29 #ifndef _GLIBCXX_TR1_COMPLEX
30 #define _GLIBCXX_TR1_COMPLEX 1
32 #pragma GCC system_header
36 namespace std _GLIBCXX_VISIBILITY(default)
38 _GLIBCXX_BEGIN_NAMESPACE_VERSION
47 #if __cplusplus >= 201103L
66 #if __cplusplus < 201103L
67 template<
typename _Tp>
72 const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
76 #if _GLIBCXX_USE_C99_COMPLEX_TR1
77 inline __complex__
float
78 __complex_acos(__complex__
float __z)
79 {
return __builtin_cacosf(__z); }
81 inline __complex__
double
82 __complex_acos(__complex__
double __z)
83 {
return __builtin_cacos(__z); }
85 inline __complex__
long double
86 __complex_acos(
const __complex__
long double& __z)
87 {
return __builtin_cacosl(__z); }
89 template<
typename _Tp>
92 {
return __complex_acos(__z.__rep()); }
97 template<
typename _Tp>
100 {
return __complex_acos(__z); }
103 template<
typename _Tp>
112 #if _GLIBCXX_USE_C99_COMPLEX_TR1
113 inline __complex__
float
114 __complex_asin(__complex__
float __z)
115 {
return __builtin_casinf(__z); }
117 inline __complex__
double
118 __complex_asin(__complex__
double __z)
119 {
return __builtin_casin(__z); }
121 inline __complex__
long double
122 __complex_asin(
const __complex__
long double& __z)
123 {
return __builtin_casinl(__z); }
125 template<
typename _Tp>
128 {
return __complex_asin(__z.__rep()); }
133 template<
typename _Tp>
136 {
return __complex_asin(__z); }
139 template<
typename _Tp>
143 const _Tp __r2 = __z.real() * __z.real();
144 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
146 _Tp __num = __z.imag() + _Tp(1.0);
147 _Tp __den = __z.imag() - _Tp(1.0);
149 __num = __r2 + __num * __num;
150 __den = __r2 + __den * __den;
153 _Tp(0.25) *
log(__num / __den));
156 #if _GLIBCXX_USE_C99_COMPLEX_TR1
157 inline __complex__
float
158 __complex_atan(__complex__
float __z)
159 {
return __builtin_catanf(__z); }
161 inline __complex__
double
162 __complex_atan(__complex__
double __z)
163 {
return __builtin_catan(__z); }
165 inline __complex__
long double
166 __complex_atan(
const __complex__
long double& __z)
167 {
return __builtin_catanl(__z); }
169 template<
typename _Tp>
172 {
return __complex_atan(__z.__rep()); }
177 template<
typename _Tp>
180 {
return __complex_atan(__z); }
183 template<
typename _Tp>
189 +
std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
192 #if _GLIBCXX_USE_C99_COMPLEX_TR1
193 inline __complex__
float
194 __complex_acosh(__complex__
float __z)
195 {
return __builtin_cacoshf(__z); }
197 inline __complex__
double
198 __complex_acosh(__complex__
double __z)
199 {
return __builtin_cacosh(__z); }
201 inline __complex__
long double
202 __complex_acosh(
const __complex__
long double& __z)
203 {
return __builtin_cacoshl(__z); }
205 template<
typename _Tp>
208 {
return __complex_acosh(__z.__rep()); }
213 template<
typename _Tp>
216 {
return __complex_acosh(__z); }
219 template<
typename _Tp>
224 * (__z.real() + __z.imag()) + _Tp(1.0),
225 _Tp(2.0) * __z.real() * __z.imag());
231 #if _GLIBCXX_USE_C99_COMPLEX_TR1
232 inline __complex__
float
233 __complex_asinh(__complex__
float __z)
234 {
return __builtin_casinhf(__z); }
236 inline __complex__
double
237 __complex_asinh(__complex__
double __z)
238 {
return __builtin_casinh(__z); }
240 inline __complex__
long double
241 __complex_asinh(
const __complex__
long double& __z)
242 {
return __builtin_casinhl(__z); }
244 template<
typename _Tp>
247 {
return __complex_asinh(__z.__rep()); }
252 template<
typename _Tp>
255 {
return __complex_asinh(__z); }
258 template<
typename _Tp>
262 const _Tp __i2 = __z.imag() * __z.imag();
263 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
265 _Tp __num = _Tp(1.0) + __z.real();
266 _Tp __den = _Tp(1.0) - __z.real();
268 __num = __i2 + __num * __num;
269 __den = __i2 + __den * __den;
272 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
275 #if _GLIBCXX_USE_C99_COMPLEX_TR1
276 inline __complex__
float
277 __complex_atanh(__complex__
float __z)
278 {
return __builtin_catanhf(__z); }
280 inline __complex__
double
281 __complex_atanh(__complex__
double __z)
282 {
return __builtin_catanh(__z); }
284 inline __complex__
long double
285 __complex_atanh(
const __complex__
long double& __z)
286 {
return __builtin_catanhl(__z); }
288 template<
typename _Tp>
291 {
return __complex_atanh(__z.__rep()); }
296 template<
typename _Tp>
299 {
return __complex_atanh(__z); }
304 template<
typename _Tp>
313 #if __cplusplus < 201103L
315 template<
typename _Tp>
316 inline typename __gnu_cxx::__promote<_Tp>::__type
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)
328 template<
typename _Tp>
329 inline typename __gnu_cxx::__promote<_Tp>::__type
333 template<
typename _Tp>
334 inline typename __gnu_cxx::__promote<_Tp>::__type
337 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
338 return __type(__x) * __type(__x);
341 template<
typename _Tp>
342 inline typename __gnu_cxx::__promote<_Tp>::__type
348 template<
typename _Tp,
typename _Up>
352 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
356 template<
typename _Tp,
typename _Up>
360 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
364 template<
typename _Tp,
typename _Up>
368 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
375 template<
typename _Tp>
380 template<
typename _Tp>
389 template<
typename _Tp,
typename _Up>
391 polar(
const _Tp& __rho,
const _Up& __theta)
393 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
394 return std::polar(__type(__rho), __type(__theta));
399 template<
typename _Tp>
404 template<
typename _Tp>
409 template<
typename _Tp>
417 _GLIBCXX_END_NAMESPACE_VERSION
420 #endif // _GLIBCXX_TR1_COMPLEX
_Tp fabs(const std::complex< _Tp > &)
fabs(__z) [8.1.8].
_Tp norm(const complex< _Tp > &)
Return z magnitude squared.
complex< _Tp > log(const complex< _Tp > &)
Return complex natural logarithm of z.
complex< _Tp > polar(const _Tp &, const _Tp &=0)
Return complex with magnitude rho and angle theta.
std::complex< _Tp > atan(const std::complex< _Tp > &)
atan(__z) [8.1.4].
std::complex< _Tp > acos(const std::complex< _Tp > &)
acos(__z) [8.1.2].
std::complex< _Tp > asin(const std::complex< _Tp > &)
asin(__z) [8.1.3].
std::complex< _Tp > asinh(const std::complex< _Tp > &)
asinh(__z) [8.1.6].
std::complex< _Tp > acosh(const std::complex< _Tp > &)
acosh(__z) [8.1.5].
complex< _Tp > pow(const complex< _Tp > &, int)
Return x to the y'th power.
_Tp arg(const complex< _Tp > &)
Return phase angle of z.
std::complex< _Tp > atanh(const std::complex< _Tp > &)
atanh(__z) [8.1.7].
complex< _Tp > conj(const complex< _Tp > &)
Return complex conjugate of z.
_Tp abs(const complex< _Tp > &)
Return magnitude of z.
complex< _Tp > sqrt(const complex< _Tp > &)
Return complex square root of z.