Does anyone know how to calculate the trajectory of something like an artillery shell, preferably over long distances?

Given: shell mass, gun elevation muzzle velocity, altitude etc...

Or know anyone who does?

Formulas would be ok because I can translate them into C++ myself. Something accurate, with aerodynamic drag, wind and humidity adjustments would be my ultimate goal but I am happy to build up to that later.

Something like the calculations that the early computers like EDVAC and COLOSSUS had to perform would be super cool.

A prize to the most helpful idea