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// Copyright 2011 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package ir
// Strongly connected components.
// Run analysis on minimal sets of mutually recursive functions
// or single non-recursive functions, bottom up.
// Finding these sets is finding strongly connected components
// by reverse topological order in the static call graph.
// The algorithm (known as Tarjan's algorithm) for doing that is taken from
// Sedgewick, Algorithms, Second Edition, p. 482, with two adaptations.
// First, a hidden closure function (n.Func.IsHiddenClosure()) cannot be the
// root of a connected component. Refusing to use it as a root
// forces it into the component of the function in which it appears.
// This is more convenient for escape analysis.
// Second, each function becomes two virtual nodes in the graph,
// with numbers n and n+1. We record the function's node number as n
// but search from node n+1. If the search tells us that the component
// number (min) is n+1, we know that this is a trivial component: one function
// plus its closures. If the search tells us that the component number is
// n, then there was a path from node n+1 back to node n, meaning that
// the function set is mutually recursive. The escape analysis can be
// more precise when analyzing a single non-recursive function than
// when analyzing a set of mutually recursive functions.
type bottomUpVisitor struct {
analyze func([]*Func, bool)
visitgen uint32
nodeID map[*Func]uint32
stack []*Func
// VisitFuncsBottomUp invokes analyze on the ODCLFUNC nodes listed in list.
// It calls analyze with successive groups of functions, working from
// the bottom of the call graph upward. Each time analyze is called with
// a list of functions, every function on that list only calls other functions
// on the list or functions that have been passed in previous invocations of
// analyze. Closures appear in the same list as their outer functions.
// The lists are as short as possible while preserving those requirements.
// (In a typical program, many invocations of analyze will be passed just
// a single function.) The boolean argument 'recursive' passed to analyze
// specifies whether the functions on the list are mutually recursive.
// If recursive is false, the list consists of only a single function and its closures.
// If recursive is true, the list may still contain only a single function,
// if that function is itself recursive.
func VisitFuncsBottomUp(list []Node, analyze func(list []*Func, recursive bool)) {
var v bottomUpVisitor
v.analyze = analyze
v.nodeID = make(map[*Func]uint32)
for _, n := range list {
if n.Op() == ODCLFUNC {
n := n.(*Func)
if !n.IsHiddenClosure() {
func (v *bottomUpVisitor) visit(n *Func) uint32 {
if id := v.nodeID[n]; id > 0 {
// already visited
return id
id := v.visitgen
v.nodeID[n] = id
min := v.visitgen
v.stack = append(v.stack, n)
do := func(defn Node) {
if defn != nil {
if m := v.visit(defn.(*Func)); m < min {
min = m
Visit(n, func(n Node) {
switch n.Op() {
case ONAME:
if n := n.(*Name); n.Class == PFUNC {
if fn := MethodExprName(n); fn != nil {
n := n.(*ClosureExpr)
if (min == id || min == id+1) && !n.IsHiddenClosure() {
// This node is the root of a strongly connected component.
// The original min was id+1. If the bottomUpVisitor found its way
// back to id, then this block is a set of mutually recursive functions.
// Otherwise, it's just a lone function that does not recurse.
recursive := min == id
// Remove connected component from stack and mark v.nodeID so that future
// visits return a large number, which will not affect the caller's min.
var i int
for i = len(v.stack) - 1; i >= 0; i-- {
x := v.stack[i]
v.nodeID[x] = ^uint32(0)
if x == n {
block := v.stack[i:]
// Call analyze on this set of functions.
v.stack = v.stack[:i]
v.analyze(block, recursive)
return min