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//===- StratifiedSets.h - Abstract stratified sets implementation. --------===//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
#include "AliasAnalysisSummary.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/Optional.h"
#include "llvm/ADT/SmallSet.h"
#include "llvm/ADT/SmallVector.h"
#include <bitset>
#include <cassert>
#include <cmath>
#include <type_traits>
#include <utility>
#include <vector>
namespace llvm {
namespace cflaa {
/// An index into Stratified Sets.
typedef unsigned StratifiedIndex;
/// NOTE: ^ This can't be a short -- bootstrapping clang has a case where
/// ~1M sets exist.
// Container of information related to a value in a StratifiedSet.
struct StratifiedInfo {
StratifiedIndex Index;
/// For field sensitivity, etc. we can tack fields on here.
/// A "link" between two StratifiedSets.
struct StratifiedLink {
/// This is a value used to signify "does not exist" where the
/// StratifiedIndex type is used.
/// This is used instead of Optional<StratifiedIndex> because
/// Optional<StratifiedIndex> would eat up a considerable amount of extra
/// memory, after struct padding/alignment is taken into account.
static const StratifiedIndex SetSentinel;
/// The index for the set "above" current
StratifiedIndex Above;
/// The link for the set "below" current
StratifiedIndex Below;
/// Attributes for these StratifiedSets.
AliasAttrs Attrs;
StratifiedLink() : Above(SetSentinel), Below(SetSentinel) {}
bool hasBelow() const { return Below != SetSentinel; }
bool hasAbove() const { return Above != SetSentinel; }
void clearBelow() { Below = SetSentinel; }
void clearAbove() { Above = SetSentinel; }
/// These are stratified sets, as described in "Fast algorithms for
/// Dyck-CFL-reachability with applications to Alias Analysis" by Zhang Q, Lyu M
/// R, Yuan H, and Su Z. -- in short, this is meant to represent different sets
/// of Value*s. If two Value*s are in the same set, or if both sets have
/// overlapping attributes, then the Value*s are said to alias.
/// Sets may be related by position, meaning that one set may be considered as
/// above or below another. In CFL Alias Analysis, this gives us an indication
/// of how two variables are related; if the set of variable A is below a set
/// containing variable B, then at some point, a variable that has interacted
/// with B (or B itself) was either used in order to extract the variable A, or
/// was used as storage of variable A.
/// Sets may also have attributes (as noted above). These attributes are
/// generally used for noting whether a variable in the set has interacted with
/// a variable whose origins we don't quite know (i.e. globals/arguments), or if
/// the variable may have had operations performed on it (modified in a function
/// call). All attributes that exist in a set A must exist in all sets marked as
/// below set A.
template <typename T> class StratifiedSets {
StratifiedSets() = default;
StratifiedSets(StratifiedSets &&) = default;
StratifiedSets &operator=(StratifiedSets &&) = default;
StratifiedSets(DenseMap<T, StratifiedInfo> Map,
std::vector<StratifiedLink> Links)
: Values(std::move(Map)), Links(std::move(Links)) {}
Optional<StratifiedInfo> find(const T &Elem) const {
auto Iter = Values.find(Elem);
if (Iter == Values.end())
return None;
return Iter->second;
const StratifiedLink &getLink(StratifiedIndex Index) const {
return Links[Index];
DenseMap<T, StratifiedInfo> Values;
std::vector<StratifiedLink> Links;
bool inbounds(StratifiedIndex Idx) const { return Idx < Links.size(); }
/// Generic Builder class that produces StratifiedSets instances.
/// The goal of this builder is to efficiently produce correct StratifiedSets
/// instances. To this end, we use a few tricks:
/// > Set chains (A method for linking sets together)
/// > Set remaps (A method for marking a set as an alias [irony?] of another)
/// ==== Set chains ====
/// This builder has a notion of some value A being above, below, or with some
/// other value B:
/// > The `A above B` relationship implies that there is a reference edge
/// going from A to B. Namely, it notes that A can store anything in B's set.
/// > The `A below B` relationship is the opposite of `A above B`. It implies
/// that there's a dereference edge going from A to B.
/// > The `A with B` relationship states that there's an assignment edge going
/// from A to B, and that A and B should be treated as equals.
/// As an example, take the following code snippet:
/// %a = alloca i32, align 4
/// %ap = alloca i32*, align 8
/// %app = alloca i32**, align 8
/// store %a, %ap
/// store %ap, %app
/// %aw = getelementptr %ap, i32 0
/// Given this, the following relations exist:
/// - %a below %ap & %ap above %a
/// - %ap below %app & %app above %ap
/// - %aw with %ap & %ap with %aw
/// These relations produce the following sets:
/// [{%a}, {%ap, %aw}, {%app}]
/// ...Which state that the only MayAlias relationship in the above program is
/// between %ap and %aw.
/// Because LLVM allows arbitrary casts, code like the following needs to be
/// supported:
/// %ip = alloca i64, align 8
/// %ipp = alloca i64*, align 8
/// %i = bitcast i64** ipp to i64
/// store i64* %ip, i64** %ipp
/// store i64 %i, i64* %ip
/// Which, because %ipp ends up *both* above and below %ip, is fun.
/// This is solved by merging %i and %ipp into a single set (...which is the
/// only way to solve this, since their bit patterns are equivalent). Any sets
/// that ended up in between %i and %ipp at the time of merging (in this case,
/// the set containing %ip) also get conservatively merged into the set of %i
/// and %ipp. In short, the resulting StratifiedSet from the above code would be
/// {%ip, %ipp, %i}.
/// ==== Set remaps ====
/// More of an implementation detail than anything -- when merging sets, we need
/// to update the numbers of all of the elements mapped to those sets. Rather
/// than doing this at each merge, we note in the BuilderLink structure that a
/// remap has occurred, and use this information so we can defer renumbering set
/// elements until build time.
template <typename T> class StratifiedSetsBuilder {
/// Represents a Stratified Set, with information about the Stratified
/// Set above it, the set below it, and whether the current set has been
/// remapped to another.
struct BuilderLink {
const StratifiedIndex Number;
BuilderLink(StratifiedIndex N) : Number(N) {
Remap = StratifiedLink::SetSentinel;
bool hasAbove() const {
return Link.hasAbove();
bool hasBelow() const {
return Link.hasBelow();
void setBelow(StratifiedIndex I) {
Link.Below = I;
void setAbove(StratifiedIndex I) {
Link.Above = I;
void clearBelow() {
void clearAbove() {
StratifiedIndex getBelow() const {
return Link.Below;
StratifiedIndex getAbove() const {
return Link.Above;
AliasAttrs getAttrs() {
return Link.Attrs;
void setAttrs(AliasAttrs Other) {
Link.Attrs |= Other;
bool isRemapped() const { return Remap != StratifiedLink::SetSentinel; }
/// For initial remapping to another set
void remapTo(StratifiedIndex Other) {
Remap = Other;
StratifiedIndex getRemapIndex() const {
return Remap;
/// Should only be called when we're already remapped.
void updateRemap(StratifiedIndex Other) {
Remap = Other;
/// Prefer the above functions to calling things directly on what's returned
/// from this -- they guard against unexpected calls when the current
/// BuilderLink is remapped.
const StratifiedLink &getLink() const { return Link; }
StratifiedLink Link;
StratifiedIndex Remap;
/// This function performs all of the set unioning/value renumbering
/// that we've been putting off, and generates a vector<StratifiedLink> that
/// may be placed in a StratifiedSets instance.
void finalizeSets(std::vector<StratifiedLink> &StratLinks) {
DenseMap<StratifiedIndex, StratifiedIndex> Remaps;
for (auto &Link : Links) {
if (Link.isRemapped())
StratifiedIndex Number = StratLinks.size();
Remaps.insert(std::make_pair(Link.Number, Number));
for (auto &Link : StratLinks) {
if (Link.hasAbove()) {
auto &Above = linksAt(Link.Above);
auto Iter = Remaps.find(Above.Number);
assert(Iter != Remaps.end());
Link.Above = Iter->second;
if (Link.hasBelow()) {
auto &Below = linksAt(Link.Below);
auto Iter = Remaps.find(Below.Number);
assert(Iter != Remaps.end());
Link.Below = Iter->second;
for (auto &Pair : Values) {
auto &Info = Pair.second;
auto &Link = linksAt(Info.Index);
auto Iter = Remaps.find(Link.Number);
assert(Iter != Remaps.end());
Info.Index = Iter->second;
/// There's a guarantee in StratifiedLink where all bits set in a
/// Link.externals will be set in all Link.externals "below" it.
static void propagateAttrs(std::vector<StratifiedLink> &Links) {
const auto getHighestParentAbove = [&Links](StratifiedIndex Idx) {
const auto *Link = &Links[Idx];
while (Link->hasAbove()) {
Idx = Link->Above;
Link = &Links[Idx];
return Idx;
SmallSet<StratifiedIndex, 16> Visited;
for (unsigned I = 0, E = Links.size(); I < E; ++I) {
auto CurrentIndex = getHighestParentAbove(I);
if (!Visited.insert(CurrentIndex).second)
while (Links[CurrentIndex].hasBelow()) {
auto &CurrentBits = Links[CurrentIndex].Attrs;
auto NextIndex = Links[CurrentIndex].Below;
auto &NextBits = Links[NextIndex].Attrs;
NextBits |= CurrentBits;
CurrentIndex = NextIndex;
/// Builds a StratifiedSet from the information we've been given since either
/// construction or the prior build() call.
StratifiedSets<T> build() {
std::vector<StratifiedLink> StratLinks;
return StratifiedSets<T>(std::move(Values), std::move(StratLinks));
bool has(const T &Elem) const { return get(Elem).hasValue(); }
bool add(const T &Main) {
if (get(Main).hasValue())
return false;
auto NewIndex = getNewUnlinkedIndex();
return addAtMerging(Main, NewIndex);
/// Restructures the stratified sets as necessary to make "ToAdd" in a
/// set above "Main". There are some cases where this is not possible (see
/// above), so we merge them such that ToAdd and Main are in the same set.
bool addAbove(const T &Main, const T &ToAdd) {
auto Index = *indexOf(Main);
if (!linksAt(Index).hasAbove())
auto Above = linksAt(Index).getAbove();
return addAtMerging(ToAdd, Above);
/// Restructures the stratified sets as necessary to make "ToAdd" in a
/// set below "Main". There are some cases where this is not possible (see
/// above), so we merge them such that ToAdd and Main are in the same set.
bool addBelow(const T &Main, const T &ToAdd) {
auto Index = *indexOf(Main);
if (!linksAt(Index).hasBelow())
auto Below = linksAt(Index).getBelow();
return addAtMerging(ToAdd, Below);
bool addWith(const T &Main, const T &ToAdd) {
auto MainIndex = *indexOf(Main);
return addAtMerging(ToAdd, MainIndex);
void noteAttributes(const T &Main, AliasAttrs NewAttrs) {
auto *Info = *get(Main);
auto &Link = linksAt(Info->Index);
DenseMap<T, StratifiedInfo> Values;
std::vector<BuilderLink> Links;
/// Adds the given element at the given index, merging sets if necessary.
bool addAtMerging(const T &ToAdd, StratifiedIndex Index) {
StratifiedInfo Info = {Index};
auto Pair = Values.insert(std::make_pair(ToAdd, Info));
if (Pair.second)
return true;
auto &Iter = Pair.first;
auto &IterSet = linksAt(Iter->second.Index);
auto &ReqSet = linksAt(Index);
// Failed to add where we wanted to. Merge the sets.
if (&IterSet != &ReqSet)
merge(IterSet.Number, ReqSet.Number);
return false;
/// Gets the BuilderLink at the given index, taking set remapping into
/// account.
BuilderLink &linksAt(StratifiedIndex Index) {
auto *Start = &Links[Index];
if (!Start->isRemapped())
return *Start;
auto *Current = Start;
while (Current->isRemapped())
Current = &Links[Current->getRemapIndex()];
auto NewRemap = Current->Number;
// Run through everything that has yet to be updated, and update them to
// remap to NewRemap
Current = Start;
while (Current->isRemapped()) {
auto *Next = &Links[Current->getRemapIndex()];
Current = Next;
return *Current;
/// Merges two sets into one another. Assumes that these sets are not
/// already one in the same.
void merge(StratifiedIndex Idx1, StratifiedIndex Idx2) {
assert(inbounds(Idx1) && inbounds(Idx2));
assert(&linksAt(Idx1) != &linksAt(Idx2) &&
"Merging a set into itself is not allowed");
// CASE 1: If the set at `Idx1` is above or below `Idx2`, we need to merge
// both the
// given sets, and all sets between them, into one.
if (tryMergeUpwards(Idx1, Idx2))
if (tryMergeUpwards(Idx2, Idx1))
// CASE 2: The set at `Idx1` is not in the same chain as the set at `Idx2`.
// We therefore need to merge the two chains together.
mergeDirect(Idx1, Idx2);
/// Merges two sets assuming that the set at `Idx1` is unreachable from
/// traversing above or below the set at `Idx2`.
void mergeDirect(StratifiedIndex Idx1, StratifiedIndex Idx2) {
assert(inbounds(Idx1) && inbounds(Idx2));
auto *LinksInto = &linksAt(Idx1);
auto *LinksFrom = &linksAt(Idx2);
// Merging everything above LinksInto then proceeding to merge everything
// below LinksInto becomes problematic, so we go as far "up" as possible!
while (LinksInto->hasAbove() && LinksFrom->hasAbove()) {
LinksInto = &linksAt(LinksInto->getAbove());
LinksFrom = &linksAt(LinksFrom->getAbove());
if (LinksFrom->hasAbove()) {
auto &NewAbove = linksAt(LinksInto->getAbove());
// Merging strategy:
// > If neither has links below, stop.
// > If only `LinksInto` has links below, stop.
// > If only `LinksFrom` has links below, reset `LinksInto.Below` to
// match `LinksFrom.Below`
// > If both have links above, deal with those next.
while (LinksInto->hasBelow() && LinksFrom->hasBelow()) {
auto FromAttrs = LinksFrom->getAttrs();
// Remap needs to happen after getBelow(), but before
// assignment of LinksFrom
auto *NewLinksFrom = &linksAt(LinksFrom->getBelow());
LinksFrom = NewLinksFrom;
LinksInto = &linksAt(LinksInto->getBelow());
if (LinksFrom->hasBelow()) {
auto &NewBelow = linksAt(LinksInto->getBelow());
/// Checks to see if lowerIndex is at a level lower than upperIndex. If so, it
/// will merge lowerIndex with upperIndex (and all of the sets between) and
/// return true. Otherwise, it will return false.
bool tryMergeUpwards(StratifiedIndex LowerIndex, StratifiedIndex UpperIndex) {
assert(inbounds(LowerIndex) && inbounds(UpperIndex));
auto *Lower = &linksAt(LowerIndex);
auto *Upper = &linksAt(UpperIndex);
if (Lower == Upper)
return true;
SmallVector<BuilderLink *, 8> Found;
auto *Current = Lower;
auto Attrs = Current->getAttrs();
while (Current->hasAbove() && Current != Upper) {
Attrs |= Current->getAttrs();
Current = &linksAt(Current->getAbove());
if (Current != Upper)
return false;
if (Lower->hasBelow()) {
auto NewBelowIndex = Lower->getBelow();
auto &NewBelow = linksAt(NewBelowIndex);
} else {
for (const auto &Ptr : Found)
return true;
Optional<const StratifiedInfo *> get(const T &Val) const {
auto Result = Values.find(Val);
if (Result == Values.end())
return None;
return &Result->second;
Optional<StratifiedInfo *> get(const T &Val) {
auto Result = Values.find(Val);
if (Result == Values.end())
return None;
return &Result->second;
Optional<StratifiedIndex> indexOf(const T &Val) {
auto MaybeVal = get(Val);
if (!MaybeVal.hasValue())
return None;
auto *Info = *MaybeVal;
auto &Link = linksAt(Info->Index);
return Link.Number;
StratifiedIndex addLinkBelow(StratifiedIndex Set) {
auto At = addLinks();
return At;
StratifiedIndex addLinkAbove(StratifiedIndex Set) {
auto At = addLinks();
return At;
StratifiedIndex getNewUnlinkedIndex() { return addLinks(); }
StratifiedIndex addLinks() {
auto Link = Links.size();
return Link;
bool inbounds(StratifiedIndex N) const { return N < Links.size(); }