cargf man page on FreeBSD

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```ATAN2(3)		 BSD Library Functions Manual		      ATAN2(3)

NAME
atan2, atan2f, atan2l, carg, cargf, cargl — arc tangent and complex phase
angle functions

LIBRARY
Math Library (libm, -lm)

SYNOPSIS
#include <math.h>

double
atan2(double y, double x);

float
atan2f(float y, float x);

long double
atan2l(long double y, long double x);

#include <complex.h>

double
carg(double complex z);

float
cargf(float complex z);

long double
cargl(long double complex z);

DESCRIPTION
The atan2(), atan2f(), and atan2l() functions compute the principal value
of the arc tangent of y/x, using the signs of both arguments to determine
the quadrant of the return value.

The carg(), cargf(), and cargl() functions compute the complex argument
(or phase angle) of z.  The complex argument is the number θ such that z
= r * e^(I * θ), where r = cabs(z).  The call carg(z) is equivalent to
atan2(cimag(z), creal(z)), and similarly for cargf() and cargl().

RETURN VALUES
The atan2(), atan2f(), and atan2l() functions, if successful, return the
arc tangent of y/x in the range [-π, +π] radians.	Here are some of the
special cases:

atan2(y, x) :=	  atan(y/x)			  if x > 0,
sign(y)*(π - atan(|y/x|))	  if x < 0,
0				  if x = y = 0, or
sign(y)*π/2			  if x = 0 ≠ y.

NOTES
The function atan2() defines "if x > 0," atan2(0, 0) = 0 despite that
previously atan2(0, 0) may have generated an error message.  The reasons
for assigning a value to atan2(0, 0) are these:

1.	Programs that test arguments to avoid computing atan2(0, 0)
must be indifferent to its value.  Programs that require it to
be invalid are vulnerable to diverse reactions to that inva‐
lidity on diverse computer systems.

2.	The atan2() function is used mostly to convert from rectangu‐
lar (x,y) to polar (r,theta) coordinates that must satisfy x =
r∗cos theta and y = r∗sin theta.  These equations are satis‐
fied when (x=0,y=0) is mapped to (r=0,theta=0).	 In general,
conversions to polar coordinates should be computed thus:

r	   := hypot(x,y);  ... := sqrt(x∗x+y∗y)
theta	:= atan2(y,x).

3.	The foregoing formulas need not be altered to cope in a rea‐
sonable way with signed zeros and infinities on a machine that
conforms to IEEE 754; the versions of hypot(3) and atan2()
provided for such a machine are designed to handle all cases.
That is why atan2(±0, -0) = ±π for instance.  In general the
formulas above are equivalent to these:

r := sqrt(x∗x+y∗y); if r = 0 then x := copysign(1,x);

acos(3), asin(3), atan(3), cabs(3), cos(3), cosh(3), math(3), sin(3),
sinh(3), tan(3), tanh(3)

STANDARDS
The atan2(), atan2f(), atan2l(), carg(), cargf(), and cargl() functions
conform to ISO/IEC 9899:1999 (“ISO C99”).

BSD				 July 31, 2008				   BSD
```
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