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> Is there any available tool for bigger (accurate) integers / for arbitrary long integers?

Try these:
	http://www.tecgraf.puc-rio.br/~lhf/ftp/lua/#lbc
	http://www.tecgraf.puc-rio.br/~lhf/ftp/lua/#lmapm

lbc does not have any external dependencies.
lmapm needs mapm but supports transcendental functions etc.