Function to always redirect home after login or logout?

Is there a function that can be dropped into functions.php to permanently change the redirect behavior after login and logout?

After logout WP by default redirects to wp-login.php, which is the absolute last place you want to go when you log out.

Log-in redirect to wp-admin, which makes sense if you’re the administrator of your own blog, but not so much in a multisite members context.

Does anyone have a function so that login/logout redirects to the homepage or, even better, just keeps you on the same page?