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.

NAME
atan2, atan2f, atan2l — arc tangent functions

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);

DESCRIPTION
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.

RETURN VALUE
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
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

  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);
    }

APPLICATION USAGE
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
None.

FUTURE DIRECTIONS
None.

SEE ALSO
acos(), asin(), atan(), feclearexcept(), fetestexcept(), hypot(), isnan(), sqrt(), tan()

The Base Definitions volume of POSIX.1-2017, Section 4.20, Treatment of Error Conditions for Mathematical Functions, <math.h>

COPYRIGHT
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 .

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