There is an "DO-178B" level A and level B certification for airborne systems. Does it prohibit using of optimizating compilers?
E.g. Some compilers will reorder instructions to get more performance. Does DO-178B lev.A or lev.B prohibits this reordering?
Most modern CPU have such reordering builtin in the hardware. Are they allowed to be used within DO-178B lev.A softare/hardware systems?
First, and critically: For this type of question, if the answer matters, you need to get a formal professional opinion from someone who is competent to provide it, or discuss this with your certification authority. Any reply you will get here should not be relied on.
With that said, I will assume you are asking from a point of curiousity and will not be relying on the answer in any meaningful way, and I will attempt to answer in that vein. I am not a professional, and this is not professional advice.
The most on-point documentation I could find online with a quick search was this FAA guideline paper about a related topic: http://www.faa.gov/aircraft/air_cert/design_approvals/air_software/cast/cast_papers/media/cast-12.pdf. This paper describes the conditions under which one must do verification of the generated object code rather than the source code. In particular, it gives a number of examples that will occur even in non-optimized code -- automatic variable initialization and exception handling are a couple of examples. On compiler optimization, it notes:
I do not have a copy of DO-178B handy to read section 4.4.2a, but I would note that (a) there are procedures for handling other cases where the object code does not correspond to the source code in a one-to-one manner, and (b) this pretty strongly implies that compiler optimization is discussed rather than outright prohibited.
It's also pretty clear from a number of the discussions in that paper that the answer to "we can't trace things between the source code and the object code" is to validate the object code in some manner -- in other words, there is a solution other than prohibiting such things.
Thus, I would conclude that at least some compiler optimizations must be permitted.
In particular, the sort of reordering that you describe is quite traceable, and it seems almost certain to me that it would be permitted.