I wish there were more explanation for why this work. There is a proof but a more opinionated description would also help. My summary of it is that parallel pre

I wish there were more explanation for why this work. There is a proof but a more opinionated description would also help. My summary of it is that parallel prefix sum is work efficient for computing general recurrences of the form xi = x_i-1 + yi. Furthermore, a product of elements can be expressed as a sum by taking the sum of the log of elements and exponentiated the result. These are two super useful properties, but merging the two operations to this general formulation is not clear. Is it simply sum the logs, and the addends via prefix sums, and then sum those two results? That seems pretty straightforward, so I suspect I am missing something that makes the solution less obvious and more complexity. Is there some fancy fixed point combinator, or solution to a differential equation of the linear system for the recurrence equation?