1//===- BalancedPartitioning.h ---------------------------------------------===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8//
9// This file implements BalancedPartitioning, a recursive balanced graph
10// partitioning algorithm.
11//
12// The algorithm is used to find an ordering of FunctionNodes while optimizing
13// a specified objective. The algorithm uses recursive bisection; it starts
14// with a collection of unordered FunctionNodes and tries to split them into
15// two sets (buckets) of equal cardinality. Each bisection step is comprised of
16// iterations that greedily swap the FunctionNodes between the two buckets while
17// there is an improvement of the objective. Once the process converges, the
18// problem is divided into two sub-problems of half the size, which are
19// recursively applied for the two buckets. The final ordering of the
20// FunctionNodes is obtained by concatenating the two (recursively computed)
21// orderings.
22//
23// In order to speed up the computation, we limit the depth of the recursive
24// tree by a specified constant (SplitDepth) and apply at most a constant
25// number of greedy iterations per split (IterationsPerSplit). The worst-case
26// time complexity of the implementation is bounded by O(M*log^2 N), where
27// N is the number of FunctionNodes and M is the number of
28// FunctionNode-UtilityNode edges; (assuming that any collection of D
29// FunctionNodes contains O(D) UtilityNodes). Notice that the two different
30// recursive sub-problems are independent and thus can be efficiently processed
31// in parallel.
32//
33// Reference:
34//   * Optimizing Function Layout for Mobile Applications,
35//     https://arxiv.org/abs/2211.09285
36//
37//===----------------------------------------------------------------------===//
38
39#ifndef LLVM_SUPPORT_BALANCED_PARTITIONING_H
40#define LLVM_SUPPORT_BALANCED_PARTITIONING_H
41
42#include "raw_ostream.h"
43#include "llvm/ADT/ArrayRef.h"
44
45#include <atomic>
46#include <condition_variable>
47#include <mutex>
48#include <random>
49#include <vector>
50
51namespace llvm {
52
53class ThreadPool;
54/// A function with a set of utility nodes where it is beneficial to order two
55/// functions close together if they have similar utility nodes
56class BPFunctionNode {
57  friend class BalancedPartitioning;
58
59public:
60  using IDT = uint64_t;
61  using UtilityNodeT = uint32_t;
62
63  /// \param UtilityNodes the set of utility nodes (must be unique'd)
64  BPFunctionNode(IDT Id, ArrayRef<UtilityNodeT> UtilityNodes)
65      : Id(Id), UtilityNodes(UtilityNodes) {}
66
67  /// The ID of this node
68  IDT Id;
69
70  void dump(raw_ostream &OS) const;
71
72protected:
73  /// The list of utility nodes associated with this node
74  SmallVector<UtilityNodeT, 4> UtilityNodes;
75  /// The bucket assigned by balanced partitioning
76  std::optional<unsigned> Bucket;
77  /// The index of the input order of the FunctionNodes
78  uint64_t InputOrderIndex = 0;
79
80  friend class BPFunctionNodeTest_Basic_Test;
81  friend class BalancedPartitioningTest_Basic_Test;
82  friend class BalancedPartitioningTest_Large_Test;
83};
84
85/// Algorithm parameters; default values are tuned on real-world binaries
86struct BalancedPartitioningConfig {
87  /// The depth of the recursive bisection
88  unsigned SplitDepth = 18;
89  /// The maximum number of bp iterations per split
90  unsigned IterationsPerSplit = 40;
91  /// The probability for a vertex to skip a move from its current bucket to
92  /// another bucket; it often helps to escape from a local optima
93  float SkipProbability = 0.1f;
94  /// Recursive subtasks up to the given depth are added to the queue and
95  /// distributed among threads by ThreadPool; all subsequent calls are executed
96  /// on the same thread
97  unsigned TaskSplitDepth = 9;
98};
99
100class BalancedPartitioning {
101public:
102  BalancedPartitioning(const BalancedPartitioningConfig &Config);
103
104  /// Run recursive graph partitioning that optimizes a given objective.
105  void run(std::vector<BPFunctionNode> &Nodes) const;
106
107private:
108  struct UtilitySignature;
109  using SignaturesT = SmallVector<UtilitySignature, 4>;
110  using FunctionNodeRange =
111      iterator_range<std::vector<BPFunctionNode>::iterator>;
112
113  /// A special ThreadPool that allows for spawning new tasks after blocking on
114  /// wait(). BalancedPartitioning recursively spawns new threads inside other
115  /// threads, so we need to track how many active threads that could spawn more
116  /// threads.
117  struct BPThreadPool {
118    ThreadPool &TheThreadPool;
119    std::mutex mtx;
120    std::condition_variable cv;
121    /// The number of threads that could spawn more threads
122    std::atomic<int> NumActiveThreads = 0;
123    /// Only true when all threads are down spawning new threads
124    bool IsFinishedSpawning = false;
125    /// Asynchronous submission of the task to the pool
126    template <typename Func> void async(Func &&F);
127    /// Blocking wait for all threads to complete. Unlike ThreadPool, it is
128    /// acceptable for other threads to add more tasks while blocking on this
129    /// call.
130    void wait();
131    BPThreadPool(ThreadPool &TheThreadPool) : TheThreadPool(TheThreadPool) {}
132  };
133
134  /// Run a recursive bisection of a given list of FunctionNodes
135  /// \param RecDepth the current depth of recursion
136  /// \param RootBucket the initial bucket of the dataVertices
137  /// \param Offset the assigned buckets are the range [Offset, Offset +
138  /// Nodes.size()]
139  void bisect(const FunctionNodeRange Nodes, unsigned RecDepth,
140              unsigned RootBucket, unsigned Offset,
141              std::optional<BPThreadPool> &TP) const;
142
143  /// Run bisection iterations
144  void runIterations(const FunctionNodeRange Nodes, unsigned RecDepth,
145                     unsigned LeftBucket, unsigned RightBucket,
146                     std::mt19937 &RNG) const;
147
148  /// Run a bisection iteration to improve the optimization goal
149  /// \returns the total number of moved FunctionNodes
150  unsigned runIteration(const FunctionNodeRange Nodes, unsigned LeftBucket,
151                        unsigned RightBucket, SignaturesT &Signatures,
152                        std::mt19937 &RNG) const;
153
154  /// Try to move \p N from one bucket to another
155  /// \returns true iff \p N is moved
156  bool moveFunctionNode(BPFunctionNode &N, unsigned LeftBucket,
157                        unsigned RightBucket, SignaturesT &Signatures,
158                        std::mt19937 &RNG) const;
159
160  /// Split all the FunctionNodes into 2 buckets, StartBucket and StartBucket +
161  /// 1 The method is used for an initial assignment before a bisection step
162  void split(const FunctionNodeRange Nodes, unsigned StartBucket) const;
163
164  /// The cost of the uniform log-gap cost, assuming a utility node has \p X
165  /// FunctionNodes in the left bucket and \p Y FunctionNodes in the right one.
166  float logCost(unsigned X, unsigned Y) const;
167
168  float log2Cached(unsigned i) const;
169
170  const BalancedPartitioningConfig &Config;
171
172  /// Precomputed values of log2(x). Table size is small enough to fit in cache.
173  static constexpr unsigned LOG_CACHE_SIZE = 16384;
174  float Log2Cache[LOG_CACHE_SIZE];
175
176  /// The signature of a particular utility node used for the bisection step,
177  /// i.e., the number of \p FunctionNodes in each of the two buckets
178  struct UtilitySignature {
179    /// The number of \p FunctionNodes in the left bucket
180    unsigned LeftCount = 0;
181    /// The number of \p FunctionNodes in the right bucket
182    unsigned RightCount = 0;
183    /// The cached gain of moving a \p FunctionNode from the left bucket to the
184    /// right bucket
185    float CachedGainLR;
186    /// The cached gain of moving a \p FunctionNode from the right bucket to the
187    /// left bucket
188    float CachedGainRL;
189    /// Whether \p CachedGainLR and \p CachedGainRL are valid
190    bool CachedGainIsValid = false;
191  };
192
193protected:
194  /// Compute the move gain for uniform log-gap cost
195  static float moveGain(const BPFunctionNode &N, bool FromLeftToRight,
196                        const SignaturesT &Signatures);
197  friend class BalancedPartitioningTest_MoveGain_Test;
198};
199
200} // end namespace llvm
201
202#endif // LLVM_SUPPORT_BALANCED_PARTITIONING_H
203