/C

# acosh, acoshf, acoshl

Defined in header `<math.h>`
`float       acoshf( float arg );`
(1) (since C99)
`double      acosh( double arg );`
(2) (since C99)
`long double acoshl( long double arg );`
(3) (since C99)
Defined in header `<tgmath.h>`
`#define acosh( arg )`
(4) (since C99)
1-3) Computes the inverse hyperbolic cosine of `arg`.
4) Type-generic macro: If the argument has type `long double`, `acoshl` is called. Otherwise, if the argument has integer type or the type `double`, `acosh` is called. Otherwise, `acoshf` is called. If the argument is complex, then the macro invokes the corresponding complex function (`cacoshf`, `cacosh`, `cacoshl`).

### Parameters

 arg - floating point value representing the area of a hyperbolic sector

### Return value

If no errors occur, the inverse hyperbolic cosine of `arg` (cosh-1
(arg), or arcosh(arg)) on the interval [0, +∞], is returned.

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

### Error handling

Errors are reported as specified in math_errhandling.

If the argument is less than 1, a domain error occurs.

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

• if the argument is less than 1, `FE_INVALID` is raised an NaN is returned
• if the argument is 1, +0 is returned
• if the argument is +∞, +∞ is returned
• if the argument is NaN, NaN is returned

### Notes

Although the C standard names this function "arc hyperbolic cosine", the inverse functions of the hyperbolic functions are the area functions. Their argument is the area of a hyperbolic sector, not an arc. The correct name is "inverse hyperbolic cosine" (used by POSIX) or "area hyperbolic cosine".

### Example

```#include <stdio.h>
#include <math.h>
#include <float.h>
#include <errno.h>
#include <fenv.h>
#pragma STDC FENV_ACCESS ON
int main(void)
{
printf("acosh(1) = %f\nacosh(10) = %f\n", acosh(1), acosh(10));
printf("acosh(DBL_MAX) = %f\nacosh(Inf) = %f\n", acosh(DBL_MAX), acosh(INFINITY));
//error handling
errno = 0; feclearexcept(FE_ALL_EXCEPT);
printf("acosh(0.5) = %f\n", acosh(0.5));
if(errno == EDOM)         perror("    errno == EDOM");
if(fetestexcept(FE_INVALID)) puts("    FE_INVALID raised");
}```

Possible output:

```acosh(1) = 0.000000
acosh(10) = 2.993223
acosh(DBL_MAX) = 710.475860
acosh(Inf) = inf
acosh(0.5) = -nan
errno == EDOM: Numerical argument out of domain
FE_INVALID raised```

### References

• C11 standard (ISO/IEC 9899:2011):
• 7.12.5.1 The acosh functions (p: 240)
• 7.25 Type-generic math <tgmath.h> (p: 373-375)
• F.10.2.1 The acosh functions (p: 520)
• C99 standard (ISO/IEC 9899:1999):
• 7.12.5.1 The acosh functions (p: 221)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• F.9.2.1 The acosh functions (p: 457)