CABS(3) BSD Library Functions Manual CABS(3)NAMEcabs — 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);
DESCRIPTIONcabs(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 [-π, π], 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.
NOTEScabs() and carg() are fully specified in terms of real functions:
cabs(x + iy) = hypot(x,y)
carg(x + iy) = atan2(y,x).
SEE ALSOhypot(3), atan2(3), fabs(3), complex(3)STANDARDS
The cabs() and carg() functions conform to ISO/IEC 9899:2011.
4th Berkeley Distribution December 11, 2006 4th Berkeley Distribution