StratifiedSets.h

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//===- 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)) {
        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