# cospi, cospif, cospil, cospid32, cospid64, cospid128

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< c‎ | numeric‎ | math

Defined in header `<math.h>` |  |
float cospif( float arg ); | (1) | (since C23)
double cospi( double arg ); | (2) | (since C23)
long double cospil( long double arg ); | (3) | (since C23)
_Decimal32 cospid32( _Decimal32 arg ); | (4) | (since C23)
_Decimal64 cospid64( _Decimal64 arg ); | (5) | (since C23)
_Decimal128 cospid128( _Decimal128 arg ); | (6) | (since C23)
Defined in header `<tgmath.h>` |  |
#define cospi( arg ) | (7) | (since C23)

1-6) Computes the cosine of `π·arg` measured in radians, thus regarding arg as a measurement in half-revolutions.
7) Type-generic macro: calls the correct function based on the type of arg. If the argument has integer type, (2) (`cospi`) 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 C23)

### Parameters

arg | - | floating-point value whose product with `π` represents an angle in radians

### Return value

If no errors occur, the cosine of `π·arg` (cos(π×arg)) in the range [-1, +1], is returned.

### Error handling

Errors are reported as specified in `math_errhandling`.

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

- if the argument is ±0, the result is 1.0;
- if the argument is ±∞, NaN is returned and FE_INVALID is raised;
- if the argument is NaN, NaN is returned.

### Example

Run this code

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

    #ifndef __GNUC__
    #pragma STDC FENV_ACCESS ON
    #endif

    #if __STDC_VERSION__ < 202311L
    // A naive implementation of a subset of cospi family
    double cospi(double arg)
    {
        return cos(arg * (double)3.1415926535897932384626433);
    }
    #endif

    int main(void)
    {
        const double pi = acos(-1);

        // typical usage
        printf("cospi(1) = %f, cos(pi) = %f\n", cospi(1), cos(pi));
        printf("cospi(0.5) = %f, cos(pi/2) = %f\n", cospi(0.5), cos(pi / 2));
        printf("cospi(-0.75) = %f, cos(-3*pi/4) = %f\n", cospi(-0.75), cos(-3 * pi / 4));

        // special values
        printf("cospi(+0) = %f\n", cospi(0.0));
        printf("cospi(-0) = %f\n", cospi(-0.0));

        // error handling
        feclearexcept(FE_ALL_EXCEPT);
        printf("cospi(INFINITY) = %f\n", cospi(INFINITY));
        if (fetestexcept(FE_INVALID))
            puts("    FE_INVALID raised");
    }

Possible output:

    cospi(1) = -1.000000, cos(pi) = -1.000000
    cospi(0.5) = 0.000000, cos(pi/2) = 0.000000
    cospi(-0.75) = -0.707107, cos(-3*pi/4) = -0.707107
    cospi(+0) = 1.000000
    cospi(-0) = 1.000000
    cospi(INFINITY) = -nan
        FE_INVALID raised

### References

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

  - 7.12.4.12 The cospi functions (p: 247)

  - 7.27 Type generic math <tgmath.h> (p: 387)

### See also

cos cosf cosl (C99)(C99) | computes cosine (\({\small\cos{x} }\)cos(x)) (function)

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