|al Battani †929ce
Al Battani, who observed the solar eclipse in the year 901CE, calculated the current year based on the data of Cl. Ptolemy the year 1212 †Alexander. The year of death (of Alexander IV, son of Alexander the Great and the Sogdian princess Roxane?) would have been -311.
In the Almagest of Ptolemy, which was authoritative for the Arab astronomers, the Earth's precession was specified with 1°/year. In fact the ecliptic longitude of Spica had increased by ~12° since Timocharis.
The exact year could be calculated from the lunar cycle.