What happens to my purchased music if I cancelled my Apple Music subscription? I have a big music library that I assembled through years of purchasing music from iTunes and CDs.

I would like to give Apple Music a try but what happens to the music that I own? Particularly worried about the music that I bought from iTunes as I paid a lot for that.
Your local iTunes library will stay the way it is—with or without an active Apple Music subscription.
If you subscribe but decide later on that you do ’t want to use Apple Music any longer, what will happen is that on other devices, that are not your main iTunes library device, you cannot stream songs any longer. Synchronising songs will still work as it did before Apple Music came out.
What you put into your iTunes library before subscribing to Apple Music will stay in there.

To quote iMore.com’s Apple Music FAQ:

What happens if I decide not to subscribe after the three month trial?
Any streaming music you've added to your library from the Apple Music catalog will no longer be playable; you'll stop having access to Connect content; you'll be skip-limited when listening to Apple Music radio stations; and unless you have iTunes Match enabled, you won't be able to stream your previously purchased and uploaded music to your devices, and any songs from your Mac's library that you've downloaded to other devices will be removed. (Your Mac's original iTunes library remains as-is.)