I don't have any experience with IIR or DIR, but I found this site indicating that you can create an IIR with two DIR's. It didn't give too many details though.
"IIR filters can be represented as two FIRs, one filtering the input, and one filtering the output - the reverse path. The results of the reverse path are added to the input. In this way, it is possible to construct IIR filters using only FIR filters and adders – which can be found in the Virtex library."
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