boost/math/special_functions/cbrt.hpp

//  (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_SF_CBRT_HPP
#define BOOST_MATH_SF_CBRT_HPP

#ifdef _MSC_VER
#pragma once
#endif

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

namespace boost{ namespace math{

namespace detail
{

   template <class T>
   struct cbrt_functor
   {
       cbrt_functor(T const& target) : a(target){}
       std::tr1::tuple<T, T, T> operator()(T const& z)
       {
         T sqr = z * z;
         return std::tr1::make_tuple(sqr * z - a, 3 * sqr, 6 * z);
       }
   private:
       T a;
   };

template <class T, class Policy>
T cbrt_imp(T z, const Policy&)
{
   BOOST_MATH_STD_USING
   int i_exp, sign(1);
   if(z < 0)
   {
      z = -z;
      sign = -sign;
   }
   if(z == 0)
      return 0;

   frexp(z, &i_exp);
   T min = static_cast<T>(ldexp(0.5, i_exp/3));
   T max = static_cast<T>(ldexp(2.0, i_exp/3));
   T guess = static_cast<T>(ldexp(1.0, i_exp/3));
   int digits = (policies::digits<T, Policy>()) / 2;
   return sign * tools::halley_iterate(detail::cbrt_functor<T>(z), guess, min, max, digits);
}

} // namespace detail

template <class T, class Policy>
inline typename tools::promote_args<T>::type cbrt(T z, const Policy& pol)
{
   typedef typename tools::promote_args<T>::type result_type;
   return detail::cbrt_imp(result_type(z), pol);
}

template <class T>
inline typename tools::promote_args<T>::type cbrt(T z)
{
   return cbrt(z, policies::policy<>());
}

} // namespace math
} // namespace boost

#endif // BOOST_MATH_SF_CBRT_HPP