From e2886d34ef54e1c36777ff14d1d43db6ac5cab4d 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] Fix precision regression when attempting to fix underflow
 issues. (transplanted from af824091be78c82212cef4b2fb085a083fbebc5e )

---
 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];