It would be interesting to generalize this with the operations available in the riscv bitmanip extension-- it might discover some strong functions for use in the future when those instructions are more widely available.
carryless multiply would also allow extending the set of reversible operations and are fast on some existent hardware (CRC too, somewhat a wider set of hardware but should be a strict subset of what CLMUL could find).
Many applications of hashes only care about the LSB or MSB of the hashes so evaluating the bias on MSB or LSB windows would be interesting (or mod varrious numbers), and some overall unbiased functions will look better or worse for metrics that don't gauge the entire output. (or for non-uniform inputs, for that matter, e.g. ascii text).
carryless multiply would also allow extending the set of reversible operations and are fast on some existent hardware (CRC too, somewhat a wider set of hardware but should be a strict subset of what CLMUL could find).
Many applications of hashes only care about the LSB or MSB of the hashes so evaluating the bias on MSB or LSB windows would be interesting (or mod varrious numbers), and some overall unbiased functions will look better or worse for metrics that don't gauge the entire output. (or for non-uniform inputs, for that matter, e.g. ascii text).