From db408fde2bdc2157c90cf00380ccb7dc4e1b88a6 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Fri, 30 Nov 2018 19:54:34 +0000
Subject: [PATCH] roots.hpp: clean up code so that there is no division by zero
 possible. Fixes: https://github.com/boostorg/math/issues/160.

---
 include/boost/math/tools/roots.hpp | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/include/boost/math/tools/roots.hpp b/include/boost/math/tools/roots.hpp
index 81e846613..804f0101c 100644
--- a/include/boost/math/tools/roots.hpp
+++ b/include/boost/math/tools/roots.hpp
@@ -514,9 +514,10 @@ namespace detail{
       template <class T>
       static T step(const T& x, const T& f0, const T& f1, const T& f2) BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T))
       {
+         using std::fabs;
          T ratio = f0 / f1;
          T delta;
-         if(ratio / x < 0.1)
+         if((x != 0) && (fabs(ratio / x) < 0.1))
          {
             delta = ratio + (f2 / (2 * f1)) * ratio * ratio;
             // check second derivative doesn't over compensate: