atan2 man page on 4.4BSD

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

     atan2 — arc tangent function of two variables

     #include <math.h>

     atan2(double y, double x);

     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.

     The atan2 function, if successful, returns the arc tangent of y/x in the
     range [-π, +π] 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)*(π - atan(|y/x|))	  if x < 0,
			  0				  if x = y = 0, or
			  sign(y)*π/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 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) on a VAX.  In
		general, conversions to polar coordinates should be computed

		      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), cos(3), cosh(3), sin(3), sinh(3), tan(3),
     tanh(3), math(3),

     The atan2() function conforms to ANSI X3.159-1989 (“ANSI C89”).

BSD				 June 4, 1993				   BSD

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