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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 [-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.

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 Distribution      December 11, 2006     4th Berkeley Distribution
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