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llvm-project/mlir/lib/Dialect/SparseTensor/Utils/Merger.cpp

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//===- Merger.cpp - Implementation of iteration lattices ------------------===//
//
// 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
//
//===----------------------------------------------------------------------===//
#include "mlir/Dialect/SparseTensor/Utils/Merger.h"
#include "mlir/IR/Operation.h"
#include "llvm/Support/Debug.h"
namespace mlir {
namespace sparse_tensor {
//
// Constructors.
//
TensorExp::TensorExp(Kind k, unsigned x, unsigned y, Value v)
: kind(k), val(v) {
switch (kind) {
case kTensor:
assert(x != -1u && y == -1u && !v);
tensor = x;
break;
case kInvariant:
assert(x == -1u && y == -1u && v);
break;
case kAbsF:
case kCeilF:
case kFloorF:
case kNegF:
case kNegI:
assert(x != -1u && y == -1u && !v);
children.e0 = x;
children.e1 = y;
break;
default:
assert(x != -1u && y != -1u && !v);
children.e0 = x;
children.e1 = y;
break;
}
}
LatPoint::LatPoint(unsigned n, unsigned e, unsigned b)
: bits(n, false), simple(), exp(e) {
bits.set(b);
}
LatPoint::LatPoint(const llvm::BitVector &b, unsigned e)
: bits(b), simple(), exp(e) {}
//
// Lattice methods.
//
unsigned Merger::addExp(Kind k, unsigned e0, unsigned e1, Value v) {
unsigned e = tensorExps.size();
tensorExps.push_back(TensorExp(k, e0, e1, v));
return e;
}
unsigned Merger::addLat(unsigned t, unsigned i, unsigned e) {
assert(t < numTensors && i < numLoops);
unsigned p = latPoints.size();
latPoints.push_back(LatPoint(numLoops * numTensors, e, numTensors * i + t));
return p;
}
unsigned Merger::addSet() {
unsigned s = latSets.size();
latSets.emplace_back(SmallVector<unsigned, 16>());
return s;
}
unsigned Merger::conjLatPoint(Kind kind, unsigned p0, unsigned p1) {
unsigned p = latPoints.size();
llvm::BitVector nb = llvm::BitVector(latPoints[p0].bits);
nb |= latPoints[p1].bits;
unsigned e = addExp(kind, latPoints[p0].exp, latPoints[p1].exp);
latPoints.push_back(LatPoint(nb, e));
return p;
}
unsigned Merger::takeConj(Kind kind, unsigned s0, unsigned s1) {
unsigned s = addSet();
for (unsigned p0 : latSets[s0])
for (unsigned p1 : latSets[s1])
latSets[s].push_back(conjLatPoint(kind, p0, p1));
return s;
}
unsigned Merger::takeDisj(Kind kind, unsigned s0, unsigned s1) {
unsigned s = takeConj(kind, s0, s1);
// Followed by all in s0.
for (unsigned p : latSets[s0])
latSets[s].push_back(p);
// Map binary 0-y to unary -y.
if (kind == kSubF)
s1 = mapSet(kNegF, s1);
else if (kind == kSubI)
s1 = mapSet(kNegI, s1);
// Followed by all in s1.
for (unsigned p : latSets[s1])
latSets[s].push_back(p);
return s;
}
unsigned Merger::mapSet(Kind kind, unsigned s0) {
assert(kAbsF <= kind && kind <= kNegI);
unsigned s = addSet();
for (unsigned p : latSets[s0]) {
unsigned e = addExp(kind, latPoints[p].exp);
latPoints.push_back(LatPoint(latPoints[p].bits, e));
latSets[s].push_back(latPoints.size() - 1);
}
return s;
}
unsigned Merger::optimizeSet(unsigned s0) {
unsigned s = addSet();
assert(latSets[s0].size() != 0);
unsigned p0 = latSets[s0][0];
for (unsigned p1 : latSets[s0]) {
bool add = true;
if (p0 != p1) {
// Is this a straightforward copy?
unsigned e = latPoints[p1].exp;
if (tensorExps[e].kind == kTensor && tensorExps[e].tensor == outTensor)
continue;
// Conjunction already covered?
for (unsigned p2 : latSets[s]) {
assert(!latGT(p1, p2)); // Lj => Li would be bad
if (onlyDenseDiff(p2, p1)) {
add = false;
break;
}
}
assert(!add || latGT(p0, p1));
}
if (add)
latSets[s].push_back(p1);
}
for (unsigned p : latSets[s])
latPoints[p].simple = simplifyCond(s, p);
return s;
}
llvm::BitVector Merger::simplifyCond(unsigned s0, unsigned p0) {
// First determine if this lattice point is a *singleton*, i.e.,
// the last point in a lattice, no other is less than this one.
bool isSingleton = true;
for (unsigned p1 : latSets[s0]) {
if (p0 != p1 && latGT(p0, p1)) {
isSingleton = false;
break;
}
}
// Now apply the two basic rules.
llvm::BitVector simple = latPoints[p0].bits;
bool reset = isSingleton && hasAnyDimOf(simple, kSparse);
for (unsigned b = 0, be = simple.size(); b < be; b++) {
if (simple[b] && !isDim(b, kSparse)) {
if (reset)
simple.reset(b);
reset = true;
}
}
return simple;
}
bool Merger::latGT(unsigned i, unsigned j) const {
const llvm::BitVector &bitsi = latPoints[i].bits;
const llvm::BitVector &bitsj = latPoints[j].bits;
assert(bitsi.size() == bitsj.size());
if (bitsi.count() > bitsj.count()) {
for (unsigned b = 0, be = bitsj.size(); b < be; b++)
if (bitsj[b] && !bitsi[b])
return false;
return true;
}
return false;
}
bool Merger::onlyDenseDiff(unsigned i, unsigned j) {
llvm::BitVector tmp = latPoints[j].bits;
tmp ^= latPoints[i].bits;
return !hasAnyDimOf(tmp, kSparse);
}
bool Merger::hasAnyDimOf(const llvm::BitVector &bits, Dim d) const {
for (unsigned b = 0, be = bits.size(); b < be; b++)
if (bits[b] && isDim(b, d))
return true;
return false;
}
bool Merger::isConjunction(unsigned t, unsigned e) const {
switch (tensorExps[e].kind) {
case kTensor:
return tensorExps[e].tensor == t;
case kAbsF:
case kCeilF:
case kFloorF:
case kNegF:
case kNegI:
return isConjunction(t, tensorExps[e].children.e0);
case kDivF: // note: x / c only
case kDivS:
case kDivU:
assert(!maybeZero(tensorExps[e].children.e1));
return isConjunction(t, tensorExps[e].children.e0);
case kShrS: // note: x >> inv only
case kShrU:
case kShlI:
assert(isInvariant(tensorExps[e].children.e1));
return isConjunction(t, tensorExps[e].children.e0);
case kMulF:
case kMulI:
case kAndI:
return isConjunction(t, tensorExps[e].children.e0) ||
isConjunction(t, tensorExps[e].children.e1);
default:
return false;
}
}
#ifndef NDEBUG
//
// Print methods (for debugging).
//
static const char *kindToOpSymbol(Kind kind) {
switch (kind) {
case kTensor:
return "tensor";
case kInvariant:
return "invariant";
case kAbsF:
return "abs";
case kCeilF:
return "ceil";
case kFloorF:
return "floor";
case kNegF:
return "-";
case kNegI:
return "-";
case kMulF:
return "*";
case kMulI:
return "*";
case kDivF:
return "/";
case kDivS:
return "/";
case kDivU:
return "/";
case kAddF:
return "+";
case kAddI:
return "+";
case kSubF:
return "-";
case kSubI:
return "-";
case kAndI:
return "&";
case kOrI:
return "|";
case kXorI:
return "^";
case kShrS:
return "a>>";
case kShrU:
return ">>";
case kShlI:
return "<<";
}
llvm_unreachable("unexpected kind for symbol");
}
void Merger::dumpExp(unsigned e) const {
switch (tensorExps[e].kind) {
case kTensor:
if (tensorExps[e].tensor == syntheticTensor)
llvm::dbgs() << "synthetic_";
else if (tensorExps[e].tensor == outTensor)
llvm::dbgs() << "output_";
llvm::dbgs() << "tensor_" << tensorExps[e].tensor;
break;
case kInvariant:
llvm::dbgs() << "invariant";
break;
case kAbsF:
case kCeilF:
case kFloorF:
case kNegF:
case kNegI:
llvm::dbgs() << kindToOpSymbol(tensorExps[e].kind) << " ";
dumpExp(tensorExps[e].children.e0);
break;
default:
llvm::dbgs() << "(";
dumpExp(tensorExps[e].children.e0);
llvm::dbgs() << " " << kindToOpSymbol(tensorExps[e].kind) << " ";
dumpExp(tensorExps[e].children.e1);
llvm::dbgs() << ")";
}
}
void Merger::dumpLat(unsigned p) const {
llvm::dbgs() << "lat(";
dumpBits(latPoints[p].bits);
llvm::dbgs() << " :";
dumpBits(latPoints[p].simple);
llvm::dbgs() << " : ";
dumpExp(latPoints[p].exp);
llvm::dbgs() << " )\n";
}
void Merger::dumpSet(unsigned s) const {
llvm::dbgs() << "{ #" << latSets[s].size() << "\n";
for (unsigned p : latSets[s]) {
llvm::dbgs() << " ";
dumpLat(p);
}
llvm::dbgs() << "}\n";
}
void Merger::dumpBits(const llvm::BitVector &bits) const {
for (unsigned b = 0, be = bits.size(); b < be; b++) {
if (bits[b]) {
unsigned t = tensor(b);
unsigned i = index(b);
llvm::dbgs() << " i_" << t << "_" << i << "_";
switch (dims[t][i]) {
case kSparse:
llvm::dbgs() << "S";
break;
case kDense:
llvm::dbgs() << "D";
break;
case kSingle:
llvm::dbgs() << "T";
break;
case kUndef:
llvm::dbgs() << "U";
break;
}
}
}
}
#endif // NDEBUG
//
// Builder methods.
//
unsigned Merger::buildLattices(unsigned e, unsigned i) {
Kind kind = tensorExps[e].kind;
switch (kind) {
case kTensor:
case kInvariant: {
// Either the index is really used in the tensor expression, or it is
// set to the undefined index in that dimension. An invariant expression
// is set to a synthetic tensor with undefined indices only.
unsigned s = addSet();
unsigned t = kind == kTensor ? tensorExps[e].tensor : syntheticTensor;
latSets[s].push_back(addLat(t, i, e));
return s;
}
case kAbsF:
case kCeilF:
case kFloorF:
case kNegF:
case kNegI:
// A zero preserving operation (viz. f(0) = 0, [Bik96,Ch5]) maps the
// lattice set of the operand through the operator into a new set.
//
// -y|!y | y |
// --+---+---+
// | 0 |-y |
return mapSet(kind, buildLattices(tensorExps[e].children.e0, i));
case kMulF:
case kMulI:
case kAndI:
// A multiplicative operation only needs to be performed
// for the conjunction of sparse iteration spaces.
//
// x*y|!y | y |
// ---+---+---+
// !x | 0 | 0 |
// x | 0 |x*y|
return takeConj(kind, // take binary conjunction
buildLattices(tensorExps[e].children.e0, i),
buildLattices(tensorExps[e].children.e1, i));
case kDivF:
case kDivS:
case kDivU:
// A division is tricky, since 0/0, 0/c, c/0 all have
// specific outcomes for floating-point and integers.
// Thus, we need to traverse the full iteration space.
//
// x/y|!y | y |
// ---+---+---+
// !x |0/0|0/y| FP: 0/0=NaN,c/0=Inf,0/c=0 with c true nonzero
// x |x/0|x/y| INT: x/0=exception for any x
//
// TODO: for now we "fixed" this by only accepting x/c cases
// during expression building, so that the conjunction
// rules applies (viz. x/c = x*(1/c) as far as lattice
// construction is concerned).
assert(!maybeZero(tensorExps[e].children.e1));
return takeConj(kind, // take binary conjunction
buildLattices(tensorExps[e].children.e0, i),
buildLattices(tensorExps[e].children.e1, i));
case kAddF:
case kAddI:
case kSubF:
case kSubI:
case kOrI:
case kXorI:
// An additive operation needs to be performed
// for the disjunction of sparse iteration spaces.
//
// x+y|!y | y | x-y|!y | y |
// ---+---+---+ ---+---+---+
// !x | 0 | y | !x | 0 |-y |
// x | x |x+y| x | x |x-y|
return takeDisj(kind, // take binary disjunction
buildLattices(tensorExps[e].children.e0, i),
buildLattices(tensorExps[e].children.e1, i));
case kShrS:
case kShrU:
case kShlI:
// A shift operation by an invariant amount (viz. tensor expressions
// can only occur at the left-hand-side of the operator) can be handled
// with the conjuction rule.
assert(isInvariant(tensorExps[e].children.e1));
return takeConj(kind, // take binary conjunction
buildLattices(tensorExps[e].children.e0, i),
buildLattices(tensorExps[e].children.e1, i));
}
llvm_unreachable("unexpected expression kind");
}
Optional<unsigned> Merger::buildTensorExpFromLinalg(linalg::GenericOp op) {
Operation *yield = op.region().front().getTerminator();
return buildTensorExp(op, yield->getOperand(0));
}
bool Merger::maybeZero(unsigned e) const {
if (tensorExps[e].kind == kInvariant) {
if (auto c = tensorExps[e].val.getDefiningOp<ConstantIntOp>())
return c.getValue() == 0;
if (auto c = tensorExps[e].val.getDefiningOp<ConstantFloatOp>())
return c.getValue().isZero();
}
return true;
}
bool Merger::isInvariant(unsigned e) const {
return tensorExps[e].kind == kInvariant;
}
Optional<unsigned> Merger::buildTensorExp(linalg::GenericOp op, Value v) {
if (auto arg = v.dyn_cast<BlockArgument>()) {
unsigned argN = arg.getArgNumber();
// Any argument of the generic op that is not marked as a scalar
// argument is considered a tensor, indexed by the implicit loop
// bounds. This includes rank-0 tensor arguments.
if (arg.getOwner()->getParentOp() == op) {
OpOperand *t = op.getInputAndOutputOperands()[argN];
if (!op.isScalar(t))
return addExp(kTensor, argN);
v = t->get(); // get scalar value
}
// Any other argument (marked as scalar argument for the generic op
// or belonging to an enveloping op) is considered invariant.
return addExp(kInvariant, v);
}
// Something defined outside is invariant.
Operation *def = v.getDefiningOp();
if (def->getBlock() != &op.region().front())
return addExp(kInvariant, v);
// Construct unary operations if subexpression can be built.
if (def->getNumOperands() == 1) {
auto x = buildTensorExp(op, def->getOperand(0));
if (x.hasValue()) {
unsigned e = x.getValue();
if (isa<AbsFOp>(def))
return addExp(kAbsF, e);
if (isa<CeilFOp>(def))
return addExp(kCeilF, e);
if (isa<FloorFOp>(def))
return addExp(kFloorF, e);
if (isa<NegFOp>(def))
return addExp(kNegF, e);
// TODO: no negi in std?
}
}
// Construct binary operations if subexpressions can be built.
// TODO: see buildLattices() for an explanation of rejecting certain divisions
if (def->getNumOperands() == 2) {
auto x = buildTensorExp(op, def->getOperand(0));
auto y = buildTensorExp(op, def->getOperand(1));
if (x.hasValue() && y.hasValue()) {
unsigned e0 = x.getValue();
unsigned e1 = y.getValue();
if (isa<MulFOp>(def))
return addExp(kMulF, e0, e1);
if (isa<MulIOp>(def))
return addExp(kMulI, e0, e1);
if (isa<DivFOp>(def) && !maybeZero(e1))
return addExp(kDivF, e0, e1);
if (isa<SignedDivIOp>(def) && !maybeZero(e1))
return addExp(kDivS, e0, e1);
if (isa<UnsignedDivIOp>(def) && !maybeZero(e1))
return addExp(kDivU, e0, e1);
if (isa<AddFOp>(def))
return addExp(kAddF, e0, e1);
if (isa<AddIOp>(def))
return addExp(kAddI, e0, e1);
if (isa<SubFOp>(def))
return addExp(kSubF, e0, e1);
if (isa<SubIOp>(def))
return addExp(kSubI, e0, e1);
if (isa<AndOp>(def))
return addExp(kAndI, e0, e1);
if (isa<OrOp>(def))
return addExp(kOrI, e0, e1);
if (isa<XOrOp>(def))
return addExp(kXorI, e0, e1);
if (isa<SignedShiftRightOp>(def) && isInvariant(e1))
return addExp(kShrS, e0, e1);
if (isa<UnsignedShiftRightOp>(def) && isInvariant(e1))
return addExp(kShrU, e0, e1);
if (isa<ShiftLeftOp>(def) && isInvariant(e1))
return addExp(kShlI, e0, e1);
}
}
// Cannot build.
return None;
}
Value Merger::buildExp(PatternRewriter &rewriter, Location loc, unsigned e,
Value v0, Value v1) {
switch (tensorExps[e].kind) {
case kTensor:
case kInvariant:
llvm_unreachable("unexpected non-op");
case kAbsF:
return rewriter.create<AbsFOp>(loc, v0);
case kCeilF:
return rewriter.create<CeilFOp>(loc, v0);
case kFloorF:
return rewriter.create<FloorFOp>(loc, v0);
case kNegF:
return rewriter.create<NegFOp>(loc, v0);
case kNegI:
assert(v1); // no negi in std
return rewriter.create<SubIOp>(loc, v0, v1);
case kMulF:
return rewriter.create<MulFOp>(loc, v0, v1);
case kMulI:
return rewriter.create<MulIOp>(loc, v0, v1);
case kDivF:
return rewriter.create<DivFOp>(loc, v0, v1);
case kDivS:
return rewriter.create<SignedDivIOp>(loc, v0, v1);
case kDivU:
return rewriter.create<UnsignedDivIOp>(loc, v0, v1);
case kAddF:
return rewriter.create<AddFOp>(loc, v0, v1);
case kAddI:
return rewriter.create<AddIOp>(loc, v0, v1);
case kSubF:
return rewriter.create<SubFOp>(loc, v0, v1);
case kSubI:
return rewriter.create<SubIOp>(loc, v0, v1);
case kAndI:
return rewriter.create<AndOp>(loc, v0, v1);
case kOrI:
return rewriter.create<OrOp>(loc, v0, v1);
case kXorI:
return rewriter.create<XOrOp>(loc, v0, v1);
case kShrS:
return rewriter.create<SignedShiftRightOp>(loc, v0, v1);
case kShrU:
return rewriter.create<UnsignedShiftRightOp>(loc, v0, v1);
case kShlI:
return rewriter.create<ShiftLeftOp>(loc, v0, v1);
}
llvm_unreachable("unexpected expression kind in build");
}
} // namespace sparse_tensor
} // namespace mlir
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