complex.cpp File Reference

#include "stlport_prefix.h"
#include <numeric>
#include <cmath>
#include <complex>

Include dependency graph for complex.cpp:

Go to the source code of this file.

Functions
_STLP_BEGIN_NAMESPACE _STLP_TEMPLATE_NULL _STLP_DECLSPEC float _STLP_CALL	abs (const complex< float > &__z)
_STLP_TEMPLATE_NULL _STLP_DECLSPEC double _STLP_CALL	abs (const complex< double > &__z)
_STLP_TEMPLATE_NULL _STLP_DECLSPEC long double _STLP_CALL	abs (const complex< long double > &__z)
_STLP_TEMPLATE_NULL _STLP_DECLSPEC float _STLP_CALL	arg (const complex< float > &__z)
_STLP_TEMPLATE_NULL _STLP_DECLSPEC double _STLP_CALL	arg (const complex< double > &__z)
_STLP_TEMPLATE_NULL _STLP_DECLSPEC long double _STLP_CALL	arg (const complex< long double > &__z)
_STLP_TEMPLATE_NULL _STLP_DECLSPEC complex< float > _STLP_CALL	polar (const float &__rho, const float &__phi)
_STLP_TEMPLATE_NULL _STLP_DECLSPEC complex< double > _STLP_CALL	polar (const double &__rho, const double &__phi)
_STLP_TEMPLATE_NULL _STLP_DECLSPEC complex< long double > _STLP_CALL	polar (const long double &__rho, const long double &__phi)
template<class _Tp >
static void	_divT (const _Tp &__z1_r, const _Tp &__z1_i, const _Tp &__z2_r, const _Tp &__z2_i, _Tp &__res_r, _Tp &__res_i)
template<class _Tp >
static void	_divT (const _Tp &__z1_r, const _Tp &__z2_r, const _Tp &__z2_i, _Tp &__res_r, _Tp &__res_i)
template<class _Tp >
static complex< _Tp >	sqrtT (const complex< _Tp > &z)
complex< float > _STLP_CALL	sqrt (const complex< float > &z)
complex< double > _STLP_CALL	sqrt (const complex< double > &z)
complex< long double > _STLP_CALL	sqrt (const complex< long double > &z)
template<class _Tp >
static complex< _Tp >	expT (const complex< _Tp > &z)
_STLP_DECLSPEC complex< float > _STLP_CALL	exp (const complex< float > &z)
_STLP_DECLSPEC complex< double > _STLP_CALL	exp (const complex< double > &z)
_STLP_DECLSPEC complex< long double > _STLP_CALL	exp (const complex< long double > &z)
template<class _Tp >
static complex< _Tp >	log10T (const complex< _Tp > &z, const _Tp &ln10_inv)
_STLP_DECLSPEC complex< float > _STLP_CALL	log10 (const complex< float > &z)
_STLP_DECLSPEC complex< double > _STLP_CALL	log10 (const complex< double > &z)
_STLP_DECLSPEC complex< long double > _STLP_CALL	log10 (const complex< long double > &z)
template<class _Tp >
static complex< _Tp >	logT (const complex< _Tp > &z)
_STLP_DECLSPEC complex< float > _STLP_CALL	log (const complex< float > &z)
_STLP_DECLSPEC complex< double > _STLP_CALL	log (const complex< double > &z)
_STLP_DECLSPEC complex< long double > _STLP_CALL	log (const complex< long double > &z)
template<class _Tp >
static complex< _Tp >	powT (const _Tp &a, const complex< _Tp > &b)
template<class _Tp >
static complex< _Tp >	powT (const complex< _Tp > &z_in, int n)
template<class _Tp >
static complex< _Tp >	powT (const complex< _Tp > &a, const _Tp &b)
template<class _Tp >
static complex< _Tp >	powT (const complex< _Tp > &a, const complex< _Tp > &b)
_STLP_DECLSPEC complex< float > _STLP_CALL	pow (const float &a, const complex< float > &b)
_STLP_DECLSPEC complex< float > _STLP_CALL	pow (const complex< float > &z_in, int n)
_STLP_DECLSPEC complex< float > _STLP_CALL	pow (const complex< float > &a, const float &b)
_STLP_DECLSPEC complex< float > _STLP_CALL	pow (const complex< float > &a, const complex< float > &b)
_STLP_DECLSPEC complex< double > _STLP_CALL	pow (const double &a, const complex< double > &b)
_STLP_DECLSPEC complex< double > _STLP_CALL	pow (const complex< double > &z_in, int n)
_STLP_DECLSPEC complex< double > _STLP_CALL	pow (const complex< double > &a, const double &b)
_STLP_DECLSPEC complex< double > _STLP_CALL	pow (const complex< double > &a, const complex< double > &b)
_STLP_DECLSPEC complex< long double > _STLP_CALL	pow (const long double &a, const complex< long double > &b)
_STLP_DECLSPEC complex< long double > _STLP_CALL	pow (const complex< long double > &z_in, int n)
_STLP_DECLSPEC complex< long double > _STLP_CALL	pow (const complex< long double > &a, const long double &b)
_STLP_DECLSPEC complex< long double > _STLP_CALL	pow (const complex< long double > &a, const complex< long double > &b)

Variables
static const float	LN10_INVF = 1.f / ::log(10.f)
static const double	LN10_INV = 1. / ::log10(10.)
static const long double	LN10_INVL = 1.l / ::log(10.l)

Function Documentation

_divT() [1/2]

template<class _Tp >

static void _divT ( const _Tp &  __z1_r, const _Tp &  __z1_i, const _Tp &  __z2_r, const _Tp &  __z2_i, _Tp &  __res_r, _Tp &  __res_i  )

static

Definition at line 84 of file complex.cpp.

                                              {
  _Tp __ar = __z2_r >= 0 ? __z2_r : -__z2_r;
  _Tp __ai = __z2_i >= 0 ? __z2_i : -__z2_i;
 
  if (__ar <= __ai) {
    _Tp __ratio = __z2_r / __z2_i;
    _Tp __denom = __z2_i * (1 + __ratio * __ratio);
    __res_r = (__z1_r * __ratio + __z1_i) / __denom;
    __res_i = (__z1_i * __ratio - __z1_r) / __denom;
  }
  else {
    _Tp __ratio = __z2_i / __z2_r;
    _Tp __denom = __z2_r * (1 + __ratio * __ratio);
    __res_r = (__z1_r + __z1_i * __ratio) / __denom;
    __res_i = (__z1_i - __z1_r * __ratio) / __denom;
  }
}

Referenced by complex< double >::_div(), and complex< float >::_div().

_divT() [2/2]

template<class _Tp >

static void _divT ( const _Tp &  __z1_r, const _Tp &  __z2_r, const _Tp &  __z2_i, _Tp &  __res_r, _Tp &  __res_i  )

static

Definition at line 105 of file complex.cpp.

                                              {
  _Tp __ar = __z2_r >= 0 ? __z2_r : -__z2_r;
  _Tp __ai = __z2_i >= 0 ? __z2_i : -__z2_i;
 
  if (__ar <= __ai) {
    _Tp __ratio = __z2_r / __z2_i;
    _Tp __denom = __z2_i * (1 + __ratio * __ratio);
    __res_r = (__z1_r * __ratio) / __denom;
    __res_i = - __z1_r / __denom;
  }
  else {
    _Tp __ratio = __z2_i / __z2_r;
    _Tp __denom = __z2_r * (1 + __ratio * __ratio);
    __res_r = __z1_r / __denom;
    __res_i = - (__z1_r * __ratio) / __denom;
  }
}

abs() [1/3]

_STLP_TEMPLATE_NULL _STLP_DECLSPEC double _STLP_CALL abs

(

const complex< double > &

__z

)

Definition at line 43 of file complex.cpp.

{ return ::hypot(__z._M_re, __z._M_im); }

abs() [2/3]

_STLP_BEGIN_NAMESPACE _STLP_TEMPLATE_NULL _STLP_DECLSPEC float _STLP_CALL abs

(

const complex< float > &

__z

)

Definition at line 40 of file complex.cpp.

{ return ::hypot(__z._M_re, __z._M_im); }

abs() [3/3]

_STLP_TEMPLATE_NULL _STLP_DECLSPEC long double _STLP_CALL abs

(

const complex< long double > &

__z

)

Definition at line 48 of file complex.cpp.

{ return ::hypot(__z._M_re, __z._M_im); }

arg() [1/3]

_STLP_TEMPLATE_NULL _STLP_DECLSPEC double _STLP_CALL arg

(

const complex< double > &

__z

)

Definition at line 59 of file complex.cpp.

{ return ::atan2(__z._M_im, __z._M_re); }

arg() [2/3]

_STLP_TEMPLATE_NULL _STLP_DECLSPEC float _STLP_CALL arg

(

const complex< float > &

__z

)

Definition at line 55 of file complex.cpp.

{ return ::atan2(__z._M_im, __z._M_re); }

arg() [3/3]

_STLP_TEMPLATE_NULL _STLP_DECLSPEC long double _STLP_CALL arg

(

const complex< long double > &

__z

)

Definition at line 64 of file complex.cpp.

{ return ::atan2(__z._M_im, __z._M_re); }

exp() [1/3]

_STLP_DECLSPEC complex< double > _STLP_CALL exp

(

const complex< double > &

z

)

Definition at line 210 of file complex.cpp.

{ return expT(z); }

exp() [2/3]

_STLP_DECLSPEC complex< float > _STLP_CALL exp

(

const complex< float > &

z

)

Definition at line 207 of file complex.cpp.

{ return expT(z); }

exp() [3/3]

_STLP_DECLSPEC complex< long double > _STLP_CALL exp

(

const complex< long double > &

z

)

Definition at line 214 of file complex.cpp.

{ return expT(z); }

expT()

template<class _Tp >

static complex< _Tp > expT ( const complex< _Tp > &  z )

static

Definition at line 202 of file complex.cpp.

                                                {
  _Tp expx = ::exp(z._M_re);
  return complex<_Tp>(expx * ::cos(z._M_im),
                      expx * ::sin(z._M_im));
}

Referenced by exp().

log() [1/3]

_STLP_DECLSPEC complex< double > _STLP_CALL log

(

const complex< double > &

z

)

Definition at line 256 of file complex.cpp.

{ return logT(z); }

log() [2/3]

_STLP_DECLSPEC complex< float > _STLP_CALL log

(

const complex< float > &

z

)

Definition at line 253 of file complex.cpp.

{ return logT(z); }

log() [3/3]

_STLP_DECLSPEC complex< long double > _STLP_CALL log

(

const complex< long double > &

z

)

Definition at line 260 of file complex.cpp.

{ return logT(z); }

log10() [1/3]

_STLP_DECLSPEC complex< double > _STLP_CALL log10

(

const complex< double > &

z

)

Definition at line 234 of file complex.cpp.

{ return log10T(z, LN10_INV); }

log10() [2/3]

_STLP_DECLSPEC complex< float > _STLP_CALL log10

(

const complex< float > &

z

)

Definition at line 230 of file complex.cpp.

{ return log10T(z, LN10_INVF); }

Referenced by log10T().

log10() [3/3]

_STLP_DECLSPEC complex< long double > _STLP_CALL log10

(

const complex< long double > &

z

)

Definition at line 239 of file complex.cpp.

{ return log10T(z, LN10_INVL); }

log10T()

template<class _Tp >

static complex< _Tp > log10T ( const complex< _Tp > &  z, const _Tp &  ln10_inv  )

static

Definition at line 221 of file complex.cpp.

                                                                       {
  complex<_Tp> r;
 
  r._M_im = ::atan2(z._M_im, z._M_re) * ln10_inv;
  r._M_re = ::log10(::hypot(z._M_re, z._M_im));
  return r;
}

Referenced by log10().

logT()

template<class _Tp >

static complex< _Tp > logT ( const complex< _Tp > &  z )

static

Definition at line 246 of file complex.cpp.

                                                {
  complex<_Tp> r;
 
  r._M_im = ::atan2(z._M_im, z._M_re);
  r._M_re = ::log(::hypot(z._M_re, z._M_im));
  return r;
}

Referenced by log().

polar() [1/3]

_STLP_TEMPLATE_NULL _STLP_DECLSPEC complex< double > _STLP_CALL polar	(	const double &	__rho,
		const double &	__phi
	)

Definition at line 73 of file complex.cpp.

{ return complex<double>(__rho * ::cos(__phi), __rho * ::sin(__phi)); }

polar() [2/3]

_STLP_TEMPLATE_NULL _STLP_DECLSPEC complex< float > _STLP_CALL polar	(	const float &	__rho,
		const float &	__phi
	)

Definition at line 70 of file complex.cpp.

{ return complex<float>(__rho * ::cos(__phi), __rho * ::sin(__phi)); }

polar() [3/3]

_STLP_TEMPLATE_NULL _STLP_DECLSPEC complex< long double > _STLP_CALL polar	(	const long double &	__rho,
		const long double &	__phi
	)

Definition at line 78 of file complex.cpp.

{ return complex<long double>(__rho * ::cos(__phi), __rho * ::sin(__phi)); }

pow() [1/12]

_STLP_DECLSPEC complex< double > _STLP_CALL pow	(	const complex< double > &	a,
		const complex< double > &	b
	)

Definition at line 326 of file complex.cpp.

{ return powT(a, b); }

pow() [2/12]

_STLP_DECLSPEC complex< double > _STLP_CALL pow	(	const complex< double > &	a,
		const double &	b
	)

Definition at line 323 of file complex.cpp.

{ return powT(a, b); }

pow() [3/12]

_STLP_DECLSPEC complex< double > _STLP_CALL pow	(	const complex< double > &	z_in,
		int	n
	)

Definition at line 320 of file complex.cpp.

{ return powT(z_in, n); }

pow() [4/12]

_STLP_DECLSPEC complex< float > _STLP_CALL pow	(	const complex< float > &	a,
		const complex< float > &	b
	)

Definition at line 314 of file complex.cpp.

{ return powT(a, b); }

pow() [5/12]

_STLP_DECLSPEC complex< float > _STLP_CALL pow	(	const complex< float > &	a,
		const float &	b
	)

Definition at line 311 of file complex.cpp.

{ return powT(a, b); }

pow() [6/12]

_STLP_DECLSPEC complex< float > _STLP_CALL pow	(	const complex< float > &	z_in,
		int	n
	)

Definition at line 308 of file complex.cpp.

{ return powT(z_in, n); }

pow() [7/12]

_STLP_DECLSPEC complex< long double > _STLP_CALL pow	(	const complex< long double > &	a,
		const complex< long double > &	b
	)

Definition at line 342 of file complex.cpp.

{ return powT(a, b); }

pow() [8/12]

_STLP_DECLSPEC complex< long double > _STLP_CALL pow	(	const complex< long double > &	a,
		const long double &	b
	)

Definition at line 338 of file complex.cpp.

{ return powT(a, b); }

pow() [9/12]

_STLP_DECLSPEC complex< long double > _STLP_CALL pow	(	const complex< long double > &	z_in,
		int	n
	)

Definition at line 335 of file complex.cpp.

{ return powT(z_in, n); }

pow() [10/12]

_STLP_DECLSPEC complex< double > _STLP_CALL pow	(	const double &	a,
		const complex< double > &	b
	)

Definition at line 317 of file complex.cpp.

{ return powT(a, b); }

pow() [11/12]

_STLP_DECLSPEC complex< float > _STLP_CALL pow	(	const float &	a,
		const complex< float > &	b
	)

Definition at line 305 of file complex.cpp.

{ return powT(a, b); }

pow() [12/12]

_STLP_DECLSPEC complex< long double > _STLP_CALL pow	(	const long double &	a,
		const complex< long double > &	b
	)

Definition at line 330 of file complex.cpp.

{ return powT(a, b); }

powT() [1/4]

template<class _Tp >

static complex< _Tp > powT ( const _Tp &  a, const complex< _Tp > &  b  )

static

Definition at line 267 of file complex.cpp.

                                                              {
  _Tp logr = ::log(a);
  _Tp x = ::exp(logr * b._M_re);
  _Tp y = logr * b._M_im;
 
  return complex<_Tp>(x * ::cos(y), x * ::sin(y));
}

Referenced by pow().

powT() [2/4]

template<class _Tp >

static complex< _Tp > powT ( const complex< _Tp > &  a, const _Tp &  b  )

static

Definition at line 286 of file complex.cpp.

                                                              {
  _Tp logr = ::log(::hypot(a._M_re,a._M_im));
  _Tp logi = ::atan2(a._M_im, a._M_re);
  _Tp x = ::exp(logr * b);
  _Tp y = logi * b;
 
  return complex<_Tp>(x * ::cos(y), x * ::sin(y));
}

powT() [3/4]

template<class _Tp >

static complex< _Tp > powT ( const complex< _Tp > &  a, const complex< _Tp > &  b  )

static

Definition at line 296 of file complex.cpp.

                                                                       {
  _Tp logr = ::log(::hypot(a._M_re,a._M_im));
  _Tp logi = ::atan2(a._M_im, a._M_re);
  _Tp x = ::exp(logr * b._M_re - logi * b._M_im);
  _Tp y = logr * b._M_im + logi * b._M_re;
 
  return complex<_Tp>(x * ::cos(y), x * ::sin(y));
}

powT() [4/4]

template<class _Tp >

static complex< _Tp > powT ( const complex< _Tp > &  z_in, int  n  )

static

Definition at line 276 of file complex.cpp.

                                                          {
  complex<_Tp> z = z_in;
  z = _STLP_PRIV __power(z, (n < 0 ? -n : n), multiplies< complex<_Tp> >());
  if (n < 0)
    return _Tp(1.0) / z;
  else
    return z;
}

sqrt() [1/3]

complex< double > _STLP_CALL sqrt

(

const complex< double > &

z

)

Definition at line 191 of file complex.cpp.

{ return sqrtT(z); }

sqrt() [2/3]

complex< float > _STLP_CALL sqrt

(

const complex< float > &

z

)

Definition at line 188 of file complex.cpp.

{ return sqrtT(z); }

Referenced by sqrtT().

sqrt() [3/3]

complex< long double > _STLP_CALL sqrt

(

const complex< long double > &

z

)

Definition at line 195 of file complex.cpp.

{ return sqrtT(z); }

sqrtT()

template<class _Tp >

static complex< _Tp > sqrtT ( const complex< _Tp > &  z )

static

Definition at line 167 of file complex.cpp.

                                                 {
  _Tp re = z._M_re;
  _Tp im = z._M_im;
  _Tp mag = ::hypot(re, im);
  complex<_Tp> result;
 
  if (mag == 0.f) {
    result._M_re = result._M_im = 0.f;
  } else if (re > 0.f) {
    result._M_re = ::sqrt(0.5f * (mag + re));
    result._M_im = im/result._M_re/2.f;
  } else {
    result._M_im = ::sqrt(0.5f * (mag - re));
    if (im < 0.f)
      result._M_im = - result._M_im;
    result._M_re = im/result._M_im/2.f;
  }
  return result;
}

Referenced by sqrt().

Variable Documentation

LN10_INV

const double LN10_INV = 1. / ::log10(10.)

static

Definition at line 233 of file complex.cpp.

Referenced by log10().

LN10_INVF

const float LN10_INVF = 1.f / ::log(10.f)

static

Definition at line 229 of file complex.cpp.

Referenced by log10().

LN10_INVL

const long double LN10_INVL = 1.l / ::log(10.l)

static

Definition at line 238 of file complex.cpp.

Referenced by log10().