1// -*- C++ -*- 2//===----------------------------------------------------------------------===// 3// 4// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 5// See https://llvm.org/LICENSE.txt for license information. 6// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 7// 8//===----------------------------------------------------------------------===// 9 10#ifndef _LIBCPP_COMPLEX 11#define _LIBCPP_COMPLEX 12 13/* 14 complex synopsis 15 16namespace std 17{ 18 19template<class T> 20class complex 21{ 22public: 23 typedef T value_type; 24 25 complex(const T& re = T(), const T& im = T()); // constexpr in C++14 26 complex(const complex&); // constexpr in C++14 27 template<class X> complex(const complex<X>&); // constexpr in C++14 28 29 T real() const; // constexpr in C++14 30 T imag() const; // constexpr in C++14 31 32 void real(T); // constexpr in C++20 33 void imag(T); // constexpr in C++20 34 35 complex<T>& operator= (const T&); // constexpr in C++20 36 complex<T>& operator+=(const T&); // constexpr in C++20 37 complex<T>& operator-=(const T&); // constexpr in C++20 38 complex<T>& operator*=(const T&); // constexpr in C++20 39 complex<T>& operator/=(const T&); // constexpr in C++20 40 41 complex& operator=(const complex&); // constexpr in C++20 42 template<class X> complex<T>& operator= (const complex<X>&); // constexpr in C++20 43 template<class X> complex<T>& operator+=(const complex<X>&); // constexpr in C++20 44 template<class X> complex<T>& operator-=(const complex<X>&); // constexpr in C++20 45 template<class X> complex<T>& operator*=(const complex<X>&); // constexpr in C++20 46 template<class X> complex<T>& operator/=(const complex<X>&); // constexpr in C++20 47}; 48 49template<> 50class complex<float> 51{ 52public: 53 typedef float value_type; 54 55 constexpr complex(float re = 0.0f, float im = 0.0f); 56 explicit constexpr complex(const complex<double>&); 57 explicit constexpr complex(const complex<long double>&); 58 59 constexpr float real() const; 60 void real(float); // constexpr in C++20 61 constexpr float imag() const; 62 void imag(float); // constexpr in C++20 63 64 complex<float>& operator= (float); // constexpr in C++20 65 complex<float>& operator+=(float); // constexpr in C++20 66 complex<float>& operator-=(float); // constexpr in C++20 67 complex<float>& operator*=(float); // constexpr in C++20 68 complex<float>& operator/=(float); // constexpr in C++20 69 70 complex<float>& operator=(const complex<float>&); // constexpr in C++20 71 template<class X> complex<float>& operator= (const complex<X>&); // constexpr in C++20 72 template<class X> complex<float>& operator+=(const complex<X>&); // constexpr in C++20 73 template<class X> complex<float>& operator-=(const complex<X>&); // constexpr in C++20 74 template<class X> complex<float>& operator*=(const complex<X>&); // constexpr in C++20 75 template<class X> complex<float>& operator/=(const complex<X>&); // constexpr in C++20 76}; 77 78template<> 79class complex<double> 80{ 81public: 82 typedef double value_type; 83 84 constexpr complex(double re = 0.0, double im = 0.0); 85 constexpr complex(const complex<float>&); 86 explicit constexpr complex(const complex<long double>&); 87 88 constexpr double real() const; 89 void real(double); // constexpr in C++20 90 constexpr double imag() const; 91 void imag(double); // constexpr in C++20 92 93 complex<double>& operator= (double); // constexpr in C++20 94 complex<double>& operator+=(double); // constexpr in C++20 95 complex<double>& operator-=(double); // constexpr in C++20 96 complex<double>& operator*=(double); // constexpr in C++20 97 complex<double>& operator/=(double); // constexpr in C++20 98 complex<double>& operator=(const complex<double>&); // constexpr in C++20 99 100 template<class X> complex<double>& operator= (const complex<X>&); // constexpr in C++20 101 template<class X> complex<double>& operator+=(const complex<X>&); // constexpr in C++20 102 template<class X> complex<double>& operator-=(const complex<X>&); // constexpr in C++20 103 template<class X> complex<double>& operator*=(const complex<X>&); // constexpr in C++20 104 template<class X> complex<double>& operator/=(const complex<X>&); // constexpr in C++20 105}; 106 107template<> 108class complex<long double> 109{ 110public: 111 typedef long double value_type; 112 113 constexpr complex(long double re = 0.0L, long double im = 0.0L); 114 constexpr complex(const complex<float>&); 115 constexpr complex(const complex<double>&); 116 117 constexpr long double real() const; 118 void real(long double); // constexpr in C++20 119 constexpr long double imag() const; 120 void imag(long double); // constexpr in C++20 121 122 complex<long double>& operator=(const complex<long double>&); // constexpr in C++20 123 complex<long double>& operator= (long double); // constexpr in C++20 124 complex<long double>& operator+=(long double); // constexpr in C++20 125 complex<long double>& operator-=(long double); // constexpr in C++20 126 complex<long double>& operator*=(long double); // constexpr in C++20 127 complex<long double>& operator/=(long double); // constexpr in C++20 128 129 template<class X> complex<long double>& operator= (const complex<X>&); // constexpr in C++20 130 template<class X> complex<long double>& operator+=(const complex<X>&); // constexpr in C++20 131 template<class X> complex<long double>& operator-=(const complex<X>&); // constexpr in C++20 132 template<class X> complex<long double>& operator*=(const complex<X>&); // constexpr in C++20 133 template<class X> complex<long double>& operator/=(const complex<X>&); // constexpr in C++20 134}; 135 136// 26.3.6 operators: 137template<class T> complex<T> operator+(const complex<T>&, const complex<T>&); // constexpr in C++20 138template<class T> complex<T> operator+(const complex<T>&, const T&); // constexpr in C++20 139template<class T> complex<T> operator+(const T&, const complex<T>&); // constexpr in C++20 140template<class T> complex<T> operator-(const complex<T>&, const complex<T>&); // constexpr in C++20 141template<class T> complex<T> operator-(const complex<T>&, const T&); // constexpr in C++20 142template<class T> complex<T> operator-(const T&, const complex<T>&); // constexpr in C++20 143template<class T> complex<T> operator*(const complex<T>&, const complex<T>&); // constexpr in C++20 144template<class T> complex<T> operator*(const complex<T>&, const T&); // constexpr in C++20 145template<class T> complex<T> operator*(const T&, const complex<T>&); // constexpr in C++20 146template<class T> complex<T> operator/(const complex<T>&, const complex<T>&); // constexpr in C++20 147template<class T> complex<T> operator/(const complex<T>&, const T&); // constexpr in C++20 148template<class T> complex<T> operator/(const T&, const complex<T>&); // constexpr in C++20 149template<class T> complex<T> operator+(const complex<T>&); // constexpr in C++20 150template<class T> complex<T> operator-(const complex<T>&); // constexpr in C++20 151template<class T> bool operator==(const complex<T>&, const complex<T>&); // constexpr in C++14 152template<class T> bool operator==(const complex<T>&, const T&); // constexpr in C++14 153template<class T> bool operator==(const T&, const complex<T>&); // constexpr in C++14, removed in C++20 154template<class T> bool operator!=(const complex<T>&, const complex<T>&); // constexpr in C++14, removed in C++20 155template<class T> bool operator!=(const complex<T>&, const T&); // constexpr in C++14, removed in C++20 156template<class T> bool operator!=(const T&, const complex<T>&); // constexpr in C++14, removed in C++20 157 158template<class T, class charT, class traits> 159 basic_istream<charT, traits>& 160 operator>>(basic_istream<charT, traits>&, complex<T>&); 161template<class T, class charT, class traits> 162 basic_ostream<charT, traits>& 163 operator<<(basic_ostream<charT, traits>&, const complex<T>&); 164 165// 26.3.7 values: 166 167template<class T> T real(const complex<T>&); // constexpr in C++14 168 long double real(long double); // constexpr in C++14 169 double real(double); // constexpr in C++14 170template<Integral T> double real(T); // constexpr in C++14 171 float real(float); // constexpr in C++14 172 173template<class T> T imag(const complex<T>&); // constexpr in C++14 174 long double imag(long double); // constexpr in C++14 175 double imag(double); // constexpr in C++14 176template<Integral T> double imag(T); // constexpr in C++14 177 float imag(float); // constexpr in C++14 178 179template<class T> T abs(const complex<T>&); 180 181template<class T> T arg(const complex<T>&); 182 long double arg(long double); 183 double arg(double); 184template<Integral T> double arg(T); 185 float arg(float); 186 187template<class T> T norm(const complex<T>&); // constexpr in C++20 188 long double norm(long double); // constexpr in C++20 189 double norm(double); // constexpr in C++20 190template<Integral T> double norm(T); // constexpr in C++20 191 float norm(float); // constexpr in C++20 192 193template<class T> complex<T> conj(const complex<T>&); // constexpr in C++20 194 complex<long double> conj(long double); // constexpr in C++20 195 complex<double> conj(double); // constexpr in C++20 196template<Integral T> complex<double> conj(T); // constexpr in C++20 197 complex<float> conj(float); // constexpr in C++20 198 199template<class T> complex<T> proj(const complex<T>&); 200 complex<long double> proj(long double); 201 complex<double> proj(double); 202template<Integral T> complex<double> proj(T); 203 complex<float> proj(float); 204 205template<class T> complex<T> polar(const T&, const T& = T()); 206 207// 26.3.8 transcendentals: 208template<class T> complex<T> acos(const complex<T>&); 209template<class T> complex<T> asin(const complex<T>&); 210template<class T> complex<T> atan(const complex<T>&); 211template<class T> complex<T> acosh(const complex<T>&); 212template<class T> complex<T> asinh(const complex<T>&); 213template<class T> complex<T> atanh(const complex<T>&); 214template<class T> complex<T> cos (const complex<T>&); 215template<class T> complex<T> cosh (const complex<T>&); 216template<class T> complex<T> exp (const complex<T>&); 217template<class T> complex<T> log (const complex<T>&); 218template<class T> complex<T> log10(const complex<T>&); 219 220template<class T> complex<T> pow(const complex<T>&, const T&); 221template<class T> complex<T> pow(const complex<T>&, const complex<T>&); 222template<class T> complex<T> pow(const T&, const complex<T>&); 223 224template<class T> complex<T> sin (const complex<T>&); 225template<class T> complex<T> sinh (const complex<T>&); 226template<class T> complex<T> sqrt (const complex<T>&); 227template<class T> complex<T> tan (const complex<T>&); 228template<class T> complex<T> tanh (const complex<T>&); 229 230 // [complex.tuple], tuple interface 231 template<class T> struct tuple_size; // Since C++26 232 template<size_t I, class T> struct tuple_element; // Since C++26 233 template<class T> struct tuple_size<complex<T>>; // Since C++26 234 template<size_t I, class T> struct tuple_element<I, complex<T>>; // Since C++26 235 template<size_t I, class T> 236 constexpr T& get(complex<T>&) noexcept; // Since C++26 237 template<size_t I, class T> 238 constexpr T&& get(complex<T>&&) noexcept; // Since C++26 239 template<size_t I, class T> 240 constexpr const T& get(const complex<T>&) noexcept; // Since C++26 241 template<size_t I, class T> 242 constexpr const T&& get(const complex<T>&&) noexcept; // Since C++26 243 244 // [complex.literals], complex literals 245 inline namespace literals { 246 inline namespace complex_literals { 247 constexpr complex<long double> operator""il(long double); // Since C++14 248 constexpr complex<long double> operator""il(unsigned long long); // Since C++14 249 constexpr complex<double> operator""i(long double); // Since C++14 250 constexpr complex<double> operator""i(unsigned long long); // Since C++14 251 constexpr complex<float> operator""if(long double); // Since C++14 252 constexpr complex<float> operator""if(unsigned long long); // Since C++14 253 } 254 } 255} // std 256 257*/ 258 259#if __cplusplus < 201103L && defined(_LIBCPP_USE_FROZEN_CXX03_HEADERS) 260# include <__cxx03/complex> 261#else 262# include <__config> 263# include <__fwd/complex.h> 264# include <__fwd/tuple.h> 265# include <__tuple/tuple_element.h> 266# include <__tuple/tuple_size.h> 267# include <__type_traits/conditional.h> 268# include <__utility/move.h> 269# include <cmath> 270# include <version> 271 272# if _LIBCPP_HAS_LOCALIZATION 273# include <sstream> // for std::basic_ostringstream 274# endif 275 276# if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 277# pragma GCC system_header 278# endif 279 280_LIBCPP_PUSH_MACROS 281# include <__undef_macros> 282 283_LIBCPP_BEGIN_NAMESPACE_STD 284 285template <class _Tp> 286class _LIBCPP_TEMPLATE_VIS complex; 287 288template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> = 0> 289_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 290operator*(const complex<_Tp>& __z, const complex<_Tp>& __w); 291 292template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> = 0> 293_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 294operator*(const complex<_Tp>& __z, const complex<_Tp>& __w); 295 296template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> = 0> 297_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 298operator/(const complex<_Tp>& __x, const complex<_Tp>& __y); 299 300template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> = 0> 301_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 302operator/(const complex<_Tp>& __x, const complex<_Tp>& __y); 303 304template <class _Tp> 305class _LIBCPP_TEMPLATE_VIS complex { 306public: 307 typedef _Tp value_type; 308 309private: 310 value_type __re_; 311 value_type __im_; 312 313public: 314 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 315 complex(const value_type& __re = value_type(), const value_type& __im = value_type()) 316 : __re_(__re), __im_(__im) {} 317 template <class _Xp> 318 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 complex(const complex<_Xp>& __c) 319 : __re_(__c.real()), __im_(__c.imag()) {} 320 321 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 value_type real() const { return __re_; } 322 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 value_type imag() const { return __im_; } 323 324 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) { __re_ = __re; } 325 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) { __im_ = __im; } 326 327 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(const value_type& __re) { 328 __re_ = __re; 329 __im_ = value_type(); 330 return *this; 331 } 332 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const value_type& __re) { 333 __re_ += __re; 334 return *this; 335 } 336 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const value_type& __re) { 337 __re_ -= __re; 338 return *this; 339 } 340 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const value_type& __re) { 341 __re_ *= __re; 342 __im_ *= __re; 343 return *this; 344 } 345 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const value_type& __re) { 346 __re_ /= __re; 347 __im_ /= __re; 348 return *this; 349 } 350 351 template <class _Xp> 352 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(const complex<_Xp>& __c) { 353 __re_ = __c.real(); 354 __im_ = __c.imag(); 355 return *this; 356 } 357 template <class _Xp> 358 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) { 359 __re_ += __c.real(); 360 __im_ += __c.imag(); 361 return *this; 362 } 363 template <class _Xp> 364 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) { 365 __re_ -= __c.real(); 366 __im_ -= __c.imag(); 367 return *this; 368 } 369 template <class _Xp> 370 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) { 371 *this = *this * complex(__c.real(), __c.imag()); 372 return *this; 373 } 374 template <class _Xp> 375 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c) { 376 *this = *this / complex(__c.real(), __c.imag()); 377 return *this; 378 } 379 380# if _LIBCPP_STD_VER >= 26 381 template <size_t _Ip, class _Xp> 382 friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp& get(complex<_Xp>&) noexcept; 383 384 template <size_t _Ip, class _Xp> 385 friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp&& get(complex<_Xp>&&) noexcept; 386 387 template <size_t _Ip, class _Xp> 388 friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp& get(const complex<_Xp>&) noexcept; 389 390 template <size_t _Ip, class _Xp> 391 friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp&& get(const complex<_Xp>&&) noexcept; 392# endif 393}; 394 395template <> 396class _LIBCPP_TEMPLATE_VIS complex<double>; 397template <> 398class _LIBCPP_TEMPLATE_VIS complex<long double>; 399 400struct __from_builtin_tag {}; 401 402template <class _Tp> 403using __complex_t _LIBCPP_NODEBUG = 404 __conditional_t<is_same<_Tp, float>::value, 405 _Complex float, 406 __conditional_t<is_same<_Tp, double>::value, _Complex double, _Complex long double> >; 407 408template <class _Tp> 409_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR __complex_t<_Tp> __make_complex(_Tp __re, _Tp __im) { 410# if __has_builtin(__builtin_complex) 411 return __builtin_complex(__re, __im); 412# else 413 return __complex_t<_Tp>{__re, __im}; 414# endif 415} 416 417template <> 418class _LIBCPP_TEMPLATE_VIS complex<float> { 419 float __re_; 420 float __im_; 421 422public: 423 typedef float value_type; 424 425 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(float __re = 0.0f, float __im = 0.0f) : __re_(__re), __im_(__im) {} 426 427 template <class _Tag, __enable_if_t<_IsSame<_Tag, __from_builtin_tag>::value, int> = 0> 428 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR explicit complex(_Tag, _Complex float __v) 429 : __re_(__real__ __v), __im_(__imag__ __v) {} 430 431 _LIBCPP_HIDE_FROM_ABI explicit _LIBCPP_CONSTEXPR complex(const complex<double>& __c); 432 _LIBCPP_HIDE_FROM_ABI explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c); 433 434 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR float real() const { return __re_; } 435 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR float imag() const { return __im_; } 436 437 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) { __re_ = __re; } 438 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) { __im_ = __im; } 439 440 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR _Complex float __builtin() const { return std::__make_complex(__re_, __im_); } 441 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 void __builtin(_Complex float __f) { 442 __re_ = __real__ __f; 443 __im_ = __imag__ __f; 444 } 445 446 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(float __re) { 447 __re_ = __re; 448 __im_ = value_type(); 449 return *this; 450 } 451 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(float __re) { 452 __re_ += __re; 453 return *this; 454 } 455 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(float __re) { 456 __re_ -= __re; 457 return *this; 458 } 459 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(float __re) { 460 __re_ *= __re; 461 __im_ *= __re; 462 return *this; 463 } 464 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(float __re) { 465 __re_ /= __re; 466 __im_ /= __re; 467 return *this; 468 } 469 470 template <class _Xp> 471 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(const complex<_Xp>& __c) { 472 __re_ = __c.real(); 473 __im_ = __c.imag(); 474 return *this; 475 } 476 template <class _Xp> 477 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) { 478 __re_ += __c.real(); 479 __im_ += __c.imag(); 480 return *this; 481 } 482 template <class _Xp> 483 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) { 484 __re_ -= __c.real(); 485 __im_ -= __c.imag(); 486 return *this; 487 } 488 template <class _Xp> 489 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) { 490 *this = *this * complex(__c.real(), __c.imag()); 491 return *this; 492 } 493 template <class _Xp> 494 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c) { 495 *this = *this / complex(__c.real(), __c.imag()); 496 return *this; 497 } 498 499# if _LIBCPP_STD_VER >= 26 500 template <size_t _Ip, class _Xp> 501 friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp& get(complex<_Xp>&) noexcept; 502 503 template <size_t _Ip, class _Xp> 504 friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp&& get(complex<_Xp>&&) noexcept; 505 506 template <size_t _Ip, class _Xp> 507 friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp& get(const complex<_Xp>&) noexcept; 508 509 template <size_t _Ip, class _Xp> 510 friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp&& get(const complex<_Xp>&&) noexcept; 511# endif 512}; 513 514template <> 515class _LIBCPP_TEMPLATE_VIS complex<double> { 516 double __re_; 517 double __im_; 518 519public: 520 typedef double value_type; 521 522 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(double __re = 0.0, double __im = 0.0) : __re_(__re), __im_(__im) {} 523 524 template <class _Tag, __enable_if_t<_IsSame<_Tag, __from_builtin_tag>::value, int> = 0> 525 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR explicit complex(_Tag, _Complex double __v) 526 : __re_(__real__ __v), __im_(__imag__ __v) {} 527 528 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(const complex<float>& __c); 529 _LIBCPP_HIDE_FROM_ABI explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c); 530 531 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR double real() const { return __re_; } 532 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR double imag() const { return __im_; } 533 534 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) { __re_ = __re; } 535 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) { __im_ = __im; } 536 537 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR _Complex double __builtin() const { 538 return std::__make_complex(__re_, __im_); 539 } 540 541 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 void __builtin(_Complex double __f) { 542 __re_ = __real__ __f; 543 __im_ = __imag__ __f; 544 } 545 546 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(double __re) { 547 __re_ = __re; 548 __im_ = value_type(); 549 return *this; 550 } 551 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(double __re) { 552 __re_ += __re; 553 return *this; 554 } 555 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(double __re) { 556 __re_ -= __re; 557 return *this; 558 } 559 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(double __re) { 560 __re_ *= __re; 561 __im_ *= __re; 562 return *this; 563 } 564 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(double __re) { 565 __re_ /= __re; 566 __im_ /= __re; 567 return *this; 568 } 569 570 template <class _Xp> 571 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(const complex<_Xp>& __c) { 572 __re_ = __c.real(); 573 __im_ = __c.imag(); 574 return *this; 575 } 576 template <class _Xp> 577 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) { 578 __re_ += __c.real(); 579 __im_ += __c.imag(); 580 return *this; 581 } 582 template <class _Xp> 583 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) { 584 __re_ -= __c.real(); 585 __im_ -= __c.imag(); 586 return *this; 587 } 588 template <class _Xp> 589 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) { 590 *this = *this * complex(__c.real(), __c.imag()); 591 return *this; 592 } 593 template <class _Xp> 594 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c) { 595 *this = *this / complex(__c.real(), __c.imag()); 596 return *this; 597 } 598 599# if _LIBCPP_STD_VER >= 26 600 template <size_t _Ip, class _Xp> 601 friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp& get(complex<_Xp>&) noexcept; 602 603 template <size_t _Ip, class _Xp> 604 friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp&& get(complex<_Xp>&&) noexcept; 605 606 template <size_t _Ip, class _Xp> 607 friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp& get(const complex<_Xp>&) noexcept; 608 609 template <size_t _Ip, class _Xp> 610 friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp&& get(const complex<_Xp>&&) noexcept; 611# endif 612}; 613 614template <> 615class _LIBCPP_TEMPLATE_VIS complex<long double> { 616 long double __re_; 617 long double __im_; 618 619public: 620 typedef long double value_type; 621 622 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(long double __re = 0.0L, long double __im = 0.0L) 623 : __re_(__re), __im_(__im) {} 624 625 template <class _Tag, __enable_if_t<_IsSame<_Tag, __from_builtin_tag>::value, int> = 0> 626 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR explicit complex(_Tag, _Complex long double __v) 627 : __re_(__real__ __v), __im_(__imag__ __v) {} 628 629 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(const complex<float>& __c); 630 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(const complex<double>& __c); 631 632 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR long double real() const { return __re_; } 633 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR long double imag() const { return __im_; } 634 635 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) { __re_ = __re; } 636 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) { __im_ = __im; } 637 638 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR _Complex long double __builtin() const { 639 return std::__make_complex(__re_, __im_); 640 } 641 642 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 void __builtin(_Complex long double __f) { 643 __re_ = __real__ __f; 644 __im_ = __imag__ __f; 645 } 646 647 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(long double __re) { 648 __re_ = __re; 649 __im_ = value_type(); 650 return *this; 651 } 652 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(long double __re) { 653 __re_ += __re; 654 return *this; 655 } 656 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(long double __re) { 657 __re_ -= __re; 658 return *this; 659 } 660 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(long double __re) { 661 __re_ *= __re; 662 __im_ *= __re; 663 return *this; 664 } 665 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(long double __re) { 666 __re_ /= __re; 667 __im_ /= __re; 668 return *this; 669 } 670 671 template <class _Xp> 672 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(const complex<_Xp>& __c) { 673 __re_ = __c.real(); 674 __im_ = __c.imag(); 675 return *this; 676 } 677 template <class _Xp> 678 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) { 679 __re_ += __c.real(); 680 __im_ += __c.imag(); 681 return *this; 682 } 683 template <class _Xp> 684 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) { 685 __re_ -= __c.real(); 686 __im_ -= __c.imag(); 687 return *this; 688 } 689 template <class _Xp> 690 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) { 691 *this = *this * complex(__c.real(), __c.imag()); 692 return *this; 693 } 694 template <class _Xp> 695 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c) { 696 *this = *this / complex(__c.real(), __c.imag()); 697 return *this; 698 } 699 700# if _LIBCPP_STD_VER >= 26 701 template <size_t _Ip, class _Xp> 702 friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp& get(complex<_Xp>&) noexcept; 703 704 template <size_t _Ip, class _Xp> 705 friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp&& get(complex<_Xp>&&) noexcept; 706 707 template <size_t _Ip, class _Xp> 708 friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp& get(const complex<_Xp>&) noexcept; 709 710 template <size_t _Ip, class _Xp> 711 friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp&& get(const complex<_Xp>&&) noexcept; 712# endif 713}; 714 715inline _LIBCPP_CONSTEXPR complex<float>::complex(const complex<double>& __c) : __re_(__c.real()), __im_(__c.imag()) {} 716 717inline _LIBCPP_CONSTEXPR complex<float>::complex(const complex<long double>& __c) 718 : __re_(__c.real()), __im_(__c.imag()) {} 719 720inline _LIBCPP_CONSTEXPR complex<double>::complex(const complex<float>& __c) : __re_(__c.real()), __im_(__c.imag()) {} 721 722inline _LIBCPP_CONSTEXPR complex<double>::complex(const complex<long double>& __c) 723 : __re_(__c.real()), __im_(__c.imag()) {} 724 725inline _LIBCPP_CONSTEXPR complex<long double>::complex(const complex<float>& __c) 726 : __re_(__c.real()), __im_(__c.imag()) {} 727 728inline _LIBCPP_CONSTEXPR complex<long double>::complex(const complex<double>& __c) 729 : __re_(__c.real()), __im_(__c.imag()) {} 730 731// 26.3.6 operators: 732 733template <class _Tp> 734inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 735operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) { 736 complex<_Tp> __t(__x); 737 __t += __y; 738 return __t; 739} 740 741template <class _Tp> 742inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 743operator+(const complex<_Tp>& __x, const _Tp& __y) { 744 complex<_Tp> __t(__x); 745 __t += __y; 746 return __t; 747} 748 749template <class _Tp> 750inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 751operator+(const _Tp& __x, const complex<_Tp>& __y) { 752 complex<_Tp> __t(__y); 753 __t += __x; 754 return __t; 755} 756 757template <class _Tp> 758inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 759operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) { 760 complex<_Tp> __t(__x); 761 __t -= __y; 762 return __t; 763} 764 765template <class _Tp> 766inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 767operator-(const complex<_Tp>& __x, const _Tp& __y) { 768 complex<_Tp> __t(__x); 769 __t -= __y; 770 return __t; 771} 772 773template <class _Tp> 774inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 775operator-(const _Tp& __x, const complex<_Tp>& __y) { 776 complex<_Tp> __t(-__y); 777 __t += __x; 778 return __t; 779} 780 781template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> > 782_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 783operator*(const complex<_Tp>& __lhs, const complex<_Tp>& __rhs) { 784 return complex<_Tp>(__from_builtin_tag(), __lhs.__builtin() * __rhs.__builtin()); 785} 786 787template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> > 788_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 789operator*(const complex<_Tp>& __z, const complex<_Tp>& __w) { 790 _Tp __a = __z.real(); 791 _Tp __b = __z.imag(); 792 _Tp __c = __w.real(); 793 _Tp __d = __w.imag(); 794 795 return complex<_Tp>((__a * __c) - (__b * __d), (__a * __d) + (__b * __c)); 796} 797 798template <class _Tp> 799inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 800operator*(const complex<_Tp>& __x, const _Tp& __y) { 801 complex<_Tp> __t(__x); 802 __t *= __y; 803 return __t; 804} 805 806template <class _Tp> 807inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 808operator*(const _Tp& __x, const complex<_Tp>& __y) { 809 complex<_Tp> __t(__y); 810 __t *= __x; 811 return __t; 812} 813 814template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> > 815_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 816operator/(const complex<_Tp>& __lhs, const complex<_Tp>& __rhs) { 817 return complex<_Tp>(__from_builtin_tag(), __lhs.__builtin() / __rhs.__builtin()); 818} 819 820template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> > 821_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 822operator/(const complex<_Tp>& __z, const complex<_Tp>& __w) { 823 _Tp __a = __z.real(); 824 _Tp __b = __z.imag(); 825 _Tp __c = __w.real(); 826 _Tp __d = __w.imag(); 827 828 _Tp __denom = __c * __c + __d * __d; 829 return complex<_Tp>((__a * __c + __b * __d) / __denom, (__b * __c - __a * __d) / __denom); 830} 831 832template <class _Tp> 833inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 834operator/(const complex<_Tp>& __x, const _Tp& __y) { 835 return complex<_Tp>(__x.real() / __y, __x.imag() / __y); 836} 837 838template <class _Tp> 839inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> 840operator/(const _Tp& __x, const complex<_Tp>& __y) { 841 complex<_Tp> __t(__x); 842 __t /= __y; 843 return __t; 844} 845 846template <class _Tp> 847inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator+(const complex<_Tp>& __x) { 848 return __x; 849} 850 851template <class _Tp> 852inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator-(const complex<_Tp>& __x) { 853 return complex<_Tp>(-__x.real(), -__x.imag()); 854} 855 856template <class _Tp> 857inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool 858operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) { 859 return __x.real() == __y.real() && __x.imag() == __y.imag(); 860} 861 862template <class _Tp> 863inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator==(const complex<_Tp>& __x, const _Tp& __y) { 864 return __x.real() == __y && __x.imag() == 0; 865} 866 867# if _LIBCPP_STD_VER <= 17 868 869template <class _Tp> 870inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator==(const _Tp& __x, const complex<_Tp>& __y) { 871 return __x == __y.real() && 0 == __y.imag(); 872} 873 874template <class _Tp> 875inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool 876operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) { 877 return !(__x == __y); 878} 879 880template <class _Tp> 881inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator!=(const complex<_Tp>& __x, const _Tp& __y) { 882 return !(__x == __y); 883} 884 885template <class _Tp> 886inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator!=(const _Tp& __x, const complex<_Tp>& __y) { 887 return !(__x == __y); 888} 889 890# endif 891 892// 26.3.7 values: 893 894template <class _Tp, bool = is_integral<_Tp>::value, bool = is_floating_point<_Tp>::value > 895struct __libcpp_complex_overload_traits {}; 896 897// Integral Types 898template <class _Tp> 899struct __libcpp_complex_overload_traits<_Tp, true, false> { 900 typedef double _ValueType; 901 typedef complex<double> _ComplexType; 902}; 903 904// Floating point types 905template <class _Tp> 906struct __libcpp_complex_overload_traits<_Tp, false, true> { 907 typedef _Tp _ValueType; 908 typedef complex<_Tp> _ComplexType; 909}; 910 911// real 912 913template <class _Tp> 914inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 _Tp real(const complex<_Tp>& __c) { 915 return __c.real(); 916} 917 918template <class _Tp> 919inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 typename __libcpp_complex_overload_traits<_Tp>::_ValueType 920real(_Tp __re) { 921 return __re; 922} 923 924// imag 925 926template <class _Tp> 927inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 _Tp imag(const complex<_Tp>& __c) { 928 return __c.imag(); 929} 930 931template <class _Tp> 932inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 typename __libcpp_complex_overload_traits<_Tp>::_ValueType 933imag(_Tp) { 934 return 0; 935} 936 937// abs 938 939template <class _Tp> 940inline _LIBCPP_HIDE_FROM_ABI _Tp abs(const complex<_Tp>& __c) { 941 return std::hypot(__c.real(), __c.imag()); 942} 943 944// arg 945 946template <class _Tp> 947inline _LIBCPP_HIDE_FROM_ABI _Tp arg(const complex<_Tp>& __c) { 948 return std::atan2(__c.imag(), __c.real()); 949} 950 951template <class _Tp, __enable_if_t<is_same<_Tp, long double>::value, int> = 0> 952inline _LIBCPP_HIDE_FROM_ABI long double arg(_Tp __re) { 953 return std::atan2l(0.L, __re); 954} 955 956template <class _Tp, __enable_if_t<is_integral<_Tp>::value || is_same<_Tp, double>::value, int> = 0> 957inline _LIBCPP_HIDE_FROM_ABI double arg(_Tp __re) { 958 return std::atan2(0., __re); 959} 960 961template <class _Tp, __enable_if_t<is_same<_Tp, float>::value, int> = 0> 962inline _LIBCPP_HIDE_FROM_ABI float arg(_Tp __re) { 963 return std::atan2f(0.F, __re); 964} 965 966// norm 967 968template <class _Tp> 969inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _Tp norm(const complex<_Tp>& __c) { 970 if (std::__constexpr_isinf(__c.real())) 971 return std::abs(__c.real()); 972 if (std::__constexpr_isinf(__c.imag())) 973 return std::abs(__c.imag()); 974 return __c.real() * __c.real() + __c.imag() * __c.imag(); 975} 976 977template <class _Tp> 978inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 typename __libcpp_complex_overload_traits<_Tp>::_ValueType 979norm(_Tp __re) { 980 typedef typename __libcpp_complex_overload_traits<_Tp>::_ValueType _ValueType; 981 return static_cast<_ValueType>(__re) * __re; 982} 983 984// conj 985 986template <class _Tp> 987inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> conj(const complex<_Tp>& __c) { 988 return complex<_Tp>(__c.real(), -__c.imag()); 989} 990 991template <class _Tp> 992inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 typename __libcpp_complex_overload_traits<_Tp>::_ComplexType 993conj(_Tp __re) { 994 typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType; 995 return _ComplexType(__re); 996} 997 998// proj 999 1000template <class _Tp> 1001inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> proj(const complex<_Tp>& __c) { 1002 complex<_Tp> __r = __c; 1003 if (std::isinf(__c.real()) || std::isinf(__c.imag())) 1004 __r = complex<_Tp>(INFINITY, std::copysign(_Tp(0), __c.imag())); 1005 return __r; 1006} 1007 1008template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> = 0> 1009inline _LIBCPP_HIDE_FROM_ABI typename __libcpp_complex_overload_traits<_Tp>::_ComplexType proj(_Tp __re) { 1010 if (std::isinf(__re)) 1011 __re = std::abs(__re); 1012 return complex<_Tp>(__re); 1013} 1014 1015template <class _Tp, __enable_if_t<is_integral<_Tp>::value, int> = 0> 1016inline _LIBCPP_HIDE_FROM_ABI typename __libcpp_complex_overload_traits<_Tp>::_ComplexType proj(_Tp __re) { 1017 typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType; 1018 return _ComplexType(__re); 1019} 1020 1021// polar 1022 1023template <class _Tp> 1024_LIBCPP_HIDE_FROM_ABI complex<_Tp> polar(const _Tp& __rho, const _Tp& __theta = _Tp()) { 1025 if (std::isnan(__rho) || std::signbit(__rho)) 1026 return complex<_Tp>(_Tp(NAN), _Tp(NAN)); 1027 if (std::isnan(__theta)) { 1028 if (std::isinf(__rho)) 1029 return complex<_Tp>(__rho, __theta); 1030 return complex<_Tp>(__theta, __theta); 1031 } 1032 if (std::isinf(__theta)) { 1033 if (std::isinf(__rho)) 1034 return complex<_Tp>(__rho, _Tp(NAN)); 1035 return complex<_Tp>(_Tp(NAN), _Tp(NAN)); 1036 } 1037 _Tp __x = __rho * std::cos(__theta); 1038 if (std::isnan(__x)) 1039 __x = 0; 1040 _Tp __y = __rho * std::sin(__theta); 1041 if (std::isnan(__y)) 1042 __y = 0; 1043 return complex<_Tp>(__x, __y); 1044} 1045 1046// log 1047 1048template <class _Tp> 1049inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> log(const complex<_Tp>& __x) { 1050 return complex<_Tp>(std::log(std::abs(__x)), std::arg(__x)); 1051} 1052 1053// log10 1054 1055template <class _Tp> 1056inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> log10(const complex<_Tp>& __x) { 1057 return std::log(__x) / std::log(_Tp(10)); 1058} 1059 1060// sqrt 1061 1062template <class _Tp> 1063_LIBCPP_HIDE_FROM_ABI complex<_Tp> sqrt(const complex<_Tp>& __x) { 1064 if (std::isinf(__x.imag())) 1065 return complex<_Tp>(_Tp(INFINITY), __x.imag()); 1066 if (std::isinf(__x.real())) { 1067 if (__x.real() > _Tp(0)) 1068 return complex<_Tp>(__x.real(), std::isnan(__x.imag()) ? __x.imag() : std::copysign(_Tp(0), __x.imag())); 1069 return complex<_Tp>(std::isnan(__x.imag()) ? __x.imag() : _Tp(0), std::copysign(__x.real(), __x.imag())); 1070 } 1071 return std::polar(std::sqrt(std::abs(__x)), std::arg(__x) / _Tp(2)); 1072} 1073 1074// exp 1075 1076template <class _Tp> 1077_LIBCPP_HIDE_FROM_ABI complex<_Tp> exp(const complex<_Tp>& __x) { 1078 _Tp __i = __x.imag(); 1079 if (__i == 0) { 1080 return complex<_Tp>(std::exp(__x.real()), std::copysign(_Tp(0), __x.imag())); 1081 } 1082 if (std::isinf(__x.real())) { 1083 if (__x.real() < _Tp(0)) { 1084 if (!std::isfinite(__i)) 1085 __i = _Tp(1); 1086 } else if (__i == 0 || !std::isfinite(__i)) { 1087 if (std::isinf(__i)) 1088 __i = _Tp(NAN); 1089 return complex<_Tp>(__x.real(), __i); 1090 } 1091 } 1092 _Tp __e = std::exp(__x.real()); 1093 return complex<_Tp>(__e * std::cos(__i), __e * std::sin(__i)); 1094} 1095 1096// pow 1097 1098template <class _Tp> 1099inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> pow(const complex<_Tp>& __x, const complex<_Tp>& __y) { 1100 return std::exp(__y * std::log(__x)); 1101} 1102 1103template <class _Tp, class _Up, __enable_if_t<is_floating_point<_Tp>::value && is_floating_point<_Up>::value, int> = 0> 1104inline _LIBCPP_HIDE_FROM_ABI complex<typename __promote<_Tp, _Up>::type> 1105pow(const complex<_Tp>& __x, const complex<_Up>& __y) { 1106 typedef complex<typename __promote<_Tp, _Up>::type> result_type; 1107 return std::pow(result_type(__x), result_type(__y)); 1108} 1109 1110template <class _Tp, class _Up, __enable_if_t<is_floating_point<_Tp>::value && is_arithmetic<_Up>::value, int> = 0> 1111inline _LIBCPP_HIDE_FROM_ABI complex<typename __promote<_Tp, _Up>::type> pow(const complex<_Tp>& __x, const _Up& __y) { 1112 typedef complex<typename __promote<_Tp, _Up>::type> result_type; 1113 return std::pow(result_type(__x), result_type(__y)); 1114} 1115 1116template <class _Tp, class _Up, __enable_if_t<is_arithmetic<_Tp>::value && is_floating_point<_Up>::value, int> = 0> 1117inline _LIBCPP_HIDE_FROM_ABI complex<typename __promote<_Tp, _Up>::type> pow(const _Tp& __x, const complex<_Up>& __y) { 1118 typedef complex<typename __promote<_Tp, _Up>::type> result_type; 1119 return std::pow(result_type(__x), result_type(__y)); 1120} 1121 1122// __sqr, computes pow(x, 2) 1123 1124template <class _Tp> 1125inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> __sqr(const complex<_Tp>& __x) { 1126 return complex<_Tp>((__x.real() - __x.imag()) * (__x.real() + __x.imag()), _Tp(2) * __x.real() * __x.imag()); 1127} 1128 1129// asinh 1130 1131template <class _Tp> 1132_LIBCPP_HIDE_FROM_ABI complex<_Tp> asinh(const complex<_Tp>& __x) { 1133 const _Tp __pi(atan2(+0., -0.)); 1134 if (std::isinf(__x.real())) { 1135 if (std::isnan(__x.imag())) 1136 return __x; 1137 if (std::isinf(__x.imag())) 1138 return complex<_Tp>(__x.real(), std::copysign(__pi * _Tp(0.25), __x.imag())); 1139 return complex<_Tp>(__x.real(), std::copysign(_Tp(0), __x.imag())); 1140 } 1141 if (std::isnan(__x.real())) { 1142 if (std::isinf(__x.imag())) 1143 return complex<_Tp>(__x.imag(), __x.real()); 1144 if (__x.imag() == 0) 1145 return __x; 1146 return complex<_Tp>(__x.real(), __x.real()); 1147 } 1148 if (std::isinf(__x.imag())) 1149 return complex<_Tp>(std::copysign(__x.imag(), __x.real()), std::copysign(__pi / _Tp(2), __x.imag())); 1150 complex<_Tp> __z = std::log(__x + std::sqrt(std::__sqr(__x) + _Tp(1))); 1151 return complex<_Tp>(std::copysign(__z.real(), __x.real()), std::copysign(__z.imag(), __x.imag())); 1152} 1153 1154// acosh 1155 1156template <class _Tp> 1157_LIBCPP_HIDE_FROM_ABI complex<_Tp> acosh(const complex<_Tp>& __x) { 1158 const _Tp __pi(atan2(+0., -0.)); 1159 if (std::isinf(__x.real())) { 1160 if (std::isnan(__x.imag())) 1161 return complex<_Tp>(std::abs(__x.real()), __x.imag()); 1162 if (std::isinf(__x.imag())) { 1163 if (__x.real() > 0) 1164 return complex<_Tp>(__x.real(), std::copysign(__pi * _Tp(0.25), __x.imag())); 1165 else 1166 return complex<_Tp>(-__x.real(), std::copysign(__pi * _Tp(0.75), __x.imag())); 1167 } 1168 if (__x.real() < 0) 1169 return complex<_Tp>(-__x.real(), std::copysign(__pi, __x.imag())); 1170 return complex<_Tp>(__x.real(), std::copysign(_Tp(0), __x.imag())); 1171 } 1172 if (std::isnan(__x.real())) { 1173 if (std::isinf(__x.imag())) 1174 return complex<_Tp>(std::abs(__x.imag()), __x.real()); 1175 return complex<_Tp>(__x.real(), __x.real()); 1176 } 1177 if (std::isinf(__x.imag())) 1178 return complex<_Tp>(std::abs(__x.imag()), std::copysign(__pi / _Tp(2), __x.imag())); 1179 complex<_Tp> __z = std::log(__x + std::sqrt(std::__sqr(__x) - _Tp(1))); 1180 return complex<_Tp>(std::copysign(__z.real(), _Tp(0)), std::copysign(__z.imag(), __x.imag())); 1181} 1182 1183// atanh 1184 1185template <class _Tp> 1186_LIBCPP_HIDE_FROM_ABI complex<_Tp> atanh(const complex<_Tp>& __x) { 1187 const _Tp __pi(atan2(+0., -0.)); 1188 if (std::isinf(__x.imag())) { 1189 return complex<_Tp>(std::copysign(_Tp(0), __x.real()), std::copysign(__pi / _Tp(2), __x.imag())); 1190 } 1191 if (std::isnan(__x.imag())) { 1192 if (std::isinf(__x.real()) || __x.real() == 0) 1193 return complex<_Tp>(std::copysign(_Tp(0), __x.real()), __x.imag()); 1194 return complex<_Tp>(__x.imag(), __x.imag()); 1195 } 1196 if (std::isnan(__x.real())) { 1197 return complex<_Tp>(__x.real(), __x.real()); 1198 } 1199 if (std::isinf(__x.real())) { 1200 return complex<_Tp>(std::copysign(_Tp(0), __x.real()), std::copysign(__pi / _Tp(2), __x.imag())); 1201 } 1202 if (std::abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0)) { 1203 return complex<_Tp>(std::copysign(_Tp(INFINITY), __x.real()), std::copysign(_Tp(0), __x.imag())); 1204 } 1205 complex<_Tp> __z = std::log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2); 1206 return complex<_Tp>(std::copysign(__z.real(), __x.real()), std::copysign(__z.imag(), __x.imag())); 1207} 1208 1209// sinh 1210 1211template <class _Tp> 1212_LIBCPP_HIDE_FROM_ABI complex<_Tp> sinh(const complex<_Tp>& __x) { 1213 if (std::isinf(__x.real()) && !std::isfinite(__x.imag())) 1214 return complex<_Tp>(__x.real(), _Tp(NAN)); 1215 if (__x.real() == 0 && !std::isfinite(__x.imag())) 1216 return complex<_Tp>(__x.real(), _Tp(NAN)); 1217 if (__x.imag() == 0 && !std::isfinite(__x.real())) 1218 return __x; 1219 return complex<_Tp>(std::sinh(__x.real()) * std::cos(__x.imag()), std::cosh(__x.real()) * std::sin(__x.imag())); 1220} 1221 1222// cosh 1223 1224template <class _Tp> 1225_LIBCPP_HIDE_FROM_ABI complex<_Tp> cosh(const complex<_Tp>& __x) { 1226 if (std::isinf(__x.real()) && !std::isfinite(__x.imag())) 1227 return complex<_Tp>(std::abs(__x.real()), _Tp(NAN)); 1228 if (__x.real() == 0 && !std::isfinite(__x.imag())) 1229 return complex<_Tp>(_Tp(NAN), __x.real()); 1230 if (__x.real() == 0 && __x.imag() == 0) 1231 return complex<_Tp>(_Tp(1), __x.imag()); 1232 if (__x.imag() == 0 && !std::isfinite(__x.real())) 1233 return complex<_Tp>(std::abs(__x.real()), __x.imag()); 1234 return complex<_Tp>(std::cosh(__x.real()) * std::cos(__x.imag()), std::sinh(__x.real()) * std::sin(__x.imag())); 1235} 1236 1237// tanh 1238 1239template <class _Tp> 1240_LIBCPP_HIDE_FROM_ABI complex<_Tp> tanh(const complex<_Tp>& __x) { 1241 if (std::isinf(__x.real())) { 1242 if (!std::isfinite(__x.imag())) 1243 return complex<_Tp>(std::copysign(_Tp(1), __x.real()), _Tp(0)); 1244 return complex<_Tp>(std::copysign(_Tp(1), __x.real()), std::copysign(_Tp(0), std::sin(_Tp(2) * __x.imag()))); 1245 } 1246 if (std::isnan(__x.real()) && __x.imag() == 0) 1247 return __x; 1248 _Tp __2r(_Tp(2) * __x.real()); 1249 _Tp __2i(_Tp(2) * __x.imag()); 1250 _Tp __d(std::cosh(__2r) + std::cos(__2i)); 1251 _Tp __2rsh(std::sinh(__2r)); 1252 if (std::isinf(__2rsh) && std::isinf(__d)) 1253 return complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1), __2i > _Tp(0) ? _Tp(0) : _Tp(-0.)); 1254 return complex<_Tp>(__2rsh / __d, std::sin(__2i) / __d); 1255} 1256 1257// asin 1258 1259template <class _Tp> 1260_LIBCPP_HIDE_FROM_ABI complex<_Tp> asin(const complex<_Tp>& __x) { 1261 complex<_Tp> __z = std::asinh(complex<_Tp>(-__x.imag(), __x.real())); 1262 return complex<_Tp>(__z.imag(), -__z.real()); 1263} 1264 1265// acos 1266 1267template <class _Tp> 1268_LIBCPP_HIDE_FROM_ABI complex<_Tp> acos(const complex<_Tp>& __x) { 1269 const _Tp __pi(atan2(+0., -0.)); 1270 if (std::isinf(__x.real())) { 1271 if (std::isnan(__x.imag())) 1272 return complex<_Tp>(__x.imag(), __x.real()); 1273 if (std::isinf(__x.imag())) { 1274 if (__x.real() < _Tp(0)) 1275 return complex<_Tp>(_Tp(0.75) * __pi, -__x.imag()); 1276 return complex<_Tp>(_Tp(0.25) * __pi, -__x.imag()); 1277 } 1278 if (__x.real() < _Tp(0)) 1279 return complex<_Tp>(__pi, std::signbit(__x.imag()) ? -__x.real() : __x.real()); 1280 return complex<_Tp>(_Tp(0), std::signbit(__x.imag()) ? __x.real() : -__x.real()); 1281 } 1282 if (std::isnan(__x.real())) { 1283 if (std::isinf(__x.imag())) 1284 return complex<_Tp>(__x.real(), -__x.imag()); 1285 return complex<_Tp>(__x.real(), __x.real()); 1286 } 1287 if (std::isinf(__x.imag())) 1288 return complex<_Tp>(__pi / _Tp(2), -__x.imag()); 1289 if (__x.real() == 0 && (__x.imag() == 0 || std::isnan(__x.imag()))) 1290 return complex<_Tp>(__pi / _Tp(2), -__x.imag()); 1291 complex<_Tp> __z = std::log(__x + std::sqrt(std::__sqr(__x) - _Tp(1))); 1292 if (std::signbit(__x.imag())) 1293 return complex<_Tp>(std::abs(__z.imag()), std::abs(__z.real())); 1294 return complex<_Tp>(std::abs(__z.imag()), -std::abs(__z.real())); 1295} 1296 1297// atan 1298 1299template <class _Tp> 1300_LIBCPP_HIDE_FROM_ABI complex<_Tp> atan(const complex<_Tp>& __x) { 1301 complex<_Tp> __z = std::atanh(complex<_Tp>(-__x.imag(), __x.real())); 1302 return complex<_Tp>(__z.imag(), -__z.real()); 1303} 1304 1305// sin 1306 1307template <class _Tp> 1308_LIBCPP_HIDE_FROM_ABI complex<_Tp> sin(const complex<_Tp>& __x) { 1309 complex<_Tp> __z = std::sinh(complex<_Tp>(-__x.imag(), __x.real())); 1310 return complex<_Tp>(__z.imag(), -__z.real()); 1311} 1312 1313// cos 1314 1315template <class _Tp> 1316inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> cos(const complex<_Tp>& __x) { 1317 return std::cosh(complex<_Tp>(-__x.imag(), __x.real())); 1318} 1319 1320// tan 1321 1322template <class _Tp> 1323_LIBCPP_HIDE_FROM_ABI complex<_Tp> tan(const complex<_Tp>& __x) { 1324 complex<_Tp> __z = std::tanh(complex<_Tp>(-__x.imag(), __x.real())); 1325 return complex<_Tp>(__z.imag(), -__z.real()); 1326} 1327 1328# if _LIBCPP_HAS_LOCALIZATION 1329template <class _Tp, class _CharT, class _Traits> 1330_LIBCPP_HIDE_FROM_ABI basic_istream<_CharT, _Traits>& 1331operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) { 1332 if (__is.good()) { 1333 std::ws(__is); 1334 if (__is.peek() == _CharT('(')) { 1335 __is.get(); 1336 _Tp __r; 1337 __is >> __r; 1338 if (!__is.fail()) { 1339 std::ws(__is); 1340 _CharT __c = __is.peek(); 1341 if (__c == _CharT(',')) { 1342 __is.get(); 1343 _Tp __i; 1344 __is >> __i; 1345 if (!__is.fail()) { 1346 std::ws(__is); 1347 __c = __is.peek(); 1348 if (__c == _CharT(')')) { 1349 __is.get(); 1350 __x = complex<_Tp>(__r, __i); 1351 } else 1352 __is.setstate(__is.failbit); 1353 } else 1354 __is.setstate(__is.failbit); 1355 } else if (__c == _CharT(')')) { 1356 __is.get(); 1357 __x = complex<_Tp>(__r, _Tp(0)); 1358 } else 1359 __is.setstate(__is.failbit); 1360 } else 1361 __is.setstate(__is.failbit); 1362 } else { 1363 _Tp __r; 1364 __is >> __r; 1365 if (!__is.fail()) 1366 __x = complex<_Tp>(__r, _Tp(0)); 1367 else 1368 __is.setstate(__is.failbit); 1369 } 1370 } else 1371 __is.setstate(__is.failbit); 1372 return __is; 1373} 1374 1375template <class _Tp, class _CharT, class _Traits> 1376_LIBCPP_HIDE_FROM_ABI basic_ostream<_CharT, _Traits>& 1377operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) { 1378 basic_ostringstream<_CharT, _Traits> __s; 1379 __s.flags(__os.flags()); 1380 __s.imbue(__os.getloc()); 1381 __s.precision(__os.precision()); 1382 __s << '(' << __x.real() << ',' << __x.imag() << ')'; 1383 return __os << __s.str(); 1384} 1385# endif // _LIBCPP_HAS_LOCALIZATION 1386 1387# if _LIBCPP_STD_VER >= 26 1388 1389// [complex.tuple], tuple interface 1390 1391template <class _Tp> 1392struct tuple_size<complex<_Tp>> : integral_constant<size_t, 2> {}; 1393 1394template <size_t _Ip, class _Tp> 1395struct tuple_element<_Ip, complex<_Tp>> { 1396 static_assert(_Ip < 2, "Index value is out of range."); 1397 using type = _Tp; 1398}; 1399 1400template <size_t _Ip, class _Xp> 1401_LIBCPP_HIDE_FROM_ABI constexpr _Xp& get(complex<_Xp>& __z) noexcept { 1402 static_assert(_Ip < 2, "Index value is out of range."); 1403 if constexpr (_Ip == 0) { 1404 return __z.__re_; 1405 } else { 1406 return __z.__im_; 1407 } 1408} 1409 1410template <size_t _Ip, class _Xp> 1411_LIBCPP_HIDE_FROM_ABI constexpr _Xp&& get(complex<_Xp>&& __z) noexcept { 1412 static_assert(_Ip < 2, "Index value is out of range."); 1413 if constexpr (_Ip == 0) { 1414 return std::move(__z.__re_); 1415 } else { 1416 return std::move(__z.__im_); 1417 } 1418} 1419 1420template <size_t _Ip, class _Xp> 1421_LIBCPP_HIDE_FROM_ABI constexpr const _Xp& get(const complex<_Xp>& __z) noexcept { 1422 static_assert(_Ip < 2, "Index value is out of range."); 1423 if constexpr (_Ip == 0) { 1424 return __z.__re_; 1425 } else { 1426 return __z.__im_; 1427 } 1428} 1429 1430template <size_t _Ip, class _Xp> 1431_LIBCPP_HIDE_FROM_ABI constexpr const _Xp&& get(const complex<_Xp>&& __z) noexcept { 1432 static_assert(_Ip < 2, "Index value is out of range."); 1433 if constexpr (_Ip == 0) { 1434 return std::move(__z.__re_); 1435 } else { 1436 return std::move(__z.__im_); 1437 } 1438} 1439 1440# endif // _LIBCPP_STD_VER >= 26 1441 1442# if _LIBCPP_STD_VER >= 14 1443// Literal suffix for complex number literals [complex.literals] 1444inline namespace literals { 1445inline namespace complex_literals { 1446_LIBCPP_HIDE_FROM_ABI inline constexpr complex<long double> operator""il(long double __im) { return {0.0l, __im}; } 1447 1448_LIBCPP_HIDE_FROM_ABI inline constexpr complex<long double> operator""il(unsigned long long __im) { 1449 return {0.0l, static_cast<long double>(__im)}; 1450} 1451 1452_LIBCPP_HIDE_FROM_ABI inline constexpr complex<double> operator""i(long double __im) { 1453 return {0.0, static_cast<double>(__im)}; 1454} 1455 1456_LIBCPP_HIDE_FROM_ABI inline constexpr complex<double> operator""i(unsigned long long __im) { 1457 return {0.0, static_cast<double>(__im)}; 1458} 1459 1460_LIBCPP_HIDE_FROM_ABI inline constexpr complex<float> operator""if(long double __im) { 1461 return {0.0f, static_cast<float>(__im)}; 1462} 1463 1464_LIBCPP_HIDE_FROM_ABI inline constexpr complex<float> operator""if(unsigned long long __im) { 1465 return {0.0f, static_cast<float>(__im)}; 1466} 1467} // namespace complex_literals 1468} // namespace literals 1469# endif 1470 1471_LIBCPP_END_NAMESPACE_STD 1472 1473_LIBCPP_POP_MACROS 1474 1475# if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20 1476# include <iosfwd> 1477# include <stdexcept> 1478# include <type_traits> 1479# endif 1480#endif // __cplusplus < 201103L && defined(_LIBCPP_USE_FROZEN_CXX03_HEADERS) 1481 1482#endif // _LIBCPP_COMPLEX 1483