VIM - Hotkey for VIMGREP on Visual Selection in current buffer

How would I go about setting up a hotkey (eg: CTRL+g) to perform a VIMGREP operation on the current visual selection in the current buffer? My intent is to show a line-numbered list in the "quickfix" window of all matching search results.

Right now, if I want to get a list of results for a regex search, I could do a command-mode query like so:

:vimgrep /foo/ %

However, there are two problems with this:

I don't want to have to type out the entire query. I could always do a visual selection, then use CTRL+r, CTRL+w, to paste the current visual selection into the command buffer, but I'd like something simpler than this.
The above approach requires that the current buffer is already saved to a file. I'd like to be able to work on a temporary buffer I've pasted into VIM rather than having to save a file buffer each time I want to do this.

Thank you.

Solution

A low-level solution

Try [I and the :ilist command:

[I                 " lists every occurrence of the word under the cursor
                   " in the current buffer (and includes)

:ilist /foo<CR>    " lists every occurrence of foo in the current buffer 
                   " (and includes)

Press : followed by a line number and <CR> to jump to that line.

You can use them on the visual selection with a simple mapping:

xnoremap <key> "vy:<C-u>ilist /<C-r>v<CR>:

You'll probably need to sanitize the register upon insertion, though.

See :help :ilist.

Another even lower-level solution

Since we are at it, let's dig even deeper and find the amazingly simple and elegant:

:g/foo/#

that you could use in the same way as :ilist above:

xnoremap <key> "vy:<C-u>g/<C-r>v/#<CR>:

Limitations

The solutions above don't use the quickfix window, obviously, but they allow you to:

see their result as a list,
use line numbers to actually get to where you want.

They have limitations, though:

the list is not cached so you must perform the search again if you want to get to a different occurrence,
the list is not transient like the quickfix list so you can't use navigation commands like :cnext or :clast to move around the result.

A higher-level solution

If those limitations are a showstopper, the function below, adapted from justinmk's answer in this /r/vim thread, gives you an almost complete solution:

press [I in normal mode to search for the word under the cursor in the whole buffer,
press ]I in normal mode to search for the word under the cursor after the current line,
press [I in visual mode to search for the selected text in the whole buffer,
press ]I in visual mode to search for the selected text after the current line.

The function below uses the quickfix list/window when the buffer is associated to a file and falls back to the regular behavior of [I and ]I otherwise. It could probably be modified to be used as part of an :Ilist command.

" Show ]I and [I results in the quickfix window.
" See :help include-search.
function! Ilist_qf(selection, start_at_cursor)

    " there's a file associated with this buffer
    if len(expand('%')) > 0

        " we are working with visually selected text
        if a:selection

            " we build a clean search pattern from the visual selection
            let old_reg = @v
            normal! gv"vy
            let search_pattern = substitute(escape(@v, '\/.*$^~[]'), '\\n', '\\n', 'g')
            let @v = old_reg

            " and we redirect the output of our command for later use
            redir => output
                silent! execute (a:start_at_cursor ? '+,$' : '') . 'ilist /' . search_pattern
            redir END

        " we are working with the word under the cursor
        else

            " we redirect the output of our command for later use
            redir => output
                silent! execute 'normal! ' . (a:start_at_cursor ? ']' : '[') . "I"
            redir END
        endif
        let lines = split(output, '\n')

        " better safe than sorry
        if lines[0] =~ '^Error detected'
            echomsg 'Could not find "' . (a:selection ? search_pattern : expand("<cword>")) . '".'
            return
        endif

        " we retrieve the filename
        let [filename, line_info] = [lines[0], lines[1:-1]]

        " we turn the :ilist output into a quickfix dictionary
        let qf_entries = map(line_info, "{
                    \ 'filename': filename,
                    \ 'lnum': split(v:val)[1],
                    \ 'text': getline(split(v:val)[1])
                    \ }")
        call setqflist(qf_entries)

        " and we finally open the quickfix window if there's something to show
        cwindow

    " there's no file associated with this buffer
    else

        " we are working with visually selected text
        if a:selection

            " we build a clean search pattern from the visual selection
            let old_reg = @v
            normal! gv"vy
            let search_pattern = substitute(escape(@v, '\/.*$^~[]'), '\\n', '\\n', 'g')
            let @v = old_reg

            " and we try to perform the search
            try
                execute (a:start_at_cursor ? '+,$' : '') . 'ilist /' .  search_pattern . '<CR>:'
            catch
                echomsg 'Could not find "' . search_pattern . '".'
                return
            endtry

        " we are working with the word under the cursor
        else

            " we try to perform the search
            try
                execute 'normal! ' . (a:start_at_cursor ? ']' : '[') . "I"
            catch
                echomsg 'Could not find "' . expand("<cword>") . '".'
                return
            endtry
        endif
    endif
endfunction

nnoremap <silent> [I :call Ilist_qf(0, 0)<CR>
nnoremap <silent> ]I :call Ilist_qf(0, 1)<CR>
xnoremap <silent> [I :<C-u>call Ilist_qf(1, 0)<CR>
xnoremap <silent> ]I :<C-u>call Ilist_qf(1, 1)<CR>

NB: <C-r><C-w> inserts the word under the cursor, not the visual selection for which there's unfortunately no such shortcut. We have no choice but to yank.