//===-- 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); } /// \brief Subtract the specified range from this range (aka relative complement /// of the sets). ConstantRange ConstantRange::difference(const ConstantRange &CR) const { return intersectWith(CR.inverse()); } /// 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.ule(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.ule(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 // 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()); }