# acos, acosf, acosl

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< c‎ | numeric‎ | math

Defined in header `<math.h>` |  |
float acosf( float arg ); | (1) | (since C99)
double acos( double arg ); | (2) |
long double acosl( long double arg ); | (3) | (since C99)
_Decimal32 acosd32( _Decimal32 arg ); | (4) | (since C23)
_Decimal64 acosd64( _Decimal64 arg ); | (5) | (since C23)
_Decimal128 acosd128( _Decimal128 arg ); | (6) | (since C23)
Defined in header `<tgmath.h>` |  |
#define acos( arg ) | (7) | (since C99)

1-6) Computes the principal value of the arc cosine of arg.
7) Type-generic macro: If the argument has type long double, (3) (`acosl`) is called. Otherwise, if the argument has integer type or the type double, (2) (`acos`) is called. Otherwise, (1) (`acosf`) is called. If the argument is complex, then the macro invokes the corresponding complex function (cacosf, cacos, cacosl).

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 C23)

### Parameters

arg | - | floating-point value

### Return value

If no errors occur, the arc cosine of arg (arccos(arg)) in the range [0 ; π], is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

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 occurs if arg is outside the range `[-1.0; 1.0]`.

If the implementation supports IEEE floating-point arithmetic (IEC 60559):

- If the argument is +1, the value `+0` is returned;
- If |arg| > 1, a domain error occurs and NaN is returned;
- if the argument is NaN, NaN is returned.

### Example

Run this code

    #include <errno.h>
    #include <fenv.h>
    #include <math.h>
    #include <stdio.h>
    #include <string.h>

    #ifndef __GNUC__
    #pragma STDC FENV_ACCESS ON
    #endif

    int main(void)
    {
        printf("acos(-1) = %f\n", acos(-1));
        printf("acos(0.0) = %f 2*acos(0.0) = %f\n", acos(0), 2 * acos(0));
        printf("acos(0.5) = %f 3*acos(0.5) = %f\n", acos(0.5), 3 * acos(0.5));
        printf("acos(1) = %f\n", acos(1));

        // error handling
        errno = 0; feclearexcept(FE_ALL_EXCEPT);
        printf("acos(1.1) = %f\n", acos(1.1));
        if (errno == EDOM)
            perror("    errno == EDOM");
        if (fetestexcept(FE_INVALID))
            puts("    FE_INVALID raised");
    }

Possible output:

    acos(-1) = 3.141593
    acos(0.0) = 1.570796 2*acos(0.0) = 3.141593
    acos(0.5) = 1.047198 3*acos(0.5) = 3.141593
    acos(1) = 0.000000
    acos(1.1) = nan
        errno == EDOM: Numerical argument out of domain
        FE_INVALID raised

### References

- C23 standard (ISO/IEC 9899:2023):

  - 7.12.4.1 The acos functions (p: TBD)

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

  - F.10.1.1 The acos functions (p: TBD)

- C17 standard (ISO/IEC 9899:2018):

  - 7.12.4.1 The acos functions (p: 173)

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

  - F.10.1.1 The acos functions (p: 378)

- C11 standard (ISO/IEC 9899:2011):

  - 7.12.4.1 The acos functions (p: 238)

  - 7.25 Type-generic math <tgmath.h> (p: 373-375)

  - F.10.1.1 The acos functions (p: 518)

- C99 standard (ISO/IEC 9899:1999):

  - 7.12.4.1 The acos functions (p: 218)

  - 7.22 Type-generic math <tgmath.h> (p: 335-337)

  - F.9.1.1 The acos functions (p: 455)

- C89/C90 standard (ISO/IEC 9899:1990):

  - 4.5.2.1 The acos function

### See also

asin asinf asinl (C99)(C99) | computes arc sine (\({\small\arcsin{x} }\)arcsin(x)) (function)
atan atanf atanl (C99)(C99) | computes arc tangent (\({\small\arctan{x} }\)arctan(x)) (function)
atan2 atan2f atan2l (C99)(C99) | computes arc tangent, using signs to determine quadrants (function)
cos cosf cosl (C99)(C99) | computes cosine (\({\small\cos{x} }\)cos(x)) (function)
cacos cacosf cacosl (C99)(C99)(C99) | computes the complex arc cosine (function)

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