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+// (C) Copyright John Maddock 2006.
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0. (See accompanying file
+// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_EXPM1_INCLUDED
+#define BOOST_MATH_EXPM1_INCLUDED
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/config/no_tr1/cmath.hpp>
+#include <math.h> // platform's ::expm1
+#include <boost/limits.hpp>
+#include <boost/math/tools/config.hpp>
+#include <boost/math/tools/series.hpp>
+#include <boost/math/tools/precision.hpp>
+#include <boost/math/tools/big_constant.hpp>
+#include <boost/math/policies/error_handling.hpp>
+#include <boost/math/tools/rational.hpp>
+#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/mpl/less_equal.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 expm1_series returns the next term in the Taylor series
+ // x^k / k!
+ // each time that operator() is invoked.
+ //
+ template <class T>
+ struct expm1_series
+ {
+ typedef T result_type;
+
+ expm1_series(T x)
+ : k(0), m_x(x), m_term(1) {}
+
+ T operator()()
+ {
+ ++k;
+ m_term *= m_x;
+ m_term /= k;
+ return m_term;
+ }
+
+ int count()const
+ {
+ return k;
+ }
+
+ private:
+ int k;
+ const T m_x;
+ T m_term;
+ expm1_series(const expm1_series&);
+ expm1_series& operator=(const expm1_series&);
+ };
+
+template <class T, bool b = boost::is_pod<T>::value>
+struct expm1_init_on_startup
+{
+ struct init
+ {
+ init()
+ {
+ boost::math::expm1(T(0.5f));
+ }
+ void do_nothing()const{}
+ };
+
+ static void do_nothing()
+ {
+ initializer.do_nothing();
+ }
+
+ static const init initializer;
+};
+
+template <class T, bool b>
+const typename expm1_init_on_startup<T, b>::init expm1_init_on_startup<T, b>::initializer;
+
+template <class T>
+struct expm1_init_on_startup<T, true>
+{
+ static void do_nothing(){}
+};
+//
+// Algorithm expm1 is part of C99, but is not yet provided by many compilers.
+//
+// This version uses a Taylor series expansion for 0.5 > |x| > epsilon.
+//
+template <class T, class Policy>
+T expm1_imp(T x, const mpl::int_<0>&, const Policy& pol)
+{
+ BOOST_MATH_STD_USING
+
+ T a = fabs(x);
+ if(a > T(0.5f))
+ {
+ if(a >= tools::log_max_value<T>())
+ {
+ if(x > 0)
+ return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
+ return -1;
+ }
+ return exp(x) - T(1);
+ }
+ if(a < tools::epsilon<T>())
+ return x;
+ detail::expm1_series<T> 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)
+ T result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter);
+#else
+ T zero = 0;
+ T result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter, zero);
+#endif
+ policies::check_series_iterations<T>("boost::math::expm1<%1%>(%1%)", max_iter, pol);
+ return result;
+}
+
+template <class T, class P>
+T expm1_imp(T x, const mpl::int_<53>&, const P& pol)
+{
+ BOOST_MATH_STD_USING
+
+ expm1_init_on_startup<T>::do_nothing();
+
+ T a = fabs(x);
+ if(a > T(0.5L))
+ {
+ if(a >= tools::log_max_value<T>())
+ {
+ if(x > 0)
+ return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
+ return -1;
+ }
+ return exp(x) - T(1);
+ }
+ if(a < tools::epsilon<T>())
+ return x;
+
+ static const float Y = 0.10281276702880859e1f;
+ static const T n[] = { -0.28127670288085937e-1, 0.51278186299064534e0, -0.6310029069350198e-1, 0.11638457975729296e-1, -0.52143390687521003e-3, 0.21491399776965688e-4 };
+ static const T d[] = { 1, -0.45442309511354755e0, 0.90850389570911714e-1, -0.10088963629815502e-1, 0.63003407478692265e-3, -0.17976570003654402e-4 };
+
+ T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
+ return result;
+}
+
+template <class T, class P>
+T expm1_imp(T x, const mpl::int_<64>&, const P& pol)
+{
+ BOOST_MATH_STD_USING
+
+ expm1_init_on_startup<T>::do_nothing();
+
+ T a = fabs(x);
+ if(a > T(0.5L))
+ {
+ if(a >= tools::log_max_value<T>())
+ {
+ if(x > 0)
+ return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
+ return -1;
+ }
+ return exp(x) - T(1);
+ }
+ if(a < tools::epsilon<T>())
+ return x;
+
+ static const float Y = 0.10281276702880859375e1f;
+ static const T n[] = {
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.281276702880859375e-1),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.512980290285154286358e0),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.667758794592881019644e-1),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.131432469658444745835e-1),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.72303795326880286965e-3),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.447441185192951335042e-4),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.714539134024984593011e-6)
+ };
+ static const T d[] = {
+ 1,
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.461477618025562520389e0),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.961237488025708540713e-1),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.116483957658204450739e-1),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.873308008461557544458e-3),
+ BOOST_MATH_BIG_CONSTANT(T, 64, -0.387922804997682392562e-4),
+ BOOST_MATH_BIG_CONSTANT(T, 64, 0.807473180049193557294e-6)
+ };
+
+ T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
+ return result;
+}
+
+template <class T, class P>
+T expm1_imp(T x, const mpl::int_<113>&, const P& pol)
+{
+ BOOST_MATH_STD_USING
+
+ expm1_init_on_startup<T>::do_nothing();
+
+ T a = fabs(x);
+ if(a > T(0.5L))
+ {
+ if(a >= tools::log_max_value<T>())
+ {
+ if(x > 0)
+ return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
+ return -1;
+ }
+ return exp(x) - T(1);
+ }
+ if(a < tools::epsilon<T>())
+ return x;
+
+ static const float Y = 0.10281276702880859375e1f;
+ static const T n[] = {
+ BOOST_MATH_BIG_CONSTANT(T, 113, -0.28127670288085937499999999999999999854e-1),
+ BOOST_MATH_BIG_CONSTANT(T, 113, 0.51278156911210477556524452177540792214e0),
+ BOOST_MATH_BIG_CONSTANT(T, 113, -0.63263178520747096729500254678819588223e-1),
+ BOOST_MATH_BIG_CONSTANT(T, 113, 0.14703285606874250425508446801230572252e-1),
+ BOOST_MATH_BIG_CONSTANT(T, 113, -0.8675686051689527802425310407898459386e-3),
+ BOOST_MATH_BIG_CONSTANT(T, 113, 0.88126359618291165384647080266133492399e-4),
+ BOOST_MATH_BIG_CONSTANT(T, 113, -0.25963087867706310844432390015463138953e-5),
+ BOOST_MATH_BIG_CONSTANT(T, 113, 0.14226691087800461778631773363204081194e-6),
+ BOOST_MATH_BIG_CONSTANT(T, 113, -0.15995603306536496772374181066765665596e-8),
+ BOOST_MATH_BIG_CONSTANT(T, 113, 0.45261820069007790520447958280473183582e-10)
+ };
+ static const T d[] = {
+ 1,
+ BOOST_MATH_BIG_CONSTANT(T, 113, -0.45441264709074310514348137469214538853e0),
+ BOOST_MATH_BIG_CONSTANT(T, 113, 0.96827131936192217313133611655555298106e-1),
+ BOOST_MATH_BIG_CONSTANT(T, 113, -0.12745248725908178612540554584374876219e-1),
+ BOOST_MATH_BIG_CONSTANT(T, 113, 0.11473613871583259821612766907781095472e-2),
+ BOOST_MATH_BIG_CONSTANT(T, 113, -0.73704168477258911962046591907690764416e-4),
+ BOOST_MATH_BIG_CONSTANT(T, 113, 0.34087499397791555759285503797256103259e-5),
+ BOOST_MATH_BIG_CONSTANT(T, 113, -0.11114024704296196166272091230695179724e-6),
+ BOOST_MATH_BIG_CONSTANT(T, 113, 0.23987051614110848595909588343223896577e-8),
+ BOOST_MATH_BIG_CONSTANT(T, 113, -0.29477341859111589208776402638429026517e-10),
+ BOOST_MATH_BIG_CONSTANT(T, 113, 0.13222065991022301420255904060628100924e-12)
+ };
+
+ T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
+ return result;
+}
+
+} // namespace detail
+
+template <class T, class Policy>
+inline typename tools::promote_args<T>::type expm1(T x, const Policy& /* pol */)
+{
+ 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_c<
+ ::std::numeric_limits<result_type>::is_specialized == 0,
+ mpl::int_<0>, // no numeric_limits, use generic solution
+ typename mpl::if_<
+ typename mpl::less_equal<precision_type, mpl::int_<53> >::type,
+ mpl::int_<53>, // double
+ typename mpl::if_<
+ typename mpl::less_equal<precision_type, mpl::int_<64> >::type,
+ mpl::int_<64>, // 80-bit long double
+ typename mpl::if_<
+ typename mpl::less_equal<precision_type, mpl::int_<113> >::type,
+ mpl::int_<113>, // 128-bit long double
+ mpl::int_<0> // too many bits, use generic version.
+ >::type
+ >::type
+ >::type
+ >::type tag_type;
+
+ return policies::checked_narrowing_cast<result_type, forwarding_policy>(detail::expm1_imp(
+ static_cast<value_type>(x),
+ tag_type(), forwarding_policy()), "boost::math::expm1<%1%>(%1%)");
+}
+
+#ifdef expm1
+# ifndef BOOST_HAS_expm1
+# define BOOST_HAS_expm1
+# endif
+# undef expm1
+#endif
+
+#if defined(BOOST_HAS_EXPM1) && !(defined(__osf__) && defined(__DECCXX_VER))
+# ifdef BOOST_MATH_USE_C99
+inline float expm1(float x, const policies::policy<>&){ return ::expm1f(x); }
+# ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+inline long double expm1(long double x, const policies::policy<>&){ return ::expm1l(x); }
+# endif
+# else
+inline float expm1(float x, const policies::policy<>&){ return ::expm1(x); }
+# endif
+inline double expm1(double x, const policies::policy<>&){ return ::expm1(x); }
+#endif
+
+template <class T>
+inline typename tools::promote_args<T>::type expm1(T x)
+{
+ return expm1(x, policies::policy<>());
+}
+
+#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x564))
+inline float expm1(float z)
+{
+ return expm1<float>(z);
+}
+inline double expm1(double z)
+{
+ return expm1<double>(z);
+}
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+inline long double expm1(long double z)
+{
+ return expm1<long double>(z);
+}
+#endif
+#endif
+
+} // namespace math
+} // namespace boost
+
+#endif // BOOST_MATH_HYPOT_INCLUDED
+
+
+
+