Here's an interesting quote from the 1911 edition of the Encyclopedia Britannica:
COMPTROLLER, the title of an official whose business primarily was to examine and take charge of accounts, hence to direct or control, e.g. the English comptroller of the household, comptroller and auditor-general (head of the exchequer and audit department), comptroller-general of patents, &c., comptro]lergeneral (head of the national debt office). On the other hand, the word is frequently spelt controller, as in controller of the navy, controller or head of the stationery office. The word is used in the same sense in the United States, as comptroller of the treasury, an official who examines accounts and signs drafts, and comptroller of the currency, who administers the law relating to the national banks.
http://47.1911encyclopedia.org/C/CO/COMPTROLLER.htm (via Onelook)

I wonder if the comp- came from computation?