source: Daodan/MSYS2/mingw32/include/c++/11.2.0/tr1/complex@ 1186

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1// TR1 complex -*- C++ -*-
2
3// Copyright (C) 2006-2021 Free Software Foundation, Inc.
4//
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 3, or (at your option)
9// any later version.
10
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.
15
16// Under Section 7 of GPL version 3, you are granted additional
17// permissions described in the GCC Runtime Library Exception, version
18// 3.1, as published by the Free Software Foundation.
19
20// You should have received a copy of the GNU General Public License and
21// a copy of the GCC Runtime Library Exception along with this program;
22// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
23// <http://www.gnu.org/licenses/>.
24
25/** @file tr1/complex
26 * This is a TR1 C++ Library header.
27 */
28
29#ifndef _GLIBCXX_TR1_COMPLEX
30#define _GLIBCXX_TR1_COMPLEX 1
31
32#pragma GCC system_header
33
34#include <complex>
35
36namespace std _GLIBCXX_VISIBILITY(default)
37{
38_GLIBCXX_BEGIN_NAMESPACE_VERSION
39
40namespace tr1
41{
42 /**
43 * @addtogroup complex_numbers
44 * @{
45 */
46
47#if __cplusplus >= 201103L
48 using std::acos;
49 using std::asin;
50 using std::atan;
51 using std::acosh;
52 using std::asinh;
53 using std::atanh;
54#else
55 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
56 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
57 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
58 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
59 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
60 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
61#endif
62
63 // The std::fabs return type in C++11 mode is different (just _Tp).
64 template<typename _Tp> std::complex<_Tp> fabs(const std::complex<_Tp>&);
65
66#if __cplusplus < 201103L
67 template<typename _Tp>
68 inline std::complex<_Tp>
69 __complex_acos(const std::complex<_Tp>& __z)
70 {
71 const std::complex<_Tp> __t = std::tr1::asin(__z);
72 const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
73 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
74 }
75
76#if _GLIBCXX_USE_C99_COMPLEX_TR1
77 inline __complex__ float
78 __complex_acos(__complex__ float __z)
79 { return __builtin_cacosf(__z); }
80
81 inline __complex__ double
82 __complex_acos(__complex__ double __z)
83 { return __builtin_cacos(__z); }
84
85 inline __complex__ long double
86 __complex_acos(const __complex__ long double& __z)
87 { return __builtin_cacosl(__z); }
88
89 template<typename _Tp>
90 inline std::complex<_Tp>
91 acos(const std::complex<_Tp>& __z)
92 { return __complex_acos(__z.__rep()); }
93#else
94 /// acos(__z) [8.1.2].
95 // Effects: Behaves the same as C99 function cacos, defined
96 // in subclause 7.3.5.1.
97 template<typename _Tp>
98 inline std::complex<_Tp>
99 acos(const std::complex<_Tp>& __z)
100 { return __complex_acos(__z); }
101#endif
102
103 template<typename _Tp>
104 inline std::complex<_Tp>
105 __complex_asin(const std::complex<_Tp>& __z)
106 {
107 std::complex<_Tp> __t(-__z.imag(), __z.real());
108 __t = std::tr1::asinh(__t);
109 return std::complex<_Tp>(__t.imag(), -__t.real());
110 }
111
112#if _GLIBCXX_USE_C99_COMPLEX_TR1
113 inline __complex__ float
114 __complex_asin(__complex__ float __z)
115 { return __builtin_casinf(__z); }
116
117 inline __complex__ double
118 __complex_asin(__complex__ double __z)
119 { return __builtin_casin(__z); }
120
121 inline __complex__ long double
122 __complex_asin(const __complex__ long double& __z)
123 { return __builtin_casinl(__z); }
124
125 template<typename _Tp>
126 inline std::complex<_Tp>
127 asin(const std::complex<_Tp>& __z)
128 { return __complex_asin(__z.__rep()); }
129#else
130 /// asin(__z) [8.1.3].
131 // Effects: Behaves the same as C99 function casin, defined
132 // in subclause 7.3.5.2.
133 template<typename _Tp>
134 inline std::complex<_Tp>
135 asin(const std::complex<_Tp>& __z)
136 { return __complex_asin(__z); }
137#endif
138
139 template<typename _Tp>
140 std::complex<_Tp>
141 __complex_atan(const std::complex<_Tp>& __z)
142 {
143 const _Tp __r2 = __z.real() * __z.real();
144 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
145
146 _Tp __num = __z.imag() + _Tp(1.0);
147 _Tp __den = __z.imag() - _Tp(1.0);
148
149 __num = __r2 + __num * __num;
150 __den = __r2 + __den * __den;
151
152 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
153 _Tp(0.25) * log(__num / __den));
154 }
155
156#if _GLIBCXX_USE_C99_COMPLEX_TR1
157 inline __complex__ float
158 __complex_atan(__complex__ float __z)
159 { return __builtin_catanf(__z); }
160
161 inline __complex__ double
162 __complex_atan(__complex__ double __z)
163 { return __builtin_catan(__z); }
164
165 inline __complex__ long double
166 __complex_atan(const __complex__ long double& __z)
167 { return __builtin_catanl(__z); }
168
169 template<typename _Tp>
170 inline std::complex<_Tp>
171 atan(const std::complex<_Tp>& __z)
172 { return __complex_atan(__z.__rep()); }
173#else
174 /// atan(__z) [8.1.4].
175 // Effects: Behaves the same as C99 function catan, defined
176 // in subclause 7.3.5.3.
177 template<typename _Tp>
178 inline std::complex<_Tp>
179 atan(const std::complex<_Tp>& __z)
180 { return __complex_atan(__z); }
181#endif
182
183 template<typename _Tp>
184 std::complex<_Tp>
185 __complex_acosh(const std::complex<_Tp>& __z)
186 {
187 // Kahan's formula.
188 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
189 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
190 }
191
192#if _GLIBCXX_USE_C99_COMPLEX_TR1
193 inline __complex__ float
194 __complex_acosh(__complex__ float __z)
195 { return __builtin_cacoshf(__z); }
196
197 inline __complex__ double
198 __complex_acosh(__complex__ double __z)
199 { return __builtin_cacosh(__z); }
200
201 inline __complex__ long double
202 __complex_acosh(const __complex__ long double& __z)
203 { return __builtin_cacoshl(__z); }
204
205 template<typename _Tp>
206 inline std::complex<_Tp>
207 acosh(const std::complex<_Tp>& __z)
208 { return __complex_acosh(__z.__rep()); }
209#else
210 /// acosh(__z) [8.1.5].
211 // Effects: Behaves the same as C99 function cacosh, defined
212 // in subclause 7.3.6.1.
213 template<typename _Tp>
214 inline std::complex<_Tp>
215 acosh(const std::complex<_Tp>& __z)
216 { return __complex_acosh(__z); }
217#endif
218
219 template<typename _Tp>
220 std::complex<_Tp>
221 __complex_asinh(const std::complex<_Tp>& __z)
222 {
223 std::complex<_Tp> __t((__z.real() - __z.imag())
224 * (__z.real() + __z.imag()) + _Tp(1.0),
225 _Tp(2.0) * __z.real() * __z.imag());
226 __t = std::sqrt(__t);
227
228 return std::log(__t + __z);
229 }
230
231#if _GLIBCXX_USE_C99_COMPLEX_TR1
232 inline __complex__ float
233 __complex_asinh(__complex__ float __z)
234 { return __builtin_casinhf(__z); }
235
236 inline __complex__ double
237 __complex_asinh(__complex__ double __z)
238 { return __builtin_casinh(__z); }
239
240 inline __complex__ long double
241 __complex_asinh(const __complex__ long double& __z)
242 { return __builtin_casinhl(__z); }
243
244 template<typename _Tp>
245 inline std::complex<_Tp>
246 asinh(const std::complex<_Tp>& __z)
247 { return __complex_asinh(__z.__rep()); }
248#else
249 /// asinh(__z) [8.1.6].
250 // Effects: Behaves the same as C99 function casin, defined
251 // in subclause 7.3.6.2.
252 template<typename _Tp>
253 inline std::complex<_Tp>
254 asinh(const std::complex<_Tp>& __z)
255 { return __complex_asinh(__z); }
256#endif
257
258 template<typename _Tp>
259 std::complex<_Tp>
260 __complex_atanh(const std::complex<_Tp>& __z)
261 {
262 const _Tp __i2 = __z.imag() * __z.imag();
263 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
264
265 _Tp __num = _Tp(1.0) + __z.real();
266 _Tp __den = _Tp(1.0) - __z.real();
267
268 __num = __i2 + __num * __num;
269 __den = __i2 + __den * __den;
270
271 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
272 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
273 }
274
275#if _GLIBCXX_USE_C99_COMPLEX_TR1
276 inline __complex__ float
277 __complex_atanh(__complex__ float __z)
278 { return __builtin_catanhf(__z); }
279
280 inline __complex__ double
281 __complex_atanh(__complex__ double __z)
282 { return __builtin_catanh(__z); }
283
284 inline __complex__ long double
285 __complex_atanh(const __complex__ long double& __z)
286 { return __builtin_catanhl(__z); }
287
288 template<typename _Tp>
289 inline std::complex<_Tp>
290 atanh(const std::complex<_Tp>& __z)
291 { return __complex_atanh(__z.__rep()); }
292#else
293 /// atanh(__z) [8.1.7].
294 // Effects: Behaves the same as C99 function catanh, defined
295 // in subclause 7.3.6.3.
296 template<typename _Tp>
297 inline std::complex<_Tp>
298 atanh(const std::complex<_Tp>& __z)
299 { return __complex_atanh(__z); }
300#endif
301
302#endif // C++11
303
304 template<typename _Tp>
305 inline std::complex<_Tp>
306 /// fabs(__z) [8.1.8].
307 // Effects: Behaves the same as C99 function cabs, defined
308 // in subclause 7.3.8.1.
309 fabs(const std::complex<_Tp>& __z)
310 { return std::abs(__z); }
311
312 /// Additional overloads [8.1.9].
313#if __cplusplus < 201103L
314
315 template<typename _Tp>
316 inline typename __gnu_cxx::__promote<_Tp>::__type
317 arg(_Tp __x)
318 {
319 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
320#if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
321 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
322 : __type();
323#else
324 return std::arg(std::complex<__type>(__x));
325#endif
326 }
327
328 template<typename _Tp>
329 inline typename __gnu_cxx::__promote<_Tp>::__type
330 imag(_Tp)
331 { return _Tp(); }
332
333 template<typename _Tp>
334 inline typename __gnu_cxx::__promote<_Tp>::__type
335 norm(_Tp __x)
336 {
337 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
338 return __type(__x) * __type(__x);
339 }
340
341 template<typename _Tp>
342 inline typename __gnu_cxx::__promote<_Tp>::__type
343 real(_Tp __x)
344 { return __x; }
345
346#endif
347
348 template<typename _Tp, typename _Up>
349 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
350 pow(const std::complex<_Tp>& __x, const _Up& __y)
351 {
352 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
353 return std::pow(std::complex<__type>(__x), __type(__y));
354 }
355
356 template<typename _Tp, typename _Up>
357 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
358 pow(const _Tp& __x, const std::complex<_Up>& __y)
359 {
360 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
361 return std::pow(__type(__x), std::complex<__type>(__y));
362 }
363
364 template<typename _Tp, typename _Up>
365 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
366 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
367 {
368 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
369 return std::pow(std::complex<__type>(__x),
370 std::complex<__type>(__y));
371 }
372
373 using std::arg;
374
375 template<typename _Tp>
376 inline std::complex<_Tp>
377 conj(const std::complex<_Tp>& __z)
378 { return std::conj(__z); }
379
380 template<typename _Tp>
381 inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
382 conj(_Tp __x)
383 { return __x; }
384
385 using std::imag;
386 using std::norm;
387 using std::polar;
388
389 template<typename _Tp, typename _Up>
390 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
391 polar(const _Tp& __rho, const _Up& __theta)
392 {
393 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
394 return std::polar(__type(__rho), __type(__theta));
395 }
396
397 using std::real;
398
399 template<typename _Tp>
400 inline std::complex<_Tp>
401 pow(const std::complex<_Tp>& __x, const _Tp& __y)
402 { return std::pow(__x, __y); }
403
404 template<typename _Tp>
405 inline std::complex<_Tp>
406 pow(const _Tp& __x, const std::complex<_Tp>& __y)
407 { return std::pow(__x, __y); }
408
409 template<typename _Tp>
410 inline std::complex<_Tp>
411 pow(const std::complex<_Tp>& __x, const std::complex<_Tp>& __y)
412 { return std::pow(__x, __y); }
413
414/// @} group complex_numbers
415}
416
417_GLIBCXX_END_NAMESPACE_VERSION
418}
419
420#endif // _GLIBCXX_TR1_COMPLEX
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