Haiku OS has added support for the "Mullins" and "Hawaii" AMD graphics processors to its basic radeon_hd graphics driver. This though is just for basic display support and goes completely untested but the developer hopes it will work for "a lot of stuff" due to commomn support with other recent Radeon GPUs. "These aren't tested, but since we go off of DCE versions for a lot of stuff, they may work."
The hopeful support for these latest-generation AMD GPUs happened with this Git commit today to Haiku. The support is based off the open-source AMD Linux Radeon graphics driver.
Under Linux there is Mullins support with Linux 3.15 while the Hawaii support has been around for a few kernel releases now. There's also Mullins Gallium3D support for these newest APUs. When it comes to open-source Radeon R9 290 "Hawaii" OpenGL/3D support, the support remains broken with the AMD developers admitting it's not a high priority item -- AMD R9 290 users are best off with the AMD Catalyst Linux driver for now.