X-Git-Url: https://git.donarmstrong.com/?p=rsem.git;a=blobdiff_plain;f=boost%2Fmath%2Fspecial_functions%2Fcbrt.hpp;fp=boost%2Fmath%2Fspecial_functions%2Fcbrt.hpp;h=0fc6e0742af6eed5f43fb08163b8b421bacd7757;hp=0000000000000000000000000000000000000000;hb=2d71eb92104693ca9baa5a2e1c23eeca776d8fd3;hpb=da57529b92adbb7ae74a89861cb39fb35ac7c62d diff --git a/boost/math/special_functions/cbrt.hpp b/boost/math/special_functions/cbrt.hpp new file mode 100644 index 0000000..0fc6e07 --- /dev/null +++ b/boost/math/special_functions/cbrt.hpp @@ -0,0 +1,180 @@ +// (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 +#include +#include +#include +#include +#include +#include +#include + +namespace boost{ namespace math{ + +namespace detail +{ + +struct big_int_type +{ + operator boost::uintmax_t()const; +}; + +template +struct largest_cbrt_int_type +{ + typedef typename mpl::if_< + boost::is_convertible, + boost::uintmax_t, + unsigned int + >::type type; +}; + +template +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(0.37568269008611818), + static_cast(1.3304968705558024), + static_cast(-1.4897101632445036), + static_cast(1.2875573098219835), + static_cast(-0.6398703759826468), + static_cast(0.13584489959258635), + }; + static const T correction[] = { + static_cast(0.62996052494743658238360530363911), // 2^-2/3 + static_cast(0.79370052598409973737585281963615), // 2^-1/3 + static_cast(1), + static_cast(1.2599210498948731647672106072782), // 2^1/3 + static_cast(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::type shift_type; + + BOOST_STATIC_ASSERT( ::std::numeric_limits::radix == 2); + + if(abs(i_exp3) < std::numeric_limits::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::type prec; + typedef typename mpl::divides >::type prec3; + typedef typename mpl::plus >::type new_prec; + typedef typename policies::normalise >::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() : ldexp(T(1), -2 - tools::digits() / 3); + T diff; + + if(original_i_exp < std::numeric_limits::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 +inline typename tools::promote_args::type cbrt(T z, const Policy& pol) +{ + typedef typename tools::promote_args::type result_type; + typedef typename policies::evaluation::type value_type; + return static_cast(detail::cbrt_imp(value_type(z), pol)); +} + +template +inline typename tools::promote_args::type cbrt(T z) +{ + return cbrt(z, policies::policy<>()); +} + +} // namespace math +} // namespace boost + +#endif // BOOST_MATH_SF_CBRT_HPP + + + +