Hi Tom,
The “gi” files are data files which contain the cache from your calculations. If they are stored the application can reuse these, instead of calculating everything again. Besides shorter render times, while reusing them, the advantage of them is given while using more than one computer to render, as each CPU has its own idea of precision.
You can read more about those files and their handling here:
CINEMA 4D Prime>> Render Menu> Edit Render Settings> Global Illumination> GI Setup
Check the point “Auto Save”
All the best
Sassi