The open-source Radeon Gallium3D compute support isn't too good yet, namely implemented through OpenCL, but Tom Stellard at AMD has been devoting many months to its upbringing. After jumping through some hoops to get it setup, it's possible to run some OpenCL demos on the GPU of Radeon hardware with a fully open-source driver stack. But these demos are far from the quality you'd expect with the NVIDIA/AMD binary blobs.
Anyhow, last month there was early compute support to this driver that succeeds R600g, and now that support has been merged to Mesa after having gone through three code revisions.
Tom Stellard merged the RadeonSI compute support on Friday afternoon. Like compute support on the R600 Gallium3D driver, the R600 LLVM back-end within a yet-to-be-out version of LLVM (not until v3.3) needs to be enabled when building Mesa. Today's merge puts RadeonSI Compute as a feature for the next Mesa release due out in H2'2013, which will likely be known as Mesa 10.0.