lib/Support/ConstantRange.cpp

   1 //===-- ConstantRange.cpp - ConstantRange implementation ------------------===//
   2 //
   3 //                     The LLVM Compiler Infrastructure
   4 //
   5 // This file was developed by the LLVM research group and is distributed under
   6 // the University of Illinois Open Source 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/Streams.h"
  26 #include <ostream>
  27 using namespace llvm;
  28
  29 /// Initialize a full (the default) or empty set for the specified type.
  30 ///
  31 ConstantRange::ConstantRange(uint32_t BitWidth, bool Full) :
  32   Lower(BitWidth, 0), Upper(BitWidth, 0) {
  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 /// isFullSet - Return true if this set contains all of the elements possible
  52 /// for this data-type
  53 bool ConstantRange::isFullSet() const {
  54   return Lower == Upper && Lower.isMaxValue();
  55 }
  56
  57 /// isEmptySet - Return true if this set contains no members.
  58 ///
  59 bool ConstantRange::isEmptySet() const {
  60   return Lower == Upper && Lower.isMinValue();
  61 }
  62
  63 /// isWrappedSet - Return true if this set wraps around the top of the range,
  64 /// for example: [100, 8)
  65 ///
  66 bool ConstantRange::isWrappedSet() const {
  67   return Lower.ugt(Upper);
  68 }
  69
  70 /// getSetSize - Return the number of elements in this set.
  71 ///
  72 APInt ConstantRange::getSetSize() const {
  73   if (isEmptySet())
  74     return APInt(getBitWidth(), 0);
  75   if (getBitWidth() == 1) {
  76     if (Lower != Upper)  // One of T or F in the set...
  77       return APInt(2, 1);
  78     return APInt(2, 2);      // Must be full set...
  79   }
  80
  81   // Simply subtract the bounds...
  82   return Upper - Lower;
  83 }
  84
  85 /// getUnsignedMax - Return the largest unsigned value contained in the
  86 /// ConstantRange.
  87 ///
  88 APInt ConstantRange::getUnsignedMax() const {
  89   if (isFullSet() || isWrappedSet())
  90     return APInt::getMaxValue(getBitWidth());
  91   else
  92     return getUpper() - 1;
  93 }
  94
  95 /// getUnsignedMin - Return the smallest unsigned value contained in the
  96 /// ConstantRange.
  97 ///
  98 APInt ConstantRange::getUnsignedMin() const {
  99   if (isFullSet() || (isWrappedSet() && getUpper() != 0))
 100     return APInt::getMinValue(getBitWidth());
 101   else
 102     return getLower();
 103 }
 104
 105 /// getSignedMax - Return the largest signed value contained in the
 106 /// ConstantRange.
 107 ///
 108 APInt ConstantRange::getSignedMax() const {
 109   APInt SignedMax(APInt::getSignedMaxValue(getBitWidth()));
 110   if (!isWrappedSet()) {
 111     if (getLower().sle(getUpper() - 1))
 112       return getUpper() - 1;
 113     else
 114       return SignedMax;
 115   } else {
 116     if ((getUpper() - 1).slt(getLower())) {
 117       if (getLower() != SignedMax)
 118         return SignedMax;
 119       else
 120         return getUpper() - 1;
 121     } else {
 122       return getUpper() - 1;
 123     }
 124   }
 125 }
 126
 127 /// getSignedMin - Return the smallest signed value contained in the
 128 /// ConstantRange.
 129 ///
 130 APInt ConstantRange::getSignedMin() const {
 131   APInt SignedMin(APInt::getSignedMinValue(getBitWidth()));
 132   if (!isWrappedSet()) {
 133     if (getLower().sle(getUpper() - 1))
 134       return getLower();
 135     else
 136       return SignedMin;
 137   } else {
 138     if ((getUpper() - 1).slt(getLower())) {
 139       if (getUpper() != SignedMin)
 140         return SignedMin;
 141       else
 142         return getLower();
 143     } else {
 144       return getLower();
 145     }
 146   }
 147 }
 148
 149 /// contains - Return true if the specified value is in the set.
 150 ///
 151 bool ConstantRange::contains(const APInt &V) const {
 152   if (Lower == Upper)
 153     return isFullSet();
 154
 155   if (!isWrappedSet())
 156     return Lower.ule(V) && V.ult(Upper);
 157   else
 158     return Lower.ule(V) || V.ult(Upper);
 159 }
 160
 161 /// subtract - Subtract the specified constant from the endpoints of this
 162 /// constant range.
 163 ConstantRange ConstantRange::subtract(const APInt &Val) const {
 164   assert(Val.getBitWidth() == getBitWidth() && "Wrong bit width");
 165   // If the set is empty or full, don't modify the endpoints.
 166   if (Lower == Upper)
 167     return *this;
 168   return ConstantRange(Lower - Val, Upper - Val);
 169 }
 170
 171
 172 // intersect1Wrapped - This helper function is used to intersect two ranges when
 173 // it is known that LHS is wrapped and RHS isn't.
 174 //
 175 ConstantRange
 176 ConstantRange::intersect1Wrapped(const ConstantRange &LHS,
 177                                  const ConstantRange &RHS) {
 178   assert(LHS.isWrappedSet() && !RHS.isWrappedSet());
 179
 180   // Check to see if we overlap on the Left side of RHS...
 181   //
 182   if (RHS.Lower.ult(LHS.Upper)) {
 183     // We do overlap on the left side of RHS, see if we overlap on the right of
 184     // RHS...
 185     if (RHS.Upper.ugt(LHS.Lower)) {
 186       // Ok, the result overlaps on both the left and right sides.  See if the
 187       // resultant interval will be smaller if we wrap or not...
 188       //
 189       if (LHS.getSetSize().ult(RHS.getSetSize()))
 190         return LHS;
 191       else
 192         return RHS;
 193
 194     } else {
 195       // No overlap on the right, just on the left.
 196       return ConstantRange(RHS.Lower, LHS.Upper);
 197     }
 198   } else {
 199     // We don't overlap on the left side of RHS, see if we overlap on the right
 200     // of RHS...
 201     if (RHS.Upper.ugt(LHS.Lower)) {
 202       // Simple overlap...
 203       return ConstantRange(LHS.Lower, RHS.Upper);
 204     } else {
 205       // No overlap...
 206       return ConstantRange(LHS.getBitWidth(), false);
 207     }
 208   }
 209 }
 210
 211 /// intersectWith - Return the range that results from the intersection of this
 212 /// range with another range.
 213 ///
 214 ConstantRange ConstantRange::intersectWith(const ConstantRange &CR) const {
 215   assert(getBitWidth() == CR.getBitWidth() &&
 216          "ConstantRange types don't agree!");
 217   // Handle common special cases
 218   if (isEmptySet() || CR.isFullSet())
 219     return *this;
 220   if (isFullSet()  || CR.isEmptySet())
 221     return CR;
 222
 223   if (!isWrappedSet()) {
 224     if (!CR.isWrappedSet()) {
 225       using namespace APIntOps;
 226       APInt L = umax(Lower, CR.Lower);
 227       APInt U = umin(Upper, CR.Upper);
 228
 229       if (L.ult(U)) // If range isn't empty...
 230         return ConstantRange(L, U);
 231       else
 232         return ConstantRange(getBitWidth(), false);// Otherwise, empty set
 233     } else
 234       return intersect1Wrapped(CR, *this);
 235   } else {   // We know "this" is wrapped...
 236     if (!CR.isWrappedSet())
 237       return intersect1Wrapped(*this, CR);
 238     else {
 239       // Both ranges are wrapped...
 240       using namespace APIntOps;
 241       APInt L = umax(Lower, CR.Lower);
 242       APInt U = umin(Upper, CR.Upper);
 243       return ConstantRange(L, U);
 244     }
 245   }
 246   return *this;
 247 }
 248
 249 /// maximalIntersectWith - Return the range that results from the intersection
 250 /// of this range with another range.  The resultant range is guaranteed to
 251 /// include all elements contained in both input ranges, and to have the
 252 /// smallest possible set size that does so.  Because there may be two
 253 /// intersections with the same set size, A.maximalIntersectWith(B) might not
 254 /// be equal to B.maximalIntersect(A).
 255 ConstantRange ConstantRange::maximalIntersectWith(const ConstantRange &CR) const {
 256   assert(getBitWidth() == CR.getBitWidth() &&
 257          "ConstantRange types don't agree!");
 258
 259   // Handle common cases.
 260   if (   isEmptySet() || CR.isFullSet()) return *this;
 261   if (CR.isEmptySet() ||    isFullSet()) return CR;
 262
 263   if (!isWrappedSet() && CR.isWrappedSet())
 264     return CR.maximalIntersectWith(*this);
 265
 266   if (!isWrappedSet() && !CR.isWrappedSet()) {
 267     if (Lower.ult(CR.Lower)) {
 268       if (Upper.ule(CR.Lower))
 269         return ConstantRange(getBitWidth(), false);
 270
 271       if (Upper.ult(CR.Upper))
 272         return ConstantRange(CR.Lower, Upper);
 273
 274       return CR;
 275     } else {
 276       if (Upper.ult(CR.Upper))
 277         return *this;
 278
 279       if (Lower.ult(CR.Upper))
 280         return ConstantRange(Lower, CR.Upper);
 281
 282       return ConstantRange(getBitWidth(), false);
 283     }
 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       else
 297         return CR;
 298     } else 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       else
 312         return CR;
 313     }
 314
 315     if (CR.Lower.ult(Lower))
 316       return ConstantRange(Lower, CR.Upper);
 317
 318     return CR;
 319   } else 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   else
 328     return CR;
 329 }
 330
 331
 332 /// unionWith - Return the range that results from the union of this range with
 333 /// another range.  The resultant range is guaranteed to include the elements of
 334 /// both sets, but may contain more.  For example, [3, 9) union [12,15) is
 335 /// [3, 15), which includes 9, 10, and 11, which were not included in either
 336 /// set before.
 337 ///
 338 ConstantRange ConstantRange::unionWith(const ConstantRange &CR) const {
 339   assert(getBitWidth() == CR.getBitWidth() &&
 340          "ConstantRange types don't agree!");
 341
 342   if (   isFullSet() || CR.isEmptySet()) return *this;
 343   if (CR.isFullSet() ||    isEmptySet()) return CR;
 344
 345   if (!isWrappedSet() && CR.isWrappedSet()) return CR.unionWith(*this);
 346
 347   APInt L = Lower, U = Upper;
 348
 349   if (!isWrappedSet() && !CR.isWrappedSet()) {
 350     if (CR.Lower.ult(L))
 351       L = CR.Lower;
 352
 353     if (CR.Upper.ugt(U))
 354       U = CR.Upper;
 355   }
 356
 357   if (isWrappedSet() && !CR.isWrappedSet()) {
 358     if ((CR.Lower.ult(Upper) && CR.Upper.ult(Upper)) ||
 359         (CR.Lower.ugt(Lower) && CR.Upper.ugt(Lower))) {
 360       return *this;
 361     }
 362
 363     if (CR.Lower.ule(Upper) && Lower.ule(CR.Upper)) {
 364       return ConstantRange(getBitWidth());
 365     }
 366
 367     if (CR.Lower.ule(Upper) && CR.Upper.ule(Lower)) {
 368       APInt d1 = CR.Upper - Upper, d2 = Lower - CR.Upper;
 369       if (d1.ult(d2)) {
 370         U = CR.Upper;
 371       } else {
 372         L = CR.Upper;
 373       }
 374     }
 375
 376     if (Upper.ult(CR.Lower) && CR.Upper.ult(Lower)) {
 377       APInt d1 = CR.Lower - Upper, d2 = Lower - CR.Upper;
 378       if (d1.ult(d2)) {
 379         U = CR.Lower + 1;
 380       } else {
 381         L = CR.Upper - 1;
 382       }
 383     }
 384
 385     if (Upper.ult(CR.Lower) && Lower.ult(CR.Upper)) {
 386       APInt d1 = CR.Lower - Upper, d2 = Lower - CR.Lower;
 387
 388       if (d1.ult(d2)) {
 389         U = CR.Lower + 1;
 390       } else {
 391         L = CR.Lower;
 392       }
 393     }
 394   }
 395
 396   if (isWrappedSet() && CR.isWrappedSet()) {
 397     if (Lower.ult(CR.Upper) || CR.Lower.ult(Upper))
 398       return ConstantRange(getBitWidth());
 399
 400     if (CR.Upper.ugt(U)) {
 401       U = CR.Upper;
 402     }
 403
 404     if (CR.Lower.ult(L)) {
 405       L = CR.Lower;
 406     }
 407
 408     if (L == U) return ConstantRange(getBitWidth());
 409   }
 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   unsigned SrcTySize = getBitWidth();
 420   assert(SrcTySize < DstTySize && "Not a value extension");
 421   if (isFullSet())
 422     // Change a source full set into [0, 1 << 8*numbytes)
 423     return ConstantRange(APInt(DstTySize,0), APInt(DstTySize,1).shl(SrcTySize));
 424
 425   APInt L = Lower; L.zext(DstTySize);
 426   APInt U = Upper; U.zext(DstTySize);
 427   return ConstantRange(L, U);
 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   unsigned SrcTySize = getBitWidth();
 436   assert(SrcTySize < DstTySize && "Not a value extension");
 437   if (isFullSet()) {
 438     return ConstantRange(APInt::getHighBitsSet(DstTySize,DstTySize-SrcTySize+1),
 439                          APInt::getLowBitsSet(DstTySize, SrcTySize-1));
 440   }
 441
 442   APInt L = Lower; L.sext(DstTySize);
 443   APInt U = Upper; U.sext(DstTySize);
 444   return ConstantRange(L, U);
 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   unsigned SrcTySize = getBitWidth();
 453   assert(SrcTySize > DstTySize && "Not a value truncation");
 454   APInt Size(APInt::getLowBitsSet(SrcTySize, DstTySize));
 455   if (isFullSet() || getSetSize().ugt(Size))
 456     return ConstantRange(DstTySize);
 457
 458   APInt L = Lower; L.trunc(DstTySize);
 459   APInt U = Upper; U.trunc(DstTySize);
 460   return ConstantRange(L, U);
 461 }
 462
 463 /// print - Print out the bounds to a stream...
 464 ///
 465 void ConstantRange::print(std::ostream &OS) const {
 466   OS << "[" << Lower.toStringSigned(10) << ","
 467             << Upper.toStringSigned(10) << " )";
 468 }
 469
 470 /// dump - Allow printing from a debugger easily...
 471 ///
 472 void ConstantRange::dump() const {
 473   print(cerr);
 474 }