510 lines
16 KiB
Plaintext
510 lines
16 KiB
Plaintext
// (C) Copyright John Maddock 2005-2006.
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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_LOG1P_INCLUDED
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#define BOOST_MATH_LOG1P_INCLUDED
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#ifdef _MSC_VER
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#pragma once
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#pragma warning(push)
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#pragma warning(disable:4702) // Unreachable code (release mode only warning)
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#endif
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#include <boost/config/no_tr1/cmath.hpp>
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#include <math.h> // platform's ::log1p
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#include <boost/limits.hpp>
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#include <boost/math/tools/config.hpp>
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#include <boost/math/tools/series.hpp>
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#include <boost/math/tools/rational.hpp>
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#include <boost/math/tools/big_constant.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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#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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# include <boost/static_assert.hpp>
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#else
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# include <boost/assert.hpp>
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#endif
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namespace boost{ namespace math{
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namespace detail
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{
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// Functor log1p_series returns the next term in the Taylor series
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// pow(-1, k-1)*pow(x, k) / k
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// each time that operator() is invoked.
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//
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template <class T>
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struct log1p_series
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{
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typedef T result_type;
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log1p_series(T x)
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: k(0), m_mult(-x), m_prod(-1){}
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T operator()()
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{
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m_prod *= m_mult;
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return m_prod / ++k;
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}
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int count()const
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{
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return k;
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}
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private:
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int k;
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const T m_mult;
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T m_prod;
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log1p_series(const log1p_series&);
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log1p_series& operator=(const log1p_series&);
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};
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// Algorithm log1p is part of C99, but is not yet provided by many compilers.
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//
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// This version uses a Taylor series expansion for 0.5 > x > epsilon, which may
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// require up to std::numeric_limits<T>::digits+1 terms to be calculated.
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// It would be much more efficient to use the equivalence:
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// log(1+x) == (log(1+x) * x) / ((1-x) - 1)
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// Unfortunately many optimizing compilers make such a mess of this, that
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// it performs no better than log(1+x): which is to say not very well at all.
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//
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template <class T, class Policy>
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T log1p_imp(T const & x, const Policy& pol, const mpl::int_<0>&)
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{ // The function returns the natural logarithm of 1 + x.
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typedef typename tools::promote_args<T>::type result_type;
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BOOST_MATH_STD_USING
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static const char* function = "boost::math::log1p<%1%>(%1%)";
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if(x < -1)
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return policies::raise_domain_error<T>(
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function, "log1p(x) requires x > -1, but got x = %1%.", x, pol);
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if(x == -1)
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return -policies::raise_overflow_error<T>(
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function, 0, pol);
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result_type a = abs(result_type(x));
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if(a > result_type(0.5f))
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return log(1 + result_type(x));
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// Note that without numeric_limits specialisation support,
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// epsilon just returns zero, and our "optimisation" will always fail:
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if(a < tools::epsilon<result_type>())
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return x;
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detail::log1p_series<result_type> s(x);
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boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
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#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) && !BOOST_WORKAROUND(__EDG_VERSION__, <= 245)
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result_type result = tools::sum_series(s, policies::get_epsilon<result_type, Policy>(), max_iter);
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#else
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result_type zero = 0;
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result_type result = tools::sum_series(s, policies::get_epsilon<result_type, Policy>(), max_iter, zero);
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#endif
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policies::check_series_iterations<T>(function, max_iter, pol);
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return result;
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}
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template <class T, class Policy>
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T log1p_imp(T const& x, const Policy& pol, const mpl::int_<53>&)
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{ // The function returns the natural logarithm of 1 + x.
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BOOST_MATH_STD_USING
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static const char* function = "boost::math::log1p<%1%>(%1%)";
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if(x < -1)
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return policies::raise_domain_error<T>(
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function, "log1p(x) requires x > -1, but got x = %1%.", x, pol);
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if(x == -1)
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return -policies::raise_overflow_error<T>(
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function, 0, pol);
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T a = fabs(x);
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if(a > 0.5f)
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return log(1 + x);
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// Note that without numeric_limits specialisation support,
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// epsilon just returns zero, and our "optimisation" will always fail:
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if(a < tools::epsilon<T>())
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return x;
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// Maximum Deviation Found: 1.846e-017
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// Expected Error Term: 1.843e-017
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// Maximum Relative Change in Control Points: 8.138e-004
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// Max Error found at double precision = 3.250766e-016
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static const T P[] = {
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0.15141069795941984e-16L,
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0.35495104378055055e-15L,
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0.33333333333332835L,
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0.99249063543365859L,
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1.1143969784156509L,
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0.58052937949269651L,
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0.13703234928513215L,
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0.011294864812099712L
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};
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static const T Q[] = {
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1L,
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3.7274719063011499L,
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5.5387948649720334L,
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4.159201143419005L,
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1.6423855110312755L,
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0.31706251443180914L,
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0.022665554431410243L,
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-0.29252538135177773e-5L
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};
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T result = 1 - x / 2 + tools::evaluate_polynomial(P, x) / tools::evaluate_polynomial(Q, x);
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result *= x;
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return result;
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}
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template <class T, class Policy>
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T log1p_imp(T const& x, const Policy& pol, const mpl::int_<64>&)
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{ // The function returns the natural logarithm of 1 + x.
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BOOST_MATH_STD_USING
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static const char* function = "boost::math::log1p<%1%>(%1%)";
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if(x < -1)
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return policies::raise_domain_error<T>(
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function, "log1p(x) requires x > -1, but got x = %1%.", x, pol);
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if(x == -1)
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return -policies::raise_overflow_error<T>(
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function, 0, pol);
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T a = fabs(x);
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if(a > 0.5f)
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return log(1 + x);
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// Note that without numeric_limits specialisation support,
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// epsilon just returns zero, and our "optimisation" will always fail:
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if(a < tools::epsilon<T>())
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return x;
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// Maximum Deviation Found: 8.089e-20
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// Expected Error Term: 8.088e-20
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// Maximum Relative Change in Control Points: 9.648e-05
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// Max Error found at long double precision = 2.242324e-19
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static const T P[] = {
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BOOST_MATH_BIG_CONSTANT(T, 64, -0.807533446680736736712e-19),
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BOOST_MATH_BIG_CONSTANT(T, 64, -0.490881544804798926426e-18),
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BOOST_MATH_BIG_CONSTANT(T, 64, 0.333333333333333373941),
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BOOST_MATH_BIG_CONSTANT(T, 64, 1.17141290782087994162),
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BOOST_MATH_BIG_CONSTANT(T, 64, 1.62790522814926264694),
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BOOST_MATH_BIG_CONSTANT(T, 64, 1.13156411870766876113),
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BOOST_MATH_BIG_CONSTANT(T, 64, 0.408087379932853785336),
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BOOST_MATH_BIG_CONSTANT(T, 64, 0.0706537026422828914622),
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BOOST_MATH_BIG_CONSTANT(T, 64, 0.00441709903782239229447)
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};
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static const T Q[] = {
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BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
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BOOST_MATH_BIG_CONSTANT(T, 64, 4.26423872346263928361),
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BOOST_MATH_BIG_CONSTANT(T, 64, 7.48189472704477708962),
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BOOST_MATH_BIG_CONSTANT(T, 64, 6.94757016732904280913),
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BOOST_MATH_BIG_CONSTANT(T, 64, 3.6493508622280767304),
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BOOST_MATH_BIG_CONSTANT(T, 64, 1.06884863623790638317),
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BOOST_MATH_BIG_CONSTANT(T, 64, 0.158292216998514145947),
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BOOST_MATH_BIG_CONSTANT(T, 64, 0.00885295524069924328658),
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BOOST_MATH_BIG_CONSTANT(T, 64, -0.560026216133415663808e-6)
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};
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T result = 1 - x / 2 + tools::evaluate_polynomial(P, x) / tools::evaluate_polynomial(Q, x);
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result *= x;
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return result;
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}
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template <class T, class Policy>
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T log1p_imp(T const& x, const Policy& pol, const mpl::int_<24>&)
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{ // The function returns the natural logarithm of 1 + x.
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BOOST_MATH_STD_USING
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static const char* function = "boost::math::log1p<%1%>(%1%)";
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if(x < -1)
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return policies::raise_domain_error<T>(
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function, "log1p(x) requires x > -1, but got x = %1%.", x, pol);
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if(x == -1)
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return -policies::raise_overflow_error<T>(
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function, 0, pol);
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T a = fabs(x);
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if(a > 0.5f)
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return log(1 + x);
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// Note that without numeric_limits specialisation support,
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// epsilon just returns zero, and our "optimisation" will always fail:
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if(a < tools::epsilon<T>())
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return x;
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// Maximum Deviation Found: 6.910e-08
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// Expected Error Term: 6.910e-08
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// Maximum Relative Change in Control Points: 2.509e-04
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// Max Error found at double precision = 6.910422e-08
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// Max Error found at float precision = 8.357242e-08
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static const T P[] = {
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-0.671192866803148236519e-7L,
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0.119670999140731844725e-6L,
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0.333339469182083148598L,
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0.237827183019664122066L
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};
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static const T Q[] = {
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1L,
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1.46348272586988539733L,
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0.497859871350117338894L,
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-0.00471666268910169651936L
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};
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T result = 1 - x / 2 + tools::evaluate_polynomial(P, x) / tools::evaluate_polynomial(Q, x);
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result *= x;
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return result;
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}
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template <class T, class Policy, class tag>
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struct log1p_initializer
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{
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struct init
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{
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init()
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{
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do_init(tag());
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}
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template <int N>
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static void do_init(const mpl::int_<N>&){}
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static void do_init(const mpl::int_<64>&)
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{
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boost::math::log1p(static_cast<T>(0.25), Policy());
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}
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void force_instantiate()const{}
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};
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static const init initializer;
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static void force_instantiate()
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{
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initializer.force_instantiate();
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}
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};
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template <class T, class Policy, class tag>
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const typename log1p_initializer<T, Policy, tag>::init log1p_initializer<T, Policy, tag>::initializer;
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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 log1p(T x, const Policy&)
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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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typedef typename policies::precision<result_type, Policy>::type precision_type;
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typedef typename policies::normalise<
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Policy,
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policies::promote_float<false>,
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policies::promote_double<false>,
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policies::discrete_quantile<>,
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policies::assert_undefined<> >::type forwarding_policy;
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typedef typename mpl::if_<
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mpl::less_equal<precision_type, mpl::int_<0> >,
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mpl::int_<0>,
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typename mpl::if_<
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mpl::less_equal<precision_type, mpl::int_<53> >,
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mpl::int_<53>, // double
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typename mpl::if_<
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mpl::less_equal<precision_type, mpl::int_<64> >,
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mpl::int_<64>, // 80-bit long double
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mpl::int_<0> // too many bits, use generic version.
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>::type
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>::type
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>::type tag_type;
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detail::log1p_initializer<value_type, forwarding_policy, tag_type>::force_instantiate();
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return policies::checked_narrowing_cast<result_type, forwarding_policy>(
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detail::log1p_imp(static_cast<value_type>(x), forwarding_policy(), tag_type()), "boost::math::log1p<%1%>(%1%)");
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}
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#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x564))
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// These overloads work around a type deduction bug:
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inline float log1p(float z)
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{
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return log1p<float>(z);
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}
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inline double log1p(double z)
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{
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return log1p<double>(z);
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}
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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inline long double log1p(long double z)
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{
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return log1p<long double>(z);
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}
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#endif
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#endif
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#ifdef log1p
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# ifndef BOOST_HAS_LOG1P
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# define BOOST_HAS_LOG1P
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# endif
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# undef log1p
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#endif
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#if defined(BOOST_HAS_LOG1P) && !(defined(__osf__) && defined(__DECCXX_VER))
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# ifdef BOOST_MATH_USE_C99
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template <class Policy>
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inline float log1p(float x, const Policy& pol)
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{
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if(x < -1)
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return policies::raise_domain_error<float>(
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"log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
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if(x == -1)
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return -policies::raise_overflow_error<float>(
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"log1p<%1%>(%1%)", 0, pol);
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return ::log1pf(x);
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}
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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template <class Policy>
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inline long double log1p(long double x, const Policy& pol)
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{
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if(x < -1)
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return policies::raise_domain_error<long double>(
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"log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
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if(x == -1)
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return -policies::raise_overflow_error<long double>(
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"log1p<%1%>(%1%)", 0, pol);
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return ::log1pl(x);
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}
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#endif
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#else
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template <class Policy>
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inline float log1p(float x, const Policy& pol)
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{
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if(x < -1)
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return policies::raise_domain_error<float>(
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"log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
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if(x == -1)
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return -policies::raise_overflow_error<float>(
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"log1p<%1%>(%1%)", 0, pol);
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return ::log1p(x);
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}
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#endif
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template <class Policy>
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inline double log1p(double x, const Policy& pol)
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{
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if(x < -1)
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return policies::raise_domain_error<double>(
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"log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
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if(x == -1)
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return -policies::raise_overflow_error<double>(
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"log1p<%1%>(%1%)", 0, pol);
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return ::log1p(x);
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}
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#elif defined(_MSC_VER) && (BOOST_MSVC >= 1400)
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//
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// You should only enable this branch if you are absolutely sure
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// that your compilers optimizer won't mess this code up!!
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// Currently tested with VC8 and Intel 9.1.
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//
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template <class Policy>
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inline double log1p(double x, const Policy& pol)
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{
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if(x < -1)
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return policies::raise_domain_error<double>(
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"log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
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if(x == -1)
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return -policies::raise_overflow_error<double>(
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"log1p<%1%>(%1%)", 0, pol);
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double u = 1+x;
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if(u == 1.0)
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return x;
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else
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return ::log(u)*(x/(u-1.0));
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}
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template <class Policy>
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inline float log1p(float x, const Policy& pol)
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{
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return static_cast<float>(boost::math::log1p(static_cast<double>(x), pol));
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}
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#ifndef _WIN32_WCE
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//
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// For some reason this fails to compile under WinCE...
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// Needs more investigation.
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//
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template <class Policy>
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inline long double log1p(long double x, const Policy& pol)
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{
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if(x < -1)
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return policies::raise_domain_error<long double>(
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"log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
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if(x == -1)
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return -policies::raise_overflow_error<long double>(
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"log1p<%1%>(%1%)", 0, pol);
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long double u = 1+x;
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if(u == 1.0)
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return x;
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else
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return ::logl(u)*(x/(u-1.0));
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}
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#endif
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#endif
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template <class T>
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inline typename tools::promote_args<T>::type log1p(T x)
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{
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return boost::math::log1p(x, policies::policy<>());
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}
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//
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// Compute log(1+x)-x:
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//
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template <class T, class Policy>
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inline typename tools::promote_args<T>::type
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log1pmx(T x, const Policy& pol)
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{
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typedef typename tools::promote_args<T>::type result_type;
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BOOST_MATH_STD_USING
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static const char* function = "boost::math::log1pmx<%1%>(%1%)";
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if(x < -1)
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return policies::raise_domain_error<T>(
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function, "log1pmx(x) requires x > -1, but got x = %1%.", x, pol);
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if(x == -1)
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return -policies::raise_overflow_error<T>(
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function, 0, pol);
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result_type a = abs(result_type(x));
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if(a > result_type(0.95f))
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return log(1 + result_type(x)) - result_type(x);
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|
// Note that without numeric_limits specialisation support,
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// epsilon just returns zero, and our "optimisation" will always fail:
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if(a < tools::epsilon<result_type>())
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return -x * x / 2;
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|
boost::math::detail::log1p_series<T> s(x);
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|
s();
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|
boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
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|
#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
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T zero = 0;
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T result = boost::math::tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter, zero);
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|
#else
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|
T result = boost::math::tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter);
|
|
#endif
|
|
policies::check_series_iterations<T>(function, max_iter, pol);
|
|
return result;
|
|
}
|
|
|
|
template <class T>
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|
inline typename tools::promote_args<T>::type log1pmx(T x)
|
|
{
|
|
return log1pmx(x, policies::policy<>());
|
|
}
|
|
|
|
} // namespace math
|
|
} // namespace boost
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|
|
|
#ifdef _MSC_VER
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|
#pragma warning(pop)
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|
#endif
|
|
|
|
#endif // BOOST_MATH_LOG1P_INCLUDED
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