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The "gzip flip" stages perform a permutation that effectively reverses the order of the inner stages. This enables one network to perform the shuffle and unshuffle operations. Otherwise we'd need two networks, one for shuffle and one for unshuffle.
You can easily find work regarding shuffle operations *used* in permutation networks from 50+ years ago. But I can not find any research regarding permutation networks that can implement a generalized form of shuffle/unshuffle operations. Pointers are very welcomed! #asktwitter
Btw, those "gzip" operations are like Inception for bit permutations: You permute the bits in your data word by permuting the bits in the bit indices. This network (used repeatedly) can performs a class of 32-bit permutations that is equivalent to all 5-bit permutations.
Interesting question. I've done some research about permutation networks for my master thesis (which involves creating sorting networks using OpenCLs shuffle operation), but I didn't come across something discussing this either.
Reminds me of stuff around crossbar design https://en.m.wikipedia.org/wiki/Clos_network … and Benes switches.
Yes, they use shuffle/unshuffle operations in all kind of networks. (And none of that is new https://dl.acm.org/citation.cfm?id=1311797 ….) But I have not found anything about networks to produce a class of shuffle/unshuffle operations.
ICYMI see Knuth 7.1.3 for a treatment of bit reversal ... swapping ... permutation ... perfect shuffle ... compress ... sheep&goats ... and arbitrary mappings (bit fanout).
Crazy idea: Did you discuss a map instruction + map function unit, for e.g. XLEN=64, somehow is set up with a context of 6 64b values = 64 6-bit bit-selectors: bit [$clog2(XLEN)-1:0] select[XLEN]; that performs for i in range(XLEN): out[i] = in[select[i]]; ? :-)
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