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ATAN2(3) FreeBSD 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 theta such
that z = r * e^(I * theta), 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 [-pi, +pi] radians. Here are some of the
special cases:
atan2(y, x) := atan(y/x) if x > 0,
sign(y)*(pi - atan(|y/x|)) if x < 0,
0 if x = y = 0, or
sign(y)*pi/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)
are satisfied 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
reasonable 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) = +-pi 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);
SEE ALSO
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").
FreeBSD 14.0-RELEASE-p11 July 31, 2008 FreeBSD 14.0-RELEASE-p11