I'm writing a package for a company using an STM32F746, and one of their wishes/requirements is a BIT for the CPU itself. Now, this is not defined well on their part. My opinion is that a test of a processor by itself isn't worth very much, but what I proposed was that I take a fixed value, stick it in one of the registers, add 1 to it and save it in another register, until I've passed through all the general purpose registers, and then return it and see if it is the expected value. This is at least testing part of the actual processor.
I then hoped that something like this, or actually, a lot better than this, exists in some library or public domain, as there are enough companies who must deem this a requirement, which would put different parts of a CPU though its paces and determine that the CPU is working. This would both save me the time of actually writing it, and also hopefully give me a test which is little more than just putting a check on a requirements checklist..