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)
5
6 #ifndef BOOST_MATH_EXPM1_INCLUDED
7 #define BOOST_MATH_EXPM1_INCLUDED
8
9 #ifdef _MSC_VER
10 #pragma once
11 #endif
12
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>
24
25 #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
26 # include <boost/static_assert.hpp>
27 #else
28 # include <boost/assert.hpp>
29 #endif
30
31 #if defined(__GNUC__) && defined(BOOST_MATH_USE_FLOAT128)
32 //
33 // This is the only way we can avoid
34 // warning: non-standard suffix on floating constant [-Wpedantic]
35 // when building with -Wall -pedantic. Neither __extension__
36 // nor #pragma diagnostic ignored work :(
37 //
38 #pragma GCC system_header
39 #endif
40
41 namespace boost{ namespace math{
42
43 namespace detail
44 {
45 // Functor expm1_series returns the next term in the Taylor series
46 // x^k / k!
47 // each time that operator() is invoked.
48 //
49 template <class T>
50 struct expm1_series
51 {
52 typedef T result_type;
53
expm1_seriesboost::math::detail::expm1_series54 expm1_series(T x)
55 : k(0), m_x(x), m_term(1) {}
56
operator ()boost::math::detail::expm1_series57 T operator()()
58 {
59 ++k;
60 m_term *= m_x;
61 m_term /= k;
62 return m_term;
63 }
64
countboost::math::detail::expm1_series65 int count()const
66 {
67 return k;
68 }
69
70 private:
71 int k;
72 const T m_x;
73 T m_term;
74 expm1_series(const expm1_series&);
75 expm1_series& operator=(const expm1_series&);
76 };
77
78 template <class T, class Policy, class tag>
79 struct expm1_initializer
80 {
81 struct init
82 {
initboost::math::detail::expm1_initializer::init83 init()
84 {
85 do_init(tag());
86 }
87 template <int N>
do_initboost::math::detail::expm1_initializer::init88 static void do_init(const boost::integral_constant<int, N>&){}
do_initboost::math::detail::expm1_initializer::init89 static void do_init(const boost::integral_constant<int, 64>&)
90 {
91 expm1(T(0.5));
92 }
do_initboost::math::detail::expm1_initializer::init93 static void do_init(const boost::integral_constant<int, 113>&)
94 {
95 expm1(T(0.5));
96 }
force_instantiateboost::math::detail::expm1_initializer::init97 void force_instantiate()const{}
98 };
99 static const init initializer;
force_instantiateboost::math::detail::expm1_initializer100 static void force_instantiate()
101 {
102 initializer.force_instantiate();
103 }
104 };
105
106 template <class T, class Policy, class tag>
107 const typename expm1_initializer<T, Policy, tag>::init expm1_initializer<T, Policy, tag>::initializer;
108
109 //
110 // Algorithm expm1 is part of C99, but is not yet provided by many compilers.
111 //
112 // This version uses a Taylor series expansion for 0.5 > |x| > epsilon.
113 //
114 template <class T, class Policy>
115 T expm1_imp(T x, const boost::integral_constant<int, 0>&, const Policy& pol)
116 {
117 BOOST_MATH_STD_USING
118
119 T a = fabs(x);
120 if((boost::math::isnan)(a))
121 {
122 return policies::raise_domain_error<T>("boost::math::expm1<%1%>(%1%)", "expm1 requires a finite argument, but got %1%", a, pol);
123 }
124 if(a > T(0.5f))
125 {
126 if(a >= tools::log_max_value<T>())
127 {
128 if(x > 0)
129 return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
130 return -1;
131 }
132 return exp(x) - T(1);
133 }
134 if(a < tools::epsilon<T>())
135 return x;
136 detail::expm1_series<T> s(x);
137 boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
138 #if !BOOST_WORKAROUND(BOOST_BORLANDC, BOOST_TESTED_AT(0x582)) && !BOOST_WORKAROUND(__EDG_VERSION__, <= 245)
139 T result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter);
140 #else
141 T zero = 0;
142 T result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter, zero);
143 #endif
144 policies::check_series_iterations<T>("boost::math::expm1<%1%>(%1%)", max_iter, pol);
145 return result;
146 }
147
148 template <class T, class P>
149 T expm1_imp(T x, const boost::integral_constant<int, 53>&, const P& pol)
150 {
151 BOOST_MATH_STD_USING
152
153 T a = fabs(x);
154 if(a > T(0.5L))
155 {
156 if(a >= tools::log_max_value<T>())
157 {
158 if(x > 0)
159 return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
160 return -1;
161 }
162 return exp(x) - T(1);
163 }
164 if(a < tools::epsilon<T>())
165 return x;
166
167 static const float Y = 0.10281276702880859e1f;
168 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) };
169 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) };
170
171 T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
172 return result;
173 }
174
175 template <class T, class P>
176 T expm1_imp(T x, const boost::integral_constant<int, 64>&, const P& pol)
177 {
178 BOOST_MATH_STD_USING
179
180 T a = fabs(x);
181 if(a > T(0.5L))
182 {
183 if(a >= tools::log_max_value<T>())
184 {
185 if(x > 0)
186 return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
187 return -1;
188 }
189 return exp(x) - T(1);
190 }
191 if(a < tools::epsilon<T>())
192 return x;
193
194 static const float Y = 0.10281276702880859375e1f;
195 static const T n[] = {
196 BOOST_MATH_BIG_CONSTANT(T, 64, -0.281276702880859375e-1),
197 BOOST_MATH_BIG_CONSTANT(T, 64, 0.512980290285154286358e0),
198 BOOST_MATH_BIG_CONSTANT(T, 64, -0.667758794592881019644e-1),
199 BOOST_MATH_BIG_CONSTANT(T, 64, 0.131432469658444745835e-1),
200 BOOST_MATH_BIG_CONSTANT(T, 64, -0.72303795326880286965e-3),
201 BOOST_MATH_BIG_CONSTANT(T, 64, 0.447441185192951335042e-4),
202 BOOST_MATH_BIG_CONSTANT(T, 64, -0.714539134024984593011e-6)
203 };
204 static const T d[] = {
205 BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
206 BOOST_MATH_BIG_CONSTANT(T, 64, -0.461477618025562520389e0),
207 BOOST_MATH_BIG_CONSTANT(T, 64, 0.961237488025708540713e-1),
208 BOOST_MATH_BIG_CONSTANT(T, 64, -0.116483957658204450739e-1),
209 BOOST_MATH_BIG_CONSTANT(T, 64, 0.873308008461557544458e-3),
210 BOOST_MATH_BIG_CONSTANT(T, 64, -0.387922804997682392562e-4),
211 BOOST_MATH_BIG_CONSTANT(T, 64, 0.807473180049193557294e-6)
212 };
213
214 T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
215 return result;
216 }
217
218 template <class T, class P>
219 T expm1_imp(T x, const boost::integral_constant<int, 113>&, const P& pol)
220 {
221 BOOST_MATH_STD_USING
222
223 T a = fabs(x);
224 if(a > T(0.5L))
225 {
226 if(a >= tools::log_max_value<T>())
227 {
228 if(x > 0)
229 return policies::raise_overflow_error<T>("boost::math::expm1<%1%>(%1%)", 0, pol);
230 return -1;
231 }
232 return exp(x) - T(1);
233 }
234 if(a < tools::epsilon<T>())
235 return x;
236
237 static const float Y = 0.10281276702880859375e1f;
238 static const T n[] = {
239 BOOST_MATH_BIG_CONSTANT(T, 113, -0.28127670288085937499999999999999999854e-1),
240 BOOST_MATH_BIG_CONSTANT(T, 113, 0.51278156911210477556524452177540792214e0),
241 BOOST_MATH_BIG_CONSTANT(T, 113, -0.63263178520747096729500254678819588223e-1),
242 BOOST_MATH_BIG_CONSTANT(T, 113, 0.14703285606874250425508446801230572252e-1),
243 BOOST_MATH_BIG_CONSTANT(T, 113, -0.8675686051689527802425310407898459386e-3),
244 BOOST_MATH_BIG_CONSTANT(T, 113, 0.88126359618291165384647080266133492399e-4),
245 BOOST_MATH_BIG_CONSTANT(T, 113, -0.25963087867706310844432390015463138953e-5),
246 BOOST_MATH_BIG_CONSTANT(T, 113, 0.14226691087800461778631773363204081194e-6),
247 BOOST_MATH_BIG_CONSTANT(T, 113, -0.15995603306536496772374181066765665596e-8),
248 BOOST_MATH_BIG_CONSTANT(T, 113, 0.45261820069007790520447958280473183582e-10)
249 };
250 static const T d[] = {
251 BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
252 BOOST_MATH_BIG_CONSTANT(T, 113, -0.45441264709074310514348137469214538853e0),
253 BOOST_MATH_BIG_CONSTANT(T, 113, 0.96827131936192217313133611655555298106e-1),
254 BOOST_MATH_BIG_CONSTANT(T, 113, -0.12745248725908178612540554584374876219e-1),
255 BOOST_MATH_BIG_CONSTANT(T, 113, 0.11473613871583259821612766907781095472e-2),
256 BOOST_MATH_BIG_CONSTANT(T, 113, -0.73704168477258911962046591907690764416e-4),
257 BOOST_MATH_BIG_CONSTANT(T, 113, 0.34087499397791555759285503797256103259e-5),
258 BOOST_MATH_BIG_CONSTANT(T, 113, -0.11114024704296196166272091230695179724e-6),
259 BOOST_MATH_BIG_CONSTANT(T, 113, 0.23987051614110848595909588343223896577e-8),
260 BOOST_MATH_BIG_CONSTANT(T, 113, -0.29477341859111589208776402638429026517e-10),
261 BOOST_MATH_BIG_CONSTANT(T, 113, 0.13222065991022301420255904060628100924e-12)
262 };
263
264 T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x);
265 return result;
266 }
267
268 } // namespace detail
269
270 template <class T, class Policy>
expm1(T x,const Policy &)271 inline typename tools::promote_args<T>::type expm1(T x, const Policy& /* pol */)
272 {
273 typedef typename tools::promote_args<T>::type result_type;
274 typedef typename policies::evaluation<result_type, Policy>::type value_type;
275 typedef typename policies::precision<result_type, Policy>::type precision_type;
276 typedef typename policies::normalise<
277 Policy,
278 policies::promote_float<false>,
279 policies::promote_double<false>,
280 policies::discrete_quantile<>,
281 policies::assert_undefined<> >::type forwarding_policy;
282
283 typedef boost::integral_constant<int,
284 precision_type::value <= 0 ? 0 :
285 precision_type::value <= 53 ? 53 :
286 precision_type::value <= 64 ? 64 :
287 precision_type::value <= 113 ? 113 : 0
288 > tag_type;
289
290 detail::expm1_initializer<value_type, forwarding_policy, tag_type>::force_instantiate();
291
292 return policies::checked_narrowing_cast<result_type, forwarding_policy>(detail::expm1_imp(
293 static_cast<value_type>(x),
294 tag_type(), forwarding_policy()), "boost::math::expm1<%1%>(%1%)");
295 }
296
297 #ifdef expm1
298 # ifndef BOOST_HAS_expm1
299 # define BOOST_HAS_expm1
300 # endif
301 # undef expm1
302 #endif
303
304 #if defined(BOOST_HAS_EXPM1) && !(defined(__osf__) && defined(__DECCXX_VER))
305 # ifdef BOOST_MATH_USE_C99
expm1(float x,const policies::policy<> &)306 inline float expm1(float x, const policies::policy<>&){ return ::expm1f(x); }
307 # ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
expm1(long double x,const policies::policy<> &)308 inline long double expm1(long double x, const policies::policy<>&){ return ::expm1l(x); }
309 # endif
310 # else
expm1(float x,const policies::policy<> &)311 inline float expm1(float x, const policies::policy<>&){ return static_cast<float>(::expm1(x)); }
312 # endif
expm1(double x,const policies::policy<> &)313 inline double expm1(double x, const policies::policy<>&){ return ::expm1(x); }
314 #endif
315
316 template <class T>
expm1(T x)317 inline typename tools::promote_args<T>::type expm1(T x)
318 {
319 return expm1(x, policies::policy<>());
320 }
321
322 #if BOOST_WORKAROUND(BOOST_BORLANDC, BOOST_TESTED_AT(0x564))
expm1(float z)323 inline float expm1(float z)
324 {
325 return expm1<float>(z);
326 }
expm1(double z)327 inline double expm1(double z)
328 {
329 return expm1<double>(z);
330 }
331 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
expm1(long double z)332 inline long double expm1(long double z)
333 {
334 return expm1<long double>(z);
335 }
336 #endif
337 #endif
338
339 } // namespace math
340 } // namespace boost
341
342 #endif // BOOST_MATH_HYPOT_INCLUDED
343
344
345
346
347