CombFolds.cpp

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//===- CombFolds.cpp - Folds + Canonicalization for Comb operations -------===//
//
// 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 "circt/Dialect/Comb/CombOps.h"
#include "circt/Dialect/HW/HWAttributes.h"
#include "circt/Dialect/HW/HWOps.h"
#include "circt/Support/Naming.h"
#include "mlir/IR/Diagnostics.h"
#include "mlir/IR/Matchers.h"
#include "mlir/IR/PatternMatch.h"
#include "llvm/ADT/SetVector.h"
#include "llvm/ADT/SmallBitVector.h"
#include "llvm/ADT/TypeSwitch.h"
#include "llvm/Support/KnownBits.h"
 
using namespace mlir;
using namespace circt;
using namespace comb;
using namespace matchers;
 
// Returns true if the op has one of its own results as an operand.
static bool isOpTriviallyRecursive(Operation *op) {
  return llvm::any_of(op->getOperands(), [op](auto operand) {
    return operand.getDefiningOp() == op;
  });
}
 
/// Create a new instance of a generic operation that only has value operands,
/// and has a single result value whose type matches the first operand.
///
/// This should not be used to create instances of ops with attributes or with
/// more complicated type signatures.
static Value createGenericOp(Location loc, OperationName name,
                             ArrayRef<Value> operands, OpBuilder &builder) {
  OperationState state(loc, name);
  state.addOperands(operands);
  state.addTypes(operands[0].getType());
  return builder.create(state)->getResult(0);
}
 
static TypedAttr getIntAttr(const APInt &value, MLIRContext *context) {
  return IntegerAttr::get(IntegerType::get(context, value.getBitWidth()),
                          value);
}
 
/// Flatten concat and mux operands into a vector.
static void getConcatOperands(Value v, SmallVectorImpl<Value> &result) {
  if (auto concat = v.getDefiningOp<ConcatOp>()) {
    for (auto op : concat.getOperands())
      getConcatOperands(op, result);
  } else if (auto repl = v.getDefiningOp<ReplicateOp>()) {
    for (size_t i = 0, e = repl.getMultiple(); i != e; ++i)
      getConcatOperands(repl.getOperand(), result);
  } else {
    result.push_back(v);
  }
}
 
// Return true if the op has SV attributes. Note that we cannot use a helper
// function `hasSVAttributes` defined under SV dialect because of a cyclic
// dependency.
static bool hasSVAttributes(Operation *op) {
  return op->hasAttr("sv.attributes");
}
 
namespace {
template <typename SubType>
struct ComplementMatcher {
  SubType lhs;
  ComplementMatcher(SubType lhs) : lhs(std::move(lhs)) {}
  bool match(Operation *op) {
    auto xorOp = dyn_cast<XorOp>(op);
    return xorOp && xorOp.isBinaryNot() &&
           mlir::detail::matchOperandOrValueAtIndex(op, 0, lhs);
  }
};
} // end anonymous namespace
 
template <typename SubType>
static inline ComplementMatcher<SubType> m_Complement(const SubType &subExpr) {
  return ComplementMatcher<SubType>(subExpr);
}
 
/// Return true if the op will be flattened afterwards. Op will be flattend if
/// it has a single user which has a same op type.  User must be in same block.
static bool shouldBeFlattened(Operation *op) {
  assert((isa<AndOp, OrOp, XorOp, AddOp, MulOp>(op) &&
          "must be commutative operations"));
  if (op->hasOneUse()) {
    auto *user = *op->getUsers().begin();
    return user->getName() == op->getName() &&
           op->getAttrOfType<UnitAttr>("twoState") ==
               user->getAttrOfType<UnitAttr>("twoState") &&
           op->getBlock() == user->getBlock();
  }
  return false;
}
 
/// Flattens a single input in `op` if `hasOneUse` is true and it can be defined
/// as an Op. Returns true if successful, and false otherwise.
///
/// Example: op(1, 2, op(3, 4), 5) -> op(1, 2, 3, 4, 5)  // returns true
///
static bool tryFlatteningOperands(Operation *op, PatternRewriter &rewriter) {
  // Skip if the operation should be flattened by another operation.
  if (shouldBeFlattened(op))
    return false;
 
  auto inputs = op->getOperands();
 
  SmallVector<Value, 4> newOperands;
  SmallVector<Location, 4> newLocations{op->getLoc()};
  newOperands.reserve(inputs.size());
  struct Element {
    decltype(inputs.begin()) current, end;
  };
 
  SmallVector<Element> worklist;
  worklist.push_back({inputs.begin(), inputs.end()});
  bool binFlag = op->hasAttrOfType<UnitAttr>("twoState");
  bool changed = false;
  while (!worklist.empty()) {
    auto &element = worklist.back(); // Do not pop. Take ref.
 
    // Pop when we finished traversing the current operand range.
    if (element.current == element.end) {
      worklist.pop_back();
      continue;
    }
 
    Value value = *element.current++;
    auto *flattenOp = value.getDefiningOp();
    // If not defined by a compatible operation of the same kind and
    // from the same block, keep this as-is.
    if (!flattenOp || flattenOp->getName() != op->getName() ||
        flattenOp == op || binFlag != op->hasAttrOfType<UnitAttr>("twoState") ||
        flattenOp->getBlock() != op->getBlock()) {
      newOperands.push_back(value);
      continue;
    }
 
    // Don't duplicate logic when it has multiple uses.
    if (!value.hasOneUse()) {
      // We can fold a multi-use binary operation into this one if this allows a
      // constant to fold though.  For example, fold
      //    (or a, b, c, (or d, cst1), cst2) --> (or a, b, c, d, cst1, cst2)
      // since the constants will both fold and we end up with the equiv cost.
      //
      // We don't do this for add/mul because the hardware won't be shared
      // between the two ops if duplicated.
      if (flattenOp->getNumOperands() != 2 || !isa<AndOp, OrOp, XorOp>(op) ||
          !flattenOp->getOperand(1).getDefiningOp<hw::ConstantOp>() ||
          !inputs.back().getDefiningOp<hw::ConstantOp>()) {
        newOperands.push_back(value);
        continue;
      }
    }
 
    changed = true;
 
    // Otherwise, push operands into worklist.
    auto flattenOpInputs = flattenOp->getOperands();
    worklist.push_back({flattenOpInputs.begin(), flattenOpInputs.end()});
    newLocations.push_back(flattenOp->getLoc());
  }
 
  if (!changed)
    return false;
 
  Value result = createGenericOp(FusedLoc::get(op->getContext(), newLocations),
                                 op->getName(), newOperands, rewriter);
  if (binFlag)
    result.getDefiningOp()->setAttr("twoState", rewriter.getUnitAttr());
 
  replaceOpAndCopyNamehint(rewriter, op, result);
  return true;
}
 
// Given a range of uses of an operation, find the lowest and highest bits
// inclusive that are ever referenced. The range of uses must not be empty.
static std::pair<size_t, size_t>
getLowestBitAndHighestBitRequired(Operation *op, bool narrowTrailingBits,
                                  size_t originalOpWidth) {
  auto users = op->getUsers();
  assert(!users.empty() &&
         "getLowestBitAndHighestBitRequired cannot operate on "
         "a empty list of uses.");
 
  // when we don't want to narrowTrailingBits (namely in arithmetic
  // operations), forcing lowestBitRequired = 0
  size_t lowestBitRequired = narrowTrailingBits ? originalOpWidth - 1 : 0;
  size_t highestBitRequired = 0;
 
  for (auto *user : users) {
    if (auto extractOp = dyn_cast<ExtractOp>(user)) {
      size_t lowBit = extractOp.getLowBit();
      size_t highBit =
          cast<IntegerType>(extractOp.getType()).getWidth() + lowBit - 1;
      highestBitRequired = std::max(highestBitRequired, highBit);
      lowestBitRequired = std::min(lowestBitRequired, lowBit);
      continue;
    }
 
    highestBitRequired = originalOpWidth - 1;
    lowestBitRequired = 0;
    break;
  }
 
  return {lowestBitRequired, highestBitRequired};
}
 
template <class OpTy>
static bool narrowOperationWidth(OpTy op, bool narrowTrailingBits,
                                 PatternRewriter &rewriter) {
  IntegerType opType = dyn_cast<IntegerType>(op.getResult().getType());
  if (!opType)
    return false;
 
  auto range = getLowestBitAndHighestBitRequired(op, narrowTrailingBits,
                                                 opType.getWidth());
  if (range.second + 1 == opType.getWidth() && range.first == 0)
    return false;
 
  SmallVector<Value> args;
  auto newType = rewriter.getIntegerType(range.second - range.first + 1);
  for (auto inop : op.getOperands()) {
    // deal with muxes here
    if (inop.getType() != op.getType())
      args.push_back(inop);
    else
      args.push_back(rewriter.createOrFold<ExtractOp>(inop.getLoc(), newType,
                                                      inop, range.first));
  }
  auto newop = OpTy::create(rewriter, op.getLoc(), newType, args);
  newop->setDialectAttrs(op->getDialectAttrs());
  if (op.getTwoState())
    newop.setTwoState(true);
 
  Value newResult = newop.getResult();
  if (range.first)
    newResult = rewriter.createOrFold<ConcatOp>(
        op.getLoc(), newResult,
        hw::ConstantOp::create(rewriter, op.getLoc(),
                               APInt::getZero(range.first)));
  if (range.second + 1 < opType.getWidth())
    newResult = rewriter.createOrFold<ConcatOp>(
        op.getLoc(),
        hw::ConstantOp::create(
            rewriter, op.getLoc(),
            APInt::getZero(opType.getWidth() - range.second - 1)),
        newResult);
  rewriter.replaceOp(op, newResult);
  return true;
}
 
//===----------------------------------------------------------------------===//
// Unary Operations
//===----------------------------------------------------------------------===//
 
OpFoldResult ReplicateOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
 
  // Replicate one time -> noop.
  if (cast<IntegerType>(getType()).getWidth() ==
      getInput().getType().getIntOrFloatBitWidth())
    return getInput();
 
  // Constant fold.
  if (auto input = dyn_cast_or_null<IntegerAttr>(adaptor.getInput())) {
    if (input.getValue().getBitWidth() == 1) {
      if (input.getValue().isZero())
        return getIntAttr(
            APInt::getZero(cast<IntegerType>(getType()).getWidth()),
            getContext());
      return getIntAttr(
          APInt::getAllOnes(cast<IntegerType>(getType()).getWidth()),
          getContext());
    }
 
    APInt result = APInt::getZeroWidth();
    for (auto i = getMultiple(); i != 0; --i)
      result = result.concat(input.getValue());
    return getIntAttr(result, getContext());
  }
 
  return {};
}
 
OpFoldResult ParityOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
 
  // Constant fold.
  if (auto input = dyn_cast_or_null<IntegerAttr>(adaptor.getInput()))
    return getIntAttr(APInt(1, input.getValue().popcount() & 1), getContext());
 
  // parity(x) -> x for single-bit values.
  if (hw::getBitWidth(getInput().getType()) == 1)
    return getInput();
 
  return {};
}
 
LogicalResult ParityOp::canonicalize(ParityOp op, PatternRewriter &rewriter) {
  if (isOpTriviallyRecursive(op))
    return failure();
 
  // Helper to check if a value has zero parity (even number of 1 bits)
  auto isParityZero = [](Value v) {
    APInt value;
    return matchPattern(v, m_ConstantInt(&value)) && value.popcount() % 2 == 0;
  };
 
  // parity(concat(c, x)) -> parity(x) when parity(c) == 0
  // parity(concat(x, c)) -> parity(x) when parity(c) == 0
  auto concat = op.getInput().getDefiningOp<ConcatOp>();
  if (!concat)
    return failure();
 
  auto operands = concat.getInputs();
  if (operands.size() != 2)
    return failure();
 
  if (isParityZero(operands[0])) {
    replaceOpWithNewOpAndCopyNamehint<ParityOp>(rewriter, op, operands[1],
                                                op.getTwoState());
    return success();
  }
 
  if (isParityZero(operands[1])) {
    replaceOpWithNewOpAndCopyNamehint<ParityOp>(rewriter, op, operands[0],
                                                op.getTwoState());
    return success();
  }
 
  return failure();
}
 
//===----------------------------------------------------------------------===//
// Binary Operations
//===----------------------------------------------------------------------===//
 
/// Performs constant folding `calculate` with element-wise behavior on the two
/// attributes in `operands` and returns the result if possible.
static Attribute constFoldBinaryOp(ArrayRef<Attribute> operands,
                                   hw::PEO paramOpcode) {
  assert(operands.size() == 2 && "binary op takes two operands");
  if (!operands[0] || !operands[1])
    return {};
 
  // Fold constants with ParamExprAttr::get which handles simple constants as
  // well as parameter expressions.
  return hw::ParamExprAttr::get(paramOpcode, cast<TypedAttr>(operands[0]),
                                cast<TypedAttr>(operands[1]));
}
 
OpFoldResult ShlOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
 
  if (auto rhs = dyn_cast_or_null<IntegerAttr>(adaptor.getRhs())) {
    if (rhs.getValue().isZero())
      return getOperand(0);
 
    unsigned width = getType().getIntOrFloatBitWidth();
    if (rhs.getValue().uge(width))
      return getIntAttr(APInt::getZero(width), getContext());
  }
  return constFoldBinaryOp(adaptor.getOperands(), hw::PEO::Shl);
}
 
LogicalResult ShlOp::canonicalize(ShlOp op, PatternRewriter &rewriter) {
  if (isOpTriviallyRecursive(op))
    return failure();
 
  // ShlOp(x, cst) -> Concat(Extract(x), zeros)
  APInt value;
  if (!matchPattern(op.getRhs(), m_ConstantInt(&value)))
    return failure();
 
  unsigned width = cast<IntegerType>(op.getLhs().getType()).getWidth();
  if (value.ugt(width))
    value = width;
  unsigned shift = value.getZExtValue();
 
  // This case is handled by fold.
  if (width <= shift || shift == 0)
    return failure();
 
  auto zeros =
      hw::ConstantOp::create(rewriter, op.getLoc(), APInt::getZero(shift));
 
  // Remove the high bits which would be removed by the Shl.
  auto extract =
      ExtractOp::create(rewriter, op.getLoc(), op.getLhs(), 0, width - shift);
 
  replaceOpWithNewOpAndCopyNamehint<ConcatOp>(rewriter, op, extract, zeros);
  return success();
}
 
OpFoldResult ShrUOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
 
  if (auto rhs = dyn_cast_or_null<IntegerAttr>(adaptor.getRhs())) {
    if (rhs.getValue().isZero())
      return getOperand(0);
 
    unsigned width = getType().getIntOrFloatBitWidth();
    if (rhs.getValue().uge(width))
      return getIntAttr(APInt::getZero(width), getContext());
  }
  return constFoldBinaryOp(adaptor.getOperands(), hw::PEO::ShrU);
}
 
LogicalResult ShrUOp::canonicalize(ShrUOp op, PatternRewriter &rewriter) {
  if (isOpTriviallyRecursive(op))
    return failure();
 
  // ShrUOp(x, cst) -> Concat(zeros, Extract(x))
  APInt value;
  if (!matchPattern(op.getRhs(), m_ConstantInt(&value)))
    return failure();
 
  unsigned width = cast<IntegerType>(op.getLhs().getType()).getWidth();
  if (value.ugt(width))
    value = width;
  unsigned shift = value.getZExtValue();
 
  // This case is handled by fold.
  if (width <= shift || shift == 0)
    return failure();
 
  auto zeros =
      hw::ConstantOp::create(rewriter, op.getLoc(), APInt::getZero(shift));
 
  // Remove the low bits which would be removed by the Shr.
  auto extract = ExtractOp::create(rewriter, op.getLoc(), op.getLhs(), shift,
                                   width - shift);
 
  replaceOpWithNewOpAndCopyNamehint<ConcatOp>(rewriter, op, zeros, extract);
  return success();
}
 
OpFoldResult ShrSOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
 
  if (auto rhs = dyn_cast_or_null<IntegerAttr>(adaptor.getRhs()))
    if (rhs.getValue().isZero())
      return getOperand(0);
  return constFoldBinaryOp(adaptor.getOperands(), hw::PEO::ShrS);
}
 
LogicalResult ShrSOp::canonicalize(ShrSOp op, PatternRewriter &rewriter) {
  if (isOpTriviallyRecursive(op))
    return failure();
 
  // ShrSOp(x, cst) -> Concat(replicate(extract(x, topbit)),extract(x))
  APInt value;
  if (!matchPattern(op.getRhs(), m_ConstantInt(&value)))
    return failure();
 
  unsigned width = cast<IntegerType>(op.getLhs().getType()).getWidth();
  if (value.ugt(width))
    value = width;
  unsigned shift = value.getZExtValue();
 
  auto topbit =
      rewriter.createOrFold<ExtractOp>(op.getLoc(), op.getLhs(), width - 1, 1);
  auto sext = rewriter.createOrFold<ReplicateOp>(op.getLoc(), topbit, shift);
 
  if (width == shift) {
    replaceOpAndCopyNamehint(rewriter, op, {sext});
    return success();
  }
 
  auto extract = ExtractOp::create(rewriter, op.getLoc(), op.getLhs(), shift,
                                   width - shift);
 
  replaceOpWithNewOpAndCopyNamehint<ConcatOp>(rewriter, op, sext, extract);
  return success();
}
 
//===----------------------------------------------------------------------===//
// Other Operations
//===----------------------------------------------------------------------===//
 
OpFoldResult ExtractOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
 
  // If we are extracting the entire input, then return it.
  if (getInput().getType() == getType())
    return getInput();
 
  // Constant fold.
  if (auto input = dyn_cast_or_null<IntegerAttr>(adaptor.getInput())) {
    unsigned dstWidth = cast<IntegerType>(getType()).getWidth();
    return getIntAttr(input.getValue().lshr(getLowBit()).trunc(dstWidth),
                      getContext());
  }
  return {};
}
 
// Transforms extract(lo, cat(a, b, c, d, e)) into
// cat(extract(lo1, b), c, extract(lo2, d)).
// innerCat must be the argument of the provided ExtractOp.
//
// When prefixWidths is non-empty it is used for O(log N) binary-search lookup
// of the first relevant concat operand instead of the default O(N) linear scan.
// The array must contain cumulative bit widths in LSB-first (reversed) order:
//   prefixWidths[i] = sum of bitwidths of concat operands [N-1, N-2, ..., N-i]
static LogicalResult
extractConcatToConcatExtract(ExtractOp op, ConcatOp innerCat,
                             PatternRewriter &rewriter,
                             ArrayRef<size_t> prefixWidths = {}) {
  auto concatInputs = innerCat.getInputs();
  size_t numOperands = concatInputs.size();
  size_t lowBit = op.getLowBit();
 
  // Find the first operand (in LSB-first order) that contains lowBit.
  size_t firstIdx;
  size_t beginOfFirst;
  if (!prefixWidths.empty()) {
    // O(log N) binary search path.
    auto it =
        std::upper_bound(prefixWidths.begin(), prefixWidths.end(), lowBit);
    assert(it != prefixWidths.end());
    firstIdx = it - prefixWidths.begin();
    beginOfFirst = (firstIdx > 0) ? prefixWidths[firstIdx - 1] : 0;
  } else {
    // O(N) linear scan path.
    firstIdx = 0;
    beginOfFirst = 0;
    for (size_t i = 0; i < numOperands; ++i) {
      size_t w =
          concatInputs[numOperands - 1 - i].getType().getIntOrFloatBitWidth();
      if (lowBit < beginOfFirst + w) {
        firstIdx = i;
        break;
      }
      beginOfFirst += w;
    }
  }
 
  SmallVector<Value> reverseConcatArgs;
  size_t widthRemaining = op.getType().getIntOrFloatBitWidth();
  size_t extractLo = lowBit - beginOfFirst;
 
  // Walk forward from firstIdx in LSB-first order, building
  // [ extract(a), b, extract(c) ], skipping an extract where possible (where
  // the whole operand is consumed).
  for (size_t i = firstIdx; widthRemaining != 0 && i < numOperands; ++i) {
    Value concatArg = concatInputs[numOperands - 1 - i];
    size_t operandWidth = concatArg.getType().getIntOrFloatBitWidth();
    size_t widthToConsume = std::min(widthRemaining, operandWidth - extractLo);
 
    if (widthToConsume == operandWidth && extractLo == 0) {
      reverseConcatArgs.push_back(concatArg);
    } else {
      auto resultType = IntegerType::get(rewriter.getContext(), widthToConsume);
      reverseConcatArgs.push_back(ExtractOp::create(
          rewriter, op.getLoc(), resultType, concatArg, extractLo));
    }
 
    widthRemaining -= widthToConsume;
    // Beyond the first element, all elements are extracted from position 0.
    extractLo = 0;
  }
 
  if (reverseConcatArgs.size() == 1) {
    replaceOpAndCopyNamehint(rewriter, op, reverseConcatArgs[0]);
  } else {
    replaceOpWithNewOpAndCopyNamehint<ConcatOp>(
        rewriter, op, SmallVector<Value>(llvm::reverse(reverseConcatArgs)));
  }
  return success();
}
 
// Transforms extract(lo, replicate(a, N)) into replicate(a, N-c).
static bool extractFromReplicate(ExtractOp op, ReplicateOp replicate,
                                 PatternRewriter &rewriter) {
  auto extractResultWidth = cast<IntegerType>(op.getType()).getWidth();
  auto replicateEltWidth =
      replicate.getOperand().getType().getIntOrFloatBitWidth();
 
  // If the extract starts at the base of an element and is an even multiple,
  // we can replace the extract with a smaller replicate.
  if (op.getLowBit() % replicateEltWidth == 0 &&
      extractResultWidth % replicateEltWidth == 0) {
    replaceOpWithNewOpAndCopyNamehint<ReplicateOp>(rewriter, op, op.getType(),
                                                   replicate.getOperand());
    return true;
  }
 
  // If the extract is completely contained in one element, extract from the
  // element.
  if (op.getLowBit() % replicateEltWidth + extractResultWidth <=
      replicateEltWidth) {
    replaceOpWithNewOpAndCopyNamehint<ExtractOp>(
        rewriter, op, op.getType(), replicate.getOperand(),
        op.getLowBit() % replicateEltWidth);
    return true;
  }
 
  // We don't currently handle the case of extracting from non-whole elements,
  // e.g. `extract (replicate 2-bit-thing, N), 1`.
  return false;
}
 
LogicalResult ExtractOp::canonicalize(ExtractOp op, PatternRewriter &rewriter) {
  if (isOpTriviallyRecursive(op))
    return failure();
  auto *inputOp = op.getInput().getDefiningOp();
 
  // This turns out to be incredibly expensive.  Disable until performance is
  // addressed.
#if 0
  // If the extracted bits are all known, then return the result.
  auto knownBits = computeKnownBits(op.getInput())
                       .extractBits(cast<IntegerType>(op.getType()).getWidth(),
                                    op.getLowBit());
  if (knownBits.isConstant()) {
    replaceOpWithNewOpAndCopyNamehint<hw::ConstantOp>(rewriter, op,
                                                  knownBits.getConstant());
    return success();
  }
#endif
 
  // extract(olo, extract(ilo, x)) = extract(olo + ilo, x)
  if (auto innerExtract = dyn_cast_or_null<ExtractOp>(inputOp)) {
    replaceOpWithNewOpAndCopyNamehint<ExtractOp>(
        rewriter, op, op.getType(), innerExtract.getInput(),
        innerExtract.getLowBit() + op.getLowBit());
    return success();
  }
 
  // extract(lo, cat(a, b, c, d, e)) = cat(extract(lo1, b), c, extract(lo2, d))
  if (auto innerCat = dyn_cast_or_null<ConcatOp>(inputOp))
    return extractConcatToConcatExtract(op, innerCat, rewriter);
 
  // extract(lo, replicate(a))
  if (auto replicate = dyn_cast_or_null<ReplicateOp>(inputOp))
    if (extractFromReplicate(op, replicate, rewriter))
      return success();
 
  // `extract(and(a, cst))` -> `extract(a)` when the relevant bits of the
  // and/or/xor are not modifying the extracted bits.
  if (inputOp && inputOp->getNumOperands() == 2 &&
      isa<AndOp, OrOp, XorOp>(inputOp)) {
    if (auto cstRHS = inputOp->getOperand(1).getDefiningOp<hw::ConstantOp>()) {
      auto extractedCst = cstRHS.getValue().extractBits(
          cast<IntegerType>(op.getType()).getWidth(), op.getLowBit());
      if (isa<OrOp, XorOp>(inputOp) && extractedCst.isZero()) {
        replaceOpWithNewOpAndCopyNamehint<ExtractOp>(
            rewriter, op, op.getType(), inputOp->getOperand(0), op.getLowBit());
        return success();
      }
 
      // `extract(and(a, cst))` -> `concat(extract(a), 0)` if we only need one
      // extract to represent the result.  Turning it into a pile of extracts is
      // always fine by our cost model, but we don't want to explode things into
      // a ton of bits because it will bloat the IR and generated Verilog.
      if (isa<AndOp>(inputOp)) {
        // For our cost model, we only do this if the bit pattern is a
        // contiguous series of ones.
        unsigned lz = extractedCst.countLeadingZeros();
        unsigned tz = extractedCst.countTrailingZeros();
        unsigned pop = extractedCst.popcount();
        if (extractedCst.getBitWidth() - lz - tz == pop) {
          auto resultTy = rewriter.getIntegerType(pop);
          SmallVector<Value> resultElts;
          if (lz)
            resultElts.push_back(hw::ConstantOp::create(rewriter, op.getLoc(),
                                                        APInt::getZero(lz)));
          resultElts.push_back(rewriter.createOrFold<ExtractOp>(
              op.getLoc(), resultTy, inputOp->getOperand(0),
              op.getLowBit() + tz));
          if (tz)
            resultElts.push_back(hw::ConstantOp::create(rewriter, op.getLoc(),
                                                        APInt::getZero(tz)));
          replaceOpWithNewOpAndCopyNamehint<ConcatOp>(rewriter, op, resultElts);
          return success();
        }
      }
    }
  }
 
  // `extract(lowBit, shl(1, x))` -> `x == lowBit` when a single bit is
  // extracted.
  if (cast<IntegerType>(op.getType()).getWidth() == 1 && inputOp)
    if (auto shlOp = dyn_cast<ShlOp>(inputOp)) {
      // Don't canonicalize if the shift is multiply used.
      if (shlOp->hasOneUse())
        if (auto lhsCst = shlOp.getLhs().getDefiningOp<hw::ConstantOp>())
          if (lhsCst.getValue().isOne()) {
            auto newCst = hw::ConstantOp::create(
                rewriter, shlOp.getLoc(),
                APInt(lhsCst.getValue().getBitWidth(), op.getLowBit()));
            replaceOpWithNewOpAndCopyNamehint<ICmpOp>(
                rewriter, op, ICmpPredicate::eq, shlOp->getOperand(1), newCst,
                false);
            return success();
          }
    }
 
  return failure();
}
 
//===----------------------------------------------------------------------===//
// Associative Variadic operations
//===----------------------------------------------------------------------===//
 
// Reduce all operands to a single value (either integer constant or parameter
// expression) if all the operands are constants.
static Attribute constFoldAssociativeOp(ArrayRef<Attribute> operands,
                                        hw::PEO paramOpcode) {
  assert(operands.size() > 1 && "caller should handle one-operand case");
  // We can only fold anything in the case where all operands are known to be
  // constants.  Check the least common one first for an early out.
  if (!operands[1] || !operands[0])
    return {};
 
  // This will fold to a simple constant if all operands are constant.
  if (llvm::all_of(operands.drop_front(2),
                   [&](Attribute in) { return !!in; })) {
    SmallVector<mlir::TypedAttr> typedOperands;
    typedOperands.reserve(operands.size());
    for (auto operand : operands) {
      if (auto typedOperand = dyn_cast<mlir::TypedAttr>(operand))
        typedOperands.push_back(typedOperand);
      else
        break;
    }
    if (typedOperands.size() == operands.size())
      return hw::ParamExprAttr::get(paramOpcode, typedOperands);
  }
 
  return {};
}
 
/// When we find a logical operation (and, or, xor) with a constant e.g.
/// `X & 42`, we want to push the constant into the computation of X if it leads
/// to simplification.
///
/// This function handles the case where the logical operation has a concat
/// operand.  We check to see if we can simplify the concat, e.g. when it has
/// constant operands.
///
/// This returns true when a simplification happens.
static bool canonicalizeLogicalCstWithConcat(Operation *logicalOp,
                                             size_t concatIdx, const APInt &cst,
                                             PatternRewriter &rewriter) {
  auto concatOp = logicalOp->getOperand(concatIdx).getDefiningOp<ConcatOp>();
  assert((isa<AndOp, OrOp, XorOp>(logicalOp) && concatOp));
 
  // Check to see if any operands can be simplified by pushing the logical op
  // into all parts of the concat.
  bool canSimplify =
      llvm::any_of(concatOp->getOperands(), [&](Value operand) -> bool {
        auto *operandOp = operand.getDefiningOp();
        if (!operandOp)
          return false;
 
        // If the concat has a constant operand then we can transform this.
        if (isa<hw::ConstantOp>(operandOp))
          return true;
        // If the concat has the same logical operation and that operation has
        // a constant operation than we can fold it into that suboperation.
        return operandOp->getName() == logicalOp->getName() &&
               operandOp->hasOneUse() && operandOp->getNumOperands() != 0 &&
               operandOp->getOperands().back().getDefiningOp<hw::ConstantOp>();
      });
 
  if (!canSimplify)
    return false;
 
  // Create a new instance of the logical operation.  We have to do this the
  // hard way since we're generic across a family of different ops.
  auto createLogicalOp = [&](ArrayRef<Value> operands) -> Value {
    return createGenericOp(logicalOp->getLoc(), logicalOp->getName(), operands,
                           rewriter);
  };
 
  // Ok, let's do the transformation.  We do this by slicing up the constant
  // for each unit of the concat and duplicate the operation into the
  // sub-operand.
  SmallVector<Value> newConcatOperands;
  newConcatOperands.reserve(concatOp->getNumOperands());
 
  // Work from MSB to LSB.
  size_t nextOperandBit = concatOp.getType().getIntOrFloatBitWidth();
  for (Value operand : concatOp->getOperands()) {
    size_t operandWidth = operand.getType().getIntOrFloatBitWidth();
    nextOperandBit -= operandWidth;
    // Take a slice of the constant.
    auto eltCst =
        hw::ConstantOp::create(rewriter, logicalOp->getLoc(),
                               cst.lshr(nextOperandBit).trunc(operandWidth));
 
    newConcatOperands.push_back(createLogicalOp({operand, eltCst}));
  }
 
  // Create the concat, and the rest of the logical op if we need it.
  Value newResult =
      ConcatOp::create(rewriter, concatOp.getLoc(), newConcatOperands);
 
  // If we had a variadic logical op on the top level, then recreate it with the
  // new concat and without the constant operand.
  if (logicalOp->getNumOperands() > 2) {
    auto origOperands = logicalOp->getOperands();
    SmallVector<Value> operands;
    // Take any stuff before the concat.
    operands.append(origOperands.begin(), origOperands.begin() + concatIdx);
    // Take any stuff after the concat but before the constant.
    operands.append(origOperands.begin() + concatIdx + 1,
                    origOperands.begin() + (origOperands.size() - 1));
    // Include the new concat.
    operands.push_back(newResult);
    newResult = createLogicalOp(operands);
  }
 
  replaceOpAndCopyNamehint(rewriter, logicalOp, newResult);
  return true;
}
 
// Determines whether the inputs to a logical element are of opposite
// comparisons and can lowered into a constant.
static bool canCombineOppositeBinCmpIntoConstant(OperandRange operands) {
  llvm::SmallDenseSet<std::tuple<ICmpPredicate, Value, Value>> seenPredicates;
 
  for (auto op : operands) {
    if (auto icmpOp = op.getDefiningOp<ICmpOp>();
        icmpOp && icmpOp.getTwoState()) {
      auto predicate = icmpOp.getPredicate();
      auto lhs = icmpOp.getLhs();
      auto rhs = icmpOp.getRhs();
      if (seenPredicates.contains(
              {ICmpOp::getNegatedPredicate(predicate), lhs, rhs}))
        return true;
 
      seenPredicates.insert({predicate, lhs, rhs});
    }
  }
  return false;
}
 
OpFoldResult AndOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
 
  APInt value = APInt::getAllOnes(cast<IntegerType>(getType()).getWidth());
 
  auto inputs = adaptor.getInputs();
 
  // and(x, 01, 10) -> 00 -- annulment.
  for (auto operand : inputs) {
    auto attr = dyn_cast_or_null<IntegerAttr>(operand);
    if (!attr)
      continue;
    value &= attr.getValue();
    if (value.isZero())
      return getIntAttr(value, getContext());
  }
 
  // and(x, -1) -> x.
  if (inputs.size() == 2)
    if (auto intAttr = dyn_cast_or_null<IntegerAttr>(inputs[1]))
      if (intAttr.getValue().isAllOnes())
        return getInputs()[0];
 
  // and(x, x, x) -> x.  This also handles and(x) -> x.
  if (llvm::all_of(getInputs(),
                   [&](auto in) { return in == this->getInputs()[0]; }))
    return getInputs()[0];
 
  // and(..., x, ..., ~x, ...) -> 0
  for (Value arg : getInputs()) {
    Value subExpr;
    if (matchPattern(arg, m_Complement(m_Any(&subExpr)))) {
      for (Value arg2 : getInputs())
        if (arg2 == subExpr)
          return getIntAttr(
              APInt::getZero(cast<IntegerType>(getType()).getWidth()),
              getContext());
    }
  }
 
  // x0 = icmp(pred, x, y)
  // x1 = icmp(!pred, x, y)
  // and(x0, x1) -> 0
  if (canCombineOppositeBinCmpIntoConstant(getInputs()))
    return getIntAttr(APInt::getZero(cast<IntegerType>(getType()).getWidth()),
                      getContext());
 
  // Constant fold
  return constFoldAssociativeOp(inputs, hw::PEO::And);
}
 
/// Returns a single common operand that all inputs of the operation `op` can
/// be traced back to, or an empty `Value` if no such operand exists.
///
/// For example for `or(a[0], a[1], ..., a[n-1])` this function returns `a`
/// (assuming the bit-width of `a` is `n`).
template <typename Op>
static Value getCommonOperand(Op op) {
  if (!op.getType().isInteger(1))
    return Value();
 
  auto inputs = op.getInputs();
  size_t size = inputs.size();
 
  auto sourceOp = inputs[0].template getDefiningOp<ExtractOp>();
  if (!sourceOp)
    return Value();
  Value source = sourceOp.getOperand();
 
  // Fast path: the input size is not equal to the width of the source.
  if (size != source.getType().getIntOrFloatBitWidth())
    return Value();
 
  // Tracks the bits that were encountered.
  llvm::BitVector bits(size);
  bits.set(sourceOp.getLowBit());
 
  for (size_t i = 1; i != size; ++i) {
    auto extractOp = inputs[i].template getDefiningOp<ExtractOp>();
    if (!extractOp || extractOp.getOperand() != source)
      return Value();
    bits.set(extractOp.getLowBit());
  }
 
  return bits.all() ? source : Value();
}
 
/// Canonicalize an idempotent operation `op` so that only one input of any kind
/// occurs.
///
/// Example: `and(x, y, x, z)` -> `and(x, y, z)`
template <typename Op>
static bool canonicalizeIdempotentInputs(Op op, PatternRewriter &rewriter) {
  // Depth limit to search, in operations.  Chosen arbitrarily, keep small.
  constexpr unsigned limit = 3;
  auto inputs = op.getInputs();
 
  llvm::SmallSetVector<Value, 8> uniqueInputs(inputs.begin(), inputs.end());
  llvm::SmallDenseSet<Op, 8> checked;
  checked.insert(op);
 
  struct OpWithDepth {
    Op op;
    unsigned depth;
  };
  llvm::SmallVector<OpWithDepth, 8> worklist;
 
  auto enqueue = [&worklist, &checked, &op](Value input, unsigned depth) {
    // Add to worklist if within depth limit, is defined in the same block by
    // the same kind of operation, has same two-state-ness, and not enqueued
    // previously.
    if (depth < limit && input.getParentBlock() == op->getBlock()) {
      auto inputOp = input.template getDefiningOp<Op>();
      if (inputOp && inputOp.getTwoState() == op.getTwoState() &&
          checked.insert(inputOp).second)
        worklist.push_back({inputOp, depth + 1});
    }
  };
 
  for (auto input : uniqueInputs)
    enqueue(input, 0);
 
  while (!worklist.empty()) {
    auto item = worklist.pop_back_val();
 
    for (auto input : item.op.getInputs()) {
      uniqueInputs.remove(input);
      enqueue(input, item.depth);
    }
  }
 
  if (uniqueInputs.size() < inputs.size()) {
    replaceOpWithNewOpAndCopyNamehint<Op>(rewriter, op, op.getType(),
                                          uniqueInputs.getArrayRef(),
                                          op.getTwoState());
    return true;
  }
 
  return false;
}
 
LogicalResult AndOp::canonicalize(AndOp op, PatternRewriter &rewriter) {
  if (isOpTriviallyRecursive(op))
    return failure();
 
  auto inputs = op.getInputs();
  auto size = inputs.size();
 
  // and(x, and(...)) -> and(x, ...) -- flatten
  if (tryFlatteningOperands(op, rewriter))
    return success();
 
  // and(..., x, ..., x) -> and(..., x, ...) -- idempotent
  // and(..., x, and(..., x, ...)) -> and(..., and(..., x, ...)) -- idempotent
  // Trivial and(x), and(x, x) cases are handled by [AndOp::fold] above.
  if (size > 1 && canonicalizeIdempotentInputs(op, rewriter))
    return success();
 
  assert(size > 1 && "expected 2 or more operands, `fold` should handle this");
 
  // Patterns for and with a constant on RHS.
  APInt value;
  if (matchPattern(inputs.back(), m_ConstantInt(&value))) {
    // and(..., '1) -> and(...) -- identity
    if (value.isAllOnes()) {
      replaceOpWithNewOpAndCopyNamehint<AndOp>(rewriter, op, op.getType(),
                                               inputs.drop_back(), false);
      return success();
    }
 
    // TODO: Combine multiple constants together even if they aren't at the
    // end. and(..., c1, c2) -> and(..., c3) where c3 = c1 & c2 -- constant
    // folding
    APInt value2;
    if (matchPattern(inputs[size - 2], m_ConstantInt(&value2))) {
      auto cst = hw::ConstantOp::create(rewriter, op.getLoc(), value & value2);
      SmallVector<Value, 4> newOperands(inputs.drop_back(/*n=*/2));
      newOperands.push_back(cst);
      replaceOpWithNewOpAndCopyNamehint<AndOp>(rewriter, op, op.getType(),
                                               newOperands, false);
      return success();
    }
 
    // Handle 'and' with a single bit constant on the RHS.
    if (size == 2 && value.isPowerOf2()) {
      // If the LHS is a replicate from a single bit, we can 'concat' it
      // into place.  e.g.:
      //   `replicate(x) & 4` -> `concat(zeros, x, zeros)`
      // TODO: Generalize this for non-single-bit operands.
      if (auto replicate = inputs[0].getDefiningOp<ReplicateOp>()) {
        auto replicateOperand = replicate.getOperand();
        if (replicateOperand.getType().isInteger(1)) {
          unsigned resultWidth = op.getType().getIntOrFloatBitWidth();
          auto trailingZeros = value.countTrailingZeros();
 
          // Don't add zero bit constants unnecessarily.
          SmallVector<Value, 3> concatOperands;
          if (trailingZeros != resultWidth - 1) {
            auto highZeros = hw::ConstantOp::create(
                rewriter, op.getLoc(),
                APInt::getZero(resultWidth - trailingZeros - 1));
            concatOperands.push_back(highZeros);
          }
          concatOperands.push_back(replicateOperand);
          if (trailingZeros != 0) {
            auto lowZeros = hw::ConstantOp::create(
                rewriter, op.getLoc(), APInt::getZero(trailingZeros));
            concatOperands.push_back(lowZeros);
          }
          replaceOpWithNewOpAndCopyNamehint<ConcatOp>(
              rewriter, op, op.getType(), concatOperands);
          return success();
        }
      }
    }
 
    // Narrow the op if the constant has leading or trailing zeros.
    //
    // and(a, 0b00101100) -> concat(0b00, and(extract(a), 0b1011), 0b00)
    unsigned leadingZeros = value.countLeadingZeros();
    unsigned trailingZeros = value.countTrailingZeros();
    if (leadingZeros > 0 || trailingZeros > 0) {
      unsigned maskLength = value.getBitWidth() - leadingZeros - trailingZeros;
 
      // Extract the non-zero regions of the operands. Look through extracts.
      SmallVector<Value> operands;
      for (auto input : inputs.drop_back()) {
        unsigned offset = trailingZeros;
        while (auto extractOp = input.getDefiningOp<ExtractOp>()) {
          input = extractOp.getInput();
          offset += extractOp.getLowBit();
        }
        operands.push_back(ExtractOp::create(rewriter, op.getLoc(), input,
                                             offset, maskLength));
      }
 
      // Add the narrowed mask if needed.
      auto narrowMask = value.extractBits(maskLength, trailingZeros);
      if (!narrowMask.isAllOnes())
        operands.push_back(hw::ConstantOp::create(
            rewriter, inputs.back().getLoc(), narrowMask));
 
      // Create the narrow and op.
      Value narrowValue = operands.back();
      if (operands.size() > 1)
        narrowValue =
            AndOp::create(rewriter, op.getLoc(), operands, op.getTwoState());
      operands.clear();
 
      // Concatenate the narrow and with the leading and trailing zeros.
      if (leadingZeros > 0)
        operands.push_back(hw::ConstantOp::create(
            rewriter, op.getLoc(), APInt::getZero(leadingZeros)));
      operands.push_back(narrowValue);
      if (trailingZeros > 0)
        operands.push_back(hw::ConstantOp::create(
            rewriter, op.getLoc(), APInt::getZero(trailingZeros)));
      replaceOpWithNewOpAndCopyNamehint<ConcatOp>(rewriter, op, operands);
      return success();
    }
 
    // and(concat(x, cst1), a, b, c, cst2)
    //    ==> and(a, b, c, concat(and(x,cst2'), and(cst1,cst2'')).
    // We do this for even more multi-use concats since they are "just wiring".
    for (size_t i = 0; i < size - 1; ++i) {
      if (auto concat = inputs[i].getDefiningOp<ConcatOp>())
        if (canonicalizeLogicalCstWithConcat(op, i, value, rewriter))
          return success();
    }
  }
 
  // extracts only of and(...) -> and(extract()...)
  if (narrowOperationWidth(op, true, rewriter))
    return success();
 
  // and(a[0], a[1], ..., a[n]) -> icmp eq(a, -1)
  if (auto source = getCommonOperand(op)) {
    auto cmpAgainst =
        hw::ConstantOp::create(rewriter, op.getLoc(), APInt::getAllOnes(size));
    replaceOpWithNewOpAndCopyNamehint<ICmpOp>(rewriter, op, ICmpPredicate::eq,
                                              source, cmpAgainst);
    return success();
  }
 
  // and(x, replicate(p : i1)) -> mux(p, x, zero)
  if (op.getTwoState() && op.getNumOperands() == 2) {
    auto isReplicateOfI1 = [](Value v) {
      auto rep = v.getDefiningOp<ReplicateOp>();
      if (!rep)
        return false;
      return rep.getOperand().getType().isInteger(1);
    };
    Value x = op.getOperand(0);
    Value y = op.getOperand(1);
    if (isReplicateOfI1(x))
      std::swap(x, y);
    if (isReplicateOfI1(y)) {
      Value p = y.getDefiningOp<ReplicateOp>().getInput();
      Value zero = hw::ConstantOp::create(
          rewriter, op.getLoc(), rewriter.getIntegerAttr(op.getType(), 0));
      replaceOpWithNewOpAndCopyNamehint<MuxOp>(rewriter, op, p, x, zero,
                                               /*isTwoState=*/true);
      return success();
    }
  }
 
  /// TODO: and(..., x, not(x)) -> and(..., 0) -- complement
  return failure();
}
 
OpFoldResult OrOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
 
  auto value = APInt::getZero(cast<IntegerType>(getType()).getWidth());
  auto inputs = adaptor.getInputs();
  // or(x, 10, 01) -> 11
  for (auto operand : inputs) {
    auto attr = dyn_cast_or_null<IntegerAttr>(operand);
    if (!attr)
      continue;
    value |= attr.getValue();
    if (value.isAllOnes())
      return getIntAttr(value, getContext());
  }
 
  // or(x, 0) -> x
  if (inputs.size() == 2)
    if (auto intAttr = dyn_cast_or_null<IntegerAttr>(inputs[1]))
      if (intAttr.getValue().isZero())
        return getInputs()[0];
 
  // or(x, x, x) -> x.  This also handles or(x) -> x
  if (llvm::all_of(getInputs(),
                   [&](auto in) { return in == this->getInputs()[0]; }))
    return getInputs()[0];
 
  // or(..., x, ..., ~x, ...) -> -1
  for (Value arg : getInputs()) {
    Value subExpr;
    if (matchPattern(arg, m_Complement(m_Any(&subExpr)))) {
      for (Value arg2 : getInputs())
        if (arg2 == subExpr)
          return getIntAttr(
              APInt::getAllOnes(cast<IntegerType>(getType()).getWidth()),
              getContext());
    }
  }
 
  // x0 = icmp(pred, x, y)
  // x1 = icmp(!pred, x, y)
  // or(x0, x1) -> 1
  if (canCombineOppositeBinCmpIntoConstant(getInputs()))
    return getIntAttr(
        APInt::getAllOnes(cast<IntegerType>(getType()).getWidth()),
        getContext());
 
  // Constant fold
  return constFoldAssociativeOp(inputs, hw::PEO::Or);
}
 
LogicalResult OrOp::canonicalize(OrOp op, PatternRewriter &rewriter) {
  if (isOpTriviallyRecursive(op))
    return failure();
 
  auto inputs = op.getInputs();
  auto size = inputs.size();
 
  // or(x, or(...)) -> or(x, ...) -- flatten
  if (tryFlatteningOperands(op, rewriter))
    return success();
 
  // or(..., x, ..., x, ...) -> or(..., x) -- idempotent
  // or(..., x, or(..., x, ...)) -> or(..., or(..., x, ...)) -- idempotent
  // Trivial or(x), or(x, x) cases are handled by [OrOp::fold].
  if (size > 1 && canonicalizeIdempotentInputs(op, rewriter))
    return success();
 
  assert(size > 1 && "expected 2 or more operands");
 
  // Patterns for and with a constant on RHS.
  APInt value;
  if (matchPattern(inputs.back(), m_ConstantInt(&value))) {
    // or(..., '0) -> or(...) -- identity
    if (value.isZero()) {
      replaceOpWithNewOpAndCopyNamehint<OrOp>(rewriter, op, op.getType(),
                                              inputs.drop_back());
      return success();
    }
 
    // or(..., c1, c2) -> or(..., c3) where c3 = c1 | c2 -- constant folding
    APInt value2;
    if (matchPattern(inputs[size - 2], m_ConstantInt(&value2))) {
      auto cst = hw::ConstantOp::create(rewriter, op.getLoc(), value | value2);
      SmallVector<Value, 4> newOperands(inputs.drop_back(/*n=*/2));
      newOperands.push_back(cst);
      replaceOpWithNewOpAndCopyNamehint<OrOp>(rewriter, op, op.getType(),
                                              newOperands);
      return success();
    }
 
    // or(concat(x, cst1), a, b, c, cst2)
    //    ==> or(a, b, c, concat(or(x,cst2'), or(cst1,cst2'')).
    // We do this for even more multi-use concats since they are "just wiring".
    for (size_t i = 0; i < size - 1; ++i) {
      if (auto concat = inputs[i].getDefiningOp<ConcatOp>())
        if (canonicalizeLogicalCstWithConcat(op, i, value, rewriter))
          return success();
    }
  }
 
  // extracts only of or(...) -> or(extract()...)
  if (narrowOperationWidth(op, true, rewriter))
    return success();
 
  // or(a[0], a[1], ..., a[n]) -> icmp ne(a, 0)
  if (auto source = getCommonOperand(op)) {
    auto cmpAgainst =
        hw::ConstantOp::create(rewriter, op.getLoc(), APInt::getZero(size));
    replaceOpWithNewOpAndCopyNamehint<ICmpOp>(rewriter, op, ICmpPredicate::ne,
                                              source, cmpAgainst);
    return success();
  }
 
  // or(mux(c_1, a, 0), mux(c_2, a, 0), ..., mux(c_n, a, 0)) -> mux(or(c_1, c_2,
  // .., c_n), a, 0)
  if (auto firstMux = op.getOperand(0).getDefiningOp<comb::MuxOp>()) {
    APInt value;
    if (op.getTwoState() && firstMux.getTwoState() &&
        matchPattern(firstMux.getFalseValue(), m_ConstantInt(&value)) &&
        value.isZero()) {
      SmallVector<Value> conditions{firstMux.getCond()};
      auto check = [&](Value v) {
        auto mux = v.getDefiningOp<comb::MuxOp>();
        if (!mux)
          return false;
        conditions.push_back(mux.getCond());
        return mux.getTwoState() &&
               firstMux.getTrueValue() == mux.getTrueValue() &&
               firstMux.getFalseValue() == mux.getFalseValue();
      };
      if (llvm::all_of(op.getOperands().drop_front(), check)) {
        auto cond = comb::OrOp::create(rewriter, op.getLoc(), conditions, true);
        replaceOpWithNewOpAndCopyNamehint<comb::MuxOp>(
            rewriter, op, cond, firstMux.getTrueValue(),
            firstMux.getFalseValue(), true);
        return success();
      }
    }
  }
 
  /// TODO: or(..., x, not(x)) -> or(..., '1) -- complement
  return failure();
}
 
OpFoldResult XorOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
 
  auto size = getInputs().size();
  auto inputs = adaptor.getInputs();
 
  // xor(x) -> x -- noop
  if (size == 1)
    return getInputs()[0];
 
  // xor(x, x) -> 0 -- idempotent
  if (size == 2 && getInputs()[0] == getInputs()[1])
    return IntegerAttr::get(getType(), 0);
 
  // xor(x, 0) -> x
  if (inputs.size() == 2)
    if (auto intAttr = dyn_cast_or_null<IntegerAttr>(inputs[1]))
      if (intAttr.getValue().isZero())
        return getInputs()[0];
 
  // xor(xor(x,1),1) -> x
  // but not self loop
  Value subExpr;
  if (matchPattern(getResult(), m_Complement(m_Complement(m_Any(&subExpr)))) &&
      subExpr != getResult())
    return subExpr;
 
  // Constant fold
  return constFoldAssociativeOp(inputs, hw::PEO::Xor);
}
 
// xor(icmp, a, b, 1) -> xor(icmp, a, b) if icmp has one user.
static void canonicalizeXorIcmpTrue(XorOp op, unsigned icmpOperand,
                                    PatternRewriter &rewriter) {
  auto icmp = op.getOperand(icmpOperand).getDefiningOp<ICmpOp>();
  auto negatedPred = ICmpOp::getNegatedPredicate(icmp.getPredicate());
 
  Value result =
      ICmpOp::create(rewriter, icmp.getLoc(), negatedPred, icmp.getOperand(0),
                     icmp.getOperand(1), icmp.getTwoState());
 
  // If the xor had other operands, rebuild it.
  if (op.getNumOperands() > 2) {
    SmallVector<Value, 4> newOperands(op.getOperands());
    newOperands.pop_back();
    newOperands.erase(newOperands.begin() + icmpOperand);
    newOperands.push_back(result);
    result =
        XorOp::create(rewriter, op.getLoc(), newOperands, op.getTwoState());
  }
 
  replaceOpAndCopyNamehint(rewriter, op, result);
}
 
LogicalResult XorOp::canonicalize(XorOp op, PatternRewriter &rewriter) {
  if (isOpTriviallyRecursive(op))
    return failure();
 
  auto inputs = op.getInputs();
  auto size = inputs.size();
  assert(size > 1 && "expected 2 or more operands");
 
  // xor(..., x, x) -> xor (...) -- idempotent
  if (inputs[size - 1] == inputs[size - 2]) {
    assert(size > 2 &&
           "expected idempotent case for 2 elements handled already.");
    replaceOpWithNewOpAndCopyNamehint<XorOp>(rewriter, op, op.getType(),
                                             inputs.drop_back(/*n=*/2), false);
    return success();
  }
 
  // Patterns for xor with a constant on RHS.
  APInt value;
  if (matchPattern(inputs.back(), m_ConstantInt(&value))) {
    // xor(..., 0) -> xor(...) -- identity
    if (value.isZero()) {
      replaceOpWithNewOpAndCopyNamehint<XorOp>(rewriter, op, op.getType(),
                                               inputs.drop_back(), false);
      return success();
    }
 
    // xor(..., c1, c2) -> xor(..., c3) where c3 = c1 ^ c2.
    APInt value2;
    if (matchPattern(inputs[size - 2], m_ConstantInt(&value2))) {
      auto cst = hw::ConstantOp::create(rewriter, op.getLoc(), value ^ value2);
      SmallVector<Value, 4> newOperands(inputs.drop_back(/*n=*/2));
      newOperands.push_back(cst);
      replaceOpWithNewOpAndCopyNamehint<XorOp>(rewriter, op, op.getType(),
                                               newOperands, false);
      return success();
    }
 
    bool isSingleBit = value.getBitWidth() == 1;
 
    // Check for subexpressions that we can simplify.
    for (size_t i = 0; i < size - 1; ++i) {
      Value operand = inputs[i];
 
      // xor(concat(x, cst1), a, b, c, cst2)
      //    ==> xor(a, b, c, concat(xor(x,cst2'), xor(cst1,cst2'')).
      // We do this for even more multi-use concats since they are "just
      // wiring".
      if (auto concat = operand.getDefiningOp<ConcatOp>())
        if (canonicalizeLogicalCstWithConcat(op, i, value, rewriter))
          return success();
 
      // xor(icmp, a, b, 1) -> xor(icmp, a, b) if icmp has one user.
      if (isSingleBit && operand.hasOneUse()) {
        assert(value == 1 && "single bit constant has to be one if not zero");
        if (auto icmp = operand.getDefiningOp<ICmpOp>())
          return canonicalizeXorIcmpTrue(op, i, rewriter), success();
      }
    }
  }
 
  // xor(sext(x), -1) -> sext(xor(x,-1))
  // More concisely: ~sext(x) = sext(~x)
  Value base;
  // Check for sext of the inverted value
  if (matchPattern(op.getResult(), m_Complement(m_Sext(m_Any(&base))))) {
    // Create negated sext: ~sext(x) = sext(~x)
    auto negBase = createOrFoldNot(rewriter, op.getLoc(), base, true);
    auto sextNegBase =
        createOrFoldSExt(rewriter, op.getLoc(), negBase, op.getType());
    replaceOpAndCopyNamehint(rewriter, op, sextNegBase);
    return success();
  }
 
  // xor(x, xor(...)) -> xor(x, ...) -- flatten
  if (tryFlatteningOperands(op, rewriter))
    return success();
 
  // extracts only of xor(...) -> xor(extract()...)
  if (narrowOperationWidth(op, true, rewriter))
    return success();
 
  // xor(a[0], a[1], ..., a[n]) -> parity(a)
  if (auto source = getCommonOperand(op)) {
    replaceOpWithNewOpAndCopyNamehint<ParityOp>(rewriter, op, source);
    return success();
  }
 
  return failure();
}
 
OpFoldResult SubOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
 
  // sub(x - x) -> 0
  if (getRhs() == getLhs())
    return getIntAttr(
        APInt::getZero(getLhs().getType().getIntOrFloatBitWidth()),
        getContext());
 
  if (adaptor.getRhs()) {
    // If both are constants, we can unconditionally fold.
    if (adaptor.getLhs()) {
      // Constant fold (c1 - c2) => (c1 + -1*c2).
      auto negOne = getIntAttr(
          APInt::getAllOnes(getLhs().getType().getIntOrFloatBitWidth()),
          getContext());
      auto rhsNeg = hw::ParamExprAttr::get(
          hw::PEO::Mul, cast<TypedAttr>(adaptor.getRhs()), negOne);
      return hw::ParamExprAttr::get(hw::PEO::Add,
                                    cast<TypedAttr>(adaptor.getLhs()), rhsNeg);
    }
 
    // sub(x - 0) -> x
    if (auto rhsC = dyn_cast<IntegerAttr>(adaptor.getRhs())) {
      if (rhsC.getValue().isZero())
        return getLhs();
    }
  }
 
  return {};
}
 
LogicalResult SubOp::canonicalize(SubOp op, PatternRewriter &rewriter) {
  if (isOpTriviallyRecursive(op))
    return failure();
 
  // sub(x, cst) -> add(x, -cst)
  APInt value;
  if (matchPattern(op.getRhs(), m_ConstantInt(&value))) {
    auto negCst = hw::ConstantOp::create(rewriter, op.getLoc(), -value);
    replaceOpWithNewOpAndCopyNamehint<AddOp>(rewriter, op, op.getLhs(), negCst,
                                             false);
    return success();
  }
 
  // extracts only of sub(...) -> sub(extract()...)
  if (narrowOperationWidth(op, false, rewriter))
    return success();
 
  return failure();
}
 
OpFoldResult AddOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
 
  auto size = getInputs().size();
 
  // add(x) -> x -- noop
  if (size == 1u)
    return getInputs()[0];
 
  // Constant fold constant operands.
  return constFoldAssociativeOp(adaptor.getOperands(), hw::PEO::Add);
}
 
LogicalResult AddOp::canonicalize(AddOp op, PatternRewriter &rewriter) {
  if (isOpTriviallyRecursive(op))
    return failure();
 
  auto inputs = op.getInputs();
  auto size = inputs.size();
  assert(size > 1 && "expected 2 or more operands");
 
  APInt value, value2;
 
  // add(..., 0) -> add(...) -- identity
  if (matchPattern(inputs.back(), m_ConstantInt(&value)) && value.isZero()) {
    replaceOpWithNewOpAndCopyNamehint<AddOp>(rewriter, op, op.getType(),
                                             inputs.drop_back(), false);
    return success();
  }
 
  // add(..., c1, c2) -> add(..., c3) where c3 = c1 + c2 -- constant folding
  if (matchPattern(inputs[size - 1], m_ConstantInt(&value)) &&
      matchPattern(inputs[size - 2], m_ConstantInt(&value2))) {
    auto cst = hw::ConstantOp::create(rewriter, op.getLoc(), value + value2);
    SmallVector<Value, 4> newOperands(inputs.drop_back(/*n=*/2));
    newOperands.push_back(cst);
    replaceOpWithNewOpAndCopyNamehint<AddOp>(rewriter, op, op.getType(),
                                             newOperands, false);
    return success();
  }
 
  // add(..., x, x) -> add(..., shl(x, 1))
  if (inputs[size - 1] == inputs[size - 2]) {
    SmallVector<Value, 4> newOperands(inputs.drop_back(/*n=*/2));
 
    auto one = hw::ConstantOp::create(rewriter, op.getLoc(), op.getType(), 1);
    auto shiftLeftOp =
        comb::ShlOp::create(rewriter, op.getLoc(), inputs.back(), one, false);
 
    newOperands.push_back(shiftLeftOp);
    replaceOpWithNewOpAndCopyNamehint<AddOp>(rewriter, op, op.getType(),
                                             newOperands, false);
    return success();
  }
 
  auto shlOp = inputs[size - 1].getDefiningOp<comb::ShlOp>();
  // add(..., x, shl(x, c)) -> add(..., mul(x, (1 << c) + 1))
  if (shlOp && shlOp.getLhs() == inputs[size - 2] &&
      matchPattern(shlOp.getRhs(), m_ConstantInt(&value))) {
 
    APInt one(/*numBits=*/value.getBitWidth(), 1, /*isSigned=*/false);
    auto rhs =
        hw::ConstantOp::create(rewriter, op.getLoc(), (one << value) + one);
 
    std::array<Value, 2> factors = {shlOp.getLhs(), rhs};
    auto mulOp = comb::MulOp::create(rewriter, op.getLoc(), factors, false);
 
    SmallVector<Value, 4> newOperands(inputs.drop_back(/*n=*/2));
    newOperands.push_back(mulOp);
    replaceOpWithNewOpAndCopyNamehint<AddOp>(rewriter, op, op.getType(),
                                             newOperands, false);
    return success();
  }
 
  auto mulOp = inputs[size - 1].getDefiningOp<comb::MulOp>();
  // add(..., x, mul(x, c)) -> add(..., mul(x, c + 1))
  if (mulOp && mulOp.getInputs().size() == 2 &&
      mulOp.getInputs()[0] == inputs[size - 2] &&
      matchPattern(mulOp.getInputs()[1], m_ConstantInt(&value))) {
 
    APInt one(/*numBits=*/value.getBitWidth(), 1, /*isSigned=*/false);
    auto rhs = hw::ConstantOp::create(rewriter, op.getLoc(), value + one);
    std::array<Value, 2> factors = {mulOp.getInputs()[0], rhs};
    auto newMulOp = comb::MulOp::create(rewriter, op.getLoc(), factors, false);
 
    SmallVector<Value, 4> newOperands(inputs.drop_back(/*n=*/2));
    newOperands.push_back(newMulOp);
    replaceOpWithNewOpAndCopyNamehint<AddOp>(rewriter, op, op.getType(),
                                             newOperands, false);
    return success();
  }
 
  // add(a, add(...)) -> add(a, ...) -- flatten
  if (tryFlatteningOperands(op, rewriter))
    return success();
 
  // extracts only of add(...) -> add(extract()...)
  if (narrowOperationWidth(op, false, rewriter))
    return success();
 
  // add(add(x, c1), c2) -> add(x, c1 + c2)
  auto addOp = inputs[0].getDefiningOp<comb::AddOp>();
  if (addOp && addOp.getInputs().size() == 2 &&
      matchPattern(addOp.getInputs()[1], m_ConstantInt(&value2)) &&
      inputs.size() == 2 && matchPattern(inputs[1], m_ConstantInt(&value))) {
 
    auto rhs = hw::ConstantOp::create(rewriter, op.getLoc(), value + value2);
    replaceOpWithNewOpAndCopyNamehint<AddOp>(
        rewriter, op, op.getType(), ArrayRef<Value>{addOp.getInputs()[0], rhs},
        /*twoState=*/op.getTwoState() && addOp.getTwoState());
    return success();
  }
 
  return failure();
}
 
OpFoldResult MulOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
 
  auto size = getInputs().size();
  auto inputs = adaptor.getInputs();
 
  // mul(x) -> x -- noop
  if (size == 1u)
    return getInputs()[0];
 
  auto width = cast<IntegerType>(getType()).getWidth();
  if (width == 0)
    return getIntAttr(APInt::getZero(0), getContext());
 
  APInt value(/*numBits=*/width, 1, /*isSigned=*/false);
 
  // mul(x, 0, 1) -> 0 -- annulment
  for (auto operand : inputs) {
    auto attr = dyn_cast_or_null<IntegerAttr>(operand);
    if (!attr)
      continue;
    value *= attr.getValue();
    if (value.isZero())
      return getIntAttr(value, getContext());
  }
 
  // Constant fold
  return constFoldAssociativeOp(inputs, hw::PEO::Mul);
}
 
LogicalResult MulOp::canonicalize(MulOp op, PatternRewriter &rewriter) {
  if (isOpTriviallyRecursive(op))
    return failure();
 
  auto inputs = op.getInputs();
  auto size = inputs.size();
  assert(size > 1 && "expected 2 or more operands");
 
  APInt value, value2;
 
  // mul(x, c) -> shl(x, log2(c)), where c is a power of two.
  if (size == 2 && matchPattern(inputs.back(), m_ConstantInt(&value)) &&
      value.isPowerOf2()) {
    auto shift = hw::ConstantOp::create(rewriter, op.getLoc(), op.getType(),
                                        value.exactLogBase2());
    auto shlOp =
        comb::ShlOp::create(rewriter, op.getLoc(), inputs[0], shift, false);
 
    replaceOpWithNewOpAndCopyNamehint<MulOp>(rewriter, op, op.getType(),
                                             ArrayRef<Value>(shlOp), false);
    return success();
  }
 
  // mul(..., 1) -> mul(...) -- identity
  if (matchPattern(inputs.back(), m_ConstantInt(&value)) && value.isOne()) {
    replaceOpWithNewOpAndCopyNamehint<MulOp>(rewriter, op, op.getType(),
                                             inputs.drop_back());
    return success();
  }
 
  // mul(..., c1, c2) -> mul(..., c3) where c3 = c1 * c2 -- constant folding
  if (matchPattern(inputs[size - 1], m_ConstantInt(&value)) &&
      matchPattern(inputs[size - 2], m_ConstantInt(&value2))) {
    auto cst = hw::ConstantOp::create(rewriter, op.getLoc(), value * value2);
    SmallVector<Value, 4> newOperands(inputs.drop_back(/*n=*/2));
    newOperands.push_back(cst);
    replaceOpWithNewOpAndCopyNamehint<MulOp>(rewriter, op, op.getType(),
                                             newOperands);
    return success();
  }
 
  // mul(a, mul(...)) -> mul(a, ...) -- flatten
  if (tryFlatteningOperands(op, rewriter))
    return success();
 
  // extracts only of mul(...) -> mul(extract()...)
  if (narrowOperationWidth(op, false, rewriter))
    return success();
 
  return failure();
}
 
template <class Op, bool isSigned>
static OpFoldResult foldDiv(Op op, ArrayRef<Attribute> constants) {
  if (auto rhsValue = dyn_cast_or_null<IntegerAttr>(constants[1])) {
    // divu(x, 1) -> x, divs(x, 1) -> x
    if (rhsValue.getValue() == 1)
      return op.getLhs();
 
    // If the divisor is zero, do not fold for now.
    if (rhsValue.getValue().isZero())
      return {};
  }
 
  return constFoldBinaryOp(constants, isSigned ? hw::PEO::DivS : hw::PEO::DivU);
}
 
OpFoldResult DivUOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
  return foldDiv<DivUOp, /*isSigned=*/false>(*this, adaptor.getOperands());
}
 
OpFoldResult DivSOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
  return foldDiv<DivSOp, /*isSigned=*/true>(*this, adaptor.getOperands());
}
 
template <class Op, bool isSigned>
static OpFoldResult foldMod(Op op, ArrayRef<Attribute> constants) {
  if (auto rhsValue = dyn_cast_or_null<IntegerAttr>(constants[1])) {
    // modu(x, 1) -> 0, mods(x, 1) -> 0
    if (rhsValue.getValue() == 1)
      return getIntAttr(APInt::getZero(op.getType().getIntOrFloatBitWidth()),
                        op.getContext());
 
    // If the divisor is zero, do not fold for now.
    if (rhsValue.getValue().isZero())
      return {};
  }
 
  if (auto lhsValue = dyn_cast_or_null<IntegerAttr>(constants[0])) {
    // modu(0, x) -> 0, mods(0, x) -> 0
    if (lhsValue.getValue().isZero())
      return getIntAttr(APInt::getZero(op.getType().getIntOrFloatBitWidth()),
                        op.getContext());
  }
 
  return constFoldBinaryOp(constants, isSigned ? hw::PEO::ModS : hw::PEO::ModU);
}
 
OpFoldResult ModUOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
  return foldMod<ModUOp, /*isSigned=*/false>(*this, adaptor.getOperands());
}
 
OpFoldResult ModSOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
  return foldMod<ModSOp, /*isSigned=*/true>(*this, adaptor.getOperands());
}
 
LogicalResult DivUOp::canonicalize(DivUOp op, PatternRewriter &rewriter) {
  if (isOpTriviallyRecursive(op) || !op.getTwoState())
    return failure();
  return convertDivUByPowerOfTwo(op, rewriter);
}
 
LogicalResult ModUOp::canonicalize(ModUOp op, PatternRewriter &rewriter) {
  if (isOpTriviallyRecursive(op) || !op.getTwoState())
    return failure();
 
  return convertModUByPowerOfTwo(op, rewriter);
}
 
//===----------------------------------------------------------------------===//
// ConcatOp
//===----------------------------------------------------------------------===//
 
// Constant folding
OpFoldResult ConcatOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
 
  if (getNumOperands() == 1)
    return getOperand(0);
 
  // If all the operands are constant, we can fold.
  for (auto attr : adaptor.getInputs())
    if (!attr || !isa<IntegerAttr>(attr))
      return {};
 
  // If we got here, we can constant fold.
  unsigned resultWidth = getType().getIntOrFloatBitWidth();
  APInt result(resultWidth, 0);
 
  unsigned nextInsertion = resultWidth;
  // Insert each chunk into the result.
  for (auto attr : adaptor.getInputs()) {
    auto chunk = cast<IntegerAttr>(attr).getValue();
    nextInsertion -= chunk.getBitWidth();
    result.insertBits(chunk, nextInsertion);
  }
 
  return getIntAttr(result, getContext());
}
 
LogicalResult ConcatOp::canonicalize(ConcatOp op, PatternRewriter &rewriter) {
  if (isOpTriviallyRecursive(op))
    return failure();
 
  auto inputs = op.getInputs();
  auto size = inputs.size();
  assert(size > 1 && "expected 2 or more operands");
 
  // Holds the not-yet-processed operands in reverse order!
  SmallVector<Value, 4> pendingOperands, processedOperands;
  bool anyOperandChanged;
 
  auto pushPendingOperands = [&](ValueRange operands) {
    auto size = operands.size();
    for (size_t i = 0; i != size; ++i)
      pendingOperands.push_back(operands[size - 1 - i]);
    anyOperandChanged = true;
  };
  auto replacePrevOperand = [&](Value replacement) {
    processedOperands.back() = replacement;
    anyOperandChanged = true;
  };
  pendingOperands.reserve(size);
  pushPendingOperands(inputs);
  anyOperandChanged = false;
 
  while (!pendingOperands.empty()) {
    Value nextOperand = pendingOperands.pop_back_val();
 
    // If an operand to the concat is itself a concat, then we can fold them
    // together.
    if (auto subConcat = nextOperand.getDefiningOp<ConcatOp>()) {
      pushPendingOperands(subConcat->getOperands());
      continue;
    }
 
    // Check for canonicalization due to neighboring operands.
    if (!processedOperands.empty()) {
      Value prevOperand = processedOperands.back();
 
      // Merge neighboring constants.
      if (auto cst = nextOperand.getDefiningOp<hw::ConstantOp>()) {
        if (auto prevCst = prevOperand.getDefiningOp<hw::ConstantOp>()) {
          unsigned prevWidth = prevCst.getValue().getBitWidth();
          unsigned thisWidth = cst.getValue().getBitWidth();
          auto resultCst = cst.getValue().zext(prevWidth + thisWidth);
          resultCst |= prevCst.getValue().zext(prevWidth + thisWidth)
                       << thisWidth;
          Value replacement =
              hw::ConstantOp::create(rewriter, op.getLoc(), resultCst);
          replacePrevOperand(replacement);
          continue;
        }
      }
 
      // If the two operands are the same, turn them into a replicate.
      if (nextOperand == prevOperand) {
        Value replacement =
            rewriter.createOrFold<ReplicateOp>(op.getLoc(), prevOperand, 2);
        replacePrevOperand(replacement);
        continue;
      }
 
      // If this input is a replicate, see if we can fold it with the previous
      // one.
      if (auto repl = nextOperand.getDefiningOp<ReplicateOp>()) {
        // ... x, repl(x, n), ...  ==> ..., repl(x, n+1), ...
        if (repl.getOperand() == prevOperand) {
          Value replacement = rewriter.createOrFold<ReplicateOp>(
              op.getLoc(), repl.getOperand(), repl.getMultiple() + 1);
          replacePrevOperand(replacement);
          continue;
        }
        // ... repl(x, n), repl(x, m), ...  ==> ..., repl(x, n+m), ...
        if (auto prevRepl = prevOperand.getDefiningOp<ReplicateOp>()) {
          if (prevRepl.getOperand() == repl.getOperand()) {
            Value replacement = rewriter.createOrFold<ReplicateOp>(
                op.getLoc(), repl.getOperand(),
                repl.getMultiple() + prevRepl.getMultiple());
            replacePrevOperand(replacement);
            continue;
          }
        }
      }
 
      // ... repl(x, n), x, ...  ==> ..., repl(x, n+1), ...
      if (auto repl = prevOperand.getDefiningOp<ReplicateOp>()) {
        if (repl.getOperand() == nextOperand) {
          Value replacement = rewriter.createOrFold<ReplicateOp>(
              op.getLoc(), nextOperand, repl.getMultiple() + 1);
          replacePrevOperand(replacement);
          continue;
        }
      }
 
      // Merge neighboring extracts of neighboring inputs, e.g.
      // {A[3], A[2]} -> A[3:2]
      if (auto extract = nextOperand.getDefiningOp<ExtractOp>()) {
        if (auto prevExtract = prevOperand.getDefiningOp<ExtractOp>()) {
          if (extract.getInput() == prevExtract.getInput()) {
            auto thisWidth = cast<IntegerType>(extract.getType()).getWidth();
            if (prevExtract.getLowBit() == extract.getLowBit() + thisWidth) {
              auto prevWidth = prevExtract.getType().getIntOrFloatBitWidth();
              auto resType = rewriter.getIntegerType(thisWidth + prevWidth);
              Value replacement =
                  ExtractOp::create(rewriter, op.getLoc(), resType,
                                    extract.getInput(), extract.getLowBit());
              replacePrevOperand(replacement);
              continue;
            }
          }
        }
      }
      // Merge neighboring array extracts of neighboring inputs, e.g.
      // {Array[4], bitcast(Array[3:2])} -> bitcast(A[4:2])
 
      // This represents a slice of an array.
      struct ArraySlice {
        Value input;
        Value index;
        size_t width;
        static std::optional<ArraySlice> get(Value value) {
          assert(isa<IntegerType>(value.getType()) && "expected integer type");
          if (auto arrayGet = value.getDefiningOp<hw::ArrayGetOp>())
            return ArraySlice{arrayGet.getInput(), arrayGet.getIndex(), 1};
          // array slice op is wrapped with bitcast.
          if (auto bitcast = value.getDefiningOp<hw::BitcastOp>())
            if (auto arraySlice =
                    bitcast.getInput().getDefiningOp<hw::ArraySliceOp>())
              return ArraySlice{
                  arraySlice.getInput(), arraySlice.getLowIndex(),
                  hw::type_cast<hw::ArrayType>(arraySlice.getType())
                      .getNumElements()};
          return std::nullopt;
        }
      };
      if (auto extractOpt = ArraySlice::get(nextOperand)) {
        if (auto prevExtractOpt = ArraySlice::get(prevOperand)) {
          // Check that two array slices are mergable.
          if (prevExtractOpt->index.getType() == extractOpt->index.getType() &&
              prevExtractOpt->input == extractOpt->input &&
              hw::isOffset(extractOpt->index, prevExtractOpt->index,
                           extractOpt->width)) {
            auto resType = hw::ArrayType::get(
                hw::type_cast<hw::ArrayType>(prevExtractOpt->input.getType())
                    .getElementType(),
                extractOpt->width + prevExtractOpt->width);
            auto resIntType = rewriter.getIntegerType(hw::getBitWidth(resType));
            Value replacement = hw::BitcastOp::create(
                rewriter, op.getLoc(), resIntType,
                hw::ArraySliceOp::create(rewriter, op.getLoc(), resType,
                                         prevExtractOpt->input,
                                         extractOpt->index));
            replacePrevOperand(replacement);
            continue;
          }
        }
      }
    }
 
    processedOperands.push_back(nextOperand);
  }
 
  // Batch-resolve all ExtractOp users of this concat using a prefix-sum array
  // and binary search. This avoids the O(M*N) cost of having each ExtractOp
  // independently do a linear scan over the concat's operands.
  //
  // Only do this when:
  //  - the concat operands are unchanged (if they changed, we'll replace the
  //    concat below and the extract users will be re-enqueued naturally)
  //  - there are enough extract users to justify batching (for small counts,
  //    the per-ExtractOp canonicalization is fine and preserves output order)
  constexpr size_t kBatchExtractThreshold = 16;
  bool anyExtractsResolved = false;
  if (!anyOperandChanged && processedOperands.size() > 1) {
    SmallVector<ExtractOp, 8> extractUsers;
    for (auto *user : op->getUsers()) {
      if (auto extract = dyn_cast<ExtractOp>(user))
        extractUsers.push_back(extract);
    }
 
    if (extractUsers.size() >= kBatchExtractThreshold) {
      // Build prefix-sum of bit widths in LSB-first (reversed) order.
      auto concatInputs = op.getInputs();
      size_t numConcatOperands = concatInputs.size();
      SmallVector<size_t> prefixWidths(numConcatOperands);
      size_t cumWidth = 0;
      for (size_t i = 0; i < numConcatOperands; ++i) {
        // Note: we can just query bitwidth here as is as the ExtractOp above's
        // type constraints means this is valid in valid IR.
        cumWidth += concatInputs[numConcatOperands - 1 - i]
                        .getType()
                        .getIntOrFloatBitWidth();
        prefixWidths[i] = cumWidth;
      }
 
      // Resolve each extract user.
      for (auto extract : extractUsers) {
        if (succeeded(extractConcatToConcatExtract(extract, op, rewriter,
                                                   prefixWidths)))
          anyExtractsResolved = true;
      }
    }
  }
 
  if (processedOperands.size() == 1) {
    // If the operands were all the same, we'll reach here with a single
    // ReplicateOp.
    replaceOpAndCopyNamehint(rewriter, op, processedOperands[0]);
  } else if (anyOperandChanged) {
    replaceOpWithNewOpAndCopyNamehint<ConcatOp>(rewriter, op, op.getType(),
                                                processedOperands);
  } else if (!anyExtractsResolved) {
    return failure();
  }
  return success();
}
 
//===----------------------------------------------------------------------===//
// MuxOp
//===----------------------------------------------------------------------===//
 
OpFoldResult MuxOp::fold(FoldAdaptor adaptor) {
  if (isOpTriviallyRecursive(*this))
    return {};
 
  // mux (c, b, b) -> b
  if (getTrueValue() == getFalseValue() && getTrueValue() != getResult())
    return getTrueValue();
  if (auto tv = adaptor.getTrueValue())
    if (tv == adaptor.getFalseValue())
      return tv;
 
  // mux(0, a, b) -> b
  // mux(1, a, b) -> a
  if (auto pred = dyn_cast_or_null<IntegerAttr>(adaptor.getCond())) {
    if (pred.getValue().isZero() && getFalseValue() != getResult())
      return getFalseValue();
    if (pred.getValue().isOne() && getTrueValue() != getResult())
      return getTrueValue();
  }
 
  // mux(cond, 1, 0) -> cond
  if (getCond().getType() == getTrueValue().getType())
    if (auto tv = dyn_cast_or_null<IntegerAttr>(adaptor.getTrueValue()))
      if (auto fv = dyn_cast_or_null<IntegerAttr>(adaptor.getFalseValue()))
        if (tv.getValue().isOne() && fv.getValue().isZero() &&
            hw::getBitWidth(getType()) == 1 && getCond() != getResult())
          return getCond();
 
  return {};
}
 
/// Check to see if the condition to the specified mux is an equality
/// comparison `indexValue` and one or more constants.  If so, put the
/// constants in the constants vector and return true, otherwise return false.
///
/// This is part of foldMuxChain.
///
static bool
getMuxChainCondConstant(Value cond, Value indexValue, bool isInverted,
                        std::function<void(hw::ConstantOp)> constantFn) {
  // Handle `idx == 42` and `idx != 42`.
  if (auto cmp = cond.getDefiningOp<ICmpOp>()) {
    // TODO: We could handle things like "x < 2" as two entries.
    auto requiredPredicate =
        (isInverted ? ICmpPredicate::eq : ICmpPredicate::ne);
    if (cmp.getLhs() == indexValue && cmp.getPredicate() == requiredPredicate) {
      if (auto cst = cmp.getRhs().getDefiningOp<hw::ConstantOp>()) {
        constantFn(cst);
        return true;
      }
    }
    return false;
  }
 
  // Handle mux(`idx == 1 || idx == 3`, value, muxchain).
  if (auto orOp = cond.getDefiningOp<OrOp>()) {
    if (!isInverted)
      return false;
    for (auto operand : orOp.getOperands())
      if (!getMuxChainCondConstant(operand, indexValue, isInverted, constantFn))
        return false;
    return true;
  }
 
  // Handle mux(`idx != 1 && idx != 3`, muxchain, value).
  if (auto andOp = cond.getDefiningOp<AndOp>()) {
    if (isInverted)
      return false;
    for (auto operand : andOp.getOperands())
      if (!getMuxChainCondConstant(operand, indexValue, isInverted, constantFn))
        return false;
    return true;
  }
 
  return false;
}
 
/// Given a mux, check to see if the "on true" value (or "on false" value if
/// isFalseSide=true) is a mux tree with the same condition.  This allows us
/// to turn things like `mux(VAL == 0, A, (mux (VAL == 1), B, C))` into
/// `array_get (array_create(A, B, C), VAL)` or a balanced mux tree which is far
/// more compact and allows synthesis tools to do more interesting
/// optimizations.
///
/// This returns false if we cannot form the mux tree (or do not want to) and
/// returns true if the mux was replaced.
bool comb::foldMuxChainWithComparison(
    PatternRewriter &rewriter, MuxOp rootMux, bool isFalseSide,
    llvm::function_ref<MuxChainWithComparisonFoldingStyle(size_t indexWidth,
                                                          size_t numEntries)>
        styleFn) {
  // Get the index value being compared.  Later we check to see if it is
  // compared to a constant with the right predicate.
  auto rootCmp = rootMux.getCond().getDefiningOp<ICmpOp>();
  if (!rootCmp)
    return false;
  Value indexValue = rootCmp.getLhs();
 
  // Return the value to use if the equality match succeeds.
  auto getCaseValue = [&](MuxOp mux) -> Value {
    return mux.getOperand(1 + unsigned(!isFalseSide));
  };
 
  // Return the value to use if the equality match fails.  This is the next
  // mux in the sequence or the "otherwise" value.
  auto getTreeValue = [&](MuxOp mux) -> Value {
    return mux.getOperand(1 + unsigned(isFalseSide));
  };
 
  // Start scanning the mux tree to see what we've got.  Keep track of the
  // constant comparison value and the SSA value to use when equal to it.
  SmallVector<Location> locationsFound;
  SmallVector<std::pair<hw::ConstantOp, Value>, 4> valuesFound;
 
  /// Extract constants and values into `valuesFound` and return true if this is
  /// part of the mux tree, otherwise return false.
  auto collectConstantValues = [&](MuxOp mux) -> bool {
    return getMuxChainCondConstant(
        mux.getCond(), indexValue, isFalseSide, [&](hw::ConstantOp cst) {
          valuesFound.push_back({cst, getCaseValue(mux)});
          locationsFound.push_back(mux.getCond().getLoc());
          locationsFound.push_back(mux->getLoc());
        });
  };
 
  // Make sure the root is a correct comparison with a constant.
  if (!collectConstantValues(rootMux))
    return false;
 
  // Make sure that we're not looking at the intermediate node in a mux tree.
  if (rootMux->hasOneUse()) {
    if (auto userMux = dyn_cast<MuxOp>(*rootMux->user_begin())) {
      if (getTreeValue(userMux) == rootMux.getResult() &&
          getMuxChainCondConstant(userMux.getCond(), indexValue, isFalseSide,
                                  [&](hw::ConstantOp cst) {}))
        return false;
    }
  }
 
  // Scan up the tree linearly.
  auto nextTreeValue = getTreeValue(rootMux);
  while (1) {
    auto nextMux = nextTreeValue.getDefiningOp<MuxOp>();
    if (!nextMux || !nextMux->hasOneUse())
      break;
    if (!collectConstantValues(nextMux))
      break;
    nextTreeValue = getTreeValue(nextMux);
  }
 
  auto indexWidth = cast<IntegerType>(indexValue.getType()).getWidth();
 
  if (indexWidth > 20)
    return false; // Too big to make a table.
 
  auto foldingStyle = styleFn(indexWidth, valuesFound.size());
  if (foldingStyle == MuxChainWithComparisonFoldingStyle::None)
    return false;
 
  uint64_t tableSize = 1ULL << indexWidth;
 
  // Ok, we're going to do the transformation, start by building the table
  // filled with the "otherwise" value.
  SmallVector<Value, 8> table(tableSize, nextTreeValue);
 
  // Fill in entries in the table from the leaf to the root of the expression.
  // This ensures that any duplicate matches end up with the ultimate value,
  // which is the one closer to the root.
  for (auto &elt : llvm::reverse(valuesFound)) {
    uint64_t idx = elt.first.getValue().getZExtValue();
    assert(idx < table.size() && "constant should be same bitwidth as index");
    table[idx] = elt.second;
  }
 
  if (foldingStyle == MuxChainWithComparisonFoldingStyle::BalancedMuxTree) {
    SmallVector<Value> bits;
    comb::extractBits(rewriter, indexValue, bits);
    auto result = constructMuxTree(rewriter, rootMux->getLoc(), bits, table,
                                   nextTreeValue);
    replaceOpAndCopyNamehint(rewriter, rootMux, result);
    return true;
  }
 
  assert(foldingStyle == MuxChainWithComparisonFoldingStyle::ArrayGet &&
         "unknown folding style");
 
  // The hw.array_create operation has the operand list in unintuitive order
  // with a[0] stored as the last element, not the first.
  std::reverse(table.begin(), table.end());
 
  // Build the array_create and the array_get.
  auto fusedLoc = rewriter.getFusedLoc(locationsFound);
  auto array = hw::ArrayCreateOp::create(rewriter, fusedLoc, table);
  replaceOpWithNewOpAndCopyNamehint<hw::ArrayGetOp>(rewriter, rootMux, array,
                                                    indexValue);
  return true;
}
 
/// Given a fully associative variadic operation like (a+b+c+d), break the
/// expression into two parts, one without the specified operand (e.g.
/// `tmp = a+b+d`) and one that combines that into the full expression (e.g.
/// `tmp+c`), and return the inner expression.
///
/// NOTE: This mutates the operation in place if it only has a single user,
/// which assumes that user will be removed.
///
static Value extractOperandFromFullyAssociative(Operation *fullyAssoc,
                                                size_t operandNo,
                                                PatternRewriter &rewriter) {
  assert(fullyAssoc->getNumOperands() >= 2 && "cannot split up unary ops");
  assert(operandNo < fullyAssoc->getNumOperands() && "Invalid operand #");
 
  // If this expression already has two operands (the common case) no splitting
  // is necessary.
  if (fullyAssoc->getNumOperands() == 2)
    return fullyAssoc->getOperand(operandNo ^ 1);
 
  // If the operation has a single use, mutate it in place.
  if (fullyAssoc->hasOneUse()) {
    rewriter.modifyOpInPlace(fullyAssoc,
                             [&]() { fullyAssoc->eraseOperand(operandNo); });
    return fullyAssoc->getResult(0);
  }
 
  // Form the new operation with the operands that remain.
  SmallVector<Value> operands;
  operands.append(fullyAssoc->getOperands().begin(),
                  fullyAssoc->getOperands().begin() + operandNo);
  operands.append(fullyAssoc->getOperands().begin() + operandNo + 1,
                  fullyAssoc->getOperands().end());
  Value opWithoutExcluded = createGenericOp(
      fullyAssoc->getLoc(), fullyAssoc->getName(), operands, rewriter);
  Value excluded = fullyAssoc->getOperand(operandNo);
 
  Value fullResult =
      createGenericOp(fullyAssoc->getLoc(), fullyAssoc->getName(),
                      ArrayRef<Value>{opWithoutExcluded, excluded}, rewriter);
  replaceOpAndCopyNamehint(rewriter, fullyAssoc, fullResult);
  return opWithoutExcluded;
}
 
/// Fold things like `mux(cond, x|y|z|a, a)` -> `(x|y|z)&replicate(cond)|a` and
/// `mux(cond, a, x|y|z|a) -> `(x|y|z)&replicate(~cond) | a` (when isTrueOperand
/// is true.  Return true on successful transformation, false if not.
///
/// These are various forms of "predicated ops" that can be handled with a
/// replicate/and combination.
static bool foldCommonMuxValue(MuxOp op, bool isTrueOperand,
                               PatternRewriter &rewriter) {
  // Check to see the operand in question is an operation.  If it is a port,
  // we can't simplify it.
  Operation *subExpr =
      (isTrueOperand ? op.getFalseValue() : op.getTrueValue()).getDefiningOp();
  if (!subExpr || subExpr->getNumOperands() < 2)
    return false;
 
  // If this isn't an operation we can handle, don't spend energy on it.
  if (!isa<AndOp, XorOp, OrOp, MuxOp>(subExpr))
    return false;
 
  // Check to see if the common value occurs in the operand list for the
  // subexpression op.  If so, then we can simplify it.
  Value commonValue = isTrueOperand ? op.getTrueValue() : op.getFalseValue();
  size_t opNo = 0, e = subExpr->getNumOperands();
  while (opNo != e && subExpr->getOperand(opNo) != commonValue)
    ++opNo;
  if (opNo == e)
    return false;
 
  // If we got a hit, then go ahead and simplify it!
  Value cond = op.getCond();
 
  // `mux(cond, a, mux(cond2, a, b))` -> `mux(cond|cond2, a, b)`
  // `mux(cond, a, mux(cond2, b, a))` -> `mux(cond|~cond2, a, b)`
  // `mux(cond, mux(cond2, a, b), a)` -> `mux(~cond|cond2, a, b)`
  // `mux(cond, mux(cond2, b, a), a)` -> `mux(~cond|~cond2, a, b)`
  if (auto subMux = dyn_cast<MuxOp>(subExpr)) {
    if (subMux == op)
      return false;
 
    Value otherValue;
    Value subCond = subMux.getCond();
 
    // Invert th subCond if needed and dig out the 'b' value.
    if (subMux.getTrueValue() == commonValue)
      otherValue = subMux.getFalseValue();
    else if (subMux.getFalseValue() == commonValue) {
      otherValue = subMux.getTrueValue();
      subCond = createOrFoldNot(rewriter, op.getLoc(), subCond);
    } else {
      // We can't fold `mux(cond, a, mux(a, x, y))`.
      return false;
    }
 
    // Invert the outer cond if needed, and combine the mux conditions.
    if (!isTrueOperand)
      cond = createOrFoldNot(rewriter, op.getLoc(), cond);
    cond = rewriter.createOrFold<OrOp>(op.getLoc(), cond, subCond, false);
    replaceOpWithNewOpAndCopyNamehint<MuxOp>(rewriter, op, cond, commonValue,
                                             otherValue, op.getTwoState());
    return true;
  }
 
  // Invert the condition if needed.  Or/Xor invert when dealing with
  // TrueOperand, And inverts for False operand.
  bool isaAndOp = isa<AndOp>(subExpr);
  if (isTrueOperand ^ isaAndOp)
    cond = createOrFoldNot(rewriter, op.getLoc(), cond);
 
  auto extendedCond =
      rewriter.createOrFold<ReplicateOp>(op.getLoc(), op.getType(), cond);
 
  // Cache this information before subExpr is erased by extraction below.
  bool isaXorOp = isa<XorOp>(subExpr);
  bool isaOrOp = isa<OrOp>(subExpr);
 
  // Handle the fully associative ops, start by pulling out the subexpression
  // from a many operand version of the op.
  auto restOfAssoc =
      extractOperandFromFullyAssociative(subExpr, opNo, rewriter);
 
  // `mux(cond, x|y|z|a, a)` -> `(x|y|z)&replicate(cond) | a`
  // `mux(cond, x^y^z^a, a)` -> `(x^y^z)&replicate(cond) ^ a`
  if (isaOrOp || isaXorOp) {
    auto masked = rewriter.createOrFold<AndOp>(op.getLoc(), extendedCond,
                                               restOfAssoc, false);
    if (isaXorOp)
      replaceOpWithNewOpAndCopyNamehint<XorOp>(rewriter, op, masked,
                                               commonValue, false);
    else
      replaceOpWithNewOpAndCopyNamehint<OrOp>(rewriter, op, masked, commonValue,
                                              false);
    return true;
  }
 
  // `mux(cond, a, x&y&z&a)` -> `((x&y&z)|replicate(cond)) & a`
  assert(isaAndOp && "unexpected operation here");
  auto masked = rewriter.createOrFold<OrOp>(op.getLoc(), extendedCond,
                                            restOfAssoc, false);
  replaceOpWithNewOpAndCopyNamehint<AndOp>(rewriter, op, masked, commonValue,
                                           false);
  return true;
}
 
/// This function is invoke when we find a mux with true/false operations that
/// have the same opcode.  Check to see if we can strength reduce the mux by
/// applying it to less data by applying this transformation:
///   `mux(cond, op(a, b), op(a, c))` -> `op(a, mux(cond, b, c))`
static bool foldCommonMuxOperation(MuxOp mux, Operation *trueOp,
                                   Operation *falseOp,
                                   PatternRewriter &rewriter) {
  // Right now we only apply to concat.
  // TODO: Generalize this to and, or, xor, icmp(!), which all occur in practice
  if (!isa<ConcatOp>(trueOp))
    return false;
 
  // Decode the operands, looking through recursive concats and replicates.
  SmallVector<Value> trueOperands, falseOperands;
  getConcatOperands(trueOp->getResult(0), trueOperands);
  getConcatOperands(falseOp->getResult(0), falseOperands);
 
  size_t numTrueOperands = trueOperands.size();
  size_t numFalseOperands = falseOperands.size();
 
  if (!numTrueOperands || !numFalseOperands ||
      (trueOperands.front() != falseOperands.front() &&
       trueOperands.back() != falseOperands.back()))
    return false;
 
  // Pull all leading shared operands out into their own op if any are common.
  if (trueOperands.front() == falseOperands.front()) {
    SmallVector<Value> operands;
    size_t i;
    for (i = 0; i < numTrueOperands; ++i) {
      Value trueOperand = trueOperands[i];
      if (trueOperand == falseOperands[i])
        operands.push_back(trueOperand);
      else
        break;
    }
    if (i == numTrueOperands) {
      // Selecting between distinct, but lexically identical, concats.
      replaceOpAndCopyNamehint(rewriter, mux, trueOp->getResult(0));
      return true;
    }
 
    Value sharedMSB;
    if (llvm::all_of(operands, [&](Value v) { return v == operands.front(); }))
      sharedMSB = rewriter.createOrFold<ReplicateOp>(
          mux->getLoc(), operands.front(), operands.size());
    else
      sharedMSB = rewriter.createOrFold<ConcatOp>(mux->getLoc(), operands);
    operands.clear();
 
    // Get a concat of the LSB's on each side.
    operands.append(trueOperands.begin() + i, trueOperands.end());
    Value trueLSB = rewriter.createOrFold<ConcatOp>(trueOp->getLoc(), operands);
    operands.clear();
    operands.append(falseOperands.begin() + i, falseOperands.end());
    Value falseLSB =
        rewriter.createOrFold<ConcatOp>(falseOp->getLoc(), operands);
    // Merge the LSBs with a new mux and concat the MSB with the LSB to be
    // done.
    Value lsb = rewriter.createOrFold<MuxOp>(
        mux->getLoc(), mux.getCond(), trueLSB, falseLSB, mux.getTwoState());
    replaceOpWithNewOpAndCopyNamehint<ConcatOp>(rewriter, mux, sharedMSB, lsb);
    return true;
  }
 
  // If trailing operands match, try to commonize them.
  if (trueOperands.back() == falseOperands.back()) {
    SmallVector<Value> operands;
    size_t i;
    for (i = 0;; ++i) {
      Value trueOperand = trueOperands[numTrueOperands - i - 1];
      if (trueOperand == falseOperands[numFalseOperands - i - 1])
        operands.push_back(trueOperand);
      else
        break;
    }
    std::reverse(operands.begin(), operands.end());
    Value sharedLSB = rewriter.createOrFold<ConcatOp>(mux->getLoc(), operands);
    operands.clear();
 
    // Get a concat of the MSB's on each side.
    operands.append(trueOperands.begin(), trueOperands.end() - i);
    Value trueMSB = rewriter.createOrFold<ConcatOp>(trueOp->getLoc(), operands);
    operands.clear();
    operands.append(falseOperands.begin(), falseOperands.end() - i);
    Value falseMSB =
        rewriter.createOrFold<ConcatOp>(falseOp->getLoc(), operands);
    // Merge the MSBs with a new mux and concat the MSB with the LSB to be done.
    Value msb = rewriter.createOrFold<MuxOp>(
        mux->getLoc(), mux.getCond(), trueMSB, falseMSB, mux.getTwoState());
    replaceOpWithNewOpAndCopyNamehint<ConcatOp>(rewriter, mux, msb, sharedLSB);
    return true;
  }
 
  return false;
}
 
// If both arguments of the mux are arrays with the same elements, sink the
// mux and return a uniform array initializing all elements to it.
static bool foldMuxOfUniformArrays(MuxOp op, PatternRewriter &rewriter) {
  auto trueVec = op.getTrueValue().getDefiningOp<hw::ArrayCreateOp>();
  auto falseVec = op.getFalseValue().getDefiningOp<hw::ArrayCreateOp>();
  if (!trueVec || !falseVec)
    return false;
  if (!trueVec.isUniform() || !falseVec.isUniform())
    return false;
 
  auto mux = MuxOp::create(rewriter, op.getLoc(), op.getCond(),
                           trueVec.getUniformElement(),
                           falseVec.getUniformElement(), op.getTwoState());
 
  SmallVector<Value> values(trueVec.getInputs().size(), mux);
  rewriter.replaceOpWithNewOp<hw::ArrayCreateOp>(op, values);
  return true;
}
 
/// If the mux condition is an operand to the op defining its true or false
/// value, replace the condition with 1 or 0.
static bool assumeMuxCondInOperand(Value muxCond, Value muxValue,
                                   bool constCond, PatternRewriter &rewriter) {
  if (!muxValue.hasOneUse())
    return false;
  auto *op = muxValue.getDefiningOp();
  if (!op || !isa_and_nonnull<CombDialect>(op->getDialect()))
    return false;
  if (!llvm::is_contained(op->getOperands(), muxCond))
    return false;
  OpBuilder::InsertionGuard guard(rewriter);
  rewriter.setInsertionPoint(op);
  auto condValue =
      hw::ConstantOp::create(rewriter, muxCond.getLoc(), APInt(1, constCond));
  rewriter.modifyOpInPlace(op, [&] {
    for (auto &use : op->getOpOperands())
      if (use.get() == muxCond)
        use.set(condValue);
  });
  return true;
}
 
namespace {
struct MuxRewriter : public mlir::OpRewritePattern<MuxOp> {
  using OpRewritePattern::OpRewritePattern;
 
  LogicalResult matchAndRewrite(MuxOp op,
                                PatternRewriter &rewriter) const override;
};
 
MuxChainWithComparisonFoldingStyle
foldToArrayCreateOnlyWhenDense(size_t indexWidth, size_t numEntries) {
  // If the array is greater that 9 bits, it will take over 512 elements and
  // it will be too large for a single expression.
  if (indexWidth >= 9 || numEntries < 3)
    return MuxChainWithComparisonFoldingStyle::None;
 
  // Next we need to see if the values are dense-ish.  We don't want to have
  // a tremendous number of replicated entries in the array.  Some sparsity is
  // ok though, so we require the table to be at least 5/8 utilized.
  uint64_t tableSize = 1ULL << indexWidth;
  if (numEntries >= tableSize * 5 / 8)
    return MuxChainWithComparisonFoldingStyle::ArrayGet;
  return MuxChainWithComparisonFoldingStyle::None;
}
 
LogicalResult MuxRewriter::matchAndRewrite(MuxOp op,
                                           PatternRewriter &rewriter) const {
  if (isOpTriviallyRecursive(op))
    return failure();
 
  bool isSignlessInt = false;
  if (auto intType = dyn_cast<IntegerType>(op.getType()))
    isSignlessInt = intType.isSignless();
 
  // If the op has a SV attribute, don't optimize it.
  if (hasSVAttributes(op))
    return failure();
  APInt value;
 
  if (matchPattern(op.getTrueValue(), m_ConstantInt(&value)) && isSignlessInt) {
    if (value.getBitWidth() == 1) {
      // mux(a, 0, b) -> and(~a, b) for single-bit values.
      if (value.isZero()) {
        auto notCond = createOrFoldNot(rewriter, op.getLoc(), op.getCond());
        replaceOpWithNewOpAndCopyNamehint<AndOp>(rewriter, op, notCond,
                                                 op.getFalseValue(), false);
        return success();
      }
 
      // mux(a, 1, b) -> or(a, b) for single-bit values.
      replaceOpWithNewOpAndCopyNamehint<OrOp>(rewriter, op, op.getCond(),
                                              op.getFalseValue(), false);
      return success();
    }
 
    // Check for mux of two constants.  There are many ways to simplify them.
    APInt value2;
    if (matchPattern(op.getFalseValue(), m_ConstantInt(&value2))) {
      // When both inputs are constants and differ by only one bit, we can
      // simplify by splitting the mux into up to three contiguous chunks: one
      // for the differing bit and up to two for the bits that are the same.
      // E.g. mux(a, 3'h2, 0) -> concat(0, mux(a, 1, 0), 0) -> concat(0, a, 0)
      APInt xorValue = value ^ value2;
      if (xorValue.isPowerOf2()) {
        unsigned leadingZeros = xorValue.countLeadingZeros();
        unsigned trailingZeros = value.getBitWidth() - leadingZeros - 1;
        SmallVector<Value, 3> operands;
 
        // Concat operands go from MSB to LSB, so we handle chunks in reverse
        // order of bit indexes.
        // For the chunks that are identical (i.e. correspond to 0s in
        // xorValue), we can extract directly from either input value, and we
        // arbitrarily pick the trueValue().
 
        if (leadingZeros > 0)
          operands.push_back(rewriter.createOrFold<ExtractOp>(
              op.getLoc(), op.getTrueValue(), trailingZeros + 1, leadingZeros));
 
        // Handle the differing bit, which should simplify into either cond or
        // ~cond.
        auto v1 = rewriter.createOrFold<ExtractOp>(
            op.getLoc(), op.getTrueValue(), trailingZeros, 1);
        auto v2 = rewriter.createOrFold<ExtractOp>(
            op.getLoc(), op.getFalseValue(), trailingZeros, 1);
        operands.push_back(rewriter.createOrFold<MuxOp>(
            op.getLoc(), op.getCond(), v1, v2, false));
 
        if (trailingZeros > 0)
          operands.push_back(rewriter.createOrFold<ExtractOp>(
              op.getLoc(), op.getTrueValue(), 0, trailingZeros));
 
        replaceOpWithNewOpAndCopyNamehint<ConcatOp>(rewriter, op, op.getType(),
                                                    operands);
        return success();
      }
 
      // If the true value is all ones and the false is all zeros then we have a
      // replicate pattern.
      if (value.isAllOnes() && value2.isZero()) {
        replaceOpWithNewOpAndCopyNamehint<ReplicateOp>(
            rewriter, op, op.getType(), op.getCond());
        return success();
      }
    }
  }
 
  if (matchPattern(op.getFalseValue(), m_ConstantInt(&value)) &&
      isSignlessInt && value.getBitWidth() == 1) {
    // mux(a, b, 0) -> and(a, b) for single-bit values.
    if (value.isZero()) {
      replaceOpWithNewOpAndCopyNamehint<AndOp>(rewriter, op, op.getCond(),
                                               op.getTrueValue(), false);
      return success();
    }
 
    // mux(a, b, 1) -> or(~a, b) for single-bit values.
    // falseValue() is known to be a single-bit 1, which we can use for
    // the 1 in the representation of ~ using xor.
    auto notCond = rewriter.createOrFold<XorOp>(op.getLoc(), op.getCond(),
                                                op.getFalseValue(), false);
    replaceOpWithNewOpAndCopyNamehint<OrOp>(rewriter, op, notCond,
                                            op.getTrueValue(), false);
    return success();
  }
 
  // mux(!a, b, c) -> mux(a, c, b)
  Value subExpr;
  Operation *condOp = op.getCond().getDefiningOp();
  if (condOp && matchPattern(condOp, m_Complement(m_Any(&subExpr))) &&
      op.getTwoState()) {
    replaceOpWithNewOpAndCopyNamehint<MuxOp>(rewriter, op, op.getType(),
                                             subExpr, op.getFalseValue(),
                                             op.getTrueValue(), true);
    return success();
  }
 
  // Same but with Demorgan's law.
  // mux(and(~a, ~b, ~c), x, y) -> mux(or(a, b, c), y, x)
  // mux(or(~a, ~b, ~c), x, y) -> mux(and(a, b, c), y, x)
  if (condOp && condOp->hasOneUse()) {
    SmallVector<Value> invertedOperands;
 
    /// Scan all the operands to see if they are complemented.  If so, build a
    /// vector of them and return true, otherwise return false.
    auto getInvertedOperands = [&]() -> bool {
      for (Value operand : condOp->getOperands()) {
        if (matchPattern(operand, m_Complement(m_Any(&subExpr))))
          invertedOperands.push_back(subExpr);
        else
          return false;
      }
      return true;
    };
 
    if (isa<AndOp>(condOp) && getInvertedOperands()) {
      auto newOr =
          rewriter.createOrFold<OrOp>(op.getLoc(), invertedOperands, false);
      replaceOpWithNewOpAndCopyNamehint<MuxOp>(
          rewriter, op, newOr, op.getFalseValue(), op.getTrueValue(),
          op.getTwoState());
      return success();
    }
    if (isa<OrOp>(condOp) && getInvertedOperands()) {
      auto newAnd =
          rewriter.createOrFold<AndOp>(op.getLoc(), invertedOperands, false);
      replaceOpWithNewOpAndCopyNamehint<MuxOp>(
          rewriter, op, newAnd, op.getFalseValue(), op.getTrueValue(),
          op.getTwoState());
      return success();
    }
  }
 
  if (auto falseMux = op.getFalseValue().getDefiningOp<MuxOp>();
      falseMux && falseMux != op) {
    // mux(selector, x, mux(selector, y, z) = mux(selector, x, z)
    if (op.getCond() == falseMux.getCond() &&
        falseMux.getFalseValue() != falseMux) {
      replaceOpWithNewOpAndCopyNamehint<MuxOp>(
          rewriter, op, op.getCond(), op.getTrueValue(),
          falseMux.getFalseValue(), op.getTwoStateAttr());
      return success();
    }
 
    // Check to see if we can fold a mux tree into an array_create/get pair.
    if (foldMuxChainWithComparison(rewriter, op, /*isFalse*/ true,
                                   foldToArrayCreateOnlyWhenDense))
      return success();
  }
 
  if (auto trueMux = op.getTrueValue().getDefiningOp<MuxOp>();
      trueMux && trueMux != op) {
    // mux(selector, mux(selector, a, b), c) = mux(selector, a, c)
    if (op.getCond() == trueMux.getCond()) {
      replaceOpWithNewOpAndCopyNamehint<MuxOp>(
          rewriter, op, op.getCond(), trueMux.getTrueValue(),
          op.getFalseValue(), op.getTwoStateAttr());
      return success();
    }
 
    // Check to see if we can fold a mux tree into an array_create/get pair.
    if (foldMuxChainWithComparison(rewriter, op, /*isFalseSide*/ false,
                                   foldToArrayCreateOnlyWhenDense))
      return success();
  }
 
  // mux(c1, mux(c2, a, b), mux(c2, a, c)) -> mux(c2, a, mux(c1, b, c))
  if (auto trueMux = dyn_cast_or_null<MuxOp>(op.getTrueValue().getDefiningOp()),
      falseMux = dyn_cast_or_null<MuxOp>(op.getFalseValue().getDefiningOp());
      trueMux && falseMux && trueMux.getCond() == falseMux.getCond() &&
      trueMux.getTrueValue() == falseMux.getTrueValue() && trueMux != op &&
      falseMux != op) {
    auto subMux = MuxOp::create(
        rewriter, rewriter.getFusedLoc({trueMux.getLoc(), falseMux.getLoc()}),
        op.getCond(), trueMux.getFalseValue(), falseMux.getFalseValue());
    replaceOpWithNewOpAndCopyNamehint<MuxOp>(rewriter, op, trueMux.getCond(),
                                             trueMux.getTrueValue(), subMux,
                                             op.getTwoStateAttr());
    return success();
  }
 
  // mux(c1, mux(c2, a, b), mux(c2, c, b)) -> mux(c2, mux(c1, a, c), b)
  if (auto trueMux = dyn_cast_or_null<MuxOp>(op.getTrueValue().getDefiningOp()),
      falseMux = dyn_cast_or_null<MuxOp>(op.getFalseValue().getDefiningOp());
      trueMux && falseMux && trueMux.getCond() == falseMux.getCond() &&
      trueMux.getFalseValue() == falseMux.getFalseValue() && trueMux != op &&
      falseMux != op) {
    auto subMux = MuxOp::create(
        rewriter, rewriter.getFusedLoc({trueMux.getLoc(), falseMux.getLoc()}),
        op.getCond(), trueMux.getTrueValue(), falseMux.getTrueValue());
    replaceOpWithNewOpAndCopyNamehint<MuxOp>(rewriter, op, trueMux.getCond(),
                                             subMux, trueMux.getFalseValue(),
                                             op.getTwoStateAttr());
    return success();
  }
 
  // mux(c1, mux(c2, a, b), mux(c3, a, b)) -> mux(mux(c1, c2, c3), a, b)
  if (auto trueMux = dyn_cast_or_null<MuxOp>(op.getTrueValue().getDefiningOp()),
      falseMux = dyn_cast_or_null<MuxOp>(op.getFalseValue().getDefiningOp());
      trueMux && falseMux &&
      trueMux.getTrueValue() == falseMux.getTrueValue() &&
      trueMux.getFalseValue() == falseMux.getFalseValue() && trueMux != op &&
      falseMux != op) {
    auto subMux =
        MuxOp::create(rewriter,
                      rewriter.getFusedLoc(
                          {op.getLoc(), trueMux.getLoc(), falseMux.getLoc()}),
                      op.getCond(), trueMux.getCond(), falseMux.getCond());
    replaceOpWithNewOpAndCopyNamehint<MuxOp>(
        rewriter, op, subMux, trueMux.getTrueValue(), trueMux.getFalseValue(),
        op.getTwoStateAttr());
    return success();
  }
 
  // mux(cond, x|y|z|a, a) -> (x|y|z)&replicate(cond) | a
  if (foldCommonMuxValue(op, false, rewriter))
    return success();
  // mux(cond, a, x|y|z|a) -> (x|y|z)&replicate(~cond) | a
  if (foldCommonMuxValue(op, true, rewriter))
    return success();
 
  // `mux(cond, op(a, b), op(a, c))` -> `op(a, mux(cond, b, c))`
  if (Operation *trueOp = op.getTrueValue().getDefiningOp())
    if (Operation *falseOp = op.getFalseValue().getDefiningOp())
      if (trueOp->getName() == falseOp->getName())
        if (foldCommonMuxOperation(op, trueOp, falseOp, rewriter))
          return success();
 
  // extracts only of mux(...) -> mux(extract()...)
  if (narrowOperationWidth(op, true, rewriter))
    return success();
 
  // mux(cond, repl(n, a1), repl(n, a2)) -> repl(n, mux(cond, a1, a2))
  if (foldMuxOfUniformArrays(op, rewriter))
    return success();
 
  // mux(cond, opA(cond), opB(cond)) -> mux(cond, opA(1), opB(0))
  if (op.getTrueValue().getDefiningOp() &&
      op.getTrueValue().getDefiningOp() != op)
    if (assumeMuxCondInOperand(op.getCond(), op.getTrueValue(), true, rewriter))
      return success();
  if (op.getFalseValue().getDefiningOp() &&
      op.getFalseValue().getDefiningOp() != op)
 
    if (assumeMuxCondInOperand(op.getCond(), op.getFalseValue(), false,
                               rewriter))
      return success();
 
  return failure();
}
 
static bool foldArrayOfMuxes(hw::ArrayCreateOp op, PatternRewriter &rewriter) {
  // Do not fold uniform or singleton arrays to avoid duplicating muxes.
  if (op.getInputs().empty() || op.isUniform())
    return false;
  auto inputs = op.getInputs();
  if (inputs.size() <= 1)
    return false;
 
  // Check the operands to the array create.  Ensure all of them are the
  // same op with the same number of operands.
  auto first = inputs[0].getDefiningOp<comb::MuxOp>();
  if (!first || hasSVAttributes(first))
    return false;
 
  // Check whether all operands are muxes with the same condition.
  for (size_t i = 1, n = inputs.size(); i < n; ++i) {
    auto input = inputs[i].getDefiningOp<comb::MuxOp>();
    if (!input || first.getCond() != input.getCond())
      return false;
  }
 
  // Collect the true and the false branches into arrays.
  SmallVector<Value> trues{first.getTrueValue()};
  SmallVector<Value> falses{first.getFalseValue()};
  SmallVector<Location> locs{first->getLoc()};
  bool isTwoState = true;
  for (size_t i = 1, n = inputs.size(); i < n; ++i) {
    auto input = inputs[i].getDefiningOp<comb::MuxOp>();
    trues.push_back(input.getTrueValue());
    falses.push_back(input.getFalseValue());
    locs.push_back(input->getLoc());
    if (!input.getTwoState())
      isTwoState = false;
  }
 
  // Define the location of the array create as the aggregate of all muxes.
  auto loc = FusedLoc::get(op.getContext(), locs);
 
  // Replace the create with an aggregate operation.  Push the create op
  // into the operands of the aggregate operation.
  auto arrayTy = op.getType();
  auto trueValues = hw::ArrayCreateOp::create(rewriter, loc, arrayTy, trues);
  auto falseValues = hw::ArrayCreateOp::create(rewriter, loc, arrayTy, falses);
  rewriter.replaceOpWithNewOp<comb::MuxOp>(op, arrayTy, first.getCond(),
                                           trueValues, falseValues, isTwoState);
  return true;
}
 
struct ArrayRewriter : public mlir::OpRewritePattern<hw::ArrayCreateOp> {
  using OpRewritePattern::OpRewritePattern;
 
  LogicalResult matchAndRewrite(hw::ArrayCreateOp op,
                                PatternRewriter &rewriter) const override {
    if (foldArrayOfMuxes(op, rewriter))
      return success();
    return failure();
  }
};
 
} // namespace
 
void MuxOp::getCanonicalizationPatterns(RewritePatternSet &results,
                                        MLIRContext *context) {
  results.insert<MuxRewriter, ArrayRewriter>(context);
}
 
//===----------------------------------------------------------------------===//
// ICmpOp
//===----------------------------------------------------------------------===//
 
// Calculate the result of a comparison when the LHS and RHS are both
// constants.
static bool applyCmpPredicate(ICmpPredicate predicate, const APInt &lhs,
                              const APInt &rhs) {
  switch (predicate) {
  case ICmpPredicate::eq:
    return lhs.eq(rhs);
  case ICmpPredicate::ne:
    return lhs.ne(rhs);
  case ICmpPredicate::slt:
    return lhs.slt(rhs);
  case ICmpPredicate::sle:
    return lhs.sle(rhs);
  case ICmpPredicate::sgt:
    return lhs.sgt(rhs);
  case ICmpPredicate::sge:
    return lhs.sge(rhs);
  case ICmpPredicate::ult:
    return lhs.ult(rhs);
  case ICmpPredicate::ule:
    return lhs.ule(rhs);
  case ICmpPredicate::ugt:
    return lhs.ugt(rhs);
  case ICmpPredicate::uge:
    return lhs.uge(rhs);
  case ICmpPredicate::ceq:
    return lhs.eq(rhs);
  case ICmpPredicate::cne:
    return lhs.ne(rhs);
  case ICmpPredicate::weq:
    return lhs.eq(rhs);
  case ICmpPredicate::wne:
    return lhs.ne(rhs);
  }
  llvm_unreachable("unknown comparison predicate");
}
 
// Returns the result of applying the predicate when the LHS and RHS are the
// exact same value.
static bool applyCmpPredicateToEqualOperands(ICmpPredicate predicate) {
  switch (predicate) {
  case ICmpPredicate::eq:
  case ICmpPredicate::sle:
  case ICmpPredicate::sge:
  case ICmpPredicate::ule:
  case ICmpPredicate::uge:
  case ICmpPredicate::ceq:
  case ICmpPredicate::weq:
    return true;
  case ICmpPredicate::ne:
  case ICmpPredicate::slt:
  case ICmpPredicate::sgt:
  case ICmpPredicate::ult:
  case ICmpPredicate::ugt:
  case ICmpPredicate::cne:
  case ICmpPredicate::wne:
    return false;
  }
  llvm_unreachable("unknown comparison predicate");
}
 
OpFoldResult ICmpOp::fold(FoldAdaptor adaptor) {
  // gt a, a -> false
  // gte a, a -> true
  if (getLhs() == getRhs()) {
    auto val = applyCmpPredicateToEqualOperands(getPredicate());
    return IntegerAttr::get(getType(), val);
  }
 
  // gt 1, 2 -> false
  if (auto lhs = dyn_cast_or_null<IntegerAttr>(adaptor.getLhs())) {
    if (auto rhs = dyn_cast_or_null<IntegerAttr>(adaptor.getRhs())) {
      auto val =
          applyCmpPredicate(getPredicate(), lhs.getValue(), rhs.getValue());
      return IntegerAttr::get(getType(), val);
    }
  }
  return {};
}
 
// Given a range of operands, computes the number of matching prefix and
// suffix elements. This does not perform cross-element matching.
template <typename Range>
static size_t computeCommonPrefixLength(const Range &a, const Range &b) {
  size_t commonPrefixLength = 0;
  auto ia = a.begin();
  auto ib = b.begin();
 
  for (; ia != a.end() && ib != b.end(); ia++, ib++, commonPrefixLength++) {
    if (*ia != *ib) {
      break;
    }
  }
 
  return commonPrefixLength;
}
 
static size_t getTotalWidth(ArrayRef<Value> operands) {
  size_t totalWidth = 0;
  for (auto operand : operands) {
    // getIntOrFloatBitWidth should never raise, since all arguments to
    // ConcatOp are integers.
    ssize_t width = operand.getType().getIntOrFloatBitWidth();
    assert(width >= 0);
    totalWidth += width;
  }
  return totalWidth;
}
 
/// Reduce the strength icmp(concat(...), concat(...)) by doing a element-wise
/// comparison on common prefix and suffixes. Returns success() if a rewriting
/// happens.  This handles both concat and replicate.
static LogicalResult matchAndRewriteCompareConcat(ICmpOp op, Operation *lhs,
                                                  Operation *rhs,
                                                  PatternRewriter &rewriter) {
  // It is safe to assume that [{lhsOperands, rhsOperands}.size() > 0] and
  // all elements have non-zero length. Both these invariants are verified
  // by the ConcatOp verifier.
  SmallVector<Value> lhsOperands, rhsOperands;
  getConcatOperands(lhs->getResult(0), lhsOperands);
  getConcatOperands(rhs->getResult(0), rhsOperands);
  ArrayRef<Value> lhsOperandsRef = lhsOperands, rhsOperandsRef = rhsOperands;
 
  auto formCatOrReplicate = [&](Location loc,
                                ArrayRef<Value> operands) -> Value {
    assert(!operands.empty());
    Value sameElement = operands[0];
    for (size_t i = 1, e = operands.size(); i != e && sameElement; ++i)
      if (sameElement != operands[i])
        sameElement = Value();
    if (sameElement)
      return rewriter.createOrFold<ReplicateOp>(loc, sameElement,
                                                operands.size());
    return rewriter.createOrFold<ConcatOp>(loc, operands);
  };
 
  auto replaceWith = [&](ICmpPredicate predicate, Value lhs,
                         Value rhs) -> LogicalResult {
    replaceOpWithNewOpAndCopyNamehint<ICmpOp>(rewriter, op, predicate, lhs, rhs,
                                              op.getTwoState());
    return success();
  };
 
  size_t commonPrefixLength =
      computeCommonPrefixLength(lhsOperands, rhsOperands);
  if (commonPrefixLength == lhsOperands.size()) {
    // cat(a, b, c) == cat(a, b, c) -> 1
    bool result = applyCmpPredicateToEqualOperands(op.getPredicate());
    replaceOpWithNewOpAndCopyNamehint<hw::ConstantOp>(rewriter, op,
                                                      APInt(1, result));
    return success();
  }
 
  size_t commonSuffixLength = computeCommonPrefixLength(
      llvm::reverse(lhsOperandsRef), llvm::reverse(rhsOperandsRef));
 
  size_t commonPrefixTotalWidth =
      getTotalWidth(lhsOperandsRef.take_front(commonPrefixLength));
  size_t commonSuffixTotalWidth =
      getTotalWidth(lhsOperandsRef.take_back(commonSuffixLength));
  auto lhsOnly = lhsOperandsRef.drop_front(commonPrefixLength)
                     .drop_back(commonSuffixLength);
  auto rhsOnly = rhsOperandsRef.drop_front(commonPrefixLength)
                     .drop_back(commonSuffixLength);
 
  auto replaceWithoutReplicatingSignBit = [&]() {
    auto newLhs = formCatOrReplicate(lhs->getLoc(), lhsOnly);
    auto newRhs = formCatOrReplicate(rhs->getLoc(), rhsOnly);
    return replaceWith(op.getPredicate(), newLhs, newRhs);
  };
 
  auto replaceWithReplicatingSignBit = [&]() {
    auto firstNonEmptyValue = lhsOperands[0];
    auto firstNonEmptyElemWidth =
        firstNonEmptyValue.getType().getIntOrFloatBitWidth();
    Value signBit = rewriter.createOrFold<ExtractOp>(
        op.getLoc(), firstNonEmptyValue, firstNonEmptyElemWidth - 1, 1);
 
    auto newLhs = ConcatOp::create(rewriter, lhs->getLoc(), signBit, lhsOnly);
    auto newRhs = ConcatOp::create(rewriter, rhs->getLoc(), signBit, rhsOnly);
    return replaceWith(op.getPredicate(), newLhs, newRhs);
  };
 
  if (ICmpOp::isPredicateSigned(op.getPredicate())) {
    // scmp(cat(..x, b), cat(..y, b)) == scmp(cat(..x), cat(..y))
    if (commonPrefixTotalWidth == 0 && commonSuffixTotalWidth > 0)
      return replaceWithoutReplicatingSignBit();
 
    // scmp(cat(a, ..x, b), cat(a, ..y, b)) == scmp(cat(sgn(a), ..x),
    // cat(sgn(b), ..y)) Note that we cannot perform this optimization if
    // [width(b) = 0 && width(a) <= 1]. since that common prefix is the sign
    // bit. Doing the rewrite can result in an infinite loop.
    if (commonPrefixTotalWidth > 1 || commonSuffixTotalWidth > 0)
      return replaceWithReplicatingSignBit();
 
  } else if (commonPrefixTotalWidth > 0 || commonSuffixTotalWidth > 0) {
    // ucmp(cat(a, ..x, b), cat(a, ..y, b)) = ucmp(cat(..x), cat(..y))
    return replaceWithoutReplicatingSignBit();
  }
 
  return failure();
}
 
/// Given an equality comparison with a constant value and some operand that has
/// known bits, simplify the comparison to check only the unknown bits of the
/// input.
///
/// One simple example of this is that `concat(0, stuff) == 0` can be simplified
/// to `stuff == 0`, or `and(x, 3) == 0` can be simplified to
/// `extract x[1:0] == 0`
static void combineEqualityICmpWithKnownBitsAndConstant(
    ICmpOp cmpOp, const KnownBits &bitAnalysis, const APInt &rhsCst,
    PatternRewriter &rewriter) {
 
  // If any of the known bits disagree with any of the comparison bits, then
  // we can constant fold this comparison right away.
  APInt bitsKnown = bitAnalysis.Zero | bitAnalysis.One;
  if ((bitsKnown & rhsCst) != bitAnalysis.One) {
    // If we discover a mismatch then we know an "eq" comparison is false
    // and a "ne" comparison is true!
    bool result = cmpOp.getPredicate() == ICmpPredicate::ne;
    replaceOpWithNewOpAndCopyNamehint<hw::ConstantOp>(rewriter, cmpOp,
                                                      APInt(1, result));
    return;
  }
 
  // Check to see if we can prove the result entirely of the comparison (in
  // which we bail out early), otherwise build a list of values to concat and a
  // smaller constant to compare against.
  SmallVector<Value> newConcatOperands;
  auto newConstant = APInt::getZeroWidth();
 
  // Ok, some (maybe all) bits are known and some others may be unknown.
  // Extract out segments of the operand and compare against the
  // corresponding bits.
  unsigned knownMSB = bitsKnown.countLeadingOnes();
 
  Value operand = cmpOp.getLhs();
 
  // Ok, some bits are known but others are not.  Extract out sequences of
  // bits that are unknown and compare just those bits.  We work from MSB to
  // LSB.
  while (knownMSB != bitsKnown.getBitWidth()) {
    // Drop any high bits that are known.
    if (knownMSB)
      bitsKnown = bitsKnown.trunc(bitsKnown.getBitWidth() - knownMSB);
 
    // Find the span of unknown bits, and extract it.
    unsigned unknownBits = bitsKnown.countLeadingZeros();
    unsigned lowBit = bitsKnown.getBitWidth() - unknownBits;
    auto spanOperand = rewriter.createOrFold<ExtractOp>(
        operand.getLoc(), operand, /*lowBit=*/lowBit,
        /*bitWidth=*/unknownBits);
    auto spanConstant = rhsCst.lshr(lowBit).trunc(unknownBits);
 
    // Add this info to the concat we're generating.
    newConcatOperands.push_back(spanOperand);
    // FIXME(llvm merge, cc697fc292b0): concat doesn't work with zero bit values
    // newConstant = newConstant.concat(spanConstant);
    if (newConstant.getBitWidth() != 0)
      newConstant = newConstant.concat(spanConstant);
    else
      newConstant = spanConstant;
 
    // Drop the unknown bits in prep for the next chunk.
    unsigned newWidth = bitsKnown.getBitWidth() - unknownBits;
    bitsKnown = bitsKnown.trunc(newWidth);
    knownMSB = bitsKnown.countLeadingOnes();
  }
 
  // If all the operands to the concat are foldable then we have an identity
  // situation where all the sub-elements equal each other.  This implies that
  // the overall result is foldable.
  if (newConcatOperands.empty()) {
    bool result = cmpOp.getPredicate() == ICmpPredicate::eq;
    replaceOpWithNewOpAndCopyNamehint<hw::ConstantOp>(rewriter, cmpOp,
                                                      APInt(1, result));
    return;
  }
 
  // If we have a single operand remaining, use it, otherwise form a concat.
  Value concatResult =
      rewriter.createOrFold<ConcatOp>(operand.getLoc(), newConcatOperands);
 
  // Form the comparison against the smaller constant.
  auto newConstantOp = hw::ConstantOp::create(
      rewriter, cmpOp.getOperand(1).getLoc(), newConstant);
 
  replaceOpWithNewOpAndCopyNamehint<ICmpOp>(rewriter, cmpOp,
                                            cmpOp.getPredicate(), concatResult,
                                            newConstantOp, cmpOp.getTwoState());
}
 
// Simplify icmp eq(xor(a,b,cst1), cst2) -> icmp eq(xor(a,b), cst1^cst2).
static void combineEqualityICmpWithXorOfConstant(ICmpOp cmpOp, XorOp xorOp,
                                                 const APInt &rhs,
                                                 PatternRewriter &rewriter) {
  auto ip = rewriter.saveInsertionPoint();
  rewriter.setInsertionPoint(xorOp);
 
  auto xorRHS = xorOp.getOperands().back().getDefiningOp<hw::ConstantOp>();
  auto newRHS = hw::ConstantOp::create(rewriter, xorRHS->getLoc(),
                                       xorRHS.getValue() ^ rhs);
  Value newLHS;
  switch (xorOp.getNumOperands()) {
  case 1:
    // This isn't common but is defined so we need to handle it.
    newLHS = hw::ConstantOp::create(rewriter, xorOp.getLoc(),
                                    APInt::getZero(rhs.getBitWidth()));
    break;
  case 2:
    // The binary case is the most common.
    newLHS = xorOp.getOperand(0);
    break;
  default:
    // The general case forces us to form a new xor with the remaining operands.
    SmallVector<Value> newOperands(xorOp.getOperands());
    newOperands.pop_back();
    newLHS = XorOp::create(rewriter, xorOp.getLoc(), newOperands, false);
    break;
  }
 
  bool xorMultipleUses = !xorOp->hasOneUse();
 
  // If the xor has multiple uses (not just the compare, then we need/want to
  // replace them as well.
  if (xorMultipleUses)
    replaceOpWithNewOpAndCopyNamehint<XorOp>(rewriter, xorOp, newLHS, xorRHS,
                                             false);
 
  // Replace the comparison.
  rewriter.restoreInsertionPoint(ip);
  replaceOpWithNewOpAndCopyNamehint<ICmpOp>(
      rewriter, cmpOp, cmpOp.getPredicate(), newLHS, newRHS, false);
}
 
LogicalResult ICmpOp::canonicalize(ICmpOp op, PatternRewriter &rewriter) {
  if (isOpTriviallyRecursive(op))
    return failure();
  APInt lhs, rhs;
 
  // icmp 1, x -> icmp x, 1
  if (matchPattern(op.getLhs(), m_ConstantInt(&lhs))) {
    assert(!matchPattern(op.getRhs(), m_ConstantInt(&rhs)) &&
           "Should be folded");
    replaceOpWithNewOpAndCopyNamehint<ICmpOp>(
        rewriter, op, ICmpOp::getFlippedPredicate(op.getPredicate()),
        op.getRhs(), op.getLhs(), op.getTwoState());
    return success();
  }
 
  // Canonicalize with RHS constant
  if (matchPattern(op.getRhs(), m_ConstantInt(&rhs))) {
    auto getConstant = [&](APInt constant) -> Value {
      return hw::ConstantOp::create(rewriter, op.getLoc(), std::move(constant));
    };
 
    auto replaceWith = [&](ICmpPredicate predicate, Value lhs,
                           Value rhs) -> LogicalResult {
      replaceOpWithNewOpAndCopyNamehint<ICmpOp>(rewriter, op, predicate, lhs,
                                                rhs, op.getTwoState());
      return success();
    };
 
    auto replaceWithConstantI1 = [&](bool constant) -> LogicalResult {
      replaceOpWithNewOpAndCopyNamehint<hw::ConstantOp>(rewriter, op,
                                                        APInt(1, constant));
      return success();
    };
 
    switch (op.getPredicate()) {
    case ICmpPredicate::slt:
      // x < max -> x != max
      if (rhs.isMaxSignedValue())
        return replaceWith(ICmpPredicate::ne, op.getLhs(), op.getRhs());
      // x < min -> false
      if (rhs.isMinSignedValue())
        return replaceWithConstantI1(0);
      // x < min+1 -> x == min
      if ((rhs - 1).isMinSignedValue())
        return replaceWith(ICmpPredicate::eq, op.getLhs(),
                           getConstant(rhs - 1));
      break;
    case ICmpPredicate::sgt:
      // x > min -> x != min
      if (rhs.isMinSignedValue())
        return replaceWith(ICmpPredicate::ne, op.getLhs(), op.getRhs());
      // x > max -> false
      if (rhs.isMaxSignedValue())
        return replaceWithConstantI1(0);
      // x > max-1 -> x == max
      if ((rhs + 1).isMaxSignedValue())
        return replaceWith(ICmpPredicate::eq, op.getLhs(),
                           getConstant(rhs + 1));
      break;
    case ICmpPredicate::ult:
      // x < max -> x != max
      if (rhs.isAllOnes())
        return replaceWith(ICmpPredicate::ne, op.getLhs(), op.getRhs());
      // x < min -> false
      if (rhs.isZero())
        return replaceWithConstantI1(0);
      // x < min+1 -> x == min
      if ((rhs - 1).isZero())
        return replaceWith(ICmpPredicate::eq, op.getLhs(),
                           getConstant(rhs - 1));
 
      // x < 0xE0 -> extract(x, 5..7) != 0b111
      if (rhs.countLeadingOnes() + rhs.countTrailingZeros() ==
          rhs.getBitWidth()) {
        auto numOnes = rhs.countLeadingOnes();
        auto smaller = ExtractOp::create(rewriter, op.getLoc(), op.getLhs(),
                                         rhs.getBitWidth() - numOnes, numOnes);
        return replaceWith(ICmpPredicate::ne, smaller,
                           getConstant(APInt::getAllOnes(numOnes)));
      }
 
      break;
    case ICmpPredicate::ugt:
      // x > min -> x != min
      if (rhs.isZero())
        return replaceWith(ICmpPredicate::ne, op.getLhs(), op.getRhs());
      // x > max -> false
      if (rhs.isAllOnes())
        return replaceWithConstantI1(0);
      // x > max-1 -> x == max
      if ((rhs + 1).isAllOnes())
        return replaceWith(ICmpPredicate::eq, op.getLhs(),
                           getConstant(rhs + 1));
 
      // x > 0x07 -> extract(x, 3..7) != 0b00000
      if ((rhs + 1).isPowerOf2()) {
        auto numOnes = rhs.countTrailingOnes();
        auto newWidth = rhs.getBitWidth() - numOnes;
        auto smaller = ExtractOp::create(rewriter, op.getLoc(), op.getLhs(),
                                         numOnes, newWidth);
        return replaceWith(ICmpPredicate::ne, smaller,
                           getConstant(APInt::getZero(newWidth)));
      }
 
      break;
    case ICmpPredicate::sle:
      // x <= max -> true
      if (rhs.isMaxSignedValue())
        return replaceWithConstantI1(1);
      // x <= c -> x < (c+1)
      return replaceWith(ICmpPredicate::slt, op.getLhs(), getConstant(rhs + 1));
    case ICmpPredicate::sge:
      // x >= min -> true
      if (rhs.isMinSignedValue())
        return replaceWithConstantI1(1);
      // x >= c -> x > (c-1)
      return replaceWith(ICmpPredicate::sgt, op.getLhs(), getConstant(rhs - 1));
    case ICmpPredicate::ule:
      // x <= max -> true
      if (rhs.isAllOnes())
        return replaceWithConstantI1(1);
      // x <= c -> x < (c+1)
      return replaceWith(ICmpPredicate::ult, op.getLhs(), getConstant(rhs + 1));
    case ICmpPredicate::uge:
      // x >= min -> true
      if (rhs.isZero())
        return replaceWithConstantI1(1);
      // x >= c -> x > (c-1)
      return replaceWith(ICmpPredicate::ugt, op.getLhs(), getConstant(rhs - 1));
    case ICmpPredicate::eq:
      if (rhs.getBitWidth() == 1) {
        if (rhs.isZero()) {
          // x == 0 -> x ^ 1
          replaceOpWithNewOpAndCopyNamehint<XorOp>(rewriter, op, op.getLhs(),
                                                   getConstant(APInt(1, 1)),
                                                   op.getTwoState());
          return success();
        }
        if (rhs.isAllOnes()) {
          // x == 1 -> x
          replaceOpAndCopyNamehint(rewriter, op, op.getLhs());
          return success();
        }
      }
      break;
    case ICmpPredicate::ne:
      if (rhs.getBitWidth() == 1) {
        if (rhs.isZero()) {
          // x != 0 -> x
          replaceOpAndCopyNamehint(rewriter, op, op.getLhs());
          return success();
        }
        if (rhs.isAllOnes()) {
          // x != 1 -> x ^ 1
          replaceOpWithNewOpAndCopyNamehint<XorOp>(rewriter, op, op.getLhs(),
                                                   getConstant(APInt(1, 1)),
                                                   op.getTwoState());
          return success();
        }
      }
      break;
    case ICmpPredicate::ceq:
    case ICmpPredicate::cne:
    case ICmpPredicate::weq:
    case ICmpPredicate::wne:
      break;
    }
 
    // We have some specific optimizations for comparison with a constant that
    // are only supported for equality comparisons.
    if (op.getPredicate() == ICmpPredicate::eq ||
        op.getPredicate() == ICmpPredicate::ne) {
      // Simplify `icmp(value_with_known_bits, rhscst)` into some extracts
      // with a smaller constant.  We only support equality comparisons for
      // this.
      auto knownBits = computeKnownBits(op.getLhs());
      if (!knownBits.isUnknown())
        return combineEqualityICmpWithKnownBitsAndConstant(op, knownBits, rhs,
                                                           rewriter),
               success();
 
      // Simplify icmp eq(xor(a,b,cst1), cst2) -> icmp eq(xor(a,b),
      // cst1^cst2).
      if (auto xorOp = op.getLhs().getDefiningOp<XorOp>())
        if (xorOp.getOperands().back().getDefiningOp<hw::ConstantOp>())
          return combineEqualityICmpWithXorOfConstant(op, xorOp, rhs, rewriter),
                 success();
 
      // Simplify icmp eq(replicate(v, n), c) -> icmp eq(v, c) if c is zero or
      // all one.
      if (auto replicateOp = op.getLhs().getDefiningOp<ReplicateOp>())
        if (rhs.isAllOnes() || rhs.isZero()) {
          auto width = replicateOp.getInput().getType().getIntOrFloatBitWidth();
          auto cst =
              hw::ConstantOp::create(rewriter, op.getLoc(),
                                     rhs.isAllOnes() ? APInt::getAllOnes(width)
                                                     : APInt::getZero(width));
          replaceOpWithNewOpAndCopyNamehint<ICmpOp>(
              rewriter, op, op.getPredicate(), replicateOp.getInput(), cst,
              op.getTwoState());
          return success();
        }
    }
  }
 
  // icmp(cat(prefix, a, b, suffix), cat(prefix, c, d, suffix)) => icmp(cat(a,
  // b), cat(c, d)). contains special handling for sign bit in signed
  // compressions.
  if (Operation *opLHS = op.getLhs().getDefiningOp())
    if (Operation *opRHS = op.getRhs().getDefiningOp())
      if (isa<ConcatOp, ReplicateOp>(opLHS) &&
          isa<ConcatOp, ReplicateOp>(opRHS)) {
        if (succeeded(matchAndRewriteCompareConcat(op, opLHS, opRHS, rewriter)))
          return success();
      }
 
  return failure();
}