1 // TR1 complex -*- C++ -*-
3 // Copyright (C) 2006 Free Software Foundation, Inc.
5 // This file is part of the GNU ISO C++ Library. This library is free
6 // software; you can redistribute it and/or modify it under the
7 // terms of the GNU General Public License as published by the
8 // Free Software Foundation; either version 2, or (at your option)
11 // This library is distributed in the hope that it will be useful,
12 // but WITHOUT ANY WARRANTY; without even the implied warranty of
13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 // GNU General Public License for more details.
16 // You should have received a copy of the GNU General Public License along
17 // with this library; see the file COPYING. If not, write to the Free
18 // Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
21 // As a special exception, you may use this file as part of a free software
22 // library without restriction. Specifically, if other files instantiate
23 // templates or use macros or inline functions from this file, or you compile
24 // this file and link it with other files to produce an executable, this
25 // file does not by itself cause the resulting executable to be covered by
26 // the GNU General Public License. This exception does not however
27 // invalidate any other reasons why the executable file might be covered by
28 // the GNU General Public License.
31 * This is a TR1 C++ Library header.
35 #define _TR1_COMPLEX 1
42 _GLIBCXX_BEGIN_NAMESPACE(tr1)
44 // Forward declarations.
45 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
46 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
47 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
49 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
50 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
51 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
52 template<typename _Tp> std::complex<_Tp> fabs(const std::complex<_Tp>&);
54 /// @brief acos(__z) [8.1.2]
55 // Effects: Behaves the same as C99 function cacos, defined
56 // in subclause 7.3.5.1.
57 template<typename _Tp>
58 inline std::complex<_Tp>
59 __complex_acos(const std::complex<_Tp>& __z)
61 const std::complex<_Tp> __t = std::tr1::asin(__z);
62 const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
63 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
66 #if _GLIBCXX_USE_C99_COMPLEX
67 inline __complex__ float
68 __complex_acos(__complex__ float __z)
69 { return __builtin_cacosf(__z); }
71 inline __complex__ double
72 __complex_acos(__complex__ double __z)
73 { return __builtin_cacos(__z); }
75 inline __complex__ long double
76 __complex_acos(const __complex__ long double& __z)
77 { return __builtin_cacosl(__z); }
79 template<typename _Tp>
80 inline std::complex<_Tp>
81 acos(const std::complex<_Tp>& __z)
82 { return __complex_acos(__z.__rep()); }
84 template<typename _Tp>
85 inline std::complex<_Tp>
86 acos(const std::complex<_Tp>& __z)
87 { return __complex_acos(__z); }
90 /// @brief asin(__z) [8.1.3]
91 // Effects: Behaves the same as C99 function casin, defined
92 // in subclause 7.3.5.2.
93 template<typename _Tp>
94 inline std::complex<_Tp>
95 __complex_asin(const std::complex<_Tp>& __z)
97 std::complex<_Tp> __t(-__z.imag(), __z.real());
98 __t = std::tr1::asinh(__t);
99 return std::complex<_Tp>(__t.imag(), -__t.real());
102 #if _GLIBCXX_USE_C99_COMPLEX
103 inline __complex__ float
104 __complex_asin(__complex__ float __z)
105 { return __builtin_casinf(__z); }
107 inline __complex__ double
108 __complex_asin(__complex__ double __z)
109 { return __builtin_casin(__z); }
111 inline __complex__ long double
112 __complex_asin(const __complex__ long double& __z)
113 { return __builtin_casinl(__z); }
115 template<typename _Tp>
116 inline std::complex<_Tp>
117 asin(const std::complex<_Tp>& __z)
118 { return __complex_asin(__z.__rep()); }
120 template<typename _Tp>
121 inline std::complex<_Tp>
122 asin(const std::complex<_Tp>& __z)
123 { return __complex_asin(__z); }
126 /// @brief atan(__z) [8.1.4]
127 // Effects: Behaves the same as C99 function catan, defined
128 // in subclause 7.3.5.3.
129 template<typename _Tp>
131 __complex_atan(const std::complex<_Tp>& __z)
133 const _Tp __r2 = __z.real() * __z.real();
134 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
136 _Tp __num = __z.imag() + _Tp(1.0);
137 _Tp __den = __z.imag() - _Tp(1.0);
139 __num = __r2 + __num * __num;
140 __den = __r2 + __den * __den;
142 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
143 _Tp(0.25) * log(__num / __den));
146 #if _GLIBCXX_USE_C99_COMPLEX
147 inline __complex__ float
148 __complex_atan(__complex__ float __z)
149 { return __builtin_catanf(__z); }
151 inline __complex__ double
152 __complex_atan(__complex__ double __z)
153 { return __builtin_catan(__z); }
155 inline __complex__ long double
156 __complex_atan(const __complex__ long double& __z)
157 { return __builtin_catanl(__z); }
159 template<typename _Tp>
160 inline std::complex<_Tp>
161 atan(const std::complex<_Tp>& __z)
162 { return __complex_atan(__z.__rep()); }
164 template<typename _Tp>
165 inline std::complex<_Tp>
166 atan(const std::complex<_Tp>& __z)
167 { return __complex_atan(__z); }
170 /// @brief acosh(__z) [8.1.5]
171 // Effects: Behaves the same as C99 function cacosh, defined
172 // in subclause 7.3.6.1.
173 template<typename _Tp>
175 __complex_acosh(const std::complex<_Tp>& __z)
177 std::complex<_Tp> __t((__z.real() - __z.imag())
178 * (__z.real() + __z.imag()) - _Tp(1.0),
179 _Tp(2.0) * __z.real() * __z.imag());
180 __t = std::sqrt(__t);
182 return std::log(__t + __z);
185 #if _GLIBCXX_USE_C99_COMPLEX
186 inline __complex__ float
187 __complex_acosh(__complex__ float __z)
188 { return __builtin_cacoshf(__z); }
190 inline __complex__ double
191 __complex_acosh(__complex__ double __z)
192 { return __builtin_cacosh(__z); }
194 inline __complex__ long double
195 __complex_acosh(const __complex__ long double& __z)
196 { return __builtin_cacoshl(__z); }
198 template<typename _Tp>
199 inline std::complex<_Tp>
200 acosh(const std::complex<_Tp>& __z)
201 { return __complex_acosh(__z.__rep()); }
203 template<typename _Tp>
204 inline std::complex<_Tp>
205 acosh(const std::complex<_Tp>& __z)
206 { return __complex_acosh(__z); }
209 /// @brief asinh(__z) [8.1.6]
210 // Effects: Behaves the same as C99 function casin, defined
211 // in subclause 7.3.6.2.
212 template<typename _Tp>
214 __complex_asinh(const std::complex<_Tp>& __z)
216 std::complex<_Tp> __t((__z.real() - __z.imag())
217 * (__z.real() + __z.imag()) + _Tp(1.0),
218 _Tp(2.0) * __z.real() * __z.imag());
219 __t = std::sqrt(__t);
221 return std::log(__t + __z);
224 #if _GLIBCXX_USE_C99_COMPLEX
225 inline __complex__ float
226 __complex_asinh(__complex__ float __z)
227 { return __builtin_casinhf(__z); }
229 inline __complex__ double
230 __complex_asinh(__complex__ double __z)
231 { return __builtin_casinh(__z); }
233 inline __complex__ long double
234 __complex_asinh(const __complex__ long double& __z)
235 { return __builtin_casinhl(__z); }
237 template<typename _Tp>
238 inline std::complex<_Tp>
239 asinh(const std::complex<_Tp>& __z)
240 { return __complex_asinh(__z.__rep()); }
242 template<typename _Tp>
243 inline std::complex<_Tp>
244 asinh(const std::complex<_Tp>& __z)
245 { return __complex_asinh(__z); }
248 /// @brief atanh(__z) [8.1.7]
249 // Effects: Behaves the same as C99 function catanh, defined
250 // in subclause 7.3.6.3.
251 template<typename _Tp>
253 __complex_atanh(const std::complex<_Tp>& __z)
255 const _Tp __i2 = __z.imag() * __z.imag();
256 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
258 _Tp __num = _Tp(1.0) + __z.real();
259 _Tp __den = _Tp(1.0) - __z.real();
261 __num = __i2 + __num * __num;
262 __den = __i2 + __den * __den;
264 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
265 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
268 #if _GLIBCXX_USE_C99_COMPLEX
269 inline __complex__ float
270 __complex_atanh(__complex__ float __z)
271 { return __builtin_catanhf(__z); }
273 inline __complex__ double
274 __complex_atanh(__complex__ double __z)
275 { return __builtin_catanh(__z); }
277 inline __complex__ long double
278 __complex_atanh(const __complex__ long double& __z)
279 { return __builtin_catanhl(__z); }
281 template<typename _Tp>
282 inline std::complex<_Tp>
283 atanh(const std::complex<_Tp>& __z)
284 { return __complex_atanh(__z.__rep()); }
286 template<typename _Tp>
287 inline std::complex<_Tp>
288 atanh(const std::complex<_Tp>& __z)
289 { return __complex_atanh(__z); }
292 /// @brief fabs(__z) [8.1.8]
293 // Effects: Behaves the same as C99 function cabs, defined
294 // in subclause 7.3.8.1.
295 template<typename _Tp>
296 inline std::complex<_Tp>
297 fabs(const std::complex<_Tp>& __z)
298 { return std::abs(__z); }
300 _GLIBCXX_END_NAMESPACE