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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)
		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) = +-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	11.2			 July 31, 2008			  FreeBSD 11.2

NAME | LIBRARY | SYNOPSIS | DESCRIPTION | RETURN VALUES | NOTES | SEE ALSO | STANDARDS

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