I've had some time to benchmark it now. Run on an input of one million strings, the multiplying version takes 35 seconds and the bitshifting version takes 28 seconds. This confirms my hunch that the bitshifting version is faster. By about 20% it seems.
Out of curiosity, I tried CountZero's XS version on the same processor, expecting it to be faster. But it took 124 seconds: significantly slower than either of the pure Perl versions. I imagine that the overhead of object construction/destruction, along with its use of regular expressions slows it down.
(PS: I know the so-called bitshifting version doesn't use the bitshift operators. My initial implementation used "N" as the template for pack and unpack and used bitshifting to separate out the head and tail parts. I tweaked it to use "nn", which allowed me to drop the bitshifting, but I've kept referring to it as the bitshifting version anyway.)
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