std:: atan2, std:: atan2f, std:: atan2l

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Defined in header <cmath>
(1)
float atan2 ( float y, float x ) ;

double atan2 ( double y, double x ) ;

long double atan2 ( long double y, long double x ) ;
(until C++23)
/* floating-point-type */

atan2 ( /* floating-point-type */ y,

/* floating-point-type */ x ) ;
(since C++23)
(constexpr since C++26)
float atan2f ( float y, float x ) ;
(2) (since C++11)
(constexpr since C++26)
long double atan2l ( long double y, long double x ) ;
(3) (since C++11)
(constexpr since C++26)
Defined in header <cmath>
template < class Integer >
double atan2 ( Integer y, Integer x ) ;
(A) (constexpr since C++26)
1-3) 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. (since C++23)
A) Additional overloads are provided for all integer types, which are treated as double .
(since C++11)

Parameters

y, x - floating-point or integer values

Return value

If no errors occur, the arc tangent of y / x ( arctan(
y
x
) ) in the range [-π, +π] radians, is returned.
y argument
Return value
x argument

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 and y are both zero, domain error does not occur.
  • If x and y are both zero, range error does not occur either.
  • If y is zero, pole error does not occur.
  • If y is ±0 and x is negative or -0, ±π is returned.
  • If y is ±0 and x is positive or +0, ±0 is returned.
  • If y is ±∞ and x is finite, ±π/2 is returned.
  • If y is ±∞ and x is -∞, ±3π/4 is returned.
  • If y is ±∞ and x is +∞, ±π/4 is returned.
  • If x is ±0 and y is negative, -π/2 is returned.
  • If x is ±0 and y is positive, +π/2 is returned.
  • If x is -∞ and y is finite and positive, +π is returned.
  • If x is -∞ and y is finite and negative, -π is returned.
  • If x is +∞ and y is finite and positive, +0 is returned.
  • If x is +∞ and y is finite and negative, -0 is returned.
  • If either x is NaN or y 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, the value y / x is 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 (A) . 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 ) )     .
  • Otherwise, if 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 ) )     .
(until 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.

(since C++23)

Example

Run this code 
#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';
}

Output: 

(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

See also

(C++11) (C++11)
computes arc sine ( arcsin(x) )
(function)
(C++11) (C++11)
computes arc cosine ( arccos(x) )
(function)
(C++11) (C++11)
computes arc tangent ( arctan(x) )
(function)
returns the phase angle
(function template)
applies the function std::atan2 to a valarray and a value
(function template)
C documentation for atan2
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