rustdoc: search URLs should be based off the documentation root

[jsha]

When you do a search on a rustdoc page, we use the history API to modify the URL bar and represent the current search. For instance if you search for "vec" from the String page, you'd get:

https://doc.rust-lang.org/std/string/struct.String.html?search=vec

But if you searched for "vec" from the slice page, you'd get:

https://doc.rust-lang.org/std/slice/index.html?search=vec

Conceptually, though, these are the same: the search results for "vec" within /std/. Since History.pushState() lets us choose whatever URL we want within the same origin, we should remove the part that's specific to the page you started on, and generate a URL like so:

https://doc.rust-lang.org/std/index.html?search=vec

(note the index.html rather than just /std/, so this works properly when loading local files).

I'm happy to work on this.

[jyn514]

Are you sure they should be based off the crate, not the actual root? https://doc.rust-lang.org/std/?search=iterator still shows results for core::iter::Iterator. I'd suggest https://doc.rust-lang.org/?search=iterator instead.

Hmm, actually I just realized that doesn't work on doc.rust-lang.org because it redirects things to https://www.rust-lang.org/learn. Maybe https://doc.rust-lang.org/settings.html?search=iterator is better.

[lolbinarycat]

There is a difference, though. You can "close" the search dialogue and go back to the underlying state by pressing escape.