/C

# atan2, atan2f, atan2l

Defined in header `<math.h>`
`float       atan2f( float y, float x );`
(1) (since C99)
`double      atan2( double y, double x );`
(2)
`long double atan2l( long double y, long double x );`
(3) (since C99)
Defined in header `<tgmath.h>`
`#define atan2( arg )`
(4) (since C99)
1-3) Computes the arc tangent of `y/x` using the signs of arguments to determine the correct quadrant.
4) Type-generic macro: If the argument has type `long double`, `atan2l` is called. Otherwise, if the argument has integer type or the type `double`, `atan2` is called. Otherwise, `atan2f` is called.

### Parameters

 x, y - floating point value

### 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.

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

`atan2(y, x)` is equivalent to `carg(x + I*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.

### Example

```#include <stdio.h>
#include <math.h>

int main(void)
{
// normal usage: the signs of the two arguments determine the quadrant
// atan2(1,1) = +pi/4, Quad I
printf("(+1,+1) cartesian is (%f,%f) polar\n", hypot( 1, 1), atan2( 1, 1));
// atan2(1, -1) = +3pi/4, Quad II
printf("(+1,-1) cartesian is (%f,%f) polar\n", hypot( 1,-1), atan2( 1,-1));
// atan2(-1,-1) = -3pi/4, Quad III
printf("(-1,-1) cartesian is (%f,%f) polar\n", hypot(-1,-1), atan2(-1,-1));
// atan2(-1,-1) = -pi/4, Quad IV
printf("(-1,+1) cartesian is (%f,%f) polar\n", hypot(-1, 1), atan2(-1, 1));

// special values
printf("atan2(0, 0) = %f atan2(0, -0)=%f\n", atan2(0,0), atan2(0,-0.0));
printf("atan2(7, 0) = %f atan2(7, -0)=%f\n", atan2(7,0), atan2(7,-0.0));
}```

Output:

```(+1,+1) cartesian is (1.414214,0.785398) polar
(+1,-1) cartesian is (1.414214,2.356194) polar
(-1,-1) cartesian is (1.414214,-2.356194) polar
(-1,+1) cartesian is (1.414214,-0.785398) polar
atan2(0, 0) = 0.000000 atan2(0, -0)=3.141593
atan2(7, 0) = 1.570796 atan2(7, -0)=1.570796```
• C11 standard (ISO/IEC 9899:2011):
• 7.12.4.4 The atan2 functions (p: 239)
• 7.25 Type-generic math <tgmath.h> (p: 373-375)
• F.10.1.4 The atan2 functions (p: 519)
• C99 standard (ISO/IEC 9899:1999):
• 7.12.4.4 The atan2 functions (p: 219)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• F.9.1.4 The atan2 functions (p: 456)
• C89/C90 standard (ISO/IEC 9899:1990):
• 4.5.2.4 The atan2 function

### See also

 asinasinfasinl (C99)(C99) computes arc sine (arcsin(x)) (function) acosacosfacosl (C99)(C99) computes arc cosine (arccos(x)) (function) atanatanfatanl (C99)(C99) computes arc tangent (arctan(x)) (function) cargcargfcargl (C99)(C99)(C99) computes the phase angle of a complex number (function)

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