Cancellation points in signal handlers?

What happens if a program calls a function which is a cancellation point from a signal handler? There are a number of functions which POSIX specifies as both async-signal-safe and cancellation points. If a signal handler calls such a function and cancellation is acted upon, the result is quite similar to what would happen if the thread had enabled asynchronous cancellation - actually much worse, because all the cancellation cleanup handlers, which are probably not async-signal-safe, would be called from a signal-handler context.

What does POSIX actually specify in this case, and what do implementations actually do? I can't find any language in POSIX that would forbid cancellation points in signal handlers from being acted upon, nor any such protection in the glibc/nptl source.