They do. It is called ROCm which is short for Radeon Open Compute. Unlike CUDA it is an open source framework. This have been part of AMDs strategy regarding computation acceleration. While NVIDIA tries to keep their framework closed source in order to lock inn software to their framework making it harder to use for example OpenCL and therefore harder to switch to AMD or Intel hardware later on. AMD embraces open source software making it easier to extend their framework to add functionality that is missing and making it possible for users to read the source code to understand how to interact with it. This does mean that developers of OpenCL have been able to see the behavior of ROCm and replicate this.
There is also a huge difference in marketing for these frameworks. NVIDIA spends a lot of money marketing their CUDA framework. A lot of people have heard about OpenCL through organic marketing. But AMD does not spend much resources marketing ROCm and tend to only mention it when marketing their hardware and not on its own.
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