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//===- LoopFusion.cpp - Code to perform loop fusion -----------------------===//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
// This file implements loop fusion.
#include "PassDetail.h"
#include "mlir/Analysis/AffineAnalysis.h"
#include "mlir/Analysis/AffineStructures.h"
#include "mlir/Analysis/LoopAnalysis.h"
#include "mlir/Analysis/Utils.h"
#include "mlir/Dialect/Affine/IR/AffineOps.h"
#include "mlir/Dialect/MemRef/IR/MemRef.h"
#include "mlir/IR/AffineExpr.h"
#include "mlir/IR/AffineMap.h"
#include "mlir/IR/Builders.h"
#include "mlir/Transforms/LoopFusionUtils.h"
#include "mlir/Transforms/LoopUtils.h"
#include "mlir/Transforms/Passes.h"
#include "mlir/Transforms/Utils.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/DenseSet.h"
#include "llvm/ADT/SetVector.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/raw_ostream.h"
#include <iomanip>
#include <sstream>
#define DEBUG_TYPE "affine-loop-fusion"
using namespace mlir;
namespace {
/// Loop fusion pass. This pass currently supports a greedy fusion policy,
/// which fuses loop nests with single-writer/single-reader memref dependences
/// with the goal of improving locality.
// TODO: Support fusion of source loop nests which write to multiple
// memrefs, where each memref can have multiple users (if profitable).
// TODO: Extend this pass to check for fusion preventing dependences,
// and add support for more general loop fusion algorithms.
struct LoopFusion : public AffineLoopFusionBase<LoopFusion> {
LoopFusion() = default;
LoopFusion(unsigned fastMemorySpace, uint64_t localBufSizeThresholdBytes,
bool maximalFusion, enum FusionMode affineFusionMode) {
this->fastMemorySpace = fastMemorySpace;
this->localBufSizeThreshold = localBufSizeThresholdBytes / 1024;
this->maximalFusion = maximalFusion;
this->affineFusionMode = affineFusionMode;
void runOnFunction() override;
} // end anonymous namespace
mlir::createLoopFusionPass(unsigned fastMemorySpace,
uint64_t localBufSizeThreshold, bool maximalFusion,
enum FusionMode affineFusionMode) {
return std::make_unique<LoopFusion>(fastMemorySpace, localBufSizeThreshold,
maximalFusion, affineFusionMode);
namespace {
// LoopNestStateCollector walks loop nests and collects load and store
// operations, and whether or not a region holding op other than ForOp and IfOp
// was encountered in the loop nest.
struct LoopNestStateCollector {
SmallVector<AffineForOp, 4> forOps;
SmallVector<Operation *, 4> loadOpInsts;
SmallVector<Operation *, 4> storeOpInsts;
bool hasNonAffineRegionOp = false;
void collect(Operation *opToWalk) {
opToWalk->walk([&](Operation *op) {
if (isa<AffineForOp>(op))
else if (op->getNumRegions() != 0 && !isa<AffineIfOp>(op))
hasNonAffineRegionOp = true;
else if (isa<AffineReadOpInterface>(op))
else if (isa<AffineWriteOpInterface>(op))
// MemRefDependenceGraph is a graph data structure where graph nodes are
// top-level operations in a FuncOp which contain load/store ops, and edges
// are memref dependences between the nodes.
// TODO: Add a more flexible dependence graph representation.
// TODO: Add a depth parameter to dependence graph construction.
struct MemRefDependenceGraph {
// Node represents a node in the graph. A Node is either an entire loop nest
// rooted at the top level which contains loads/stores, or a top level
// load/store.
struct Node {
// The unique identifier of this node in the graph.
unsigned id;
// The top-level statement which is (or contains) a load/store.
Operation *op;
// List of load operations.
SmallVector<Operation *, 4> loads;
// List of store op insts.
SmallVector<Operation *, 4> stores;
Node(unsigned id, Operation *op) : id(id), op(op) {}
// Returns the load op count for 'memref'.
unsigned getLoadOpCount(Value memref) {
unsigned loadOpCount = 0;
for (auto *loadOpInst : loads) {
if (memref == cast<AffineReadOpInterface>(loadOpInst).getMemRef())
return loadOpCount;
// Returns the store op count for 'memref'.
unsigned getStoreOpCount(Value memref) {
unsigned storeOpCount = 0;
for (auto *storeOpInst : stores) {
if (memref == cast<AffineWriteOpInterface>(storeOpInst).getMemRef())
return storeOpCount;
// Returns all store ops in 'storeOps' which access 'memref'.
void getStoreOpsForMemref(Value memref,
SmallVectorImpl<Operation *> *storeOps) {
for (auto *storeOpInst : stores) {
if (memref == cast<AffineWriteOpInterface>(storeOpInst).getMemRef())
// Returns all load ops in 'loadOps' which access 'memref'.
void getLoadOpsForMemref(Value memref,
SmallVectorImpl<Operation *> *loadOps) {
for (auto *loadOpInst : loads) {
if (memref == cast<AffineReadOpInterface>(loadOpInst).getMemRef())
// Returns all memrefs in 'loadAndStoreMemrefSet' for which this node
// has at least one load and store operation.
void getLoadAndStoreMemrefSet(DenseSet<Value> *loadAndStoreMemrefSet) {
llvm::SmallDenseSet<Value, 2> loadMemrefs;
for (auto *loadOpInst : loads) {
for (auto *storeOpInst : stores) {
auto memref = cast<AffineWriteOpInterface>(storeOpInst).getMemRef();
if (loadMemrefs.count(memref) > 0)
// Edge represents a data dependence between nodes in the graph.
struct Edge {
// The id of the node at the other end of the edge.
// If this edge is stored in Edge = Node.inEdges[i], then
// 'Node.inEdges[i].id' is the identifier of the source node of the edge.
// If this edge is stored in Edge = Node.outEdges[i], then
// 'Node.outEdges[i].id' is the identifier of the dest node of the edge.
unsigned id;
// The SSA value on which this edge represents a dependence.
// If the value is a memref, then the dependence is between graph nodes
// which contain accesses to the same memref 'value'. If the value is a
// non-memref value, then the dependence is between a graph node which
// defines an SSA value and another graph node which uses the SSA value
// (e.g. a constant or load operation defining a value which is used inside
// a loop nest).
Value value;
// Map from node id to Node.
DenseMap<unsigned, Node> nodes;
// Map from node id to list of input edges.
DenseMap<unsigned, SmallVector<Edge, 2>> inEdges;
// Map from node id to list of output edges.
DenseMap<unsigned, SmallVector<Edge, 2>> outEdges;
// Map from memref to a count on the dependence edges associated with that
// memref.
DenseMap<Value, unsigned> memrefEdgeCount;
// The next unique identifier to use for newly created graph nodes.
unsigned nextNodeId = 0;
MemRefDependenceGraph() {}
// Initializes the dependence graph based on operations in 'f'.
// Returns true on success, false otherwise.
bool init(FuncOp f);
// Returns the graph node for 'id'.
Node *getNode(unsigned id) {
auto it = nodes.find(id);
assert(it != nodes.end());
return &it->second;
// Returns the graph node for 'forOp'.
Node *getForOpNode(AffineForOp forOp) {
for (auto &idAndNode : nodes)
if (idAndNode.second.op == forOp.getOperation())
return &idAndNode.second;
return nullptr;
// Adds a node with 'op' to the graph and returns its unique identifier.
unsigned addNode(Operation *op) {
Node node(nextNodeId++, op);
nodes.insert({, node});
// Remove node 'id' (and its associated edges) from graph.
void removeNode(unsigned id) {
// Remove each edge in 'inEdges[id]'.
if (inEdges.count(id) > 0) {
SmallVector<Edge, 2> oldInEdges = inEdges[id];
for (auto &inEdge : oldInEdges) {
removeEdge(, id, inEdge.value);
// Remove each edge in 'outEdges[id]'.
if (outEdges.count(id) > 0) {
SmallVector<Edge, 2> oldOutEdges = outEdges[id];
for (auto &outEdge : oldOutEdges) {
removeEdge(id,, outEdge.value);
// Erase remaining node state.
// Returns true if node 'id' writes to any memref which escapes (or is an
// argument to) the function/block. Returns false otherwise.
bool writesToLiveInOrEscapingMemrefs(unsigned id) {
Node *node = getNode(id);
for (auto *storeOpInst : node->stores) {
auto memref = cast<AffineWriteOpInterface>(storeOpInst).getMemRef();
auto *op = memref.getDefiningOp();
// Return true if 'memref' is a block argument.
if (!op)
return true;
// Return true if any use of 'memref' escapes the function.
for (auto *user : memref.getUsers())
if (!isa<AffineMapAccessInterface>(*user))
return true;
return false;
// Returns true iff there is an edge from node 'srcId' to node 'dstId' which
// is for 'value' if non-null, or for any value otherwise. Returns false
// otherwise.
bool hasEdge(unsigned srcId, unsigned dstId, Value value = nullptr) {
if (outEdges.count(srcId) == 0 || inEdges.count(dstId) == 0) {
return false;
bool hasOutEdge = llvm::any_of(outEdges[srcId], [=](Edge &edge) {
return == dstId && (!value || edge.value == value);
bool hasInEdge = llvm::any_of(inEdges[dstId], [=](Edge &edge) {
return == srcId && (!value || edge.value == value);
return hasOutEdge && hasInEdge;
// Adds an edge from node 'srcId' to node 'dstId' for 'value'.
void addEdge(unsigned srcId, unsigned dstId, Value value) {
if (!hasEdge(srcId, dstId, value)) {
outEdges[srcId].push_back({dstId, value});
inEdges[dstId].push_back({srcId, value});
if (value.getType().isa<MemRefType>())
// Removes an edge from node 'srcId' to node 'dstId' for 'value'.
void removeEdge(unsigned srcId, unsigned dstId, Value value) {
assert(inEdges.count(dstId) > 0);
assert(outEdges.count(srcId) > 0);
if (value.getType().isa<MemRefType>()) {
assert(memrefEdgeCount.count(value) > 0);
// Remove 'srcId' from 'inEdges[dstId]'.
for (auto it = inEdges[dstId].begin(); it != inEdges[dstId].end(); ++it) {
if ((*it).id == srcId && (*it).value == value) {
// Remove 'dstId' from 'outEdges[srcId]'.
for (auto it = outEdges[srcId].begin(); it != outEdges[srcId].end(); ++it) {
if ((*it).id == dstId && (*it).value == value) {
// Returns true if there is a path in the dependence graph from node 'srcId'
// to node 'dstId'. Returns false otherwise.
bool hasDependencePath(unsigned srcId, unsigned dstId) {
// Worklist state is: <node-id, next-output-edge-index-to-visit>
SmallVector<std::pair<unsigned, unsigned>, 4> worklist;
worklist.push_back({srcId, 0});
// Run DFS traversal to see if 'dstId' is reachable from 'srcId'.
while (!worklist.empty()) {
auto &idAndIndex = worklist.back();
// Return true if we have reached 'dstId'.
if (idAndIndex.first == dstId)
return true;
// Pop and continue if node has no out edges, or if all out edges have
// already been visited.
if (outEdges.count(idAndIndex.first) == 0 ||
idAndIndex.second == outEdges[idAndIndex.first].size()) {
// Get graph edge to traverse.
Edge edge = outEdges[idAndIndex.first][idAndIndex.second];
// Increment next output edge index for 'idAndIndex'.
// Add node at '' to worklist.
worklist.push_back({, 0});
return false;
// Returns the input edge count for node 'id' and 'memref' from src nodes
// which access 'memref' with a store operation.
unsigned getIncomingMemRefAccesses(unsigned id, Value memref) {
unsigned inEdgeCount = 0;
if (inEdges.count(id) > 0)
for (auto &inEdge : inEdges[id])
if (inEdge.value == memref) {
Node *srcNode = getNode(;
// Only count in edges from 'srcNode' if 'srcNode' accesses 'memref'
if (srcNode->getStoreOpCount(memref) > 0)
return inEdgeCount;
// Returns the output edge count for node 'id' and 'memref' (if non-null),
// otherwise returns the total output edge count from node 'id'.
unsigned getOutEdgeCount(unsigned id, Value memref = nullptr) {
unsigned outEdgeCount = 0;
if (outEdges.count(id) > 0)
for (auto &outEdge : outEdges[id])
if (!memref || outEdge.value == memref)
return outEdgeCount;
/// Return all nodes which define SSA values used in node 'id'.
void gatherDefiningNodes(unsigned id, DenseSet<unsigned> &definingNodes) {
for (MemRefDependenceGraph::Edge edge : inEdges[id])
// By definition of edge, if the edge value is a non-memref value,
// then the dependence is between a graph node which defines an SSA value
// and another graph node which uses the SSA value.
if (!edge.value.getType().isa<MemRefType>())
// Computes and returns an insertion point operation, before which the
// the fused <srcId, dstId> loop nest can be inserted while preserving
// dependences. Returns nullptr if no such insertion point is found.
Operation *getFusedLoopNestInsertionPoint(unsigned srcId, unsigned dstId) {
if (outEdges.count(srcId) == 0)
return getNode(dstId)->op;
// Skip if there is any defining node of 'dstId' that depends on 'srcId'.
DenseSet<unsigned> definingNodes;
gatherDefiningNodes(dstId, definingNodes);
if (llvm::any_of(definingNodes, [&](unsigned id) {
return hasDependencePath(srcId, id);
})) {
<< "Can't fuse: a defining op with a user in the dst "
"loop has dependence from the src loop\n");
return nullptr;
// Build set of insts in range (srcId, dstId) which depend on 'srcId'.
SmallPtrSet<Operation *, 2> srcDepInsts;
for (auto &outEdge : outEdges[srcId])
if ( != dstId)
// Build set of insts in range (srcId, dstId) on which 'dstId' depends.
SmallPtrSet<Operation *, 2> dstDepInsts;
for (auto &inEdge : inEdges[dstId])
if ( != srcId)
Operation *srcNodeInst = getNode(srcId)->op;
Operation *dstNodeInst = getNode(dstId)->op;
// Computing insertion point:
// *) Walk all operation positions in Block operation list in the
// range (src, dst). For each operation 'op' visited in this search:
// *) Store in 'firstSrcDepPos' the first position where 'op' has a
// dependence edge from 'srcNode'.
// *) Store in 'lastDstDepPost' the last position where 'op' has a
// dependence edge to 'dstNode'.
// *) Compare 'firstSrcDepPos' and 'lastDstDepPost' to determine the
// operation insertion point (or return null pointer if no such
// insertion point exists: 'firstSrcDepPos' <= 'lastDstDepPos').
SmallVector<Operation *, 2> depInsts;
Optional<unsigned> firstSrcDepPos;
Optional<unsigned> lastDstDepPos;
unsigned pos = 0;
for (Block::iterator it = std::next(Block::iterator(srcNodeInst));
it != Block::iterator(dstNodeInst); ++it) {
Operation *op = &(*it);
if (srcDepInsts.count(op) > 0 && firstSrcDepPos == None)
firstSrcDepPos = pos;
if (dstDepInsts.count(op) > 0)
lastDstDepPos = pos;
if (firstSrcDepPos.hasValue()) {
if (lastDstDepPos.hasValue()) {
if (firstSrcDepPos.getValue() <= lastDstDepPos.getValue()) {
// No valid insertion point exists which preserves dependences.
return nullptr;
// Return the insertion point at 'firstSrcDepPos'.
return depInsts[firstSrcDepPos.getValue()];
// No dependence targets in range (or only dst deps in range), return
// 'dstNodInst' insertion point.
return dstNodeInst;
// Updates edge mappings from node 'srcId' to node 'dstId' after fusing them,
// taking into account that:
// *) if 'removeSrcId' is true, 'srcId' will be removed after fusion,
// *) memrefs in 'privateMemRefs' has been replaced in node at 'dstId' by a
// private memref.
void updateEdges(unsigned srcId, unsigned dstId,
const DenseSet<Value> &privateMemRefs, bool removeSrcId) {
// For each edge in 'inEdges[srcId]': add new edge remapping to 'dstId'.
if (inEdges.count(srcId) > 0) {
SmallVector<Edge, 2> oldInEdges = inEdges[srcId];
for (auto &inEdge : oldInEdges) {
// Add edge from '' to 'dstId' if it's not a private memref.
if (privateMemRefs.count(inEdge.value) == 0)
addEdge(, dstId, inEdge.value);
// For each edge in 'outEdges[srcId]': remove edge from 'srcId' to 'dstId'.
// If 'srcId' is going to be removed, remap all the out edges to 'dstId'.
if (outEdges.count(srcId) > 0) {
SmallVector<Edge, 2> oldOutEdges = outEdges[srcId];
for (auto &outEdge : oldOutEdges) {
// Remove any out edges from 'srcId' to 'dstId' across memrefs.
if ( == dstId)
removeEdge(srcId,, outEdge.value);
else if (removeSrcId) {
addEdge(dstId,, outEdge.value);
removeEdge(srcId,, outEdge.value);
// Remove any edges in 'inEdges[dstId]' on 'oldMemRef' (which is being
// replaced by a private memref). These edges could come from nodes
// other than 'srcId' which were removed in the previous step.
if (inEdges.count(dstId) > 0 && !privateMemRefs.empty()) {
SmallVector<Edge, 2> oldInEdges = inEdges[dstId];
for (auto &inEdge : oldInEdges)
if (privateMemRefs.count(inEdge.value) > 0)
removeEdge(, dstId, inEdge.value);
// Update edge mappings for nodes 'sibId' and 'dstId' to reflect fusion
// of sibling node 'sibId' into node 'dstId'.
void updateEdges(unsigned sibId, unsigned dstId) {
// For each edge in 'inEdges[sibId]':
// *) Add new edge from source node '' to 'dstNode'.
// *) Remove edge from source node '' to 'sibNode'.
if (inEdges.count(sibId) > 0) {
SmallVector<Edge, 2> oldInEdges = inEdges[sibId];
for (auto &inEdge : oldInEdges) {
addEdge(, dstId, inEdge.value);
removeEdge(, sibId, inEdge.value);
// For each edge in 'outEdges[sibId]' to node 'id'
// *) Add new edge from 'dstId' to ''.
// *) Remove edge from 'sibId' to ''.
if (outEdges.count(sibId) > 0) {
SmallVector<Edge, 2> oldOutEdges = outEdges[sibId];
for (auto &outEdge : oldOutEdges) {
addEdge(dstId,, outEdge.value);
removeEdge(sibId,, outEdge.value);
// Adds ops in 'loads' and 'stores' to node at 'id'.
void addToNode(unsigned id, const SmallVectorImpl<Operation *> &loads,
const SmallVectorImpl<Operation *> &stores) {
Node *node = getNode(id);
for (auto *loadOpInst : loads)
for (auto *storeOpInst : stores)
void clearNodeLoadAndStores(unsigned id) {
Node *node = getNode(id);
// Calls 'callback' for each input edge incident to node 'id' which carries a
// memref dependence.
void forEachMemRefInputEdge(unsigned id,
const std::function<void(Edge)> &callback) {
if (inEdges.count(id) > 0)
forEachMemRefEdge(inEdges[id], callback);
// Calls 'callback' for each output edge from node 'id' which carries a
// memref dependence.
void forEachMemRefOutputEdge(unsigned id,
const std::function<void(Edge)> &callback) {
if (outEdges.count(id) > 0)
forEachMemRefEdge(outEdges[id], callback);
// Calls 'callback' for each edge in 'edges' which carries a memref
// dependence.
void forEachMemRefEdge(ArrayRef<Edge> edges,
const std::function<void(Edge)> &callback) {
for (const auto &edge : edges) {
// Skip if 'edge' is not a memref dependence edge.
if (!edge.value.getType().isa<MemRefType>())
assert(nodes.count( > 0);
// Skip if '' is not a loop nest.
if (!isa<AffineForOp>(getNode(>op))
// Visit current input edge 'edge'.
void print(raw_ostream &os) const {
os << "\nMemRefDependenceGraph\n";
os << "\nNodes:\n";
for (const auto &idAndNode : nodes) {
os << "Node: " << idAndNode.first << "\n";
auto it = inEdges.find(idAndNode.first);
if (it != inEdges.end()) {
for (const auto &e : it->second)
os << " InEdge: " << << " " << e.value << "\n";
it = outEdges.find(idAndNode.first);
if (it != outEdges.end()) {
for (const auto &e : it->second)
os << " OutEdge: " << << " " << e.value << "\n";
void dump() const { print(llvm::errs()); }
/// Returns true if node 'srcId' can be removed after fusing it with node
/// 'dstId'. The node can be removed if any of the following conditions are met:
/// 1. 'srcId' has no output dependences after fusion and no escaping memrefs.
/// 2. 'srcId' has no output dependences after fusion, has escaping memrefs
/// and the fusion slice is maximal.
/// 3. 'srcId' has output dependences after fusion, the fusion slice is
/// maximal and the fusion insertion point dominates all the dependences.
static bool canRemoveSrcNodeAfterFusion(
unsigned srcId, unsigned dstId, const ComputationSliceState &fusionSlice,
Operation *fusedLoopInsPoint, const DenseSet<Value> &escapingMemRefs,
MemRefDependenceGraph *mdg) {
Operation *dstNodeOp = mdg->getNode(dstId)->op;
bool hasOutDepsAfterFusion = false;
for (auto &outEdge : mdg->outEdges[srcId]) {
Operation *depNodeOp = mdg->getNode(>op;
// Skip dependence with dstOp since it will be removed after fusion.
if (depNodeOp == dstNodeOp)
// Only fusion within the same block is supported. Use domination analysis
// when needed.
if (depNodeOp->getBlock() != dstNodeOp->getBlock())
return false;
// Check if the insertion point of the fused loop dominates the dependence.
// Otherwise, the src loop can't be removed.
if (fusedLoopInsPoint != depNodeOp &&
!fusedLoopInsPoint->isBeforeInBlock(depNodeOp)) {
LLVM_DEBUG(llvm::dbgs() << "Src loop can't be removed: dst loop doesn't "
"dominate dependence\n");
return false;
hasOutDepsAfterFusion = true;
// If src loop has dependences after fusion or it writes to an live-out or
// escaping memref, we can only remove it if the fusion slice is maximal so
// that all the dependences are preserved.
if (hasOutDepsAfterFusion || !escapingMemRefs.empty()) {
Optional<bool> isMaximal = fusionSlice.isMaximal();
if (!isMaximal.hasValue()) {
LLVM_DEBUG(llvm::dbgs() << "Src loop can't be removed: can't determine "
"if fusion is maximal\n");
return false;
if (!isMaximal.getValue()) {
<< "Src loop can't be removed: fusion is not maximal\n");
return false;
return true;
/// Returns in 'srcIdCandidates' the producer fusion candidates for consumer
/// 'dstId'. Candidates are sorted by node id order. This order corresponds to
/// the program order when the 'mdg' is created. However, program order is not
/// guaranteed and must not be required by the client. Program order won't be
/// held if the 'mdg' is reused from a previous fusion step or if the node
/// creation order changes in the future to support more advance cases.
// TODO: Move this to a loop fusion utility once 'mdg' is also moved.
static void getProducerCandidates(unsigned dstId, MemRefDependenceGraph *mdg,
SmallVectorImpl<unsigned> &srcIdCandidates) {
// Skip if no input edges along which to fuse.
if (mdg->inEdges.count(dstId) == 0)
// Gather memrefs from loads in 'dstId'.
auto *dstNode = mdg->getNode(dstId);
DenseSet<Value> consumedMemrefs;
for (Operation *load : dstNode->loads)
// Traverse 'dstId' incoming edges and gather the nodes that contain a store
// to one of the consumed memrefs.
for (auto &srcEdge : mdg->inEdges[dstId]) {
auto *srcNode = mdg->getNode(;
// Skip if 'srcNode' is not a loop nest.
if (!isa<AffineForOp>(srcNode->op))
if (any_of(srcNode->stores, [&](Operation *op) {
auto storeOp = cast<AffineWriteOpInterface>(op);
return consumedMemrefs.count(storeOp.getMemRef()) > 0;
std::sort(srcIdCandidates.begin(), srcIdCandidates.end());
std::unique(srcIdCandidates.begin(), srcIdCandidates.end()),
/// Returns in 'producerConsumerMemrefs' the memrefs involved in a
/// producer-consumer dependence between 'srcId' and 'dstId'.
static void
gatherProducerConsumerMemrefs(unsigned srcId, unsigned dstId,
MemRefDependenceGraph *mdg,
DenseSet<Value> &producerConsumerMemrefs) {
auto *dstNode = mdg->getNode(dstId);
auto *srcNode = mdg->getNode(srcId);
gatherProducerConsumerMemrefs(srcNode->stores, dstNode->loads,
/// Returns in 'escapingMemRefs' the memrefs from affine store ops in node 'id'
/// that escape the function. A memref escapes the function if either:
/// 1. It's a function argument, or
/// 2. It's used by a non-affine op (e.g., std load/store, std call, etc.)
void gatherEscapingMemrefs(unsigned id, MemRefDependenceGraph *mdg,
DenseSet<Value> &escapingMemRefs) {
auto *node = mdg->getNode(id);
for (auto *storeOpInst : node->stores) {
auto memref = cast<AffineWriteOpInterface>(storeOpInst).getMemRef();
if (escapingMemRefs.count(memref))
// Check if 'memref' escapes because it's a block argument.
if (memref.isa<BlockArgument>()) {
// Check if 'memref' escapes through a non-affine op (e.g., std load/store,
// call op, etc.).
for (Operation *user : memref.getUsers())
if (!isa<AffineMapAccessInterface>(*user))
} // end anonymous namespace
// Initializes the data dependence graph by walking operations in 'f'.
// Assigns each node in the graph a node id based on program order in 'f'.
// TODO: Add support for taking a Block arg to construct the
// dependence graph at a different depth.
bool MemRefDependenceGraph::init(FuncOp f) {
LLVM_DEBUG(llvm::dbgs() << "--- Initializing MDG ---\n");
DenseMap<Value, SetVector<unsigned>> memrefAccesses;
// TODO: support multi-block functions.
if (!llvm::hasSingleElement(f))
return false;
DenseMap<Operation *, unsigned> forToNodeMap;
for (auto &op : f.front()) {
if (auto forOp = dyn_cast<AffineForOp>(op)) {
// Create graph node 'id' to represent top-level 'forOp' and record
// all loads and store accesses it contains.
LoopNestStateCollector collector;
// Return false if a region holding op other than 'affine.for' and
// 'affine.if' was found (not currently supported).
if (collector.hasNonAffineRegionOp)
return false;
Node node(nextNodeId++, &op);
for (auto *opInst : collector.loadOpInsts) {
auto memref = cast<AffineReadOpInterface>(opInst).getMemRef();
for (auto *opInst : collector.storeOpInsts) {
auto memref = cast<AffineWriteOpInterface>(opInst).getMemRef();
forToNodeMap[&op] =;
nodes.insert({, node});
} else if (auto loadOp = dyn_cast<AffineReadOpInterface>(op)) {
// Create graph node for top-level load op.
Node node(nextNodeId++, &op);
auto memref = cast<AffineReadOpInterface>(op).getMemRef();
nodes.insert({, node});
} else if (auto storeOp = dyn_cast<AffineWriteOpInterface>(op)) {
// Create graph node for top-level store op.
Node node(nextNodeId++, &op);
auto memref = cast<AffineWriteOpInterface>(op).getMemRef();
nodes.insert({, node});
} else if (op.getNumRegions() != 0) {
// Return false if another region is found (not currently supported).
return false;
} else if (op.getNumResults() > 0 && !op.use_empty()) {
// Create graph node for top-level producer of SSA values, which
// could be used by loop nest nodes.
Node node(nextNodeId++, &op);
nodes.insert({, node});
} else if (isa<CallOpInterface>(op)) {
// Create graph node for top-level Call Op that takes any argument of
// memref type. Call Op that returns one or more memref type results
// is already taken care of, by the previous conditions.
if (llvm::any_of(op.getOperandTypes(),
[&](Type t) { return t.isa<MemRefType>(); })) {
Node node(nextNodeId++, &op);
nodes.insert({, node});
} else if (auto effectInterface = dyn_cast<MemoryEffectOpInterface>(op)) {
// Create graph node for top-level op, which could have a memory write
// side effect.
SmallVector<MemoryEffects::EffectInstance, 1> effects;
if (llvm::any_of(effects, [](const MemoryEffects::EffectInstance &it) {
return isa<MemoryEffects::Write, MemoryEffects::Free>(
})) {
Node node(nextNodeId++, &op);
nodes.insert({, node});
for (auto &idAndNode : nodes) {
LLVM_DEBUG(llvm::dbgs() << "Create node " << idAndNode.first << " for:\n"
<< *(idAndNode.second.op) << "\n");
// Add dependence edges between nodes which produce SSA values and their
// users. Load ops can be considered as the ones producing SSA values.
for (auto &idAndNode : nodes) {
const Node &node = idAndNode.second;
// Stores don't define SSA values, skip them.
if (!node.stores.empty())
auto *opInst = node.op;
for (auto value : opInst->getResults()) {
for (auto *user : value.getUsers()) {
SmallVector<AffineForOp, 4> loops;
getLoopIVs(*user, &loops);
if (loops.empty())
assert(forToNodeMap.count(loops[0].getOperation()) > 0);
unsigned userLoopNestId = forToNodeMap[loops[0].getOperation()];
addEdge(, userLoopNestId, value);
// Walk memref access lists and add graph edges between dependent nodes.
for (auto &memrefAndList : memrefAccesses) {
unsigned n = memrefAndList.second.size();
for (unsigned i = 0; i < n; ++i) {
unsigned srcId = memrefAndList.second[i];
bool srcHasStore =
getNode(srcId)->getStoreOpCount(memrefAndList.first) > 0;
for (unsigned j = i + 1; j < n; ++j) {
unsigned dstId = memrefAndList.second[j];
bool dstHasStore =
getNode(dstId)->getStoreOpCount(memrefAndList.first) > 0;
if (srcHasStore || dstHasStore)
addEdge(srcId, dstId, memrefAndList.first);
return true;
// Sinks all sequential loops to the innermost levels (while preserving
// relative order among them) and moves all parallel loops to the
// outermost (while again preserving relative order among them).
// This can increase the loop depth at which we can fuse a slice, since we are
// pushing loop carried dependence to a greater depth in the loop nest.
static void sinkSequentialLoops(MemRefDependenceGraph::Node *node) {
AffineForOp newRootForOp = sinkSequentialLoops(cast<AffineForOp>(node->op));
node->op = newRootForOp.getOperation();
// TODO: improve/complete this when we have target data.
static unsigned getMemRefEltSizeInBytes(MemRefType memRefType) {
auto elementType = memRefType.getElementType();
unsigned sizeInBits;
if (elementType.isIntOrFloat()) {
sizeInBits = elementType.getIntOrFloatBitWidth();
} else {
auto vectorType = elementType.cast<VectorType>();
sizeInBits =
vectorType.getElementTypeBitWidth() * vectorType.getNumElements();
return llvm::divideCeil(sizeInBits, 8);
// Creates and returns a private (single-user) memref for fused loop rooted
// at 'forOp', with (potentially reduced) memref size based on the
// MemRefRegion written to by 'srcStoreOpInst' at depth 'dstLoopDepth'.
// TODO: consider refactoring the common code from generateDma and
// this one.
static Value createPrivateMemRef(AffineForOp forOp, Operation *srcStoreOpInst,
unsigned dstLoopDepth,
Optional<unsigned> fastMemorySpace,
uint64_t localBufSizeThreshold) {
auto *forInst = forOp.getOperation();
// Create builder to insert alloc op just before 'forOp'.
OpBuilder b(forInst);
// Builder to create constants at the top level.
OpBuilder top(forInst->getParentOfType<FuncOp>().getBody());
// Create new memref type based on slice bounds.
auto oldMemRef = cast<AffineWriteOpInterface>(srcStoreOpInst).getMemRef();
auto oldMemRefType = oldMemRef.getType().cast<MemRefType>();
unsigned rank = oldMemRefType.getRank();
// Compute MemRefRegion for 'srcStoreOpInst' at depth 'dstLoopDepth'.
MemRefRegion region(srcStoreOpInst->getLoc());
bool validRegion = succeeded(region.compute(srcStoreOpInst, dstLoopDepth));
assert(validRegion && "unexpected memref region failure");
SmallVector<int64_t, 4> newShape;
std::vector<SmallVector<int64_t, 4>> lbs;
SmallVector<int64_t, 8> lbDivisors;
// Query 'region' for 'newShape' and lower bounds of MemRefRegion accessed
// by 'srcStoreOpInst' at depth 'dstLoopDepth'.
Optional<int64_t> numElements =
region.getConstantBoundingSizeAndShape(&newShape, &lbs, &lbDivisors);
assert(numElements.hasValue() &&
"non-constant number of elts in local buffer");
const FlatAffineValueConstraints *cst = region.getConstraints();
// 'outerIVs' holds the values that this memory region is symbolic/parametric
// on; this would correspond to loop IVs surrounding the level at which the
// slice is being materialized.
SmallVector<Value, 8> outerIVs;
cst->getValues(rank, cst->getNumIds(), &outerIVs);
// Build 'rank' AffineExprs from MemRefRegion 'lbs'
SmallVector<AffineExpr, 4> offsets;
for (unsigned d = 0; d < rank; ++d) {
assert(lbs[d].size() == cst->getNumCols() - rank && "incorrect bound size");
AffineExpr offset = top.getAffineConstantExpr(0);
for (unsigned j = 0, e = cst->getNumCols() - rank - 1; j < e; j++) {
offset = offset + lbs[d][j] * top.getAffineDimExpr(j);
assert(lbDivisors[d] > 0);
offset =
(offset + lbs[d][cst->getNumCols() - 1 - rank]).floorDiv(lbDivisors[d]);
// Create 'newMemRefType' using 'newShape' from MemRefRegion accessed
// by 'srcStoreOpInst'.
uint64_t bufSize =
getMemRefEltSizeInBytes(oldMemRefType) * numElements.getValue();
unsigned newMemSpace;
if (bufSize <= localBufSizeThreshold && fastMemorySpace.hasValue()) {
newMemSpace = fastMemorySpace.getValue();
} else {
newMemSpace = oldMemRefType.getMemorySpaceAsInt();
auto newMemRefType = MemRefType::get(newShape, oldMemRefType.getElementType(),
{}, newMemSpace);
// Create new private memref for fused loop 'forOp'. 'newShape' is always
// a constant shape.
// TODO: Create/move alloc ops for private memrefs closer to their
// consumer loop nests to reduce their live range. Currently they are added
// at the beginning of the function, because loop nests can be reordered
// during the fusion pass.
Value newMemRef = top.create<memref::AllocOp>(forOp.getLoc(), newMemRefType);
// Build an AffineMap to remap access functions based on lower bound offsets.
SmallVector<AffineExpr, 4> remapExprs;
for (unsigned i = 0; i < rank; i++) {
auto dimExpr = b.getAffineDimExpr(outerIVs.size() + i);
auto remapExpr =
simplifyAffineExpr(dimExpr - offsets[i], outerIVs.size() + rank, 0);
auto indexRemap =
AffineMap::get(outerIVs.size() + rank, 0, remapExprs, forOp.getContext());
// Replace all users of 'oldMemRef' with 'newMemRef'.
LogicalResult res =
replaceAllMemRefUsesWith(oldMemRef, newMemRef, {}, indexRemap,
assert(succeeded(res) &&
"replaceAllMemrefUsesWith should always succeed here");
return newMemRef;
/// Walking from node 'srcId' to node 'dstId' (exclusive of 'srcId' and
/// 'dstId'), if there is any non-affine operation accessing 'memref', return
/// true. Otherwise, return false.
static bool hasNonAffineUsersOnThePath(unsigned srcId, unsigned dstId,
Value memref,
MemRefDependenceGraph *mdg) {
auto *srcNode = mdg->getNode(srcId);
auto *dstNode = mdg->getNode(dstId);
Value::user_range users = memref.getUsers();
// For each MemRefDependenceGraph's node that is between 'srcNode' and
// 'dstNode' (exclusive of 'srcNodes' and 'dstNode'), check whether any
// non-affine operation in the node accesses the 'memref'.
for (auto &idAndNode : mdg->nodes) {
Operation *op = idAndNode.second.op;
// Take care of operations between 'srcNode' and 'dstNode'.
if (srcNode->op->isBeforeInBlock(op) && op->isBeforeInBlock(dstNode->op)) {
// Walk inside the operation to find any use of the memref.
// Interrupt the walk if found.
auto walkResult = op->walk([&](Operation *user) {
// Skip affine ops.
if (isa<AffineMapAccessInterface>(*user))
return WalkResult::advance();
// Find a non-affine op that uses the memref.
if (llvm::is_contained(users, user))
return WalkResult::interrupt();
return WalkResult::advance();
if (walkResult.wasInterrupted())
return true;
return false;
/// Check whether a memref value in node 'srcId' has a non-affine that
/// is between node 'srcId' and node 'dstId' (exclusive of 'srcNode' and
/// 'dstNode').
static bool hasNonAffineUsersOnThePath(unsigned srcId, unsigned dstId,
MemRefDependenceGraph *mdg) {
// Collect memref values in node 'srcId'.
auto *srcNode = mdg->getNode(srcId);
llvm::SmallDenseSet<Value, 2> memRefValues;
srcNode->op->walk([&](Operation *op) {
// Skip affine ops.
if (isa<AffineForOp>(op))
return WalkResult::advance();
for (Value v : op->getOperands())
// Collect memref values only.
if (v.getType().isa<MemRefType>())
return WalkResult::advance();
// Looking for users between node 'srcId' and node 'dstId'.
for (Value memref : memRefValues)
if (hasNonAffineUsersOnThePath(srcId, dstId, memref, mdg))
return true;
return false;
// Checks the profitability of fusing a backwards slice of the loop nest
// surrounding 'srcOpInst' into the loop nest surrounding 'dstLoadOpInsts'.
// The argument 'srcStoreOpInst' is used to calculate the storage reduction on
// the memref being produced and consumed, which is an input to the cost model.
// For producer-consumer fusion, 'srcStoreOpInst' will be the same as
// 'srcOpInst', as we are slicing w.r.t to that producer. For input-reuse
// fusion, 'srcOpInst' will be the src loop nest LoadOp which reads from the
// same memref as dst loop nest load ops, and 'srcStoreOpInst' will be the
// unique store op in the src node, which will be used to check that the write
// region is the same after input-reuse fusion. Computation slices are provided
// in 'depthSliceUnions' for each legal fusion depth. The maximal depth at which
// fusion is legal is provided in 'maxLegalFusionDepth'. Returns true if it is
// profitable to fuse the candidate loop nests. Returns false otherwise.
// `dstLoopDepth` is set to the most profitable depth at which to materialize
// the source loop nest slice.
// The profitability model executes the following steps:
// *) Computes the backward computation slice at 'srcOpInst'. This
// computation slice of the loop nest surrounding 'srcOpInst' is
// represented by modified src loop bounds in 'sliceState', which are
// functions of loop IVs in the loop nest surrounding 'srcOpInst'.
// *) Computes the cost of unfused src/dst loop nests (currently the cost of a
// loop nest is the total number of dynamic operation instances in the loop
// nest).
// *) Computes the cost of fusing a slice of the src loop nest into the dst
// loop nest at various values of dst loop depth, attempting to fuse
// the largest computation slice at the maximal dst loop depth (closest to
// the load) to minimize reuse distance and potentially enable subsequent
// load/store forwarding.
// NOTE: 'dstLoopDepth' refers to the loop depth within the destination loop
// nest, at which the src computation slice is inserted/fused.
// NOTE: We attempt to maximize the dst loop depth, but there are cases
// where a particular setting for 'dstLoopNest' might fuse an unsliced
// loop (within the src computation slice) at a depth which results in
// excessive recomputation (see unit tests for examples).
// *) Compares the total cost of the unfused loop nests to the min cost fused
// loop nest computed in the previous step, and returns true if the latter
// is lower.
// TODO: Extend profitability analysis to support scenarios with multiple
// stores.
static bool isFusionProfitable(Operation *srcOpInst, Operation *srcStoreOpInst,
AffineForOp dstForOp,
ArrayRef<ComputationSliceState> depthSliceUnions,
unsigned maxLegalFusionDepth,
unsigned *dstLoopDepth,
double computeToleranceThreshold) {
llvm::dbgs() << "Checking whether fusion is profitable between src op:\n";
llvm::dbgs() << ' ' << *srcOpInst << " and destination loop:\n";
llvm::dbgs() << dstForOp << "\n";
if (maxLegalFusionDepth == 0) {
LLVM_DEBUG(llvm::dbgs() << "Can't fuse: maxLegalFusionDepth == 0 .\n");
return false;
// Compute cost of sliced and unsliced src loop nest.
SmallVector<AffineForOp, 4> srcLoopIVs;
getLoopIVs(*srcOpInst, &srcLoopIVs);
// Walk src loop nest and collect stats.
LoopNestStats srcLoopNestStats;
if (!getLoopNestStats(srcLoopIVs[0], &srcLoopNestStats))
return false;
// Compute cost of dst loop nest.
LoopNestStats dstLoopNestStats;
if (!getLoopNestStats(dstForOp, &dstLoopNestStats))
return false;
// Search for min cost value for 'dstLoopDepth'. At each value of
// 'dstLoopDepth' from 'maxLegalLoopDepth' to '1', compute computation slice
// bounds between 'srcOpInst' and each op in 'dstOpinsts' (taking the union
// of these bounds). Next the union slice bounds are used to calculate
// the cost of the slice and the cost of the slice inserted into the dst
// loop nest at 'dstLoopDepth'.
uint64_t minFusedLoopNestComputeCost = std::numeric_limits<uint64_t>::max();
double maxStorageReduction = 0.0;
Optional<uint64_t> sliceMemEstimate = None;
// The best loop depth at which to materialize the slice.
Optional<unsigned> bestDstLoopDepth = None;
// Compute op instance count for the src loop nest without iteration slicing.
uint64_t srcLoopNestCost = getComputeCost(srcLoopIVs[0], srcLoopNestStats);
// Compute src loop nest write region size.
MemRefRegion srcWriteRegion(srcStoreOpInst->getLoc());
if (failed(srcWriteRegion.compute(srcStoreOpInst, /*loopDepth=*/0))) {
<< "Unable to compute MemRefRegion for source operation\n.");
return false;
Optional<int64_t> maybeSrcWriteRegionSizeBytes =
if (!maybeSrcWriteRegionSizeBytes.hasValue())
return false;
int64_t srcWriteRegionSizeBytes = maybeSrcWriteRegionSizeBytes.getValue();
// Compute op instance count for the src loop nest.
uint64_t dstLoopNestCost = getComputeCost(dstForOp, dstLoopNestStats);
// Evaluate all depth choices for materializing the slice in the destination
// loop nest.
for (unsigned i = maxLegalFusionDepth; i >= 1; --i) {
const ComputationSliceState &slice = depthSliceUnions[i - 1];
// Skip slice union if it wasn't computed for this depth.
if (slice.isEmpty())
int64_t fusedLoopNestComputeCost;
if (!getFusionComputeCost(srcLoopIVs[0], srcLoopNestStats, dstForOp,
dstLoopNestStats, slice,
&fusedLoopNestComputeCost)) {
LLVM_DEBUG(llvm::dbgs() << "Unable to compute fusion compute cost.\n.");
double additionalComputeFraction =
fusedLoopNestComputeCost /
(static_cast<double>(srcLoopNestCost) + dstLoopNestCost) -
// Determine what the slice write MemRefRegion would be, if the src loop
// nest slice 'slice' were to be inserted into the dst loop nest at loop
// depth 'i'.
MemRefRegion sliceWriteRegion(srcStoreOpInst->getLoc());
if (failed(sliceWriteRegion.compute(srcStoreOpInst, /*loopDepth=*/0,
&slice))) {
<< "Failed to compute slice write region at loopDepth: " << i
<< "\n");
Optional<int64_t> maybeSliceWriteRegionSizeBytes =
if (!maybeSliceWriteRegionSizeBytes.hasValue() ||
maybeSliceWriteRegionSizeBytes.getValue() == 0) {
<< "Failed to get slice write region size at loopDepth: " << i
<< "\n");
int64_t sliceWriteRegionSizeBytes =
// If we are fusing for reuse, check that write regions remain the same.
// TODO: Write region check should check sizes and offsets in
// each dimension, so that we are sure they are covering the same memref
// region. Also, move this out to a isMemRefRegionSuperSet helper function.
if (srcOpInst != srcStoreOpInst &&
sliceWriteRegionSizeBytes != srcWriteRegionSizeBytes)
double storageReduction = static_cast<double>(srcWriteRegionSizeBytes) /
std::stringstream msg;
msg << " evaluating fusion profitability at depth : " << i << "\n"
<< std::fixed << std::setprecision(2)
<< " additional compute fraction: "
<< 100.0 * additionalComputeFraction << "%\n"
<< " storage reduction factor: " << storageReduction << "x\n"
<< " fused nest cost: " << fusedLoopNestComputeCost << "\n"
<< " src write region size: " << srcWriteRegionSizeBytes << "\n"
<< " slice write region size: " << sliceWriteRegionSizeBytes
<< "\n";
llvm::dbgs() << msg.str();
// TODO: This is a placeholder cost model.
// Among all choices that add an acceptable amount of redundant computation
// (as per computeToleranceThreshold), we will simply pick the one that
// reduces the intermediary size the most.
if ((storageReduction > maxStorageReduction) &&
(additionalComputeFraction < computeToleranceThreshold)) {
maxStorageReduction = storageReduction;
bestDstLoopDepth = i;
minFusedLoopNestComputeCost = fusedLoopNestComputeCost;
sliceMemEstimate = sliceWriteRegionSizeBytes;
// A simple cost model: fuse if it reduces the memory footprint.
if (!bestDstLoopDepth.hasValue()) {
<< "All fusion choices involve more than the threshold amount of "
"redundant computation; NOT fusing.\n");
return false;
if (!bestDstLoopDepth.hasValue()) {
LLVM_DEBUG(llvm::dbgs() << "no fusion depth could be evaluated.\n");
return false;
// Set dstLoopDepth based on best values from search.
*dstLoopDepth = bestDstLoopDepth.getValue();
llvm::dbgs() << " LoopFusion fusion stats:"
<< "\n best loop depth: " << bestDstLoopDepth
<< "\n src loop nest compute cost: " << srcLoopNestCost
<< "\n dst loop nest compute cost: " << dstLoopNestCost
<< "\n fused loop nest compute cost: "
<< minFusedLoopNestComputeCost << "\n");
auto dstMemSize = getMemoryFootprintBytes(dstForOp);
auto srcMemSize = getMemoryFootprintBytes(srcLoopIVs[0]);
Optional<double> storageReduction = None;
if (!dstMemSize.hasValue() || !srcMemSize.hasValue()) {
<< " fusion memory benefit cannot be evaluated; NOT fusing.\n");
return false;
auto srcMemSizeVal = srcMemSize.getValue();
auto dstMemSizeVal = dstMemSize.getValue();
assert(sliceMemEstimate.hasValue() && "expected value");
auto fusedMem = dstMemSizeVal + sliceMemEstimate.getValue();
LLVM_DEBUG(llvm::dbgs() << " src mem: " << srcMemSizeVal << "\n"
<< " dst mem: " << dstMemSizeVal << "\n"
<< " fused mem: " << fusedMem << "\n"
<< " slice mem: " << sliceMemEstimate << "\n");
if (static_cast<long>(fusedMem) > srcMemSizeVal + dstMemSizeVal) {
LLVM_DEBUG(llvm::dbgs() << "Fusion is not profitable; NOT fusing.\n");
return false;
storageReduction =
100.0 *
(1.0 - fusedMem / (static_cast<double>(srcMemSizeVal) + dstMemSizeVal));
double additionalComputeFraction =
100.0 * (minFusedLoopNestComputeCost /
(static_cast<double>(srcLoopNestCost) + dstLoopNestCost) -
std::stringstream msg;
msg << " fusion is most profitable at depth " << *dstLoopDepth << " with "
<< std::setprecision(2) << additionalComputeFraction
<< "% redundant computation and a ";
msg << (storageReduction.hasValue()
? std::to_string(storageReduction.getValue())
: "<unknown>");
msg << "% storage reduction.\n";
llvm::dbgs() << msg.str();
return true;
namespace {
// GreedyFusion greedily fuses loop nests which have a producer/consumer or
// input-reuse relationship on a memref, with the goal of improving locality.
// The steps of the producer-consumer fusion algorithm are as follows:
// *) A worklist is initialized with node ids from the dependence graph.
// *) For each node id in the worklist:
// *) Pop an AffineForOp of the worklist. This 'dstAffineForOp' will be a
// candidate destination AffineForOp into which fusion will be attempted.
// *) Add each LoadOp currently in 'dstAffineForOp' into list 'dstLoadOps'.
// *) For each LoadOp in 'dstLoadOps' do:
// *) Look up dependent loop nests which have a single store op to the same
// memref.
// *) Check if dependences would be violated by the fusion.
// *) Get a computation slice of 'srcLoopNest', which adjusts its loop
// bounds to be functions of 'dstLoopNest' IVs and symbols.
// *) Fuse the 'srcLoopNest' computation slice into the 'dstLoopNest',
// at a loop depth determined by the cost model in 'isFusionProfitable'.
// *) Add the newly fused load/store operations to the state,
// and also add newly fused load ops to 'dstLoopOps' to be considered
// as fusion dst load ops in another iteration.
// *) Remove old src loop nest and its associated state.
// The steps of the input-reuse fusion algorithm are as follows:
// *) Initialize 'worklist' with node ids from the dependence graph.
// *) For each 'dstNode' in the worklist:
// *) Find a candidate sibling node 'sibNode' to fuse with 'dstNode' which
// loads from the same memref, but which has no dependence paths to/from.
// *) Get a computation slice of 'sibLoopNest', which adjusts its loop
// bounds to be functions of 'dstLoopNest' IVs and symbols.
// *) Fuse the 'sibLoopNest' computation slice into the 'dstLoopNest',
// at a loop depth determined by the cost model in 'isFusionProfitable'.
// This function also checks that the memref write region of 'sibLoopNest',
// is preserved in the fused loop nest.
// *) Update graph state to reflect the fusion of 'sibNode' into 'dstNode'.
// Given a graph where top-level operations are vertices in the set 'V' and
// edges in the set 'E' are dependences between vertices, this algorithm
// takes O(V) time for initialization, and has runtime O(V + E).
// This greedy algorithm is not 'maximal' due to the current restriction of
// fusing along single producer consumer edges, but there is a TODO: to fix
// this.
// TODO: Experiment with other fusion policies.
struct GreedyFusion {
// The data dependence graph to traverse during fusion.
MemRefDependenceGraph *mdg;
// Worklist of graph nodes visited during the fusion pass.
SmallVector<unsigned, 8> worklist;
// Parameter for local buffer size threshold.
unsigned localBufSizeThreshold;
// Parameter for fast memory space.
Optional<unsigned> fastMemorySpace;
// If true, ignore any additional (redundant) computation tolerance threshold
// that would have prevented fusion.
bool maximalFusion;
// The amount of additional computation that is tolerated while fusing
// pair-wise as a fraction of the total computation.
double computeToleranceThreshold;
using Node = MemRefDependenceGraph::Node;
GreedyFusion(MemRefDependenceGraph *mdg, unsigned localBufSizeThreshold,
Optional<unsigned> fastMemorySpace, bool maximalFusion,
double computeToleranceThreshold)
: mdg(mdg), localBufSizeThreshold(localBufSizeThreshold),
fastMemorySpace(fastMemorySpace), maximalFusion(maximalFusion),
computeToleranceThreshold(computeToleranceThreshold) {}
/// Initializes 'worklist' with nodes from 'mdg'.
void init() {
// TODO: Add a priority queue for prioritizing nodes by different
// metrics (e.g. arithmetic intensity/flops-to-bytes ratio).
for (auto &idAndNode : mdg->nodes) {
const Node &node = idAndNode.second;
/// Run only sibling fusion on the `mdg`.
void runSiblingFusionOnly() {
/// Run only producer/consumer fusion on the `mdg`.
void runProducerConsumerFusionOnly() {
// Run the GreedyFusion pass.
// *) First pass through the nodes fuses single-use producer nodes into their
// unique consumer.
// *) Second pass fuses sibling nodes which share no dependence edges.
// *) Third pass fuses any remaining producer nodes into their users.
void runGreedyFusion() {
// TODO: Run this repeatedly until a fixed-point is reached.
void fuseProducerConsumerNodes(unsigned maxSrcUserCount) {
LLVM_DEBUG(llvm::dbgs() << "--- Producer/Consumer Fusion ---\n");
while (!worklist.empty()) {
unsigned dstId = worklist.back();
// Skip if this node was removed (fused into another node).
if (mdg->nodes.count(dstId) == 0)
// Get 'dstNode' into which to attempt fusion.
auto *dstNode = mdg->getNode(dstId);
// Skip if 'dstNode' is not a loop nest.
if (!isa<AffineForOp>(dstNode->op))
// Skip if 'dstNode' is a loop nest returning values.
// TODO: support loop nests that return values.
if (dstNode->op->getNumResults() > 0)
LLVM_DEBUG(llvm::dbgs() << "Evaluating dst loop " << dstId << "\n");
// Sink sequential loops in 'dstNode' (and thus raise parallel loops)
// while preserving relative order. This can increase the maximum loop
// depth at which we can fuse a slice of a producer loop nest into a
// consumer loop nest.
auto dstAffineForOp = cast<AffineForOp>(dstNode->op);
// Try to fuse 'dstNode' with candidate producer loops until a fixed point
// is reached. Fusing two loops may expose new fusion opportunities.
bool dstNodeChanged;
do {
// Gather src loop candidates for 'dstNode' and visit them in "quasi"
// reverse program order to minimize the number of iterations needed to
// reach the fixed point. Note that this is a best effort approach since
// 'getProducerCandidates' does not always guarantee that program order
// in 'srcIdCandidates'.
dstNodeChanged = false;
SmallVector<unsigned, 16> srcIdCandidates;
getProducerCandidates(dstId, mdg, srcIdCandidates);
for (unsigned srcId : llvm::reverse(srcIdCandidates)) {
// Get 'srcNode' from which to attempt fusion into 'dstNode'.
auto *srcNode = mdg->getNode(srcId);
auto srcAffineForOp = cast<AffineForOp>(srcNode->op);
LLVM_DEBUG(llvm::dbgs() << "Evaluating src loop " << srcId
<< " for dst loop " << dstId << "\n");
// Skip if 'srcNode' is a loop nest returning values.
// TODO: support loop nests that return values.
if (isa<AffineForOp>(srcNode->op) && srcNode->op->getNumResults() > 0)
DenseSet<Value> producerConsumerMemrefs;
gatherProducerConsumerMemrefs(srcId, dstId, mdg,
// Skip if 'srcNode' out edge count on any memref is greater than
// 'maxSrcUserCount'.
if (any_of(producerConsumerMemrefs, [&](Value memref) {
return mdg->getOutEdgeCount(srcNode->id, memref) >
// Gather memrefs in 'srcNode' that are written and escape to the
// function (e.g., memref function arguments, returned memrefs,
// memrefs passed to function calls, etc.).
DenseSet<Value> srcEscapingMemRefs;
gatherEscapingMemrefs(srcNode->id, mdg, srcEscapingMemRefs);
// Skip if there are non-affine operations in between the 'srcNode'
// and 'dstNode' using their memrefs. If so, we wouldn't be able to
// compute a legal insertion point for now. 'srcNode' and 'dstNode'
// memrefs with non-affine operation users would be considered
// escaping memrefs so we can limit this check to only scenarios with
// escaping memrefs.
if (!srcEscapingMemRefs.empty() &&
hasNonAffineUsersOnThePath(srcId, dstId, mdg)) {
<< "Can't fuse: non-affine users in between the loops\n.");
// Compute an operation list insertion point for the fused loop
// nest which preserves dependences.
Operation *fusedLoopInsPoint =
mdg->getFusedLoopNestInsertionPoint(srcNode->id, dstNode->id);
if (fusedLoopInsPoint == nullptr)
// Compute the innermost common loop depth for dstNode
// producer-consumer loads/stores.
SmallVector<Operation *, 2> dstMemrefOps;
for (Operation *op : dstNode->loads)
if (producerConsumerMemrefs.count(
cast<AffineReadOpInterface>(op).getMemRef()) > 0)
for (Operation *op : dstNode->stores)
if (producerConsumerMemrefs.count(
unsigned dstLoopDepthTest = getInnermostCommonLoopDepth(dstMemrefOps);
// Check the feasibility of fusing src loop nest into dst loop nest
// at loop depths in range [1, dstLoopDepthTest].
unsigned maxLegalFusionDepth = 0;
SmallVector<ComputationSliceState, 8> depthSliceUnions;
FusionStrategy strategy(FusionStrategy::ProducerConsumer);
for (unsigned i = 1; i <= dstLoopDepthTest; ++i) {
FusionResult result = mlir::canFuseLoops(
srcAffineForOp, dstAffineForOp,
/*dstLoopDepth=*/i, &depthSliceUnions[i - 1], strategy);
if (result.value == FusionResult::Success)
maxLegalFusionDepth = i;
if (maxLegalFusionDepth == 0) {
<< "Can't fuse: fusion is not legal at any depth\n");
// Check if fusion would be profitable. We skip profitability analysis
// for maximal fusion since we already know the maximal legal depth to
// fuse.
unsigned bestDstLoopDepth = maxLegalFusionDepth;
if (!maximalFusion) {
// Retrieve producer stores from the src loop.
SmallVector<Operation *, 2> producerStores;
for (Operation *op : srcNode->stores)
if (producerConsumerMemrefs.count(
// TODO: Suppport multiple producer stores in profitability
// analysis. We limit profitability analysis to only scenarios with
// a single producer store for now. Note that some multi-store
// producer scenarios will still go through profitability analysis
// if only one of the stores is involved the producer-consumer
// relationship of the candidate loops.
assert(!producerStores.empty() && "Expected producer store");
if (producerStores.size() > 1)
LLVM_DEBUG(llvm::dbgs() << "Skipping profitability analysis. Not "
"supported for this case\n");
else if (!isFusionProfitable(producerStores[0], producerStores[0],
dstAffineForOp, depthSliceUnions,
maxLegalFusionDepth, &bestDstLoopDepth,
assert(bestDstLoopDepth > 0 && "Unexpected loop fusion depth");
ComputationSliceState &bestSlice =
depthSliceUnions[bestDstLoopDepth - 1];
assert(!bestSlice.isEmpty() && "Missing slice union for depth");
// Determine if 'srcId' can be removed after fusion, taking into
// account remaining dependences, escaping memrefs and the fusion
// insertion point.
bool removeSrcNode = canRemoveSrcNodeAfterFusion(
srcId, dstId, bestSlice, fusedLoopInsPoint, srcEscapingMemRefs,
DenseSet<Value> privateMemrefs;
for (Value memref : producerConsumerMemrefs) {
// If `memref` is an escaping one, do not create a private memref
// for the below scenarios, since doing so will leave the escaping
// memref unmodified as all the writes originally meant for the
// escaping memref would be performed on the private memref:
// 1. The source is to be removed after fusion,
// OR
// 2. The destination writes to `memref`.
if (srcEscapingMemRefs.count(memref) > 0 &&
(removeSrcNode || dstNode->getStoreOpCount(memref) > 0))
// Don't create a private memref if 'srcNode' has in edges on
// 'memref' or 'dstNode' has out edges on 'memref'.
if (mdg->getIncomingMemRefAccesses(srcId, memref) > 0 ||
mdg->getOutEdgeCount(dstId, memref) > 0)
// If 'srcNode' will be removed but it has out edges on 'memref' to
// nodes other than 'dstNode', we have to preserve dependences and
// cannot create a private memref.
if (removeSrcNode &&
any_of(mdg->outEdges[srcId], [&](const auto &edge) {
return edge.value == memref && != dstId;
// Create a private version of this memref.
// Fuse computation slice of 'srcLoopNest' into 'dstLoopNest'.
fuseLoops(srcAffineForOp, dstAffineForOp, bestSlice);
dstNodeChanged = true;
<< "Fused src loop " << srcId << " into dst loop " << dstId
<< " at depth " << bestDstLoopDepth << ":\n"
<< dstAffineForOp << "\n");
// Move 'dstAffineForOp' before 'insertPointInst' if needed.
if (fusedLoopInsPoint != dstAffineForOp.getOperation())
// Update edges between 'srcNode' and 'dstNode'.
mdg->updateEdges(srcNode->id, dstNode->id, privateMemrefs,
// Create private memrefs.
if (!privateMemrefs.empty()) {
// Gather stores for all the private-to-be memrefs.
DenseMap<Value, SmallVector<Operation *, 4>> privateMemRefToStores;
dstAffineForOp.walk([&](AffineWriteOpInterface storeOp) {
Value storeMemRef = storeOp.getMemRef();
if (privateMemrefs.count(storeMemRef) > 0)
// Replace original memrefs with private memrefs. Note that all the
// loads and stores on these memrefs will be replaced with a new
// loads and stores. Any reference to the original ones becomes
// invalid after this point.
for (auto &memrefToStoresPair : privateMemRefToStores) {
// TODO: Use union of memref write regions to compute
// private memref footprint.
SmallVector<Operation *, 4> &storesForMemref =
Value newMemRef = createPrivateMemRef(
dstAffineForOp, storesForMemref[0], bestDstLoopDepth,
fastMemorySpace, localBufSizeThreshold);
// Create new node in dependence graph for 'newMemRef' alloc op.
unsigned newMemRefNodeId =
// Add edge from 'newMemRef' node to dstNode.
mdg->addEdge(newMemRefNodeId, dstId, newMemRef);
// One or more entries for 'newMemRef' alloc op are inserted into
// the DenseMap mdg->nodes. Since an insertion may cause DenseMap to
// reallocate, update dstNode.
dstNode = mdg->getNode(dstId);
// Collect dst loop stats after memref privatization transformation.
LoopNestStateCollector dstLoopCollector;
// Clear and add back loads and stores.
mdg->addToNode(dstId, dstLoopCollector.loadOpInsts,
if (removeSrcNode) {
<< "Removing src loop " << srcId << " after fusion\n");
// srcNode is no longer valid after it is removed from mdg.
srcNode = nullptr;
} while (dstNodeChanged);
// Visits each node in the graph, and for each node, attempts to fuse it with
// its sibling nodes (nodes which share a parent, but no dependence edges).
void fuseSiblingNodes() {
LLVM_DEBUG(llvm::dbgs() << "--- Sibling Fusion ---\n");
while (!worklist.empty()) {
unsigned dstId = worklist.back();
// Skip if this node was removed (fused into another node).
if (mdg->nodes.count(dstId) == 0)
// Get 'dstNode' into which to attempt fusion.
auto *dstNode = mdg->getNode(dstId);
// Skip if 'dstNode' is not a loop nest.
if (!isa<AffineForOp>(dstNode->op))
// Attempt to fuse 'dstNode' with its sibling nodes in the graph.
// Attempt to fuse 'dstNode' with sibling nodes in the graph.
void fuseWithSiblingNodes(Node *dstNode) {
DenseSet<unsigned> visitedSibNodeIds;
std::pair<unsigned, Value> idAndMemref;
auto dstAffineForOp = cast<AffineForOp>(dstNode->op);
while (findSiblingNodeToFuse(dstNode, &visitedSibNodeIds, &idAndMemref)) {
unsigned sibId = idAndMemref.first;
Value memref = idAndMemref.second;
// TODO: Check that 'sibStoreOpInst' post-dominates all other
// stores to the same memref in 'sibNode' loop nest.
auto *sibNode = mdg->getNode(sibId);
// Compute an operation list insertion point for the fused loop
// nest which preserves dependences.
assert(sibNode->op->getBlock() == dstNode->op->getBlock());
Operation *insertPointInst =
? mdg->getFusedLoopNestInsertionPoint(sibNode->id, dstNode->id)
: mdg->getFusedLoopNestInsertionPoint(dstNode->id, sibNode->id);
if (insertPointInst == nullptr)
// Check if fusion would be profitable and at what depth.
// Get unique 'sibNode' load op to 'memref'.
SmallVector<Operation *, 2> sibLoadOpInsts;
sibNode->getLoadOpsForMemref(memref, &sibLoadOpInsts);
// Currently findSiblingNodeToFuse searches for siblings with one load.
assert(sibLoadOpInsts.size() == 1);
Operation *sibLoadOpInst = sibLoadOpInsts[0];
// TODO: Choose the store which postdominates all other stores.
auto *sibStoreOpInst = sibNode->stores.back();
// Gather 'dstNode' load ops to 'memref'.
SmallVector<Operation *, 2> dstLoadOpInsts;
dstNode->getLoadOpsForMemref(memref, &dstLoadOpInsts);
SmallVector<AffineForOp, 4> dstLoopIVs;
getLoopIVs(*dstLoadOpInsts[0], &dstLoopIVs);
unsigned dstLoopDepthTest = dstLoopIVs.size();
auto sibAffineForOp = cast<AffineForOp>(sibNode->op);
// Compute loop depth and slice union for fusion.
SmallVector<ComputationSliceState, 8> depthSliceUnions;
unsigned maxLegalFusionDepth = 0;
FusionStrategy strategy(memref);
for (unsigned i = 1; i <= dstLoopDepthTest; ++i) {
FusionResult result = mlir::canFuseLoops(
sibAffineForOp, dstAffineForOp,
/*dstLoopDepth=*/i, &depthSliceUnions[i - 1], strategy);
if (result.value == FusionResult::Success)
maxLegalFusionDepth = i;
// Skip if fusion is not feasible at any loop depths.
if (maxLegalFusionDepth == 0)
unsigned bestDstLoopDepth = maxLegalFusionDepth;
if (!maximalFusion) {
// Check if fusion would be profitable.
if (!isFusionProfitable(sibLoadOpInst, sibStoreOpInst, dstAffineForOp,
depthSliceUnions, maxLegalFusionDepth,
&bestDstLoopDepth, computeToleranceThreshold))
assert(bestDstLoopDepth > 0 && "Unexpected loop fusion depth");
assert(!depthSliceUnions[bestDstLoopDepth - 1].isEmpty() &&
"Fusion depth has no computed slice union");
// Check if source loop is being inserted in the innermost
// destination loop. Based on this, the fused loop may be optimized
// further inside `fuseLoops`.
bool isInnermostInsertion = (bestDstLoopDepth == dstLoopDepthTest);
// Fuse computation slice of 'sibLoopNest' into 'dstLoopNest'.
mlir::fuseLoops(sibAffineForOp, dstAffineForOp,
depthSliceUnions[bestDstLoopDepth - 1],
auto dstForInst = cast<AffineForOp>(dstNode->op);
// Update operation position of fused loop nest (if needed).
if (insertPointInst != dstForInst.getOperation()) {
// Update data dependence graph state post fusion.
updateStateAfterSiblingFusion(sibNode, dstNode);
// Searches function argument uses and the graph from 'dstNode' looking for a
// fusion candidate sibling node which shares no dependences with 'dstNode'
// but which loads from the same memref. Returns true and sets
// 'idAndMemrefToFuse' on success. Returns false otherwise.
bool findSiblingNodeToFuse(Node *dstNode,
DenseSet<unsigned> *visitedSibNodeIds,
std::pair<unsigned, Value> *idAndMemrefToFuse) {
// Returns true if 'sibNode' can be fused with 'dstNode' for input reuse
// on 'memref'.
auto canFuseWithSibNode = [&](Node *sibNode, Value memref) {
// Skip if 'outEdge' is not a read-after-write dependence.
// TODO: Remove restrict to single load op restriction.
if (sibNode->getLoadOpCount(memref) != 1)
return false;
// Skip if there exists a path of dependent edges between
// 'sibNode' and 'dstNode'.
if (mdg->hasDependencePath(sibNode->id, dstNode->id) ||
mdg->hasDependencePath(dstNode->id, sibNode->id))
return false;
// Skip sib node if it loads to (and stores from) the same memref on
// which it also has an input dependence edge.
DenseSet<Value> loadAndStoreMemrefSet;
if (llvm::any_of(loadAndStoreMemrefSet, [=](Value memref) {
return mdg->getIncomingMemRefAccesses(sibNode->id, memref) > 0;
return false;
// Check that all stores are to the same memref.
DenseSet<Value> storeMemrefs;
for (auto *storeOpInst : sibNode->stores) {
if (storeMemrefs.size() != 1)
return false;
// Skip if a memref value in one node is used by a non-affine memref
// access that lies between 'dstNode' and 'sibNode'.
if (hasNonAffineUsersOnThePath(dstNode->id, sibNode->id, mdg) ||
hasNonAffineUsersOnThePath(sibNode->id, dstNode->id, mdg))
return false;
return true;
// Search for siblings which load the same memref function argument.
auto fn = dstNode->op->getParentOfType<FuncOp>();
for (unsigned i = 0, e = fn.getNumArguments(); i != e; ++i) {
for (auto *user : fn.getArgument(i).getUsers()) {
if (auto loadOp = dyn_cast<AffineReadOpInterface>(user)) {
// Gather loops surrounding 'use'.
SmallVector<AffineForOp, 4> loops;
getLoopIVs(*user, &loops);
// Skip 'use' if it is not within a loop nest.
if (loops.empty())
Node *sibNode = mdg->getForOpNode(loops[0]);
assert(sibNode != nullptr);
// Skip 'use' if it not a sibling to 'dstNode'.
if (sibNode->id == dstNode->id)
// Skip 'use' if it has been visited.
if (visitedSibNodeIds->count(sibNode->id) > 0)
// Skip 'use' if it does not load from the same memref as 'dstNode'.
auto memref = loadOp.getMemRef();
if (dstNode->getLoadOpCount(memref) == 0)
// Check if 'sibNode/dstNode' can be input-reuse fused on 'memref'.
if (canFuseWithSibNode(sibNode, memref)) {
idAndMemrefToFuse->first = sibNode->id;
idAndMemrefToFuse->second = memref;
return true;
// Search for siblings by following edges through an intermediate src node.
// Collect candidate 'dstNode' input edges in 'inEdges'.
SmallVector<MemRefDependenceGraph::Edge, 2> inEdges;
dstNode->id, [&](MemRefDependenceGraph::Edge inEdge) {
// Add 'inEdge' if it is a read-after-write dependence.
if (dstNode->getLoadOpCount(inEdge.value) > 0 &&
mdg->getNode(>getStoreOpCount(inEdge.value) > 0)
// Search for sibling nodes to fuse by visiting output edges from each input
// edge in 'inEdges'.
for (auto &inEdge : inEdges) {
// Collect candidate output edges from each node '' in 'inEdges'.
SmallVector<MemRefDependenceGraph::Edge, 2> outEdges;
mdg->forEachMemRefOutputEdge(, [&](MemRefDependenceGraph::Edge outEdge) {
unsigned sibNodeId =;
if (visitedSibNodeIds->count(sibNodeId) > 0)
// Skip output edge if not a sibling using the same memref.
if ( == dstNode->id || outEdge.value != inEdge.value)
auto *sibNode = mdg->getNode(sibNodeId);
if (!isa<AffineForOp>(sibNode->op))
// Check if 'sibNode/dstNode' can be input-reuse fused on 'memref'.
if (canFuseWithSibNode(sibNode, outEdge.value)) {
// Add candidate 'outEdge' to sibling node.
// Add first candidate if any were returned.
if (!outEdges.empty()) {
idAndMemrefToFuse->first = outEdges[0].id;
idAndMemrefToFuse->second = outEdges[0].value;
return true;
return false;
/// Update data dependence graph state to reflect sibling fusion of 'sibNode'
/// into 'dstNode'.
void updateStateAfterSiblingFusion(Node *sibNode, Node *dstNode) {
// Update 'sibNode' and 'dstNode' input/output edges to reflect fusion.
mdg->updateEdges(sibNode->id, dstNode->id);
// Collect dst loop stats after memref privatization transformation.
auto dstForInst = cast<AffineForOp>(dstNode->op);
LoopNestStateCollector dstLoopCollector;
// Clear and add back loads and stores
mdg->addToNode(dstNode->id, dstLoopCollector.loadOpInsts,
// Remove old sibling loop nest if it no longer has outgoing dependence
// edges, and it does not write to a memref which escapes the
// function.
if (mdg->getOutEdgeCount(sibNode->id) == 0) {
// Clean up any allocs with no users.
void eraseUnusedMemRefAllocations() {
for (auto &pair : mdg->memrefEdgeCount) {
if (pair.second > 0)
auto memref = pair.first;
// Skip if there exist other uses (return operation or function calls).
if (!memref.use_empty())
// Use list expected to match the dep graph info.
auto *op = memref.getDefiningOp();
if (isa_and_nonnull<memref::AllocOp>(op))
} // end anonymous namespace
void LoopFusion::runOnFunction() {
MemRefDependenceGraph g;
if (!g.init(getFunction()))
Optional<unsigned> fastMemorySpaceOpt;
if (fastMemorySpace.hasValue())
fastMemorySpaceOpt = fastMemorySpace;
unsigned localBufSizeThresholdBytes = localBufSizeThreshold * 1024;
GreedyFusion fusion(&g, localBufSizeThresholdBytes, fastMemorySpaceOpt,
maximalFusion, computeToleranceThreshold);
if (affineFusionMode == FusionMode::ProducerConsumer)
else if (affineFusionMode == FusionMode::Sibling)