I had a similar issue on Radeon HD4350 (RV710) when the RLC microcode was introduced. It was later fixed, I used Trisquel and Parabola on that machine. It's probably worse with newer cards.
Linux-libre has working modesetting for more Radeons than Debian without firmware: Debian intentionally disables it [0] despite it working on some cards. While it works on e.g. HD3200 and HD4350, all h-node.org reports of it working with HD6310 are with Trisquel (one fails on Parabola), so it's probably due to vesa, not radeon driver. [0] http://anonscm.debian.org/viewvc/kernel/dists/trunk/linux/debian/patches/bugfix/all/radeon-firmware-is-required-for-drm-and-kms-on-r600-onward.patch?view=markup
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