atan2, atan2f, atan2l
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                    | 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.| Contents | 
[edit] Parameters
| x, y | - | floating point value | 
[edit] Return value
If no errors occur, the arc tangent ofy/x (arctan(| y | 
| x | 
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.
[edit] 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 xandyare both zero, domain error does not occur
-  If xandyare both zero, range error does not occur either
-  If yis zero, pole error does not occur
-  If yis±0andxis negative or-0,±πis returned
-  If yis±0andxis negative or+0,±0is returned
-  If yis±∞andxis finite,±π/2is returned
-  If yis±∞andxis-∞,±3π/4is returned
-  If yis±∞andxis+∞,±π/4is returned
-  If xis±0andyis negative,-π/2is returned
-  If xis±0andyis positive,+π/2is returned
-  If xis-∞andyis finite and positive,+πis returned
-  If xis-∞andyis finite and negative,-πis returned
-  If xis+∞andyis finite and positive,+0is returned
-  If xis+∞andyis finite and negative,-0is returned
-  If either xis NaN oryis NaN, NaN is returned
[edit] Notes
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.
[edit] Example
Run this code
#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
[edit] References
- 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
 
[edit] See also
| (C99)(C99) | computes arc sine (arcsin(x)) (function) | 
| (C99)(C99) | computes arc cosine (arccos(x)) (function) | 
| (C99)(C99) | computes arc tangent (arctan(x)) (function) | 
| (C99)(C99)(C99) | computes the phase angle of a complex number (function) | 
| C++ documentation for atan2 | |



