std::atan2,std::atan2f,std::atan2l(3)

NAME
std::atan2,std::atan2f,std::atan2l - std::atan2,std::atan2f,std::atan2l

Synopsis
   Defined in header <cmath>
   float atan2 ( float y, float x );
   double atan2 ( double y, double x ); (until C++23)
   long double atan2 ( long double y, long double x );
   /* floating-point-type */
                        (since C++23)
               atan2 ( /* floating-point-type */ y, (constexpr since C++26)
                        (1)
                       /* floating-point-type */ x );
   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)
   Additional overloads (since C++11)
   Defined in header <cmath>
   template< class Integer > (A) (constexpr since C++26)
   double atan2 ( Integer y, Integer x );
   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 (since C++11)
   treated as double.

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
   math-atan2.png
   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 (until C++23)
       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)).
   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 (since C++23)
   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.

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
   asin
   asinf computes arc sine (\({\small\arcsin{x}}\)arcsin(x))
   asinl (function)
   (C++11)
   (C++11)
   acos
   acosf computes arc cosine (\({\small\arccos{x}}\)arccos(x))
   acosl (function)
   (C++11)
   (C++11)
   atan
   atanf computes arc tangent (\({\small\arctan{x}}\)arctan(x))
   atanl (function)
   (C++11)
   (C++11)
   arg returns the phase angle
                        (function template)
   atan2(std::valarray) applies the function std::atan2 to a valarray and a value
                        (function template)
   C documentation for
   atan2