boost/math/special_functions/log1p.hpp
// (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 #pragma warning(push) #pragma warning(disable:4702) // Unreachable code (release mode only warning) #endif #include <cmath> #include <cstdint> #include <limits> #include <boost/math/tools/config.hpp> #include <boost/math/tools/series.hpp> #include <boost/math/tools/rational.hpp> #include <boost/math/tools/big_constant.hpp> #include <boost/math/policies/error_handling.hpp> #include <boost/math/special_functions/math_fwd.hpp> #include <boost/math/tools/assert.hpp> #include <boost/math/special_functions/fpclassify.hpp> #if defined(__GNUC__) && defined(BOOST_MATH_USE_FLOAT128) // // This is the only way we can avoid // warning: non-standard suffix on floating constant [-Wpedantic] // when building with -Wall -pedantic. Neither __extension__ // nor #pragma diagnostic ignored work :( // #pragma GCC system_header #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&) = delete; log1p_series& operator=(const log1p_series&) = delete; }; // 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 std::integral_constant<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) || (boost::math::isnan)(x)) 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, nullptr, 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); std::uintmax_t max_iter = policies::get_max_series_iterations<Policy>(); result_type result = tools::sum_series(s, policies::get_epsilon<result_type, Policy>(), max_iter); policies::check_series_iterations<T>(function, max_iter, pol); return result; } template <class T, class Policy> T log1p_imp(T const& x, const Policy& pol, const std::integral_constant<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, nullptr, 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 std::integral_constant<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, nullptr, 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[] = { BOOST_MATH_BIG_CONSTANT(T, 64, -0.807533446680736736712e-19), BOOST_MATH_BIG_CONSTANT(T, 64, -0.490881544804798926426e-18), BOOST_MATH_BIG_CONSTANT(T, 64, 0.333333333333333373941), BOOST_MATH_BIG_CONSTANT(T, 64, 1.17141290782087994162), BOOST_MATH_BIG_CONSTANT(T, 64, 1.62790522814926264694), BOOST_MATH_BIG_CONSTANT(T, 64, 1.13156411870766876113), BOOST_MATH_BIG_CONSTANT(T, 64, 0.408087379932853785336), BOOST_MATH_BIG_CONSTANT(T, 64, 0.0706537026422828914622), BOOST_MATH_BIG_CONSTANT(T, 64, 0.00441709903782239229447) }; static const T Q[] = { BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), BOOST_MATH_BIG_CONSTANT(T, 64, 4.26423872346263928361), BOOST_MATH_BIG_CONSTANT(T, 64, 7.48189472704477708962), BOOST_MATH_BIG_CONSTANT(T, 64, 6.94757016732904280913), BOOST_MATH_BIG_CONSTANT(T, 64, 3.6493508622280767304), BOOST_MATH_BIG_CONSTANT(T, 64, 1.06884863623790638317), BOOST_MATH_BIG_CONSTANT(T, 64, 0.158292216998514145947), BOOST_MATH_BIG_CONSTANT(T, 64, 0.00885295524069924328658), BOOST_MATH_BIG_CONSTANT(T, 64, -0.560026216133415663808e-6) }; 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 std::integral_constant<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, nullptr, 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; } template <class T, class Policy, class tag> struct log1p_initializer { struct init { init() { do_init(tag()); } template <int N> static void do_init(const std::integral_constant<int, N>&){} static void do_init(const std::integral_constant<int, 64>&) { boost::math::log1p(static_cast<T>(0.25), Policy()); } void force_instantiate()const{} }; static const init initializer; static void force_instantiate() { initializer.force_instantiate(); } }; template <class T, class Policy, class tag> const typename log1p_initializer<T, Policy, tag>::init log1p_initializer<T, Policy, tag>::initializer; } // 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 std::integral_constant<int, precision_type::value <= 0 ? 0 : precision_type::value <= 53 ? 53 : precision_type::value <= 64 ? 64 : 0 > tag_type; detail::log1p_initializer<value_type, forwarding_policy, tag_type>::force_instantiate(); 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%)"); } #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%)", nullptr, 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%)", nullptr, 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%)", nullptr, 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%)", nullptr, 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%)", nullptr, 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%)", nullptr, 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, nullptr, 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(); std::uintmax_t max_iter = policies::get_max_series_iterations<Policy>(); T result = boost::math::tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter); policies::check_series_iterations<T>(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 #ifdef _MSC_VER #pragma warning(pop) #endif #endif // BOOST_MATH_LOG1P_INCLUDED