/Src/Dependencies/Boost/boost/math/special_functions/log1p.hpp
C++ Header | 471 lines | 368 code | 50 blank | 53 comment | 51 complexity | e1fd72f704ca0c39c19d1726ff8a906e MD5 | raw file
Possible License(s): GPL-3.0, LGPL-2.0, Apache-2.0, LGPL-3.0
- // (C) Copyright John Maddock 2005-2006.
- // 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_LOG1P_INCLUDED
- #define BOOST_MATH_LOG1P_INCLUDED
- #ifdef _MSC_VER
- #pragma once
- #endif
- #include <boost/config/no_tr1/cmath.hpp>
- #include <math.h> // platform's ::log1p
- #include <boost/limits.hpp>
- #include <boost/math/tools/config.hpp>
- #include <boost/math/tools/series.hpp>
- #include <boost/math/tools/rational.hpp>
- #include <boost/math/policies/error_handling.hpp>
- #include <boost/math/special_functions/math_fwd.hpp>
- #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
- # include <boost/static_assert.hpp>
- #else
- # include <boost/assert.hpp>
- #endif
- namespace boost{ namespace math{
- namespace detail
- {
- // Functor log1p_series returns the next term in the Taylor series
- // pow(-1, k-1)*pow(x, k) / k
- // each time that operator() is invoked.
- //
- template <class T>
- struct log1p_series
- {
- typedef T result_type;
- log1p_series(T x)
- : k(0), m_mult(-x), m_prod(-1){}
- T operator()()
- {
- m_prod *= m_mult;
- return m_prod / ++k;
- }
- int count()const
- {
- return k;
- }
- private:
- int k;
- const T m_mult;
- T m_prod;
- log1p_series(const log1p_series&);
- log1p_series& operator=(const log1p_series&);
- };
- // Algorithm log1p is part of C99, but is not yet provided by many compilers.
- //
- // This version uses a Taylor series expansion for 0.5 > x > epsilon, which may
- // require up to std::numeric_limits<T>::digits+1 terms to be calculated.
- // It would be much more efficient to use the equivalence:
- // log(1+x) == (log(1+x) * x) / ((1-x) - 1)
- // Unfortunately many optimizing compilers make such a mess of this, that
- // it performs no better than log(1+x): which is to say not very well at all.
- //
- template <class T, class Policy>
- T log1p_imp(T const & x, const Policy& pol, const mpl::int_<0>&)
- { // The function returns the natural logarithm of 1 + x.
- typedef typename tools::promote_args<T>::type result_type;
- BOOST_MATH_STD_USING
- static const char* function = "boost::math::log1p<%1%>(%1%)";
- if(x < -1)
- return policies::raise_domain_error<T>(
- function, "log1p(x) requires x > -1, but got x = %1%.", x, pol);
- if(x == -1)
- return -policies::raise_overflow_error<T>(
- function, 0, pol);
- result_type a = abs(result_type(x));
- if(a > result_type(0.5f))
- return log(1 + result_type(x));
- // Note that without numeric_limits specialisation support,
- // epsilon just returns zero, and our "optimisation" will always fail:
- if(a < tools::epsilon<result_type>())
- return x;
- detail::log1p_series<result_type> s(x);
- boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
- #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) && !BOOST_WORKAROUND(__EDG_VERSION__, <= 245)
- result_type result = tools::sum_series(s, policies::get_epsilon<result_type, Policy>(), max_iter);
- #else
- result_type zero = 0;
- result_type result = tools::sum_series(s, policies::get_epsilon<result_type, Policy>(), max_iter, zero);
- #endif
- policies::check_series_iterations(function, max_iter, pol);
- return result;
- }
- template <class T, class Policy>
- T log1p_imp(T const& x, const Policy& pol, const mpl::int_<53>&)
- { // The function returns the natural logarithm of 1 + x.
- BOOST_MATH_STD_USING
- static const char* function = "boost::math::log1p<%1%>(%1%)";
- if(x < -1)
- return policies::raise_domain_error<T>(
- function, "log1p(x) requires x > -1, but got x = %1%.", x, pol);
- if(x == -1)
- return -policies::raise_overflow_error<T>(
- function, 0, pol);
- T a = fabs(x);
- if(a > 0.5f)
- return log(1 + x);
- // Note that without numeric_limits specialisation support,
- // epsilon just returns zero, and our "optimisation" will always fail:
- if(a < tools::epsilon<T>())
- return x;
- // Maximum Deviation Found: 1.846e-017
- // Expected Error Term: 1.843e-017
- // Maximum Relative Change in Control Points: 8.138e-004
- // Max Error found at double precision = 3.250766e-016
- static const T P[] = {
- 0.15141069795941984e-16L,
- 0.35495104378055055e-15L,
- 0.33333333333332835L,
- 0.99249063543365859L,
- 1.1143969784156509L,
- 0.58052937949269651L,
- 0.13703234928513215L,
- 0.011294864812099712L
- };
- static const T Q[] = {
- 1L,
- 3.7274719063011499L,
- 5.5387948649720334L,
- 4.159201143419005L,
- 1.6423855110312755L,
- 0.31706251443180914L,
- 0.022665554431410243L,
- -0.29252538135177773e-5L
- };
- T result = 1 - x / 2 + tools::evaluate_polynomial(P, x) / tools::evaluate_polynomial(Q, x);
- result *= x;
- return result;
- }
- template <class T, class Policy>
- T log1p_imp(T const& x, const Policy& pol, const mpl::int_<64>&)
- { // The function returns the natural logarithm of 1 + x.
- BOOST_MATH_STD_USING
- static const char* function = "boost::math::log1p<%1%>(%1%)";
- if(x < -1)
- return policies::raise_domain_error<T>(
- function, "log1p(x) requires x > -1, but got x = %1%.", x, pol);
- if(x == -1)
- return -policies::raise_overflow_error<T>(
- function, 0, pol);
- T a = fabs(x);
- if(a > 0.5f)
- return log(1 + x);
- // Note that without numeric_limits specialisation support,
- // epsilon just returns zero, and our "optimisation" will always fail:
- if(a < tools::epsilon<T>())
- return x;
- // Maximum Deviation Found: 8.089e-20
- // Expected Error Term: 8.088e-20
- // Maximum Relative Change in Control Points: 9.648e-05
- // Max Error found at long double precision = 2.242324e-19
- static const T P[] = {
- -0.807533446680736736712e-19L,
- -0.490881544804798926426e-18L,
- 0.333333333333333373941L,
- 1.17141290782087994162L,
- 1.62790522814926264694L,
- 1.13156411870766876113L,
- 0.408087379932853785336L,
- 0.0706537026422828914622L,
- 0.00441709903782239229447L
- };
- static const T Q[] = {
- 1L,
- 4.26423872346263928361L,
- 7.48189472704477708962L,
- 6.94757016732904280913L,
- 3.6493508622280767304L,
- 1.06884863623790638317L,
- 0.158292216998514145947L,
- 0.00885295524069924328658L,
- -0.560026216133415663808e-6L
- };
- T result = 1 - x / 2 + tools::evaluate_polynomial(P, x) / tools::evaluate_polynomial(Q, x);
- result *= x;
- return result;
- }
- template <class T, class Policy>
- T log1p_imp(T const& x, const Policy& pol, const mpl::int_<24>&)
- { // The function returns the natural logarithm of 1 + x.
- BOOST_MATH_STD_USING
- static const char* function = "boost::math::log1p<%1%>(%1%)";
- if(x < -1)
- return policies::raise_domain_error<T>(
- function, "log1p(x) requires x > -1, but got x = %1%.", x, pol);
- if(x == -1)
- return -policies::raise_overflow_error<T>(
- function, 0, pol);
- T a = fabs(x);
- if(a > 0.5f)
- return log(1 + x);
- // Note that without numeric_limits specialisation support,
- // epsilon just returns zero, and our "optimisation" will always fail:
- if(a < tools::epsilon<T>())
- return x;
- // Maximum Deviation Found: 6.910e-08
- // Expected Error Term: 6.910e-08
- // Maximum Relative Change in Control Points: 2.509e-04
- // Max Error found at double precision = 6.910422e-08
- // Max Error found at float precision = 8.357242e-08
- static const T P[] = {
- -0.671192866803148236519e-7L,
- 0.119670999140731844725e-6L,
- 0.333339469182083148598L,
- 0.237827183019664122066L
- };
- static const T Q[] = {
- 1L,
- 1.46348272586988539733L,
- 0.497859871350117338894L,
- -0.00471666268910169651936L
- };
- T result = 1 - x / 2 + tools::evaluate_polynomial(P, x) / tools::evaluate_polynomial(Q, x);
- result *= x;
- return result;
- }
- } // namespace detail
- template <class T, class Policy>
- inline typename tools::promote_args<T>::type log1p(T x, const Policy&)
- {
- typedef typename tools::promote_args<T>::type result_type;
- typedef typename policies::evaluation<result_type, Policy>::type value_type;
- typedef typename policies::precision<result_type, Policy>::type precision_type;
- typedef typename policies::normalise<
- Policy,
- policies::promote_float<false>,
- policies::promote_double<false>,
- policies::discrete_quantile<>,
- policies::assert_undefined<> >::type forwarding_policy;
- typedef typename mpl::if_<
- mpl::less_equal<precision_type, mpl::int_<0> >,
- mpl::int_<0>,
- typename mpl::if_<
- mpl::less_equal<precision_type, mpl::int_<53> >,
- mpl::int_<53>, // double
- typename mpl::if_<
- mpl::less_equal<precision_type, mpl::int_<64> >,
- mpl::int_<64>, // 80-bit long double
- mpl::int_<0> // too many bits, use generic version.
- >::type
- >::type
- >::type tag_type;
- return policies::checked_narrowing_cast<result_type, forwarding_policy>(
- detail::log1p_imp(static_cast<value_type>(x), forwarding_policy(), tag_type()), "boost::math::log1p<%1%>(%1%)");
- }
- #if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x564))
- // These overloads work around a type deduction bug:
- inline float log1p(float z)
- {
- return log1p<float>(z);
- }
- inline double log1p(double z)
- {
- return log1p<double>(z);
- }
- #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
- inline long double log1p(long double z)
- {
- return log1p<long double>(z);
- }
- #endif
- #endif
- #ifdef log1p
- # ifndef BOOST_HAS_LOG1P
- # define BOOST_HAS_LOG1P
- # endif
- # undef log1p
- #endif
- #if defined(BOOST_HAS_LOG1P) && !(defined(__osf__) && defined(__DECCXX_VER))
- # ifdef BOOST_MATH_USE_C99
- template <class Policy>
- inline float log1p(float x, const Policy& pol)
- {
- if(x < -1)
- return policies::raise_domain_error<float>(
- "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
- if(x == -1)
- return -policies::raise_overflow_error<float>(
- "log1p<%1%>(%1%)", 0, pol);
- return ::log1pf(x);
- }
- #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
- template <class Policy>
- inline long double log1p(long double x, const Policy& pol)
- {
- if(x < -1)
- return policies::raise_domain_error<long double>(
- "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
- if(x == -1)
- return -policies::raise_overflow_error<long double>(
- "log1p<%1%>(%1%)", 0, pol);
- return ::log1pl(x);
- }
- #endif
- #else
- template <class Policy>
- inline float log1p(float x, const Policy& pol)
- {
- if(x < -1)
- return policies::raise_domain_error<float>(
- "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
- if(x == -1)
- return -policies::raise_overflow_error<float>(
- "log1p<%1%>(%1%)", 0, pol);
- return ::log1p(x);
- }
- #endif
- template <class Policy>
- inline double log1p(double x, const Policy& pol)
- {
- if(x < -1)
- return policies::raise_domain_error<double>(
- "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
- if(x == -1)
- return -policies::raise_overflow_error<double>(
- "log1p<%1%>(%1%)", 0, pol);
- return ::log1p(x);
- }
- #elif defined(_MSC_VER) && (BOOST_MSVC >= 1400)
- //
- // You should only enable this branch if you are absolutely sure
- // that your compilers optimizer won't mess this code up!!
- // Currently tested with VC8 and Intel 9.1.
- //
- template <class Policy>
- inline double log1p(double x, const Policy& pol)
- {
- if(x < -1)
- return policies::raise_domain_error<double>(
- "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
- if(x == -1)
- return -policies::raise_overflow_error<double>(
- "log1p<%1%>(%1%)", 0, pol);
- double u = 1+x;
- if(u == 1.0)
- return x;
- else
- return ::log(u)*(x/(u-1.0));
- }
- template <class Policy>
- inline float log1p(float x, const Policy& pol)
- {
- return static_cast<float>(boost::math::log1p(static_cast<double>(x), pol));
- }
- #ifndef _WIN32_WCE
- //
- // For some reason this fails to compile under WinCE...
- // Needs more investigation.
- //
- template <class Policy>
- inline long double log1p(long double x, const Policy& pol)
- {
- if(x < -1)
- return policies::raise_domain_error<long double>(
- "log1p<%1%>(%1%)", "log1p(x) requires x > -1, but got x = %1%.", x, pol);
- if(x == -1)
- return -policies::raise_overflow_error<long double>(
- "log1p<%1%>(%1%)", 0, pol);
- long double u = 1+x;
- if(u == 1.0)
- return x;
- else
- return ::logl(u)*(x/(u-1.0));
- }
- #endif
- #endif
- template <class T>
- inline typename tools::promote_args<T>::type log1p(T x)
- {
- return boost::math::log1p(x, policies::policy<>());
- }
- //
- // Compute log(1+x)-x:
- //
- template <class T, class Policy>
- inline typename tools::promote_args<T>::type
- log1pmx(T x, const Policy& pol)
- {
- typedef typename tools::promote_args<T>::type result_type;
- BOOST_MATH_STD_USING
- static const char* function = "boost::math::log1pmx<%1%>(%1%)";
- if(x < -1)
- return policies::raise_domain_error<T>(
- function, "log1pmx(x) requires x > -1, but got x = %1%.", x, pol);
- if(x == -1)
- return -policies::raise_overflow_error<T>(
- function, 0, pol);
- result_type a = abs(result_type(x));
- if(a > result_type(0.95f))
- return log(1 + result_type(x)) - result_type(x);
- // Note that without numeric_limits specialisation support,
- // epsilon just returns zero, and our "optimisation" will always fail:
- if(a < tools::epsilon<result_type>())
- return -x * x / 2;
- boost::math::detail::log1p_series<T> s(x);
- s();
- boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
- #if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
- T zero = 0;
- T result = boost::math::tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter, zero);
- #else
- T result = boost::math::tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter);
- #endif
- policies::check_series_iterations(function, max_iter, pol);
- return result;
- }
- template <class T>
- inline typename tools::promote_args<T>::type log1pmx(T x)
- {
- return log1pmx(x, policies::policy<>());
- }
- } // namespace math
- } // namespace boost
- #endif // BOOST_MATH_LOG1P_INCLUDED