Complex Numbers

Collaboration diagram for Complex Numbers:

Classes

• struct std::complex< _Tp >
• struct std::complex< double >

  26.2.3 complex specializations complex<double> specialization More...
  

• struct std::complex< float >

  26.2.3 complex specializations complex<float> specialization More...
  

• struct std::complex< long double >

  26.2.3 complex specializations complex<long double> specialization More...
  

Functions

• constexpr std::complex< float >::complex (const complex< long double > &)
• template<typename _Tp > _Tp std::__complex_abs (const complex< _Tp > &__z)
• template<typename _Tp > std::complex< _Tp > std::tr1::__complex_acosh (const std::complex< _Tp > &__z)
• template<typename _Tp > _Tp std::__complex_arg (const complex< _Tp > &__z)
• template<typename _Tp > std::complex< _Tp > std::tr1::__complex_asinh (const std::complex< _Tp > &__z)
• template<typename _Tp > std::complex< _Tp > std::tr1::__complex_atanh (const std::complex< _Tp > &__z)
• template<typename _Tp > complex< _Tp > std::__complex_cos (const complex< _Tp > &__z)
• template<typename _Tp > complex< _Tp > std::__complex_cosh (const complex< _Tp > &__z)
• template<typename _Tp > complex< _Tp > std::__complex_exp (const complex< _Tp > &__z)
• template<typename _Tp > complex< _Tp > std::__complex_log (const complex< _Tp > &__z)
• template<typename _Tp > complex< _Tp > std::__complex_pow (const complex< _Tp > &__x, const complex< _Tp > &__y)
• template<typename _Tp > complex< _Tp > std::__complex_sin (const complex< _Tp > &__z)
• template<typename _Tp > complex< _Tp > std::__complex_sinh (const complex< _Tp > &__z)
• template<typename _Tp > complex< _Tp > std::__complex_sqrt (const complex< _Tp > &__z)
• template<typename _Tp > complex< _Tp > std::__complex_tan (const complex< _Tp > &__z)
• template<typename _Tp > complex< _Tp > std::__complex_tanh (const complex< _Tp > &__z)
• template<typename _Tp > _Tp std::abs (const complex< _Tp > &)
• template<typename _Tp > std::complex< _Tp > std::tr1::acosh (const std::complex< _Tp > &__z)
• template<typename _Tp > _Tp std::arg (const complex< _Tp > &)
• template<typename _Tp > std::complex< _Tp > std::tr1::asinh (const std::complex< _Tp > &__z)
• template<typename _Tp > std::complex< _Tp > std::tr1::atanh (const std::complex< _Tp > &__z)
• template<typename _Tp > complex< _Tp > std::conj (const complex< _Tp > &)
• template<typename _Tp > std::complex< _Tp > std::tr1::conj (const std::complex< _Tp > &__z)
• template<typename _Tp > std::complex< typename
  __gnu_cxx::__promote< _Tp >
  ::__type > std::tr1::conj (_Tp __x)
• template<typename _Tp > complex< _Tp > std::cos (const complex< _Tp > &)
• template<typename _Tp > complex< _Tp > std::cosh (const complex< _Tp > &)
• template<typename _Tp > complex< _Tp > std::exp (const complex< _Tp > &)
• template<typename _Tp > std::complex< _Tp > std::tr1::fabs (const std::complex< _Tp > &__z)
• template<typename _Tp > constexpr _Tp std::imag (const complex< _Tp > &__z)
• template<typename _Tp > complex< _Tp > std::log (const complex< _Tp > &)
• template<typename _Tp > complex< _Tp > std::log10 (const complex< _Tp > &)
• template<typename _Tp > _Tp std::norm (const complex< _Tp > &)
• complex< _Tp > & std::complex< _Tp >::operator*= (const _Tp &)
• template<typename _Up > complex< _Tp > & std::complex< _Tp >::operator*= (const complex< _Up > &)
• template<typename _Tp > complex< _Tp > std::operator+ (const complex< _Tp > &__x)
• template<typename _Up > complex< _Tp > & std::complex< _Tp >::operator+= (const complex< _Up > &)
• template<typename _Tp > complex< _Tp > std::operator- (const complex< _Tp > &__x)
• template<typename _Up > complex< _Tp > & std::complex< _Tp >::operator-= (const complex< _Up > &)
• complex< _Tp > & std::complex< _Tp >::operator/= (const _Tp &)
• template<typename _Up > complex< _Tp > & std::complex< _Tp >::operator/= (const complex< _Up > &)
• template<typename _Tp , typename _CharT , class _Traits > basic_ostream< _CharT, _Traits > & std::operator<< (basic_ostream< _CharT, _Traits > &__os, const complex< _Tp > &__x)
• complex< _Tp > & std::complex< _Tp >::operator= (const _Tp &)
• template<typename _Up > complex< _Tp > & std::complex< _Tp >::operator= (const complex< _Up > &)
• template<typename _Tp , typename _CharT , class _Traits > basic_istream< _CharT, _Traits > & std::operator>> (basic_istream< _CharT, _Traits > &__is, complex< _Tp > &__x)
• template<typename _Tp > complex< _Tp > std::polar (const _Tp &, const _Tp &=0)
• template<typename _Tp , typename _Up > std::complex< typename
  __gnu_cxx::__promote_2< _Tp,
  _Up >::__type > std::tr1::polar (const _Tp &__rho, const _Up &__theta)
• template<typename _Tp > complex< _Tp > std::pow (const complex< _Tp > &, const _Tp &)
• template<typename _Tp > complex< _Tp > std::pow (const complex< _Tp > &, const complex< _Tp > &)
• template<typename _Tp > complex< _Tp > std::pow (const _Tp &, const complex< _Tp > &)
• template<typename _Tp , typename _Up > std::complex< typename
  __gnu_cxx::__promote_2< _Tp,
  _Up >::__type > std::tr1::pow (const std::complex< _Tp > &__x, const _Up &__y)
• template<typename _Tp , typename _Up > std::complex< typename
  __gnu_cxx::__promote_2< _Tp,
  _Up >::__type > std::tr1::pow (const _Tp &__x, const std::complex< _Up > &__y)
• template<typename _Tp , typename _Up > std::complex< typename
  __gnu_cxx::__promote_2< _Tp,
  _Up >::__type > std::tr1::pow (const std::complex< _Tp > &__x, const std::complex< _Up > &__y)
• template<typename _Tp > std::complex< _Tp > std::tr1::pow (const std::complex< _Tp > &__x, const _Tp &__y)
• template<typename _Tp > std::complex< _Tp > std::tr1::pow (const _Tp &__x, const std::complex< _Tp > &__y)
• template<typename _Tp > std::complex< _Tp > std::tr1::pow (const std::complex< _Tp > &__x, const std::complex< _Tp > &__y)
• template<typename _Tp > constexpr _Tp std::real (const complex< _Tp > &__z)
• template<typename _Tp > complex< _Tp > std::sin (const complex< _Tp > &)
• template<typename _Tp > complex< _Tp > std::sinh (const complex< _Tp > &)
• template<typename _Tp > complex< _Tp > std::sqrt (const complex< _Tp > &)
• template<typename _Tp > complex< _Tp > std::tan (const complex< _Tp > &)
• template<typename _Tp > complex< _Tp > std::tanh (const complex< _Tp > &)

• template<typename _Tp > complex< _Tp > std::operator+ (const complex< _Tp > &__x, const complex< _Tp > &__y)
• template<typename _Tp > complex< _Tp > std::operator+ (const complex< _Tp > &__x, const _Tp &__y)
• template<typename _Tp > complex< _Tp > std::operator+ (const _Tp &__x, const complex< _Tp > &__y)

• template<typename _Tp > complex< _Tp > std::operator- (const complex< _Tp > &__x, const complex< _Tp > &__y)
• template<typename _Tp > complex< _Tp > std::operator- (const complex< _Tp > &__x, const _Tp &__y)
• template<typename _Tp > complex< _Tp > std::operator- (const _Tp &__x, const complex< _Tp > &__y)

• template<typename _Tp > complex< _Tp > std::operator* (const complex< _Tp > &__x, const complex< _Tp > &__y)
• template<typename _Tp > complex< _Tp > std::operator* (const complex< _Tp > &__x, const _Tp &__y)
• template<typename _Tp > complex< _Tp > std::operator* (const _Tp &__x, const complex< _Tp > &__y)

• template<typename _Tp > complex< _Tp > std::operator/ (const complex< _Tp > &__x, const complex< _Tp > &__y)
• template<typename _Tp > complex< _Tp > std::operator/ (const complex< _Tp > &__x, const _Tp &__y)
• template<typename _Tp > complex< _Tp > std::operator/ (const _Tp &__x, const complex< _Tp > &__y)

• template<typename _Tp > constexpr bool std::operator== (const complex< _Tp > &__x, const complex< _Tp > &__y)
• template<typename _Tp > constexpr bool std::operator== (const complex< _Tp > &__x, const _Tp &__y)
• template<typename _Tp > constexpr bool std::operator== (const _Tp &__x, const complex< _Tp > &__y)

• template<typename _Tp > constexpr bool std::operator!= (const complex< _Tp > &__x, const complex< _Tp > &__y)
• template<typename _Tp > constexpr bool std::operator!= (const complex< _Tp > &__x, const _Tp &__y)
• template<typename _Tp > constexpr bool std::operator!= (const _Tp &__x, const complex< _Tp > &__y)

---

Detailed Description

Classes and functions for complex numbers.

---

Function Documentation

template<typename _Tp >

_Tp std::abs

(

const complex< _Tp > &

__z

)

[inline]

Return magnitude of z.

Definition at line 596 of file complex.

Referenced by std::tr1::fabs(), std::fabs(), std::binomial_distribution< _IntType >::operator()(), and std::poisson_distribution< _IntType >::operator()().

template<typename _Tp >

std::complex< _Tp > std::tr1::acosh

(

const std::complex< _Tp > &

__z

)

[inline]

acosh(__z) [8.1.5].

Definition at line 216 of file tr1/complex.

template<typename _Tp >

_Tp std::arg

(

const complex< _Tp > &

__z

)

[inline]

Return phase angle of z.

Definition at line 623 of file complex.

Referenced by std::arg().

template<typename _Tp >

std::complex< _Tp > std::tr1::asinh

(

const std::complex< _Tp > &

__z

)

[inline]

asinh(__z) [8.1.6].

Definition at line 255 of file tr1/complex.

template<typename _Tp >

std::complex< _Tp > std::tr1::atanh

(

const std::complex< _Tp > &

__z

)

[inline]

atanh(__z) [8.1.7].

Definition at line 299 of file tr1/complex.

template<typename _Tp >

complex< _Tp > std::conj

(

const complex< _Tp > &

__z

)

[inline]

Return complex conjugate of z.

Definition at line 669 of file complex.

template<typename _Tp >

complex< _Tp > std::cos

(

const complex< _Tp > &

__z

)

[inline]

Return complex cosine of z.

Definition at line 701 of file complex.

Referenced by std::polar().

template<typename _Tp >

complex< _Tp > std::cosh

(

const complex< _Tp > &

__z

)

[inline]

Return complex hyperbolic cosine of z.

Definition at line 731 of file complex.

template<typename _Tp >

complex< _Tp > std::exp

(

const complex< _Tp > &

__z

)

[inline]

Return complex base e exponential of z.

Definition at line 757 of file complex.

Referenced by std::pow().

template<typename _Tp >

std::complex< _Tp > std::tr1::fabs

(

const std::complex< _Tp > &

__z

)

[inline]

fabs(__z) [8.1.8].

Definition at line 308 of file tr1/complex.

References std::abs().

template<typename _Tp >

complex< _Tp > std::log

(

const complex< _Tp > &

__z

)

[inline]

Return complex natural logarithm of z.

Definition at line 784 of file complex.

Referenced by std::generate_canonical(), std::log10(), std::independent_bits_engine< _RandomNumberEngine, __w, _UIntType >::operator()(), std::normal_distribution< _RealType >::operator()(), std::gamma_distribution< _RealType >::operator()(), std::binomial_distribution< _IntType >::operator()(), std::poisson_distribution< _IntType >::operator()(), and std::pow().

template<typename _Tp >

complex< _Tp > std::log10

(

const complex< _Tp > &

__z

)

[inline]

Return complex base 10 logarithm of z.

Definition at line 789 of file complex.

References std::log().

template<typename _Tp >

_Tp std::norm

(

const complex< _Tp > &

__z

)

[inline]

Return z magnitude squared.

Definition at line 656 of file complex.

Referenced by std::complex< _Tp >::operator/=().

template<typename _Tp >

constexpr bool std::operator!=	(	const complex< _Tp > &	__x,
		const complex< _Tp > &	__y
	)		[inline]

Return false if x is equal to y.

Definition at line 471 of file complex.

template<typename _Tp >

constexpr bool std::operator!=	(	const complex< _Tp > &	__x,
		const _Tp &	__y
	)		[inline]

Return false if x is equal to y.

Definition at line 476 of file complex.

template<typename _Tp >

constexpr bool std::operator!=	(	const _Tp &	__x,
		const complex< _Tp > &	__y
	)		[inline]

Return false if x is equal to y.

Definition at line 481 of file complex.

template<typename _Tp >

complex<_Tp> std::operator*	(	const complex< _Tp > &	__x,
		const complex< _Tp > &	__y
	)		[inline]

Return new complex value x times y.

Definition at line 381 of file complex.

template<typename _Tp >

complex<_Tp> std::operator*	(	const complex< _Tp > &	__x,
		const _Tp &	__y
	)		[inline]

Return new complex value x times y.

Definition at line 390 of file complex.

template<typename _Tp >

complex<_Tp> std::operator*	(	const _Tp &	__x,
		const complex< _Tp > &	__y
	)		[inline]

Return new complex value x times y.

Definition at line 399 of file complex.

template<typename _Tp >

complex< _Tp > & std::complex< _Tp >::operator*=

(

const _Tp &

__t

)

Multiply this complex number by t.

Definition at line 240 of file complex.

template<typename _Tp >

template<typename _Up >

complex< _Tp > & std::complex< _Tp >::operator*=

(

const complex< _Up > &

__z

)

Multiply this complex number by z.

Definition at line 294 of file complex.

template<typename _Tp >

complex<_Tp> std::operator+	(	const complex< _Tp > &	__x,
		const complex< _Tp > &	__y
	)		[inline]

Return new complex value x plus y.

Definition at line 321 of file complex.

template<typename _Tp >

complex<_Tp> std::operator+	(	const complex< _Tp > &	__x,
		const _Tp &	__y
	)		[inline]

Return new complex value x plus y.

Definition at line 330 of file complex.

template<typename _Tp >

complex<_Tp> std::operator+	(	const _Tp &	__x,
		const complex< _Tp > &	__y
	)		[inline]

Return new complex value x plus y.

Definition at line 339 of file complex.

template<typename _Tp >

complex<_Tp> std::operator+

(

const complex< _Tp > &

__x

)

[inline]

Return x.

Definition at line 440 of file complex.

template<typename _Tp >

template<typename _Up >

complex< _Tp > & std::complex< _Tp >::operator+=

(

const complex< _Up > &

__z

)

Add z to this complex number.

Definition at line 271 of file complex.

template<typename _Tp >

complex<_Tp> std::operator-	(	const complex< _Tp > &	__x,
		const complex< _Tp > &	__y
	)		[inline]

Return new complex value x minus y.

Definition at line 351 of file complex.

template<typename _Tp >

complex<_Tp> std::operator-	(	const complex< _Tp > &	__x,
		const _Tp &	__y
	)		[inline]

Return new complex value x minus y.

Definition at line 360 of file complex.

template<typename _Tp >

complex<_Tp> std::operator-	(	const _Tp &	__x,
		const complex< _Tp > &	__y
	)		[inline]

Return new complex value x minus y.

Definition at line 369 of file complex.

template<typename _Tp >

complex<_Tp> std::operator-

(

const complex< _Tp > &

__x

)

[inline]

Return complex negation of x.

Definition at line 446 of file complex.

template<typename _Tp >

template<typename _Up >

complex< _Tp > & std::complex< _Tp >::operator-=

(

const complex< _Up > &

__z

)

Subtract z from this complex number.

Definition at line 282 of file complex.

template<typename _Tp >

complex<_Tp> std::operator/	(	const complex< _Tp > &	__x,
		const complex< _Tp > &	__y
	)		[inline]

Return new complex value x divided by y.

Definition at line 411 of file complex.

template<typename _Tp >

complex<_Tp> std::operator/	(	const complex< _Tp > &	__x,
		const _Tp &	__y
	)		[inline]

Return new complex value x divided by y.

Definition at line 420 of file complex.

template<typename _Tp >

complex<_Tp> std::operator/	(	const _Tp &	__x,
		const complex< _Tp > &	__y
	)		[inline]

Return new complex value x divided by y.

Definition at line 429 of file complex.

template<typename _Tp >

complex< _Tp > & std::complex< _Tp >::operator/=

(

const _Tp &

__t

)

Divide this complex number by t.

Definition at line 250 of file complex.

template<typename _Tp >

template<typename _Up >

complex< _Tp > & std::complex< _Tp >::operator/=

(

const complex< _Up > &

__z

)

Divide this complex number by z.

Definition at line 307 of file complex.

References std::norm().

template<typename _Tp , typename _CharT , class _Traits >

basic_ostream<_CharT, _Traits>& std::operator<<	(	basic_ostream< _CharT, _Traits > &	__os,
		const complex< _Tp > &	__x
	)

Insertion operator for complex values.

Definition at line 521 of file complex.

References std::ios_base::flags(), std::basic_ios< _CharT, _Traits >::imbue(), std::ios_base::precision(), and std::basic_ostringstream< _CharT, _Traits, _Alloc >::str().

template<typename _Tp >

complex< _Tp > & std::complex< _Tp >::operator=

(

const _Tp &

__t

)

Assign this complex number to scalar t.

Definition at line 230 of file complex.

template<typename _Tp >

template<typename _Up >

complex< _Tp > & std::complex< _Tp >::operator=

(

const complex< _Up > &

__z

)

Assign this complex number to complex z.

Definition at line 260 of file complex.

template<typename _Tp >

constexpr bool std::operator==	(	const complex< _Tp > &	__x,
		const complex< _Tp > &	__y
	)		[inline]

Return true if x is equal to y.

Definition at line 453 of file complex.

template<typename _Tp >

constexpr bool std::operator==	(	const complex< _Tp > &	__x,
		const _Tp &	__y
	)		[inline]

Return true if x is equal to y.

Definition at line 458 of file complex.

template<typename _Tp >

constexpr bool std::operator==	(	const _Tp &	__x,
		const complex< _Tp > &	__y
	)		[inline]

Return true if x is equal to y.

Definition at line 463 of file complex.

template<typename _Tp , typename _CharT , class _Traits >

basic_istream<_CharT, _Traits>& std::operator>>	(	basic_istream< _CharT, _Traits > &	__is,
		complex< _Tp > &	__x
	)

Extraction operator for complex values.

Definition at line 488 of file complex.

References std::ios_base::failbit, std::basic_istream< _CharT, _Traits >::putback(), and std::basic_ios< _CharT, _Traits >::setstate().

template<typename _Tp >

complex< _Tp > std::polar	(	const _Tp &	__rho,
		const _Tp &	__theta = 0
	)		[inline]

Return complex with magnitude rho and angle theta.

Definition at line 664 of file complex.

References std::cos(), and std::sin().

Referenced by std::pow().

template<typename _Tp >

complex< _Tp > std::pow	(	const complex< _Tp > &	__x,
		const _Tp &	__y
	)

Return x to the y'th power.

Definition at line 986 of file complex.

References std::exp(), std::log(), and std::polar().

Referenced by std::gamma_distribution< _RealType >::operator()(), std::pow(), and std::tr1::pow().

template<typename _Tp >

complex< _Tp > std::pow	(	const complex< _Tp > &	__x,
		const complex< _Tp > &	__y
	)		[inline]

Return x to the y'th power.

Definition at line 1025 of file complex.

template<typename _Tp >

complex< _Tp > std::pow	(	const _Tp &	__x,
		const complex< _Tp > &	__y
	)		[inline]

Return x to the y'th power.

Definition at line 1031 of file complex.

References std::log(), std::polar(), and std::pow().

template<typename _Tp , typename _Up >

std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> std::tr1::pow	(	const std::complex< _Tp > &	__x,
		const _Up &	__y
	)		[inline]

Additional overloads [8.1.9].

Definition at line 349 of file tr1/complex.

References std::pow().

template<typename _Tp >

complex< _Tp > std::sin

(

const complex< _Tp > &

__z

)

[inline]

Return complex sine of z.

Definition at line 819 of file complex.

Referenced by std::polar().

template<typename _Tp >

complex< _Tp > std::sinh

(

const complex< _Tp > &

__z

)

[inline]

Return complex hyperbolic sine of z.

Definition at line 849 of file complex.

template<typename _Tp >

complex< _Tp > std::sqrt

(

const complex< _Tp > &

__z

)

[inline]

Return complex square root of z.

Definition at line 893 of file complex.

Referenced by std::normal_distribution< _RealType >::operator()(), and std::student_t_distribution< _RealType >::operator()().

template<typename _Tp >

complex< _Tp > std::tan

(

const complex< _Tp > &

__z

)

[inline]

Return complex tangent of z.

Definition at line 920 of file complex.

template<typename _Tp >

complex< _Tp > std::tanh

(

const complex< _Tp > &

__z

)

[inline]

Return complex hyperbolic tangent of z.

Definition at line 948 of file complex.