There is a group of PDL libraries that are not thread-safe. I am referring to those associated with dimension manipulation as indicated in the PDL::Internals documentation:
Certain types of transformations can be optimized very efficiently obviating the need for explicit readdata and writebackdata methods. Those transformations are called pdl_vaffine. Most dimension manipulating functions (e.g., slice, xchg) belong to this class.
The basic trick is that parent and child of such a transformation work on the same (shared) block of data which they just choose to interpret differently (by dusing different dims, dimincs and offs on the same data, compare the pdl structure above). Each operation on a piddle sharing data with another one in this way is therefore automatically flown from child to parent and back -- after all they are reading and writing the same block of memory. This is currently not perl thread safe --
The same documentation goes on to indicate that "no big loss since the whole PDL core is not reentrant". Therefore, the PDL core would not be thread safe