1 // (C) Copyright John Maddock 2006.
2 // Use, modification and distribution are subject to the
3 // Boost Software License, Version 1.0. (See accompanying file
4 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
6 #ifndef BOOST_MATH_EXPM1_INCLUDED
7 #define BOOST_MATH_EXPM1_INCLUDED
13 #include <boost/config/no_tr1/cmath.hpp>
14 #include <math.h> // platform's ::expm1
15 #include <boost/limits.hpp>
16 #include <boost/math/tools/config.hpp>
17 #include <boost/math/tools/series.hpp>
18 #include <boost/math/tools/precision.hpp>
19 #include <boost/math/policies/error_handling.hpp>
20 #include <boost/math/tools/rational.hpp>
21 #include <boost/math/special_functions/math_fwd.hpp>
22 #include <boost/mpl/less_equal.hpp>
24 #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
25 # include <boost/static_assert.hpp>
27 # include <boost/assert.hpp>
30 namespace boost{ namespace math{
34 // Functor expm1_series returns the next term in the Taylor series
36 // each time that operator() is invoked.
41 typedef T result_type;
44 : k(0), m_x(x), m_term(1) {}
63 expm1_series(const expm1_series&);
64 expm1_series& operator=(const expm1_series&);
68 // Algorithm expm1 is part of C99, but is not yet provided by many compilers.
70 // This version uses a Taylor series expansion for 0.5 > |x| > epsilon.
72 template <class T, class Policy>
73 T expm1_imp(T x, const mpl::int_<0>&, const Policy& pol)
80 if(a >= tools::log_max_value<T>())
83 return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
88 if(a < tools::epsilon<T>())
90 detail::expm1_series<T> s(x);
91 boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
92 #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) && !BOOST_WORKAROUND(__EDG_VERSION__, <= 245)
93 T result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter);
96 T result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter, zero);
98 policies::check_series_iterations("boost::math::expm1<%1%>(%1%)", max_iter, pol);
102 template <class T, class P>
103 T expm1_imp(T x, const mpl::int_<53>&, const P& pol)
110 if(a >= tools::log_max_value<T>())
113 return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
116 return exp(x) - T(1);
118 if(a < tools::epsilon<T>())
121 static const float Y = 0.10281276702880859e1f;
122 static const T n[] = { -0.28127670288085937e-1, 0.51278186299064534e0, -0.6310029069350198e-1, 0.11638457975729296e-1, -0.52143390687521003e-3, 0.21491399776965688e-4 };
123 static const T d[] = { 1, -0.45442309511354755e0, 0.90850389570911714e-1, -0.10088963629815502e-1, 0.63003407478692265e-3, -0.17976570003654402e-4 };
125 T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
129 template <class T, class P>
130 T expm1_imp(T x, const mpl::int_<64>&, const P& pol)
137 if(a >= tools::log_max_value<T>())
140 return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
143 return exp(x) - T(1);
145 if(a < tools::epsilon<T>())
148 static const float Y = 0.10281276702880859375e1f;
149 static const T n[] = {
150 -0.281276702880859375e-1L,
151 0.512980290285154286358e0L,
152 -0.667758794592881019644e-1L,
153 0.131432469658444745835e-1L,
154 -0.72303795326880286965e-3L,
155 0.447441185192951335042e-4L,
156 -0.714539134024984593011e-6L
158 static const T d[] = {
160 -0.461477618025562520389e0L,
161 0.961237488025708540713e-1L,
162 -0.116483957658204450739e-1L,
163 0.873308008461557544458e-3L,
164 -0.387922804997682392562e-4L,
165 0.807473180049193557294e-6L
168 T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
172 template <class T, class P>
173 T expm1_imp(T x, const mpl::int_<113>&, const P& pol)
180 if(a >= tools::log_max_value<T>())
183 return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
186 return exp(x) - T(1);
188 if(a < tools::epsilon<T>())
191 static const float Y = 0.10281276702880859375e1f;
192 static const T n[] = {
193 -0.28127670288085937499999999999999999854e-1L,
194 0.51278156911210477556524452177540792214e0L,
195 -0.63263178520747096729500254678819588223e-1L,
196 0.14703285606874250425508446801230572252e-1L,
197 -0.8675686051689527802425310407898459386e-3L,
198 0.88126359618291165384647080266133492399e-4L,
199 -0.25963087867706310844432390015463138953e-5L,
200 0.14226691087800461778631773363204081194e-6L,
201 -0.15995603306536496772374181066765665596e-8L,
202 0.45261820069007790520447958280473183582e-10L
204 static const T d[] = {
206 -0.45441264709074310514348137469214538853e0L,
207 0.96827131936192217313133611655555298106e-1L,
208 -0.12745248725908178612540554584374876219e-1L,
209 0.11473613871583259821612766907781095472e-2L,
210 -0.73704168477258911962046591907690764416e-4L,
211 0.34087499397791555759285503797256103259e-5L,
212 -0.11114024704296196166272091230695179724e-6L,
213 0.23987051614110848595909588343223896577e-8L,
214 -0.29477341859111589208776402638429026517e-10L,
215 0.13222065991022301420255904060628100924e-12L
218 T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
222 } // namespace detail
224 template <class T, class Policy>
225 inline typename tools::promote_args<T>::type expm1(T x, const Policy& /* pol */)
227 typedef typename tools::promote_args<T>::type result_type;
228 typedef typename policies::evaluation<result_type, Policy>::type value_type;
229 typedef typename policies::precision<result_type, Policy>::type precision_type;
230 typedef typename policies::normalise<
232 policies::promote_float<false>,
233 policies::promote_double<false>,
234 policies::discrete_quantile<>,
235 policies::assert_undefined<> >::type forwarding_policy;
237 typedef typename mpl::if_c<
238 ::std::numeric_limits<result_type>::is_specialized == 0,
239 mpl::int_<0>, // no numeric_limits, use generic solution
241 typename mpl::less_equal<precision_type, mpl::int_<53> >::type,
242 mpl::int_<53>, // double
244 typename mpl::less_equal<precision_type, mpl::int_<64> >::type,
245 mpl::int_<64>, // 80-bit long double
247 typename mpl::less_equal<precision_type, mpl::int_<113> >::type,
248 mpl::int_<113>, // 128-bit long double
249 mpl::int_<0> // too many bits, use generic version.
255 return policies::checked_narrowing_cast<result_type, forwarding_policy>(detail::expm1_imp(
256 static_cast<value_type>(x),
257 tag_type(), forwarding_policy()), "boost::math::expm1<%1%>(%1%)");
261 # ifndef BOOST_HAS_expm1
262 # define BOOST_HAS_expm1
267 #if defined(BOOST_HAS_EXPM1) && !(defined(__osf__) && defined(__DECCXX_VER))
268 # ifdef BOOST_MATH_USE_C99
269 inline float expm1(float x, const policies::policy<>&){ return ::expm1f(x); }
270 # ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
271 inline long double expm1(long double x, const policies::policy<>&){ return ::expm1l(x); }
274 inline float expm1(float x, const policies::policy<>&){ return ::expm1(x); }
276 inline double expm1(double x, const policies::policy<>&){ return ::expm1(x); }
280 inline typename tools::promote_args<T>::type expm1(T x)
282 return expm1(x, policies::policy<>());
285 #if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x564))
286 inline float expm1(float z)
288 return expm1<float>(z);
290 inline double expm1(double z)
292 return expm1<double>(z);
294 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
295 inline long double expm1(long double z)
297 return expm1<long double>(z);
305 #endif // BOOST_MATH_HYPOT_INCLUDED