NAME
cplxexp, exp, log, log10, pow, sqrt - functions in the C++
complex number math library
SYNOPSIS
#include <complex.h>
class complex {
public:
friend complex exp(const complex);
friend complex log(const complex);
friend complex log10(const complex);
friend complex pow(double base, const complex exp);
friend complex pow(const complex base, int exp);
friend complex pow(const complex base, double exp);
friend complex pow(const complex base, const complex exp);
friend complex sqrt(const complex);
... // remainder not shown here
};
DESCRIPTION
These functions are versions of the corresponding floating-
point math library functions, overloaded for use with com-
plex numbers.
complex z = exp(x)
Returns e raised to the x power, where x is a complex
number, and e is the base of the natural logarithms.
complex z = log(x)
Returns the natural logarithm (base e) of x, where x is
a complex number.
complex z = log10(x)
Returns the common logarithm (base 10) of x, where x is
a complex number.
complex z = pow(x, y)
Returns x raised to the y power, where x or y (or both)
are complex numbers. The library provides versions of
this function optimized for various combinations of
integer, floating-point, and complex arguments.
complex z = sqrt(x)
Returns the square root of x, where x is a complex
number. The real part of the result will be non-
negative.
SEE ALSO
cplx.intro(3C++), cartpol(3C++), cplxerr(3C++),
cplxops(3C++), cplxtrig(3C++), intro(2), C++ Library Refer-
ence Manual, Chapter 3, "The Complex Arithmetic Library."
DIAGNOSTICS
exp(x)
If the real part of x is small enough or the imaginary
part is large enough to cause overflow, exp() returns
(0,0). If the real part is large enough to cause over-
flow, returns a value depending on the sine and cosine
of the imaginary part of x:
______________________________________________
| x.imag()| x.imag()| returned value |
|_________|__________|________________________|
| sin>=0 | cos>=0 | (HUGE_VAL, HUGE_VAL) |
|_________|__________|________________________|
| sin< 0 | cos>=0 | (HUGE_VAL, -HUGE_VAL)|
|_________|__________|________________________|
| sin>=0 | cos< 0 | (-HUGE_VAL, HUGE_VAL) |
|_________|__________|________________________|
| sin< 0 | cos< 0 | (-HUGE_VAL, -HUGE_VAL)|
|_________|__________|________________________|
In all cases, errno is set to ERANGE (see intro(2)).
log(x), log10(x)
If x is (0,0), returns (-HUGE_VAL, 0), sets errno to
EDOM (see intro(2)), and generates a SING error (see
cplxerr(3C++)).
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