diff --git a/Eigen/Core b/Eigen/Core
index a897e4f45..79b326792 100644
--- a/Eigen/Core
+++ b/Eigen/Core
@@ -1,3 +1,5 @@
+#include <cstdlib>
+#include <cmath>
 #include <complex>
 #include <cassert>
 #include <iostream>
diff --git a/Eigen/src/Core/Conjugate.h b/Eigen/src/Core/Conjugate.h
index 839a43bc7..21f256c76 100644
--- a/Eigen/src/Core/Conjugate.h
+++ b/Eigen/src/Core/Conjugate.h
@@ -63,7 +63,7 @@ template<typename MatrixType> class Conjugate : NoOperatorEquals,
     
     Scalar _coeff(int row, int col) const
     {
-      return conj(m_matrix.coeff(row, col));
+      return ei_conj(m_matrix.coeff(row, col));
     }
     
   protected:
diff --git a/Eigen/src/Core/DiagonalMatrix.h b/Eigen/src/Core/DiagonalMatrix.h
index b8ce5d2d5..583eb68c5 100644
--- a/Eigen/src/Core/DiagonalMatrix.h
+++ b/Eigen/src/Core/DiagonalMatrix.h
@@ -109,14 +109,14 @@ bool MatrixBase<Scalar, Derived>::isDiagonal
   RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
   for(int j = 0; j < cols(); j++)
   {
-    RealScalar absOnDiagonal = abs(coeff(j,j));
+    RealScalar absOnDiagonal = ei_abs(coeff(j,j));
     if(absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;
   }
   for(int j = 0; j < cols(); j++)
     for(int i = 0; i < j; i++)
     {
-      if(!Eigen::isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false;
-      if(!Eigen::isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false;
+      if(!ei_isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false;
+      if(!ei_isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false;
     }
   return true;
 }
diff --git a/Eigen/src/Core/Dot.h b/Eigen/src/Core/Dot.h
index 3ff416fba..168cf65a3 100644
--- a/Eigen/src/Core/Dot.h
+++ b/Eigen/src/Core/Dot.h
@@ -32,7 +32,7 @@ struct DotUnroller
   static void run(const Derived1 &v1, const Derived2& v2, typename Derived1::Scalar &dot)
   {
     DotUnroller<Index-1, Size, Derived1, Derived2>::run(v1, v2, dot);
-    dot += v1.coeff(Index) * conj(v2.coeff(Index));
+    dot += v1.coeff(Index) * ei_conj(v2.coeff(Index));
   }
 };
 
@@ -41,7 +41,7 @@ struct DotUnroller<0, Size, Derived1, Derived2>
 {
   static void run(const Derived1 &v1, const Derived2& v2, typename Derived1::Scalar &dot)
   {
-    dot = v1.coeff(0) * conj(v2.coeff(0));
+    dot = v1.coeff(0) * ei_conj(v2.coeff(0));
   }
 };
 
@@ -84,9 +84,9 @@ Scalar MatrixBase<Scalar, Derived>::dot(const OtherDerived& other) const
       ::run(*static_cast<const Derived*>(this), other, res);
   else
   {
-    res = (*this).coeff(0) * conj(other.coeff(0));
+    res = (*this).coeff(0) * ei_conj(other.coeff(0));
     for(int i = 1; i < size(); i++)
-      res += (*this).coeff(i)* conj(other.coeff(i));
+      res += (*this).coeff(i)* ei_conj(other.coeff(i));
   }
   return res;
 }
@@ -100,7 +100,7 @@ Scalar MatrixBase<Scalar, Derived>::dot(const OtherDerived& other) const
 template<typename Scalar, typename Derived>
 typename NumTraits<Scalar>::Real MatrixBase<Scalar, Derived>::norm2() const
 {
-  return real(dot(*this));
+  return ei_real(dot(*this));
 }
 
 /** \returns the norm of *this, i.e. the square root of the dot product of *this with itself.
@@ -112,7 +112,7 @@ typename NumTraits<Scalar>::Real MatrixBase<Scalar, Derived>::norm2() const
 template<typename Scalar, typename Derived>
 typename NumTraits<Scalar>::Real MatrixBase<Scalar, Derived>::norm() const
 {
-  return sqrt(norm2());
+  return ei_sqrt(norm2());
 }
 
 /** \returns an expression of the quotient of *this by its own norm.
@@ -140,7 +140,7 @@ bool MatrixBase<Scalar, Derived>::isOrtho
 (const OtherDerived& other,
  typename NumTraits<Scalar>::Real prec) const
 {
-  return abs2(dot(other)) <= prec * prec * norm2() * other.norm2();
+  return ei_abs2(dot(other)) <= prec * prec * norm2() * other.norm2();
 }
 
 /** \returns true if *this is approximately an unitary matrix,
@@ -160,10 +160,10 @@ bool MatrixBase<Scalar, Derived>::isOrtho
 {
   for(int i = 0; i < cols(); i++)
   {
-    if(!Eigen::isApprox(col(i).norm2(), static_cast<Scalar>(1), prec))
+    if(!ei_isApprox(col(i).norm2(), static_cast<Scalar>(1), prec))
       return false;
     for(int j = 0; j < i; j++)
-      if(!Eigen::isMuchSmallerThan(col(i).dot(col(j)), static_cast<Scalar>(1), prec))
+      if(!ei_isMuchSmallerThan(col(i).dot(col(j)), static_cast<Scalar>(1), prec))
         return false;
   }
   return true;
diff --git a/Eigen/src/Core/Fuzzy.h b/Eigen/src/Core/Fuzzy.h
index 261f14b4a..c16438a2c 100644
--- a/Eigen/src/Core/Fuzzy.h
+++ b/Eigen/src/Core/Fuzzy.h
@@ -37,10 +37,10 @@
   * \note Because of the multiplicativeness of this comparison, one can't use this function
   * to check whether \c *this is approximately equal to the zero matrix or vector.
   * Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix
-  * or vector. If you want to test whether \c *this is zero, use isMuchSmallerThan(const
+  * or vector. If you want to test whether \c *this is zero, use ei_isMuchSmallerThan(const
   * RealScalar&, RealScalar) instead.
   *
-  * \sa isMuchSmallerThan(const RealScalar&, RealScalar) const
+  * \sa ei_isMuchSmallerThan(const RealScalar&, RealScalar) const
   */
 template<typename Scalar, typename Derived>
 template<typename OtherDerived>
@@ -82,12 +82,12 @@ bool MatrixBase<Scalar, Derived>::isMuchSmallerThan(
 {
   if(Traits::IsVectorAtCompileTime)
   {
-    return(norm2() <= abs2(other * prec));
+    return(norm2() <= ei_abs2(other * prec));
   }
   else
   {
     for(int i = 0; i < cols(); i++)
-      if(col(i).norm2() > abs2(other * prec))
+      if(col(i).norm2() > ei_abs2(other * prec))
         return false;
     return true;
   }
diff --git a/Eigen/src/Core/Identity.h b/Eigen/src/Core/Identity.h
index a74ad0247..4cb9073a6 100644
--- a/Eigen/src/Core/Identity.h
+++ b/Eigen/src/Core/Identity.h
@@ -125,12 +125,12 @@ bool MatrixBase<Scalar, Derived>::isIdentity
     {
       if(i == j)
       {
-        if(!Eigen::isApprox(coeff(i, j), static_cast<Scalar>(1), prec))
+        if(!ei_isApprox(coeff(i, j), static_cast<Scalar>(1), prec))
           return false;
       }
       else
       {
-        if(!Eigen::isMuchSmallerThan(coeff(i, j), static_cast<RealScalar>(1), prec))
+        if(!ei_isMuchSmallerThan(coeff(i, j), static_cast<RealScalar>(1), prec))
           return false;
       }
     }
diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
index 3b72a29c0..e8348dd6f 100644
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
@@ -27,16 +27,16 @@
 #define EIGEN_MATHFUNCTIONS_H
 
 template<typename T> inline typename NumTraits<T>::Real precision();
-template<typename T> inline T random(T a, T b);
-template<typename T> inline T random();
+template<typename T> inline T ei_random(T a, T b);
+template<typename T> inline T ei_random();
 
 template<> inline int precision<int>() { return 0; }
-inline int real(int x)  { return x; }
-inline int imag(int)    { return 0; }
-inline int conj(int x)  { return x; }
-inline int abs(int x)   { return std::abs(x); }
-inline int abs2(int x)  { return x*x; }
-inline int sqrt(int)
+inline int ei_real(int x)  { return x; }
+inline int ei_imag(int)    { return 0; }
+inline int ei_conj(int x)  { return x; }
+inline int ei_abs(int x)   { return abs(x); }
+inline int ei_abs2(int x)  { return x*x; }
+inline int ei_sqrt(int)
 {
   // Taking the square root of integers is not allowed
   // (the square root does not always exist within the integers).
@@ -44,91 +44,91 @@ inline int sqrt(int)
   assert(false);
   return 0;
 }
-template<> inline int random(int a, int b)
+template<> inline int ei_random(int a, int b)
 {
   // We can't just do rand()%n as only the high-order bits are really random
   return a + static_cast<int>((b-a+1) * (rand() / (RAND_MAX + 1.0)));
 }
-template<> inline int random()
+template<> inline int ei_random()
 {
-  return random<int>(-10, 10);
+  return ei_random<int>(-10, 10);
 }
-inline bool isMuchSmallerThan(int a, int, int = precision<int>())
+inline bool ei_isMuchSmallerThan(int a, int, int = precision<int>())
 {
   return a == 0;
 }
-inline bool isApprox(int a, int b, int = precision<int>())
+inline bool ei_isApprox(int a, int b, int = precision<int>())
 {
   return a == b;
 }
-inline bool isApproxOrLessThan(int a, int b, int = precision<int>())
+inline bool ei_isApproxOrLessThan(int a, int b, int = precision<int>())
 {
   return a <= b;
 }
 
 template<> inline float precision<float>() { return 1e-5f; }
-inline float real(float x)  { return x; }
-inline float imag(float)    { return 0.f; }
-inline float conj(float x)  { return x; }
-inline float abs(float x)   { return std::abs(x); }
-inline float abs2(float x)  { return x*x; }
-inline float sqrt(float x)  { return std::sqrt(x); }
-template<> inline float random(float a, float b)
+inline float ei_real(float x)  { return x; }
+inline float ei_imag(float)    { return 0.f; }
+inline float ei_conj(float x)  { return x; }
+inline float ei_abs(float x)   { return std::abs(x); }
+inline float ei_abs2(float x)  { return x*x; }
+inline float ei_sqrt(float x)  { return std::sqrt(x); }
+template<> inline float ei_random(float a, float b)
 {
   return a + (b-a) * std::rand() / RAND_MAX;
 }
-template<> inline float random()
+template<> inline float ei_random()
 {
-  return random<float>(-10.0f, 10.0f);
+  return ei_random<float>(-10.0f, 10.0f);
 }
-inline bool isMuchSmallerThan(float a, float b, float prec = precision<float>())
+inline bool ei_isMuchSmallerThan(float a, float b, float prec = precision<float>())
 {
-  return std::abs(a) <= std::abs(b) * prec;
+  return ei_abs(a) <= ei_abs(b) * prec;
 }
-inline bool isApprox(float a, float b, float prec = precision<float>())
+inline bool ei_isApprox(float a, float b, float prec = precision<float>())
 {
-  return std::abs(a - b) <= std::min(std::abs(a), std::abs(b)) * prec;
+  return ei_abs(a - b) <= std::min(ei_abs(a), ei_abs(b)) * prec;
 }
-inline bool isApproxOrLessThan(float a, float b, float prec = precision<float>())
+inline bool ei_isApproxOrLessThan(float a, float b, float prec = precision<float>())
 {
-  return a <= b || isApprox(a, b, prec);
+  return a <= b || ei_isApprox(a, b, prec);
 }
 
 template<> inline double precision<double>() { return 1e-11; }
-inline double real(double x)  { return x; }
-inline double imag(double)    { return 0.; }
-inline double conj(double x)  { return x; }
-inline double abs(double x)   { return std::abs(x); }
-inline double abs2(double x)  { return x*x; }
-inline double sqrt(double x)  { return std::sqrt(x); }
-template<> inline double random(double a, double b)
+inline double ei_real(double x)  { return x; }
+inline double ei_imag(double)    { return 0.; }
+inline double ei_conj(double x)  { return x; }
+inline double ei_abs(double x)   { return std::abs(x); }
+inline double ei_abs2(double x)  { return x*x; }
+inline double ei_sqrt(double x)  { return std::sqrt(x); }
+template<> inline double ei_random(double a, double b)
 {
   return a + (b-a) * std::rand() / RAND_MAX;
 }
-template<> inline double random()
+template<> inline double ei_random()
 {
-  return random<double>(-10.0, 10.0);
+  return ei_random<double>(-10.0, 10.0);
 }
-inline bool isMuchSmallerThan(double a, double b, double prec = precision<double>())
+inline bool ei_isMuchSmallerThan(double a, double b, double prec = precision<double>())
 {
-  return std::abs(a) <= std::abs(b) * prec;
+  return ei_abs(a) <= ei_abs(b) * prec;
 }
-inline bool isApprox(double a, double b, double prec = precision<double>())
+inline bool ei_isApprox(double a, double b, double prec = precision<double>())
 {
-  return std::abs(a - b) <= std::min(std::abs(a), std::abs(b)) * prec;
+  return ei_abs(a - b) <= std::min(ei_abs(a), ei_abs(b)) * prec;
 }
-inline bool isApproxOrLessThan(double a, double b, double prec = precision<double>())
+inline bool ei_isApproxOrLessThan(double a, double b, double prec = precision<double>())
 {
-  return a <= b || isApprox(a, b, prec);
+  return a <= b || ei_isApprox(a, b, prec);
 }
 
 template<> inline float precision<std::complex<float> >() { return precision<float>(); }
-inline float real(const std::complex<float>& x) { return std::real(x); }
-inline float imag(const std::complex<float>& x) { return std::imag(x); }
-inline std::complex<float> conj(const std::complex<float>& x) { return std::conj(x); }
-inline float abs(const std::complex<float>& x) { return std::abs(x); }
-inline float abs2(const std::complex<float>& x) { return std::norm(x); }
-inline std::complex<float> sqrt(const std::complex<float>&)
+inline float ei_real(const std::complex<float>& x) { return std::real(x); }
+inline float ei_imag(const std::complex<float>& x) { return std::imag(x); }
+inline std::complex<float> ei_conj(const std::complex<float>& x) { return std::conj(x); }
+inline float ei_abs(const std::complex<float>& x) { return std::abs(x); }
+inline float ei_abs2(const std::complex<float>& x) { return std::norm(x); }
+inline std::complex<float> ei_sqrt(const std::complex<float>&)
 {
   // Taking the square roots of complex numbers is not allowed,
   // as this is ambiguous (there are two square roots).
@@ -136,49 +136,49 @@ inline std::complex<float> sqrt(const std::complex<float>&)
   assert(false);
   return 0;
 }
-template<> inline std::complex<float> random()
+template<> inline std::complex<float> ei_random()
 {
-  return std::complex<float>(random<float>(), random<float>());
+  return std::complex<float>(ei_random<float>(), ei_random<float>());
 }
-inline bool isMuchSmallerThan(const std::complex<float>& a, const std::complex<float>& b, float prec = precision<float>())
+inline bool ei_isMuchSmallerThan(const std::complex<float>& a, const std::complex<float>& b, float prec = precision<float>())
 {
-  return abs2(a) <= abs2(b) * prec * prec;
+  return ei_abs2(a) <= ei_abs2(b) * prec * prec;
 }
-inline bool isMuchSmallerThan(const std::complex<float>& a, float b, float prec = precision<float>())
+inline bool ei_isMuchSmallerThan(const std::complex<float>& a, float b, float prec = precision<float>())
 {
-  return abs2(a) <= abs2(b) * prec * prec;
+  return ei_abs2(a) <= ei_abs2(b) * prec * prec;
 }
-inline bool isApprox(const std::complex<float>& a, const std::complex<float>& b, float prec = precision<float>())
+inline bool ei_isApprox(const std::complex<float>& a, const std::complex<float>& b, float prec = precision<float>())
 {
-  return isApprox(std::real(a), std::real(b), prec)
-      && isApprox(std::imag(a), std::imag(b), prec);
+  return ei_isApprox(ei_real(a), ei_real(b), prec)
+      && ei_isApprox(ei_imag(a), ei_imag(b), prec);
 }
-// isApproxOrLessThan wouldn't make sense for complex numbers
+// ei_isApproxOrLessThan wouldn't make sense for complex numbers
 
 template<> inline double precision<std::complex<double> >() { return precision<double>(); }
-inline double real(const std::complex<double>& x) { return std::real(x); }
-inline double imag(const std::complex<double>& x) { return std::imag(x); }
-inline std::complex<double> conj(const std::complex<double>& x) { return std::conj(x); }
-inline double abs(const std::complex<double>& x) { return std::abs(x); }
-inline double abs2(const std::complex<double>& x) { return std::norm(x); }
-template<> inline std::complex<double> random()
+inline double ei_real(const std::complex<double>& x) { return std::real(x); }
+inline double ei_imag(const std::complex<double>& x) { return std::imag(x); }
+inline std::complex<double> ei_conj(const std::complex<double>& x) { return std::conj(x); }
+inline double ei_abs(const std::complex<double>& x) { return std::abs(x); }
+inline double ei_abs2(const std::complex<double>& x) { return std::norm(x); }
+template<> inline std::complex<double> ei_random()
 {
-  return std::complex<double>(random<double>(), random<double>());
+  return std::complex<double>(ei_random<double>(), ei_random<double>());
 }
-inline bool isMuchSmallerThan(const std::complex<double>& a, const std::complex<double>& b, double prec = precision<double>())
+inline bool ei_isMuchSmallerThan(const std::complex<double>& a, const std::complex<double>& b, double prec = precision<double>())
 {
-  return abs2(a) <= abs2(b) * prec * prec;
+  return ei_abs2(a) <= ei_abs2(b) * prec * prec;
 }
-inline bool isMuchSmallerThan(const std::complex<double>& a, double b, double prec = precision<double>())
+inline bool ei_isMuchSmallerThan(const std::complex<double>& a, double b, double prec = precision<double>())
 {
-  return abs2(a) <= abs2(b) * prec * prec;
+  return ei_abs2(a) <= ei_abs2(b) * prec * prec;
 }
-inline bool isApprox(const std::complex<double>& a, const std::complex<double>& b, double prec = precision<double>())
+inline bool ei_isApprox(const std::complex<double>& a, const std::complex<double>& b, double prec = precision<double>())
 {
-  return isApprox(std::real(a), std::real(b), prec)
-      && isApprox(std::imag(a), std::imag(b), prec);
+  return ei_isApprox(ei_real(a), ei_real(b), prec)
+      && ei_isApprox(ei_imag(a), ei_imag(b), prec);
 }
-// isApproxOrLessThan wouldn't make sense for complex numbers
+// ei_isApproxOrLessThan wouldn't make sense for complex numbers
 
 #define EIGEN_MAKE_MORE_OVERLOADED_COMPLEX_OPERATOR_STAR(T,U) \
 inline std::complex<T> operator*(U a, const std::complex<T>& b) \
diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h
index fce3a441d..cb7186729 100644
--- a/Eigen/src/Core/MatrixBase.h
+++ b/Eigen/src/Core/MatrixBase.h
@@ -314,7 +314,7 @@ template<typename Scalar, typename Derived> class MatrixBase
       for(int j = 0; j < cols(); j++)
         for(int i = 0; i < rows(); i++)
         {
-          RealScalar x = abs(coeff(i,j));
+          RealScalar x = ei_abs(coeff(i,j));
           if(x > biggest)
           {
             biggest = x;
diff --git a/Eigen/src/Core/Ones.h b/Eigen/src/Core/Ones.h
index 4e5a2e7ca..cd7f5903a 100644
--- a/Eigen/src/Core/Ones.h
+++ b/Eigen/src/Core/Ones.h
@@ -146,7 +146,7 @@ bool MatrixBase<Scalar, Derived>::isOnes
 {
   for(int j = 0; j < cols(); j++)
     for(int i = 0; i < rows(); i++)
-      if(!Eigen::isApprox(coeff(i, j), static_cast<Scalar>(1), prec))
+      if(!ei_isApprox(coeff(i, j), static_cast<Scalar>(1), prec))
         return false;
   return true;
 }
diff --git a/Eigen/src/Core/Random.h b/Eigen/src/Core/Random.h
index 89febe4f3..793e45505 100644
--- a/Eigen/src/Core/Random.h
+++ b/Eigen/src/Core/Random.h
@@ -55,7 +55,7 @@ template<typename MatrixType> class Random : NoOperatorEquals,
     
     Scalar _coeff(int, int) const
     {
-      return Eigen::random<Scalar>();
+      return ei_random<Scalar>();
     }
   
   public:
@@ -78,13 +78,13 @@ template<typename MatrixType> class Random : NoOperatorEquals,
   * the returned matrix. Must be compatible with this MatrixBase type.
   *
   * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
-  * it is redundant to pass \a rows and \a cols as arguments, so random() should be used
+  * it is redundant to pass \a rows and \a cols as arguments, so ei_random() should be used
   * instead.
   *
   * Example: \include MatrixBase_random_int_int.cpp
   * Output: \verbinclude MatrixBase_random_int_int.out
   *
-  * \sa random(), random(int)
+  * \sa ei_random(), ei_random(int)
   */
 template<typename Scalar, typename Derived>
 const Eval<Random<Derived> >
@@ -101,13 +101,13 @@ MatrixBase<Scalar, Derived>::random(int rows, int cols)
   * \only_for_vectors
   *
   * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
-  * it is redundant to pass \a size as argument, so random() should be used
+  * it is redundant to pass \a size as argument, so ei_random() should be used
   * instead.
   *
   * Example: \include MatrixBase_random_int.cpp
   * Output: \verbinclude MatrixBase_random_int.out
   *
-  * \sa random(), random(int,int)
+  * \sa ei_random(), ei_random(int,int)
   */
 template<typename Scalar, typename Derived>
 const Eval<Random<Derived> >
@@ -127,7 +127,7 @@ MatrixBase<Scalar, Derived>::random(int size)
   * Example: \include MatrixBase_random.cpp
   * Output: \verbinclude MatrixBase_random.out
   *
-  * \sa random(int), random(int,int)
+  * \sa ei_random(int), ei_random(int,int)
   */
 template<typename Scalar, typename Derived>
 const Eval<Random<Derived> >
@@ -141,7 +141,7 @@ MatrixBase<Scalar, Derived>::random()
   * Example: \include MatrixBase_setRandom.cpp
   * Output: \verbinclude MatrixBase_setRandom.out
   *
-  * \sa class Random, random()
+  * \sa class Random, ei_random()
   */
 template<typename Scalar, typename Derived>
 Derived& MatrixBase<Scalar, Derived>::setRandom()
diff --git a/Eigen/src/Core/Zero.h b/Eigen/src/Core/Zero.h
index 625804059..a8b003493 100644
--- a/Eigen/src/Core/Zero.h
+++ b/Eigen/src/Core/Zero.h
@@ -146,7 +146,7 @@ bool MatrixBase<Scalar, Derived>::isZero
 {
   for(int j = 0; j < cols(); j++)
     for(int i = 0; i < rows(); i++)
-      if(!Eigen::isMuchSmallerThan(coeff(i, j), static_cast<Scalar>(1), prec))
+      if(!ei_isMuchSmallerThan(coeff(i, j), static_cast<Scalar>(1), prec))
         return false;
   return true;
 }
diff --git a/doc/benchmark.cpp b/doc/benchmark.cpp
index b2ab9a3b0..ad515e04e 100644
--- a/doc/benchmark.cpp
+++ b/doc/benchmark.cpp
@@ -1,8 +1,9 @@
 // g++ -O3 -DNDEBUG benchmark.cpp -o benchmark && time ./benchmark
-
+#include <cstdlib>
+#include <cmath>
 #include <Eigen/Core>
 
-using namespace std;
+//using namespace std;
 USING_PART_OF_NAMESPACE_EIGEN
 
 int main(int argc, char *argv[])
@@ -18,6 +19,6 @@ int main(int argc, char *argv[])
 	{
 		m = I + 0.00005 * (m + m*m);
 	}
-	cout << m << endl;
+	std::cout << m << std::endl;
 	return 0;
 }
diff --git a/test/adjoint.cpp b/test/adjoint.cpp
index f6cd53631..b30deb6a9 100644
--- a/test/adjoint.cpp
+++ b/test/adjoint.cpp
@@ -51,8 +51,8 @@ template<typename MatrixType> void adjoint(const MatrixType& m)
              v3 = VectorType::random(rows),
              vzero = VectorType::zero(rows);
 
-  Scalar s1 = random<Scalar>(),
-         s2 = random<Scalar>();
+  Scalar s1 = ei_random<Scalar>(),
+         s2 = ei_random<Scalar>();
   
   // check involutivity of adjoint, transpose, conjugate
   VERIFY_IS_APPROX(m1.transpose().transpose(),              m1);
@@ -70,18 +70,18 @@ template<typename MatrixType> void adjoint(const MatrixType& m)
   VERIFY_IS_APPROX((m1.adjoint() * m2).adjoint(),           m2.adjoint() * m1);
   VERIFY_IS_APPROX((m1.transpose() * m2).conjugate(),       m1.adjoint() * m2.conjugate());
   VERIFY_IS_APPROX((s1 * m1).transpose(),                   s1 * m1.transpose());
-  VERIFY_IS_APPROX((s1 * m1).conjugate(),                   conj(s1) * m1.conjugate());
-  VERIFY_IS_APPROX((s1 * m1).adjoint(),                     conj(s1) * m1.adjoint());
+  VERIFY_IS_APPROX((s1 * m1).conjugate(),                   ei_conj(s1) * m1.conjugate());
+  VERIFY_IS_APPROX((s1 * m1).adjoint(),                     ei_conj(s1) * m1.adjoint());
   
   // check basic properties of dot, norm, norm2
   typedef typename NumTraits<Scalar>::Real RealScalar;
   VERIFY_IS_APPROX((s1 * v1 + s2 * v2).dot(v3),      s1 * v1.dot(v3) + s2 * v2.dot(v3));
-  VERIFY_IS_APPROX(v3.dot(s1 * v1 + s2 * v2),        conj(s1)*v3.dot(v1)+conj(s2)*v3.dot(v2));
-  VERIFY_IS_APPROX(conj(v1.dot(v2)),                 v2.dot(v1));
-  VERIFY_IS_APPROX(abs(v1.dot(v1)),                  v1.norm2());
+  VERIFY_IS_APPROX(v3.dot(s1 * v1 + s2 * v2),        ei_conj(s1)*v3.dot(v1)+ei_conj(s2)*v3.dot(v2));
+  VERIFY_IS_APPROX(ei_conj(v1.dot(v2)),                 v2.dot(v1));
+  VERIFY_IS_APPROX(ei_abs(v1.dot(v1)),                  v1.norm2());
   if(NumTraits<Scalar>::HasFloatingPoint)
     VERIFY_IS_APPROX(v1.norm2(),                     v1.norm() * v1.norm());
-  VERIFY_IS_MUCH_SMALLER_THAN(abs(vzero.dot(v1)),    static_cast<RealScalar>(1));
+  VERIFY_IS_MUCH_SMALLER_THAN(ei_abs(vzero.dot(v1)),    static_cast<RealScalar>(1));
   if(NumTraits<Scalar>::HasFloatingPoint)
     VERIFY_IS_MUCH_SMALLER_THAN(vzero.norm(),        static_cast<RealScalar>(1));
   
@@ -89,10 +89,10 @@ template<typename MatrixType> void adjoint(const MatrixType& m)
   VERIFY_IS_APPROX(v1.dot(square * v2),              (square.adjoint() * v1).dot(v2));
   
   // like in testBasicStuff, test operator() to check const-qualification
-  int r = random<int>(0, rows-1),
-      c = random<int>(0, cols-1);
-  VERIFY_IS_APPROX(m1.conjugate()(r,c), conj(m1(r,c)));
-  VERIFY_IS_APPROX(m1.adjoint()(c,r), conj(m1(r,c)));
+  int r = ei_random<int>(0, rows-1),
+      c = ei_random<int>(0, cols-1);
+  VERIFY_IS_APPROX(m1.conjugate()(r,c), ei_conj(m1(r,c)));
+  VERIFY_IS_APPROX(m1.adjoint()(c,r), ei_conj(m1(r,c)));
   
 }
 
diff --git a/test/basicstuff.cpp b/test/basicstuff.cpp
index f8a651a73..456275a09 100644
--- a/test/basicstuff.cpp
+++ b/test/basicstuff.cpp
@@ -49,8 +49,8 @@ template<typename MatrixType> void basicStuff(const MatrixType& m)
              v2 = VectorType::random(rows),
              vzero = VectorType::zero(rows);
 
-  int r = random<int>(0, rows-1),
-      c = random<int>(0, cols-1);
+  int r = ei_random<int>(0, rows-1),
+      c = ei_random<int>(0, cols-1);
   
   VERIFY_IS_APPROX(               v1,    v1);
   VERIFY_IS_NOT_APPROX(           v1,    2*v1);
diff --git a/test/linearstructure.cpp b/test/linearstructure.cpp
index 682315c7a..f1869f5d1 100644
--- a/test/linearstructure.cpp
+++ b/test/linearstructure.cpp
@@ -53,11 +53,11 @@ template<typename MatrixType> void linearStructure(const MatrixType& m)
              v2 = VectorType::random(rows),
              vzero = VectorType::zero(rows);
 
-  Scalar s1 = random<Scalar>(),
-         s2 = random<Scalar>();
+  Scalar s1 = ei_random<Scalar>(),
+         s2 = ei_random<Scalar>();
   
-  int r = random<int>(0, rows-1),
-      c = random<int>(0, cols-1);
+  int r = ei_random<int>(0, rows-1),
+      c = ei_random<int>(0, cols-1);
   
   VERIFY_IS_APPROX(-(-m1),                  m1);
   VERIFY_IS_APPROX(m1+m1,                   2*m1);
diff --git a/test/main.h b/test/main.h
index d914a14f5..2699e4bae 100644
--- a/test/main.h
+++ b/test/main.h
@@ -38,12 +38,12 @@
 #define DEFAULT_REPEAT 50
 
 #define VERIFY(a) QVERIFY(a)
-#define VERIFY_IS_APPROX(a, b) QVERIFY(test_isApprox(a, b))
-#define VERIFY_IS_NOT_APPROX(a, b) QVERIFY(!test_isApprox(a, b))
-#define VERIFY_IS_MUCH_SMALLER_THAN(a, b) QVERIFY(test_isMuchSmallerThan(a, b))
-#define VERIFY_IS_NOT_MUCH_SMALLER_THAN(a, b) QVERIFY(!test_isMuchSmallerThan(a, b))
-#define VERIFY_IS_APPROX_OR_LESS_THAN(a, b) QVERIFY(test_isApproxOrLessThan(a, b))
-#define VERIFY_IS_NOT_APPROX_OR_LESS_THAN(a, b) QVERIFY(!test_isApproxOrLessThan(a, b))
+#define VERIFY_IS_APPROX(a, b) QVERIFY(test_ei_isApprox(a, b))
+#define VERIFY_IS_NOT_APPROX(a, b) QVERIFY(!test_ei_isApprox(a, b))
+#define VERIFY_IS_MUCH_SMALLER_THAN(a, b) QVERIFY(test_ei_isMuchSmallerThan(a, b))
+#define VERIFY_IS_NOT_MUCH_SMALLER_THAN(a, b) QVERIFY(!test_ei_isMuchSmallerThan(a, b))
+#define VERIFY_IS_APPROX_OR_LESS_THAN(a, b) QVERIFY(test_ei_isApproxOrLessThan(a, b))
+#define VERIFY_IS_NOT_APPROX_OR_LESS_THAN(a, b) QVERIFY(!test_ei_isApproxOrLessThan(a, b))
 
 namespace Eigen {
 
@@ -54,53 +54,53 @@ template<> inline double test_precision<double>() { return 1e-5; }
 template<> inline float test_precision<std::complex<float> >() { return test_precision<float>(); }
 template<> inline double test_precision<std::complex<double> >() { return test_precision<double>(); }
 
-inline bool test_isApprox(const int& a, const int& b)
-{ return isApprox(a, b, test_precision<int>()); }
-inline bool test_isMuchSmallerThan(const int& a, const int& b)
-{ return isMuchSmallerThan(a, b, test_precision<int>()); }
-inline bool test_isApproxOrLessThan(const int& a, const int& b)
-{ return isApproxOrLessThan(a, b, test_precision<int>()); }
+inline bool test_ei_isApprox(const int& a, const int& b)
+{ return ei_isApprox(a, b, test_precision<int>()); }
+inline bool test_ei_isMuchSmallerThan(const int& a, const int& b)
+{ return ei_isMuchSmallerThan(a, b, test_precision<int>()); }
+inline bool test_ei_isApproxOrLessThan(const int& a, const int& b)
+{ return ei_isApproxOrLessThan(a, b, test_precision<int>()); }
 
-inline bool test_isApprox(const float& a, const float& b)
-{ return isApprox(a, b, test_precision<float>()); }
-inline bool test_isMuchSmallerThan(const float& a, const float& b)
-{ return isMuchSmallerThan(a, b, test_precision<float>()); }
-inline bool test_isApproxOrLessThan(const float& a, const float& b)
-{ return isApproxOrLessThan(a, b, test_precision<float>()); }
+inline bool test_ei_isApprox(const float& a, const float& b)
+{ return ei_isApprox(a, b, test_precision<float>()); }
+inline bool test_ei_isMuchSmallerThan(const float& a, const float& b)
+{ return ei_isMuchSmallerThan(a, b, test_precision<float>()); }
+inline bool test_ei_isApproxOrLessThan(const float& a, const float& b)
+{ return ei_isApproxOrLessThan(a, b, test_precision<float>()); }
 
-inline bool test_isApprox(const double& a, const double& b)
-{ return isApprox(a, b, test_precision<double>()); }
-inline bool test_isMuchSmallerThan(const double& a, const double& b)
-{ return isMuchSmallerThan(a, b, test_precision<double>()); }
-inline bool test_isApproxOrLessThan(const double& a, const double& b)
-{ return isApproxOrLessThan(a, b, test_precision<double>()); }
+inline bool test_ei_isApprox(const double& a, const double& b)
+{ return ei_isApprox(a, b, test_precision<double>()); }
+inline bool test_ei_isMuchSmallerThan(const double& a, const double& b)
+{ return ei_isMuchSmallerThan(a, b, test_precision<double>()); }
+inline bool test_ei_isApproxOrLessThan(const double& a, const double& b)
+{ return ei_isApproxOrLessThan(a, b, test_precision<double>()); }
 
-inline bool test_isApprox(const std::complex<float>& a, const std::complex<float>& b)
-{ return isApprox(a, b, test_precision<std::complex<float> >()); }
-inline bool test_isMuchSmallerThan(const std::complex<float>& a, const std::complex<float>& b)
-{ return isMuchSmallerThan(a, b, test_precision<std::complex<float> >()); }
+inline bool test_ei_isApprox(const std::complex<float>& a, const std::complex<float>& b)
+{ return ei_isApprox(a, b, test_precision<std::complex<float> >()); }
+inline bool test_ei_isMuchSmallerThan(const std::complex<float>& a, const std::complex<float>& b)
+{ return ei_isMuchSmallerThan(a, b, test_precision<std::complex<float> >()); }
 
-inline bool test_isApprox(const std::complex<double>& a, const std::complex<double>& b)
-{ return isApprox(a, b, test_precision<std::complex<double> >()); }
-inline bool test_isMuchSmallerThan(const std::complex<double>& a, const std::complex<double>& b)
-{ return isMuchSmallerThan(a, b, test_precision<std::complex<double> >()); }
+inline bool test_ei_isApprox(const std::complex<double>& a, const std::complex<double>& b)
+{ return ei_isApprox(a, b, test_precision<std::complex<double> >()); }
+inline bool test_ei_isMuchSmallerThan(const std::complex<double>& a, const std::complex<double>& b)
+{ return ei_isMuchSmallerThan(a, b, test_precision<std::complex<double> >()); }
 
 template<typename Scalar, typename Derived1, typename Derived2>
-inline bool test_isApprox(const MatrixBase<Scalar, Derived1>& m1,
+inline bool test_ei_isApprox(const MatrixBase<Scalar, Derived1>& m1,
                    const MatrixBase<Scalar, Derived2>& m2)
 {
   return m1.isApprox(m2, test_precision<Scalar>());
 }
 
 template<typename Scalar, typename Derived1, typename Derived2>
-inline bool test_isMuchSmallerThan(const MatrixBase<Scalar, Derived1>& m1,
+inline bool test_ei_isMuchSmallerThan(const MatrixBase<Scalar, Derived1>& m1,
                                    const MatrixBase<Scalar, Derived2>& m2)
 {
   return m1.isMuchSmallerThan(m2, test_precision<Scalar>());
 }
 
 template<typename Scalar, typename Derived>
-inline bool test_isMuchSmallerThan(const MatrixBase<Scalar, Derived>& m,
+inline bool test_ei_isMuchSmallerThan(const MatrixBase<Scalar, Derived>& m,
                                    const typename NumTraits<Scalar>::Real& s)
 {
   return m.isMuchSmallerThan(s, test_precision<Scalar>());
diff --git a/test/miscmatrices.cpp b/test/miscmatrices.cpp
index 42f808b1a..70e77403d 100644
--- a/test/miscmatrices.cpp
+++ b/test/miscmatrices.cpp
@@ -39,7 +39,7 @@ template<typename MatrixType> void miscMatrices(const MatrixType& m)
   int rows = m.rows();
   int cols = m.cols();
   
-  int r = random<int>(0, rows-1), r2 = random<int>(0, rows-1), c = random<int>(0, cols-1);
+  int r = ei_random<int>(0, rows-1), r2 = ei_random<int>(0, rows-1), c = ei_random<int>(0, cols-1);
   VERIFY_IS_APPROX(MatrixType::ones(rows,cols)(r,c), static_cast<Scalar>(1));
   MatrixType m1 = MatrixType::ones(rows,cols);
   VERIFY_IS_APPROX(m1(r,c), static_cast<Scalar>(1));
diff --git a/test/product.cpp b/test/product.cpp
index 9bba45c48..2ee39acab 100644
--- a/test/product.cpp
+++ b/test/product.cpp
@@ -53,10 +53,10 @@ template<typename MatrixType> void product(const MatrixType& m)
              v2 = VectorType::random(rows),
              vzero = VectorType::zero(rows);
 
-  Scalar s1 = random<Scalar>();
+  Scalar s1 = ei_random<Scalar>();
   
-  int r = random<int>(0, rows-1),
-      c = random<int>(0, cols-1);
+  int r = ei_random<int>(0, rows-1),
+      c = ei_random<int>(0, cols-1);
   
   // begin testing Product.h: only associativity for now
   // (we use Transpose.h but this doesn't count as a test for it)
diff --git a/test/smallvectors.cpp b/test/smallvectors.cpp
index 3496733e2..458b79ce7 100644
--- a/test/smallvectors.cpp
+++ b/test/smallvectors.cpp
@@ -32,10 +32,10 @@ template<typename Scalar> void smallVectors()
   typedef Matrix<Scalar, 1, 2> V2;
   typedef Matrix<Scalar, 3, 1> V3;
   typedef Matrix<Scalar, 1, 4> V4;
-  Scalar x1 = random<Scalar>(),
-         x2 = random<Scalar>(),
-         x3 = random<Scalar>(),
-         x4 = random<Scalar>();
+  Scalar x1 = ei_random<Scalar>(),
+         x2 = ei_random<Scalar>(),
+         x3 = ei_random<Scalar>(),
+         x4 = ei_random<Scalar>();
   V2 v2(x1, x2);
   V3 v3(x1, x2, x3);
   V4 v4(x1, x2, x3, x4);
diff --git a/test/submatrices.cpp b/test/submatrices.cpp
index aa189476e..633bcb302 100644
--- a/test/submatrices.cpp
+++ b/test/submatrices.cpp
@@ -52,12 +52,12 @@ template<typename MatrixType> void submatrices(const MatrixType& m)
              v3 = VectorType::random(rows),
              vzero = VectorType::zero(rows);
 
-  Scalar s1 = random<Scalar>();
+  Scalar s1 = ei_random<Scalar>();
   
-  int r1 = random<int>(0,rows-1);
-  int r2 = random<int>(r1,rows-1);
-  int c1 = random<int>(0,cols-1);
-  int c2 = random<int>(c1,cols-1);
+  int r1 = ei_random<int>(0,rows-1);
+  int r2 = ei_random<int>(r1,rows-1);
+  int c1 = ei_random<int>(0,cols-1);
+  int c2 = ei_random<int>(c1,cols-1);
   
   //check row() and col()
   VERIFY_IS_APPROX(m1.col(c1).transpose(), m1.transpose().row(c1));
@@ -108,7 +108,7 @@ void EigenTest::testSubmatrices()
     // being called as a member of a class that is itself a template parameter
     // (at least as of g++ 4.2)
     Matrix<float, 6, 8> m = Matrix<float, 6, 8>::random();
-    float s = random<float>();
+    float s = ei_random<float>();
     // test fixedBlock() as lvalue
     m.fixedBlock<2,5>(1,1) *= s;
     // test operator() on fixedBlock() both as constant and non-constant