Node Splitting

Transformation used for converting non-reducible flow graphs to reducible flow graphs. If there is a node n with k predecessors:

• Split n into k nodes generating nodes n1, n2, ..., nk
• The ith predecessor of n becomes the predecessors of ni
• All the successors of n become successors of all of the ni’s

Interval Analysis

• Divides flow graph into various regions
• Consolidate each region into a (abstract) node
• Resulting flow graph is an abstract flow graph
• Result of transformations produce control tree
  • Root represents the original graph
  • Leaf of control tree are basic blocks
  • Internal nodes are abstract nodes
  • Edges represent relationship between abstract nodes

Intervals

• Each interval has a header node that dominates all the nodes in the interval.
• Given a flow graph with initial node n0, the interval with header n is denoted by I(n) and is defined as:
  • N is in I(n)
  • If all the predecessors of a node m are in I(n) then m is in I(n)
  • No other node is in I(n)