atan2l(3) [mojave man page]

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

NAME

     atan2 -- arc tangent function of two variables

SYNOPSIS

     #include <math.h>

     double
     atan2(double y, double x);

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

     float
     atan2f(float y, float x);

DESCRIPTION

     The atan2() function computes the principal value of the arc tangent of y/x, using the signs of both arguments to determine the quadrant of
     the return value.

SPECIAL VALUES

     atan2(+-0, -0) returns +-pi.

     atan2(+-0, +0) returns +-0.

     atan2(+-0, x) returns +-pi for x < 0.

     atan2(+-0, x) returns +-0 for x > 0.

     atan2(y, +-0) returns +pi/2 for y > 0.

     atan2(y, +-0) returns -pi/2 for y < 0.

     atan2(+-y, -infinity) returns +-pi for finite y > 0.

     atan2(+-y, +infinity) returns +-0 for finite y > 0.

     atan2(+-infinity, x) returns +-pi/2 for finite x.

     atan2(+-infinity, -infinity) returns +-3*pi/4.

     atan2(+-infinity, +infinity) returns +-pi/4.

NOTES

     The atan2() function is used mostly to convert from rectangular (x,y) to polar (r,theta) coordinates that must satisfy x = r*cos theta and y
     = r*sin theta.  In general, conversions to polar coordinates should be computed thus:

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

VECTOR OPERATIONS

     If you need to apply the atan2() function to SIMD vectors or arrays, using the following functions provided by the Accelerate.framework may
     give significantly better performance:

     #include <Accelerate/Accelerate.h>

     vFloat atan2f(vFloat y, vFloat x);
     void vvatan2f(float *z, const float *y, const float *x, const int *n);
     void vvatan2(double *z, const double *y, const double *x, const int *n);

SEE ALSO

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

STANDARDS

     The atan2() function conforms to ISO/IEC 9899:2011.

BSD
								 December 11, 2006							       BSD

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

NAME

     atan2, atan2f -- arc tangent function of two variables

LIBRARY

     Math Library (libm, -lm)

SYNOPSIS

     #include <math.h>

     double
     atan2(double y, double x);

     float
     atan2f(float y, float x);

DESCRIPTION

     The atan2() and atan2f() 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.

RETURN VALUES

     The atan2() function, if successful, returns the arc tangent of y/x in the range [-pi, +pi] radians.  If both x and y are zero, the global
     variable errno is set to EDOM.  On the VAX:

     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 on a VAX 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 invalidity on diverse computer systems.

	   2.	The atan2() function is used mostly to convert from rectangular (x,y) to polar (r,theta) coordinates that must satisfy x = r*cos
		theta and y = r*sin theta.  These equations are satisfied when (x=0,y=0) is mapped to (r=0,theta=0) on a VAX.  In general, conver-
		sions 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), cos(3), cosh(3), math(3), sin(3), sinh(3), tan(3), tanh(3)

STANDARDS

     The atan2() function conforms to ANSI X3.159-1989 (``ANSI C89'').

BSD
								    May 2, 1991 							       BSD