Automatic Complexity Analysis of Explicitly Parallel Programs

The doubling of cores every two years requires programmers to expose maximum parallelism. Applications that are de-veloped on today’s machines will often be required to run on many more cores. Thus, it is necessary to understand how much parallelism codes can expose. The work and depth model provides a convenient mental framework to assess the required work and the maximum parallelism of algorithms and their parallel efficiency. We propose an automatic anal-ysis to extract work and depth from a source-code. We do this by statically counting the number of loop iterations de-pending on the set of input parameters. The resulting ex-pression can be used to assess work and depth with regards to the program inputs. Our method supports the large class of practically relevant loops with affine update functions and generates additional parameters for other expressions. We demonstrate how this method can be used to determine work and depth of several real-world applications. Our technique enables us to prove if the theoretically maximum parallelism is exposed in a practical implementation of a problem. This will be most important for future-proof software develop-ment