```ATAN2(3P)                 POSIX Programmer's Manual                ATAN2(3P)
```

## PROLOG         top

```       This manual page is part of the POSIX Programmer's Manual.  The Linux
implementation of this interface may differ (consult the
corresponding Linux manual page for details of Linux behavior), or
the interface may not be implemented on Linux.
```

## NAME         top

```       atan2, atan2f, atan2l — arc tangent functions
```

## SYNOPSIS         top

```       #include <math.h>

double atan2(double y, double x);
float atan2f(float y, float x);
long double atan2l(long double y, long double x);
```

## DESCRIPTION         top

```       The functionality described on this reference page is aligned with
the ISO C standard. Any conflict between the requirements described
here and the ISO C standard is unintentional. This volume of
POSIX.1‐2008 defers to the ISO C standard.

These functions shall 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.

An application wishing to check for error situations should set errno
to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these
functions. On return, if errno is non-zero or fetestexcept(FE_INVALID
| FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error
has occurred.
```

## RETURN VALUE         top

```       Upon successful completion, these functions shall return the arc
tangent of y/x in the range [−π,π] radians.

If y is ±0 and x is < 0, ±π shall be returned.

If y is ±0 and x is > 0, ±0 shall be returned.

If y is < 0 and x is ±0, −π/2 shall be returned.

If y is > 0 and x is ±0, π/2 shall be returned.

If x is 0, a pole error shall not occur.

If either x or y is NaN, a NaN shall be returned.

If the correct value would cause underflow, a range error may occur,
and atan(), atan2f(), and atan2l() shall return an implementation-
defined value no greater in magnitude than DBL_MIN, FLT_MIN, and
LDBL_MIN, respectively.

If the IEC 60559 Floating-Point option is supported, y/x should be
returned.

If y is ±0 and x is −0, ±π shall be returned.

If y is ±0 and x is +0, ±0 shall be returned.

For finite values of ±y > 0, if x is −Inf, ±π shall be returned.

For finite values of ±y > 0, if x is +Inf, ±0 shall be returned.

For finite values of x, if y is ±Inf, ±π/2 shall be returned.

If y is ±Inf and x is −Inf, ±3π/4 shall be returned.

If y is ±Inf and x is +Inf, ±π/4 shall be returned.

If both arguments are 0, a domain error shall not occur.
```

## ERRORS         top

```       These functions may fail if:

Range Error The result underflows.

If the integer expression (math_errhandling & MATH_ERRNO)
is non-zero, then errno shall be set to [ERANGE].  If the
integer expression (math_errhandling & MATH_ERREXCEPT) is
non-zero, then the underflow floating-point exception
shall be raised.

The following sections are informative.
```

## EXAMPLES         top

```   Converting Cartesian to Polar Coordinates System
The function below uses atan2() to convert a 2d vector expressed in
cartesian coordinates (x,y) to the polar coordinates (rho,theta).
There are other ways to compute the angle theta, using asin() acos(),
or atan().  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 uses hypot() rather than sqrt() since it is

#include <math.h>

void
cartesian_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         top

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

## RATIONALE         top

```       None.
```

## FUTURE DIRECTIONS         top

```       None.
```

```       acos(3p), asin(3p), atan(3p), feclearexcept(3p), fetestexcept(3p),
hypot(3p), isnan(3p), sqrt(3p), tan(3p)

The Base Definitions volume of POSIX.1‐2008, Section 4.19, Treatment
of Error Conditions for Mathematical Functions, math.h(0p)
```

```       Portions of this text are reprinted and reproduced in electronic form
from IEEE Std 1003.1, 2013 Edition, Standard for Information
Technology -- Portable Operating System Interface (POSIX), The Open
Group Base Specifications Issue 7, Copyright (C) 2013 by the
Institute of Electrical and Electronics Engineers, Inc and The Open
Group.  (This is POSIX.1-2008 with the 2013 Technical Corrigendum 1
applied.) In the event of any discrepancy between this version and
the original IEEE and The Open Group Standard, the original IEEE and
The Open Group Standard is the referee document. The original
Standard can be obtained online at http://www.unix.org/online.html .