lib/Support/ConstantRange.cpp

   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/Support/ConstantRange.h"
  25 #include "llvm/Support/raw_ostream.h"
  26 using namespace llvm;
  27
  28 /// Initialize a full (the default) or empty set for the specified type.
  29 ///
  30 ConstantRange::ConstantRange(uint32_t BitWidth, bool Full) :
  31   Lower(BitWidth, 0), Upper(BitWidth, 0) {
  32   if (Full)
  33     Lower = Upper = APInt::getMaxValue(BitWidth);
  34   else
  35     Lower = Upper = APInt::getMinValue(BitWidth);
  36 }
  37
  38 /// Initialize a range to hold the single specified value.
  39 ///
  40 ConstantRange::ConstantRange(const APInt & V) : Lower(V), Upper(V + 1) { }
  41
  42 ConstantRange::ConstantRange(const APInt &L, const APInt &U) :
  43   Lower(L), Upper(U) {
  44   assert(L.getBitWidth() == U.getBitWidth() &&
  45          "ConstantRange with unequal bit widths");
  46   assert((L != U || (L.isMaxValue() || L.isMinValue())) &&
  47          "Lower == Upper, but they aren't min or max value!");
  48 }
  49
  50 /// isFullSet - Return true if this set contains all of the elements possible
  51 /// for this data-type
  52 bool ConstantRange::isFullSet() const {
  53   return Lower == Upper && Lower.isMaxValue();
  54 }
  55
  56 /// isEmptySet - Return true if this set contains no members.
  57 ///
  58 bool ConstantRange::isEmptySet() const {
  59   return Lower == Upper && Lower.isMinValue();
  60 }
  61
  62 /// isWrappedSet - Return true if this set wraps around the top of the range,
  63 /// for example: [100, 8)
  64 ///
  65 bool ConstantRange::isWrappedSet() const {
  66   return Lower.ugt(Upper);
  67 }
  68
  69 /// getSetSize - Return the number of elements in this set.
  70 ///
  71 APInt ConstantRange::getSetSize() const {
  72   if (isEmptySet())
  73     return APInt(getBitWidth(), 0);
  74   if (getBitWidth() == 1) {
  75     if (Lower != Upper)  // One of T or F in the set...
  76       return APInt(2, 1);
  77     return APInt(2, 2);      // Must be full set...
  78   }
  79
  80   // Simply subtract the bounds...
  81   return Upper - Lower;
  82 }
  83
  84 /// getUnsignedMax - Return the largest unsigned value contained in the
  85 /// ConstantRange.
  86 ///
  87 APInt ConstantRange::getUnsignedMax() const {
  88   if (isFullSet() || isWrappedSet())
  89     return APInt::getMaxValue(getBitWidth());
  90   else
  91     return getUpper() - 1;
  92 }
  93
  94 /// getUnsignedMin - Return the smallest unsigned value contained in the
  95 /// ConstantRange.
  96 ///
  97 APInt ConstantRange::getUnsignedMin() const {
  98   if (isFullSet() || (isWrappedSet() && getUpper() != 0))
  99     return APInt::getMinValue(getBitWidth());
 100   else
 101     return getLower();
 102 }
 103
 104 /// getSignedMax - Return the largest signed value contained in the
 105 /// ConstantRange.
 106 ///
 107 APInt ConstantRange::getSignedMax() const {
 108   APInt SignedMax(APInt::getSignedMaxValue(getBitWidth()));
 109   if (!isWrappedSet()) {
 110     if (getLower().sle(getUpper() - 1))
 111       return getUpper() - 1;
 112     else
 113       return SignedMax;
 114   } else {
 115     if ((getUpper() - 1).slt(getLower())) {
 116       if (getLower() != SignedMax)
 117         return SignedMax;
 118       else
 119         return getUpper() - 1;
 120     } else {
 121       return getUpper() - 1;
 122     }
 123   }
 124 }
 125
 126 /// getSignedMin - Return the smallest signed value contained in the
 127 /// ConstantRange.
 128 ///
 129 APInt ConstantRange::getSignedMin() const {
 130   APInt SignedMin(APInt::getSignedMinValue(getBitWidth()));
 131   if (!isWrappedSet()) {
 132     if (getLower().sle(getUpper() - 1))
 133       return getLower();
 134     else
 135       return SignedMin;
 136   } else {
 137     if ((getUpper() - 1).slt(getLower())) {
 138       if (getUpper() != SignedMin)
 139         return SignedMin;
 140       else
 141         return getLower();
 142     } else {
 143       return getLower();
 144     }
 145   }
 146 }
 147
 148 /// contains - Return true if the specified value is in the set.
 149 ///
 150 bool ConstantRange::contains(const APInt &V) const {
 151   if (Lower == Upper)
 152     return isFullSet();
 153
 154   if (!isWrappedSet())
 155     return Lower.ule(V) && V.ult(Upper);
 156   else
 157     return Lower.ule(V) || V.ult(Upper);
 158 }
 159
 160 /// subtract - Subtract the specified constant from the endpoints of this
 161 /// constant range.
 162 ConstantRange ConstantRange::subtract(const APInt &Val) const {
 163   assert(Val.getBitWidth() == getBitWidth() && "Wrong bit width");
 164   // If the set is empty or full, don't modify the endpoints.
 165   if (Lower == Upper)
 166     return *this;
 167   return ConstantRange(Lower - Val, Upper - Val);
 168 }
 169
 170
 171 // intersect1Wrapped - This helper function is used to intersect two ranges when
 172 // it is known that LHS is wrapped and RHS isn't.
 173 //
 174 ConstantRange
 175 ConstantRange::intersect1Wrapped(const ConstantRange &LHS,
 176                                  const ConstantRange &RHS) {
 177   assert(LHS.isWrappedSet() && !RHS.isWrappedSet());
 178
 179   // Check to see if we overlap on the Left side of RHS...
 180   //
 181   if (RHS.Lower.ult(LHS.Upper)) {
 182     // We do overlap on the left side of RHS, see if we overlap on the right of
 183     // RHS...
 184     if (RHS.Upper.ugt(LHS.Lower)) {
 185       // Ok, the result overlaps on both the left and right sides.  See if the
 186       // resultant interval will be smaller if we wrap or not...
 187       //
 188       if (LHS.getSetSize().ult(RHS.getSetSize()))
 189         return LHS;
 190       else
 191         return RHS;
 192
 193     } else {
 194       // No overlap on the right, just on the left.
 195       return ConstantRange(RHS.Lower, LHS.Upper);
 196     }
 197   } else {
 198     // We don't overlap on the left side of RHS, see if we overlap on the right
 199     // of RHS...
 200     if (RHS.Upper.ugt(LHS.Lower)) {
 201       // Simple overlap...
 202       return ConstantRange(LHS.Lower, RHS.Upper);
 203     } else {
 204       // No overlap...
 205       return ConstantRange(LHS.getBitWidth(), false);
 206     }
 207   }
 208 }
 209
 210 /// intersectWith - Return the range that results from the intersection of this
 211 /// range with another range.
 212 ///
 213 ConstantRange ConstantRange::intersectWith(const ConstantRange &CR) const {
 214   assert(getBitWidth() == CR.getBitWidth() &&
 215          "ConstantRange types don't agree!");
 216   // Handle common special cases
 217   if (isEmptySet() || CR.isFullSet())
 218     return *this;
 219   if (isFullSet()  || CR.isEmptySet())
 220     return CR;
 221
 222   if (!isWrappedSet()) {
 223     if (!CR.isWrappedSet()) {
 224       using namespace APIntOps;
 225       APInt L = umax(Lower, CR.Lower);
 226       APInt U = umin(Upper, CR.Upper);
 227
 228       if (L.ult(U)) // If range isn't empty...
 229         return ConstantRange(L, U);
 230       else
 231         return ConstantRange(getBitWidth(), false);// Otherwise, empty set
 232     } else
 233       return intersect1Wrapped(CR, *this);
 234   } else {   // We know "this" is wrapped...
 235     if (!CR.isWrappedSet())
 236       return intersect1Wrapped(*this, CR);
 237     else {
 238       // Both ranges are wrapped...
 239       using namespace APIntOps;
 240       APInt L = umax(Lower, CR.Lower);
 241       APInt U = umin(Upper, CR.Upper);
 242       return ConstantRange(L, U);
 243     }
 244   }
 245   return *this;
 246 }
 247
 248 /// maximalIntersectWith - Return the range that results from the intersection
 249 /// of this range with another range.  The resultant range is guaranteed to
 250 /// include all elements contained in both input ranges, and to have the
 251 /// smallest possible set size that does so.  Because there may be two
 252 /// intersections with the same set size, A.maximalIntersectWith(B) might not
 253 /// be equal to B.maximalIntersect(A).
 254 ConstantRange ConstantRange::maximalIntersectWith(const ConstantRange &CR) const {
 255   assert(getBitWidth() == CR.getBitWidth() &&
 256          "ConstantRange types don't agree!");
 257
 258   // Handle common cases.
 259   if (   isEmptySet() || CR.isFullSet()) return *this;
 260   if (CR.isEmptySet() ||    isFullSet()) return CR;
 261
 262   if (!isWrappedSet() && CR.isWrappedSet())
 263     return CR.maximalIntersectWith(*this);
 264
 265   if (!isWrappedSet() && !CR.isWrappedSet()) {
 266     if (Lower.ult(CR.Lower)) {
 267       if (Upper.ule(CR.Lower))
 268         return ConstantRange(getBitWidth(), false);
 269
 270       if (Upper.ult(CR.Upper))
 271         return ConstantRange(CR.Lower, Upper);
 272
 273       return CR;
 274     } else {
 275       if (Upper.ult(CR.Upper))
 276         return *this;
 277
 278       if (Lower.ult(CR.Upper))
 279         return ConstantRange(Lower, CR.Upper);
 280
 281       return ConstantRange(getBitWidth(), false);
 282     }
 283   }
 284
 285   if (isWrappedSet() && !CR.isWrappedSet()) {
 286     if (CR.Lower.ult(Upper)) {
 287       if (CR.Upper.ult(Upper))
 288         return CR;
 289
 290       if (CR.Upper.ult(Lower))
 291         return ConstantRange(CR.Lower, Upper);
 292
 293       if (getSetSize().ult(CR.getSetSize()))
 294         return *this;
 295       else
 296         return CR;
 297     } else if (CR.Lower.ult(Lower)) {
 298       if (CR.Upper.ule(Lower))
 299         return ConstantRange(getBitWidth(), false);
 300
 301       return ConstantRange(Lower, CR.Upper);
 302     }
 303     return CR;
 304   }
 305
 306   if (CR.Upper.ult(Upper)) {
 307     if (CR.Lower.ult(Upper)) {
 308       if (getSetSize().ult(CR.getSetSize()))
 309         return *this;
 310       else
 311         return CR;
 312     }
 313
 314     if (CR.Lower.ult(Lower))
 315       return ConstantRange(Lower, CR.Upper);
 316
 317     return CR;
 318   } else if (CR.Upper.ult(Lower)) {
 319     if (CR.Lower.ult(Lower))
 320       return *this;
 321
 322     return ConstantRange(CR.Lower, Upper);
 323   }
 324   if (getSetSize().ult(CR.getSetSize()))
 325     return *this;
 326   else
 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   APInt L = Lower, U = Upper;
 347
 348   if (!isWrappedSet() && !CR.isWrappedSet()) {
 349     if (CR.Lower.ult(L))
 350       L = CR.Lower;
 351
 352     if (CR.Upper.ugt(U))
 353       U = CR.Upper;
 354   }
 355
 356   if (isWrappedSet() && !CR.isWrappedSet()) {
 357     if ((CR.Lower.ult(Upper) && CR.Upper.ult(Upper)) ||
 358         (CR.Lower.ugt(Lower) && CR.Upper.ugt(Lower))) {
 359       return *this;
 360     }
 361
 362     if (CR.Lower.ule(Upper) && Lower.ule(CR.Upper)) {
 363       return ConstantRange(getBitWidth());
 364     }
 365
 366     if (CR.Lower.ule(Upper) && CR.Upper.ule(Lower)) {
 367       APInt d1 = CR.Upper - Upper, d2 = Lower - CR.Upper;
 368       if (d1.ult(d2)) {
 369         U = CR.Upper;
 370       } else {
 371         L = CR.Upper;
 372       }
 373     }
 374
 375     if (Upper.ult(CR.Lower) && CR.Upper.ult(Lower)) {
 376       APInt d1 = CR.Lower - Upper, d2 = Lower - CR.Upper;
 377       if (d1.ult(d2)) {
 378         U = CR.Lower + 1;
 379       } else {
 380         L = CR.Upper - 1;
 381       }
 382     }
 383
 384     if (Upper.ult(CR.Lower) && Lower.ult(CR.Upper)) {
 385       APInt d1 = CR.Lower - Upper, d2 = Lower - CR.Lower;
 386
 387       if (d1.ult(d2)) {
 388         U = CR.Lower + 1;
 389       } else {
 390         L = CR.Lower;
 391       }
 392     }
 393   }
 394
 395   if (isWrappedSet() && CR.isWrappedSet()) {
 396     if (Lower.ult(CR.Upper) || CR.Lower.ult(Upper))
 397       return ConstantRange(getBitWidth());
 398
 399     if (CR.Upper.ugt(U)) {
 400       U = CR.Upper;
 401     }
 402
 403     if (CR.Lower.ult(L)) {
 404       L = CR.Lower;
 405     }
 406
 407     if (L == U) return ConstantRange(getBitWidth());
 408   }
 409
 410   return ConstantRange(L, U);
 411 }
 412
 413 /// zeroExtend - Return a new range in the specified integer type, which must
 414 /// be strictly larger than the current type.  The returned range will
 415 /// correspond to the possible range of values as if the source range had been
 416 /// zero extended.
 417 ConstantRange ConstantRange::zeroExtend(uint32_t DstTySize) const {
 418   unsigned SrcTySize = getBitWidth();
 419   assert(SrcTySize < DstTySize && "Not a value extension");
 420   if (isFullSet())
 421     // Change a source full set into [0, 1 << 8*numbytes)
 422     return ConstantRange(APInt(DstTySize,0), APInt(DstTySize,1).shl(SrcTySize));
 423
 424   APInt L = Lower; L.zext(DstTySize);
 425   APInt U = Upper; U.zext(DstTySize);
 426   return ConstantRange(L, U);
 427 }
 428
 429 /// signExtend - Return a new range in the specified integer type, which must
 430 /// be strictly larger than the current type.  The returned range will
 431 /// correspond to the possible range of values as if the source range had been
 432 /// sign extended.
 433 ConstantRange ConstantRange::signExtend(uint32_t DstTySize) const {
 434   unsigned SrcTySize = getBitWidth();
 435   assert(SrcTySize < DstTySize && "Not a value extension");
 436   if (isFullSet()) {
 437     return ConstantRange(APInt::getHighBitsSet(DstTySize,DstTySize-SrcTySize+1),
 438                          APInt::getLowBitsSet(DstTySize, SrcTySize-1));
 439   }
 440
 441   APInt L = Lower; L.sext(DstTySize);
 442   APInt U = Upper; U.sext(DstTySize);
 443   return ConstantRange(L, U);
 444 }
 445
 446 /// truncate - Return a new range in the specified integer type, which must be
 447 /// strictly smaller than the current type.  The returned range will
 448 /// correspond to the possible range of values as if the source range had been
 449 /// truncated to the specified type.
 450 ConstantRange ConstantRange::truncate(uint32_t DstTySize) const {
 451   unsigned SrcTySize = getBitWidth();
 452   assert(SrcTySize > DstTySize && "Not a value truncation");
 453   APInt Size(APInt::getLowBitsSet(SrcTySize, DstTySize));
 454   if (isFullSet() || getSetSize().ugt(Size))
 455     return ConstantRange(DstTySize);
 456
 457   APInt L = Lower; L.trunc(DstTySize);
 458   APInt U = Upper; U.trunc(DstTySize);
 459   return ConstantRange(L, U);
 460 }
 461
 462 /// print - Print out the bounds to a stream...
 463 ///
 464 void ConstantRange::print(raw_ostream &OS) const {
 465   OS << "[" << Lower << "," << Upper << ")";
 466 }
 467
 468 /// dump - Allow printing from a debugger easily...
 469 ///
 470 void ConstantRange::dump() const {
 471   print(errs());
 472 }