Legacy Document

asinh

You can use the asinh function to compute the inverse hyperbolic sine of a real number.

double_t asinh (double_t x);

x

Any floating-point number.

DESCRIPTION

The asinh function returns the inverse hyperbolic sine of its argument. This function is antisymmetric.

$asinh(x)\; =\; arcsinhx\; =\; y$ such that $sinhy\; =\; x$

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

EXCEPTIONS

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

• inexact (for all finite, nonzero values of x)
• underflow (if the result is inexact and must be represented as a denormalized number or 0)

SPECIAL CASES

Table 10-31 shows the results when the argument to the asinh function is a zero, a NaN, or an Infinity.

Special cases for the asinh function

Operation	Result	Exceptions raised
$asinh(+0)$	+0	None
$asinh(-0)$	$-0$	None
$asinh(NaN)$	NaN	None[53]
$asinh(+$ )	+	None
$asinh(-$ )	$-$	None

EXAMPLES

z = asinh(1.0);   /* z  0.881374. The inexact exception is 
                     raised. */
z = asinh(-1.0);  /* z  0.881374. The inexact exception is 
                     raised. */

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