The Parable of the Square-Dancing Witches and Wizards

Abstract

In this presentation I will tell The Parable of the Square-Dancing Witches and Wizards. This parable explains how to perform the bit-permutation operation that compresses the selected bits to the LSB end of the word, while the remaining bits are pushed to the MSB end of the word in reversed bit order. This operation is referred to as “sheep and goats” (SAG) operation with reversed goat bits by other authors, in reference to The Parable of the Sheep and the Goats, found in Matthew 25:31-46. Mentalising and discussing routing networks using symbolism from scripture is awkward or even problematic for many reasons. The Parable of the Square-Dancing Witches and Wizards on the other hand is loosely based on symbolisms from The Wizard of Oz, and does not only provide a mental image for what this bit-permutation operation does, but also how that can be achieved in an efficient manner using a Reverse Omega Network.