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complex(3C++)			       -			 complex(3C++)

Standard C++ Library Copyright 1998, Rogue Wave Software, Inc.

NAME
       complex

	- C++ complex number library

SPECIALIZATIONS
       complex <float>
       complex <double>
       complex <long double>

SYNOPSIS
       #include <complex>
       template <class T>
       class complex;
       class complex<float>;
       class complex<double>;
       class complex<long double>;

DESCRIPTION
       complex<T>  is  a class that supports complex numbers. A complex number
       has a real part and an  imaginary  part.	 The  complex  class  supports
       equality,  comparison  and  basic  arithmetic  operations. In addition,
       mathematical functions  such  as	 exponents,  logarithms,  powers,  and
       square roots are also available.

INTERFACE
       template <class T>
       class complex {

       public:
  typedef T value_type;

  complex (const T& re = T(), const T& im = T());
  complex (const complex&);
  template <class X> complex
    (const complex<X>&);

  T real () const;
  T imag () const;

  complex<T>& operator= (const T&);
  complex<T>& operator+=(const T&);
  complex<T>& operator-=(const T&);
  complex<T>& operator*=(const T&);
  complex<T>& operator/=(const T&);

  template <class X>
   complex<T>& operator= (const complex<X>&);

  template <class X>
   complex<T>& operator+= (const complex<X>&);
  template <class X>
   complex<T>& operator-= (const complex<X>&);
  template <class X>
   complex<T>& operator*= (const complex<X>&);
  template <class X>
   complex<T>& operator/= (const complex<X>&);
};
// Non-member Operators

template<;class T>
complex<;T> operator+ (const complex<T>&,
		      const complex<T>&);
template<;class T>
complex<;T> operator+ (const complex<T>&, T&);
template<;class T>
complex<;T> operator+ (T, const complex<T>&);

template<;class T>
complex<;T> operator- (const complex<T>&,
		      const complex<T>&);
template<;class T>
complex<;T> operator- (const complex<T>&, T&);
template<;classT>
complex<;T> operator- (T, const complex<T>&);

template<;class T>
complex<;T> operator* (const complex<T>&,
		      const complex<T>&);
template<;class T>
complex<;T> operator* (const complex<T>&, T&);
template<;class T>
complex<;T> operator* (T, const complex<T>&);

template<;class T>
complex<;T> operator/ (const complex<T>&,
		      const complex<T>&);
template<;class T>
complex<;T> operator/ (const complex<T>&, T&);
template<;class T>
complex<;T> operator/ (T, const complex<T>&);

template<;class T>
complex<;T> operator+ (const complex<T>&);
template<;class T>
complex<;T> operator- (const complex<T>&);

template<;class T>
bool operator== (const complex<T>&, const complex<T>&);
template<;class T>
bool operator== (const complex<T>&, T&);
template<;class T>
bool operator== (T, const complex<T>&);

template<;class T>
bool operator!= (const complex<T>&, const complex<T>&);
template<;class T>
bool operator!= (const complex<T>&, T&);
template<;class T>
bool operator!= (T, const complex<T>&);

template <;class T, class charT, class traits>
basic_istream<;charT, traits>& operator>>
	      (istream&, complex<T>&);
template <;class T, class charT, class traits>
basic_ostream<;charT, traits>& operator<<
	      (ostream&, const complex<T>&);

// Values
template<;class T> T real (const complex<T>&);
template<;class T> T imag (const complex<T>&);

template<;class T> T abs (const complex<T>&);
template<;class T> T arg (const complex<T>&);
template<;class T> T norm (const complex<T>&);

template<;class T> complex<T> conj (const complex<T>&);
template<;class T> complex<T> polar (const T&, const T&);

// Transcendentals
template<;class T> complex<T> cos (const complex<T>&);
template<;class T> complex<T> cosh (const complex<T>&);
template<;class T> complex<T> exp (const complex<T>&);
template<;class T> complex<T> log (const complex<T>&);

template<;class T> complex<T> log10 (const complex<T>&);

template<;class T> complex<T> pow (const complex<T>&, int);
template<;class T> complex<T> pow (const complex<T>&, T&);
template<;class T> complex<T> pow (const complex<T>&,
				 const complex<T>&);
template<;class T> complex<T> pow (const T&,
				 const complex<T>&);

template<;class T> complex<T> sin (const complex<T>&);
template<;class T> complex<T> sinh (const complex<T>&);
template<;class T> complex<T> sqrt (const complex<T>&);
template<;class T> complex<T> tan (const complex<T>&);
template<;class T> complex<T> tanh (const complex<T>&);

CONSTRUCTORS
       complex
       (const T& re_arg = T(), const T& im_arg = T());

   Constructs an object of class complex, initializing re_arg to the real part
   and im_arg to the imaginary part.

template <;class X> complex
(const complex<X>&);

   Constructs a complex number from another complex number.

ASSIGNMENT OPERATORS
       complex<T>& operator=(const T& v);

   Assigns v to the real part of itself, setting the imaginary part to 0.

complex<;T>& operator+=(const T& v);

   Adds v to the real part of itself, then returns the result.

complex<;T>& operator-=(const T& v);

   Subtracts v from the real part of itself, then returns the result.

complex<;T>& operator*=(const T& v);

   Multiplies v by the real part of itself, then returns the result.

complex<;T>& operator/=(const T& v);

   Divides v by the real part of itself, then returns the result.

template <;class X>
complex<;T>
operator=(const complex<X>& c);

   Assigns c to itself.

template <;class X>
complex<;T>
operator+=(const complex<X>& c);

   Adds c to itself, then returns the result.

template <;class X>
complex<;T>
operator-=(const complex<X>& c);

   Subtracts c from itself, then returns the result.

template <;class X>
complex<;T>
operator*=(const complex<X>& c);

   Multiplies itself by c, then returns the result.

template <;class X>
complex<;T>
operator/=(const complex<X>& c);

   Divides itself by c, then returns the result.

MEMBER FUNCTIONS
       T
       imag() const;

   Returns the imaginary part of the complex number.

T
real() const;

   Returns the real part of the complex number.

NON-MEMBER OPERATORS
       template<class T> complex<T>
       operator+(const complex<T>& lhs,const complex<T>& rhs);
       template<class T> complex<T>
       operator+(const complex<T>& lhs, const T& rhs);
       template<class T> complex<T>
       operator+(const T& lhs, const complex<T>& rhs);

   Returns the sum of lhs and rhs.

template<;class T> complex<T>
operator-(const complex<T>& lhs,const complex<T>& rhs);
template<;class T> complex<T>
operator-(const complex<T>& lhs, const T& rhs);
template<;class T> complex<T>
operator-(const T& lhs, const complex<T>& rhs);

   Returns the difference of lhs and rhs.

template<;class T> complex<T>
operator*(const complex<;T>& lhs,const complex<T>& rhs);
template<;class T> complex<T>
operator*(const complex<;T>& lhs, const T& rhs);
template<;class T> complex<T>
operator* (const T& lhs, const complex<T>& rhs);

   Returns the product of lhs and rhs.

template<;class T> complex<T>
operator/(const complex<T>& lhs,const complex<T>& rhs);
template<;class T> complex<T>
operator/(const complex<T>& lhs, const T& rhs);
template<;class T> complex<T>
operator/(const T& lhs, const complex<T>& rhs);

   Returns the quotient of lhs divided by rhs.

template<;class T> complex<T>
operator+(const complex<;T>& rhs);

   Returns rhs.

template<;class T> complex<T>
operator-(const complex<T>& lhs);

   Returns complex<T>(-lhs.real(), -lhs.imag()).

template<;class T> bool
operator==(const complex<T>& x, const complex<T>& y);

   Returns true if the real and imaginary parts of x and y are equal.

template<;class T> bool
operator==(const complex<T>& x, const T& y);

   Returns true if y is equal to the real part of x and the imaginary part  of
   x is equal to 0.

template<;class T> bool
operator==(const T& x, const complex<T>& y);

   Returns  true if x is equal to the real part of y and the imaginary part of
   y is equal to 0.

template<;class T> bool
operator!=(const complex<T>& x, const complex<T>& y);

   Returns true if either the real or the imaginary part of x and  y  are  not
   equal.

template<;class T> bool
operator!=(const complex<T>& x, const T& y);

   Returns  true if y is not equal to the real part of x or the imaginary part
   of x is not equal to 0.

template<;class T> bool
operator!=(const T& x, const complex<T>& y);

   Returns true if x is not equal to the real part of y or the imaginary  part
   of y is not equal to 0.

template <;class T, class charT, class traits>
	 basic_istream<charT, traits>&
operator>>(basic_istream<charT, traits>& is, complex<T>& x);

   Reads  a complex number x into the input stream is. x may be of the form u,
   (u), or (u,v) where u is the real part and v is the imaginary part. If  bad
   input is encountered, is.setstate(ios::failbit) is called.

template <;class T, class charT, class traits>
	 basic_ostream<charT, traits>&
operator<;<(basic_ostream<charT, traits>& os,
	  const complex<T>& x);

   Returns os << "(" << x.real() << ","	 << x.imag() << ")".

NON-MEMBER FUNCTIONS
template<;class T> T
abs(const complex<;T>& c);

   Returns the absolute value or magnitude of c (the square root of the norm).

template<;class T> T
arg(const complex<;T>& x);

   Returns the phase angle of x or atan2(imag(x), real(x)).

template<;class T> complex<T>
conj(const complex<;T>& c);

   Returns the conjugate of c.

template<;class T> complex<T>
cos(const complex<;T>& c);

   Returns the cosine of c.

template<;class T> complex<T>
cosh(const complex<;T>& c);

   Returns the hyperbolic cosine of c.

template<;class T> complex<T>
exp(const complex<;T>& x);

   Returns e raised to the x power.

template<;class T> T
imag(const complex<;T>& c) const;

   Returns the imaginary part of c.

template<;class T> complex<T>
log(const complex<;T>& x);

   Returns  the	 complex  natural  (base  e) logarithm of x, in the range of a
   strip mathematically unbounded along the real axis and in the interval  [-i
   times  pi,  i  times	 pi ] along the imaginary axis. When x is a nega- tive
   real number, imag(log(x)) is pi.

   The branch cuts are along the negative real axis.

template<;class T> complex<T>
log10(const complex<;T>& x);

   Returns  the	 complex  common  (base	 10)  logarithm	 of  x,	  defined   as
   log(x)/log(10).

   The branch cuts are along the negative real axis.

template<;class T> T
norm(const complex<;T>& c);

   Returns the squared magnitude of c. (The sum of the squares of the real and
   imaginary parts.)

template<;class T> complex<T>
polar(const T& m, const T& a = 0);

   Returns the complex value of a complex number  whose	 magnitude  is	m  and
   phase angle is a, measured in radians.

template<;class T> complex<T>
pow(const complex<;T>& x, int y);
template<;class T> complex<T>
pow(const complex<;T>& x, const T& y);
template<;class T> complex<T>
pow(const complex<;T>& x, const complex<T>& y);
template<;class T> complex<T>
pow(const T& x, const complex<T>& y);

   Returns  x  raised  to  the	y  power;  or,	if called with (0, 0), returns
   complex <T>(1,0). The branch cuts are along the negative real axis.

template<;class T> T
real(const complex<;T>& c);

   Returns the real part of c.

template<;class T> complex<T>
sin(const complex<;T>& c);

   Returns the sine of c.

template<;class T> complex<T>
sinh(const complex<;T>& c);

   Returns the hyperbolic sine of c.

template<;class T> complex<T>
sqrt(const complex<;T>& x);

   Returns the complex square root of x, in the range of the right half-plane.
   If  the  argument is a negative real number, the value returned lies on the
   positive imaginary axis. The branch cuts are along the negative real axis.

template<;class T> complex<T>
tan(const complex<;T>& x);

   Returns the tangent of x.

template<;class T> complex<T>
tanh(const complex<;T>& x);

   Returns the hyperbolic tangent of x.

EXAMPLE
       //
       // complex.cpp
       //
 #include <complex>
 #include <iostream>
using namespace std;

int main()
 {
  complex<double> a(1.2, 3.4);
  complex<double> b(-9.8, -7.6);

  a += b;
  a /= sin(b) * cos(a);
  b *= log(a) + pow(b, a);

  cout << "a = " << a << ", b = " << b << endl;

  return 0;
 }

Program Output

a = (1.42804e-06,-0.0002873), b = (58.2199,69.7354)

WARNINGS
       On compilers that don't support member function templates,  the	arith‐
       metic  operators	 do  not work on any arbitrary type; they work only on
       float, double and long doubles. Also, you can perform binary arithmetic
       only on types that are the same.

       Compilers  that don't support non-converting constructors permit unsafe
       downcasts (for example, long double to double, double  to  float,  long
       double to float).

       If  your compiler does not support namespaces, then you do not need the
       using declaration for std.

Rogue Wave Software		  02 Apr 1998			 complex(3C++)
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