text: //  (C) Copyright Matt Borland 2021.
  //  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)
  //
  //  Constexpr implementation of sqrt function
  
  #ifndef BOOST_MATH_CCMATH_SQRT
  #define BOOST_MATH_CCMATH_SQRT
  
  #include <cmath>
  #include <limits>
  #include <type_traits>
  #include <boost/math/ccmath/isnan.hpp>
  #include <boost/math/ccmath/isinf.hpp>
  #include <boost/math/tools/is_constant_evaluated.hpp>
  
  namespace boost::math::ccmath { 
  
  namespace detail {
  
  template <typename Real>
  inline constexpr Real sqrt_impl_2(Real x, Real s, Real s2)
  {
      return !(s < s2) ? s2 : sqrt_impl_2(x, (x / s + s) / 2, s);
  }
  
  template <typename Real>
  inline constexpr Real sqrt_impl_1(Real x, Real s)
  {
      return sqrt_impl_2(x, (x / s + s) / 2, s);
  }
  
  template <typename Real>
  inline constexpr Real sqrt_impl(Real x)
  {
      return sqrt_impl_1(x, x > 1 ? x : Real(1));
  }
  
  } // namespace detail
  
  template <typename Real, std::enable_if_t<!std::is_integral_v<Real>, bool> = true>
  inline constexpr Real sqrt(Real x)
  {
      if(BOOST_MATH_IS_CONSTANT_EVALUATED(x))
      {
          return boost::math::ccmath::isnan(x) ? std::numeric_limits<Real>::quiet_NaN() : 
                 boost::math::ccmath::isinf(x) ? std::numeric_limits<Real>::infinity() : 
                 detail::sqrt_impl<Real>(x);
      }
      else
      {
          using std::sqrt;
          return sqrt(x);
      }
  }
  
  template <typename Z, std::enable_if_t<std::is_integral_v<Z>, bool> = true>
  inline constexpr double sqrt(Z x)
  {
      return detail::sqrt_impl<double>(static_cast<double>(x));
  }
  
  } // Namespaces
  
  #endif // BOOST_MATH_CCMATH_SQRT
  