Legacy Document

atanh

You can use the atanh function to perform the inverse hyperbolic tangent of a real number.

double_t atanh (double_t x);

x

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

DESCRIPTION

The atanh function returns the inverse hyperbolic tangent of its argument. This function is antisymmetric.

$atanh(x)\; =\; arctanhx\; =\; y$ such that $tanhy\; =\; x$

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

EXCEPTIONS

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

• inexact (for all finite, nonzero values of x other than +1 and -1)
• invalid (if |x| > 1)
• underflow (if the result is inexact and must be represented as a denormalized number or 0)

SPECIAL CASES

Table 10-32 shows the results when the argument to the atanh function is a zero, a NaN, or an Infinity, plus other special cases for the atanh function.

Special cases for the atanh function

Operation	Result	Exceptions raised
$atanh(x)$ for |x| > 1	NaN	Invalid
$atanh(-1)$	$-$	None
$atanh(+1)$	+	None
$atanh(+0)$	+0	None
$atanh(-0)$	$-0$	None
$atanh(NaN)$	NaN	None[54]
$atanh(+$ )	NaN	Invalid
$atanh(-$ )	NaN	Invalid

EXAMPLES

z = atanh(1.0);   /* z = +INFINITY */
z = atanh(-1.0);  /* z = -INFINITY */

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