+++ /dev/null
-// 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)
- }
-}
projects / dotfiles / .git / blobdiff