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

 

C++

Language

Standard Library Headers

Freestanding and hosted implementations

Named requirements

Language support library

Concepts library (C++20)

Diagnostics library

Utilities library

Strings library

Containers library

Iterators library

Ranges library (C++20)

Algorithms library

Numerics library

Input/output library

Localizations library

Regular expressions library (C++11)

Atomic operations library (C++11)

Thread support library (C++11)

Filesystem library (C++17)

Technical Specifications

 

Numerics library

Common mathematical functions

Mathematical special functions (C++17)

Mathematical constants (C++20)

Floating-point environment (C++11)

Complex numbers

Numeric arrays

Pseudo-random number generation

Compile-time rational arithmetic (C++11)

Numeric algorithms

gcd (C++17)

lcm (C++17)

Interpolations

midpoint (C++20)

lerp (C++20)

Generic numeric operations

iota (C++11)

accumulate

inner_product

adjacent_difference

partial_sum

reduce (C++17)

transform_reduce (C++17)

inclusive_scan (C++17)

exclusive_scan (C++17)

transform_inclusive_scan (C++17)

transform_exclusive_scan (C++17)

Bit operations

bit_cast (C++20)

has_single_bit (C++20)

bit_ceil (C++20)

bit_floor (C++20)

bit_width (C++20)

rotl (C++20)

rotr (C++20)

countl_zero (C++20)

countl_one (C++20)

countr_zero (C++20)

countr_one (C++20)

popcount (C++20)

endian (C++20)

 

Common mathematical functions

Functions
Basic operations
abs(int)labsllabsimaxabs (C++11) abs(float)fabs divldivlldivimaxdiv (C++11) fmod	remainder (C++11) remquo (C++11) fma (C++11) fmax (C++11) fmin (C++11) fdim (C++11) nannanfnanl (C++11)(C++11)(C++11)
Exponential functions
exp exp2 (C++11) expm1 (C++11)	log log10 log1p (C++11) log2 (C++11)
Power functions
sqrt cbrt (C++11)	hypot (C++11) pow
Trigonometric and hyperbolic functions
sin cos tan asin acos atan atan2	sinh cosh tanh asinh (C++11) acosh (C++11) atanh (C++11)

Error and gamma functions
erf (C++11) erfc (C++11)	lgamma (C++11) tgamma (C++11)
Nearest integer floating point operations
ceil floor roundlroundllround (C++11)(C++11)(C++11)	trunc (C++11) nearbyint (C++11) rintlrintllrint (C++11)(C++11)(C++11)
Floating point manipulation functions
ldexp scalbnscalbln (C++11)(C++11) ilogb (C++11) logb (C++11)	frexp modf nextafternexttoward (C++11)(C++11) copysign (C++11)
Classification/Comparison
fpclassify (C++11) isfinite (C++11) isinf (C++11) isnan (C++11) isnormal (C++11) signbit (C++11)	isgreater (C++11) isgreaterequal (C++11) isless (C++11) islessequal (C++11) islessgreater (C++11) isunordered (C++11)
Macro constants
HUGE_VALFHUGE_VALHUGE_VALL (C++11)(C++11) INFINITY (C++11) NAN (C++11) math_errhandlingMATH_ERRNOMATH_ERREXCEPT (C++11)	FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C++11)(C++11)(C++11)(C++11)(C++11)

 

Defined in header <cmath>
	(1)
float       atan2 ( float y, float x );
float       atan2f( float y, float x );			(since C++11)
double      atan2 ( double y, double x );		(2)
		(3)
long double atan2 ( long double y, long double x );
long double atan2l( long double y, long double x );				(since C++11)
Promoted    atan2 ( Arithmetic1 y, Arithmetic2 x );			(4)	(since C++11)

1-3) Computes the arc tangent of y/x using the signs of arguments to determine the correct quadrant.

4) A set of overloads or a function template for all combinations of arguments of arithmetic type not covered by 1-3). If any argument has integral type, it is cast to double. If any argument is long double, then the return type Promoted is also long double, otherwise the return type is always double.

Parameters

x, y

-

values of floating-point or integral types

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<double>(x,y))

POSIX specifies that in case of underflow, y/x is the value returned, and if that is not supported, and implementation-defined value no greater than DBL_MIN, FLT_MIN, and LDBL_MIN is returned.

Example

Run this code

#include <iostream>
#include <cmath>
 
int main()
{
    // normal usage: the signs of the two arguments determine the quadrant
    std::cout << "(x:+1,y:+1) cartesian is (r:" << hypot(1,1)
              << ",phi:" << atan2(1,1) << ") polar\n"  // atan2(1,1) = +pi/4, Quad I
              << "(x:-1,y:+1) cartesian is (r:" << hypot(1,-1)
              << ",phi:" << atan2(1,-1) << ") polar\n" // atan2(1, -1) = +3pi/4, Quad II
              << "(x:-1,y:-1) cartesian is (r:" << hypot(-1,-1)
              << ",phi:" << atan2(-1,-1) << ") polar\n" // atan2(-1,-1) = -3pi/4, Quad III
              << "(x:+1,y:-1) cartesian is (r:" << hypot(-1,1)
              << ",phi:" << atan2(-1,1) << ") polar\n"; // atan2(-1, 1) = -pi/4, Quad IV
    // special values
    std::cout << "atan2(0, 0) = " << atan2(0,0)
              << " atan2(0,-0) = " << atan2(0,-0.0) << '\n'
              << "atan2(7, 0) = " << atan2(7,0)
              << " 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

asinasinfasinl (C++11)(C++11)	computes arc sine (\({\small\arcsin{x} }\)arcsin(x)) (function)
acosacosfacosl (C++11)(C++11)	computes arc cosine (\({\small\arccos{x} }\)arccos(x)) (function)
atanatanfatanl (C++11)(C++11)	computes arc tangent (\({\small\arctan{x} }\)arctan(x)) (function)
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