Chris@16: //  (C) Copyright John Maddock 2006.
Chris@16: //  Use, modification and distribution are subject to the
Chris@16: //  Boost Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_MATH_SQRT1PM1
Chris@16: #define BOOST_MATH_SQRT1PM1
Chris@16: 
Chris@16: #ifdef _MSC_VER
Chris@16: #pragma once
Chris@16: #endif
Chris@16: 
Chris@101: #include <boost/math/special_functions/math_fwd.hpp>
Chris@16: #include <boost/math/special_functions/log1p.hpp>
Chris@16: #include <boost/math/special_functions/expm1.hpp>
Chris@16: 
Chris@16: //
Chris@16: // This algorithm computes sqrt(1+x)-1 for small x:
Chris@16: //
Chris@16: 
Chris@16: namespace boost{ namespace math{
Chris@16: 
Chris@16: template <class T, class Policy>
Chris@16: inline typename tools::promote_args<T>::type sqrt1pm1(const T& val, const Policy& pol)
Chris@16: {
Chris@16:    typedef typename tools::promote_args<T>::type result_type;
Chris@16:    BOOST_MATH_STD_USING
Chris@16: 
Chris@16:    if(fabs(result_type(val)) > 0.75)
Chris@16:       return sqrt(1 + result_type(val)) - 1;
Chris@16:    return boost::math::expm1(boost::math::log1p(val, pol) / 2, pol);
Chris@16: }
Chris@16: 
Chris@16: template <class T>
Chris@16: inline typename tools::promote_args<T>::type sqrt1pm1(const T& val)
Chris@16: {
Chris@16:    return sqrt1pm1(val, policies::policy<>());
Chris@16: }
Chris@16: 
Chris@16: } // namespace math
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #endif // BOOST_MATH_SQRT1PM1
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: