| Defined in header <math.h> | ||||
|---|---|---|---|---|
| (1) | (since C99) | ||
| (2) | |||
| (3) | (since C99) | ||
| Defined in header <tgmath.h> | ||||
| (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
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
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.
Example
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | #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 2 3 4 5 6 | (+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) polaratan2(0, 0) = 0.000000 atan2(0, -0)=3.141593atan2(7, 0) = 1.570796 atan2(7, -0)=1.570796 |
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
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 | |
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