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loops.Software pipelining has been known to assembly language programmers of machines with instruction-level parallelism since such architectures existed. Effective compiler generation of such code dates to the invention of modulo scheduling by Rau and Glaeser.Lam showed that special hardware is unnecessary for effective modulo scheduling. Her technique, modulo variable expansion is widely used in practice.Gao et al. formulated optimal software pipelining in integer linear programming, culminating

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