//  (C) Copyright John Maddock 2006.

//  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 BOOST_MATH_SQRT1PM1

#define BOOST_MATH_SQRT1PM1



#include <boost/math/special_functions/log1p.hpp>

#include <boost/math/special_functions/expm1.hpp>

#include <boost/math/special_functions/math_fwd.hpp>



//

// This algorithm computes sqrt(1+x)-1 for small x:

//



namespace boost{ namespace math{



template <class T, class Policy>

inline typename tools::promote_args<T>::type sqrt1pm1(const T& val, const Policy& pol)

{

   typedef typename tools::promote_args<T>::type result_type;

   BOOST_MATH_STD_USING



   if(fabs(result_type(val)) > 0.75)

      return sqrt(1 + result_type(val)) - 1;

   return boost::math::expm1(boost::math::log1p(val, pol) / 2, pol);

}



template <class T>

inline typename tools::promote_args<T>::type sqrt1pm1(const T& val)

{

   return sqrt1pm1(val, policies::policy<>());

}



} // namespace math

} // namespace boost



#endif // BOOST_MATH_SQRT1PM1









