cabs(3) BSD Library Functions Manual cabs(3)
NAME
cabs -- complex norm (absolute value) function
carg -- complex argument function
SYNOPSIS
#include <complex.h>
double
cabs(double complex z);
long double
cabsl(long double complex z);
float
cabsf(float complex z);
double
carg(double complex z);
long double
cargl(long double complex z);
float
cargf(float complex z);
DESCRIPTION
cabs(z) computes the norm (absolute value) of the complex floating-point
number z.
carg(z) computes the argument (also called phase angle) of the complex
floating-point number z, with a branch cut on the negative real axis.
The result is in the range [-pi, pi], and has the same sign as the imagi-
nary part of z.
EXAMPLES
The function foo defined in the example below applies a non-linear rota-
tion to the complex plane, such that points near the origin are not much
affected, and points far from the origin are rotated by about pi/2.
This is accomplished by using cabs and carg to convert to polar coordi-
nates, then computing the transformation in that coordinate system, and
finally converting back to the usual rectangular coordinate system.
#include <complex.h>
#include <math.h>
double complex foo(double complex z) {
// get the polar coordinates of z
double r = cabs(z);
double theta = carg(z);
// add a value dependent on r to theta
theta += atan(r);
// now change back to rectangular coordinates and
// return the new complex number
return r*cos(theta) + r*sin(theta)*I;
}
SPECIAL VALUES
cabs(x + yi), cabs(y + xi), and cabs(x - yi) are equivalent. This is
used to abbreviate the specification of special values.
cabs(x +- 0i) is equivalent to fabs(x).
cabs(+-inf + yi) returns inf even if y is a NaN.
cabs(x + NaN i) returns NaN, for finite x.
cabs(NaN + NaN i) returns NaN.
carg(-0 +- 0i) returns +-pi.
carg(+0 +- 0i) returns +-0.
carg(x +- 0i) returns +-pi for x < 0.
carg(x +- 0i) returns +-0 for x > 0.
carg(+-0 + yi) returns -pi/2 for y < 0.
carg(+-0 + yi) returns +pi/2 for y > 0.
carg(-inf +- yi) returns +-pi for finite y > 0.
carg(+inf +- yi) returns +-0 for finite y > 0.
carg(x +- inf i) returns +-pi/2 for finite x.
carg(-inf +- inf i) returns +-3*pi/4.
carg(+inf +- inf i) returns +-pi/4.
carg(x + yi) returns NaN if either of x or y is NaN.
NOTES
cabs() and carg() are fully specified in terms of real functions:
cabs(x + iy) = hypot(x,y)
carg(x + iy) = atan2(y,x).
SEE ALSO
hypot(3), atan2(3), fabs(3), complex(3)
STANDARDS
The cabs() and carg() functions conform to ISO/IEC 9899:1999(E).
4th Berkeley Distribution December 11, 2006 4th Berkeley Distribution
Mac OS X 10.6 - Generated Thu Sep 17 20:18:40 CDT 2009