<snip>
I could search for the zero bytes using SRST but
presumably that would hit the same problem going off the end of a page
</snip>

Do not presume anything. Read the POp. Carefully.

"May or may not" means exactly what it says. It is allowed to do it and it is 
allowed not to do it, architecturally. In practice, a given machine will choose 
one way or the other but even that is not guaranteed. It would architecturally 
be allowed to do it one way on Mondays and the other way on Tuesdays.

If you use SRST with a big enough range you will eventually encounter storage 
to which you are not authorized to read (unless you are key 0), or storage that 
is not allocated and will blow up. The x'7FFFF000' page in the address space is 
intentionally left as one that will always blow up on reference.

Peter Relson
z/OS Core Technology Design


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