Collected fixes for test_autodiff_8

[ci skip]

include/boost/math/special_functions/erf.hpp

@@ -204,7 +204,7 @@ T erf_imp(T z, bool invert, const Policy& pol, const std::integral_constant<int,
    {
       if(!invert)
          return -erf_imp(T(-z), invert, pol, t);
-      else if(z < -0.5)
+      else if(z < T(-0.5))
          return 2 - erf_imp(T(-z), invert, pol, t);
       else
          return 1 + erf_imp(T(-z), false, pol, t);
@@ -217,12 +217,12 @@ T erf_imp(T z, bool invert, const Policy& pol, const std::integral_constant<int,
    // which implementation to use,
    // try to put most likely options first:
    //
-   if(z < 0.5)
+   if(z < T(0.5))
    {
       //
       // We're going to calculate erf:
       //
-      if(z < 1e-10)
+      if(z < T(1e-10))
       {
          if(z == 0)
          {
@@ -294,7 +294,7 @@ T erf_imp(T z, bool invert, const Policy& pol, const std::integral_constant<int,
          BOOST_MATH_INSTRUMENT_VARIABLE(P[0]);
          BOOST_MATH_INSTRUMENT_VARIABLE(Q[0]);
          BOOST_MATH_INSTRUMENT_VARIABLE(z);
-         result = Y + tools::evaluate_polynomial(P, T(z - 0.5)) / tools::evaluate_polynomial(Q, T(z - 0.5));
+         result = Y + tools::evaluate_polynomial(P, T(z - T(0.5))) / tools::evaluate_polynomial(Q, T(z - T(0.5)));
          BOOST_MATH_INSTRUMENT_VARIABLE(result);
          result *= exp(-z * z) / z;
          BOOST_MATH_INSTRUMENT_VARIABLE(result);
@@ -322,7 +322,7 @@ T erf_imp(T z, bool invert, const Policy& pol, const std::integral_constant<int,
             BOOST_MATH_BIG_CONSTANT(T, 53, 0.0563921837420478160373),
             BOOST_MATH_BIG_CONSTANT(T, 53, 0.00410369723978904575884),
          };
-         result = Y + tools::evaluate_polynomial(P, T(z - 1.5)) / tools::evaluate_polynomial(Q, z - T(1.5));
+         result = Y + tools::evaluate_polynomial(P, T(z - T(1.5))) / tools::evaluate_polynomial(Q, z - T(1.5));
          T hi, lo;
          int expon;
          hi = floor(ldexp(frexp(z, &expon), 26));
@@ -355,7 +355,7 @@ T erf_imp(T z, bool invert, const Policy& pol, const std::integral_constant<int,
             BOOST_MATH_BIG_CONSTANT(T, 53, 0.0105982906484876531489),
             BOOST_MATH_BIG_CONSTANT(T, 53, 0.000479411269521714493907),
          };
-         result = Y + tools::evaluate_polynomial(P, T(z - 3.5)) / tools::evaluate_polynomial(Q, z - T(3.5));
+         result = Y + tools::evaluate_polynomial(P, T(z - T(3.5))) / tools::evaluate_polynomial(Q, z - T(3.5));
          T hi, lo;
          int expon;
          hi = floor(ldexp(frexp(z, &expon), 26));

include/boost/math/special_functions/hermite.hpp

@@ -23,7 +23,8 @@ template <class T1, class T2, class T3>
 inline typename tools::promote_args<T1, T2, T3>::type 
    hermite_next(unsigned n, T1 x, T2 Hn, T3 Hnm1)
 {
-   return (2 * x * Hn - 2 * n * Hnm1);
+   using promoted_type = tools::promote_args_t<T1, T2, T3>;
+   return (2 * promoted_type(x) * promoted_type(Hn) - 2 * n * promoted_type(Hnm1));
 }
 
 namespace detail{

include/boost/math/special_functions/lambert_w.hpp

@@ -1043,7 +1043,7 @@ T lambert_w_positive_rational_float(T z)
    BOOST_MATH_STD_USING
    if (z < 2)
    {
-      if (z < 0.5)
+      if (z < T(0.5))
       { // 0.05 < z < 0.5
         // Maximum Deviation Found:                     2.993e-08
         // Expected Error Term : 2.993e-08
@@ -1119,7 +1119,7 @@ T lambert_w_positive_rational_float(T z)
       };
       return Y + boost::math::tools::evaluate_rational(P, Q, z);
    }
-   else if (z < 9897.12905874)  // 2.8 < log(z) < 9.2
+   else if (z < T(9897.12905874))  // 2.8 < log(z) < 9.2
    {
       // Max error in interpolated form: 1.771e-08
       static const T Y = -1.402973175e+00f;
@@ -1139,7 +1139,7 @@ T lambert_w_positive_rational_float(T z)
       T log_w = log(z);
       return log_w + Y + boost::math::tools::evaluate_polynomial(P, log_w) / boost::math::tools::evaluate_polynomial(Q, log_w);
    }
-   else if (z < 7.896296e+13)  // 9.2 < log(z) <= 32
+   else if (z < T(7.896296e+13))  // 9.2 < log(z) <= 32
    {
       // Max error in interpolated form: 5.821e-08
       static const T Y = -2.735729218e+00f;
@@ -1184,9 +1184,9 @@ template <typename T, typename Policy>
 T lambert_w_negative_rational_float(T z, const Policy& pol)
 {
    BOOST_MATH_STD_USING
-   if (z > -0.27)
+   if (z > T(-0.27))
    {
-      if (z < -0.051)
+      if (z < T(-0.051))
       {
          // -0.27 < z < -0.051
          // Max error in interpolated form: 5.080e-08
@@ -1211,7 +1211,7 @@ T lambert_w_negative_rational_float(T z, const Policy& pol)
          return lambert_w0_small_z(z, pol);
       }
    }
-   else if (z > -0.3578794411714423215955237701)
+   else if (z > T(-0.3578794411714423215955237701))
    { // Very close to branch singularity.
      // Max error in interpolated form: 5.269e-08
       static const T Y = 1.220928431e-01f;

include/boost/math/special_functions/sin_pi.hpp

@@ -27,7 +27,7 @@ inline T sin_pi_imp(T x, const Policy& pol)
    if(x < 0)
       return -sin_pi_imp(T(-x), pol);
    // sin of pi*x:
-   if(x < 0.5)
+   if(x < T(0.5))
       return sin(constants::pi<T>() * x);
    bool invert;
    if(x < 1)