--- /dev/null
+// (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
+
+
+
+