The true explanation for Peter Eisentraut's report of inexact asind results
seems to be that (a) he's compiling into x87 instruction set, which uses
wider-than-double float registers, plus (b) the library function asin() on
his platform returns a result that is wider than double and is not rounded
to double width.  To fix, we have to force the function's result to be
rounded comparably to what happened to the scaling constant asin_0_5.
Experimentation suggests that storing it into a volatile local variable is
the least ugly way of making that happen.  Although only asin() is known to
exhibit an observable inexact result, we'd better do this in all the places
where we're hoping to get an exact result by scaling.