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//===- ConstantRange.h - Represent a range ----------------------*- C++ -*-===//

//

// 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

//

//===----------------------------------------------------------------------===//

//

// Represent a range of possible values that may occur when the program is run

// for an integral value.  This keeps track of a lower and upper bound for the

// constant, which MAY wrap around the end of the numeric range.  To do this, it

// keeps track of a [lower, upper) bound, which specifies an interval just like

// STL iterators.  When used with boolean values, the following are important

// ranges: :

//

//  [F, F) = {}     = Empty set

//  [T, F) = {T}

//  [F, T) = {F}

//  [T, T) = {F, T} = Full set

//

// The other integral ranges use min/max values for special range values. For

// example, for 8-bit types, it uses:

// [0, 0)     = {}       = Empty set

// [255, 255) = {0..255} = Full Set

//

// Note that ConstantRange can be used to represent either signed or

// unsigned ranges.

//

//===----------------------------------------------------------------------===//

#ifndef LLVM_IR_CONSTANTRANGE_H

#define LLVM_IR_CONSTANTRANGE_H

#include "llvm/ADT/APInt.h"

#include "llvm/IR/InstrTypes.h"

#include "llvm/IR/Instruction.h"

#include "llvm/Support/Compiler.h"

#include <cstdint>

namespace llvm {

class MDNode;

class raw_ostream;

struct KnownBits;

/// This class represents a range of values.

class [[nodiscard]] ConstantRange {

  APInt Lower, Upper;

  /// Create empty constant range with same bitwidth.

  ConstantRange getEmpty() const {

    return ConstantRange(getBitWidth(), false);

  }

  /// Create full constant range with same bitwidth.

  ConstantRange getFull() const {

    return ConstantRange(getBitWidth(), true);

  }

public:

  /// Initialize a full or empty set for the specified bit width.

  explicit ConstantRange(uint32_t BitWidth, bool isFullSet);

  /// Initialize a range to hold the single specified value.

  ConstantRange(APInt Value);

  /// Initialize a range of values explicitly. This will assert out if

  /// Lower==Upper and Lower != Min or Max value for its type. It will also

  /// assert out if the two APInt's are not the same bit width.

  ConstantRange(APInt Lower, APInt Upper);

  /// Create empty constant range with the given bit width.

  static ConstantRange getEmpty(uint32_t BitWidth) {

    return ConstantRange(BitWidth, false);

  }

  /// Create full constant range with the given bit width.

  static ConstantRange getFull(uint32_t BitWidth) {

    return ConstantRange(BitWidth, true);

  }

  /// Create non-empty constant range with the given bounds. If Lower and

  /// Upper are the same, a full range is returned.

  static ConstantRange getNonEmpty(APInt Lower, APInt Upper) {

    if (Lower == Upper)

      return getFull(Lower.getBitWidth());

    return ConstantRange(std::move(Lower), std::move(Upper));

  }

  /// Initialize a range based on a known bits constraint. The IsSigned flag

  /// indicates whether the constant range should not wrap in the signed or

  /// unsigned domain.

  static ConstantRange fromKnownBits(const KnownBits &Known, bool IsSigned);

  /// Produce the smallest range such that all values that may satisfy the given

  /// predicate with any value contained within Other is contained in the

  /// returned range.  Formally, this returns a superset of

  /// 'union over all y in Other . { x : icmp op x y is true }'.  If the exact

  /// answer is not representable as a ConstantRange, the return value will be a

  /// proper superset of the above.

  ///

  /// Example: Pred = ult and Other = i8 [2, 5) returns Result = [0, 4)

  static ConstantRange makeAllowedICmpRegion(CmpInst::Predicate Pred,

                                             const ConstantRange &Other);

  /// Produce the largest range such that all values in the returned range

  /// satisfy the given predicate with all values contained within Other.

  /// Formally, this returns a subset of

  /// 'intersection over all y in Other . { x : icmp op x y is true }'.  If the

  /// exact answer is not representable as a ConstantRange, the return value

  /// will be a proper subset of the above.

  ///

  /// Example: Pred = ult and Other = i8 [2, 5) returns [0, 2)

  static ConstantRange makeSatisfyingICmpRegion(CmpInst::Predicate Pred,

                                                const ConstantRange &Other);

  /// Produce the exact range such that all values in the returned range satisfy

  /// the given predicate with any value contained within Other. Formally, this

  /// returns the exact answer when the superset of 'union over all y in Other

  /// is exactly same as the subset of intersection over all y in Other.

  /// { x : icmp op x y is true}'.

  ///

  /// Example: Pred = ult and Other = i8 3 returns [0, 3)

  static ConstantRange makeExactICmpRegion(CmpInst::Predicate Pred,

                                           const APInt &Other);

  /// Does the predicate \p Pred hold between ranges this and \p Other?

  /// NOTE: false does not mean that inverse predicate holds!

  bool icmp(CmpInst::Predicate Pred, const ConstantRange &Other) const;

  /// Return true iff CR1 ult CR2 is equivalent to CR1 slt CR2.

  /// Does not depend on strictness/direction of the predicate.

  static bool

  areInsensitiveToSignednessOfICmpPredicate(const ConstantRange &CR1,

                                            const ConstantRange &CR2);

  /// Return true iff CR1 ult CR2 is equivalent to CR1 sge CR2.

  /// Does not depend on strictness/direction of the predicate.

  static bool

  areInsensitiveToSignednessOfInvertedICmpPredicate(const ConstantRange &CR1,

                                                    const ConstantRange &CR2);

  /// If the comparison between constant ranges this and Other

  /// is insensitive to the signedness of the comparison predicate,

  /// return a predicate equivalent to \p Pred, with flipped signedness

  /// (i.e. unsigned instead of signed or vice versa), and maybe inverted,

  /// otherwise returns CmpInst::Predicate::BAD_ICMP_PREDICATE.

  static CmpInst::Predicate

  getEquivalentPredWithFlippedSignedness(CmpInst::Predicate Pred,

                                         const ConstantRange &CR1,

                                         const ConstantRange &CR2);

  /// Produce the largest range containing all X such that "X BinOp Y" is

  /// guaranteed not to wrap (overflow) for *all* Y in Other. However, there may

  /// be *some* Y in Other for which additional X not contained in the result

  /// also do not overflow.

  ///

  /// NoWrapKind must be one of OBO::NoUnsignedWrap or OBO::NoSignedWrap.

  ///

  /// Examples:

  ///  typedef OverflowingBinaryOperator OBO;

  ///  #define MGNR makeGuaranteedNoWrapRegion

  ///  MGNR(Add, [i8 1, 2), OBO::NoSignedWrap) == [-128, 127)

  ///  MGNR(Add, [i8 1, 2), OBO::NoUnsignedWrap) == [0, -1)

  ///  MGNR(Add, [i8 0, 1), OBO::NoUnsignedWrap) == Full Set

  ///  MGNR(Add, [i8 -1, 6), OBO::NoSignedWrap) == [INT_MIN+1, INT_MAX-4)

  ///  MGNR(Sub, [i8 1, 2), OBO::NoSignedWrap) == [-127, 128)

  ///  MGNR(Sub, [i8 1, 2), OBO::NoUnsignedWrap) == [1, 0)

  static ConstantRange makeGuaranteedNoWrapRegion(Instruction::BinaryOps BinOp,

                                                  const ConstantRange &Other,

                                                  unsigned NoWrapKind);

  /// Produce the range that contains X if and only if "X BinOp Other" does

  /// not wrap.

  static ConstantRange makeExactNoWrapRegion(Instruction::BinaryOps BinOp,

                                             const APInt &Other,

                                             unsigned NoWrapKind);

  /// Returns true if ConstantRange calculations are supported for intrinsic

  /// with \p IntrinsicID.

  static bool isIntrinsicSupported(Intrinsic::ID IntrinsicID);

  /// Compute range of intrinsic result for the given operand ranges.

  static ConstantRange intrinsic(Intrinsic::ID IntrinsicID,

                                 ArrayRef<ConstantRange> Ops);

  /// Set up \p Pred and \p RHS such that

  /// ConstantRange::makeExactICmpRegion(Pred, RHS) == *this.  Return true if

  /// successful.

  bool getEquivalentICmp(CmpInst::Predicate &Pred, APInt &RHS) const;

  /// Set up \p Pred, \p RHS and \p Offset such that (V + Offset) Pred RHS

  /// is true iff V is in the range. Prefers using Offset == 0 if possible.

  void

  getEquivalentICmp(CmpInst::Predicate &Pred, APInt &RHS, APInt &Offset) const;

  /// Return the lower value for this range.

  const APInt &getLower() const { return Lower; }

  /// Return the upper value for this range.

  const APInt &getUpper() const { return Upper; }

  /// Get the bit width of this ConstantRange.

  uint32_t getBitWidth() const { return Lower.getBitWidth(); }

  /// Return true if this set contains all of the elements possible

  /// for this data-type.

  bool isFullSet() const;

  /// Return true if this set contains no members.

  bool isEmptySet() const;

  /// Return true if this set wraps around the unsigned domain. Special cases:

  ///  * Empty set: Not wrapped.

  ///  * Full set: Not wrapped.

  ///  * [X, 0) == [X, Max]: Not wrapped.

  bool isWrappedSet() const;

  /// Return true if the exclusive upper bound wraps around the unsigned

  /// domain. Special cases:

  ///  * Empty set: Not wrapped.

  ///  * Full set: Not wrapped.

  ///  * [X, 0): Wrapped.

  bool isUpperWrapped() const;

  /// Return true if this set wraps around the signed domain. Special cases:

  ///  * Empty set: Not wrapped.

  ///  * Full set: Not wrapped.

  ///  * [X, SignedMin) == [X, SignedMax]: Not wrapped.

  bool isSignWrappedSet() const;

  /// Return true if the (exclusive) upper bound wraps around the signed

  /// domain. Special cases:

  ///  * Empty set: Not wrapped.

  ///  * Full set: Not wrapped.

  ///  * [X, SignedMin): Wrapped.

  bool isUpperSignWrapped() const;

  /// Return true if the specified value is in the set.

  bool contains(const APInt &Val) const;

  /// Return true if the other range is a subset of this one.

  bool contains(const ConstantRange &CR) const;

  /// If this set contains a single element, return it, otherwise return null.

  const APInt *getSingleElement() const {

    if (Upper == Lower + 1)

      return &Lower;

    return nullptr;

  }

  /// If this set contains all but a single element, return it, otherwise return

  /// null.

  const APInt *getSingleMissingElement() const {

    if (Lower == Upper + 1)

      return &Upper;

    return nullptr;

  }

  /// Return true if this set contains exactly one member.

  bool isSingleElement() const { return getSingleElement() != nullptr; }

  /// Compare set size of this range with the range CR.

  bool isSizeStrictlySmallerThan(const ConstantRange &CR) const;

  /// Compare set size of this range with Value.

  bool isSizeLargerThan(uint64_t MaxSize) const;

  /// Return true if all values in this range are negative.

  bool isAllNegative() const;

  /// Return true if all values in this range are non-negative.

  bool isAllNonNegative() const;

  /// Return the largest unsigned value contained in the ConstantRange.

  APInt getUnsignedMax() const;

  /// Return the smallest unsigned value contained in the ConstantRange.

  APInt getUnsignedMin() const;

  /// Return the largest signed value contained in the ConstantRange.

  APInt getSignedMax() const;

  /// Return the smallest signed value contained in the ConstantRange.

  APInt getSignedMin() const;

  /// Return true if this range is equal to another range.

  bool operator==(const ConstantRange &CR) const {

    return Lower == CR.Lower && Upper == CR.Upper;

  }

  bool operator!=(const ConstantRange &CR) const {

    return !operator==(CR);

  }

  /// Compute the maximal number of active bits needed to represent every value

  /// in this range.

  unsigned getActiveBits() const;

  /// Compute the maximal number of bits needed to represent every value

  /// in this signed range.

  unsigned getMinSignedBits() const;

  /// Subtract the specified constant from the endpoints of this constant range.

  ConstantRange subtract(const APInt &CI) const;

  /// Subtract the specified range from this range (aka relative complement of

  /// the sets).

  ConstantRange difference(const ConstantRange &CR) const;

  /// If represented precisely, the result of some range operations may consist

  /// of multiple disjoint ranges. As only a single range may be returned, any

  /// range covering these disjoint ranges constitutes a valid result, but some

  /// may be more useful than others depending on context. The preferred range

  /// type specifies whether a range that is non-wrapping in the unsigned or

  /// signed domain, or has the smallest size, is preferred. If a signedness is

  /// preferred but all ranges are non-wrapping or all wrapping, then the

  /// smallest set size is preferred. If there are multiple smallest sets, any

  /// one of them may be returned.

  enum PreferredRangeType { Smallest, Unsigned, Signed };

  /// Return the range that results from the intersection of this range with

  /// another range. If the intersection is disjoint, such that two results

  /// are possible, the preferred range is determined by the PreferredRangeType.

  ConstantRange intersectWith(const ConstantRange &CR,

                              PreferredRangeType Type = Smallest) const;

  /// Return the range that results from the union of this range

  /// with another range.  The resultant range is guaranteed to include the

  /// elements of both sets, but may contain more.  For example, [3, 9) union

  /// [12,15) is [3, 15), which includes 9, 10, and 11, which were not included

  /// in either set before.

  ConstantRange unionWith(const ConstantRange &CR,

                          PreferredRangeType Type = Smallest) const;

  /// Intersect the two ranges and return the result if it can be represented

  /// exactly, otherwise return std::nullopt.

  std::optional<ConstantRange>

  exactIntersectWith(const ConstantRange &CR) const;

  /// Union the two ranges and return the result if it can be represented

  /// exactly, otherwise return std::nullopt.

  std::optional<ConstantRange> exactUnionWith(const ConstantRange &CR) const;

  /// Return a new range representing the possible values resulting

  /// from an application of the specified cast operator to this range. \p

  /// BitWidth is the target bitwidth of the cast.  For casts which don't

  /// change bitwidth, it must be the same as the source bitwidth.  For casts

  /// which do change bitwidth, the bitwidth must be consistent with the

  /// requested cast and source bitwidth.

  ConstantRange castOp(Instruction::CastOps CastOp,

                       uint32_t BitWidth) const;

  /// Return a new range in the specified integer type, which must

  /// be strictly larger than the current type.  The returned range will

  /// correspond to the possible range of values if the source range had been

  /// zero extended to BitWidth.

  ConstantRange zeroExtend(uint32_t BitWidth) const;

  /// Return a new range in the specified integer type, which must

  /// be strictly larger than the current type.  The returned range will

  /// correspond to the possible range of values if the source range had been

  /// sign extended to BitWidth.

  ConstantRange signExtend(uint32_t BitWidth) const;

  /// Return a new range in the specified integer type, which must be

  /// strictly smaller than the current type.  The returned range will

  /// correspond to the possible range of values if the source range had been

  /// truncated to the specified type.

  ConstantRange truncate(uint32_t BitWidth) const;

  /// Make this range have the bit width given by \p BitWidth. The

  /// value is zero extended, truncated, or left alone to make it that width.

  ConstantRange zextOrTrunc(uint32_t BitWidth) const;

  /// Make this range have the bit width given by \p BitWidth. The

  /// value is sign extended, truncated, or left alone to make it that width.

  ConstantRange sextOrTrunc(uint32_t BitWidth) const;

  /// Return a new range representing the possible values resulting

  /// from an application of the specified binary operator to an left hand side

  /// of this range and a right hand side of \p Other.

  ConstantRange binaryOp(Instruction::BinaryOps BinOp,

                         const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting

  /// from an application of the specified overflowing binary operator to a

  /// left hand side of this range and a right hand side of \p Other given

  /// the provided knowledge about lack of wrapping \p NoWrapKind.

  ConstantRange overflowingBinaryOp(Instruction::BinaryOps BinOp,

                                    const ConstantRange &Other,

                                    unsigned NoWrapKind) const;

  /// Return a new range representing the possible values resulting

  /// from an addition of a value in this range and a value in \p Other.

  ConstantRange add(const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting

  /// from an addition with wrap type \p NoWrapKind of a value in this

  /// range and a value in \p Other.

  /// If the result range is disjoint, the preferred range is determined by the

  /// \p PreferredRangeType.

  ConstantRange addWithNoWrap(const ConstantRange &Other, unsigned NoWrapKind,

                              PreferredRangeType RangeType = Smallest) const;

  /// Return a new range representing the possible values resulting

  /// from a subtraction of a value in this range and a value in \p Other.

  ConstantRange sub(const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting

  /// from an subtraction with wrap type \p NoWrapKind of a value in this

  /// range and a value in \p Other.

  /// If the result range is disjoint, the preferred range is determined by the

  /// \p PreferredRangeType.

  ConstantRange subWithNoWrap(const ConstantRange &Other, unsigned NoWrapKind,

                              PreferredRangeType RangeType = Smallest) const;

  /// Return a new range representing the possible values resulting

  /// from a multiplication of a value in this range and a value in \p Other,

  /// treating both this and \p Other as unsigned ranges.

  ConstantRange multiply(const ConstantRange &Other) const;

  /// Return range of possible values for a signed multiplication of this and

  /// \p Other. However, if overflow is possible always return a full range

  /// rather than trying to determine a more precise result.

  ConstantRange smul_fast(const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting

  /// from a signed maximum of a value in this range and a value in \p Other.

  ConstantRange smax(const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting

  /// from an unsigned maximum of a value in this range and a value in \p Other.

  ConstantRange umax(const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting

  /// from a signed minimum of a value in this range and a value in \p Other.

  ConstantRange smin(const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting

  /// from an unsigned minimum of a value in this range and a value in \p Other.

  ConstantRange umin(const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting

  /// from an unsigned division of a value in this range and a value in

  /// \p Other.

  ConstantRange udiv(const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting

  /// from a signed division of a value in this range and a value in

  /// \p Other. Division by zero and division of SignedMin by -1 are considered

  /// undefined behavior, in line with IR, and do not contribute towards the

  /// result.

  ConstantRange sdiv(const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting

  /// from an unsigned remainder operation of a value in this range and a

  /// value in \p Other.

  ConstantRange urem(const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting

  /// from a signed remainder operation of a value in this range and a

  /// value in \p Other.

  ConstantRange srem(const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting from

  /// a binary-xor of a value in this range by an all-one value,

  /// aka bitwise complement operation.

  ConstantRange binaryNot() const;

  /// Return a new range representing the possible values resulting

  /// from a binary-and of a value in this range by a value in \p Other.

  ConstantRange binaryAnd(const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting

  /// from a binary-or of a value in this range by a value in \p Other.

  ConstantRange binaryOr(const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting

  /// from a binary-xor of a value in this range by a value in \p Other.

  ConstantRange binaryXor(const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting

  /// from a left shift of a value in this range by a value in \p Other.

  /// TODO: This isn't fully implemented yet.

  ConstantRange shl(const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting from a

  /// logical right shift of a value in this range and a value in \p Other.

  ConstantRange lshr(const ConstantRange &Other) const;

  /// Return a new range representing the possible values resulting from a

  /// arithmetic right shift of a value in this range and a value in \p Other.

  ConstantRange ashr(const ConstantRange &Other) const;

  /// Perform an unsigned saturating addition of two constant ranges.

  ConstantRange uadd_sat(const ConstantRange &Other) const;

  /// Perform a signed saturating addition of two constant ranges.

  ConstantRange sadd_sat(const ConstantRange &Other) const;

  /// Perform an unsigned saturating subtraction of two constant ranges.

  ConstantRange usub_sat(const ConstantRange &Other) const;

  /// Perform a signed saturating subtraction of two constant ranges.

  ConstantRange ssub_sat(const ConstantRange &Other) const;

  /// Perform an unsigned saturating multiplication of two constant ranges.

  ConstantRange umul_sat(const ConstantRange &Other) const;

  /// Perform a signed saturating multiplication of two constant ranges.

  ConstantRange smul_sat(const ConstantRange &Other) const;

  /// Perform an unsigned saturating left shift of this constant range by a

  /// value in \p Other.

  ConstantRange ushl_sat(const ConstantRange &Other) const;

  /// Perform a signed saturating left shift of this constant range by a

  /// value in \p Other.

  ConstantRange sshl_sat(const ConstantRange &Other) const;

  /// Return a new range that is the logical not of the current set.

  ConstantRange inverse() const;

  /// Calculate absolute value range. If the original range contains signed

  /// min, then the resulting range will contain signed min if and only if

  /// \p IntMinIsPoison is false.

  ConstantRange abs(bool IntMinIsPoison = false) const;

  /// Represents whether an operation on the given constant range is known to

  /// always or never overflow.

  enum class OverflowResult {

    /// Always overflows in the direction of signed/unsigned min value.

    AlwaysOverflowsLow,

    /// Always overflows in the direction of signed/unsigned max value.

    AlwaysOverflowsHigh,

    /// May or may not overflow.

    MayOverflow,

    /// Never overflows.

    NeverOverflows,

  };

  /// Return whether unsigned add of the two ranges always/never overflows.

  OverflowResult unsignedAddMayOverflow(const ConstantRange &Other) const;

  /// Return whether signed add of the two ranges always/never overflows.

  OverflowResult signedAddMayOverflow(const ConstantRange &Other) const;

  /// Return whether unsigned sub of the two ranges always/never overflows.

  OverflowResult unsignedSubMayOverflow(const ConstantRange &Other) const;

  /// Return whether signed sub of the two ranges always/never overflows.

  OverflowResult signedSubMayOverflow(const ConstantRange &Other) const;

  /// Return whether unsigned mul of the two ranges always/never overflows.

  OverflowResult unsignedMulMayOverflow(const ConstantRange &Other) const;

  /// Return known bits for values in this range.

  KnownBits toKnownBits() const;

  /// Print out the bounds to a stream.

  void print(raw_ostream &OS) const;

  /// Allow printing from a debugger easily.

  void dump() const;

};

inline raw_ostream &operator<<(raw_ostream &OS, const ConstantRange &CR) {

  CR.print(OS);

  return OS;

}

/// Parse out a conservative ConstantRange from !range metadata.

///

/// E.g. if RangeMD is !{i32 0, i32 10, i32 15, i32 20} then return [0, 20).

ConstantRange getConstantRangeFromMetadata(const MDNode &RangeMD);

} // end namespace llvm

#endif // LLVM_IR_CONSTANTRANGE_H