Gov contribution to open software

How much of open software was built with gov funding? Either directly or indirectly through funding academics and students who then wrote either for use in their work or even in their spare time (basic income like!)?

What about if we include even more indirect sources like AT&T labs which was quasi-governmental and where government regulation ensured they shared stuff very openly?

My guess is that the answer is: a lot! Probably most of all open software was funded in whole or in part by gov. I also think a lot of this was not

Note: this is a question I've been asking for a long time. I've even repeatedly made claims about the answer in talks – e.g. stating that gov are responsible for a lot, probably the majority)!