AMD Berlin is said to be a server variant of the "Kaveri" and the company's first APU built around their much talked about Heterogeneous System Architecture (HSA). The graphics core on Berlin is of the "GCN" (HD 7000 generation) so from the open-source driver side there isn't too much to hook up.
The Radeon DRM in Linux 3.12 has the necessary kernel bits while all of the user-space support was merged hours ago. There's the Mesa commit for RadeonSI Gallium3D and libdrm and xf86-video-ati DDX. With Berlin building upon GCN, these commits aren't exciting and nothing more than adding in the new PCI IDs.
The AMD Berlin open-source graphics are using the RadeonSI Gallium3D driver and taking the same code-paths as the forthcoming "Kaveri" APU. The initial PCI IDs (or at least what AMD is reserving for Berlin parts) include 0x1304, 0x1305, 0x1306, 0x1307, 0x1309, 0x130A, 0x130B, 0x130C, 0x130D, 0x130E, 0x130F, 0x1310, 0x1311, 0x1312, 0x1313, 0x1314, 0x1315, 0x1316, 0x1317, 0x131B, 0x131C, and 0x131D.
AMD Berlin APUs aren't expected until 2014 and hopefully by then there will be more improvements to the open-source RadeonSI Gallium3D driver. Only this week the RadeonSI driver gained OpenGL 3.0 support while the performance is still improving. Berlin server customers will most likely be interested in OpenCL on the graphics side, from where the open-source GPGPU/CL support is still very much in a growing process. The AMD Catalyst binary driver will also be around for launch-day support delivering first-rate performance and features.