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/tools/big_constant.hpp>
20 #include <boost/math/policies/error_handling.hpp>
21 #include <boost/math/tools/rational.hpp>
22 #include <boost/math/special_functions/math_fwd.hpp>
23 #include <boost/mpl/less_equal.hpp>
25 #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
26 # include <boost/static_assert.hpp>
28 # include <boost/assert.hpp>
31 namespace boost{ namespace math{
35 // Functor expm1_series returns the next term in the Taylor series
37 // each time that operator() is invoked.
42 typedef T result_type;
45 : k(0), m_x(x), m_term(1) {}
64 expm1_series(const expm1_series&);
65 expm1_series& operator=(const expm1_series&);
68 template <class T, class Policy, class tag>
69 struct expm1_initializer
78 static void do_init(const mpl::int_<N>&){}
79 static void do_init(const mpl::int_<64>&)
83 static void do_init(const mpl::int_<113>&)
87 void force_instantiate()const{}
89 static const init initializer;
90 static void force_instantiate()
92 initializer.force_instantiate();
96 template <class T, class Policy, class tag>
97 const typename expm1_initializer<T, Policy, tag>::init expm1_initializer<T, Policy, tag>::initializer;
100 // Algorithm expm1 is part of C99, but is not yet provided by many compilers.
102 // This version uses a Taylor series expansion for 0.5 > |x| > epsilon.
104 template <class T, class Policy>
105 T expm1_imp(T x, const mpl::int_<0>&, const Policy& pol)
110 if((boost::math::isnan)(a))
112 return policies::raise_domain_error<T>("boost::math::expm1<%1%>(%1%)", "expm1 requires a finite argument, but got %1%", a, pol);
116 if(a >= tools::log_max_value<T>())
119 return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
122 return exp(x) - T(1);
124 if(a < tools::epsilon<T>())
126 detail::expm1_series<T> s(x);
127 boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
128 #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) && !BOOST_WORKAROUND(__EDG_VERSION__, <= 245)
129 T result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter);
132 T result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter, zero);
134 policies::check_series_iterations<T>("boost::math::expm1<%1%>(%1%)", max_iter, pol);
138 template <class T, class P>
139 T expm1_imp(T x, const mpl::int_<53>&, const P& pol)
146 if(a >= tools::log_max_value<T>())
149 return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
152 return exp(x) - T(1);
154 if(a < tools::epsilon<T>())
157 static const float Y = 0.10281276702880859e1f;
158 static const T n[] = { static_cast<T>(-0.28127670288085937e-1), static_cast<T>(0.51278186299064534e0), static_cast<T>(-0.6310029069350198e-1), static_cast<T>(0.11638457975729296e-1), static_cast<T>(-0.52143390687521003e-3), static_cast<T>(0.21491399776965688e-4) };
159 static const T d[] = { 1, static_cast<T>(-0.45442309511354755e0), static_cast<T>(0.90850389570911714e-1), static_cast<T>(-0.10088963629815502e-1), static_cast<T>(0.63003407478692265e-3), static_cast<T>(-0.17976570003654402e-4) };
161 T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
165 template <class T, class P>
166 T expm1_imp(T x, const mpl::int_<64>&, const P& pol)
173 if(a >= tools::log_max_value<T>())
176 return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
179 return exp(x) - T(1);
181 if(a < tools::epsilon<T>())
184 static const float Y = 0.10281276702880859375e1f;
185 static const T n[] = {
186 BOOST_MATH_BIG_CONSTANT(T, 64, -0.281276702880859375e-1),
187 BOOST_MATH_BIG_CONSTANT(T, 64, 0.512980290285154286358e0),
188 BOOST_MATH_BIG_CONSTANT(T, 64, -0.667758794592881019644e-1),
189 BOOST_MATH_BIG_CONSTANT(T, 64, 0.131432469658444745835e-1),
190 BOOST_MATH_BIG_CONSTANT(T, 64, -0.72303795326880286965e-3),
191 BOOST_MATH_BIG_CONSTANT(T, 64, 0.447441185192951335042e-4),
192 BOOST_MATH_BIG_CONSTANT(T, 64, -0.714539134024984593011e-6)
194 static const T d[] = {
195 BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
196 BOOST_MATH_BIG_CONSTANT(T, 64, -0.461477618025562520389e0),
197 BOOST_MATH_BIG_CONSTANT(T, 64, 0.961237488025708540713e-1),
198 BOOST_MATH_BIG_CONSTANT(T, 64, -0.116483957658204450739e-1),
199 BOOST_MATH_BIG_CONSTANT(T, 64, 0.873308008461557544458e-3),
200 BOOST_MATH_BIG_CONSTANT(T, 64, -0.387922804997682392562e-4),
201 BOOST_MATH_BIG_CONSTANT(T, 64, 0.807473180049193557294e-6)
204 T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
208 template <class T, class P>
209 T expm1_imp(T x, const mpl::int_<113>&, const P& pol)
216 if(a >= tools::log_max_value<T>())
219 return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
222 return exp(x) - T(1);
224 if(a < tools::epsilon<T>())
227 static const float Y = 0.10281276702880859375e1f;
228 static const T n[] = {
229 BOOST_MATH_BIG_CONSTANT(T, 113, -0.28127670288085937499999999999999999854e-1),
230 BOOST_MATH_BIG_CONSTANT(T, 113, 0.51278156911210477556524452177540792214e0),
231 BOOST_MATH_BIG_CONSTANT(T, 113, -0.63263178520747096729500254678819588223e-1),
232 BOOST_MATH_BIG_CONSTANT(T, 113, 0.14703285606874250425508446801230572252e-1),
233 BOOST_MATH_BIG_CONSTANT(T, 113, -0.8675686051689527802425310407898459386e-3),
234 BOOST_MATH_BIG_CONSTANT(T, 113, 0.88126359618291165384647080266133492399e-4),
235 BOOST_MATH_BIG_CONSTANT(T, 113, -0.25963087867706310844432390015463138953e-5),
236 BOOST_MATH_BIG_CONSTANT(T, 113, 0.14226691087800461778631773363204081194e-6),
237 BOOST_MATH_BIG_CONSTANT(T, 113, -0.15995603306536496772374181066765665596e-8),
238 BOOST_MATH_BIG_CONSTANT(T, 113, 0.45261820069007790520447958280473183582e-10)
240 static const T d[] = {
241 BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
242 BOOST_MATH_BIG_CONSTANT(T, 113, -0.45441264709074310514348137469214538853e0),
243 BOOST_MATH_BIG_CONSTANT(T, 113, 0.96827131936192217313133611655555298106e-1),
244 BOOST_MATH_BIG_CONSTANT(T, 113, -0.12745248725908178612540554584374876219e-1),
245 BOOST_MATH_BIG_CONSTANT(T, 113, 0.11473613871583259821612766907781095472e-2),
246 BOOST_MATH_BIG_CONSTANT(T, 113, -0.73704168477258911962046591907690764416e-4),
247 BOOST_MATH_BIG_CONSTANT(T, 113, 0.34087499397791555759285503797256103259e-5),
248 BOOST_MATH_BIG_CONSTANT(T, 113, -0.11114024704296196166272091230695179724e-6),
249 BOOST_MATH_BIG_CONSTANT(T, 113, 0.23987051614110848595909588343223896577e-8),
250 BOOST_MATH_BIG_CONSTANT(T, 113, -0.29477341859111589208776402638429026517e-10),
251 BOOST_MATH_BIG_CONSTANT(T, 113, 0.13222065991022301420255904060628100924e-12)
254 T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
258 } // namespace detail
260 template <class T, class Policy>
261 inline typename tools::promote_args<T>::type expm1(T x, const Policy& /* pol */)
263 typedef typename tools::promote_args<T>::type result_type;
264 typedef typename policies::evaluation<result_type, Policy>::type value_type;
265 typedef typename policies::precision<result_type, Policy>::type precision_type;
266 typedef typename policies::normalise<
268 policies::promote_float<false>,
269 policies::promote_double<false>,
270 policies::discrete_quantile<>,
271 policies::assert_undefined<> >::type forwarding_policy;
273 typedef typename mpl::if_c<
274 ::std::numeric_limits<result_type>::is_specialized == 0,
275 mpl::int_<0>, // no numeric_limits, use generic solution
277 typename mpl::less_equal<precision_type, mpl::int_<53> >::type,
278 mpl::int_<53>, // double
280 typename mpl::less_equal<precision_type, mpl::int_<64> >::type,
281 mpl::int_<64>, // 80-bit long double
283 typename mpl::less_equal<precision_type, mpl::int_<113> >::type,
284 mpl::int_<113>, // 128-bit long double
285 mpl::int_<0> // too many bits, use generic version.
291 detail::expm1_initializer<value_type, forwarding_policy, tag_type>::force_instantiate();
293 return policies::checked_narrowing_cast<result_type, forwarding_policy>(detail::expm1_imp(
294 static_cast<value_type>(x),
295 tag_type(), forwarding_policy()), "boost::math::expm1<%1%>(%1%)");
299 # ifndef BOOST_HAS_expm1
300 # define BOOST_HAS_expm1
305 #if defined(BOOST_HAS_EXPM1) && !(defined(__osf__) && defined(__DECCXX_VER))
306 # ifdef BOOST_MATH_USE_C99
307 inline float expm1(float x, const policies::policy<>&){ return ::expm1f(x); }
308 # ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
309 inline long double expm1(long double x, const policies::policy<>&){ return ::expm1l(x); }
312 inline float expm1(float x, const policies::policy<>&){ return static_cast<float>(::expm1(x)); }
314 inline double expm1(double x, const policies::policy<>&){ return ::expm1(x); }
318 inline typename tools::promote_args<T>::type expm1(T x)
320 return expm1(x, policies::policy<>());
323 #if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x564))
324 inline float expm1(float z)
326 return expm1<float>(z);
328 inline double expm1(double z)
330 return expm1<double>(z);
332 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
333 inline long double expm1(long double z)
335 return expm1<long double>(z);
343 #endif // BOOST_MATH_HYPOT_INCLUDED