lib/Support/SCEVValidator.cpp

#include "polly/Support/SCEVValidator.h"
#include "polly/ScopInfo.h"
#include "llvm/Analysis/ScalarEvolution.h"
#include "llvm/Analysis/ScalarEvolutionExpressions.h"
#include "llvm/Analysis/RegionInfo.h"
#include "llvm/Support/Debug.h"

#include <vector>

using namespace llvm;

#define DEBUG_TYPE "polly-scev-validator"

namespace SCEVType {
/// @brief The type of a SCEV
///
/// To check for the validity of a SCEV we assign to each SCEV a type. The
/// possible types are INT, PARAM, IV and INVALID. The order of the types is
/// important. The subexpressions of SCEV with a type X can only have a type
/// that is smaller or equal than X.
enum TYPE {
  // An integer value.
  INT,

  // An expression that is constant during the execution of the Scop,
  // but that may depend on parameters unknown at compile time.
  PARAM,

  // An expression that may change during the execution of the SCoP.
  IV,

  // An invalid expression.
  INVALID
};
}

/// @brief The result the validator returns for a SCEV expression.
class ValidatorResult {
  /// @brief The type of the expression
  SCEVType::TYPE Type;

  /// @brief The set of Parameters in the expression.
  std::vector<const SCEV *> Parameters;

public:
  /// @brief The copy constructor
  ValidatorResult(const ValidatorResult &Source) {
    Type = Source.Type;
    Parameters = Source.Parameters;
  }

  /// @brief Construct a result with a certain type and no parameters.
  ValidatorResult(SCEVType::TYPE Type) : Type(Type) {
    assert(Type != SCEVType::PARAM && "Did you forget to pass the parameter");
  }

  /// @brief Construct a result with a certain type and a single parameter.
  ValidatorResult(SCEVType::TYPE Type, const SCEV *Expr) : Type(Type) {
    Parameters.push_back(Expr);
  }

  /// @brief Get the type of the ValidatorResult.
  SCEVType::TYPE getType() { return Type; }

  /// @brief Is the analyzed SCEV constant during the execution of the SCoP.
  bool isConstant() { return Type == SCEVType::INT || Type == SCEVType::PARAM; }

  /// @brief Is the analyzed SCEV valid.
  bool isValid() { return Type != SCEVType::INVALID; }

  /// @brief Is the analyzed SCEV of Type IV.
  bool isIV() { return Type == SCEVType::IV; }

  /// @brief Is the analyzed SCEV of Type INT.
  bool isINT() { return Type == SCEVType::INT; }

  /// @brief Is the analyzed SCEV of Type PARAM.
  bool isPARAM() { return Type == SCEVType::PARAM; }

  /// @brief Get the parameters of this validator result.
  std::vector<const SCEV *> getParameters() { return Parameters; }

  /// @brief Add the parameters of Source to this result.
  void addParamsFrom(const ValidatorResult &Source) {
    Parameters.insert(Parameters.end(), Source.Parameters.begin(),
                      Source.Parameters.end());
  }

  /// @brief Merge a result.
  ///
  /// This means to merge the parameters and to set the Type to the most
  /// specific Type that matches both.
  ValidatorResult &merge(const ValidatorResult &ToMerge) {
    Type = std::max(Type, ToMerge.Type);
    addParamsFrom(ToMerge);
    return *this;
  }

  void print(raw_ostream &OS) {
    switch (Type) {
    case SCEVType::INT:
      OS << "SCEVType::INT";
      break;
    case SCEVType::PARAM:
      OS << "SCEVType::PARAM";
      break;
    case SCEVType::IV:
      OS << "SCEVType::IV";
      break;
    case SCEVType::INVALID:
      OS << "SCEVType::INVALID";
      break;
    }
  }
};

raw_ostream &operator<<(raw_ostream &OS, class ValidatorResult &VR) {
  VR.print(OS);
  return OS;
}

/// Check if a SCEV is valid in a SCoP.
struct SCEVValidator
    : public SCEVVisitor<SCEVValidator, class ValidatorResult> {
private:
  const Region *R;
  ScalarEvolution &SE;
  const Value *BaseAddress;

public:
  SCEVValidator(const Region *R, ScalarEvolution &SE, const Value *BaseAddress)
      : R(R), SE(SE), BaseAddress(BaseAddress) {}

  class ValidatorResult visitConstant(const SCEVConstant *Constant) {
    return ValidatorResult(SCEVType::INT);
  }

  class ValidatorResult visitTruncateExpr(const SCEVTruncateExpr *Expr) {
    ValidatorResult Op = visit(Expr->getOperand());

    switch (Op.getType()) {
    case SCEVType::INT:
    case SCEVType::PARAM:
      // We currently do not represent a truncate expression as an affine
      // expression. If it is constant during Scop execution, we treat it as a
      // parameter.
      return ValidatorResult(SCEVType::PARAM, Expr);
    case SCEVType::IV:
      DEBUG(dbgs() << "INVALID: Truncation of SCEVType::IV expression");
      return ValidatorResult(SCEVType::INVALID);
    case SCEVType::INVALID:
      return Op;
    }

    llvm_unreachable("Unknown SCEVType");
  }

  class ValidatorResult visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {

    // Pattern matching rules to capture some bit and modulo computations:
    //
    //       EXP   %  2^C      <==>
    // [A] (i + c) & (2^C - 1)  ==> zext iC {c,+,1}<%for_i> to IXX
    // [B] (p + q) & (2^C - 1)  ==> zext iC (trunc iXX %p_add_q to iC) to iXX
    // [C] (i + p) & (2^C - 1)  ==> zext iC {p & (2^C - 1),+,1}<%for_i> to iXX
    //                          ==> zext iC {trunc iXX %p to iC,+,1}<%for_i> to

    // Check for [A] and [C].
    const SCEV *OpS = Expr->getOperand();
    if (auto *OpAR = dyn_cast<SCEVAddRecExpr>(OpS)) {
      const SCEV *OpARStart = OpAR->getStart();

      // Special case for [C].
      if (auto *OpARStartTR = dyn_cast<SCEVTruncateExpr>(OpARStart))
        OpARStart = OpARStartTR->getOperand();

      ValidatorResult OpARStartVR = visit(OpARStart);
      if (OpARStartVR.isConstant() && OpAR->getStepRecurrence(SE)->isOne())
        return OpARStartVR;
    }

    // Check for [B].
    if (auto *OpTR = dyn_cast<SCEVTruncateExpr>(OpS)) {
      ValidatorResult OpTRVR = visit(OpTR->getOperand());
      if (OpTRVR.isConstant())
        return OpTRVR;
    }

    ValidatorResult Op = visit(OpS);
    switch (Op.getType()) {
    case SCEVType::INT:
    case SCEVType::PARAM:
      // We currently do not represent a truncate expression as an affine
      // expression. If it is constant during Scop execution, we treat it as a
      // parameter.
      return ValidatorResult(SCEVType::PARAM, Expr);
    case SCEVType::IV:
      DEBUG(dbgs() << "INVALID: ZeroExtend of SCEVType::IV expression");
      return ValidatorResult(SCEVType::INVALID);
    case SCEVType::INVALID:
      return Op;
    }

    llvm_unreachable("Unknown SCEVType");
  }

  class ValidatorResult visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
    // We currently allow only signed SCEV expressions. In the case of a
    // signed value, a sign extend is a noop.
    //
    // TODO: Reconsider this when we add support for unsigned values.
    return visit(Expr->getOperand());
  }

  class ValidatorResult visitAddExpr(const SCEVAddExpr *Expr) {
    ValidatorResult Return(SCEVType::INT);

    for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
      ValidatorResult Op = visit(Expr->getOperand(i));
      Return.merge(Op);

      // Early exit.
      if (!Return.isValid())
        break;
    }

    // TODO: Check for NSW and NUW.
    return Return;
  }

  class ValidatorResult visitMulExpr(const SCEVMulExpr *Expr) {
    ValidatorResult Return(SCEVType::INT);

    bool HasMultipleParams = false;

    for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
      ValidatorResult Op = visit(Expr->getOperand(i));

      if (Op.isINT())
        continue;

      if (Op.isPARAM() && Return.isPARAM()) {
        HasMultipleParams = true;
        continue;
      }

      if ((Op.isIV() || Op.isPARAM()) && !Return.isINT()) {
        DEBUG(dbgs() << "INVALID: More than one non-int operand in MulExpr\n"
                     << "\tExpr: " << *Expr << "\n"
                     << "\tPrevious expression type: " << Return << "\n"
                     << "\tNext operand (" << Op
                     << "): " << *Expr->getOperand(i) << "\n");

        return ValidatorResult(SCEVType::INVALID);
      }

      Return.merge(Op);
    }

    if (HasMultipleParams)
      return ValidatorResult(SCEVType::PARAM, Expr);

    // TODO: Check for NSW and NUW.
    return Return;
  }

  class ValidatorResult visitUDivExpr(const SCEVUDivExpr *Expr) {
    ValidatorResult LHS = visit(Expr->getLHS());
    ValidatorResult RHS = visit(Expr->getRHS());

    // We currently do not represent an unsigned division as an affine
    // expression. If the division is constant during Scop execution we treat it
    // as a parameter, otherwise we bail out.
    if (LHS.isConstant() && RHS.isConstant())
      return ValidatorResult(SCEVType::PARAM, Expr);

    DEBUG(dbgs() << "INVALID: unsigned division of non-constant expressions");
    return ValidatorResult(SCEVType::INVALID);
  }

  class ValidatorResult visitAddRecExpr(const SCEVAddRecExpr *Expr) {
    if (!Expr->isAffine()) {
      DEBUG(dbgs() << "INVALID: AddRec is not affine");
      return ValidatorResult(SCEVType::INVALID);
    }

    ValidatorResult Start = visit(Expr->getStart());
    ValidatorResult Recurrence = visit(Expr->getStepRecurrence(SE));

    if (!Start.isValid())
      return Start;

    if (!Recurrence.isValid())
      return Recurrence;

    if (R->contains(Expr->getLoop())) {
      if (Recurrence.isINT()) {
        ValidatorResult Result(SCEVType::IV);
        Result.addParamsFrom(Start);
        return Result;
      }

      DEBUG(dbgs() << "INVALID: AddRec within scop has non-int"
                      "recurrence part");
      return ValidatorResult(SCEVType::INVALID);
    }

    assert(Start.isConstant() && Recurrence.isConstant() &&
           "Expected 'Start' and 'Recurrence' to be constant");

    // Directly generate ValidatorResult for Expr if 'start' is zero.
    if (Expr->getStart()->isZero())
      return ValidatorResult(SCEVType::PARAM, Expr);

    // Translate AddRecExpr from '{start, +, inc}' into 'start + {0, +, inc}'
    // if 'start' is not zero.
    const SCEV *ZeroStartExpr = SE.getAddRecExpr(
        SE.getConstant(Expr->getStart()->getType(), 0),
        Expr->getStepRecurrence(SE), Expr->getLoop(), SCEV::FlagAnyWrap);

    ValidatorResult ZeroStartResult =
        ValidatorResult(SCEVType::PARAM, ZeroStartExpr);
    ZeroStartResult.addParamsFrom(Start);

    return ZeroStartResult;
  }

  class ValidatorResult visitSMaxExpr(const SCEVSMaxExpr *Expr) {
    ValidatorResult Return(SCEVType::INT);

    for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
      ValidatorResult Op = visit(Expr->getOperand(i));

      if (!Op.isValid())
        return Op;

      Return.merge(Op);
    }

    return Return;
  }

  class ValidatorResult visitUMaxExpr(const SCEVUMaxExpr *Expr) {
    // We do not support unsigned operations. If 'Expr' is constant during Scop
    // execution we treat this as a parameter, otherwise we bail out.
    for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
      ValidatorResult Op = visit(Expr->getOperand(i));

      if (!Op.isConstant()) {
        DEBUG(dbgs() << "INVALID: UMaxExpr has a non-constant operand");
        return ValidatorResult(SCEVType::INVALID);
      }
    }

    return ValidatorResult(SCEVType::PARAM, Expr);
  }

  ValidatorResult visitUnknown(const SCEVUnknown *Expr) {
    Value *V = Expr->getValue();

    // We currently only support integer types. It may be useful to support
    // pointer types, e.g. to support code like:
    //
    //   if (A)
    //     A[i] = 1;
    //
    // See test/CodeGen/20120316-InvalidCast.ll
    if (!Expr->getType()->isIntegerTy()) {
      DEBUG(dbgs() << "INVALID: UnknownExpr is not an integer type");
      return ValidatorResult(SCEVType::INVALID);
    }

    if (isa<UndefValue>(V)) {
      DEBUG(dbgs() << "INVALID: UnknownExpr references an undef value");
      return ValidatorResult(SCEVType::INVALID);
    }

    if (auto *I = dyn_cast<Instruction>(Expr->getValue())) {
      if (I->getOpcode() == Instruction::SRem) {

        ValidatorResult Op0 = visit(SE.getSCEV(I->getOperand(0)));
        if (!Op0.isValid())
          return ValidatorResult(SCEVType::INVALID);

        ValidatorResult Op1 = visit(SE.getSCEV(I->getOperand(1)));
        if (!Op1.isValid() || !Op1.isINT())
          return ValidatorResult(SCEVType::INVALID);

        Op0.merge(Op1);
        return Op0;
      }

      if (R->contains(I)) {
        DEBUG(dbgs() << "INVALID: UnknownExpr references an instruction "
                        "within the region\n");
        return ValidatorResult(SCEVType::INVALID);
      }
    }

    if (BaseAddress == V) {
      DEBUG(dbgs() << "INVALID: UnknownExpr references BaseAddress\n");
      return ValidatorResult(SCEVType::INVALID);
    }

    return ValidatorResult(SCEVType::PARAM, Expr);
  }
};

/// @brief Check whether a SCEV refers to an SSA name defined inside a region.
///
struct SCEVInRegionDependences
    : public SCEVVisitor<SCEVInRegionDependences, bool> {
public:
  /// Returns true when the SCEV has SSA names defined in region R.
  static bool hasDependences(const SCEV *S, const Region *R) {
    SCEVInRegionDependences Ignore(R);
    return Ignore.visit(S);
  }

  SCEVInRegionDependences(const Region *R) : R(R) {}

  bool visit(const SCEV *Expr) {
    return SCEVVisitor<SCEVInRegionDependences, bool>::visit(Expr);
  }

  bool visitConstant(const SCEVConstant *Constant) { return false; }

  bool visitTruncateExpr(const SCEVTruncateExpr *Expr) {
    return visit(Expr->getOperand());
  }

  bool visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
    return visit(Expr->getOperand());
  }

  bool visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
    return visit(Expr->getOperand());
  }

  bool visitAddExpr(const SCEVAddExpr *Expr) {
    for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
      if (visit(Expr->getOperand(i)))
        return true;

    return false;
  }

  bool visitMulExpr(const SCEVMulExpr *Expr) {
    for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
      if (visit(Expr->getOperand(i)))
        return true;

    return false;
  }

  bool visitUDivExpr(const SCEVUDivExpr *Expr) {
    if (visit(Expr->getLHS()))
      return true;

    if (visit(Expr->getRHS()))
      return true;

    return false;
  }

  bool visitAddRecExpr(const SCEVAddRecExpr *Expr) {
    if (visit(Expr->getStart()))
      return true;

    for (size_t i = 0; i < Expr->getNumOperands(); ++i)
      if (visit(Expr->getOperand(i)))
        return true;

    return false;
  }

  bool visitSMaxExpr(const SCEVSMaxExpr *Expr) {
    for (size_t i = 0; i < Expr->getNumOperands(); ++i)
      if (visit(Expr->getOperand(i)))
        return true;

    return false;
  }

  bool visitUMaxExpr(const SCEVUMaxExpr *Expr) {
    for (size_t i = 0; i < Expr->getNumOperands(); ++i)
      if (visit(Expr->getOperand(i)))
        return true;

    return false;
  }

  bool visitUnknown(const SCEVUnknown *Expr) {
    Instruction *Inst = dyn_cast<Instruction>(Expr->getValue());

    // Return true when Inst is defined inside the region R.
    if (Inst && R->contains(Inst))
      return true;

    return false;
  }

private:
  const Region *R;
};

namespace polly {
bool hasScalarDepsInsideRegion(const SCEV *Expr, const Region *R) {
  return SCEVInRegionDependences::hasDependences(Expr, R);
}

bool isAffineExpr(const Region *R, const SCEV *Expr, ScalarEvolution &SE,
                  const Value *BaseAddress) {
  if (isa<SCEVCouldNotCompute>(Expr))
    return false;

  SCEVValidator Validator(R, SE, BaseAddress);
  DEBUG(dbgs() << "\n"; dbgs() << "Expr: " << *Expr << "\n";
        dbgs() << "Region: " << R->getNameStr() << "\n"; dbgs() << " -> ");

  ValidatorResult Result = Validator.visit(Expr);

  DEBUG(if (Result.isValid()) dbgs() << "VALID\n"; dbgs() << "\n";);

  return Result.isValid();
}

std::vector<const SCEV *> getParamsInAffineExpr(const Region *R,
                                                const SCEV *Expr,
                                                ScalarEvolution &SE,
                                                const Value *BaseAddress) {
  if (isa<SCEVCouldNotCompute>(Expr))
    return std::vector<const SCEV *>();

  SCEVValidator Validator(R, SE, BaseAddress);
  ValidatorResult Result = Validator.visit(Expr);

  return Result.getParameters();
}
}