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TouchDevelop/ast/dataflow.ts

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95 KiB
TypeScript
Исходник Ответственный История

///<reference path='refs.ts'/>
module TDev.AST {
// a visitor to find the set of ``next'' statements after provided one
// the next finder is conservative and can find false nodes!
export class NextFinder
extends NodeVisitor {
constructor()
{
super();
}
static enclosingStmt(stmt: Stmt) {
return stmt.parentBlock() && stmt.parentBlock().parent;
}
static asLoop(stmt: Stmt): LoopStmt{
if (stmt instanceof While || stmt instanceof For || stmt instanceof Foreach) return <LoopStmt><any>stmt;
else return null;
}
private nextInBlock(stmt: Stmt) {
if (!stmt || !stmt.parentBlock()) return [];
var container = stmt.parentBlock().stmts;
var ix = container.indexOf(stmt);
var enclosing = NextFinder.enclosingStmt(stmt);
++ix;
while ((ix < container.length) && (container[ix].isPlaceholder() || container[ix].nodeType() === "comment")) ++ix;
var ret = []
if(ix >= container.length) {
// we are last child
ret = this.nextInBlock(enclosing);
} else {
ret = [container[ix]];
}
return ret.concat(this.visitLoop(NextFinder.asLoop(enclosing)));
}
static firstInCodeBlock(body: CodeBlock) {
if (body == null) return null;
var ix = 0;
var container = body.stmts;
while ((ix < container.length) && (container[ix].isPlaceholder() || container[ix].nodeType() === "comment"))++ix;
if (ix >= container.length) {
// nothing useful inside
return null;
}
return container[ix];
}
public visitCodeBlock(body: CodeBlock) {
var ret = NextFinder.firstInCodeBlock(body);
return ret ? [ret] : [];
}
private visitLoop(stmt: LoopStmt) {
if (stmt == null) return [];
var ret = this.visitCodeBlock(stmt.body);
return ret.concat(this.nextInBlock(<Stmt><any>stmt));
}
public visitFor(stmt: For) { return this.visitLoop(stmt); }
public visitForeach(stmt: Foreach) { return this.visitLoop(stmt); }
public visitWhile(stmt: While) { return this.visitLoop(stmt); }
// TODO this is wrong for Return and Break
public visitExprStmt(stmt: ExprStmt) {
return this.nextInBlock(stmt);
}
public visitBox(box: Box) {
return this.visitCodeBlock(box.body);
}
public visitInlineActions(ia: InlineActions) {
return this.visitExprStmt(ia);
}
public visitAnyIf(stmt: If) {
var arrs = stmt.parentIf.bodies().map(b => this.visitCodeBlock(b))
arrs.push(this.nextInBlock(stmt)) // this is not really the case most of the time, but whatever
return Util.concatArraysVA(arrs)
}
static find(stmt: Stmt): Stmt[]{
if (!stmt) return [];
var ret = new NextFinder().dispatch(stmt);
if (!ret) {
return [];
}
return ret;
}
}
export class InnerNextFinder
extends NodeVisitor {
called: Action[] = [];
visitAstNode(n: AstNode) {
this.visitChildren(n);
return null;
}
visitCall(n: Call) {
var act = n.calledAction();
if (act && this.called.indexOf(act) < 0) {
this.called.push(act);
} else {
super.visitCall(n);
}
}
visitExprHolder(n: ExprHolder) {
if (n.parsed) this.dispatch(n.parsed);
}
static find(stmt: Stmt): Stmt[]{
if (!stmt) return [];
var finder = new InnerNextFinder();
finder.dispatch(stmt);
return finder.called.filter(a => !!a.body).map(a => {
var fst = NextFinder.firstInCodeBlock(a.body);
return fst ? [fst] : [];
}).reduce((a,b) => a.concat(b), []);
}
}
class AwaitChecker extends NodeVisitor {
private res = false;
visitAstNode(n: AstNode) {
if (!n) return;
this.visitChildren(n);
}
visitExprHolder(eh: ExprHolder) {
if (!eh) return;
this.dispatch(eh.parsed);
}
visitCall(n: Call) {
if (!n) return;
super.visitCall(n);
if (n.awaits()) this.res = true;
}
static isAwait(n: Stmt) {
if (!n) return;
var checker = new AwaitChecker();
checker.dispatch(n);
return checker.res;
}
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
// Visitor classes that enable Dataflow Analyses to walk through the AST
// PredecessorsFinder extracts the list of predecessors statements of another statement
// by walking the AST. These are the predecessors when converting the AST to a CFG.
// NOTE: Valid nodes for all dataflow analyses are Statement nodes
// that contain an ExprHolder instance (therefore, consumes an expression).
// PredecessorsFinder and SuccessorsFinder both walk through these nodes
// and bypasses the rest (Box es, for instance).
export class PredecessorsFinder
extends NodeVisitor {
constructor() {
super();
}
// Convenience methods
static enclosingStmt(stmt: Stmt): Stmt {
return stmt.parentBlock() && stmt.parentBlock().parent;
}
static asLoop(stmt: Stmt): Stmt {
if (stmt instanceof While || stmt instanceof For || stmt instanceof Foreach) return stmt;
else return null;
}
// Tries to dig the last statement of a block that belongs to the
// current stmt. If it does not contain a block, returns itself.
static unpeelAndGetLast(stmt: Stmt): Stmt[]{
var ret: Stmt[] = [];
// Comments and placeholders are not excluded from the dataflow
// visiting path. They just propagate the information through,
// but we need to handle them.
if (stmt instanceof Comment) {
ret = [stmt];
} else if (stmt instanceof For) {
ret = ret.concat(PredecessorsFinder.lastInCodeBlock((<For>stmt).body));
} else if (stmt instanceof Foreach) {
ret = ret.concat(PredecessorsFinder.lastInCodeBlock((<Foreach>stmt).body));
} else if (stmt instanceof While) {
ret = ret.concat(PredecessorsFinder.lastInCodeBlock((<While>stmt).body));
} else if (stmt instanceof If) {
Util.assert(!((<If>stmt).isElseIf));
// "If" nodes contains many last statements, one for each block. This should
// always return at least two nodes, even when else is empty - in this
// case it returns the placeholder.
ret = ret.concat(Util.concatArraysVA((<If>stmt).bodies().map(PredecessorsFinder.lastInCodeBlock)))
} else if (stmt instanceof Box) {
ret = ret.concat(PredecessorsFinder.lastInCodeBlock((<Box>stmt).body));
} else if (stmt instanceof ExprStmt) {
ret = [stmt];
}
if (ret.length == 0)
ret = [stmt];
return ret;
}
// Find the previous IF statement (used only to find predecessors
// of ifelse conditions).
private findPreviousIf(ifstmt: If): Stmt[] {
Util.assert(!!ifstmt && !!(ifstmt.parentBlock()));
var container = ifstmt.parentBlock().stmts;
var ix = container.indexOf(ifstmt);
--ix;
Util.assert(ix >= 0);
var previous = container[ix];
Util.assert(previous instanceof If);
return [previous];
}
// Find the previous statement considering the enclosing block
private previousInBlock(stmt: Stmt): Stmt[] {
if (!stmt || !stmt.parentBlock()) return [];
var container = stmt.parentBlock().stmts;
var ix = container.indexOf(stmt);
var enclosing = PredecessorsFinder.enclosingStmt(stmt);
--ix;
var ret = [];
if (ix < 0) {
// We are the first statement in a block
// The previous is the loop condition check or if statement,
// if they exist. Otherwise, we need to dig further and go for
// the previous statement of the enclosing block.
var l = PredecessorsFinder.asLoop(enclosing);
if (!!l || (enclosing instanceof If)) {
ret = ret.concat(enclosing);
} else if (enclosing instanceof InlineAction) {
ret = [];
} else {
ret = ret.concat(this.previousInBlock(enclosing));
}
} else {
var prev = container[ix];
// In case of a block of statements, we need to unpeel and go
// inside it. For loops, the loop itself is the statement.
if ((prev instanceof For)
|| (prev instanceof While)
|| (prev instanceof Foreach)) {
ret = ret.concat([prev]);
} else if ((prev instanceof If)
&& ((<If>prev).isElseIf)) {
ret = ret.concat(PredecessorsFinder.unpeelAndGetLast((<If>prev).parentIf));
} else {
ret = ret.concat(PredecessorsFinder.unpeelAndGetLast(prev));
}
if (ret.length == 0)
ret = this.previousInBlock(prev);
}
return ret;
}
// Extracts the last statement in a code block. Useful for finding
// predecessors of loop structures.
static lastInCodeBlock(body: CodeBlock): Stmt[] {
if (body == null) return [];
var enclosing = PredecessorsFinder.enclosingStmt(body);
var container = body.stmts;
var ix = container.length - 1;
if (ix < 0) {
return [];
}
var last = container[ix];
// In case of a block of statements, we need to unpeel and go
// inside it. For loops, the loop itself is the statement.
if ((last instanceof For)
|| (last instanceof While)
|| (last instanceof Foreach))
return [last];
if (last instanceof If && (<If>last).isElseIf) {
return PredecessorsFinder.unpeelAndGetLast((<If>last).parentIf);
}
return PredecessorsFinder.unpeelAndGetLast(last);
}
public visitCodeBlock(body: CodeBlock): Stmt[] {
return PredecessorsFinder.lastInCodeBlock(body);
}
// The predecessor of a loop is the pair of the previous statement in
// its enclosing block and the last statement inside the loop
private visitLoop(stmt: Stmt): Stmt[] {
if (stmt == null) return [];
var ret = this.previousInBlock(<Stmt><any>stmt);
return ret.concat(PredecessorsFinder.unpeelAndGetLast(stmt));
}
public visitFor(stmt: For): Stmt[] { return this.visitLoop(stmt); }
public visitForeach(stmt: Foreach): Stmt[] { return this.visitLoop(stmt); }
public visitWhile(stmt: While): Stmt[] { return this.visitLoop(stmt); }
// The predecessor of a regular statement is simply the previous
// statement in the block
public visitStmt(stmt: Stmt): Stmt[] {
return this.previousInBlock(stmt);
}
// The predecessor of an If is simply the previous statement in its
// enclosing block.
public visitIf(stmt: If): Stmt[]{
Util.assert(!stmt.isElseIf);
return this.previousInBlock(stmt);
}
// If it is an Ifelse, then its predecessor is the previous If.
public visitElseIf(n: If) {
return this.findPreviousIf(n);
}
// Returns the list of predecessor statements for "stmt". Uses a
// visitor to handle different node types.
static find(stmt: Stmt): Stmt[] {
if (!stmt) return [];
return new PredecessorsFinder().dispatch(stmt);
}
}
// Used for dataflow equations, analogous to the PredecessorFinder.
// Predecessor and Successors Finders must satisfy the property that
// Succs[ Preds[x] ] = x
// Otherwise analyses will break. Successors are not just used in backward
// analysis, but also in regular forward analysis in order to discover
// which nodes to analyze when its Outs[] set is update, and vice-versa.
//
// NOTE: Valid nodes for all dataflow analyses are Statement nodes
// that contain an ExprHolder instance (therefore, consumes an expression).
// PredecessorsFinder and SuccessorsFinder both walk through these nodes
// and bypasses the rest (Box es, for instance).
export class SuccessorsFinder
extends NodeVisitor {
constructor() {
super();
}
// Convenience methods
static enclosingStmt(stmt: Stmt): Stmt {
return stmt.parentBlock() && stmt.parentBlock().parent;
}
static asLoop(stmt: Stmt): Stmt {
if (stmt instanceof While || stmt instanceof For || stmt instanceof Foreach) return stmt;
else return null;
}
// This is not the same as "unpeelAndGetLast" of Predecessors because
// it rarely needs to actually unpeel and get the statements inside a
// block. The reason is that the first statement of a "If" or loop node
// are really the "If" or loop themselves, except for Boxes.
static unpeelAndGetFirst(stmt: Stmt): Stmt[]{
var ret: Stmt[] = [];
if (stmt instanceof Comment) {
ret = ret.concat(stmt);
} else if (stmt instanceof For)
ret = ret.concat(stmt);
else if (stmt instanceof Foreach) {
ret = ret.concat(stmt);
} else if (stmt instanceof While) {
ret = ret.concat(stmt);
} else if (stmt instanceof If) {
ret = ret.concat(stmt);
} else if (stmt instanceof Box) {
ret = ret.concat(SuccessorsFinder.firstInCodeBlock((<Box>stmt).body));
} else if (stmt instanceof ExprStmt) {
ret = ret.concat(stmt);
}
if (ret.length == 0)
ret = [stmt];
return ret;
}
// Find the next IF statement (used only to find successors
// of if/ifelse nodes).
private findNextIf(ifstmt: If): Stmt[] {
Util.assert(!!ifstmt && !!(ifstmt.parentBlock()));
var container = ifstmt.parentBlock().stmts;
var ix = container.indexOf(ifstmt);
++ix;
if (ix >= container.length)
return [];
var next = container[ix];
if (!(next instanceof If) || !((<If>next).isElseIf))
return [];
return [next];
}
// clone of nextInBlock, but jumps over IFELSE stmts.
// Goes to the next stmt after a sequence of ifelse. Useful to
// jump to the end of the structure when finding the successors of
// the last statement of a codeblock inside an if.
private jumpToEndOfIfElse(ifstmt: Stmt): Stmt[] {
Util.assert(!!ifstmt && !!(ifstmt.parentBlock()));
var container = ifstmt.parentBlock().stmts;
var ix = container.indexOf(ifstmt);
var enclosing = PredecessorsFinder.enclosingStmt(ifstmt);
++ix;
while (container[ix] && container[ix] instanceof If && (<If>(container[ix])).isElseIf) ++ix;
var ret = [];
if (ix >= container.length) {
// We are the last statement, so we can only find the next
// statement looking for our parents: it is either the
// enclosing loop or the successor of our parent. NOTE: We do not
// jump directly from the last statement of a loop to outside
// the loop: it must first go to the loop node to check the
// condition, therefore we only have a single successor in
// this case.
var l = SuccessorsFinder.asLoop(enclosing);
if (!!l) {
ret = ret.concat(enclosing);
} else if (enclosing instanceof If) {
ret = ret.concat(this.jumpToEndOfIfElse(enclosing));
} else if (enclosing instanceof InlineAction) {
ret = [];
} else {
ret = ret.concat(this.nextInBlock(enclosing));
}
} else {
var next = container[ix];
// If this is a statement that contains statements, we want its children,
// but first check if it is an statement that contains an ExprHolder
ret = ret.concat(SuccessorsFinder.unpeelAndGetFirst(next));
if (ret.length == 0)
ret = this.nextInBlock(next);
}
return ret;
}
// Look for the next statement considering its enclosing block.
private nextInBlock(stmt: Stmt): Stmt[] {
if (!stmt || !stmt.parentBlock()) return [];
var container = stmt.parentBlock().stmts;
var ix = container.indexOf(stmt);
var enclosing = PredecessorsFinder.enclosingStmt(stmt);
++ix;
var ret = [];
if (ix >= container.length) {
// We are the last statement, so we can only find the next
// statement looking for our parents: it is either the
// enclosing loop or the successor of our parent. NOTE: We do not
// jump directly from the last statement of a loop to outside
// the loop: it must first go to the loop node to check the
// condition, therefore we only have a single successor in
// this case.
var l = SuccessorsFinder.asLoop(enclosing);
if (!!l) {
ret = ret.concat(enclosing);
} else if (enclosing instanceof If) {
ret = ret.concat(this.jumpToEndOfIfElse(enclosing));
} else if (enclosing instanceof InlineAction) {
ret = [];
} else {
ret = ret.concat(this.nextInBlock(enclosing));
}
} else {
var next = container[ix];
// If this is a statement that contains statements, we want its children,
// but first check if it is an statement that contains an ExprHolder
ret = ret.concat(SuccessorsFinder.unpeelAndGetFirst(next));
if (ret.length == 0)
ret = this.nextInBlock(next);
}
return ret;
}
// Extracts the first statement in a code block, useful for finding
// successors of loop structures.
static firstInCodeBlock(body: CodeBlock): Stmt[] {
if (body == null) return [];
var container = body.stmts;
var ix = 0;
var enclosing = SuccessorsFinder.enclosingStmt(body);
if (ix >= container.length) {
// nothing useful inside
return [];
}
var first = container[ix];
return SuccessorsFinder.unpeelAndGetFirst(first);
}
public visitCodeBlock(body: CodeBlock): Stmt[] {
return SuccessorsFinder.firstInCodeBlock(body);
}
// The successors of a loop is the pair of the first statement in its
// body and the next statement after the loop, since the execution flow
// skips the loop body after its condition evaluates to false.
private visitLoop(stmt: Stmt): Stmt[] {
if (stmt == null) return [];
var ret = this.nextInBlock(stmt);
return ret.concat(this.visitCodeBlock((<LoopStmt><any>stmt).body));
}
public visitFor(stmt: For): Stmt[] { return this.visitLoop(stmt); }
public visitForeach(stmt: Foreach): Stmt[] { return this.visitLoop(stmt); }
public visitWhile(stmt: While): Stmt[] { return this.visitLoop(stmt); }
// The succ for a generic statement is the next stmt in its enclosing
// block.
public visitStmt(stmt: Stmt): Stmt[] {
return this.nextInBlock(stmt);
}
// Successors of the "If" node are the first statements of its child
// code blocks ("then" and "else"). If the else path includes another
// condition check (ifelse node), then the first statement of "then"
// block and the next ifelse node are the successors.
public visitIf(stmt: If): Stmt[]{
var ret = SuccessorsFinder.firstInCodeBlock(stmt.rawThenBody);
if (stmt.displayElse)
return ret.concat(SuccessorsFinder.firstInCodeBlock(stmt.rawElseBody));
return ret.concat(this.findNextIf(stmt));
}
public visitElseIf(n: If) { return this.visitIf(n); }
// Returns the list of successor statements for "stmt". Only returns
// "valid" nodes as described in the note above (Statement nodes that
// contains ExprHolder instances).
static find(stmt: Stmt): Stmt[] {
if (!stmt) return [];
return new SuccessorsFinder().dispatch(stmt);
}
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
// Dataflow set data strucutes
// An element may be anything worth storing in Ins/Outs sets for each point
// of the program and depends on the analysis. Reaching definitions will
// store the stringified def expression as the "key" and a reference to the
// def expression itself. "Id" is bookkeeping maintained by the
// SetElementsPool class.
export class SetElement {
constructor(public id: number, public key: string, public refNode: Expr) { }
}
// The pool keeps the elements alive and assign the lowest possible id
// to reference them, and Set instances reference them using a lightweight
// bitset representation. If IDs are large, more memory will be necessary
// to represent the bitset.
// After an analysis is done, a pool contains all elements generated by
// Gen equations.
class SetElementsPool {
private map: { [s: string]: number; };
private pool: SetElement[];
constructor(private curId = 0) {
this.map = {};
this.pool = [];
}
// Builds a new SetElement and assign to it the lowest possible id. Get
// it if an element with the same id already exists.
public getElm(key: string, refNode: Expr): SetElement {
var idx = this.map[["a_", key].join("")];
if (idx == undefined) {
idx = this.curId++;
var elm = new SetElement(idx, key, refNode);
this.pool.push(elm);
this.map[["a_", key].join("")] = idx;
}
return this.pool[idx];
}
public getElmById(id: number): SetElement {
if (id >= this.pool.length) return null;
return this.pool[id];
}
public size(): number {
return this.pool.length;
}
}
// The memory representation of all Ins/Outs sets for all points of the
// programs.
export class BitSet {
private _myset: number[];
private setSize: number;
// largestIndex is important for bookkeeping and directly reflects
// our current size, signaling when it should be expanded. It is also
// used to limit which indexes to traverse when forEach is called for
// an allSet set (that is supposed to contain all known elements).
private largestIndex: number;
// The allSet flag is meant to be used in a set that is supposed to
// start containing all possible elements. Therefore, it expands
// with 1s, meaning it contains even those elements that it has never
// seen before. Useful for intersection-confluence analyses.
constructor(public allSet = false) {
this._myset = [];
if (allSet)
this._myset.push(0xFFFFFFFF);
else
this._myset.push(0);
this.setSize = 1;
this.largestIndex = -1;
}
// Helper function to expand the set when a large index is used
// to access an element that is currently not being represented.
private growSet(idx: number): void {
idx -= this.setSize * 32;
while (idx >= 0) {
if (this.allSet)
this._myset.push(0xFFFFFFFF);
else
this._myset.push(0);
++this.setSize;
idx -= 32;
}
}
private cloneSet(): number[]{
var a: number[] = [];
for (var i = 0; i < this.setSize; ++i) {
a.push(this._myset[i]);
}
return a;
}
// Makes this an allSet set (contains all elements).
public makeAllSet(): void {
this._myset = [0xFFFFFFFF];
this.setSize = 1;
this.allSet = true;
this.largestIndex = -1;
}
public add(elm: number): void {
if (elm >= this.setSize * 32)
this.growSet(elm);
if (elm > this.largestIndex)
this.largestIndex = elm;
this._myset[Math.floor(elm / 32)] |= 1 << elm % 32;
}
public setLargestIndex(idx: number): void {
if (idx > this.setSize * 32)
this.growSet(idx);
this.largestIndex = idx;
}
public remove(elm: number): void {
if (elm >= this.setSize * 32)
this.growSet(elm);
if (elm > this.largestIndex)
this.largestIndex = elm;
this._myset[Math.floor(elm / 32)] &= ~(1 << elm % 32);
}
public contains(elm: number): boolean {
if (elm >= this.setSize * 32)
this.growSet(elm);
if (elm > this.largestIndex)
this.largestIndex = elm;
return !!(this._myset[Math.floor(elm / 32)] & (1 << elm % 32));
}
public union(a: BitSet): void {
if (a.largestIndex > this.largestIndex) {
this.setLargestIndex(a.largestIndex);
} else if (this.largestIndex > a.largestIndex) {
a.setLargestIndex(this.largestIndex);
}
for (var i = 0; i < a.setSize; ++i) {
this._myset[i] |= a._myset[i];
}
if (a.allSet)
this.allSet = true;
}
public intersection(a: BitSet): void {
if (a.largestIndex > this.largestIndex) {
this.setLargestIndex(a.largestIndex);
} else if (this.largestIndex > a.largestIndex) {
a.setLargestIndex(this.largestIndex);
}
for (var i = 0; i < a.setSize; ++i) {
this._myset[i] &= a._myset[i];
}
if (this.allSet && !a.allSet)
this.allSet = false;
}
public forEach(cb: (elm: number) => void ): void {
if (this.largestIndex < 0)
return;
for (var i = 0; i <= this.largestIndex / 32; ++i) {
var idx = i * 32;
var val = this._myset[i];
while (val != 0 && idx <= this.largestIndex) {
if (val & 1)
cb(idx);
++idx; val = val >>> 1;
}
}
}
public clone(): BitSet {
var a = new BitSet(this.allSet);
a._myset = this.cloneSet();
a.setSize = this.setSize;
a.largestIndex = this.largestIndex;
return a;
}
public equals(a: BitSet): boolean {
if ((this.allSet && !a.allSet) || (!this.allSet && a.allSet))
return false;
if (a.largestIndex > this.largestIndex) {
this.setLargestIndex(a.largestIndex);
} else if (this.largestIndex > a.largestIndex) {
a.setLargestIndex(this.largestIndex);
}
for (var i = 0; i < a.setSize; ++i) {
if (this._myset[i] != a._myset[i])
return false;
}
return true;
}
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
// Dataflow framework classes
// Every dataflow analysis should implement this interface.
// DataflowVisitor will call your analysis for every Statement that
// contains expressions (ExprHolder instances) to calculate gen/kill
// sets.
export interface IDataflowAnalysis {
// Change _set to reflect the In set of the entry node of
// the action (or exit node if backwards analysis).
buildStartNodeSet(a: Action, _set: BitSet): void;
// All sets are intialized by cloning the set specified by this
// function. You should start with an allSet set for analysis that
// use intersection confluence.
buildStartingSet(a: Action, _set: BitSet): void;
// Change _set to reflect Gen[n], where n is an expression.
// inSet: the original set before Kill kicked in
// isIV: true when this expression does not actually exist, but was
// generated to simulate the behavior experienced by induction
// variables of "For" nodes.
gen(n: ExprHolder, _set: BitSet, inSet: BitSet, isIV: boolean): void;
// Change _set to reflext Kill[n], where n is an expression.
// isIV: true when this expression does not actually exist, but was
// generated to simulate the behavior experienced by induction
// variables when "For" nodes are executed.
kill(n: ExprHolder, _set: BitSet, isIV: boolean): void;
// Attach the calculated information from expression "n" in node "s",
// which owns this expression. This should be the result of this
// analysis and remains attached to the AST.
updateNode(s: Stmt, n: ExprHolder): void;
}
// DataflowVisitor manages all common duties of a dataflow analysis, leaving
// only the gen/kill sets calculation for the analysis itself. It works once
// per Action and starts by determining the order of nodes to visit in this
// action, but only consider nodes that are Statement and that contains
// expressions (ExprHolder instances), skipping other nodes.
// Uses BitSet for union and intersection set operations, topological sort
// for the initial visit order and a worklist for the remaining visits
// NOTE: If the analysis is backwards, notice that Ins/Outs sets are
// reversed.
class DataflowVisitor
extends NodeVisitor {
private worklist: Stmt[] = [];
public Ins: { [k: number]: BitSet; } = {};
public Outs: { [k: number]: BitSet; } = {};
private startingSet: BitSet;
private startNodeSet: BitSet;
private starting: boolean = false;
private changed: boolean = false;
private visited: { [id: number]: boolean; } = {};
// df: Reference to the actual Analysis that will be called for each
// expression.
// pool: Reference to the pool to create/reference elements of sets.
// backwards: direction, true if backwards.
// intersection: confluence operator, false if union, true if
// intersection
// useWorklist: true if uses a worklist to visit nodes, false will
// use the blind algorithm of revisiting all nodes each time a
// modification is detected.
constructor(public df: IDataflowAnalysis, public pool: SetElementsPool,
public backwards: boolean = false, public intersection: boolean = false,
public useWorklist = true) {
super();
}
// Keep the same id for generated assignzero expressions
private genZeroMap: { [name: string]: Expr; } = {};
// Helper function to generate an expression that mimics the behavior
// of a "For" node, initializing the induction variable with zero.
private generateAssignZero(l: LocalDef): Expr {
var res = this.genZeroMap[["d_", l.getName()].join("")];
if (res != undefined)
return res;
var localThing = mkThing(l.getName());
(<ThingRef>localThing).def = l;
var initialVal = mkLit(0);
res = mkCall(PropertyRef.mkProp(api.core.AssignmentProp),
[localThing, initialVal]);
this.genZeroMap[["d_", l.getName()].join("")] = res;
return res;
}
// Keep the same id for generated inc expressions
private genIncMap: { [name: string]: Expr; } = {};
// Helper function to generate an expression that mimics the behavior
// of a "For" node, incrementing the induction variable
private generateInc(l: LocalDef): Expr {
var res = this.genIncMap[["d_", l.getName()].join("")];
if (res != undefined)
return res;
var localThing = mkThing(l.getName());
(<ThingRef>localThing).def = l;
var incVal = mkLit(1);
var sum = mkCall(PropertyRef.mkProp(api.core.Number.getProperty("+")),
[localThing, incVal]);
res = mkCall(PropertyRef.mkProp(api.core.AssignmentProp),
[localThing, sum]);
this.genIncMap[["d_", l.getName()].join("")] = res;
return res;
}
public visitAstNode(node: AstNode): any {
this.visitChildren(node);
}
// This is the core of DataflowVisitor and handles our subject of
// interest: AST Statements that contains ExprHolder instances.
private visitExprHolderHolder(stmt: Stmt) {
var preds = this.backwards ? AST.SuccessorsFinder.find(stmt) : AST.PredecessorsFinder.find(stmt);
var newIn: BitSet;
if (this.starting) {
newIn = this.startNodeSet.clone();
this.starting = false;
} else {
var validPreds = 0;
newIn = this.intersection ? new BitSet(/*allset*/true) : new BitSet();
preds.forEach((x: Stmt) => {
var nOut = this.Outs[x.nodeId];
if (nOut != undefined) {
++validPreds;
if (this.intersection)
newIn.intersection(nOut);
else
newIn.union(nOut);
}
});
if (validPreds == 0) {
newIn = this.startingSet.clone();
}
}
this.Ins[stmt.nodeId] = newIn;
var newOut = newIn.clone();
// Calculate kill/gen sets. Ignore placeholders.
if (stmt instanceof ExprStmt && !stmt.isPlaceholder()) {
this.df.kill((<ExprStmt>stmt).expr, newOut, false);
this.df.gen((<ExprStmt>stmt).expr, newOut, newIn, false);
} else if (!!stmt.calcNode()) {
// A "For" node implicitly updates the induction variable each
// time it is run, and some analyses need to know about this.
// We generate fake expressions that represent this behavior.
if (stmt instanceof For) {
var forInitialAssgn = exprToStmt(this.generateAssignZero((<For>stmt).boundLocal));
var forIncAssgn = exprToStmt(this.generateInc((<For>stmt).boundLocal));
this.df.kill(forInitialAssgn.expr, newOut, true);
this.df.kill(forIncAssgn.expr, newOut, true);
this.df.gen(forIncAssgn.expr, newOut, newIn, true);
this.df.gen(forInitialAssgn.expr, newOut, newIn, true);
}
this.df.kill(stmt.calcNode(), newOut, false);
this.df.gen(stmt.calcNode(), newOut, newIn, false);
}
// Check to see if we are stuck at a fixed point or if we need
// to continue running the analysis for succs nodes.
var oldOut = this.Outs[stmt.nodeId];
if (!oldOut || !oldOut.equals(newOut)) {
if (this.useWorklist) {
if (this.backwards) {
AST.PredecessorsFinder.find(stmt).forEach((s: Stmt) => {
this.worklist.push(s);
this.visited[s.nodeId] = false;
});
} else {
AST.SuccessorsFinder.find(stmt).forEach((s: Stmt) => {
this.worklist.push(s);
this.visited[s.nodeId] = false;
});
}
} else {
this.changed = true;
}
this.Outs[stmt.nodeId] = newOut;
}
// Attach the analysis info into the AST
if (stmt instanceof ExprStmt) {
this.df.updateNode(stmt, (<ExprStmt>stmt).expr);
} else if (!!stmt.calcNode()) {
this.df.updateNode(stmt, stmt.calcNode());
}
if (!this.useWorklist)
this.visitChildren(stmt);
}
visitComment(n: Comment) {
this.visitExprHolderHolder(n);
}
visitFor(n: For) {
this.visitExprHolderHolder(n);
}
visitIf(n: If) {
this.visitExprHolderHolder(n);
}
visitElseIf(n: If) {
this.visitExprHolderHolder(n);
}
visitForeach(n: Foreach) {
this.visitExprHolderHolder(n);
}
visitWhile(n: While) {
this.visitExprHolderHolder(n);
}
visitExprStmt(n: ExprStmt) {
this.visitExprHolderHolder(n);
}
// Non-recursive version of a topological sort to order our first
// visit to the Action's nodes. Recursive versions are simpler
// and more elegant but crash on shallow stack mobile Safari browsers.
private topologicalSort(a: Action) {
var incomingEdges : { [id: number]: number; } = { };
var visited: { [id: number]: boolean; } = {};
var noIncomingEdges: { [id: number]: boolean; } = {};
var idToNode: { [id: number]: Stmt; } = {};
var numNodesVisited = 0;
// Populate map with frequency of incoming edges
a.body.forEach((s: Stmt) => {
var todo = this.backwards ? PredecessorsFinder.unpeelAndGetLast(s) :
SuccessorsFinder.unpeelAndGetFirst(s);
while (todo.length > 0) {
var cur = todo.shift();
if (visited[cur.nodeId])
continue;
visited[cur.nodeId] = true;
++numNodesVisited;
idToNode[cur.nodeId] = cur;
if (!(incomingEdges[cur.nodeId] > 0)) {
noIncomingEdges[cur.nodeId] = true;
}
var succs = this.backwards ? AST.PredecessorsFinder.find(cur)
: AST.SuccessorsFinder.find(cur);
succs.forEach((x: ExprStmt) => {
if (incomingEdges[x.nodeId] == undefined)
incomingEdges[x.nodeId] = 1;
else
incomingEdges[x.nodeId]++;
noIncomingEdges[x.nodeId] = false;
todo.push(x);
});
}
});
// Get nodes with no incoming edges
var s: Stmt[] = [];
for (var key in noIncomingEdges) {
if (noIncomingEdges[key]) {
var node = idToNode[key];
Util.assert(node !== undefined);
s.push(node);
}
}
// Sort
while (this.worklist.length < numNodesVisited) {
if (s.length == 0) {
var found = false;
for (var key in visited) {
var cand = idToNode[key];
if (cand !== undefined && incomingEdges[key] > 0) {
incomingEdges[key] = 0;
s.push(cand);
found = true;
break;
}
}
Util.assert(found);
}
var cur = s.shift();
this.worklist.push(cur);
var succs = this.backwards ? AST.PredecessorsFinder.find(cur)
: AST.SuccessorsFinder.find(cur);
for (var i = 0; i < succs.length; ++i) {
var x = succs[i];
if (--incomingEdges[x.nodeId] == 0)
s.unshift(x);
else if (incomingEdges[x.nodeId] > 0 && i == succs.length - 1 && s.length == 0) {
// break the cycle
incomingEdges[x.nodeId] = 0;
s.push(x);
}
}
}
}
private dfTesting(s: Stmt) {
// Testing to ensure x C Succs[Preds[x]]
var preds = AST.PredecessorsFinder.find(s);
var succs;
for (var i = 0; i < preds.length; ++i) {
var elmi = preds[i];
succs = AST.SuccessorsFinder.find(elmi);
var found = false;
for (var j = 0; j < succs.length; ++j) {
var elmj = succs[j];
if (elmj === s)
found = true;
}
Util.assert(found);
}
// Testing to ensure x C Preds[Succs[x]]
succs = AST.SuccessorsFinder.find(s);
for (var i = 0; i < succs.length; ++i) {
var elmi2 = succs[i];
preds = AST.PredecessorsFinder.find(elmi2);
var found = false;
for (var j = 0; j < preds.length; ++j) {
var elmj2 = preds[j];
if (elmj2 === s)
found = true;
}
Util.assert(found);
}
}
// Entry point for the dataflow analysis. Initialize all data
// structures and start visiting the statements of Action n.
visitAction(n: Action) {
if (n instanceof LibraryRefAction)
return;
if (n.isPage())
return;
if (this.useWorklist) {
this.worklist = [];
this.topologicalSort(n);
this.visited = {};
this.startNodeSet = new BitSet();
this.df.buildStartNodeSet(n, this.startNodeSet);
this.startingSet = new BitSet();
this.df.buildStartingSet(n, this.startingSet);
this.starting = true;
while (this.worklist.length > 0) {
var cur = this.worklist.shift();
if (this.visited[cur.nodeId])
continue;
this.visited[cur.nodeId] = true;
//this.dfTesting(cur); // Check if preds/succs are alright
cur.accept(this);
}
} else {
this.startNodeSet = new BitSet();
this.df.buildStartNodeSet(n, this.startNodeSet);
this.startingSet = new BitSet();
this.df.buildStartingSet(n, this.startingSet);
this.changed = true;
this.starting = true;
while (this.changed) {
this.changed = false;
n.body.forEach((c) => {
c.accept(this);
});
}
}
}
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
// Dataflow Analyses
// * REACHING DEFINITIONS *
// Motivation: RD seeks to eliminate "ok checks" that slows down script
// execution in IE and Firefox by checking if the invalid definition
// reaches an expression.
// Flags to activate: options.okElimination, URL ?okElimination
// Manages Reaching Definitions data attached to the AST as the result
// of the analysis.
export class ReachingDefsMgr {
constructor(public defs: Expr[], public node: Stmt) { }
private getLocal(e: Token): String {
if (e instanceof ThingRef) {
var d = (<ThingRef>e).def;
if (d instanceof LocalDef) return (<LocalDef>d).getName();
}
return null;
}
public toString(): string {
return "RD #" + this.node.nodeId + ": {" + this.defs.join() + "}";
}
// The compiler will ask whether this definition may be invalid, at
// this point of the program. If it may be, then it needs to put an
// "ok check".
public mayBeInvalid(d: LocalDef): boolean {
var ret = false;
this.defs.forEach((e: Expr) => {
var refcall = <Call>e;
if (refcall.prop() != api.core.AssignmentProp)
return;
refcall.args[0].flatten(api.core.TupleProp).forEach((a) => {
var l = this.getLocal(a);
if (l && l == d.getName()) {
if (refcall.args.length > 1) {
refcall.args.slice(1).forEach((val: Expr) => {
// check for invalid
if (val instanceof Call &&
(<Call>val).args.length > 0 &&
(<Call>val).args[0] instanceof ThingRef &&
(<ThingRef>(<Call>val).args[0]).data == "invalid") {
ret = true;
}
// check for non-robust call
if (val instanceof Call &&
!((<Call>val).prop().getFlags() & PropertyFlags.Robust)) {
ret = true;
}
});
}
}
});
});
return ret;
}
}
// ReachingDefinitions is the classic analysis to compute local variable
// definitions that reaches a certain point. It is used by the compiler
// to detect whether an "invalid" definition reaches some point, in which
// case we need to emit an "ok check" to dynamically detect if it is truly
// invalid value and stop the script before it is used.
//
// Main characteristics: Forward, union confluence
export class ReachingDefinitions
implements IDataflowAnalysis {
private df: DataflowVisitor;
private curNode: Stmt;
private pool: SetElementsPool;
constructor() {
}
// Convenience methods
private getLocal(e: Token): LocalDef {
if (e instanceof ThingRef) {
var d = (<ThingRef>e).def;
if (d instanceof LocalDef) return <LocalDef>d;
}
return null;
}
private getLocalName(e: Token): String {
var ld = this.getLocal(e);
if (ld != null) {
return ld.getName();
}
return null;
}
// Helper function to calculate the Gen set when the expression
// is a variable copy. We need to copy all the definitions of the
// source variable to the destination variable.
private handleCopy(c: Call, _set: BitSet): boolean {
var bypassGen = false;
// Check for a regular copy
if (c.prop() == api.core.AssignmentProp
&& c.args.length == 2
&& c.args[0] instanceof ThingRef
&& c.args[1] instanceof ThingRef) {
var dst = this.getLocal(c.args[0]);
var src = this.getLocal(c.args[1]);
if (src != null && dst != null) {
_set.forEach((idx: number) => {
var elm = this.pool.getElmById(idx);
var refcall = <Call> elm.refNode;
if (refcall) {
refcall.args[0].flatten(api.core.TupleProp).forEach((a) => {
var l2 = this.getLocalName(a);
if (l2 == src.getName()) {
var newCall = this.cloneAndChangeDst(refcall, dst);
var newElm = this.pool.getElm(newCall.getText(), newCall);
_set.add(newElm.id);
bypassGen = true; // we dont need to keep "x = y" definitions
}
});
}
});
}
}
// Check for a conditional copy (or/and)
if (c.prop() == api.core.AssignmentProp
&& c.args.length == 2
&& c.args[0] instanceof ThingRef
&& c.args[1] instanceof Call) {
var dst = this.getLocal(c.args[0]);
var srcCall = <Call> c.args[1];
if (dst != null && srcCall != null
&& srcCall.args.length == 2
&& (srcCall.prop() == api.core.AndProp ||
srcCall.prop() == api.core.OrProp)
&& srcCall.args[1] instanceof ThingRef) {
var src = this.getLocal(srcCall.args[1]);
if (src != null && dst != null) {
_set.forEach((idx: number) => {
var elm = this.pool.getElmById(idx);
var refcall = <Call> elm.refNode;
if (refcall) {
refcall.args[0].flatten(api.core.TupleProp).forEach((a) => {
var l2 = this.getLocalName(a);
if (l2 == src.getName()) {
var newCall = this.cloneAndChangeDst(refcall, dst);
var newElm = this.pool.getElm(newCall.getText(), newCall);
_set.add(newElm.id);
}
});
}
});
}
}
}
return bypassGen;
}
// The core function of this Analysis, calculates the GEN and KILL sets
// for the expression "n". Updates "_set" to reflect this.
private updateSet(n: ExprHolder, _set: BitSet, genKill: boolean): void {
if (!n.parsed || !(n.parsed instanceof Call))
return;
var c = <Call>n.parsed;
//... Traverse nodes non-recursively
var exprVisitQueue: Expr[] = [];
exprVisitQueue.push(c);
while (exprVisitQueue.length > 0) {
var cur = exprVisitQueue.shift();
if (!(cur instanceof Call))
continue;
var curCall = <Call> cur;
exprVisitQueue = exprVisitQueue.concat(curCall.children());
var prop = curCall.prop();
// We are only looking for assignments to local variables
if (prop == api.core.AssignmentProp) {
c.args[0].flatten(api.core.TupleProp).forEach((e) => {
var l = this.getLocalName(e);
if (l) {
if (genKill) { // Generate
// First check if it is a local copy expression
if (!this.handleCopy(curCall, _set)) {
// If it is not, put this assignment into the Out set
var elm = this.pool.getElm(curCall.getText(), curCall);
_set.add(elm.id);
}
} else { // Remove all defs of the same var from the In set
_set.forEach((idx: number) => {
var elm = this.pool.getElmById(idx);
var refcall = <Call> elm.refNode;
var remove = false;
if (refcall) {
refcall.args[0].flatten(api.core.TupleProp).forEach((a) => {
var l2 = this.getLocalName(a);
if (l2 == l)
remove = true;
});
}
if (remove)
_set.remove(idx);
});
}
}
});
}
}
}
// Wrappers for updateSet
gen(n: ExprHolder, _set: BitSet, inSet: BitSet, isIV = false): void {
this.updateSet(n, _set, true);
}
kill(n: ExprHolder, _set: BitSet, isIV = false): void {
this.updateSet(n, _set, false);
}
// Extract our calculated RD set by using Set and SetElementsPool data
// structure, then stick this into the AST.
updateNode(s: Stmt, n: ExprHolder) {
n.reachingDefs = null;
var defs:Expr[] = [];
this.df.Ins[s.nodeId].forEach((idx: number) => {
defs.push(this.pool.getElmById(idx).refNode);
});
if (defs.length > 0)
n.reachingDefs = new ReachingDefsMgr(defs, s);
}
// Helper function to generate a fake invalid assignment.
private generateInvalidAssignmentFor(l: LocalDef): Expr {
var localThing = mkThing(l.getName());
(<ThingRef>localThing).def = l;
var invalidThing = mkThing("invalid");
(<ThingRef>invalidThing).def = api.getKind("Invalid").singleton;
return mkCall(PropertyRef.mkProp(api.core.AssignmentProp),
[localThing, mkCall(PropertyRef.mkProp(api.getKind("Invalid").getProperty("number")), [invalidThing])]);
}
// Helper function used when handling copy expressions, necessary
// when copying all the definitions of the source variable to the
// destination variable.
private cloneAndChangeDst(c: Call, dst: LocalDef): Expr {
var args = c.args.slice(0);
args[0] = mkThing(dst.getName());
(<ThingRef>args[0]).def = dst;
return mkCall(c.propRef, args);
}
// Our start node for the action assigns all input parameters to
// invalid, assuming (conservatively) that they are undefined.
buildStartNodeSet(a: Action, _set: BitSet): void {
a.allLocals.forEach((e: Decl) => {
if (!(e instanceof LocalDef))
return;
var l = (<LocalDef>e).getName();
var elm = this.pool.getElm(l, this.generateInvalidAssignmentFor(<LocalDef>e));
_set.add(elm.id);
});
}
// All nodes start empty in this analysis.
buildStartingSet(a: Action, _set: BitSet): void {
}
// Entry point for this analysis. Analyze the App Action-wise.
visitApp(n: App) {
n.things.forEach((a: Decl) => {
if (a instanceof Action && !(<Action>a).isPage()) {
this.pool = new SetElementsPool();
this.df = new DataflowVisitor(this, this.pool,/*backwards*/false, /*intersection*/false, /*useWorklist*/true);
this.df.dispatch(a);
}
});
}
}
// * DOMINATOR SET *
// Motivation:
// The Dominator Set Analysis is used only to debug intersection-confluence
// analysis, since it is the simplest analysis you can build with the
// intersection confluence operator. May be used as boilerplate code for
// other analyses as well.
// Flags to activate: no one
export class DominatorsMgr {
constructor(public doms: Expr[], public node: Stmt) { }
public toString() {
var str = "DOMS(" + this.node.nodeId + ") : {";
str += this.doms.map((e: Expr) => {
return e.nodeId.toString();
}).join();
return str + "}";
}
}
// Dominators will compute the set of statements that dominate each
// other. A statement x dominates y if all paths from the start of
// the action to y includes x.
//
// Main characteristics: Forward, intersection confluence
export class Dominators
implements IDataflowAnalysis {
private df: DataflowVisitor;
private curNode: Stmt;
private pool: SetElementsPool;
constructor() {
}
// Our gen set is simply our own expression id.
gen(n: ExprHolder, _set: BitSet, inSet: BitSet, isIV = false): void {
if (!n.parsed)
return;
var elm = this.pool.getElm(n.parsed.nodeId.toString(), n.parsed);
_set.add(elm.id);
}
// We do not need to kill. The intersection confluence operator takes
// care of eliminating IDs that do not dominate this statement.
kill(n: ExprHolder, _set: BitSet, isIV = false): void {
}
// Put our calculated set into the AST node of this statement
updateNode(s: Stmt, n: ExprHolder) {
n.dominators = null;
var doms: Expr[] = [];
this.df.Ins[s.nodeId].forEach((idx: number) => {
doms.push(this.pool.getElmById(idx).refNode);
});
if (doms.length > 0)
n.dominators = new DominatorsMgr(doms, s);
}
// We assume no one dominates the first node.
buildStartNodeSet(a: Action, _set: BitSet): void {
}
// All nodes must be initialized with the set that contains all
// elements (allSet), otherwise we will not reach the maximum
// fixed point solution.
buildStartingSet(a: Action, _set: BitSet): void {
_set.makeAllSet();
}
// Entry point for this analysis. Analyze the App Action-wise.
visitApp(n: App) {
n.things.forEach((a: Decl) => {
if (a instanceof Action && !(<Action>a).isPage()) {
this.pool = new SetElementsPool();
this.df = new DataflowVisitor(this, this.pool,/*backwards*/false, /*intersection*/true, /*useWorklist*/true);
this.df.dispatch(a);
}
});
}
}
// * USED SET ANALYSIS *
// Motivation:
// ReachingDefinitions is not enough to eliminate all unnecessary "ok
// checks". Since all checks are done once a value is used, there are
// time in which the program already used the value and thus it was
// already checked, and all the remaining checks may be eliminated.
// Uset set analysis calculates the set of local variables that were
// already used at a certain point of the program, but were not
// redefined since the last use, therefore, enabling us to remove
// redundant "ok checks".
// Flags to activate: options.okElimination, URL ?okElimination
// Manages the information we stick into the AST statament nodes.
export class UsedSetMgr {
constructor(public used: Expr[], public node: Stmt) { }
// Convenience methods accessible for everyone
public static getLocal(e: Token): LocalDef {
if (e instanceof ThingRef) {
var d = (<ThingRef>e).def;
if (d instanceof LocalDef) return <LocalDef>d;
}
return null;
}
public static getLocalName(e: Token): String {
var ld = this.getLocal(e);
if (ld != null) {
return ld.getName();
}
return null;
}
// The compiler asks whether the local ld was already used at this
// point in order to eliminate redundant "ok checks".
public alreadyUsed(ld: LocalDef): boolean {
var res = false;
this.used.forEach((e: Expr) => {
var name1 = UsedSetMgr.getLocalName(e);
if (name1 && name1 == ld.getName()) {
res = true;
}
});
return res;
}
// Debugging
public toString() {
var str = "USED(" + this.node.nodeId + ") : {";
str += this.used.map((e: Expr) => {
return UsedSetMgr.getLocalName(e);
}).join();
return str + "}";
}
}
// UsedAnalysis main class
//
// Main characteristics: Forward, intersection confluence
// NOTE: gen/kill functions are reversed in order to compensate for the
// calling order of DataflowVisitor.
export class UsedAnalysis
implements IDataflowAnalysis {
private df: DataflowVisitor;
private curNode: Stmt;
private pool: SetElementsPool;
constructor() {
}
// This is actually the kill set. Since, for UsedAnalysis, we need to
// kill after generation (as opposed to the common case), we reverse
// the gen/kill functions.
gen(n: ExprHolder, _set: BitSet, inSet: BitSet, isIV = false): void {
// We are only interested in Call expressions
if (!n.parsed || !(n.parsed instanceof Call))
return;
// .. Traverse nodes non-recursively
var c = <Call>n.parsed;
var exprVisitQueue: Expr[] = [];
exprVisitQueue.push(c);
while (exprVisitQueue.length > 0) {
var cur = exprVisitQueue.shift();
if (!(cur instanceof Call))
continue;
var curCall = <Call> cur;
exprVisitQueue = exprVisitQueue.concat(curCall.children());
var prop = curCall.prop();
// We are only interested in assignments
if (prop == api.core.AssignmentProp) {
c.args[0].flatten(api.core.TupleProp).forEach((e) => {
var l = UsedSetMgr.getLocalName(e);
if (l) {
{ // Kill all uses of the var that was defined
// in this expression, since it was redefined
_set.forEach((idx: number) => {
var elm = this.pool.getElmById(idx);
if (elm.key == l)
_set.remove(idx);
});
}
}
});
}
}
}
// This is actually the gen set. We look for all uses of local
// variables and add them to the set.
kill(n: ExprHolder, _set: BitSet, isIV = false): void {
if (!n.parsed)
return;
var exprVisitQueue: Expr[] = [];
exprVisitQueue.push(n.parsed);
while (exprVisitQueue.length > 0) {
var e = exprVisitQueue.shift();
var refcall = <Call>e;
if (!(e instanceof Call)) {
if (e instanceof ThingRef) {
var ed = (<ThingRef> e).def;
if (ed instanceof LocalDef) {
var elm = this.pool.getElm((<LocalDef>ed).getName(), e);
_set.add(elm.id);
}
}
} else {
if (refcall.prop() && refcall.prop().getName() == "is invalid") {
// x->is_invalid is not a use of x
} else if (refcall.prop() != api.core.AssignmentProp) {
exprVisitQueue = exprVisitQueue.concat(refcall.children());
} else {
exprVisitQueue = exprVisitQueue.concat(refcall.args.slice(1));
}
}
}
}
// Put our calculated UsedSet into the AST, so the compiler can query
// later.
updateNode(s: Stmt, n: ExprHolder) {
n.usedSet = null;
var usedSet: Expr[] = [];
this.df.Ins[s.nodeId].forEach((idx: number) => {
usedSet.push(this.pool.getElmById(idx).refNode);
});
if (usedSet.length > 0)
n.usedSet = new UsedSetMgr(usedSet, s);
}
// Our start node begins with no used variables.
buildStartNodeSet(a: Action, _set: BitSet): void {
}
// All remaining nodes are initialized with allSet, necessary for
// intersection analyses.
buildStartingSet(a: Action, _set: BitSet): void {
_set.makeAllSet();
}
// Entry point for this analysis. Analyze the App Action-wise.
visitApp(n: App) {
n.things.forEach((a: Decl) => {
if (a instanceof Action && !(<Action>a).isPage()) {
this.pool = new SetElementsPool();
this.df = new DataflowVisitor(this, this.pool,/*backwards*/false, /*intersection*/true, /*useWorklist*/true);
this.df.dispatch(a);
}
});
}
}
// * AVAILABLE EXPRESSIONS *
// Motivation:
// The Available Expressions classic analysis is used to detect
// opportunities for common subexpression elimination. Since the compiler
// may separate an action into several steps, each one being a different
// native JavaScript function, the JIT engine will miss optimization
// opportunities beyond the step granularity, and this analysis can help
// in these cases by performing global common subexpression elimination.
// Flags to activate: options.commonSubexprElim, URL ?commonSubexprElim
export class AvailableExpressionsMgr {
constructor(public aeSet: Expr[], public node: Stmt) { }
// Helper method to check if the entire expression is idempotent,
// which means there is no effect in recalculating it or not.
private hasOnlyIdempotentNodes(e: Expr) {
var exprVisitQueue: Expr[] = [];
exprVisitQueue.push(e);
while (exprVisitQueue.length > 0) {
var e = exprVisitQueue.shift();
var refcall = <Call>e;
if (!(e instanceof Call)) {
if (!(e instanceof Literal || (e instanceof ThingRef
&& (<ThingRef>e).def.nodeType() == "localDef")))
return false;
} else {
if (refcall.prop() != api.core.AssignmentProp &&
refcall.prop().getFlags() & PropertyFlags.Idempotent) {
exprVisitQueue = exprVisitQueue.concat(refcall.children());
} else {
return false;
}
}
}
return true;
}
// The compiler will ask if this expression was already calculated at
// this point and if they are idempotent. Returns the set of all such
// expressions.
public checkForIdenticalExpressions(e: Expr): Expr[]{
var res: Expr[] = [];
if (e == undefined)
return;
this.aeSet.forEach((ae: Expr) => {
if (ae.toString() == e.toString()
&& this.hasOnlyIdempotentNodes(e))
res.push(ae);
});
return res;
}
// Debugging
public toString() {
var str = "AE(" + this.node.nodeId + ") : {";
str += this.aeSet.join();
return str + "}";
}
}
// Main characteriscs: Forward, intersection confluence
// NOTE: gen/kill functions are reversed in order to compensate for the
// calling order of DataflowVisitor.
export class AvailableExpressions
implements IDataflowAnalysis {
private df: DataflowVisitor;
private curNode: Stmt;
private pool: SetElementsPool;
constructor() {
}
// Helper function to detect whether expression "e" uses local variable
// "l"
private usesLocal(e: Expr, l: String): boolean {
var exprVisitQueue: Expr[] = [];
exprVisitQueue.push(e);
while (exprVisitQueue.length > 0) {
var e = exprVisitQueue.shift();
var refcall = <Call>e;
if (!(e instanceof Call)) {
if (UsedSetMgr.getLocalName(e) == l)
return true;
} else {
if (refcall.prop() != api.core.AssignmentProp) {
exprVisitQueue = exprVisitQueue.concat(refcall.children());
} else {
exprVisitQueue = exprVisitQueue.concat(refcall.args.slice(1));
}
}
}
return false;
}
// This is actually the kill set. Since, for AvailableExpressions, we
// need to kill after generation (as opposed to the common case), we
// reverse the gen/kill functions.
gen(n: ExprHolder, _set: BitSet, inSet: BitSet, isIV = false): void {
if (isIV)
return;
if (!n.parsed || !(n.parsed instanceof Call))
return;
var c = <Call>n.parsed;
var exprVisitQueue: Expr[] = [];
exprVisitQueue.push(c);
while (exprVisitQueue.length > 0) {
var cur = exprVisitQueue.shift();
if (!(cur instanceof Call))
continue;
var curCall = <Call> cur;
exprVisitQueue = exprVisitQueue.concat(curCall.children());
var prop = curCall.prop();
if (prop == api.core.AssignmentProp) {
c.args[0].flatten(api.core.TupleProp).forEach((e) => {
var l = UsedSetMgr.getLocalName(e);
if (l) {
{ // Kill all expressions that the same var
_set.forEach((idx: number) => {
var elm = this.pool.getElmById(idx);
if (this.usesLocal(elm.refNode, l))
_set.remove(idx);
});
}
}
});
}
}
}
// This is actually the gen set. We look for all uses of local
// variables and add them to the set.
kill(n: ExprHolder, _set: BitSet, isIV = false): void {
if (isIV)
return;
if (!n.parsed)
return;
var exprVisitQueue: Expr[] = [];
exprVisitQueue.push(n.parsed);
while (exprVisitQueue.length > 0) {
var e = exprVisitQueue.shift();
var refcall = <Call>e;
if (e instanceof Call) {
if (refcall.prop() != api.core.AssignmentProp) {
var elm = this.pool.getElm(refcall.toString(), refcall);
_set.add(elm.id);
exprVisitQueue = exprVisitQueue.concat(refcall.args.slice(1));
} else {
exprVisitQueue = exprVisitQueue.concat(refcall.children());
}
}
}
}
// Put our calculated UsedSet into the AST, so the compiler can query
// later.
updateNode(s: Stmt, n: ExprHolder) {
n.aeSet = null;
var aeSet: Expr[] = [];
this.df.Ins[s.nodeId].forEach((idx: number) => {
aeSet.push(this.pool.getElmById(idx).refNode);
});
if (aeSet.length > 0)
n.aeSet = new AvailableExpressionsMgr(aeSet, s);
}
// Our start node begins with no available expressions.
buildStartNodeSet(a: Action, _set: BitSet): void {
}
// All remaining nodes are initialized with allSet, necessary for
// intersection analyses.
buildStartingSet(a: Action, _set: BitSet): void {
_set.makeAllSet();
}
// Entry point for this analysis. Analyze the App Action-wise.
visitApp(n: App) {
n.things.forEach((a: Decl) => {
if (a instanceof Action && !(<Action>a).isPage()) {
this.pool = new SetElementsPool();
this.df = new DataflowVisitor(this, this.pool,/*backwards*/false, /*intersection*/true, /*useWorklist*/true);
this.df.dispatch(a);
}
});
}
}
// * CONSTANT FOLDING/PROPAGATION FRAMEWORK *
// Motivation:
// This analysis computes the set of locals defined as constants, yielding
// pairs <local, constant value>, and also folds an idempotent expression
// that works with constants. A pair <local, constant value> may be the
// result of many folded expressions. As with CSE, since the compiler
// may separate an action into several steps, each one being a different
// native JavaScript function, the JIT engine will miss optimization
// opportunities beyond the step granularity, and this analysis can help
// in these cases by performing global constant folding.
// Flags to activate: options.constantPropagation, URL ?constantPropagation
// Manages the information we stick into the AST statement nodes. It also
// has the logic to perform folding for selected idempotent operators.
export class ConstantPropagationMgr {
constructor(public constantSet: Expr[], public node: Stmt) { }
// Helper function.
// Get the constant value of the local "d" by using the information
// computed for this point of the program.
public getLiteralValueFor(d: LocalDef) {
var res = null;
this.constantSet.forEach((e: Expr) => {
if (e instanceof Call
&& (<Call>e).prop() == api.core.AssignmentProp
&& (<Call>e).args.length == 2
&& (<Call>e).args[0] instanceof ThingRef
&& (<ThingRef>((<Call>e).args[0])).def instanceof LocalDef
&& (<LocalDef>((<ThingRef>((<Call>e).args[0])).def)).getName() == d.getName()
&& (<Call>e).args[1] instanceof Literal
&& (<Literal>((<Call>e).args[1])).data != null)
res = (<Literal>((<Call>e).args[1])).data;
});
return res;
}
// Helper function.
// Avoids using JavaScript's "eval" and implement our own function
// to evaluate expressions. Return null if we don't know how to
// calculate this at compile time.
public static evaluate(c: Call, args: any[]) {
if (c.prop().getCategory() == PropertyCategory.Builtin) {
if (c.prop().getSpecialApply() == "+")
return args[0] + args[1];
else if (c.prop().getSpecialApply() == "-")
return args[0] - args[1];
else if (c.prop().getSpecialApply() == "/")
return args[0] / args[1];
else if (c.prop().getSpecialApply() == "*")
return args[0] * args[1];
else if (c.prop().getSpecialApply() == "===")
return args[0] === args[1];
}
return null;
}
// Entry point for expression evaluation. By using the information
// available at this point of the program (pairs <local, value>),
// tries to evaluate the result of the expression "e". If it is
// possible to know this at compile time, returns the value,
// otherwise returns null.
public precomputeLiteralExpression(e: Expr) {
var visitExpr = (exp: Expr) => {
var refcall = <Call>exp;
if (!(exp instanceof Call)) {
if (exp instanceof Literal)
return (<Literal>exp).data;
if (exp instanceof ThingRef
&& (<ThingRef>exp).def.nodeType() == "localDef"
&& this.getLiteralValueFor(<LocalDef>(<ThingRef>exp).def) != null)
return this.getLiteralValueFor(<LocalDef>(<ThingRef>exp).def);
} else {
if (refcall.prop() != api.core.AssignmentProp &&
refcall.prop().getFlags() & PropertyFlags.Idempotent) {
var values = refcall.children().map((ea: Expr) => visitExpr(ea));
var hasNull = false;
values.forEach((ea: Expr) => {
if (ea == null) hasNull = true;
});
if (!hasNull) {
return ConstantPropagationMgr.evaluate(refcall, values);
}
}
return null;
}
};
return visitExpr(e);
}
// Debugging purposes
public toString() {
var str = "CP(" + this.node.nodeId + ") : {";
str += this.constantSet.join();
return str + "}";
}
}
// ConstantPropagation will compute gen/kill sets to achieve the maximum
// number of constant folding/propagation for locals of the action. It
// uses ConstantPropagationMgr methods to help fold expressions with
// literal leaves, which are also used by the compiler when emitting
// code. This differs from the other analysis because they leave their
// Manager to be used solely by the compiler.
//
// Main characteristics: Forward, intersection confluence
export class ConstantPropagation
implements IDataflowAnalysis {
private df: DataflowVisitor;
private curNode: Stmt;
private pool: SetElementsPool;
constructor() {
}
// Helper function to generate a fake assignment of literal "value"
// to local "l". We need to generate these assingments to express
// the result of folding, since they don't really exist in the original
// source code.
private generateAssignmentFor(l: LocalDef, value: any): Expr {
var localThing = mkThing(l.getName());
(<ThingRef>localThing).def = l;
var literal = mkLit(value);
return mkCall(PropertyRef.mkProp(api.core.AssignmentProp),
[localThing, literal]);
}
// Helper function to handle copy assignments
private cloneAndChangeDst(c: Call, dst: LocalDef): Expr {
var args = c.args.slice(0);
args[0] = mkThing(dst.getName());
(<ThingRef>args[0]).def = dst;
return mkCall(c.propRef, args);
}
// Convenience methods
private getLocal(e: Token): LocalDef {
if (e instanceof ThingRef) {
var d = (<ThingRef>e).def;
if (d instanceof LocalDef) return <LocalDef>d;
}
return null;
}
private getLocalName(e: Token): String {
var ld = this.getLocal(e);
if (ld != null) {
return ld.getName();
}
return null;
}
// Handle copy. Copies the literal value of src to dst.
private handleCopy(c: Call, _set: BitSet): boolean {
var bypassGen = false;
// Check for a regular copy
if (c.prop() == api.core.AssignmentProp
&& c.args.length == 2
&& c.args[0] instanceof ThingRef
&& c.args[1] instanceof ThingRef) {
var dst = this.getLocal(c.args[0]);
var src = this.getLocal(c.args[1]);
if (src != null && dst != null) {
// Find the literal value of src, if any
_set.forEach((idx: number) => {
var elm = this.pool.getElmById(idx);
var refcall = <Call> elm.refNode;
if (refcall) {
refcall.args[0].flatten(api.core.TupleProp).forEach((a) => {
var l2 = this.getLocalName(a);
if (l2 == src.getName()) { // Found
// Copy to the destination generating a fake assingment
var newCall = this.cloneAndChangeDst(refcall, dst);
var newElm = this.pool.getElm(newCall.getText(), newCall);
_set.add(newElm.id);
bypassGen = true;
}
});
}
});
}
}
return bypassGen;
}
// Entry point for generating/killing elements.
private updateSet(n: ExprHolder, _set: BitSet, genKill: boolean): void {
if (!n.parsed || !(n.parsed instanceof Call))
return;
var c = <Call>n.parsed;
// Traverse all nodes of the expression non-recursively
var exprVisitQueue: Expr[] = [];
exprVisitQueue.push(c);
while (exprVisitQueue.length > 0) {
var cur = exprVisitQueue.shift();
if (!(cur instanceof Call))
continue;
var curCall = <Call> cur;
exprVisitQueue = exprVisitQueue.concat(curCall.children());
var prop = curCall.prop();
// Look for assignments
if (prop == api.core.AssignmentProp) {
c.args[0].flatten(api.core.TupleProp).forEach((e) => {
var l = this.getLocalName(e);
if (l) {
if (genKill) { // Generate
if (!this.handleCopy(curCall, _set)) {
// Try to fold the src expression with the information we currently have
// at this point and, if successful, assign it to the local
var lit = (new ConstantPropagationMgr(this.generateCpSet(_set), null)).precomputeLiteralExpression(c.args[1]);
if (lit != null) {
var assgn = this.generateAssignmentFor(this.getLocal(e), lit);
var elm = this.pool.getElm(assgn.getText(), assgn);
_set.add(elm.id);
}
}
} else { /// Kill all locals that this expression redefined
_set.forEach((idx: number) => {
var elm = this.pool.getElmById(idx);
var refcall = <Call> elm.refNode;
var remove = false;
if (refcall) {
refcall.args[0].flatten(api.core.TupleProp).forEach((a) => {
var l2 = this.getLocalName(a);
if (l2 == l)
remove = true;
});
}
if (remove)
_set.remove(idx);
});
}
}
});
}
}
}
// Wrappers to updateSet
gen(n: ExprHolder, _set: BitSet, inSet: BitSet, isIV = false): void {
if (!isIV)
this.updateSet(n, _set, true);
}
kill(n: ExprHolder, _set: BitSet, isIV = false): void {
if (!isIV)
this.updateSet(n, _set, false);
}
// Helper function to compute the information the
// ConstantPropagationMgr instance needs, converting the elements
// of the BitSet into a regular JavaScript object array.
private generateCpSet(_set: BitSet): Expr[] {
var cpSet: Expr[] = [];
_set.forEach((idx: number) => {
cpSet.push(this.pool.getElmById(idx).refNode);
});
return cpSet;
}
// Update the AST with the info we calculated for this node,
// use generateCpSet
updateNode(s: Stmt, n: ExprHolder) {
var cpSet = this.generateCpSet(this.df.Ins[s.nodeId]);
n.cpSet = new ConstantPropagationMgr(cpSet, s);
}
// We start with no definitions
buildStartNodeSet(a: Action, _set: BitSet): void {
}
// Sets are initialized full
buildStartingSet(a: Action, _set: BitSet): void {
_set.makeAllSet();
}
// Entry point for this analysis. Analyze the App Action-wise.
visitApp(n: App) {
n.things.forEach((a: Decl) => {
if (a instanceof Action && !(<Action>a).isPage()) {
this.pool = new SetElementsPool();
this.df = new DataflowVisitor(this, this.pool,/*backwards*/false, /*intersection*/true, /*useWorklist*/true);
this.df.dispatch(a);
}
});
}
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
// Non-Dataflow Analyses
// * INLINE ANALYSIS *
// Motivation:
// The inline analysis looks for actions that can be inlined and flags them
// to the compiler. This means these actions will be called as native
// JavaScript functions in the final code, bypassing the interpreter and
// saving time.
// Flags to activate: options.inlining or URL: ?inlining
export class CallGraphNode
{
constructor(public action: Action, public succs: CallGraphNode[], public preds: CallGraphNode[],
public canInline: boolean = false) { }
public addSucc(succ: CallGraphNode)
{
for (var i = 0; i < this.succs.length; ++i)
{
if (this.succs[i] == succ)
return;
}
this.succs.push(succ);
}
public addPred(pred: CallGraphNode)
{
for (var i = 0; i < this.preds.length; ++i)
{
if (this.preds[i] == pred)
return;
}
this.preds.push(pred);
}
}
// InlineAnalysis (multi-level)
//
// Step1: Build a callgraph for the App using the
// visitor pattern. While it is visiting each Action, it checks not only
// for calls that helps to build the callgraph, but also for statements
// that precludes an action from being inlined (i.e. loop statements).
//
// Step2: Afterwards, it sorts the callgraph using topological
// sort, allowing it to easily perform a bottom-up traversal of the tree.
// Then, it marks actions as inlined if they satisfy some
// predefined properties in "actionHasDesiredProperties()", if it doesn't
// have any unwanted statements and finally if all the actions it calls
// are also inlined.
export class InlineAnalysis
extends NodeVisitor {
public hasChanged = false;
private nodeMap: { [s: string]: CallGraphNode; };
private nodes: CallGraphNode[];
private nowVisiting: CallGraphNode;
constructor() {
super();
this.nodes = [];
this.nodeMap = {};
}
visitAstNode(n: AstNode) {
this.visitChildren(n);
}
visitExprHolder(n: ExprHolder) {
if (n.parsed)
this.dispatch(n.parsed);
this.visitChildren(n);
}
// Unwanted statements in an inlined action
visitFor(n: For) {
this.nowVisiting.canInline = false;
this.visitChildren(n);
}
visitForeach(n: Foreach) {
this.nowVisiting.canInline = false;
this.visitChildren(n);
}
visitWhile(n: While) {
this.nowVisiting.canInline = false;
this.visitChildren(n);
}
visitBox(n: Box) {
this.nowVisiting.canInline = false;
this.visitChildren(n);
}
visitForeachClause(n: ForeachClause) {
this.nowVisiting.canInline = false;
this.visitChildren(n);
}
visitInlineActions(n: InlineActions) {
this.nowVisiting.canInline = false;
this.visitChildren(n);
}
visitInlineAction(n: InlineAction) {
this.nowVisiting.canInline = false;
this.visitChildren(n);
}
visitOptionalParameter(n: OptionalParameter) {
this.nowVisiting.canInline = false;
this.visitChildren(n);
}
visitContinue(n: Call) {
this.nowVisiting.canInline = false;
this.visitChildren(n);
}
visitBreak(n: Call) {
this.nowVisiting.canInline = false;
this.visitChildren(n);
}
visitReturn(n: Call) {
this.nowVisiting.canInline = false;
this.visitChildren(n);
}
// Build a new edge of the callgraph if calling another action
visitCall(n: Call) {
var a = n.calledAction();
var prop = n.prop();
// Check for unwanted calls
if (prop && prop.getCategory() == PropertyCategory.Library) {
this.nowVisiting.canInline = false;
return;
}
if (prop && prop.shouldPauseInterperter()) {
this.nowVisiting.canInline = false;
return;
}
if (prop && prop.getName() == "run" && prop.parentKind.isAction) {
this.nowVisiting.canInline = false;
return;
}
if (a == null) {
this.visitChildren(n);
return;
}
if (a instanceof LibraryRefAction) {
this.nowVisiting.canInline = false;
return;
}
// This is a call to another action inside this App, create the
// callgraph node if not available and create the edge to it.
var cgNode = this.nodeMap[["a_", a.getName()].join("")];
if (cgNode == undefined) {
cgNode = new CallGraphNode(a, [], []);
this.nodeMap[["a_", a.getName()].join("")] = cgNode;
this.nodes.push(cgNode);
}
this.nowVisiting.addSucc(cgNode);
cgNode.addPred(this.nowVisiting);
this.visitChildren(n);
}
// Check if this action can be inlined (apart from the callgraph
// analysis)
actionHasDesiredProperties(a: Action) {
return (a.isNormalAction()
&& a.isPrivate
&& !a.isLambda
&& !a.isTest()
&& a.isAtomic
&& a.getOutParameters().length <= 1);
}
// Create a new callgraph node to this action and start visiting it.
visitAction(n: Action) {
if (n instanceof LibraryRefAction)
return;
var cgNode = this.nodeMap[["a_", n.getName()].join("")];
if (cgNode == undefined) {
cgNode = new CallGraphNode(n, [], []);
this.nodeMap[["a_", n.getName()].join("")] = cgNode;
this.nodes.push(cgNode);
}
this.nowVisiting = cgNode;
this.nowVisiting.canInline = true;
this.visitChildren(n);
if (this.nowVisiting.canInline
&& this.actionHasDesiredProperties(n)
&& this.nowVisiting.succs.length == 0) {
n.canBeInlined = true;
}
}
// Sort the callgraph node to allow an easy bottom-up traversal of
// of the call tree.
public topologicalSort() : CallGraphNode[] {
var traversalOrder : CallGraphNode[] = [];
var visited : { [idx: number] : boolean; } = <any>{};
var indexMap: { [name: string] : number;} = {};
for (var i = 0; i < this.nodes.length; ++i) {
visited[i] = false;
indexMap[["a_", this.nodes[i].action.getName()].join("")] = i;
}
var visit = (cur: number) => {
if (visited[cur])
return;
visited[cur] = true;
for (var i = 0; i < this.nodes[cur].preds.length; ++i) {
visit(indexMap[["a_", this.nodes[cur].preds[i].action.getName()].join("")]);
}
traversalOrder.unshift(this.nodes[cur]);
}
for (var i = 0; i < this.nodes.length; ++i) {
visit(i);
}
return traversalOrder;
}
// Entry point for the inline analysis.
public nestedInlineAnalysis() {
var sorted = this.topologicalSort();
for (var i = 0; i < sorted.length; ++i) {
if (sorted[i].action.canBeInlined)
continue;
var canInline = this.actionHasDesiredProperties(sorted[i].action)
&& sorted[i].canInline;
if (!canInline)
continue;
for (var j = 0; j < sorted[i].succs.length; ++j) {
if (!sorted[i].succs[j].action.canBeInlined)
canInline = false;
}
sorted[i].action.canBeInlined = canInline;
}
}
// Debugging purposes
public dumpCallGraph() {
for (var i = 0; i < this.nodes.length; ++i) {
if (this.nodes[i].action.canBeInlined)
Util.log("Node " + i + ": " + this.nodes[i].action.toString()
+ " [can be inlined]");
else
Util.log("Node " + i + ": " + this.nodes[i].action.toString());
for (var j = 0; j < this.nodes[i].succs.length; ++j) {
Util.log(" |-> calls " + this.nodes[i].succs[j].action.toString());
}
}
}
}
}
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