Computer Science 313 – Advanced Programming Topics

Knuth's Rules Of Optimization

Problem We Face

Static Single Assignment  Ignore programmer since they are dumb  Go through and rewrite all local variables NOT  But NOT fields (other threads may use them)  Change code so each variable assigned once (def)  Tie value (use) to definition for that line of code  Names unimportant, since only used by compiler  Optimizations easier & need not fix humans

Examples of SSA Form a = 2; b = a + 1; a = 3; b = a + 1; a 1 = 2; b 1 = a 1 + 1; a 2 = 3; b 2 = a 2 + 1; if (…) { d = 2; } else { c = 3; } b = a + 1; if (…) { d 1 = 2; } else { c 1 = 3; } b 1 = a 1 + 1;

Control Flow Graph  Common technique showing program structure  Visualizes execution paths possible in a method  Also referred to as flow of a program’s control  Vertices are “basic blocks” found in method  Basic block is code that must be executed together  Edges represent transfer of flow between blocks  Normally result from start & end of loops or branches  Goes to block could come next during a method run

Example of a CFG a 1 = 2; b 1 = a 1 + 1; a 2 = 3; b 2 = a 2 + 1; if (b 2 > 20) { System.out.println(“Woot”); } else { System.err.print(“Doh”); foo(a 2 ); } b 3 = a 2 + b 2 ;

Example of a CFG a 1 = 2; b 1 = a 1 + 1; a 2 = 3; b 2 = a 2 + 1; if (b 2 > 20) System.err.print(“Woot”); System.err.print(“Doh”); foo(a 2 ); T F b 3 = a 2 + b 2 ;

Example of a CFG + SSA a 1 = 2; b 1 = a 1 + 1; a 2 = 3; b 2 = a 2 + 1; if (b 2 > 20) System.err.print(“Woot”); System.err.print(“Doh”); foo(a 2 ); T F b 3 = a 2 + b 2 ;

Limits of SSA Form a 1 = 2; b 1 = a 1 + 1; a 2 = 3; b 2 = a 2 + 1; if (b 2 > 20) b 3 = 21 foo(a 2 ); T F b 5 = a 2 + b ???? ;

Ф Functions Are Fun!  SSA has problems when code branches  What if variable assigned – cannot know defs to use  Ф function merges values along multiple paths  Ф function has one input for each incoming vertex  1 def for all future use of variable now exists  Remember that Ф function does not exist  Simple bookkeeping to allow SSA to work  Compiler also uses to track related values

Examples of SSA Form a 1 = 2; b 1 = a 1 + 1; a 2 = 3; b 2 = a 2 + 1; if (b 2 > 20) b 3 = 21 foo(a 2 ); T F b 4 = Ф (b 3, b 2 ); b 5 = a 2 + b 4 ;

Dominators  X dominates Y if and only if ALL PATHS X on ALL PATHS to Y  Must find for good time on weekends

Dominators  X dominates Y if and only if ALL PATHS X on ALL PATHS to Y  Must find for good time on weekends

Dominators  X dominates Y if and only if ALL PATHS X on ALL PATHS to Y  Each basic block needs this to convert to SSA

Dominators  X dominates Y if and only if ALL PATHS X on ALL PATHS to Y  Each basic block needs this to convert to SSA

Dominators  X dominates Y if and only if ALL PATHS X on ALL PATHS to Y  Each basic block needs this to convert to SSA  Reflexive & transitive & fun relation defined  dom(Y) defines dominators of Y  To know when to add Ф nodes for Y use dom(Y)  Must be computed

Dominators  X dominates Y if and only if ALL PATHS X on ALL PATHS to Y  Each basic block needs this to convert to SSA  Reflexive & transitive & fun relation defined  dom(Y) defines dominators of Y  To know when to add Ф nodes for Y use dom(Y)  Must be computed (unless you’ve been a bad coder)

Dominator Tree Example START a b c d END START CFG DT

Dominator Tree Example START a b c d END START CFG DT a

Dominator Tree Example START a b c d END START CFG DT a b c

Dominator Tree Example START a b c d END START CFG DT a b c d

Dominator Tree Example START a b c d END START CFG DT a b c d END

Next Step for SSA Form  Dominance frontier for node X in CFG  Defines set such that for each node Y in the d.f.: X != Y AND X dominates predecessor of Y AND X does not dominate Y

Next Step for SSA Form  Dominance frontier for node X in CFG  Defines set such that for each node Y in the d.f.: X != Y AND X dominates predecessor of Y AND X does not dominate Y

DF Computation  Algorithm to compute dominance frontier for (Vertex b : CFG.vertices()) if ( CFG.countInEdges( b ) ≥ 2) for (Vertex p : CFG.hasEdgeTargetting( b )) runner  p while ( runner != dominatorTree. parent (b)) // Add runner to b ’s dominance frontier runner  dominatorTree. parent (b)

DF Example START a bc d END CFG DT START a bc d END for (Vertex b : CFG.vertices()) if ( CFG.countInEdges( b ) ≥ 2) for (Vertex p : CFG.hasEdgeTargetting( b )) runner  p while ( runner != dominatorTree. parent (b)) // Add b to runner ’s dominance frontier runner  dominatorTree. parent (runner)

DF Example START a bc d END CFG DT START a bc d END for (Vertex b : CFG.vertices()) if ( CFG.countInEdges( b ) ≥ 2) for (Vertex p : CFG.hasEdgeTargetting( b )) runner  p while ( runner != dominatorTree. parent (b)) // Add b to runner ’s dominance frontier runner  dominatorTree. parent (runner)

Placing Φ Nodes  If a basic block X has assignment to variable a  May need Φ function for a but where to place it?  Add Φ to all blocks with X in dominance frontier  Repeat algorithm for each assignment & block  No shortcuts here: must compute iteratively  Quick for computer to do & so can spare the whip

Placing Φ Nodes  If a basic block X has assignment to variable a  May need Φ function for a but where to place it?  Add Φ to all blocks with X in dominance frontier  Repeat algorithm for each assignment & block  No shortcuts here: must compute iteratively  Quick for computer to do & so can spare the whip

Why Should You Care?  Do you understand how programs optimized?  Many common beliefs wrong & ridiculous  Avoid looking like poseur & write useless speedups  May confuse compiler and prevent real optimizations

For Next Lecture  Read pages  What do you when must talk about a program?  What do you document (when it matters?)  What do wish others documentation would say?  Good design means what? Why? How do you know?  Ever seen beautiful code? What made it pretty?