commands → arctanh

arctanh(x)

The arctanh command computes the inverse hyperbolic tangent of x where x is in radians. If x is a floating point number then a floating point result is computed, otherwise the result is an exact symbolic value.

Examples 

# hardware floating point
arctanh(0.5);
	0.549306144334055

# symbolic
arctanh(1/2);
	arctanh(1/2)

Algorithm

To compute arctanh in extended precision we express it as a natural logarithm.

References

Gullberg, Jan. Mathematics: From the Birth of Numbers. Norton, 1996.