Atan2
Defined in header <cmath>
.
Description
Computes the arc tangent of y / x
using the signs of arguments to determine the correct quadrant.
The library provides overloads of std::atan2 for all cv-unqualified floating-point types as the type of the parameters y
and x
(od C++23).
Additional Overloads are provided for all other combinations of arithmetic types (od C++11).
Declarations
- C++23
- C++11
// 1)
/* floating-point-type */ atan2( /* floating-point-type */ y,
/* floating-point-type */ x );
// 2)
float atan2f( float y, float x );
// 3)
long double atan2l( long double y, long double x );
// 4)
template< class Arithmetic1, class Arithmetic2 >
/* common-floating-point-type */ atan2( Arithmetic1 y, Arithmetic2 x );
// 1)
float atan2 ( float y, float x );
// 2)
double atan2 ( double y, double x );
// 3)
long double atan2 ( long double y, long double x );
// 4)
float atan2f( float y, float x );
// 5)
long double atan2l( long double y, long double x );
// 6)
template< class Arithmetic1, class Arithmetic2 >
/* common-floating-point-type */ atan2( Arithmetic1 y, Arithmetic2 x );
Parameters
y
, x
- floating-point or integer values
Return value
If no errors occur, the arc tangent of y / x
(arctan(x/y)) in the range [-π, +π]
radians, is returned.
If a domain error occurs, an implementation-defined value is returned (NaN where supported).
If a range error occurs due to underflow, the correct result (after rounding) is returned.
Error handling
Errors are reported as specified in math_errhandling.
Domain error may occur if x
and y
are both zero.
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
- If
x
andy
are both zero, domain error does not occur - If
x
andy
are both zero, range error does not occur either - If
y
is zero, pole error does not occur - If
y
is±0
andx
is negative or-0
,±π
is returned - If
y
is±0
andx
is positive or+0
,±0
is returned - If
y
is±∞
andx
is finite,±π/2
is returned - If
y
is±∞
andx
is-∞
,±3π/4
is returned - If
y
is±∞
andx
is+∞
,±π/4
is returned - If
x
is±0
andy
is negative,-π/2
is returned - If
x
is±0
andy
is positive,+π/2
is returned - If
x
is-∞
andy
is finite and positive,+π
is returned - If
x
is-∞
andy
is finite and negative,-π
is returned - If
x
is+∞
andy
is finite and positive,+0
is returned - If
x
is+∞
andy
is finite and negative,-0
is returned - If either
x
is NaN ory
is NaN, NaN is returned
Notes
std::atan2(y, x)
is equivalent to
std::arg(std::complex<std::common_type_t<decltype(x), decltype(y)>>(x, y))
POSIX
specifies that in case of underflow, y / x
is the value returned, and if that is not supported, an implementation-defined value no
greater than DBL_MIN
, FLT_MIN
, and LDBL_MIN
is returned.
The additional overloads are not required to be provided exactly as Additional Overloads.
They only need to be sufficient to ensure that for their first argument num1
and second argument num2
:
If num1
or num2
has type long double, then
std::atan2(num1, num2)
has the same effect as
std::atan2(static_cast<long double>(num1), static_cast<long double>(num2))
.
Otherwise, if num1
and/or num2
has type double or an integer type, then
std::atan2(num1, num2)
has the same effect as
std::atan2(static_cast<double>(num1), static_cast<double>(num2))
.
num1
or num2
has type float
, then std::atan2(num1, num2)
has the same effect as
std::atan2(static_cast<float>(num1), static_cast<float>(num2))
. (do C++23)
If num1
and num2
have arithmetic types, then
std::atan2(num1, num2)
has the same effect as
std::atan2(static_cast</* common-floating-point-type */>(num1), static_cast</* common-floating-point-type */>(num2))
.
where /* common-floating-point-type */ is the floating-point type with the greatest floating-point conversion rank and
greatest floating-point conversion subrank between the types of num1
and num2
,
arguments of integer type are considered to have the same floating-point conversion rank as double.
If no such floating-point type with the greatest rank and subrank exists, then overload resolution does not result in a usable candidate from the overloads provided.
Examples
#include <cmath>
#include <iostream>
void print_coordinates(int x, int y)
{
std::cout
<< std::showpos
<< "(x:" << x << ", y:"
<< y << ") cartesian is "
<< "(r:" << std::hypot(x, y)
<< ", phi:" << std::atan2(y, x)
<< ") polar\n";
}
int main()
{
// normal usage: the signs of the two arguments determine the quadrant
print_coordinates(+1, +1);
// atan2( 1, 1) = +pi/4, Quad I
print_coordinates(-1, +1);
// atan2( 1, -1) = +3pi/4, Quad II
print_coordinates(-1, -1);
// atan2(-1, -1) = -3pi/4, Quad III
print_coordinates(+1, -1);
// atan2(-1, 1) = -pi/4, Quad IV
// special values
std::cout
<< std::noshowpos
<< "atan2(0, 0) = "
<< atan2(0, 0) << '\n'
<< "atan2(0,-0) = "
<< atan2(0, -0.0) << '\n'
<< "atan2(7, 0) = "
<< atan2(7, 0) << '\n'
<< "atan2(7,-0) = "
<< atan2(7, -0.0) << '\n';
}
(x:+1, y:+1) cartesian is (r:1.41421, phi:0.785398) polar
(x:-1, y:+1) cartesian is (r:1.41421, phi:2.35619) polar
(x:-1, y:-1) cartesian is (r:1.41421, phi:-2.35619) polar
(x:+1, y:-1) cartesian is (r:1.41421, phi:-0.785398) polar
atan2(0, 0) = 0
atan2(0,-0) = 3.14159
atan2(7, 0) = 1.5708
atan2(7,-0) = 1.5708