diff --git a/include/boost/math/quadrature/detail/quadrature_constant.hpp b/include/boost/math/quadrature/detail/quadrature_constant.hpp
new file mode 100644
index 0000000000..ea09288a9d
--- /dev/null
+++ b/include/boost/math/quadrature/detail/quadrature_constant.hpp
@@ -0,0 +1,61 @@
+//  Copyright John Maddock 2015.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+
+#ifndef BOOST_MATH_QUADRATURE_DETAIL_QUADRATURE_CONSTANT_HPP
+#define BOOST_MATH_QUADRATURE_DETAIL_QUADRATURE_CONSTANT_HPP
+
+#ifndef BOOST_MATH_BUILD_MODULE
+#include <limits>
+#include <type_traits>
+#endif
+
+BOOST_MATH_NAMESPACE_BEGIN namespace quadrature{ namespace detail {
+
+template <class T>
+struct quadrature_constant_category
+{
+   static const unsigned value =
+      (std::numeric_limits<T>::is_specialized == 0) ? 999 :
+      (std::numeric_limits<T>::radix == 2) ?
+      (
+#ifdef BOOST_HAS_FLOAT128
+         (std::numeric_limits<T>::digits <= 113) && std::is_constructible<T, __float128>::value ? 0 :
+#else
+         (std::numeric_limits<T>::digits <= std::numeric_limits<long double>::digits) && std::is_constructible<T, long double>::value ? 0 :
+#endif
+         (std::numeric_limits<T>::digits10 <= 110) && std::is_constructible<T, const char*>::value ? 4 : 999
+      ) : (std::numeric_limits<T>::digits10 <= 110) && std::is_constructible<T, const char*>::value ? 4 : 999;
+
+   using storage_type =
+      std::conditional_t<(std::numeric_limits<T>::is_specialized == 0), T,
+         std::conditional_t<(std::numeric_limits<T>::radix == 2),
+            std::conditional_t< ((std::numeric_limits<T>::digits <= std::numeric_limits<float>::digits) && std::is_constructible<T, float>::value),
+               float,
+               std::conditional_t<((std::numeric_limits<T>::digits <= std::numeric_limits<double>::digits) && std::is_constructible<T, double>::value),
+                  double,
+                  std::conditional_t<((std::numeric_limits<T>::digits <= std::numeric_limits<long double>::digits) && std::is_constructible<T, long double>::value),
+                     long double,
+#ifdef BOOST_HAS_FLOAT128
+                     std::conditional_t<((std::numeric_limits<T>::digits <= 113) && std::is_constructible<T, __float128>::value),
+                        __float128,
+                        T
+                     >
+                  >
+#else
+                     T
+                  >
+#endif
+               >
+            >, T
+         >
+      >;
+};
+
+} // namespace detail
+} // namespace quadrature
+BOOST_MATH_NAMESPACE_END
+
+#endif // BOOST_MATH_QUADRATURE_DETAIL_QUADRATURE_CONSTANT_HPP
\ No newline at end of file
diff --git a/include/boost/math/quadrature/gauss.hpp b/include/boost/math/quadrature/gauss.hpp
index 80d800c870..6d12cfdc75 100644
--- a/include/boost/math/quadrature/gauss.hpp
+++ b/include/boost/math/quadrature/gauss.hpp
@@ -16,53 +16,14 @@
 #endif
 #include <boost/math/special_functions/legendre.hpp>
 #include <boost/math/constants/constants.hpp>
+#include <boost/math/quadrature/detail/quadrature_constant.hpp>
 
 #ifdef _MSC_VER
 #pragma warning(push)
 #pragma warning(disable:4127)
 #endif
 
-BOOST_MATH_NAMESPACE_BEGIN namespace quadrature{ namespace detail{
-
-template <class T>
-struct gauss_constant_category
-{
-   static const unsigned value =
-      (std::numeric_limits<T>::is_specialized == 0) ? 999 :
-      (std::numeric_limits<T>::radix == 2) ?
-      (
-#ifdef BOOST_HAS_FLOAT128
-         (std::numeric_limits<T>::digits <= 113) && std::is_constructible<T, __float128>::value ? 0 :
-#else
-         (std::numeric_limits<T>::digits <= std::numeric_limits<long double>::digits) && std::is_constructible<T, long double>::value ? 0 :
-#endif
-         (std::numeric_limits<T>::digits10 <= 110) && std::is_constructible<T, const char*>::value ? 4 : 999
-      ) : (std::numeric_limits<T>::digits10 <= 110) && std::is_constructible<T, const char*>::value ? 4 : 999;
-   
-   using storage_type =
-      std::conditional_t<(std::numeric_limits<T>::is_specialized == 0), T,
-         std::conditional_t<(std::numeric_limits<T>::radix == 2),
-            std::conditional_t< ((std::numeric_limits<T>::digits <= std::numeric_limits<float>::digits) && std::is_constructible<T, float>::value),
-               float,
-               std::conditional_t<((std::numeric_limits<T>::digits <= std::numeric_limits<double>::digits) && std::is_constructible<T, double>::value),
-                  double,
-                  std::conditional_t<((std::numeric_limits<T>::digits <= std::numeric_limits<long double>::digits) && std::is_constructible<T, long double>::value),
-                     long double,
-#ifdef BOOST_HAS_FLOAT128
-                     std::conditional_t<((std::numeric_limits<T>::digits <= 113) && std::is_constructible<T, __float128>::value),
-                        __float128,
-                        T
-                     >
-                  >
-#else
-                     T
-                  >
-#endif
-               >
-            >, T
-         >
-      >;
-};
+BOOST_MATH_NAMESPACE_BEGIN namespace quadrature{ namespace detail {
 
 #ifndef BOOST_MATH_GAUSS_NO_COMPUTE_ON_DEMAND
 
@@ -103,7 +64,7 @@ class gauss_detail;
 template <class T>
 class gauss_detail<T, 7, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 4> const & abscissa()
    {
@@ -130,7 +91,7 @@ class gauss_detail<T, 7, 0>
 template <class T>
 class gauss_detail<T, 7, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 4> const & abscissa()
    {
@@ -183,7 +144,7 @@ class gauss_detail<T, 7, 4>
 template <class T>
 class gauss_detail<T, 10, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 5> const & abscissa()
    {
@@ -212,7 +173,7 @@ class gauss_detail<T, 10, 0>
 template <class T>
 class gauss_detail<T, 10, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 5> const & abscissa()
    {
@@ -270,7 +231,7 @@ class gauss_detail<T, 10, 4>
 template <class T>
 class gauss_detail<T, 15, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 8> const & abscissa()
    {
@@ -305,7 +266,7 @@ class gauss_detail<T, 15, 0>
 template <class T>
 class gauss_detail<T, 15, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 8> const & abscissa()
    {
@@ -375,7 +336,7 @@ class gauss_detail<T, 15, 4>
 template <class T>
 class gauss_detail<T, 20, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 10> const & abscissa()
    {
@@ -414,7 +375,7 @@ class gauss_detail<T, 20, 0>
 template <class T>
 class gauss_detail<T, 20, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 10> const & abscissa()
    {
@@ -492,7 +453,7 @@ class gauss_detail<T, 20, 4>
 template <class T>
 class gauss_detail<T, 25, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 13> const & abscissa()
    {
@@ -537,7 +498,7 @@ class gauss_detail<T, 25, 0>
 template <class T>
 class gauss_detail<T, 25, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 13> const & abscissa()
    {
@@ -628,7 +589,7 @@ class gauss_detail<T, 25, 4>
 template <class T>
 class gauss_detail<T, 30, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 15> const & abscissa()
    {
@@ -677,7 +638,7 @@ class gauss_detail<T, 30, 0>
 template <class T>
 class gauss_detail<T, 30, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 15> const & abscissa()
    {
@@ -774,9 +735,9 @@ class gauss_detail<T, 30, 4>
 }
 
 BOOST_MATH_EXPORT template <class Real, unsigned N, class Policy = BOOST_MATH_NAMESPACE::policies::policy<> >
-class gauss : public detail::gauss_detail<Real, N, detail::gauss_constant_category<Real>::value>
+class gauss : public detail::gauss_detail<Real, N, detail::quadrature_constant_category<Real>::value>
 {
-   typedef detail::gauss_detail<Real, N, detail::gauss_constant_category<Real>::value> base;
+   typedef detail::gauss_detail<Real, N, detail::quadrature_constant_category<Real>::value> base;
 public:
 
    template <class F>
diff --git a/include/boost/math/quadrature/gauss_hermite.hpp b/include/boost/math/quadrature/gauss_hermite.hpp
index a8bd05a002..2330983a7a 100644
--- a/include/boost/math/quadrature/gauss_hermite.hpp
+++ b/include/boost/math/quadrature/gauss_hermite.hpp
@@ -32,49 +32,10 @@
 #include <boost/math/special_functions/fpclassify.hpp>
 #include <boost/math/tools/big_constant.hpp>
 #include <boost/math/tools/precision.hpp>
+#include <boost/math/quadrature/detail/quadrature_constant.hpp>
 
 BOOST_MATH_NAMESPACE_BEGIN namespace quadrature { namespace detail {
 
-template <class T>
-struct gauss_hermite_constant_category
-{
-   static const unsigned value =
-      (std::numeric_limits<T>::is_specialized == 0) ? 999 :
-      (std::numeric_limits<T>::radix == 2) ?
-      (
-#ifdef BOOST_HAS_FLOAT128
-         (std::numeric_limits<T>::digits <= 113) && std::is_constructible<T, __float128>::value ? 0 :
-#else
-         (std::numeric_limits<T>::digits <= std::numeric_limits<long double>::digits) && std::is_constructible<T, long double>::value ? 0 :
-#endif
-         (std::numeric_limits<T>::digits10 <= 110) && std::is_constructible<T, const char*>::value ? 4 : 999
-      ) : (std::numeric_limits<T>::digits10 <= 110) && std::is_constructible<T, const char*>::value ? 4 : 999;
-
-   using storage_type =
-      std::conditional_t<(std::numeric_limits<T>::is_specialized == 0), T,
-         std::conditional_t<(std::numeric_limits<T>::radix == 2),
-            std::conditional_t< ((std::numeric_limits<T>::digits <= std::numeric_limits<float>::digits) && std::is_constructible<T, float>::value),
-               float,
-               std::conditional_t<((std::numeric_limits<T>::digits <= std::numeric_limits<double>::digits) && std::is_constructible<T, double>::value),
-                  double,
-                  std::conditional_t<((std::numeric_limits<T>::digits <= std::numeric_limits<long double>::digits) && std::is_constructible<T, long double>::value),
-                     long double,
-#ifdef BOOST_HAS_FLOAT128
-                     std::conditional_t<((std::numeric_limits<T>::digits <= 113) && std::is_constructible<T, __float128>::value),
-                        __float128,
-                        T
-                     >
-                  >
-#else
-                     T
-                  >
-#endif
-               >
-            >, T
-         >
-      >;
-};
-
 #ifndef BOOST_MATH_GAUSS_NO_COMPUTE_ON_DEMAND
 
 template <class Real, unsigned N, unsigned Category>
@@ -252,7 +213,7 @@ class gauss_hermite_detail;
 template <class T>
 class gauss_hermite_detail<T, 7, 0>
 {
-   using storage_type = typename gauss_hermite_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
    public:
       static std::array<storage_type, 4> const & abscissa()
       {
@@ -280,7 +241,7 @@ class gauss_hermite_detail<T, 7, 0>
 template <class T>
 class gauss_hermite_detail<T, 7, 0>
 {
-   using storage_type = typename gauss_hermite_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
    public:
       static std::array<storage_type, 4> const & abscissa()
       {
@@ -308,7 +269,7 @@ class gauss_hermite_detail<T, 7, 0>
 template <class T>
 class gauss_hermite_detail<T, 7, 4>
 {
-   using storage_type = typename gauss_hermite_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
    public:
       static std::array<T, 4> const & abscissa()
       {
@@ -336,7 +297,7 @@ class gauss_hermite_detail<T, 7, 4>
 template <class T>
 class gauss_hermite_detail<T, 10, 0>
 {
-   using storage_type = typename gauss_hermite_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
    public:
       static std::array<storage_type, 5> const & abscissa()
       {
@@ -366,7 +327,7 @@ class gauss_hermite_detail<T, 10, 0>
 template <class T>
 class gauss_hermite_detail<T, 10, 0>
 {
-   using storage_type = typename gauss_hermite_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
    public:
       static std::array<storage_type, 5> const & abscissa()
       {
@@ -396,7 +357,7 @@ class gauss_hermite_detail<T, 10, 0>
 template <class T>
 class gauss_hermite_detail<T, 10, 4>
 {
-   using storage_type = typename gauss_hermite_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
    public:
       static std::array<T, 5> const & abscissa()
       {
@@ -426,7 +387,7 @@ class gauss_hermite_detail<T, 10, 4>
 template <class T>
 class gauss_hermite_detail<T, 15, 0>
 {
-   using storage_type = typename gauss_hermite_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
    public:
       static std::array<storage_type, 8> const & abscissa()
       {
@@ -462,7 +423,7 @@ class gauss_hermite_detail<T, 15, 0>
 template <class T>
 class gauss_hermite_detail<T, 15, 0>
 {
-   using storage_type = typename gauss_hermite_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
    public:
       static std::array<storage_type, 8> const & abscissa()
       {
@@ -498,7 +459,7 @@ class gauss_hermite_detail<T, 15, 0>
 template <class T>
 class gauss_hermite_detail<T, 15, 4>
 {
-   using storage_type = typename gauss_hermite_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
    public:
       static std::array<T, 8> const & abscissa()
       {
@@ -533,9 +494,9 @@ class gauss_hermite_detail<T, 15, 4>
 } // namespace detail
 
 template <class Real, unsigned N, class Policy = BOOST_MATH_NAMESPACE::policies::policy<> >
-class gauss_hermite : public detail::gauss_hermite_detail<Real, N, detail::gauss_hermite_constant_category<Real>::value>
+class gauss_hermite : public detail::gauss_hermite_detail<Real, N, detail::quadrature_constant_category<Real>::value>
 {
-   using base = detail::gauss_hermite_detail<Real, N, detail::gauss_hermite_constant_category<Real>::value>;
+   using base = detail::gauss_hermite_detail<Real, N, detail::quadrature_constant_category<Real>::value>;
 
    // Abscissas computed on demand are NaN when the recurrence overflows Real.
    static bool overflowed()
diff --git a/include/boost/math/quadrature/gauss_kronrod.hpp b/include/boost/math/quadrature/gauss_kronrod.hpp
index e776f5bb7a..f66b9de5d0 100644
--- a/include/boost/math/quadrature/gauss_kronrod.hpp
+++ b/include/boost/math/quadrature/gauss_kronrod.hpp
@@ -21,6 +21,7 @@
 #include <boost/math/special_functions/legendre.hpp>
 #include <boost/math/special_functions/legendre_stieltjes.hpp>
 #include <boost/math/quadrature/gauss.hpp>
+#include <boost/math/quadrature/detail/quadrature_constant.hpp>
 
 BOOST_MATH_NAMESPACE_BEGIN namespace quadrature{ namespace detail{
 
@@ -88,7 +89,7 @@ class gauss_kronrod_detail;
 template <class T>
 class gauss_kronrod_detail<T, 15, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 8> const & abscissa()
    {
@@ -124,7 +125,7 @@ class gauss_kronrod_detail<T, 15, 0>
 template <class T>
 class gauss_kronrod_detail<T, 15, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 8> const & abscissa()
    {
@@ -196,7 +197,7 @@ class gauss_kronrod_detail<T, 15, 4>
 template <class T>
 class gauss_kronrod_detail<T, 21, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 11> const & abscissa()
    {
@@ -238,7 +239,7 @@ class gauss_kronrod_detail<T, 21, 0>
 template <class T>
 class gauss_kronrod_detail<T, 21, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 11> const & abscissa()
    {
@@ -322,7 +323,7 @@ class gauss_kronrod_detail<T, 21, 4>
 template <class T>
 class gauss_kronrod_detail<T, 31, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 16> const & abscissa()
    {
@@ -375,7 +376,7 @@ class gauss_kronrod_detail<T, 31, 0>
 template <class T>
 class gauss_kronrod_detail<T, 31, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 16> const & abscissa()
    {
@@ -479,7 +480,7 @@ class gauss_kronrod_detail<T, 31, 4>
 template <class T>
 class gauss_kronrod_detail<T, 41, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 21> const & abscissa()
    {
@@ -542,7 +543,7 @@ class gauss_kronrod_detail<T, 41, 0>
 template <class T>
 class gauss_kronrod_detail<T, 41, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 21> const & abscissa()
    {
@@ -666,7 +667,7 @@ class gauss_kronrod_detail<T, 41, 4>
 template <class T>
 class gauss_kronrod_detail<T, 51, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 26> const & abscissa()
    {
@@ -739,7 +740,7 @@ class gauss_kronrod_detail<T, 51, 0>
 template <class T>
 class gauss_kronrod_detail<T, 51, 3>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 26> const & abscissa()
    {
@@ -883,7 +884,7 @@ class gauss_kronrod_detail<T, 51, 4>
 template <class T>
 class gauss_kronrod_detail<T, 61, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 31> const & abscissa()
    {
@@ -966,7 +967,7 @@ class gauss_kronrod_detail<T, 61, 0>
 template <class T>
 class gauss_kronrod_detail<T, 61, 0>
 {
-   using storage_type = typename gauss_constant_category<T>::storage_type;
+   using storage_type = typename quadrature_constant_category<T>::storage_type;
 public:
    static std::array<storage_type, 31> const & abscissa()
    {
@@ -1128,9 +1129,9 @@ class gauss_kronrod_detail<T, 61, 4>
 }
 
 BOOST_MATH_EXPORT template <class Real, unsigned N, class Policy = BOOST_MATH_NAMESPACE::policies::policy<> >
-class gauss_kronrod : public detail::gauss_kronrod_detail<Real, N, detail::gauss_constant_category<Real>::value>
+class gauss_kronrod : public detail::gauss_kronrod_detail<Real, N, detail::quadrature_constant_category<Real>::value>
 {
-   typedef detail::gauss_kronrod_detail<Real, N, detail::gauss_constant_category<Real>::value> base;
+   typedef detail::gauss_kronrod_detail<Real, N, detail::quadrature_constant_category<Real>::value> base;
 public:
   typedef Real value_type;
 private: