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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/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::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 ConstantRange(W);
case CmpInst::ICMP_ULT: {
APInt UMax(CR.getUnsignedMax());
if (UMax.isMinValue())
return ConstantRange(W, /* empty */ false);
return ConstantRange(APInt::getMinValue(W), std::move(UMax));
}
case CmpInst::ICMP_SLT: {
APInt SMax(CR.getSignedMax());
if (SMax.isMinSignedValue())
return ConstantRange(W, /* empty */ false);
return ConstantRange(APInt::getSignedMinValue(W), std::move(SMax));
}
case CmpInst::ICMP_ULE: {
APInt UMax(CR.getUnsignedMax());
if (UMax.isMaxValue())
return ConstantRange(W);
return ConstantRange(APInt::getMinValue(W), std::move(UMax) + 1);
}
case CmpInst::ICMP_SLE: {
APInt SMax(CR.getSignedMax());
if (SMax.isMaxSignedValue())
return ConstantRange(W);
return ConstantRange(APInt::getSignedMinValue(W), std::move(SMax) + 1);
}
case CmpInst::ICMP_UGT: {
APInt UMin(CR.getUnsignedMin());
if (UMin.isMaxValue())
return ConstantRange(W, /* empty */ false);
return ConstantRange(std::move(UMin) + 1, APInt::getNullValue(W));
}
case CmpInst::ICMP_SGT: {
APInt SMin(CR.getSignedMin());
if (SMin.isMaxSignedValue())
return ConstantRange(W, /* empty */ false);
return ConstantRange(std::move(SMin) + 1, APInt::getSignedMinValue(W));
}
case CmpInst::ICMP_UGE: {
APInt UMin(CR.getUnsignedMin());
if (UMin.isMinValue())
return ConstantRange(W);
return ConstantRange(std::move(UMin), APInt::getNullValue(W));
}
case CmpInst::ICMP_SGE: {
APInt SMin(CR.getSignedMin());
if (SMin.isMinSignedValue())
return ConstantRange(W);
return ConstantRange(std::move(SMin), 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;
}
ConstantRange
ConstantRange::makeGuaranteedNoWrapRegion(Instruction::BinaryOps BinOp,
const ConstantRange &Other,
unsigned NoWrapKind) {
using OBO = OverflowingBinaryOperator;
// Computes the intersection of CR0 and CR1. It is different from
// intersectWith in that the ConstantRange returned will only contain elements
// in both CR0 and CR1 (i.e. SubsetIntersect(X, Y) is a *subset*, proper or
// not, of both X and Y).
auto SubsetIntersect =
[](const ConstantRange &CR0, const ConstantRange &CR1) {
return CR0.inverse().unionWith(CR1.inverse()).inverse();
};
assert(Instruction::isBinaryOp(BinOp) && "Binary operators only!");
assert((NoWrapKind == OBO::NoSignedWrap ||
NoWrapKind == OBO::NoUnsignedWrap ||
NoWrapKind == (OBO::NoUnsignedWrap | OBO::NoSignedWrap)) &&
"NoWrapKind invalid!");
unsigned BitWidth = Other.getBitWidth();
ConstantRange Result(BitWidth);
switch (BinOp) {
default:
// Conservative answer: empty set
return ConstantRange(BitWidth, false);
case Instruction::Add:
if (auto *C = Other.getSingleElement())
if (C->isNullValue())
// Full set: nothing signed / unsigned wraps when added to 0.
return ConstantRange(BitWidth);
if (NoWrapKind & OBO::NoUnsignedWrap)
Result =
SubsetIntersect(Result, ConstantRange(APInt::getNullValue(BitWidth),
-Other.getUnsignedMax()));
if (NoWrapKind & OBO::NoSignedWrap) {
const APInt &SignedMin = Other.getSignedMin();
const APInt &SignedMax = Other.getSignedMax();
if (SignedMax.isStrictlyPositive())
Result = SubsetIntersect(
Result,
ConstantRange(APInt::getSignedMinValue(BitWidth),
APInt::getSignedMinValue(BitWidth) - SignedMax));
if (SignedMin.isNegative())
Result = SubsetIntersect(
Result,
ConstantRange(APInt::getSignedMinValue(BitWidth) - SignedMin,
APInt::getSignedMinValue(BitWidth)));
}
return Result;
case Instruction::Sub:
if (auto *C = Other.getSingleElement())
if (C->isNullValue())
// Full set: nothing signed / unsigned wraps when subtracting 0.
return ConstantRange(BitWidth);
if (NoWrapKind & OBO::NoUnsignedWrap)
Result =
SubsetIntersect(Result, ConstantRange(Other.getUnsignedMax(),
APInt::getMinValue(BitWidth)));
if (NoWrapKind & OBO::NoSignedWrap) {
const APInt &SignedMin = Other.getSignedMin();
const APInt &SignedMax = Other.getSignedMax();
if (SignedMax.isStrictlyPositive())
Result = SubsetIntersect(
Result,
ConstantRange(APInt::getSignedMinValue(BitWidth) + SignedMax,
APInt::getSignedMinValue(BitWidth)));
if (SignedMin.isNegative())
Result = SubsetIntersect(
Result,
ConstantRange(APInt::getSignedMinValue(BitWidth),
APInt::getSignedMinValue(BitWidth) + SignedMin));
}
return Result;
case Instruction::Mul: {
if (NoWrapKind == (OBO::NoSignedWrap | OBO::NoUnsignedWrap)) {
return SubsetIntersect(
makeGuaranteedNoWrapRegion(BinOp, Other, OBO::NoSignedWrap),
makeGuaranteedNoWrapRegion(BinOp, Other, OBO::NoUnsignedWrap));
}
// Equivalent to calling makeGuaranteedNoWrapRegion() on [V, V+1).
const bool Unsigned = NoWrapKind == OBO::NoUnsignedWrap;
const auto makeSingleValueRegion = [Unsigned,
BitWidth](APInt V) -> ConstantRange {
// Handle special case for 0, -1 and 1. See the last for reason why we
// specialize -1 and 1.
if (V == 0 || V.isOneValue())
return ConstantRange(BitWidth, true);
APInt MinValue, MaxValue;
if (Unsigned) {
MinValue = APInt::getMinValue(BitWidth);
MaxValue = APInt::getMaxValue(BitWidth);
} else {
MinValue = APInt::getSignedMinValue(BitWidth);
MaxValue = APInt::getSignedMaxValue(BitWidth);
}
// e.g. Returning [-127, 127], represented as [-127, -128).
if (!Unsigned && V.isAllOnesValue())
return ConstantRange(-MaxValue, MinValue);
APInt Lower, Upper;
if (!Unsigned && V.isNegative()) {
Lower = APIntOps::RoundingSDiv(MaxValue, V, APInt::Rounding::UP);
Upper = APIntOps::RoundingSDiv(MinValue, V, APInt::Rounding::DOWN);
} else if (Unsigned) {
Lower = APIntOps::RoundingUDiv(MinValue, V, APInt::Rounding::UP);
Upper = APIntOps::RoundingUDiv(MaxValue, V, APInt::Rounding::DOWN);
} else {
Lower = APIntOps::RoundingSDiv(MinValue, V, APInt::Rounding::UP);
Upper = APIntOps::RoundingSDiv(MaxValue, V, APInt::Rounding::DOWN);
}
if (Unsigned) {
Lower = Lower.zextOrSelf(BitWidth);
Upper = Upper.zextOrSelf(BitWidth);
} else {
Lower = Lower.sextOrSelf(BitWidth);
Upper = Upper.sextOrSelf(BitWidth);
}
// ConstantRange ctor take a half inclusive interval [Lower, Upper + 1).
// Upper + 1 is guanranteed not to overflow, because |divisor| > 1. 0, -1,
// and 1 are already handled as special cases.
return ConstantRange(Lower, Upper + 1);
};
if (Unsigned)
return makeSingleValueRegion(Other.getUnsignedMax());
return SubsetIntersect(makeSingleValueRegion(Other.getSignedMin()),
makeSingleValueRegion(Other.getSignedMax()));
}
}
}
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);
}
bool ConstantRange::isSignWrappedSet() const {
return contains(APInt::getSignedMaxValue(getBitWidth())) &&
contains(APInt::getSignedMinValue(getBitWidth()));
}
APInt ConstantRange::getSetSize() const {
if (isFullSet())
return APInt::getOneBitSet(getBitWidth()+1, getBitWidth());
// This is also correct for wrapped sets.
return (Upper - Lower).zext(getBitWidth()+1);
}
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);
}
APInt ConstantRange::getUnsignedMax() const {
if (isFullSet() || isWrappedSet())
return APInt::getMaxValue(getBitWidth());
return getUpper() - 1;
}
APInt ConstantRange::getUnsignedMin() const {
if (isFullSet() || (isWrappedSet() && !getUpper().isNullValue()))
return APInt::getMinValue(getBitWidth());
return getLower();
}
APInt ConstantRange::getSignedMax() const {
if (isFullSet() || Lower.sgt(Upper))
return APInt::getSignedMaxValue(getBitWidth());
return getUpper() - 1;
}
APInt ConstantRange::getSignedMin() const {
if (isFullSet() || (Lower.sgt(Upper) && !getUpper().isMinSignedValue()))
return APInt::getSignedMinValue(getBitWidth());
return getLower();
}
bool ConstantRange::contains(const APInt &V) const {
if (Lower == Upper)
return isFullSet();
if (!isWrappedSet())
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 (!isWrappedSet()) {
if (Other.isWrappedSet())
return false;
return Lower.ule(Other.getLower()) && Other.getUpper().ule(Upper);
}
if (!Other.isWrappedSet())
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());
}
ConstantRange ConstantRange::intersectWith(const ConstantRange &CR) 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 (!isWrappedSet() && CR.isWrappedSet())
return CR.intersectWith(*this);
if (!isWrappedSet() && !CR.isWrappedSet()) {
if (Lower.ult(CR.Lower)) {
if (Upper.ule(CR.Lower))
return ConstantRange(getBitWidth(), false);
if (Upper.ult(CR.Upper))
return ConstantRange(CR.Lower, Upper);
return CR;
}
if (Upper.ult(CR.Upper))
return *this;
if (Lower.ult(CR.Upper))
return ConstantRange(Lower, CR.Upper);
return ConstantRange(getBitWidth(), false);
}
if (isWrappedSet() && !CR.isWrappedSet()) {
if (CR.Lower.ult(Upper)) {
if (CR.Upper.ult(Upper))
return CR;
if (CR.Upper.ule(Lower))
return ConstantRange(CR.Lower, Upper);
if (isSizeStrictlySmallerThan(CR))
return *this;
return CR;
}
if (CR.Lower.ult(Lower)) {
if (CR.Upper.ule(Lower))
return ConstantRange(getBitWidth(), false);
return ConstantRange(Lower, CR.Upper);
}
return CR;
}
if (CR.Upper.ult(Upper)) {
if (CR.Lower.ult(Upper)) {
if (isSizeStrictlySmallerThan(CR))
return *this;
return CR;
}
if (CR.Lower.ult(Lower))
return ConstantRange(Lower, CR.Upper);
return CR;
}
if (CR.Upper.ule(Lower)) {
if (CR.Lower.ult(Lower))
return *this;
return ConstantRange(CR.Lower, Upper);
}
if (isSizeStrictlySmallerThan(CR))
return *this;
return CR;
}
ConstantRange ConstantRange::unionWith(const ConstantRange &CR) const {
assert(getBitWidth() == CR.getBitWidth() &&
"ConstantRange types don't agree!");
if ( isFullSet() || CR.isEmptySet()) return *this;
if (CR.isFullSet() || isEmptySet()) return CR;
if (!isWrappedSet() && CR.isWrappedSet()) return CR.unionWith(*this);
if (!isWrappedSet() && !CR.isWrappedSet()) {
if (CR.Upper.ult(Lower) || Upper.ult(CR.Lower)) {
// If the two ranges are disjoint, find the smaller gap and bridge it.
APInt d1 = CR.Lower - Upper, d2 = Lower - CR.Upper;
if (d1.ult(d2))
return ConstantRange(Lower, CR.Upper);
return ConstantRange(CR.Lower, Upper);
}
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 ConstantRange(getBitWidth());
return ConstantRange(std::move(L), std::move(U));
}
if (!CR.isWrappedSet()) {
// ------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 ConstantRange(getBitWidth());
// ----U L---- : this
// L---U : CR
// <d1> <d2>
if (Upper.ule(CR.Lower) && CR.Upper.ule(Lower)) {
APInt d1 = CR.Lower - Upper, d2 = Lower - CR.Upper;
if (d1.ult(d2))
return ConstantRange(Lower, CR.Upper);
return ConstantRange(CR.Lower, Upper);
}
// ----U L----- : this
// L----U : CR
if (Upper.ult(CR.Lower) && Lower.ult(CR.Upper))
return ConstantRange(CR.Lower, Upper);
// ------U L---- : this
// L-----U : CR
assert(CR.Lower.ult(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 ConstantRange(getBitWidth());
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 ConstantRange(getBitWidth(), /*isFullSet=*/true);
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 full set.
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
};
}
ConstantRange ConstantRange::zeroExtend(uint32_t DstTySize) const {
if (isEmptySet()) return ConstantRange(DstTySize, /*isFullSet=*/false);
unsigned SrcTySize = getBitWidth();
assert(SrcTySize < DstTySize && "Not a value extension");
if (isFullSet() || isWrappedSet()) {
// 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 ConstantRange(DstTySize, /*isFullSet=*/false);
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 ConstantRange(DstTySize, /*isFullSet=*/false);
if (isFullSet())
return ConstantRange(DstTySize, /*isFullSet=*/true);
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 (isWrappedSet()) {
// If Upper is greater than or equal to MaxValue(DstTy), it covers the whole
// truncated range.
if (Upper.getActiveBits() > DstTySize ||
Upper.countTrailingOnes() == DstTySize)
return ConstantRange(DstTySize, /*isFullSet=*/true);
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 ConstantRange(DstTySize, /*isFullSet=*/true);
}
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::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 full set.
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
}
}
ConstantRange
ConstantRange::add(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
if (isFullSet() || Other.isFullSet())
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
APInt NewLower = getLower() + Other.getLower();
APInt NewUpper = getUpper() + Other.getUpper() - 1;
if (NewLower == NewUpper)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
ConstantRange X = ConstantRange(std::move(NewLower), std::move(NewUpper));
if (X.isSizeStrictlySmallerThan(*this) ||
X.isSizeStrictlySmallerThan(Other))
// We've wrapped, therefore, full set.
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
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.
// makeGuaranteedNoWrapRegion will produce an exact NSW range since we are
// passing a single element range.
auto NSWRange = ConstantRange::makeGuaranteedNoWrapRegion(BinaryOperator::Add,
ConstantRange(Other),
OverflowingBinaryOperator::NoSignedWrap);
auto NSWConstrainedRange = intersectWith(NSWRange);
return NSWConstrainedRange.add(ConstantRange(Other));
}
ConstantRange
ConstantRange::sub(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
if (isFullSet() || Other.isFullSet())
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
APInt NewLower = getLower() - Other.getUpper() + 1;
APInt NewUpper = getUpper() - Other.getLower();
if (NewLower == NewUpper)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
ConstantRange X = ConstantRange(std::move(NewLower), std::move(NewUpper));
if (X.isSizeStrictlySmallerThan(*this) ||
X.isSizeStrictlySmallerThan(Other))
// We've wrapped, therefore, full set.
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
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 ConstantRange(getBitWidth(), /*isFullSet=*/false);
// 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.isWrappedSet() &&
(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 ConstantRange(getBitWidth(), /*isFullSet=*/false);
APInt NewL = APIntOps::smax(getSignedMin(), Other.getSignedMin());
APInt NewU = APIntOps::smax(getSignedMax(), Other.getSignedMax()) + 1;
if (NewU == NewL)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(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 ConstantRange(getBitWidth(), /*isFullSet=*/false);
APInt NewL = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
APInt NewU = APIntOps::umax(getUnsignedMax(), Other.getUnsignedMax()) + 1;
if (NewU == NewL)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(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 ConstantRange(getBitWidth(), /*isFullSet=*/false);
APInt NewL = APIntOps::smin(getSignedMin(), Other.getSignedMin());
APInt NewU = APIntOps::smin(getSignedMax(), Other.getSignedMax()) + 1;
if (NewU == NewL)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(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 ConstantRange(getBitWidth(), /*isFullSet=*/false);
APInt NewL = APIntOps::umin(getUnsignedMin(), Other.getUnsignedMin());
APInt NewU = APIntOps::umin(getUnsignedMax(), Other.getUnsignedMax()) + 1;
if (NewU == NewL)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(std::move(NewL), std::move(NewU));
}
ConstantRange
ConstantRange::udiv(const ConstantRange &RHS) const {
if (isEmptySet() || RHS.isEmptySet() || RHS.getUnsignedMax().isNullValue())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
if (RHS.isFullSet())
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
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;
// If the LHS is Full and the RHS is a wrapped interval containing 1 then
// this could occur.
if (Lower == Upper)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(std::move(Lower), std::move(Upper));
}
ConstantRange
ConstantRange::binaryAnd(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
// TODO: replace this with something less conservative
APInt umin = APIntOps::umin(Other.getUnsignedMax(), getUnsignedMax());
if (umin.isAllOnesValue())
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(APInt::getNullValue(getBitWidth()), std::move(umin) + 1);
}
ConstantRange
ConstantRange::binaryOr(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
// TODO: replace this with something less conservative
APInt umax = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
if (umax.isNullValue())
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(std::move(umax), APInt::getNullValue(getBitWidth()));
}
ConstantRange
ConstantRange::shl(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
APInt max = getUnsignedMax();
APInt Other_umax = Other.getUnsignedMax();
// there's overflow!
if (Other_umax.uge(max.countLeadingZeros()))
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
// 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 ConstantRange(getBitWidth(), /*isFullSet=*/false);
APInt max = getUnsignedMax().lshr(Other.getUnsignedMin()) + 1;
APInt min = getUnsignedMin().lshr(Other.getUnsignedMax());