#include "triton/Analysis/Allocation.h" #include "mlir/Analysis/Liveness.h" #include "mlir/Analysis/SliceAnalysis.h" #include "mlir/Dialect/Tensor/IR/Tensor.h" #include "triton/Analysis/Alias.h" #include "triton/Analysis/Utility.h" #include "triton/Dialect/TritonGPU/IR/Dialect.h" #include "llvm/ADT/SmallVector.h" #include #include #include using ::mlir::triton::gpu::BlockedEncodingAttr; using ::mlir::triton::gpu::DotOperandEncodingAttr; using ::mlir::triton::gpu::getContigPerThread; using ::mlir::triton::gpu::getOrder; using ::mlir::triton::gpu::getShapePerCTA; using ::mlir::triton::gpu::getSizePerThread; using ::mlir::triton::gpu::MmaEncodingAttr; using ::mlir::triton::gpu::SharedEncodingAttr; using ::mlir::triton::gpu::SliceEncodingAttr; namespace mlir { //===----------------------------------------------------------------------===// // Shared Memory Allocation Analysis //===----------------------------------------------------------------------===// namespace triton { // Bitwidth of pointers constexpr int kPtrBitWidth = 64; static std::pair, SmallVector> getCvtOrder(const Attribute &srcLayout, const Attribute &dstLayout) { auto srcBlockedLayout = srcLayout.dyn_cast(); auto srcMmaLayout = srcLayout.dyn_cast(); auto srcDotLayout = srcLayout.dyn_cast(); auto dstBlockedLayout = dstLayout.dyn_cast(); auto dstMmaLayout = dstLayout.dyn_cast(); auto dstDotLayout = dstLayout.dyn_cast(); assert(!(srcMmaLayout && dstMmaLayout) && "Unexpected mma -> mma layout conversion"); // mma or dot layout does not have an order, so the order depends on the // layout of the other operand. auto inOrd = (srcMmaLayout || srcDotLayout) ? getOrder(dstLayout) : getOrder(srcLayout); auto outOrd = (dstMmaLayout || dstDotLayout) ? getOrder(srcLayout) : getOrder(dstLayout); return {inOrd, outOrd}; } SmallVector getScratchConfigForCvtLayout(triton::gpu::ConvertLayoutOp op, unsigned &inVec, unsigned &outVec) { auto srcTy = op.src().getType().cast(); auto dstTy = op.result().getType().cast(); Attribute srcLayout = srcTy.getEncoding(); Attribute dstLayout = dstTy.getEncoding(); assert(srcLayout && dstLayout && "Unexpect layout in getScratchConfigForCvtLayout()"); auto [inOrd, outOrd] = getCvtOrder(srcLayout, dstLayout); unsigned srcContigPerThread = getContigPerThread(srcLayout)[inOrd[0]]; unsigned dstContigPerThread = getContigPerThread(dstLayout)[outOrd[0]]; // TODO: Fix the legacy issue that ourOrd[0] == 0 always means // that we cannot do vectorization. inVec = outOrd[0] == 0 ? 1 : inOrd[0] == 0 ? 1 : srcContigPerThread; outVec = outOrd[0] == 0 ? 1 : dstContigPerThread; auto srcShapePerCTA = getShapePerCTA(srcLayout); auto dstShapePerCTA = getShapePerCTA(dstLayout); unsigned rank = dstTy.getRank(); SmallVector paddedRepShape(rank); unsigned pad = std::max(inVec, outVec); for (unsigned d = 0; d < rank; ++d) { paddedRepShape[d] = std::max(std::min(srcTy.getShape()[d], srcShapePerCTA[d]), std::min(dstTy.getShape()[d], dstShapePerCTA[d])); } if (rank == 1) return paddedRepShape; unsigned paddedDim = 1; if (auto dstBlockedLayout = dstLayout.dyn_cast()) { paddedDim = dstBlockedLayout.getOrder()[0]; } paddedRepShape[paddedDim] += pad; return paddedRepShape; } // TODO: extend beyond scalars SmallVector getScratchConfigForAtomicRMW(triton::AtomicRMWOp op) { SmallVector smemShape; if (op.ptr().getType().isa()) { // do nothing or just assert because shared memory is not used in tensor up // to now } else { // need only bytes for scalar // always vec = 1 and elemsPerThread = 1 for scalar? smemShape.push_back(1); } return smemShape; } SmallVector getScratchConfigForAtomicCAS(triton::AtomicCASOp op) { return SmallVector{1}; } class AllocationAnalysis { public: AllocationAnalysis(Operation *operation, Allocation *allocation) : operation(operation), allocation(allocation) { run(); } private: using BufferT = Allocation::BufferT; /// Value -> Liveness Range /// Use MapVector to ensure determinism. using BufferRangeMapT = llvm::MapVector>; /// Nodes -> Nodes using GraphT = DenseMap>; void run() { getValuesAndSizes(); resolveLiveness(); computeOffsets(); } /// Initializes explicitly defined shared memory values for a given operation. void getExplicitValueSize(Operation *op) { // Values returned from scf.yield will not be allocated even though they // have the shared encoding. // For example: %a = scf.if -> yield // %a must be allocated elsewhere by other operations. // FIXME(Keren): extract and insert are always alias for now if (!maybeSharedAllocationOp(op) || maybeAliasOp(op)) { return; } for (Value result : op->getResults()) { if (isSharedEncoding(result)) { // Bytes could be a different value once we support padding or other // allocation policies. auto tensorType = result.getType().dyn_cast(); auto bytes = tensorType.getNumElements() * tensorType.getElementTypeBitWidth() / 8; allocation->addBuffer(result, bytes); } } } /// Initializes temporary shared memory for a given operation. void getScratchValueSize(Operation *op) { if (auto reduceOp = dyn_cast(op)) { ReduceOpHelper helper(reduceOp); unsigned bytes = helper.getScratchSizeInBytes(); allocation->addBuffer(op, bytes); } else if (auto cvtLayout = dyn_cast(op)) { auto srcTy = cvtLayout.src().getType().cast(); auto dstTy = cvtLayout.result().getType().cast(); auto srcEncoding = srcTy.getEncoding(); auto dstEncoding = dstTy.getEncoding(); if (srcEncoding.isa() || dstEncoding.isa()) { // Conversions from/to shared memory do not need scratch memory. return; } // ConvertLayoutOp with both input/output non-shared_layout // TODO: Besides of implementing ConvertLayoutOp via shared memory, it's // also possible to realize it with other approaches in restricted // conditions, such as warp-shuffle unsigned inVec = 0; unsigned outVec = 0; auto smemShape = getScratchConfigForCvtLayout(cvtLayout, inVec, outVec); unsigned elems = std::accumulate(smemShape.begin(), smemShape.end(), 1, std::multiplies{}); auto bytes = srcTy.getElementType().isa() ? elems * kPtrBitWidth / 8 : elems * std::max(8, srcTy.getElementTypeBitWidth()) / 8; allocation->addBuffer(op, bytes); } else if (auto atomicRMWOp = dyn_cast(op)) { auto value = op->getOperand(0); // only scalar requires scratch memory // make it explicit for readability if (value.getType().dyn_cast()) { // nothing to do } else { auto smemShape = getScratchConfigForAtomicRMW(atomicRMWOp); unsigned elems = std::accumulate(smemShape.begin(), smemShape.end(), 1, std::multiplies{}); auto elemTy = value.getType().cast().getPointeeType(); auto bytes = elemTy.isa() ? elems * kPtrBitWidth / 8 : elems * std::max(8, elemTy.getIntOrFloatBitWidth()) / 8; allocation->addBuffer(op, bytes); } } else if (auto atomicCASOp = dyn_cast(op)) { auto value = op->getOperand(0); auto smemShape = getScratchConfigForAtomicCAS(atomicCASOp); unsigned elems = std::accumulate(smemShape.begin(), smemShape.end(), 1, std::multiplies{}); auto elemTy = value.getType().cast().getPointeeType(); auto bytes = elemTy.isa() ? elems * kPtrBitWidth / 8 : elems * elemTy.getIntOrFloatBitWidth() / 8; allocation->addBuffer(op, bytes); } } void getValueAlias(Value value, SharedMemoryAliasAnalysis &analysis) { LatticeElement *latticeElement = analysis.lookupLatticeElement(value); if (latticeElement) { auto &info = latticeElement->getValue(); if (!info.getAllocs().empty()) { for (auto alloc : info.getAllocs()) { allocation->addAlias(value, alloc); } } } } /// Extract all shared memory values and their sizes void getValuesAndSizes() { // Get the alloc values operation->walk([&](Operation *op) { getExplicitValueSize(op); getScratchValueSize(op); }); // Get the alias values SharedMemoryAliasAnalysis aliasAnalysis(operation->getContext()); aliasAnalysis.run(operation); operation->walk([&](Operation *op) { for (auto operand : op->getOperands()) { getValueAlias(operand, aliasAnalysis); } for (auto value : op->getResults()) { getValueAlias(value, aliasAnalysis); } }); } /// Computes the liveness range of the allocated value. /// Each buffer is allocated only once. void resolveExplicitBufferLiveness( function_ref(Value value)> getLiveness) { for (auto valueBufferIter : allocation->valueBuffer) { auto value = valueBufferIter.first; auto *buffer = valueBufferIter.second; bufferRange[buffer] = getLiveness(value); } } /// Extends the liveness range by unionizing the liveness range of the aliased /// values because each allocated buffer could be an alias of others, if block /// arguments are involved. void resolveAliasBufferLiveness( function_ref(Value value)> getLiveness) { for (auto aliasBufferIter : allocation->aliasBuffer) { auto value = aliasBufferIter.first; auto buffers = aliasBufferIter.second; auto range = getLiveness(value); for (auto *buffer : buffers) { auto minId = range.start(); auto maxId = range.end(); if (bufferRange.count(buffer)) { // Extend the allocated buffer's range minId = std::min(minId, bufferRange[buffer].start()); maxId = std::max(maxId, bufferRange[buffer].end()); } bufferRange[buffer] = Interval(minId, maxId); } } } /// Computes the liveness range of scratched buffers. /// Some operations may have a temporary buffer that is not explicitly /// allocated, but is used to store intermediate results. void resolveScratchBufferLiveness( const DenseMap &operationId) { // Analyze liveness of scratch buffers for (auto opScratchIter : allocation->opScratch) { // Any scratch memory's live range is the current operation's live // range. auto *op = opScratchIter.first; auto *buffer = opScratchIter.second; bufferRange.insert({buffer, Interval(operationId.lookup(op), operationId.lookup(op) + 1)}); } } /// Resolves liveness of all values involved under the root operation. void resolveLiveness() { // In the SCF dialect, we always have a sequentially nested structure of // blocks DenseMap operationId; operation->walk( [&](Operation *op) { operationId[op] = operationId.size(); }); // Analyze liveness of explicit buffers Liveness liveness(operation); auto getValueLivenessRange = [&](Value value) { auto liveOperations = liveness.resolveLiveness(value); auto minId = std::numeric_limits::max(); auto maxId = std::numeric_limits::min(); std::for_each(liveOperations.begin(), liveOperations.end(), [&](Operation *liveOp) { if (operationId[liveOp] < minId) { minId = operationId[liveOp]; } if ((operationId[liveOp] + 1) > maxId) { maxId = operationId[liveOp] + 1; } }); return Interval(minId, maxId); }; resolveExplicitBufferLiveness(getValueLivenessRange); resolveAliasBufferLiveness(getValueLivenessRange); resolveScratchBufferLiveness(operationId); } /// Computes the shared memory offsets for all related values. /// Paper: Algorithms for Compile-Time Memory Optimization /// (https://www.cs.utexas.edu/users/harrison/papers/compile-time.pdf) void computeOffsets() { SmallVector buffers; for (auto bufferIter : bufferRange) { buffers.emplace_back(bufferIter.first); } DenseMap bufferStart; calculateStarts(buffers, bufferStart); GraphT interference; buildInterferenceGraph(buffers, bufferStart, interference); allocate(buffers, bufferStart, interference); } /// Computes the initial shared memory offsets. void calculateStarts(const SmallVector &buffers, DenseMap &bufferStart) { // v = values in shared memory // t = triplet of (size, start, end) // shared memory space // - // | *******t4 // | /|\ v2 inserts t4, t5, and t6 // | | // | ******t5 ************t6 // | ^^^^^v2^^^^^^ // | | *********************t2 // | \|/ v2 erases t1 // | ******t1 ^^^^^^^^^v1^^^^^^^^^ ************t3 // |---------------------------------------------| liveness range // 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ... /// Start -> Liveness Range using TripleMapT = std::multimap>; TripleMapT tripleMap; tripleMap.insert(std::make_pair(0, Interval())); SmallVector xBuffers = buffers; while (!xBuffers.empty()) { auto tripleIt = tripleMap.begin(); auto size = tripleIt->first; auto range = tripleIt->second; tripleMap.erase(tripleIt); auto bufferIt = std::find_if(xBuffers.begin(), xBuffers.end(), [&](auto *buffer) { auto xRange = bufferRange[buffer]; bool res = xRange.intersects(range); for (auto val : tripleMap) res = res && !val.second.intersects(xRange); return res; }); if (bufferIt != xBuffers.end()) { auto buffer = *bufferIt; auto xSize = buffer->size; auto xRange = bufferRange.lookup(buffer); bufferStart[buffer] = size; tripleMap.insert( {size + xSize, Interval{std::max(range.start(), xRange.start()), std::min(range.end(), xRange.end())}}); if (range.start() < xRange.start()) tripleMap.insert({size, Interval{range.start(), xRange.end()}}); if (xRange.end() < range.end()) tripleMap.insert({size, Interval{xRange.start(), range.end()}}); xBuffers.erase(bufferIt); } } } /// Builds a graph of all shared memory values. Edges are created between /// shared memory values that are overlapping. void buildInterferenceGraph(const SmallVector &buffers, const DenseMap &bufferStart, GraphT &interference) { for (auto x : buffers) { for (auto y : buffers) { if (x == y) continue; auto xStart = bufferStart.lookup(x); auto yStart = bufferStart.lookup(y); auto xSize = x->size; auto ySize = y->size; Interval xSizeRange = {xStart, xStart + xSize}; Interval ySizeRange = {yStart, yStart + ySize}; auto xOpRange = bufferRange.lookup(x); auto yOpRange = bufferRange.lookup(y); if (xOpRange.intersects(yOpRange) && xSizeRange.intersects(ySizeRange)) { interference[x].insert(y); } } } } /// Finalizes shared memory offsets considering interference. void allocate(const SmallVector &buffers, const DenseMap &bufferStart, const GraphT &interference) { // First-fit graph coloring // Neighbors are nodes that interfere with each other. // We color a node by finding the index of the first available // non-neighboring node or the first neighboring node without any color. // Nodes with the same color do not interfere with each other. DenseMap colors; for (auto value : buffers) { colors[value] = (value == buffers[0]) ? 0 : -1; } SmallVector available(buffers.size()); for (auto x : buffers) { std::fill(available.begin(), available.end(), true); for (auto y : interference.lookup(x)) { int color = colors[y]; if (color >= 0) { available[color] = false; } } auto it = std::find(available.begin(), available.end(), true); colors[x] = std::distance(available.begin(), it); } // Finalize allocation // color0: [0, 7), [0, 8), [0, 15) -> [0, 7), [0, 8), [0, 15) // color1: [7, 9) -> [0 + 1 * 15, 9 + 1 * 15) -> [15, 24) // color2: [8, 12) -> [8 + 2 * 15, 12 + 2 * 15) -> [38, 42) // TODO(Keren): We are wasting memory here. // Nodes with color2 can actually start with 24. for (auto x : buffers) { size_t adj = 0; for (auto y : interference.lookup(x)) { adj = std::max(adj, bufferStart.lookup(y) + y->size); } x->offset = bufferStart.lookup(x) + colors.lookup(x) * adj; allocation->sharedMemorySize = std::max(allocation->sharedMemorySize, x->offset + x->size); } } private: Operation *operation; Allocation *allocation; BufferRangeMapT bufferRange; }; } // namespace triton void Allocation::run() { triton::AllocationAnalysis(getOperation(), this); } } // namespace mlir