1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
|
// TR1 complex -*- C++ -*-
// Copyright (C) 2006-2017 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library. This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.
// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
// <http://www.gnu.org/licenses/>.
/** @file tr1/complex
* This is a TR1 C++ Library header.
*/
#ifndef _GLIBCXX_TR1_COMPLEX
#define _GLIBCXX_TR1_COMPLEX 1
#pragma GCC system_header
#include <complex>
namespace std _GLIBCXX_VISIBILITY(default)
{
namespace tr1
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
/**
* @addtogroup complex_numbers
* @{
*/
#if __cplusplus >= 201103L
using std::acos;
using std::asin;
using std::atan;
using std::acosh;
using std::asinh;
using std::atanh;
#else
template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
#endif
// The std::fabs return type in C++11 mode is different (just _Tp).
template<typename _Tp> std::complex<_Tp> fabs(const std::complex<_Tp>&);
#if __cplusplus < 201103L
template<typename _Tp>
inline std::complex<_Tp>
__complex_acos(const std::complex<_Tp>& __z)
{
const std::complex<_Tp> __t = std::tr1::asin(__z);
const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
}
#if _GLIBCXX_USE_C99_COMPLEX_TR1
inline __complex__ float
__complex_acos(__complex__ float __z)
{ return __builtin_cacosf(__z); }
inline __complex__ double
__complex_acos(__complex__ double __z)
{ return __builtin_cacos(__z); }
inline __complex__ long double
__complex_acos(const __complex__ long double& __z)
{ return __builtin_cacosl(__z); }
template<typename _Tp>
inline std::complex<_Tp>
acos(const std::complex<_Tp>& __z)
{ return __complex_acos(__z.__rep()); }
#else
/// acos(__z) [8.1.2].
// Effects: Behaves the same as C99 function cacos, defined
// in subclause 7.3.5.1.
template<typename _Tp>
inline std::complex<_Tp>
acos(const std::complex<_Tp>& __z)
{ return __complex_acos(__z); }
#endif
template<typename _Tp>
inline std::complex<_Tp>
__complex_asin(const std::complex<_Tp>& __z)
{
std::complex<_Tp> __t(-__z.imag(), __z.real());
__t = std::tr1::asinh(__t);
return std::complex<_Tp>(__t.imag(), -__t.real());
}
#if _GLIBCXX_USE_C99_COMPLEX_TR1
inline __complex__ float
__complex_asin(__complex__ float __z)
{ return __builtin_casinf(__z); }
inline __complex__ double
__complex_asin(__complex__ double __z)
{ return __builtin_casin(__z); }
inline __complex__ long double
__complex_asin(const __complex__ long double& __z)
{ return __builtin_casinl(__z); }
template<typename _Tp>
inline std::complex<_Tp>
asin(const std::complex<_Tp>& __z)
{ return __complex_asin(__z.__rep()); }
#else
/// asin(__z) [8.1.3].
// Effects: Behaves the same as C99 function casin, defined
// in subclause 7.3.5.2.
template<typename _Tp>
inline std::complex<_Tp>
asin(const std::complex<_Tp>& __z)
{ return __complex_asin(__z); }
#endif
template<typename _Tp>
std::complex<_Tp>
__complex_atan(const std::complex<_Tp>& __z)
{
const _Tp __r2 = __z.real() * __z.real();
const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
_Tp __num = __z.imag() + _Tp(1.0);
_Tp __den = __z.imag() - _Tp(1.0);
__num = __r2 + __num * __num;
__den = __r2 + __den * __den;
return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
_Tp(0.25) * log(__num / __den));
}
#if _GLIBCXX_USE_C99_COMPLEX_TR1
inline __complex__ float
__complex_atan(__complex__ float __z)
{ return __builtin_catanf(__z); }
inline __complex__ double
__complex_atan(__complex__ double __z)
{ return __builtin_catan(__z); }
inline __complex__ long double
__complex_atan(const __complex__ long double& __z)
{ return __builtin_catanl(__z); }
template<typename _Tp>
inline std::complex<_Tp>
atan(const std::complex<_Tp>& __z)
{ return __complex_atan(__z.__rep()); }
#else
/// atan(__z) [8.1.4].
// Effects: Behaves the same as C99 function catan, defined
// in subclause 7.3.5.3.
template<typename _Tp>
inline std::complex<_Tp>
atan(const std::complex<_Tp>& __z)
{ return __complex_atan(__z); }
#endif
template<typename _Tp>
std::complex<_Tp>
__complex_acosh(const std::complex<_Tp>& __z)
{
// Kahan's formula.
return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
+ std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
}
#if _GLIBCXX_USE_C99_COMPLEX_TR1
inline __complex__ float
__complex_acosh(__complex__ float __z)
{ return __builtin_cacoshf(__z); }
inline __complex__ double
__complex_acosh(__complex__ double __z)
{ return __builtin_cacosh(__z); }
inline __complex__ long double
__complex_acosh(const __complex__ long double& __z)
{ return __builtin_cacoshl(__z); }
template<typename _Tp>
inline std::complex<_Tp>
acosh(const std::complex<_Tp>& __z)
{ return __complex_acosh(__z.__rep()); }
#else
/// acosh(__z) [8.1.5].
// Effects: Behaves the same as C99 function cacosh, defined
// in subclause 7.3.6.1.
template<typename _Tp>
inline std::complex<_Tp>
acosh(const std::complex<_Tp>& __z)
{ return __complex_acosh(__z); }
#endif
template<typename _Tp>
std::complex<_Tp>
__complex_asinh(const std::complex<_Tp>& __z)
{
std::complex<_Tp> __t((__z.real() - __z.imag())
* (__z.real() + __z.imag()) + _Tp(1.0),
_Tp(2.0) * __z.real() * __z.imag());
__t = std::sqrt(__t);
return std::log(__t + __z);
}
#if _GLIBCXX_USE_C99_COMPLEX_TR1
inline __complex__ float
__complex_asinh(__complex__ float __z)
{ return __builtin_casinhf(__z); }
inline __complex__ double
__complex_asinh(__complex__ double __z)
{ return __builtin_casinh(__z); }
inline __complex__ long double
__complex_asinh(const __complex__ long double& __z)
{ return __builtin_casinhl(__z); }
template<typename _Tp>
inline std::complex<_Tp>
asinh(const std::complex<_Tp>& __z)
{ return __complex_asinh(__z.__rep()); }
#else
/// asinh(__z) [8.1.6].
// Effects: Behaves the same as C99 function casin, defined
// in subclause 7.3.6.2.
template<typename _Tp>
inline std::complex<_Tp>
asinh(const std::complex<_Tp>& __z)
{ return __complex_asinh(__z); }
#endif
template<typename _Tp>
std::complex<_Tp>
__complex_atanh(const std::complex<_Tp>& __z)
{
const _Tp __i2 = __z.imag() * __z.imag();
const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
_Tp __num = _Tp(1.0) + __z.real();
_Tp __den = _Tp(1.0) - __z.real();
__num = __i2 + __num * __num;
__den = __i2 + __den * __den;
return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
_Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
}
#if _GLIBCXX_USE_C99_COMPLEX_TR1
inline __complex__ float
__complex_atanh(__complex__ float __z)
{ return __builtin_catanhf(__z); }
inline __complex__ double
__complex_atanh(__complex__ double __z)
{ return __builtin_catanh(__z); }
inline __complex__ long double
__complex_atanh(const __complex__ long double& __z)
{ return __builtin_catanhl(__z); }
template<typename _Tp>
inline std::complex<_Tp>
atanh(const std::complex<_Tp>& __z)
{ return __complex_atanh(__z.__rep()); }
#else
/// atanh(__z) [8.1.7].
// Effects: Behaves the same as C99 function catanh, defined
// in subclause 7.3.6.3.
template<typename _Tp>
inline std::complex<_Tp>
atanh(const std::complex<_Tp>& __z)
{ return __complex_atanh(__z); }
#endif
#endif // C++11
template<typename _Tp>
inline std::complex<_Tp>
/// fabs(__z) [8.1.8].
// Effects: Behaves the same as C99 function cabs, defined
// in subclause 7.3.8.1.
fabs(const std::complex<_Tp>& __z)
{ return std::abs(__z); }
/// Additional overloads [8.1.9].
#if __cplusplus < 201103L
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
arg(_Tp __x)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
#if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
: __type();
#else
return std::arg(std::complex<__type>(__x));
#endif
}
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
imag(_Tp)
{ return _Tp(); }
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
norm(_Tp __x)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __type(__x) * __type(__x);
}
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
real(_Tp __x)
{ return __x; }
#endif
template<typename _Tp, typename _Up>
inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
pow(const std::complex<_Tp>& __x, const _Up& __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return std::pow(std::complex<__type>(__x), __type(__y));
}
template<typename _Tp, typename _Up>
inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
pow(const _Tp& __x, const std::complex<_Up>& __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return std::pow(__type(__x), std::complex<__type>(__y));
}
template<typename _Tp, typename _Up>
inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return std::pow(std::complex<__type>(__x),
std::complex<__type>(__y));
}
using std::arg;
template<typename _Tp>
inline std::complex<_Tp>
conj(const std::complex<_Tp>& __z)
{ return std::conj(__z); }
template<typename _Tp>
inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
conj(_Tp __x)
{ return __x; }
using std::imag;
using std::norm;
using std::polar;
template<typename _Tp, typename _Up>
inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
polar(const _Tp& __rho, const _Up& __theta)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return std::polar(__type(__rho), __type(__theta));
}
using std::real;
template<typename _Tp>
inline std::complex<_Tp>
pow(const std::complex<_Tp>& __x, const _Tp& __y)
{ return std::pow(__x, __y); }
template<typename _Tp>
inline std::complex<_Tp>
pow(const _Tp& __x, const std::complex<_Tp>& __y)
{ return std::pow(__x, __y); }
template<typename _Tp>
inline std::complex<_Tp>
pow(const std::complex<_Tp>& __x, const std::complex<_Tp>& __y)
{ return std::pow(__x, __y); }
// @} group complex_numbers
_GLIBCXX_END_NAMESPACE_VERSION
}
}
#endif // _GLIBCXX_TR1_COMPLEX
|
