diff --git a/include/boost/math/tools/detail/polynomial_horner1_10.hpp b/include/boost/math/tools/detail/polynomial_horner1_10.hpp
index 37e4cba01..04ad90b69 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_10.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_10.hpp
@@ -12,67 +12,67 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_11.hpp b/include/boost/math/tools/detail/polynomial_horner1_11.hpp
index 885490f22..f99ab8250 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_11.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_11.hpp
@@ -12,73 +12,73 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_12.hpp b/include/boost/math/tools/detail/polynomial_horner1_12.hpp
index f54034592..3006ebe51 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_12.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_12.hpp
@@ -12,79 +12,79 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_13.hpp b/include/boost/math/tools/detail/polynomial_horner1_13.hpp
index e9e13bd52..0f1118909 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_13.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_13.hpp
@@ -12,85 +12,85 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_14.hpp b/include/boost/math/tools/detail/polynomial_horner1_14.hpp
index eaa18bdc5..caba4b97e 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_14.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_14.hpp
@@ -12,91 +12,91 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_15.hpp b/include/boost/math/tools/detail/polynomial_horner1_15.hpp
index c4a880449..c8f42ac81 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_15.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_15.hpp
@@ -12,97 +12,97 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_16.hpp b/include/boost/math/tools/detail/polynomial_horner1_16.hpp
index 5c262cc63..2ed591ccf 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_16.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_16.hpp
@@ -12,103 +12,103 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_17.hpp b/include/boost/math/tools/detail/polynomial_horner1_17.hpp
index 90d49a0bd..5e9fc8cd7 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_17.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_17.hpp
@@ -12,109 +12,109 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_18.hpp b/include/boost/math/tools/detail/polynomial_horner1_18.hpp
index 58fb83fd3..ffb62ff04 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_18.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_18.hpp
@@ -12,115 +12,115 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_19.hpp b/include/boost/math/tools/detail/polynomial_horner1_19.hpp
index 18a6af2d3..56df108ac 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_19.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_19.hpp
@@ -12,121 +12,121 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((((a[18] * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_2.hpp b/include/boost/math/tools/detail/polynomial_horner1_2.hpp
index 645e3f878..63091ebdd 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_2.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_2.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_20.hpp b/include/boost/math/tools/detail/polynomial_horner1_20.hpp
index 47584e787..c16e5143e 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_20.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_20.hpp
@@ -12,127 +12,127 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((((((((((((a[18] * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((((((((((((((a[19] * x + a[18]) * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_3.hpp b/include/boost/math/tools/detail/polynomial_horner1_3.hpp
index 420bbcc28..0aeccc111 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_3.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_3.hpp
@@ -12,25 +12,25 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_4.hpp b/include/boost/math/tools/detail/polynomial_horner1_4.hpp
index 930798e74..61058fce8 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_4.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_4.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_5.hpp b/include/boost/math/tools/detail/polynomial_horner1_5.hpp
index b97a8f9eb..47021bc50 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_5.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_5.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_6.hpp b/include/boost/math/tools/detail/polynomial_horner1_6.hpp
index 6a699f517..bfd24371d 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_6.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_6.hpp
@@ -12,43 +12,43 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_7.hpp b/include/boost/math/tools/detail/polynomial_horner1_7.hpp
index 2aceeeca1..50ddca63f 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_7.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_7.hpp
@@ -12,49 +12,49 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_8.hpp b/include/boost/math/tools/detail/polynomial_horner1_8.hpp
index 0486d642f..3be7ba4d1 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_8.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_8.hpp
@@ -12,55 +12,55 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner1_9.hpp b/include/boost/math/tools/detail/polynomial_horner1_9.hpp
index b0838014b..4ec53c48b 100644
--- a/include/boost/math/tools/detail/polynomial_horner1_9.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner1_9.hpp
@@ -12,61 +12,61 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner2_10.hpp b/include/boost/math/tools/detail/polynomial_horner2_10.hpp
index 2a680d756..f242d7464 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_10.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_10.hpp
@@ -12,72 +12,72 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_11.hpp b/include/boost/math/tools/detail/polynomial_horner2_11.hpp
index 7036eec3f..edf7f86c5 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_11.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_11.hpp
@@ -12,79 +12,79 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_12.hpp b/include/boost/math/tools/detail/polynomial_horner2_12.hpp
index fbbf2a3fa..969c9c4dd 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_12.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_12.hpp
@@ -12,86 +12,86 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_13.hpp b/include/boost/math/tools/detail/polynomial_horner2_13.hpp
index 46fb3859d..ed4559d11 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_13.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_13.hpp
@@ -12,93 +12,93 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_14.hpp b/include/boost/math/tools/detail/polynomial_horner2_14.hpp
index d1c326e0f..4b79eb78a 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_14.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_14.hpp
@@ -12,100 +12,100 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_15.hpp b/include/boost/math/tools/detail/polynomial_horner2_15.hpp
index d679cfeaf..28b62eee7 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_15.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_15.hpp
@@ -12,107 +12,107 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_16.hpp b/include/boost/math/tools/detail/polynomial_horner2_16.hpp
index 0f3ed8f6c..6368b4054 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_16.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_16.hpp
@@ -12,114 +12,114 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_17.hpp b/include/boost/math/tools/detail/polynomial_horner2_17.hpp
index 7783c4c81..551e6191c 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_17.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_17.hpp
@@ -12,121 +12,121 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_18.hpp b/include/boost/math/tools/detail/polynomial_horner2_18.hpp
index 4e3b57f98..19cfdc19e 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_18.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_18.hpp
@@ -12,128 +12,128 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((((a[17] * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_19.hpp b/include/boost/math/tools/detail/polynomial_horner2_19.hpp
index 9eca8ef11..9ea87fd93 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_19.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_19.hpp
@@ -12,135 +12,135 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((((a[17] * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((((a[18] * x2 + a[16]) * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((((a[17] * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_2.hpp b/include/boost/math/tools/detail/polynomial_horner2_2.hpp
index 857d43fdb..1982a81f3 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_2.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_2.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner2_20.hpp b/include/boost/math/tools/detail/polynomial_horner2_20.hpp
index 2a8359025..23afe55e0 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_20.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_20.hpp
@@ -12,142 +12,142 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((a[10] * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((a[11] * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((a[12] * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((a[13] * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((a[14] * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((((((a[15] * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((((a[17] * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((((((a[16] * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((((((((a[18] * x2 + a[16]) * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((((((((a[17] * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((((((((a[19] * x2 + a[17]) * x2 + a[15]) * x2 + a[13]) * x2 + a[11]) * x2 + a[9]) * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((((((((a[18] * x2 + a[16]) * x2 + a[14]) * x2 + a[12]) * x2 + a[10]) * x2 + a[8]) * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_3.hpp b/include/boost/math/tools/detail/polynomial_horner2_3.hpp
index b5956cdaf..f9d6953b8 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_3.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_3.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner2_4.hpp b/include/boost/math/tools/detail/polynomial_horner2_4.hpp
index 9194a1868..8f11de5b3 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_4.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_4.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner2_5.hpp b/include/boost/math/tools/detail/polynomial_horner2_5.hpp
index 4e20c214a..eba9ee9e6 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_5.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_5.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_6.hpp b/include/boost/math/tools/detail/polynomial_horner2_6.hpp
index a33168d5e..ef77c6255 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_6.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_6.hpp
@@ -12,44 +12,44 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_7.hpp b/include/boost/math/tools/detail/polynomial_horner2_7.hpp
index 2f135756c..fe8d21b95 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_7.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_7.hpp
@@ -12,51 +12,51 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_8.hpp b/include/boost/math/tools/detail/polynomial_horner2_8.hpp
index 4c59602f9..de1810a94 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_8.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_8.hpp
@@ -12,58 +12,58 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
diff --git a/include/boost/math/tools/detail/polynomial_horner2_9.hpp b/include/boost/math/tools/detail/polynomial_horner2_9.hpp
index 0b60c3c04..5c53b7329 100644
--- a/include/boost/math/tools/detail/polynomial_horner2_9.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner2_9.hpp
@@ -12,65 +12,65 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>(((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    return static_cast<V>((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x);
diff --git a/include/boost/math/tools/detail/polynomial_horner3_10.hpp b/include/boost/math/tools/detail/polynomial_horner3_10.hpp
index 3386fcae4..7fb5bb474 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_10.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_10.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_11.hpp b/include/boost/math/tools/detail/polynomial_horner3_11.hpp
index f24ebb024..9f22820de 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_11.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_11.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_12.hpp b/include/boost/math/tools/detail/polynomial_horner3_12.hpp
index 73916940d..b04961376 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_12.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_12.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_13.hpp b/include/boost/math/tools/detail/polynomial_horner3_13.hpp
index 44ec9a84c..f39a33cc9 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_13.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_13.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_14.hpp b/include/boost/math/tools/detail/polynomial_horner3_14.hpp
index 4d4e9e21c..32b9e7db2 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_14.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_14.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_15.hpp b/include/boost/math/tools/detail/polynomial_horner3_15.hpp
index b7cf83dd1..55325c84b 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_15.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_15.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_16.hpp b/include/boost/math/tools/detail/polynomial_horner3_16.hpp
index fbf504f3f..f71d62f50 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_16.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_16.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -295,7 +295,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_17.hpp b/include/boost/math/tools/detail/polynomial_horner3_17.hpp
index c7af11b65..783a34558 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_17.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_17.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -295,7 +295,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -330,7 +330,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_18.hpp b/include/boost/math/tools/detail/polynomial_horner3_18.hpp
index feceac694..b10b270c4 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_18.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_18.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -295,7 +295,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -330,7 +330,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -367,7 +367,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_19.hpp b/include/boost/math/tools/detail/polynomial_horner3_19.hpp
index 6a9a4ea6f..21147591c 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_19.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_19.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -295,7 +295,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -330,7 +330,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -367,7 +367,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -406,7 +406,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_2.hpp b/include/boost/math/tools/detail/polynomial_horner3_2.hpp
index 69925be1c..ee3e35e6c 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_2.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_2.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner3_20.hpp b/include/boost/math/tools/detail/polynomial_horner3_20.hpp
index 8dda51139..338aeb7db 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_20.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_20.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -127,7 +127,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -150,7 +150,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -175,7 +175,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -231,7 +231,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -262,7 +262,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -295,7 +295,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -330,7 +330,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -367,7 +367,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -406,7 +406,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -447,7 +447,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_3.hpp b/include/boost/math/tools/detail/polynomial_horner3_3.hpp
index 30e68ac2a..1eee0cfac 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_3.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_3.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner3_4.hpp b/include/boost/math/tools/detail/polynomial_horner3_4.hpp
index e3c9b16f3..efa7fba48 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_4.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_4.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
diff --git a/include/boost/math/tools/detail/polynomial_horner3_5.hpp b/include/boost/math/tools/detail/polynomial_horner3_5.hpp
index c02467da0..f150e2a4a 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_5.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_5.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_6.hpp b/include/boost/math/tools/detail/polynomial_horner3_6.hpp
index ad71255bf..fe679e74d 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_6.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_6.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_7.hpp b/include/boost/math/tools/detail/polynomial_horner3_7.hpp
index 31e0afa66..76f080ad9 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_7.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_7.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_8.hpp b/include/boost/math/tools/detail/polynomial_horner3_8.hpp
index 33121b204..75634bdfc 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_8.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_8.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/polynomial_horner3_9.hpp b/include/boost/math/tools/detail/polynomial_horner3_9.hpp
index c9f717133..63a40580d 100644
--- a/include/boost/math/tools/detail/polynomial_horner3_9.hpp
+++ b/include/boost/math/tools/detail/polynomial_horner3_9.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[1] * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[2] * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -55,7 +55,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -70,7 +70,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -87,7 +87,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x
 }
 
 template <class T, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    V x2 = x * x;
    V t[2];
diff --git a/include/boost/math/tools/detail/rational_horner1_10.hpp b/include/boost/math/tools/detail/rational_horner1_10.hpp
index 346ac34ec..e2f6c6d2f 100644
--- a/include/boost/math/tools/detail/rational_horner1_10.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_10.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_11.hpp b/include/boost/math/tools/detail/rational_horner1_11.hpp
index 74ed24a74..31d480a65 100644
--- a/include/boost/math/tools/detail/rational_horner1_11.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_11.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_12.hpp b/include/boost/math/tools/detail/rational_horner1_12.hpp
index 9072d1698..c08a85b3a 100644
--- a/include/boost/math/tools/detail/rational_horner1_12.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_12.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_13.hpp b/include/boost/math/tools/detail/rational_horner1_13.hpp
index 1e5c75092..cc87ec2dc 100644
--- a/include/boost/math/tools/detail/rational_horner1_13.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_13.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_14.hpp b/include/boost/math/tools/detail/rational_horner1_14.hpp
index 75b9bde42..256473710 100644
--- a/include/boost/math/tools/detail/rational_horner1_14.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_14.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_15.hpp b/include/boost/math/tools/detail/rational_horner1_15.hpp
index 47f18a3c4..2ab24814e 100644
--- a/include/boost/math/tools/detail/rational_horner1_15.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_15.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_16.hpp b/include/boost/math/tools/detail/rational_horner1_16.hpp
index fec9a51a2..dce0b5e9b 100644
--- a/include/boost/math/tools/detail/rational_horner1_16.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_16.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -192,7 +192,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((b[15] * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_17.hpp b/include/boost/math/tools/detail/rational_horner1_17.hpp
index b26dac95c..8e875d657 100644
--- a/include/boost/math/tools/detail/rational_horner1_17.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_17.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -192,7 +192,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((b[15] * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -204,7 +204,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((b[16] * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_18.hpp b/include/boost/math/tools/detail/rational_horner1_18.hpp
index 074a6359b..ab67a970b 100644
--- a/include/boost/math/tools/detail/rational_horner1_18.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_18.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -192,7 +192,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((b[15] * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -204,7 +204,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((b[16] * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -216,7 +216,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((((b[17] * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_19.hpp b/include/boost/math/tools/detail/rational_horner1_19.hpp
index a1cceaeab..dc300343a 100644
--- a/include/boost/math/tools/detail/rational_horner1_19.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_19.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -192,7 +192,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((b[15] * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -204,7 +204,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((b[16] * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -216,7 +216,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((((b[17] * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -228,7 +228,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((((((a[18] * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((((b[18] * x + b[17]) * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_2.hpp b/include/boost/math/tools/detail/rational_horner1_2.hpp
index 81250ba10..c6b1ef9ef 100644
--- a/include/boost/math/tools/detail/rational_horner1_2.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_2.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_20.hpp b/include/boost/math/tools/detail/rational_horner1_20.hpp
index 63763fd8c..5b8b170c1 100644
--- a/include/boost/math/tools/detail/rational_horner1_20.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_20.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -120,7 +120,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((a[9] * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((b[9] * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -132,7 +132,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((a[10] * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((b[10] * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -144,7 +144,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((a[11] * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((b[11] * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -156,7 +156,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((a[12] * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((b[12] * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -168,7 +168,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((a[13] * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((b[13] * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((a[14] * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((b[14] * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -192,7 +192,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((a[15] * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((b[15] * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -204,7 +204,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((((a[16] * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((b[16] * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -216,7 +216,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((((a[17] * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((((b[17] * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -228,7 +228,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((((((((((((a[18] * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((((((((((((b[18] * x + b[17]) * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -240,7 +240,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((((((((((((((a[19] * x + a[18]) * x + a[17]) * x + a[16]) * x + a[15]) * x + a[14]) * x + a[13]) * x + a[12]) * x + a[11]) * x + a[10]) * x + a[9]) * x + a[8]) * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((((((((((((((b[19] * x + b[18]) * x + b[17]) * x + b[16]) * x + b[15]) * x + b[14]) * x + b[13]) * x + b[12]) * x + b[11]) * x + b[10]) * x + b[9]) * x + b[8]) * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_3.hpp b/include/boost/math/tools/detail/rational_horner1_3.hpp
index 1aebe20d3..6933e22bf 100644
--- a/include/boost/math/tools/detail/rational_horner1_3.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_3.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_4.hpp b/include/boost/math/tools/detail/rational_horner1_4.hpp
index 8175f348c..49b983577 100644
--- a/include/boost/math/tools/detail/rational_horner1_4.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_4.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_5.hpp b/include/boost/math/tools/detail/rational_horner1_5.hpp
index 93c11c1ef..91e97ff44 100644
--- a/include/boost/math/tools/detail/rational_horner1_5.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_5.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_6.hpp b/include/boost/math/tools/detail/rational_horner1_6.hpp
index a59cceb24..876b026cd 100644
--- a/include/boost/math/tools/detail/rational_horner1_6.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_6.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_7.hpp b/include/boost/math/tools/detail/rational_horner1_7.hpp
index eaa023a50..bcac18293 100644
--- a/include/boost/math/tools/detail/rational_horner1_7.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_7.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_8.hpp b/include/boost/math/tools/detail/rational_horner1_8.hpp
index 5624c814f..55e30a53e 100644
--- a/include/boost/math/tools/detail/rational_horner1_8.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_8.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner1_9.hpp b/include/boost/math/tools/detail/rational_horner1_9.hpp
index c94e7ed42..c7087de50 100644
--- a/include/boost/math/tools/detail/rational_horner1_9.hpp
+++ b/include/boost/math/tools/detail/rational_horner1_9.hpp
@@ -12,19 +12,19 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
@@ -36,7 +36,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
@@ -48,7 +48,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
@@ -60,7 +60,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((a[4] * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((b[4] * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -72,7 +72,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((a[5] * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((b[5] * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -84,7 +84,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((a[6] * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((b[6] * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -96,7 +96,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>((((((((a[7] * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / (((((((b[7] * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
@@ -108,7 +108,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
      return static_cast<V>(((((((((a[8] * x + a[7]) * x + a[6]) * x + a[5]) * x + a[4]) * x + a[3]) * x + a[2]) * x + a[1]) * x + a[0]) / ((((((((b[8] * x + b[7]) * x + b[6]) * x + b[5]) * x + b[4]) * x + b[3]) * x + b[2]) * x + b[1]) * x + b[0]));
diff --git a/include/boost/math/tools/detail/rational_horner2_10.hpp b/include/boost/math/tools/detail/rational_horner2_10.hpp
index 0e4fd54ea..4d74a714d 100644
--- a/include/boost/math/tools/detail/rational_horner2_10.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_10.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_11.hpp b/include/boost/math/tools/detail/rational_horner2_11.hpp
index 841c8bd49..15f1cf255 100644
--- a/include/boost/math/tools/detail/rational_horner2_11.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_11.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_12.hpp b/include/boost/math/tools/detail/rational_horner2_12.hpp
index 3e783c577..24e9d9e7f 100644
--- a/include/boost/math/tools/detail/rational_horner2_12.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_12.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_13.hpp b/include/boost/math/tools/detail/rational_horner2_13.hpp
index a3afa653d..495f88525 100644
--- a/include/boost/math/tools/detail/rational_horner2_13.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_13.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -170,7 +170,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_14.hpp b/include/boost/math/tools/detail/rational_horner2_14.hpp
index 377c1ad42..273e723b6 100644
--- a/include/boost/math/tools/detail/rational_horner2_14.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_14.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -170,7 +170,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -186,7 +186,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_15.hpp b/include/boost/math/tools/detail/rational_horner2_15.hpp
index 9082d03f8..c7e24ec7d 100644
--- a/include/boost/math/tools/detail/rational_horner2_15.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_15.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -170,7 +170,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -186,7 +186,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_16.hpp b/include/boost/math/tools/detail/rational_horner2_16.hpp
index 64173bffe..2eebd702b 100644
--- a/include/boost/math/tools/detail/rational_horner2_16.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_16.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -170,7 +170,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -186,7 +186,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -218,7 +218,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_17.hpp b/include/boost/math/tools/detail/rational_horner2_17.hpp
index 5ae8cb428..1fee63047 100644
--- a/include/boost/math/tools/detail/rational_horner2_17.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_17.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -170,7 +170,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -186,7 +186,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -218,7 +218,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -234,7 +234,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_18.hpp b/include/boost/math/tools/detail/rational_horner2_18.hpp
index ebe440e62..7aedbf2aa 100644
--- a/include/boost/math/tools/detail/rational_horner2_18.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_18.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -170,7 +170,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -186,7 +186,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -218,7 +218,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -234,7 +234,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -250,7 +250,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_19.hpp b/include/boost/math/tools/detail/rational_horner2_19.hpp
index c1a2d4383..1c36a267c 100644
--- a/include/boost/math/tools/detail/rational_horner2_19.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_19.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -170,7 +170,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -186,7 +186,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -218,7 +218,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -234,7 +234,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -250,7 +250,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -266,7 +266,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_2.hpp b/include/boost/math/tools/detail/rational_horner2_2.hpp
index e1dd400ae..bb2e2c4dc 100644
--- a/include/boost/math/tools/detail/rational_horner2_2.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_2.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/include/boost/math/tools/detail/rational_horner2_20.hpp b/include/boost/math/tools/detail/rational_horner2_20.hpp
index 50a63c128..a591b901c 100644
--- a/include/boost/math/tools/detail/rational_horner2_20.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_20.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -122,7 +122,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -138,7 +138,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -154,7 +154,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -170,7 +170,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -186,7 +186,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -202,7 +202,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -218,7 +218,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -234,7 +234,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -250,7 +250,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -266,7 +266,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -282,7 +282,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_3.hpp b/include/boost/math/tools/detail/rational_horner2_3.hpp
index ab0d029aa..0b410d8bb 100644
--- a/include/boost/math/tools/detail/rational_horner2_3.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_3.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/include/boost/math/tools/detail/rational_horner2_4.hpp b/include/boost/math/tools/detail/rational_horner2_4.hpp
index 147f5d1da..07a9a2c5a 100644
--- a/include/boost/math/tools/detail/rational_horner2_4.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_4.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/include/boost/math/tools/detail/rational_horner2_5.hpp b/include/boost/math/tools/detail/rational_horner2_5.hpp
index db5907b6f..0933ddfbc 100644
--- a/include/boost/math/tools/detail/rational_horner2_5.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_5.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_6.hpp b/include/boost/math/tools/detail/rational_horner2_6.hpp
index b71bc150a..dee9c6e16 100644
--- a/include/boost/math/tools/detail/rational_horner2_6.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_6.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_7.hpp b/include/boost/math/tools/detail/rational_horner2_7.hpp
index da5b1476a..6f9a85838 100644
--- a/include/boost/math/tools/detail/rational_horner2_7.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_7.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_8.hpp b/include/boost/math/tools/detail/rational_horner2_8.hpp
index b047ad948..33dda23bb 100644
--- a/include/boost/math/tools/detail/rational_horner2_8.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_8.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner2_9.hpp b/include/boost/math/tools/detail/rational_horner2_9.hpp
index 4eed1c430..a9025a890 100644
--- a/include/boost/math/tools/detail/rational_horner2_9.hpp
+++ b/include/boost/math/tools/detail/rational_horner2_9.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -58,7 +58,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -74,7 +74,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -90,7 +90,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -106,7 +106,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_10.hpp b/include/boost/math/tools/detail/rational_horner3_10.hpp
index 1fe94f8e3..b7cec124e 100644
--- a/include/boost/math/tools/detail/rational_horner3_10.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_10.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_11.hpp b/include/boost/math/tools/detail/rational_horner3_11.hpp
index 1a4277a82..579f0e486 100644
--- a/include/boost/math/tools/detail/rational_horner3_11.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_11.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_12.hpp b/include/boost/math/tools/detail/rational_horner3_12.hpp
index 5deb0f374..54300dd08 100644
--- a/include/boost/math/tools/detail/rational_horner3_12.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_12.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_13.hpp b/include/boost/math/tools/detail/rational_horner3_13.hpp
index 6c6857f31..d2fc7b633 100644
--- a/include/boost/math/tools/detail/rational_horner3_13.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_13.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -570,7 +570,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_14.hpp b/include/boost/math/tools/detail/rational_horner3_14.hpp
index 1aadb35de..0b7675f49 100644
--- a/include/boost/math/tools/detail/rational_horner3_14.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_14.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -570,7 +570,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -672,7 +672,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_15.hpp b/include/boost/math/tools/detail/rational_horner3_15.hpp
index 0f79e5b0d..8286caed0 100644
--- a/include/boost/math/tools/detail/rational_horner3_15.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_15.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -570,7 +570,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -672,7 +672,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -782,7 +782,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_16.hpp b/include/boost/math/tools/detail/rational_horner3_16.hpp
index b7c6e96c1..fc823e416 100644
--- a/include/boost/math/tools/detail/rational_horner3_16.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_16.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -570,7 +570,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -672,7 +672,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -782,7 +782,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -900,7 +900,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_17.hpp b/include/boost/math/tools/detail/rational_horner3_17.hpp
index 25328e7ff..cf7f75a70 100644
--- a/include/boost/math/tools/detail/rational_horner3_17.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_17.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -570,7 +570,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -672,7 +672,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -782,7 +782,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -900,7 +900,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1026,7 +1026,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_18.hpp b/include/boost/math/tools/detail/rational_horner3_18.hpp
index 335b895c4..f853ed3e0 100644
--- a/include/boost/math/tools/detail/rational_horner3_18.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_18.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -570,7 +570,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -672,7 +672,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -782,7 +782,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -900,7 +900,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1026,7 +1026,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1160,7 +1160,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_19.hpp b/include/boost/math/tools/detail/rational_horner3_19.hpp
index 22d24403e..d44e22c90 100644
--- a/include/boost/math/tools/detail/rational_horner3_19.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_19.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -570,7 +570,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -672,7 +672,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -782,7 +782,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -900,7 +900,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1026,7 +1026,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1160,7 +1160,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1302,7 +1302,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_2.hpp b/include/boost/math/tools/detail/rational_horner3_2.hpp
index e1dd400ae..bb2e2c4dc 100644
--- a/include/boost/math/tools/detail/rational_horner3_2.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_2.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/include/boost/math/tools/detail/rational_horner3_20.hpp b/include/boost/math/tools/detail/rational_horner3_20.hpp
index f97124afb..967edf083 100644
--- a/include/boost/math/tools/detail/rational_horner3_20.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_20.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -312,7 +312,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -390,7 +390,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 11>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -476,7 +476,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 12>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -570,7 +570,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 13>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -672,7 +672,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 14>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -782,7 +782,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 15>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -900,7 +900,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 16>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1026,7 +1026,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 17>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1160,7 +1160,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 18>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1302,7 +1302,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 19>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -1452,7 +1452,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 20>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_3.hpp b/include/boost/math/tools/detail/rational_horner3_3.hpp
index ab0d029aa..0b410d8bb 100644
--- a/include/boost/math/tools/detail/rational_horner3_3.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_3.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/include/boost/math/tools/detail/rational_horner3_4.hpp b/include/boost/math/tools/detail/rational_horner3_4.hpp
index 147f5d1da..07a9a2c5a 100644
--- a/include/boost/math/tools/detail/rational_horner3_4.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_4.hpp
@@ -12,31 +12,31 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
diff --git a/include/boost/math/tools/detail/rational_horner3_5.hpp b/include/boost/math/tools/detail/rational_horner3_5.hpp
index af1c76f1c..62c76dd50 100644
--- a/include/boost/math/tools/detail/rational_horner3_5.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_5.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_6.hpp b/include/boost/math/tools/detail/rational_horner3_6.hpp
index 05d626ac8..f81a068ac 100644
--- a/include/boost/math/tools/detail/rational_horner3_6.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_6.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_7.hpp b/include/boost/math/tools/detail/rational_horner3_7.hpp
index 2d91a5c50..fea457ccf 100644
--- a/include/boost/math/tools/detail/rational_horner3_7.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_7.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_8.hpp b/include/boost/math/tools/detail/rational_horner3_8.hpp
index 3a6ea4ff0..306e2a41d 100644
--- a/include/boost/math/tools/detail/rational_horner3_8.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_8.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/detail/rational_horner3_9.hpp b/include/boost/math/tools/detail/rational_horner3_9.hpp
index d20149b22..93a3527c1 100644
--- a/include/boost/math/tools/detail/rational_horner3_9.hpp
+++ b/include/boost/math/tools/detail/rational_horner3_9.hpp
@@ -12,37 +12,37 @@
 namespace boost{ namespace math{ namespace tools{ namespace detail{
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(0);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
 {
    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -80,7 +80,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -126,7 +126,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -180,7 +180,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
@@ -242,7 +242,7 @@ BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b,
 }
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
 {
    if((-1 <= x) && (x <= 1))
    {
diff --git a/include/boost/math/tools/rational.hpp b/include/boost/math/tools/rational.hpp
index b65700f62..e3c3e7e33 100644
--- a/include/boost/math/tools/rational.hpp
+++ b/include/boost/math/tools/rational.hpp
@@ -10,9 +10,13 @@
 #pragma once
 #endif
 
-#include <array>
 #include <boost/math/tools/config.hpp>
 #include <boost/math/tools/assert.hpp>
+#include <boost/math/tools/type_traits.hpp>
+
+#ifndef BOOST_MATH_HAS_NVRTC
+#include <array>
+#endif
 
 #if BOOST_MATH_POLY_METHOD == 1
 #  define BOOST_HEADER() <BOOST_MATH_JOIN(boost/math/tools/detail/polynomial_horner1_, BOOST_MATH_MAX_POLY_ORDER).hpp>
@@ -168,7 +172,7 @@ namespace boost{ namespace math{ namespace tools{
 // Forward declaration to keep two phase lookup happy:
 //
 template <class T, class U>
-BOOST_MATH_GPU_ENABLED U evaluate_polynomial(const T* poly, U const& z, std::size_t count) BOOST_MATH_NOEXCEPT(U);
+BOOST_MATH_GPU_ENABLED U evaluate_polynomial(const T* poly, U const& z, BOOST_MATH_SIZE_T count) BOOST_MATH_NOEXCEPT(U);
 
 namespace detail{
 
@@ -186,7 +190,7 @@ BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp
 // the loop expanded versions above:
 //
 template <class T, class U>
-BOOST_MATH_GPU_ENABLED inline U evaluate_polynomial(const T* poly, U const& z, std::size_t count) BOOST_MATH_NOEXCEPT(U)
+BOOST_MATH_GPU_ENABLED inline U evaluate_polynomial(const T* poly, U const& z, BOOST_MATH_SIZE_T count) BOOST_MATH_NOEXCEPT(U)
 {
    BOOST_MATH_ASSERT(count > 0);
    U sum = static_cast<U>(poly[count - 1]);
@@ -201,64 +205,70 @@ BOOST_MATH_GPU_ENABLED inline U evaluate_polynomial(const T* poly, U const& z, s
 // Compile time sized polynomials, just inline forwarders to the
 // implementations above:
 //
-template <std::size_t N, class T, class V>
+template <BOOST_MATH_SIZE_T N, class T, class V>
 BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial(const T(&a)[N], const V& val) BOOST_MATH_NOEXCEPT(V)
 {
-   typedef std::integral_constant<int, N> tag_type;
+   typedef boost::math::integral_constant<int, N> tag_type;
    return detail::evaluate_polynomial_c_imp(static_cast<const T*>(a), val, static_cast<tag_type const*>(nullptr));
 }
 
-template <std::size_t N, class T, class V>
+#ifndef BOOST_MATH_HAS_NVRTC
+template <BOOST_MATH_SIZE_T N, class T, class V>
 BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial(const std::array<T,N>& a, const V& val) BOOST_MATH_NOEXCEPT(V)
 {
-   typedef std::integral_constant<int, N> tag_type;
+   typedef boost::math::integral_constant<int, N> tag_type;
    return detail::evaluate_polynomial_c_imp(static_cast<const T*>(a.data()), val, static_cast<tag_type const*>(nullptr));
 }
+#endif
 //
 // Even polynomials are trivial: just square the argument!
 //
 template <class T, class U>
-BOOST_MATH_GPU_ENABLED inline U evaluate_even_polynomial(const T* poly, U z, std::size_t count) BOOST_MATH_NOEXCEPT(U)
+BOOST_MATH_GPU_ENABLED inline U evaluate_even_polynomial(const T* poly, U z, BOOST_MATH_SIZE_T count) BOOST_MATH_NOEXCEPT(U)
 {
    return evaluate_polynomial(poly, U(z*z), count);
 }
 
-template <std::size_t N, class T, class V>
+template <BOOST_MATH_SIZE_T N, class T, class V>
 BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_even_polynomial(const T(&a)[N], const V& z) BOOST_MATH_NOEXCEPT(V)
 {
    return evaluate_polynomial(a, V(z*z));
 }
 
-template <std::size_t N, class T, class V>
+#ifndef BOOST_MATH_HAS_NVRTC
+template <BOOST_MATH_SIZE_T N, class T, class V>
 BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_even_polynomial(const std::array<T,N>& a, const V& z) BOOST_MATH_NOEXCEPT(V)
 {
    return evaluate_polynomial(a, V(z*z));
 }
+#endif
 //
 // Odd polynomials come next:
 //
 template <class T, class U>
-BOOST_MATH_GPU_ENABLED inline U evaluate_odd_polynomial(const T* poly, U z, std::size_t count) BOOST_MATH_NOEXCEPT(U)
+BOOST_MATH_GPU_ENABLED inline U evaluate_odd_polynomial(const T* poly, U z, BOOST_MATH_SIZE_T count) BOOST_MATH_NOEXCEPT(U)
 {
    return poly[0] + z * evaluate_polynomial(poly+1, U(z*z), count-1);
 }
 
-template <std::size_t N, class T, class V>
+template <BOOST_MATH_SIZE_T N, class T, class V>
 BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_odd_polynomial(const T(&a)[N], const V& z) BOOST_MATH_NOEXCEPT(V)
 {
-   typedef std::integral_constant<int, N-1> tag_type;
+   typedef boost::math::integral_constant<int, N-1> tag_type;
    return a[0] + z * detail::evaluate_polynomial_c_imp(static_cast<const T*>(a) + 1, V(z*z), static_cast<tag_type const*>(nullptr));
 }
 
-template <std::size_t N, class T, class V>
+#ifndef BOOST_MATH_HAS_NVRTC
+template <BOOST_MATH_SIZE_T N, class T, class V>
 BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_odd_polynomial(const std::array<T,N>& a, const V& z) BOOST_MATH_NOEXCEPT(V)
 {
-   typedef std::integral_constant<int, N-1> tag_type;
+   typedef boost::math::integral_constant<int, N-1> tag_type;
    return a[0] + z * detail::evaluate_polynomial_c_imp(static_cast<const T*>(a.data()) + 1, V(z*z), static_cast<tag_type const*>(nullptr));
 }
+#endif
 
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED V evaluate_rational(const T* num, const U* denom, const V& z_, std::size_t count) BOOST_MATH_NOEXCEPT(V);
+BOOST_MATH_GPU_ENABLED V evaluate_rational(const T* num, const U* denom, const V& z_, BOOST_MATH_SIZE_T count) BOOST_MATH_NOEXCEPT(V);
 
 namespace detail{
 
@@ -278,7 +288,7 @@ BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(c
 // in our Lanczos code for example.
 //
 template <class T, class U, class V>
-BOOST_MATH_GPU_ENABLED V evaluate_rational(const T* num, const U* denom, const V& z_, std::size_t count) BOOST_MATH_NOEXCEPT(V)
+BOOST_MATH_GPU_ENABLED V evaluate_rational(const T* num, const U* denom, const V& z_, BOOST_MATH_SIZE_T count) BOOST_MATH_NOEXCEPT(V)
 {
    V z(z_);
    V s1, s2;
@@ -310,17 +320,19 @@ BOOST_MATH_GPU_ENABLED V evaluate_rational(const T* num, const U* denom, const V
    return s1 / s2;
 }
 
-template <std::size_t N, class T, class U, class V>
+template <BOOST_MATH_SIZE_T N, class T, class U, class V>
 BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_rational(const T(&a)[N], const U(&b)[N], const V& z) BOOST_MATH_NOEXCEPT(V)
 {
-   return detail::evaluate_rational_c_imp(a, b, z, static_cast<const std::integral_constant<int, N>*>(nullptr));
+   return detail::evaluate_rational_c_imp(a, b, z, static_cast<const boost::math::integral_constant<int, N>*>(nullptr));
 }
 
-template <std::size_t N, class T, class U, class V>
+#ifndef BOOST_MATH_HAS_NVRTC
+template <BOOST_MATH_SIZE_T N, class T, class U, class V>
 BOOST_MATH_GPU_ENABLED BOOST_MATH_GPU_ENABLED inline V evaluate_rational(const std::array<T,N>& a, const std::array<U,N>& b, const V& z) BOOST_MATH_NOEXCEPT(V)
 {
-   return detail::evaluate_rational_c_imp(a.data(), b.data(), z, static_cast<std::integral_constant<int, N>*>(nullptr));
+   return detail::evaluate_rational_c_imp(a.data(), b.data(), z, static_cast<boost::math::integral_constant<int, N>*>(nullptr));
 }
+#endif
 
 } // namespace tools
 } // namespace math
diff --git a/tools/generate_rational_code.cpp b/tools/generate_rational_code.cpp
index 92b7da9a1..20ffde850 100644
--- a/tools/generate_rational_code.cpp
+++ b/tools/generate_rational_code.cpp
@@ -40,13 +40,13 @@ void print_polynomials(int max_order)
          "#define BOOST_MATH_TOOLS_POLY_EVAL_" << i << "_HPP\n\n"
          "namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*)\n"
          "{\n"
          "   return static_cast<V>(0);\n"
          "}\n"
          "\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*)\n"
          "{\n"
          "   return static_cast<V>(a[0]);\n"
          "}\n\n";
@@ -55,7 +55,7 @@ void print_polynomials(int max_order)
       {
          ofs << 
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, " << order << ">*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, " << order << ">*)\n"
          "{\n"
          "   return static_cast<V>(";
          
@@ -90,28 +90,28 @@ void print_polynomials(int max_order)
          "#define BOOST_MATH_TOOLS_POLY_EVAL_" << i << "_HPP\n\n"
          "namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*)\n"
          "{\n"
          "   return static_cast<V>(0);\n"
          "}\n"
          "\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*)\n"
          "{\n"
          "   return static_cast<V>(a[0]);\n"
          "}\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*)\n"
          "{\n"
          "   return static_cast<V>(a[1] * x + a[0]);\n"
          "}\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*)\n"
          "{\n"
          "   return static_cast<V>((a[2] * x + a[1]) * x + a[0]);\n"
          "}\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*)\n"
          "{\n"
          "   return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);\n"
          "}\n\n";
@@ -120,7 +120,7 @@ void print_polynomials(int max_order)
       {
          ofs << 
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, " << order << ">*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, " << order << ">*)\n"
          "{\n"
          "   V x2 = x * x;\n"
          "   return static_cast<V>(";
@@ -186,28 +186,28 @@ void print_polynomials(int max_order)
          "#define BOOST_MATH_TOOLS_POLY_EVAL_" << i << "_HPP\n\n"
          "namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const std::integral_constant<int, 0>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T*, const V&, const boost::math::integral_constant<int, 0>*)\n"
          "{\n"
          "   return static_cast<V>(0);\n"
          "}\n"
          "\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const std::integral_constant<int, 1>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V&, const boost::math::integral_constant<int, 1>*)\n"
          "{\n"
          "   return static_cast<V>(a[0]);\n"
          "}\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 2>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 2>*)\n"
          "{\n"
          "   return static_cast<V>(a[1] * x + a[0]);\n"
          "}\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 3>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 3>*)\n"
          "{\n"
          "   return static_cast<V>((a[2] * x + a[1]) * x + a[0]);\n"
          "}\n\n"
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, 4>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, 4>*)\n"
          "{\n"
          "   return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);\n"
          "}\n\n";
@@ -216,7 +216,7 @@ void print_polynomials(int max_order)
       {
          ofs << 
          "template <class T, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const std::integral_constant<int, " << order << ">*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_polynomial_c_imp(const T* a, const V& x, const boost::math::integral_constant<int, " << order << ">*)\n"
          "{\n"
          "   V x2 = x * x;\n"
          "   V t[2];\n";
@@ -281,13 +281,13 @@ void print_rationals(int max_order)
          "#define BOOST_MATH_TOOLS_POLY_RAT_" << i << "_HPP\n\n"
          "namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*)\n"
          "{\n"
          "   return static_cast<V>(0);\n"
          "}\n"
          "\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*)\n"
          "{\n"
          "   return static_cast<V>(a[0]) / static_cast<V>(b[0]);\n"
          "}\n\n";
@@ -296,7 +296,7 @@ void print_rationals(int max_order)
       {
          ofs << 
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, " << order << ">*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, " << order << ">*)\n"
          "{\n"
          "   if((-1 <= x) && (x <= 1))\n"
          "     return static_cast<V>((";
@@ -361,28 +361,28 @@ void print_rationals(int max_order)
          "#define BOOST_MATH_TOOLS_RAT_EVAL_" << i << "_HPP\n\n"
          "namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*)\n"
          "{\n"
          "   return static_cast<V>(0);\n"
          "}\n"
          "\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*)\n"
          "{\n"
          "   return static_cast<V>(a[0]) / static_cast<V>(b[0]);\n"
          "}\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*)\n"
          "{\n"
          "   return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));\n"
          "}\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*)\n"
          "{\n"
          "   return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));\n"
          "}\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*)\n"
          "{\n"
          "   return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));\n"
          "}\n\n";
@@ -391,7 +391,7 @@ void print_rationals(int max_order)
       {
          ofs << 
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, " << order << ">*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, " << order << ">*)\n"
          "{\n"
          "   if((-1 <= x) && (x <= 1))\n   {\n"
          "      V x2 = x * x;\n"
@@ -577,28 +577,28 @@ void print_rationals(int max_order)
          "#define BOOST_MATH_TOOLS_RAT_EVAL_" << i << "_HPP\n\n"
          "namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::math::integral_constant<int, 0>*)\n"
          "{\n"
          "   return static_cast<V>(0);\n"
          "}\n"
          "\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::math::integral_constant<int, 1>*)\n"
          "{\n"
          "   return static_cast<V>(a[0]) / static_cast<V>(b[0]);\n"
          "}\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 2>*)\n"
          "{\n"
          "   return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));\n"
          "}\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 3>*)\n"
          "{\n"
          "   return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));\n"
          "}\n\n"
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, 4>*)\n"
          "{\n"
          "   return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));\n"
          "}\n\n";
@@ -607,7 +607,7 @@ void print_rationals(int max_order)
       {
          ofs << 
          "template <class T, class U, class V>\n"
-         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, " << order << ">*)\n"
+         "BOOST_MATH_GPU_ENABLED inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::math::integral_constant<int, " << order << ">*)\n"
          "{\n"
          "   if((-1 <= x) && (x <= 1))\n   {\n"
          "      V x2 = x * x;\n"