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471 lines
14 KiB
471 lines
14 KiB
// (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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#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/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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-0.807533446680736736712e-19L, |
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-0.490881544804798926426e-18L, |
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0.333333333333333373941L, |
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1.17141290782087994162L, |
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1.62790522814926264694L, |
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1.13156411870766876113L, |
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0.408087379932853785336L, |
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0.0706537026422828914622L, |
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0.00441709903782239229447L |
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}; |
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static const T Q[] = { |
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1L, |
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4.26423872346263928361L, |
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7.48189472704477708962L, |
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6.94757016732904280913L, |
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3.6493508622280767304L, |
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1.06884863623790638317L, |
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0.158292216998514145947L, |
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0.00885295524069924328658L, |
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-0.560026216133415663808e-6L |
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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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} // 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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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); |
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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> |
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inline typename tools::promote_args<T>::type log1pmx(T x) |
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{ |
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return log1pmx(x, 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_LOG1P_INCLUDED |
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