//===- StratifiedSets.h - Abstract stratified sets implementation. --------===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
#ifndef LLVM_ADT_STRATIFIEDSETS_H
#define LLVM_ADT_STRATIFIEDSETS_H
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/Optional.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/SmallSet.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/Support/Compiler.h"
#include <bitset>
#include <cassert>
#include <cmath>
#include <limits>
#include <type_traits>
#include <utility>
#include <vector>
namespace llvm {
// \brief An index into Stratified Sets.
typedef unsigned StratifiedIndex;
// NOTE: ^ This can't be a short -- bootstrapping clang has a case where
// ~1M sets exist.
// \brief Container of information related to a value in a StratifiedSet.
struct StratifiedInfo {
StratifiedIndex Index;
// For field sensitivity, etc. we can tack attributes on to this struct.
};
// The number of attributes that StratifiedAttrs should contain. Attributes are
// described below, and 32 was an arbitrary choice because it fits nicely in 32
// bits (because we use a bitset for StratifiedAttrs).
static const unsigned NumStratifiedAttrs = 32;
// These are attributes that the users of StratifiedSets/StratifiedSetBuilders
// may use for various purposes. These also have the special property of that
// they are merged down. So, if set A is above set B, and one decides to set an
// attribute in set A, then the attribute will automatically be set in set B.
typedef std::bitset<NumStratifiedAttrs> StratifiedAttrs;
// \brief A "link" between two StratifiedSets.
struct StratifiedLink {
// \brief 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;
// \brief The index for the set "above" current
StratifiedIndex Above;
// \brief The link for the set "below" current
StratifiedIndex Below;
// \brief Attributes for these StratifiedSets.
StratifiedAttrs 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; }
};
// \brief 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 {
public:
StratifiedSets() {}
StratifiedSets(DenseMap<T, StratifiedInfo> Map,
std::vector<StratifiedLink> Links)
: Values(std::move(Map)), Links(std::move(Links)) {}
StratifiedSets(StratifiedSets<T> &&Other) { *this = std::move(Other); }
StratifiedSets &operator=(StratifiedSets<T> &&Other) {
Values = std::move(Other.Values);
Links = std::move(Other.Links);
return *this;
}
Optional<StratifiedInfo> find(const T &Elem) const {
auto Iter = Values.find(Elem);
if (Iter == Values.end()) {
return NoneType();
}
return Iter->second;
}
const StratifiedLink &getLink(StratifiedIndex Index) const {
assert(inbounds(Index));
return Links[Index];
}
private:
DenseMap<T, StratifiedInfo> Values;
std::vector<StratifiedLink> Links;
bool inbounds(StratifiedIndex Idx) const { return Idx < Links.size(); }
};
// \brief 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, 0
//
// Given this, the follow 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 states that the only MayAlias relationship in the above program is
// between %ap and %aw.
//
// Life gets more complicated when we actually have logic in our programs. So,
// we either must remove this logic from our programs, or make consessions for
// it in our AA algorithms. In this case, we have decided to select the latter
// option.
//
// First complication: Conditionals
// Motivation:
// %ad = alloca int, align 4
// %a = alloca int*, align 8
// %b = alloca int*, align 8
// %bp = alloca int**, align 8
// %c = call i1 @SomeFunc()
// %k = select %c, %ad, %bp
// store %ad, %a
// store %b, %bp
//
// %k has 'with' edges to both %a and %b, which ordinarily would not be linked
// together. So, we merge the set that contains %a with the set that contains
// %b. We then recursively merge the set above %a with the set above %b, and
// the set below %a with the set below %b, etc. Ultimately, the sets for this
// program would end up like: {%ad}, {%a, %b, %k}, {%bp}, where {%ad} is below
// {%a, %b, %c} is below {%ad}.
//
// Second complication: Arbitrary casts
// Motivation:
// %ip = alloca int*, align 8
// %ipp = alloca int**, align 8
// %i = bitcast ipp to int
// store %ip, %ipp
// store %i, %ip
//
// This is impossible to construct with any of the rules above, because a set
// containing both {%i, %ipp} is supposed to exist, the set with %i is supposed
// to be below the set with %ip, and the set with %ip is supposed to be below
// the set with %ipp. Because we don't allow circular relationships like this,
// we merge all concerned sets into one. So, the above code would generate a
// single StratifiedSet: {%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 {
// \brief 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 {
assert(!isRemapped());
return Link.hasAbove();
}
bool hasBelow() const {
assert(!isRemapped());
return Link.hasBelow();
}
void setBelow(StratifiedIndex I) {
assert(!isRemapped());
Link.Below = I;
}
void setAbove(StratifiedIndex I) {
assert(!isRemapped());
Link.Above = I;
}
void clearBelow() {
assert(!isRemapped());
Link.clearBelow();
}
void clearAbove() {
assert(!isRemapped());
Link.clearAbove();
}
StratifiedIndex getBelow() const {
assert(!isRemapped());
assert(hasBelow());
return Link.Below;
}
StratifiedIndex getAbove() const {
assert(!isRemapped());
assert(hasAbove());
return Link.Above;
}
StratifiedAttrs &getAttrs() {
assert(!isRemapped());
return Link.Attrs;
}
void setAttr(unsigned index) {
assert(!isRemapped());
assert(index < NumStratifiedAttrs);
Link.Attrs.set(index);
}
void setAttrs(const StratifiedAttrs &other) {
assert(!isRemapped());
Link.Attrs |= other;
}
bool isRemapped() const { return Remap != StratifiedLink::SetSentinel; }
// \brief For initial remapping to another set
void remapTo(StratifiedIndex Other) {
assert(!isRemapped());
Remap = Other;
}
StratifiedIndex getRemapIndex() const {
assert(isRemapped());
return Remap;
}
// \brief Should only be called when we're already remapped.
void updateRemap(StratifiedIndex Other) {
assert(isRemapped());
Remap = Other;
}
// \brief 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; }
private:
StratifiedLink Link;
StratifiedIndex Remap;
};
// \brief 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()) {
continue;
}
StratifiedIndex Number = StratLinks.size();
Remaps.insert(std::make_pair(Link.Number, Number));
StratLinks.push_back(Link.getLink());
}
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;
}
}
// \brief 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) {
continue;
}
while (Links[CurrentIndex].hasBelow()) {
auto &CurrentBits = Links[CurrentIndex].Attrs;
auto NextIndex = Links[CurrentIndex].Below;
auto &NextBits = Links[NextIndex].Attrs;
NextBits |= CurrentBits;
CurrentIndex = NextIndex;
}
}
}
public:
// \brief 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;
finalizeSets(StratLinks);
propagateAttrs(StratLinks);
Links.clear();
return StratifiedSets<T>(std::move(Values), std::move(StratLinks));
}
std::size_t size() const { return Values.size(); }
std::size_t numSets() const { return Links.size(); }
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);
}
// \brief 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) {
assert(has(Main));
auto Index = *indexOf(Main);
if (!linksAt(Index).hasAbove())
addLinkAbove(Index);
auto Above = linksAt(Index).getAbove();
return addAtMerging(ToAdd, Above);
}
// \brief 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) {
assert(has(Main));
auto Index = *indexOf(Main);
if (!linksAt(Index).hasBelow())
addLinkBelow(Index);
auto Below = linksAt(Index).getBelow();
return addAtMerging(ToAdd, Below);
}
bool addWith(const T &Main, const T &ToAdd) {
assert(has(Main));
auto MainIndex = *indexOf(Main);
return addAtMerging(ToAdd, MainIndex);
}
void noteAttribute(const T &Main, unsigned AttrNum) {
assert(has(Main));
assert(AttrNum < StratifiedLink::SetSentinel);
auto *Info = *get(Main);
auto &Link = linksAt(Info->Index);
Link.setAttr(AttrNum);
}
void noteAttributes(const T &Main, const StratifiedAttrs &NewAttrs) {
assert(has(Main));
auto *Info = *get(Main);
auto &Link = linksAt(Info->Index);
Link.setAttrs(NewAttrs);
}
StratifiedAttrs getAttributes(const T &Main) {
assert(has(Main));
auto *Info = *get(Main);
auto *Link = &linksAt(Info->Index);
auto Attrs = Link->getAttrs();
while (Link->hasAbove()) {
Link = &linksAt(Link->getAbove());
Attrs |= Link->getAttrs();
}
return Attrs;
}
bool getAttribute(const T &Main, unsigned AttrNum) {
assert(AttrNum < StratifiedLink::SetSentinel);
auto Attrs = getAttributes(Main);
return Attrs[AttrNum];
}
// \brief Gets the attributes that have been applied to the set that Main
// belongs to. It ignores attributes in any sets above the one that Main
// resides in.
StratifiedAttrs getRawAttributes(const T &Main) {
assert(has(Main));
auto *Info = *get(Main);
auto &Link = linksAt(Info->Index);
return Link.getAttrs();
}
// \brief Gets an attribute from the attributes that have been applied to the
// set that Main belongs to. It ignores attributes in any sets above the one
// that Main resides in.
bool getRawAttribute(const T &Main, unsigned AttrNum) {
assert(AttrNum < StratifiedLink::SetSentinel);
auto Attrs = getRawAttributes(Main);
return Attrs[AttrNum];
}
private:
DenseMap<T, StratifiedInfo> Values;
std::vector<BuilderLink> Links;
// \brief 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;
}
// \brief 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->updateRemap(NewRemap);
Current = Next;
}
return *Current;
}
// \brief 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))
return;
if (tryMergeUpwards(Idx2, Idx1))
return;
// 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);
}
// \brief 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()) {
LinksInto->setAbove(LinksFrom->getAbove());
auto &NewAbove = linksAt(LinksInto->getAbove());
NewAbove.setBelow(LinksInto->Number);
}
// 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();
LinksInto->setAttrs(FromAttrs);
// Remap needs to happen after getBelow(), but before
// assignment of LinksFrom
auto *NewLinksFrom = &linksAt(LinksFrom->getBelow());
LinksFrom->remapTo(LinksInto->Number);
LinksFrom = NewLinksFrom;
LinksInto = &linksAt(LinksInto->getBelow());
}
if (LinksFrom->hasBelow()) {
LinksInto->setBelow(LinksFrom->getBelow());
auto &NewBelow = linksAt(LinksInto->getBelow());
NewBelow.setAbove(LinksInto->Number);
}
LinksFrom->remapTo(LinksInto->Number);
}
// \brief 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) {
Found.push_back(Current);
Attrs |= Current->getAttrs();
Current = &linksAt(Current->getAbove());
}
if (Current != Upper)
return false;
Upper->setAttrs(Attrs);
if (Lower->hasBelow()) {
auto NewBelowIndex = Lower->getBelow();
Upper->setBelow(NewBelowIndex);
auto &NewBelow = linksAt(NewBelowIndex);
NewBelow.setAbove(UpperIndex);
} else {
Upper->clearBelow();
}
for (const auto &Ptr : Found)
Ptr->remapTo(Upper->Number);
return true;
}
Optional<const StratifiedInfo *> get(const T &Val) const {
auto Result = Values.find(Val);
if (Result == Values.end())
return NoneType();
return &Result->second;
}
Optional<StratifiedInfo *> get(const T &Val) {
auto Result = Values.find(Val);
if (Result == Values.end())
return NoneType();
return &Result->second;
}
Optional<StratifiedIndex> indexOf(const T &Val) {
auto MaybeVal = get(Val);
if (!MaybeVal.hasValue())
return NoneType();
auto *Info = *MaybeVal;
auto &Link = linksAt(Info->Index);
return Link.Number;
}
StratifiedIndex addLinkBelow(StratifiedIndex Set) {
auto At = addLinks();
Links[Set].setBelow(At);
Links[At].setAbove(Set);
return At;
}
StratifiedIndex addLinkAbove(StratifiedIndex Set) {
auto At = addLinks();
Links[At].setBelow(Set);
Links[Set].setAbove(At);
return At;
}
StratifiedIndex getNewUnlinkedIndex() { return addLinks(); }
StratifiedIndex addLinks() {
auto Link = Links.size();
Links.push_back(BuilderLink(Link));
return Link;
}
bool inbounds(StratifiedIndex N) const { return N < Links.size(); }
};
}
#endif // LLVM_ADT_STRATIFIEDSETS_H