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> Lua provides an arbitrary(as far as I can tell) subset of POSIX math
> functions and a constant (pi), which are in turn are a random subset of
> the universe of useful functions and constants.

Lua is not intended to POSIX machines. Lua provides a subset of the
ANSI C math functions. The subset does not sound arbitrary to me; it
contains the most used functions (from our point of view, of course)
from that library.  If there is a really great demand for an hyperbolic
sine function we can add it to the library without problems. If there is
great demand for a HUGE_VAL constant, we can add it to the library too.

NaN is not part of ANSI C89. So, I wouldn't say that its absence is an
arbitrary decision. (Maybe bad, but not arbitrary :)

-- Roberto