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+// Copyright 2017 The Abseil Authors.
+//
+// Licensed 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
+//
+// https://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.
+
+// GraphCycles provides incremental cycle detection on a dynamic
+// graph using the following algorithm:
+//
+// A dynamic topological sort algorithm for directed acyclic graphs
+// David J. Pearce, Paul H. J. Kelly
+// Journal of Experimental Algorithmics (JEA) JEA Homepage archive
+// Volume 11, 2006, Article No. 1.7
+//
+// Brief summary of the algorithm:
+//
+// (1) Maintain a rank for each node that is consistent
+// with the topological sort of the graph. I.e., path from x to y
+// implies rank[x] < rank[y].
+// (2) When a new edge (x->y) is inserted, do nothing if rank[x] < rank[y].
+// (3) Otherwise: adjust ranks in the neighborhood of x and y.
+
+#include "absl/base/attributes.h"
+// This file is a no-op if the required LowLevelAlloc support is missing.
+#include "absl/base/internal/low_level_alloc.h"
+#ifndef ABSL_LOW_LEVEL_ALLOC_MISSING
+
+#include "absl/synchronization/internal/graphcycles.h"
+
+#include <algorithm>
+#include <array>
+#include "absl/base/internal/hide_ptr.h"
+#include "absl/base/internal/raw_logging.h"
+#include "absl/base/internal/spinlock.h"
+
+// Do not use STL. This module does not use standard memory allocation.
+
+namespace absl {
+ABSL_NAMESPACE_BEGIN
+namespace synchronization_internal {
+
+namespace {
+
+// Avoid LowLevelAlloc's default arena since it calls malloc hooks in
+// which people are doing things like acquiring Mutexes.
+static absl::base_internal::SpinLock arena_mu(
+ absl::base_internal::kLinkerInitialized);
+static base_internal::LowLevelAlloc::Arena* arena;
+
+static void InitArenaIfNecessary() {
+ arena_mu.Lock();
+ if (arena == nullptr) {
+ arena = base_internal::LowLevelAlloc::NewArena(0);
+ }
+ arena_mu.Unlock();
+}
+
+// Number of inlined elements in Vec. Hash table implementation
+// relies on this being a power of two.
+static const uint32_t kInline = 8;
+
+// A simple LowLevelAlloc based resizable vector with inlined storage
+// for a few elements. T must be a plain type since constructor
+// and destructor are not run on elements of type T managed by Vec.
+template <typename T>
+class Vec {
+ public:
+ Vec() { Init(); }
+ ~Vec() { Discard(); }
+
+ void clear() {
+ Discard();
+ Init();
+ }
+
+ bool empty() const { return size_ == 0; }
+ uint32_t size() const { return size_; }
+ T* begin() { return ptr_; }
+ T* end() { return ptr_ + size_; }
+ const T& operator[](uint32_t i) const { return ptr_[i]; }
+ T& operator[](uint32_t i) { return ptr_[i]; }
+ const T& back() const { return ptr_[size_-1]; }
+ void pop_back() { size_--; }
+
+ void push_back(const T& v) {
+ if (size_ == capacity_) Grow(size_ + 1);
+ ptr_[size_] = v;
+ size_++;
+ }
+
+ void resize(uint32_t n) {
+ if (n > capacity_) Grow(n);
+ size_ = n;
+ }
+
+ void fill(const T& val) {
+ for (uint32_t i = 0; i < size(); i++) {
+ ptr_[i] = val;
+ }
+ }
+
+ // Guarantees src is empty at end.
+ // Provided for the hash table resizing code below.
+ void MoveFrom(Vec<T>* src) {
+ if (src->ptr_ == src->space_) {
+ // Need to actually copy
+ resize(src->size_);
+ std::copy(src->ptr_, src->ptr_ + src->size_, ptr_);
+ src->size_ = 0;
+ } else {
+ Discard();
+ ptr_ = src->ptr_;
+ size_ = src->size_;
+ capacity_ = src->capacity_;
+ src->Init();
+ }
+ }
+
+ private:
+ T* ptr_;
+ T space_[kInline];
+ uint32_t size_;
+ uint32_t capacity_;
+
+ void Init() {
+ ptr_ = space_;
+ size_ = 0;
+ capacity_ = kInline;
+ }
+
+ void Discard() {
+ if (ptr_ != space_) base_internal::LowLevelAlloc::Free(ptr_);
+ }
+
+ void Grow(uint32_t n) {
+ while (capacity_ < n) {
+ capacity_ *= 2;
+ }
+ size_t request = static_cast<size_t>(capacity_) * sizeof(T);
+ T* copy = static_cast<T*>(
+ base_internal::LowLevelAlloc::AllocWithArena(request, arena));
+ std::copy(ptr_, ptr_ + size_, copy);
+ Discard();
+ ptr_ = copy;
+ }
+
+ Vec(const Vec&) = delete;
+ Vec& operator=(const Vec&) = delete;
+};
+
+// A hash set of non-negative int32_t that uses Vec for its underlying storage.
+class NodeSet {
+ public:
+ NodeSet() { Init(); }
+
+ void clear() { Init(); }
+ bool contains(int32_t v) const { return table_[FindIndex(v)] == v; }
+
+ bool insert(int32_t v) {
+ uint32_t i = FindIndex(v);
+ if (table_[i] == v) {
+ return false;
+ }
+ if (table_[i] == kEmpty) {
+ // Only inserting over an empty cell increases the number of occupied
+ // slots.
+ occupied_++;
+ }
+ table_[i] = v;
+ // Double when 75% full.
+ if (occupied_ >= table_.size() - table_.size()/4) Grow();
+ return true;
+ }
+
+ void erase(uint32_t v) {
+ uint32_t i = FindIndex(v);
+ if (static_cast<uint32_t>(table_[i]) == v) {
+ table_[i] = kDel;
+ }
+ }
+
+ // Iteration: is done via HASH_FOR_EACH
+ // Example:
+ // HASH_FOR_EACH(elem, node->out) { ... }
+#define HASH_FOR_EACH(elem, eset) \
+ for (int32_t elem, _cursor = 0; (eset).Next(&_cursor, &elem); )
+ bool Next(int32_t* cursor, int32_t* elem) {
+ while (static_cast<uint32_t>(*cursor) < table_.size()) {
+ int32_t v = table_[*cursor];
+ (*cursor)++;
+ if (v >= 0) {
+ *elem = v;
+ return true;
+ }
+ }
+ return false;
+ }
+
+ private:
+ enum : int32_t { kEmpty = -1, kDel = -2 };
+ Vec<int32_t> table_;
+ uint32_t occupied_; // Count of non-empty slots (includes deleted slots)
+
+ static uint32_t Hash(uint32_t a) { return a * 41; }
+
+ // Return index for storing v. May return an empty index or deleted index
+ int FindIndex(int32_t v) const {
+ // Search starting at hash index.
+ const uint32_t mask = table_.size() - 1;
+ uint32_t i = Hash(v) & mask;
+ int deleted_index = -1; // If >= 0, index of first deleted element we see
+ while (true) {
+ int32_t e = table_[i];
+ if (v == e) {
+ return i;
+ } else if (e == kEmpty) {
+ // Return any previously encountered deleted slot.
+ return (deleted_index >= 0) ? deleted_index : i;
+ } else if (e == kDel && deleted_index < 0) {
+ // Keep searching since v might be present later.
+ deleted_index = i;
+ }
+ i = (i + 1) & mask; // Linear probing; quadratic is slightly slower.
+ }
+ }
+
+ void Init() {
+ table_.clear();
+ table_.resize(kInline);
+ table_.fill(kEmpty);
+ occupied_ = 0;
+ }
+
+ void Grow() {
+ Vec<int32_t> copy;
+ copy.MoveFrom(&table_);
+ occupied_ = 0;
+ table_.resize(copy.size() * 2);
+ table_.fill(kEmpty);
+
+ for (const auto& e : copy) {
+ if (e >= 0) insert(e);
+ }
+ }
+
+ NodeSet(const NodeSet&) = delete;
+ NodeSet& operator=(const NodeSet&) = delete;
+};
+
+// We encode a node index and a node version in GraphId. The version
+// number is incremented when the GraphId is freed which automatically
+// invalidates all copies of the GraphId.
+
+inline GraphId MakeId(int32_t index, uint32_t version) {
+ GraphId g;
+ g.handle =
+ (static_cast<uint64_t>(version) << 32) | static_cast<uint32_t>(index);
+ return g;
+}
+
+inline int32_t NodeIndex(GraphId id) {
+ return static_cast<uint32_t>(id.handle & 0xfffffffful);
+}
+
+inline uint32_t NodeVersion(GraphId id) {
+ return static_cast<uint32_t>(id.handle >> 32);
+}
+
+struct Node {
+ int32_t rank; // rank number assigned by Pearce-Kelly algorithm
+ uint32_t version; // Current version number
+ int32_t next_hash; // Next entry in hash table
+ bool visited; // Temporary marker used by depth-first-search
+ uintptr_t masked_ptr; // User-supplied pointer
+ NodeSet in; // List of immediate predecessor nodes in graph
+ NodeSet out; // List of immediate successor nodes in graph
+ int priority; // Priority of recorded stack trace.
+ int nstack; // Depth of recorded stack trace.
+ void* stack[40]; // stack[0,nstack-1] holds stack trace for node.
+};
+
+// Hash table for pointer to node index lookups.
+class PointerMap {
+ public:
+ explicit PointerMap(const Vec<Node*>* nodes) : nodes_(nodes) {
+ table_.fill(-1);
+ }
+
+ int32_t Find(void* ptr) {
+ auto masked = base_internal::HidePtr(ptr);
+ for (int32_t i = table_[Hash(ptr)]; i != -1;) {
+ Node* n = (*nodes_)[i];
+ if (n->masked_ptr == masked) return i;
+ i = n->next_hash;
+ }
+ return -1;
+ }
+
+ void Add(void* ptr, int32_t i) {
+ int32_t* head = &table_[Hash(ptr)];
+ (*nodes_)[i]->next_hash = *head;
+ *head = i;
+ }
+
+ int32_t Remove(void* ptr) {
+ // Advance through linked list while keeping track of the
+ // predecessor slot that points to the current entry.
+ auto masked = base_internal::HidePtr(ptr);
+ for (int32_t* slot = &table_[Hash(ptr)]; *slot != -1; ) {
+ int32_t index = *slot;
+ Node* n = (*nodes_)[index];
+ if (n->masked_ptr == masked) {
+ *slot = n->next_hash; // Remove n from linked list
+ n->next_hash = -1;
+ return index;
+ }
+ slot = &n->next_hash;
+ }
+ return -1;
+ }
+
+ private:
+ // Number of buckets in hash table for pointer lookups.
+ static constexpr uint32_t kHashTableSize = 8171; // should be prime
+
+ const Vec<Node*>* nodes_;
+ std::array<int32_t, kHashTableSize> table_;
+
+ static uint32_t Hash(void* ptr) {
+ return reinterpret_cast<uintptr_t>(ptr) % kHashTableSize;
+ }
+};
+
+} // namespace
+
+struct GraphCycles::Rep {
+ Vec<Node*> nodes_;
+ Vec<int32_t> free_nodes_; // Indices for unused entries in nodes_
+ PointerMap ptrmap_;
+
+ // Temporary state.
+ Vec<int32_t> deltaf_; // Results of forward DFS
+ Vec<int32_t> deltab_; // Results of backward DFS
+ Vec<int32_t> list_; // All nodes to reprocess
+ Vec<int32_t> merged_; // Rank values to assign to list_ entries
+ Vec<int32_t> stack_; // Emulates recursion stack for depth-first searches
+
+ Rep() : ptrmap_(&nodes_) {}
+};
+
+static Node* FindNode(GraphCycles::Rep* rep, GraphId id) {
+ Node* n = rep->nodes_[NodeIndex(id)];
+ return (n->version == NodeVersion(id)) ? n : nullptr;
+}
+
+GraphCycles::GraphCycles() {
+ InitArenaIfNecessary();
+ rep_ = new (base_internal::LowLevelAlloc::AllocWithArena(sizeof(Rep), arena))
+ Rep;
+}
+
+GraphCycles::~GraphCycles() {
+ for (auto* node : rep_->nodes_) {
+ node->Node::~Node();
+ base_internal::LowLevelAlloc::Free(node);
+ }
+ rep_->Rep::~Rep();
+ base_internal::LowLevelAlloc::Free(rep_);
+}
+
+bool GraphCycles::CheckInvariants() const {
+ Rep* r = rep_;
+ NodeSet ranks; // Set of ranks seen so far.
+ for (uint32_t x = 0; x < r->nodes_.size(); x++) {
+ Node* nx = r->nodes_[x];
+ void* ptr = base_internal::UnhidePtr<void>(nx->masked_ptr);
+ if (ptr != nullptr && static_cast<uint32_t>(r->ptrmap_.Find(ptr)) != x) {
+ ABSL_RAW_LOG(FATAL, "Did not find live node in hash table %u %p", x, ptr);
+ }
+ if (nx->visited) {
+ ABSL_RAW_LOG(FATAL, "Did not clear visited marker on node %u", x);
+ }
+ if (!ranks.insert(nx->rank)) {
+ ABSL_RAW_LOG(FATAL, "Duplicate occurrence of rank %d", nx->rank);
+ }
+ HASH_FOR_EACH(y, nx->out) {
+ Node* ny = r->nodes_[y];
+ if (nx->rank >= ny->rank) {
+ ABSL_RAW_LOG(FATAL, "Edge %u->%d has bad rank assignment %d->%d", x, y,
+ nx->rank, ny->rank);
+ }
+ }
+ }
+ return true;
+}
+
+GraphId GraphCycles::GetId(void* ptr) {
+ int32_t i = rep_->ptrmap_.Find(ptr);
+ if (i != -1) {
+ return MakeId(i, rep_->nodes_[i]->version);
+ } else if (rep_->free_nodes_.empty()) {
+ Node* n =
+ new (base_internal::LowLevelAlloc::AllocWithArena(sizeof(Node), arena))
+ Node;
+ n->version = 1; // Avoid 0 since it is used by InvalidGraphId()
+ n->visited = false;
+ n->rank = rep_->nodes_.size();
+ n->masked_ptr = base_internal::HidePtr(ptr);
+ n->nstack = 0;
+ n->priority = 0;
+ rep_->nodes_.push_back(n);
+ rep_->ptrmap_.Add(ptr, n->rank);
+ return MakeId(n->rank, n->version);
+ } else {
+ // Preserve preceding rank since the set of ranks in use must be
+ // a permutation of [0,rep_->nodes_.size()-1].
+ int32_t r = rep_->free_nodes_.back();
+ rep_->free_nodes_.pop_back();
+ Node* n = rep_->nodes_[r];
+ n->masked_ptr = base_internal::HidePtr(ptr);
+ n->nstack = 0;
+ n->priority = 0;
+ rep_->ptrmap_.Add(ptr, r);
+ return MakeId(r, n->version);
+ }
+}
+
+void GraphCycles::RemoveNode(void* ptr) {
+ int32_t i = rep_->ptrmap_.Remove(ptr);
+ if (i == -1) {
+ return;
+ }
+ Node* x = rep_->nodes_[i];
+ HASH_FOR_EACH(y, x->out) {
+ rep_->nodes_[y]->in.erase(i);
+ }
+ HASH_FOR_EACH(y, x->in) {
+ rep_->nodes_[y]->out.erase(i);
+ }
+ x->in.clear();
+ x->out.clear();
+ x->masked_ptr = base_internal::HidePtr<void>(nullptr);
+ if (x->version == std::numeric_limits<uint32_t>::max()) {
+ // Cannot use x any more
+ } else {
+ x->version++; // Invalidates all copies of node.
+ rep_->free_nodes_.push_back(i);
+ }
+}
+
+void* GraphCycles::Ptr(GraphId id) {
+ Node* n = FindNode(rep_, id);
+ return n == nullptr ? nullptr
+ : base_internal::UnhidePtr<void>(n->masked_ptr);
+}
+
+bool GraphCycles::HasNode(GraphId node) {
+ return FindNode(rep_, node) != nullptr;
+}
+
+bool GraphCycles::HasEdge(GraphId x, GraphId y) const {
+ Node* xn = FindNode(rep_, x);
+ return xn && FindNode(rep_, y) && xn->out.contains(NodeIndex(y));
+}
+
+void GraphCycles::RemoveEdge(GraphId x, GraphId y) {
+ Node* xn = FindNode(rep_, x);
+ Node* yn = FindNode(rep_, y);
+ if (xn && yn) {
+ xn->out.erase(NodeIndex(y));
+ yn->in.erase(NodeIndex(x));
+ // No need to update the rank assignment since a previous valid
+ // rank assignment remains valid after an edge deletion.
+ }
+}
+
+static bool ForwardDFS(GraphCycles::Rep* r, int32_t n, int32_t upper_bound);
+static void BackwardDFS(GraphCycles::Rep* r, int32_t n, int32_t lower_bound);
+static void Reorder(GraphCycles::Rep* r);
+static void Sort(const Vec<Node*>&, Vec<int32_t>* delta);
+static void MoveToList(
+ GraphCycles::Rep* r, Vec<int32_t>* src, Vec<int32_t>* dst);
+
+bool GraphCycles::InsertEdge(GraphId idx, GraphId idy) {
+ Rep* r = rep_;
+ const int32_t x = NodeIndex(idx);
+ const int32_t y = NodeIndex(idy);
+ Node* nx = FindNode(r, idx);
+ Node* ny = FindNode(r, idy);
+ if (nx == nullptr || ny == nullptr) return true; // Expired ids
+
+ if (nx == ny) return false; // Self edge
+ if (!nx->out.insert(y)) {
+ // Edge already exists.
+ return true;
+ }
+
+ ny->in.insert(x);
+
+ if (nx->rank <= ny->rank) {
+ // New edge is consistent with existing rank assignment.
+ return true;
+ }
+
+ // Current rank assignments are incompatible with the new edge. Recompute.
+ // We only need to consider nodes that fall in the range [ny->rank,nx->rank].
+ if (!ForwardDFS(r, y, nx->rank)) {
+ // Found a cycle. Undo the insertion and tell caller.
+ nx->out.erase(y);
+ ny->in.erase(x);
+ // Since we do not call Reorder() on this path, clear any visited
+ // markers left by ForwardDFS.
+ for (const auto& d : r->deltaf_) {
+ r->nodes_[d]->visited = false;
+ }
+ return false;
+ }
+ BackwardDFS(r, x, ny->rank);
+ Reorder(r);
+ return true;
+}
+
+static bool ForwardDFS(GraphCycles::Rep* r, int32_t n, int32_t upper_bound) {
+ // Avoid recursion since stack space might be limited.
+ // We instead keep a stack of nodes to visit.
+ r->deltaf_.clear();
+ r->stack_.clear();
+ r->stack_.push_back(n);
+ while (!r->stack_.empty()) {
+ n = r->stack_.back();
+ r->stack_.pop_back();
+ Node* nn = r->nodes_[n];
+ if (nn->visited) continue;
+
+ nn->visited = true;
+ r->deltaf_.push_back(n);
+
+ HASH_FOR_EACH(w, nn->out) {
+ Node* nw = r->nodes_[w];
+ if (nw->rank == upper_bound) {
+ return false; // Cycle
+ }
+ if (!nw->visited && nw->rank < upper_bound) {
+ r->stack_.push_back(w);
+ }
+ }
+ }
+ return true;
+}
+
+static void BackwardDFS(GraphCycles::Rep* r, int32_t n, int32_t lower_bound) {
+ r->deltab_.clear();
+ r->stack_.clear();
+ r->stack_.push_back(n);
+ while (!r->stack_.empty()) {
+ n = r->stack_.back();
+ r->stack_.pop_back();
+ Node* nn = r->nodes_[n];
+ if (nn->visited) continue;
+
+ nn->visited = true;
+ r->deltab_.push_back(n);
+
+ HASH_FOR_EACH(w, nn->in) {
+ Node* nw = r->nodes_[w];
+ if (!nw->visited && lower_bound < nw->rank) {
+ r->stack_.push_back(w);
+ }
+ }
+ }
+}
+
+static void Reorder(GraphCycles::Rep* r) {
+ Sort(r->nodes_, &r->deltab_);
+ Sort(r->nodes_, &r->deltaf_);
+
+ // Adds contents of delta lists to list_ (backwards deltas first).
+ r->list_.clear();
+ MoveToList(r, &r->deltab_, &r->list_);
+ MoveToList(r, &r->deltaf_, &r->list_);
+
+ // Produce sorted list of all ranks that will be reassigned.
+ r->merged_.resize(r->deltab_.size() + r->deltaf_.size());
+ std::merge(r->deltab_.begin(), r->deltab_.end(),
+ r->deltaf_.begin(), r->deltaf_.end(),
+ r->merged_.begin());
+
+ // Assign the ranks in order to the collected list.
+ for (uint32_t i = 0; i < r->list_.size(); i++) {
+ r->nodes_[r->list_[i]]->rank = r->merged_[i];
+ }
+}
+
+static void Sort(const Vec<Node*>& nodes, Vec<int32_t>* delta) {
+ struct ByRank {
+ const Vec<Node*>* nodes;
+ bool operator()(int32_t a, int32_t b) const {
+ return (*nodes)[a]->rank < (*nodes)[b]->rank;
+ }
+ };
+ ByRank cmp;
+ cmp.nodes = &nodes;
+ std::sort(delta->begin(), delta->end(), cmp);
+}
+
+static void MoveToList(
+ GraphCycles::Rep* r, Vec<int32_t>* src, Vec<int32_t>* dst) {
+ for (auto& v : *src) {
+ int32_t w = v;
+ v = r->nodes_[w]->rank; // Replace v entry with its rank
+ r->nodes_[w]->visited = false; // Prepare for future DFS calls
+ dst->push_back(w);
+ }
+}
+
+int GraphCycles::FindPath(GraphId idx, GraphId idy, int max_path_len,
+ GraphId path[]) const {
+ Rep* r = rep_;
+ if (FindNode(r, idx) == nullptr || FindNode(r, idy) == nullptr) return 0;
+ const int32_t x = NodeIndex(idx);
+ const int32_t y = NodeIndex(idy);
+
+ // Forward depth first search starting at x until we hit y.
+ // As we descend into a node, we push it onto the path.
+ // As we leave a node, we remove it from the path.
+ int path_len = 0;
+
+ NodeSet seen;
+ r->stack_.clear();
+ r->stack_.push_back(x);
+ while (!r->stack_.empty()) {
+ int32_t n = r->stack_.back();
+ r->stack_.pop_back();
+ if (n < 0) {
+ // Marker to indicate that we are leaving a node
+ path_len--;
+ continue;
+ }
+
+ if (path_len < max_path_len) {
+ path[path_len] = MakeId(n, rep_->nodes_[n]->version);
+ }
+ path_len++;
+ r->stack_.push_back(-1); // Will remove tentative path entry
+
+ if (n == y) {
+ return path_len;
+ }
+
+ HASH_FOR_EACH(w, r->nodes_[n]->out) {
+ if (seen.insert(w)) {
+ r->stack_.push_back(w);
+ }
+ }
+ }
+
+ return 0;
+}
+
+bool GraphCycles::IsReachable(GraphId x, GraphId y) const {
+ return FindPath(x, y, 0, nullptr) > 0;
+}
+
+void GraphCycles::UpdateStackTrace(GraphId id, int priority,
+ int (*get_stack_trace)(void** stack, int)) {
+ Node* n = FindNode(rep_, id);
+ if (n == nullptr || n->priority >= priority) {
+ return;
+ }
+ n->nstack = (*get_stack_trace)(n->stack, ABSL_ARRAYSIZE(n->stack));
+ n->priority = priority;
+}
+
+int GraphCycles::GetStackTrace(GraphId id, void*** ptr) {
+ Node* n = FindNode(rep_, id);
+ if (n == nullptr) {
+ *ptr = nullptr;
+ return 0;
+ } else {
+ *ptr = n->stack;
+ return n->nstack;
+ }
+}
+
+} // namespace synchronization_internal
+ABSL_NAMESPACE_END
+} // namespace absl
+
+#endif // ABSL_LOW_LEVEL_ALLOC_MISSING