Forgive the quirkiness of the title; I am not aware of a name for this concept, therefore I just made a few up.

This blogpost is about a particular way to construct what I call a "pseudorandom permuter". It is distinct from a regular pseudorandom number generator (PRNG) in that it is constructed such that the sequence will never repeat until all $$$M = 2^k$$$ integers in its machine-integer state space (32- or 64-bit) has been used. In other words, it's a way to produce a permutation of $$$[0, M)$$$ that's (hopefully) statistically indistinguishable from a truly random permutation.

The generator is made up of two parts, a "discrete Weyl sequence", and an "avalanching perfect hash function".

A "discrete Weyl sequence" is defined by a parameterized function $$$W_{s, \gamma}: [0, M) \rightarrow [0, M)$$$ where the $$$i$$$-th member of the sequence is $$$W_{s, \gamma}(i) = (s + \gamma \cdot i) \mod M$$$. The two parameters can be chosen using a standard random generator, with the caveat that $$$\gamma$$$ must be odd (this can be easily ensured by a | 1 instruction). This ensures it is coprime with the machine integer size $$$M$$$.