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//===-- ConstantRange.cpp - ConstantRange implementation ------------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// 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/InstrTypes.h"
#include "llvm/Support/ConstantRange.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/raw_ostream.h"
using namespace llvm;
/// Initialize a full (the default) or empty set for the specified type.
///
ConstantRange::ConstantRange(uint32_t BitWidth, bool Full) {
if (Full)
Lower = Upper = APInt::getMaxValue(BitWidth);
else
Lower = Upper = APInt::getMinValue(BitWidth);
}
/// Initialize a range to hold the single specified value.
///
ConstantRange::ConstantRange(const APInt &V) : Lower(V), Upper(V + 1) {}
ConstantRange::ConstantRange(const APInt &L, const APInt &U) :
Lower(L), Upper(U) {
assert(L.getBitWidth() == U.getBitWidth() &&
"ConstantRange with unequal bit widths");
assert((L != U || (L.isMaxValue() || L.isMinValue())) &&
"Lower == Upper, but they aren't min or max value!");
}
ConstantRange ConstantRange::makeICmpRegion(unsigned Pred,
const ConstantRange &CR) {
if (CR.isEmptySet())
return CR;
uint32_t W = CR.getBitWidth();
switch (Pred) {
default: llvm_unreachable("Invalid ICmp predicate to makeICmpRegion()");
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), UMax);
}
case CmpInst::ICMP_SLT: {
APInt SMax(CR.getSignedMax());
if (SMax.isMinSignedValue())
return ConstantRange(W, /* empty */ false);
return ConstantRange(APInt::getSignedMinValue(W), SMax);
}
case CmpInst::ICMP_ULE: {
APInt UMax(CR.getUnsignedMax());
if (UMax.isMaxValue())
return ConstantRange(W);
return ConstantRange(APInt::getMinValue(W), UMax + 1);
}
case CmpInst::ICMP_SLE: {
APInt SMax(CR.getSignedMax());
if (SMax.isMaxSignedValue())
return ConstantRange(W);
return ConstantRange(APInt::getSignedMinValue(W), SMax + 1);
}
case CmpInst::ICMP_UGT: {
APInt UMin(CR.getUnsignedMin());
if (UMin.isMaxValue())
return ConstantRange(W, /* empty */ false);
return ConstantRange(UMin + 1, APInt::getNullValue(W));
}
case CmpInst::ICMP_SGT: {
APInt SMin(CR.getSignedMin());
if (SMin.isMaxSignedValue())
return ConstantRange(W, /* empty */ false);
return ConstantRange(SMin + 1, APInt::getSignedMinValue(W));
}
case CmpInst::ICMP_UGE: {
APInt UMin(CR.getUnsignedMin());
if (UMin.isMinValue())
return ConstantRange(W);
return ConstantRange(UMin, APInt::getNullValue(W));
}
case CmpInst::ICMP_SGE: {
APInt SMin(CR.getSignedMin());
if (SMin.isMinSignedValue())
return ConstantRange(W);
return ConstantRange(SMin, APInt::getSignedMinValue(W));
}
}
}
/// isFullSet - Return true if this set contains all of the elements possible
/// for this data-type
bool ConstantRange::isFullSet() const {
return Lower == Upper && Lower.isMaxValue();
}
/// isEmptySet - Return true if this set contains no members.
///
bool ConstantRange::isEmptySet() const {
return Lower == Upper && Lower.isMinValue();
}
/// isWrappedSet - Return true if this set wraps around the top of the range,
/// for example: [100, 8)
///
bool ConstantRange::isWrappedSet() const {
return Lower.ugt(Upper);
}
/// isSignWrappedSet - Return true if this set wraps around the INT_MIN of
/// its bitwidth, for example: i8 [120, 140).
///
bool ConstantRange::isSignWrappedSet() const {
return contains(APInt::getSignedMaxValue(getBitWidth())) &&
contains(APInt::getSignedMinValue(getBitWidth()));
}
/// getSetSize - Return the number of elements in this set.
///
APInt ConstantRange::getSetSize() const {
if (isEmptySet())
return APInt(getBitWidth(), 0);
if (getBitWidth() == 1) {
if (Lower != Upper) // One of T or F in the set...
return APInt(2, 1);
return APInt(2, 2); // Must be full set...
}
// Simply subtract the bounds...
return Upper - Lower;
}
/// getUnsignedMax - Return the largest unsigned value contained in the
/// ConstantRange.
///
APInt ConstantRange::getUnsignedMax() const {
if (isFullSet() || isWrappedSet())
return APInt::getMaxValue(getBitWidth());
return getUpper() - 1;
}
/// getUnsignedMin - Return the smallest unsigned value contained in the
/// ConstantRange.
///
APInt ConstantRange::getUnsignedMin() const {
if (isFullSet() || (isWrappedSet() && getUpper() != 0))
return APInt::getMinValue(getBitWidth());
return getLower();
}
/// getSignedMax - Return the largest signed value contained in the
/// ConstantRange.
///
APInt ConstantRange::getSignedMax() const {
APInt SignedMax(APInt::getSignedMaxValue(getBitWidth()));
if (!isWrappedSet()) {
if (getLower().sle(getUpper() - 1))
return getUpper() - 1;
return SignedMax;
}
if (getLower().isNegative() == getUpper().isNegative())
return SignedMax;
return getUpper() - 1;
}
/// getSignedMin - Return the smallest signed value contained in the
/// ConstantRange.
///
APInt ConstantRange::getSignedMin() const {
APInt SignedMin(APInt::getSignedMinValue(getBitWidth()));
if (!isWrappedSet()) {
if (getLower().sle(getUpper() - 1))
return getLower();
return SignedMin;
}
if ((getUpper() - 1).slt(getLower())) {
if (getUpper() != SignedMin)
return SignedMin;
}
return getLower();
}
/// contains - Return true if the specified value is in the set.
///
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);
}
/// contains - Return true if the argument is a subset of this range.
/// Two equal sets contain each other. The empty set contained by all other
/// sets.
///
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());
}
/// subtract - Subtract the specified constant from the endpoints of this
/// constant range.
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);
}
/// intersectWith - Return the range that results from the intersection of this
/// range with another range. The resultant range is guaranteed to include all
/// elements contained in both input ranges, and to have the smallest possible
/// set size that does so. Because there may be two intersections with the
/// same set size, A.intersectWith(B) might not be equal to B.intersectWith(A).
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.ult(Lower))
return ConstantRange(CR.Lower, Upper);
if (getSetSize().ult(CR.getSetSize()))
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 (getSetSize().ult(CR.getSetSize()))
return *this;
return CR;
}
if (CR.Lower.ult(Lower))
return ConstantRange(Lower, CR.Upper);
return CR;
}
if (CR.Upper.ult(Lower)) {
if (CR.Lower.ult(Lower))
return *this;
return ConstantRange(CR.Lower, Upper);
}
if (getSetSize().ult(CR.getSetSize()))
return *this;
return CR;
}
/// unionWith - 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 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 = Lower, U = Upper;
if (CR.Lower.ult(L))
L = CR.Lower;
if ((CR.Upper - 1).ugt(U - 1))
U = CR.Upper;
if (L == 0 && U == 0)
return ConstantRange(getBitWidth());
return ConstantRange(L, 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 = Lower, U = Upper;
if (CR.Upper.ugt(U))
U = CR.Upper;
if (CR.Lower.ult(L))
L = CR.Lower;
return ConstantRange(L, U);
}
/// zeroExtend - 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 as if the source range had been
/// zero extended.
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)
return ConstantRange(APInt(DstTySize,0), APInt(DstTySize,1).shl(SrcTySize));
return ConstantRange(Lower.zext(DstTySize), Upper.zext(DstTySize));
}
/// signExtend - 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 as if the source range had been
/// sign extended.
ConstantRange ConstantRange::signExtend(uint32_t DstTySize) const {
if (isEmptySet()) return ConstantRange(DstTySize, /*isFullSet=*/false);
unsigned SrcTySize = getBitWidth();
assert(SrcTySize < DstTySize && "Not a value extension");
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));
}
/// truncate - 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 as if the source range had been
/// truncated to the specified type.
ConstantRange ConstantRange::truncate(uint32_t DstTySize) const {
assert(getBitWidth() > DstTySize && "Not a value truncation");
if (isFullSet() || getSetSize().getActiveBits() > DstTySize)
return ConstantRange(DstTySize, /*isFullSet=*/true);
return ConstantRange(Lower.trunc(DstTySize), Upper.trunc(DstTySize));
}
/// zextOrTrunc - make this range have the bit width given by \p DstTySize. The
/// value is zero extended, truncated, or left alone to make it that width.
ConstantRange ConstantRange::zextOrTrunc(uint32_t DstTySize) const {
unsigned SrcTySize = getBitWidth();
if (SrcTySize > DstTySize)
return truncate(DstTySize);
if (SrcTySize < DstTySize)
return zeroExtend(DstTySize);
return *this;
}
/// sextOrTrunc - make this range have the bit width given by \p DstTySize. The
/// value is sign extended, truncated, or left alone to make it that width.
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::add(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
if (isFullSet() || Other.isFullSet())
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
APInt Spread_X = getSetSize(), Spread_Y = Other.getSetSize();
APInt NewLower = getLower() + Other.getLower();
APInt NewUpper = getUpper() + Other.getUpper() - 1;
if (NewLower == NewUpper)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
ConstantRange X = ConstantRange(NewLower, NewUpper);
if (X.getSetSize().ult(Spread_X) || X.getSetSize().ult(Spread_Y))
// We've wrapped, therefore, full set.
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return X;
}
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 Spread_X = getSetSize(), Spread_Y = Other.getSetSize();
APInt NewLower = getLower() - Other.getUpper() + 1;
APInt NewUpper = getUpper() - Other.getLower();
if (NewLower == NewUpper)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
ConstantRange X = ConstantRange(NewLower, NewUpper);
if (X.getSetSize().ult(Spread_X) || X.getSetSize().ult(Spread_Y))
// 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);
if (isFullSet() || Other.isFullSet())
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
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);
return Result_zext.truncate(getBitWidth());
}
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(NewL, 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(NewL, NewU);
}
ConstantRange
ConstantRange::udiv(const ConstantRange &RHS) const {
if (isEmptySet() || RHS.isEmptySet() || RHS.getUnsignedMax() == 0)
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 == 0) {
// 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 = APInt(getBitWidth(), 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(Lower, 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()), 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.isMinValue())
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(umax, APInt::getNullValue(getBitWidth()));
}
ConstantRange
ConstantRange::shl(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
APInt min = getUnsignedMin().shl(Other.getUnsignedMin());
APInt max = getUnsignedMax().shl(Other.getUnsignedMax());
// there's no overflow!
APInt Zeros(getBitWidth(), getUnsignedMax().countLeadingZeros());
if (Zeros.ugt(Other.getUnsignedMax()))
return ConstantRange(min, max + 1);
// FIXME: implement the other tricky cases
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
}
ConstantRange
ConstantRange::lshr(const ConstantRange &Other) const {
if (isEmptySet() || Other.isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
APInt max = getUnsignedMax().lshr(Other.getUnsignedMin());
APInt min = getUnsignedMin().lshr(Other.getUnsignedMax());
if (min == max + 1)
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(min, max + 1);
}
ConstantRange ConstantRange::inverse() const {
if (isFullSet())
return ConstantRange(getBitWidth(), /*isFullSet=*/false);
if (isEmptySet())
return ConstantRange(getBitWidth(), /*isFullSet=*/true);
return ConstantRange(Upper, Lower);
}
/// print - Print out the bounds to a stream...
///
void ConstantRange::print(raw_ostream &OS) const {
if (isFullSet())
OS << "full-set";
else if (isEmptySet())
OS << "empty-set";
else
OS << "[" << Lower << "," << Upper << ")";
}
/// dump - Allow printing from a debugger easily...
///
void ConstantRange::dump() const {
print(dbgs());
}