Optimizing compiler Scalar optimizations

SSA (Static single assignment form)

SSA form proposes unique name for each variable definition and introduction of special pseudo-assignments.

Рис. 3.15.

SSA is designed to save developers from building complex use / def chains for local variables. Power of SSA is that each variable has only one definition in the program. Therefore, use / def chain is trivial.

SSA introduces special presentation of Phi-functions in places with uncertainty, to create a new variable. This so-called pseudo-assignment. In the construction is necessary to place Phi - functions and create new unique variables.

The new variables are generated by completing the variable name with a unique option. In order to correctly insert the Phi function is necessary to consider some of the concepts of graph theory.

Рис. 3.16.

Рис. 3.17.

Node N dominates node M if all ways to M pass through N. A node is an immediate dominator of node M if it is the last dominator on any path from entry node to M.

Рис. 3.18.

Dominance frontier of node x is set w of all nodes where x dominates all predecessors nodes from w, but doesn’t dominates nodes from w.

Example:

 
Dom[5] = {5,6,7,8}
DF[5] ={5,4,12,11} 

In SSA form, each variable definition must dominate the use of this variable.

Construction of the dominators set for each basic block can be the following:

The set of dominators for a node N is the intersection of the dominators set of all his predecessors, and the node itself.

Strict dominator N, this dominator!= N. Immediate dominator – the closest node from the set of dominators.

idom (N) - the immediate dominator for basic block N

children (N) - the set of basic blocks for N, which it dominates

Рис. 3.19.

Criterion of dominance frontier: if the basic block N contains a definition of variable A, then every node on the dominance frontier of node N requires Phi function for A. Each Phi function is also the definition, so you must apply the criterion while there are nodes which requires Phi function.

Рис. 3.20.

Inserting ? functions for the node 5 of the scheme on slide 25

Optimization using the SSA form:

• Dead code elimination
  • If the variable a_ver is not used than it should be removed.
• Constant propagation
  • If there is an assignment a_ver = const, then all of a_ver should be replaced by const
  • If there is a Phi-function a_next = Phi (c, c) than Phi should be replaced by c.
• Copy propagation
• If there is an assignment a_n = b_k than all usages of a_n should be replaced with b_k.
• If there is an assignment a_n = Phi (b_k, b_k) than Phi should be replaced with b_k.