From e2aa58b6316ba869be039e49dce73f99647f4139 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Tue, 12 Jul 2016 17:21:03 +0200
Subject: [PATCH] Consider denormals as zero in makeJacobi and 2x2 SVD. This
 also fix serious issues with x387 for which values can be much smaller than
 the smallest denormal!

---
 Eigen/src/Jacobi/Jacobi.h   | 5 +++--
 Eigen/src/misc/RealSvd2x2.h | 3 ++-
 2 files changed, 5 insertions(+), 3 deletions(-)

diff --git a/Eigen/src/Jacobi/Jacobi.h b/Eigen/src/Jacobi/Jacobi.h
index 55de15e87..d25af8e90 100644
--- a/Eigen/src/Jacobi/Jacobi.h
+++ b/Eigen/src/Jacobi/Jacobi.h
@@ -85,7 +85,8 @@ bool JacobiRotation<Scalar>::makeJacobi(const RealScalar& x, const Scalar& y, co
   using std::sqrt;
   using std::abs;
   typedef typename NumTraits<Scalar>::Real RealScalar;
-  if(y == Scalar(0))
+  RealScalar deno = RealScalar(2)*abs(y);
+  if(deno < (std::numeric_limits<RealScalar>::min)())
   {
     m_c = Scalar(1);
     m_s = Scalar(0);
@@ -93,7 +94,7 @@ bool JacobiRotation<Scalar>::makeJacobi(const RealScalar& x, const Scalar& y, co
   }
   else
   {
-    RealScalar tau = (x-z)/(RealScalar(2)*abs(y));
+    RealScalar tau = (x-z)/deno;
     RealScalar w = sqrt(numext::abs2(tau) + RealScalar(1));
     RealScalar t;
     if(tau>RealScalar(0))
diff --git a/Eigen/src/misc/RealSvd2x2.h b/Eigen/src/misc/RealSvd2x2.h
index dfaaa0b17..abb4d3c2f 100644
--- a/Eigen/src/misc/RealSvd2x2.h
+++ b/Eigen/src/misc/RealSvd2x2.h
@@ -28,7 +28,8 @@ 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))
+
+  if(abs(d) < (std::numeric_limits<RealScalar>::min)())
   {
     rot1.s() = RealScalar(0);
     rot1.c() = RealScalar(1);