## Parallel programming with opencl and python: parallel scan

This post will continue the subject of how to implement common algorithms in a parallel processor, which I started to discuss here. Today we come to the second pattern, the scan. An example is the cumulative sum, where you iterate over an array and calculate the sum of all elements up to the current one. Like reduce, the algorithm we’ll talk about is not exclusive for the sum operation, but for any binary associative operation (the max is another common example). There are two ways to do a parallel scan:  the hills steele scan, which needs $\log n$ steps; and the blelloch scan, requiring $2 \log n$ steps. The blelloch scan is useful if you have more data than processors, because it only needs to do $\mathcal{O}(n)$ operations (this quantity is also referred to as the work efficiency); while the hillis steele scan needs $\mathcal{O}(n \log n)$ operations. So let’s look at how to implement both of them with opencl kernels.

## Parallel programming with opencl and python: parallel reduce

Once you know how to use python to run opencl kernels on your device (read Part I and Part II of this series) you need to start thinking about the programming patterns you will use. While many tasks are inherently parallel (like calculating the value of a function for N different values) and you can just straightforwardly run N copies on your processors, most interesting tasks involve dependencies in the data. For instance if you want to simply sum N numbers in the simplest possible way, the thread doing the summing needs to know about all N numbers, so you can only run one thread, leaving most of your cores unused. So what we need to come up with are clever ways to decompose the problem into individual parts which can be run in parallel, and then combine them all in the end.