Grok it, steampunks.

The Antikythera Mechanism is a unique Greek geared device, constructed around the end of the second century BC. It is known that it calculated and displayed celestial information, particularly cycles such as the phases of the moon and a luni-solar calendar. … Named after its place of discovery in 1901 in a Roman shipwreck, the Antikythera Mechanism is technically more complex than any known device for at least a millennium afterwards. http://www.nature.com/nature/journal/v444/n7119/full/nature05357.html

• http://en.wikipedia.org/wiki/Antikythera_mechanism
• http://dlib.nyu.edu/awdl/isaw/isaw-papers/4/

By way of footnote:

When assembled precisely, analog computers can be much more accurate than digital computers on these types of questions. Because they use physical rather than digital inputs and outputs, they can represent curves and other geometric elements of calculations with an infinite level of resolution (though the precision of those calculations is based on how well their parts are machined, and loss from friction and slippage). There are no least significant digits dropped, and answers are continuous rather than dependent on “for-next” clock-driven computing cycles. http://arstechnica.com/information-technology/2014/03/gears-of-war-when-mechanical-analog-computers-ruled-the-waves/