path: root/mlir/lib/Transforms/RemoveDeadValues.cpp

//===- RemoveDeadValues.cpp - Remove Dead Values --------------------------===//
//
// 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
//
//===----------------------------------------------------------------------===//
//
// The goal of this pass is optimization (reducing runtime) by removing
// unnecessary instructions. Unlike other passes that rely on local information
// gathered from patterns to accomplish optimization, this pass uses a full
// analysis of the IR, specifically, liveness analysis, and is thus more
// powerful.
//
// Currently, this pass performs the following optimizations:
// (A) Removes function arguments that are not live,
// (B) Removes function return values that are not live across all callers of
// the function,
// (C) Removes unneccesary operands, results, region arguments, and region
// terminator operands of region branch ops, and,
// (D) Removes simple and region branch ops that have all non-live results and
// don't affect memory in any way,
//
// iff
//
// the IR doesn't have any non-function symbol ops, non-call symbol user ops and
// branch ops.
//
// Here, a "simple op" refers to an op that isn't a symbol op, symbol-user op,
// region branch op, branch op, region branch terminator op, or return-like.
//
//===----------------------------------------------------------------------===//

#include "mlir/Analysis/DataFlow/DeadCodeAnalysis.h"
#include "mlir/Analysis/DataFlow/LivenessAnalysis.h"
#include "mlir/IR/Builders.h"
#include "mlir/IR/BuiltinAttributes.h"
#include "mlir/IR/Dialect.h"
#include "mlir/IR/Operation.h"
#include "mlir/IR/OperationSupport.h"
#include "mlir/IR/SymbolTable.h"
#include "mlir/IR/Value.h"
#include "mlir/IR/ValueRange.h"
#include "mlir/IR/Visitors.h"
#include "mlir/Interfaces/CallInterfaces.h"
#include "mlir/Interfaces/ControlFlowInterfaces.h"
#include "mlir/Interfaces/FunctionInterfaces.h"
#include "mlir/Interfaces/SideEffectInterfaces.h"
#include "mlir/Pass/Pass.h"
#include "mlir/Support/LLVM.h"
#include "mlir/Transforms/FoldUtils.h"
#include "mlir/Transforms/Passes.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/DebugLog.h"
#include <cassert>
#include <cstddef>
#include <memory>
#include <optional>
#include <vector>

#define DEBUG_TYPE "remove-dead-values"

namespace mlir {
#define GEN_PASS_DEF_REMOVEDEADVALUES
#include "mlir/Transforms/Passes.h.inc"
} // namespace mlir

using namespace mlir;
using namespace mlir::dataflow;

//===----------------------------------------------------------------------===//
// RemoveDeadValues Pass
//===----------------------------------------------------------------------===//

namespace {

// Set of structures below to be filled with operations and arguments to erase.
// This is done to separate analysis and tree modification phases,
// otherwise analysis is operating on half-deleted tree which is incorrect.

struct FunctionToCleanUp {
  FunctionOpInterface funcOp;
  BitVector nonLiveArgs;
  BitVector nonLiveRets;
};

struct OperationToCleanup {
  Operation *op;
  BitVector nonLive;
};

struct BlockArgsToCleanup {
  Block *b;
  BitVector nonLiveArgs;
};

struct SuccessorOperandsToCleanup {
  BranchOpInterface branch;
  unsigned successorIndex;
  BitVector nonLiveOperands;
};

struct RDVFinalCleanupList {
  SmallVector<Operation *> operations;
  SmallVector<Value> values;
  SmallVector<FunctionToCleanUp> functions;
  SmallVector<OperationToCleanup> operands;
  SmallVector<OperationToCleanup> results;
  SmallVector<BlockArgsToCleanup> blocks;
  SmallVector<SuccessorOperandsToCleanup> successorOperands;
};

// Some helper functions...

/// Return true iff at least one value in `values` is live, given the liveness
/// information in `la`.
static bool hasLive(ValueRange values, const DenseSet<Value> &nonLiveSet,
                    RunLivenessAnalysis &la) {
  for (Value value : values) {
    if (nonLiveSet.contains(value)) {
      LDBG() << "Value " << value << " is already marked non-live (dead)";
      continue;
    }

    const Liveness *liveness = la.getLiveness(value);
    if (!liveness) {
      LDBG() << "Value " << value
             << " has no liveness info, conservatively considered live";
      return true;
    }
    if (liveness->isLive) {
      LDBG() << "Value " << value << " is live according to liveness analysis";
      return true;
    } else {
      LDBG() << "Value " << value << " is dead according to liveness analysis";
    }
  }
  return false;
}

/// Return a BitVector of size `values.size()` where its i-th bit is 1 iff the
/// i-th value in `values` is live, given the liveness information in `la`.
static BitVector markLives(ValueRange values, const DenseSet<Value> &nonLiveSet,
                           RunLivenessAnalysis &la) {
  BitVector lives(values.size(), true);

  for (auto [index, value] : llvm::enumerate(values)) {
    if (nonLiveSet.contains(value)) {
      lives.reset(index);
      LDBG() << "Value " << value
             << " is already marked non-live (dead) at index " << index;
      continue;
    }

    const Liveness *liveness = la.getLiveness(value);
    // It is important to note that when `liveness` is null, we can't tell if
    // `value` is live or not. So, the safe option is to consider it live. Also,
    // the execution of this pass might create new SSA values when erasing some
    // of the results of an op and we know that these new values are live
    // (because they weren't erased) and also their liveness is null because
    // liveness analysis ran before their creation.
    if (!liveness) {
      LDBG() << "Value " << value << " at index " << index
             << " has no liveness info, conservatively considered live";
      continue;
    }
    if (!liveness->isLive) {
      lives.reset(index);
      LDBG() << "Value " << value << " at index " << index
             << " is dead according to liveness analysis";
    } else {
      LDBG() << "Value " << value << " at index " << index
             << " is live according to liveness analysis";
    }
  }

  return lives;
}

/// Collects values marked as "non-live" in the provided range and inserts them
/// into the nonLiveSet. A value is considered "non-live" if the corresponding
/// index in the `nonLive` bit vector is set.
static void collectNonLiveValues(DenseSet<Value> &nonLiveSet, ValueRange range,
                                 const BitVector &nonLive) {
  for (auto [index, result] : llvm::enumerate(range)) {
    if (!nonLive[index])
      continue;
    nonLiveSet.insert(result);
    LDBG() << "Marking value " << result << " as non-live (dead) at index "
           << index;
  }
}

/// Drop the uses of the i-th result of `op` and then erase it iff toErase[i]
/// is 1.
static void dropUsesAndEraseResults(Operation *op, BitVector toErase) {
  assert(op->getNumResults() == toErase.size() &&
         "expected the number of results in `op` and the size of `toErase` to "
         "be the same");

  std::vector<Type> newResultTypes;
  for (OpResult result : op->getResults())
    if (!toErase[result.getResultNumber()])
      newResultTypes.push_back(result.getType());
  OpBuilder builder(op);
  builder.setInsertionPointAfter(op);
  OperationState state(op->getLoc(), op->getName().getStringRef(),
                       op->getOperands(), newResultTypes, op->getAttrs());
  for (unsigned i = 0, e = op->getNumRegions(); i < e; ++i)
    state.addRegion();
  Operation *newOp = builder.create(state);
  for (const auto &[index, region] : llvm::enumerate(op->getRegions())) {
    Region &newRegion = newOp->getRegion(index);
    // Move all blocks of `region` into `newRegion`.
    Block *temp = new Block();
    newRegion.push_back(temp);
    while (!region.empty())
      region.front().moveBefore(temp);
    temp->erase();
  }

  unsigned indexOfNextNewCallOpResultToReplace = 0;
  for (auto [index, result] : llvm::enumerate(op->getResults())) {
    assert(result && "expected result to be non-null");
    if (toErase[index]) {
      result.dropAllUses();
    } else {
      result.replaceAllUsesWith(
          newOp->getResult(indexOfNextNewCallOpResultToReplace++));
    }
  }
  op->erase();
}

/// Convert a list of `Operand`s to a list of `OpOperand`s.
static SmallVector<OpOperand *> operandsToOpOperands(OperandRange operands) {
  OpOperand *values = operands.getBase();
  SmallVector<OpOperand *> opOperands;
  for (unsigned i = 0, e = operands.size(); i < e; i++)
    opOperands.push_back(&values[i]);
  return opOperands;
}

/// Process a simple operation `op` using the liveness analysis `la`.
/// If the operation has no memory effects and none of its results are live:
///   1. Add the operation to a list for future removal, and
///   2. Mark all its results as non-live values
///
/// The operation `op` is assumed to be simple. A simple operation is one that
/// is NOT:
///   - Function-like
///   - Call-like
///   - A region branch operation
///   - A branch operation
///   - A region branch terminator
///   - Return-like
static void processSimpleOp(Operation *op, RunLivenessAnalysis &la,
                            DenseSet<Value> &nonLiveSet,
                            RDVFinalCleanupList &cl) {
  LDBG() << "Processing simple op: " << *op;
  if (!isMemoryEffectFree(op) || hasLive(op->getResults(), nonLiveSet, la)) {
    LDBG()
        << "Simple op is not memory effect free or has live results, skipping: "
        << *op;
    return;
  }

  LDBG()
      << "Simple op has all dead results and is memory effect free, scheduling "
         "for removal: "
      << *op;
  cl.operations.push_back(op);
  collectNonLiveValues(nonLiveSet, op->getResults(),
                       BitVector(op->getNumResults(), true));
}

/// Process a function-like operation `funcOp` using the liveness analysis `la`
/// and the IR in `module`. If it is not public or external:
///   (1) Adding its non-live arguments to a list for future removal.
///   (2) Marking their corresponding operands in its callers for removal.
///   (3) Identifying and enqueueing unnecessary terminator operands
///       (return values that are non-live across all callers) for removal.
///   (4) Enqueueing the non-live arguments and return values for removal.
///   (5) Collecting the uses of these return values in its callers for future
///       removal.
///   (6) Marking all its results as non-live values.
static void processFuncOp(FunctionOpInterface funcOp, Operation *module,
                          RunLivenessAnalysis &la, DenseSet<Value> &nonLiveSet,
                          RDVFinalCleanupList &cl) {
  LDBG() << "Processing function op: " << funcOp.getOperation()->getName();
  if (funcOp.isPublic() || funcOp.isExternal()) {
    LDBG() << "Function is public or external, skipping: "
           << funcOp.getOperation()->getName();
    return;
  }

  // Get the list of unnecessary (non-live) arguments in `nonLiveArgs`.
  SmallVector<Value> arguments(funcOp.getArguments());
  BitVector nonLiveArgs = markLives(arguments, nonLiveSet, la);
  nonLiveArgs = nonLiveArgs.flip();

  // Do (1).
  for (auto [index, arg] : llvm::enumerate(arguments))
    if (arg && nonLiveArgs[index]) {
      cl.values.push_back(arg);
      nonLiveSet.insert(arg);
    }

  // Do (2).
  SymbolTable::UseRange uses = *funcOp.getSymbolUses(module);
  for (SymbolTable::SymbolUse use : uses) {
    Operation *callOp = use.getUser();
    assert(isa<CallOpInterface>(callOp) && "expected a call-like user");
    // The number of operands in the call op may not match the number of
    // arguments in the func op.
    BitVector nonLiveCallOperands(callOp->getNumOperands(), false);
    SmallVector<OpOperand *> callOpOperands =
        operandsToOpOperands(cast<CallOpInterface>(callOp).getArgOperands());
    for (int index : nonLiveArgs.set_bits())
      nonLiveCallOperands.set(callOpOperands[index]->getOperandNumber());
    cl.operands.push_back({callOp, nonLiveCallOperands});
  }

  // Do (3).
  // Get the list of unnecessary terminator operands (return values that are
  // non-live across all callers) in `nonLiveRets`. There is a very important
  // subtlety here. Unnecessary terminator operands are NOT the operands of the
  // terminator that are non-live. Instead, these are the return values of the
  // callers such that a given return value is non-live across all callers. Such
  // corresponding operands in the terminator could be live. An example to
  // demonstrate this:
  //  func.func private @f(%arg0: memref<i32>) -> (i32, i32) {
  //    %c0_i32 = arith.constant 0 : i32
  //    %0 = arith.addi %c0_i32, %c0_i32 : i32
  //    memref.store %0, %arg0[] : memref<i32>
  //    return %c0_i32, %0 : i32, i32
  //  }
  //  func.func @main(%arg0: i32, %arg1: memref<i32>) -> (i32) {
  //    %1:2 = call @f(%arg1) : (memref<i32>) -> i32
  //    return %1#0 : i32
  //  }
  // Here, we can see that %1#1 is never used. It is non-live. Thus, @f doesn't
  // need to return %0. But, %0 is live. And, still, we want to stop it from
  // being returned, in order to optimize our IR. So, this demonstrates how we
  // can make our optimization strong by even removing a live return value (%0),
  // since it forwards only to non-live value(s) (%1#1).
  Operation *lastReturnOp = funcOp.back().getTerminator();
  size_t numReturns = lastReturnOp->getNumOperands();
  BitVector nonLiveRets(numReturns, true);
  for (SymbolTable::SymbolUse use : uses) {
    Operation *callOp = use.getUser();
    assert(isa<CallOpInterface>(callOp) && "expected a call-like user");
    BitVector liveCallRets = markLives(callOp->getResults(), nonLiveSet, la);
    nonLiveRets &= liveCallRets.flip();
  }

  // Note that in the absence of control flow ops forcing the control to go from
  // the entry (first) block to the other blocks, the control never reaches any
  // block other than the entry block, because every block has a terminator.
  for (Block &block : funcOp.getBlocks()) {
    Operation *returnOp = block.getTerminator();
    if (returnOp && returnOp->getNumOperands() == numReturns)
      cl.operands.push_back({returnOp, nonLiveRets});
  }

  // Do (4).
  cl.functions.push_back({funcOp, nonLiveArgs, nonLiveRets});

  // Do (5) and (6).
  if (numReturns == 0)
    return;
  for (SymbolTable::SymbolUse use : uses) {
    Operation *callOp = use.getUser();
    assert(isa<CallOpInterface>(callOp) && "expected a call-like user");
    cl.results.push_back({callOp, nonLiveRets});
    collectNonLiveValues(nonLiveSet, callOp->getResults(), nonLiveRets);
  }
}

/// Process a region branch operation `regionBranchOp` using the liveness
/// information in `la`. The processing involves two scenarios:
///
/// Scenario 1: If the operation has no memory effects and none of its results
/// are live:
///   (1') Enqueue all its uses for deletion.
///   (2') Enqueue the branch itself for deletion.
///
/// Scenario 2: Otherwise:
///   (1) Collect its unnecessary operands (operands forwarded to unnecessary
///       results or arguments).
///   (2) Process each of its regions.
///   (3) Collect the uses of its unnecessary results (results forwarded from
///       unnecessary operands
///       or terminator operands).
///   (4) Add these results to the deletion list.
///
/// Processing a region includes:
///   (a) Collecting the uses of its unnecessary arguments (arguments forwarded
///       from unnecessary operands
///       or terminator operands).
///   (b) Collecting these unnecessary arguments.
///   (c) Collecting its unnecessary terminator operands (terminator operands
///       forwarded to unnecessary results
///       or arguments).
///
/// Value Flow Note: In this operation, values flow as follows:
/// - From operands and terminator operands (successor operands)
/// - To arguments and results (successor inputs).
static void processRegionBranchOp(RegionBranchOpInterface regionBranchOp,
                                  RunLivenessAnalysis &la,
                                  DenseSet<Value> &nonLiveSet,
                                  RDVFinalCleanupList &cl) {
  LDBG() << "Processing region branch op: "
         << OpWithFlags(regionBranchOp, OpPrintingFlags().skipRegions());
  // Mark live results of `regionBranchOp` in `liveResults`.
  auto markLiveResults = [&](BitVector &liveResults) {
    liveResults = markLives(regionBranchOp->getResults(), nonLiveSet, la);
  };

  // Mark live arguments in the regions of `regionBranchOp` in `liveArgs`.
  auto markLiveArgs = [&](DenseMap<Region *, BitVector> &liveArgs) {
    for (Region &region : regionBranchOp->getRegions()) {
      if (region.empty())
        continue;
      SmallVector<Value> arguments(region.front().getArguments());
      BitVector regionLiveArgs = markLives(arguments, nonLiveSet, la);
      liveArgs[&region] = regionLiveArgs;
    }
  };

  // Return the successors of `region` if the latter is not null. Else return
  // the successors of `regionBranchOp`.
  auto getSuccessors = [&](Region *region = nullptr) {
    auto point = region ? region : RegionBranchPoint::parent();
    SmallVector<RegionSuccessor> successors;
    regionBranchOp.getSuccessorRegions(point, successors);
    return successors;
  };

  // Return the operands of `terminator` that are forwarded to `successor` if
  // the former is not null. Else return the operands of `regionBranchOp`
  // forwarded to `successor`.
  auto getForwardedOpOperands = [&](const RegionSuccessor &successor,
                                    Operation *terminator = nullptr) {
    OperandRange operands =
        terminator ? cast<RegionBranchTerminatorOpInterface>(terminator)
                         .getSuccessorOperands(successor)
                   : regionBranchOp.getEntrySuccessorOperands(successor);
    SmallVector<OpOperand *> opOperands = operandsToOpOperands(operands);
    return opOperands;
  };

  // Mark the non-forwarded operands of `regionBranchOp` in
  // `nonForwardedOperands`.
  auto markNonForwardedOperands = [&](BitVector &nonForwardedOperands) {
    nonForwardedOperands.resize(regionBranchOp->getNumOperands(), true);
    for (const RegionSuccessor &successor : getSuccessors()) {
      for (OpOperand *opOperand : getForwardedOpOperands(successor))
        nonForwardedOperands.reset(opOperand->getOperandNumber());
    }
  };

  // Mark the non-forwarded terminator operands of the various regions of
  // `regionBranchOp` in `nonForwardedRets`.
  auto markNonForwardedReturnValues =
      [&](DenseMap<Operation *, BitVector> &nonForwardedRets) {
        for (Region &region : regionBranchOp->getRegions()) {
          if (region.empty())
            continue;
          Operation *terminator = region.front().getTerminator();
          nonForwardedRets[terminator] =
              BitVector(terminator->getNumOperands(), true);
          for (const RegionSuccessor &successor : getSuccessors(&region)) {
            for (OpOperand *opOperand :
                 getForwardedOpOperands(successor, terminator))
              nonForwardedRets[terminator].reset(opOperand->getOperandNumber());
          }
        }
      };

  // Update `valuesToKeep` (which is expected to correspond to operands or
  // terminator operands) based on `resultsToKeep` and `argsToKeep`, given
  // `region`. When `valuesToKeep` correspond to operands, `region` is null.
  // Else, `region` is the parent region of the terminator.
  auto updateOperandsOrTerminatorOperandsToKeep =
      [&](BitVector &valuesToKeep, BitVector &resultsToKeep,
          DenseMap<Region *, BitVector> &argsToKeep, Region *region = nullptr) {
        Operation *terminator =
            region ? region->front().getTerminator() : nullptr;

        for (const RegionSuccessor &successor : getSuccessors(region)) {
          Region *successorRegion = successor.getSuccessor();
          for (auto [opOperand, input] :
               llvm::zip(getForwardedOpOperands(successor, terminator),
                         successor.getSuccessorInputs())) {
            size_t operandNum = opOperand->getOperandNumber();
            bool updateBasedOn =
                successorRegion
                    ? argsToKeep[successorRegion]
                                [cast<BlockArgument>(input).getArgNumber()]
                    : resultsToKeep[cast<OpResult>(input).getResultNumber()];
            valuesToKeep[operandNum] = valuesToKeep[operandNum] | updateBasedOn;
          }
        }
      };

  // Recompute `resultsToKeep` and `argsToKeep` based on `operandsToKeep` and
  // `terminatorOperandsToKeep`. Store true in `resultsOrArgsToKeepChanged` if a
  // value is modified, else, false.
  auto recomputeResultsAndArgsToKeep =
      [&](BitVector &resultsToKeep, DenseMap<Region *, BitVector> &argsToKeep,
          BitVector &operandsToKeep,
          DenseMap<Operation *, BitVector> &terminatorOperandsToKeep,
          bool &resultsOrArgsToKeepChanged) {
        resultsOrArgsToKeepChanged = false;

        // Recompute `resultsToKeep` and `argsToKeep` based on `operandsToKeep`.
        for (const RegionSuccessor &successor : getSuccessors()) {
          Region *successorRegion = successor.getSuccessor();
          for (auto [opOperand, input] :
               llvm::zip(getForwardedOpOperands(successor),
                         successor.getSuccessorInputs())) {
            bool recomputeBasedOn =
                operandsToKeep[opOperand->getOperandNumber()];
            bool toRecompute =
                successorRegion
                    ? argsToKeep[successorRegion]
                                [cast<BlockArgument>(input).getArgNumber()]
                    : resultsToKeep[cast<OpResult>(input).getResultNumber()];
            if (!toRecompute && recomputeBasedOn)
              resultsOrArgsToKeepChanged = true;
            if (successorRegion) {
              argsToKeep[successorRegion][cast<BlockArgument>(input)
                                              .getArgNumber()] =
                  argsToKeep[successorRegion]
                            [cast<BlockArgument>(input).getArgNumber()] |
                  recomputeBasedOn;
            } else {
              resultsToKeep[cast<OpResult>(input).getResultNumber()] =
                  resultsToKeep[cast<OpResult>(input).getResultNumber()] |
                  recomputeBasedOn;
            }
          }
        }

        // Recompute `resultsToKeep` and `argsToKeep` based on
        // `terminatorOperandsToKeep`.
        for (Region &region : regionBranchOp->getRegions()) {
          if (region.empty())
            continue;
          Operation *terminator = region.front().getTerminator();
          for (const RegionSuccessor &successor : getSuccessors(&region)) {
            Region *successorRegion = successor.getSuccessor();
            for (auto [opOperand, input] :
                 llvm::zip(getForwardedOpOperands(successor, terminator),
                           successor.getSuccessorInputs())) {
              bool recomputeBasedOn =
                  terminatorOperandsToKeep[region.back().getTerminator()]
                                          [opOperand->getOperandNumber()];
              bool toRecompute =
                  successorRegion
                      ? argsToKeep[successorRegion]
                                  [cast<BlockArgument>(input).getArgNumber()]
                      : resultsToKeep[cast<OpResult>(input).getResultNumber()];
              if (!toRecompute && recomputeBasedOn)
                resultsOrArgsToKeepChanged = true;
              if (successorRegion) {
                argsToKeep[successorRegion][cast<BlockArgument>(input)
                                                .getArgNumber()] =
                    argsToKeep[successorRegion]
                              [cast<BlockArgument>(input).getArgNumber()] |
                    recomputeBasedOn;
              } else {
                resultsToKeep[cast<OpResult>(input).getResultNumber()] =
                    resultsToKeep[cast<OpResult>(input).getResultNumber()] |
                    recomputeBasedOn;
              }
            }
          }
        }
      };

  // Mark the values that we want to keep in `resultsToKeep`, `argsToKeep`,
  // `operandsToKeep`, and `terminatorOperandsToKeep`.
  auto markValuesToKeep =
      [&](BitVector &resultsToKeep, DenseMap<Region *, BitVector> &argsToKeep,
          BitVector &operandsToKeep,
          DenseMap<Operation *, BitVector> &terminatorOperandsToKeep) {
        bool resultsOrArgsToKeepChanged = true;
        // We keep updating and recomputing the values until we reach a point
        // where they stop changing.
        while (resultsOrArgsToKeepChanged) {
          // Update the operands that need to be kept.
          updateOperandsOrTerminatorOperandsToKeep(operandsToKeep,
                                                   resultsToKeep, argsToKeep);

          // Update the terminator operands that need to be kept.
          for (Region &region : regionBranchOp->getRegions()) {
            if (region.empty())
              continue;
            updateOperandsOrTerminatorOperandsToKeep(
                terminatorOperandsToKeep[region.back().getTerminator()],
                resultsToKeep, argsToKeep, &region);
          }

          // Recompute the results and arguments that need to be kept.
          recomputeResultsAndArgsToKeep(
              resultsToKeep, argsToKeep, operandsToKeep,
              terminatorOperandsToKeep, resultsOrArgsToKeepChanged);
        }
      };

  // Scenario 1. This is the only case where the entire `regionBranchOp`
  // is removed. It will not happen in any other scenario. Note that in this
  // case, a non-forwarded operand of `regionBranchOp` could be live/non-live.
  // It could never be live because of this op but its liveness could have been
  // attributed to something else.
  // Do (1') and (2').
  if (isMemoryEffectFree(regionBranchOp.getOperation()) &&
      !hasLive(regionBranchOp->getResults(), nonLiveSet, la)) {
    cl.operations.push_back(regionBranchOp.getOperation());
    return;
  }

  // Scenario 2.
  // At this point, we know that every non-forwarded operand of `regionBranchOp`
  // is live.

  // Stores the results of `regionBranchOp` that we want to keep.
  BitVector resultsToKeep;
  // Stores the mapping from regions of `regionBranchOp` to their arguments that
  // we want to keep.
  DenseMap<Region *, BitVector> argsToKeep;
  // Stores the operands of `regionBranchOp` that we want to keep.
  BitVector operandsToKeep;
  // Stores the mapping from region terminators in `regionBranchOp` to their
  // operands that we want to keep.
  DenseMap<Operation *, BitVector> terminatorOperandsToKeep;

  // Initializing the above variables...

  // The live results of `regionBranchOp` definitely need to be kept.
  markLiveResults(resultsToKeep);
  // Similarly, the live arguments of the regions in `regionBranchOp` definitely
  // need to be kept.
  markLiveArgs(argsToKeep);
  // The non-forwarded operands of `regionBranchOp` definitely need to be kept.
  // A live forwarded operand can be removed but no non-forwarded operand can be
  // removed since it "controls" the flow of data in this control flow op.
  markNonForwardedOperands(operandsToKeep);
  // Similarly, the non-forwarded terminator operands of the regions in
  // `regionBranchOp` definitely need to be kept.
  markNonForwardedReturnValues(terminatorOperandsToKeep);

  // Mark the values (results, arguments, operands, and terminator operands)
  // that we want to keep.
  markValuesToKeep(resultsToKeep, argsToKeep, operandsToKeep,
                   terminatorOperandsToKeep);

  // Do (1).
  cl.operands.push_back({regionBranchOp, operandsToKeep.flip()});

  // Do (2.a) and (2.b).
  for (Region &region : regionBranchOp->getRegions()) {
    if (region.empty())
      continue;
    BitVector argsToRemove = argsToKeep[&region].flip();
    cl.blocks.push_back({&region.front(), argsToRemove});
    collectNonLiveValues(nonLiveSet, region.front().getArguments(),
                         argsToRemove);
  }

  // Do (2.c).
  for (Region &region : regionBranchOp->getRegions()) {
    if (region.empty())
      continue;
    Operation *terminator = region.front().getTerminator();
    cl.operands.push_back(
        {terminator, terminatorOperandsToKeep[terminator].flip()});
  }

  // Do (3) and (4).
  BitVector resultsToRemove = resultsToKeep.flip();
  collectNonLiveValues(nonLiveSet, regionBranchOp.getOperation()->getResults(),
                       resultsToRemove);
  cl.results.push_back({regionBranchOp.getOperation(), resultsToRemove});
}

/// Steps to process a `BranchOpInterface` operation:
/// Iterate through each successor block of `branchOp`.
/// (1) For each successor block, gather all operands from all successors.
/// (2) Fetch their associated liveness analysis data and collect for future
///     removal.
/// (3) Identify and collect the dead operands from the successor block
///     as well as their corresponding arguments.

static void processBranchOp(BranchOpInterface branchOp, RunLivenessAnalysis &la,
                            DenseSet<Value> &nonLiveSet,
                            RDVFinalCleanupList &cl) {
  LDBG() << "Processing branch op: " << *branchOp;
  unsigned numSuccessors = branchOp->getNumSuccessors();

  for (unsigned succIdx = 0; succIdx < numSuccessors; ++succIdx) {
    Block *successorBlock = branchOp->getSuccessor(succIdx);

    // Do (1)
    SuccessorOperands successorOperands =
        branchOp.getSuccessorOperands(succIdx);
    SmallVector<Value> operandValues;
    for (unsigned operandIdx = 0; operandIdx < successorOperands.size();
         ++operandIdx) {
      operandValues.push_back(successorOperands[operandIdx]);
    }

    // Do (2)
    BitVector successorNonLive =
        markLives(operandValues, nonLiveSet, la).flip();
    collectNonLiveValues(nonLiveSet, successorBlock->getArguments(),
                         successorNonLive);

    // Do (3)
    cl.blocks.push_back({successorBlock, successorNonLive});
    cl.successorOperands.push_back({branchOp, succIdx, successorNonLive});
  }
}

/// Removes dead values collected in RDVFinalCleanupList.
/// To be run once when all dead values have been collected.
static void cleanUpDeadVals(RDVFinalCleanupList &list) {
  // 1. Operations
  for (auto &op : list.operations) {
    op->dropAllUses();
    op->erase();
  }

  // 2. Values
  for (auto &v : list.values) {
    v.dropAllUses();
  }

  // 3. Functions
  for (auto &f : list.functions) {
    // Some functions may not allow erasing arguments or results. These calls
    // return failure in such cases without modifying the function, so it's okay
    // to proceed.
    (void)f.funcOp.eraseArguments(f.nonLiveArgs);
    (void)f.funcOp.eraseResults(f.nonLiveRets);
  }

  // 4. Operands
  for (OperationToCleanup &o : list.operands) {
    if (o.op->getNumOperands() > 0)
      o.op->eraseOperands(o.nonLive);
  }

  // 5. Results
  for (auto &r : list.results) {
    dropUsesAndEraseResults(r.op, r.nonLive);
  }

  // 6. Blocks
  for (auto &b : list.blocks) {
    // blocks that are accessed via multiple codepaths processed once
    if (b.b->getNumArguments() != b.nonLiveArgs.size())
      continue;
    // it iterates backwards because erase invalidates all successor indexes
    for (int i = b.nonLiveArgs.size() - 1; i >= 0; --i) {
      if (!b.nonLiveArgs[i])
        continue;
      b.b->getArgument(i).dropAllUses();
      b.b->eraseArgument(i);
    }
  }

  // 7. Successor Operands
  for (auto &op : list.successorOperands) {
    SuccessorOperands successorOperands =
        op.branch.getSuccessorOperands(op.successorIndex);
    // blocks that are accessed via multiple codepaths processed once
    if (successorOperands.size() != op.nonLiveOperands.size())
      continue;
    // it iterates backwards because erase invalidates all successor indexes
    for (int i = successorOperands.size() - 1; i >= 0; --i) {
      if (!op.nonLiveOperands[i])
        continue;
      successorOperands.erase(i);
    }
  }
}

struct RemoveDeadValues : public impl::RemoveDeadValuesBase<RemoveDeadValues> {
  void runOnOperation() override;
};
} // namespace

void RemoveDeadValues::runOnOperation() {
  auto &la = getAnalysis<RunLivenessAnalysis>();
  Operation *module = getOperation();

  // Tracks values eligible for erasure - complements liveness analysis to
  // identify "droppable" values.
  DenseSet<Value> deadVals;

  // Maintains a list of Ops, values, branches, etc., slated for cleanup at the
  // end of this pass.
  RDVFinalCleanupList finalCleanupList;

  module->walk([&](Operation *op) {
    if (auto funcOp = dyn_cast<FunctionOpInterface>(op)) {
      processFuncOp(funcOp, module, la, deadVals, finalCleanupList);
    } else if (auto regionBranchOp = dyn_cast<RegionBranchOpInterface>(op)) {
      processRegionBranchOp(regionBranchOp, la, deadVals, finalCleanupList);
    } else if (auto branchOp = dyn_cast<BranchOpInterface>(op)) {
      processBranchOp(branchOp, la, deadVals, finalCleanupList);
    } else if (op->hasTrait<::mlir::OpTrait::IsTerminator>()) {
      // Nothing to do here because this is a terminator op and it should be
      // honored with respect to its parent
    } else if (isa<CallOpInterface>(op)) {
      // Nothing to do because this op is associated with a function op and gets
      // cleaned when the latter is cleaned.
    } else {
      processSimpleOp(op, la, deadVals, finalCleanupList);
    }
  });

  cleanUpDeadVals(finalCleanupList);
}

std::unique_ptr<Pass> mlir::createRemoveDeadValuesPass() {
  return std::make_unique<RemoveDeadValues>();
}