//===- 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 LLVM_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); | |

/// 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); | |

/// 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; | |

/// 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); | |

} | |

/// 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; | |

/// 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 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 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 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-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 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; | |

/// 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 also contain signed min. | |

ConstantRange abs() 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; | |

/// 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 |