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// Copyright 2013 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 pointer
// This file implements Hash-Value Numbering (HVN), a pre-solver
// constraint optimization described in Hardekopf & Lin, SAS'07 (see
// doc.go) that analyses the graph topology to determine which sets of
// variables are "pointer equivalent" (PE), i.e. must have identical
// points-to sets in the solution.
//
// A separate ("offline") graph is constructed. Its nodes are those of
// the main-graph, plus an additional node *X for each pointer node X.
// With this graph we can reason about the unknown points-to set of
// dereferenced pointers. (We do not generalize this to represent
// unknown fields x->f, perhaps because such fields would be numerous,
// though it might be worth an experiment.)
//
// Nodes whose points-to relations are not entirely captured by the
// graph are marked as "indirect": the *X nodes, the parameters of
// address-taken functions (which includes all functions in method
// sets), or nodes updated by the solver rules for reflection, etc.
//
// All addr (y=&x) nodes are initially assigned a pointer-equivalence
// (PE) label equal to x's nodeid in the main graph. (These are the
// only PE labels that are less than len(a.nodes).)
//
// All offsetAddr (y=&x.f) constraints are initially assigned a PE
// label; such labels are memoized, keyed by (x, f), so that equivalent
// nodes y as assigned the same label.
//
// Then we process each strongly connected component (SCC) of the graph
// in topological order, assigning it a PE label based on the set P of
// PE labels that flow to it from its immediate dependencies.
//
// If any node in P is "indirect", the entire SCC is assigned a fresh PE
// label. Otherwise:
//
// |P|=0 if P is empty, all nodes in the SCC are non-pointers (e.g.
// uninitialized variables, or formal params of dead functions)
// and the SCC is assigned the PE label of zero.
//
// |P|=1 if P is a singleton, the SCC is assigned the same label as the
// sole element of P.
//
// |P|>1 if P contains multiple labels, a unique label representing P is
// invented and recorded in an hash table, so that other
// equivalent SCCs may also be assigned this label, akin to
// conventional hash-value numbering in a compiler.
//
// Finally, a renumbering is computed such that each node is replaced by
// the lowest-numbered node with the same PE label. All constraints are
// renumbered, and any resulting duplicates are eliminated.
//
// The only nodes that are not renumbered are the objects x in addr
// (y=&x) constraints, since the ids of these nodes (and fields derived
// from them via offsetAddr rules) are the elements of all points-to
// sets, so they must remain as they are if we want the same solution.
//
// The solverStates (node.solve) for nodes in the same equivalence class
// are linked together so that all nodes in the class have the same
// solution. This avoids the need to renumber nodeids buried in
// Queries, cgnodes, etc (like (*analysis).renumber() does) since only
// the solution is needed.
//
// The result of HVN is that the number of distinct nodes and
// constraints is reduced, but the solution is identical (almost---see
// CROSS-CHECK below). In particular, both linear and cyclic chains of
// copies are each replaced by a single node.
//
// Nodes and constraints created "online" (e.g. while solving reflection
// constraints) are not subject to this optimization.
//
// PERFORMANCE
//
// In two benchmarks (guru and godoc), HVN eliminates about two thirds
// of nodes, the majority accounted for by non-pointers: nodes of
// non-pointer type, pointers that remain nil, formal parameters of dead
// functions, nodes of untracked types, etc. It also reduces the number
// of constraints, also by about two thirds, and the solving time by
// 30--42%, although we must pay about 15% for the running time of HVN
// itself. The benefit is greater for larger applications.
//
// There are many possible optimizations to improve the performance:
// * Use fewer than 1:1 onodes to main graph nodes: many of the onodes
// we create are not needed.
// * HU (HVN with Union---see paper): coalesce "union" peLabels when
// their expanded-out sets are equal.
// * HR (HVN with deReference---see paper): this will require that we
// apply HVN until fixed point, which may need more bookkeeping of the
// correspondence of main nodes to onodes.
// * Location Equivalence (see paper): have points-to sets contain not
// locations but location-equivalence class labels, each representing
// a set of locations.
// * HVN with field-sensitive ref: model each of the fields of a
// pointer-to-struct.
//
// CROSS-CHECK
//
// To verify the soundness of the optimization, when the
// debugHVNCrossCheck option is enabled, we run the solver twice, once
// before and once after running HVN, dumping the solution to disk, and
// then we compare the results. If they are not identical, the analysis
// panics.
//
// The solution dumped to disk includes only the N*N submatrix of the
// complete solution where N is the number of nodes after generation.
// In other words, we ignore pointer variables and objects created by
// the solver itself, since their numbering depends on the solver order,
// which is affected by the optimization. In any case, that's the only
// part the client cares about.
//
// The cross-check is too strict and may fail spuriously. Although the
// H&L paper describing HVN states that the solutions obtained should be
// identical, this is not the case in practice because HVN can collapse
// cycles involving *p even when pts(p)={}. Consider this example
// distilled from testdata/hello.go:
//
// var x T
// func f(p **T) {
// t0 = *p
// ...
// t1 = φ(t0, &x)
// *p = t1
// }
//
// If f is dead code, we get:
// unoptimized: pts(p)={} pts(t0)={} pts(t1)={&x}
// optimized: pts(p)={} pts(t0)=pts(t1)=pts(*p)={&x}
//
// It's hard to argue that this is a bug: the result is sound and the
// loss of precision is inconsequential---f is dead code, after all.
// But unfortunately it limits the usefulness of the cross-check since
// failures must be carefully analyzed. Ben Hardekopf suggests (in
// personal correspondence) some approaches to mitigating it:
//
// If there is a node with an HVN points-to set that is a superset
// of the NORM points-to set, then either it's a bug or it's a
// result of this issue. If it's a result of this issue, then in
// the offline constraint graph there should be a REF node inside
// some cycle that reaches this node, and in the NORM solution the
// pointer being dereferenced by that REF node should be the empty
// set. If that isn't true then this is a bug. If it is true, then
// you can further check that in the NORM solution the "extra"
// points-to info in the HVN solution does in fact come from that
// purported cycle (if it doesn't, then this is still a bug). If
// you're doing the further check then you'll need to do it for
// each "extra" points-to element in the HVN points-to set.
//
// There are probably ways to optimize these checks by taking
// advantage of graph properties. For example, extraneous points-to
// info will flow through the graph and end up in many
// nodes. Rather than checking every node with extra info, you
// could probably work out the "origin point" of the extra info and
// just check there. Note that the check in the first bullet is
// looking for soundness bugs, while the check in the second bullet
// is looking for precision bugs; depending on your needs, you may
// care more about one than the other.
//
// which we should evaluate. The cross-check is nonetheless invaluable
// for all but one of the programs in the pointer_test suite.
import (
"fmt"
"go/types"
"io"
"reflect"
"golang.org/x/tools/container/intsets"
)
// A peLabel is a pointer-equivalence label: two nodes with the same
// peLabel have identical points-to solutions.
//
// The numbers are allocated consecutively like so:
// 0 not a pointer
// 1..N-1 addrConstraints (equals the constraint's .src field, hence sparse)
// ... offsetAddr constraints
// ... SCCs (with indirect nodes or multiple inputs)
//
// Each PE label denotes a set of pointers containing a single addr, a
// single offsetAddr, or some set of other PE labels.
//
type peLabel int
type hvn struct {
a *analysis
N int // len(a.nodes) immediately after constraint generation
log io.Writer // (optional) log of HVN lemmas
onodes []*onode // nodes of the offline graph
label peLabel // the next available PE label
hvnLabel map[string]peLabel // hash-value numbering (PE label) for each set of onodeids
stack []onodeid // DFS stack
index int32 // next onode.index, from Tarjan's SCC algorithm
// For each distinct offsetAddrConstraint (src, offset) pair,
// offsetAddrLabels records a unique PE label >= N.
offsetAddrLabels map[offsetAddr]peLabel
}
// The index of an node in the offline graph.
// (Currently the first N align with the main nodes,
// but this may change with HRU.)
type onodeid uint32
// An onode is a node in the offline constraint graph.
// (Where ambiguous, members of analysis.nodes are referred to as
// "main graph" nodes.)
//
// Edges in the offline constraint graph (edges and implicit) point to
// the source, i.e. against the flow of values: they are dependencies.
// Implicit edges are used for SCC computation, but not for gathering
// incoming labels.
//
type onode struct {
rep onodeid // index of representative of SCC in offline constraint graph
edges intsets.Sparse // constraint edges X-->Y (this onode is X)
implicit intsets.Sparse // implicit edges *X-->*Y (this onode is X)
peLabels intsets.Sparse // set of peLabels are pointer-equivalent to this one
indirect bool // node has points-to relations not represented in graph
// Tarjan's SCC algorithm
index, lowlink int32 // Tarjan numbering
scc int32 // -ve => on stack; 0 => unvisited; +ve => node is root of a found SCC
}
type offsetAddr struct {
ptr nodeid
offset uint32
}
// nextLabel issues the next unused pointer-equivalence label.
func (h *hvn) nextLabel() peLabel {
h.label++
return h.label
}
// ref(X) returns the index of the onode for *X.
func (h *hvn) ref(id onodeid) onodeid {
return id + onodeid(len(h.a.nodes))
}
// hvn computes pointer-equivalence labels (peLabels) using the Hash-based
// Value Numbering (HVN) algorithm described in Hardekopf & Lin, SAS'07.
//
func (a *analysis) hvn() {
start("HVN")
if a.log != nil {
fmt.Fprintf(a.log, "\n\n==== Pointer equivalence optimization\n\n")
}
h := hvn{
a: a,
N: len(a.nodes),
log: a.log,
hvnLabel: make(map[string]peLabel),
offsetAddrLabels: make(map[offsetAddr]peLabel),
}
if h.log != nil {
fmt.Fprintf(h.log, "\nCreating offline graph nodes...\n")
}
// Create offline nodes. The first N nodes correspond to main
// graph nodes; the next N are their corresponding ref() nodes.
h.onodes = make([]*onode, 2*h.N)
for id := range a.nodes {
id := onodeid(id)
h.onodes[id] = &onode{}
h.onodes[h.ref(id)] = &onode{indirect: true}
}
// Each node initially represents just itself.
for id, o := range h.onodes {
o.rep = onodeid(id)
}
h.markIndirectNodes()
// Reserve the first N PE labels for addrConstraints.
h.label = peLabel(h.N)
// Add offline constraint edges.
if h.log != nil {
fmt.Fprintf(h.log, "\nAdding offline graph edges...\n")
}
for _, c := range a.constraints {
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "; %s\n", c)
}
c.presolve(&h)
}
// Find and collapse SCCs.
if h.log != nil {
fmt.Fprintf(h.log, "\nFinding SCCs...\n")
}
h.index = 1
for id, o := range h.onodes {
if id > 0 && o.index == 0 {
// Start depth-first search at each unvisited node.
h.visit(onodeid(id))
}
}
// Dump the solution
// (NB: somewhat redundant with logging from simplify().)
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "\nPointer equivalences:\n")
for id, o := range h.onodes {
if id == 0 {
continue
}
if id == int(h.N) {
fmt.Fprintf(h.log, "---\n")
}
fmt.Fprintf(h.log, "o%d\t", id)
if o.rep != onodeid(id) {
fmt.Fprintf(h.log, "rep=o%d", o.rep)
} else {
fmt.Fprintf(h.log, "p%d", o.peLabels.Min())
if o.indirect {
fmt.Fprint(h.log, " indirect")
}
}
fmt.Fprintln(h.log)
}
}
// Simplify the main constraint graph
h.simplify()
a.showCounts()
stop("HVN")
}
// ---- constraint-specific rules ----
// dst := &src
func (c *addrConstraint) presolve(h *hvn) {
// Each object (src) is an initial PE label.
label := peLabel(c.src) // label < N
if debugHVNVerbose && h.log != nil {
// duplicate log messages are possible
fmt.Fprintf(h.log, "\tcreate p%d: {&n%d}\n", label, c.src)
}
odst := onodeid(c.dst)
osrc := onodeid(c.src)
// Assign dst this label.
h.onodes[odst].peLabels.Insert(int(label))
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "\to%d has p%d\n", odst, label)
}
h.addImplicitEdge(h.ref(odst), osrc) // *dst ~~> src.
}
// dst = src
func (c *copyConstraint) presolve(h *hvn) {
odst := onodeid(c.dst)
osrc := onodeid(c.src)
h.addEdge(odst, osrc) // dst --> src
h.addImplicitEdge(h.ref(odst), h.ref(osrc)) // *dst ~~> *src
}
// dst = *src + offset
func (c *loadConstraint) presolve(h *hvn) {
odst := onodeid(c.dst)
osrc := onodeid(c.src)
if c.offset == 0 {
h.addEdge(odst, h.ref(osrc)) // dst --> *src
} else {
// We don't interpret load-with-offset, e.g. results
// of map value lookup, R-block of dynamic call, slice
// copy/append, reflection.
h.markIndirect(odst, "load with offset")
}
}
// *dst + offset = src
func (c *storeConstraint) presolve(h *hvn) {
odst := onodeid(c.dst)
osrc := onodeid(c.src)
if c.offset == 0 {
h.onodes[h.ref(odst)].edges.Insert(int(osrc)) // *dst --> src
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "\to%d --> o%d\n", h.ref(odst), osrc)
}
}
// We don't interpret store-with-offset.
// See discussion of soundness at markIndirectNodes.
}
// dst = &src.offset
func (c *offsetAddrConstraint) presolve(h *hvn) {
// Give each distinct (addr, offset) pair a fresh PE label.
// The cache performs CSE, effectively.
key := offsetAddr{c.src, c.offset}
label, ok := h.offsetAddrLabels[key]
if !ok {
label = h.nextLabel()
h.offsetAddrLabels[key] = label
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "\tcreate p%d: {&n%d.#%d}\n",
label, c.src, c.offset)
}
}
// Assign dst this label.
h.onodes[c.dst].peLabels.Insert(int(label))
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "\to%d has p%d\n", c.dst, label)
}
}
// dst = src.(typ) where typ is an interface
func (c *typeFilterConstraint) presolve(h *hvn) {
h.markIndirect(onodeid(c.dst), "typeFilter result")
}
// dst = src.(typ) where typ is concrete
func (c *untagConstraint) presolve(h *hvn) {
odst := onodeid(c.dst)
for end := odst + onodeid(h.a.sizeof(c.typ)); odst < end; odst++ {
h.markIndirect(odst, "untag result")
}
}
// dst = src.method(c.params...)
func (c *invokeConstraint) presolve(h *hvn) {
// All methods are address-taken functions, so
// their formal P-blocks were already marked indirect.
// Mark the caller's targets node as indirect.
sig := c.method.Type().(*types.Signature)
id := c.params
h.markIndirect(onodeid(c.params), "invoke targets node")
id++
id += nodeid(h.a.sizeof(sig.Params()))
// Mark the caller's R-block as indirect.
end := id + nodeid(h.a.sizeof(sig.Results()))
for id < end {
h.markIndirect(onodeid(id), "invoke R-block")
id++
}
}
// markIndirectNodes marks as indirect nodes whose points-to relations
// are not entirely captured by the offline graph, including:
//
// (a) All address-taken nodes (including the following nodes within
// the same object). This is described in the paper.
//
// The most subtle cause of indirect nodes is the generation of
// store-with-offset constraints since the offline graph doesn't
// represent them. A global audit of constraint generation reveals the
// following uses of store-with-offset:
//
// (b) genDynamicCall, for P-blocks of dynamically called functions,
// to which dynamic copy edges will be added to them during
// solving: from storeConstraint for standalone functions,
// and from invokeConstraint for methods.
// All such P-blocks must be marked indirect.
// (c) MakeUpdate, to update the value part of a map object.
// All MakeMap objects's value parts must be marked indirect.
// (d) copyElems, to update the destination array.
// All array elements must be marked indirect.
//
// Not all indirect marking happens here. ref() nodes are marked
// indirect at construction, and each constraint's presolve() method may
// mark additional nodes.
//
func (h *hvn) markIndirectNodes() {
// (a) all address-taken nodes, plus all nodes following them
// within the same object, since these may be indirectly
// stored or address-taken.
for _, c := range h.a.constraints {
if c, ok := c.(*addrConstraint); ok {
start := h.a.enclosingObj(c.src)
end := start + nodeid(h.a.nodes[start].obj.size)
for id := c.src; id < end; id++ {
h.markIndirect(onodeid(id), "A-T object")
}
}
}
// (b) P-blocks of all address-taken functions.
for id := 0; id < h.N; id++ {
obj := h.a.nodes[id].obj
// TODO(adonovan): opt: if obj.cgn.fn is a method and
// obj.cgn is not its shared contour, this is an
// "inlined" static method call. We needn't consider it
// address-taken since no invokeConstraint will affect it.
if obj != nil && obj.flags&otFunction != 0 && h.a.atFuncs[obj.cgn.fn] {
// address-taken function
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "n%d is address-taken: %s\n", id, obj.cgn.fn)
}
h.markIndirect(onodeid(id), "A-T func identity")
id++
sig := obj.cgn.fn.Signature
psize := h.a.sizeof(sig.Params())
if sig.Recv() != nil {
psize += h.a.sizeof(sig.Recv().Type())
}
for end := id + int(psize); id < end; id++ {
h.markIndirect(onodeid(id), "A-T func P-block")
}
id--
continue
}
}
// (c) all map objects' value fields.
for _, id := range h.a.mapValues {
h.markIndirect(onodeid(id), "makemap.value")
}
// (d) all array element objects.
// TODO(adonovan): opt: can we do better?
for id := 0; id < h.N; id++ {
// Identity node for an object of array type?
if tArray, ok := h.a.nodes[id].typ.(*types.Array); ok {
// Mark the array element nodes indirect.
// (Skip past the identity field.)
for range h.a.flatten(tArray.Elem()) {
id++
h.markIndirect(onodeid(id), "array elem")
}
}
}
}
func (h *hvn) markIndirect(oid onodeid, comment string) {
h.onodes[oid].indirect = true
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "\to%d is indirect: %s\n", oid, comment)
}
}
// Adds an edge dst-->src.
// Note the unusual convention: edges are dependency (contraflow) edges.
func (h *hvn) addEdge(odst, osrc onodeid) {
h.onodes[odst].edges.Insert(int(osrc))
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "\to%d --> o%d\n", odst, osrc)
}
}
func (h *hvn) addImplicitEdge(odst, osrc onodeid) {
h.onodes[odst].implicit.Insert(int(osrc))
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "\to%d ~~> o%d\n", odst, osrc)
}
}
// visit implements the depth-first search of Tarjan's SCC algorithm.
// Precondition: x is canonical.
func (h *hvn) visit(x onodeid) {
h.checkCanonical(x)
xo := h.onodes[x]
xo.index = h.index
xo.lowlink = h.index
h.index++
h.stack = append(h.stack, x) // push
assert(xo.scc == 0, "node revisited")
xo.scc = -1
var deps []int
deps = xo.edges.AppendTo(deps)
deps = xo.implicit.AppendTo(deps)
for _, y := range deps {
// Loop invariant: x is canonical.
y := h.find(onodeid(y))
if x == y {
continue // nodes already coalesced
}
xo := h.onodes[x]
yo := h.onodes[y]
switch {
case yo.scc > 0:
// y is already a collapsed SCC
case yo.scc < 0:
// y is on the stack, and thus in the current SCC.
if yo.index < xo.lowlink {
xo.lowlink = yo.index
}
default:
// y is unvisited; visit it now.
h.visit(y)
// Note: x and y are now non-canonical.
x = h.find(onodeid(x))
if yo.lowlink < xo.lowlink {
xo.lowlink = yo.lowlink
}
}
}
h.checkCanonical(x)
// Is x the root of an SCC?
if xo.lowlink == xo.index {
// Coalesce all nodes in the SCC.
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "scc o%d\n", x)
}
for {
// Pop y from stack.
i := len(h.stack) - 1
y := h.stack[i]
h.stack = h.stack[:i]
h.checkCanonical(x)
xo := h.onodes[x]
h.checkCanonical(y)
yo := h.onodes[y]
if xo == yo {
// SCC is complete.
xo.scc = 1
h.labelSCC(x)
break
}
h.coalesce(x, y)
}
}
}
// Precondition: x is canonical.
func (h *hvn) labelSCC(x onodeid) {
h.checkCanonical(x)
xo := h.onodes[x]
xpe := &xo.peLabels
// All indirect nodes get new labels.
if xo.indirect {
label := h.nextLabel()
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "\tcreate p%d: indirect SCC\n", label)
fmt.Fprintf(h.log, "\to%d has p%d\n", x, label)
}
// Remove pre-labeling, in case a direct pre-labeled node was
// merged with an indirect one.
xpe.Clear()
xpe.Insert(int(label))
return
}
// Invariant: all peLabels sets are non-empty.
// Those that are logically empty contain zero as their sole element.
// No other sets contains zero.
// Find all labels coming in to the coalesced SCC node.
for _, y := range xo.edges.AppendTo(nil) {
y := h.find(onodeid(y))
if y == x {
continue // already coalesced
}
ype := &h.onodes[y].peLabels
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "\tedge from o%d = %s\n", y, ype)
}
if ype.IsEmpty() {
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "\tnode has no PE label\n")
}
}
assert(!ype.IsEmpty(), "incoming node has no PE label")
if ype.Has(0) {
// {0} represents a non-pointer.
assert(ype.Len() == 1, "PE set contains {0, ...}")
} else {
xpe.UnionWith(ype)
}
}
switch xpe.Len() {
case 0:
// SCC has no incoming non-zero PE labels: it is a non-pointer.
xpe.Insert(0)
case 1:
// already a singleton
default:
// SCC has multiple incoming non-zero PE labels.
// Find the canonical label representing this set.
// We use String() as a fingerprint consistent with Equals().
key := xpe.String()
label, ok := h.hvnLabel[key]
if !ok {
label = h.nextLabel()
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "\tcreate p%d: union %s\n", label, xpe.String())
}
h.hvnLabel[key] = label
}
xpe.Clear()
xpe.Insert(int(label))
}
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "\to%d has p%d\n", x, xpe.Min())
}
}
// coalesce combines two nodes in the offline constraint graph.
// Precondition: x and y are canonical.
func (h *hvn) coalesce(x, y onodeid) {
xo := h.onodes[x]
yo := h.onodes[y]
// x becomes y's canonical representative.
yo.rep = x
if debugHVNVerbose && h.log != nil {
fmt.Fprintf(h.log, "\tcoalesce o%d into o%d\n", y, x)
}
// x accumulates y's edges.
xo.edges.UnionWith(&yo.edges)
yo.edges.Clear()
// x accumulates y's implicit edges.
xo.implicit.UnionWith(&yo.implicit)
yo.implicit.Clear()
// x accumulates y's pointer-equivalence labels.
xo.peLabels.UnionWith(&yo.peLabels)
yo.peLabels.Clear()
// x accumulates y's indirect flag.
if yo.indirect {
xo.indirect = true
}
}
// simplify computes a degenerate renumbering of nodeids from the PE
// labels assigned by the hvn, and uses it to simplify the main
// constraint graph, eliminating non-pointer nodes and duplicate
// constraints.
//
func (h *hvn) simplify() {
// canon maps each peLabel to its canonical main node.
canon := make([]nodeid, h.label)
for i := range canon {
canon[i] = nodeid(h.N) // indicates "unset"
}
// mapping maps each main node index to the index of the canonical node.
mapping := make([]nodeid, len(h.a.nodes))
for id := range h.a.nodes {
id := nodeid(id)
if id == 0 {
canon[0] = 0
mapping[0] = 0
continue
}
oid := h.find(onodeid(id))
peLabels := &h.onodes[oid].peLabels
assert(peLabels.Len() == 1, "PE class is not a singleton")
label := peLabel(peLabels.Min())
canonID := canon[label]
if canonID == nodeid(h.N) {
// id becomes the representative of the PE label.
canonID = id
canon[label] = canonID
if h.a.log != nil {
fmt.Fprintf(h.a.log, "\tpts(n%d) is canonical : \t(%s)\n",
id, h.a.nodes[id].typ)
}
} else {
// Link the solver states for the two nodes.
assert(h.a.nodes[canonID].solve != nil, "missing solver state")
h.a.nodes[id].solve = h.a.nodes[canonID].solve
if h.a.log != nil {
// TODO(adonovan): debug: reorganize the log so it prints
// one line:
// pe y = x1, ..., xn
// for each canonical y. Requires allocation.
fmt.Fprintf(h.a.log, "\tpts(n%d) = pts(n%d) : %s\n",
id, canonID, h.a.nodes[id].typ)
}
}
mapping[id] = canonID
}
// Renumber the constraints, eliminate duplicates, and eliminate
// any containing non-pointers (n0).
addrs := make(map[addrConstraint]bool)
copys := make(map[copyConstraint]bool)
loads := make(map[loadConstraint]bool)
stores := make(map[storeConstraint]bool)
offsetAddrs := make(map[offsetAddrConstraint]bool)
untags := make(map[untagConstraint]bool)
typeFilters := make(map[typeFilterConstraint]bool)
invokes := make(map[invokeConstraint]bool)
nbefore := len(h.a.constraints)
cc := h.a.constraints[:0] // in-situ compaction
for _, c := range h.a.constraints {
// Renumber.
switch c := c.(type) {
case *addrConstraint:
// Don't renumber c.src since it is the label of
// an addressable object and will appear in PT sets.
c.dst = mapping[c.dst]
default:
c.renumber(mapping)
}
if c.ptr() == 0 {
continue // skip: constraint attached to non-pointer
}
var dup bool
switch c := c.(type) {
case *addrConstraint:
_, dup = addrs[*c]
addrs[*c] = true
case *copyConstraint:
if c.src == c.dst {
continue // skip degenerate copies
}
if c.src == 0 {
continue // skip copy from non-pointer
}
_, dup = copys[*c]
copys[*c] = true
case *loadConstraint:
if c.src == 0 {
continue // skip load from non-pointer
}
_, dup = loads[*c]
loads[*c] = true
case *storeConstraint:
if c.src == 0 {
continue // skip store from non-pointer
}
_, dup = stores[*c]
stores[*c] = true
case *offsetAddrConstraint:
if c.src == 0 {
continue // skip offset from non-pointer
}
_, dup = offsetAddrs[*c]
offsetAddrs[*c] = true
case *untagConstraint:
if c.src == 0 {
continue // skip untag of non-pointer
}
_, dup = untags[*c]
untags[*c] = true
case *typeFilterConstraint:
if c.src == 0 {
continue // skip filter of non-pointer
}
_, dup = typeFilters[*c]
typeFilters[*c] = true
case *invokeConstraint:
if c.params == 0 {
panic("non-pointer invoke.params")
}
if c.iface == 0 {
continue // skip invoke on non-pointer
}
_, dup = invokes[*c]
invokes[*c] = true
default:
// We don't bother de-duping advanced constraints
// (e.g. reflection) since they are uncommon.
// Eliminate constraints containing non-pointer nodeids.
//
// We use reflection to find the fields to avoid
// adding yet another method to constraint.
//
// TODO(adonovan): experiment with a constraint
// method that returns a slice of pointers to
// nodeids fields to enable uniform iteration;
// the renumber() method could be removed and
// implemented using the new one.
//
// TODO(adonovan): opt: this is unsound since
// some constraints still have an effect if one
// of the operands is zero: rVCall, rVMapIndex,
// rvSetMapIndex. Handle them specially.
rtNodeid := reflect.TypeOf(nodeid(0))
x := reflect.ValueOf(c).Elem()
for i, nf := 0, x.NumField(); i < nf; i++ {
f := x.Field(i)
if f.Type() == rtNodeid {
if f.Uint() == 0 {
dup = true // skip it
break
}
}
}
}
if dup {
continue // skip duplicates
}
cc = append(cc, c)
}
h.a.constraints = cc
if h.log != nil {
fmt.Fprintf(h.log, "#constraints: was %d, now %d\n", nbefore, len(h.a.constraints))
}
}
// find returns the canonical onodeid for x.
// (The onodes form a disjoint set forest.)
func (h *hvn) find(x onodeid) onodeid {
// TODO(adonovan): opt: this is a CPU hotspot. Try "union by rank".
xo := h.onodes[x]
rep := xo.rep
if rep != x {
rep = h.find(rep) // simple path compression
xo.rep = rep
}
return rep
}
func (h *hvn) checkCanonical(x onodeid) {
if debugHVN {
assert(x == h.find(x), "not canonical")
}
}
func assert(p bool, msg string) {
if debugHVN && !p {
panic("assertion failed: " + msg)
}
}