[Collage] PartitionRule (though without CombinePartitionRule)

See https://github.com/apache/tvm-rfcs/blob/main/rfcs/0062-collage.md.

(Special thanks to Matthew Barrett for authoring partition_rule_test.cc and suggesting a PR
partitioning strategy.)

Collage uses a small 'combinator library' of PartitionRule to decribe how candidate partitions
can be extracted from a model for measurement and comparison. This introduces most of that
machinery, however we defer the all important 'CombinerPartitionRule' for the next PR. Thus
the rules at this stage can only express the sorts of DFPattern-based rules we find in most
BYOC integrations, and cannot describe rules more traditionally associated with operator fusion.

Based on #11981.

src/relay/collage/candidate_partition.cc

@@ -0,0 +1,258 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *   http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing,
+ * software distributed under the License is distributed on an
+ * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.  See the License for the
+ * specific language governing permissions and limitations
+ * under the License.
+ */
+
+/*!
+ * \file src/relay/collage/candidate_partition.cc
+ * \brief A potential partition in the Collage search.
+ */
+
+#include "./candidate_partition.h"
+
+#include <tvm/relay/attrs/memory.h>
+
+#include "./candidate_set.h"
+#include "./partition_rule.h"
+#include "./partition_spec.h"
+#include "./utils.h"
+
+namespace tvm {
+namespace relay {
+namespace collage {
+
+TVM_REGISTER_NODE_TYPE(CandidatePartitionNode);
+
+void CandidatePartitionNode::VisitAttrs(AttrVisitor* v) {
+  v->Visit("rule_name", &rule_name_);
+  v->Visit("sub_graph", &sub_graph_);
+  v->Visit("spec", &spec_);
+  // TODO(mbs): cost_
+}
+
+PartitionSpec CandidatePartitionNode::partition_spec() const {
+  return Downcast<PartitionSpec>(spec_);
+}
+
+std::string CandidatePartitionNode::partition_spec_name() const {
+  return Downcast<PartitionSpec>(spec_)->spec_name_;
+}
+
+Target CandidatePartitionNode::target() const { return Downcast<PartitionSpec>(spec_)->target_; }
+
+std::string CandidatePartitionNode::ToSummary(const DataflowGraph& dataflow_graph) const {
+  std::ostringstream os;
+  os << sub_graph_->label_;
+  os << " | (";
+  bool first = true;
+  for (PostDfsIndex index : sub_graph_->input_) {
+    Expr sub_expr = dataflow_graph.index_to_node(index)->ref();
+    if (CanInline(sub_expr)) {
+      continue;
+    }
+    if (first) {
+      first = false;
+    } else {
+      os << ", ";
+    }
+    os << PrettyPrint(sub_expr->checked_type());
+  }
+  os << ") -> (";
+  first = true;
+  for (PostDfsIndex index : sub_graph_->exit_) {
+    Expr sub_expr = dataflow_graph.index_to_node(index)->ref();
+    if (CanInline(sub_expr)) {
+      continue;
+    }
+    if (first) {
+      first = false;
+    } else {
+      os << ", ";
+    }
+    os << PrettyPrint(sub_expr->checked_type());
+  }
+  os << ") | ";
+  os << sub_graph_->inside_.ToString();
+  os << " | ";
+  os << partition_spec_name();
+  os << " | ";
+  os << cost_.ToString();
+  return os.str();
+}
+
+std::string CandidatePartitionNode::ToString() const {
+  std::ostringstream os;
+  os << "{rule_name=" << rule_name_;
+  os << ",sub_graph=" << sub_graph_->ToString();
+  os << ",spec_name=" << partition_spec_name();
+  if (!cost_.is_unknown()) {
+    os << ",cost=" << cost_.ToString();
+  }
+  os << "}";
+  return os.str();
+}
+
+CandidatePartition::CandidatePartition(String rule_name, SubGraph sub_graph,
+                                       ObjectRef /* actually PartitionSpec */ spec, Cost cost) {
+  auto node = runtime::make_object<CandidatePartitionNode>();
+  node->rule_name_ = std::move(rule_name);
+  node->sub_graph_ = std::move(sub_graph);
+  node->spec_ = std::move(spec);
+  node->cost_ = cost;
+  data_ = std::move(node);
+}
+
+CandidatePartition WithRuleName(CandidatePartition candidate, String rule_name) {
+  if (rule_name == candidate->rule_name_) {
+    return candidate;
+  }
+  auto* node = candidate.CopyOnWrite();
+  node->rule_name_ = std::move(rule_name);
+  return GetRef<CandidatePartition>(node);
+}
+
+CandidatePartition WithSubGraph(CandidatePartition candidate, SubGraph sub_graph) {
+  if (sub_graph == candidate->sub_graph_) {
+    return candidate;
+  }
+  auto* node = candidate.CopyOnWrite();
+  node->sub_graph_ = std::move(sub_graph);
+  return GetRef<CandidatePartition>(node);
+}
+
+bool CandidatePartition::operator<(const CandidatePartition& that) const {
+  // Order lexicographically on sub-graphs.
+  if (*get()->sub_graph_.get() < *that->sub_graph_.get()) {
+    return true;
+  }
+  if (*that->sub_graph_.get() < *get()->sub_graph_.get()) {
+    return false;
+  }
+  // Break ties by rule name.
+  return get()->rule_name_ < that->rule_name_;
+}
+
+bool CandidatePartition::AreTouching(const DataflowGraph& dataflow_graph,
+                                     const CandidatePartition& that) const {
+  return get()->spec_ == that->spec_ &&
+         get()->sub_graph_.AreTouching(dataflow_graph, that->sub_graph_);
+}
+
+CandidatePartition CandidatePartition::DisjointUnion(const DataflowGraph& dataflow_graph,
+                                                     const CandidatePartition& that) const {
+  ICHECK_EQ(get()->spec_, that->spec_);
+  return CandidatePartition(UnionLabels(get()->rule_name_, that->rule_name_),
+                            get()->sub_graph_.DisjointUnion(dataflow_graph, that->sub_graph_),
+                            get()->spec_, get()->cost_ + that->cost_);
+}
+
+/*static*/
+CandidatePartition CandidatePartition::DisjointUnion(const DataflowGraph& dataflow_graph,
+                                                     std::vector<CandidatePartition> candidates) {
+  ICHECK_GT(candidates.size(), 1);
+  CandidatePartition result = candidates.front();
+  for (size_t i = 1; i < candidates.size(); ++i) {
+    result = result.DisjointUnion(dataflow_graph, candidates[i]);
+  }
+  return result;
+}
+
+/*static*/
+Expr CandidatePartition::ParallelRewrite(const DataflowGraph& dataflow_graph,
+                                         const std::vector<CandidatePartition>& candidates) {
+  std::vector<SubGraph> sub_graphs;
+  sub_graphs.reserve(candidates.size());
+  for (const auto& candidate : candidates) {
+    sub_graphs.emplace_back(candidate->sub_graph_);
+  }
+  return SubGraph::ParallelRewrite(dataflow_graph, sub_graphs);
+}
+
+/*static*/
+std::vector<CandidatePartition> CandidatePartition::MaxCoalesce(
+    const DataflowGraph& dataflow_graph, std::vector<CandidatePartition> candidates) {
+  VLOG(1) << "Running MaxCoalesce over " << candidates.size() << " candidates";
+  // This is an eager version of using the simple (kOpaque, kOpaque) combiner.
+
+  // Switch to set representation.
+  CandidateSet result_set(std::move(candidates));
+
+  // Until fixed point...
+  size_t num_rounds = 0;
+  while (result_set.PrepareForNextRound()) {
+    VLOG_CONTEXT << "round " << ++num_rounds;
+    VLOG(1) << "checking " << result_set.size() << " candidates (" << result_set.first_new_index()
+            << " existing)";
+    IndexSet removed_this_round(result_set.size());  // over candidate indexes!
+
+    // Build map from post-dfs indices to the indices of candidates with corresponding entry node.
+    // NOTE: the index set is over candidate indices not post-dfs indices!
+    std::vector<IndexSet> entry_map(dataflow_graph.size(), IndexSet(result_set.size()));
+    for (size_t i = 0; i < result_set.size(); ++i) {
+      CandidatePartition candidate = result_set.at(i);
+      for (PostDfsIndex entry_index : candidate->sub_graph_->entry_) {
+        entry_map[entry_index].Add(i);
+      }
+    }
+
+    for (size_t i = 0; i < result_set.size(); ++i) {
+      if (removed_this_round[i]) {
+        // Already merged.
+        continue;
+      }
+      CandidatePartition upstream = result_set.at(i);
+      // Narrow our search to just those candidates which could touch.
+      IndexSet possible_downstream(result_set.size());  // over candidate indexes!
+      for (PostDfsIndex output_index : upstream->sub_graph_->output_) {
+        possible_downstream = possible_downstream | entry_map[output_index];
+      }
+      for (size_t j : possible_downstream) {
+        if (removed_this_round[j]) {
+          // Already merged.
+          continue;
+        }
+        if (i == j) {
+          // Ignore self.
+          continue;
+        }
+        CandidatePartition downstream = result_set.at(j);
+        if (!upstream.AreTouching(dataflow_graph, downstream)) {
+          continue;
+        }
+        CandidatePartition new_candidate = upstream.DisjointUnion(dataflow_graph, downstream);
+        VLOG(2) << "Merging upstream candidate " << upstream->ToString()
+                << " and downstream candidate " << downstream->ToString() << " to yield "
+                << new_candidate->ToString();
+        result_set.Add(dataflow_graph, new_candidate);
+        result_set.Remove(upstream);
+        removed_this_round.Add(i);
+        result_set.Remove(downstream);
+        removed_this_round.Add(j);
+      }
+    }
+  }
+
+  // Restore canonical order.
+  result_set.sort();
+
+  VLOG(1) << "MaxCoalesce produced " << result_set.size() << " candidates";
+  return result_set.MovedCurrentCandidates();
+}
+
+}  // namespace collage
+}  // namespace relay
+}  // namespace tvm