According to Wikipedia, Zacharias Dase "calculated a 7-digit logarithm table and extended a table of integer factorizations from 7,000,000 to 10,000,000." It also says he "calculated $\pi$ to 200 decimal places in his head, a record for the time," but it's not clear to me whether that was a record for calculating $\pi$, or just a record for calculating $\pi$ in one's head. I don't know whether Dase qualifies as a savant.
EDIT: Perhaps I should have mentioned that Dase did this in the 1830s or thereabouts, hence, without mechanical aids to computation.