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llvm / llvm-project / llvm / c1994972438f3c054f9ded8b710d91e3a0c93775 / . / lib / Transforms / Utils / SampleProfileInference.cpp
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//===- SampleProfileInference.cpp - Adjust sample profiles in the IR ------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// This file implements a profile inference algorithm. Given an incomplete and
// possibly imprecise block counts, the algorithm reconstructs realistic block
// and edge counts that satisfy flow conservation rules, while minimally modify
// input block counts.
//
//===----------------------------------------------------------------------===//
#include "llvm/Transforms/Utils/SampleProfileInference.h"
#include "llvm/ADT/BitVector.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Debug.h"
#include <queue>
#include <set>
#include <stack>
using namespace llvm;
#define DEBUG_TYPE "sample-profile-inference"
namespace {
static cl::opt<bool> SampleProfileEvenCountDistribution(
"sample-profile-even-count-distribution", cl::init(true), cl::Hidden,
cl::desc("Try to evenly distribute counts when there are multiple equally "
"likely options."));
static cl::opt<unsigned> SampleProfileMaxDfsCalls(
"sample-profile-max-dfs-calls", cl::init(10), cl::Hidden,
cl::desc("Maximum number of dfs iterations for even count distribution."));
static cl::opt<unsigned> SampleProfileProfiCostInc(
"sample-profile-profi-cost-inc", cl::init(10), cl::Hidden,
cl::desc("A cost of increasing a block's count by one."));
static cl::opt<unsigned> SampleProfileProfiCostDec(
"sample-profile-profi-cost-dec", cl::init(20), cl::Hidden,
cl::desc("A cost of decreasing a block's count by one."));
static cl::opt<unsigned> SampleProfileProfiCostIncZero(
"sample-profile-profi-cost-inc-zero", cl::init(11), cl::Hidden,
cl::desc("A cost of increasing a count of zero-weight block by one."));
static cl::opt<unsigned> SampleProfileProfiCostIncEntry(
"sample-profile-profi-cost-inc-entry", cl::init(40), cl::Hidden,
cl::desc("A cost of increasing the entry block's count by one."));
static cl::opt<unsigned> SampleProfileProfiCostDecEntry(
"sample-profile-profi-cost-dec-entry", cl::init(10), cl::Hidden,
cl::desc("A cost of decreasing the entry block's count by one."));
/// A value indicating an infinite flow/capacity/weight of a block/edge.
/// Not using numeric_limits<int64_t>::max(), as the values can be summed up
/// during the execution.
static constexpr int64_t INF = ((int64_t)1) << 50;
/// The minimum-cost maximum flow algorithm.
///
/// The algorithm finds the maximum flow of minimum cost on a given (directed)
/// network using a modified version of the classical Moore-Bellman-Ford
/// approach. The algorithm applies a number of augmentation iterations in which
/// flow is sent along paths of positive capacity from the source to the sink.
/// The worst-case time complexity of the implementation is O(v(f)*m*n), where
/// where m is the number of edges, n is the number of vertices, and v(f) is the
/// value of the maximum flow. However, the observed running time on typical
/// instances is sub-quadratic, that is, o(n^2).
///
/// The input is a set of edges with specified costs and capacities, and a pair
/// of nodes (source and sink). The output is the flow along each edge of the
/// minimum total cost respecting the given edge capacities.
class MinCostMaxFlow {
public:
// Initialize algorithm's data structures for a network of a given size.
void initialize(uint64_t NodeCount, uint64_t SourceNode, uint64_t SinkNode) {
Source = SourceNode;
Target = SinkNode;
Nodes = std::vector<Node>(NodeCount);
Edges = std::vector<std::vector<Edge>>(NodeCount, std::vector<Edge>());
if (SampleProfileEvenCountDistribution)
AugmentingEdges =
std::vector<std::vector<Edge *>>(NodeCount, std::vector<Edge *>());
}
// Run the algorithm.
int64_t run() {
// Iteratively find an augmentation path/dag in the network and send the
// flow along its edges
size_t AugmentationIters = applyFlowAugmentation();
// Compute the total flow and its cost
int64_t TotalCost = 0;
int64_t TotalFlow = 0;
for (uint64_t Src = 0; Src < Nodes.size(); Src++) {
for (auto &Edge : Edges[Src]) {
if (Edge.Flow > 0) {
TotalCost += Edge.Cost * Edge.Flow;
if (Src == Source)
TotalFlow += Edge.Flow;
}
}
}
LLVM_DEBUG(dbgs() << "Completed profi after " << AugmentationIters
<< " iterations with " << TotalFlow << " total flow"
<< " of " << TotalCost << " cost\n");
(void)TotalFlow;
(void)AugmentationIters;
return TotalCost;
}
/// Adding an edge to the network with a specified capacity and a cost.
/// Multiple edges between a pair of nodes are allowed but self-edges
/// are not supported.
void addEdge(uint64_t Src, uint64_t Dst, int64_t Capacity, int64_t Cost) {
assert(Capacity > 0 && "adding an edge of zero capacity");
assert(Src != Dst && "loop edge are not supported");
Edge SrcEdge;
SrcEdge.Dst = Dst;
SrcEdge.Cost = Cost;
SrcEdge.Capacity = Capacity;
SrcEdge.Flow = 0;
SrcEdge.RevEdgeIndex = Edges[Dst].size();
Edge DstEdge;
DstEdge.Dst = Src;
DstEdge.Cost = -Cost;
DstEdge.Capacity = 0;
DstEdge.Flow = 0;
DstEdge.RevEdgeIndex = Edges[Src].size();
Edges[Src].push_back(SrcEdge);
Edges[Dst].push_back(DstEdge);
}
/// Adding an edge to the network of infinite capacity and a given cost.
void addEdge(uint64_t Src, uint64_t Dst, int64_t Cost) {
addEdge(Src, Dst, INF, Cost);
}
/// Get the total flow from a given source node.
/// Returns a list of pairs (target node, amount of flow to the target).
const std::vector<std::pair<uint64_t, int64_t>> getFlow(uint64_t Src) const {
std::vector<std::pair<uint64_t, int64_t>> Flow;
for (auto &Edge : Edges[Src]) {
if (Edge.Flow > 0)
Flow.push_back(std::make_pair(Edge.Dst, Edge.Flow));
}
return Flow;
}
/// Get the total flow between a pair of nodes.
int64_t getFlow(uint64_t Src, uint64_t Dst) const {
int64_t Flow = 0;
for (auto &Edge : Edges[Src]) {
if (Edge.Dst == Dst) {
Flow += Edge.Flow;
}
}
return Flow;
}
/// A cost of taking an unlikely jump.
static constexpr int64_t AuxCostUnlikely = ((int64_t)1) << 30;
/// Minimum BaseDistance for the jump distance values in island joining.
static constexpr uint64_t MinBaseDistance = 10000;
private:
/// Iteratively find an augmentation path/dag in the network and send the
/// flow along its edges. The method returns the number of applied iterations.
size_t applyFlowAugmentation() {
size_t AugmentationIters = 0;
while (findAugmentingPath()) {
uint64_t PathCapacity = computeAugmentingPathCapacity();
while (PathCapacity > 0) {
bool Progress = false;
if (SampleProfileEvenCountDistribution) {
// Identify node/edge candidates for augmentation
identifyShortestEdges(PathCapacity);
// Find an augmenting DAG
auto AugmentingOrder = findAugmentingDAG();
// Apply the DAG augmentation
Progress = augmentFlowAlongDAG(AugmentingOrder);
PathCapacity = computeAugmentingPathCapacity();
}
if (!Progress) {
augmentFlowAlongPath(PathCapacity);
PathCapacity = 0;
}
AugmentationIters++;
}
}
return AugmentationIters;
}
/// Compute the capacity of the cannonical augmenting path. If the path is
/// saturated (that is, no flow can be sent along the path), then return 0.
uint64_t computeAugmentingPathCapacity() {
uint64_t PathCapacity = INF;
uint64_t Now = Target;
while (Now != Source) {
uint64_t Pred = Nodes[Now].ParentNode;
auto &Edge = Edges[Pred][Nodes[Now].ParentEdgeIndex];
assert(Edge.Capacity >= Edge.Flow && "incorrect edge flow");
uint64_t EdgeCapacity = uint64_t(Edge.Capacity - Edge.Flow);
PathCapacity = std::min(PathCapacity, EdgeCapacity);
Now = Pred;
}
return PathCapacity;
}
/// Check for existence of an augmenting path with a positive capacity.
bool findAugmentingPath() {
// Initialize data structures
for (auto &Node : Nodes) {
Node.Distance = INF;
Node.ParentNode = uint64_t(-1);
Node.ParentEdgeIndex = uint64_t(-1);
Node.Taken = false;
}
std::queue<uint64_t> Queue;
Queue.push(Source);
Nodes[Source].Distance = 0;
Nodes[Source].Taken = true;
while (!Queue.empty()) {
uint64_t Src = Queue.front();
Queue.pop();
Nodes[Src].Taken = false;
// Although the residual network contains edges with negative costs
// (in particular, backward edges), it can be shown that there are no
// negative-weight cycles and the following two invariants are maintained:
// (i) Dist[Source, V] >= 0 and (ii) Dist[V, Target] >= 0 for all nodes V,
// where Dist is the length of the shortest path between two nodes. This
// allows to prune the search-space of the path-finding algorithm using
// the following early-stop criteria:
// -- If we find a path with zero-distance from Source to Target, stop the
// search, as the path is the shortest since Dist[Source, Target] >= 0;
// -- If we have Dist[Source, V] > Dist[Source, Target], then do not
// process node V, as it is guaranteed _not_ to be on a shortest path
// from Source to Target; it follows from inequalities
// Dist[Source, Target] >= Dist[Source, V] + Dist[V, Target]
// >= Dist[Source, V]
if (!SampleProfileEvenCountDistribution && Nodes[Target].Distance == 0)
break;
if (Nodes[Src].Distance > Nodes[Target].Distance)
continue;
// Process adjacent edges
for (uint64_t EdgeIdx = 0; EdgeIdx < Edges[Src].size(); EdgeIdx++) {
auto &Edge = Edges[Src][EdgeIdx];
if (Edge.Flow < Edge.Capacity) {
uint64_t Dst = Edge.Dst;
int64_t NewDistance = Nodes[Src].Distance + Edge.Cost;
if (Nodes[Dst].Distance > NewDistance) {
// Update the distance and the parent node/edge
Nodes[Dst].Distance = NewDistance;
Nodes[Dst].ParentNode = Src;
Nodes[Dst].ParentEdgeIndex = EdgeIdx;
// Add the node to the queue, if it is not there yet
if (!Nodes[Dst].Taken) {
Queue.push(Dst);
Nodes[Dst].Taken = true;
}
}
}
}
}
return Nodes[Target].Distance != INF;
}
/// Update the current flow along the augmenting path.
void augmentFlowAlongPath(uint64_t PathCapacity) {
assert(PathCapacity > 0 && "found an incorrect augmenting path");
uint64_t Now = Target;
while (Now != Source) {
uint64_t Pred = Nodes[Now].ParentNode;
auto &Edge = Edges[Pred][Nodes[Now].ParentEdgeIndex];
auto &RevEdge = Edges[Now][Edge.RevEdgeIndex];
Edge.Flow += PathCapacity;
RevEdge.Flow -= PathCapacity;
Now = Pred;
}
}
/// Find an Augmenting DAG order using a modified version of DFS in which we
/// can visit a node multiple times. In the DFS search, when scanning each
/// edge out of a node, continue search at Edge.Dst endpoint if it has not
/// been discovered yet and its NumCalls < MaxDfsCalls. The algorithm
/// runs in O(MaxDfsCalls * |Edges| + |Nodes|) time.
/// It returns an Augmenting Order (Taken nodes in decreasing Finish time)
/// that starts with Source and ends with Target.
std::vector<uint64_t> findAugmentingDAG() {
// We use a stack based implemenation of DFS to avoid recursion.
// Defining DFS data structures:
// A pair (NodeIdx, EdgeIdx) at the top of the Stack denotes that
// - we are currently visiting Nodes[NodeIdx] and
// - the next edge to scan is Edges[NodeIdx][EdgeIdx]
typedef std::pair<uint64_t, uint64_t> StackItemType;
std::stack<StackItemType> Stack;
std::vector<uint64_t> AugmentingOrder;
// Phase 0: Initialize Node attributes and Time for DFS run
for (auto &Node : Nodes) {
Node.Discovery = 0;
Node.Finish = 0;
Node.NumCalls = 0;
Node.Taken = false;
}
uint64_t Time = 0;
// Mark Target as Taken
// Taken attribute will be propagated backwards from Target towards Source
Nodes[Target].Taken = true;
// Phase 1: Start DFS traversal from Source
Stack.emplace(Source, 0);
Nodes[Source].Discovery = ++Time;
while (!Stack.empty()) {
auto NodeIdx = Stack.top().first;
auto EdgeIdx = Stack.top().second;
// If we haven't scanned all edges out of NodeIdx, continue scanning
if (EdgeIdx < Edges[NodeIdx].size()) {
auto &Edge = Edges[NodeIdx][EdgeIdx];
auto &Dst = Nodes[Edge.Dst];
Stack.top().second++;
if (Edge.OnShortestPath) {
// If we haven't seen Edge.Dst so far, continue DFS search there
if (Dst.Discovery == 0 && Dst.NumCalls < SampleProfileMaxDfsCalls) {
Dst.Discovery = ++Time;
Stack.emplace(Edge.Dst, 0);
Dst.NumCalls++;
} else if (Dst.Taken && Dst.Finish != 0) {
// Else, if Edge.Dst already have a path to Target, so that NodeIdx
Nodes[NodeIdx].Taken = true;
}
}
} else {
// If we are done scanning all edge out of NodeIdx
Stack.pop();
// If we haven't found a path from NodeIdx to Target, forget about it
if (!Nodes[NodeIdx].Taken) {
Nodes[NodeIdx].Discovery = 0;
} else {
// If we have found a path from NodeIdx to Target, then finish NodeIdx
// and propagate Taken flag to DFS parent unless at the Source
Nodes[NodeIdx].Finish = ++Time;
// NodeIdx == Source if and only if the stack is empty
if (NodeIdx != Source) {
assert(!Stack.empty() && "empty stack while running dfs");
Nodes[Stack.top().first].Taken = true;
}
AugmentingOrder.push_back(NodeIdx);
}
}
}
// Nodes are collected decreasing Finish time, so the order is reversed
std::reverse(AugmentingOrder.begin(), AugmentingOrder.end());
// Phase 2: Extract all forward (DAG) edges and fill in AugmentingEdges
for (size_t Src : AugmentingOrder) {
AugmentingEdges[Src].clear();
for (auto &Edge : Edges[Src]) {
uint64_t Dst = Edge.Dst;
if (Edge.OnShortestPath && Nodes[Src].Taken && Nodes[Dst].Taken &&
Nodes[Dst].Finish < Nodes[Src].Finish) {
AugmentingEdges[Src].push_back(&Edge);
}
}
assert((Src == Target || !AugmentingEdges[Src].empty()) &&
"incorrectly constructed augmenting edges");
}
return AugmentingOrder;
}
/// Update the current flow along the given (acyclic) subgraph specified by
/// the vertex order, AugmentingOrder. The objective is to send as much flow
/// as possible while evenly distributing flow among successors of each node.
/// After the update at least one edge is saturated.
bool augmentFlowAlongDAG(const std::vector<uint64_t> &AugmentingOrder) {
// Phase 0: Initialization
for (uint64_t Src : AugmentingOrder) {
Nodes[Src].FracFlow = 0;
Nodes[Src].IntFlow = 0;
for (auto &Edge : AugmentingEdges[Src]) {
Edge->AugmentedFlow = 0;
}
}
// Phase 1: Send a unit of fractional flow along the DAG
uint64_t MaxFlowAmount = INF;
Nodes[Source].FracFlow = 1.0;
for (uint64_t Src : AugmentingOrder) {
assert((Src == Target || Nodes[Src].FracFlow > 0.0) &&
"incorrectly computed fractional flow");
// Distribute flow evenly among successors of Src
uint64_t Degree = AugmentingEdges[Src].size();
for (auto &Edge : AugmentingEdges[Src]) {
double EdgeFlow = Nodes[Src].FracFlow / Degree;
Nodes[Edge->Dst].FracFlow += EdgeFlow;
if (Edge->Capacity == INF)
continue;
uint64_t MaxIntFlow = double(Edge->Capacity - Edge->Flow) / EdgeFlow;
MaxFlowAmount = std::min(MaxFlowAmount, MaxIntFlow);
}
}
// Stop early if we cannot send any (integral) flow from Source to Target
if (MaxFlowAmount == 0)
return false;
// Phase 2: Send an integral flow of MaxFlowAmount
Nodes[Source].IntFlow = MaxFlowAmount;
for (uint64_t Src : AugmentingOrder) {
if (Src == Target)
break;
// Distribute flow evenly among successors of Src, rounding up to make
// sure all flow is sent
uint64_t Degree = AugmentingEdges[Src].size();
// We are guaranteeed that Node[Src].IntFlow <= SuccFlow * Degree
uint64_t SuccFlow = (Nodes[Src].IntFlow + Degree - 1) / Degree;
for (auto &Edge : AugmentingEdges[Src]) {
uint64_t Dst = Edge->Dst;
uint64_t EdgeFlow = std::min(Nodes[Src].IntFlow, SuccFlow);
EdgeFlow = std::min(EdgeFlow, uint64_t(Edge->Capacity - Edge->Flow));
Nodes[Dst].IntFlow += EdgeFlow;
Nodes[Src].IntFlow -= EdgeFlow;
Edge->AugmentedFlow += EdgeFlow;
}
}
assert(Nodes[Target].IntFlow <= MaxFlowAmount);
Nodes[Target].IntFlow = 0;
// Phase 3: Send excess flow back traversing the nodes backwards.
// Because of rounding, not all flow can be sent along the edges of Src.
// Hence, sending the remaining flow back to maintain flow conservation
for (size_t Idx = AugmentingOrder.size() - 1; Idx > 0; Idx--) {
uint64_t Src = AugmentingOrder[Idx - 1];
// Try to send excess flow back along each edge.
// Make sure we only send back flow we just augmented (AugmentedFlow).
for (auto &Edge : AugmentingEdges[Src]) {
uint64_t Dst = Edge->Dst;
if (Nodes[Dst].IntFlow == 0)
continue;
uint64_t EdgeFlow = std::min(Nodes[Dst].IntFlow, Edge->AugmentedFlow);
Nodes[Dst].IntFlow -= EdgeFlow;
Nodes[Src].IntFlow += EdgeFlow;
Edge->AugmentedFlow -= EdgeFlow;
}
}
// Phase 4: Update flow values along all edges
bool HasSaturatedEdges = false;
for (uint64_t Src : AugmentingOrder) {
// Verify that we have sent all the excess flow from the node
assert(Src == Source || Nodes[Src].IntFlow == 0);
for (auto &Edge : AugmentingEdges[Src]) {
assert(uint64_t(Edge->Capacity - Edge->Flow) >= Edge->AugmentedFlow);
// Update flow values along the edge and its reverse copy
auto &RevEdge = Edges[Edge->Dst][Edge->RevEdgeIndex];
Edge->Flow += Edge->AugmentedFlow;
RevEdge.Flow -= Edge->AugmentedFlow;
if (Edge->Capacity == Edge->Flow && Edge->AugmentedFlow > 0)
HasSaturatedEdges = true;
}
}
// The augmentation is successful iff at least one edge becomes saturated
return HasSaturatedEdges;
}
/// Identify candidate (shortest) edges for augmentation.
void identifyShortestEdges(uint64_t PathCapacity) {
assert(PathCapacity > 0 && "found an incorrect augmenting DAG");
// To make sure the augmentation DAG contains only edges with large residual
// capacity, we prune all edges whose capacity is below a fraction of
// the capacity of the augmented path.
// (All edges of the path itself are always in the DAG)
uint64_t MinCapacity = std::max(PathCapacity / 2, uint64_t(1));
// Decide which edges are on a shortest path from Source to Target
for (size_t Src = 0; Src < Nodes.size(); Src++) {
// An edge cannot be augmenting if the endpoint has large distance
if (Nodes[Src].Distance > Nodes[Target].Distance)
continue;
for (auto &Edge : Edges[Src]) {
uint64_t Dst = Edge.Dst;
Edge.OnShortestPath =
Src != Target && Dst != Source &&
Nodes[Dst].Distance <= Nodes[Target].Distance &&
Nodes[Dst].Distance == Nodes[Src].Distance + Edge.Cost &&
Edge.Capacity > Edge.Flow &&
uint64_t(Edge.Capacity - Edge.Flow) >= MinCapacity;
}
}
}
/// A node in a flow network.
struct Node {
/// The cost of the cheapest path from the source to the current node.
int64_t Distance;
/// The node preceding the current one in the path.
uint64_t ParentNode;
/// The index of the edge between ParentNode and the current node.
uint64_t ParentEdgeIndex;
/// An indicator of whether the current node is in a queue.
bool Taken;
/// Data fields utilized in DAG-augmentation:
/// Fractional flow.
double FracFlow;
/// Integral flow.
uint64_t IntFlow;
/// Discovery time.
uint64_t Discovery;
/// Finish time.
uint64_t Finish;
/// NumCalls.
uint64_t NumCalls;
};
/// An edge in a flow network.
struct Edge {
/// The cost of the edge.
int64_t Cost;
/// The capacity of the edge.
int64_t Capacity;
/// The current flow on the edge.
int64_t Flow;
/// The destination node of the edge.
uint64_t Dst;
/// The index of the reverse edge between Dst and the current node.
uint64_t RevEdgeIndex;
/// Data fields utilized in DAG-augmentation:
/// Whether the edge is currently on a shortest path from Source to Target.
bool OnShortestPath;
/// Extra flow along the edge.
uint64_t AugmentedFlow;
};
/// The set of network nodes.
std::vector<Node> Nodes;
/// The set of network edges.
std::vector<std::vector<Edge>> Edges;
/// Source node of the flow.
uint64_t Source;
/// Target (sink) node of the flow.
uint64_t Target;
/// Augmenting edges.
std::vector<std::vector<Edge *>> AugmentingEdges;
};
constexpr int64_t MinCostMaxFlow::AuxCostUnlikely;
constexpr uint64_t MinCostMaxFlow::MinBaseDistance;
/// A post-processing adjustment of control flow. It applies two steps by
/// rerouting some flow and making it more realistic:
///
/// - First, it removes all isolated components ("islands") with a positive flow
/// that are unreachable from the entry block. For every such component, we
/// find the shortest from the entry to an exit passing through the component,
/// and increase the flow by one unit along the path.
///
/// - Second, it identifies all "unknown subgraphs" consisting of basic blocks
/// with no sampled counts. Then it rebalnces the flow that goes through such
/// a subgraph so that each branch is taken with probability 50%.
/// An unknown subgraph is such that for every two nodes u and v:
/// - u dominates v and u is not unknown;
/// - v post-dominates u; and
/// - all inner-nodes of all (u,v)-paths are unknown.
///
class FlowAdjuster {
public:
FlowAdjuster(FlowFunction &Func) : Func(Func) {
assert(Func.Blocks[Func.Entry].isEntry() &&
"incorrect index of the entry block");
}
// Run the post-processing
void run() {
/// Adjust the flow to get rid of isolated components.
joinIsolatedComponents();
/// Rebalance the flow inside unknown subgraphs.
rebalanceUnknownSubgraphs();
}
private:
void joinIsolatedComponents() {
// Find blocks that are reachable from the source
auto Visited = BitVector(NumBlocks(), false);
findReachable(Func.Entry, Visited);
// Iterate over all non-reachable blocks and adjust their weights
for (uint64_t I = 0; I < NumBlocks(); I++) {
auto &Block = Func.Blocks[I];
if (Block.Flow > 0 && !Visited[I]) {
// Find a path from the entry to an exit passing through the block I
auto Path = findShortestPath(I);
// Increase the flow along the path
assert(Path.size() > 0 && Path[0]->Source == Func.Entry &&
"incorrectly computed path adjusting control flow");
Func.Blocks[Func.Entry].Flow += 1;
for (auto &Jump : Path) {
Jump->Flow += 1;
Func.Blocks[Jump->Target].Flow += 1;
// Update reachability
findReachable(Jump->Target, Visited);
}
}
}
}
/// Run BFS from a given block along the jumps with a positive flow and mark
/// all reachable blocks.
void findReachable(uint64_t Src, BitVector &Visited) {
if (Visited[Src])
return;
std::queue<uint64_t> Queue;
Queue.push(Src);
Visited[Src] = true;
while (!Queue.empty()) {
Src = Queue.front();
Queue.pop();
for (auto Jump : Func.Blocks[Src].SuccJumps) {
uint64_t Dst = Jump->Target;
if (Jump->Flow > 0 && !Visited[Dst]) {
Queue.push(Dst);
Visited[Dst] = true;
}
}
}
}
/// Find the shortest path from the entry block to an exit block passing
/// through a given block.
std::vector<FlowJump *> findShortestPath(uint64_t BlockIdx) {
// A path from the entry block to BlockIdx
auto ForwardPath = findShortestPath(Func.Entry, BlockIdx);
// A path from BlockIdx to an exit block
auto BackwardPath = findShortestPath(BlockIdx, AnyExitBlock);
// Concatenate the two paths
std::vector<FlowJump *> Result;
Result.insert(Result.end(), ForwardPath.begin(), ForwardPath.end());
Result.insert(Result.end(), BackwardPath.begin(), BackwardPath.end());
return Result;
}
/// Apply the Dijkstra algorithm to find the shortest path from a given
/// Source to a given Target block.
/// If Target == -1, then the path ends at an exit block.
std::vector<FlowJump *> findShortestPath(uint64_t Source, uint64_t Target) {
// Quit early, if possible
if (Source == Target)
return std::vector<FlowJump *>();
if (Func.Blocks[Source].isExit() && Target == AnyExitBlock)
return std::vector<FlowJump *>();
// Initialize data structures
auto Distance = std::vector<int64_t>(NumBlocks(), INF);
auto Parent = std::vector<FlowJump *>(NumBlocks(), nullptr);
Distance[Source] = 0;
std::set<std::pair<uint64_t, uint64_t>> Queue;
Queue.insert(std::make_pair(Distance[Source], Source));
// Run the Dijkstra algorithm
while (!Queue.empty()) {
uint64_t Src = Queue.begin()->second;
Queue.erase(Queue.begin());
// If we found a solution, quit early
if (Src == Target ||
(Func.Blocks[Src].isExit() && Target == AnyExitBlock))
break;
for (auto Jump : Func.Blocks[Src].SuccJumps) {
uint64_t Dst = Jump->Target;
int64_t JumpDist = jumpDistance(Jump);
if (Distance[Dst] > Distance[Src] + JumpDist) {
Queue.erase(std::make_pair(Distance[Dst], Dst));
Distance[Dst] = Distance[Src] + JumpDist;
Parent[Dst] = Jump;
Queue.insert(std::make_pair(Distance[Dst], Dst));
}
}
}
// If Target is not provided, find the closest exit block
if (Target == AnyExitBlock) {
for (uint64_t I = 0; I < NumBlocks(); I++) {
if (Func.Blocks[I].isExit() && Parent[I] != nullptr) {
if (Target == AnyExitBlock || Distance[Target] > Distance[I]) {
Target = I;
}
}
}
}
assert(Parent[Target] != nullptr && "a path does not exist");
// Extract the constructed path
std::vector<FlowJump *> Result;
uint64_t Now = Target;
while (Now != Source) {
assert(Now == Parent[Now]->Target && "incorrect parent jump");
Result.push_back(Parent[Now]);
Now = Parent[Now]->Source;
}
// Reverse the path, since it is extracted from Target to Source
std::reverse(Result.begin(), Result.end());
return Result;
}
/// A distance of a path for a given jump.
/// In order to incite the path to use blocks/jumps with large positive flow,
/// and avoid changing branch probability of outgoing edges drastically,
/// set the jump distance so as:
/// - to minimize the number of unlikely jumps used and subject to that,
/// - to minimize the number of Flow == 0 jumps used and subject to that,
/// - minimizes total multiplicative Flow increase for the remaining edges.
/// To capture this objective with integer distances, we round off fractional
/// parts to a multiple of 1 / BaseDistance.
int64_t jumpDistance(FlowJump *Jump) const {
uint64_t BaseDistance =
std::max(MinCostMaxFlow::MinBaseDistance,
std::min(Func.Blocks[Func.Entry].Flow,
MinCostMaxFlow::AuxCostUnlikely / NumBlocks()));
if (Jump->IsUnlikely)
return MinCostMaxFlow::AuxCostUnlikely;
if (Jump->Flow > 0)
return BaseDistance + BaseDistance / Jump->Flow;
return BaseDistance * NumBlocks();
};
uint64_t NumBlocks() const { return Func.Blocks.size(); }
/// Rebalance unknown subgraphs so that the flow is split evenly across the
/// outgoing branches of every block of the subgraph. The method iterates over
/// blocks with known weight and identifies unknown subgraphs rooted at the
/// blocks. Then it verifies if flow rebalancing is feasible and applies it.
void rebalanceUnknownSubgraphs() {
// Try to find unknown subgraphs from each block
for (uint64_t I = 0; I < Func.Blocks.size(); I++) {
auto SrcBlock = &Func.Blocks[I];
// Verify if rebalancing rooted at SrcBlock is feasible
if (!canRebalanceAtRoot(SrcBlock))
continue;
// Find an unknown subgraphs starting at SrcBlock. Along the way,
// fill in known destinations and intermediate unknown blocks.
std::vector<FlowBlock *> UnknownBlocks;
std::vector<FlowBlock *> KnownDstBlocks;
findUnknownSubgraph(SrcBlock, KnownDstBlocks, UnknownBlocks);
// Verify if rebalancing of the subgraph is feasible. If the search is
// successful, find the unique destination block (which can be null)
FlowBlock *DstBlock = nullptr;
if (!canRebalanceSubgraph(SrcBlock, KnownDstBlocks, UnknownBlocks,
DstBlock))
continue;
// We cannot rebalance subgraphs containing cycles among unknown blocks
if (!isAcyclicSubgraph(SrcBlock, DstBlock, UnknownBlocks))
continue;
// Rebalance the flow
rebalanceUnknownSubgraph(SrcBlock, DstBlock, UnknownBlocks);
}
}
/// Verify if rebalancing rooted at a given block is possible.
bool canRebalanceAtRoot(const FlowBlock *SrcBlock) {
// Do not attempt to find unknown subgraphs from an unknown or a
// zero-flow block
if (SrcBlock->UnknownWeight || SrcBlock->Flow == 0)
return false;
// Do not attempt to process subgraphs from a block w/o unknown sucessors
bool HasUnknownSuccs = false;
for (auto Jump : SrcBlock->SuccJumps) {
if (Func.Blocks[Jump->Target].UnknownWeight) {
HasUnknownSuccs = true;
break;
}
}
if (!HasUnknownSuccs)
return false;
return true;
}
/// Find an unknown subgraph starting at block SrcBlock. The method sets
/// identified destinations, KnownDstBlocks, and intermediate UnknownBlocks.
void findUnknownSubgraph(const FlowBlock *SrcBlock,
std::vector<FlowBlock *> &KnownDstBlocks,
std::vector<FlowBlock *> &UnknownBlocks) {
// Run BFS from SrcBlock and make sure all paths are going through unknown
// blocks and end at a known DstBlock
auto Visited = BitVector(NumBlocks(), false);
std::queue<uint64_t> Queue;
Queue.push(SrcBlock->Index);
Visited[SrcBlock->Index] = true;
while (!Queue.empty()) {
auto &Block = Func.Blocks[Queue.front()];
Queue.pop();
// Process blocks reachable from Block
for (auto Jump : Block.SuccJumps) {
// If Jump can be ignored, skip it
if (ignoreJump(SrcBlock, nullptr, Jump))
continue;
uint64_t Dst = Jump->Target;
// If Dst has been visited, skip Jump
if (Visited[Dst])
continue;
// Process block Dst
Visited[Dst] = true;
if (!Func.Blocks[Dst].UnknownWeight) {
KnownDstBlocks.push_back(&Func.Blocks[Dst]);
} else {
Queue.push(Dst);
UnknownBlocks.push_back(&Func.Blocks[Dst]);
}
}
}
}
/// Verify if rebalancing of the subgraph is feasible. If the checks are
/// successful, set the unique destination block, DstBlock (can be null).
bool canRebalanceSubgraph(const FlowBlock *SrcBlock,
const std::vector<FlowBlock *> &KnownDstBlocks,
const std::vector<FlowBlock *> &UnknownBlocks,
FlowBlock *&DstBlock) {
// If the list of unknown blocks is empty, we don't need rebalancing
if (UnknownBlocks.empty())
return false;
// If there are multiple known sinks, we can't rebalance
if (KnownDstBlocks.size() > 1)
return false;
DstBlock = KnownDstBlocks.empty() ? nullptr : KnownDstBlocks.front();
// Verify sinks of the subgraph
for (auto Block : UnknownBlocks) {
if (Block->SuccJumps.empty()) {
// If there are multiple (known and unknown) sinks, we can't rebalance
if (DstBlock != nullptr)
return false;
continue;
}
size_t NumIgnoredJumps = 0;
for (auto Jump : Block->SuccJumps) {
if (ignoreJump(SrcBlock, DstBlock, Jump))
NumIgnoredJumps++;
}
// If there is a non-sink block in UnknownBlocks with all jumps ignored,
// then we can't rebalance
if (NumIgnoredJumps == Block->SuccJumps.size())
return false;
}
return true;
}
/// Decide whether the Jump is ignored while processing an unknown subgraphs
/// rooted at basic block SrcBlock with the destination block, DstBlock.
bool ignoreJump(const FlowBlock *SrcBlock, const FlowBlock *DstBlock,
const FlowJump *Jump) {
// Ignore unlikely jumps with zero flow
if (Jump->IsUnlikely && Jump->Flow == 0)
return true;
auto JumpSource = &Func.Blocks[Jump->Source];
auto JumpTarget = &Func.Blocks[Jump->Target];
// Do not ignore jumps coming into DstBlock
if (DstBlock != nullptr && JumpTarget == DstBlock)
return false;
// Ignore jumps out of SrcBlock to known blocks
if (!JumpTarget->UnknownWeight && JumpSource == SrcBlock)
return true;
// Ignore jumps to known blocks with zero flow
if (!JumpTarget->UnknownWeight && JumpTarget->Flow == 0)
return true;
return false;
}
/// Verify if the given unknown subgraph is acyclic, and if yes, reorder
/// UnknownBlocks in the topological order (so that all jumps are "forward").
bool isAcyclicSubgraph(const FlowBlock *SrcBlock, const FlowBlock *DstBlock,
std::vector<FlowBlock *> &UnknownBlocks) {
// Extract local in-degrees in the considered subgraph
auto LocalInDegree = std::vector<uint64_t>(NumBlocks(), 0);
auto fillInDegree = [&](const FlowBlock *Block) {
for (auto Jump : Block->SuccJumps) {
if (ignoreJump(SrcBlock, DstBlock, Jump))
continue;
LocalInDegree[Jump->Target]++;
}
};
fillInDegree(SrcBlock);
for (auto Block : UnknownBlocks) {
fillInDegree(Block);
}
// A loop containing SrcBlock
if (LocalInDegree[SrcBlock->Index] > 0)
return false;
std::vector<FlowBlock *> AcyclicOrder;
std::queue<uint64_t> Queue;
Queue.push(SrcBlock->Index);
while (!Queue.empty()) {
FlowBlock *Block = &Func.Blocks[Queue.front()];
Queue.pop();
// Stop propagation once we reach DstBlock, if any
if (DstBlock != nullptr && Block == DstBlock)
break;
// Keep an acyclic order of unknown blocks
if (Block->UnknownWeight && Block != SrcBlock)
AcyclicOrder.push_back(Block);
// Add to the queue all successors with zero local in-degree
for (auto Jump : Block->SuccJumps) {
if (ignoreJump(SrcBlock, DstBlock, Jump))
continue;
uint64_t Dst = Jump->Target;
LocalInDegree[Dst]--;
if (LocalInDegree[Dst] == 0) {
Queue.push(Dst);
}
}
}
// If there is a cycle in the subgraph, AcyclicOrder contains only a subset
// of all blocks
if (UnknownBlocks.size() != AcyclicOrder.size())
return false;
UnknownBlocks = AcyclicOrder;
return true;
}
/// Rebalance a given subgraph rooted at SrcBlock, ending at DstBlock and
/// having UnknownBlocks intermediate blocks.
void rebalanceUnknownSubgraph(const FlowBlock *SrcBlock,
const FlowBlock *DstBlock,
const std::vector<FlowBlock *> &UnknownBlocks) {
assert(SrcBlock->Flow > 0 && "zero-flow block in unknown subgraph");
// Ditribute flow from the source block
uint64_t BlockFlow = 0;
// SrcBlock's flow is the sum of outgoing flows along non-ignored jumps
for (auto Jump : SrcBlock->SuccJumps) {
if (ignoreJump(SrcBlock, DstBlock, Jump))
continue;
BlockFlow += Jump->Flow;
}
rebalanceBlock(SrcBlock, DstBlock, SrcBlock, BlockFlow);
// Ditribute flow from the remaining blocks
for (auto Block : UnknownBlocks) {
assert(Block->UnknownWeight && "incorrect unknown subgraph");
uint64_t BlockFlow = 0;
// Block's flow is the sum of incoming flows
for (auto Jump : Block->PredJumps) {
BlockFlow += Jump->Flow;
}
Block->Flow = BlockFlow;
rebalanceBlock(SrcBlock, DstBlock, Block, BlockFlow);
}
}
/// Redistribute flow for a block in a subgraph rooted at SrcBlock,
/// and ending at DstBlock.
void rebalanceBlock(const FlowBlock *SrcBlock, const FlowBlock *DstBlock,
const FlowBlock *Block, uint64_t BlockFlow) {
// Process all successor jumps and update corresponding flow values
size_t BlockDegree = 0;
for (auto Jump : Block->SuccJumps) {
if (ignoreJump(SrcBlock, DstBlock, Jump))
continue;
BlockDegree++;
}
// If all successor jumps of the block are ignored, skip it
if (DstBlock == nullptr && BlockDegree == 0)
return;
assert(BlockDegree > 0 && "all outgoing jumps are ignored");
// Each of the Block's successors gets the following amount of flow.
// Rounding the value up so that all flow is propagated
uint64_t SuccFlow = (BlockFlow + BlockDegree - 1) / BlockDegree;
for (auto Jump : Block->SuccJumps) {
if (ignoreJump(SrcBlock, DstBlock, Jump))
continue;
uint64_t Flow = std::min(SuccFlow, BlockFlow);
Jump->Flow = Flow;
BlockFlow -= Flow;
}
assert(BlockFlow == 0 && "not all flow is propagated");
}
/// A constant indicating an arbitrary exit block of a function.
static constexpr uint64_t AnyExitBlock = uint64_t(-1);
/// The function.
FlowFunction &Func;
};
/// Initializing flow network for a given function.
///
/// Every block is split into three nodes that are responsible for (i) an
/// incoming flow, (ii) an outgoing flow, and (iii) penalizing an increase or
/// reduction of the block weight.
void initializeNetwork(MinCostMaxFlow &Network, FlowFunction &Func) {
uint64_t NumBlocks = Func.Blocks.size();
assert(NumBlocks > 1 && "Too few blocks in a function");
LLVM_DEBUG(dbgs() << "Initializing profi for " << NumBlocks << " blocks\n");
// Pre-process data: make sure the entry weight is at least 1
if (Func.Blocks[Func.Entry].Weight == 0) {
Func.Blocks[Func.Entry].Weight = 1;
}
// Introducing dummy source/sink pairs to allow flow circulation.
// The nodes corresponding to blocks of Func have indicies in the range
// [0..3 * NumBlocks); the dummy nodes are indexed by the next four values.
uint64_t S = 3 * NumBlocks;
uint64_t T = S + 1;
uint64_t S1 = S + 2;
uint64_t T1 = S + 3;
Network.initialize(3 * NumBlocks + 4, S1, T1);
// Create three nodes for every block of the function
for (uint64_t B = 0; B < NumBlocks; B++) {
auto &Block = Func.Blocks[B];
assert((!Block.UnknownWeight || Block.Weight == 0 || Block.isEntry()) &&
"non-zero weight of a block w/o weight except for an entry");
// Split every block into two nodes
uint64_t Bin = 3 * B;
uint64_t Bout = 3 * B + 1;
uint64_t Baux = 3 * B + 2;
if (Block.Weight > 0) {
Network.addEdge(S1, Bout, Block.Weight, 0);
Network.addEdge(Bin, T1, Block.Weight, 0);
}
// Edges from S and to T
assert((!Block.isEntry() || !Block.isExit()) &&
"a block cannot be an entry and an exit");
if (Block.isEntry()) {
Network.addEdge(S, Bin, 0);
} else if (Block.isExit()) {
Network.addEdge(Bout, T, 0);
}
// An auxiliary node to allow increase/reduction of block counts:
// We assume that decreasing block counts is more expensive than increasing,
// and thus, setting separate costs here. In the future we may want to tune
// the relative costs so as to maximize the quality of generated profiles.
int64_t AuxCostInc = SampleProfileProfiCostInc;
int64_t AuxCostDec = SampleProfileProfiCostDec;
if (Block.UnknownWeight) {
// Do not penalize changing weights of blocks w/o known profile count
AuxCostInc = 0;
AuxCostDec = 0;
} else {
// Increasing the count for "cold" blocks with zero initial count is more
// expensive than for "hot" ones
if (Block.Weight == 0) {
AuxCostInc = SampleProfileProfiCostIncZero;
}
// Modifying the count of the entry block is expensive
if (Block.isEntry()) {
AuxCostInc = SampleProfileProfiCostIncEntry;
AuxCostDec = SampleProfileProfiCostDecEntry;
}
}
// For blocks with self-edges, do not penalize a reduction of the count,
// as all of the increase can be attributed to the self-edge
if (Block.HasSelfEdge) {
AuxCostDec = 0;
}
Network.addEdge(Bin, Baux, AuxCostInc);
Network.addEdge(Baux, Bout, AuxCostInc);
if (Block.Weight > 0) {
Network.addEdge(Bout, Baux, AuxCostDec);
Network.addEdge(Baux, Bin, AuxCostDec);
}
}
// Creating edges for every jump
for (auto &Jump : Func.Jumps) {
uint64_t Src = Jump.Source;
uint64_t Dst = Jump.Target;
if (Src != Dst) {
uint64_t SrcOut = 3 * Src + 1;
uint64_t DstIn = 3 * Dst;
uint64_t Cost = Jump.IsUnlikely ? MinCostMaxFlow::AuxCostUnlikely : 0;
Network.addEdge(SrcOut, DstIn, Cost);
}
}
// Make sure we have a valid flow circulation
Network.addEdge(T, S, 0);
}
/// Extract resulting block and edge counts from the flow network.
void extractWeights(MinCostMaxFlow &Network, FlowFunction &Func) {
uint64_t NumBlocks = Func.Blocks.size();
// Extract resulting block counts
for (uint64_t Src = 0; Src < NumBlocks; Src++) {
auto &Block = Func.Blocks[Src];
uint64_t SrcOut = 3 * Src + 1;
int64_t Flow = 0;
for (auto &Adj : Network.getFlow(SrcOut)) {
uint64_t DstIn = Adj.first;
int64_t DstFlow = Adj.second;
bool IsAuxNode = (DstIn < 3 * NumBlocks && DstIn % 3 == 2);
if (!IsAuxNode || Block.HasSelfEdge) {
Flow += DstFlow;
}
}
Block.Flow = Flow;
assert(Flow >= 0 && "negative block flow");
}
// Extract resulting jump counts
for (auto &Jump : Func.Jumps) {
uint64_t Src = Jump.Source;
uint64_t Dst = Jump.Target;
int64_t Flow = 0;
if (Src != Dst) {
uint64_t SrcOut = 3 * Src + 1;
uint64_t DstIn = 3 * Dst;
Flow = Network.getFlow(SrcOut, DstIn);
} else {
uint64_t SrcOut = 3 * Src + 1;
uint64_t SrcAux = 3 * Src + 2;
int64_t AuxFlow = Network.getFlow(SrcOut, SrcAux);
if (AuxFlow > 0)
Flow = AuxFlow;
}
Jump.Flow = Flow;
assert(Flow >= 0 && "negative jump flow");
}
}
#ifndef NDEBUG
/// Verify that the computed flow values satisfy flow conservation rules
void verifyWeights(const FlowFunction &Func) {
const uint64_t NumBlocks = Func.Blocks.size();
auto InFlow = std::vector<uint64_t>(NumBlocks, 0);
auto OutFlow = std::vector<uint64_t>(NumBlocks, 0);
for (auto &Jump : Func.Jumps) {
InFlow[Jump.Target] += Jump.Flow;
OutFlow[Jump.Source] += Jump.Flow;
}
uint64_t TotalInFlow = 0;
uint64_t TotalOutFlow = 0;
for (uint64_t I = 0; I < NumBlocks; I++) {
auto &Block = Func.Blocks[I];
if (Block.isEntry()) {
TotalInFlow += Block.Flow;
assert(Block.Flow == OutFlow[I] && "incorrectly computed control flow");
} else if (Block.isExit()) {
TotalOutFlow += Block.Flow;
assert(Block.Flow == InFlow[I] && "incorrectly computed control flow");
} else {
assert(Block.Flow == OutFlow[I] && "incorrectly computed control flow");
assert(Block.Flow == InFlow[I] && "incorrectly computed control flow");
}
}
assert(TotalInFlow == TotalOutFlow && "incorrectly computed control flow");
// Verify that there are no isolated flow components
// One could modify FlowFunction to hold edges indexed by the sources, which
// will avoid a creation of the object
auto PositiveFlowEdges = std::vector<std::vector<uint64_t>>(NumBlocks);
for (auto &Jump : Func.Jumps) {
if (Jump.Flow > 0) {
PositiveFlowEdges[Jump.Source].push_back(Jump.Target);
}
}
// Run BFS from the source along edges with positive flow
std::queue<uint64_t> Queue;
auto Visited = BitVector(NumBlocks, false);
Queue.push(Func.Entry);
Visited[Func.Entry] = true;
while (!Queue.empty()) {
uint64_t Src = Queue.front();
Queue.pop();
for (uint64_t Dst : PositiveFlowEdges[Src]) {
if (!Visited[Dst]) {
Queue.push(Dst);
Visited[Dst] = true;
}
}
}
// Verify that every block that has a positive flow is reached from the source
// along edges with a positive flow
for (uint64_t I = 0; I < NumBlocks; I++) {
auto &Block = Func.Blocks[I];
assert((Visited[I] || Block.Flow == 0) && "an isolated flow component");
}
}
#endif
} // end of anonymous namespace
/// Apply the profile inference algorithm for a given flow function
void llvm::applyFlowInference(FlowFunction &Func) {
// Create and apply an inference network model
auto InferenceNetwork = MinCostMaxFlow();
initializeNetwork(InferenceNetwork, Func);
InferenceNetwork.run();
// Extract flow values for every block and every edge
extractWeights(InferenceNetwork, Func);
// Post-processing adjustments to the flow
auto Adjuster = FlowAdjuster(Func);
Adjuster.run();
#ifndef NDEBUG
// Verify the result
verifyWeights(Func);
#endif
}