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> Why 5.1 support negative and 5.2 do not support negative operating it?

Only Lua authors can really answer this question. I can just make a guess.
IMHO, Lua 5.1 _tolerates_ negative values for format %X rather that
_supports_ them.
You have to realize that the result of string.format("%X",-1) is not
defined : is it 0xFF, 0xFFFF, 0xFFFFFFFF, 0xFFFFFFFFFFFFFFFF, ... ?
Lua 5.2 is more strict concerning range of accepted numerical values.