I can read about function and the I want search for another function, so I click on to the browser scrooler and drag to the bottom of page and than i write another function name. It can be there some kind of anchor than I can click it and go to the top automatically.
Just another suggestion (not sure if this is the correct place), when a documentation page is loaded up the input field at the top gets the focus automatically - this isn’t really useful especially if you prefer to use keyboard navigation!
I think it would be better if the "scroll to top" button is always available on the right bottom of the page. Means position:fixed like thinkt4nk suggested. See this for example (scroll down to see effect).