Lecture 2: SSA Form

Computer Science 313 – Advanced Programming Topics Lecture 2:SSA Form

Knuth's Rules Of Optimization NO!

Knuth's Rules Of Optimization NO! Not yet!

Knuth's Rules Of Optimization NO! Not yet! For experts only!

Problem We Face • Want to optimize code, but face problems: Programmers are stupid • Code awful: contains variable reassigned regularly • Hard to know value at any single point in code • Would be much easier if many variables used

Problem We Face • Want to optimize code, but face problems: Programmers are human • Maintenance & readabilityprobably important • But only for humans; compiler wants to go zooom

Static Single Assignment • Ignore programmer since they are dumb • Go through and rewrite all local variables • But NOTfields (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; a1 = 2; b1 = a1 + 1; a2 = 3; b2 = a2 + 1; if (…) {d1= 2;} else {c1= 3;} b1= a1+ 1; if (…) {d= 2;} else {c = 3;} b = a + 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 a1 = 2; b1 = a1 + 1; a2 = 3; b2 = a2 + 1; if (b2 > 20) { System.out.println(“Woot”); } else { System.err.print(“Doh”); foo(a2); } b3 = a2+ b2 ;

Example of a CFG a1 = 2; b1 = a1 + 1; a2 = 3; b2 = a2 + 1; if (b2 > 20) F T System.err.print(“Woot”); System.err.print(“Doh”); foo(a2); b3 = a2+ b2;

Example of a CFG + SSA a1 = 2; b1 = a1 + 1; a2 = 3; b2 = a2 + 1; if (b2 > 20) F T System.err.print(“Woot”); System.err.print(“Doh”); foo(a2); b3 = a2 + b2;

Limits of SSA Form a1 = 2; b1 = a1 + 1; a2 = 3; b2 = a2 + 1; if (b2 > 20) F T b3 = 21 foo(a2); b5 = a2 + 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 • 1def for all future useof 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 a1 = 2; b1 = a1 + 1; a2 = 3; b2 = a2 + 1; if (b2 > 20) F T b3 = 21 foo(a2); b4 = Ф (b3, b2); b5 = a2 + b4;

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

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

Dominators • X dominates Yif and only if 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 Yif and only if 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 START a c b d CFG DT END

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

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

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

Dominator Tree Example START START END a a d b c c b d CFG DT 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 ANDXdominates predecessor of Y ANDX 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 ANDX dominates predecessor of Y ANDX 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’sdominance frontier runner  dominatorTree.parent(b)

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

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 26 - 32 • What do you when musttalk 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?

Lecture 2: SSA Form