comparison DEPENDENCIES/generic/include/boost/math/special_functions/cbrt.hpp @ 16:2665513ce2d3

Add boost headers

+//  (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/rational.hpp>
+#include <boost/math/policies/error_handling.hpp>
+#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/math/special_functions/fpclassify.hpp>
+#include <boost/mpl/divides.hpp>
+#include <boost/mpl/plus.hpp>
+#include <boost/mpl/if.hpp>
+#include <boost/type_traits/is_convertible.hpp>
+
+namespace boost{ namespace math{
+
+namespace detail
+{
+
+struct big_int_type
+{
+   operator boost::uintmax_t()const;
+};
+
+template <class T>
+struct largest_cbrt_int_type
+{
+   typedef typename mpl::if_<
+      boost::is_convertible<big_int_type, T>,
+      boost::uintmax_t,
+      unsigned int
+   >::type type;
+};
+
+template <class T, class Policy>
+T cbrt_imp(T z, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   //
+   // cbrt approximation for z in the range [0.5,1]
+   // It's hard to say what number of terms gives the optimum
+   // trade off between precision and performance, this seems
+   // to be about the best for double precision.
+   //
+   // Maximum Deviation Found:                     1.231e-006
+   // Expected Error Term:                         -1.231e-006
+   // Maximum Relative Change in Control Points:   5.982e-004
+   //
+   static const T P[] = { 
+      static_cast<T>(0.37568269008611818),
+      static_cast<T>(1.3304968705558024),
+      static_cast<T>(-1.4897101632445036),
+      static_cast<T>(1.2875573098219835),
+      static_cast<T>(-0.6398703759826468),
+      static_cast<T>(0.13584489959258635),
+   };
+   static const T correction[] = {
+      static_cast<T>(0.62996052494743658238360530363911),  // 2^-2/3
+      static_cast<T>(0.79370052598409973737585281963615),  // 2^-1/3
+      static_cast<T>(1),
+      static_cast<T>(1.2599210498948731647672106072782),   // 2^1/3
+      static_cast<T>(1.5874010519681994747517056392723),   // 2^2/3
+   };
+
+   if(!(boost::math::isfinite)(z))
+   {
+      return policies::raise_domain_error("boost::math::cbrt<%1%>(%1%)", "Argument to function must be finite but got %1%.", z, pol);
+   }
+
+   int i_exp, sign(1);
+   if(z < 0)
+   {
+      z = -z;
+      sign = -sign;
+   }
+   if(z == 0)
+      return 0;
+
+   T guess = frexp(z, &i_exp);
+   int original_i_exp = i_exp; // save for later
+   guess = tools::evaluate_polynomial(P, guess);
+   int i_exp3 = i_exp / 3;
+
+   typedef typename largest_cbrt_int_type<T>::type shift_type;
+
+   BOOST_STATIC_ASSERT( ::std::numeric_limits<shift_type>::radix == 2);
+
+   if(abs(i_exp3) < std::numeric_limits<shift_type>::digits)
+   {
+      if(i_exp3 > 0)
+         guess *= shift_type(1u) << i_exp3;
+      else
+         guess /= shift_type(1u) << -i_exp3;
+   }
+   else
+   {
+      guess = ldexp(guess, i_exp3);
+   }
+   i_exp %= 3;
+   guess *= correction[i_exp + 2];
+   //
+   // Now inline Halley iteration.
+   // We do this here rather than calling tools::halley_iterate since we can
+   // simplify the expressions algebraically, and don't need most of the error
+   // checking of the boilerplate version as we know in advance that the function
+   // is well behaved...
+   //
+   typedef typename policies::precision<T, Policy>::type prec;
+   typedef typename mpl::divides<prec, mpl::int_<3> >::type prec3;
+   typedef typename mpl::plus<prec3, mpl::int_<3> >::type new_prec;
+   typedef typename policies::normalise<Policy, policies::digits2<new_prec::value> >::type new_policy;
+   //
+   // Epsilon calculation uses compile time arithmetic when it's available for type T,
+   // otherwise uses ldexp to calculate at runtime:
+   //
+   T eps = (new_prec::value > 3) ? policies::get_epsilon<T, new_policy>() : ldexp(T(1), -2 - tools::digits<T>() / 3);
+   T diff;
+
+   if(original_i_exp < std::numeric_limits<T>::max_exponent - 3)
+   {
+      //
+      // Safe from overflow, use the fast method:
+      //
+      do
+      {
+         T g3 = guess * guess * guess;
+         diff = (g3 + z + z) / (g3 + g3 + z);
+         guess *= diff;
+      }
+      while(fabs(1 - diff) > eps);
+   }
+   else
+   {
+      //
+      // Either we're ready to overflow, or we can't tell because numeric_limits isn't
+      // available for type T:
+      //
+      do
+      {
+         T g2 = guess * guess;
+         diff = (g2 - z / guess) / (2 * guess + z / g2);
+         guess -= diff;
+      }
+      while((guess * eps) < fabs(diff));
+   }
+
+   return sign * guess;
+}
+
+} // 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;
+   typedef typename policies::evaluation<result_type, Policy>::type value_type;
+   return static_cast<result_type>(detail::cbrt_imp(value_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
+
+
+
+