Loops are pervasive in computer programs, and a great proportion of the execution time of a typical program is spent in one loop or another. Hence it is worthwhile devising optimizations to make loops go faster. Intuitively, a loop is a sequence of instructions that ends by jumping back to the beginning. But to be able to optimize loops effectively we will use a more precise definition.

A loop in a control-flow graph is a set of nodes S including a header node h with the following properties:

• From any node in S there is a path of directed edges leading to h.

• There is a path of directed edges from h to any node in S.

• There is no edge from any node outside S to any node in S other than h.

Thus, the dictionary definition (from Webster's) is not the same as the technical definition.

Figure 18.1 shows some loops. A loop entry node is one with some predecessor outside the loop; a loop exit node is one with a successor outside the loop. Figures 18.1c, 18.1d, and 18.1e illustrate that a loop may have multiple exits, but may have only one entry. Figures 18.1e and 18.1f contain nested loops.

REDUCIBLE FLOW GRAPHS

A reducible flow graph is one in which the dictionary definition of loop corresponds more closely to the technical definition; but let us develop a more precise definition.