atan2, atan2f, atan2l

Types

div_tldiv_tlldiv_timaxdiv_t (哋它亢99)(哋它亢99)

float_tdouble_t (哋它亢99)(哋它亢99)
_Decimal32_t_Decimal64_t (哋它亢23)(哋它亢23)

Functions

Basic operations

abslabsllabsimaxabs (哋它亢99)(哋它亢99)
fabs
divldivlldivimaxdiv (哋它亢99)(哋它亢99)

fmod
remainder (哋它亢99)
remquo (哋它亢99)
fma (哋它亢99)
fdim (哋它亢99)
nannanfnanlnandN (哋它亢99)(哋它亢99)(哋它亢99)(哋它亢23)

Maximum/minimum operations

fmax (哋它亢99)
fmaximum (哋它亢23)
fmaximum_mag (哋它亢23)
fmaximum_num (哋它亢23)
fmaximum_mag_num (哋它亢23)

fmin (哋它亢99)
fminimum (哋它亢23)
fminimum_mag (哋它亢23)
fminimum_num (哋它亢23)
fminimum_mag_num (哋它亢23)

Exponential functions

exp
exp10 (哋它亢23)
exp2 (哋它亢99)
expm1 (哋它亢99)
exp10m1 (哋它亢23)
exp2m1 (哋它亢23)

log
log10
log2 (哋它亢99)
log1plogp1 (哋它亢99)(哋它亢23)
log10p1 (哋它亢23)
log2p1 (哋它亢23)

Power functions

sqrt
cbrt (哋它亢99)
rootn (哋它亢23)
rsqrt (哋它亢23)

hypot (哋它亢99)
compound (哋它亢23)
pow
pown (哋它亢23)
powr (哋它亢23)

Trigonometric and hyperbolic functions

sin
cos
tan
asin
acos
atan
atan2
sinpi (哋它亢23)
cospi (哋它亢23)
tanpi (哋它亢23)

asinpi (哋它亢23)
acospi (哋它亢23)
atanpi (哋它亢23)
atan2pi (哋它亢23)
sinh
cosh
tanh
asinh (哋它亢99)
acosh (哋它亢99)
atanh (哋它亢99)

Error and gamma functions

erf (哋它亢99)
erfc (哋它亢99)

lgamma (哋它亢99)
tgamma (哋它亢99)

Nearest integer floating-point operations

ceil
floor
roundlroundllround (哋它亢99)(哋它亢99)(哋它亢99)
roundeven (哋它亢23)
trunc (哋它亢99)

nearbyint (哋它亢99)
rintlrintllrint (哋它亢99)(哋它亢99)(哋它亢99)
fromfpfromfpxufromfpufromfpx (哋它亢23)(哋它亢23)(哋它亢23)(哋它亢23)

Floating-point manipulation functions

ldexp
frexp
scalbnscalbln (哋它亢99)(哋它亢99)
ilogbllogb (哋它亢99)(哋它亢23)
logb (哋它亢99)

modf
nextafternexttoward (哋它亢99)(哋它亢99)
nextupnextdown (哋它亢23)(哋它亢23)
copysign (哋它亢99)
canonicalize (哋它亢23)

Narrowing operations

fadd (哋它亢23)
fsub (哋它亢23)
fmul (哋它亢23)

fdiv (哋它亢23)
ffma (哋它亢23)
fsqrt (哋它亢23)

Quantum and quantum exponent functions

quantizedN (哋它亢23)
samequantumdN (哋它亢23)

quantumdN (哋它亢23)
llquantexpdN (哋它亢23)

Decimal re-encoding functions

encodedecdN (哋它亢23)
decodedecdN (哋它亢23)

encodebindN (哋它亢23)
decodebindN (哋它亢23)

Total order and payload functions

totalorder (哋它亢23)
getpayload (哋它亢23)

setpayload (哋它亢23)
setpayloadsig (哋它亢23)

Classification

fpclassify (哋它亢99)
iscanonical (哋它亢23)
isfinite (哋它亢99)
isinf (哋它亢99)
isnan (哋它亢99)
isnormal (哋它亢99)
signbit (哋它亢99)
issubnormal (哋它亢23)
iszero (哋它亢23)

isgreater (哋它亢99)
isgreaterequal (哋它亢99)
isless (哋它亢99)
islessequal (哋它亢99)
islessgreater (哋它亢99)
isunordered (哋它亢99)
issignaling (哋它亢23)
iseqsig (哋它亢23)

Macro constants

Special floating-point values

HUGE_VALFHUGE_VALHUGE_VALLHUGE_VALDN

(哋它亢99)(哋它亢99)(哋它亢23)

INFINITYDEC_INFINITY (哋它亢99)(哋它亢23)
NANDEC_NAN (哋它亢99)(哋它亢23)

Arguments and return values

FP_ILOGB0FP_ILOGBNAN (哋它亢99)(哋它亢99)
FP_INT_UPWARDFP_INT_DOWNWARDFP_INT_TOWARDZEROFP_INT_TONEARESTFROMZEROFP_INT_TONEAREST (哋它亢23)(哋它亢23)(哋它亢23)(哋它亢23)(哋它亢23)

FP_LLOGB0FP_LLOGBNAN (哋它亢23)(哋它亢23)
FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (哋它亢99)(哋它亢99)(哋它亢99)(哋它亢99)(哋它亢99)

Error handling

MATH_ERRNOMATH_ERRNOEXCEPT

(哋它亢99)(哋它亢99)

math_errhandling (哋它亢99)

Fast operation indicators

FP_FAST_FMAFFP_FAST_FMA (哋它亢99)(哋它亢99)
FP_FAST_FADDFP_FAST_FADDLFP_FAST_DADDLFP_FAST_DMADDDN (哋它亢23)(哋它亢23)(哋它亢23)(哋它亢23)
FP_FAST_FMULFP_FAST_FMULLFP_FAST_DMULLFP_FAST_DMMULDN (哋它亢23)(哋它亢23)(哋它亢23)(哋它亢23)
FP_FAST_FFMAFP_FAST_FFMALFP_FAST_DFMALFP_FAST_DMFMADN (哋它亢23)(哋它亢23)(哋它亢23)(哋它亢23)

FP_FAST_FMALFP_FAST_FMADN (哋它亢99)(哋它亢23)
FP_FAST_FSUBFP_FAST_FSUBLFP_FAST_DSUBLFP_FAST_DMSUBDN (哋它亢23)(哋它亢23)(哋它亢23)(哋它亢23)
FP_FAST_FDIVFP_FAST_FDIVLFP_FAST_DDIVLFP_FAST_DMDIVDN (哋它亢23)(哋它亢23)(哋它亢23)(哋它亢23)
FP_FAST_FSQRTFP_FAST_FSQRTLFP_FAST_DSQRTLFP_FAST_DMSQRTDN (哋它亢23)(哋它亢23)(哋它亢23)(哋它亢23)

Defined in header `<math.h>`
float atan2f( float y, float x );	(1)	(since 哋它亢99)
double atan2( double y, double x );	(2)
long double atan2l( long double y, long double x );	(3)	(since 哋它亢99)
_Decimal32 atan2d32( _Decimal32 y, _Decimal32 x );	(4)	(since 哋它亢23)
_Decimal64 atan2d64( _Decimal64 y, _Decimal64 x );	(5)	(since 哋它亢23)
_Decimal128 atan2d128( _Decimal128 y, _Decimal128 x );	(6)	(since 哋它亢23)
Defined in header `<tgmath.h>`
#define atan2( y, x )	(7)	(since 哋它亢99)

1-6) Computes the arc tangent of y / x using the signs of arguments to determine the correct quadrant.

7) Type-generic macro: If any argument has type long double, (3) (atan2l) is called. Otherwise, if any argument has integer type or has type double, (2) (atan2) is called. Otherwise, (1) (atan2f) is called.

The functions (4-6) are declared if and only if the implementation predefines __STDC_IEC_60559_DFP__ (i.e. the implementation supports decimal floating-point numbers).

(since 哋它亢23)

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 <math.h>
#include <stdio.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

哋它亢23 standard (ISO/IEC 9899:2023):

7.12.4.4 The atan2 functions (p: TBD)

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

F.10.1.4 The atan2 functions (p: TBD)

哋它亢17 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)

哋它亢11 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)

哋它亢99 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)

哋它亢89/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 (哋它亢11)
Technical Specifications
Symbol index

Common mathematical functions
Floating-point environment (哋它亢99)
Pseudo-random number generation
Complex number arithmetic (哋它亢99)
Type-generic math (哋它亢99)

asinasinfasinl (哋它亢99)(哋它亢99)	computes arc sine (\({\small\arcsin{x} }\) $arcsin(x)$ ) (function)
acosacosfacosl (哋它亢99)(哋它亢99)	computes arc cosine (\({\small\arccos{x} }\) $arccos(x)$ ) (function)
atanatanfatanl (哋它亢99)(哋它亢99)	computes arc tangent (\({\small\arctan{x} }\) $arctan(x)$ ) (function)
cargcargfcargl (哋它亢99)(哋它亢99)(哋它亢99)	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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