Legacy Document

acosh

You can use the acosh function to compute the inverse hyperbolic cosine of a real number.

double_t acosh (double_t x);

x

Any floating-point number in the range 1 x + .

DESCRIPTION

The acosh function returns the inverse hyperbolic cosine of its argument. This function is antisymmetric.

$acosh(x)\; =\; arccoshx\; =\; y$ such that $coshy\; =\; x$

The cosh function performs the inverse operation $(cosh(y))$ .

EXCEPTIONS

When x is finite and nonzero, the result of $acosh(x)$ might raise one of the following exceptions:

• inexact (for all finite values of x > 1)
• invalid (if x < 1)

SPECIAL CASES

Table 10-30 shows the results when the argument to the acosh function is a zero, a NaN, or an Infinity, plus other special cases for the acosh function.

Special cases for the acosh function

Operation	Result	Exceptions raised
$acosh(x)$ for x < 1	NaN	Invalid
$acosh(1)$	+0	None
$acosh(+0)$	NaN	Invalid
$acosh(-0)$	NaN	Invalid
$acosh(NaN)$	NaN	None[52]
$acosh(+$ )	+	None
$acosh(-$ )	NaN	Invalid

EXAMPLES

z = acosh(1.0);   /* z = +0 */
z = acosh(0.0);   /* z = NAN. The invalid exception is raised. */

---

[52] If the NaN is a signaling NaN, the invalid exception is raised.