We use "async-signal-safe" (not "async-signal safe") elsewhere, and so does POSIX.
http://pubs.opengroup.org/onlinepubs/9699919799/functions/sigaction.html Index: sigaction.2 =================================================================== RCS file: /cvs/src/lib/libc/sys/sigaction.2,v retrieving revision 1.61 diff -u -p -r1.61 sigaction.2 --- sigaction.2 31 Aug 2014 01:42:36 -0000 1.61 +++ sigaction.2 15 Sep 2014 04:30:54 -0000 @@ -463,7 +463,7 @@ and .Dv SA_SIGINFO flags are options commonly found in other operating systems. The following functions are either reentrant or not interruptible -by signals and are async-signal safe. +by signals and are async-signal-safe. Therefore applications may invoke them, without restriction, from signal-catching functions: .Pp