diff --git a/Eigen/src/Core/arch/CUDA/Half.h b/Eigen/src/Core/arch/CUDA/Half.h
index 482b654ac..9ecc4fd88 100644
--- a/Eigen/src/Core/arch/CUDA/Half.h
+++ b/Eigen/src/Core/arch/CUDA/Half.h
@@ -510,6 +510,11 @@ static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC int (isfinite)(const Eigen::half& a
 
 namespace std {
 
+EIGEN_ALWAYS_INLINE ostream& operator << (ostream& os, const Eigen::half& v) {
+  os << static_cast<float>(v);
+  return os;
+}
+
 #if __cplusplus > 199711L
 template <>
 struct hash<Eigen::half> {
diff --git a/Eigen/src/SVD/JacobiSVD.h b/Eigen/src/SVD/JacobiSVD.h
index f08776bc6..1940c8294 100644
--- a/Eigen/src/SVD/JacobiSVD.h
+++ b/Eigen/src/SVD/JacobiSVD.h
@@ -350,7 +350,8 @@ template<typename MatrixType, int QRPreconditioner>
 struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, false>
 {
   typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;
-  static bool run(typename SVD::WorkMatrixType&, SVD&, Index, Index, const typename MatrixType::RealScalar&) { return true; }
+  typedef typename MatrixType::RealScalar RealScalar;
+  static bool run(typename SVD::WorkMatrixType&, SVD&, Index, Index, RealScalar&) { return true; }
 };
 
 template<typename MatrixType, int QRPreconditioner>
@@ -359,25 +360,30 @@ struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
   typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;
   typedef typename MatrixType::Scalar Scalar;
   typedef typename MatrixType::RealScalar RealScalar;
-  static bool run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q, const typename MatrixType::RealScalar& precision)
+  static bool run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q, RealScalar& maxDiagEntry)
   {
     using std::sqrt;
+    using std::abs;
     Scalar z;
     JacobiRotation<Scalar> rot;
     RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p)));
-    
+
+    const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)();
+    const RealScalar precision = NumTraits<Scalar>::epsilon();
+
     if(n==0)
     {
       // make sure first column is zero
       work_matrix.coeffRef(p,p) = work_matrix.coeffRef(q,p) = Scalar(0);
-      if(work_matrix.coeff(p,q)!=Scalar(0))
+
+      if(abs(numext::imag(work_matrix.coeff(p,q)))>considerAsZero)
       {
         // work_matrix.coeff(p,q) can be zero if work_matrix.coeff(q,p) is not zero but small enough to underflow when computing n
         z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
         work_matrix.row(p) *= z;
         if(svd.computeU()) svd.m_matrixU.col(p) *= conj(z);
       }
-      if(work_matrix.coeff(q,q)!=Scalar(0))
+      if(abs(numext::imag(work_matrix.coeff(q,q)))>considerAsZero)
       {
         z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
         work_matrix.row(q) *= z;
@@ -391,13 +397,13 @@ struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
       rot.s() = work_matrix.coeff(q,p) / n;
       work_matrix.applyOnTheLeft(p,q,rot);
       if(svd.computeU()) svd.m_matrixU.applyOnTheRight(p,q,rot.adjoint());
-      if(work_matrix.coeff(p,q) != Scalar(0))
+      if(abs(numext::imag(work_matrix.coeff(p,q)))>considerAsZero)
       {
         z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
         work_matrix.col(q) *= z;
         if(svd.computeV()) svd.m_matrixV.col(q) *= z;
       }
-      if(work_matrix.coeff(q,q) != Scalar(0))
+      if(abs(numext::imag(work_matrix.coeff(q,q)))>considerAsZero)
       {
         z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
         work_matrix.row(q) *= z;
@@ -405,11 +411,11 @@ struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
       }
     }
 
-    const RealScalar considerAsZero = RealScalar(2) * std::numeric_limits<RealScalar>::denorm_min();
-    RealScalar threshold = numext::maxi<RealScalar>(considerAsZero,
-                           precision * numext::maxi<RealScalar>(abs(work_matrix.coeff(p,p)), abs(work_matrix.coeff(q,q))));
-    // return true if we still have some work to do
-    return numext::abs(work_matrix(p,q)) > threshold || numext::abs(work_matrix(q,p)) > threshold;
+    // update largest diagonal entry
+    maxDiagEntry = numext::maxi(maxDiagEntry,numext::maxi(abs(work_matrix.coeff(p,p)), abs(work_matrix.coeff(q,q))));
+    // and check whether the 2x2 block is already diagonal
+    RealScalar threshold = numext::maxi<RealScalar>(considerAsZero, precision * maxDiagEntry);
+    return abs(work_matrix.coeff(p,q))>threshold || abs(work_matrix.coeff(q,p)) > threshold;
   }
 };
 
@@ -426,7 +432,6 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
   JacobiRotation<RealScalar> rot1;
   RealScalar t = m.coeff(0,0) + m.coeff(1,1);
   RealScalar d = m.coeff(1,0) - m.coeff(0,1);
-  
   if(d == RealScalar(0))
   {
     rot1.s() = RealScalar(0);
@@ -719,6 +724,7 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig
   }
 
   /*** step 2. The main Jacobi SVD iteration. ***/
+  RealScalar maxDiagEntry = m_workMatrix.cwiseAbs().diagonal().maxCoeff();
 
   bool finished = false;
   while(!finished)
@@ -734,16 +740,13 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig
         // if this 2x2 sub-matrix is not diagonal already...
         // notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN's don't
         // keep us iterating forever. Similarly, small denormal numbers are considered zero.
-        RealScalar threshold = numext::maxi<RealScalar>(considerAsZero,
-                   precision * numext::maxi<RealScalar>(abs(m_workMatrix.coeff(p,p)),
-                                                        abs(m_workMatrix.coeff(q,q))));
-        // We compare both values to threshold instead of calling max to be robust to NaN (See bug 791)
+        RealScalar threshold = numext::maxi<RealScalar>(considerAsZero, precision * maxDiagEntry);
         if(abs(m_workMatrix.coeff(p,q))>threshold || abs(m_workMatrix.coeff(q,p)) > threshold)
         {
           finished = false;
           // perform SVD decomposition of 2x2 sub-matrix corresponding to indices p,q to make it diagonal
           // the complex to real operation returns true is the updated 2x2 block is not already diagonal
-          if(internal::svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner>::run(m_workMatrix, *this, p, q, precision))
+          if(internal::svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner>::run(m_workMatrix, *this, p, q, maxDiagEntry))
           {
             JacobiRotation<RealScalar> j_left, j_right;
             internal::real_2x2_jacobi_svd(m_workMatrix, p, q, &j_left, &j_right);
@@ -754,6 +757,9 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig
 
             m_workMatrix.applyOnTheRight(p,q,j_right);
             if(computeV()) m_matrixV.applyOnTheRight(p,q,j_right);
+
+            // keep track of the largest diagonal coefficient
+            maxDiagEntry = numext::maxi(maxDiagEntry,numext::maxi(abs(m_workMatrix.coeff(p,p)), abs(m_workMatrix.coeff(q,q))));
           }
         }
       }
diff --git a/test/main.h b/test/main.h
index bba5e7570..dbb496b89 100644
--- a/test/main.h
+++ b/test/main.h
@@ -316,9 +316,9 @@ inline bool test_isMuchSmallerThan(const float& a, const float& b)
 { return internal::isMuchSmallerThan(a, b, test_precision<float>()); }
 inline bool test_isApproxOrLessThan(const float& a, const float& b)
 { return internal::isApproxOrLessThan(a, b, test_precision<float>()); }
+
 inline bool test_isApprox(const double& a, const double& b)
 { return internal::isApprox(a, b, test_precision<double>()); }
-
 inline bool test_isMuchSmallerThan(const double& a, const double& b)
 { return internal::isMuchSmallerThan(a, b, test_precision<double>()); }
 inline bool test_isApproxOrLessThan(const double& a, const double& b)
@@ -359,6 +359,12 @@ inline bool test_isApproxOrLessThan(const long double& a, const long double& b)
 { return internal::isApproxOrLessThan(a, b, test_precision<long double>()); }
 #endif // EIGEN_TEST_NO_LONGDOUBLE
 
+inline bool test_isApprox(const half& a, const half& b)
+{ return internal::isApprox(a, b, test_precision<half>()); }
+inline bool test_isMuchSmallerThan(const half& a, const half& b)
+{ return internal::isMuchSmallerThan(a, b, test_precision<half>()); }
+inline bool test_isApproxOrLessThan(const half& a, const half& b)
+{ return internal::isApproxOrLessThan(a, b, test_precision<half>()); }
 
 // test_relative_error returns the relative difference between a and b as a real scalar as used in isApprox.
 template<typename T1,typename T2>
@@ -426,9 +432,7 @@ template<typename T1,typename T2>
 typename NumTraits<T1>::Real test_relative_error(const T1 &a, const T2 &b, typename internal::enable_if<internal::is_arithmetic<typename NumTraits<T1>::Real>::value, T1>::type* = 0)
 {
   typedef typename NumTraits<T1>::Real RealScalar; 
-  using std::min;
-  using std::sqrt;
-  return sqrt(RealScalar(numext::abs2(a-b))/RealScalar((min)(numext::abs2(a),numext::abs2(b))));
+  return numext::sqrt(RealScalar(numext::abs2(a-b))/RealScalar((numext::mini)(numext::abs2(a),numext::abs2(b))));
 }
 
 template<typename T>
diff --git a/test/svd_fill.h b/test/svd_fill.h
index 7e44b3d05..1bbe645ee 100644
--- a/test/svd_fill.h
+++ b/test/svd_fill.h
@@ -80,6 +80,8 @@ void svd_fill_random(MatrixType &m, int Option = 0)
           Index i = internal::random<Index>(0,m.rows()-1);
           Index j = internal::random<Index>(0,m.cols()-1);
           m(j,i) = m(i,j) = samples(internal::random<Index>(0,samples.size()-1));
+          if(NumTraits<Scalar>::IsComplex)
+            *(&numext::real_ref(m(j,i))+1) = *(&numext::real_ref(m(i,j))+1) = samples.real()(internal::random<Index>(0,samples.size()-1));
         }
       }
     }
@@ -91,8 +93,14 @@ void svd_fill_random(MatrixType &m, int Option = 0)
     if(!(dup && unit_uv))
     {
       Index n = internal::random<Index>(0,m.size()-1);
-      for(Index i=0; i<n; ++i)
-        m(internal::random<Index>(0,m.rows()-1), internal::random<Index>(0,m.cols()-1)) = samples(internal::random<Index>(0,samples.size()-1));
+      for(Index k=0; k<n; ++k)
+      {
+        Index i = internal::random<Index>(0,m.rows()-1);
+        Index j = internal::random<Index>(0,m.cols()-1);
+        m(i,j) = samples(internal::random<Index>(0,samples.size()-1));
+        if(NumTraits<Scalar>::IsComplex)
+          *(&numext::real_ref(m(i,j))+1) = samples.real()(internal::random<Index>(0,samples.size()-1));
+      }
     }
   }
 }
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h b/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h
index ccaa757d1..44dc2d730 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h
@@ -64,7 +64,7 @@ struct scalar_sigmoid_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_sigmoid_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T operator()(const T& x) const {
     const T one = T(1);
-    return one / (one + std::exp(-x));
+    return one / (one + numext::exp(-x));
   }
 
   template <typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
@@ -803,7 +803,7 @@ class GaussianGenerator {
       T offset = coordinates[i] - m_means[i];
       tmp += offset * offset / m_two_sigmas[i];
     }
-    return std::exp(-tmp);
+    return numext::exp(-tmp);
   }
 
  private:
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorUInt128.h b/unsupported/Eigen/CXX11/src/Tensor/TensorUInt128.h
index 3e56589c3..5950f38e2 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorUInt128.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorUInt128.h
@@ -53,9 +53,7 @@ struct TensorUInt128
   template<typename T>
   EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
   explicit TensorUInt128(const T& x) : high(0), low(x) {
-    typedef typename conditional<sizeof(T) == 8, uint64_t, uint32_t>::type UnsignedT;
-    typedef typename conditional<sizeof(LOW) == 8, uint64_t, uint32_t>::type UnsignedLow;
-    eigen_assert(static_cast<UnsignedT>(x) <= static_cast<UnsignedLow>(NumTraits<LOW>::highest()));
+    eigen_assert((static_cast<typename conditional<sizeof(T) == 8, uint64_t, uint32_t>::type>(x) <= static_cast<typename conditional<sizeof(LOW) == 8, uint64_t, uint32_t>::type>(NumTraits<LOW>::highest())));
     eigen_assert(x >= 0);
   }
 
diff --git a/unsupported/test/cxx11_float16.cpp b/unsupported/test/cxx11_float16.cpp
index 2dc0872d8..273dcbc11 100644
--- a/unsupported/test/cxx11_float16.cpp
+++ b/unsupported/test/cxx11_float16.cpp
@@ -122,6 +122,8 @@ void test_comparison()
   VERIFY(half(1.0f) != half(2.0f));
 
   // Comparisons with NaNs and infinities.
+#if !EIGEN_COMP_MSVC
+  // Visual Studio errors out on divisions by 0
   VERIFY(!(half(0.0 / 0.0) == half(0.0 / 0.0)));
   VERIFY(half(0.0 / 0.0) != half(0.0 / 0.0));
 
@@ -132,13 +134,26 @@ void test_comparison()
 
   VERIFY(half(1.0) < half(1.0 / 0.0));
   VERIFY(half(1.0) > half(-1.0 / 0.0));
+#endif
 }
 
-void test_functions()
+void test_basic_functions()
 {
   VERIFY_IS_EQUAL(float(numext::abs(half(3.5f))), 3.5f);
   VERIFY_IS_EQUAL(float(numext::abs(half(-3.5f))), 3.5f);
 
+  VERIFY_IS_EQUAL(float(numext::floor(half(3.5f))), 3.0f);
+  VERIFY_IS_EQUAL(float(numext::floor(half(-3.5f))), -4.0f);
+
+  VERIFY_IS_EQUAL(float(numext::ceil(half(3.5f))), 4.0f);
+  VERIFY_IS_EQUAL(float(numext::ceil(half(-3.5f))), -3.0f);
+
+  VERIFY_IS_APPROX(float(numext::sqrt(half(0.0f))), 0.0f);
+  VERIFY_IS_APPROX(float(numext::sqrt(half(4.0f))), 2.0f);
+
+  VERIFY_IS_APPROX(float(numext::pow(half(0.0f), half(1.0f))), 0.0f);
+  VERIFY_IS_APPROX(float(numext::pow(half(2.0f), half(2.0f))), 4.0f);
+
   VERIFY_IS_EQUAL(float(numext::exp(half(0.0f))), 1.0f);
   VERIFY_IS_APPROX(float(numext::exp(half(EIGEN_PI))), float(20.0 + EIGEN_PI));
 
@@ -146,10 +161,32 @@ void test_functions()
   VERIFY_IS_APPROX(float(numext::log(half(10.0f))), 2.30273f);
 }
 
+void test_trigonometric_functions()
+{
+  VERIFY_IS_APPROX(numext::cos(half(0.0f)), half(cosf(0.0f)));
+  VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI)), half(cosf(EIGEN_PI)));
+  //VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI/2)), half(cosf(EIGEN_PI/2)));
+  //VERIFY_IS_APPROX(numext::cos(half(3*EIGEN_PI/2)), half(cosf(3*EIGEN_PI/2)));
+  VERIFY_IS_APPROX(numext::cos(half(3.5f)), half(cosf(3.5f)));
+
+  VERIFY_IS_APPROX(numext::sin(half(0.0f)), half(sinf(0.0f)));
+  //  VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI)), half(sinf(EIGEN_PI)));
+  VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI/2)), half(sinf(EIGEN_PI/2)));
+  VERIFY_IS_APPROX(numext::sin(half(3*EIGEN_PI/2)), half(sinf(3*EIGEN_PI/2)));
+  VERIFY_IS_APPROX(numext::sin(half(3.5f)), half(sinf(3.5f)));
+
+  VERIFY_IS_APPROX(numext::tan(half(0.0f)), half(tanf(0.0f)));
+  //  VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI)), half(tanf(EIGEN_PI)));
+  //  VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI/2)), half(tanf(EIGEN_PI/2)));
+  //VERIFY_IS_APPROX(numext::tan(half(3*EIGEN_PI/2)), half(tanf(3*EIGEN_PI/2)));
+  VERIFY_IS_APPROX(numext::tan(half(3.5f)), half(tanf(3.5f)));
+}
+
 void test_cxx11_float16()
 {
   CALL_SUBTEST(test_conversion());
   CALL_SUBTEST(test_arithmetic());
   CALL_SUBTEST(test_comparison());
-  CALL_SUBTEST(test_functions());
+  CALL_SUBTEST(test_basic_functions());
+  CALL_SUBTEST(test_trigonometric_functions());
 }