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llvm-project/llvm/lib/IR/ConstantRange.cpp

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//===- ConstantRange.cpp - ConstantRange implementation -------------------===//
//
// 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 (other integral ranges use min/max values for special range values):
//
// [F, F) = {} = Empty set
// [T, F) = {T}
// [F, T) = {F}
// [T, T) = {F, T} = Full set
//
//===----------------------------------------------------------------------===//
#include "llvm/ADT/APInt.h"
#include "llvm/Config/llvm-config.h"
#include "llvm/IR/ConstantRange.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/InstrTypes.h"
#include "llvm/IR/Instruction.h"
#include "llvm/IR/Metadata.h"
#include "llvm/IR/Operator.h"
#include "llvm/Support/Compiler.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/ErrorHandling.h"
#include "llvm/Support/KnownBits.h"
#include "llvm/Support/raw_ostream.h"
#include <algorithm>
#include <cassert>
#include <cstdint>
using namespace llvm;
ConstantRange::ConstantRange(uint32_t BitWidth, bool Full)
: Lower(Full ? APInt::getMaxValue(BitWidth) : APInt::getMinValue(BitWidth)),
Upper(Lower) {}
ConstantRange::ConstantRange(APInt V)
: Lower(std::move(V)), Upper(Lower + 1) {}
ConstantRange::ConstantRange(APInt L, APInt U)
: Lower(std::move(L)), Upper(std::move(U)) {
assert(Lower.getBitWidth() == Upper.getBitWidth() &&
"ConstantRange with unequal bit widths");
assert((Lower != Upper || (Lower.isMaxValue() || Lower.isMinValue())) &&
"Lower == Upper, but they aren't min or max value!");
}
ConstantRange ConstantRange::fromKnownBits(const KnownBits &Known,
bool IsSigned) {
assert(!Known.hasConflict() && "Expected valid KnownBits");
if (Known.isUnknown())
return getFull(Known.getBitWidth());
// For unsigned ranges, or signed ranges with known sign bit, create a simple
// range between the smallest and largest possible value.
if (!IsSigned || Known.isNegative() || Known.isNonNegative())
return ConstantRange(Known.One, ~Known.Zero + 1);
// If we don't know the sign bit, pick the lower bound as a negative number
// and the upper bound as a non-negative one.
APInt Lower = Known.One, Upper = ~Known.Zero;
Lower.setSignBit();
Upper.clearSignBit();
return ConstantRange(Lower, Upper + 1);
}
ConstantRange ConstantRange::makeAllowedICmpRegion(CmpInst::Predicate Pred,
const ConstantRange &CR) {
if (CR.isEmptySet())
return CR;
uint32_t W = CR.getBitWidth();
switch (Pred) {
default:
llvm_unreachable("Invalid ICmp predicate to makeAllowedICmpRegion()");
case CmpInst::ICMP_EQ:
return CR;
case CmpInst::ICMP_NE:
if (CR.isSingleElement())
return ConstantRange(CR.getUpper(), CR.getLower());
return getFull(W);
case CmpInst::ICMP_ULT: {
APInt UMax(CR.getUnsignedMax());
if (UMax.isMinValue())
return getEmpty(W);
return ConstantRange(APInt::getMinValue(W), std::move(UMax));
}
case CmpInst::ICMP_SLT: {
APInt SMax(CR.getSignedMax());
if (SMax.isMinSignedValue())
return getEmpty(W);
return ConstantRange(APInt::getSignedMinValue(W), std::move(SMax));
}
case CmpInst::ICMP_ULE:
return getNonEmpty(APInt::getMinValue(W), CR.getUnsignedMax() + 1);
case CmpInst::ICMP_SLE:
return getNonEmpty(APInt::getSignedMinValue(W), CR.getSignedMax() + 1);
case CmpInst::ICMP_UGT: {
APInt UMin(CR.getUnsignedMin());
if (UMin.isMaxValue())
return getEmpty(W);
return ConstantRange(std::move(UMin) + 1, APInt::getNullValue(W));
}
case CmpInst::ICMP_SGT: {
APInt SMin(CR.getSignedMin());
if (SMin.isMaxSignedValue())
return getEmpty(W);
return ConstantRange(std::move(SMin) + 1, APInt::getSignedMinValue(W));
}
case CmpInst::ICMP_UGE:
return getNonEmpty(CR.getUnsignedMin(), APInt::getNullValue(W));
case CmpInst::ICMP_SGE:
return getNonEmpty(CR.getSignedMin(), APInt::getSignedMinValue(W));
}
}
ConstantRange ConstantRange::makeSatisfyingICmpRegion(CmpInst::Predicate Pred,
const ConstantRange &CR) {
// Follows from De-Morgan's laws:
//
// ~(~A union ~B) == A intersect B.
//
return makeAllowedICmpRegion(CmpInst::getInversePredicate(Pred), CR)
.inverse();
}
ConstantRange ConstantRange::makeExactICmpRegion(CmpInst::Predicate Pred,
const APInt &C) {
// Computes the exact range that is equal to both the constant ranges returned
// by makeAllowedICmpRegion and makeSatisfyingICmpRegion. This is always true
// when RHS is a singleton such as an APInt and so the assert is valid.
// However for non-singleton RHS, for example ult [2,5) makeAllowedICmpRegion
// returns [0,4) but makeSatisfyICmpRegion returns [0,2).
//
assert(makeAllowedICmpRegion(Pred, C) == makeSatisfyingICmpRegion(Pred, C));
return makeAllowedICmpRegion(Pred, C);
}
bool ConstantRange::getEquivalentICmp(CmpInst::Predicate &Pred,
APInt &RHS) const {
bool Success = false;
if (isFullSet() || isEmptySet()) {
Pred = isEmptySet() ? CmpInst::ICMP_ULT : CmpInst::ICMP_UGE;
RHS = APInt(getBitWidth(), 0);
Success = true;
} else if (auto *OnlyElt = getSingleElement()) {
Pred = CmpInst::ICMP_EQ;
RHS = *OnlyElt;
Success = true;
} else if (auto *OnlyMissingElt = getSingleMissingElement()) {
Pred = CmpInst::ICMP_NE;
RHS = *OnlyMissingElt;
Success = true;
} else if (getLower().isMinSignedValue() || getLower().isMinValue()) {
Pred =
getLower().isMinSignedValue() ? CmpInst::ICMP_SLT : CmpInst::ICMP_ULT;
RHS = getUpper();
Success = true;
} else if (getUpper().isMinSignedValue() || getUpper().isMinValue()) {
Pred =
getUpper().isMinSignedValue() ? CmpInst::ICMP_SGE : CmpInst::ICMP_UGE;
RHS = getLower();
Success = true;
}
assert((!Success || ConstantRange::makeExactICmpRegion(Pred, RHS) == *this) &&
"Bad result!");
return Success;
}
/// Exact mul nuw region for single element RHS.
static ConstantRange makeExactMulNUWRegion(const APInt &V) {
unsigned BitWidth = V.getBitWidth();
if (V == 0)
return ConstantRange::getFull(V.getBitWidth());
return ConstantRange::getNonEmpty(
APIntOps::RoundingUDiv(APInt::getMinValue(BitWidth), V,
APInt::Rounding::UP),
APIntOps::RoundingUDiv(APInt::getMaxValue(BitWidth), V,
APInt::Rounding::DOWN) + 1);
}
/// Exact mul nsw region for single element RHS.
static ConstantRange makeExactMulNSWRegion(const APInt &V) {
// Handle special case for 0, -1 and 1. See the last for reason why we
// specialize -1 and 1.
unsigned BitWidth = V.getBitWidth();
if (V == 0 || V.isOneValue())
return ConstantRange::getFull(BitWidth);
APInt MinValue = APInt::getSignedMinValue(BitWidth);
APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
// e.g. Returning [-127, 127], represented as [-127, -128).
if (V.isAllOnesValue())
return ConstantRange(-MaxValue, MinValue);
APInt Lower, Upper;
if (V.isNegative()) {
Lower = APIntOps::RoundingSDiv(MaxValue, V, APInt::Rounding::UP);
Upper = APIntOps::RoundingSDiv(MinValue, V, APInt::Rounding::DOWN);
} else {
Lower = APIntOps::RoundingSDiv(MinValue, V, APInt::Rounding::UP);
Upper = APIntOps::RoundingSDiv(MaxValue, V, APInt::Rounding::DOWN);
}
// ConstantRange ctor take a half inclusive interval [Lower, Upper + 1).
// Upper + 1 is guaranteed not to overflow, because |divisor| > 1. 0, -1,
// and 1 are already handled as special cases.
return ConstantRange(Lower, Upper + 1);
}
ConstantRange
ConstantRange::makeGuaranteedNoWrapRegion(Instruction::BinaryOps BinOp,
const ConstantRange &Other,
unsigned NoWrapKind) {
using OBO = OverflowingBinaryOperator;
assert(Instruction::isBinaryOp(BinOp) && "Binary operators only!");
assert((NoWrapKind == OBO::NoSignedWrap ||
NoWrapKind == OBO::NoUnsignedWrap) &&
"NoWrapKind invalid!");
bool Unsigned = NoWrapKind == OBO::NoUnsignedWrap;
unsigned BitWidth = Other.getBitWidth();
switch (BinOp) {
default:
// Conservative answer: empty set
return getEmpty(BitWidth);
case Instruction::Add: {
if (Unsigned)
return getNonEmpty(APInt::getNullValue(BitWidth),
-Other.getUnsignedMax());
APInt SignedMinVal = APInt::getSignedMinValue(BitWidth);
APInt SMin = Other.getSignedMin(), SMax = Other.getSignedMax();
return getNonEmpty(
SMin.isNegative() ? SignedMinVal - SMin : SignedMinVal,
SMax.isStrictlyPositive() ? SignedMinVal - SMax : SignedMinVal);
}
case Instruction::Sub: {
if (Unsigned)
return getNonEmpty(Other.getUnsignedMax(), APInt::getMinValue(BitWidth));
APInt SignedMinVal = APInt::getSignedMinValue(BitWidth);
APInt SMin = Other.getSignedMin(), SMax = Other.getSignedMax();
return getNonEmpty(
SMax.isStrictlyPositive() ? SignedMinVal + SMax : SignedMinVal,
SMin.isNegative() ? SignedMinVal + SMin : SignedMinVal);
}
case Instruction::Mul:
if (Unsigned)
return makeExactMulNUWRegion(Other.getUnsignedMax());
return makeExactMulNSWRegion(Other.getSignedMin())
.intersectWith(makeExactMulNSWRegion(Other.getSignedMax()));
}
}
ConstantRange ConstantRange::makeExactNoWrapRegion(Instruction::BinaryOps BinOp,
const APInt &Other,
unsigned NoWrapKind) {
// makeGuaranteedNoWrapRegion() is exact for single-element ranges, as
// "for all" and "for any" coincide in this case.
return makeGuaranteedNoWrapRegion(BinOp, ConstantRange(Other), NoWrapKind);
}
bool ConstantRange::isFullSet() const {
return Lower == Upper && Lower.isMaxValue();
}
bool ConstantRange::isEmptySet() const {
return Lower == Upper && Lower.isMinValue();
}
bool ConstantRange::isWrappedSet() const {
return Lower.ugt(Upper) && !Upper.isNullValue();
}
bool ConstantRange::isUpperWrapped() const {
return Lower.ugt(Upper);
}
bool ConstantRange::isSignWrappedSet() const {
return Lower.sgt(Upper) && !Upper.isMinSignedValue();
}
bool ConstantRange::isUpperSignWrapped() const {
return Lower.sgt(Upper);
}
bool
ConstantRange::isSizeStrictlySmallerThan(const ConstantRange &Other) const {
assert(getBitWidth() == Other.getBitWidth());
if (isFullSet())
return false;
if (Other.isFullSet())
return true;
return (Upper - Lower).ult(Other.Upper - Other.Lower);
}
bool
ConstantRange::isSizeLargerThan(uint64_t MaxSize) const {
assert(MaxSize && "MaxSize can't be 0.");
// If this a full set, we need special handling to avoid needing an extra bit
// to represent the size.
if (isFullSet())
return APInt::getMaxValue(getBitWidth()).ugt(MaxSize - 1);
return (Upper - Lower).ugt(MaxSize);
}
bool ConstantRange::isAllNegative() const {
// Empty set is all negative, full set is not.
if (isEmptySet())
return true;
if (isFullSet())
return false;
return !isUpperSignWrapped() && !Upper.isStrictlyPositive();
}
bool ConstantRange::isAllNonNegative() const {
// Empty and full set are automatically treated correctly.
return !isSignWrappedSet() && Lower.isNonNegative();
}
APInt ConstantRange::getUnsignedMax() const {
if (isFullSet() || isUpperWrapped())
return APInt::getMaxValue(getBitWidth());
return getUpper() - 1;
}
APInt ConstantRange::getUnsignedMin() const {
if (isFullSet() || isWrappedSet())
return APInt::getMinValue(getBitWidth());
return getLower();
}
APInt ConstantRange::getSignedMax() const {
if (isFullSet() || isUpperSignWrapped())
return APInt::getSignedMaxValue(getBitWidth());
return getUpper() - 1;
}
APInt ConstantRange::getSignedMin() const {
if (isFullSet() || isSignWrappedSet())
return APInt::getSignedMinValue(getBitWidth());
return getLower();
}
bool ConstantRange::contains(const APInt &V) const {
if (Lower == Upper)
return isFullSet();
if (!isUpperWrapped())
return Lower.ule(V) && V.ult(Upper);
return Lower.ule(V) || V.ult(Upper);
}
bool ConstantRange::contains(const ConstantRange &Other) const {
if (isFullSet() || Other.isEmptySet()) return true;
if (isEmptySet() || Other.isFullSet()) return false;
if (!isUpperWrapped()) {
if (Other.isUpperWrapped())
return false;
return Lower.ule(Other.getLower()) && Other.getUpper().ule(Upper);
}
if (!Other.isUpperWrapped())
return Other.getUpper().ule(Upper) ||
Lower.ule(Other.getLower());
return Other.getUpper().ule(Upper) && Lower.ule(Other.getLower());
}
ConstantRange ConstantRange::subtract(const APInt &Val) const {
assert(Val.getBitWidth() == getBitWidth() && "Wrong bit width");
// If the set is empty or full, don't modify the endpoints.
if (Lower == Upper)
return *this;
return ConstantRange(Lower - Val, Upper - Val);
}
ConstantRange ConstantRange::difference(const ConstantRange &CR) const {
return intersectWith(CR.inverse());
}
static ConstantRange getPreferredRange(
const ConstantRange &CR1, const ConstantRange &CR2,
ConstantRange::PreferredRangeType Type) {
if (Type == ConstantRange::Unsigned) {
if (!CR1.isWrappedSet() && CR2.isWrappedSet())
return CR1;
if (CR1.isWrappedSet() && !CR2.isWrappedSet())
return CR2;
} else if (Type == ConstantRange::Signed) {
if (!CR1.isSignWrappedSet() && CR2.isSignWrappedSet())
return CR1;
if (CR1.isSignWrappedSet() && !CR2.isSignWrappedSet())
return CR2;
}
if (CR1.isSizeStrictlySmallerThan(CR2))
return CR1;
return CR2;
}
ConstantRange ConstantRange::intersectWith(const ConstantRange &CR,
PreferredRangeType Type) const {
assert(getBitWidth() == CR.getBitWidth() &&
"ConstantRange types don't agree!");
// Handle common cases.
if ( isEmptySet() || CR.isFullSet()) return *this;
if (CR.isEmptySet() || isFullSet()) return CR;
if (!isUpperWrapped() && CR.isUpperWrapped())
return CR.intersectWith(*this, Type);
if (!isUpperWrapped() && !CR.isUpperWrapped()) {
if (Lower.ult(CR.Lower)) {
// L---U : this
// L---U : CR
if (Upper.ule(CR.Lower))
return getEmpty();
// L---U : this
// L---U : CR
if (Upper.ult(CR.Upper))
return ConstantRange(CR.Lower, Upper);
// L-------U : this
// L---U : CR
return CR;
}
// L---U : this
// L-------U : CR
if (Upper.ult(CR.Upper))
return *this;
// L-----U : this
// L-----U : CR
if (Lower.ult(CR.Upper))
return ConstantRange(Lower, CR.Upper);
// L---U : this
// L---U : CR
return getEmpty();
}
if (isUpperWrapped() && !CR.isUpperWrapped()) {
if (CR.Lower.ult(Upper)) {
// ------U L--- : this
// L--U : CR
if (CR.Upper.ult(Upper))
return CR;
// ------U L--- : this
// L------U : CR
if (CR.Upper.ule(Lower))
return ConstantRange(CR.Lower, Upper);
// ------U L--- : this
// L----------U : CR
return getPreferredRange(*this, CR, Type);
}
if (CR.Lower.ult(Lower)) {
// --U L---- : this
// L--U : CR
if (CR.Upper.ule(Lower))
return getEmpty();
// --U L---- : this
// L------U : CR
return ConstantRange(Lower, CR.Upper);
}
// --U L------ : this
// L--U : CR
return CR;
}
if (CR.Upper.ult(Upper)) {
// ------U L-- : this
// --U L------ : CR
if (CR.Lower.ult(Upper))
return getPreferredRange(*this, CR, Type);
// ----U L-- : this
// --U L---- : CR
if (CR.Lower.ult(Lower))
return ConstantRange(Lower, CR.Upper);
// ----U L---- : this
// --U L-- : CR
return CR;
}
if (CR.Upper.ule(Lower)) {
// --U L-- : this
// ----U L---- : CR
if (CR.Lower.ult(Lower))
return *this;
// --U L---- : this
// ----U L-- : CR
return ConstantRange(CR.Lower, Upper);
}
// --U L------ : this
// ------U L-- : CR
return getPreferredRange(*this, CR, Type);
}
ConstantRange ConstantRange::unionWith(const ConstantRange &CR,
PreferredRangeType Type) const {
assert(getBitWidth() == CR.getBitWidth() &&
"ConstantRange types don't agree!");
if ( isFullSet() || CR.isEmptySet()) return *this;
if (CR.isFullSet() || isEmptySet()) return CR;
if (!isUpperWrapped() && CR.isUpperWrapped())
return CR.unionWith(*this, Type);
if (!isUpperWrapped() && !CR.isUpperWrapped()) {
// L---U and L---U : this
// L---U L---U : CR
// result in one of
// L---------U
// -----U L-----
if (CR.Upper.ult(Lower) || Upper.ult(CR.Lower))
return getPreferredRange(
ConstantRange(Lower, CR.Upper), ConstantRange(CR.Lower, Upper), Type);
APInt L = CR.Lower.ult(Lower) ? CR.Lower : Lower;
APInt U = (CR.Upper - 1).ugt(Upper - 1) ? CR.Upper : Upper;
if (L.isNullValue() && U.isNullValue())
return getFull();
return ConstantRange(std::move(L), std::move(U));
}
if (!CR.isUpperWrapped()) {
// ------U L----- and ------U L----- : this
// L--U L--U : CR
if (CR.Upper.ule(Upper) || CR.Lower.uge(Lower))
return *this;
// ------U L----- : this
// L---------U : CR
if (CR.Lower.ule(Upper) && Lower.ule(CR.Upper))
return getFull();
// ----U L---- : this
// L---U : CR
// results in one of
// ----------U L----
// ----U L----------
if (Upper.ult(CR.Lower) && CR.Upper.ult(Lower))
return getPreferredRange(
ConstantRange(Lower, CR.Upper), ConstantRange(CR.Lower, Upper), Type);
// ----U L----- : this
// L----U : CR
if (Upper.ult(CR.Lower) && Lower.ule(CR.Upper))
return ConstantRange(CR.Lower, Upper);
// ------U L---- : this
// L-----U : CR
assert(CR.Lower.ule(Upper) && CR.Upper.ult(Lower) &&
"ConstantRange::unionWith missed a case with one range wrapped");
return ConstantRange(Lower, CR.Upper);
}
// ------U L---- and ------U L---- : this
// -U L----------- and ------------U L : CR
if (CR.Lower.ule(Upper) || Lower.ule(CR.Upper))
return getFull();
APInt L = CR.Lower.ult(Lower) ? CR.Lower : Lower;
APInt U = CR.Upper.ugt(Upper) ? CR.Upper : Upper;
return ConstantRange(std::move(L), std::move(U));
}
ConstantRange ConstantRange::castOp(Instruction::CastOps CastOp,
uint32_t ResultBitWidth) const {
switch (CastOp) {
default:
llvm_unreachable("unsupported cast type");
case Instruction::Trunc:
return truncate(ResultBitWidth);
case Instruction::SExt:
return signExtend(ResultBitWidth);
case Instruction::ZExt:
return zeroExtend(ResultBitWidth);
case Instruction::BitCast:
return *this;
case Instruction::FPToUI:
case Instruction::FPToSI:
if (getBitWidth() == ResultBitWidth)
return *this;
else
return getFull();
case Instruction::UIToFP: {
// TODO: use input range if available
auto BW = getBitWidth();
APInt Min = APInt::getMinValue(BW).zextOrSelf(ResultBitWidth);
APInt Max = APInt::getMaxValue(BW).zextOrSelf(ResultBitWidth);
return ConstantRange(std::move(Min), std::move(Max));
}
case Instruction::SIToFP: {
// TODO: use input range if available
auto BW = getBitWidth();
APInt SMin = APInt::getSignedMinValue(BW).sextOrSelf(ResultBitWidth);
APInt SMax = APInt::getSignedMaxValue(BW).sextOrSelf(ResultBitWidth);
return ConstantRange(std::move(SMin), std::move(SMax));
}
case Instruction::FPTrunc:
case Instruction::FPExt:
case Instruction::IntToPtr:
case Instruction::PtrToInt:
case Instruction::AddrSpaceCast:
// Conservatively return getFull set.
return getFull();
};
}
ConstantRange ConstantRange::zeroExtend(uint32_t DstTySize) const {
if (isEmptySet()) return getEmpty(DstTySize);
unsigned SrcTySize = getBitWidth();
assert(SrcTySize < DstTySize && "Not a value extension");
if (isFullSet() || isUpperWrapped()) {
// Change into [0, 1 << src bit width)
APInt LowerExt(DstTySize, 0);
if (!Upper) // special case: [X, 0) -- not really wrapping around
LowerExt = Lower.zext(DstTySize);
return ConstantRange(std::move(LowerExt),
APInt::getOneBitSet(DstTySize, SrcTySize));
}
return ConstantRange(Lower.zext(DstTySize), Upper.zext(DstTySize));
}
ConstantRange ConstantRange::signExtend(uint32_t DstTySize) const {
if (isEmptySet()) return getEmpty(DstTySize);
unsigned SrcTySize = getBitWidth();
assert(SrcTySize < DstTySize && "Not a value extension");
// special case: [X, INT_MIN) -- not really wrapping around
if (Upper.isMinSignedValue())
return ConstantRange(Lower.sext(DstTySize), Upper.zext(DstTySize));
if (isFullSet() || isSignWrappedSet()) {
return ConstantRange(APInt::getHighBitsSet(DstTySize,DstTySize-SrcTySize+1),
APInt::getLowBitsSet(DstTySize, SrcTySize-1) + 1);
}
return ConstantRange(Lower.sext(DstTySize), Upper.sext(DstTySize));
}
ConstantRange ConstantRange::truncate(uint32_t DstTySize) const {
assert(getBitWidth() > DstTySize && "Not a value truncation");
if (isEmptySet())
return getEmpty(DstTySize);
if (isFullSet())
return getFull(DstTySize);
APInt LowerDiv(Lower), UpperDiv(Upper);
ConstantRange Union(DstTySize, /*isFullSet=*/false);
// Analyze wrapped sets in their two parts: [0, Upper) \/ [Lower, MaxValue]
// We use the non-wrapped set code to analyze the [Lower, MaxValue) part, and
// then we do the union with [MaxValue, Upper)
if (isUpperWrapped()) {
// If Upper is greater than or equal to MaxValue(DstTy), it covers the whole
// truncated range.
if (Upper.getActiveBits() > DstTySize ||
Upper.countTrailingOnes() == DstTySize)
return getFull(DstTySize);
Union = ConstantRange(APInt::getMaxValue(DstTySize),Upper.trunc(DstTySize));
UpperDiv.setAllBits();
// Union covers the MaxValue case, so return if the remaining range is just
// MaxValue(DstTy).
if (LowerDiv == UpperDiv)
return Union;
}
// Chop off the most significant bits that are past the destination bitwidth.
if (LowerDiv.getActiveBits() > DstTySize) {
// Mask to just the signficant bits and subtract from LowerDiv/UpperDiv.
APInt Adjust = LowerDiv & APInt::getBitsSetFrom(getBitWidth(), DstTySize);
LowerDiv -= Adjust;
UpperDiv -= Adjust;
}
unsigned UpperDivWidth = UpperDiv.getActiveBits();
if (UpperDivWidth <= DstTySize)
return ConstantRange(LowerDiv.trunc(DstTySize),
UpperDiv.trunc(DstTySize)).unionWith(Union);
// The truncated value wraps around. Check if we can do better than fullset.
if (UpperDivWidth == DstTySize + 1) {
// Clear the MSB so that UpperDiv wraps around.
UpperDiv.clearBit(DstTySize);
if (UpperDiv.ult(LowerDiv))
return ConstantRange(LowerDiv.trunc(DstTySize),
UpperDiv.trunc(DstTySize)).unionWith(Union);
}
return getFull(DstTySize);
}
ConstantRange ConstantRange::zextOrTrunc(uint32_t DstTySize) const {
unsigned SrcTySize = getBitWidth();
if (SrcTySize > DstTySize)
return truncate(DstTySize);
if (SrcTySize < DstTySize)
return zeroExtend(DstTySize);
return *this;
}
ConstantRange ConstantRange::sextOrTrunc(uint32_t DstTySize) const {
unsigned SrcTySize = getBitWidth();
if (SrcTySize > DstTySize)
return truncate(DstTySize);
if (SrcTySize < DstTySize)
return signExtend(DstTySize);
return *this;
}
ConstantRange ConstantRange::binaryOp(Instruction::BinaryOps BinOp,
const ConstantRange &Other) const {
assert(Instruction::isBinaryOp(BinOp) && "Binary operators only!");
switch (BinOp) {
case Instruction::Add:
return add(Other);
case Instruction::Sub:
return sub(Other);
case Instruction::Mul:
return multiply(Other);
case Instruction::UDiv:
return udiv(Other);
case Instruction::URem:
return urem(Other);
case Instruction::SRem:
return srem(Other);
case Instruction::Shl:
return shl(Other);
case Instruction::LShr:
return lshr(Other);
case Instruction::AShr:
return ashr(Other);
case Instruction::And:
return binaryAnd(Other);
case Instruction::Or:
return binaryOr(Other);
// Note: floating point operations applied to abstract ranges are just
// ideal integer operations with a lossy representation
case Instruction::FAdd:
return add(Other);
case Instruction::FSub:
return sub(Other);
case Instruction::FMul:
return multiply(Other);
default:
// Conservatively return getFull set.
return getFull();
}
}
ConstantRange
ConstantRange::add(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return getEmpty();
if (isFullSet() || Other.isFullSet())
return getFull();
APInt NewLower = getLower() + Other.getLower();
APInt NewUpper = getUpper() + Other.getUpper() - 1;
if (NewLower == NewUpper)
return getFull();
ConstantRange X = ConstantRange(std::move(NewLower), std::move(NewUpper));
if (X.isSizeStrictlySmallerThan(*this) ||
X.isSizeStrictlySmallerThan(Other))
// We've wrapped, therefore, full set.
return getFull();
return X;
}
ConstantRange ConstantRange::addWithNoSignedWrap(const APInt &Other) const {
// Calculate the subset of this range such that "X + Other" is
// guaranteed not to wrap (overflow) for all X in this subset.
auto NSWRange = ConstantRange::makeExactNoWrapRegion(
BinaryOperator::Add, Other, OverflowingBinaryOperator::NoSignedWrap);
auto NSWConstrainedRange = intersectWith(NSWRange);
return NSWConstrainedRange.add(ConstantRange(Other));
}
ConstantRange
ConstantRange::sub(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return getEmpty();
if (isFullSet() || Other.isFullSet())
return getFull();
APInt NewLower = getLower() - Other.getUpper() + 1;
APInt NewUpper = getUpper() - Other.getLower();
if (NewLower == NewUpper)
return getFull();
ConstantRange X = ConstantRange(std::move(NewLower), std::move(NewUpper));
if (X.isSizeStrictlySmallerThan(*this) ||
X.isSizeStrictlySmallerThan(Other))
// We've wrapped, therefore, full set.
return getFull();
return X;
}
ConstantRange
ConstantRange::multiply(const ConstantRange &Other) const {
// TODO: If either operand is a single element and the multiply is known to
// be non-wrapping, round the result min and max value to the appropriate
// multiple of that element. If wrapping is possible, at least adjust the
// range according to the greatest power-of-two factor of the single element.
if (isEmptySet() || Other.isEmptySet())
return getEmpty();
// Multiplication is signedness-independent. However different ranges can be
// obtained depending on how the input ranges are treated. These different
// ranges are all conservatively correct, but one might be better than the
// other. We calculate two ranges; one treating the inputs as unsigned
// and the other signed, then return the smallest of these ranges.
// Unsigned range first.
APInt this_min = getUnsignedMin().zext(getBitWidth() * 2);
APInt this_max = getUnsignedMax().zext(getBitWidth() * 2);
APInt Other_min = Other.getUnsignedMin().zext(getBitWidth() * 2);
APInt Other_max = Other.getUnsignedMax().zext(getBitWidth() * 2);
ConstantRange Result_zext = ConstantRange(this_min * Other_min,
this_max * Other_max + 1);
ConstantRange UR = Result_zext.truncate(getBitWidth());
// If the unsigned range doesn't wrap, and isn't negative then it's a range
// from one positive number to another which is as good as we can generate.
// In this case, skip the extra work of generating signed ranges which aren't
// going to be better than this range.
if (!UR.isUpperWrapped() &&
(UR.getUpper().isNonNegative() || UR.getUpper().isMinSignedValue()))
return UR;
// Now the signed range. Because we could be dealing with negative numbers
// here, the lower bound is the smallest of the cartesian product of the
// lower and upper ranges; for example:
// [-1,4) * [-2,3) = min(-1*-2, -1*2, 3*-2, 3*2) = -6.
// Similarly for the upper bound, swapping min for max.
this_min = getSignedMin().sext(getBitWidth() * 2);
this_max = getSignedMax().sext(getBitWidth() * 2);
Other_min = Other.getSignedMin().sext(getBitWidth() * 2);
Other_max = Other.getSignedMax().sext(getBitWidth() * 2);
auto L = {this_min * Other_min, this_min * Other_max,
this_max * Other_min, this_max * Other_max};
auto Compare = [](const APInt &A, const APInt &B) { return A.slt(B); };
ConstantRange Result_sext(std::min(L, Compare), std::max(L, Compare) + 1);
ConstantRange SR = Result_sext.truncate(getBitWidth());
return UR.isSizeStrictlySmallerThan(SR) ? UR : SR;
}
ConstantRange
ConstantRange::smax(const ConstantRange &Other) const {
// X smax Y is: range(smax(X_smin, Y_smin),
// smax(X_smax, Y_smax))
if (isEmptySet() || Other.isEmptySet())
return getEmpty();
APInt NewL = APIntOps::smax(getSignedMin(), Other.getSignedMin());
APInt NewU = APIntOps::smax(getSignedMax(), Other.getSignedMax()) + 1;
return getNonEmpty(std::move(NewL), std::move(NewU));
}
ConstantRange
ConstantRange::umax(const ConstantRange &Other) const {
// X umax Y is: range(umax(X_umin, Y_umin),
// umax(X_umax, Y_umax))
if (isEmptySet() || Other.isEmptySet())
return getEmpty();
APInt NewL = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
APInt NewU = APIntOps::umax(getUnsignedMax(), Other.getUnsignedMax()) + 1;
return getNonEmpty(std::move(NewL), std::move(NewU));
}
ConstantRange
ConstantRange::smin(const ConstantRange &Other) const {
// X smin Y is: range(smin(X_smin, Y_smin),
// smin(X_smax, Y_smax))
if (isEmptySet() || Other.isEmptySet())
return getEmpty();
APInt NewL = APIntOps::smin(getSignedMin(), Other.getSignedMin());
APInt NewU = APIntOps::smin(getSignedMax(), Other.getSignedMax()) + 1;
return getNonEmpty(std::move(NewL), std::move(NewU));
}
ConstantRange
ConstantRange::umin(const ConstantRange &Other) const {
// X umin Y is: range(umin(X_umin, Y_umin),
// umin(X_umax, Y_umax))
if (isEmptySet() || Other.isEmptySet())
return getEmpty();
APInt NewL = APIntOps::umin(getUnsignedMin(), Other.getUnsignedMin());
APInt NewU = APIntOps::umin(getUnsignedMax(), Other.getUnsignedMax()) + 1;
return getNonEmpty(std::move(NewL), std::move(NewU));
}
ConstantRange
ConstantRange::udiv(const ConstantRange &RHS) const {
if (isEmptySet() || RHS.isEmptySet() || RHS.getUnsignedMax().isNullValue())
return getEmpty();
APInt Lower = getUnsignedMin().udiv(RHS.getUnsignedMax());
APInt RHS_umin = RHS.getUnsignedMin();
if (RHS_umin.isNullValue()) {
// We want the lowest value in RHS excluding zero. Usually that would be 1
// except for a range in the form of [X, 1) in which case it would be X.
if (RHS.getUpper() == 1)
RHS_umin = RHS.getLower();
else
RHS_umin = 1;
}
APInt Upper = getUnsignedMax().udiv(RHS_umin) + 1;
return getNonEmpty(std::move(Lower), std::move(Upper));
}
ConstantRange ConstantRange::urem(const ConstantRange &RHS) const {
if (isEmptySet() || RHS.isEmptySet() || RHS.getUnsignedMax().isNullValue())
return getEmpty();
// L % R for L < R is L.
if (getUnsignedMax().ult(RHS.getUnsignedMin()))
return *this;
// L % R is <= L and < R.
APInt Upper = APIntOps::umin(getUnsignedMax(), RHS.getUnsignedMax() - 1) + 1;
return getNonEmpty(APInt::getNullValue(getBitWidth()), std::move(Upper));
}
ConstantRange ConstantRange::srem(const ConstantRange &RHS) const {
if (isEmptySet() || RHS.isEmptySet())
return getEmpty();
ConstantRange AbsRHS = RHS.abs();
APInt MinAbsRHS = AbsRHS.getUnsignedMin();
APInt MaxAbsRHS = AbsRHS.getUnsignedMax();
// Modulus by zero is UB.
if (MaxAbsRHS.isNullValue())
return getEmpty();
if (MinAbsRHS.isNullValue())
++MinAbsRHS;
APInt MinLHS = getSignedMin(), MaxLHS = getSignedMax();
if (MinLHS.isNonNegative()) {
// L % R for L < R is L.
if (MaxLHS.ult(MinAbsRHS))
return *this;
// L % R is <= L and < R.
APInt Upper = APIntOps::umin(MaxLHS, MaxAbsRHS - 1) + 1;
return ConstantRange(APInt::getNullValue(getBitWidth()), std::move(Upper));
}
// Same basic logic as above, but the result is negative.
if (MaxLHS.isNegative()) {
if (MinLHS.ugt(-MinAbsRHS))
return *this;
APInt Lower = APIntOps::umax(MinLHS, -MaxAbsRHS + 1);
return ConstantRange(std::move(Lower), APInt(getBitWidth(), 1));
}
// LHS range crosses zero.
APInt Lower = APIntOps::umax(MinLHS, -MaxAbsRHS + 1);
APInt Upper = APIntOps::umin(MaxLHS, MaxAbsRHS - 1) + 1;
return ConstantRange(std::move(Lower), std::move(Upper));
}
ConstantRange
ConstantRange::binaryAnd(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return getEmpty();
// TODO: replace this with something less conservative
APInt umin = APIntOps::umin(Other.getUnsignedMax(), getUnsignedMax());
return getNonEmpty(APInt::getNullValue(getBitWidth()), std::move(umin) + 1);
}
ConstantRange
ConstantRange::binaryOr(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return getEmpty();
// TODO: replace this with something less conservative
APInt umax = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
return getNonEmpty(std::move(umax), APInt::getNullValue(getBitWidth()));
}
ConstantRange
ConstantRange::shl(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return getEmpty();
APInt max = getUnsignedMax();
APInt Other_umax = Other.getUnsignedMax();
// If we are shifting by maximum amount of
// zero return return the original range.
if (Other_umax.isNullValue())
return *this;
// there's overflow!
if (Other_umax.ugt(max.countLeadingZeros()))
return getFull();
// FIXME: implement the other tricky cases
APInt min = getUnsignedMin();
min <<= Other.getUnsignedMin();
max <<= Other_umax;
return ConstantRange(std::move(min), std::move(max) + 1);
}
ConstantRange
ConstantRange::lshr(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return getEmpty();
APInt max = getUnsignedMax().lshr(Other.getUnsignedMin()) + 1;
APInt min = getUnsignedMin().lshr(Other.getUnsignedMax());
return getNonEmpty(std::move(min), std::move(max));
}
ConstantRange
ConstantRange::ashr(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return getEmpty();
// May straddle zero, so handle both positive and negative cases.
// 'PosMax' is the upper bound of the result of the ashr
// operation, when Upper of the LHS of ashr is a non-negative.
// number. Since ashr of a non-negative number will result in a
// smaller number, the Upper value of LHS is shifted right with
// the minimum value of 'Other' instead of the maximum value.
APInt PosMax = getSignedMax().ashr(Other.getUnsignedMin()) + 1;
// 'PosMin' is the lower bound of the result of the ashr
// operation, when Lower of the LHS is a non-negative number.
// Since ashr of a non-negative number will result in a smaller
// number, the Lower value of LHS is shifted right with the
// maximum value of 'Other'.
APInt PosMin = getSignedMin().ashr(Other.getUnsignedMax());
// 'NegMax' is the upper bound of the result of the ashr
// operation, when Upper of the LHS of ashr is a negative number.
// Since 'ashr' of a negative number will result in a bigger
// number, the Upper value of LHS is shifted right with the
// maximum value of 'Other'.
APInt NegMax = getSignedMax().ashr(Other.getUnsignedMax()) + 1;
// 'NegMin' is the lower bound of the result of the ashr
// operation, when Lower of the LHS of ashr is a negative number.
// Since 'ashr' of a negative number will result in a bigger
// number, the Lower value of LHS is shifted right with the
// minimum value of 'Other'.
APInt NegMin = getSignedMin().ashr(Other.getUnsignedMin());
APInt max, min;
if (getSignedMin().isNonNegative()) {
// Upper and Lower of LHS are non-negative.
min = PosMin;
max = PosMax;
} else if (getSignedMax().isNegative()) {
// Upper and Lower of LHS are negative.
min = NegMin;
max = NegMax;
} else {
// Upper is non-negative and Lower is negative.
min = NegMin;
max = PosMax;
}
return getNonEmpty(std::move(min), std::move(max));
}
ConstantRange ConstantRange::uadd_sat(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return getEmpty();
APInt NewL = getUnsignedMin().uadd_sat(Other.getUnsignedMin());
APInt NewU = getUnsignedMax().uadd_sat(Other.getUnsignedMax()) + 1;
return getNonEmpty(std::move(NewL), std::move(NewU));
}
ConstantRange ConstantRange::sadd_sat(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return getEmpty();
APInt NewL = getSignedMin().sadd_sat(Other.getSignedMin());
APInt NewU = getSignedMax().sadd_sat(Other.getSignedMax()) + 1;
return getNonEmpty(std::move(NewL), std::move(NewU));
}
ConstantRange ConstantRange::usub_sat(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return getEmpty();
APInt NewL = getUnsignedMin().usub_sat(Other.getUnsignedMax());
APInt NewU = getUnsignedMax().usub_sat(Other.getUnsignedMin()) + 1;
return getNonEmpty(std::move(NewL), std::move(NewU));
}
ConstantRange ConstantRange::ssub_sat(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return getEmpty();
APInt NewL = getSignedMin().ssub_sat(Other.getSignedMax());
APInt NewU = getSignedMax().ssub_sat(Other.getSignedMin()) + 1;
return getNonEmpty(std::move(NewL), std::move(NewU));
}
ConstantRange ConstantRange::inverse() const {
if (isFullSet())
return getEmpty();
if (isEmptySet())
return getFull();
return ConstantRange(Upper, Lower);
}
ConstantRange ConstantRange::abs() const {
if (isEmptySet())
return getEmpty();
if (isSignWrappedSet()) {
APInt Lo;
// Check whether the range crosses zero.
if (Upper.isStrictlyPositive() || !Lower.isStrictlyPositive())
Lo = APInt::getNullValue(getBitWidth());
else
Lo = APIntOps::umin(Lower, -Upper + 1);
// SignedMin is included in the result range.
return ConstantRange(Lo, APInt::getSignedMinValue(getBitWidth()) + 1);
}
APInt SMin = getSignedMin(), SMax = getSignedMax();
// All non-negative.
if (SMin.isNonNegative())
return *this;
// All negative.
if (SMax.isNegative())
return ConstantRange(-SMax, -SMin + 1);
// Range crosses zero.
return ConstantRange(APInt::getNullValue(getBitWidth()),
APIntOps::umax(-SMin, SMax) + 1);
}
ConstantRange::OverflowResult ConstantRange::unsignedAddMayOverflow(
const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return OverflowResult::MayOverflow;
APInt Min = getUnsignedMin(), Max = getUnsignedMax();
APInt OtherMin = Other.getUnsignedMin(), OtherMax = Other.getUnsignedMax();
// a u+ b overflows iff a u> ~b.
if (Min.ugt(~OtherMin))
return OverflowResult::AlwaysOverflows;
if (Max.ugt(~OtherMax))
return OverflowResult::MayOverflow;
return OverflowResult::NeverOverflows;
}
ConstantRange::OverflowResult ConstantRange::signedAddMayOverflow(
const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return OverflowResult::MayOverflow;
APInt Min = getSignedMin(), Max = getSignedMax();
APInt OtherMin = Other.getSignedMin(), OtherMax = Other.getSignedMax();
APInt SignedMin = APInt::getSignedMinValue(getBitWidth());
APInt SignedMax = APInt::getSignedMaxValue(getBitWidth());
// a s+ b overflows high iff a s>=0 && b s>= 0 && a s> smax - b.
// a s+ b overflows low iff a s< 0 && b s< 0 && a s< smin - b.
if (Min.isNonNegative() && OtherMin.isNonNegative() &&
Min.sgt(SignedMax - OtherMin))
return OverflowResult::AlwaysOverflows;
if (Max.isNegative() && OtherMax.isNegative() &&
Max.slt(SignedMin - OtherMax))
return OverflowResult::AlwaysOverflows;
if (Max.isNonNegative() && OtherMax.isNonNegative() &&
Max.sgt(SignedMax - OtherMax))
return OverflowResult::MayOverflow;
if (Min.isNegative() && OtherMin.isNegative() &&
Min.slt(SignedMin - OtherMin))
return OverflowResult::MayOverflow;
return OverflowResult::NeverOverflows;
}
ConstantRange::OverflowResult ConstantRange::unsignedSubMayOverflow(
const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return OverflowResult::MayOverflow;
APInt Min = getUnsignedMin(), Max = getUnsignedMax();
APInt OtherMin = Other.getUnsignedMin(), OtherMax = Other.getUnsignedMax();
// a u- b overflows iff a u< b.
if (Max.ult(OtherMin))
return OverflowResult::AlwaysOverflows;
if (Min.ult(OtherMax))
return OverflowResult::MayOverflow;
return OverflowResult::NeverOverflows;
}
ConstantRange::OverflowResult ConstantRange::signedSubMayOverflow(
const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return OverflowResult::MayOverflow;
APInt Min = getSignedMin(), Max = getSignedMax();
APInt OtherMin = Other.getSignedMin(), OtherMax = Other.getSignedMax();
APInt SignedMin = APInt::getSignedMinValue(getBitWidth());
APInt SignedMax = APInt::getSignedMaxValue(getBitWidth());
// a s- b overflows high iff a s>=0 && b s< 0 && a s> smax + b.
// a s- b overflows low iff a s< 0 && b s>= 0 && a s< smin + b.
if (Min.isNonNegative() && OtherMax.isNegative() &&
Min.sgt(SignedMax + OtherMax))
return OverflowResult::AlwaysOverflows;
if (Max.isNegative() && OtherMin.isNonNegative() &&
Max.slt(SignedMin + OtherMin))
return OverflowResult::AlwaysOverflows;
if (Max.isNonNegative() && OtherMin.isNegative() &&
Max.sgt(SignedMax + OtherMin))
return OverflowResult::MayOverflow;
if (Min.isNegative() && OtherMax.isNonNegative() &&
Min.slt(SignedMin + OtherMax))
return OverflowResult::MayOverflow;
return OverflowResult::NeverOverflows;
}
ConstantRange::OverflowResult ConstantRange::unsignedMulMayOverflow(
const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return OverflowResult::MayOverflow;
APInt Min = getUnsignedMin(), Max = getUnsignedMax();
APInt OtherMin = Other.getUnsignedMin(), OtherMax = Other.getUnsignedMax();
bool Overflow;
(void) Min.umul_ov(OtherMin, Overflow);
if (Overflow)
return OverflowResult::AlwaysOverflows;
(void) Max.umul_ov(OtherMax, Overflow);
if (Overflow)
return OverflowResult::MayOverflow;
return OverflowResult::NeverOverflows;
}
void ConstantRange::print(raw_ostream &OS) const {
if (isFullSet())
OS << "full-set";
else if (isEmptySet())
OS << "empty-set";
else
OS << "[" << Lower << "," << Upper << ")";
}
#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
LLVM_DUMP_METHOD void ConstantRange::dump() const {
print(dbgs());
}
#endif
ConstantRange llvm::getConstantRangeFromMetadata(const MDNode &Ranges) {
const unsigned NumRanges = Ranges.getNumOperands() / 2;
assert(NumRanges >= 1 && "Must have at least one range!");
assert(Ranges.getNumOperands() % 2 == 0 && "Must be a sequence of pairs");
auto *FirstLow = mdconst::extract<ConstantInt>(Ranges.getOperand(0));
auto *FirstHigh = mdconst::extract<ConstantInt>(Ranges.getOperand(1));
ConstantRange CR(FirstLow->getValue(), FirstHigh->getValue());
for (unsigned i = 1; i < NumRanges; ++i) {
auto *Low = mdconst::extract<ConstantInt>(Ranges.getOperand(2 * i + 0));
auto *High = mdconst::extract<ConstantInt>(Ranges.getOperand(2 * i + 1));
// Note: unionWith will potentially create a range that contains values not
// contained in any of the original N ranges.
CR = CR.unionWith(ConstantRange(Low->getValue(), High->getValue()));
}
return CR;
}
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