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<strong>
Mike Speciner
</strong>
on 2011-07-20 03:45:02 <br />
This does not work for negative arg. It also suffers from poor precision for |arg| &lt;&lt; 1.

To fix the first problem, try
return Math.log(Math.abs(arg) + Math.sqrt(arg * arg + 1))*(arg&lt;0?-1:1);

The second problem is much harder to fix; best might be a rational function approximation for small args.
If there were a builtin function log1p(x) := log(1+x), and similarly
expm1(x) := exp(x)-1, things would be much simpler for all the hyperbolic functions and their inverses.
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