Most programs are repetitive, where similar behavior can be seen at different execution times. Proposed algorithms automatically group these similar intervals of execution into phases, where the intervals in a phase have homogeneous behavior and similar resource requirements. These prior techniques have focused on using fixed intervals for finding phase behavior. Using fixed length intervals can make finding the true periodic repeating phase behavior difficult, since the fixed length intervals can be out of sync with the size of the ideal phase behavior. In addition, focusing only on a single fixed interval size limits the phase behavior to the phase behavior seen at that interval size, when in reality there is a whole hierarchy of phase behavior at many different intervals sizes. In this paper, we present an automated approach for breaking the program's execution up into variable length intervals that match the phase behavior of the program. We then provide an algorithm for creating a hierarchy of variable length intervals and use this hierarchy to expose a program's phase behavior from small to large time scales.
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