Photos question - moving the system library

Let's say I have my iCloud Photo Library set up and all uploaded, etc., and the master library file being wherever it is.

Now, what would happen if I were to reformat my computer, reinstall OS X, move the library file, or buy a new computer? Would Photos then see the library, see my iCloud credentials, and merge the library, or re-upload all pictures?

I ask because if I have a 40GB+ library, I wouldn't want to have it re-upload all pictures just because I moved the library file or bought a new computer there.

Can anyone tell me anecdotally what happens in those scenarios? Thanks!

Thanks for your reply. I'm a bit nervous because when I originally uploaded about 5,000~ pictures then an error occurred, I repaired my library with Photos. After completion of the repair, Photos wanted to re-upload ALL my photos all over again, even though they were already in iCloud!

That's why I'm not sure what the standard behavior is when moving the library file to a different location, either on the same computer or a new one, but using the same iCloud credentials. Can anyone with real life experience confirm?