diff --git a/Eigen/src/QR/ColPivHouseholderQR.h b/Eigen/src/QR/ColPivHouseholderQR.h
index ae7c1775f..5270eaca2 100644
--- a/Eigen/src/QR/ColPivHouseholderQR.h
+++ b/Eigen/src/QR/ColPivHouseholderQR.h
@@ -552,10 +552,10 @@ void ColPivHouseholderQR<MatrixType>::computeInPlace()
       // http://www.netlib.org/lapack/lawnspdf/lawn176.pdf
       // and used in LAPACK routines xGEQPF and xGEQP3.
       // See lines 278-297 in http://www.netlib.org/lapack/explore-html/dc/df4/sgeqpf_8f_source.html
-      if (m_colNormsUpdated.coeffRef(j) != 0) {
+      if (m_colNormsUpdated.coeffRef(j) != RealScalar(0)) {
         RealScalar temp = abs(m_qr.coeffRef(k, j)) / m_colNormsUpdated.coeffRef(j);
         temp = (RealScalar(1) + temp) * (RealScalar(1) - temp);
-        temp = temp < 0 ? RealScalar(0) : temp;
+        temp = temp <  RealScalar(0) ? RealScalar(0) : temp;
         RealScalar temp2 = temp * numext::abs2<RealScalar>(m_colNormsUpdated.coeffRef(j) /
                                                            m_colNormsDirect.coeffRef(j));
         if (temp2 <= norm_downdate_threshold) {
diff --git a/Eigen/src/SVD/BDCSVD.h b/Eigen/src/SVD/BDCSVD.h
index 25fca6f4d..d7a4271cb 100644
--- a/Eigen/src/SVD/BDCSVD.h
+++ b/Eigen/src/SVD/BDCSVD.h
@@ -77,6 +77,7 @@ public:
   typedef _MatrixType MatrixType;
   typedef typename MatrixType::Scalar Scalar;
   typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+  typedef typename NumTraits<RealScalar>::Literal Literal;
   enum {
     RowsAtCompileTime = MatrixType::RowsAtCompileTime, 
     ColsAtCompileTime = MatrixType::ColsAtCompileTime, 
@@ -259,7 +260,7 @@ BDCSVD<MatrixType>& BDCSVD<MatrixType>::compute(const MatrixType& matrix, unsign
   
   //**** step 0 - Copy the input matrix and apply scaling to reduce over/under-flows
   RealScalar scale = matrix.cwiseAbs().maxCoeff();
-  if(scale==RealScalar(0)) scale = RealScalar(1);
+  if(scale==Literal(0)) scale = Literal(1);
   MatrixX copy;
   if (m_isTranspose) copy = matrix.adjoint()/scale;
   else               copy = matrix/scale;
@@ -351,13 +352,13 @@ void BDCSVD<MatrixType>::structured_update(Block<MatrixXr,Dynamic,Dynamic> A, co
     Index k1=0, k2=0;
     for(Index j=0; j<n; ++j)
     {
-      if( (A.col(j).head(n1).array()!=0).any() )
+      if( (A.col(j).head(n1).array()!=Literal(0)).any() )
       {
         A1.col(k1) = A.col(j).head(n1);
         B1.row(k1) = B.row(j);
         ++k1;
       }
-      if( (A.col(j).tail(n2).array()!=0).any() )
+      if( (A.col(j).tail(n2).array()!=Literal(0)).any() )
       {
         A2.col(k2) = A.col(j).tail(n2);
         B2.row(k2) = B.row(j);
@@ -449,11 +450,11 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
     l = m_naiveU.row(1).segment(firstCol, k);
     f = m_naiveU.row(0).segment(firstCol + k + 1, n - k - 1);
   }
-  if (m_compV) m_naiveV(firstRowW+k, firstColW) = 1;
+  if (m_compV) m_naiveV(firstRowW+k, firstColW) = Literal(1);
   if (r0<considerZero)
   {
-    c0 = 1;
-    s0 = 0;
+    c0 = Literal(1);
+    s0 = Literal(0);
   }
   else
   {
@@ -574,7 +575,7 @@ void BDCSVD<MatrixType>::computeSVDofM(Index firstCol, Index n, MatrixXr& U, Vec
   ArrayRef col0 = m_computed.col(firstCol).segment(firstCol, n);
   m_workspace.head(n) =  m_computed.block(firstCol, firstCol, n, n).diagonal();
   ArrayRef diag = m_workspace.head(n);
-  diag(0) = 0;
+  diag(0) = Literal(0);
 
   // Allocate space for singular values and vectors
   singVals.resize(n);
@@ -590,7 +591,7 @@ void BDCSVD<MatrixType>::computeSVDofM(Index firstCol, Index n, MatrixXr& U, Vec
   // but others are interleaved and we must ignore them at this stage.
   // To this end, let's compute a permutation skipping them:
   Index actual_n = n;
-  while(actual_n>1 && diag(actual_n-1)==0) --actual_n;
+  while(actual_n>1 && diag(actual_n-1)==Literal(0)) --actual_n;
   Index m = 0; // size of the deflated problem
   for(Index k=0;k<actual_n;++k)
     if(abs(col0(k))>considerZero)
@@ -691,7 +692,7 @@ template <typename MatrixType>
 typename BDCSVD<MatrixType>::RealScalar BDCSVD<MatrixType>::secularEq(RealScalar mu, const ArrayRef& col0, const ArrayRef& diag, const IndicesRef &perm, const ArrayRef& diagShifted, RealScalar shift)
 {
   Index m = perm.size();
-  RealScalar res = 1;
+  RealScalar res = Literal(1);
   for(Index i=0; i<m; ++i)
   {
     Index j = perm(i);
@@ -710,16 +711,16 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayRef& col0, const ArrayRef& d
 
   Index n = col0.size();
   Index actual_n = n;
-  while(actual_n>1 && col0(actual_n-1)==0) --actual_n;
+  while(actual_n>1 && col0(actual_n-1)==Literal(0)) --actual_n;
 
   for (Index k = 0; k < n; ++k)
   {
-    if (col0(k) == 0 || actual_n==1)
+    if (col0(k) == Literal(0) || actual_n==1)
     {
       // if col0(k) == 0, then entry is deflated, so singular value is on diagonal
       // if actual_n==1, then the deflated problem is already diagonalized
       singVals(k) = k==0 ? col0(0) : diag(k);
-      mus(k) = 0;
+      mus(k) = Literal(0);
       shifts(k) = k==0 ? col0(0) : diag(k);
       continue;
     } 
@@ -733,13 +734,13 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayRef& col0, const ArrayRef& d
     {
       // Skip deflated singular values
       Index l = k+1;
-      while(col0(l)==0) { ++l; eigen_internal_assert(l<actual_n); }
+      while(col0(l)==Literal(0)) { ++l; eigen_internal_assert(l<actual_n); }
       right = diag(l);
     }
 
     // first decide whether it's closer to the left end or the right end
-    RealScalar mid = left + (right-left) / 2;
-    RealScalar fMid = secularEq(mid, col0, diag, perm, diag, 0);
+    RealScalar mid = left + (right-left) / Literal(2);
+    RealScalar fMid = secularEq(mid, col0, diag, perm, diag, Literal(0));
 #ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
     std::cout << right-left << "\n";
     std::cout << "fMid = " << fMid << " " << secularEq(mid-left, col0, diag, perm, diag-left, left) << " " << secularEq(mid-right, col0, diag, perm, diag-right, right)   << "\n";
@@ -755,7 +756,7 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayRef& col0, const ArrayRef& d
               << " "       << secularEq(0.8*(left+right), col0, diag, perm, diag, 0)
               << " "       << secularEq(0.9*(left+right), col0, diag, perm, diag, 0) << "\n";
 #endif
-    RealScalar shift = (k == actual_n-1 || fMid > 0) ? left : right;
+    RealScalar shift = (k == actual_n-1 || fMid > Literal(0)) ? left : right;
     
     // measure everything relative to shift
     Map<ArrayXr> diagShifted(m_workspace.data()+4*n, n);
@@ -785,13 +786,13 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayRef& col0, const ArrayRef& d
 
     // rational interpolation: fit a function of the form a / mu + b through the two previous
     // iterates and use its zero to compute the next iterate
-    bool useBisection = fPrev*fCur>0;
-    while (fCur!=0 && abs(muCur - muPrev) > 8 * NumTraits<RealScalar>::epsilon() * numext::maxi<RealScalar>(abs(muCur), abs(muPrev)) && abs(fCur - fPrev)>NumTraits<RealScalar>::epsilon() && !useBisection)
+    bool useBisection = fPrev*fCur>Literal(0);
+    while (fCur!=Literal(0) && abs(muCur - muPrev) > Literal(8) * NumTraits<RealScalar>::epsilon() * numext::maxi<RealScalar>(abs(muCur), abs(muPrev)) && abs(fCur - fPrev)>NumTraits<RealScalar>::epsilon() && !useBisection)
     {
       ++m_numIters;
 
       // Find a and b such that the function f(mu) = a / mu + b matches the current and previous samples.
-      RealScalar a = (fCur - fPrev) / (1/muCur - 1/muPrev);
+      RealScalar a = (fCur - fPrev) / (Literal(1)/muCur - Literal(1)/muPrev);
       RealScalar b = fCur - a / muCur;
       // And find mu such that f(mu)==0:
       RealScalar muZero = -a/b;
@@ -803,8 +804,8 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayRef& col0, const ArrayRef& d
       fCur = fZero;
       
       
-      if (shift == left  && (muCur < 0 || muCur > right - left)) useBisection = true;
-      if (shift == right && (muCur < -(right - left) || muCur > 0)) useBisection = true;
+      if (shift == left  && (muCur < Literal(0) || muCur > right - left)) useBisection = true;
+      if (shift == right && (muCur < -(right - left) || muCur > Literal(0))) useBisection = true;
       if (abs(fCur)>abs(fPrev)) useBisection = true;
     }
 
@@ -841,13 +842,13 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayRef& col0, const ArrayRef& d
         std::cout << k << " : " <<  fLeft << " * " << fRight << " == " << fLeft * fRight << "  ;  " << left << " - " << right << " -> " <<  leftShifted << " " << rightShifted << "   shift=" << shift << "\n";
       }
 #endif
-      eigen_internal_assert(fLeft * fRight < 0);
+      eigen_internal_assert(fLeft * fRight < Literal(0));
       
-      while (rightShifted - leftShifted > 2 * NumTraits<RealScalar>::epsilon() * numext::maxi<RealScalar>(abs(leftShifted), abs(rightShifted)))
+      while (rightShifted - leftShifted > Literal(2) * NumTraits<RealScalar>::epsilon() * numext::maxi<RealScalar>(abs(leftShifted), abs(rightShifted)))
       {
-        RealScalar midShifted = (leftShifted + rightShifted) / 2;
+        RealScalar midShifted = (leftShifted + rightShifted) / Literal(2);
         fMid = secularEq(midShifted, col0, diag, perm, diagShifted, shift);
-        if (fLeft * fMid < 0)
+        if (fLeft * fMid < Literal(0))
         {
           rightShifted = midShifted;
         }
@@ -858,7 +859,7 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayRef& col0, const ArrayRef& d
         }
       }
 
-      muCur = (leftShifted + rightShifted) / 2;
+      muCur = (leftShifted + rightShifted) / Literal(2);
     }
       
     singVals[k] = shift + muCur;
@@ -892,8 +893,8 @@ void BDCSVD<MatrixType>::perturbCol0
   // The offset permits to skip deflated entries while computing zhat
   for (Index k = 0; k < n; ++k)
   {
-    if (col0(k) == 0) // deflated
-      zhat(k) = 0;
+    if (col0(k) == Literal(0)) // deflated
+      zhat(k) = Literal(0);
     else
     {
       // see equation (3.6)
@@ -918,7 +919,7 @@ void BDCSVD<MatrixType>::perturbCol0
       std::cout << "zhat(" << k << ") =  sqrt( " << prod << ")  ;  " << (singVals(last) + dk) << " * " << mus(last) + shifts(last) << " - " << dk << "\n";
 #endif
       RealScalar tmp = sqrt(prod);
-      zhat(k) = col0(k) > 0 ? tmp : -tmp;
+      zhat(k) = col0(k) > Literal(0) ? tmp : -tmp;
     }
   }
 }
@@ -934,7 +935,7 @@ void BDCSVD<MatrixType>::computeSingVecs
   
   for (Index k = 0; k < n; ++k)
   {
-    if (zhat(k) == 0)
+    if (zhat(k) == Literal(0))
     {
       U.col(k) = VectorType::Unit(n+1, k);
       if (m_compV) V.col(k) = VectorType::Unit(n, k);
@@ -947,7 +948,7 @@ void BDCSVD<MatrixType>::computeSingVecs
         Index i = perm(l);
         U(i,k) = zhat(i)/(((diag(i) - shifts(k)) - mus(k)) )/( (diag(i) + singVals[k]));
       }
-      U(n,k) = 0;      
+      U(n,k) = Literal(0);
       U.col(k).normalize();
     
       if (m_compV)
@@ -958,7 +959,7 @@ void BDCSVD<MatrixType>::computeSingVecs
           Index i = perm(l);
           V(i,k) = diag(i) * zhat(i) / (((diag(i) - shifts(k)) - mus(k)) )/( (diag(i) + singVals[k]));
         }
-        V(0,k) = -1;
+        V(0,k) = Literal(-1);
         V.col(k).normalize();
       }
     }
@@ -980,14 +981,14 @@ void BDCSVD<MatrixType>::deflation43(Index firstCol, Index shift, Index i, Index
   RealScalar c = m_computed(start, start);
   RealScalar s = m_computed(start+i, start);
   RealScalar r = sqrt(numext::abs2(c) + numext::abs2(s));
-  if (r == 0)
+  if (r == Literal(0))
   {
-    m_computed(start+i, start+i) = 0;
+    m_computed(start+i, start+i) = Literal(0);
     return;
   }
   m_computed(start,start) = r;  
-  m_computed(start+i, start) = 0;
-  m_computed(start+i, start+i) = 0;
+  m_computed(start+i, start) = Literal(0);
+  m_computed(start+i, start+i) = Literal(0);
   
   JacobiRotation<RealScalar> J(c/r,-s/r);
   if (m_compU)  m_naiveU.middleRows(firstCol, size+1).applyOnTheRight(firstCol, firstCol+i, J);
@@ -1020,7 +1021,7 @@ void BDCSVD<MatrixType>::deflation44(Index firstColu , Index firstColm, Index fi
     << m_computed(firstColm + i+1, firstColm+i+1) << " "
     << m_computed(firstColm + i+2, firstColm+i+2) << "\n";
 #endif
-  if (r==0)
+  if (r==Literal(0))
   {
     m_computed(firstColm + i, firstColm + i) = m_computed(firstColm + j, firstColm + j);
     return;
@@ -1029,7 +1030,7 @@ void BDCSVD<MatrixType>::deflation44(Index firstColu , Index firstColm, Index fi
   s/=r;
   m_computed(firstColm + i, firstColm) = r;  
   m_computed(firstColm + j, firstColm + j) = m_computed(firstColm + i, firstColm + i);
-  m_computed(firstColm + j, firstColm) = 0;
+  m_computed(firstColm + j, firstColm) = Literal(0);
 
   JacobiRotation<RealScalar> J(c,-s);
   if (m_compU)  m_naiveU.middleRows(firstColu, size+1).applyOnTheRight(firstColu + i, firstColu + j, J);
@@ -1053,7 +1054,7 @@ void BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index
   const RealScalar considerZero = (std::numeric_limits<RealScalar>::min)();
   RealScalar maxDiag = diag.tail((std::max)(Index(1),length-1)).cwiseAbs().maxCoeff();
   RealScalar epsilon_strict = numext::maxi<RealScalar>(considerZero,NumTraits<RealScalar>::epsilon() * maxDiag);
-  RealScalar epsilon_coarse = 8 * NumTraits<RealScalar>::epsilon() * numext::maxi<RealScalar>(col0.cwiseAbs().maxCoeff(), maxDiag);
+  RealScalar epsilon_coarse = Literal(8) * NumTraits<RealScalar>::epsilon() * numext::maxi<RealScalar>(col0.cwiseAbs().maxCoeff(), maxDiag);
   
 #ifdef EIGEN_BDCSVD_SANITY_CHECKS
   assert(m_naiveU.allFinite());
@@ -1081,7 +1082,7 @@ void BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index
 #ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE
       std::cout << "deflation 4.2, set z(" << i << ") to zero because " << abs(col0(i)) << " < " << epsilon_strict << "  (diag(" << i << ")=" << diag(i) << ")\n";
 #endif
-      col0(i) = 0;
+      col0(i) = Literal(0);
     }
 
   //condition 4.3
diff --git a/Eigen/src/SVD/UpperBidiagonalization.h b/Eigen/src/SVD/UpperBidiagonalization.h
index 0b1460894..11ac847e1 100644
--- a/Eigen/src/SVD/UpperBidiagonalization.h
+++ b/Eigen/src/SVD/UpperBidiagonalization.h
@@ -159,6 +159,8 @@ void upperbidiagonalization_blocked_helper(MatrixType& A,
                                                       traits<MatrixType>::Flags & RowMajorBit> > Y)
 {
   typedef typename MatrixType::Scalar Scalar;
+  typedef typename MatrixType::RealScalar RealScalar;
+  typedef typename NumTraits<RealScalar>::Literal Literal;
   enum { StorageOrder = traits<MatrixType>::Flags & RowMajorBit };
   typedef InnerStride<int(StorageOrder) == int(ColMajor) ? 1 : Dynamic> ColInnerStride;
   typedef InnerStride<int(StorageOrder) == int(ColMajor) ? Dynamic : 1> RowInnerStride;
@@ -263,7 +265,7 @@ void upperbidiagonalization_blocked_helper(MatrixType& A,
     SubMatType A10( A.block(bs,0, brows-bs,bs) );
     SubMatType A01( A.block(0,bs, bs,bcols-bs) );
     Scalar tmp = A01(bs-1,0);
-    A01(bs-1,0) = 1;
+    A01(bs-1,0) = Literal(1);
     A11.noalias() -= A10 * Y.topLeftCorner(bcols,bs).bottomRows(bcols-bs).adjoint();
     A11.noalias() -= X.topLeftCorner(brows,bs).bottomRows(brows-bs) * A01;
     A01(bs-1,0) = tmp;