1 /* Boost interval/transc.hpp template implementation file
2 *
3 * Copyright 2000 Jens Maurer
4 * Copyright 2002 Herv� Br�nnimann, Guillaume Melquiond, Sylvain Pion
5 *
6 * Distributed under the Boost Software License, Version 1.0.
7 * (See accompanying file LICENSE_1_0.txt or
8 * copy at http://www.boost.org/LICENSE_1_0.txt)
9 */
10
11 #ifndef BOOST_NUMERIC_INTERVAL_TRANSC_HPP
12 #define BOOST_NUMERIC_INTERVAL_TRANSC_HPP
13
14 #include <boost/config.hpp>
15 #include <boost/numeric/interval/detail/interval_prototype.hpp>
16 #include <boost/numeric/interval/detail/bugs.hpp>
17 #include <boost/numeric/interval/detail/test_input.hpp>
18 #include <boost/numeric/interval/rounding.hpp>
19 #include <boost/numeric/interval/constants.hpp>
20 #include <boost/numeric/interval/arith.hpp>
21 #include <boost/numeric/interval/arith2.hpp>
22 #include <algorithm>
23
24 namespace boost {
25 namespace numeric {
26
27 template<class T, class Policies> inline
exp(const interval<T,Policies> & x)28 interval<T, Policies> exp(const interval<T, Policies>& x)
29 {
30 typedef interval<T, Policies> I;
31 if (interval_lib::detail::test_input(x))
32 return I::empty();
33 typename Policies::rounding rnd;
34 return I(rnd.exp_down(x.lower()), rnd.exp_up(x.upper()), true);
35 }
36
37 template<class T, class Policies> inline
log(const interval<T,Policies> & x)38 interval<T, Policies> log(const interval<T, Policies>& x)
39 {
40 typedef interval<T, Policies> I;
41 if (interval_lib::detail::test_input(x) ||
42 !interval_lib::user::is_pos(x.upper()))
43 return I::empty();
44 typename Policies::rounding rnd;
45 typedef typename Policies::checking checking;
46 T l = !interval_lib::user::is_pos(x.lower())
47 ? checking::neg_inf() : rnd.log_down(x.lower());
48 return I(l, rnd.log_up(x.upper()), true);
49 }
50
51 template<class T, class Policies> inline
cos(const interval<T,Policies> & x)52 interval<T, Policies> cos(const interval<T, Policies>& x)
53 {
54 if (interval_lib::detail::test_input(x))
55 return interval<T, Policies>::empty();
56 typename Policies::rounding rnd;
57 typedef interval<T, Policies> I;
58 typedef typename interval_lib::unprotect<I>::type R;
59
60 // get lower bound within [0, pi]
61 const R pi2 = interval_lib::pi_twice<R>();
62 R tmp = fmod((const R&)x, pi2);
63 if (width(tmp) >= pi2.lower())
64 return I(static_cast<T>(-1), static_cast<T>(1), true); // we are covering a full period
65 if (tmp.lower() >= interval_lib::constants::pi_upper<T>())
66 return -cos(tmp - interval_lib::pi<R>());
67 T l = tmp.lower();
68 T u = tmp.upper();
69
70 BOOST_USING_STD_MIN();
71 // separate into monotone subintervals
72 if (u <= interval_lib::constants::pi_lower<T>())
73 return I(rnd.cos_down(u), rnd.cos_up(l), true);
74 else if (u <= pi2.lower())
75 return I(static_cast<T>(-1), rnd.cos_up(min BOOST_PREVENT_MACRO_SUBSTITUTION(rnd.sub_down(pi2.lower(), u), l)), true);
76 else
77 return I(static_cast<T>(-1), static_cast<T>(1), true);
78 }
79
80 template<class T, class Policies> inline
sin(const interval<T,Policies> & x)81 interval<T, Policies> sin(const interval<T, Policies>& x)
82 {
83 typedef interval<T, Policies> I;
84 if (interval_lib::detail::test_input(x))
85 return I::empty();
86 typename Policies::rounding rnd;
87 typedef typename interval_lib::unprotect<I>::type R;
88 I r = cos((const R&)x - interval_lib::pi_half<R>());
89 (void)&rnd;
90 return r;
91 }
92
93 template<class T, class Policies> inline
tan(const interval<T,Policies> & x)94 interval<T, Policies> tan(const interval<T, Policies>& x)
95 {
96 typedef interval<T, Policies> I;
97 if (interval_lib::detail::test_input(x))
98 return I::empty();
99 typename Policies::rounding rnd;
100 typedef typename interval_lib::unprotect<I>::type R;
101
102 // get lower bound within [-pi/2, pi/2]
103 const R pi = interval_lib::pi<R>();
104 R tmp = fmod((const R&)x, pi);
105 const T pi_half_d = interval_lib::constants::pi_half_lower<T>();
106 if (tmp.lower() >= pi_half_d)
107 tmp -= pi;
108 if (tmp.lower() <= -pi_half_d || tmp.upper() >= pi_half_d)
109 return I::whole();
110 return I(rnd.tan_down(tmp.lower()), rnd.tan_up(tmp.upper()), true);
111 }
112
113 template<class T, class Policies> inline
asin(const interval<T,Policies> & x)114 interval<T, Policies> asin(const interval<T, Policies>& x)
115 {
116 typedef interval<T, Policies> I;
117 if (interval_lib::detail::test_input(x)
118 || x.upper() < static_cast<T>(-1) || x.lower() > static_cast<T>(1))
119 return I::empty();
120 typename Policies::rounding rnd;
121 T l = (x.lower() <= static_cast<T>(-1))
122 ? -interval_lib::constants::pi_half_upper<T>()
123 : rnd.asin_down(x.lower());
124 T u = (x.upper() >= static_cast<T>(1) )
125 ? interval_lib::constants::pi_half_upper<T>()
126 : rnd.asin_up (x.upper());
127 return I(l, u, true);
128 }
129
130 template<class T, class Policies> inline
acos(const interval<T,Policies> & x)131 interval<T, Policies> acos(const interval<T, Policies>& x)
132 {
133 typedef interval<T, Policies> I;
134 if (interval_lib::detail::test_input(x)
135 || x.upper() < static_cast<T>(-1) || x.lower() > static_cast<T>(1))
136 return I::empty();
137 typename Policies::rounding rnd;
138 T l = (x.upper() >= static_cast<T>(1) )
139 ? static_cast<T>(0)
140 : rnd.acos_down(x.upper());
141 T u = (x.lower() <= static_cast<T>(-1))
142 ? interval_lib::constants::pi_upper<T>()
143 : rnd.acos_up (x.lower());
144 return I(l, u, true);
145 }
146
147 template<class T, class Policies> inline
atan(const interval<T,Policies> & x)148 interval<T, Policies> atan(const interval<T, Policies>& x)
149 {
150 typedef interval<T, Policies> I;
151 if (interval_lib::detail::test_input(x))
152 return I::empty();
153 typename Policies::rounding rnd;
154 return I(rnd.atan_down(x.lower()), rnd.atan_up(x.upper()), true);
155 }
156
157 template<class T, class Policies> inline
sinh(const interval<T,Policies> & x)158 interval<T, Policies> sinh(const interval<T, Policies>& x)
159 {
160 typedef interval<T, Policies> I;
161 if (interval_lib::detail::test_input(x))
162 return I::empty();
163 typename Policies::rounding rnd;
164 return I(rnd.sinh_down(x.lower()), rnd.sinh_up(x.upper()), true);
165 }
166
167 template<class T, class Policies> inline
cosh(const interval<T,Policies> & x)168 interval<T, Policies> cosh(const interval<T, Policies>& x)
169 {
170 typedef interval<T, Policies> I;
171 if (interval_lib::detail::test_input(x))
172 return I::empty();
173 typename Policies::rounding rnd;
174 if (interval_lib::user::is_neg(x.upper()))
175 return I(rnd.cosh_down(x.upper()), rnd.cosh_up(x.lower()), true);
176 else if (!interval_lib::user::is_neg(x.lower()))
177 return I(rnd.cosh_down(x.lower()), rnd.cosh_up(x.upper()), true);
178 else
179 return I(static_cast<T>(0), rnd.cosh_up(-x.lower() > x.upper() ? x.lower() : x.upper()), true);
180 }
181
182 template<class T, class Policies> inline
tanh(const interval<T,Policies> & x)183 interval<T, Policies> tanh(const interval<T, Policies>& x)
184 {
185 typedef interval<T, Policies> I;
186 if (interval_lib::detail::test_input(x))
187 return I::empty();
188 typename Policies::rounding rnd;
189 return I(rnd.tanh_down(x.lower()), rnd.tanh_up(x.upper()), true);
190 }
191
192 template<class T, class Policies> inline
asinh(const interval<T,Policies> & x)193 interval<T, Policies> asinh(const interval<T, Policies>& x)
194 {
195 typedef interval<T, Policies> I;
196 if (interval_lib::detail::test_input(x))
197 return I::empty();
198 typename Policies::rounding rnd;
199 return I(rnd.asinh_down(x.lower()), rnd.asinh_up(x.upper()), true);
200 }
201
202 template<class T, class Policies> inline
acosh(const interval<T,Policies> & x)203 interval<T, Policies> acosh(const interval<T, Policies>& x)
204 {
205 typedef interval<T, Policies> I;
206 if (interval_lib::detail::test_input(x) || x.upper() < static_cast<T>(1))
207 return I::empty();
208 typename Policies::rounding rnd;
209 T l = x.lower() <= static_cast<T>(1) ? static_cast<T>(0) : rnd.acosh_down(x.lower());
210 return I(l, rnd.acosh_up(x.upper()), true);
211 }
212
213 template<class T, class Policies> inline
atanh(const interval<T,Policies> & x)214 interval<T, Policies> atanh(const interval<T, Policies>& x)
215 {
216 typedef interval<T, Policies> I;
217 if (interval_lib::detail::test_input(x)
218 || x.upper() < static_cast<T>(-1) || x.lower() > static_cast<T>(1))
219 return I::empty();
220 typename Policies::rounding rnd;
221 typedef typename Policies::checking checking;
222 T l = (x.lower() <= static_cast<T>(-1))
223 ? checking::neg_inf() : rnd.atanh_down(x.lower());
224 T u = (x.upper() >= static_cast<T>(1) )
225 ? checking::pos_inf() : rnd.atanh_up (x.upper());
226 return I(l, u, true);
227 }
228
229 } // namespace numeric
230 } // namespace boost
231
232 #endif // BOOST_NUMERIC_INTERVAL_TRANSC_HPP
233