diff --git a/libstdc++-v3/include/std/limits b/libstdc++-v3/include/std/limits
index 898406f91ee..c27350c9ec4 100644
--- a/libstdc++-v3/include/std/limits
+++ b/libstdc++-v3/include/std/limits
@@ -1714,8 +1714,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
       static _GLIBCXX_CONSTEXPR float
       denorm_min() _GLIBCXX_USE_NOEXCEPT { return __FLT_DENORM_MIN__; }
 
-      static _GLIBCXX_USE_CONSTEXPR bool is_iec559
-	= has_infinity && has_quiet_NaN && has_denorm == denorm_present;
+      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = __GCC_IEC_559 >= 2;
       static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
       static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
 
@@ -1789,8 +1788,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
       static _GLIBCXX_CONSTEXPR double
       denorm_min() _GLIBCXX_USE_NOEXCEPT { return __DBL_DENORM_MIN__; }
 
-      static _GLIBCXX_USE_CONSTEXPR bool is_iec559
-	= has_infinity && has_quiet_NaN && has_denorm == denorm_present;
+      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = __GCC_IEC_559 >= 2;
       static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
       static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
 
@@ -1864,8 +1862,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
       static _GLIBCXX_CONSTEXPR long double
       denorm_min() _GLIBCXX_USE_NOEXCEPT { return __LDBL_DENORM_MIN__; }
 
-      static _GLIBCXX_USE_CONSTEXPR bool is_iec559
-	= has_infinity && has_quiet_NaN && has_denorm == denorm_present;
+      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = __GCC_IEC_559 >= 2;
       static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
       static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
 
diff --git a/libstdc++-v3/testsuite/18_support/numeric_limits/denorm_min-1.cc b/libstdc++-v3/testsuite/18_support/numeric_limits/denorm_min-1.cc
new file mode 100644
index 00000000000..8ff2950d77e
--- /dev/null
+++ b/libstdc++-v3/testsuite/18_support/numeric_limits/denorm_min-1.cc
@@ -0,0 +1,2 @@
+// { dg-options "-ffast-math" }
+#include "denorm_min.cc"
diff --git a/libstdc++-v3/testsuite/18_support/numeric_limits/epsilon-1.cc b/libstdc++-v3/testsuite/18_support/numeric_limits/epsilon-1.cc
new file mode 100644
index 00000000000..34548976bea
--- /dev/null
+++ b/libstdc++-v3/testsuite/18_support/numeric_limits/epsilon-1.cc
@@ -0,0 +1,2 @@
+// { dg-options "-ffast-math" }
+#include "epsilon.cc"
diff --git a/libstdc++-v3/testsuite/18_support/numeric_limits/infinity-1.cc b/libstdc++-v3/testsuite/18_support/numeric_limits/infinity-1.cc
new file mode 100644
index 00000000000..7ff8ea81242
--- /dev/null
+++ b/libstdc++-v3/testsuite/18_support/numeric_limits/infinity-1.cc
@@ -0,0 +1,2 @@
+// { dg-options "-ffast-math" }
+#include "infinity.cc"
diff --git a/libstdc++-v3/testsuite/18_support/numeric_limits/infinity.cc b/libstdc++-v3/testsuite/18_support/numeric_limits/infinity.cc
index 3a5bce57c35..9585ab38216 100644
--- a/libstdc++-v3/testsuite/18_support/numeric_limits/infinity.cc
+++ b/libstdc++-v3/testsuite/18_support/numeric_limits/infinity.cc
@@ -33,10 +33,10 @@ test_infinity()
 {
   bool test;
 
-  if (std::numeric_limits<T>::has_infinity)
+  if (std::numeric_limits<T>::has_infinity && std::numeric_limits<T>::is_iec559)
     {
       T inf = std::numeric_limits<T>::infinity();
-      test = (inf + inf == inf);
+      test  = (inf + inf == inf);
     }
   else
     test = true;
diff --git a/libstdc++-v3/testsuite/18_support/numeric_limits/is_iec559-1.cc b/libstdc++-v3/testsuite/18_support/numeric_limits/is_iec559-1.cc
new file mode 100644
index 00000000000..91dd8163126
--- /dev/null
+++ b/libstdc++-v3/testsuite/18_support/numeric_limits/is_iec559-1.cc
@@ -0,0 +1,2 @@
+// { dg-options "-ffast-math" }
+#include "is_iec559.cc"
diff --git a/libstdc++-v3/testsuite/18_support/numeric_limits/is_iec559.cc b/libstdc++-v3/testsuite/18_support/numeric_limits/is_iec559.cc
index d15ae5cae14..c71da192d1d 100644
--- a/libstdc++-v3/testsuite/18_support/numeric_limits/is_iec559.cc
+++ b/libstdc++-v3/testsuite/18_support/numeric_limits/is_iec559.cc
@@ -27,28 +27,50 @@
 #include <cwchar>
 #include <testsuite_hooks.h>
 
+// make these values "invisible" to the optimizer so that we really test the FPU
+template <typename T>
+T min = std::numeric_limits<T>::min();
+template <typename T>
+T denorm_min = std::numeric_limits<T>::denorm_min();
+template <typename T>
+T inf = std::numeric_limits<T>::infinity();
+template <typename T>
+T max = std::numeric_limits<T>::max();
+template <typename T>
+T qnan = std::numeric_limits<T>::quiet_NaN();
+
 template<typename T>
 void
 test_is_iec559()
 {
-  bool test;
-
   if (std::numeric_limits<T>::is_iec559)
     {
       // IEC 559 requires all of the following.
-      test = (std::numeric_limits<T>::has_infinity
-	      && std::numeric_limits<T>::has_quiet_NaN
-	      && std::numeric_limits<T>::has_signaling_NaN);
+      VERIFY(std::numeric_limits<T>::has_infinity &&
+	     std::numeric_limits<T>::has_quiet_NaN &&
+	     std::numeric_limits<T>::has_signaling_NaN);
+
+      // Test a few random IEC559 features
+      VERIFY(min<T> / 2 > T());         // min/2 is denormal, but not 0
+      VERIFY(denorm_min<T> / 3 == T()); // calculation with denormals works
+      T x = denorm_min<T>;
+      for (int i = 1; i < std::numeric_limits<T>::digits; ++i)
+	x *= 2;
+      VERIFY(x == min<T>);
+      VERIFY(inf<T> * 2 == inf<T>); // infinity saturates
+      VERIFY(max<T> * 2 == inf<T>); // max*2 saturates to infinity
+      T inf0 = inf<T> * T();        // NaN
+      VERIFY(inf0 != inf<T>);
+      VERIFY(inf0 != 0);
+      VERIFY((inf0 == inf0) == false);
+      VERIFY(qnan<T> != qnan<T>);
     }
   else
     {
-      // If we had all of the following, why didn't we set IEC 559?
-      test = (!std::numeric_limits<T>::has_infinity
-	      || !std::numeric_limits<T>::has_quiet_NaN
-	      || !std::numeric_limits<T>::has_signaling_NaN);
+      // We could have representations for inf, NaN, and SNaN and still not be
+      // IEC559 compliant. At this point, the meaning of operations on NaNs and
+      // infinities is unspecified.
     }
-
-  VERIFY (test);
 }
 
 // libstdc++/8949
diff --git a/libstdc++-v3/testsuite/18_support/numeric_limits/quiet_NaN-1.cc b/libstdc++-v3/testsuite/18_support/numeric_limits/quiet_NaN-1.cc
new file mode 100644
index 00000000000..45bef204a65
--- /dev/null
+++ b/libstdc++-v3/testsuite/18_support/numeric_limits/quiet_NaN-1.cc
@@ -0,0 +1,2 @@
+// { dg-options "-ffast-math" }
+#include "quiet_NaN.cc"
diff --git a/libstdc++-v3/testsuite/18_support/numeric_limits/quiet_NaN.cc b/libstdc++-v3/testsuite/18_support/numeric_limits/quiet_NaN.cc
index 97406aed2b3..b17df1cc3d7 100644
--- a/libstdc++-v3/testsuite/18_support/numeric_limits/quiet_NaN.cc
+++ b/libstdc++-v3/testsuite/18_support/numeric_limits/quiet_NaN.cc
@@ -33,10 +33,11 @@ test_qnan()
 {
   bool test;
 
-  if (std::numeric_limits<T>::has_quiet_NaN)
+  if (std::numeric_limits<T>::has_quiet_NaN &&
+      std::numeric_limits<T>::is_iec559)
     {
       T nan = std::numeric_limits<T>::quiet_NaN();
-      test = (nan != nan);
+      test  = (nan != nan);
     }
   else
     test = true;