функции арктангенса (arc tangent functions)
Пролог (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.
Имя (Name)
atan2, atan2f, atan2l — arc tangent functions
Синопсис (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);
Описание (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.
Возвращаемое значение (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.
Ошибки (Error)
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.
Примеры (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);
}
Использование в приложениях (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.
Обоснование (Rationale)
None.
Будущие направления (Future directions)
None.
Смотри также (See also)
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)
