ATAN2(3P) POSIX Programmer's Manual ATAN2(3P)PROLOG
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
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.1‐2008
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
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
Upon successful completion, these functions shall return the arc tan‐
gent 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
If the IEC 60559 Floating-Point option is supported, y/x should be
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
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 bet‐
ter for special cases; see hypot() for more information.
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.
SEE ALSOacos(), asin(), atan(), feclearexcept(), fetestexcept(), hypot(),
isnan(), sqrt(), tan()
The Base Definitions volume of POSIX.1‐2008, Section 4.19, Treatment of
Error Conditions for Mathematical Functions, <math.h>
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 Electri‐
cal 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 .
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IEEE/The Open Group 2013 ATAN2(3P)