atan2, atan2f, atan2l

C

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Error handling

Dynamic memory management

Date and time utilities

Strings library

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Numerics

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Localization support

Atomic operations (C11)

Thread support (C11)

Technical Specifications

Numerics

Common mathematical functions

Floating-point environment

Complex number arithmetics

Random number generation

Type-generic math

Common mathematical functions

Functions
Basic operations
abslabsllabsimaxabs (C99) fabs divldivlldivimaxdiv (C99) fmod	remainder (C99) remquo (C99) fma (C99) fmax (C99) fmin (C99) fdim (C99) nannanfnanl (C99)(C99)(C99)
Exponential functions
exp exp2 (C99) expm1 (C99)	log log10 log1p (C99) log2 (C99)
Power functions
sqrt cbrt (C99)	hypot (C99) pow
Trigonometric and hyperbolic functions
sin cos tan asin acos atan atan2	sinh cosh tanh asinh (C99) acosh (C99) atanh (C99)
Error and gamma functions
erf (C99) erfc (C99)	lgamma (C99) tgamma (C99)
Nearest integer floating point operations
ceil floor roundlroundllround (C99)(C99)(C99)	trunc (C99) nearbyint (C99) rintlrintllrint (C99)(C99)(C99)
Floating point manipulation functions
ldexp scalbnscalbln (C99)(C99) ilogb (C99) logb (C99)	frexp modf nextafternexttoward (C99)(C99) copysign (C99)
Classification
fpclassify (C99) isfinite (C99) isinf (C99) isnan (C99) isnormal (C99) signbit (C99)	isgreater (C99) isgreaterequal (C99) isless (C99) islessequal (C99) islessgreater (C99) isunordered (C99)
Types
div_tldiv_tlldiv_timaxdiv_t (C99)(C99)	float_tdouble_t (C99)(C99)
Macro constants
HUGE_VALFHUGE_VALHUGE_VALL (C99)(C99) FP_FAST_FMAFFP_FAST_FMAFP_FAST_FMAL (C99)(C99)(C99) math_errhandlingMATH_ERRNOMATH_ERRNOEXCEPT (C99)(C99)(C99)	INFINITY (C99) NAN (C99) FP_ILOGB0FP_ILOGBNAN (C99)(C99) FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C99)(C99)(C99)(C99)(C99)

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 [-; +] 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, is returned
• If y is 0 and x is positive or +0, 0 is returned
• If y is and x is finite, /2 is returned
• If y is and x is -, 3/4 is returned
• If y is and x is +, /4 is returned
• If x is 0 and y is negative, -/2 is returned
• If x is 0 and y is positive, +/2 is returned
• If x is - and y is finite and positive, + is returned
• If x is - and y is finite and negative, - 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

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

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

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

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)