# cabs(3) [opendarwin man page]

CABS(3) BSD Library Functions Manual CABS(3)NAME

cabscomplex absolute value function--SYNOPSIS

#include <math.h> struct {double x, y;} z; double cabs(z);DESCRIPTION

The cabs() function computes the complex absolute value (also called norm, modulus, or magnitude) of z, without undue underflow or overflow. It is specified by cabs(x+iy) = hypot(x, y)SEE ALSO

hypot(3), math(3), sqrt(3), cabsfSTANDARDS

The cabs() function conforms to ISO/IEC 9899:1999(E).4th Berkeley DistributionJanuary 28, 2003 4th Berkeley Distribution

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CABS(3) BSD Library Functions Manual CABS(3)NAME

cabscomplex 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], and has the same sign as the imaginary part of z.-piEXAMPLES

The function foo defined in the example below applies a non-linear rotation 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 coordinates, 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 9899:2011.4th Berkeley DistributionDecember 11, 2006 4th Berkeley Distribution