 * Implementation of cast                                                 *
 ****************************************************************************/
@@ -422,12 +369,6 @@ struct atanh2_retval
   typedef Scalar type;
 };
 
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(atanh2, Scalar) atanh2(const Scalar& x, const Scalar& y)
-{
-  return EIGEN_MATHFUNC_IMPL(atanh2, Scalar)::run(x, y);
-}
-
 /****************************************************************************
 * Implementation of pow                                                  *
 ****************************************************************************/
@@ -471,12 +412,6 @@ struct pow_retval
   typedef Scalar type;
 };
 
-template<typename Scalar>
-inline EIGEN_MATHFUNC_RETVAL(pow, Scalar) pow(const Scalar& x, const Scalar& y)
-{
-  return EIGEN_MATHFUNC_IMPL(pow, Scalar)::run(x, y);
-}
-
 /****************************************************************************
 * Implementation of random                                               *
 ****************************************************************************/
@@ -611,6 +546,97 @@ inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random()
   return EIGEN_MATHFUNC_IMPL(random, Scalar)::run();
 }
 
+} // end namespace internal
+
+/****************************************************************************
+* Generic math function                                                    *
+****************************************************************************/
+
+namespace numext {
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);
+}  
+
+template<typename Scalar>
+inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(const Scalar& x)
+{
+  return internal::real_ref_impl<Scalar>::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(const Scalar& x)
+{
+  return internal::imag_ref_impl<Scalar>::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y)
+{
+  return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(atanh2, Scalar) atanh2(const Scalar& x, const Scalar& y)
+{
+  return EIGEN_MATHFUNC_IMPL(atanh2, Scalar)::run(x, y);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(pow, Scalar) pow(const Scalar& x, const Scalar& y)
+{
+  return EIGEN_MATHFUNC_IMPL(pow, Scalar)::run(x, y);
+}
+
+// std::isfinite is non standard, so let's define our own version,
+// even though it is not very efficient.
+template<typename T> bool (isfinite)(const T& x)
+{
+  return x<NumTraits<T>::highest() && x>NumTraits<T>::lowest();
+}
+
+} // end namespace numext
+
+namespace internal {
+
 /****************************************************************************
 * Implementation of fuzzy comparisons                                       *
 ****************************************************************************/
@@ -668,12 +694,12 @@ struct scalar_fuzzy_default_impl<Scalar, true, false>
   template<typename OtherScalar>
   static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
   {
-    return abs2(x) <= abs2(y) * prec * prec;
+    return numext::abs2(x) <= numext::abs2(y) * prec * prec;
   }
   static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
   {
     using std::min;
-    return abs2(x - y) <= (min)(abs2(x), abs2(y)) * prec * prec;
+    return numext::abs2(x - y) <= (min)(numext::abs2(x), numext::abs2(y)) * prec * prec;
   }
 };
 
@@ -735,17 +761,7 @@ template<> struct scalar_fuzzy_impl<bool>
   
 };
 
-/****************************************************************************
-* Special functions                                                          *
-****************************************************************************/
-
-// std::isfinite is non standard, so let's define our own version,
-// even though it is not very efficient.
-template<typename T> bool (isfinite)(const T& x)
-{
-  return x<NumTraits<T>::highest() && x>NumTraits<T>::lowest();
-}
-
+  
 } // end namespace internal
 
 } // end namespace Eigen
diff --git a/Eigen/src/Core/SelfAdjointView.h b/Eigen/src/Core/SelfAdjointView.h
index d43789123..6fa7cd15e 100644
--- a/Eigen/src/Core/SelfAdjointView.h
+++ b/Eigen/src/Core/SelfAdjointView.h
@@ -214,9 +214,9 @@ struct triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Upper), U
     triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Upper), UnrollCount-1, ClearOpposite>::run(dst, src);
 
     if(row == col)
-      dst.coeffRef(row, col) = real(src.coeff(row, col));
+      dst.coeffRef(row, col) = numext::real(src.coeff(row, col));
     else if(row < col)
-      dst.coeffRef(col, row) = conj(dst.coeffRef(row, col) = src.coeff(row, col));
+      dst.coeffRef(col, row) = numext::conj(dst.coeffRef(row, col) = src.coeff(row, col));
   }
 };
 
@@ -239,9 +239,9 @@ struct triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Lower), U
     triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Lower), UnrollCount-1, ClearOpposite>::run(dst, src);
 
     if(row == col)
-      dst.coeffRef(row, col) = real(src.coeff(row, col));
+      dst.coeffRef(row, col) = numext::real(src.coeff(row, col));
     else if(row > col)
-      dst.coeffRef(col, row) = conj(dst.coeffRef(row, col) = src.coeff(row, col));
+      dst.coeffRef(col, row) = numext::conj(dst.coeffRef(row, col) = src.coeff(row, col));
   }
 };
 
@@ -262,7 +262,7 @@ struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Upper, Dyn
       for(Index i = 0; i < j; ++i)
       {
         dst.copyCoeff(i, j, src);
-        dst.coeffRef(j,i) = conj(dst.coeff(i,j));
+        dst.coeffRef(j,i) = numext::conj(dst.coeff(i,j));
       }
       dst.copyCoeff(j, j, src);
     }
@@ -280,7 +280,7 @@ struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Lower, Dyn
       for(Index j = 0; j < i; ++j)
       {
         dst.copyCoeff(i, j, src);
-        dst.coeffRef(j,i) = conj(dst.coeff(i,j));
+        dst.coeffRef(j,i) = numext::conj(dst.coeff(i,j));
       }
       dst.copyCoeff(i, i, src);
     }
diff --git a/Eigen/src/Core/StableNorm.h b/Eigen/src/Core/StableNorm.h
index f57bbb772..c83e955ee 100644
--- a/Eigen/src/Core/StableNorm.h
+++ b/Eigen/src/Core/StableNorm.h
@@ -20,7 +20,7 @@ inline void stable_norm_kernel(const ExpressionType& bl, Scalar& ssq, Scalar& sc
   Scalar max = bl.cwiseAbs().maxCoeff();
   if (max>scale)
   {
-    ssq = ssq * abs2(scale/max);
+    ssq = ssq * numext::abs2(scale/max);
     scale = max;
     invScale = Scalar(1)/scale;
   }
@@ -84,9 +84,9 @@ blueNorm_impl(const EigenBase<Derived>& _vec)
   for(typename Derived::InnerIterator it(vec, 0); it; ++it)
   {
     RealScalar ax = abs(it.value());
-    if(ax > ab2)     abig += internal::abs2(ax*s2m);
-    else if(ax < b1) asml += internal::abs2(ax*s1m);
-    else             amed += internal::abs2(ax);
+    if(ax > ab2)     abig += numext::abs2(ax*s2m);
+    else if(ax < b1) asml += numext::abs2(ax*s1m);
+    else             amed += numext::abs2(ax);
   }
   if(abig > RealScalar(0))
   {
@@ -120,7 +120,7 @@ blueNorm_impl(const EigenBase<Derived>& _vec)
   if(asml <= abig*relerr)
     return abig;
   else
-    return abig * sqrt(RealScalar(1) + internal::abs2(asml/abig));
+    return abig * sqrt(RealScalar(1) + numext::abs2(asml/abig));
 }
 
 } // end namespace internal
diff --git a/Eigen/src/Core/arch/SSE/Complex.h b/Eigen/src/Core/arch/SSE/Complex.h
index bd76d75ed..91bba5e38 100644
--- a/Eigen/src/Core/arch/SSE/Complex.h
+++ b/Eigen/src/Core/arch/SSE/Complex.h
@@ -81,8 +81,8 @@ template<> EIGEN_STRONG_INLINE Packet2cf por    <Packet2cf>(const Packet2cf& a,
 template<> EIGEN_STRONG_INLINE Packet2cf pxor   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_xor_ps(a.v,b.v)); }
 template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_andnot_ps(a.v,b.v)); }
 
-template<> EIGEN_STRONG_INLINE Packet2cf pload <Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>(&real_ref(*from))); }
-template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>(&real_ref(*from))); }
+template<> EIGEN_STRONG_INLINE Packet2cf pload <Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>(&numext::real_ref(*from))); }
+template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>(&numext::real_ref(*from))); }
 
 template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>&  from)
 {
@@ -104,8 +104,8 @@ template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<flo
 
 template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from) { return pset1<Packet2cf>(*from); }
 
-template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore(&real_ref(*to), from.v); }
-template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(&real_ref(*to), from.v); }
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore(&numext::real_ref(*to), from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(&numext::real_ref(*to), from.v); }
 
 template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> *   addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
 
diff --git a/Eigen/src/Core/products/GeneralMatrixVector.h b/Eigen/src/Core/products/GeneralMatrixVector.h
index 9bdd588df..c1cb78498 100644
--- a/Eigen/src/Core/products/GeneralMatrixVector.h
+++ b/Eigen/src/Core/products/GeneralMatrixVector.h
@@ -86,7 +86,7 @@ EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,ColMajor,Co
   conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;
   conj_helper<LhsPacket,RhsPacket,ConjugateLhs,ConjugateRhs> pcj;
   if(ConjugateRhs)
-    alpha = conj(alpha);
+    alpha = numext::conj(alpha);
 
   enum { AllAligned = 0, EvenAligned, FirstAligned, NoneAligned };
   const Index columnsAtOnce = 4;
diff --git a/Eigen/src/Core/products/SelfadjointMatrixMatrix.h b/Eigen/src/Core/products/SelfadjointMatrixMatrix.h
index ee619df99..99cf9e0ae 100644
--- a/Eigen/src/Core/products/SelfadjointMatrixMatrix.h
+++ b/Eigen/src/Core/products/SelfadjointMatrixMatrix.h
@@ -30,9 +30,9 @@ struct symm_pack_lhs
     for(Index k=i; k<i+BlockRows; k++)
     {
       for(Index w=0; w<h; w++)
-        blockA[count++] = conj(lhs(k, i+w)); // transposed
+        blockA[count++] = numext::conj(lhs(k, i+w)); // transposed
 
-      blockA[count++] = real(lhs(k,k));   // real (diagonal)
+      blockA[count++] = numext::real(lhs(k,k));   // real (diagonal)
 
       for(Index w=h+1; w<BlockRows; w++)
         blockA[count++] = lhs(i+w, k);          // normal
@@ -41,7 +41,7 @@ struct symm_pack_lhs
     // transposed copy
     for(Index k=i+BlockRows; k<cols; k++)
       for(Index w=0; w<BlockRows; w++)
-        blockA[count++] = conj(lhs(k, i+w)); // transposed
+        blockA[count++] = numext::conj(lhs(k, i+w)); // transposed
   }
   void operator()(Scalar* blockA, const Scalar* _lhs, Index lhsStride, Index cols, Index rows)
   {
@@ -65,10 +65,10 @@ struct symm_pack_lhs
       for(Index k=0; k<i; k++)
         blockA[count++] = lhs(i, k);              // normal
 
-      blockA[count++] = real(lhs(i, i));       // real (diagonal)
+      blockA[count++] = numext::real(lhs(i, i));       // real (diagonal)
 
       for(Index k=i+1; k<cols; k++)
-        blockA[count++] = conj(lhs(k, i));     // transposed
+        blockA[count++] = numext::conj(lhs(k, i));     // transposed
     }
   }
 };
@@ -107,12 +107,12 @@ struct symm_pack_rhs
       // transpose
       for(Index k=k2; k<j2; k++)
       {
-        blockB[count+0] = conj(rhs(j2+0,k));
-        blockB[count+1] = conj(rhs(j2+1,k));
+        blockB[count+0] = numext::conj(rhs(j2+0,k));
+        blockB[count+1] = numext::conj(rhs(j2+1,k));
         if (nr==4)
         {
-          blockB[count+2] = conj(rhs(j2+2,k));
-          blockB[count+3] = conj(rhs(j2+3,k));
+          blockB[count+2] = numext::conj(rhs(j2+2,k));
+          blockB[count+3] = numext::conj(rhs(j2+3,k));
         }
         count += nr;
       }
@@ -124,11 +124,11 @@ struct symm_pack_rhs
         for (Index w=0 ; w<h; ++w)
           blockB[count+w] = rhs(k,j2+w);
 
-        blockB[count+h] = real(rhs(k,k));
+        blockB[count+h] = numext::real(rhs(k,k));
 
         // transpose
         for (Index w=h+1 ; w<nr; ++w)
-          blockB[count+w] = conj(rhs(j2+w,k));
+          blockB[count+w] = numext::conj(rhs(j2+w,k));
         count += nr;
         ++h;
       }
@@ -151,12 +151,12 @@ struct symm_pack_rhs
     {
       for(Index k=k2; k<end_k; k++)
       {
-        blockB[count+0] = conj(rhs(j2+0,k));
-        blockB[count+1] = conj(rhs(j2+1,k));
+        blockB[count+0] = numext::conj(rhs(j2+0,k));
+        blockB[count+1] = numext::conj(rhs(j2+1,k));
         if (nr==4)
         {
-          blockB[count+2] = conj(rhs(j2+2,k));
-          blockB[count+3] = conj(rhs(j2+3,k));
+          blockB[count+2] = numext::conj(rhs(j2+2,k));
+          blockB[count+3] = numext::conj(rhs(j2+3,k));
         }
         count += nr;
       }
@@ -169,13 +169,13 @@ struct symm_pack_rhs
       Index half = (std::min)(end_k,j2);
       for(Index k=k2; k<half; k++)
       {
-        blockB[count] = conj(rhs(j2,k));
+        blockB[count] = numext::conj(rhs(j2,k));
         count += 1;
       }
 
       if(half==j2 && half<k2+rows)
       {
-        blockB[count] = real(rhs(j2,j2));
+        blockB[count] = numext::real(rhs(j2,j2));
         count += 1;
       }
       else
diff --git a/Eigen/src/Core/products/SelfadjointMatrixVector.h b/Eigen/src/Core/products/SelfadjointMatrixVector.h
index f70f4894c..c40e80f53 100644
--- a/Eigen/src/Core/products/SelfadjointMatrixVector.h
+++ b/Eigen/src/Core/products/SelfadjointMatrixVector.h
@@ -59,7 +59,7 @@ EIGEN_DONT_INLINE void selfadjoint_matrix_vector_product<Scalar,Index,StorageOrd
   conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs,  IsRowMajor), ConjugateRhs> pcj0;
   conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, !IsRowMajor), ConjugateRhs> pcj1;
 
-  Scalar cjAlpha = ConjugateRhs ? conj(alpha) : alpha;
+  Scalar cjAlpha = ConjugateRhs ? numext::conj(alpha) : alpha;
 
   // FIXME this copy is now handled outside product_selfadjoint_vector, so it could probably be removed.
   // if the rhs is not sequentially stored in memory we copy it to a temporary buffer,
@@ -98,8 +98,8 @@ EIGEN_DONT_INLINE void selfadjoint_matrix_vector_product<Scalar,Index,StorageOrd
     size_t alignedEnd = alignedStart + ((endi-alignedStart)/(PacketSize))*(PacketSize);
 
     // TODO make sure this product is a real * complex and that the rhs is properly conjugated if needed
-    res[j]   += cjd.pmul(internal::real(A0[j]), t0);
-    res[j+1] += cjd.pmul(internal::real(A1[j+1]), t1);
+    res[j]   += cjd.pmul(numext::real(A0[j]), t0);
+    res[j+1] += cjd.pmul(numext::real(A1[j+1]), t1);
     if(FirstTriangular)
     {
       res[j]   += cj0.pmul(A1[j],   t1);
@@ -114,8 +114,8 @@ EIGEN_DONT_INLINE void selfadjoint_matrix_vector_product<Scalar,Index,StorageOrd
     for (size_t i=starti; i<alignedStart; ++i)
     {
       res[i] += t0 * A0[i] + t1 * A1[i];
-      t2 += conj(A0[i]) * rhs[i];
-      t3 += conj(A1[i]) * rhs[i];
+      t2 += numext::conj(A0[i]) * rhs[i];
+      t3 += numext::conj(A1[i]) * rhs[i];
     }
     // Yes this an optimization for gcc 4.3 and 4.4 (=> huge speed up)
     // gcc 4.2 does this optimization automatically.
@@ -152,7 +152,7 @@ EIGEN_DONT_INLINE void selfadjoint_matrix_vector_product<Scalar,Index,StorageOrd
     Scalar t1 = cjAlpha * rhs[j];
     Scalar t2(0);
     // TODO make sure this product is a real * complex and that the rhs is properly conjugated if needed
-    res[j] += cjd.pmul(internal::real(A0[j]), t1);
+    res[j] += cjd.pmul(numext::real(A0[j]), t1);
     for (Index i=FirstTriangular ? 0 : j+1; i<(FirstTriangular ? j : size); i++)
     {
       res[i] += cj0.pmul(A0[i], t1);
diff --git a/Eigen/src/Core/products/SelfadjointRank2Update.h b/Eigen/src/Core/products/SelfadjointRank2Update.h
index 4b57f189d..8594a97ce 100644
--- a/Eigen/src/Core/products/SelfadjointRank2Update.h
+++ b/Eigen/src/Core/products/SelfadjointRank2Update.h
@@ -30,8 +30,8 @@ struct selfadjoint_rank2_update_selector<Scalar,Index,UType,VType,Lower>
     for (Index i=0; i<size; ++i)
     {
       Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i+i, size-i) +=
-                        (conj(alpha)  * conj(u.coeff(i))) * v.tail(size-i)
-                      + (alpha * conj(v.coeff(i))) * u.tail(size-i);
+                        (numext::conj(alpha) * numext::conj(u.coeff(i))) * v.tail(size-i)
+                      + (alpha * numext::conj(v.coeff(i))) * u.tail(size-i);
     }
   }
 };
@@ -44,8 +44,8 @@ struct selfadjoint_rank2_update_selector<Scalar,Index,UType,VType,Upper>
     const Index size = u.size();
     for (Index i=0; i<size; ++i)
       Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i, i+1) +=
-                        (conj(alpha)  * conj(u.coeff(i))) * v.head(i+1)
-                      + (alpha * conj(v.coeff(i))) * u.head(i+1);
+                        (numext::conj(alpha)  * numext::conj(u.coeff(i))) * v.head(i+1)
+                      + (alpha * numext::conj(v.coeff(i))) * u.head(i+1);
   }
 };
 
@@ -75,9 +75,9 @@ SelfAdjointView<MatrixType,UpLo>& SelfAdjointView<MatrixType,UpLo>
 
   enum { IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0 };
   Scalar actualAlpha = alpha * UBlasTraits::extractScalarFactor(u.derived())
-                             * internal::conj(VBlasTraits::extractScalarFactor(v.derived()));
+                             * numext::conj(VBlasTraits::extractScalarFactor(v.derived()));
   if (IsRowMajor)
-    actualAlpha = internal::conj(actualAlpha);
+    actualAlpha = numext::conj(actualAlpha);
 
   internal::selfadjoint_rank2_update_selector<Scalar, Index,
     typename internal::remove_all<typename internal::conj_expr_if<IsRowMajor ^ UBlasTraits::NeedToConjugate,_ActualUType>::type>::type,
diff --git a/Eigen/src/Core/products/TriangularMatrixVector.h b/Eigen/src/Core/products/TriangularMatrixVector.h
index c8b7d28c4..6117d5a82 100644
--- a/Eigen/src/Core/products/TriangularMatrixVector.h
+++ b/Eigen/src/Core/products/TriangularMatrixVector.h
@@ -245,7 +245,7 @@ template<> struct trmv_selector<ColMajor>
 
     gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
 
-    bool alphaIsCompatible = (!ComplexByReal) || (imag(actualAlpha)==RealScalar(0));
+    bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));
     bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
     
     RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
diff --git a/Eigen/src/Core/util/BlasUtil.h b/Eigen/src/Core/util/BlasUtil.h
index 91496651c..a28f16fa0 100644
--- a/Eigen/src/Core/util/BlasUtil.h
+++ b/Eigen/src/Core/util/BlasUtil.h
@@ -42,7 +42,7 @@ template<bool Conjugate> struct conj_if;
 
 template<> struct conj_if<true> {
   template<typename T>
-  inline T operator()(const T& x) { return conj(x); }
+  inline T operator()(const T& x) { return numext::conj(x); }
   template<typename T>
   inline T pconj(const T& x) { return internal::pconj(x); }
 };
@@ -67,7 +67,7 @@ template<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::
   { return c + pmul(x,y); }
 
   EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const Scalar& y) const
-  { return Scalar(real(x)*real(y) + imag(x)*imag(y), imag(x)*real(y) - real(x)*imag(y)); }
+  { return Scalar(numext::real(x)*numext::real(y) + numext::imag(x)*numext::imag(y), numext::imag(x)*numext::real(y) - numext::real(x)*numext::imag(y)); }
 };
 
 template<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::complex<RealScalar>, true,false>
@@ -77,7 +77,7 @@ template<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::
   { return c + pmul(x,y); }
 
   EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const Scalar& y) const
-  { return Scalar(real(x)*real(y) + imag(x)*imag(y), real(x)*imag(y) - imag(x)*real(y)); }
+  { return Scalar(numext::real(x)*numext::real(y) + numext::imag(x)*numext::imag(y), numext::real(x)*numext::imag(y) - numext::imag(x)*numext::real(y)); }
 };
 
 template<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::complex<RealScalar>, true,true>
@@ -87,7 +87,7 @@ template<typename RealScalar> struct conj_helper<std::complex<RealScalar>, std::
   { return c + pmul(x,y); }
 
   EIGEN_STRONG_INLINE Scalar pmul(const Scalar& x, const Scalar& y) const
-  { return Scalar(real(x)*real(y) - imag(x)*imag(y), - real(x)*imag(y) - imag(x)*real(y)); }
+  { return Scalar(numext::real(x)*numext::real(y) - numext::imag(x)*numext::imag(y), - numext::real(x)*numext::imag(y) - numext::imag(x)*numext::real(y)); }
 };
 
 template<typename RealScalar,bool Conj> struct conj_helper<std::complex<RealScalar>, RealScalar, Conj,false>
@@ -113,7 +113,7 @@ template<typename From,typename To> struct get_factor {
 };
 
 template<typename Scalar> struct get_factor<Scalar,typename NumTraits<Scalar>::Real> {
-  static EIGEN_STRONG_INLINE typename NumTraits<Scalar>::Real run(const Scalar& x) { return real(x); }
+  static EIGEN_STRONG_INLINE typename NumTraits<Scalar>::Real run(const Scalar& x) { return numext::real(x); }
 };
 
 // Lightweight helper class to access matrix coefficients.
diff --git a/Eigen/src/Eigen2Support/MathFunctions.h b/Eigen/src/Eigen2Support/MathFunctions.h
index bde5dd441..3544af253 100644
--- a/Eigen/src/Eigen2Support/MathFunctions.h
+++ b/Eigen/src/Eigen2Support/MathFunctions.h
@@ -12,18 +12,18 @@
 
 namespace Eigen { 
 
-template<typename T> inline typename NumTraits<T>::Real ei_real(const T& x) { return internal::real(x); }
-template<typename T> inline typename NumTraits<T>::Real ei_imag(const T& x) { return internal::imag(x); }
-template<typename T> inline T ei_conj(const T& x) { return internal::conj(x); }
+template<typename T> inline typename NumTraits<T>::Real ei_real(const T& x) { return numext::real(x); }
+template<typename T> inline typename NumTraits<T>::Real ei_imag(const T& x) { return numext::imag(x); }
+template<typename T> inline T ei_conj(const T& x) { return numext::conj(x); }
 template<typename T> inline typename NumTraits<T>::Real ei_abs (const T& x) { using std::abs; return abs(x); }
-template<typename T> inline typename NumTraits<T>::Real ei_abs2(const T& x) { return internal::abs2(x); }
+template<typename T> inline typename NumTraits<T>::Real ei_abs2(const T& x) { return numext::abs2(x); }
 template<typename T> inline T ei_sqrt(const T& x) { using std::sqrt; return sqrt(x); }
 template<typename T> inline T ei_exp (const T& x) { using std::exp;  return exp(x); }
 template<typename T> inline T ei_log (const T& x) { using std::log;  return log(x); }
 template<typename T> inline T ei_sin (const T& x) { using std::sin;  return sin(x); }
 template<typename T> inline T ei_cos (const T& x) { using std::cos;  return cos(x); }
 template<typename T> inline T ei_atan2(const T& x,const T& y) { using std::atan2; return atan2(x,y); }
-template<typename T> inline T ei_pow (const T& x,const T& y) { return internal::pow(x,y); }
+template<typename T> inline T ei_pow (const T& x,const T& y) { return numext::pow(x,y); }
 template<typename T> inline T ei_random () { return internal::random<T>(); }
 template<typename T> inline T ei_random (const T& x, const T& y) { return internal::random(x, y); }
 
diff --git a/Eigen/src/Eigen2Support/SVD.h b/Eigen/src/Eigen2Support/SVD.h
index a08b695a4..077d26d54 100644
--- a/Eigen/src/Eigen2Support/SVD.h
+++ b/Eigen/src/Eigen2Support/SVD.h
@@ -315,7 +315,7 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
         e[p-2] = 0.0;
         for (j = p-2; j >= k; --j)
         {
-          Scalar t(internal::hypot(m_sigma[j],f));
+          Scalar t(numext::hypot(m_sigma[j],f));
           Scalar cs(m_sigma[j]/t);
           Scalar sn(f/t);
           m_sigma[j] = t;
@@ -344,7 +344,7 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
         e[k-1] = 0.0;
         for (j = k; j < p; ++j)
         {
-          Scalar t(internal::hypot(m_sigma[j],f));
+          Scalar t(numext::hypot(m_sigma[j],f));
           Scalar cs( m_sigma[j]/t);
           Scalar sn(f/t);
           m_sigma[j] = t;
@@ -392,7 +392,7 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
 
         for (j = k; j < p-1; ++j)
         {
-          Scalar t = internal::hypot(f,g);
+          Scalar t = numext::hypot(f,g);
           Scalar cs = f/t;
           Scalar sn = g/t;
           if (j != k)
@@ -410,7 +410,7 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
               m_matV(i,j) = t;
             }
           }
-          t = internal::hypot(f,g);
+          t = numext::hypot(f,g);
           cs = f/t;
           sn = g/t;
           m_sigma[j] = t;
diff --git a/Eigen/src/Eigenvalues/ComplexEigenSolver.h b/Eigen/src/Eigenvalues/ComplexEigenSolver.h
index bd41bf7ed..af434bc9b 100644
--- a/Eigen/src/Eigenvalues/ComplexEigenSolver.h
+++ b/Eigen/src/Eigenvalues/ComplexEigenSolver.h
@@ -294,7 +294,7 @@ void ComplexEigenSolver<MatrixType>::doComputeEigenvectors(const RealScalar& mat
       {
         // If the i-th and k-th eigenvalue are equal, then z equals 0.
         // Use a small value instead, to prevent division by zero.
-        internal::real_ref(z) = NumTraits<RealScalar>::epsilon() * matrixnorm;
+        numext::real_ref(z) = NumTraits<RealScalar>::epsilon() * matrixnorm;
       }
       m_matX.coeffRef(i,k) = m_matX.coeff(i,k) / z;
     }
diff --git a/Eigen/src/Eigenvalues/ComplexSchur.h b/Eigen/src/Eigenvalues/ComplexSchur.h
index 62b57ff66..89e6cade3 100644
--- a/Eigen/src/Eigenvalues/ComplexSchur.h
+++ b/Eigen/src/Eigenvalues/ComplexSchur.h
@@ -263,8 +263,8 @@ template<typename _MatrixType> class ComplexSchur
 template<typename MatrixType>
 inline bool ComplexSchur<MatrixType>::subdiagonalEntryIsNeglegible(Index i)
 {
-  RealScalar d = internal::norm1(m_matT.coeff(i,i)) + internal::norm1(m_matT.coeff(i+1,i+1));
-  RealScalar sd = internal::norm1(m_matT.coeff(i+1,i));
+  RealScalar d = numext::norm1(m_matT.coeff(i,i)) + numext::norm1(m_matT.coeff(i+1,i+1));
+  RealScalar sd = numext::norm1(m_matT.coeff(i+1,i));
   if (internal::isMuchSmallerThan(sd, d, NumTraits<RealScalar>::epsilon()))
   {
     m_matT.coeffRef(i+1,i) = ComplexScalar(0);
@@ -282,7 +282,7 @@ typename ComplexSchur<MatrixType>::ComplexScalar ComplexSchur<MatrixType>::compu
   if (iter == 10 || iter == 20) 
   {
     // exceptional shift, taken from http://www.netlib.org/eispack/comqr.f
-    return abs(internal::real(m_matT.coeff(iu,iu-1))) + abs(internal::real(m_matT.coeff(iu-1,iu-2)));
+    return abs(numext::real(m_matT.coeff(iu,iu-1))) + abs(numext::real(m_matT.coeff(iu-1,iu-2)));
   }
 
   // compute the shift as one of the eigenvalues of t, the 2x2
@@ -299,13 +299,13 @@ typename ComplexSchur<MatrixType>::ComplexScalar ComplexSchur<MatrixType>::compu
   ComplexScalar eival1 = (trace + disc) / RealScalar(2);
   ComplexScalar eival2 = (trace - disc) / RealScalar(2);
 
-  if(internal::norm1(eival1) > internal::norm1(eival2))
+  if(numext::norm1(eival1) > numext::norm1(eival2))
     eival2 = det / eival1;
   else
     eival1 = det / eival2;
 
   // choose the eigenvalue closest to the bottom entry of the diagonal
-  if(internal::norm1(eival1-t.coeff(1,1)) < internal::norm1(eival2-t.coeff(1,1)))
+  if(numext::norm1(eival1-t.coeff(1,1)) < numext::norm1(eival2-t.coeff(1,1)))
     return normt * eival1;
   else
     return normt * eival2;
diff --git a/Eigen/src/Eigenvalues/EigenSolver.h b/Eigen/src/Eigenvalues/EigenSolver.h
index f0d4e5afa..6e7150685 100644
--- a/Eigen/src/Eigenvalues/EigenSolver.h
+++ b/Eigen/src/Eigenvalues/EigenSolver.h
@@ -317,12 +317,12 @@ MatrixType EigenSolver<MatrixType>::pseudoEigenvalueMatrix() const
   MatrixType matD = MatrixType::Zero(n,n);
   for (Index i=0; i<n; ++i)
   {
-    if (internal::isMuchSmallerThan(internal::imag(m_eivalues.coeff(i)), internal::real(m_eivalues.coeff(i))))
-      matD.coeffRef(i,i) = internal::real(m_eivalues.coeff(i));
+    if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i))))
+      matD.coeffRef(i,i) = numext::real(m_eivalues.coeff(i));
     else
     {
-      matD.template block<2,2>(i,i) <<  internal::real(m_eivalues.coeff(i)), internal::imag(m_eivalues.coeff(i)),
-                                       -internal::imag(m_eivalues.coeff(i)), internal::real(m_eivalues.coeff(i));
+      matD.template block<2,2>(i,i) <<  numext::real(m_eivalues.coeff(i)), numext::imag(m_eivalues.coeff(i)),
+                                       -numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i));
       ++i;
     }
   }
@@ -338,7 +338,7 @@ typename EigenSolver<MatrixType>::EigenvectorsType EigenSolver<MatrixType>::eige
   EigenvectorsType matV(n,n);
   for (Index j=0; j<n; ++j)
   {
-    if (internal::isMuchSmallerThan(internal::imag(m_eivalues.coeff(j)), internal::real(m_eivalues.coeff(j))) || j+1==n)
+    if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(j)), numext::real(m_eivalues.coeff(j))) || j+1==n)
     {
       // we have a real eigen value
       matV.col(j) = m_eivec.col(j).template cast<ComplexScalar>();
@@ -515,8 +515,8 @@ void EigenSolver<MatrixType>::doComputeEigenvectors()
       else
       {
         std::complex<Scalar> cc = cdiv<Scalar>(0.0,-m_matT.coeff(n-1,n),m_matT.coeff(n-1,n-1)-p,q);
-        m_matT.coeffRef(n-1,n-1) = internal::real(cc);
-        m_matT.coeffRef(n-1,n) = internal::imag(cc);
+        m_matT.coeffRef(n-1,n-1) = numext::real(cc);
+        m_matT.coeffRef(n-1,n) = numext::imag(cc);
       }
       m_matT.coeffRef(n,n-1) = 0.0;
       m_matT.coeffRef(n,n) = 1.0;
@@ -538,8 +538,8 @@ void EigenSolver<MatrixType>::doComputeEigenvectors()
           if (m_eivalues.coeff(i).imag() == RealScalar(0))
           {
             std::complex<Scalar> cc = cdiv(-ra,-sa,w,q);
-            m_matT.coeffRef(i,n-1) = internal::real(cc);
-            m_matT.coeffRef(i,n) = internal::imag(cc);
+            m_matT.coeffRef(i,n-1) = numext::real(cc);
+            m_matT.coeffRef(i,n) = numext::imag(cc);
           }
           else
           {
@@ -552,8 +552,8 @@ void EigenSolver<MatrixType>::doComputeEigenvectors()
               vr = eps * norm * (abs(w) + abs(q) + abs(x) + abs(y) + abs(lastw));
 
             std::complex<Scalar> cc = cdiv(x*lastra-lastw*ra+q*sa,x*lastsa-lastw*sa-q*ra,vr,vi);
-            m_matT.coeffRef(i,n-1) = internal::real(cc);
-            m_matT.coeffRef(i,n) = internal::imag(cc);
+            m_matT.coeffRef(i,n-1) = numext::real(cc);
+            m_matT.coeffRef(i,n) = numext::imag(cc);
             if (abs(x) > (abs(lastw) + abs(q)))
             {
               m_matT.coeffRef(i+1,n-1) = (-ra - w * m_matT.coeff(i,n-1) + q * m_matT.coeff(i,n)) / x;
@@ -562,8 +562,8 @@ void EigenSolver<MatrixType>::doComputeEigenvectors()
             else
             {
               cc = cdiv(-lastra-y*m_matT.coeff(i,n-1),-lastsa-y*m_matT.coeff(i,n),lastw,q);
-              m_matT.coeffRef(i+1,n-1) = internal::real(cc);
-              m_matT.coeffRef(i+1,n) = internal::imag(cc);
+              m_matT.coeffRef(i+1,n-1) = numext::real(cc);
+              m_matT.coeffRef(i+1,n) = numext::imag(cc);
             }
           }
 
diff --git a/Eigen/src/Eigenvalues/HessenbergDecomposition.h b/Eigen/src/Eigenvalues/HessenbergDecomposition.h
index ebd8ae908..afa636ffa 100644
--- a/Eigen/src/Eigenvalues/HessenbergDecomposition.h
+++ b/Eigen/src/Eigenvalues/HessenbergDecomposition.h
@@ -313,7 +313,7 @@ void HessenbergDecomposition<MatrixType>::_compute(MatrixType& matA, CoeffVector
 
     // A = A H'
     matA.rightCols(remainingSize)
-        .applyHouseholderOnTheRight(matA.col(i).tail(remainingSize-1).conjugate(), internal::conj(h), &temp.coeffRef(0));
+        .applyHouseholderOnTheRight(matA.col(i).tail(remainingSize-1).conjugate(), numext::conj(h), &temp.coeffRef(0));
   }
 }
 
diff --git a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
index 03c024927..3993046a8 100644
--- a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
+++ b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
@@ -395,7 +395,7 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
 
   if(n==1)
   {
-    m_eivalues.coeffRef(0,0) = internal::real(matrix.coeff(0,0));
+    m_eivalues.coeffRef(0,0) = numext::real(matrix.coeff(0,0));
     if(computeEigenvectors)
       m_eivec.setOnes(n,n);
     m_info = Success;
@@ -669,7 +669,7 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,2
   static inline void computeRoots(const MatrixType& m, VectorType& roots)
   {
     using std::sqrt;
-    const Scalar t0 = Scalar(0.5) * sqrt( abs2(m(0,0)-m(1,1)) + Scalar(4)*m(1,0)*m(1,0));
+    const Scalar t0 = Scalar(0.5) * sqrt( numext::abs2(m(0,0)-m(1,1)) + Scalar(4)*m(1,0)*m(1,0));
     const Scalar t1 = Scalar(0.5) * (m(0,0) + m(1,1));
     roots(0) = t1 - t0;
     roots(1) = t1 + t0;
@@ -699,9 +699,9 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,2
     if(computeEigenvectors)
     {
       scaledMat.diagonal().array () -= eivals(1);
-      Scalar a2 = abs2(scaledMat(0,0));
-      Scalar c2 = abs2(scaledMat(1,1));
-      Scalar b2 = abs2(scaledMat(1,0));
+      Scalar a2 = numext::abs2(scaledMat(0,0));
+      Scalar c2 = numext::abs2(scaledMat(1,1));
+      Scalar b2 = numext::abs2(scaledMat(1,0));
       if(a2>c2)
       {
         eivecs.col(1) << -scaledMat(1,0), scaledMat(0,0);
@@ -744,7 +744,7 @@ static void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index sta
   RealScalar e = subdiag[end-1];
   // Note that thanks to scaling, e^2 or td^2 cannot overflow, however they can still
   // underflow thus leading to inf/NaN values when using the following commented code:
-//   RealScalar e2 = abs2(subdiag[end-1]);
+//   RealScalar e2 = numext::abs2(subdiag[end-1]);
 //   RealScalar mu = diag[end] - e2 / (td + (td>0 ? 1 : -1) * sqrt(td*td + e2));
   // This explain the following, somewhat more complicated, version:
   RealScalar mu = diag[end];
@@ -752,8 +752,8 @@ static void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index sta
     mu -= abs(e);
   else
   {
-    RealScalar e2 = abs2(subdiag[end-1]);
-    RealScalar h = hypot(td,e);
+    RealScalar e2 = numext::abs2(subdiag[end-1]);
+    RealScalar h = numext::hypot(td,e);
     if(e2==0)  mu -= (e / (td + (td>0 ? 1 : -1))) * (e / h);
     else       mu -= e2 / (td + (td>0 ? h : -h));
   }
diff --git a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver_MKL.h b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver_MKL.h
index 5de5f15d6..17c0dadd2 100644
--- a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver_MKL.h
+++ b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver_MKL.h
@@ -56,7 +56,7 @@ SelfAdjointEigenSolver<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(c
 \
   if(n==1) \
   { \
-    m_eivalues.coeffRef(0,0) = internal::real(matrix.coeff(0,0)); \
+    m_eivalues.coeffRef(0,0) = numext::real(matrix.coeff(0,0)); \
     if(computeEigenvectors) m_eivec.setOnes(n,n); \
     m_info = Success; \
     m_isInitialized = true; \
diff --git a/Eigen/src/Eigenvalues/Tridiagonalization.h b/Eigen/src/Eigenvalues/Tridiagonalization.h
index e8408761d..b55a01d3a 100644
--- a/Eigen/src/Eigenvalues/Tridiagonalization.h
+++ b/Eigen/src/Eigenvalues/Tridiagonalization.h
@@ -345,7 +345,7 @@ namespace internal {
 template<typename MatrixType, typename CoeffVectorType>
 void tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs)
 {
-  using internal::conj;
+  using numext::conj;
   typedef typename MatrixType::Index Index;
   typedef typename MatrixType::Scalar Scalar;
   typedef typename MatrixType::RealScalar RealScalar;
@@ -468,7 +468,7 @@ struct tridiagonalization_inplace_selector<MatrixType,3,false>
   {
     using std::sqrt;
     diag[0] = mat(0,0);
-    RealScalar v1norm2 = abs2(mat(2,0));
+    RealScalar v1norm2 = numext::abs2(mat(2,0));
     if(v1norm2 == RealScalar(0))
     {
       diag[1] = mat(1,1);
@@ -480,7 +480,7 @@ struct tridiagonalization_inplace_selector<MatrixType,3,false>
     }
     else
     {
-      RealScalar beta = sqrt(abs2(mat(1,0)) + v1norm2);
+      RealScalar beta = sqrt(numext::abs2(mat(1,0)) + v1norm2);
       RealScalar invBeta = RealScalar(1)/beta;
       Scalar m01 = mat(1,0) * invBeta;
       Scalar m02 = mat(2,0) * invBeta;
@@ -510,7 +510,7 @@ struct tridiagonalization_inplace_selector<MatrixType,1,IsComplex>
   template<typename DiagonalType, typename SubDiagonalType>
   static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType&, bool extractQ)
   {
-    diag(0,0) = real(mat(0,0));
+    diag(0,0) = numext::real(mat(0,0));
     if(extractQ)
       mat(0,0) = Scalar(1);
   }
diff --git a/Eigen/src/Geometry/OrthoMethods.h b/Eigen/src/Geometry/OrthoMethods.h
index 4c1bf5fcd..556bc8160 100644
--- a/Eigen/src/Geometry/OrthoMethods.h
+++ b/Eigen/src/Geometry/OrthoMethods.h
@@ -33,9 +33,9 @@ MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
   typename internal::nested<Derived,2>::type lhs(derived());
   typename internal::nested<OtherDerived,2>::type rhs(other.derived());
   return typename cross_product_return_type<OtherDerived>::type(
-    internal::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
-    internal::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
-    internal::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
+    numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
+    numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
+    numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
   );
 }
 
@@ -49,9 +49,9 @@ struct cross3_impl {
   run(const VectorLhs& lhs, const VectorRhs& rhs)
   {
     return typename internal::plain_matrix_type<VectorLhs>::type(
-      internal::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
-      internal::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
-      internal::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),
+      numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
+      numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
+      numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),
       0
     );
   }
@@ -141,8 +141,8 @@ struct unitOrthogonal_selector
     if (maxi==0)
       sndi = 1;
     RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm();
-    perp.coeffRef(maxi) = -conj(src.coeff(sndi)) * invnm;
-    perp.coeffRef(sndi) =  conj(src.coeff(maxi)) * invnm;
+    perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm;
+    perp.coeffRef(sndi) =  numext::conj(src.coeff(maxi)) * invnm;
 
     return perp;
    }
@@ -168,8 +168,8 @@ struct unitOrthogonal_selector<Derived,3>
     || (!isMuchSmallerThan(src.y(), src.z())))
     {
       RealScalar invnm = RealScalar(1)/src.template head<2>().norm();
-      perp.coeffRef(0) = -conj(src.y())*invnm;
-      perp.coeffRef(1) = conj(src.x())*invnm;
+      perp.coeffRef(0) = -numext::conj(src.y())*invnm;
+      perp.coeffRef(1) = numext::conj(src.x())*invnm;
       perp.coeffRef(2) = 0;
     }
     /* if both x and y are close to zero, then the vector is close
@@ -180,8 +180,8 @@ struct unitOrthogonal_selector<Derived,3>
     {
       RealScalar invnm = RealScalar(1)/src.template tail<2>().norm();
       perp.coeffRef(0) = 0;
-      perp.coeffRef(1) = -conj(src.z())*invnm;
-      perp.coeffRef(2) = conj(src.y())*invnm;
+      perp.coeffRef(1) = -numext::conj(src.z())*invnm;
+      perp.coeffRef(2) = numext::conj(src.y())*invnm;
     }
 
     return perp;
@@ -193,7 +193,7 @@ struct unitOrthogonal_selector<Derived,2>
 {
   typedef typename plain_matrix_type<Derived>::type VectorType;
   static inline VectorType run(const Derived& src)
-  { return VectorType(-conj(src.y()), conj(src.x())).normalized(); }
+  { return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); }
 };
 
 } // end namespace internal
diff --git a/Eigen/src/Householder/Householder.h b/Eigen/src/Householder/Householder.h
index b7cfa9b2b..32112af9b 100644
--- a/Eigen/src/Householder/Householder.h
+++ b/Eigen/src/Householder/Householder.h
@@ -68,7 +68,7 @@ void MatrixBase<Derived>::makeHouseholder(
   RealScalar& beta) const
 {
   using std::sqrt;
-  using internal::conj;
+  using numext::conj;
   
   EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)
   VectorBlock<const Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1);
@@ -76,16 +76,16 @@ void MatrixBase<Derived>::makeHouseholder(
   RealScalar tailSqNorm = size()==1 ? RealScalar(0) : tail.squaredNorm();
   Scalar c0 = coeff(0);
 
-  if(tailSqNorm == RealScalar(0) && internal::imag(c0)==RealScalar(0))
+  if(tailSqNorm == RealScalar(0) && numext::imag(c0)==RealScalar(0))
   {
     tau = RealScalar(0);
-    beta = internal::real(c0);
+    beta = numext::real(c0);
     essential.setZero();
   }
   else
   {
-    beta = sqrt(internal::abs2(c0) + tailSqNorm);
-    if (internal::real(c0)>=RealScalar(0))
+    beta = sqrt(numext::abs2(c0) + tailSqNorm);
+    if (numext::real(c0)>=RealScalar(0))
       beta = -beta;
     essential = tail / (c0 - beta);
     tau = conj((beta - c0) / beta);
diff --git a/Eigen/src/IterativeLinearSolvers/ConjugateGradient.h b/Eigen/src/IterativeLinearSolvers/ConjugateGradient.h
index 00b5647c6..a74a8155e 100644
--- a/Eigen/src/IterativeLinearSolvers/ConjugateGradient.h
+++ b/Eigen/src/IterativeLinearSolvers/ConjugateGradient.h
@@ -63,7 +63,7 @@ void conjugate_gradient(const MatrixType& mat, const Rhs& rhs, Dest& x,
   p = precond.solve(residual);      //initial search direction
 
   VectorType z(n), tmp(n);
-  RealScalar absNew = internal::real(residual.dot(p));  // the square of the absolute value of r scaled by invM
+  RealScalar absNew = numext::real(residual.dot(p));  // the square of the absolute value of r scaled by invM
   int i = 0;
   while(i < maxIters)
   {
@@ -80,7 +80,7 @@ void conjugate_gradient(const MatrixType& mat, const Rhs& rhs, Dest& x,
     z = precond.solve(residual);          // approximately solve for "A z = residual"
 
     RealScalar absOld = absNew;
-    absNew = internal::real(residual.dot(z));     // update the absolute value of r
+    absNew = numext::real(residual.dot(z));     // update the absolute value of r
     RealScalar beta = absNew / absOld;            // calculate the Gram-Schmidt value used to create the new search direction
     p = z + beta * p;                             // update search direction
     i++;
diff --git a/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h b/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h
index 17d18ef58..50a870aec 100644
--- a/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h
+++ b/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h
@@ -310,7 +310,7 @@ void IncompleteLUT<Scalar>::factorize(const _MatrixType& amat)
         jr(k) = jpos;
         ++sizeu;
       }
-      rownorm += internal::abs2(j_it.value());
+      rownorm += numext::abs2(j_it.value());
     }
 
     // 2 - detect possible zero row
diff --git a/Eigen/src/Jacobi/Jacobi.h b/Eigen/src/Jacobi/Jacobi.h
index d9d75196c..956f72d57 100644
--- a/Eigen/src/Jacobi/Jacobi.h
+++ b/Eigen/src/Jacobi/Jacobi.h
@@ -50,16 +50,16 @@ template<typename Scalar> class JacobiRotation
     /** Concatenates two planar rotation */
     JacobiRotation operator*(const JacobiRotation& other)
     {
-      using internal::conj;
+      using numext::conj;
       return JacobiRotation(m_c * other.m_c - conj(m_s) * other.m_s,
                             conj(m_c * conj(other.m_s) + conj(m_s) * conj(other.m_c)));
     }
 
     /** Returns the transposed transformation */
-    JacobiRotation transpose() const { using internal::conj; return JacobiRotation(m_c, -conj(m_s)); }
+    JacobiRotation transpose() const { using numext::conj; return JacobiRotation(m_c, -conj(m_s)); }
 
     /** Returns the adjoint transformation */
-    JacobiRotation adjoint() const { using internal::conj; return JacobiRotation(conj(m_c), -m_s); }
+    JacobiRotation adjoint() const { using numext::conj; return JacobiRotation(conj(m_c), -m_s); }
 
     template<typename Derived>
     bool makeJacobi(const MatrixBase<Derived>&, typename Derived::Index p, typename Derived::Index q);
@@ -94,7 +94,7 @@ bool JacobiRotation<Scalar>::makeJacobi(const RealScalar& x, const Scalar& y, co
   else
   {
     RealScalar tau = (x-z)/(RealScalar(2)*abs(y));
-    RealScalar w = sqrt(internal::abs2(tau) + RealScalar(1));
+    RealScalar w = sqrt(numext::abs2(tau) + RealScalar(1));
     RealScalar t;
     if(tau>RealScalar(0))
     {
@@ -105,8 +105,8 @@ bool JacobiRotation<Scalar>::makeJacobi(const RealScalar& x, const Scalar& y, co
       t = RealScalar(1) / (tau - w);
     }
     RealScalar sign_t = t > RealScalar(0) ? RealScalar(1) : RealScalar(-1);
-    RealScalar n = RealScalar(1) / sqrt(internal::abs2(t)+RealScalar(1));
-    m_s = - sign_t * (internal::conj(y) / abs(y)) * abs(t) * n;
+    RealScalar n = RealScalar(1) / sqrt(numext::abs2(t)+RealScalar(1));
+    m_s = - sign_t * (numext::conj(y) / abs(y)) * abs(t) * n;
     m_c = n;
     return true;
   }
@@ -125,7 +125,7 @@ template<typename Scalar>
 template<typename Derived>
 inline bool JacobiRotation<Scalar>::makeJacobi(const MatrixBase<Derived>& m, typename Derived::Index p, typename Derived::Index q)
 {
-  return makeJacobi(internal::real(m.coeff(p,p)), m.coeff(p,q), internal::real(m.coeff(q,q)));
+  return makeJacobi(numext::real(m.coeff(p,p)), m.coeff(p,q), numext::real(m.coeff(q,q)));
 }
 
 /** Makes \c *this as a Givens rotation \c G such that applying \f$ G^* \f$ to the left of the vector
@@ -157,11 +157,11 @@ void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar
 {
   using std::sqrt;
   using std::abs;
-  using internal::conj;
+  using numext::conj;
   
   if(q==Scalar(0))
   {
-    m_c = internal::real(p)<0 ? Scalar(-1) : Scalar(1);
+    m_c = numext::real(p)<0 ? Scalar(-1) : Scalar(1);
     m_s = 0;
     if(r) *r = m_c * p;
   }
@@ -173,17 +173,17 @@ void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar
   }
   else
   {
-    RealScalar p1 = internal::norm1(p);
-    RealScalar q1 = internal::norm1(q);
+    RealScalar p1 = numext::norm1(p);
+    RealScalar q1 = numext::norm1(q);
     if(p1>=q1)
     {
       Scalar ps = p / p1;
-      RealScalar p2 = internal::abs2(ps);
+      RealScalar p2 = numext::abs2(ps);
       Scalar qs = q / p1;
-      RealScalar q2 = internal::abs2(qs);
+      RealScalar q2 = numext::abs2(qs);
 
       RealScalar u = sqrt(RealScalar(1) + q2/p2);
-      if(internal::real(p)<RealScalar(0))
+      if(numext::real(p)<RealScalar(0))
         u = -u;
 
       m_c = Scalar(1)/u;
@@ -193,12 +193,12 @@ void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar
     else
     {
       Scalar ps = p / q1;
-      RealScalar p2 = internal::abs2(ps);
+      RealScalar p2 = numext::abs2(ps);
       Scalar qs = q / q1;
-      RealScalar q2 = internal::abs2(qs);
+      RealScalar q2 = numext::abs2(qs);
 
       RealScalar u = q1 * sqrt(p2 + q2);
-      if(internal::real(p)<RealScalar(0))
+      if(numext::real(p)<RealScalar(0))
         u = -u;
 
       p1 = abs(p);
@@ -231,7 +231,7 @@ void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar
   else if(abs(p) > abs(q))
   {
     Scalar t = q/p;
-    Scalar u = sqrt(Scalar(1) + internal::abs2(t));
+    Scalar u = sqrt(Scalar(1) + numext::abs2(t));
     if(p<Scalar(0))
       u = -u;
     m_c = Scalar(1)/u;
@@ -241,7 +241,7 @@ void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar
   else
   {
     Scalar t = p/q;
-    Scalar u = sqrt(Scalar(1) + internal::abs2(t));
+    Scalar u = sqrt(Scalar(1) + numext::abs2(t));
     if(q<Scalar(0))
       u = -u;
     m_s = -Scalar(1)/u;
@@ -337,8 +337,8 @@ void /*EIGEN_DONT_INLINE*/ apply_rotation_in_the_plane(VectorX& _x, VectorY& _y,
     {
       Scalar xi = x[i];
       Scalar yi = y[i];
-      x[i] =  c * xi + conj(s) * yi;
-      y[i] = -s * xi + conj(c) * yi;
+      x[i] =  c * xi + numext::conj(s) * yi;
+      y[i] = -s * xi + numext::conj(c) * yi;
     }
 
     Scalar* EIGEN_RESTRICT px = x + alignedStart;
@@ -385,8 +385,8 @@ void /*EIGEN_DONT_INLINE*/ apply_rotation_in_the_plane(VectorX& _x, VectorY& _y,
     {
       Scalar xi = x[i];
       Scalar yi = y[i];
-      x[i] =  c * xi + conj(s) * yi;
-      y[i] = -s * xi + conj(c) * yi;
+      x[i] =  c * xi + numext::conj(s) * yi;
+      y[i] = -s * xi + numext::conj(c) * yi;
     }
   }
 
@@ -418,8 +418,8 @@ void /*EIGEN_DONT_INLINE*/ apply_rotation_in_the_plane(VectorX& _x, VectorY& _y,
     {
       Scalar xi = *x;
       Scalar yi = *y;
-      *x =  c * xi + conj(s) * yi;
-      *y = -s * xi + conj(c) * yi;
+      *x =  c * xi + numext::conj(s) * yi;
+      *y = -s * xi + numext::conj(c) * yi;
       x += incrx;
       y += incry;
     }
diff --git a/Eigen/src/MetisSupport/MetisSupport.h b/Eigen/src/MetisSupport/MetisSupport.h
index 818355e79..f2bbef20c 100644
--- a/Eigen/src/MetisSupport/MetisSupport.h
+++ b/Eigen/src/MetisSupport/MetisSupport.h
@@ -134,4 +134,4 @@ public:
 };
 
 }// end namespace eigen 
-#endif
\ No newline at end of file
+#endif
diff --git a/Eigen/src/QR/ColPivHouseholderQR.h b/Eigen/src/QR/ColPivHouseholderQR.h
index 07e75d6f0..7d475b936 100644
--- a/Eigen/src/QR/ColPivHouseholderQR.h
+++ b/Eigen/src/QR/ColPivHouseholderQR.h
@@ -441,7 +441,7 @@ ColPivHouseholderQR<MatrixType>& ColPivHouseholderQR<MatrixType>::compute(const
   for(Index k = 0; k < cols; ++k)
     m_colSqNorms.coeffRef(k) = m_qr.col(k).squaredNorm();
 
-  RealScalar threshold_helper = m_colSqNorms.maxCoeff() * internal::abs2(NumTraits<Scalar>::epsilon()) / RealScalar(rows);
+  RealScalar threshold_helper = m_colSqNorms.maxCoeff() * numext::abs2(NumTraits<Scalar>::epsilon()) / RealScalar(rows);
 
   m_nonzero_pivots = size; // the generic case is that in which all pivots are nonzero (invertible case)
   m_maxpivot = RealScalar(0);
diff --git a/Eigen/src/QR/FullPivHouseholderQR.h b/Eigen/src/QR/FullPivHouseholderQR.h
index f82126494..0dd5ad347 100644
--- a/Eigen/src/QR/FullPivHouseholderQR.h
+++ b/Eigen/src/QR/FullPivHouseholderQR.h
@@ -572,7 +572,7 @@ public:
   template <typename ResultType>
   void evalTo(ResultType& result, WorkVectorType& workspace) const
   {
-    using internal::conj;
+    using numext::conj;
     // compute the product H'_0 H'_1 ... H'_n-1,
     // where H_k is the k-th Householder transformation I - h_k v_k v_k'
     // and v_k is the k-th Householder vector [1,m_qr(k+1,k), m_qr(k+2,k), ...]
diff --git a/Eigen/src/SVD/JacobiSVD.h b/Eigen/src/SVD/JacobiSVD.h
index 495d3fabf..c7a7eeda0 100644
--- a/Eigen/src/SVD/JacobiSVD.h
+++ b/Eigen/src/SVD/JacobiSVD.h
@@ -374,7 +374,7 @@ struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
     using std::sqrt;
     Scalar z;
     JacobiRotation<Scalar> rot;
-    RealScalar n = sqrt(abs2(work_matrix.coeff(p,p)) + abs2(work_matrix.coeff(q,p)));
+    RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p)));
     if(n==0)
     {
       z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
@@ -413,8 +413,8 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
 {
   using std::sqrt;
   Matrix<RealScalar,2,2> m;
-  m << real(matrix.coeff(p,p)), real(matrix.coeff(p,q)),
-       real(matrix.coeff(q,p)), real(matrix.coeff(q,q));
+  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);
@@ -426,7 +426,7 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
   else
   {
     RealScalar u = d / t;
-    rot1.c() = RealScalar(1) / sqrt(RealScalar(1) + abs2(u));
+    rot1.c() = RealScalar(1) / sqrt(RealScalar(1) + numext::abs2(u));
     rot1.s() = rot1.c() * u;
   }
   m.applyOnTheLeft(0,1,rot1);
diff --git a/Eigen/src/SparseCholesky/SimplicialCholesky.h b/Eigen/src/SparseCholesky/SimplicialCholesky.h
index 62747279d..f41d7e010 100644
--- a/Eigen/src/SparseCholesky/SimplicialCholesky.h
+++ b/Eigen/src/SparseCholesky/SimplicialCholesky.h
@@ -364,7 +364,7 @@ public:
     Scalar determinant() const
     {
       Scalar detL = Base::m_matrix.diagonal().prod();
-      return internal::abs2(detL);
+      return numext::abs2(detL);
     }
 };
 
@@ -599,7 +599,7 @@ public:
       else
       {
         Scalar detL = Diagonal<const CholMatrixType>(Base::m_matrix).prod();
-        return internal::abs2(detL);
+        return numext::abs2(detL);
       }
     }
     
diff --git a/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h b/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h
index 4b249868f..7aaf702be 100644
--- a/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h
+++ b/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h
@@ -131,7 +131,7 @@ void SimplicialCholeskyBase<Derived>::factorize_preordered(const CholMatrixType&
       Index i = it.index();
       if(i <= k)
       {
-        y[i] += internal::conj(it.value());            /* scatter A(i,k) into Y (sum duplicates) */
+        y[i] += numext::conj(it.value());            /* scatter A(i,k) into Y (sum duplicates) */
         Index len;
         for(len = 0; tags[i] != k; i = m_parent[i])
         {
@@ -145,7 +145,7 @@ void SimplicialCholeskyBase<Derived>::factorize_preordered(const CholMatrixType&
 
     /* compute numerical values kth row of L (a sparse triangular solve) */
 
-    RealScalar d = internal::real(y[k]) * m_shiftScale + m_shiftOffset;    // get D(k,k), apply the shift function, and clear Y(k)
+    RealScalar d = numext::real(y[k]) * m_shiftScale + m_shiftOffset;    // get D(k,k), apply the shift function, and clear Y(k)
     y[k] = 0.0;
     for(; top < size; ++top)
     {
@@ -163,8 +163,8 @@ void SimplicialCholeskyBase<Derived>::factorize_preordered(const CholMatrixType&
       Index p2 = Lp[i] + m_nonZerosPerCol[i];
       Index p;
       for(p = Lp[i] + (DoLDLT ? 0 : 1); p < p2; ++p)
-        y[Li[p]] -= internal::conj(Lx[p]) * yi;
-      d -= internal::real(l_ki * internal::conj(yi));
+        y[Li[p]] -= numext::conj(Lx[p]) * yi;
+      d -= numext::real(l_ki * numext::conj(yi));
       Li[p] = k;                          /* store L(k,i) in column form of L */
       Lx[p] = l_ki;
       ++m_nonZerosPerCol[i];              /* increment count of nonzeros in col i */
diff --git a/Eigen/src/SparseCore/SparseDot.h b/Eigen/src/SparseCore/SparseDot.h
index dfeb3a8df..db39c9aec 100644
--- a/Eigen/src/SparseCore/SparseDot.h
+++ b/Eigen/src/SparseCore/SparseDot.h
@@ -30,7 +30,7 @@ SparseMatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const
   Scalar res(0);
   while (i)
   {
-    res += internal::conj(i.value()) * other.coeff(i.index());
+    res += numext::conj(i.value()) * other.coeff(i.index());
     ++i;
   }
   return res;
@@ -64,7 +64,7 @@ SparseMatrixBase<Derived>::dot(const SparseMatrixBase<OtherDerived>& other) cons
   {
     if (i.index()==j.index())
     {
-      res += internal::conj(i.value()) * j.value();
+      res += numext::conj(i.value()) * j.value();
       ++i; ++j;
     }
     else if (i.index()<j.index())
@@ -79,7 +79,7 @@ template<typename Derived>
 inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
 SparseMatrixBase<Derived>::squaredNorm() const
 {
-  return internal::real((*this).cwiseAbs2().sum());
+  return numext::real((*this).cwiseAbs2().sum());
 }
 
 template<typename Derived>
diff --git a/Eigen/src/SparseCore/SparseSelfAdjointView.h b/Eigen/src/SparseCore/SparseSelfAdjointView.h
index 9630b60f5..d2e170410 100644
--- a/Eigen/src/SparseCore/SparseSelfAdjointView.h
+++ b/Eigen/src/SparseCore/SparseSelfAdjointView.h
@@ -240,7 +240,7 @@ class SparseSelfAdjointTimeDenseProduct
           Index b = LhsIsRowMajor ? i.index() : j;
           typename Lhs::Scalar v = i.value();
           dest.row(a) += (v) * m_rhs.row(b);
-          dest.row(b) += internal::conj(v) * m_rhs.row(a);
+          dest.row(b) += numext::conj(v) * m_rhs.row(a);
         }
         if (ProcessFirstHalf && i && (i.index()==j))
           dest.row(j) += i.value() * m_rhs.row(j);
@@ -367,7 +367,7 @@ void permute_symm_to_fullsymm(const MatrixType& mat, SparseMatrix<typename Matri
         dest.valuePtr()[k] = it.value();
         k = count[ip]++;
         dest.innerIndexPtr()[k] = jp;
-        dest.valuePtr()[k] = internal::conj(it.value());
+        dest.valuePtr()[k] = numext::conj(it.value());
       }
     }
   }
@@ -428,7 +428,7 @@ void permute_symm_to_symm(const MatrixType& mat, SparseMatrix<typename MatrixTyp
       
       if(!StorageOrderMatch) std::swap(ip,jp);
       if( ((int(DstUpLo)==int(Lower) && ip<jp) || (int(DstUpLo)==int(Upper) && ip>jp)))
-        dest.valuePtr()[k] = conj(it.value());
+        dest.valuePtr()[k] = numext::conj(it.value());
       else
         dest.valuePtr()[k] = it.value();
     }
@@ -461,7 +461,10 @@ class SparseSymmetricPermutationProduct
     template<typename DestScalar, int Options, typename DstIndex>
     void evalTo(SparseMatrix<DestScalar,Options,DstIndex>& _dest) const
     {
-      internal::permute_symm_to_fullsymm<UpLo>(m_matrix,_dest,m_perm.indices().data());
+//       internal::permute_symm_to_fullsymm<UpLo>(m_matrix,_dest,m_perm.indices().data());
+      SparseMatrix<DestScalar,(Options&RowMajor)==RowMajor ? ColMajor : RowMajor, DstIndex> tmp;
+      internal::permute_symm_to_fullsymm<UpLo>(m_matrix,tmp,m_perm.indices().data());
+      _dest = tmp;
     }
     
     template<typename DestType,unsigned int DestUpLo> void evalTo(SparseSelfAdjointView<DestType,DestUpLo>& dest) const
diff --git a/Eigen/src/SparseCore/SparseView.h b/Eigen/src/SparseCore/SparseView.h
index 4fd0cb3d8..67eb93245 100644
--- a/Eigen/src/SparseCore/SparseView.h
+++ b/Eigen/src/SparseCore/SparseView.h
@@ -18,7 +18,7 @@ namespace internal {
 template<typename MatrixType>
 struct traits<SparseView<MatrixType> > : traits<MatrixType>
 {
-  typedef int Index;
+  typedef typename MatrixType::Index Index;
   typedef Sparse StorageKind;
   enum {
     Flags = int(traits<MatrixType>::Flags) & (RowMajorBit)
diff --git a/Eigen/src/SparseQR/SparseQR.h b/Eigen/src/SparseQR/SparseQR.h
index 1bf631507..07c46e4b9 100644
--- a/Eigen/src/SparseQR/SparseQR.h
+++ b/Eigen/src/SparseQR/SparseQR.h
@@ -435,23 +435,23 @@ void SparseQR<MatrixType,OrderingType>::factorize(const MatrixType& mat)
     
     // First, the squared norm of Q((col+1):m, col)
     RealScalar sqrNorm = 0.;
-    for (Index itq = 1; itq < nzcolQ; ++itq) sqrNorm += internal::abs2(tval(Qidx(itq)));
+    for (Index itq = 1; itq < nzcolQ; ++itq) sqrNorm += numext::abs2(tval(Qidx(itq)));
     
-    if(sqrNorm == RealScalar(0) && internal::imag(c0) == RealScalar(0))
+    if(sqrNorm == RealScalar(0) && numext::imag(c0) == RealScalar(0))
     {
       tau = RealScalar(0);
-      beta = internal::real(c0);
+      beta = numext::real(c0);
       tval(Qidx(0)) = 1;
      }
     else
     {
-      beta = std::sqrt(internal::abs2(c0) + sqrNorm);
-      if(internal::real(c0) >= RealScalar(0))
+      beta = std::sqrt(numext::abs2(c0) + sqrNorm);
+      if(numext::real(c0) >= RealScalar(0))
         beta = -beta;
       tval(Qidx(0)) = 1;
       for (Index itq = 1; itq < nzcolQ; ++itq)
         tval(Qidx(itq)) /= (c0 - beta);
-      tau = internal::conj((beta-c0) / beta);
+      tau = numext::conj((beta-c0) / beta);
         
     }
 
diff --git a/Eigen/src/UmfPackSupport/UmfPackSupport.h b/Eigen/src/UmfPackSupport/UmfPackSupport.h
index d85b8be85..3a48cecf7 100644
--- a/Eigen/src/UmfPackSupport/UmfPackSupport.h
+++ b/Eigen/src/UmfPackSupport/UmfPackSupport.h
@@ -39,7 +39,7 @@ inline int umfpack_symbolic(int n_row,int n_col,
                             const int Ap[], const int Ai[], const std::complex<double> Ax[], void **Symbolic,
                             const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
 {
-  return umfpack_zi_symbolic(n_row,n_col,Ap,Ai,&internal::real_ref(Ax[0]),0,Symbolic,Control,Info);
+  return umfpack_zi_symbolic(n_row,n_col,Ap,Ai,&numext::real_ref(Ax[0]),0,Symbolic,Control,Info);
 }
 
 inline int umfpack_numeric( const int Ap[], const int Ai[], const double Ax[],
@@ -53,7 +53,7 @@ inline int umfpack_numeric( const int Ap[], const int Ai[], const std::complex<d
                             void *Symbolic, void **Numeric,
                             const double Control[UMFPACK_CONTROL],double Info [UMFPACK_INFO])
 {
-  return umfpack_zi_numeric(Ap,Ai,&internal::real_ref(Ax[0]),0,Symbolic,Numeric,Control,Info);
+  return umfpack_zi_numeric(Ap,Ai,&numext::real_ref(Ax[0]),0,Symbolic,Numeric,Control,Info);
 }
 
 inline int umfpack_solve( int sys, const int Ap[], const int Ai[], const double Ax[],
@@ -67,7 +67,7 @@ inline int umfpack_solve( int sys, const int Ap[], const int Ai[], const std::co
                           std::complex<double> X[], const std::complex<double> B[], void *Numeric,
                           const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])
 {
-  return umfpack_zi_solve(sys,Ap,Ai,&internal::real_ref(Ax[0]),0,&internal::real_ref(X[0]),0,&internal::real_ref(B[0]),0,Numeric,Control,Info);
+  return umfpack_zi_solve(sys,Ap,Ai,&numext::real_ref(Ax[0]),0,&numext::real_ref(X[0]),0,&numext::real_ref(B[0]),0,Numeric,Control,Info);
 }
 
 inline int umfpack_get_lunz(int *lnz, int *unz, int *n_row, int *n_col, int *nz_udiag, void *Numeric, double)
@@ -89,9 +89,9 @@ inline int umfpack_get_numeric(int Lp[], int Lj[], double Lx[], int Up[], int Ui
 inline int umfpack_get_numeric(int Lp[], int Lj[], std::complex<double> Lx[], int Up[], int Ui[], std::complex<double> Ux[],
                                int P[], int Q[], std::complex<double> Dx[], int *do_recip, double Rs[], void *Numeric)
 {
-  double& lx0_real = internal::real_ref(Lx[0]);
-  double& ux0_real = internal::real_ref(Ux[0]);
-  double& dx0_real = internal::real_ref(Dx[0]);
+  double& lx0_real = numext::real_ref(Lx[0]);
+  double& ux0_real = numext::real_ref(Ux[0]);
+  double& dx0_real = numext::real_ref(Dx[0]);
   return umfpack_zi_get_numeric(Lp,Lj,Lx?&lx0_real:0,0,Up,Ui,Ux?&ux0_real:0,0,P,Q,
                                 Dx?&dx0_real:0,0,do_recip,Rs,Numeric);
 }
@@ -103,7 +103,7 @@ inline int umfpack_get_determinant(double *Mx, double *Ex, void *NumericHandle,
 
 inline int umfpack_get_determinant(std::complex<double> *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO])
 {
-  double& mx_real = internal::real_ref(*Mx);
+  double& mx_real = numext::real_ref(*Mx);
   return umfpack_zi_get_determinant(&mx_real,0,Ex,NumericHandle,User_Info);
 }