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> OTOH, sinh & cosh can be defined as oneliner functions of exp just 
> checking wikipedia.

There are subtle numerical reasons to avoid these definitions. These
are handled in libc, as they should. See for instance the Cephes
Mathematical Library at http://www.netlib.org/cephes/ .

This is the main reason why providing a math library in Lua is probably
not a good idea: the result would either have low quality or be quite
complex and obscure, in the interest of precision.