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

^[CX] 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.1-2024 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.

^[MX] 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. ^[MXX]  If the IEC 60559 Floating-Point option is supported, y/x should be returned.

^[MX] 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

^[MX] 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.

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

XBD 4.23 Treatment of Error Conditions for Mathematical Functions, <math.h>

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 the APPLICATION USAGE section.

Issue 6

The atan2f() and atan2l() 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 9899:1999 standard, 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.

Issue 7

POSIX.1-2008, Technical Corrigendum 1, XSH/TC1-2008/0038 [68,428] is applied.

Issue 8

Austin Group Defect 1178 is applied, removing MX shading from a paragraph in the RETURN VALUE section and joining it with the following paragraph.