New adjustment method for Courgette....

courgette/adjustment_method_2.cc

+// Copyright (c) 2009 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+#include "courgette/adjustment_method.h"
+
+#include <algorithm>
+#include <limits>
+#include <list>
+#include <map>
+#include <set>
+#include <string>
+#include <vector>
+
+#include <iostream>
+
+#include "base/basictypes.h"
+#include "base/logging.h"
+#include "base/string_util.h"
+
+#include "courgette/assembly_program.h"
+#include "courgette/courgette.h"
+#include "courgette/encoded_program.h"
+#include "courgette/image_info.h"
+
+/*
+
+Shingle weighting matching.
+
+We have a sequence S1 of symbols from alphabet A1={A,B,C,...} called the 'model'
+and a second sequence of S2 of symbols from alphabet A2={U,V,W,....} called the
+'program'.  Each symbol in A1 has a unique numerical name or index.  We can
+transcribe the sequence S1 to a sequence T1 of indexes of the symbols. We wish
+to assign indexes to the symbols in A2 so that when we transcribe S2 into T2, T2
+has long subsequences that occur in T1.  This will ensure that the sequence
+T1;T2 compresses to be only slightly larger than the compressed T1.
+
+The algorithm for matching members of S2 with members of S1 is eager - it makes
+matches without backtracking, until no more matches can be made.  Each variable
+(symbol) U,V,... in A2 has a set of candidates from A1, each candidate with a
+weight summarizing the evidence for the match.  We keep a VariableQueue of
+U,V,... sorted by how much the evidence for the best choice outweighs the
+evidence for the second choice, i.e. prioritized by how 'clear cut' the best
+assignment is.  We pick the variable with the most clear-cut candidate, make the
+assignment, adjust the evidence and repeat.
+
+What has not been described so far is how the evidence is gathered and
+maintained.  We are working under the assumption that S1 and S2 are largely
+similar.  (A different assumption might be that S1 and S2 are dissimilar except
+for many long subsequences.)
+
+A naive algorithm would consider all pairs (A,U) and for each pair assess the
+benefit, or score, the assignment U:=A.  The score might count the number of
+occurrences of U in S2 which appear in similar contexts to A in S1.
+
+To distinguish contexts we view S1 and S2 as a sequence of overlapping k-length
+substrings or 'shingles'.  Two shingles are compatible if the symbols in one
+shingle could be matched with the symbols in the other symbol.  For example, ABC
+is *not* compatible with UVU because it would require conflicting matches A=U
+and C=U.  ABC is compatible with UVW, UWV, WUV, VUW etc.  We can't tell which
+until we make an assignment - the compatible shingles form an equivalence class.
+After assigning U:=A then only UVW and UWV (equivalently AVW, AWV) are
+compatible.  As we make assignments the number of equivalence classes of
+shingles increases and the number of members of each equivalence class
+decreases.  The compatibility test becomes more restrictive.
+
+We gather evidence for the potential assignment U:=A by counting how many
+shingles containing U are compatible with shingles containing A.  Thus symbols
+occurring a large number of times in compatible contexts will be assigned first.
+
+Finding the 'most clear-cut' assignment by considering all pairs symbols and for
+each pair comparing the contexts of each pair of occurrences of the symbols is
+computationally infeasible.  We get the job done in a reasonable time by
+approaching it 'backwards' and making incremental changes as we make
+assignments.
+
+First the shingles are partitioned according to compatibility.  In S1=ABCDD and
+S2=UVWXX we have a total of 6 shingles, each occuring once. (ABC:1 BCD:1 CDD:1;
+UVW:1 VWX: WXX:1) all fit the pattern <V0 V1 V2> or the pattern <V0 V1 V1>.  The
+first pattern indicates that each position matches a different symbol, the
+second pattern indicates that the second symbol is repeated.
+
+  pattern      S1 members      S2 members
+  <V0 V1 V2>:  {ABC:1, BCD:1}; {UVW:1, VWX:1}
+  <V0 V1 V1>:  {CDD:1}         {WXX:1}
+
+The second pattern appears to have a unique assignment but we don't make the
+assignment on such scant evidence.  If S1 and S2 do not match exactly, there
+will be numerous spurious low-score matches like this.  Instead we must see what
+assignments are indicated by considering all of the evidence.
+
+First pattern has 2 x 2 = 4 shingle pairs.  For each pair we count the number
+of symbol assignments.  For ABC:a * UVW:b accumulate min(a,b) to each of
+  {U:=A, V:=B, W:=C}.
+After accumulating over all 2 x 2 pairs:
+  U: {A:1  B:1}
+  V: {A:1  B:2  C:1}
+  W: {B:1  C:2  D:1 }
+  X: {C:1  D:1}
+The second pattern contributes:
+  W: {C:1}
+  X: {D:2}
+Sum:
+  U: {A:1  B:1}
+  V: {A:1  B:2  C:1}
+  W: {B:1  C:3  D:1}
+  X: {C:1  D:3}
+
+From this we decide to assign X:=D (because this assignment has both the largest
+difference above the next candidate (X:=C) and this is also the largest
+proportionately over the sum of alternatives).
+
+Lets assume D has numerical 'name' 77.  The assignment X:=D sets X to 77 too.
+Next we repartition all the shingles containing X or D:
+
+  pattern      S1 members      S2 members
+  <V0 V1 V2>:  {ABC:1};        {UVW:1}
+  <V0 V1 77>:  {BCD:1};        {VWX:1}
+  <V0 77 77>:  {CDD:1}         {WXX:1}
+As we repartition, we recalculate the contributions to the scores:
+  U: {A:1}
+  V: {B:2}
+  W: {C:3}
+All the remaining assignments are now fixed.
+
+There is one step in the incremental algorithm that is still infeasibly
+expensive: the contributions due to the cross product of large equivalence
+classes.  We settle for making an approximation by computing the contribution of
+the cross product of only the most common shingles.  The hope is that the noise
+from the long tail of uncounted shingles is well below the scores being used to
+pick assignments.  The second hope is that as assignment are made, the large
+equivalence class will be partitioned into smaller equivalence classes, reducing
+the noise over time.
+
+In the code below the shingles are bigger (Shingle::kWidth = 5).
+Class ShinglePattern holds the data for one pattern.
+
+There is an optimization for this case:
+  <V0 V1 V1>:  {CDD:1}         {WXX:1}
+
+Above we said that we don't make an assignment on this "scant evidence".  There
+is an exception: if there is only one variable unassigned (more like the <V0 77
+77> pattern) AND there are no occurrences of C and W other than those counted in
+this pattern, then there is no competing evidence and we go ahead with the
+assignment immediately.  This produces slightly better results because these
+cases tend to be low-scoring and susceptible to small mistakes made in
+low-scoring assignments in the approximation for large equivalence classes.
+
+*/
+
+namespace courgette {
+namespace adjustment_method_2 {
+
+// We have three discretionary information logging levels for algorithm
+// development.  For now just configure with #defines.
+// TODO(sra): make dependent of some configurable setting.
+struct LogToCout {
+  LogToCout() {}
+  ~LogToCout() { std::cout << std::endl; }
+  std::ostream& stream() { return std::cout; }
+};
+#define LOG_TO_COUT (LogToCout().stream())
+#define NO_LOG DLOG_IF(INFO, false)
+
+#if 0   // Log to log file.
+#define ALOG1 LOG(INFO)
+#define ALOG2 LOG(INFO)
+#define ALOG3 LOG(INFO)
+#elif 0  // Log to stdout.
+#define ALOG1 LOG_TO_COUT
+#define ALOG2 LOG_TO_COUT
+#define ALOG3 LOG_TO_COUT
+#else   // Log to nowhere.
+#define ALOG1 NO_LOG
+#define ALOG2 NO_LOG
+#define ALOG3 NO_LOG
+#endif
+
+////////////////////////////////////////////////////////////////////////////////
+
+class AssignmentCandidates;
+class LabelInfoMaker;
+class Shingle;
+class ShinglePattern;
+
+// The purpose of adjustment is to assign indexes to Labels of a program 'p' to
+// make the sequence of indexes similar to a 'model' program 'm'.  Labels
+// themselves don't have enough information to do this job, so we work with a
+// LabelInfo surrogate for each label.
+//
+class LabelInfo {
+ public:
+  // Just a no-argument constructor and copy constructor.  Actual LabelInfo
+  // objects are allocated in std::pair structs in a std::map.
+  LabelInfo()
+      : label_(NULL), is_model_(false), debug_index_(0), refs_(0),
+        assignment_(NULL), candidates_(NULL)
+  {}
+
+  ~LabelInfo();
+
+  AssignmentCandidates* candidates();
+
+  Label* label_;             // The label that this info a surrogate for.
+
+  uint32 is_model_ : 1;      // Is the label in the model?
+  uint32 debug_index_ : 31;  // A small number for naming the label in debug
+                             // output. The pair (is_model_, debug_index_) is
+                             // unique.
+
+  uint32 refs_;              // Number of times this Label is referenced.
+
+  LabelInfo* assignment_;    // Label from other program corresponding to this.
+
+  std::vector<uint32> positions_;  // Offsets into the trace of references.
+
+ private:
+  AssignmentCandidates* candidates_;
+
+  void operator=(const LabelInfo*);  // Disallow assignment only.
+  // Public compiler generated copy constructor is needed to constuct
+  // std::pair<Label*, LabelInfo> so that fresh LabelInfos can be allocated
+  // inside a std::map.
+};
+
+typedef std::vector<LabelInfo*> Trace;
+
+std::string ToString(const LabelInfo* info) {
+  std::string s;
+  StringAppendF(&s, "%c%d", "pm"[info->is_model_], info->debug_index_);
+  if (info->label_->index_ != Label::kNoIndex)
+    StringAppendF(&s, " (%d)", info->label_->index_);
+
+  StringAppendF(&s, " #%u", info->refs_);
+  return s;
+}
+
+// LabelInfoMaker maps labels to their surrogate LabelInfo objects.
+class LabelInfoMaker {
+ public:
+  LabelInfoMaker() : debug_label_index_gen_(0) {}
+
+  LabelInfo* MakeLabelInfo(Label* label, bool is_model, uint32 position) {
+    LabelInfo& slot = label_infos_[label];
+    if (slot.label_ == NULL) {
+      slot.label_ = label;
+      slot.is_model_ = is_model;
+      slot.debug_index_ = ++debug_label_index_gen_;
+    }
+    slot.positions_.push_back(position);
+    ++slot.refs_;
+    return &slot;
+  }
+
+  void ResetDebugLabel() { debug_label_index_gen_ = 0; }
+
+ private:
+  int debug_label_index_gen_;
+
+  // Note LabelInfo is allocated 'flat' inside map::value_type, so the LabelInfo
+  // lifetimes are managed by the map.
+  std::map<Label*, LabelInfo> label_infos_;
+
+  DISALLOW_COPY_AND_ASSIGN(LabelInfoMaker);
+};
+
+struct OrderLabelInfo {
+  bool operator()(const LabelInfo* a, const LabelInfo* b) const {
+    if (a->label_->rva_ < b->label_->rva_) return true;
+    if (a->label_->rva_ > b->label_->rva_) return false;
+    if (a == b) return false;
+    return a->positions_ < b->positions_;  // Lexicographic ordering of vector.
+  }
+};
+
+// AssignmentCandidates is a priority queue of candidate assignments to
+// a single program LabelInfo, |program_info_|.
+class AssignmentCandidates {
+ public:
+  explicit AssignmentCandidates(LabelInfo* program_info)
+      : program_info_(program_info) {}
+
+  LabelInfo* program_info() const { return program_info_; }
+
+  bool empty() const { return label_to_score_.empty(); }
+
+  LabelInfo* top_candidate() const { return queue_.begin()->second; }
+
+  void Update(LabelInfo* model_info, int delta_score) {
+    LOG_ASSERT(delta_score != 0);
+    int old_score = 0;
+    int new_score = 0;
+    LabelToScore::iterator p = label_to_score_.find(model_info);
+    if (p != label_to_score_.end()) {
+      old_score = p->second;
+      new_score = old_score + delta_score;
+      queue_.erase(ScoreAndLabel(old_score, p->first));
+      if (new_score == 0) {
+        label_to_score_.erase(p);
+      } else {
+        p->second = new_score;
+        queue_.insert(ScoreAndLabel(new_score, model_info));
+      }
+    } else {
+      new_score = delta_score;
+      label_to_score_.insert(std::make_pair(model_info, new_score));
+      queue_.insert(ScoreAndLabel(new_score, model_info));
+    }
+    LOG_ASSERT(queue_.size() == label_to_score_.size());
+  }
+
+  int TopScore() const {
+    int first_value = 0;
+    int second_value = 0;
+    Queue::const_iterator p = queue_.begin();
+    if (p != queue_.end()) {
+      first_value = p->first;
+      ++p;
+      if (p != queue_.end()) {
+        second_value = p->first;
+      }
+    }
+    return first_value - second_value;
+  }
+
+  bool HasPendingUpdates() { return !pending_updates_.empty(); }
+
+  void AddPendingUpdate(LabelInfo* model_info, int delta_score) {
+    LOG_ASSERT(delta_score != 0);
+    pending_updates_[model_info] += delta_score;
+  }
+
+  void ApplyPendingUpdates() {
+    // TODO(sra): try to walk |pending_updates_| and |label_to_score_| in
+    // lockstep.  Try to batch updates to |queue_|.
+    size_t zeroes = 0;
+    for (LabelToScore::iterator p = pending_updates_.begin();
+         p != pending_updates_.end();
+         ++p) {
+      if (p->second != 0)
+        Update(p->first, p->second);
+      else
+        ++zeroes;
+    }
+    pending_updates_.clear();
+  }
+
+  void Print(int max) {
+    ALOG1 << "score "  << TopScore() << "  " << ToString(program_info_)
+          << " := ?";
+    if (!pending_updates_.empty())
+      ALOG1 << pending_updates_.size() << " pending";
+    int count = 0;
+    for (Queue::iterator q = queue_.begin();  q != queue_.end();  ++q) {
+      if (++count > max) break;
+      ALOG1 << "   " << q->first << "  " << ToString(q->second);
+    }
+  }
+
+ private:
+  typedef std::map<LabelInfo*, int, OrderLabelInfo> LabelToScore;
+  typedef std::pair<int, LabelInfo*> ScoreAndLabel;
+  struct OrderScoreAndLabelByScoreDecreasing {
+    OrderLabelInfo tie_breaker;
+    bool operator()(const ScoreAndLabel& a, const ScoreAndLabel& b) const {
+      if (a.first > b.first) return true;
+      if (a.first < b.first) return false;
+      return tie_breaker(a.second, b.second);
+    }
+  };
+  typedef std::set<ScoreAndLabel, OrderScoreAndLabelByScoreDecreasing> Queue;
+
+  LabelInfo* program_info_;
+  LabelToScore label_to_score_;
+  LabelToScore pending_updates_;
+  Queue queue_;
+};
+
+AssignmentCandidates* LabelInfo::candidates() {
+  if (candidates_ == NULL)
+    candidates_ = new AssignmentCandidates(this);
+  return candidates_;
+}
+
+LabelInfo::~LabelInfo() {
+  delete candidates_;
+}
+
+// A Shingle is a short fixed-length string of LabelInfos that actually occurs
+// in a Trace.  A Shingle may occur many times.  We repesent the Shingle by the
+// position of one of the occurrences in the Trace.
+class Shingle {
+ public:
+  static const size_t kWidth = 5;
+
+  struct InterningLess {
+    bool operator()(const Shingle& a, const Shingle& b) const;
+  };
+
+  typedef std::set<Shingle, InterningLess> OwningSet;
+
+  static Shingle* Find(const Trace& trace, size_t position,
+                       OwningSet* owning_set) {
+    std::pair<OwningSet::iterator, bool> pair =
+        owning_set->insert(Shingle(trace, position));
+    // pair.first is the newly inserted Shingle or the previouly inserted one
+    // that looks the same according to the comparator.
+    pair.first->add_position(position);
+    return &*pair.first;
+  }
+
+  LabelInfo* at(size_t i) const { return trace_[exemplar_position_ + i]; }
+  void add_position(size_t position) { positions_.push_back(position); }
+  size_t position_count() const { return positions_.size(); }
+
+  bool InModel() const { return at(0)->is_model_; }
+
+  ShinglePattern* pattern() const { return pattern_; }
+  void set_pattern(ShinglePattern* pattern) { pattern_ = pattern; }
+
+  struct PointerLess {
+    bool operator()(const Shingle* a, const Shingle* b) const {
+      // Arbitrary but repeatable (memory-address) independent ordering:
+      return a->exemplar_position_ < b->exemplar_position_;
+      // return InterningLess()(*a, *b);
+    }
+  };
+
+ private:
+  Shingle(const Trace& trace, size_t exemplar_position)
+      : trace_(trace),
+        exemplar_position_(exemplar_position),
+        pattern_(NULL) {
+  }
+
+  const Trace& trace_;             // The shingle lives inside trace_.
+  size_t exemplar_position_;       // At this position (and other positions).
+  std::vector<uint32> positions_;  // Includes exemplar_position_.
+
+  ShinglePattern* pattern_;       // Pattern changes as LabelInfos are assigned.
+
+  friend std::string ToString(const Shingle* instance);
+
+  // We can't disallow the copy constructor because we use std::set<Shingle> and
+  // VS2005's implementation of std::set<T>::set() requires T to have a copy
+  // constructor.
+  //   DISALLOW_COPY_AND_ASSIGN(Shingle);
+  void operator=(const Shingle&);  // Disallow assignment only.
+};
+
+std::string ToString(const Shingle* instance) {
+  std::string s;
+  const char* sep = "<";
+  for (size_t i = 0; i < Shingle::kWidth; ++i) {
+    // StringAppendF(&s, "%s%x ", sep, instance.at(i)->label_->rva_);
+    s += sep;
+    s += ToString(instance->at(i));
+    sep = ", ";
+  }
+  StringAppendF(&s, ">(%u)@{%d}", instance->exemplar_position_,
+                static_cast<int>(instance->position_count()));
+  return s;
+}
+
+
+bool Shingle::InterningLess::operator()(
+    const Shingle& a,
+    const Shingle& b) const {
+  for (size_t i = 0;  i < kWidth;  ++i) {
+    LabelInfo* info_a = a.at(i);
+    LabelInfo* info_b = b.at(i);
+    if (info_a->label_->rva_ < info_b->label_->rva_)
+      return true;
+    if (info_a->label_->rva_ > info_b->label_->rva_)
+      return false;
+    if (info_a->is_model_ < info_b->is_model_)
+      return true;
+    if (info_a->is_model_ > info_b->is_model_)
+      return false;
+    if (info_a != info_b) {
+      NOTREACHED();
+    }
+  }
+  return false;
+}
+
+class ShinglePattern {
+ public:
+  enum { kOffsetMask = 7,  // Offset lives in low bits.
+         kFixed    = 0,    // kind & kVariable == 0  => fixed.
+         kVariable = 8     // kind & kVariable == 1  => variable.
+         };
+  // sequence[position + (kinds_[i] & kOffsetMask)] gives LabelInfo for position
+  // i of shingle.  Below, second 'A' is duplicate of position 1, second '102'
+  // is duplicate of position 0.
+  //
+  //   <102, A, 103, A , 102>
+  //      --> <kFixed+0, kVariable+1, kFixed+2, kVariable+1, kFixed+0>
+  struct Index {
+    explicit Index(const Shingle* instance);
+    uint8 kinds_[Shingle::kWidth];
+    uint8 variables_;
+    uint8 unique_variables_;
+    uint8 first_variable_index_;
+    uint32 hash_;
+    int assigned_indexes_[Shingle::kWidth];
+  };
+
+  // ShinglePattern keeps histograms of member Shingle instances, ordered by
+  // decreasing number of occurrences.  We don't have a pair (occurrence count,
+  // Shingle instance), so we use a FreqView adapter to make the instance
+  // pointer look like the pair.
+  class FreqView {
+   public:
+    explicit FreqView(const Shingle* instance) : instance_(instance) {}
+    size_t count() const { return instance_->position_count(); }
+    const Shingle* instance() const { return instance_; }
+    struct Greater {
+      bool operator()(const FreqView& a, const FreqView& b) const {
+        if (a.count() > b.count()) return true;
+        if (a.count() < b.count()) return false;
+        return resolve_ties(a.instance(), b.instance());
+      }
+     private:
+      Shingle::PointerLess resolve_ties;
+    };
+   private:
+    const Shingle* instance_;
+  };
+
+  typedef std::set<FreqView, FreqView::Greater> Histogram;
+
+  ShinglePattern() : index_(NULL), model_coverage_(0), program_coverage_(0) {}
+
+  const Index* index_;  // Points to the key in the owning map value_type.
+  Histogram model_histogram_;
+  Histogram program_histogram_;
+  int model_coverage_;
+  int program_coverage_;
+};
+
+std::string ToString(const ShinglePattern::Index* index) {
+  std::string s;
+  if (index == NULL) {
+    s = "<null>";
+  } else {
+    StringAppendF(&s, "<%d: ", index->variables_);
+    const char* sep = "";
+    for (size_t i = 0;  i < Shingle::kWidth;  ++i) {
+      s += sep;
+      sep = ", ";
+      uint32 kind = index->kinds_[i];
+      int offset = kind & ShinglePattern::kOffsetMask;
+      if (kind & ShinglePattern::kVariable)
+        StringAppendF(&s, "V%d", offset);
+      else
+        StringAppendF(&s, "%d", index->assigned_indexes_[offset]);
+     }
+    StringAppendF(&s, " %x", index->hash_);
+    s += ">";
+  }
+  return s;
+}
+
+std::string HistogramToString(const ShinglePattern::Histogram& histogram,
+                              size_t snippet_max) {
+  std::string s;
+  size_t histogram_size = histogram.size();
+  size_t snippet_size = 0;
+  for (ShinglePattern::Histogram::const_iterator p = histogram.begin();
+       p != histogram.end();
+       ++p) {
+    if (++snippet_size > snippet_max && snippet_size != histogram_size) {
+      s += " ...";
+      break;
+    }
+    StringAppendF(&s, " %d", p->count());
+  }
+  return s;
+}
+
+std::string HistogramToStringFull(const ShinglePattern::Histogram& histogram,
+                                  const char* indent,
+                                  size_t snippet_max) {
+  std::string s;
+
+  size_t histogram_size = histogram.size();
+  size_t snippet_size = 0;
+  for (ShinglePattern::Histogram::const_iterator p = histogram.begin();
+       p != histogram.end();
+       ++p) {
+    s += indent;
+    if (++snippet_size > snippet_max && snippet_size != histogram_size) {
+      s += "...\n";
+      break;
+    }
+    StringAppendF(&s, "(%d) ", p->count());
+    s += ToString(&(*p->instance()));
+    s += "\n";
+  }
+  return s;
+}
+
+std::string ToString(const ShinglePattern* pattern, size_t snippet_max = 3) {
+  std::string s;
+  if (pattern == NULL) {
+    s = "<null>";
+  } else {
+    s = "{";
+    s += ToString(pattern->index_);
+    StringAppendF(&s, ";  %d(%d):",
+                  static_cast<int>(pattern->model_histogram_.size()),
+                  pattern->model_coverage_);
+
+    s += HistogramToString(pattern->model_histogram_, snippet_max);
+    StringAppendF(&s, ";  %d(%d):",
+                  static_cast<int>(pattern->program_histogram_.size()),
+                  pattern->program_coverage_);
+    s += HistogramToString(pattern->program_histogram_, snippet_max);
+    s += "}";
+  }
+  return s;
+}
+
+std::string ShinglePatternToStringFull(const ShinglePattern* pattern,
+                                       size_t max) {
+  std::string s;
+  s += ToString(pattern->index_);
+  s += "\n";
+  size_t model_size = pattern->model_histogram_.size();
+  size_t program_size = pattern->program_histogram_.size();
+  StringAppendF(&s, "  model shingles %u\n", model_size);
+  s += HistogramToStringFull(pattern->model_histogram_, "    ", max);
+  StringAppendF(&s, "  program shingles %u\n", program_size);
+  s += HistogramToStringFull(pattern->program_histogram_, "    ", max);
+  return s;
+}
+
+struct ShinglePatternIndexLess {
+  bool operator()(const ShinglePattern::Index& a,
+                  const ShinglePattern::Index& b) const {
+    if (a.hash_ < b.hash_) return true;
+    if (a.hash_ > b.hash_) return false;
+
+    for (size_t i = 0;  i < Shingle::kWidth;  ++i) {
+      if (a.kinds_[i] < b.kinds_[i]) return true;
+      if (a.kinds_[i] > b.kinds_[i]) return false;
+      if ((a.kinds_[i] & ShinglePattern::kVariable) == 0) {
+        if (a.assigned_indexes_[i] < b.assigned_indexes_[i])
+          return true;
+        if (a.assigned_indexes_[i] > b.assigned_indexes_[i])
+          return false;
+      }
+    }
+    return false;
+  }
+};
+
+static uint32 hash_combine(uint32 h, uint32 v) {
+  h += v;
+  return (h * (37 + 0x0000d100)) ^ (h >> 13);
+}
+
+ShinglePattern::Index::Index(const Shingle* instance) {
+  uint32 hash = 0;
+  variables_ = 0;
+  unique_variables_ = 0;
+  first_variable_index_ = 255;
+
+  for (size_t i = 0; i < Shingle::kWidth; ++i) {
+    LabelInfo* info = instance->at(i);
+    uint32 kind;
+    int code = -1;
+    size_t j = 0;
+    for ( ; j < i; ++j) {
+      if (info == instance->at(j)) {  // Duplicate LabelInfo
+        kind = kinds_[j];
+        break;
+      }
+    }
+    if (j == i) {  // Not found above.
+      if (info->assignment_) {
+        code = info->label_->index_;
+        assigned_indexes_[i] = code;
+        kind = kFixed + i;
+      } else {
+        kind = kVariable + i;
+        ++unique_variables_;
+        if (i < first_variable_index_)
+          first_variable_index_ = i;
+      }
+    }
+    if (kind & kVariable) ++variables_;
+    hash = hash_combine(hash, code);
+    hash = hash_combine(hash, kind);
+    kinds_[i] = kind;
+    assigned_indexes_[i] = code;
+  }
+  hash_ = hash;
+}
+
+struct ShinglePatternLess {
+  bool operator()(const ShinglePattern& a, const ShinglePattern& b) const {
+    return index_less(*a.index_, *b.index_);
+  }
+  ShinglePatternIndexLess index_less;
+};
+
+struct ShinglePatternPointerLess {
+  bool operator()(const ShinglePattern* a, const ShinglePattern* b) const {
+    return pattern_less(*a, *b);
+  }
+  ShinglePatternLess pattern_less;
+};
+
+template<int (*Scorer)(const ShinglePattern*)>
+struct OrderShinglePatternByScoreDescending {
+  bool operator()(const ShinglePattern* a, const ShinglePattern* b) const {
+    int score_a = Scorer(a);
+    int score_b = Scorer(b);
+    if (score_a > score_b) return true;
+    if (score_a < score_b) return false;
+    return break_ties(a, b);
+  }
+  ShinglePatternPointerLess break_ties;
+};
+
+// Returns a score for a 'Single Use' rule.  Returns -1 if the rule is not
+// applicable.
+int SingleUseScore(const ShinglePattern* pattern) {
+  if (pattern->index_->variables_ != 1)
+    return -1;
+
+  if (pattern->model_histogram_.size() != 1 ||
+      pattern->program_histogram_.size() != 1)
+    return -1;
+
+  // Does this pattern account for all uses of the variable?
+  const ShinglePattern::FreqView& program_freq =
+      *pattern->program_histogram_.begin();
+  const ShinglePattern::FreqView& model_freq =
+      *pattern->model_histogram_.begin();
+  int p1 = program_freq.count();
+  int m1 = model_freq.count();
+  if (p1 == m1) {
+    const Shingle* program_instance = program_freq.instance();
+    const Shingle* model_instance = model_freq.instance();
+    size_t variable_index = pattern->index_->first_variable_index_;
+    LabelInfo* program_info = program_instance->at(variable_index);
+    LabelInfo* model_info = model_instance->at(variable_index);
+    if (!program_info->assignment_) {
+      if (program_info->refs_ == p1 && model_info->refs_ == m1) {
+        return p1;
+      }
+    }
+  }
+  return -1;
+}
+
+// The VariableQueue is a priority queue of unassigned LabelInfos from
+// the 'program' (the 'variables') and their AssignmentCandidates.
+class VariableQueue {
+ public:
+  typedef std::pair<int, LabelInfo*> ScoreAndLabel;
+
+  VariableQueue() {}
+
+  bool empty() const { return queue_.empty(); }
+
+  const ScoreAndLabel& first() const { return *queue_.begin(); }
+
+  // For debugging only.
+  void Print() const {
+    for (Queue::const_iterator p = queue_.begin();  p != queue_.end();  ++p) {
+      AssignmentCandidates* candidates = p->second->candidates();
+      candidates->Print(std::numeric_limits<int>::max());
+    }
+  }
+
+  void AddPendingUpdate(LabelInfo* program_info, LabelInfo* model_info,
+                        int delta_score) {
+    AssignmentCandidates* candidates = program_info->candidates();
+    if (!candidates->HasPendingUpdates()) {
+      pending_update_candidates_.push_back(candidates);
+    }
+    candidates->AddPendingUpdate(model_info, delta_score);
+  }
+
+  void ApplyPendingUpdates() {
+    for (size_t i = 0;  i < pending_update_candidates_.size();  ++i) {
+      AssignmentCandidates* candidates = pending_update_candidates_[i];
+      int old_score = candidates->TopScore();
+      queue_.erase(ScoreAndLabel(old_score, candidates->program_info()));
+      candidates->ApplyPendingUpdates();
+      if (!candidates->empty()) {
+        int new_score = candidates->TopScore();
+        queue_.insert(ScoreAndLabel(new_score, candidates->program_info()));
+      }
+    }
+    pending_update_candidates_.clear();
+  }
+
+ private:
+  struct OrderScoreAndLabelByScoreDecreasing {
+    bool operator()(const ScoreAndLabel& a, const ScoreAndLabel& b) const {
+      if (a.first > b.first) return true;
+      if (a.first < b.first) return false;
+      return OrderLabelInfo()(a.second, b.second);
+    }
+  };
+  typedef std::set<ScoreAndLabel, OrderScoreAndLabelByScoreDecreasing> Queue;
+
+  Queue queue_;
+  std::vector<AssignmentCandidates*> pending_update_candidates_;
+
+  DISALLOW_COPY_AND_ASSIGN(VariableQueue);
+};
+
+
+class AssignmentProblem {
+ public:
+  AssignmentProblem(const Trace& trace, size_t model_end)
+      : trace_(trace),
+        model_end_(model_end) {
+    ALOG1 << "AssignmentProblem::AssignmentProblem  " << model_end << ", "
+          << trace.size();
+  }
+
+  bool Solve() {
+    if (model_end_ < Shingle::kWidth ||
+        trace_.size() - model_end_ < Shingle::kWidth) {
+      // Nothing much we can do with such a short problem.
+      return true;
+    }
+    instances_.resize(trace_.size() - Shingle::kWidth + 1, NULL);
+    AddShingles(0, model_end_);
+    AddShingles(model_end_, trace_.size());
+    InitialClassify();
+    AddPatternsNeedingUpdatesToQueues();
+
+    patterns_needing_updates_.clear();
+    while (FindAndAssignBestLeader()) {
+      NO_LOG << "Updated " << patterns_needing_updates_.size() << " patterns";
+      patterns_needing_updates_.clear();
+    }
+    PrintActivePatterns();
+
+    return true;
+  }
+
+ private:
+  typedef std::set<Shingle*, Shingle::PointerLess> ShingleSet;
+
+  typedef std::set<const ShinglePattern*, ShinglePatternPointerLess>
+      ShinglePatternSet;
+
+  // Patterns are partitioned into the following sets:
+
+  // * Retired patterns (not stored).  No shingles exist for this pattern (they
+  //   all now match more specialized patterns).
+  // * Useless patterns (not stored).  There are no 'program' shingles for this
+  //   pattern (they all now match more specialized patterns).
+  // * Single-use patterns - single_use_pattern_queue_.
+  // * Other patterns - active_non_single_use_patterns_ / variable_queue_.
+
+  typedef std::set<const ShinglePattern*,
+                   OrderShinglePatternByScoreDescending<&SingleUseScore> >
+      SingleUsePatternQueue;
+
+  void PrintPatternsHeader() const {
+    ALOG1 << shingle_instances_.size() << " instances  "
+          << trace_.size() << " trace length  "
+          << patterns_.size() << " shingle indexes  "
+          << single_use_pattern_queue_.size() << " single use patterns  "
+          << active_non_single_use_patterns_.size() << " active patterns";
+  }
+
+  void PrintActivePatterns() const {
+    for (ShinglePatternSet::const_iterator p =
+             active_non_single_use_patterns_.begin();
+         p != active_non_single_use_patterns_.end();
+         ++p) {
+      const ShinglePattern* pattern = *p;
+      ALOG1 << ToString(pattern, 10);
+    }
+  }
+
+  void PrintPatterns() const {
+    PrintAllPatterns();
+    PrintActivePatterns();
+    PrintAllShingles();
+  }
+
+  void PrintAllPatterns() const {
+    for (IndexToPattern::const_iterator p = patterns_.begin();
+         p != patterns_.end();
+         ++p) {
+      const ShinglePattern& pattern = p->second;
+      ALOG1 << ToString(&pattern, 10);
+    }
+  }
+
+  void PrintAllShingles() const {
+    for (Shingle::OwningSet::const_iterator p = shingle_instances_.begin();
+         p != shingle_instances_.end();
+         ++p) {
+      const Shingle& instance = *p;
+      ALOG1 << ToString(&instance) << "   " << ToString(instance.pattern());
+    }
+  }
+
+
+  void AddShingles(size_t begin, size_t end) {
+    for (size_t i = begin;  i + Shingle::kWidth - 1 < end;  ++i) {
+      instances_[i] = Shingle::Find(trace_, i, &shingle_instances_);
+    }
+  }
+
+  void Declassify(Shingle* shingle) {
+    ShinglePattern* pattern = shingle->pattern();
+    if (shingle->InModel()) {
+      pattern->model_histogram_.erase(ShinglePattern::FreqView(shingle));
+      pattern->model_coverage_ -= shingle->position_count();
+    } else {
+      pattern->program_histogram_.erase(ShinglePattern::FreqView(shingle));
+      pattern->program_coverage_ -= shingle->position_count();
+    }
+    shingle->set_pattern(NULL);
+  }
+
+  void Reclassify(Shingle* shingle) {
+    ShinglePattern* pattern = shingle->pattern();
+    LOG_ASSERT(pattern == NULL);
+
+    ShinglePattern::Index index(shingle);
+    if (index.variables_ == 0)
+      return;
+
+    std::pair<IndexToPattern::iterator, bool> inserted =
+        patterns_.insert(std::make_pair(index, ShinglePattern()));
+
+    pattern = &inserted.first->second;
+    pattern->index_ = &inserted.first->first;
+    shingle->set_pattern(pattern);
+    patterns_needing_updates_.insert(pattern);
+
+    if (shingle->InModel()) {
+      pattern->model_histogram_.insert(ShinglePattern::FreqView(shingle));
+      pattern->model_coverage_ += shingle->position_count();
+    } else {
+      pattern->program_histogram_.insert(ShinglePattern::FreqView(shingle));
+      pattern->program_coverage_ += shingle->position_count();
+    }
+  }
+
+  void InitialClassify() {
+    for (Shingle::OwningSet::iterator p = shingle_instances_.begin();
+         p != shingle_instances_.end();
+         ++p) {
+      Reclassify(&*p);
+    }
+  }
+
+  // For the positions in |info|, find the shingles that overlap that position.
+  void AddAffectedPositions(LabelInfo* info, ShingleSet* affected_shingles) {
+    const size_t kWidth = Shingle::kWidth;
+    for (size_t i = 0;  i < info->positions_.size();  ++i) {
+      size_t position = info->positions_[i];
+      // Find bounds to the subrange of |trace_| we are in.
+      size_t start = position < model_end_ ? 0 : model_end_;
+      size_t end = position < model_end_ ? model_end_ : trace_.size();
+
+      // Clip [position-kWidth+1, position+1)
+      size_t low = position > start + kWidth - 1
+          ? position - kWidth + 1
+          : start;
+      size_t high = position + kWidth < end ? position + 1 : end - kWidth + 1;
+
+      for (size_t shingle_position = low;
+           shingle_position < high;
+           ++shingle_position) {
+        Shingle* overlapping_shingle = instances_.at(shingle_position);
+        affected_shingles->insert(overlapping_shingle);
+      }
+    }
+  }
+
+  void RemovePatternsNeedingUpdatesFromQueues() {
+    for (ShinglePatternSet::iterator p = patterns_needing_updates_.begin();
+         p != patterns_needing_updates_.end();
+         ++p) {
+      RemovePatternFromQueues(*p);
+    }
+  }
+
+  void AddPatternsNeedingUpdatesToQueues() {
+    for (ShinglePatternSet::iterator p = patterns_needing_updates_.begin();
+         p != patterns_needing_updates_.end();
+         ++p) {
+      AddPatternToQueues(*p);
+    }
+    variable_queue_.ApplyPendingUpdates();
+  }
+
+  void RemovePatternFromQueues(const ShinglePattern* pattern) {
+    int single_use_score = SingleUseScore(pattern);
+    if (single_use_score > 0) {
+      size_t n = single_use_pattern_queue_.erase(pattern);
+      LOG_ASSERT(n == 1);
+    } else if (pattern->program_histogram_.size() == 0 &&
+               pattern->model_histogram_.size() == 0) {
+      NOTREACHED();  // Should not come back to life.
+    } else if (pattern->program_histogram_.size() == 0) {
+      // Useless pattern.
+    } else {
+      active_non_single_use_patterns_.erase(pattern);
+      AddPatternToLabelQueue(pattern, -1);
+    }
+  }
+
+  void AddPatternToQueues(const ShinglePattern* pattern) {
+    int single_use_score = SingleUseScore(pattern);
+    if (single_use_score > 0) {
+      single_use_pattern_queue_.insert(pattern);
+    } else if (pattern->program_histogram_.size() == 0 &&
+               pattern->model_histogram_.size() == 0) {
+    } else if (pattern->program_histogram_.size() == 0) {
+      // Useless pattern.
+    } else {
+      active_non_single_use_patterns_.insert(pattern);
+      AddPatternToLabelQueue(pattern, +1);
+    }
+  }
+
+  void AddPatternToLabelQueue(const ShinglePattern* pattern, int sign) {
+    // For each possible assignment in this pattern, update the potential
+    // contributions to the LabelInfo queues.
+    size_t model_histogram_size = pattern->model_histogram_.size();
+    size_t program_histogram_size = pattern->program_histogram_.size();
+
+    // We want to find for each symbol (LabelInfo) the maximum contribution that
+    // could be achieved by making shingle-wise assignments between shingles in
+    // the model and shingles in the program.
+    //
+    // If the shingles in the histograms are independent (no two shingles have a
+    // symbol in common) then any permutation of the assignments is possible,
+    // and the maximum contribution can be found by taking the maximum over all
+    // the pairs.
+    //
+    // If the shingles are dependent two things happen.  The maximum
+    // contribution to any given symbol is a sum because the symbol has
+    // contributions from all the shingles containing it.  Second, some
+    // assignments are blocked by previous incompatible assignments.  We want to
+    // avoid a combinatorial search, so we ignore the blocking.
+
+    const int kUnwieldy = 5;
+
+    typedef std::map<LabelInfo*, int> LabelToScore;
+    typedef std::map<LabelInfo*, LabelToScore > ScoreSet;
+    ScoreSet maxima;
+
+    size_t n_model_samples = 0;
+    for (ShinglePattern::Histogram::const_iterator model_iter =
+             pattern->model_histogram_.begin();
+         model_iter != pattern->model_histogram_.end();
+         ++model_iter) {
+      if (++n_model_samples > kUnwieldy) break;
+      const ShinglePattern::FreqView& model_freq = *model_iter;
+      int m1 = model_freq.count();
+      const Shingle* model_instance = model_freq.instance();
+
+      ScoreSet sums;
+      size_t n_program_samples = 0;
+      for (ShinglePattern::Histogram::const_iterator program_iter =
+               pattern->program_histogram_.begin();
+           program_iter != pattern->program_histogram_.end();
+           ++program_iter) {
+        if (++n_program_samples > kUnwieldy) break;
+        const ShinglePattern::FreqView& program_freq = *program_iter;
+        int p1 = program_freq.count();
+        const Shingle* program_instance = program_freq.instance();
+
+        // int score = p1;  // ? weigh all equally??
+        int score = std::min(p1, m1);
+
+        for (size_t i = 0;  i < Shingle::kWidth;  ++i) {
+          LabelInfo* program_info = program_instance->at(i);
+          LabelInfo* model_info = model_instance->at(i);
+          if ((model_info->assignment_ == NULL) !=
+              (program_info->assignment_ == NULL)) {
+            ALOG1 << "ERROR " << i
+                  << "\n\t"  << ToString(pattern, 10)
+                  << "\n\t" << ToString(program_instance)
+                  << "\n\t" << ToString(model_instance);
+          }
+          if (!program_info->assignment_ && !model_info->assignment_) {
+            sums[program_info][model_info] += score;
+          }
+        }
+
+        for (ScoreSet::iterator assignee_iterator = sums.begin();
+             assignee_iterator != sums.end();
+             ++assignee_iterator) {
+          LabelInfo* program_info = assignee_iterator->first;
+          for (LabelToScore::iterator p = assignee_iterator->second.begin();
+               p != assignee_iterator->second.end();
+               ++p) {
+            LabelInfo* model_info = p->first;
+            int score = p->second;
+            int* slot = &maxima[program_info][model_info];
+            *slot = std::max(*slot, score);
+          }
+        }
+      }
+    }
+
+    for (ScoreSet::iterator assignee_iterator = maxima.begin();
+         assignee_iterator != maxima.end();
+         ++assignee_iterator) {
+      LabelInfo* program_info = assignee_iterator->first;
+      for (LabelToScore::iterator p = assignee_iterator->second.begin();
+           p != assignee_iterator->second.end();
+           ++p) {
+        LabelInfo* model_info = p->first;
+        int score = sign * p->second;
+        variable_queue_.AddPendingUpdate(program_info, model_info, score);
+      }
+    }
+  }
+
+  void AssignOne(LabelInfo* model_info, LabelInfo* program_info) {
+    LOG_ASSERT(!model_info->assignment_);
+    LOG_ASSERT(!program_info->assignment_);
+    LOG_ASSERT(model_info->is_model_);
+    LOG_ASSERT(!program_info->is_model_);
+
+    ALOG2 << "Assign " << ToString(program_info)
+          << " := " << ToString(model_info);
+
+    ShingleSet affected_shingles;
+    AddAffectedPositions(model_info, &affected_shingles);
+    AddAffectedPositions(program_info, &affected_shingles);
+
+    for (ShingleSet::iterator p = affected_shingles.begin();
+         p != affected_shingles.end();
+         ++p) {
+      patterns_needing_updates_.insert((*p)->pattern());
+    }
+
+    RemovePatternsNeedingUpdatesFromQueues();
+
+    for (ShingleSet::iterator p = affected_shingles.begin();
+         p != affected_shingles.end();
+         ++p) {
+      Declassify(*p);
+    }
+
+    program_info->label_->index_ = model_info->label_->index_;
+    // Mark as assigned
+    model_info->assignment_ = program_info;
+    program_info->assignment_ = model_info;
+
+    for (ShingleSet::iterator p = affected_shingles.begin();
+         p != affected_shingles.end();
+         ++p) {
+      Reclassify(*p);
+    }
+
+    AddPatternsNeedingUpdatesToQueues();
+  }
+
+  bool AssignFirstVariableOfHistogramHead(const ShinglePattern& pattern) {
+    const ShinglePattern::FreqView& program_1 =
+        *pattern.program_histogram_.begin();
+    const ShinglePattern::FreqView& model_1 = *pattern.model_histogram_.begin();
+    const Shingle* program_instance = program_1.instance();
+    const Shingle* model_instance = model_1.instance();
+    size_t variable_index = pattern.index_->first_variable_index_;
+    LabelInfo* program_info = program_instance->at(variable_index);
+    LabelInfo* model_info = model_instance->at(variable_index);
+    AssignOne(model_info, program_info);
+    return true;
+  }
+
+  bool FindAndAssignBestLeader() {
+    LOG_ASSERT(patterns_needing_updates_.empty());
+
+    if (!single_use_pattern_queue_.empty()) {
+      const ShinglePattern& pattern = **single_use_pattern_queue_.begin();
+      return AssignFirstVariableOfHistogramHead(pattern);
+    }
+
+    if (variable_queue_.empty())
+      return false;
+
+    const VariableQueue::ScoreAndLabel best = variable_queue_.first();
+    int score = best.first;
+    LabelInfo* assignee = best.second;
+
+    // TODO(sra): score (best.first) can be zero.  A zero score means we are
+    // blindly picking between two (or more) alternatives which look the same.
+    // If we exit on the first zero-score we sometimes get 3-4% better total
+    // compression.  This indicates that 'infill' is doing a better job than
+    // picking blindly.  Perhaps we can use an extended region around the
+    // undistinguished competing alternatives to break the tie.
+    if (score == 0) {
+      variable_queue_.Print();
+      return false;
+    }
+
+    AssignmentCandidates* candidates = assignee->candidates();
+    if (candidates->empty())
+      return false;  // Should not happen.
+
+    AssignOne(candidates->top_candidate(), assignee);
+    return true;
+  }
+
+ private:
+  // The trace vector contains the model sequence [0, model_end_) followed by
+  // the program sequence [model_end_, trace.end())
+  const Trace& trace_;
+  size_t model_end_;
+
+  // |shingle_instances_| is the set of 'interned' shingles.
+  Shingle::OwningSet shingle_instances_;
+
+  // |instances_| maps from position in |trace_| to Shingle at that position.
+  std::vector<Shingle*> instances_;
+
+  SingleUsePatternQueue single_use_pattern_queue_;
+  ShinglePatternSet active_non_single_use_patterns_;
+  VariableQueue variable_queue_;
+
+  // Transient information: when we make an assignment, we need to recompute
+  // priority queue information derived from these ShinglePatterns.
+  ShinglePatternSet patterns_needing_updates_;
+
+  typedef std::map<ShinglePattern::Index,
+                   ShinglePattern, ShinglePatternIndexLess> IndexToPattern;
+  IndexToPattern patterns_;
+
+  DISALLOW_COPY_AND_ASSIGN(AssignmentProblem);
+};
+
+class Adjuster : public AdjustmentMethod {
+ public:
+  Adjuster() {}
+  ~Adjuster() {}
+
+  bool Adjust(const AssemblyProgram& model, AssemblyProgram* program) {
+    LOG(INFO) << "Adjuster::Adjust";
+    prog_ = program;
+    model_ = &model;
+    return Finish();
+  }
+
+  bool Finish() {
+    prog_->UnassignIndexes();
+    Trace abs32_trace_;
+    Trace rel32_trace_;
+    CollectTraces(model_, &abs32_trace_, &rel32_trace_, true);
+    size_t abs32_model_end = abs32_trace_.size();
+    size_t rel32_model_end = rel32_trace_.size();
+    CollectTraces(prog_,  &abs32_trace_,  &rel32_trace_,  false);
+    Solve(abs32_trace_, abs32_model_end);
+    Solve(rel32_trace_, rel32_model_end);
+    prog_->AssignRemainingIndexes();
+    return true;
+  }
+
+ private:
+  void CollectTraces(const AssemblyProgram* program, Trace* abs32, Trace* rel32,
+                     bool is_model) {
+    label_info_maker_.ResetDebugLabel();
+    const std::vector<Instruction*>& instructions = program->instructions();
+    for (size_t i = 0;  i < instructions.size();  ++i) {
+      Instruction* instruction = instructions.at(i);
+      if (Label* label = program->InstructionAbs32Label(instruction))
+        ReferenceLabel(abs32, label, is_model);
+      if (Label* label = program->InstructionRel32Label(instruction))
+        ReferenceLabel(rel32, label, is_model);
+    }
+    // TODO(sra): we could simply append all the labels in index order to
+    // incorporate some costing for entropy (bigger deltas) that will be
+    // introduced into the label address table by non-monotonic ordering.  This
+    // would have some knock-on effects to parts of the algorithm that work on
+    // single-occurrence labels.
+  }
+
+  void Solve(const Trace& model, size_t model_end) {
+    AssignmentProblem a(model, model_end);
+    a.Solve();
+  }
+
+  void ReferenceLabel(Trace* trace, Label* label, bool is_model) {
+    trace->push_back(
+        label_info_maker_.MakeLabelInfo(label, is_model, trace->size()));
+  }
+
+  AssemblyProgram* prog_;         // Program to be adjusted, owned by caller.
+  const AssemblyProgram* model_;  // Program to be mimicked, owned by caller.
+
+  LabelInfoMaker label_info_maker_;
+
+ private:
+  DISALLOW_COPY_AND_ASSIGN(Adjuster);
+};
+
+////////////////////////////////////////////////////////////////////////////////
+
+}  // namespace adjustment_method_2
+
+AdjustmentMethod* AdjustmentMethod::MakeShingleAdjustmentMethod() {
+  return new adjustment_method_2::Adjuster();
+}
+
+}  // namespace courgette