//===- 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 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. LLVM_ABI explicit ConstantRange(uint32_t BitWidth, bool isFullSet); /// Initialize a range to hold the single specified value. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI static ConstantRange fromKnownBits(const KnownBits &Known, bool IsSigned); /// Split the ConstantRange into positive and negative components, ignoring /// zero values. LLVM_ABI std::pair splitPosNeg() const; /// 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) LLVM_ABI 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) LLVM_ABI 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) LLVM_ABI 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! LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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) LLVM_ABI 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. LLVM_ABI static ConstantRange makeExactNoWrapRegion(Instruction::BinaryOps BinOp, const APInt &Other, unsigned NoWrapKind); /// Initialize a range containing all values X that satisfy `(X & Mask) /// != C`. Note that the range returned may contain values where `(X & Mask) /// == C` holds, making it less precise, but still conservative. LLVM_ABI static ConstantRange makeMaskNotEqualRange(const APInt &Mask, const APInt &C); /// Returns true if ConstantRange calculations are supported for intrinsic /// with \p IntrinsicID. LLVM_ABI static bool isIntrinsicSupported(Intrinsic::ID IntrinsicID); /// Compute range of intrinsic result for the given operand ranges. LLVM_ABI static ConstantRange intrinsic(Intrinsic::ID IntrinsicID, ArrayRef Ops); /// Set up \p Pred and \p RHS such that /// ConstantRange::makeExactICmpRegion(Pred, RHS) == *this. Return true if /// successful. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI bool isFullSet() const; /// Return true if this set contains no members. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI bool isUpperSignWrapped() const; /// Return true if the specified value is in the set. LLVM_ABI bool contains(const APInt &Val) const; /// Return true if the other range is a subset of this one. LLVM_ABI 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. LLVM_ABI bool isSizeStrictlySmallerThan(const ConstantRange &CR) const; /// Compare set size of this range with Value. LLVM_ABI bool isSizeLargerThan(uint64_t MaxSize) const; /// Return true if all values in this range are negative. LLVM_ABI bool isAllNegative() const; /// Return true if all values in this range are non-negative. LLVM_ABI bool isAllNonNegative() const; /// Return true if all values in this range are positive. LLVM_ABI bool isAllPositive() const; /// Return the largest unsigned value contained in the ConstantRange. LLVM_ABI APInt getUnsignedMax() const; /// Return the smallest unsigned value contained in the ConstantRange. LLVM_ABI APInt getUnsignedMin() const; /// Return the largest signed value contained in the ConstantRange. LLVM_ABI APInt getSignedMax() const; /// Return the smallest signed value contained in the ConstantRange. LLVM_ABI 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. LLVM_ABI unsigned getActiveBits() const; /// Compute the maximal number of bits needed to represent every value /// in this signed range. LLVM_ABI unsigned getMinSignedBits() const; /// Subtract the specified constant from the endpoints of this constant range. LLVM_ABI ConstantRange subtract(const APInt &CI) const; /// Subtract the specified range from this range (aka relative complement of /// the sets). LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI std::optional exactIntersectWith(const ConstantRange &CR) const; /// Union the two ranges and return the result if it can be represented /// exactly, otherwise return std::nullopt. LLVM_ABI std::optional 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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 with wrap type \p NoWrapKind. /// Note that the result of trunc nuw is exact. LLVM_ABI ConstantRange truncate(uint32_t BitWidth, unsigned NoWrapKind = 0) 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI ConstantRange multiply(const ConstantRange &Other) const; /// Return a new range representing the possible values resulting /// from a multiplication 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. LLVM_ABI ConstantRange multiplyWithNoWrap(const ConstantRange &Other, unsigned NoWrapKind, PreferredRangeType RangeType = Smallest) 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI 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. LLVM_ABI ConstantRange shl(const ConstantRange &Other) const; /// Return a new range representing the possible values resulting /// from a left shift 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. LLVM_ABI ConstantRange shlWithNoWrap(const ConstantRange &Other, unsigned NoWrapKind, PreferredRangeType RangeType = Smallest) 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. LLVM_ABI 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. LLVM_ABI ConstantRange ashr(const ConstantRange &Other) const; /// Perform an unsigned saturating addition of two constant ranges. LLVM_ABI ConstantRange uadd_sat(const ConstantRange &Other) const; /// Perform a signed saturating addition of two constant ranges. LLVM_ABI ConstantRange sadd_sat(const ConstantRange &Other) const; /// Perform an unsigned saturating subtraction of two constant ranges. LLVM_ABI ConstantRange usub_sat(const ConstantRange &Other) const; /// Perform a signed saturating subtraction of two constant ranges. LLVM_ABI ConstantRange ssub_sat(const ConstantRange &Other) const; /// Perform an unsigned saturating multiplication of two constant ranges. LLVM_ABI ConstantRange umul_sat(const ConstantRange &Other) const; /// Perform a signed saturating multiplication of two constant ranges. LLVM_ABI ConstantRange smul_sat(const ConstantRange &Other) const; /// Perform an unsigned saturating left shift of this constant range by a /// value in \p Other. LLVM_ABI ConstantRange ushl_sat(const ConstantRange &Other) const; /// Perform a signed saturating left shift of this constant range by a /// value in \p Other. LLVM_ABI ConstantRange sshl_sat(const ConstantRange &Other) const; /// Return a new range that is the logical not of the current set. LLVM_ABI 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. LLVM_ABI ConstantRange abs(bool IntMinIsPoison = false) const; /// Calculate ctlz range. If \p ZeroIsPoison is set, the range is computed /// ignoring a possible zero value contained in the input range. LLVM_ABI ConstantRange ctlz(bool ZeroIsPoison = false) const; /// Calculate cttz range. If \p ZeroIsPoison is set, the range is computed /// ignoring a possible zero value contained in the input range. LLVM_ABI ConstantRange cttz(bool ZeroIsPoison = false) const; /// Calculate ctpop range. LLVM_ABI ConstantRange ctpop() 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. LLVM_ABI OverflowResult unsignedAddMayOverflow(const ConstantRange &Other) const; /// Return whether signed add of the two ranges always/never overflows. LLVM_ABI OverflowResult signedAddMayOverflow(const ConstantRange &Other) const; /// Return whether unsigned sub of the two ranges always/never overflows. LLVM_ABI OverflowResult unsignedSubMayOverflow(const ConstantRange &Other) const; /// Return whether signed sub of the two ranges always/never overflows. LLVM_ABI OverflowResult signedSubMayOverflow(const ConstantRange &Other) const; /// Return whether unsigned mul of the two ranges always/never overflows. LLVM_ABI OverflowResult unsignedMulMayOverflow(const ConstantRange &Other) const; /// Return known bits for values in this range. LLVM_ABI KnownBits toKnownBits() const; /// Print out the bounds to a stream. LLVM_ABI void print(raw_ostream &OS) const; /// Allow printing from a debugger easily. LLVM_ABI 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). LLVM_ABI ConstantRange getConstantRangeFromMetadata(const MDNode &RangeMD); } // end namespace llvm #endif // LLVM_IR_CONSTANTRANGE_H