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Er, shouldn't the C library be able to handle large files using FILE?
Depends. fseek() takes a long (i.e. a signed long) as the file offset, so if long is 32-bits then you can't get past 2GB-1.
Anyway, a default build of Lua on my 32-bit Linux has a 2GB-1 size limit on files it can process. (My QEMU virtual machine disk images are often bigger than that.)