There is an excellent existing plugin that does this work pretty well.

I am already using this plugin and to be honest I see no sense in implementing the same fuctionality in theme. Why authors should spend their time coding the feature which is already available? The plugin is working good and it’s lightweight, so it can’t be made much better. Although there’s a lot of sense in dropping heavyweight overcomplicated freemium plugins like YITH Compare and YITH Wishlist, I suppose there’s no sense in adding functionality of good plugins into the theme.