Midnight GMT positions (Tropical) for 1700-2100 are derived from the Jet Propulsion Laboratories (JPL) DE406 ephemerides and the US Naval Observatory equivalent for Asteroids. These are stored in a small binary database of our own devising. From that database positions for other times are interpolated using algorithms specified by Jean Meeus. Sidereal positions are derived by correcting Tropical positions to the selected Ayanamsa.
iPhemeris uses a New Style calendar with all dates according to the Gregorian Calendar adopted October 1582. However, be aware that various locales adopted the Gregorian calendar at other times; for example, Great Britain didn't switch until September 1752. Therefore, adjust your dates accordingly.