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NetBSD 6.1.5 - man page for atan2f (netbsd section 3)

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

     atan2, atan2f -- arc tangent function of two variables

     Math Library (libm, -lm)

     #include <math.h>

     atan2(double y, double x);

     atan2f(float y, float x);

     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.

     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.

     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, 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);

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

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

BSD					   May 2, 1991					      BSD

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