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>  I think it should be simple to provide my own custom allocator

This is trivial in 5.1 and pretty simple in 5.0
(you have to change 2 macros in lmem.c and recompile).

>  Some mobile phone platforms don't provide a complete C standard library.

The Lua core tries to avoid as much as possible of the C standard library.
Not so with the Lua libraries, though...

>  I guess it is possible to replace all double usage with equivalent
> fixed point operations.

This is simple in 5.1 because there are macros for all numeric operations.
In 5.0 (and also in 5.1) you cal compile Lua to use int instead of double,
though I'm not sure that'd fit your needs.
--lhf