From 0b2aa546dd4d0b895b592df6da53b96953b3761e Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Thu, 23 May 2024 19:05:39 +0100
Subject: [PATCH 01/13] Prevent passing denormals in calculation. Refs
 https://github.com/scipy/scipy/issues/20693

---
 include/boost/math/distributions/non_central_beta.hpp | 4 ++--
 include/boost/math/distributions/non_central_t.hpp    | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/include/boost/math/distributions/non_central_beta.hpp b/include/boost/math/distributions/non_central_beta.hpp
index 33d9150572..2361b58298 100644
--- a/include/boost/math/distributions/non_central_beta.hpp
+++ b/include/boost/math/distributions/non_central_beta.hpp
@@ -63,7 +63,7 @@ namespace boost
                ? detail::ibeta_imp(T(a + k), b, x, pol, false, true, &xterm)
                : detail::ibeta_imp(b, T(a + k), y, pol, true, true, &xterm);
 
-            while (beta * pois == 0)
+            while (beta * pois < tools::min_value<T>())
             {
                if ((k == 0) || (pois == 0))
                   return init_val;
@@ -554,7 +554,7 @@ namespace boost
                ibeta_derivative(a + k, b, x, pol)
                : ibeta_derivative(b, a + k, y, pol);
 
-            while (beta * pois == 0)
+            while (beta * pois < tools::min_value<T>())
             {
                if ((k == 0) || (pois == 0))
                   return 0;  // Nothing else we can do!
diff --git a/include/boost/math/distributions/non_central_t.hpp b/include/boost/math/distributions/non_central_t.hpp
index 59cb5d14d8..4841b9d832 100644
--- a/include/boost/math/distributions/non_central_t.hpp
+++ b/include/boost/math/distributions/non_central_t.hpp
@@ -59,7 +59,7 @@ namespace boost
                ? detail::ibeta_imp(T(k + 1), T(v / 2), x, pol, false, true, &xterm)
                : detail::ibeta_imp(T(v / 2), T(k + 1), y, pol, true, true, &xterm);
 
-            while (beta * pois == 0)
+            while (beta * pois < tools::min_value<T>())
             {
                if ((k == 0) || (pois == 0))
                   return init_val;
@@ -419,7 +419,7 @@ namespace boost
                : ibeta_derivative(n / 2, T(k + 1), y, pol);
             BOOST_MATH_INSTRUMENT_VARIABLE(xterm);
 
-            while (xterm * pois == 0)
+            while (fabs(xterm * pois) < tools::min_value<T>())
             {
                if (k == 0)
                   return init_val;

From 5e7fec6a11b06ee89eddabc293887e3bb1446120 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Fri, 24 May 2024 10:22:35 +0100
Subject: [PATCH 02/13] Poisson part can be negative, take fabs of product when
 checking for small values.

---
 include/boost/math/distributions/non_central_beta.hpp | 4 ++--
 include/boost/math/distributions/non_central_t.hpp    | 2 +-
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/include/boost/math/distributions/non_central_beta.hpp b/include/boost/math/distributions/non_central_beta.hpp
index 2361b58298..592ac19517 100644
--- a/include/boost/math/distributions/non_central_beta.hpp
+++ b/include/boost/math/distributions/non_central_beta.hpp
@@ -63,7 +63,7 @@ namespace boost
                ? detail::ibeta_imp(T(a + k), b, x, pol, false, true, &xterm)
                : detail::ibeta_imp(b, T(a + k), y, pol, true, true, &xterm);
 
-            while (beta * pois < tools::min_value<T>())
+            while (fabs(beta * pois) < tools::min_value<T>())
             {
                if ((k == 0) || (pois == 0))
                   return init_val;
@@ -554,7 +554,7 @@ namespace boost
                ibeta_derivative(a + k, b, x, pol)
                : ibeta_derivative(b, a + k, y, pol);
 
-            while (beta * pois < tools::min_value<T>())
+            while (fabs(beta * pois) < tools::min_value<T>())
             {
                if ((k == 0) || (pois == 0))
                   return 0;  // Nothing else we can do!
diff --git a/include/boost/math/distributions/non_central_t.hpp b/include/boost/math/distributions/non_central_t.hpp
index 4841b9d832..ca3e9d53f2 100644
--- a/include/boost/math/distributions/non_central_t.hpp
+++ b/include/boost/math/distributions/non_central_t.hpp
@@ -59,7 +59,7 @@ namespace boost
                ? detail::ibeta_imp(T(k + 1), T(v / 2), x, pol, false, true, &xterm)
                : detail::ibeta_imp(T(v / 2), T(k + 1), y, pol, true, true, &xterm);
 
-            while (beta * pois < tools::min_value<T>())
+            while (fabs(beta * pois) < tools::min_value<T>())
             {
                if ((k == 0) || (pois == 0))
                   return init_val;

From f28c7764f12143732a7a52241d07141d2e4916df Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Thu, 30 May 2024 12:29:35 +0100
Subject: [PATCH 03/13] Add non central t PDF integral tests. Fix exp_sinh
 issues so that it does actually find the integral.

---
 .../quadrature/detail/exp_sinh_detail.hpp     | 20 ++++++++-
 test/exp_sinh_quadrature_test.cpp             | 38 +++++++++++++++++
 test/tanh_sinh_quadrature_test.cpp            | 42 ++++++++++++++++++-
 3 files changed, 97 insertions(+), 3 deletions(-)

diff --git a/include/boost/math/quadrature/detail/exp_sinh_detail.hpp b/include/boost/math/quadrature/detail/exp_sinh_detail.hpp
index e829fa3285..d0438a8236 100644
--- a/include/boost/math/quadrature/detail/exp_sinh_detail.hpp
+++ b/include/boost/math/quadrature/detail/exp_sinh_detail.hpp
@@ -198,13 +198,29 @@ auto exp_sinh_detail<Real, Policy>::integrate(const F& f, Real* error, Real* L1,
         if (!have_first_j && (I1_last == I1))
         {
            // No change to the sum, disregard these values on the LHS:
-           min_abscissa = m_abscissas[1][i];
-           first_j = i;
+           if ((i < m_abscissas[1].size() - 1) && (m_abscissas[1][i + 1] > max_abscissa))
+           {
+              // The summit is so high, that we found nothing in this row which added to the integral!!
+              have_first_j = true;
+           }
+           else
+           {
+              min_abscissa = m_abscissas[1][i];
+              first_j = i;
+           }
         }
         else
            have_first_j = true;
     }
 
+    if (I0 == static_cast<Real>(0))
+    {
+       // We failed to find anything, is the integral zero, or have we just not found it yet?
+       // We'll try one more level, if that still finds nothing then it'll terminate.
+       min_abscissa = 0;
+       max_abscissa = boost::math::tools::max_value<Real>();
+    }
+
     I1 *= half<Real>();
     L1_I1 *= half<Real>();
     Real err = abs(I0 - I1);
diff --git a/test/exp_sinh_quadrature_test.cpp b/test/exp_sinh_quadrature_test.cpp
index d39ec4c5dc..7c958d5d8e 100644
--- a/test/exp_sinh_quadrature_test.cpp
+++ b/test/exp_sinh_quadrature_test.cpp
@@ -573,6 +573,37 @@ void test_complex_exponential_integral_E1(){
     }
 }
 
+template <class T>
+void test_non_central_t()
+{
+   //
+   // Bug case from the non-central t distribution:
+   //
+   using std::pow;
+   using std::exp;
+   using std::sqrt;
+
+   std::cout << "Testing non-central T PDF integral" << std::endl;
+
+   T x = -1.882352352142334;
+   T v = 77.384613037109375;
+   T mu = 8.1538467407226562;
+   T expected = static_cast<T>(4.5098555913703146875364186893655197e+49L);
+
+   boost::math::quadrature::exp_sinh<T> integrator;
+   T err;
+   T L1;
+   std::size_t levels;
+   T integral = integrator.integrate([&x, v, mu](T y)
+      {
+         return pow(y, v) * exp(boost::math::pow<2>((y - mu * x / sqrt(x * x + v))) / -2);
+      },
+      boost::math::tools::root_epsilon<T>(), &err, &L1, &levels);
+
+   T tol = 100 * boost::math::tools::epsilon<T>();
+   BOOST_CHECK_CLOSE_FRACTION(integral, expected, tol);
+}
+
 
 BOOST_AUTO_TEST_CASE(exp_sinh_quadrature_test)
 {
@@ -596,11 +627,13 @@ BOOST_AUTO_TEST_CASE(exp_sinh_quadrature_test)
     test_right_limit_infinite<std::float32_t>();
     test_nr_examples<std::float32_t>();
     test_crc<std::float32_t>();
+    //test_non_central_t<float32_t>();
 #else
     test_left_limit_infinite<float>();
     test_right_limit_infinite<float>();
     test_nr_examples<float>();
     test_crc<float>();
+    //test_non_central_t<float>();
 #endif
 
 #endif
@@ -611,11 +644,13 @@ BOOST_AUTO_TEST_CASE(exp_sinh_quadrature_test)
     test_right_limit_infinite<std::float64_t>();
     test_nr_examples<std::float64_t>();
     test_crc<std::float64_t>();
+    test_non_central_t<float64_t>();
 #else
     test_left_limit_infinite<double>();
     test_right_limit_infinite<double>();
     test_nr_examples<double>();
     test_crc<double>();
+    test_non_central_t<double>();
 #endif
 
 #endif
@@ -626,6 +661,7 @@ BOOST_AUTO_TEST_CASE(exp_sinh_quadrature_test)
     test_right_limit_infinite<long double>();
     test_nr_examples<long double>();
     test_crc<long double>();
+    test_non_central_t<long double>();
 #endif
 #endif
 #endif
@@ -634,6 +670,7 @@ BOOST_AUTO_TEST_CASE(exp_sinh_quadrature_test)
     test_right_limit_infinite<cpp_bin_float_quad>();
     test_nr_examples<cpp_bin_float_quad>();
     test_crc<cpp_bin_float_quad>();
+    test_non_central_t<cpp_bin_float_quad>();
 #endif
 
 #if !defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS) && !defined(BOOST_MATH_NO_REAL_CONCEPT_TESTS)
@@ -642,6 +679,7 @@ BOOST_AUTO_TEST_CASE(exp_sinh_quadrature_test)
     test_right_limit_infinite<boost::math::concepts::real_concept>();
     test_nr_examples<boost::math::concepts::real_concept>();
     test_crc<boost::math::concepts::real_concept>();
+    test_non_central_t<boost::math::concepts::real_concept>();
 #endif
 #endif
 #if defined(TEST6) && defined(BOOST_MATH_RUN_MP_TESTS)
diff --git a/test/tanh_sinh_quadrature_test.cpp b/test/tanh_sinh_quadrature_test.cpp
index ceccb29ebb..534abfdfa2 100644
--- a/test/tanh_sinh_quadrature_test.cpp
+++ b/test/tanh_sinh_quadrature_test.cpp
@@ -883,6 +883,41 @@ void test_complex()
    }
 }
 
+template <class T>
+void test_non_central_t()
+{
+   //
+   // Bug case from the non-central t distribution:
+   //
+   using std::pow;
+   using std::exp;
+   using std::sqrt;
+
+   std::cout << "Testing non-central T PDF integral" << std::endl;
+
+   T x = -1.882352352142334;
+   T v = 77.384613037109375;
+   T mu = 8.1538467407226562;
+   T expected = static_cast<T>(4.5098555913703146875364186893655197e+49L);
+
+   T left = 0;
+   T right = std::numeric_limits<T>::has_infinity ? std::numeric_limits<T>::infinity() : boost::math::tools::max_value<T>();
+
+   boost::math::quadrature::tanh_sinh<T> integrator;
+   T err;
+   T L1;
+   std::size_t levels;
+   T integral = integrator.integrate([&x, v, mu](T y)
+      {
+         return pow(y, v) * exp(boost::math::pow<2>((y - mu * x / sqrt(x * x + v))) / -2);
+      },
+      left, right,
+      boost::math::tools::root_epsilon<T>(), &err, &L1, &levels);
+
+   T tol = 100 * boost::math::tools::epsilon<T>();
+   BOOST_CHECK_CLOSE_FRACTION(integral, expected, tol);
+}
+
 
 BOOST_AUTO_TEST_CASE(tanh_sinh_quadrature_test)
 {
@@ -944,6 +979,7 @@ BOOST_AUTO_TEST_CASE(tanh_sinh_quadrature_test)
     test_early_termination<double>();
     test_sf<double>();
     test_2_arg<double>();
+    test_non_central_t<double>();
 #endif
 #ifdef TEST2A
    #ifndef BOOST_MATH_STANDALONE
@@ -967,6 +1003,7 @@ BOOST_AUTO_TEST_CASE(tanh_sinh_quadrature_test)
     test_early_termination<long double>();
     test_sf<long double>();
     test_2_arg<long double>();
+    test_non_central_t<long double>();
 #endif
 #ifdef TEST3A
    #ifndef BOOST_MATH_STANDALONE
@@ -991,7 +1028,8 @@ BOOST_AUTO_TEST_CASE(tanh_sinh_quadrature_test)
     test_crc<cpp_bin_float_quad>();
     test_sf<cpp_bin_float_quad>();
     test_2_arg<cpp_bin_float_quad>();
-   #endif
+    test_non_central_t<cpp_bin_float_quad>();
+#endif
 #endif
 #ifdef TEST5
    #ifdef BOOST_MATH_RUN_MP_TESTS
@@ -1017,6 +1055,7 @@ BOOST_AUTO_TEST_CASE(tanh_sinh_quadrature_test)
     test_early_termination<boost::math::concepts::real_concept>();
     test_sf<boost::math::concepts::real_concept>();
     test_2_arg<boost::math::concepts::real_concept>();
+    test_non_central_t<boost::math::concepts::real_concept>();
 #endif
 #ifdef TEST6A
     test_crc<boost::math::concepts::real_concept>();
@@ -1044,6 +1083,7 @@ BOOST_AUTO_TEST_CASE(tanh_sinh_quadrature_test)
     test_crc<boost::multiprecision::float128>();
     test_sf<boost::multiprecision::float128>();
     test_2_arg<boost::multiprecision::float128>();
+    test_non_central_t<boost::multiprecision::float128>();
 
 #endif
 #ifdef TEST9

From 9e6f2b1b401c28a7eed0be4aa816027646a14a4b Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Fri, 31 May 2024 11:54:52 +0100
Subject: [PATCH 04/13] Update Non central T PDF: Lot's more tests, especially
 in the tails. Added Hypergeometric and Integration methods as fallbacks.

---
 .../math/distributions/non_central_beta.hpp   |  17 ++-
 .../math/distributions/non_central_t.hpp      | 107 +++++++++++++++---
 test/test_nc_t.cpp                            |  14 +++
 test/test_nc_t.hpp                            |  30 +++++
 tools/non_central_t_pdf_data.cpp              |  92 +++++++++++++++
 5 files changed, 242 insertions(+), 18 deletions(-)
 create mode 100644 tools/non_central_t_pdf_data.cpp

diff --git a/include/boost/math/distributions/non_central_beta.hpp b/include/boost/math/distributions/non_central_beta.hpp
index 592ac19517..66b12e870a 100644
--- a/include/boost/math/distributions/non_central_beta.hpp
+++ b/include/boost/math/distributions/non_central_beta.hpp
@@ -91,7 +91,7 @@ namespace boost
             {
                T term = beta * pois;
                sum += term;
-               if(((fabs(term/sum) < errtol) && (last_term >= term)) || (term == 0))
+               if(((fabs(term/sum) < errtol) && (fabs(last_term) >= fabs(term))) || (term == 0))
                {
                   count = k - i;
                   break;
@@ -106,6 +106,7 @@ namespace boost
                
                last_term = term;
             }
+            last_term = 0;
             for(auto i = k + 1; ; ++i)
             {
                poisf *= l2 / i;
@@ -114,10 +115,11 @@ namespace boost
 
                T term = poisf * betaf;
                sum += term;
-               if((fabs(term/sum) < errtol) || (term == 0))
+               if(((fabs(term/sum) < errtol) && (fabs(last_term) >= fabs(term))) || (term == 0))
                {
                   break;
                }
+               last_term = term;
                if(static_cast<std::uintmax_t>(count + i - k) > max_iter)
                {
                   return policies::raise_evaluation_error("cdf(non_central_beta_distribution<%1%>, %1%)", "Series did not converge, closest value was %1%", sum, pol); // LCOV_EXCL_LINE
@@ -579,15 +581,19 @@ namespace boost
             // Stable backwards recursion first:
             //
             std::uintmax_t count = k;
+            T ratio = 0;
+            T old_ratio = 0;
             for(auto i = k; i >= 0; --i)
             {
                T term = beta * pois;
                sum += term;
-               if((fabs(term/sum) < errtol) || (term == 0))
+               ratio = fabs(term / sum);
+               if(((ratio < errtol) && (ratio < old_ratio)) || (term == 0))
                {
                   count = k - i;
                   break;
                }
+               ratio = old_ratio;
                pois *= i / l2;
 
                if (a + b + i != 1)
@@ -595,6 +601,7 @@ namespace boost
                   beta *= (a + i - 1) / (x * (a + i + b - 1));
                }
             }
+            old_ratio = 0;
             for(auto i = k + 1; ; ++i)
             {
                poisf *= l2 / i;
@@ -602,10 +609,12 @@ namespace boost
 
                T term = poisf * betaf;
                sum += term;
-               if((fabs(term/sum) < errtol) || (term == 0))
+               ratio = fabs(term / sum);
+               if(((ratio < errtol) && (ratio < old_ratio)) || (term == 0))
                {
                   break;
                }
+               old_ratio = ratio;
                if(static_cast<std::uintmax_t>(count + i - k) > max_iter)
                {
                   return policies::raise_evaluation_error("pdf(non_central_beta_distribution<%1%>, %1%)", "Series did not converge, closest value was %1%", sum, pol); // LCOV_EXCL_LINE
diff --git a/include/boost/math/distributions/non_central_t.hpp b/include/boost/math/distributions/non_central_t.hpp
index ca3e9d53f2..d3d58cd206 100644
--- a/include/boost/math/distributions/non_central_t.hpp
+++ b/include/boost/math/distributions/non_central_t.hpp
@@ -16,6 +16,8 @@
 #include <boost/math/distributions/students_t.hpp>
 #include <boost/math/distributions/detail/generic_quantile.hpp> // quantile
 #include <boost/math/special_functions/trunc.hpp>
+#include <boost/math/special_functions/detail/hypergeometric_series.hpp>
+#include <boost/math/quadrature/exp_sinh.hpp>
 
 namespace boost
 {
@@ -390,6 +392,60 @@ namespace boost
                function);
          }
 
+         template <class T, class Policy>
+         T non_central_t_pdf_integral(T x, T v, T mu, const Policy& pol)
+         {
+            BOOST_MATH_STD_USING
+            boost::math::quadrature::exp_sinh<T, Policy> integrator;
+            T integral = pow(v, v / 2) * exp(-v * mu * mu / (2 * (x * x + v)));
+            if (integral != 0)
+            {
+               integral *= integrator.integrate([&x, v, mu](T y) 
+                  {
+                     T p;
+                     if (v * log(y) < tools::log_max_value<T>())
+                        p = pow(y, v) * exp(boost::math::pow<2>((y - mu * x / sqrt(x * x + v))) / -2);
+                     else
+                        p = exp(log(y) * v + boost::math::pow<2>((y - mu * x / sqrt(x * x + v))) / -2);
+                     return p; 
+                  });
+            }
+            integral /= boost::math::constants::root_pi<T>() * boost::math::tgamma(v / 2, pol) * pow(T(2), (v - 1) / 2) * pow(x * x + v, (v + 1) / 2);
+            return integral;
+         }
+
+         template <class T, class Policy>
+         T non_central_t_pdf_hypergeometric(T x, T v, T mu, const Policy& pol)
+         {
+            BOOST_MATH_STD_USING
+            long long scale = 0;
+            const char* function = "non central T PDF";
+            //
+            // We only call this routine when we know that the series form of 1F1 is cheap to evaluate,
+            // so no need to call the whole 1F1 function, just the series will do:
+            //
+            T Av = hypergeometric_1F1_generic_series((v + 1) / 2, boost::math::constants::half<T>(), mu * mu * x * x / (2 * (x * x + v)), pol, scale, function);
+            Av = ldexp(Av, static_cast<int>(scale));
+            scale = 0;
+            T Bv = hypergeometric_1F1_generic_series(v / 2 + T(1), T(3) / 2, mu * mu * x * x / (2 * (x * x + v)), pol, scale, function);
+            Bv = ldexp(Bv, static_cast<int>(scale));
+            Bv *= boost::math::tgamma_delta_ratio(v / 2 + T(1), -constants::half<T>(), pol);
+            Bv *= boost::math::constants::root_two<T>() * mu * x / sqrt(x * x + v);
+
+            T tolerance = tools::root_epsilon<T>() * Av * 4;
+            Av += Bv;
+
+            if (Av < tolerance)
+            {
+               // More than half the digits have cancelled, fall back to the integral method:
+               return non_central_t_pdf_integral(x, v, mu, pol);
+            }
+
+            Av *= exp(-mu * mu / 2) * pow(1 + x * x / v, -(v + 1) / 2) * boost::math::tgamma_delta_ratio(v / 2 + constants::half<T>(), -constants::half<T>(), pol);
+            Av /= sqrt(v) * boost::math::constants::root_pi<T>();
+            return Av;
+         }
+
          template <class T, class Policy>
          T non_central_t2_pdf(T n, T delta, T x, T y, const Policy& pol, T init_val)
          {
@@ -462,15 +518,18 @@ namespace boost
                }
             }
             BOOST_MATH_INSTRUMENT_VARIABLE(sum);
+            old_ratio = 0;
             for(auto i = k + 1; ; ++i)
             {
                poisf *= d2 / (i + 0.5f);
                xtermf *= (x * (n / 2 + i)) / (i);
                T term = poisf * xtermf;
                sum += term;
-               if((fabs(term/sum) < errtol) || (term == 0))
+               T ratio = fabs(term / sum);
+               if(((ratio < errtol) && (ratio < old_ratio)) || (term == 0))
                   break;
                ++count;
+               old_ratio = ratio;
                if(count > max_iter)
                {
                   return policies::raise_evaluation_error("pdf(non_central_t_distribution<%1%>, %1%)", "Series did not converge, closest value was %1%", sum, pol); // LCOV_EXCL_LINE
@@ -489,14 +548,7 @@ namespace boost
                normal_distribution<T, Policy> norm(delta, 1);
                return pdf(norm, t);
             }
-            //
-            // Otherwise, for t < 0 we have to use the reflection formula:
-            if(t < 0)
-            {
-               t = -t;
-               delta = -delta;
-            }
-            if(t * t == 0)
+            if(t * t < tools::epsilon<T>())
             {
                //
                // Handle this as a special case, using the formula
@@ -527,13 +579,30 @@ namespace boost
                return pdf(students_t_distribution<T, Policy>(n), t - delta);
             }
             //
+            // Figure out if the hypergeometric formula will be efficient or not, 
+            // based on where the summit of the series.
+            //
+            T a = (n + 1) / 2;
+            T x = delta * delta * t * t / (2 * (t * t + n));
+            T summit = (sqrt(x * (4 * a + x)) + x) / 2;
+            if (summit < 40)
+               return non_central_t_pdf_hypergeometric(t, n, delta, pol);
+            // 
+            // Otherwise, for t < 0 we have to use the reflection formula:
+            //
+            if (t < 0)
+            {
+               t = -t;
+               delta = -delta;
+            }
+            //
             // x and y are the corresponding random
             // variables for the noncentral beta distribution,
             // with y = 1 - x:
             //
-            T x = t * t / (n + t * t);
+            x = t * t / (n + t * t);
             T y = n / (n + t * t);
-            T a = 0.5f;
+            a = 0.5f;
             T b = n / 2;
             T d2 = delta * delta;
             //
@@ -543,12 +612,22 @@ namespace boost
             BOOST_MATH_INSTRUMENT_VARIABLE(dt);
             T result = non_central_beta_pdf(a, b, d2, x, y, pol);
             BOOST_MATH_INSTRUMENT_VARIABLE(result);
-            T tol = tools::epsilon<T>() * result * 500;
+            T tol = tools::root_epsilon<T>() * result;
             result = non_central_t2_pdf(n, delta, x, y, pol, result);
             BOOST_MATH_INSTRUMENT_VARIABLE(result);
-            if(result <= tol)
-               result = 0;
             result *= dt;
+            if (result <= tol)
+            {
+               // More than half the digits in the result have cancelled, 
+               // Try direct integration... super slow but reliable as far as we can tell...
+               if (delta < 0)
+               {
+                  // reflect back:
+                  delta = -delta;
+                  t = -t;
+               }
+               result = non_central_t_pdf_integral(t, n, delta, pol);
+            }
             return result;
          }
 
diff --git a/test/test_nc_t.cpp b/test/test_nc_t.cpp
index d9a8d4ed77..8a12635de7 100644
--- a/test/test_nc_t.cpp
+++ b/test/test_nc_t.cpp
@@ -113,6 +113,20 @@ void expected_results()
       largest_type,                     // test type(s)
       "[^|]*",                          // test data group
       "[^|]*", 400, 100);               // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      "double",                         // test type(s)
+      "[^|]*PDF",                  // test data group
+      "[^|]*", static_cast<std::uintmax_t>(1 / boost::math::tools::root_epsilon<double>()), static_cast<std::uintmax_t>(1 / boost::math::tools::root_epsilon<double>())); // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      "long double",                         // test type(s)
+      "[^|]*PDF",                  // test data group
+      "[^|]*", static_cast<std::uintmax_t>(1 / boost::math::tools::root_epsilon<long double>()), static_cast<std::uintmax_t>(1 / boost::math::tools::root_epsilon<long double>())); // test function
    add_expected_result(
       "[^|]*",                          // compiler
       "[^|]*",                          // stdlib
diff --git a/test/test_nc_t.hpp b/test/test_nc_t.hpp
index b4fd17fb73..65af7e647a 100644
--- a/test/test_nc_t.hpp
+++ b/test/test_nc_t.hpp
@@ -353,6 +353,12 @@ T nct_cdf(T df, T nc, T x)
    return cdf(boost::math::non_central_t_distribution<T>(df, nc), x);
 }
 
+template <class T>
+T nct_pdf(T df, T nc, T x)
+{
+   return pdf(boost::math::non_central_t_distribution<T>(df, nc), x);
+}
+
 template <class T>
 T nct_ccdf(T df, T nc, T x)
 {
@@ -399,6 +405,27 @@ void do_test_nc_t(T& data, const char* type_name, const char* test)
 #endif
 }
 
+template <typename Real, typename T>
+void do_test_nc_t_pdf(T& data, const char* type_name, const char* test)
+{
+   typedef Real                   value_type;
+
+   std::cout << "Testing: " << test << std::endl;
+
+   value_type(*fp1)(value_type, value_type, value_type) = nct_pdf;
+
+   boost::math::tools::test_result<value_type> result;
+
+   result = boost::math::tools::test_hetero<Real>(
+      data,
+      bind_func<Real>(fp1, 0, 1, 2),
+      extract_result<Real>(3));
+   handle_test_result(result, data[result.worst()], result.worst(),
+      type_name, "non central t PDF", test);
+
+   std::cout << std::endl;
+}
+
 template <typename Real, typename T>
 void quantile_sanity_check(T& data, const char* type_name, const char* test)
 {
@@ -522,6 +549,9 @@ void test_accuracy(T, const char* type_name)
 #include "nct_asym.ipp"
       do_test_nc_t<T>(nct_asym, type_name, "Non Central T (large parameters)");
       quantile_sanity_check<T>(nct_asym, type_name, "Non Central T (large parameters)");
+
+#include "nc_t_pdf_data.ipp"
+      do_test_nc_t_pdf<T>(nc_t_pdf_data, type_name, "Non Central T PDF");
    }
 }
 
diff --git a/tools/non_central_t_pdf_data.cpp b/tools/non_central_t_pdf_data.cpp
new file mode 100644
index 0000000000..7d50f00808
--- /dev/null
+++ b/tools/non_central_t_pdf_data.cpp
@@ -0,0 +1,92 @@
+//  (C) Copyright John Maddock 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_MAX_SERIES_ITERATION_POLICY 10000000
+#define BOOST_MATH_USE_MPFR
+
+#include "mp_t.hpp"
+#include <boost/math/special_functions/hypergeometric_1F1.hpp>
+#include <boost/math/distributions/non_central_t.hpp>
+#include <boost/lexical_cast.hpp>
+#include <fstream>
+#include <map>
+#include <boost/math/tools/test_data.hpp>
+#include <boost/random.hpp>
+
+using namespace boost::math::tools;
+using namespace boost::math;
+using namespace std;
+
+struct nc_t_pdf_gen
+{
+   mp_t operator()(mp_t v, mp_t mu, mp_t x)
+   {
+      //
+      // Arbitrary smallest value we accept, below this, we will likely underflow to zero
+      // when computing at double precision:
+      //
+      static const mp_t minimum = 1e-270;
+
+      mp_t Av = boost::math::hypergeometric_1F1((v + 1) / 2, boost::math::constants::half<mp_t>(), mu * mu * x * x / (2 * (x * x + v)));
+      mp_t Bv = boost::math::hypergeometric_1F1(v / 2 + mp_t(1), mp_t(3) / 2, mu * mu * x * x / (2 * (x * x + v)));
+      Bv *= boost::math::tgamma_ratio(v / 2 + mp_t(1), (v + mp_t(1)) / 2);
+      Bv *= boost::math::constants::root_two<mp_t>() * mu * x / sqrt(x * x + v);
+
+      Av += Bv;
+      Av *= exp(-mu * mu / 2) * pow(1 + x * x / v, -(v + 1) / 2) * boost::math::tgamma_ratio((v + mp_t(1)) / 2, v / 2);
+      Av /= sqrt(v) * boost::math::constants::root_pi<mp_t>();
+
+      if (Av < minimum)
+         throw std::domain_error("Result too small!");
+
+      return Av;
+   }
+};
+
+
+int main(int, char* [])
+{
+   parameter_info<mp_t> arg1, arg2, arg3;
+   test_data<mp_t> data;
+
+   std::cout << "Welcome.\n"
+      "This program will generate spot tests for the non central t PDF:\n";
+
+   std::string line;
+   bool cont;
+
+   random_ns::mt19937 rnd;
+   random_ns::uniform_real_distribution<float> ur_a(0, 20);
+
+
+   do
+   {
+      if (0 == get_user_parameter_info(arg1, "v"))
+         return 1;
+      if (0 == get_user_parameter_info(arg2, "nc"))
+         return 1;
+
+      arg3 = make_periodic_param(mp_t(-20), mp_t(200), 170);
+
+      data.insert(nc_t_pdf_gen(), arg1, arg2, arg3);
+      std::cout << "Any more data [y/n]?";
+      std::getline(std::cin, line);
+      boost::algorithm::trim(line);
+      cont = (line == "y");
+   } while (cont);
+
+   std::cout << "Enter name of test data file [default=nc_t_pdf_data.ipp]";
+   std::getline(std::cin, line);
+   boost::algorithm::trim(line);
+   if (line == "")
+      line = "nc_t_pdf_data.ipp";
+   std::ofstream ofs(line.c_str());
+   ofs << std::scientific << std::setprecision(40);
+   write_code(ofs, data, line.c_str());
+
+   return 0;
+}
+
+

From 70b6ab76e38316d2e0c6c79276a3a3c9dca5191b Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Fri, 31 May 2024 11:55:38 +0100
Subject: [PATCH 05/13] Jacobi Zeta: remove unused variable.

---
 include/boost/math/special_functions/jacobi_zeta.hpp | 1 -
 1 file changed, 1 deletion(-)

diff --git a/include/boost/math/special_functions/jacobi_zeta.hpp b/include/boost/math/special_functions/jacobi_zeta.hpp
index 1bdf7f0f6e..c4ba7d23d2 100644
--- a/include/boost/math/special_functions/jacobi_zeta.hpp
+++ b/include/boost/math/special_functions/jacobi_zeta.hpp
@@ -43,7 +43,6 @@ T jacobi_zeta_imp(T phi, T k, const Policy& pol, T kp)
     T result;
     T sinp = sin(phi);
     T cosp = cos(phi);
-    T s2 = sinp * sinp;
     T c2 = cosp * cosp;
     T one_minus_ks2 = kp + c2 - kp * c2;
     T k2 = k * k;

From 18f49f94f5b76aab052fb79729347dd08e3fb664 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Fri, 31 May 2024 16:58:41 +0100
Subject: [PATCH 06/13] Allow exp_sinh to be used on non-exception
 environments.

---
 include/boost/math/quadrature/exp_sinh.hpp | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/include/boost/math/quadrature/exp_sinh.hpp b/include/boost/math/quadrature/exp_sinh.hpp
index 14970bfdb5..f28493737e 100644
--- a/include/boost/math/quadrature/exp_sinh.hpp
+++ b/include/boost/math/quadrature/exp_sinh.hpp
@@ -91,8 +91,7 @@ auto exp_sinh<Real, Policy>::integrate(const F& f, Real tolerance, Real* error,
     static const char* function = "boost::math::quadrature::exp_sinh<%1%>::integrate";
     using std::abs;
     if (abs(tolerance) > 1) {
-        std::string msg = std::string(__FILE__) + ":" + std::to_string(__LINE__) + ":" + std::string(function) + ": The tolerance provided is unusually large; did you confuse it with a domain bound?";
-        throw std::domain_error(msg);
+        return policies::raise_domain_error(function, "The tolerance provided (%1%) is unusually large; did you confuse it with a domain bound?", tolerance, Policy());
     }
     return m_imp->integrate(f, error, L1, function, tolerance, levels);
 }

From 5ec5c6759aba30950f8e62ac606be0b4c407107a Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Fri, 31 May 2024 16:59:16 +0100
Subject: [PATCH 07/13] Add missing test file.

---
 test/nc_t_pdf_data.ipp | 12121 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 12121 insertions(+)
 create mode 100644 test/nc_t_pdf_data.ipp

diff --git a/test/nc_t_pdf_data.ipp b/test/nc_t_pdf_data.ipp
new file mode 100644
index 0000000000..ce4626113e
--- /dev/null
+++ b/test/nc_t_pdf_data.ipp
@@ -0,0 +1,12121 @@
+#ifndef SC_
+#  define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
+#endif
+   static const std::array<std::array<T, 4>, 12112> nc_t_pdf_data = {{
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(-2.0000000000000000000000000000000000000000e+01), SC_(1.4381813277523004272343589190146201842804e-06) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(-1.8705886840820312500000000000000000000000e+01), SC_(1.7570993138850640675881332555246167625001e-06) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(-1.7411766052246093750000000000000000000000e+01), SC_(2.1776624749602608724215749701932540495194e-06) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(-1.6117652893066406250000000000000000000000e+01), SC_(2.7437748471563251651810419842608555823112e-06) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(-1.4823532104492187500000000000000000000000e+01), SC_(3.5242068285498268064856885581705033301522e-06) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(-1.3529411315917968750000000000000000000000e+01), SC_(4.6306441321775042248572523975297685709043e-06) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(-1.2235294342041015625000000000000000000000e+01), SC_(6.2524582986546127466128626136898551304061e-06) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(-1.0941177368164062500000000000000000000000e+01), SC_(8.7277004154694400993170850522354837910928e-06) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(-9.6470603942871093750000000000000000000000e+00), SC_(1.2698822611984500166119118630224410637015e-05) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(-8.3529434204101562500000000000000000000000e+00), SC_(1.9485879183139325712134962445161030227791e-05) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(-7.0588245391845703125000000000000000000000e+00), SC_(3.2086387152381181297690359790022815747067e-05) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(-5.7647056579589843750000000000000000000000e+00), SC_(5.8273840556190222406296411457432136139729e-05) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(-4.4705886840820312500000000000000000000000e+00), SC_(1.2231493859692107909954847981598455305555e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(-3.1764707565307617187500000000000000000000e+00), SC_(3.2419501327949399831436883948257874465481e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(-1.8823523521423339843750000000000000000000e+00), SC_(1.3150870759896782842146518731597698204537e-03) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(-5.8823466300964355468750000000000000000000e-01), SC_(1.2502536175677130652478644413803447848099e-02) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(7.0588302612304687500000000000000000000000e-01), SC_(1.7392658805528147996492784000917750482146e-01) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.5505237245131592879465049509558564339510e-01) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(3.2941179275512695312500000000000000000000e+00), SC_(1.3891484344063819340920397074590876366327e-01) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(4.5882358551025390625000000000000000000000e+00), SC_(7.0573515208378571098450697999426970255806e-02) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(5.8823528289794921875000000000000000000000e+00), SC_(3.8659108941274892704939877688209596486522e-02) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(7.1764717102050781250000000000000000000000e+00), SC_(2.2972870175517668819501307839139439765597e-02) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(8.4705886840820312500000000000000000000000e+00), SC_(1.4612138020671884199410920956065499300964e-02) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(9.7647056579589843750000000000000000000000e+00), SC_(9.8155803353488957527588448888355653147470e-03) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(1.1058822631835937500000000000000000000000e+01), SC_(6.8892329703213950547819353284115218987106e-03) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(1.2352939605712890625000000000000000000000e+01), SC_(5.0110055005455076612933152412755070324156e-03) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(1.3647060394287109375000000000000000000000e+01), SC_(3.7537643616370592501494430511246425118804e-03) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(1.4941177368164062500000000000000000000000e+01), SC_(2.8820947300776745522732463222576655813809e-03) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(1.6235290527343750000000000000000000000000e+01), SC_(2.2595114796970283273606264072755840851385e-03) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(1.7529411315917968750000000000000000000000e+01), SC_(1.8033857138844883616646264529329275269992e-03) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(1.8823524475097656250000000000000000000000e+01), SC_(1.4618023277491700254576904946550613071766e-03) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0117645263671875000000000000000000000000e+01), SC_(1.2010567922668599338034822360685891048573e-03) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.1411766052246093750000000000000000000000e+01), SC_(9.9864909838274633148295747522888074251920e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.2705879211425781250000000000000000000000e+01), SC_(8.3917577421362860751024209004037584513413e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.4000000000000000000000000000000000000000e+01), SC_(7.1185408035729552160450145203995363226997e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.5294113159179687500000000000000000000000e+01), SC_(6.0899023174638864536541511117915647815923e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.6588233947753906250000000000000000000000e+01), SC_(5.2499209036812976210490530247988827336209e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.7882354736328125000000000000000000000000e+01), SC_(4.5573301166456967934784270104383263818628e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.9176467895507812500000000000000000000000e+01), SC_(3.9812211483809037366198434952769852429178e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(3.0470588684082031250000000000000000000000e+01), SC_(3.4981290070150162434927481887970003801838e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(3.1764701843261718750000000000000000000000e+01), SC_(3.0900423801167881959448575122971810717785e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(3.3058822631835937500000000000000000000000e+01), SC_(2.7429648942571774824427815556237965522167e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(3.4352935791015625000000000000000000000000e+01), SC_(2.4459244769146319507415060872541619816038e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(3.5647048950195312500000000000000000000000e+01), SC_(2.1902271781867434879475079615325359430352e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(3.6941177368164062500000000000000000000000e+01), SC_(1.9689277701848234503083782721650057769639e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(3.8235290527343750000000000000000000000000e+01), SC_(1.7764407568114622135559094754607699381020e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(3.9529403686523437500000000000000000000000e+01), SC_(1.6082275635651116139041564271947395438616e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(4.0823532104492187500000000000000000000000e+01), SC_(1.4605807481783500715849221562776584303156e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(4.2117645263671875000000000000000000000000e+01), SC_(1.3304561423706586533888117869501400880892e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(4.3411758422851562500000000000000000000000e+01), SC_(1.2153301121523862313482574820783060724421e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(4.4705871582031250000000000000000000000000e+01), SC_(1.1131039103922523427411533756220334101415e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(4.6000000000000000000000000000000000000000e+01), SC_(1.0220203298224593537874082685745363929158e-04) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(4.7294113159179687500000000000000000000000e+01), SC_(9.4060441082441367396037390083438962186616e-05) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(4.8588226318359375000000000000000000000000e+01), SC_(8.6760664627983602056469845771199465786538e-05) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(4.9882354736328125000000000000000000000000e+01), SC_(8.0196639915530512247358832167502790702000e-05) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(5.1176467895507812500000000000000000000000e+01), SC_(7.4278141405871561824392218467923377775258e-05) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(5.2470581054687500000000000000000000000000e+01), SC_(6.8927702334717041005168417775838360518285e-05) }, 
+      { SC_(2.0000000000000000000000000000000000000000e+00), SC_(2.0000000000000000000000000000000000000000e+00), SC_(5.3764709472656250000000000000000000000000e+01), SC_(6.4078749802564052275781318760033026037582e-05) }, 
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+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.7282348632812500000000000000000000000000e+02), SC_(1.4838718106789964650285160766740948294170e-13) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.7411761474609375000000000000000000000000e+02), SC_(9.0549499400150439520970960357347653495766e-14) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.7541174316406250000000000000000000000000e+02), SC_(5.5314174544117514596751372988680027657517e-14) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.7670587158203125000000000000000000000000e+02), SC_(3.3827131096932843458260135152431231385248e-14) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.7800000000000000000000000000000000000000e+02), SC_(2.0710414809112452326805622686016389974919e-14) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.7929412841796875000000000000000000000000e+02), SC_(1.2694711987255190137539254528086373197784e-14) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.8058819580078125000000000000000000000000e+02), SC_(7.7909760162316637681773623129245784566004e-15) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.8188232421875000000000000000000000000000e+02), SC_(4.7872870129783953121119602921557868570950e-15) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.8317645263671875000000000000000000000000e+02), SC_(2.9453601502745647300958274986092401013423e-15) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.8447058105468750000000000000000000000000e+02), SC_(1.8144733978107203604881459002270045172080e-15) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.8576470947265625000000000000000000000000e+02), SC_(1.1192759873753187997635200674242323510561e-15) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.8705883789062500000000000000000000000000e+02), SC_(6.9136680890239356450295002788403772818145e-16) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.8835290527343750000000000000000000000000e+02), SC_(4.2764570424287083657113563344728118028216e-16) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.8964703369140625000000000000000000000000e+02), SC_(2.6488249529511590876715779383566908540448e-16) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.9094116210937500000000000000000000000000e+02), SC_(1.6429871390040407686383662243973678780041e-16) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.9223529052734375000000000000000000000000e+02), SC_(1.0205506613529281545453710313734561196657e-16) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.9352941894531250000000000000000000000000e+02), SC_(6.3483612951656433465759601453127921733732e-17) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.9482348632812500000000000000000000000000e+02), SC_(3.9548649390453189371949399360399900113814e-17) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.9611761474609375000000000000000000000000e+02), SC_(2.4673532864744022371074780269124638469264e-17) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.9741174316406250000000000000000000000000e+02), SC_(1.5416152118734838320357169475425327590953e-17) }, 
+      { SC_(8.9111114501953125000000000000000000000000e+01), SC_(8.9111114501953125000000000000000000000000e+01), SC_(1.9870587158203125000000000000000000000000e+02), SC_(9.6465214102301022955827217656166174060445e-18) }
+   }};
+//#undef SC_
+

From eb42cba0c4579dfc3b0649a1a0e883f521c0a88e Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Fri, 31 May 2024 18:03:27 +0100
Subject: [PATCH 08/13] Lots of warning suppressions.

---
 include/boost/math/concepts/distributions.hpp |  2 +-
 .../detail/hypergeometric_pdf.hpp             | 28 ++++++++--------
 .../detail/hypergeometric_quantile.hpp        | 32 +++++++++----------
 3 files changed, 31 insertions(+), 31 deletions(-)

diff --git a/include/boost/math/concepts/distributions.hpp b/include/boost/math/concepts/distributions.hpp
index 538bbe702b..7f9af2dd5a 100644
--- a/include/boost/math/concepts/distributions.hpp
+++ b/include/boost/math/concepts/distributions.hpp
@@ -343,7 +343,7 @@ struct DistributionConcept
    template <class R, class P>
    static void test_extra_members(const boost::math::hypergeometric_distribution<R, P>& d)
    {
-      unsigned u = d.defective();
+      std::uint64_t u = d.defective();
       u = d.sample_count();
       u = d.total();
       suppress_unused_variable_warning(u);
diff --git a/include/boost/math/distributions/detail/hypergeometric_pdf.hpp b/include/boost/math/distributions/detail/hypergeometric_pdf.hpp
index 9eeef270d8..0ec3065eb3 100644
--- a/include/boost/math/distributions/detail/hypergeometric_pdf.hpp
+++ b/include/boost/math/distributions/detail/hypergeometric_pdf.hpp
@@ -297,7 +297,7 @@ T hypergeometric_pdf_prime_loop_imp(hypergeometric_pdf_prime_loop_data& data, hy
    while(data.current_prime <= data.N)
    {
       std::uint64_t base = data.current_prime;
-      std::int64_t prime_powers = 0;
+      std::uint64_t prime_powers = 0;
       while(base <= data.N)
       {
          prime_powers += data.n / base;
@@ -313,7 +313,7 @@ T hypergeometric_pdf_prime_loop_imp(hypergeometric_pdf_prime_loop_data& data, hy
       }
       if(prime_powers)
       {
-         T p = integer_power<T>(static_cast<T>(data.current_prime), prime_powers);
+         T p = integer_power<T>(static_cast<T>(data.current_prime), static_cast<int>(prime_powers));
          if((p > 1) && (tools::max_value<T>() / p < result.value))
          {
             //
@@ -321,7 +321,7 @@ T hypergeometric_pdf_prime_loop_imp(hypergeometric_pdf_prime_loop_data& data, hy
             // to sidestep the issue:
             //
             hypergeometric_pdf_prime_loop_result_entry<T> t = { p, &result };
-            data.current_prime = prime(++data.prime_index);
+            data.current_prime = prime(static_cast<unsigned>(++data.prime_index));
             return hypergeometric_pdf_prime_loop_imp<T>(data, t);
          }
          if((p < 1) && (tools::min_value<T>() / p > result.value))
@@ -331,12 +331,12 @@ T hypergeometric_pdf_prime_loop_imp(hypergeometric_pdf_prime_loop_data& data, hy
             // to sidestep the issue:
             //
             hypergeometric_pdf_prime_loop_result_entry<T> t = { p, &result };
-            data.current_prime = prime(++data.prime_index);
+            data.current_prime = prime(static_cast<unsigned>(++data.prime_index));
             return hypergeometric_pdf_prime_loop_imp<T>(data, t);
          }
          result.value *= p;
       }
-      data.current_prime = prime(++data.prime_index);
+      data.current_prime = prime(static_cast<unsigned>(++data.prime_index));
    }
    //
    // When we get to here we have run out of prime factors,
@@ -395,18 +395,18 @@ T hypergeometric_pdf_factorial_imp(std::uint64_t x, std::uint64_t r, std::uint64
 {
    BOOST_MATH_STD_USING
    BOOST_MATH_ASSERT(N <= boost::math::max_factorial<T>::value);
-   T result = boost::math::unchecked_factorial<T>(n);
+   T result = boost::math::unchecked_factorial<T>(static_cast<unsigned>(n));
    T num[3] = {
-      boost::math::unchecked_factorial<T>(r),
-      boost::math::unchecked_factorial<T>(N - n),
-      boost::math::unchecked_factorial<T>(N - r)
+      boost::math::unchecked_factorial<T>(static_cast<unsigned>(r)),
+      boost::math::unchecked_factorial<T>(static_cast<unsigned>(N - n)),
+      boost::math::unchecked_factorial<T>(static_cast<unsigned>(N - r))
    };
    T denom[5] = {
-      boost::math::unchecked_factorial<T>(N),
-      boost::math::unchecked_factorial<T>(x),
-      boost::math::unchecked_factorial<T>(n - x),
-      boost::math::unchecked_factorial<T>(r - x),
-      boost::math::unchecked_factorial<T>(N - n - r + x)
+      boost::math::unchecked_factorial<T>(static_cast<unsigned>(N)),
+      boost::math::unchecked_factorial<T>(static_cast<unsigned>(x)),
+      boost::math::unchecked_factorial<T>(static_cast<unsigned>(n - x)),
+      boost::math::unchecked_factorial<T>(static_cast<unsigned>(r - x)),
+      boost::math::unchecked_factorial<T>(static_cast<unsigned>(N - n - r + x))
    };
    std::size_t i = 0;
    std::size_t j = 0;
diff --git a/include/boost/math/distributions/detail/hypergeometric_quantile.hpp b/include/boost/math/distributions/detail/hypergeometric_quantile.hpp
index 7ab85fb144..2441a73309 100644
--- a/include/boost/math/distributions/detail/hypergeometric_quantile.hpp
+++ b/include/boost/math/distributions/detail/hypergeometric_quantile.hpp
@@ -14,7 +14,7 @@
 namespace boost{ namespace math{ namespace detail{
 
 template <class T>
-inline unsigned round_x_from_p(unsigned x, T p, T cum, T fudge_factor, unsigned lbound, unsigned /*ubound*/, const policies::discrete_quantile<policies::integer_round_down>&)
+inline std::uint64_t round_x_from_p(std::uint64_t x, T p, T cum, T fudge_factor, std::uint64_t lbound, std::uint64_t /*ubound*/, const policies::discrete_quantile<policies::integer_round_down>&)
 {
    if((p < cum * fudge_factor) && (x != lbound))
    {
@@ -25,7 +25,7 @@ inline unsigned round_x_from_p(unsigned x, T p, T cum, T fudge_factor, unsigned
 }
 
 template <class T>
-inline unsigned round_x_from_p(unsigned x, T p, T cum, T fudge_factor, unsigned /*lbound*/, unsigned ubound, const policies::discrete_quantile<policies::integer_round_up>&)
+inline std::uint64_t round_x_from_p(std::uint64_t x, T p, T cum, T fudge_factor, std::uint64_t /*lbound*/, std::uint64_t ubound, const policies::discrete_quantile<policies::integer_round_up>&)
 {
    if((cum < p * fudge_factor) && (x != ubound))
    {
@@ -36,7 +36,7 @@ inline unsigned round_x_from_p(unsigned x, T p, T cum, T fudge_factor, unsigned
 }
 
 template <class T>
-inline unsigned round_x_from_p(unsigned x, T p, T cum, T fudge_factor, unsigned lbound, unsigned ubound, const policies::discrete_quantile<policies::integer_round_inwards>&)
+inline std::uint64_t round_x_from_p(std::uint64_t x, T p, T cum, T fudge_factor, std::uint64_t lbound, std::uint64_t ubound, const policies::discrete_quantile<policies::integer_round_inwards>&)
 {
    if(p >= 0.5)
       return round_x_from_p(x, p, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_down>());
@@ -44,7 +44,7 @@ inline unsigned round_x_from_p(unsigned x, T p, T cum, T fudge_factor, unsigned
 }
 
 template <class T>
-inline unsigned round_x_from_p(unsigned x, T p, T cum, T fudge_factor, unsigned lbound, unsigned ubound, const policies::discrete_quantile<policies::integer_round_outwards>&)
+inline std::uint64_t round_x_from_p(std::uint64_t x, T p, T cum, T fudge_factor, std::uint64_t lbound, std::uint64_t ubound, const policies::discrete_quantile<policies::integer_round_outwards>&)
 {
    if(p >= 0.5)
       return round_x_from_p(x, p, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_up>());
@@ -52,13 +52,13 @@ inline unsigned round_x_from_p(unsigned x, T p, T cum, T fudge_factor, unsigned
 }
 
 template <class T>
-inline unsigned round_x_from_p(unsigned x, T /*p*/, T /*cum*/, T /*fudge_factor*/, unsigned /*lbound*/, unsigned /*ubound*/, const policies::discrete_quantile<policies::integer_round_nearest>&)
+inline std::uint64_t round_x_from_p(std::uint64_t x, T /*p*/, T /*cum*/, T /*fudge_factor*/, std::uint64_t /*lbound*/, std::uint64_t /*ubound*/, const policies::discrete_quantile<policies::integer_round_nearest>&)
 {
    return x;
 }
 
 template <class T>
-inline unsigned round_x_from_q(unsigned x, T q, T cum, T fudge_factor, unsigned lbound, unsigned /*ubound*/, const policies::discrete_quantile<policies::integer_round_down>&)
+inline std::uint64_t round_x_from_q(std::uint64_t x, T q, T cum, T fudge_factor, std::uint64_t lbound, std::uint64_t /*ubound*/, const policies::discrete_quantile<policies::integer_round_down>&)
 {
    if((q * fudge_factor > cum) && (x != lbound))
    {
@@ -69,7 +69,7 @@ inline unsigned round_x_from_q(unsigned x, T q, T cum, T fudge_factor, unsigned
 }
 
 template <class T>
-inline unsigned round_x_from_q(unsigned x, T q, T cum, T fudge_factor, unsigned /*lbound*/, unsigned ubound, const policies::discrete_quantile<policies::integer_round_up>&)
+inline std::uint64_t round_x_from_q(std::uint64_t x, T q, T cum, T fudge_factor, std::uint64_t /*lbound*/, std::uint64_t ubound, const policies::discrete_quantile<policies::integer_round_up>&)
 {
    if((q < cum * fudge_factor) && (x != ubound))
    {
@@ -80,7 +80,7 @@ inline unsigned round_x_from_q(unsigned x, T q, T cum, T fudge_factor, unsigned
 }
 
 template <class T>
-inline unsigned round_x_from_q(unsigned x, T q, T cum, T fudge_factor, unsigned lbound, unsigned ubound, const policies::discrete_quantile<policies::integer_round_inwards>&)
+inline std::uint64_t round_x_from_q(std::uint64_t x, T q, T cum, T fudge_factor, std::uint64_t lbound, std::uint64_t ubound, const policies::discrete_quantile<policies::integer_round_inwards>&)
 {
    if(q < 0.5)
       return round_x_from_q(x, q, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_down>());
@@ -88,7 +88,7 @@ inline unsigned round_x_from_q(unsigned x, T q, T cum, T fudge_factor, unsigned
 }
 
 template <class T>
-inline unsigned round_x_from_q(unsigned x, T q, T cum, T fudge_factor, unsigned lbound, unsigned ubound, const policies::discrete_quantile<policies::integer_round_outwards>&)
+inline std::uint64_t round_x_from_q(std::uint64_t x, T q, T cum, T fudge_factor, std::uint64_t lbound, std::uint64_t ubound, const policies::discrete_quantile<policies::integer_round_outwards>&)
 {
    if(q >= 0.5)
       return round_x_from_q(x, q, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_down>());
@@ -96,13 +96,13 @@ inline unsigned round_x_from_q(unsigned x, T q, T cum, T fudge_factor, unsigned
 }
 
 template <class T>
-inline unsigned round_x_from_q(unsigned x, T /*q*/, T /*cum*/, T /*fudge_factor*/, unsigned /*lbound*/, unsigned /*ubound*/, const policies::discrete_quantile<policies::integer_round_nearest>&)
+inline std::uint64_t round_x_from_q(std::uint64_t x, T /*q*/, T /*cum*/, T /*fudge_factor*/, std::uint64_t /*lbound*/, std::uint64_t /*ubound*/, const policies::discrete_quantile<policies::integer_round_nearest>&)
 {
    return x;
 }
 
 template <class T, class Policy>
-unsigned hypergeometric_quantile_imp(T p, T q, unsigned r, unsigned n, unsigned N, const Policy& pol)
+std::uint64_t hypergeometric_quantile_imp(T p, T q, std::uint64_t r, std::uint64_t n, std::uint64_t N, const Policy& pol)
 {
 #ifdef _MSC_VER
 #  pragma warning(push)
@@ -113,8 +113,8 @@ unsigned hypergeometric_quantile_imp(T p, T q, unsigned r, unsigned n, unsigned
    BOOST_FPU_EXCEPTION_GUARD
    T result;
    T fudge_factor = 1 + tools::epsilon<T>() * ((N <= boost::math::prime(boost::math::max_prime - 1)) ? 50 : 2 * N);
-   unsigned base = static_cast<unsigned>((std::max)(0, static_cast<int>(n + r) - static_cast<int>(N)));
-   unsigned lim = (std::min)(r, n);
+   std::uint64_t base = static_cast<std::uint64_t>((std::max)(0, static_cast<int>(n + r) - static_cast<int>(N)));
+   std::uint64_t lim = (std::min)(r, n);
 
    BOOST_MATH_INSTRUMENT_VARIABLE(p);
    BOOST_MATH_INSTRUMENT_VARIABLE(q);
@@ -127,7 +127,7 @@ unsigned hypergeometric_quantile_imp(T p, T q, unsigned r, unsigned n, unsigned
 
    if(p <= 0.5)
    {
-      unsigned x = base;
+      std::uint64_t x = base;
       result = hypergeometric_pdf<T>(x, r, n, N, pol);
       T diff = result;
       if (diff == 0)
@@ -175,7 +175,7 @@ unsigned hypergeometric_quantile_imp(T p, T q, unsigned r, unsigned n, unsigned
    }
    else
    {
-      unsigned x = lim;
+      std::uint64_t x = lim;
       result = 0;
       T diff = hypergeometric_pdf<T>(x, r, n, N, pol);
       if (diff == 0)
@@ -225,7 +225,7 @@ unsigned hypergeometric_quantile_imp(T p, T q, unsigned r, unsigned n, unsigned
 }
 
 template <class T, class Policy>
-inline unsigned hypergeometric_quantile(T p, T q, unsigned r, unsigned n, unsigned N, const Policy&)
+inline std::uint64_t hypergeometric_quantile(T p, T q, std::uint64_t r, std::uint64_t n, std::uint64_t N, const Policy&)
 {
    BOOST_FPU_EXCEPTION_GUARD
    typedef typename tools::promote_args<T>::type result_type;

From 69443ab9a5e8c454c1c033c94b47f5ba06ac2e36 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Fri, 31 May 2024 18:04:04 +0100
Subject: [PATCH 09/13] Correct isfinite call.

---
 include/boost/math/quadrature/detail/exp_sinh_detail.hpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/include/boost/math/quadrature/detail/exp_sinh_detail.hpp b/include/boost/math/quadrature/detail/exp_sinh_detail.hpp
index d0438a8236..2df07b6ecc 100644
--- a/include/boost/math/quadrature/detail/exp_sinh_detail.hpp
+++ b/include/boost/math/quadrature/detail/exp_sinh_detail.hpp
@@ -259,7 +259,7 @@ auto exp_sinh_detail<Real, Policy>::integrate(const F& f, Real* error, Real* L1,
         err = abs(I0 - I1);
         //std::cout << "Estimate:        " << I1 << " Error estimate at level " << i  << " = " << err << std::endl;
         // Use L1_I1 here to make it work with both complex and real valued integrands:
-        if (!isfinite(L1_I1))
+        if (!(boost::math::isfinite)(L1_I1))
         {
             return static_cast<K>(policies::raise_evaluation_error(function, "The exp_sinh quadrature evaluated your function at a singular point and returned %1%. Please ensure your function evaluates to a finite number over its entire domain.", I1, Policy()));
         }

From 7439011b06fffde0041cb0d85c5e35c09281a4b7 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Fri, 31 May 2024 18:04:31 +0100
Subject: [PATCH 10/13] Set quad precision error rates.

---
 test/test_nc_t_quad.cpp | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/test/test_nc_t_quad.cpp b/test/test_nc_t_quad.cpp
index 044f9d290e..0f0179c458 100644
--- a/test/test_nc_t_quad.cpp
+++ b/test/test_nc_t_quad.cpp
@@ -54,6 +54,13 @@ void expected_results()
       "cpp_bin_float_quad",             // test type(s)
       ".*large parameters.*",           // test data group
       "[^|]*", 300000, 100000);         // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      "cpp_bin_float_quad",                         // test type(s)
+      "[^|]*PDF",                  // test data group
+      "[^|]*", static_cast<std::uintmax_t>(1 / boost::math::tools::root_epsilon<boost::multiprecision::cpp_bin_float_quad>()), static_cast<std::uintmax_t>(1 / boost::math::tools::root_epsilon<boost::multiprecision::cpp_bin_float_quad>())); // test function
    add_expected_result(
       "[^|]*",                          // compiler
       "[^|]*",                          // stdlib

From 2bea451ac8debb55de3b78a4ce30a960c2247947 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Fri, 31 May 2024 18:57:37 +0100
Subject: [PATCH 11/13] Correct conceptual failings, remove tests which can't
 possibly succeed.

---
 include/boost/math/distributions/non_central_t.hpp | 4 ++--
 test/exp_sinh_quadrature_test.cpp                  | 1 -
 test/tanh_sinh_quadrature_test.cpp                 | 2 --
 3 files changed, 2 insertions(+), 5 deletions(-)

diff --git a/include/boost/math/distributions/non_central_t.hpp b/include/boost/math/distributions/non_central_t.hpp
index d3d58cd206..a6c988d758 100644
--- a/include/boost/math/distributions/non_central_t.hpp
+++ b/include/boost/math/distributions/non_central_t.hpp
@@ -424,10 +424,10 @@ namespace boost
             // We only call this routine when we know that the series form of 1F1 is cheap to evaluate,
             // so no need to call the whole 1F1 function, just the series will do:
             //
-            T Av = hypergeometric_1F1_generic_series((v + 1) / 2, boost::math::constants::half<T>(), mu * mu * x * x / (2 * (x * x + v)), pol, scale, function);
+            T Av = hypergeometric_1F1_generic_series(static_cast<T>((v + 1) / 2), boost::math::constants::half<T>(), static_cast<T>(mu * mu * x * x / (2 * (x * x + v))), pol, scale, function);
             Av = ldexp(Av, static_cast<int>(scale));
             scale = 0;
-            T Bv = hypergeometric_1F1_generic_series(v / 2 + T(1), T(3) / 2, mu * mu * x * x / (2 * (x * x + v)), pol, scale, function);
+            T Bv = hypergeometric_1F1_generic_series(static_cast<T>(v / 2 + T(1)), static_cast<T>(T(3) / 2), static_cast<T>(mu * mu * x * x / (2 * (x * x + v))), pol, scale, function);
             Bv = ldexp(Bv, static_cast<int>(scale));
             Bv *= boost::math::tgamma_delta_ratio(v / 2 + T(1), -constants::half<T>(), pol);
             Bv *= boost::math::constants::root_two<T>() * mu * x / sqrt(x * x + v);
diff --git a/test/exp_sinh_quadrature_test.cpp b/test/exp_sinh_quadrature_test.cpp
index 7c958d5d8e..7bba2298af 100644
--- a/test/exp_sinh_quadrature_test.cpp
+++ b/test/exp_sinh_quadrature_test.cpp
@@ -670,7 +670,6 @@ BOOST_AUTO_TEST_CASE(exp_sinh_quadrature_test)
     test_right_limit_infinite<cpp_bin_float_quad>();
     test_nr_examples<cpp_bin_float_quad>();
     test_crc<cpp_bin_float_quad>();
-    test_non_central_t<cpp_bin_float_quad>();
 #endif
 
 #if !defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS) && !defined(BOOST_MATH_NO_REAL_CONCEPT_TESTS)
diff --git a/test/tanh_sinh_quadrature_test.cpp b/test/tanh_sinh_quadrature_test.cpp
index 534abfdfa2..ffd55352b1 100644
--- a/test/tanh_sinh_quadrature_test.cpp
+++ b/test/tanh_sinh_quadrature_test.cpp
@@ -1028,7 +1028,6 @@ BOOST_AUTO_TEST_CASE(tanh_sinh_quadrature_test)
     test_crc<cpp_bin_float_quad>();
     test_sf<cpp_bin_float_quad>();
     test_2_arg<cpp_bin_float_quad>();
-    test_non_central_t<cpp_bin_float_quad>();
 #endif
 #endif
 #ifdef TEST5
@@ -1083,7 +1082,6 @@ BOOST_AUTO_TEST_CASE(tanh_sinh_quadrature_test)
     test_crc<boost::multiprecision::float128>();
     test_sf<boost::multiprecision::float128>();
     test_2_arg<boost::multiprecision::float128>();
-    test_non_central_t<boost::multiprecision::float128>();
 
 #endif
 #ifdef TEST9

From 7d56997a99b5ddc06150ea2023650aabbbc13479 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Sat, 1 Jun 2024 10:32:11 +0100
Subject: [PATCH 12/13] tentative CI failure fixes.

---
 test/Jamfile.v2        | 2 +-
 test/nc_t_pdf_data.ipp | 4 ++++
 2 files changed, 5 insertions(+), 1 deletion(-)

diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 9571cd4ea4..a6e181ac23 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -888,7 +888,7 @@ test-suite new_floats :
 
 test-suite mp :
 
-   [ run test_nc_t_quad.cpp  pch ../../test/build//boost_unit_test_framework : : : release [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
+   [ run test_nc_t_quad.cpp  pch ../../test/build//boost_unit_test_framework : : : release <toolset>gcc-mingw:<cxxflags>-Wa,-mbig-obj <debug-symbols>off [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run test_polynomial.cpp ../../test/build//boost_unit_test_framework : : : <define>TEST1 : test_polynomial_1  ]
    [ run test_polynomial.cpp ../../test/build//boost_unit_test_framework : : : <define>TEST2 : test_polynomial_2  ]
    [ run test_polynomial.cpp ../../test/build//boost_unit_test_framework : : : <define>TEST3 : test_polynomial_3  ]
diff --git a/test/nc_t_pdf_data.ipp b/test/nc_t_pdf_data.ipp
index ce4626113e..e427206ce8 100644
--- a/test/nc_t_pdf_data.ipp
+++ b/test/nc_t_pdf_data.ipp
@@ -1,3 +1,7 @@
+//  (C) Copyright John Maddock 2024.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
 #ifndef SC_
 #  define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
 #endif

From 20f44d1275334d7b8b513fd9d8331cccf5248841 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Sun, 2 Jun 2024 12:04:09 +0100
Subject: [PATCH 13/13] Work through more CI failures.

---
 include/boost/math/concepts/std_real_concept.hpp |  3 +++
 test/exp_sinh_quadrature_test.cpp                |  2 +-
 test/test_nc_t_quad.cpp                          | 10 ++++++++++
 3 files changed, 14 insertions(+), 1 deletion(-)

diff --git a/include/boost/math/concepts/std_real_concept.hpp b/include/boost/math/concepts/std_real_concept.hpp
index 277c35cafd..f77935c7fb 100644
--- a/include/boost/math/concepts/std_real_concept.hpp
+++ b/include/boost/math/concepts/std_real_concept.hpp
@@ -90,6 +90,9 @@ class std_real_concept
    std_real_concept& operator=(float c) { m_value = c; return *this; }
    std_real_concept& operator=(double c) { m_value = c; return *this; }
    std_real_concept& operator=(long double c) { m_value = c; return *this; }
+#ifdef BOOST_MATH_USE_FLOAT128
+   std_real_concept& operator=(BOOST_MATH_FLOAT128_TYPE c) { m_value = c; return *this; }
+#endif
 
    // Access:
    std_real_concept_base_type value()const{ return m_value; }
diff --git a/test/exp_sinh_quadrature_test.cpp b/test/exp_sinh_quadrature_test.cpp
index 7bba2298af..deed18c922 100644
--- a/test/exp_sinh_quadrature_test.cpp
+++ b/test/exp_sinh_quadrature_test.cpp
@@ -644,7 +644,7 @@ BOOST_AUTO_TEST_CASE(exp_sinh_quadrature_test)
     test_right_limit_infinite<std::float64_t>();
     test_nr_examples<std::float64_t>();
     test_crc<std::float64_t>();
-    test_non_central_t<float64_t>();
+    test_non_central_t<std::float64_t>();
 #else
     test_left_limit_infinite<double>();
     test_right_limit_infinite<double>();
diff --git a/test/test_nc_t_quad.cpp b/test/test_nc_t_quad.cpp
index 0f0179c458..5b7ac27d34 100644
--- a/test/test_nc_t_quad.cpp
+++ b/test/test_nc_t_quad.cpp
@@ -40,6 +40,14 @@ using std::endl;
 #include <limits>
 using std::numeric_limits;
 
+#if defined(__GNUC__) && (__GNUC__ < 13) && (defined(__CYGWIN__) || defined(_WIN32))
+//
+// We either get an internal compiler error, or worse, the compiler prints nothing at all
+// and exits with an error code :(
+//
+# define DISABLE_THIS_TEST
+#endif
+
 
 void expected_results()
 {
@@ -83,10 +91,12 @@ BOOST_AUTO_TEST_CASE( test_main )
   BOOST_MATH_CONTROL_FP;
    // Basic sanity-check spot values.
    expected_results();
+#ifndef DISABLE_THIS_TEST
 #if !BOOST_WORKAROUND(BOOST_MSVC, < 1920)
    test_spots(boost::multiprecision::cpp_bin_float_quad(0));
 #endif
    test_accuracy(boost::multiprecision::cpp_bin_float_quad(0), "cpp_bin_float_quad");
+#endif
    // double precision tests only:
    //test_big_df(boost::multiprecision::cpp_bin_float_quad(0));
 } // BOOST_AUTO_TEST_CASE( test_main )