Equality Saturation: A New Approach to Optimization

Optimizations in a traditional compiler are applied sequentially, with each optimization destructively modifying the program to produce a transformed program that is then passed to the next optimization. We present a new approach for structuring the optimization phase of a compiler. In our approach, optimizations take the form of equality analyses that add equality information to a common intermediate representation. The optimizer works by repeatedly applying these analyses to infer equivalences between program fragments, thus saturating the intermediate representation with equalities. Once saturated, the intermediate representation encodes multiple optimized versions of the input program. At this point, a profitability heuristic picks the final optimized program from the various programs represented in the saturated representation. Our proposed way of structuring optimizers has a variety of benefits over previous approaches: our approach obviates the need to worry about optimization ordering, enables the use of a global optimization heuristic that selects among fully optimized programs, and can be used to perform translation validation, even on compilers other than our own. We present our approach, formalize it, and describe our choice of intermediate representation. We also present experimental results showing that our approach is practical in terms of time and space overhead, is effective at discovering intricate optimization opportunities, and is effective at performing translation validation for a realistic optimizer.Comment: 80 pages, 39 figure

American College of Cardiology; American Heart Association Task Force; European Society of Cardiology Committee for Practice Guidelines. ACC/AHA/ESC 2006 guidelines for management of patients with ventricular arrhythmias and the prevention of sudden cardiac death: a report of the American College of Cardiology/American Heart Association Task Force and the European Society of Cardiology Committee for Practice Guidelines (Writing Committee to Develop Guidelines for Management of Patients With Ventricular Arrhythmias and the Prevention of Sudden Cardiac Death).

The purpose this document is to update and combine the previously published recommendations into one source approved by the major cardiology organizations in the United States and Europe. We have consciously attempted to create a streamlined document, not a textbook, that would be useful specifically to locate recommendations on the evaluation and treatment of patients who have or may be at risk for ventricular arrhythmias. Thus, sections on epidemiology, mechanisms and substrates, and clinical presentations are brief, because there are no recommendations for those sections. For the other sections, the wording has been kept to a minimum, and clinical presentations have been confined to those aspects relevant to forming recommendations