diff --git a/include/boost/multiprecision/cpp_bin_float.hpp b/include/boost/multiprecision/cpp_bin_float.hpp
index e393d131..f988fb47 100644
--- a/include/boost/multiprecision/cpp_bin_float.hpp
+++ b/include/boost/multiprecision/cpp_bin_float.hpp
@@ -581,8 +581,8 @@ inline void do_eval_subtract(cpp_bin_float<Digits, DigitBase, Allocator, Exponen
       res = a;
       return;
    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
-      res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan;
-      res.sign() = false;
+      res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity;
+      res.sign() = true;
       res.bits() = static_cast<limb_type>(0u);
       return; // result is a NaN.
    case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
diff --git a/include/boost/multiprecision/cpp_dec_float.hpp b/include/boost/multiprecision/cpp_dec_float.hpp
index 4c469190..26fe9815 100644
--- a/include/boost/multiprecision/cpp_dec_float.hpp
+++ b/include/boost/multiprecision/cpp_dec_float.hpp
@@ -662,6 +662,12 @@ cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, Expone
       return operator=(v);
    }
 
+   if((v.isnan)() || (v.isinf)())
+   {
+      *this = v;
+      return *this;
+   }
+
    // Get the offset for the add/sub operation.
    static const ExponentType max_delta_exp = static_cast<ExponentType>((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10);
 
diff --git a/test/test_arithmetic.hpp b/test/test_arithmetic.hpp
index 52e0a592..340afaad 100644
--- a/test/test_arithmetic.hpp
+++ b/test/test_arithmetic.hpp
@@ -993,6 +993,74 @@ void test_float_ops(const boost::mpl::int_<boost::multiprecision::number_kind_fl
       }
    }
 
+   //
+   // Operations involving NaN's as one argument:
+   //
+   if(std::numeric_limits<Real>::has_quiet_NaN)
+   {
+      v = 20.25;
+      r = std::numeric_limits<Real>::quiet_NaN();
+      BOOST_CHECK((boost::math::isnan)(v + r));
+      BOOST_CHECK((boost::math::isnan)(r + v));
+      BOOST_CHECK((boost::math::isnan)(r - v));
+      BOOST_CHECK((boost::math::isnan)(v - r));
+      BOOST_CHECK((boost::math::isnan)(r * v));
+      BOOST_CHECK((boost::math::isnan)(v * r));
+      BOOST_CHECK((boost::math::isnan)(r / v));
+      BOOST_CHECK((boost::math::isnan)(v / r));
+      Real t = v;
+      BOOST_CHECK((boost::math::isnan)(t += r));
+      t = r;
+      BOOST_CHECK((boost::math::isnan)(t += v));
+      t = r;
+      BOOST_CHECK((boost::math::isnan)(t -= v));
+      t = v;
+      BOOST_CHECK((boost::math::isnan)(t -= r));
+      t = r;
+      BOOST_CHECK((boost::math::isnan)(t *= v));
+      t = v;
+      BOOST_CHECK((boost::math::isnan)(t *= r));
+      t = r;
+      BOOST_CHECK((boost::math::isnan)(t /= v));
+      t = v;
+      BOOST_CHECK((boost::math::isnan)(t /= r));
+   }
+   //
+   // Operations involving infinities as one argument:
+   //
+   if(std::numeric_limits<Real>::has_infinity)
+   {
+      v = 20.25;
+      r = std::numeric_limits<Real>::infinity();
+      BOOST_CHECK((boost::math::isinf)(v + r));
+      BOOST_CHECK((boost::math::isinf)(r + v));
+      BOOST_CHECK((boost::math::isinf)(r - v));
+      BOOST_CHECK((boost::math::isinf)(v - r));
+      BOOST_CHECK_LT(v - r, 0);
+      BOOST_CHECK((boost::math::isinf)(r * v));
+      BOOST_CHECK((boost::math::isinf)(v * r));
+      BOOST_CHECK((boost::math::isinf)(r / v));
+      BOOST_CHECK_EQUAL(v / r, 0);
+      Real t = v;
+      BOOST_CHECK((boost::math::isinf)(t += r));
+      t = r;
+      BOOST_CHECK((boost::math::isinf)(t += v));
+      t = r;
+      BOOST_CHECK((boost::math::isinf)(t -= v));
+      t = v;
+      BOOST_CHECK((boost::math::isinf)(t -= r));
+      t = v;
+      BOOST_CHECK(t -= r < 0);
+      t = r;
+      BOOST_CHECK((boost::math::isinf)(t *= v));
+      t = v;
+      BOOST_CHECK((boost::math::isinf)(t *= r));
+      t = r;
+      BOOST_CHECK((boost::math::isinf)(t /= v));
+      t = v;
+      BOOST_CHECK((t /= r) == 0);
+   }
+
    test_float_funcs<Real>(boost::mpl::bool_<std::numeric_limits<Real>::is_specialized>());
 }