atan2, atan2f, atan2l

Functions

Basic operations

abslabsllabsimaxabs (C99)(C99)
fabs
divldivlldivimaxdiv (C99)(C99)

fmod
remainder (C99)
remquo (C99)
fma (C99)
fdim (C99)
nannanfnanlnandN (C99)(C99)(C99)(C23)

Maximum/minimum operations

fmax (C99)
fmaximum (C23)
fmaximum_mag (C23)
fmaximum_num (C23)
fmaximum_mag_num (C23)

fmin (C99)
fminimum (C23)
fminimum_mag (C23)
fminimum_num (C23)
fminimum_mag_num (C23)

Exponential functions

exp
exp10 (C23)
exp2 (C99)
expm1 (C99)
exp10m1 (C23)
exp2m1 (C23)

log
log10
log2 (C99)
log1plogp1 (C99)(C23)
log10p1 (C23)
log2p1 (C23)

Power functions

sqrt
cbrt (C99)
rootn (C23)
rsqrt (C23)

hypot (C99)
compound (C23)
pow
pown (C23)
powr (C23)

Trigonometric and hyperbolic functions

sin
cos
tan
asin
acos
atan
atan2
sinpi (C23)
cospi (C23)
tanpi (C23)

asinpi (C23)
acospi (C23)
atanpi (C23)
atan2pi (C23)
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)
roundeven (C23)
trunc (C99)

nearbyint (C99)
rintlrintllrint (C99)(C99)(C99)
fromfpfromfpxufromfpufromfpx (C23)(C23)(C23)(C23)

Floating-point manipulation functions

ldexp
frexp
scalbnscalbln (C99)(C99)
ilogbllogb (C99)(C23)
logb (C99)

modf
nextafternexttoward (C99)(C99)
nextupnextdown (C23)(C23)
copysign (C99)
canonicalize (C23)

Narrowing operations

fadd (C23)
fsub (C23)
fmul (C23)

fdiv (C23)
ffma (C23)
fsqrt (C23)

Quantum and quantum exponent functions

quantizedN (C23)
samequantumdN (C23)

quantumdN (C23)
llquantexpdN (C23)

Decimal re-encoding functions

encodedecdN (C23)
decodedecdN (C23)

encodebindN (C23)
decodebindN (C23)

Total order and payload functions

totalorder (C23)
getpayload (C23)

setpayload (C23)
setpayloadsig (C23)

Classification

fpclassify (C99)
iscanonical (C23)
isfinite (C99)
isinf (C99)
isnan (C99)
isnormal (C99)
signbit (C99)
issubnormal (C23)
iszero (C23)

isgreater (C99)
isgreaterequal (C99)
isless (C99)
islessequal (C99)
islessgreater (C99)
isunordered (C99)
issignaling (C23)
iseqsig (C23)

Types

div_tldiv_tlldiv_timaxdiv_t

(C99)(C99)

float_tdouble_t (C99)(C99)
_Decimal32_t_Decimal64_t (C23)(C23)

Macro constants

Special floating-point values

HUGE_VALFHUGE_VALHUGE_VALLHUGE_VALDN

(C99)(C99)(C23)

INFINITYDEC_INFINITY (C99)(C23)
NANDEC_NAN (C99)(C23)

Arguments and return values

FP_ILOGB0FP_ILOGBNAN (C99)(C99)
FP_INT_UPWARDFP_INT_DOWNWARDFP_INT_TOWARDZEROFP_INT_TONEARSTFROMZEROFP_INT_TONEARST (C23)(C23)(C23)(C23)(C23)

FP_LLOGB0FP_LLOGBNAN (C23)(C23)
FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C99)(C99)(C99)(C99)(C99)

Error handling

math_errhandlingMATH_ERRNOMATH_ERRNOEXCEPT

(C99)(C99)(C99)

Fast operation indicators

FP_FAST_FMAFFP_FAST_FMA (C99)(C99)
FP_FAST_FADDFP_FAST_FADDLFP_FAST_DADDLFP_FAST_DMADDDN (C23)(C23)(C23)(C23)
FP_FAST_FMULFP_FAST_FMULLFP_FAST_DMULLFP_FAST_DMMULDN (C23)(C23)(C23)(C23)
FP_FAST_FFMAFP_FAST_FFMALFP_FAST_DFMALFP_FAST_DMFMADN (C23)(C23)(C23)(C23)

FP_FAST_FMALFP_FAST_FMADN (C99)(C23)
FP_FAST_FSUBFP_FAST_FSUBLFP_FAST_DSUBLFP_FAST_DMSUBDN (C23)(C23)(C23)(C23)
FP_FAST_FDIVFP_FAST_FDIVLFP_FAST_DDIVLFP_FAST_DMDIVDN (C23)(C23)(C23)(C23)
FP_FAST_FSQRTFP_FAST_FSQRTLFP_FAST_DSQRTLFP_FAST_DMSQRTDN (C23)(C23)(C23)(C23)

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( y, x )	(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 any argument has type long double, atan2l is called. Otherwise, if any argument has integer type or has 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

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

C17 standard (ISO/IEC 9899:2018):

7.12.4.4 The atan2 functions (p: 174)

7.25 Type-generic math <tgmath.h> (p: 272-273)

F.10.1.4 The atan2 functions (p: 378)

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

Language
Headers
Type support
Program utilities
Variadic function support
Error handling
Dynamic memory management
Strings library
Algorithms
Numerics
Date and time utilities
Input/output support
Localization support
Concurrency support (C11)
Technical Specifications
Symbol index

Common mathematical functions
Floating-point environment (C99)
Pseudo-random number generation
Complex number arithmetics (C99)
Type-generic math (C99)

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

atan2, atan2f, atan2l

Parameters

Return value

Error handling

Notes

Example

References

See also

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