1// TR1 complex -*- C++ -*-
2
3// Copyright (C) 2006-2015 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{
38namespace tr1
39{
40_GLIBCXX_BEGIN_NAMESPACE_VERSION
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#else
52  template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
53  template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
54  template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
55#endif
56
57  template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
58  template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
59  template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
60
61  // The std::fabs return type in C++0x mode is different (just _Tp).
62  template<typename _Tp> std::complex<_Tp> fabs(const std::complex<_Tp>&);
63
64#if __cplusplus < 201103L
65  template<typename _Tp>
66    inline std::complex<_Tp>
67    __complex_acos(const std::complex<_Tp>& __z)
68    {
69      const std::complex<_Tp> __t = std::tr1::asin(__z);
70      const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
71      return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
72    }
73
74#if _GLIBCXX_USE_C99_COMPLEX_TR1
75  inline __complex__ float
76  __complex_acos(__complex__ float __z)
77  { return __builtin_cacosf(__z); }
78
79  inline __complex__ double
80  __complex_acos(__complex__ double __z)
81  { return __builtin_cacos(__z); }
82
83  inline __complex__ long double
84  __complex_acos(const __complex__ long double& __z)
85  { return __builtin_cacosl(__z); }
86
87  template<typename _Tp>
88    inline std::complex<_Tp>
89    acos(const std::complex<_Tp>& __z)
90    { return __complex_acos(__z.__rep()); }
91#else
92  /// acos(__z) [8.1.2].
93  //  Effects:  Behaves the same as C99 function cacos, defined
94  //            in subclause 7.3.5.1.
95  template<typename _Tp>
96    inline std::complex<_Tp>
97    acos(const std::complex<_Tp>& __z)
98    { return __complex_acos(__z); }
99#endif
100
101  template<typename _Tp>
102    inline std::complex<_Tp>
103    __complex_asin(const std::complex<_Tp>& __z)
104    {
105      std::complex<_Tp> __t(-__z.imag(), __z.real());
106      __t = std::tr1::asinh(__t);
107      return std::complex<_Tp>(__t.imag(), -__t.real());
108    }
109
110#if _GLIBCXX_USE_C99_COMPLEX_TR1
111  inline __complex__ float
112  __complex_asin(__complex__ float __z)
113  { return __builtin_casinf(__z); }
114
115  inline __complex__ double
116  __complex_asin(__complex__ double __z)
117  { return __builtin_casin(__z); }
118
119  inline __complex__ long double
120  __complex_asin(const __complex__ long double& __z)
121  { return __builtin_casinl(__z); }
122
123  template<typename _Tp>
124    inline std::complex<_Tp>
125    asin(const std::complex<_Tp>& __z)
126    { return __complex_asin(__z.__rep()); }
127#else
128  /// asin(__z) [8.1.3].
129  //  Effects:  Behaves the same as C99 function casin, defined
130  //            in subclause 7.3.5.2.
131  template<typename _Tp>
132    inline std::complex<_Tp>
133    asin(const std::complex<_Tp>& __z)
134    { return __complex_asin(__z); }
135#endif
136
137  template<typename _Tp>
138    std::complex<_Tp>
139    __complex_atan(const std::complex<_Tp>& __z)
140    {
141      const _Tp __r2 = __z.real() * __z.real();
142      const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
143
144      _Tp __num = __z.imag() + _Tp(1.0);
145      _Tp __den = __z.imag() - _Tp(1.0);
146
147      __num = __r2 + __num * __num;
148      __den = __r2 + __den * __den;
149
150      return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
151			       _Tp(0.25) * log(__num / __den));
152    }
153
154#if _GLIBCXX_USE_C99_COMPLEX_TR1
155  inline __complex__ float
156  __complex_atan(__complex__ float __z)
157  { return __builtin_catanf(__z); }
158
159  inline __complex__ double
160  __complex_atan(__complex__ double __z)
161  { return __builtin_catan(__z); }
162
163  inline __complex__ long double
164  __complex_atan(const __complex__ long double& __z)
165  { return __builtin_catanl(__z); }
166
167  template<typename _Tp>
168    inline std::complex<_Tp>
169    atan(const std::complex<_Tp>& __z)
170    { return __complex_atan(__z.__rep()); }
171#else
172  /// atan(__z) [8.1.4].
173  //  Effects:  Behaves the same as C99 function catan, defined
174  //            in subclause 7.3.5.3.
175  template<typename _Tp>
176    inline std::complex<_Tp>
177    atan(const std::complex<_Tp>& __z)
178    { return __complex_atan(__z); }
179#endif
180
181#endif // C++11
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  template<typename _Tp>
303    inline std::complex<_Tp>
304    /// fabs(__z) [8.1.8].
305    //  Effects:  Behaves the same as C99 function cabs, defined
306    //            in subclause 7.3.8.1.
307    fabs(const std::complex<_Tp>& __z)
308    { return std::abs(__z); }
309
310  /// Additional overloads [8.1.9].
311#if __cplusplus < 201103L
312
313  template<typename _Tp>
314    inline typename __gnu_cxx::__promote<_Tp>::__type
315    arg(_Tp __x)
316    {
317      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
318#if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
319      return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
320	                       : __type();
321#else
322      return std::arg(std::complex<__type>(__x));
323#endif
324    }
325
326  template<typename _Tp>
327    inline typename __gnu_cxx::__promote<_Tp>::__type
328    imag(_Tp)
329    { return _Tp(); }
330
331  template<typename _Tp>
332    inline typename __gnu_cxx::__promote<_Tp>::__type
333    norm(_Tp __x)
334    {
335      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
336      return __type(__x) * __type(__x);
337    }
338
339  template<typename _Tp>
340    inline typename __gnu_cxx::__promote<_Tp>::__type
341    real(_Tp __x)
342    { return __x; }
343
344#endif
345
346  template<typename _Tp, typename _Up>
347    inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
348    pow(const std::complex<_Tp>& __x, const _Up& __y)
349    {
350      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
351      return std::pow(std::complex<__type>(__x), __type(__y));
352    }
353
354  template<typename _Tp, typename _Up>
355    inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
356    pow(const _Tp& __x, const std::complex<_Up>& __y)
357    {
358      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
359      return std::pow(__type(__x), std::complex<__type>(__y));
360    }
361
362  template<typename _Tp, typename _Up>
363    inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
364    pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
365    {
366      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
367      return std::pow(std::complex<__type>(__x),
368		      std::complex<__type>(__y));
369    }
370
371  using std::arg;
372
373  template<typename _Tp>
374    inline std::complex<_Tp>
375    conj(const std::complex<_Tp>& __z)
376    { return std::conj(__z); }
377
378  template<typename _Tp>
379    inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
380    conj(_Tp __x)
381    { return __x; }
382
383  using std::imag;
384  using std::norm;
385  using std::polar;
386
387  template<typename _Tp, typename _Up>
388    inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
389    polar(const _Tp& __rho, const _Up& __theta)
390    {
391      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
392      return std::polar(__type(__rho), __type(__theta));
393    }
394
395  using std::real;
396
397  template<typename _Tp>
398    inline std::complex<_Tp>
399    pow(const std::complex<_Tp>& __x, const _Tp& __y)
400    { return std::pow(__x, __y); }
401
402  template<typename _Tp>
403    inline std::complex<_Tp>
404    pow(const _Tp& __x, const std::complex<_Tp>& __y)
405    { return std::pow(__x, __y); }
406
407  template<typename _Tp>
408    inline std::complex<_Tp>
409    pow(const std::complex<_Tp>& __x, const std::complex<_Tp>& __y)
410    { return std::pow(__x, __y); }
411
412// @} group complex_numbers
413
414_GLIBCXX_END_NAMESPACE_VERSION
415}
416}
417
418#endif // _GLIBCXX_TR1_COMPLEX
419