text: 
  // Copyright Christopher Kormanyos 2002 - 2011.
  // Copyright 2011 John Maddock. Distributed under the Boost
  // Distributed under 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)
  
  // This work is based on an earlier work:
  // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
  // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
  //
  // This file has no include guards or namespaces - it's expanded inline inside default_ops.hpp
  // 
  
  #ifdef BOOST_MSVC
  #pragma warning(push)
  #pragma warning(disable:6326)  // comparison of two constants
  #endif
  
  template <class T>
  void hyp0F1(T& result, const T& b, const T& x)
  {
     typedef typename boost::multiprecision::detail::canonical<boost::int32_t, T>::type si_type;
     typedef typename boost::multiprecision::detail::canonical<boost::uint32_t, T>::type ui_type;
  
     // Compute the series representation of Hypergeometric0F1 taken from
     // http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric0F1/06/01/01/
     // There are no checks on input range or parameter boundaries.
  
     T x_pow_n_div_n_fact(x);
     T pochham_b         (b);
     T bp                (b);
  
     eval_divide(result, x_pow_n_div_n_fact, pochham_b);
     eval_add(result, ui_type(1));
  
     si_type n;
  
     T tol;
     tol = ui_type(1);
     eval_ldexp(tol, tol, 1 - boost::multiprecision::detail::digits2<number<T, et_on> >::value);
     eval_multiply(tol, result);
     if(eval_get_sign(tol) < 0)
        tol.negate();
     T term;
  
     static const int series_limit = 
        boost::multiprecision::detail::digits2<number<T, et_on> >::value < 100
        ? 100 : boost::multiprecision::detail::digits2<number<T, et_on> >::value;
     // Series expansion of hyperg_0f1(; b; x).
     for(n = 2; n < series_limit; ++n)
     {
        eval_multiply(x_pow_n_div_n_fact, x);
        eval_divide(x_pow_n_div_n_fact, n);
        eval_increment(bp);
        eval_multiply(pochham_b, bp);
  
        eval_divide(term, x_pow_n_div_n_fact, pochham_b);
        eval_add(result, term);
  
        bool neg_term = eval_get_sign(term) < 0;
        if(neg_term)
           term.negate();
        if(term.compare(tol) <= 0)
           break;
     }
  
     if(n >= series_limit)
        BOOST_THROW_EXCEPTION(std::runtime_error("H0F1 Failed to Converge"));
  }
  
  
  template <class T>
  void eval_sin(T& result, const T& x)
  {
     BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The sin function is only valid for floating point types.");
     if(&result == &x)
     {
        T temp;
        eval_sin(temp, x);
        result = temp;
        return;
     }
  
     typedef typename boost::multiprecision::detail::canonical<boost::int32_t, T>::type si_type;
     typedef typename boost::multiprecision::detail::canonical<boost::uint32_t, T>::type ui_type;
     typedef typename mpl::front<typename T::float_types>::type fp_type;
  
     switch(eval_fpclassify(x))
     {
     case FP_INFINITE:
     case FP_NAN:
        if(std::numeric_limits<number<T, et_on> >::has_quiet_NaN)
           result = std::numeric_limits<number<T, et_on> >::quiet_NaN().backend();
        else
           BOOST_THROW_EXCEPTION(std::domain_error("Result is undefined or complex and there is no NaN for this number type."));
        return;
     case FP_ZERO:
        result = ui_type(0);
        return;
     default: ;
     }
  
     // Local copy of the argument
     T xx = x;
  
     // Analyze and prepare the phase of the argument.
     // Make a local, positive copy of the argument, xx.
     // The argument xx will be reduced to 0 <= xx <= pi/2.
     bool b_negate_sin = false;
  
     if(eval_get_sign(x) < 0)
     {
        xx.negate();
        b_negate_sin = !b_negate_sin;
     }
  
     T n_pi, t;
     // Remove even multiples of pi.
     if(xx.compare(get_constant_pi<T>()) > 0)
     {
        eval_divide(n_pi, xx, get_constant_pi<T>());
        eval_trunc(n_pi, n_pi);
        t = ui_type(2);
        eval_fmod(t, n_pi, t);
        const bool b_n_pi_is_even = eval_get_sign(t) == 0;
        eval_multiply(n_pi, get_constant_pi<T>());
        eval_subtract(xx, n_pi);
  
        BOOST_MATH_INSTRUMENT_CODE(xx.str(0, std::ios_base::scientific));
        BOOST_MATH_INSTRUMENT_CODE(n_pi.str(0, std::ios_base::scientific));
  
        // Adjust signs if the multiple of pi is not even.
        if(!b_n_pi_is_even)
        {
           b_negate_sin = !b_negate_sin;
        }
     }
  
     // Reduce the argument to 0 <= xx <= pi/2.
     eval_ldexp(t, get_constant_pi<T>(), -1);
     if(xx.compare(t) > 0)
     {
        eval_subtract(xx, get_constant_pi<T>(), xx);
        BOOST_MATH_INSTRUMENT_CODE(xx.str(0, std::ios_base::scientific));
     }
  
     eval_subtract(t, xx);
     const bool b_zero    = eval_get_sign(xx) == 0;
     const bool b_pi_half = eval_get_sign(t) == 0;
  
     // Check if the reduced argument is very close to 0 or pi/2.
     const bool    b_near_zero    = xx.compare(fp_type(1e-1)) < 0;
     const bool    b_near_pi_half = t.compare(fp_type(1e-1)) < 0;;
  
     if(b_zero)
     {
        result = ui_type(0);
     }
     else if(b_pi_half)
     {
        result = ui_type(1);
     }
     else if(b_near_zero)
     {
        eval_multiply(t, xx, xx);
        eval_divide(t, si_type(-4));
        T t2;
        t2 = fp_type(1.5);
        hyp0F1(result, t2, t);
        BOOST_MATH_INSTRUMENT_CODE(result.str(0, std::ios_base::scientific));
        eval_multiply(result, xx);
     }
     else if(b_near_pi_half)
     {
        eval_multiply(t, t);
        eval_divide(t, si_type(-4));
        T t2;
        t2 = fp_type(0.5);
        hyp0F1(result, t2, t);
        BOOST_MATH_INSTRUMENT_CODE(result.str(0, std::ios_base::scientific));
     }
     else
     {
        // Scale to a small argument for an efficient Taylor series,
        // implemented as a hypergeometric function. Use a standard
        // divide by three identity a certain number of times.
        // Here we use division by 3^9 --> (19683 = 3^9).
  
        static const si_type n_scale = 9;
        static const si_type n_three_pow_scale = static_cast<si_type>(19683L);
  
        eval_divide(xx, n_three_pow_scale);
  
        // Now with small arguments, we are ready for a series expansion.
        eval_multiply(t, xx, xx);
        eval_divide(t, si_type(-4));
        T t2;
        t2 = fp_type(1.5);
        hyp0F1(result, t2, t);
        BOOST_MATH_INSTRUMENT_CODE(result.str(0, std::ios_base::scientific));
        eval_multiply(result, xx);
  
        // Convert back using multiple angle identity.
        for(boost::int32_t k = static_cast<boost::int32_t>(0); k < n_scale; k++)
        {
           // Rescale the cosine value using the multiple angle identity.
           eval_multiply(t2, result, ui_type(3));
           eval_multiply(t, result, result);
           eval_multiply(t, result);
           eval_multiply(t, ui_type(4));
           eval_subtract(result, t2, t);
        }
     }
  
     if(b_negate_sin)
        result.negate();
  }
  
  template <class T>
  void eval_cos(T& result, const T& x)
  {
     BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The cos function is only valid for floating point types.");
     if(&result == &x)
     {
        T temp;
        eval_cos(temp, x);
        result = temp;
        return;
     }
  
     typedef typename boost::multiprecision::detail::canonical<boost::int32_t, T>::type si_type;
     typedef typename boost::multiprecision::detail::canonical<boost::uint32_t, T>::type ui_type;
     typedef typename mpl::front<typename T::float_types>::type fp_type;
  
     switch(eval_fpclassify(x))
     {
     case FP_INFINITE:
     case FP_NAN:
        if(std::numeric_limits<number<T, et_on> >::has_quiet_NaN)
           result = std::numeric_limits<number<T, et_on> >::quiet_NaN().backend();
        else
           BOOST_THROW_EXCEPTION(std::domain_error("Result is undefined or complex and there is no NaN for this number type."));
        return;
     case FP_ZERO:
        result = ui_type(1);
        return;
     default: ;
     }
  
     // Local copy of the argument
     T xx = x;
  
     // Analyze and prepare the phase of the argument.
     // Make a local, positive copy of the argument, xx.
     // The argument xx will be reduced to 0 <= xx <= pi/2.
     bool b_negate_cos = false;
  
     if(eval_get_sign(x) < 0)
     {
        xx.negate();
     }
  
     T n_pi, t;
     // Remove even multiples of pi.
     if(xx.compare(get_constant_pi<T>()) > 0)
     {
        eval_divide(t, xx, get_constant_pi<T>());
        eval_trunc(n_pi, t);
        BOOST_MATH_INSTRUMENT_CODE(n_pi.str(0, std::ios_base::scientific));
        eval_multiply(t, n_pi, get_constant_pi<T>());
        BOOST_MATH_INSTRUMENT_CODE(t.str(0, std::ios_base::scientific));
        eval_subtract(xx, t);
        BOOST_MATH_INSTRUMENT_CODE(xx.str(0, std::ios_base::scientific));
  
        // Adjust signs if the multiple of pi is not even.
        t = ui_type(2);
        eval_fmod(t, n_pi, t);
        const bool b_n_pi_is_even = eval_get_sign(t) == 0;
  
        if(!b_n_pi_is_even)
        {
           b_negate_cos = !b_negate_cos;
        }
     }
  
     // Reduce the argument to 0 <= xx <= pi/2.
     eval_ldexp(t, get_constant_pi<T>(), -1);
     int com = xx.compare(t);
     if(com > 0)
     {
        eval_subtract(xx, get_constant_pi<T>(), xx);
        b_negate_cos = !b_negate_cos;
        BOOST_MATH_INSTRUMENT_CODE(xx.str(0, std::ios_base::scientific));
     }
  
     const bool b_zero    = eval_get_sign(xx) == 0;
     const bool b_pi_half = com == 0;
  
     // Check if the reduced argument is very close to 0.
     const bool    b_near_zero    = xx.compare(fp_type(1e-1)) < 0;
  
     if(b_zero)
     {
        result = si_type(1);
     }
     else if(b_pi_half)
     {
        result = si_type(0);
     }
     else if(b_near_zero)
     {
        eval_multiply(t, xx, xx);
        eval_divide(t, si_type(-4));
        n_pi = fp_type(0.5f);
        hyp0F1(result, n_pi, t);
        BOOST_MATH_INSTRUMENT_CODE(result.str(0, std::ios_base::scientific));
     }
     else
     {
        eval_subtract(t, xx);
        eval_sin(result, t);
     }
     if(b_negate_cos)
        result.negate();
  }
  
  template <class T>
  void eval_tan(T& result, const T& x)
  {
     BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The tan function is only valid for floating point types.");
     if(&result == &x)
     {
        T temp;
        eval_tan(temp, x);
        result = temp;
        return;
     }
     T t;
     eval_sin(result, x);
     eval_cos(t, x);
     eval_divide(result, t);
  }
  
  template <class T>
  void hyp2F1(T& result, const T& a, const T& b, const T& c, const T& x)
  {
    // Compute the series representation of hyperg_2f1 taken from
    // Abramowitz and Stegun 15.1.1.
    // There are no checks on input range or parameter boundaries.
  
     typedef typename boost::multiprecision::detail::canonical<boost::uint32_t, T>::type ui_type;
  
     T x_pow_n_div_n_fact(x);
     T pochham_a         (a);
     T pochham_b         (b);
     T pochham_c         (c);
     T ap                (a);
     T bp                (b);
     T cp                (c);
  
     eval_multiply(result, pochham_a, pochham_b);
     eval_divide(result, pochham_c);
     eval_multiply(result, x_pow_n_div_n_fact);
     eval_add(result, ui_type(1));
  
     T lim;
     eval_ldexp(lim, result, 1 - boost::multiprecision::detail::digits2<number<T, et_on> >::value);
  
     if(eval_get_sign(lim) < 0)
        lim.negate();
  
     ui_type n;
     T term;
  
     static const unsigned series_limit = 
        boost::multiprecision::detail::digits2<number<T, et_on> >::value < 100
        ? 100 : boost::multiprecision::detail::digits2<number<T, et_on> >::value;
     // Series expansion of hyperg_2f1(a, b; c; x).
     for(n = 2; n < series_limit; ++n)
     {
        eval_multiply(x_pow_n_div_n_fact, x);
        eval_divide(x_pow_n_div_n_fact, n);
  
        eval_increment(ap);
        eval_multiply(pochham_a, ap);
        eval_increment(bp);
        eval_multiply(pochham_b, bp);
        eval_increment(cp);
        eval_multiply(pochham_c, cp);
  
        eval_multiply(term, pochham_a, pochham_b);
        eval_divide(term, pochham_c);
        eval_multiply(term, x_pow_n_div_n_fact);
        eval_add(result, term);
  
        if(eval_get_sign(term) < 0)
           term.negate();
        if(lim.compare(term) >= 0)
           break;
     }
     if(n > series_limit)
        BOOST_THROW_EXCEPTION(std::runtime_error("H2F1 failed to converge."));
  }
  
  template <class T>
  void eval_asin(T& result, const T& x)
  {
     BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The asin function is only valid for floating point types.");
     typedef typename boost::multiprecision::detail::canonical<boost::uint32_t, T>::type ui_type;
     typedef typename mpl::front<typename T::float_types>::type fp_type;
  
     if(&result == &x)
     {
        T t(x);
        eval_asin(result, t);
        return;
     }
  
     switch(eval_fpclassify(x))
     {
     case FP_NAN:
     case FP_INFINITE:
        if(std::numeric_limits<number<T, et_on> >::has_quiet_NaN)
           result = std::numeric_limits<number<T, et_on> >::quiet_NaN().backend();
        else
           BOOST_THROW_EXCEPTION(std::domain_error("Result is undefined or complex and there is no NaN for this number type."));
        return;
     case FP_ZERO:
        result = ui_type(0);
        return;
     default: ;
     }
  
     const bool b_neg = eval_get_sign(x) < 0;
  
     T xx(x);
     if(b_neg)
        xx.negate();
  
     int c = xx.compare(ui_type(1));
     if(c > 0)
     {
        if(std::numeric_limits<number<T, et_on> >::has_quiet_NaN)
           result = std::numeric_limits<number<T, et_on> >::quiet_NaN().backend();
        else
           BOOST_THROW_EXCEPTION(std::domain_error("Result is undefined or complex and there is no NaN for this number type."));
        return;
     }
     else if(c == 0)
     {
        result = get_constant_pi<T>();
        eval_ldexp(result, result, -1);
        if(b_neg)
           result.negate();
        return;
     }
  
     if(xx.compare(fp_type(1e-4)) < 0)
     {
        // http://functions.wolfram.com/ElementaryFunctions/ArcSin/26/01/01/
        eval_multiply(xx, xx);
        T t1, t2;
        t1 = fp_type(0.5f);
        t2 = fp_type(1.5f);
        hyp2F1(result, t1, t1, t2, xx);
        eval_multiply(result, x);
        return;
     }
     else if(xx.compare(fp_type(1 - 1e-4f)) > 0)
     {
        T dx1;
        T t1, t2;
        eval_subtract(dx1, ui_type(1), xx);
        t1 = fp_type(0.5f);
        t2 = fp_type(1.5f);
        eval_ldexp(dx1, dx1, -1);
        hyp2F1(result, t1, t1, t2, dx1);
        eval_ldexp(dx1, dx1, 2);
        eval_sqrt(t1, dx1);
        eval_multiply(result, t1);
        eval_ldexp(t1, get_constant_pi<T>(), -1);
        result.negate();
        eval_add(result, t1);
        if(b_neg)
           result.negate();
        return;
     }
  #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
     typedef typename boost::multiprecision::detail::canonical<long double, T>::type guess_type;
  #else
     typedef fp_type guess_type;
  #endif
     // Get initial estimate using standard math function asin.
     guess_type dd;
     eval_convert_to(&dd, xx);
  
     result = (guess_type)(std::asin(dd));
  
     unsigned current_digits = std::numeric_limits<guess_type>::digits - 5;
     unsigned target_precision = boost::multiprecision::detail::digits2<number<T, et_on> >::value;
  
     // Newton-Raphson iteration
     while(current_digits < target_precision)
     {
        T sine, cosine;
        eval_sin(sine, result);
        eval_cos(cosine, result);
        eval_subtract(sine, xx);
        eval_divide(sine, cosine);
        eval_subtract(result, sine);
  
        current_digits *= 2;
        /*
        T lim;
        eval_ldexp(lim, result, 1 - boost::multiprecision::detail::digits2<number<T, et_on> >::value);
        if(eval_get_sign(s) < 0)
           s.negate();
        if(eval_get_sign(lim) < 0)
           lim.negate();
        if(lim.compare(s) >= 0)
           break;
           */
     }
     if(b_neg)
        result.negate();
  }
  
  template <class T>
  inline void eval_acos(T& result, const T& x)
  {
     BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The acos function is only valid for floating point types.");
     typedef typename boost::multiprecision::detail::canonical<boost::uint32_t, T>::type ui_type;
  
     switch(eval_fpclassify(x))
     {
     case FP_NAN:
     case FP_INFINITE:
        if(std::numeric_limits<number<T, et_on> >::has_quiet_NaN)
           result = std::numeric_limits<number<T, et_on> >::quiet_NaN().backend();
        else
           BOOST_THROW_EXCEPTION(std::domain_error("Result is undefined or complex and there is no NaN for this number type."));
        return;
     case FP_ZERO:
        result = get_constant_pi<T>();
        eval_ldexp(result, result, -1); // divide by two.
        return;
     }
  
     eval_abs(result, x);
     int c = result.compare(ui_type(1));
  
     if(c > 0)
     {
        if(std::numeric_limits<number<T, et_on> >::has_quiet_NaN)
           result = std::numeric_limits<number<T, et_on> >::quiet_NaN().backend();
        else
           BOOST_THROW_EXCEPTION(std::domain_error("Result is undefined or complex and there is no NaN for this number type."));
        return;
     }
     else if(c == 0)
     {
        if(eval_get_sign(x) < 0)
           result = get_constant_pi<T>();
        else
           result = ui_type(0);
        return;
     }
  
     eval_asin(result, x);
     T t;
     eval_ldexp(t, get_constant_pi<T>(), -1);
     eval_subtract(result, t);
     result.negate();
  }
  
  template <class T>
  void eval_atan(T& result, const T& x)
  {
     BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The atan function is only valid for floating point types.");
     typedef typename boost::multiprecision::detail::canonical<boost::int32_t, T>::type si_type;
     typedef typename boost::multiprecision::detail::canonical<boost::uint32_t, T>::type ui_type;
     typedef typename mpl::front<typename T::float_types>::type fp_type;
  
     switch(eval_fpclassify(x))
     {
     case FP_NAN:
        result = x;
        return;
     case FP_ZERO:
        result = ui_type(0);
        return;
     case FP_INFINITE:
        if(eval_get_sign(x) < 0)
        {
           eval_ldexp(result, get_constant_pi<T>(), -1);
           result.negate();
        }
        else
           eval_ldexp(result, get_constant_pi<T>(), -1);
        return;
     default: ;
     }
  
     const bool b_neg = eval_get_sign(x) < 0;
  
     T xx(x);
     if(b_neg)
        xx.negate();
  
     if(xx.compare(fp_type(0.1)) < 0)
     {
        T t1, t2, t3;
        t1 = ui_type(1);
        t2 = fp_type(0.5f);
        t3 = fp_type(1.5f);
        eval_multiply(xx, xx);
        xx.negate();
        hyp2F1(result, t1, t2, t3, xx);
        eval_multiply(result, x);
        return;
     }
  
     if(xx.compare(fp_type(10)) > 0)
     {
        T t1, t2, t3;
        t1 = fp_type(0.5f);
        t2 = ui_type(1u);
        t3 = fp_type(1.5f);
        eval_multiply(xx, xx);
        eval_divide(xx, si_type(-1), xx);
        hyp2F1(result, t1, t2, t3, xx);
        eval_divide(result, x);
        if(!b_neg)
           result.negate();
        eval_ldexp(t1, get_constant_pi<T>(), -1);
        eval_add(result, t1);
        if(b_neg)
           result.negate();
        return;
     }
  
  
     // Get initial estimate using standard math function atan.
     fp_type d;
     eval_convert_to(&d, xx);
     result = fp_type(std::atan(d));
  
     // Newton-Raphson iteration
     static const boost::int32_t double_digits10_minus_a_few = std::numeric_limits<double>::digits10 - 3;
  
     T s, c, t;
     for(boost::int32_t digits = double_digits10_minus_a_few; digits <= std::numeric_limits<number<T, et_on> >::digits10; digits *= 2)
     {
        eval_sin(s, result);
        eval_cos(c, result);
        eval_multiply(t, xx, c);
        eval_subtract(t, s);
        eval_multiply(s, t, c);
        eval_add(result, s);
     }
     if(b_neg)
        result.negate();
  }
  
  template <class T>
  void eval_atan2(T& result, const T& y, const T& x)
  {
     BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The atan2 function is only valid for floating point types.");
     if(&result == &y)
     {
        T temp(y);
        eval_atan2(result, temp, x);
        return;
     }
     else if(&result == &x)
     {
        T temp(x);
        eval_atan2(result, y, temp);
        return;
     }
  
     typedef typename boost::multiprecision::detail::canonical<boost::uint32_t, T>::type ui_type;
  
     switch(eval_fpclassify(y))
     {
     case FP_NAN:
        result = y;
        return;
     case FP_ZERO:
        {
           int c = eval_get_sign(x);
           if(c < 0)
              result = get_constant_pi<T>();
           else if(c >= 0)
              result = ui_type(0); // Note we allow atan2(0,0) to be zero, even though it's mathematically undefined
           return;
        }
     case FP_INFINITE:
        {
           if(eval_fpclassify(x) == FP_INFINITE)
           {
              if(std::numeric_limits<number<T, et_on> >::has_quiet_NaN)
                 result = std::numeric_limits<number<T, et_on> >::quiet_NaN().backend();
              else
                 BOOST_THROW_EXCEPTION(std::domain_error("Result is undefined or complex and there is no NaN for this number type."));
           }
           else
           {
              eval_ldexp(result, get_constant_pi<T>(), -1);
              if(eval_get_sign(y) < 0)
                 result.negate();
           }
           return;
        }
     }
  
     switch(eval_fpclassify(x))
     {
     case FP_NAN:
        result = x;
        return;
     case FP_ZERO:
        {
           eval_ldexp(result, get_constant_pi<T>(), -1);
           if(eval_get_sign(y) < 0)
              result.negate();
           return;
        }
     case FP_INFINITE:
        if(eval_get_sign(x) > 0)
           result = ui_type(0);
        else
           result = get_constant_pi<T>();
        if(eval_get_sign(y) < 0)
           result.negate();
        return;
     }
  
     T xx;
     eval_divide(xx, y, x);
     if(eval_get_sign(xx) < 0)
        xx.negate();
  
     eval_atan(result, xx);
  
     // Determine quadrant (sign) based on signs of x, y
     const bool y_neg = eval_get_sign(y) < 0;
     const bool x_neg = eval_get_sign(x) < 0;
  
     if(y_neg != x_neg)
        result.negate();
  
     if(x_neg)
     {
        if(y_neg)
           eval_subtract(result, get_constant_pi<T>());
        else
           eval_add(result, get_constant_pi<T>());
     }
  }
  template<class T, class A> 
  inline typename enable_if<is_arithmetic<A>, void>::type eval_atan2(T& result, const T& x, const A& a)
  {
     typedef typename boost::multiprecision::detail::canonical<A, T>::type canonical_type;
     typedef typename mpl::if_<is_same<A, canonical_type>, T, canonical_type>::type cast_type;
     cast_type c;
     c = a;
     eval_atan2(result, x, c);
  }
  
  template<class T, class A> 
  inline typename enable_if<is_arithmetic<A>, void>::type eval_atan2(T& result, const A& x, const T& a)
  {
     typedef typename boost::multiprecision::detail::canonical<A, T>::type canonical_type;
     typedef typename mpl::if_<is_same<A, canonical_type>, T, canonical_type>::type cast_type;
     cast_type c;
     c = x;
     eval_atan2(result, c, a);
  }
  
  #ifdef BOOST_MSVC
  #pragma warning(pop)
  #endif
  