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// Copyright 2021 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 vta
import (
"go/types"
"golang.org/x/tools/go/callgraph/vta/internal/trie"
"golang.org/x/tools/go/ssa"
"golang.org/x/tools/go/types/typeutil"
)
// scc computes strongly connected components (SCCs) of `g` using the
// classical Tarjan's algorithm for SCCs. The result is a pair <m, id>
// where m is a map from nodes to unique id of their SCC in the range
// [0, id). The SCCs are sorted in reverse topological order: for SCCs
// with ids X and Y s.t. X < Y, Y comes before X in the topological order.
func scc(g vtaGraph) (map[node]int, int) {
// standard data structures used by Tarjan's algorithm.
var index uint64
var stack []node
indexMap := make(map[node]uint64)
lowLink := make(map[node]uint64)
onStack := make(map[node]bool)
nodeToSccID := make(map[node]int)
sccID := 0
var doSCC func(node)
doSCC = func(n node) {
indexMap[n] = index
lowLink[n] = index
index = index + 1
onStack[n] = true
stack = append(stack, n)
for s := range g[n] {
if _, ok := indexMap[s]; !ok {
// Analyze successor s that has not been visited yet.
doSCC(s)
lowLink[n] = min(lowLink[n], lowLink[s])
} else if onStack[s] {
// The successor is on the stack, meaning it has to be
// in the current SCC.
lowLink[n] = min(lowLink[n], indexMap[s])
}
}
// if n is a root node, pop the stack and generate a new SCC.
if lowLink[n] == indexMap[n] {
for {
w := stack[len(stack)-1]
stack = stack[:len(stack)-1]
onStack[w] = false
nodeToSccID[w] = sccID
if w == n {
break
}
}
sccID++
}
}
index = 0
for n := range g {
if _, ok := indexMap[n]; !ok {
doSCC(n)
}
}
return nodeToSccID, sccID
}
func min(x, y uint64) uint64 {
if x < y {
return x
}
return y
}
// propType represents type information being propagated
// over the vta graph. f != nil only for function nodes
// and nodes reachable from function nodes. There, we also
// remember the actual *ssa.Function in order to more
// precisely model higher-order flow.
type propType struct {
typ types.Type
f *ssa.Function
}
// propTypeMap is an auxiliary structure that serves
// the role of a map from nodes to a set of propTypes.
type propTypeMap struct {
nodeToScc map[node]int
sccToTypes map[int]*trie.MutMap
}
// propTypes returns a list of propTypes associated with
// node `n`. If `n` is not in the map `ptm`, nil is returned.
func (ptm propTypeMap) propTypes(n node) []propType {
id, ok := ptm.nodeToScc[n]
if !ok {
return nil
}
var pts []propType
for _, elem := range trie.Elems(ptm.sccToTypes[id].M) {
pts = append(pts, elem.(propType))
}
return pts
}
// propagate reduces the `graph` based on its SCCs and
// then propagates type information through the reduced
// graph. The result is a map from nodes to a set of types
// and functions, stemming from higher-order data flow,
// reaching the node. `canon` is used for type uniqueness.
func propagate(graph vtaGraph, canon *typeutil.Map) propTypeMap {
nodeToScc, sccID := scc(graph)
// We also need the reverse map, from ids to SCCs.
sccs := make(map[int][]node, sccID)
for n, id := range nodeToScc {
sccs[id] = append(sccs[id], n)
}
// propTypeIds are used to create unique ids for
// propType, to be used for trie-based type sets.
propTypeIds := make(map[propType]uint64)
// Id creation is based on == equality, which works
// as types are canonicalized (see getPropType).
propTypeId := func(p propType) uint64 {
if id, ok := propTypeIds[p]; ok {
return id
}
id := uint64(len(propTypeIds))
propTypeIds[p] = id
return id
}
builder := trie.NewBuilder()
// Initialize sccToTypes to avoid repeated check
// for initialization later.
sccToTypes := make(map[int]*trie.MutMap, sccID)
for i := 0; i <= sccID; i++ {
sccToTypes[i] = nodeTypes(sccs[i], builder, propTypeId, canon)
}
for i := len(sccs) - 1; i >= 0; i-- {
nextSccs := make(map[int]struct{})
for _, node := range sccs[i] {
for succ := range graph[node] {
nextSccs[nodeToScc[succ]] = struct{}{}
}
}
// Propagate types to all successor SCCs.
for nextScc := range nextSccs {
sccToTypes[nextScc].Merge(sccToTypes[i].M)
}
}
return propTypeMap{nodeToScc: nodeToScc, sccToTypes: sccToTypes}
}
// nodeTypes returns a set of propTypes for `nodes`. These are the
// propTypes stemming from the type of each node in `nodes` plus.
func nodeTypes(nodes []node, builder *trie.Builder, propTypeId func(p propType) uint64, canon *typeutil.Map) *trie.MutMap {
typeSet := builder.MutEmpty()
for _, n := range nodes {
if hasInitialTypes(n) {
pt := getPropType(n, canon)
typeSet.Update(propTypeId(pt), pt)
}
}
return &typeSet
}
// getPropType creates a propType for `node` based on its type.
// propType.typ is always node.Type(). If node is function, then
// propType.val is the underlying function; nil otherwise.
func getPropType(node node, canon *typeutil.Map) propType {
t := canonicalize(node.Type(), canon)
if fn, ok := node.(function); ok {
return propType{f: fn.f, typ: t}
}
return propType{f: nil, typ: t}
}
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