The status of support of GPUs not only depend on the GPU vendor and family but in some case also on if there are free replacements for the video BIOS or equivalent.
Fully free software status
This page summarize the research on which GPU and display controllers can work with fully free software.
Many SOCs have a display controller that work fine and doesn't need a GPU. That enables to use various displays without necessarily needing to support the GPU. When the GPU is unsupported you typically don't have 3D acceleration.
|GPUs||driver||OS or software||can work with only free software?||missing parts to work with only free software||status / features|
|Many Nvidia GPUs||nouveau||GNU/Linux||No||
|Many ATI and AMD GPUs||Radeon||GNU/Linux||No||
|Lemote ATI Radeon GPU||GRUB||Yes|
|Many older ATI/AMD GPUs||RadeonHD||GNU/Linux||Yes?||
|xgi_z9s||Coreboot until 4.12||Yes||
|Intel GPUs found in I945 and GM45 chipsets||gma||Coreboot||Yes||
|Intel GPUs found in I945 and GM45 chipsets||i915||GNU/Linux when booting with Libreboot or Coreboot||Yes||Everything seem to work fine|
This set of pages talks about GPUs.
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