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NAME

atan2, atan2f, atan2l - arc tangent functions

SYNOPSIS

#include <math.h> double atan2(doubley, doublex); float atan2f(floaty, floatx); long double atan2l(long doubley, long doublex);

DESCRIPTION

^[CX] The functionality described on this reference page is aligned with the ISO C standard. Any conflict between therequirements described here and the ISO C standard is unintentional. This volume of POSIX.1-2017 defers to the ISO Cstandard.
These functions shall compute the principal value of the arc tangent ofy/x, using the signs of both arguments todetermine the quadrant of the return value.
An application wishing to check for error situations should seterrno to zero and callfeclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, iferrno is non-zero orfetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

RETURN VALUE

Upon successful completion, these functions shall return the arc tangent ofy/x in the range [-,] radians.
Ify is ±0 andx is < 0, ± shall be returned.
Ify is ±0 andx is > 0, ±0 shall be returned.
Ify is < 0 andx is ±0, -/2 shall be returned.
Ify is > 0 andx is ±0,/2 shall be returned.
Ifx is 0, a pole error shall not occur.
^[MX] Ifeitherx ory is NaN, a NaN shall be returned.
If the correct value would cause underflow, a range error may occur, andatan(),atan2f(), andatan2l() shall return an implementation-defined value no greater in magnitude than DBL_MIN, FLT_MIN,and LDBL_MIN, respectively.
^[MXX]If the IEC 60559 Floating-Point option is supported,y/x should be returned.
^[MX] Ify is ±0 andx is -0, ± shall be returned.
Ify is ±0 andx is +0, ±0 shall be returned.
For finite values of ±y > 0, ifx is -Inf, ± shall bereturned.
For finite values of ±y > 0, ifx is +Inf, ±0 shall be returned.
For finite values ofx, ify is ±Inf, ±/2 shall bereturned.
Ify is ±Inf andx is -Inf, ±3/4 shall be returned.
Ify is ±Inf andx is +Inf, ±/4 shall be returned.
If both arguments are 0, a domain error shall not occur.

ERRORS

These functions may fail if:
Range Error
^[MX]The result underflows.
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, thenerrno shall be set to [ERANGE]. Ifthe integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the underflow floating-point exceptionshall be raised.

The following sections are informative.

EXAMPLES

Converting Cartesian to Polar Coordinates System
The function below usesatan2() to convert a 2d vector expressed in cartesian coordinates (x,y) to thepolar coordinates (rho,theta). There are other ways to compute the angletheta, usingasin()acos(), oratan(). However,atan2() presents here two advantages:
The angle's quadrant is automatically determined.
The singular cases (0,y) are taken into account.
Finally, this example useshypot() rather thansqrt() since it is better for special cases; seehypot() for more information.
#include <math.h>
voidcartesian_to_polar(const double x, const double y,                   double *rho, double *theta    ){    *rho   = hypot (x,y); /* better than sqrt(x*x+y*y) */    *theta = atan2 (y,x);}

APPLICATION USAGE

On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) areindependent of each other, but at least one of them must be non-zero.

RATIONALE

None.

FUTURE DIRECTIONS

None.

CHANGE HISTORY

First released in Issue 1. Derived from Issue 1 of the SVID.

Issue 5

The DESCRIPTION is updated to indicate how an application should check for an error. This text was previously published in theAPPLICATION USAGE section.

Issue 6

Theatan2f() andatan2l() functions are added for alignment with the ISO/IEC 9899:1999 standard.
The DESCRIPTION, RETURN VALUE, ERRORS, and APPLICATION USAGE sections are revised to align with the ISO/IEC 9899:1999standard, and the IEC 60559:1989 standard floating-point extensions over the ISO/IEC 9899:1999 standard are marked.
IEEE Std 1003.1-2001/Cor 2-2004, item XSH/TC2/D6/18 is applied, adding to the EXAMPLES section.