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The Manual says, under lua_tointegerx:

   If the number is not an integer, it is truncated in some non-specified way.

A more accurate description of the present behaviour on at least one commonly
used system would be:

   If the number is not an integer, it is rounded in some non-specified way.

The code in llimits.h defining the process is heavy with #ifdef's and commented
with copious use of the word "trick". Suffice to say that it is strongly
implementation-dependent.

Maybe a neutral term would be more appropriate.

   If the number is not an integer, it is convered to an integer in
some non-specified way.