acosh

float       acoshf( float arg );

double      acosh( double arg );

long double acoshl( long double arg );

#define acosh( arg )

Parameters

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");
}

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)

See also

External links

Weisstein, Eric W. "Inverse Hyperbolic Cosine." From MathWorld--A Wolfram Web Resource.