Improve Coverage Part 4

include/boost/math/special_functions/airy.hpp

@@ -187,7 +187,7 @@ BOOST_MATH_GPU_ENABLED T airy_ai_zero_imp(int m, const Policy& pol)
    // of decimal digits in the numeric type T, being at least 12.
    const int my_digits10 = static_cast<int>(static_cast<float>(policies::digits<T, Policy>() * 0.301F));
 
-   const std::uintmax_t iterations_allowed = static_cast<std::uintmax_t>((std::max)(12, my_digits10 * 2));
+   const std::uintmax_t iterations_allowed = static_cast<std::uintmax_t>(BOOST_MATH_GPU_SAFE_MAX(12, my_digits10 * 2));
 
    std::uintmax_t iterations_used = iterations_allowed;
 
@@ -239,7 +239,7 @@ BOOST_MATH_GPU_ENABLED T airy_bi_zero_imp(int m, const Policy& pol)
    // of decimal digits in the numeric type T, being at least 12.
    const int my_digits10 = static_cast<int>(static_cast<float>(policies::digits<T, Policy>() * 0.301F));
 
-   const std::uintmax_t iterations_allowed = static_cast<std::uintmax_t>((std::max)(12, my_digits10 * 2));
+   const std::uintmax_t iterations_allowed = static_cast<std::uintmax_t>(BOOST_MATH_GPU_SAFE_MAX(12, my_digits10 * 2));
 
    std::uintmax_t iterations_used = iterations_allowed;
 

include/boost/math/special_functions/beta.hpp

@@ -1132,7 +1132,7 @@ BOOST_MATH_GPU_ENABLED T binomial_ccdf(T n, T k, T x, T y, const Policy& pol)
 }
 
 template <class T, class Policy>
-T ibeta_large_ab(T a, T b, T x, T y, bool invert, bool normalised, const Policy& pol)
+BOOST_MATH_GPU_ENABLED T ibeta_large_ab(T a, T b, T x, T y, bool invert, bool normalised, const Policy& pol)
 {
    //
    // Large arguments, symetric case, see https://dlmf.nist.gov/8.18
@@ -1571,11 +1571,11 @@ BOOST_MATH_GPU_ENABLED T ibeta_imp(T a, T b, T x, const Policy& pol, bool inv, b
       {
          // a and b both large:
          bool use_asym = false;
-         T ma = (std::max)(a, b);
+         T ma = BOOST_MATH_GPU_SAFE_MAX(a, b);
          T xa = ma == a ? x : y;
          T saddle = ma / (a + b);
          T powers = 0;
-         if ((ma > 1e-5f / tools::epsilon<T>()) && (ma / (std::min)(a, b) < (xa < saddle ? 2 : 15)))
+         if ((ma > 1e-5f / tools::epsilon<T>()) && (ma / BOOST_MATH_GPU_SAFE_MIN(a, b) < (xa < saddle ? 2 : 15)))
          {
             if (a == b)
                use_asym = true;

include/boost/math/special_functions/detail/ibeta_inverse.hpp

@@ -683,16 +683,16 @@ BOOST_MATH_GPU_ENABLED T ibeta_inv_imp(T a, T b, T p, T q, const Policy& pol, T*
             }
             else
                y = 1;
-            if((y > 1e-5) && (std::min)(a, b) < 1000)
+            if((y > 1e-5) && BOOST_MATH_GPU_SAFE_MIN(a, b) < 1000)
             {
                x = temme_method_3_ibeta_inverse(a, b, p, q, pol);
                y = 1 - x;
             }
-            else if ((y > 1e-5) && (std::min)(a, b) > 1000)
+            else if ((y > 1e-5) && BOOST_MATH_GPU_SAFE_MIN(a, b) > 1000)
             {
                // All options have failed, use the saddle point as a starting location:
-               x = (std::max)(a, b) / (a + b);
-               y = (std::min)(a, b) / (a + b);
+               x = BOOST_MATH_GPU_SAFE_MAX(a, b) / (a + b);
+               y = BOOST_MATH_GPU_SAFE_MIN(a, b) / (a + b);
             }
          }
       }

include/boost/math/special_functions/expint.hpp

@@ -562,6 +562,7 @@ BOOST_MATH_GPU_ENABLED T expint_i_imp(T z, const Policy& pol, const boost::math:
       // Maximum Deviation Found:                     2.852e-18
       // Expected Error Term:                         2.852e-18
       // Max Error found at double precision =        Poly: 2.636335e-16   Cheb: 4.187027e-16
+      // LCOV_EXCL_START
       BOOST_MATH_STATIC const T P[10] = {
          BOOST_MATH_BIG_CONSTANT(T, 53, 2.98677224343598593013),
          BOOST_MATH_BIG_CONSTANT(T, 53, 0.356343618769377415068),
@@ -590,6 +591,7 @@ BOOST_MATH_GPU_ENABLED T expint_i_imp(T z, const Policy& pol, const boost::math:
       BOOST_MATH_STATIC_LOCAL_VARIABLE const T r1 = static_cast<T>(c1 / c2);
       BOOST_MATH_STATIC_LOCAL_VARIABLE const T r2 = BOOST_MATH_BIG_CONSTANT(T, 53, 0.131401834143860282009280387409357165515556574352422001206362e-16);
       BOOST_MATH_STATIC_LOCAL_VARIABLE const T r = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 53, 0.372507410781366634461991866580119133535689497771654051555657435242200120636201854384926049951548942392));
+      // LCOV_EXCL_STOP
       T t = (z / 3) - 1;
       result = tools::evaluate_polynomial(P, t)
          / tools::evaluate_polynomial(Q, t);
@@ -609,6 +611,7 @@ BOOST_MATH_GPU_ENABLED T expint_i_imp(T z, const Policy& pol, const boost::math:
       // Maximum Deviation Found:                     6.546e-17
       // Expected Error Term:                         6.546e-17
       // Max Error found at double precision =        Poly: 6.890169e-17   Cheb: 6.772128e-17
+      // LCOV_EXCL_START
       BOOST_MATH_STATIC_LOCAL_VARIABLE const T Y = 1.158985137939453125F;
       BOOST_MATH_STATIC const T P[8] = {
          BOOST_MATH_BIG_CONSTANT(T, 53, 0.00139324086199402804173),
@@ -630,6 +633,7 @@ BOOST_MATH_GPU_ENABLED T expint_i_imp(T z, const Policy& pol, const boost::math:
          BOOST_MATH_BIG_CONSTANT(T, 53, 0.000402453408512476836472),
          BOOST_MATH_BIG_CONSTANT(T, 53, 0.263649630720255691787e-4)
       };
+      // LCOV_EXCL_STOP
       T t = z / 2 - 4;
       result = Y + tools::evaluate_polynomial(P, t)
          / tools::evaluate_polynomial(Q, t);
@@ -641,7 +645,7 @@ BOOST_MATH_GPU_ENABLED T expint_i_imp(T z, const Policy& pol, const boost::math:
       // Maximum Deviation Found:                     1.843e-17
       // Expected Error Term:                         -1.842e-17
       // Max Error found at double precision =        Poly: 4.375868e-17   Cheb: 5.860967e-17
-
+      // LCOV_EXCL_START
       BOOST_MATH_STATIC_LOCAL_VARIABLE const T Y = 1.0869731903076171875F;
       BOOST_MATH_STATIC const T P[9] = {
          BOOST_MATH_BIG_CONSTANT(T, 53, -0.00893891094356945667451),
@@ -665,6 +669,7 @@ BOOST_MATH_GPU_ENABLED T expint_i_imp(T z, const Policy& pol, const boost::math:
          BOOST_MATH_BIG_CONSTANT(T, 53, 0.00278170769163303669021),
          BOOST_MATH_BIG_CONSTANT(T, 53, 0.000159150281166108755531)
       };
+      // LCOV_EXCL_STOP
       T t = z / 5 - 3;
       result = Y + tools::evaluate_polynomial(P, t)
          / tools::evaluate_polynomial(Q, t);
@@ -676,8 +681,7 @@ BOOST_MATH_GPU_ENABLED T expint_i_imp(T z, const Policy& pol, const boost::math:
       // Maximum Deviation Found:                     5.102e-18
       // Expected Error Term:                         5.101e-18
       // Max Error found at double precision =        Poly: 1.441088e-16   Cheb: 1.864792e-16
-
-
+      // LCOV_EXCL_START
       BOOST_MATH_STATIC_LOCAL_VARIABLE const T Y = 1.03937530517578125F;
       BOOST_MATH_STATIC const T P[9] = {
          BOOST_MATH_BIG_CONSTANT(T, 53, -0.00356165148914447597995),
@@ -700,6 +704,7 @@ BOOST_MATH_GPU_ENABLED T expint_i_imp(T z, const Policy& pol, const boost::math:
          BOOST_MATH_BIG_CONSTANT(T, 53, 0.0651165455496281337831),
          BOOST_MATH_BIG_CONSTANT(T, 53, 0.00488071077519227853585)
       };
+      // LCOV_EXCL_STOP
       T t = z / 10 - 3;
       result = Y + tools::evaluate_polynomial(P, t)
          / tools::evaluate_polynomial(Q, t);
@@ -709,6 +714,7 @@ BOOST_MATH_GPU_ENABLED T expint_i_imp(T z, const Policy& pol, const boost::math:
    else
    {
       // Max Error found at double precision =        3.381886e-17
+      // LCOV_EXCL_START
       BOOST_MATH_STATIC_LOCAL_VARIABLE const T exp40 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 53, 2.35385266837019985407899910749034804508871617254555467236651e17));
       BOOST_MATH_STATIC_LOCAL_VARIABLE const T Y= 1.013065338134765625F;
       BOOST_MATH_STATIC const T P[6] = {
@@ -728,6 +734,7 @@ BOOST_MATH_GPU_ENABLED T expint_i_imp(T z, const Policy& pol, const boost::math:
          BOOST_MATH_BIG_CONSTANT(T, 53, 54738.2833147775537106),
          BOOST_MATH_BIG_CONSTANT(T, 53, 8297.16296356518409347)
       };
+      // LCOV_EXCL_STOP
       T t = 1 / z;
       result = Y + tools::evaluate_polynomial(P, t)
          / tools::evaluate_polynomial(Q, t);

include/boost/math/special_functions/fpclassify.hpp

@@ -127,7 +127,7 @@ template<> inline BOOST_MATH_GPU_ENABLED int (fpclassify)(float t)
    }
    else if(at > FLT_MAX)
       return FP_INFINITE;
-   return FP_NAN;
+   return FP_NAN;    // LCOV_EXCL_LINE  should not normally be reachable.
 }
 
 template<> inline BOOST_MATH_GPU_ENABLED int (fpclassify)(double t)

include/boost/math/special_functions/jacobi_elliptic.hpp

@@ -41,9 +41,7 @@ T jacobi_imp(const T& x, const T& k, T* cn, T* dn, const Policy& pol, const char
    BOOST_MATH_STD_USING
    if(k < 0)
    {
-      *cn = policies::raise_domain_error<T>(function, "Modulus k must be positive but got %1%.", k, pol);
-      *dn = *cn;
-      return *cn;
+      return *dn = *cn = policies::raise_domain_error<T>(function, "Modulus k must be positive but got %1%.", k, pol);
    }
    if(k > 1)
    {