181 lines
5.2 KiB
Plaintext
181 lines
5.2 KiB
Plaintext
// (C) Copyright John Maddock 2006.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_MATH_SF_CBRT_HPP
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#define BOOST_MATH_SF_CBRT_HPP
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#ifdef _MSC_VER
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#pragma once
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#endif
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#include <boost/math/tools/rational.hpp>
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#include <boost/math/policies/error_handling.hpp>
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#include <boost/math/special_functions/math_fwd.hpp>
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#include <boost/math/special_functions/fpclassify.hpp>
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#include <boost/mpl/divides.hpp>
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#include <boost/mpl/plus.hpp>
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#include <boost/mpl/if.hpp>
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#include <boost/type_traits/is_convertible.hpp>
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namespace boost{ namespace math{
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namespace detail
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{
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struct big_int_type
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{
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operator boost::uintmax_t()const;
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};
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template <class T>
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struct largest_cbrt_int_type
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{
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typedef typename mpl::if_<
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boost::is_convertible<big_int_type, T>,
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boost::uintmax_t,
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unsigned int
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>::type type;
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};
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template <class T, class Policy>
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T cbrt_imp(T z, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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//
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// cbrt approximation for z in the range [0.5,1]
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// It's hard to say what number of terms gives the optimum
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// trade off between precision and performance, this seems
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// to be about the best for double precision.
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//
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// Maximum Deviation Found: 1.231e-006
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// Expected Error Term: -1.231e-006
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// Maximum Relative Change in Control Points: 5.982e-004
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//
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static const T P[] = {
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static_cast<T>(0.37568269008611818),
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static_cast<T>(1.3304968705558024),
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static_cast<T>(-1.4897101632445036),
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static_cast<T>(1.2875573098219835),
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static_cast<T>(-0.6398703759826468),
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static_cast<T>(0.13584489959258635),
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};
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static const T correction[] = {
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static_cast<T>(0.62996052494743658238360530363911), // 2^-2/3
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static_cast<T>(0.79370052598409973737585281963615), // 2^-1/3
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static_cast<T>(1),
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static_cast<T>(1.2599210498948731647672106072782), // 2^1/3
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static_cast<T>(1.5874010519681994747517056392723), // 2^2/3
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};
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if(!(boost::math::isfinite)(z))
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{
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return policies::raise_domain_error("boost::math::cbrt<%1%>(%1%)", "Argument to function must be finite but got %1%.", z, pol);
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}
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int i_exp, sign(1);
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if(z < 0)
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{
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z = -z;
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sign = -sign;
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}
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if(z == 0)
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return 0;
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T guess = frexp(z, &i_exp);
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int original_i_exp = i_exp; // save for later
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guess = tools::evaluate_polynomial(P, guess);
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int i_exp3 = i_exp / 3;
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typedef typename largest_cbrt_int_type<T>::type shift_type;
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BOOST_STATIC_ASSERT( ::std::numeric_limits<shift_type>::radix == 2);
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if(abs(i_exp3) < std::numeric_limits<shift_type>::digits)
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{
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if(i_exp3 > 0)
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guess *= shift_type(1u) << i_exp3;
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else
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guess /= shift_type(1u) << -i_exp3;
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}
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else
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{
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guess = ldexp(guess, i_exp3);
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}
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i_exp %= 3;
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guess *= correction[i_exp + 2];
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//
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// Now inline Halley iteration.
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// We do this here rather than calling tools::halley_iterate since we can
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// simplify the expressions algebraically, and don't need most of the error
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// checking of the boilerplate version as we know in advance that the function
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// is well behaved...
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//
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typedef typename policies::precision<T, Policy>::type prec;
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typedef typename mpl::divides<prec, mpl::int_<3> >::type prec3;
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typedef typename mpl::plus<prec3, mpl::int_<3> >::type new_prec;
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typedef typename policies::normalise<Policy, policies::digits2<new_prec::value> >::type new_policy;
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//
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// Epsilon calculation uses compile time arithmetic when it's available for type T,
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// otherwise uses ldexp to calculate at runtime:
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//
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T eps = (new_prec::value > 3) ? policies::get_epsilon<T, new_policy>() : ldexp(T(1), -2 - tools::digits<T>() / 3);
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T diff;
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if(original_i_exp < std::numeric_limits<T>::max_exponent - 3)
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{
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//
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// Safe from overflow, use the fast method:
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//
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do
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{
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T g3 = guess * guess * guess;
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diff = (g3 + z + z) / (g3 + g3 + z);
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guess *= diff;
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}
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while(fabs(1 - diff) > eps);
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}
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else
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{
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//
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// Either we're ready to overflow, or we can't tell because numeric_limits isn't
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// available for type T:
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//
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do
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{
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T g2 = guess * guess;
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diff = (g2 - z / guess) / (2 * guess + z / g2);
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guess -= diff;
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}
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while((guess * eps) < fabs(diff));
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}
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return sign * guess;
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}
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} // namespace detail
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template <class T, class Policy>
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inline typename tools::promote_args<T>::type cbrt(T z, const Policy& pol)
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{
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typedef typename tools::promote_args<T>::type result_type;
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typedef typename policies::evaluation<result_type, Policy>::type value_type;
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return static_cast<result_type>(detail::cbrt_imp(value_type(z), pol));
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}
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template <class T>
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inline typename tools::promote_args<T>::type cbrt(T z)
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{
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return cbrt(z, policies::policy<>());
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}
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} // namespace math
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} // namespace boost
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#endif // BOOST_MATH_SF_CBRT_HPP
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