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PROLOG | NAME | SYNOPSIS | DESCRIPTION | RETURN VALUE | ERRORS | EXAMPLES | APPLICATION USAGE | RATIONALE | FUTURE DIRECTIONS | SEE ALSO | COPYRIGHT |
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ATAN2(3P) POSIX Programmer's Manual ATAN2(3P)
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.
atan2, atan2f, atan2l — arc tangent functions
#include <math.h>
double atan2(double y, double x);
float atan2f(float y, float x);
long double atan2l(long double y, long double x);
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.1‐2017 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.
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.
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.
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
better for special cases; see hypot() for more information.
#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);
}
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.
None.
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.1‐2017, Section 4.20,
Treatment of Error Conditions for Mathematical Functions,
math.h(0p)
Portions of this text are reprinted and reproduced in electronic
form from IEEE Std 1003.1-2017, Standard for Information
Technology -- Portable Operating System Interface (POSIX), The
Open Group Base Specifications Issue 7, 2018 Edition, Copyright
(C) 2018 by the Institute of Electrical and Electronics Engineers,
Inc and The Open Group. 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.opengroup.org/unix/online.html .
Any typographical or formatting errors that appear in this page
are most likely to have been introduced during the conversion of
the source files to man page format. To report such errors, see
https://www.kernel.org/doc/man-pages/reporting_bugs.html .
IEEE/The Open Group 2017 ATAN2(3P)
Pages that refer to this page: math.h(0p), atan(3p), hypot(3p)
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HTML rendering created 2025-09-06 by Michael Kerrisk, author of The Linux Programming Interface. For details of in-depth Linux/UNIX system programming training courses that I teach, look here. Hosting by jambit GmbH. |
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