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1 424 jeremybenn 
// The template and inlines for the -*- C++ -*- complex number classes.
2 
 
3 
// Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005,
4 
// 2006, 2007, 2008, 2009, 2010
5 
// Free Software Foundation, Inc.
6 
//
7 
// This file is part of the GNU ISO C++ Library.  This library is free
8 
// software; you can redistribute it and/or modify it under the
9 
// terms of the GNU General Public License as published by the
10 
// Free Software Foundation; either version 3, or (at your option)
11 
// any later version.
12 
 
13 
// This library is distributed in the hope that it will be useful,
14 
// but WITHOUT ANY WARRANTY; without even the implied warranty of
15 
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
16 
// GNU General Public License for more details.
17 
 
18 
// Under Section 7 of GPL version 3, you are granted additional
19 
// permissions described in the GCC Runtime Library Exception, version
20 
// 3.1, as published by the Free Software Foundation.
21 
 
22 
// You should have received a copy of the GNU General Public License and
23 
// a copy of the GCC Runtime Library Exception along with this program;
24 
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
25 
// .
26 
 
27 
/** @file include/complex
28 
 *  This is a Standard C++ Library header.
29 
 */
30 
 
31 
//
32 
// ISO C++ 14882: 26.2  Complex Numbers
33 
// Note: this is not a conforming implementation.
34 
// Initially implemented by Ulrich Drepper
35 
// Improved by Gabriel Dos Reis
36 
//
37 
 
38 
#ifndef _GLIBCXX_COMPLEX
39 
#define _GLIBCXX_COMPLEX 1
40 
 
41 
#pragma GCC system_header
42 
 
43 
#include
44 
#include
45 
#include
46 
#include
47 
#include
48 
 
49 
_GLIBCXX_BEGIN_NAMESPACE(std)
50 
 
51 
  /**
52 
   * @defgroup complex_numbers Complex Numbers
53 
   * @ingroup numerics
54 
   *
55 
   * Classes and functions for complex numbers.
56 
   * @{
57 
   */
58 
 
59 
  // Forward declarations.
60 
  template class complex;
61 
  template<> class complex;
62 
  template<> class complex;
63 
  template<> class complex;
64 
 
65 
  ///  Return magnitude of @a z.
66 
  template _Tp abs(const complex<_Tp>&);
67 
  ///  Return phase angle of @a z.
68 
  template _Tp arg(const complex<_Tp>&);
69 
  ///  Return @a z magnitude squared.
70 
  template _Tp norm(const complex<_Tp>&);
71 
 
72 
  ///  Return complex conjugate of @a z.
73 
  template complex<_Tp> conj(const complex<_Tp>&);
74 
  ///  Return complex with magnitude @a rho and angle @a theta.
75 
  template complex<_Tp> polar(const _Tp&, const _Tp& = 0);
76 
 
77 
  // Transcendentals:
78 
  /// Return complex cosine of @a z.
79 
  template complex<_Tp> cos(const complex<_Tp>&);
80 
  /// Return complex hyperbolic cosine of @a z.
81 
  template complex<_Tp> cosh(const complex<_Tp>&);
82 
  /// Return complex base e exponential of @a z.
83 
  template complex<_Tp> exp(const complex<_Tp>&);
84 
  /// Return complex natural logarithm of @a z.
85 
  template complex<_Tp> log(const complex<_Tp>&);
86 
  /// Return complex base 10 logarithm of @a z.
87 
  template complex<_Tp> log10(const complex<_Tp>&);
88 
#ifndef __GXX_EXPERIMENTAL_CXX0X__
89 
  // DR 844.
90 
  /// Return @a x to the @a y'th power.
91 
  template complex<_Tp> pow(const complex<_Tp>&, int);
92 
#endif
93 
  /// Return @a x to the @a y'th power.
94 
  template complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
95 
  /// Return @a x to the @a y'th power.
96 
  template complex<_Tp> pow(const complex<_Tp>&,
97 
                                          const complex<_Tp>&);
98 
  /// Return @a x to the @a y'th power.
99 
  template complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
100 
  /// Return complex sine of @a z.
101 
  template complex<_Tp> sin(const complex<_Tp>&);
102 
  /// Return complex hyperbolic sine of @a z.
103 
  template complex<_Tp> sinh(const complex<_Tp>&);
104 
  /// Return complex square root of @a z.
105 
  template complex<_Tp> sqrt(const complex<_Tp>&);
106 
  /// Return complex tangent of @a z.
107 
  template complex<_Tp> tan(const complex<_Tp>&);
108 
  /// Return complex hyperbolic tangent of @a z.
109 
  template complex<_Tp> tanh(const complex<_Tp>&);
110 
 
111 
 
112 
  // 26.2.2  Primary template class complex
113 
  /**
114 
   *  Template to represent complex numbers.
115 
   *
116 
   *  Specializations for float, double, and long double are part of the
117 
   *  library.  Results with any other type are not guaranteed.
118 
   *
119 
   *  @param  Tp  Type of real and imaginary values.
120 
  */
121 
  template
122 
    struct complex
123 
    {
124 
      /// Value typedef.
125 
      typedef _Tp value_type;
126 
 
127 
      ///  Default constructor.  First parameter is x, second parameter is y.
128 
      ///  Unspecified parameters default to 0.
129 
      complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp())
130 
      : _M_real(__r), _M_imag(__i) { }
131 
 
132 
      // Lets the compiler synthesize the copy constructor
133 
      // complex (const complex<_Tp>&);
134 
      ///  Copy constructor.
135 
      template
136 
        complex(const complex<_Up>& __z)
137 
        : _M_real(__z.real()), _M_imag(__z.imag()) { }
138 
 
139 
#ifdef __GXX_EXPERIMENTAL_CXX0X__
140 
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
141 
      // DR 387. std::complex over-encapsulated.
142 
      _Tp real() const
143 
      { return _M_real; }
144 
 
145 
      _Tp imag() const
146 
      { return _M_imag; }
147 
#else
148 
      ///  Return real part of complex number.
149 
      _Tp& real()
150 
      { return _M_real; }
151 
 
152 
      ///  Return real part of complex number.
153 
      const _Tp& real() const
154 
      { return _M_real; }
155 
 
156 
      ///  Return imaginary part of complex number.
157 
      _Tp& imag()
158 
      { return _M_imag; }
159 
 
160 
      ///  Return imaginary part of complex number.
161 
      const _Tp& imag() const
162 
      { return _M_imag; }
163 
#endif
164 
 
165 
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
166 
      // DR 387. std::complex over-encapsulated.
167 
      void real(_Tp __val)
168 
      { _M_real = __val; }
169 
 
170 
      void imag(_Tp __val)
171 
      { _M_imag = __val; }
172 
 
173 
      /// Assign this complex number to scalar @a t.
174 
      complex<_Tp>& operator=(const _Tp&);
175 
 
176 
      /// Add @a t to this complex number.
177 
      // 26.2.5/1
178 
      complex<_Tp>&
179 
      operator+=(const _Tp& __t)
180 
      {
181 
        _M_real += __t;
182 
        return *this;
183 
      }
184 
 
185 
      /// Subtract @a t from this complex number.
186 
      // 26.2.5/3
187 
      complex<_Tp>&
188 
      operator-=(const _Tp& __t)
189 
      {
190 
        _M_real -= __t;
191 
        return *this;
192 
      }
193 
 
194 
      /// Multiply this complex number by @a t.
195 
      complex<_Tp>& operator*=(const _Tp&);
196 
      /// Divide this complex number by @a t.
197 
      complex<_Tp>& operator/=(const _Tp&);
198 
 
199 
      // Lets the compiler synthesize the
200 
      // copy and assignment operator
201 
      // complex<_Tp>& operator= (const complex<_Tp>&);
202 
      /// Assign this complex number to complex @a z.
203 
      template
204 
        complex<_Tp>& operator=(const complex<_Up>&);
205 
      /// Add @a z to this complex number.
206 
      template
207 
        complex<_Tp>& operator+=(const complex<_Up>&);
208 
      /// Subtract @a z from this complex number.
209 
      template
210 
        complex<_Tp>& operator-=(const complex<_Up>&);
211 
      /// Multiply this complex number by @a z.
212 
      template
213 
        complex<_Tp>& operator*=(const complex<_Up>&);
214 
      /// Divide this complex number by @a z.
215 
      template
216 
        complex<_Tp>& operator/=(const complex<_Up>&);
217 
 
218 
      const complex& __rep() const
219 
      { return *this; }
220 
 
221 
    private:
222 
      _Tp _M_real;
223 
      _Tp _M_imag;
224 
    };
225 
 
226 
  template
227 
    complex<_Tp>&
228 
    complex<_Tp>::operator=(const _Tp& __t)
229 
    {
230 
     _M_real = __t;
231 
     _M_imag = _Tp();
232 
     return *this;
233 
    }
234 
 
235 
  // 26.2.5/5
236 
  template
237 
    complex<_Tp>&
238 
    complex<_Tp>::operator*=(const _Tp& __t)
239 
    {
240 
      _M_real *= __t;
241 
      _M_imag *= __t;
242 
      return *this;
243 
    }
244 
 
245 
  // 26.2.5/7
246 
  template
247 
    complex<_Tp>&
248 
    complex<_Tp>::operator/=(const _Tp& __t)
249 
    {
250 
      _M_real /= __t;
251 
      _M_imag /= __t;
252 
      return *this;
253 
    }
254 
 
255 
  template
256 
    template
257 
    complex<_Tp>&
258 
    complex<_Tp>::operator=(const complex<_Up>& __z)
259 
    {
260 
      _M_real = __z.real();
261 
      _M_imag = __z.imag();
262 
      return *this;
263 
    }
264 
 
265 
  // 26.2.5/9
266 
  template
267 
    template
268 
    complex<_Tp>&
269 
    complex<_Tp>::operator+=(const complex<_Up>& __z)
270 
    {
271 
      _M_real += __z.real();
272 
      _M_imag += __z.imag();
273 
      return *this;
274 
    }
275 
 
276 
  // 26.2.5/11
277 
  template
278 
    template
279 
    complex<_Tp>&
280 
    complex<_Tp>::operator-=(const complex<_Up>& __z)
281 
    {
282 
      _M_real -= __z.real();
283 
      _M_imag -= __z.imag();
284 
      return *this;
285 
    }
286 
 
287 
  // 26.2.5/13
288 
  // XXX: This is a grammar school implementation.
289 
  template
290 
    template
291 
    complex<_Tp>&
292 
    complex<_Tp>::operator*=(const complex<_Up>& __z)
293 
    {
294 
      const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
295 
      _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
296 
      _M_real = __r;
297 
      return *this;
298 
    }
299 
 
300 
  // 26.2.5/15
301 
  // XXX: This is a grammar school implementation.
302 
  template
303 
    template
304 
    complex<_Tp>&
305 
    complex<_Tp>::operator/=(const complex<_Up>& __z)
306 
    {
307 
      const _Tp __r =  _M_real * __z.real() + _M_imag * __z.imag();
308 
      const _Tp __n = std::norm(__z);
309 
      _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
310 
      _M_real = __r / __n;
311 
      return *this;
312 
    }
313 
 
314 
  // Operators:
315 
  //@{
316 
  ///  Return new complex value @a x plus @a y.
317 
  template
318 
    inline complex<_Tp>
319 
    operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
320 
    {
321 
      complex<_Tp> __r = __x;
322 
      __r += __y;
323 
      return __r;
324 
    }
325 
 
326 
  template
327 
    inline complex<_Tp>
328 
    operator+(const complex<_Tp>& __x, const _Tp& __y)
329 
    {
330 
      complex<_Tp> __r = __x;
331 
      __r += __y;
332 
      return __r;
333 
    }
334 
 
335 
  template
336 
    inline complex<_Tp>
337 
    operator+(const _Tp& __x, const complex<_Tp>& __y)
338 
    {
339 
      complex<_Tp> __r = __y;
340 
      __r += __x;
341 
      return __r;
342 
    }
343 
  //@}
344 
 
345 
  //@{
346 
  ///  Return new complex value @a x minus @a y.
347 
  template
348 
    inline complex<_Tp>
349 
    operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
350 
    {
351 
      complex<_Tp> __r = __x;
352 
      __r -= __y;
353 
      return __r;
354 
    }
355 
 
356 
  template
357 
    inline complex<_Tp>
358 
    operator-(const complex<_Tp>& __x, const _Tp& __y)
359 
    {
360 
      complex<_Tp> __r = __x;
361 
      __r -= __y;
362 
      return __r;
363 
    }
364 
 
365 
  template
366 
    inline complex<_Tp>
367 
    operator-(const _Tp& __x, const complex<_Tp>& __y)
368 
    {
369 
      complex<_Tp> __r(__x, -__y.imag());
370 
      __r -= __y.real();
371 
      return __r;
372 
    }
373 
  //@}
374 
 
375 
  //@{
376 
  ///  Return new complex value @a x times @a y.
377 
  template
378 
    inline complex<_Tp>
379 
    operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
380 
    {
381 
      complex<_Tp> __r = __x;
382 
      __r *= __y;
383 
      return __r;
384 
    }
385 
 
386 
  template
387 
    inline complex<_Tp>
388 
    operator*(const complex<_Tp>& __x, const _Tp& __y)
389 
    {
390 
      complex<_Tp> __r = __x;
391 
      __r *= __y;
392 
      return __r;
393 
    }
394 
 
395 
  template
396 
    inline complex<_Tp>
397 
    operator*(const _Tp& __x, const complex<_Tp>& __y)
398 
    {
399 
      complex<_Tp> __r = __y;
400 
      __r *= __x;
401 
      return __r;
402 
    }
403 
  //@}
404 
 
405 
  //@{
406 
  ///  Return new complex value @a x divided by @a y.
407 
  template
408 
    inline complex<_Tp>
409 
    operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
410 
    {
411 
      complex<_Tp> __r = __x;
412 
      __r /= __y;
413 
      return __r;
414 
    }
415 
 
416 
  template
417 
    inline complex<_Tp>
418 
    operator/(const complex<_Tp>& __x, const _Tp& __y)
419 
    {
420 
      complex<_Tp> __r = __x;
421 
      __r /= __y;
422 
      return __r;
423 
    }
424 
 
425 
  template
426 
    inline complex<_Tp>
427 
    operator/(const _Tp& __x, const complex<_Tp>& __y)
428 
    {
429 
      complex<_Tp> __r = __x;
430 
      __r /= __y;
431 
      return __r;
432 
    }
433 
  //@}
434 
 
435 
  ///  Return @a x.
436 
  template
437 
    inline complex<_Tp>
438 
    operator+(const complex<_Tp>& __x)
439 
    { return __x; }
440 
 
441 
  ///  Return complex negation of @a x.
442 
  template
443 
    inline complex<_Tp>
444 
    operator-(const complex<_Tp>& __x)
445 
    {  return complex<_Tp>(-__x.real(), -__x.imag()); }
446 
 
447 
  //@{
448 
  ///  Return true if @a x is equal to @a y.
449 
  template
450 
    inline bool
451 
    operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
452 
    { return __x.real() == __y.real() && __x.imag() == __y.imag(); }
453 
 
454 
  template
455 
    inline bool
456 
    operator==(const complex<_Tp>& __x, const _Tp& __y)
457 
    { return __x.real() == __y && __x.imag() == _Tp(); }
458 
 
459 
  template
460 
    inline bool
461 
    operator==(const _Tp& __x, const complex<_Tp>& __y)
462 
    { return __x == __y.real() && _Tp() == __y.imag(); }
463 
  //@}
464 
 
465 
  //@{
466 
  ///  Return false if @a x is equal to @a y.
467 
  template
468 
    inline bool
469 
    operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
470 
    { return __x.real() != __y.real() || __x.imag() != __y.imag(); }
471 
 
472 
  template
473 
    inline bool
474 
    operator!=(const complex<_Tp>& __x, const _Tp& __y)
475 
    { return __x.real() != __y || __x.imag() != _Tp(); }
476 
 
477 
  template
478 
    inline bool
479 
    operator!=(const _Tp& __x, const complex<_Tp>& __y)
480 
    { return __x != __y.real() || _Tp() != __y.imag(); }
481 
  //@}
482 
 
483 
  ///  Extraction operator for complex values.
484 
  template
485 
    basic_istream<_CharT, _Traits>&
486 
    operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
487 
    {
488 
      _Tp __re_x, __im_x;
489 
      _CharT __ch;
490 
      __is >> __ch;
491 
      if (__ch == '(')
492 
        {
493 
          __is >> __re_x >> __ch;
494 
          if (__ch == ',')
495 
            {
496 
              __is >> __im_x >> __ch;
497 
              if (__ch == ')')
498 
                __x = complex<_Tp>(__re_x, __im_x);
499 
              else
500 
                __is.setstate(ios_base::failbit);
501 
            }
502 
          else if (__ch == ')')
503 
            __x = __re_x;
504 
          else
505 
            __is.setstate(ios_base::failbit);
506 
        }
507 
      else
508 
        {
509 
          __is.putback(__ch);
510 
          __is >> __re_x;
511 
          __x = __re_x;
512 
        }
513 
      return __is;
514 
    }
515 
 
516 
  ///  Insertion operator for complex values.
517 
  template
518 
    basic_ostream<_CharT, _Traits>&
519 
    operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
520 
    {
521 
      basic_ostringstream<_CharT, _Traits> __s;
522 
      __s.flags(__os.flags());
523 
      __s.imbue(__os.getloc());
524 
      __s.precision(__os.precision());
525 
      __s << '(' << __x.real() << ',' << __x.imag() << ')';
526 
      return __os << __s.str();
527 
    }
528 
 
529 
  // Values
530 
#ifdef __GXX_EXPERIMENTAL_CXX0X__
531 
  template
532 
    inline _Tp
533 
    real(const complex<_Tp>& __z)
534 
    { return __z.real(); }
535 
 
536 
  template
537 
    inline _Tp
538 
    imag(const complex<_Tp>& __z)
539 
    { return __z.imag(); }
540 
#else
541 
  template
542 
    inline _Tp&
543 
    real(complex<_Tp>& __z)
544 
    { return __z.real(); }
545 
 
546 
  template
547 
    inline const _Tp&
548 
    real(const complex<_Tp>& __z)
549 
    { return __z.real(); }
550 
 
551 
  template
552 
    inline _Tp&
553 
    imag(complex<_Tp>& __z)
554 
    { return __z.imag(); }
555 
 
556 
  template
557 
    inline const _Tp&
558 
    imag(const complex<_Tp>& __z)
559 
    { return __z.imag(); }
560 
#endif
561 
 
562 
  // 26.2.7/3 abs(__z):  Returns the magnitude of __z.
563 
  template
564 
    inline _Tp
565 
    __complex_abs(const complex<_Tp>& __z)
566 
    {
567 
      _Tp __x = __z.real();
568 
      _Tp __y = __z.imag();
569 
      const _Tp __s = std::max(abs(__x), abs(__y));
570 
      if (__s == _Tp())  // well ...
571 
        return __s;
572 
      __x /= __s;
573 
      __y /= __s;
574 
      return __s * sqrt(__x * __x + __y * __y);
575 
    }
576 
 
577 
#if _GLIBCXX_USE_C99_COMPLEX
578 
  inline float
579 
  __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); }
580 
 
581 
  inline double
582 
  __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); }
583 
 
584 
  inline long double
585 
  __complex_abs(const __complex__ long double& __z)
586 
  { return __builtin_cabsl(__z); }
587 
 
588 
  template
589 
    inline _Tp
590 
    abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); }
591 
#else
592 
  template
593 
    inline _Tp
594 
    abs(const complex<_Tp>& __z) { return __complex_abs(__z); }
595 
#endif
596 
 
597 
 
598 
  // 26.2.7/4: arg(__z): Returns the phase angle of __z.
599 
  template
600 
    inline _Tp
601 
    __complex_arg(const complex<_Tp>& __z)
602 
    { return  atan2(__z.imag(), __z.real()); }
603 
 
604 
#if _GLIBCXX_USE_C99_COMPLEX
605 
  inline float
606 
  __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); }
607 
 
608 
  inline double
609 
  __complex_arg(__complex__ double __z) { return __builtin_carg(__z); }
610 
 
611 
  inline long double
612 
  __complex_arg(const __complex__ long double& __z)
613 
  { return __builtin_cargl(__z); }
614 
 
615 
  template
616 
    inline _Tp
617 
    arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); }
618 
#else
619 
  template
620 
    inline _Tp
621 
    arg(const complex<_Tp>& __z) { return __complex_arg(__z); }
622 
#endif
623 
 
624 
  // 26.2.7/5: norm(__z) returns the squared magnitude of __z.
625 
  //     As defined, norm() is -not- a norm is the common mathematical
626 
  //     sens used in numerics.  The helper class _Norm_helper<> tries to
627 
  //     distinguish between builtin floating point and the rest, so as
628 
  //     to deliver an answer as close as possible to the real value.
629 
  template
630 
    struct _Norm_helper
631 
    {
632 
      template
633 
        static inline _Tp _S_do_it(const complex<_Tp>& __z)
634 
        {
635 
          const _Tp __x = __z.real();
636 
          const _Tp __y = __z.imag();
637 
          return __x * __x + __y * __y;
638 
        }
639 
    };
640 
 
641 
  template<>
642 
    struct _Norm_helper
643 
    {
644 
      template
645 
        static inline _Tp _S_do_it(const complex<_Tp>& __z)
646 
        {
647 
          _Tp __res = std::abs(__z);
648 
          return __res * __res;
649 
        }
650 
    };
651 
 
652 
  template
653 
    inline _Tp
654 
    norm(const complex<_Tp>& __z)
655 
    {
656 
      return _Norm_helper<__is_floating<_Tp>::__value
657 
        && !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
658 
    }
659 
 
660 
  template
661 
    inline complex<_Tp>
662 
    polar(const _Tp& __rho, const _Tp& __theta)
663 
    { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); }
664 
 
665 
  template
666 
    inline complex<_Tp>
667 
    conj(const complex<_Tp>& __z)
668 
    { return complex<_Tp>(__z.real(), -__z.imag()); }
669 
 
670 
  // Transcendentals
671 
 
672 
  // 26.2.8/1 cos(__z):  Returns the cosine of __z.
673 
  template
674 
    inline complex<_Tp>
675 
    __complex_cos(const complex<_Tp>& __z)
676 
    {
677 
      const _Tp __x = __z.real();
678 
      const _Tp __y = __z.imag();
679 
      return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
680 
    }
681 
 
682 
#if _GLIBCXX_USE_C99_COMPLEX
683 
  inline __complex__ float
684 
  __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); }
685 
 
686 
  inline __complex__ double
687 
  __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); }
688 
 
689 
  inline __complex__ long double
690 
  __complex_cos(const __complex__ long double& __z)
691 
  { return __builtin_ccosl(__z); }
692 
 
693 
  template
694 
    inline complex<_Tp>
695 
    cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); }
696 
#else
697 
  template
698 
    inline complex<_Tp>
699 
    cos(const complex<_Tp>& __z) { return __complex_cos(__z); }
700 
#endif
701 
 
702 
  // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z.
703 
  template
704 
    inline complex<_Tp>
705 
    __complex_cosh(const complex<_Tp>& __z)
706 
    {
707 
      const _Tp __x = __z.real();
708 
      const _Tp __y = __z.imag();
709 
      return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
710 
    }
711 
 
712 
#if _GLIBCXX_USE_C99_COMPLEX
713 
  inline __complex__ float
714 
  __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); }
715 
 
716 
  inline __complex__ double
717 
  __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); }
718 
 
719 
  inline __complex__ long double
720 
  __complex_cosh(const __complex__ long double& __z)
721 
  { return __builtin_ccoshl(__z); }
722 
 
723 
  template
724 
    inline complex<_Tp>
725 
    cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); }
726 
#else
727 
  template
728 
    inline complex<_Tp>
729 
    cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); }
730 
#endif
731 
 
732 
  // 26.2.8/3 exp(__z): Returns the complex base e exponential of x
733 
  template
734 
    inline complex<_Tp>
735 
    __complex_exp(const complex<_Tp>& __z)
736 
    { return std::polar(exp(__z.real()), __z.imag()); }
737 
 
738 
#if _GLIBCXX_USE_C99_COMPLEX
739 
  inline __complex__ float
740 
  __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); }
741 
 
742 
  inline __complex__ double
743 
  __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); }
744 
 
745 
  inline __complex__ long double
746 
  __complex_exp(const __complex__ long double& __z)
747 
  { return __builtin_cexpl(__z); }
748 
 
749 
  template
750 
    inline complex<_Tp>
751 
    exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); }
752 
#else
753 
  template
754 
    inline complex<_Tp>
755 
    exp(const complex<_Tp>& __z) { return __complex_exp(__z); }
756 
#endif
757 
 
758 
  // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z.
759 
  //                    The branch cut is along the negative axis.
760 
  template
761 
    inline complex<_Tp>
762 
    __complex_log(const complex<_Tp>& __z)
763 
    { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
764 
 
765 
#if _GLIBCXX_USE_C99_COMPLEX
766 
  inline __complex__ float
767 
  __complex_log(__complex__ float __z) { return __builtin_clogf(__z); }
768 
 
769 
  inline __complex__ double
770 
  __complex_log(__complex__ double __z) { return __builtin_clog(__z); }
771 
 
772 
  inline __complex__ long double
773 
  __complex_log(const __complex__ long double& __z)
774 
  { return __builtin_clogl(__z); }
775 
 
776 
  template
777 
    inline complex<_Tp>
778 
    log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); }
779 
#else
780 
  template
781 
    inline complex<_Tp>
782 
    log(const complex<_Tp>& __z) { return __complex_log(__z); }
783 
#endif
784 
 
785 
  template
786 
    inline complex<_Tp>
787 
    log10(const complex<_Tp>& __z)
788 
    { return std::log(__z) / log(_Tp(10.0)); }
789 
 
790 
  // 26.2.8/10 sin(__z): Returns the sine of __z.
791 
  template
792 
    inline complex<_Tp>
793 
    __complex_sin(const complex<_Tp>& __z)
794 
    {
795 
      const _Tp __x = __z.real();
796 
      const _Tp __y = __z.imag();
797 
      return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
798 
    }
799 
 
800 
#if _GLIBCXX_USE_C99_COMPLEX
801 
  inline __complex__ float
802 
  __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); }
803 
 
804 
  inline __complex__ double
805 
  __complex_sin(__complex__ double __z) { return __builtin_csin(__z); }
806 
 
807 
  inline __complex__ long double
808 
  __complex_sin(const __complex__ long double& __z)
809 
  { return __builtin_csinl(__z); }
810 
 
811 
  template
812 
    inline complex<_Tp>
813 
    sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); }
814 
#else
815 
  template
816 
    inline complex<_Tp>
817 
    sin(const complex<_Tp>& __z) { return __complex_sin(__z); }
818 
#endif
819 
 
820 
  // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z.
821 
  template
822 
    inline complex<_Tp>
823 
    __complex_sinh(const complex<_Tp>& __z)
824 
    {
825 
      const _Tp __x = __z.real();
826 
      const _Tp  __y = __z.imag();
827 
      return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
828 
    }
829 
 
830 
#if _GLIBCXX_USE_C99_COMPLEX
831 
  inline __complex__ float
832 
  __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
833 
 
834 
  inline __complex__ double
835 
  __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
836 
 
837 
  inline __complex__ long double
838 
  __complex_sinh(const __complex__ long double& __z)
839 
  { return __builtin_csinhl(__z); }
840 
 
841 
  template
842 
    inline complex<_Tp>
843 
    sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); }
844 
#else
845 
  template
846 
    inline complex<_Tp>
847 
    sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); }
848 
#endif
849 
 
850 
  // 26.2.8/13 sqrt(__z): Returns the complex square root of __z.
851 
  //                     The branch cut is on the negative axis.
852 
  template
853 
    complex<_Tp>
854 
    __complex_sqrt(const complex<_Tp>& __z)
855 
    {
856 
      _Tp __x = __z.real();
857 
      _Tp __y = __z.imag();
858 
 
859 
      if (__x == _Tp())
860 
        {
861 
          _Tp __t = sqrt(abs(__y) / 2);
862 
          return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
863 
        }
864 
      else
865 
        {
866 
          _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
867 
          _Tp __u = __t / 2;
868 
          return __x > _Tp()
869 
            ? complex<_Tp>(__u, __y / __t)
870 
            : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
871 
        }
872 
    }
873 
 
874 
#if _GLIBCXX_USE_C99_COMPLEX
875 
  inline __complex__ float
876 
  __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); }
877 
 
878 
  inline __complex__ double
879 
  __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); }
880 
 
881 
  inline __complex__ long double
882 
  __complex_sqrt(const __complex__ long double& __z)
883 
  { return __builtin_csqrtl(__z); }
884 
 
885 
  template
886 
    inline complex<_Tp>
887 
    sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); }
888 
#else
889 
  template
890 
    inline complex<_Tp>
891 
    sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); }
892 
#endif
893 
 
894 
  // 26.2.8/14 tan(__z):  Return the complex tangent of __z.
895 
 
896 
  template
897 
    inline complex<_Tp>
898 
    __complex_tan(const complex<_Tp>& __z)
899 
    { return std::sin(__z) / std::cos(__z); }
900 
 
901 
#if _GLIBCXX_USE_C99_COMPLEX
902 
  inline __complex__ float
903 
  __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); }
904 
 
905 
  inline __complex__ double
906 
  __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); }
907 
 
908 
  inline __complex__ long double
909 
  __complex_tan(const __complex__ long double& __z)
910 
  { return __builtin_ctanl(__z); }
911 
 
912 
  template
913 
    inline complex<_Tp>
914 
    tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); }
915 
#else
916 
  template
917 
    inline complex<_Tp>
918 
    tan(const complex<_Tp>& __z) { return __complex_tan(__z); }
919 
#endif
920 
 
921 
 
922 
  // 26.2.8/15 tanh(__z):  Returns the hyperbolic tangent of __z.
923 
 
924 
  template
925 
    inline complex<_Tp>
926 
    __complex_tanh(const complex<_Tp>& __z)
927 
    { return std::sinh(__z) / std::cosh(__z); }
928 
 
929 
#if _GLIBCXX_USE_C99_COMPLEX
930 
  inline __complex__ float
931 
  __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); }
932 
 
933 
  inline __complex__ double
934 
  __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); }
935 
 
936 
  inline __complex__ long double
937 
  __complex_tanh(const __complex__ long double& __z)
938 
  { return __builtin_ctanhl(__z); }
939 
 
940 
  template
941 
    inline complex<_Tp>
942 
    tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); }
943 
#else
944 
  template
945 
    inline complex<_Tp>
946 
    tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); }
947 
#endif
948 
 
949 
 
950 
  // 26.2.8/9  pow(__x, __y): Returns the complex power base of __x
951 
  //                          raised to the __y-th power.  The branch
952 
  //                          cut is on the negative axis.
953 
#ifndef __GXX_EXPERIMENTAL_CXX0X__
954 
  // _GLIBCXX_RESOLVE_LIB_DEFECTS
955 
  // DR 844. complex pow return type is ambiguous.
956 
  template
957 
    inline complex<_Tp>
958 
    pow(const complex<_Tp>& __z, int __n)
959 
    { return std::__pow_helper(__z, __n); }
960 
#endif
961 
 
962 
  template
963 
    complex<_Tp>
964 
    pow(const complex<_Tp>& __x, const _Tp& __y)
965 
    {
966 
#ifndef _GLIBCXX_USE_C99_COMPLEX
967 
      if (__x == _Tp())
968 
        return _Tp();
969 
#endif
970 
      if (__x.imag() == _Tp() && __x.real() > _Tp())
971 
        return pow(__x.real(), __y);
972 
 
973 
      complex<_Tp> __t = std::log(__x);
974 
      return std::polar(exp(__y * __t.real()), __y * __t.imag());
975 
    }
976 
 
977 
  template
978 
    inline complex<_Tp>
979 
    __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
980 
    { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); }
981 
 
982 
#if _GLIBCXX_USE_C99_COMPLEX
983 
  inline __complex__ float
984 
  __complex_pow(__complex__ float __x, __complex__ float __y)
985 
  { return __builtin_cpowf(__x, __y); }
986 
 
987 
  inline __complex__ double
988 
  __complex_pow(__complex__ double __x, __complex__ double __y)
989 
  { return __builtin_cpow(__x, __y); }
990 
 
991 
  inline __complex__ long double
992 
  __complex_pow(const __complex__ long double& __x,
993 
                const __complex__ long double& __y)
994 
  { return __builtin_cpowl(__x, __y); }
995 
 
996 
  template
997 
    inline complex<_Tp>
998 
    pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
999 
    { return __complex_pow(__x.__rep(), __y.__rep()); }
1000 
#else
1001 
  template
1002 
    inline complex<_Tp>
1003 
    pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1004 
    { return __complex_pow(__x, __y); }
1005 
#endif
1006 
 
1007 
  template
1008 
    inline complex<_Tp>
1009 
    pow(const _Tp& __x, const complex<_Tp>& __y)
1010 
    {
1011 
      return __x > _Tp() ? std::polar(pow(__x, __y.real()),
1012 
                                      __y.imag() * log(__x))
1013 
                         : std::pow(complex<_Tp>(__x), __y);
1014 
    }
1015 
 
1016 
  // 26.2.3  complex specializations
1017 
  // complex specialization
1018 
  template<>
1019 
    struct complex
1020 
    {
1021 
      typedef float value_type;
1022 
      typedef __complex__ float _ComplexT;
1023 
 
1024 
      complex(_ComplexT __z) : _M_value(__z) { }
1025 
 
1026 
      complex(float __r = 0.0f, float __i = 0.0f)
1027 
      {
1028 
        __real__ _M_value = __r;
1029 
        __imag__ _M_value = __i;
1030 
      }
1031 
 
1032 
      explicit complex(const complex&);
1033 
      explicit complex(const complex&);
1034 
 
1035 
#ifdef __GXX_EXPERIMENTAL_CXX0X__
1036 
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
1037 
      // DR 387. std::complex over-encapsulated.
1038 
      float real() const
1039 
      { return __real__ _M_value; }
1040 
 
1041 
      float imag() const
1042 
      { return __imag__ _M_value; }
1043 
#else
1044 
      float& real()
1045 
      { return __real__ _M_value; }
1046 
 
1047 
      const float& real() const
1048 
      { return __real__ _M_value; }
1049 
 
1050 
      float& imag()
1051 
      { return __imag__ _M_value; }
1052 
 
1053 
      const float& imag() const
1054 
      { return __imag__ _M_value; }
1055 
#endif
1056 
 
1057 
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
1058 
      // DR 387. std::complex over-encapsulated.
1059 
      void real(float __val)
1060 
      { __real__ _M_value = __val; }
1061 
 
1062 
      void imag(float __val)
1063 
      { __imag__ _M_value = __val; }
1064 
 
1065 
      complex&
1066 
      operator=(float __f)
1067 
      {
1068 
        __real__ _M_value = __f;
1069 
        __imag__ _M_value = 0.0f;
1070 
        return *this;
1071 
      }
1072 
 
1073 
      complex&
1074 
      operator+=(float __f)
1075 
      {
1076 
        __real__ _M_value += __f;
1077 
        return *this;
1078 
      }
1079 
 
1080 
      complex&
1081 
      operator-=(float __f)
1082 
      {
1083 
        __real__ _M_value -= __f;
1084 
        return *this;
1085 
      }
1086 
 
1087 
      complex&
1088 
      operator*=(float __f)
1089 
      {
1090 
        _M_value *= __f;
1091 
        return *this;
1092 
      }
1093 
 
1094 
      complex&
1095 
      operator/=(float __f)
1096 
      {
1097 
        _M_value /= __f;
1098 
        return *this;
1099 
      }
1100 
 
1101 
      // Let the compiler synthesize the copy and assignment
1102 
      // operator.  It always does a pretty good job.
1103 
      // complex& operator=(const complex&);
1104 
 
1105 
      template
1106 
        complex&
1107 
        operator=(const complex<_Tp>&  __z)
1108 
        {
1109 
          __real__ _M_value = __z.real();
1110 
          __imag__ _M_value = __z.imag();
1111 
          return *this;
1112 
        }
1113 
 
1114 
      template
1115 
        complex&
1116 
        operator+=(const complex<_Tp>& __z)
1117 
        {
1118 
          __real__ _M_value += __z.real();
1119 
          __imag__ _M_value += __z.imag();
1120 
          return *this;
1121 
        }
1122 
 
1123 
      template
1124 
        complex&
1125 
        operator-=(const complex<_Tp>& __z)
1126 
        {
1127 
          __real__ _M_value -= __z.real();
1128 
          __imag__ _M_value -= __z.imag();
1129 
          return *this;
1130 
        }
1131 
 
1132 
      template
1133 
        complex&
1134 
        operator*=(const complex<_Tp>& __z)
1135 
        {
1136 
          _ComplexT __t;
1137 
          __real__ __t = __z.real();
1138 
          __imag__ __t = __z.imag();
1139 
          _M_value *= __t;
1140 
          return *this;
1141 
        }
1142 
 
1143 
      template
1144 
        complex&
1145 
        operator/=(const complex<_Tp>& __z)
1146 
        {
1147 
          _ComplexT __t;
1148 
          __real__ __t = __z.real();
1149 
          __imag__ __t = __z.imag();
1150 
          _M_value /= __t;
1151 
          return *this;
1152 
        }
1153 
 
1154 
      const _ComplexT& __rep() const { return _M_value; }
1155 
 
1156 
    private:
1157 
      _ComplexT _M_value;
1158 
    };
1159 
 
1160 
  // 26.2.3  complex specializations
1161 
  // complex specialization
1162 
  template<>
1163 
    struct complex
1164 
    {
1165 
      typedef double value_type;
1166 
      typedef __complex__ double _ComplexT;
1167 
 
1168 
      complex(_ComplexT __z) : _M_value(__z) { }
1169 
 
1170 
      complex(double __r = 0.0, double __i = 0.0)
1171 
      {
1172 
        __real__ _M_value = __r;
1173 
        __imag__ _M_value = __i;
1174 
      }
1175 
 
1176 
      complex(const complex& __z)
1177 
      : _M_value(__z.__rep()) { }
1178 
 
1179 
      explicit complex(const complex&);
1180 
 
1181 
#ifdef __GXX_EXPERIMENTAL_CXX0X__
1182 
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
1183 
      // DR 387. std::complex over-encapsulated.
1184 
      double real() const
1185 
      { return __real__ _M_value; }
1186 
 
1187 
      double imag() const
1188 
      { return __imag__ _M_value; }
1189 
#else
1190 
      double& real()
1191 
      { return __real__ _M_value; }
1192 
 
1193 
      const double& real() const
1194 
      { return __real__ _M_value; }
1195 
 
1196 
      double& imag()
1197 
      { return __imag__ _M_value; }
1198 
 
1199 
      const double& imag() const
1200 
      { return __imag__ _M_value; }
1201 
#endif
1202 
 
1203 
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
1204 
      // DR 387. std::complex over-encapsulated.
1205 
      void real(double __val)
1206 
      { __real__ _M_value = __val; }
1207 
 
1208 
      void imag(double __val)
1209 
      { __imag__ _M_value = __val; }
1210 
 
1211 
      complex&
1212 
      operator=(double __d)
1213 
      {
1214 
        __real__ _M_value = __d;
1215 
        __imag__ _M_value = 0.0;
1216 
        return *this;
1217 
      }
1218 
 
1219 
      complex&
1220 
      operator+=(double __d)
1221 
      {
1222 
        __real__ _M_value += __d;
1223 
        return *this;
1224 
      }
1225 
 
1226 
      complex&
1227 
      operator-=(double __d)
1228 
      {
1229 
        __real__ _M_value -= __d;
1230 
        return *this;
1231 
      }
1232 
 
1233 
      complex&
1234 
      operator*=(double __d)
1235 
      {
1236 
        _M_value *= __d;
1237 
        return *this;
1238 
      }
1239 
 
1240 
      complex&
1241 
      operator/=(double __d)
1242 
      {
1243 
        _M_value /= __d;
1244 
        return *this;
1245 
      }
1246 
 
1247 
      // The compiler will synthesize this, efficiently.
1248 
      // complex& operator=(const complex&);
1249 
 
1250 
      template
1251 
        complex&
1252 
        operator=(const complex<_Tp>& __z)
1253 
        {
1254 
          __real__ _M_value = __z.real();
1255 
          __imag__ _M_value = __z.imag();
1256 
          return *this;
1257 
        }
1258 
 
1259 
      template
1260 
        complex&
1261 
        operator+=(const complex<_Tp>& __z)
1262 
        {
1263 
          __real__ _M_value += __z.real();
1264 
          __imag__ _M_value += __z.imag();
1265 
          return *this;
1266 
        }
1267 
 
1268 
      template
1269 
        complex&
1270 
        operator-=(const complex<_Tp>& __z)
1271 
        {
1272 
          __real__ _M_value -= __z.real();
1273 
          __imag__ _M_value -= __z.imag();
1274 
          return *this;
1275 
        }
1276 
 
1277 
      template
1278 
        complex&
1279 
        operator*=(const complex<_Tp>& __z)
1280 
        {
1281 
          _ComplexT __t;
1282 
          __real__ __t = __z.real();
1283 
          __imag__ __t = __z.imag();
1284 
          _M_value *= __t;
1285 
          return *this;
1286 
        }
1287 
 
1288 
      template
1289 
        complex&
1290 
        operator/=(const complex<_Tp>& __z)
1291 
        {
1292 
          _ComplexT __t;
1293 
          __real__ __t = __z.real();
1294 
          __imag__ __t = __z.imag();
1295 
          _M_value /= __t;
1296 
          return *this;
1297 
        }
1298 
 
1299 
      const _ComplexT& __rep() const { return _M_value; }
1300 
 
1301 
    private:
1302 
      _ComplexT _M_value;
1303 
    };
1304 
 
1305 
  // 26.2.3  complex specializations
1306 
  // complex specialization
1307 
  template<>
1308 
    struct complex
1309 
    {
1310 
      typedef long double value_type;
1311 
      typedef __complex__ long double _ComplexT;
1312 
 
1313 
      complex(_ComplexT __z) : _M_value(__z) { }
1314 
 
1315 
      complex(long double __r = 0.0L, long double __i = 0.0L)
1316 
      {
1317 
        __real__ _M_value = __r;
1318 
        __imag__ _M_value = __i;
1319 
      }
1320 
 
1321 
      complex(const complex& __z)
1322 
      : _M_value(__z.__rep()) { }
1323 
 
1324 
      complex(const complex& __z)
1325 
      : _M_value(__z.__rep()) { }
1326 
 
1327 
#ifdef __GXX_EXPERIMENTAL_CXX0X__
1328 
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
1329 
      // DR 387. std::complex over-encapsulated.
1330 
      long double real() const
1331 
      { return __real__ _M_value; }
1332 
 
1333 
      long double imag() const
1334 
      { return __imag__ _M_value; }
1335 
#else
1336 
      long double& real()
1337 
      { return __real__ _M_value; }
1338 
 
1339 
      const long double& real() const
1340 
      { return __real__ _M_value; }
1341 
 
1342 
      long double& imag()
1343 
      { return __imag__ _M_value; }
1344 
 
1345 
      const long double& imag() const
1346 
      { return __imag__ _M_value; }
1347 
#endif
1348 
 
1349 
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
1350 
      // DR 387. std::complex over-encapsulated.
1351 
      void real(long double __val)
1352 
      { __real__ _M_value = __val; }
1353 
 
1354 
      void imag(long double __val)
1355 
      { __imag__ _M_value = __val; }
1356 
 
1357 
      complex&
1358 
      operator=(long double __r)
1359 
      {
1360 
        __real__ _M_value = __r;
1361 
        __imag__ _M_value = 0.0L;
1362 
        return *this;
1363 
      }
1364 
 
1365 
      complex&
1366 
      operator+=(long double __r)
1367 
      {
1368 
        __real__ _M_value += __r;
1369 
        return *this;
1370 
      }
1371 
 
1372 
      complex&
1373 
      operator-=(long double __r)
1374 
      {
1375 
        __real__ _M_value -= __r;
1376 
        return *this;
1377 
      }
1378 
 
1379 
      complex&
1380 
      operator*=(long double __r)
1381 
      {
1382 
        _M_value *= __r;
1383 
        return *this;
1384 
      }
1385 
 
1386 
      complex&
1387 
      operator/=(long double __r)
1388 
      {
1389 
        _M_value /= __r;
1390 
        return *this;
1391 
      }
1392 
 
1393 
      // The compiler knows how to do this efficiently
1394 
      // complex& operator=(const complex&);
1395 
 
1396 
      template
1397 
        complex&
1398 
        operator=(const complex<_Tp>& __z)
1399 
        {
1400 
          __real__ _M_value = __z.real();
1401 
          __imag__ _M_value = __z.imag();
1402 
          return *this;
1403 
        }
1404 
 
1405 
      template
1406 
        complex&
1407 
        operator+=(const complex<_Tp>& __z)
1408 
        {
1409 
          __real__ _M_value += __z.real();
1410 
          __imag__ _M_value += __z.imag();
1411 
          return *this;
1412 
        }
1413 
 
1414 
      template
1415 
        complex&
1416 
        operator-=(const complex<_Tp>& __z)
1417 
        {
1418 
          __real__ _M_value -= __z.real();
1419 
          __imag__ _M_value -= __z.imag();
1420 
          return *this;
1421 
        }
1422 
 
1423 
      template
1424 
        complex&
1425 
        operator*=(const complex<_Tp>& __z)
1426 
        {
1427 
          _ComplexT __t;
1428 
          __real__ __t = __z.real();
1429 
          __imag__ __t = __z.imag();
1430 
          _M_value *= __t;
1431 
          return *this;
1432 
        }
1433 
 
1434 
      template
1435 
        complex&
1436 
        operator/=(const complex<_Tp>& __z)
1437 
        {
1438 
          _ComplexT __t;
1439 
          __real__ __t = __z.real();
1440 
          __imag__ __t = __z.imag();
1441 
          _M_value /= __t;
1442 
          return *this;
1443 
        }
1444 
 
1445 
      const _ComplexT& __rep() const { return _M_value; }
1446 
 
1447 
    private:
1448 
      _ComplexT _M_value;
1449 
    };
1450 
 
1451 
  // These bits have to be at the end of this file, so that the
1452 
  // specializations have all been defined.
1453 
  inline
1454 
  complex::complex(const complex& __z)
1455 
  : _M_value(__z.__rep()) { }
1456 
 
1457 
  inline
1458 
  complex::complex(const complex& __z)
1459 
  : _M_value(__z.__rep()) { }
1460 
 
1461 
  inline
1462 
  complex::complex(const complex& __z)
1463 
  : _M_value(__z.__rep()) { }
1464 
 
1465 
  // Inhibit implicit instantiations for required instantiations,
1466 
  // which are defined via explicit instantiations elsewhere.
1467 
  // NB:  This syntax is a GNU extension.
1468 
#if _GLIBCXX_EXTERN_TEMPLATE
1469 
  extern template istream& operator>>(istream&, complex&);
1470 
  extern template ostream& operator<<(ostream&, const complex&);
1471 
  extern template istream& operator>>(istream&, complex&);
1472 
  extern template ostream& operator<<(ostream&, const complex&);
1473 
  extern template istream& operator>>(istream&, complex&);
1474 
  extern template ostream& operator<<(ostream&, const complex&);
1475 
 
1476 
#ifdef _GLIBCXX_USE_WCHAR_T
1477 
  extern template wistream& operator>>(wistream&, complex&);
1478 
  extern template wostream& operator<<(wostream&, const complex&);
1479 
  extern template wistream& operator>>(wistream&, complex&);
1480 
  extern template wostream& operator<<(wostream&, const complex&);
1481 
  extern template wistream& operator>>(wistream&, complex&);
1482 
  extern template wostream& operator<<(wostream&, const complex&);
1483 
#endif
1484 
#endif
1485 
 
1486 
  // @} group complex_numbers
1487 
 
1488 
_GLIBCXX_END_NAMESPACE
1489 
 
1490 
_GLIBCXX_BEGIN_NAMESPACE(__gnu_cxx)
1491 
 
1492 
  // See ext/type_traits.h for the primary template.
1493 
  template
1494 
    struct __promote_2, _Up>
1495 
    {
1496 
    public:
1497 
      typedef std::complex::__type> __type;
1498 
    };
1499 
 
1500 
  template
1501 
    struct __promote_2<_Tp, std::complex<_Up> >
1502 
    {
1503 
    public:
1504 
      typedef std::complex::__type> __type;
1505 
    };
1506 
 
1507 
  template
1508 
    struct __promote_2, std::complex<_Up> >
1509 
    {
1510 
    public:
1511 
      typedef std::complex::__type> __type;
1512 
    };
1513 
 
1514 
_GLIBCXX_END_NAMESPACE
1515 
 
1516 
#ifdef __GXX_EXPERIMENTAL_CXX0X__
1517 
#  if defined(_GLIBCXX_INCLUDE_AS_TR1)
1518 
#    error C++0x header cannot be included from TR1 header
1519 
#  endif
1520 
#  if defined(_GLIBCXX_INCLUDE_AS_CXX0X)
1521 
#    include
1522 
#  else
1523 
#    define _GLIBCXX_INCLUDE_AS_CXX0X
1524 
#    define _GLIBCXX_BEGIN_NAMESPACE_TR1
1525 
#    define _GLIBCXX_END_NAMESPACE_TR1
1526 
#    define _GLIBCXX_TR1
1527 
#    include
1528 
#    undef _GLIBCXX_TR1
1529 
#    undef _GLIBCXX_END_NAMESPACE_TR1
1530 
#    undef _GLIBCXX_BEGIN_NAMESPACE_TR1
1531 
#    undef _GLIBCXX_INCLUDE_AS_CXX0X
1532 
#  endif
1533 
 
1534 
_GLIBCXX_BEGIN_NAMESPACE(std)
1535 
 
1536 
  // Forward declarations.
1537 
  // DR 781.
1538 
  template std::complex<_Tp> proj(const std::complex<_Tp>&);
1539 
 
1540 
  template
1541 
    std::complex<_Tp>
1542 
    __complex_proj(const std::complex<_Tp>& __z)
1543 
    {
1544 
      const _Tp __den = (__z.real() * __z.real()
1545 
                         + __z.imag() * __z.imag() + _Tp(1.0));
1546 
 
1547 
      return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den,
1548 
                               (_Tp(2.0) * __z.imag()) / __den);
1549 
    }
1550 
 
1551 
#if _GLIBCXX_USE_C99_COMPLEX
1552 
  inline __complex__ float
1553 
  __complex_proj(__complex__ float __z)
1554 
  { return __builtin_cprojf(__z); }
1555 
 
1556 
  inline __complex__ double
1557 
  __complex_proj(__complex__ double __z)
1558 
  { return __builtin_cproj(__z); }
1559 
 
1560 
  inline __complex__ long double
1561 
  __complex_proj(const __complex__ long double& __z)
1562 
  { return __builtin_cprojl(__z); }
1563 
 
1564 
  template
1565 
    inline std::complex<_Tp>
1566 
    proj(const std::complex<_Tp>& __z)
1567 
    { return __complex_proj(__z.__rep()); }
1568 
#else
1569 
  template
1570 
    inline std::complex<_Tp>
1571 
    proj(const std::complex<_Tp>& __z)
1572 
    { return __complex_proj(__z); }
1573 
#endif
1574 
 
1575 
  // DR 1137.
1576 
  template
1577 
    inline typename __gnu_cxx::__promote<_Tp>::__type
1578 
    proj(_Tp __x)
1579 
    { return __x; }
1580 
 
1581 
  template
1582 
    inline typename __gnu_cxx::__promote<_Tp>::__type
1583 
    conj(_Tp __x)
1584 
    { return __x; }
1585 
 
1586 
_GLIBCXX_END_NAMESPACE
1587 
 
1588 
#endif
1589 
 
1590 
#endif  /* _GLIBCXX_COMPLEX */

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