From cppreference.com
Defined in header
floatatan2(floaty,floatx);doubleatan2(doubley,doublex);longdoubleatan2(longdoubley,longdoublex); (1)(until C++23)/*floating-point-type*/atan2(/*floating-point-type*/y,/*floating-point-type*/x);(since C++23)
(constexpr since C++26)floatatan2f(floaty,floatx); (2)(since C++11)
(constexpr since C++26)longdoubleatan2l(longdoubley,longdoublex); (3)(since C++11)
(constexpr since C++26)
(since C++26)
Defined in header
template<classV0,classV1>constexpr/*math-common-simd-t*/<V0,V1>atan2(constV0&v_y,constV1&v_x); (S) (since C++26)
(since C++11)
Defined in header
template<classInteger>doubleatan2(Integery,Integerx); (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)
S) The SIMD overload performs an element-wise std::atan2 on v_yand v_x.
(See
for its definition.)(since C++26)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(yx)
) 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
.
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)).
that in case of underflow, the value y/x is returned, and if that is not supported, an implementation-defined value no greater than
,
, and
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 longdouble, then std::atan2(num1,num2) has the same effect as std::atan2(static_cast<longdouble>(num1),
static_cast<longdouble>(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
does not result in a usable candidate from the overloads provided.
(since C++23)Example
Run this code
#include<cmath>#include<iostream>voidprint_coordinates(intx,inty){std::cout<<std::showpos<<"(x:"<<x<<", y:"<<y<<") cartesian is "<<"(r:"<<std::hypot(x,y)<<", phi:"<<std::atan2(y,x)<<") polar\n";}intmain(){// normal usage: the signs of the two arguments determine the quadrantprint_coordinates(+1,+1);// atan2( 1, 1) = +pi/4, Quad Iprint_coordinates(-1,+1);// atan2( 1, -1) = +3pi/4, Quad IIprint_coordinates(-1,-1);// atan2(-1, -1) = -3pi/4, Quad IIIprint_coordinates(+1,-1);// atan2(-1, 1) = -pi/4, Quad IV// special valuesstd::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
to a valarray and a value
(function template)
for atan2