libstdc++
tr1/complex
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1 // TR1 complex -*- C++ -*-
2 
3 // Copyright (C) 2006-2014 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 
36 namespace std _GLIBCXX_VISIBILITY(default)
37 {
38 namespace 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>
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>
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>
216  { return __complex_acosh(__z); }
217 #endif
218 
219  template<typename _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>
255  { return __complex_asinh(__z); }
256 #endif
257 
258  template<typename _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>
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.
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>
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>
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>
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>
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>
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
std::complex< _Tp > atanh(const std::complex< _Tp > &)
atanh(__z) [8.1.7].
Definition: tr1/complex:298
std::complex< _Tp > acosh(const std::complex< _Tp > &)
acosh(__z) [8.1.5].
Definition: tr1/complex:215
std::complex< _Tp > asin(const std::complex< _Tp > &)
asin(__z) [8.1.3].
Definition: complex:1645
std::complex< _Tp > fabs(const std::complex< _Tp > &)
fabs(__z) [8.1.8].
Definition: tr1/complex:307
complex< _Tp > sqrt(const complex< _Tp > &)
Return complex square root of z.
Definition: complex:893
complex< _Tp > pow(const complex< _Tp > &, int)
Return x to the y&#39;th power.
Definition: complex:979
_Tp norm(const complex< _Tp > &)
Return z magnitude squared.
Definition: complex:656
std::complex< _Tp > asinh(const std::complex< _Tp > &)
asinh(__z) [8.1.6].
Definition: tr1/complex:254
std::complex< _Tp > acos(const std::complex< _Tp > &)
acos(__z) [8.1.2].
Definition: complex:1609
complex< _Tp > polar(const _Tp &, const _Tp &=0)
Return complex with magnitude rho and angle theta.
Definition: complex:664
_Tp abs(const complex< _Tp > &)
Return magnitude of z.
Definition: complex:596
_Tp arg(const complex< _Tp > &)
Return phase angle of z.
Definition: complex:623
complex< _Tp > conj(const complex< _Tp > &)
Return complex conjugate of z.
Definition: complex:669
std::complex< _Tp > atan(const std::complex< _Tp > &)
atan(__z) [8.1.4].
Definition: complex:1689
complex< _Tp > log(const complex< _Tp > &)
Return complex natural logarithm of z.
Definition: complex:784