Why do programs have heavy tails?

Abstract

Designing and optimizing computer systems require deep understanding of the underlying system. Historically many important observations that led to the development of essential hardware and software optimizations were driven by empirical studies of program behavior. In this paper we report an interesting property of dynamic program execution by viewing it as a changing (or social) network. In a program social network, two instructions are friends if there is a producer-consumer relationship between them. One prominent result is that the outdegree of instructions follow heavy tails or power law distributions, i.e., a few instructions produce values for many instructions while most instructions do so for very few instructions. In other words, the number of instruction dependencies is highly skewed. In this paper we investigate this curious phenomenon. By analyzing a large set of workloads under different compilers, compilation options, ISAs and inputs we find that the dependence skew is widespread, suggesting that it is fundamental. We also observe that the skew is fractal across time and space. Finally, we describe conditions under which skew emerges within programs and provide evidence that suggests that the heavy-tailed distributions are a unique program property.