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1. Checking code (or anything else, e.g. a Usenet posting) for completely stupid mistakes. Implies that the check is to make sure the author was sane when it was written; e.g. if a piece of scientific software relied on a particular formula and was giving unexpected results, one might first look at the nesting of parentheses or the coding of the formula, as a "sanity check", before looking at the more complex I/O or data structure manipulation routines, much less the algorithm itself.
Compare reality check.
2. A run-time test, either validating input or ensuring that the program hasn't screwed up internally (producing an inconsistent value or state).