From af824091be78c82212cef4b2fb085a083fbebc5e Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Sun, 5 Aug 2012 09:57:31 +0200
Subject: [PATCH 1/2] Fix precision regression when attempting to fix underflow
 issues.

---
 Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h | 11 ++++++++++-
 1 file changed, 10 insertions(+), 1 deletion(-)

diff --git a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
index acc5576fe..24c78b4b2 100644
--- a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
+++ b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
@@ -743,7 +743,16 @@ static void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index sta
 //   RealScalar e2 = 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] - (e / (td + (td>0 ? 1 : -1))) * (e / hypot(td,e));
+  RealScalar mu = diag[end];
+  if(td==0)
+    mu -= abs(e);
+  else
+  {
+    RealScalar e2 = abs2(subdiag[end-1]);
+    RealScalar h = hypot(td,e);
+    if(e2==0)  mu -= (e / (td + (td>0 ? 1 : -1))) * (e / h);
+    else       mu -= e2 / (td + (td>0 ? h : -h));
+  }
   
   RealScalar x = diag[start] - mu;
   RealScalar z = subdiag[start];

From a1b405c92ec22289f5454328646bc845dc204cf6 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Sun, 5 Aug 2012 10:40:46 +0200
Subject: [PATCH 2/2] Add missing const in some casts

---
 Eigen/src/Core/Transpose.h | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Eigen/src/Core/Transpose.h b/Eigen/src/Core/Transpose.h
index fdb1dc6e2..34944e055 100644
--- a/Eigen/src/Core/Transpose.h
+++ b/Eigen/src/Core/Transpose.h
@@ -353,7 +353,7 @@ struct check_transpose_aliasing_run_time_selector
 {
   static bool run(const Scalar* dest, const OtherDerived& src)
   {
-    return (bool(blas_traits<OtherDerived>::IsTransposed) != DestIsTransposed) && (dest!=0 && dest==(Scalar*)extract_data(src));
+    return (bool(blas_traits<OtherDerived>::IsTransposed) != DestIsTransposed) && (dest!=0 && dest==(const Scalar*)extract_data(src));
   }
 };
 
@@ -362,8 +362,8 @@ struct check_transpose_aliasing_run_time_selector<Scalar,DestIsTransposed,CwiseB
 {
   static bool run(const Scalar* dest, const CwiseBinaryOp<BinOp,DerivedA,DerivedB>& src)
   {
-    return ((blas_traits<DerivedA>::IsTransposed != DestIsTransposed) && (dest!=0 && dest==(Scalar*)extract_data(src.lhs())))
-        || ((blas_traits<DerivedB>::IsTransposed != DestIsTransposed) && (dest!=0 && dest==(Scalar*)extract_data(src.rhs())));
+    return ((blas_traits<DerivedA>::IsTransposed != DestIsTransposed) && (dest!=0 && dest==(const Scalar*)extract_data(src.lhs())))
+        || ((blas_traits<DerivedB>::IsTransposed != DestIsTransposed) && (dest!=0 && dest==(const Scalar*)extract_data(src.rhs())));
   }
 };