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

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

     Math Library (libm, -lm)

     #include <math.h>

     atan2(double y, double x);

     atan2f(float y, float x);

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

     #include <complex.h>

     carg(double complex z);

     cargf(float complex z);

     long double
     cargl(long double complex z);

     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().

     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.

     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)

     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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