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      1 //===-- ConstantRange.cpp - ConstantRange implementation ------------------===//
      2 //
      3 //                     The LLVM Compiler Infrastructure
      4 //
      5 // This file is distributed under the University of Illinois Open Source
      6 // License. See LICENSE.TXT for details.
      7 //
      8 //===----------------------------------------------------------------------===//
      9 //
     10 // Represent a range of possible values that may occur when the program is run
     11 // for an integral value.  This keeps track of a lower and upper bound for the
     12 // constant, which MAY wrap around the end of the numeric range.  To do this, it
     13 // keeps track of a [lower, upper) bound, which specifies an interval just like
     14 // STL iterators.  When used with boolean values, the following are important
     15 // ranges (other integral ranges use min/max values for special range values):
     16 //
     17 //  [F, F) = {}     = Empty set
     18 //  [T, F) = {T}
     19 //  [F, T) = {F}
     20 //  [T, T) = {F, T} = Full set
     21 //
     22 //===----------------------------------------------------------------------===//
     23 
     24 #include "llvm/InstrTypes.h"
     25 #include "llvm/Support/ConstantRange.h"
     26 #include "llvm/Support/Debug.h"
     27 #include "llvm/Support/raw_ostream.h"
     28 using namespace llvm;
     29 
     30 /// Initialize a full (the default) or empty set for the specified type.
     31 ///
     32 ConstantRange::ConstantRange(uint32_t BitWidth, bool Full) {
     33   if (Full)
     34     Lower = Upper = APInt::getMaxValue(BitWidth);
     35   else
     36     Lower = Upper = APInt::getMinValue(BitWidth);
     37 }
     38 
     39 /// Initialize a range to hold the single specified value.
     40 ///
     41 ConstantRange::ConstantRange(const APInt &V) : Lower(V), Upper(V + 1) {}
     42 
     43 ConstantRange::ConstantRange(const APInt &L, const APInt &U) :
     44   Lower(L), Upper(U) {
     45   assert(L.getBitWidth() == U.getBitWidth() &&
     46          "ConstantRange with unequal bit widths");
     47   assert((L != U || (L.isMaxValue() || L.isMinValue())) &&
     48          "Lower == Upper, but they aren't min or max value!");
     49 }
     50 
     51 ConstantRange ConstantRange::makeICmpRegion(unsigned Pred,
     52                                             const ConstantRange &CR) {
     53   if (CR.isEmptySet())
     54     return CR;
     55 
     56   uint32_t W = CR.getBitWidth();
     57   switch (Pred) {
     58     default: llvm_unreachable("Invalid ICmp predicate to makeICmpRegion()");
     59     case CmpInst::ICMP_EQ:
     60       return CR;
     61     case CmpInst::ICMP_NE:
     62       if (CR.isSingleElement())
     63         return ConstantRange(CR.getUpper(), CR.getLower());
     64       return ConstantRange(W);
     65     case CmpInst::ICMP_ULT: {
     66       APInt UMax(CR.getUnsignedMax());
     67       if (UMax.isMinValue())
     68         return ConstantRange(W, /* empty */ false);
     69       return ConstantRange(APInt::getMinValue(W), UMax);
     70     }
     71     case CmpInst::ICMP_SLT: {
     72       APInt SMax(CR.getSignedMax());
     73       if (SMax.isMinSignedValue())
     74         return ConstantRange(W, /* empty */ false);
     75       return ConstantRange(APInt::getSignedMinValue(W), SMax);
     76     }
     77     case CmpInst::ICMP_ULE: {
     78       APInt UMax(CR.getUnsignedMax());
     79       if (UMax.isMaxValue())
     80         return ConstantRange(W);
     81       return ConstantRange(APInt::getMinValue(W), UMax + 1);
     82     }
     83     case CmpInst::ICMP_SLE: {
     84       APInt SMax(CR.getSignedMax());
     85       if (SMax.isMaxSignedValue())
     86         return ConstantRange(W);
     87       return ConstantRange(APInt::getSignedMinValue(W), SMax + 1);
     88     }
     89     case CmpInst::ICMP_UGT: {
     90       APInt UMin(CR.getUnsignedMin());
     91       if (UMin.isMaxValue())
     92         return ConstantRange(W, /* empty */ false);
     93       return ConstantRange(UMin + 1, APInt::getNullValue(W));
     94     }
     95     case CmpInst::ICMP_SGT: {
     96       APInt SMin(CR.getSignedMin());
     97       if (SMin.isMaxSignedValue())
     98         return ConstantRange(W, /* empty */ false);
     99       return ConstantRange(SMin + 1, APInt::getSignedMinValue(W));
    100     }
    101     case CmpInst::ICMP_UGE: {
    102       APInt UMin(CR.getUnsignedMin());
    103       if (UMin.isMinValue())
    104         return ConstantRange(W);
    105       return ConstantRange(UMin, APInt::getNullValue(W));
    106     }
    107     case CmpInst::ICMP_SGE: {
    108       APInt SMin(CR.getSignedMin());
    109       if (SMin.isMinSignedValue())
    110         return ConstantRange(W);
    111       return ConstantRange(SMin, APInt::getSignedMinValue(W));
    112     }
    113   }
    114 }
    115 
    116 /// isFullSet - Return true if this set contains all of the elements possible
    117 /// for this data-type
    118 bool ConstantRange::isFullSet() const {
    119   return Lower == Upper && Lower.isMaxValue();
    120 }
    121 
    122 /// isEmptySet - Return true if this set contains no members.
    123 ///
    124 bool ConstantRange::isEmptySet() const {
    125   return Lower == Upper && Lower.isMinValue();
    126 }
    127 
    128 /// isWrappedSet - Return true if this set wraps around the top of the range,
    129 /// for example: [100, 8)
    130 ///
    131 bool ConstantRange::isWrappedSet() const {
    132   return Lower.ugt(Upper);
    133 }
    134 
    135 /// isSignWrappedSet - Return true if this set wraps around the INT_MIN of
    136 /// its bitwidth, for example: i8 [120, 140).
    137 ///
    138 bool ConstantRange::isSignWrappedSet() const {
    139   return contains(APInt::getSignedMaxValue(getBitWidth())) &&
    140          contains(APInt::getSignedMinValue(getBitWidth()));
    141 }
    142 
    143 /// getSetSize - Return the number of elements in this set.
    144 ///
    145 APInt ConstantRange::getSetSize() const {
    146   if (isEmptySet())
    147     return APInt(getBitWidth(), 0);
    148   if (getBitWidth() == 1) {
    149     if (Lower != Upper)  // One of T or F in the set...
    150       return APInt(2, 1);
    151     return APInt(2, 2);      // Must be full set...
    152   }
    153 
    154   // Simply subtract the bounds...
    155   return Upper - Lower;
    156 }
    157 
    158 /// getUnsignedMax - Return the largest unsigned value contained in the
    159 /// ConstantRange.
    160 ///
    161 APInt ConstantRange::getUnsignedMax() const {
    162   if (isFullSet() || isWrappedSet())
    163     return APInt::getMaxValue(getBitWidth());
    164   return getUpper() - 1;
    165 }
    166 
    167 /// getUnsignedMin - Return the smallest unsigned value contained in the
    168 /// ConstantRange.
    169 ///
    170 APInt ConstantRange::getUnsignedMin() const {
    171   if (isFullSet() || (isWrappedSet() && getUpper() != 0))
    172     return APInt::getMinValue(getBitWidth());
    173   return getLower();
    174 }
    175 
    176 /// getSignedMax - Return the largest signed value contained in the
    177 /// ConstantRange.
    178 ///
    179 APInt ConstantRange::getSignedMax() const {
    180   APInt SignedMax(APInt::getSignedMaxValue(getBitWidth()));
    181   if (!isWrappedSet()) {
    182     if (getLower().sle(getUpper() - 1))
    183       return getUpper() - 1;
    184     return SignedMax;
    185   }
    186   if (getLower().isNegative() == getUpper().isNegative())
    187     return SignedMax;
    188   return getUpper() - 1;
    189 }
    190 
    191 /// getSignedMin - Return the smallest signed value contained in the
    192 /// ConstantRange.
    193 ///
    194 APInt ConstantRange::getSignedMin() const {
    195   APInt SignedMin(APInt::getSignedMinValue(getBitWidth()));
    196   if (!isWrappedSet()) {
    197     if (getLower().sle(getUpper() - 1))
    198       return getLower();
    199     return SignedMin;
    200   }
    201   if ((getUpper() - 1).slt(getLower())) {
    202     if (getUpper() != SignedMin)
    203       return SignedMin;
    204   }
    205   return getLower();
    206 }
    207 
    208 /// contains - Return true if the specified value is in the set.
    209 ///
    210 bool ConstantRange::contains(const APInt &V) const {
    211   if (Lower == Upper)
    212     return isFullSet();
    213 
    214   if (!isWrappedSet())
    215     return Lower.ule(V) && V.ult(Upper);
    216   return Lower.ule(V) || V.ult(Upper);
    217 }
    218 
    219 /// contains - Return true if the argument is a subset of this range.
    220 /// Two equal sets contain each other. The empty set contained by all other
    221 /// sets.
    222 ///
    223 bool ConstantRange::contains(const ConstantRange &Other) const {
    224   if (isFullSet() || Other.isEmptySet()) return true;
    225   if (isEmptySet() || Other.isFullSet()) return false;
    226 
    227   if (!isWrappedSet()) {
    228     if (Other.isWrappedSet())
    229       return false;
    230 
    231     return Lower.ule(Other.getLower()) && Other.getUpper().ule(Upper);
    232   }
    233 
    234   if (!Other.isWrappedSet())
    235     return Other.getUpper().ule(Upper) ||
    236            Lower.ule(Other.getLower());
    237 
    238   return Other.getUpper().ule(Upper) && Lower.ule(Other.getLower());
    239 }
    240 
    241 /// subtract - Subtract the specified constant from the endpoints of this
    242 /// constant range.
    243 ConstantRange ConstantRange::subtract(const APInt &Val) const {
    244   assert(Val.getBitWidth() == getBitWidth() && "Wrong bit width");
    245   // If the set is empty or full, don't modify the endpoints.
    246   if (Lower == Upper)
    247     return *this;
    248   return ConstantRange(Lower - Val, Upper - Val);
    249 }
    250 
    251 /// intersectWith - Return the range that results from the intersection of this
    252 /// range with another range.  The resultant range is guaranteed to include all
    253 /// elements contained in both input ranges, and to have the smallest possible
    254 /// set size that does so.  Because there may be two intersections with the
    255 /// same set size, A.intersectWith(B) might not be equal to B.intersectWith(A).
    256 ConstantRange ConstantRange::intersectWith(const ConstantRange &CR) const {
    257   assert(getBitWidth() == CR.getBitWidth() &&
    258          "ConstantRange types don't agree!");
    259 
    260   // Handle common cases.
    261   if (   isEmptySet() || CR.isFullSet()) return *this;
    262   if (CR.isEmptySet() ||    isFullSet()) return CR;
    263 
    264   if (!isWrappedSet() && CR.isWrappedSet())
    265     return CR.intersectWith(*this);
    266 
    267   if (!isWrappedSet() && !CR.isWrappedSet()) {
    268     if (Lower.ult(CR.Lower)) {
    269       if (Upper.ule(CR.Lower))
    270         return ConstantRange(getBitWidth(), false);
    271 
    272       if (Upper.ult(CR.Upper))
    273         return ConstantRange(CR.Lower, Upper);
    274 
    275       return CR;
    276     }
    277     if (Upper.ult(CR.Upper))
    278       return *this;
    279 
    280     if (Lower.ult(CR.Upper))
    281       return ConstantRange(Lower, CR.Upper);
    282 
    283     return ConstantRange(getBitWidth(), false);
    284   }
    285 
    286   if (isWrappedSet() && !CR.isWrappedSet()) {
    287     if (CR.Lower.ult(Upper)) {
    288       if (CR.Upper.ult(Upper))
    289         return CR;
    290 
    291       if (CR.Upper.ult(Lower))
    292         return ConstantRange(CR.Lower, Upper);
    293 
    294       if (getSetSize().ult(CR.getSetSize()))
    295         return *this;
    296       return CR;
    297     }
    298     if (CR.Lower.ult(Lower)) {
    299       if (CR.Upper.ule(Lower))
    300         return ConstantRange(getBitWidth(), false);
    301 
    302       return ConstantRange(Lower, CR.Upper);
    303     }
    304     return CR;
    305   }
    306 
    307   if (CR.Upper.ult(Upper)) {
    308     if (CR.Lower.ult(Upper)) {
    309       if (getSetSize().ult(CR.getSetSize()))
    310         return *this;
    311       return CR;
    312     }
    313 
    314     if (CR.Lower.ult(Lower))
    315       return ConstantRange(Lower, CR.Upper);
    316 
    317     return CR;
    318   }
    319   if (CR.Upper.ult(Lower)) {
    320     if (CR.Lower.ult(Lower))
    321       return *this;
    322 
    323     return ConstantRange(CR.Lower, Upper);
    324   }
    325   if (getSetSize().ult(CR.getSetSize()))
    326     return *this;
    327   return CR;
    328 }
    329 
    330 
    331 /// unionWith - Return the range that results from the union of this range with
    332 /// another range.  The resultant range is guaranteed to include the elements of
    333 /// both sets, but may contain more.  For example, [3, 9) union [12,15) is
    334 /// [3, 15), which includes 9, 10, and 11, which were not included in either
    335 /// set before.
    336 ///
    337 ConstantRange ConstantRange::unionWith(const ConstantRange &CR) const {
    338   assert(getBitWidth() == CR.getBitWidth() &&
    339          "ConstantRange types don't agree!");
    340 
    341   if (   isFullSet() || CR.isEmptySet()) return *this;
    342   if (CR.isFullSet() ||    isEmptySet()) return CR;
    343 
    344   if (!isWrappedSet() && CR.isWrappedSet()) return CR.unionWith(*this);
    345 
    346   if (!isWrappedSet() && !CR.isWrappedSet()) {
    347     if (CR.Upper.ult(Lower) || Upper.ult(CR.Lower)) {
    348       // If the two ranges are disjoint, find the smaller gap and bridge it.
    349       APInt d1 = CR.Lower - Upper, d2 = Lower - CR.Upper;
    350       if (d1.ult(d2))
    351         return ConstantRange(Lower, CR.Upper);
    352       return ConstantRange(CR.Lower, Upper);
    353     }
    354 
    355     APInt L = Lower, U = Upper;
    356     if (CR.Lower.ult(L))
    357       L = CR.Lower;
    358     if ((CR.Upper - 1).ugt(U - 1))
    359       U = CR.Upper;
    360 
    361     if (L == 0 && U == 0)
    362       return ConstantRange(getBitWidth());
    363 
    364     return ConstantRange(L, U);
    365   }
    366 
    367   if (!CR.isWrappedSet()) {
    368     // ------U   L-----  and  ------U   L----- : this
    369     //   L--U                            L--U  : CR
    370     if (CR.Upper.ule(Upper) || CR.Lower.uge(Lower))
    371       return *this;
    372 
    373     // ------U   L----- : this
    374     //    L---------U   : CR
    375     if (CR.Lower.ule(Upper) && Lower.ule(CR.Upper))
    376       return ConstantRange(getBitWidth());
    377 
    378     // ----U       L---- : this
    379     //       L---U       : CR
    380     //    <d1>  <d2>
    381     if (Upper.ule(CR.Lower) && CR.Upper.ule(Lower)) {
    382       APInt d1 = CR.Lower - Upper, d2 = Lower - CR.Upper;
    383       if (d1.ult(d2))
    384         return ConstantRange(Lower, CR.Upper);
    385       return ConstantRange(CR.Lower, Upper);
    386     }
    387 
    388     // ----U     L----- : this
    389     //        L----U    : CR
    390     if (Upper.ult(CR.Lower) && Lower.ult(CR.Upper))
    391       return ConstantRange(CR.Lower, Upper);
    392 
    393     // ------U    L---- : this
    394     //    L-----U       : CR
    395     assert(CR.Lower.ult(Upper) && CR.Upper.ult(Lower) &&
    396            "ConstantRange::unionWith missed a case with one range wrapped");
    397     return ConstantRange(Lower, CR.Upper);
    398   }
    399 
    400   // ------U    L----  and  ------U    L---- : this
    401   // -U  L-----------  and  ------------U  L : CR
    402   if (CR.Lower.ule(Upper) || Lower.ule(CR.Upper))
    403     return ConstantRange(getBitWidth());
    404 
    405   APInt L = Lower, U = Upper;
    406   if (CR.Upper.ugt(U))
    407     U = CR.Upper;
    408   if (CR.Lower.ult(L))
    409     L = CR.Lower;
    410 
    411   return ConstantRange(L, U);
    412 }
    413 
    414 /// zeroExtend - Return a new range in the specified integer type, which must
    415 /// be strictly larger than the current type.  The returned range will
    416 /// correspond to the possible range of values as if the source range had been
    417 /// zero extended.
    418 ConstantRange ConstantRange::zeroExtend(uint32_t DstTySize) const {
    419   if (isEmptySet()) return ConstantRange(DstTySize, /*isFullSet=*/false);
    420 
    421   unsigned SrcTySize = getBitWidth();
    422   assert(SrcTySize < DstTySize && "Not a value extension");
    423   if (isFullSet() || isWrappedSet())
    424     // Change into [0, 1 << src bit width)
    425     return ConstantRange(APInt(DstTySize,0), APInt(DstTySize,1).shl(SrcTySize));
    426 
    427   return ConstantRange(Lower.zext(DstTySize), Upper.zext(DstTySize));
    428 }
    429 
    430 /// signExtend - Return a new range in the specified integer type, which must
    431 /// be strictly larger than the current type.  The returned range will
    432 /// correspond to the possible range of values as if the source range had been
    433 /// sign extended.
    434 ConstantRange ConstantRange::signExtend(uint32_t DstTySize) const {
    435   if (isEmptySet()) return ConstantRange(DstTySize, /*isFullSet=*/false);
    436 
    437   unsigned SrcTySize = getBitWidth();
    438   assert(SrcTySize < DstTySize && "Not a value extension");
    439   if (isFullSet() || isSignWrappedSet()) {
    440     return ConstantRange(APInt::getHighBitsSet(DstTySize,DstTySize-SrcTySize+1),
    441                          APInt::getLowBitsSet(DstTySize, SrcTySize-1) + 1);
    442   }
    443 
    444   return ConstantRange(Lower.sext(DstTySize), Upper.sext(DstTySize));
    445 }
    446 
    447 /// truncate - Return a new range in the specified integer type, which must be
    448 /// strictly smaller than the current type.  The returned range will
    449 /// correspond to the possible range of values as if the source range had been
    450 /// truncated to the specified type.
    451 ConstantRange ConstantRange::truncate(uint32_t DstTySize) const {
    452   assert(getBitWidth() > DstTySize && "Not a value truncation");
    453   if (isFullSet() || getSetSize().getActiveBits() > DstTySize)
    454     return ConstantRange(DstTySize, /*isFullSet=*/true);
    455 
    456   return ConstantRange(Lower.trunc(DstTySize), Upper.trunc(DstTySize));
    457 }
    458 
    459 /// zextOrTrunc - make this range have the bit width given by \p DstTySize. The
    460 /// value is zero extended, truncated, or left alone to make it that width.
    461 ConstantRange ConstantRange::zextOrTrunc(uint32_t DstTySize) const {
    462   unsigned SrcTySize = getBitWidth();
    463   if (SrcTySize > DstTySize)
    464     return truncate(DstTySize);
    465   if (SrcTySize < DstTySize)
    466     return zeroExtend(DstTySize);
    467   return *this;
    468 }
    469 
    470 /// sextOrTrunc - make this range have the bit width given by \p DstTySize. The
    471 /// value is sign extended, truncated, or left alone to make it that width.
    472 ConstantRange ConstantRange::sextOrTrunc(uint32_t DstTySize) const {
    473   unsigned SrcTySize = getBitWidth();
    474   if (SrcTySize > DstTySize)
    475     return truncate(DstTySize);
    476   if (SrcTySize < DstTySize)
    477     return signExtend(DstTySize);
    478   return *this;
    479 }
    480 
    481 ConstantRange
    482 ConstantRange::add(const ConstantRange &Other) const {
    483   if (isEmptySet() || Other.isEmptySet())
    484     return ConstantRange(getBitWidth(), /*isFullSet=*/false);
    485   if (isFullSet() || Other.isFullSet())
    486     return ConstantRange(getBitWidth(), /*isFullSet=*/true);
    487 
    488   APInt Spread_X = getSetSize(), Spread_Y = Other.getSetSize();
    489   APInt NewLower = getLower() + Other.getLower();
    490   APInt NewUpper = getUpper() + Other.getUpper() - 1;
    491   if (NewLower == NewUpper)
    492     return ConstantRange(getBitWidth(), /*isFullSet=*/true);
    493 
    494   ConstantRange X = ConstantRange(NewLower, NewUpper);
    495   if (X.getSetSize().ult(Spread_X) || X.getSetSize().ult(Spread_Y))
    496     // We've wrapped, therefore, full set.
    497     return ConstantRange(getBitWidth(), /*isFullSet=*/true);
    498 
    499   return X;
    500 }
    501 
    502 ConstantRange
    503 ConstantRange::sub(const ConstantRange &Other) const {
    504   if (isEmptySet() || Other.isEmptySet())
    505     return ConstantRange(getBitWidth(), /*isFullSet=*/false);
    506   if (isFullSet() || Other.isFullSet())
    507     return ConstantRange(getBitWidth(), /*isFullSet=*/true);
    508 
    509   APInt Spread_X = getSetSize(), Spread_Y = Other.getSetSize();
    510   APInt NewLower = getLower() - Other.getUpper() + 1;
    511   APInt NewUpper = getUpper() - Other.getLower();
    512   if (NewLower == NewUpper)
    513     return ConstantRange(getBitWidth(), /*isFullSet=*/true);
    514 
    515   ConstantRange X = ConstantRange(NewLower, NewUpper);
    516   if (X.getSetSize().ult(Spread_X) || X.getSetSize().ult(Spread_Y))
    517     // We've wrapped, therefore, full set.
    518     return ConstantRange(getBitWidth(), /*isFullSet=*/true);
    519 
    520   return X;
    521 }
    522 
    523 ConstantRange
    524 ConstantRange::multiply(const ConstantRange &Other) const {
    525   // TODO: If either operand is a single element and the multiply is known to
    526   // be non-wrapping, round the result min and max value to the appropriate
    527   // multiple of that element. If wrapping is possible, at least adjust the
    528   // range according to the greatest power-of-two factor of the single element.
    529 
    530   if (isEmptySet() || Other.isEmptySet())
    531     return ConstantRange(getBitWidth(), /*isFullSet=*/false);
    532   if (isFullSet() || Other.isFullSet())
    533     return ConstantRange(getBitWidth(), /*isFullSet=*/true);
    534 
    535   APInt this_min = getUnsignedMin().zext(getBitWidth() * 2);
    536   APInt this_max = getUnsignedMax().zext(getBitWidth() * 2);
    537   APInt Other_min = Other.getUnsignedMin().zext(getBitWidth() * 2);
    538   APInt Other_max = Other.getUnsignedMax().zext(getBitWidth() * 2);
    539 
    540   ConstantRange Result_zext = ConstantRange(this_min * Other_min,
    541                                             this_max * Other_max + 1);
    542   return Result_zext.truncate(getBitWidth());
    543 }
    544 
    545 ConstantRange
    546 ConstantRange::smax(const ConstantRange &Other) const {
    547   // X smax Y is: range(smax(X_smin, Y_smin),
    548   //                    smax(X_smax, Y_smax))
    549   if (isEmptySet() || Other.isEmptySet())
    550     return ConstantRange(getBitWidth(), /*isFullSet=*/false);
    551   APInt NewL = APIntOps::smax(getSignedMin(), Other.getSignedMin());
    552   APInt NewU = APIntOps::smax(getSignedMax(), Other.getSignedMax()) + 1;
    553   if (NewU == NewL)
    554     return ConstantRange(getBitWidth(), /*isFullSet=*/true);
    555   return ConstantRange(NewL, NewU);
    556 }
    557 
    558 ConstantRange
    559 ConstantRange::umax(const ConstantRange &Other) const {
    560   // X umax Y is: range(umax(X_umin, Y_umin),
    561   //                    umax(X_umax, Y_umax))
    562   if (isEmptySet() || Other.isEmptySet())
    563     return ConstantRange(getBitWidth(), /*isFullSet=*/false);
    564   APInt NewL = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
    565   APInt NewU = APIntOps::umax(getUnsignedMax(), Other.getUnsignedMax()) + 1;
    566   if (NewU == NewL)
    567     return ConstantRange(getBitWidth(), /*isFullSet=*/true);
    568   return ConstantRange(NewL, NewU);
    569 }
    570 
    571 ConstantRange
    572 ConstantRange::udiv(const ConstantRange &RHS) const {
    573   if (isEmptySet() || RHS.isEmptySet() || RHS.getUnsignedMax() == 0)
    574     return ConstantRange(getBitWidth(), /*isFullSet=*/false);
    575   if (RHS.isFullSet())
    576     return ConstantRange(getBitWidth(), /*isFullSet=*/true);
    577 
    578   APInt Lower = getUnsignedMin().udiv(RHS.getUnsignedMax());
    579 
    580   APInt RHS_umin = RHS.getUnsignedMin();
    581   if (RHS_umin == 0) {
    582     // We want the lowest value in RHS excluding zero. Usually that would be 1
    583     // except for a range in the form of [X, 1) in which case it would be X.
    584     if (RHS.getUpper() == 1)
    585       RHS_umin = RHS.getLower();
    586     else
    587       RHS_umin = APInt(getBitWidth(), 1);
    588   }
    589 
    590   APInt Upper = getUnsignedMax().udiv(RHS_umin) + 1;
    591 
    592   // If the LHS is Full and the RHS is a wrapped interval containing 1 then
    593   // this could occur.
    594   if (Lower == Upper)
    595     return ConstantRange(getBitWidth(), /*isFullSet=*/true);
    596 
    597   return ConstantRange(Lower, Upper);
    598 }
    599 
    600 ConstantRange
    601 ConstantRange::binaryAnd(const ConstantRange &Other) const {
    602   if (isEmptySet() || Other.isEmptySet())
    603     return ConstantRange(getBitWidth(), /*isFullSet=*/false);
    604 
    605   // TODO: replace this with something less conservative
    606 
    607   APInt umin = APIntOps::umin(Other.getUnsignedMax(), getUnsignedMax());
    608   if (umin.isAllOnesValue())
    609     return ConstantRange(getBitWidth(), /*isFullSet=*/true);
    610   return ConstantRange(APInt::getNullValue(getBitWidth()), umin + 1);
    611 }
    612 
    613 ConstantRange
    614 ConstantRange::binaryOr(const ConstantRange &Other) const {
    615   if (isEmptySet() || Other.isEmptySet())
    616     return ConstantRange(getBitWidth(), /*isFullSet=*/false);
    617 
    618   // TODO: replace this with something less conservative
    619 
    620   APInt umax = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
    621   if (umax.isMinValue())
    622     return ConstantRange(getBitWidth(), /*isFullSet=*/true);
    623   return ConstantRange(umax, APInt::getNullValue(getBitWidth()));
    624 }
    625 
    626 ConstantRange
    627 ConstantRange::shl(const ConstantRange &Other) const {
    628   if (isEmptySet() || Other.isEmptySet())
    629     return ConstantRange(getBitWidth(), /*isFullSet=*/false);
    630 
    631   APInt min = getUnsignedMin().shl(Other.getUnsignedMin());
    632   APInt max = getUnsignedMax().shl(Other.getUnsignedMax());
    633 
    634   // there's no overflow!
    635   APInt Zeros(getBitWidth(), getUnsignedMax().countLeadingZeros());
    636   if (Zeros.ugt(Other.getUnsignedMax()))
    637     return ConstantRange(min, max + 1);
    638 
    639   // FIXME: implement the other tricky cases
    640   return ConstantRange(getBitWidth(), /*isFullSet=*/true);
    641 }
    642 
    643 ConstantRange
    644 ConstantRange::lshr(const ConstantRange &Other) const {
    645   if (isEmptySet() || Other.isEmptySet())
    646     return ConstantRange(getBitWidth(), /*isFullSet=*/false);
    647 
    648   APInt max = getUnsignedMax().lshr(Other.getUnsignedMin());
    649   APInt min = getUnsignedMin().lshr(Other.getUnsignedMax());
    650   if (min == max + 1)
    651     return ConstantRange(getBitWidth(), /*isFullSet=*/true);
    652 
    653   return ConstantRange(min, max + 1);
    654 }
    655 
    656 ConstantRange ConstantRange::inverse() const {
    657   if (isFullSet())
    658     return ConstantRange(getBitWidth(), /*isFullSet=*/false);
    659   if (isEmptySet())
    660     return ConstantRange(getBitWidth(), /*isFullSet=*/true);
    661   return ConstantRange(Upper, Lower);
    662 }
    663 
    664 /// print - Print out the bounds to a stream...
    665 ///
    666 void ConstantRange::print(raw_ostream &OS) const {
    667   if (isFullSet())
    668     OS << "full-set";
    669   else if (isEmptySet())
    670     OS << "empty-set";
    671   else
    672     OS << "[" << Lower << "," << Upper << ")";
    673 }
    674 
    675 /// dump - Allow printing from a debugger easily...
    676 ///
    677 void ConstantRange::dump() const {
    678   print(dbgs());
    679 }
    680