ATAN2(3P)

πŸ“¦ version 2017a, in alpine 3.22, alpine 3.23, alpine 3.24, arch rolling, nixpkgs unstable, opensuse-leap 16.0

🌸 ATAN2(3P) β€” POSIX Programmer's Manual 🌸

okay bestie, welcome to the POSIX Programmer's Manual πŸ’– we're doing trig today and honestly? it's giving ✨geometry✨

πŸ’« PROLOG πŸ’«

Real talk first: this manual page is part of the POSIX Programmer's Manual. The Linux implementation of this interface may differ (so like, go consult the corresponding Linux manual page for the deets on Linux behavior), or β€” plot twist β€” the interface might not even be implemented on Linux at all. πŸ™ˆ

πŸ‘‘ NAME πŸ‘‘

atan2, atan2f, atan2l β€” arc tangent functions πŸŽ€

✨ 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);

three flavors, one vibe. pick your precision. πŸ’…

πŸ¦‹ DESCRIPTION πŸ¦‹

so the functionality described on this reference page is aligned with the ISO C standard. if there's any conflict between what's required here and what the ISO C standard says, that conflict is unintentional β€” no drama intended. this volume of POSIX.1‐2017 defers to the ISO C standard, periodt.

These functions shall compute the principal value of the arc tangent of y/x, using the signs of both arguments to figure out which quadrant the return value lives in. yesss, both signs matter, that's the whole point of this function, don't skip it 🫢

okay and if your application wants to check for error situations, here's the little ritual: set errno to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these functions. then on return, if errno is non-zero or fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred. πŸ”

🌈 RETURN VALUE 🌈

Upon successful completion, these functions shall return the arc tangent of y/x in the range [-Ο€,Ο€] radians. ✨

now the special cases, and bestie there are a lot of them, so buckle up:

  • If y is Β±0 and x is < 0, Β±Ο€ shall be returned.
  • If y is Β±0 and x is > 0, Β±0 shall be returned.
  • If y is < 0 and x is Β±0, -Ο€/2 shall be returned.
  • If y is > 0 and x is Β±0, Ο€/2 shall be returned.
  • If x is 0, a pole error shall not occur. (iconic behavior honestly)
  • 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 Β±0 and x is -0, Β±Ο€ shall be returned.
  • If y is Β±0 and x is +0, Β±0 shall be returned.
  • For finite values of Β±y > 0, if x is -Inf, Β±Ο€ shall be returned.
  • For finite values of Β±y > 0, if x is +Inf, Β±0 shall be returned.
  • For finite values of x, if y is Β±Inf, Β±Ο€/2 shall be returned.
  • If y is Β±Inf and x is -Inf, Β±3Ο€/4 shall be returned.
  • If y is Β±Inf and x is +Inf, Β±Ο€/4 shall be returned.
  • If both arguments are 0, a domain error shall not occur.
πŸ’€ zero and infinity edge cases really said "we contain multitudes" and they were right

πŸ”₯ ERRORS πŸ”₯

These functions may fail if:

  • Range Error β€” 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. (so like, the juicy lore, not the law πŸ’…)

🧚 EXAMPLES 🧚

πŸ“ 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. πŸ‘‘
  • 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. no cap.

πŸŽ€ RATIONALE πŸŽ€

None.

the void. the silence. we respect it 🫢

⭐ FUTURE DIRECTIONS ⭐

None.

πŸ’œ SEE ALSO πŸ’œ

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>

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 .

and that's the whole page, bestie!! πŸ’–βœ¨πŸŽ€

this absolute banger of a page dropped via IEEE/The Open Group, 2017 β€” and yes, ATAN2(3P) is the name, the legend, the moment. go forth and compute your quadrants correctly. mwah πŸ’…πŸ¦‹

πŸ“¦ where this page comes from