lib/IR/ConstantRange.cpp

   1 //===- ConstantRange.cpp - ConstantRange implementation -------------------===//
   2 //
   3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
   4 // See https://llvm.org/LICENSE.txt for license information.
   5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
   6 //
   7 //===----------------------------------------------------------------------===//
   8 //
   9 // Represent a range of possible values that may occur when the program is run
  10 // for an integral value.  This keeps track of a lower and upper bound for the
  11 // constant, which MAY wrap around the end of the numeric range.  To do this, it
  12 // keeps track of a [lower, upper) bound, which specifies an interval just like
  13 // STL iterators.  When used with boolean values, the following are important
  14 // ranges (other integral ranges use min/max values for special range values):
  15 //
  16 //  [F, F) = {}     = Empty set
  17 //  [T, F) = {T}
  18 //  [F, T) = {F}
  19 //  [T, T) = {F, T} = Full set
  20 //
  21 //===----------------------------------------------------------------------===//
  22
  23 #include "llvm/ADT/APInt.h"
  24 #include "llvm/Config/llvm-config.h"
  25 #include "llvm/IR/ConstantRange.h"
  26 #include "llvm/IR/Constants.h"
  27 #include "llvm/IR/InstrTypes.h"
  28 #include "llvm/IR/Instruction.h"
  29 #include "llvm/IR/Metadata.h"
  30 #include "llvm/IR/Operator.h"
  31 #include "llvm/Support/Compiler.h"
  32 #include "llvm/Support/Debug.h"
  33 #include "llvm/Support/ErrorHandling.h"
  34 #include "llvm/Support/KnownBits.h"
  35 #include "llvm/Support/raw_ostream.h"
  36 #include <algorithm>
  37 #include <cassert>
  38 #include <cstdint>
  39
  40 using namespace llvm;
  41
  42 ConstantRange::ConstantRange(uint32_t BitWidth, bool Full)
  43     : Lower(Full ? APInt::getMaxValue(BitWidth) : APInt::getMinValue(BitWidth)),
  44       Upper(Lower) {}
  45
  46 ConstantRange::ConstantRange(APInt V)
  47     : Lower(std::move(V)), Upper(Lower + 1) {}
  48
  49 ConstantRange::ConstantRange(APInt L, APInt U)
  50     : Lower(std::move(L)), Upper(std::move(U)) {
  51   assert(Lower.getBitWidth() == Upper.getBitWidth() &&
  52          "ConstantRange with unequal bit widths");
  53   assert((Lower != Upper || (Lower.isMaxValue() || Lower.isMinValue())) &&
  54          "Lower == Upper, but they aren't min or max value!");
  55 }
  56
  57 ConstantRange ConstantRange::fromKnownBits(const KnownBits &Known,
  58                                            bool IsSigned) {
  59   assert(!Known.hasConflict() && "Expected valid KnownBits");
  60
  61   if (Known.isUnknown())
  62     return getFull(Known.getBitWidth());
  63
  64   // For unsigned ranges, or signed ranges with known sign bit, create a simple
  65   // range between the smallest and largest possible value.
  66   if (!IsSigned || Known.isNegative() || Known.isNonNegative())
  67     return ConstantRange(Known.One, ~Known.Zero + 1);
  68
  69   // If we don't know the sign bit, pick the lower bound as a negative number
  70   // and the upper bound as a non-negative one.
  71   APInt Lower = Known.One, Upper = ~Known.Zero;
  72   Lower.setSignBit();
  73   Upper.clearSignBit();
  74   return ConstantRange(Lower, Upper + 1);
  75 }
  76
  77 ConstantRange ConstantRange::makeAllowedICmpRegion(CmpInst::Predicate Pred,
  78                                                    const ConstantRange &CR) {
  79   if (CR.isEmptySet())
  80     return CR;
  81
  82   uint32_t W = CR.getBitWidth();
  83   switch (Pred) {
  84   default:
  85     llvm_unreachable("Invalid ICmp predicate to makeAllowedICmpRegion()");
  86   case CmpInst::ICMP_EQ:
  87     return CR;
  88   case CmpInst::ICMP_NE:
  89     if (CR.isSingleElement())
  90       return ConstantRange(CR.getUpper(), CR.getLower());
  91     return getFull(W);
  92   case CmpInst::ICMP_ULT: {
  93     APInt UMax(CR.getUnsignedMax());
  94     if (UMax.isMinValue())
  95       return getEmpty(W);
  96     return ConstantRange(APInt::getMinValue(W), std::move(UMax));
  97   }
  98   case CmpInst::ICMP_SLT: {
  99     APInt SMax(CR.getSignedMax());
 100     if (SMax.isMinSignedValue())
 101       return getEmpty(W);
 102     return ConstantRange(APInt::getSignedMinValue(W), std::move(SMax));
 103   }
 104   case CmpInst::ICMP_ULE:
 105     return getNonEmpty(APInt::getMinValue(W), CR.getUnsignedMax() + 1);
 106   case CmpInst::ICMP_SLE:
 107     return getNonEmpty(APInt::getSignedMinValue(W), CR.getSignedMax() + 1);
 108   case CmpInst::ICMP_UGT: {
 109     APInt UMin(CR.getUnsignedMin());
 110     if (UMin.isMaxValue())
 111       return getEmpty(W);
 112     return ConstantRange(std::move(UMin) + 1, APInt::getNullValue(W));
 113   }
 114   case CmpInst::ICMP_SGT: {
 115     APInt SMin(CR.getSignedMin());
 116     if (SMin.isMaxSignedValue())
 117       return getEmpty(W);
 118     return ConstantRange(std::move(SMin) + 1, APInt::getSignedMinValue(W));
 119   }
 120   case CmpInst::ICMP_UGE:
 121     return getNonEmpty(CR.getUnsignedMin(), APInt::getNullValue(W));
 122   case CmpInst::ICMP_SGE:
 123     return getNonEmpty(CR.getSignedMin(), APInt::getSignedMinValue(W));
 124   }
 125 }
 126
 127 ConstantRange ConstantRange::makeSatisfyingICmpRegion(CmpInst::Predicate Pred,
 128                                                       const ConstantRange &CR) {
 129   // Follows from De-Morgan's laws:
 130   //
 131   // ~(~A union ~B) == A intersect B.
 132   //
 133   return makeAllowedICmpRegion(CmpInst::getInversePredicate(Pred), CR)
 134       .inverse();
 135 }
 136
 137 ConstantRange ConstantRange::makeExactICmpRegion(CmpInst::Predicate Pred,
 138                                                  const APInt &C) {
 139   // Computes the exact range that is equal to both the constant ranges returned
 140   // by makeAllowedICmpRegion and makeSatisfyingICmpRegion. This is always true
 141   // when RHS is a singleton such as an APInt and so the assert is valid.
 142   // However for non-singleton RHS, for example ult [2,5) makeAllowedICmpRegion
 143   // returns [0,4) but makeSatisfyICmpRegion returns [0,2).
 144   //
 145   assert(makeAllowedICmpRegion(Pred, C) == makeSatisfyingICmpRegion(Pred, C));
 146   return makeAllowedICmpRegion(Pred, C);
 147 }
 148
 149 bool ConstantRange::getEquivalentICmp(CmpInst::Predicate &Pred,
 150                                       APInt &RHS) const {
 151   bool Success = false;
 152
 153   if (isFullSet() || isEmptySet()) {
 154     Pred = isEmptySet() ? CmpInst::ICMP_ULT : CmpInst::ICMP_UGE;
 155     RHS = APInt(getBitWidth(), 0);
 156     Success = true;
 157   } else if (auto *OnlyElt = getSingleElement()) {
 158     Pred = CmpInst::ICMP_EQ;
 159     RHS = *OnlyElt;
 160     Success = true;
 161   } else if (auto *OnlyMissingElt = getSingleMissingElement()) {
 162     Pred = CmpInst::ICMP_NE;
 163     RHS = *OnlyMissingElt;
 164     Success = true;
 165   } else if (getLower().isMinSignedValue() || getLower().isMinValue()) {
 166     Pred =
 167         getLower().isMinSignedValue() ? CmpInst::ICMP_SLT : CmpInst::ICMP_ULT;
 168     RHS = getUpper();
 169     Success = true;
 170   } else if (getUpper().isMinSignedValue() || getUpper().isMinValue()) {
 171     Pred =
 172         getUpper().isMinSignedValue() ? CmpInst::ICMP_SGE : CmpInst::ICMP_UGE;
 173     RHS = getLower();
 174     Success = true;
 175   }
 176
 177   assert((!Success || ConstantRange::makeExactICmpRegion(Pred, RHS) == *this) &&
 178          "Bad result!");
 179
 180   return Success;
 181 }
 182
 183 /// Exact mul nuw region for single element RHS.
 184 static ConstantRange makeExactMulNUWRegion(const APInt &V) {
 185   unsigned BitWidth = V.getBitWidth();
 186   if (V == 0)
 187     return ConstantRange::getFull(V.getBitWidth());
 188
 189   return ConstantRange::getNonEmpty(
 190       APIntOps::RoundingUDiv(APInt::getMinValue(BitWidth), V,
 191                              APInt::Rounding::UP),
 192       APIntOps::RoundingUDiv(APInt::getMaxValue(BitWidth), V,
 193                              APInt::Rounding::DOWN) + 1);
 194 }
 195
 196 /// Exact mul nsw region for single element RHS.
 197 static ConstantRange makeExactMulNSWRegion(const APInt &V) {
 198   // Handle special case for 0, -1 and 1. See the last for reason why we
 199   // specialize -1 and 1.
 200   unsigned BitWidth = V.getBitWidth();
 201   if (V == 0 || V.isOneValue())
 202     return ConstantRange::getFull(BitWidth);
 203
 204   APInt MinValue = APInt::getSignedMinValue(BitWidth);
 205   APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
 206   // e.g. Returning [-127, 127], represented as [-127, -128).
 207   if (V.isAllOnesValue())
 208     return ConstantRange(-MaxValue, MinValue);
 209
 210   APInt Lower, Upper;
 211   if (V.isNegative()) {
 212     Lower = APIntOps::RoundingSDiv(MaxValue, V, APInt::Rounding::UP);
 213     Upper = APIntOps::RoundingSDiv(MinValue, V, APInt::Rounding::DOWN);
 214   } else {
 215     Lower = APIntOps::RoundingSDiv(MinValue, V, APInt::Rounding::UP);
 216     Upper = APIntOps::RoundingSDiv(MaxValue, V, APInt::Rounding::DOWN);
 217   }
 218   // ConstantRange ctor take a half inclusive interval [Lower, Upper + 1).
 219   // Upper + 1 is guaranteed not to overflow, because |divisor| > 1. 0, -1,
 220   // and 1 are already handled as special cases.
 221   return ConstantRange(Lower, Upper + 1);
 222 }
 223
 224 ConstantRange
 225 ConstantRange::makeGuaranteedNoWrapRegion(Instruction::BinaryOps BinOp,
 226                                           const ConstantRange &Other,
 227                                           unsigned NoWrapKind) {
 228   using OBO = OverflowingBinaryOperator;
 229
 230   assert(Instruction::isBinaryOp(BinOp) && "Binary operators only!");
 231
 232   assert((NoWrapKind == OBO::NoSignedWrap ||
 233           NoWrapKind == OBO::NoUnsignedWrap) &&
 234          "NoWrapKind invalid!");
 235
 236   bool Unsigned = NoWrapKind == OBO::NoUnsignedWrap;
 237   unsigned BitWidth = Other.getBitWidth();
 238
 239   switch (BinOp) {
 240   default:
 241     llvm_unreachable("Unsupported binary op");
 242
 243   case Instruction::Add: {
 244     if (Unsigned)
 245       return getNonEmpty(APInt::getNullValue(BitWidth),
 246                          -Other.getUnsignedMax());
 247
 248     APInt SignedMinVal = APInt::getSignedMinValue(BitWidth);
 249     APInt SMin = Other.getSignedMin(), SMax = Other.getSignedMax();
 250     return getNonEmpty(
 251         SMin.isNegative() ? SignedMinVal - SMin : SignedMinVal,
 252         SMax.isStrictlyPositive() ? SignedMinVal - SMax : SignedMinVal);
 253   }
 254
 255   case Instruction::Sub: {
 256     if (Unsigned)
 257       return getNonEmpty(Other.getUnsignedMax(), APInt::getMinValue(BitWidth));
 258
 259     APInt SignedMinVal = APInt::getSignedMinValue(BitWidth);
 260     APInt SMin = Other.getSignedMin(), SMax = Other.getSignedMax();
 261     return getNonEmpty(
 262         SMax.isStrictlyPositive() ? SignedMinVal + SMax : SignedMinVal,
 263         SMin.isNegative() ? SignedMinVal + SMin : SignedMinVal);
 264   }
 265
 266   case Instruction::Mul:
 267     if (Unsigned)
 268       return makeExactMulNUWRegion(Other.getUnsignedMax());
 269
 270     return makeExactMulNSWRegion(Other.getSignedMin())
 271         .intersectWith(makeExactMulNSWRegion(Other.getSignedMax()));
 272
 273   case Instruction::Shl: {
 274     // For given range of shift amounts, if we ignore all illegal shift amounts
 275     // (that always produce poison), what shift amount range is left?
 276     ConstantRange ShAmt = Other.intersectWith(
 277         ConstantRange(APInt(BitWidth, 0), APInt(BitWidth, (BitWidth - 1) + 1)));
 278     if (ShAmt.isEmptySet()) {
 279       // If the entire range of shift amounts is already poison-producing,
 280       // then we can freely add more poison-producing flags ontop of that.
 281       return getFull(BitWidth);
 282     }
 283     // There are some legal shift amounts, we can compute conservatively-correct
 284     // range of no-wrap inputs. Note that by now we have clamped the ShAmtUMax
 285     // to be at most bitwidth-1, which results in most conservative range.
 286     APInt ShAmtUMax = ShAmt.getUnsignedMax();
 287     if (Unsigned)
 288       return getNonEmpty(APInt::getNullValue(BitWidth),
 289                          APInt::getMaxValue(BitWidth).lshr(ShAmtUMax) + 1);
 290     return getNonEmpty(APInt::getSignedMinValue(BitWidth).ashr(ShAmtUMax),
 291                        APInt::getSignedMaxValue(BitWidth).ashr(ShAmtUMax) + 1);
 292   }
 293   }
 294 }
 295
 296 ConstantRange ConstantRange::makeExactNoWrapRegion(Instruction::BinaryOps BinOp,
 297                                                    const APInt &Other,
 298                                                    unsigned NoWrapKind) {
 299   // makeGuaranteedNoWrapRegion() is exact for single-element ranges, as
 300   // "for all" and "for any" coincide in this case.
 301   return makeGuaranteedNoWrapRegion(BinOp, ConstantRange(Other), NoWrapKind);
 302 }
 303
 304 bool ConstantRange::isFullSet() const {
 305   return Lower == Upper && Lower.isMaxValue();
 306 }
 307
 308 bool ConstantRange::isEmptySet() const {
 309   return Lower == Upper && Lower.isMinValue();
 310 }
 311
 312 bool ConstantRange::isWrappedSet() const {
 313   return Lower.ugt(Upper) && !Upper.isNullValue();
 314 }
 315
 316 bool ConstantRange::isUpperWrapped() const {
 317   return Lower.ugt(Upper);
 318 }
 319
 320 bool ConstantRange::isSignWrappedSet() const {
 321   return Lower.sgt(Upper) && !Upper.isMinSignedValue();
 322 }
 323
 324 bool ConstantRange::isUpperSignWrapped() const {
 325   return Lower.sgt(Upper);
 326 }
 327
 328 bool
 329 ConstantRange::isSizeStrictlySmallerThan(const ConstantRange &Other) const {
 330   assert(getBitWidth() == Other.getBitWidth());
 331   if (isFullSet())
 332     return false;
 333   if (Other.isFullSet())
 334     return true;
 335   return (Upper - Lower).ult(Other.Upper - Other.Lower);
 336 }
 337
 338 bool
 339 ConstantRange::isSizeLargerThan(uint64_t MaxSize) const {
 340   assert(MaxSize && "MaxSize can't be 0.");
 341   // If this a full set, we need special handling to avoid needing an extra bit
 342   // to represent the size.
 343   if (isFullSet())
 344     return APInt::getMaxValue(getBitWidth()).ugt(MaxSize - 1);
 345
 346   return (Upper - Lower).ugt(MaxSize);
 347 }
 348
 349 bool ConstantRange::isAllNegative() const {
 350   // Empty set is all negative, full set is not.
 351   if (isEmptySet())
 352     return true;
 353   if (isFullSet())
 354     return false;
 355
 356   return !isUpperSignWrapped() && !Upper.isStrictlyPositive();
 357 }
 358
 359 bool ConstantRange::isAllNonNegative() const {
 360   // Empty and full set are automatically treated correctly.
 361   return !isSignWrappedSet() && Lower.isNonNegative();
 362 }
 363
 364 APInt ConstantRange::getUnsignedMax() const {
 365   if (isFullSet() || isUpperWrapped())
 366     return APInt::getMaxValue(getBitWidth());
 367   return getUpper() - 1;
 368 }
 369
 370 APInt ConstantRange::getUnsignedMin() const {
 371   if (isFullSet() || isWrappedSet())
 372     return APInt::getMinValue(getBitWidth());
 373   return getLower();
 374 }
 375
 376 APInt ConstantRange::getSignedMax() const {
 377   if (isFullSet() || isUpperSignWrapped())
 378     return APInt::getSignedMaxValue(getBitWidth());
 379   return getUpper() - 1;
 380 }
 381
 382 APInt ConstantRange::getSignedMin() const {
 383   if (isFullSet() || isSignWrappedSet())
 384     return APInt::getSignedMinValue(getBitWidth());
 385   return getLower();
 386 }
 387
 388 bool ConstantRange::contains(const APInt &V) const {
 389   if (Lower == Upper)
 390     return isFullSet();
 391
 392   if (!isUpperWrapped())
 393     return Lower.ule(V) && V.ult(Upper);
 394   return Lower.ule(V) || V.ult(Upper);
 395 }
 396
 397 bool ConstantRange::contains(const ConstantRange &Other) const {
 398   if (isFullSet() || Other.isEmptySet()) return true;
 399   if (isEmptySet() || Other.isFullSet()) return false;
 400
 401   if (!isUpperWrapped()) {
 402     if (Other.isUpperWrapped())
 403       return false;
 404
 405     return Lower.ule(Other.getLower()) && Other.getUpper().ule(Upper);
 406   }
 407
 408   if (!Other.isUpperWrapped())
 409     return Other.getUpper().ule(Upper) ||
 410            Lower.ule(Other.getLower());
 411
 412   return Other.getUpper().ule(Upper) && Lower.ule(Other.getLower());
 413 }
 414
 415 ConstantRange ConstantRange::subtract(const APInt &Val) const {
 416   assert(Val.getBitWidth() == getBitWidth() && "Wrong bit width");
 417   // If the set is empty or full, don't modify the endpoints.
 418   if (Lower == Upper)
 419     return *this;
 420   return ConstantRange(Lower - Val, Upper - Val);
 421 }
 422
 423 ConstantRange ConstantRange::difference(const ConstantRange &CR) const {
 424   return intersectWith(CR.inverse());
 425 }
 426
 427 static ConstantRange getPreferredRange(
 428     const ConstantRange &CR1, const ConstantRange &CR2,
 429     ConstantRange::PreferredRangeType Type) {
 430   if (Type == ConstantRange::Unsigned) {
 431     if (!CR1.isWrappedSet() && CR2.isWrappedSet())
 432       return CR1;
 433     if (CR1.isWrappedSet() && !CR2.isWrappedSet())
 434       return CR2;
 435   } else if (Type == ConstantRange::Signed) {
 436     if (!CR1.isSignWrappedSet() && CR2.isSignWrappedSet())
 437       return CR1;
 438     if (CR1.isSignWrappedSet() && !CR2.isSignWrappedSet())
 439       return CR2;
 440   }
 441
 442   if (CR1.isSizeStrictlySmallerThan(CR2))
 443     return CR1;
 444   return CR2;
 445 }
 446
 447 ConstantRange ConstantRange::intersectWith(const ConstantRange &CR,
 448                                            PreferredRangeType Type) const {
 449   assert(getBitWidth() == CR.getBitWidth() &&
 450          "ConstantRange types don't agree!");
 451
 452   // Handle common cases.
 453   if (   isEmptySet() || CR.isFullSet()) return *this;
 454   if (CR.isEmptySet() ||    isFullSet()) return CR;
 455
 456   if (!isUpperWrapped() && CR.isUpperWrapped())
 457     return CR.intersectWith(*this, Type);
 458
 459   if (!isUpperWrapped() && !CR.isUpperWrapped()) {
 460     if (Lower.ult(CR.Lower)) {
 461       // L---U       : this
 462       //       L---U : CR
 463       if (Upper.ule(CR.Lower))
 464         return getEmpty();
 465
 466       // L---U       : this
 467       //   L---U     : CR
 468       if (Upper.ult(CR.Upper))
 469         return ConstantRange(CR.Lower, Upper);
 470
 471       // L-------U   : this
 472       //   L---U     : CR
 473       return CR;
 474     }
 475     //   L---U     : this
 476     // L-------U   : CR
 477     if (Upper.ult(CR.Upper))
 478       return *this;
 479
 480     //   L-----U   : this
 481     // L-----U     : CR
 482     if (Lower.ult(CR.Upper))
 483       return ConstantRange(Lower, CR.Upper);
 484
 485     //       L---U : this
 486     // L---U       : CR
 487     return getEmpty();
 488   }
 489
 490   if (isUpperWrapped() && !CR.isUpperWrapped()) {
 491     if (CR.Lower.ult(Upper)) {
 492       // ------U   L--- : this
 493       //  L--U          : CR
 494       if (CR.Upper.ult(Upper))
 495         return CR;
 496
 497       // ------U   L--- : this
 498       //  L------U      : CR
 499       if (CR.Upper.ule(Lower))
 500         return ConstantRange(CR.Lower, Upper);
 501
 502       // ------U   L--- : this
 503       //  L----------U  : CR
 504       return getPreferredRange(*this, CR, Type);
 505     }
 506     if (CR.Lower.ult(Lower)) {
 507       // --U      L---- : this
 508       //     L--U       : CR
 509       if (CR.Upper.ule(Lower))
 510         return getEmpty();
 511
 512       // --U      L---- : this
 513       //     L------U   : CR
 514       return ConstantRange(Lower, CR.Upper);
 515     }
 516
 517     // --U  L------ : this
 518     //        L--U  : CR
 519     return CR;
 520   }
 521
 522   if (CR.Upper.ult(Upper)) {
 523     // ------U L-- : this
 524     // --U L------ : CR
 525     if (CR.Lower.ult(Upper))
 526       return getPreferredRange(*this, CR, Type);
 527
 528     // ----U   L-- : this
 529     // --U   L---- : CR
 530     if (CR.Lower.ult(Lower))
 531       return ConstantRange(Lower, CR.Upper);
 532
 533     // ----U L---- : this
 534     // --U     L-- : CR
 535     return CR;
 536   }
 537   if (CR.Upper.ule(Lower)) {
 538     // --U     L-- : this
 539     // ----U L---- : CR
 540     if (CR.Lower.ult(Lower))
 541       return *this;
 542
 543     // --U   L---- : this
 544     // ----U   L-- : CR
 545     return ConstantRange(CR.Lower, Upper);
 546   }
 547
 548   // --U L------ : this
 549   // ------U L-- : CR
 550   return getPreferredRange(*this, CR, Type);
 551 }
 552
 553 ConstantRange ConstantRange::unionWith(const ConstantRange &CR,
 554                                        PreferredRangeType Type) const {
 555   assert(getBitWidth() == CR.getBitWidth() &&
 556          "ConstantRange types don't agree!");
 557
 558   if (   isFullSet() || CR.isEmptySet()) return *this;
 559   if (CR.isFullSet() ||    isEmptySet()) return CR;
 560
 561   if (!isUpperWrapped() && CR.isUpperWrapped())
 562     return CR.unionWith(*this, Type);
 563
 564   if (!isUpperWrapped() && !CR.isUpperWrapped()) {
 565     //        L---U  and  L---U        : this
 566     //  L---U                   L---U  : CR
 567     // result in one of
 568     //  L---------U
 569     // -----U L-----
 570     if (CR.Upper.ult(Lower) || Upper.ult(CR.Lower))
 571       return getPreferredRange(
 572           ConstantRange(Lower, CR.Upper), ConstantRange(CR.Lower, Upper), Type);
 573
 574     APInt L = CR.Lower.ult(Lower) ? CR.Lower : Lower;
 575     APInt U = (CR.Upper - 1).ugt(Upper - 1) ? CR.Upper : Upper;
 576
 577     if (L.isNullValue() && U.isNullValue())
 578       return getFull();
 579
 580     return ConstantRange(std::move(L), std::move(U));
 581   }
 582
 583   if (!CR.isUpperWrapped()) {
 584     // ------U   L-----  and  ------U   L----- : this
 585     //   L--U                            L--U  : CR
 586     if (CR.Upper.ule(Upper) || CR.Lower.uge(Lower))
 587       return *this;
 588
 589     // ------U   L----- : this
 590     //    L---------U   : CR
 591     if (CR.Lower.ule(Upper) && Lower.ule(CR.Upper))
 592       return getFull();
 593
 594     // ----U       L---- : this
 595     //       L---U       : CR
 596     // results in one of
 597     // ----------U L----
 598     // ----U L----------
 599     if (Upper.ult(CR.Lower) && CR.Upper.ult(Lower))
 600       return getPreferredRange(
 601           ConstantRange(Lower, CR.Upper), ConstantRange(CR.Lower, Upper), Type);
 602
 603     // ----U     L----- : this
 604     //        L----U    : CR
 605     if (Upper.ult(CR.Lower) && Lower.ule(CR.Upper))
 606       return ConstantRange(CR.Lower, Upper);
 607
 608     // ------U    L---- : this
 609     //    L-----U       : CR
 610     assert(CR.Lower.ule(Upper) && CR.Upper.ult(Lower) &&
 611            "ConstantRange::unionWith missed a case with one range wrapped");
 612     return ConstantRange(Lower, CR.Upper);
 613   }
 614
 615   // ------U    L----  and  ------U    L---- : this
 616   // -U  L-----------  and  ------------U  L : CR
 617   if (CR.Lower.ule(Upper) || Lower.ule(CR.Upper))
 618     return getFull();
 619
 620   APInt L = CR.Lower.ult(Lower) ? CR.Lower : Lower;
 621   APInt U = CR.Upper.ugt(Upper) ? CR.Upper : Upper;
 622
 623   return ConstantRange(std::move(L), std::move(U));
 624 }
 625
 626 ConstantRange ConstantRange::castOp(Instruction::CastOps CastOp,
 627                                     uint32_t ResultBitWidth) const {
 628   switch (CastOp) {
 629   default:
 630     llvm_unreachable("unsupported cast type");
 631   case Instruction::Trunc:
 632     return truncate(ResultBitWidth);
 633   case Instruction::SExt:
 634     return signExtend(ResultBitWidth);
 635   case Instruction::ZExt:
 636     return zeroExtend(ResultBitWidth);
 637   case Instruction::BitCast:
 638     return *this;
 639   case Instruction::FPToUI:
 640   case Instruction::FPToSI:
 641     if (getBitWidth() == ResultBitWidth)
 642       return *this;
 643     else
 644       return getFull();
 645   case Instruction::UIToFP: {
 646     // TODO: use input range if available
 647     auto BW = getBitWidth();
 648     APInt Min = APInt::getMinValue(BW).zextOrSelf(ResultBitWidth);
 649     APInt Max = APInt::getMaxValue(BW).zextOrSelf(ResultBitWidth);
 650     return ConstantRange(std::move(Min), std::move(Max));
 651   }
 652   case Instruction::SIToFP: {
 653     // TODO: use input range if available
 654     auto BW = getBitWidth();
 655     APInt SMin = APInt::getSignedMinValue(BW).sextOrSelf(ResultBitWidth);
 656     APInt SMax = APInt::getSignedMaxValue(BW).sextOrSelf(ResultBitWidth);
 657     return ConstantRange(std::move(SMin), std::move(SMax));
 658   }
 659   case Instruction::FPTrunc:
 660   case Instruction::FPExt:
 661   case Instruction::IntToPtr:
 662   case Instruction::PtrToInt:
 663   case Instruction::AddrSpaceCast:
 664     // Conservatively return getFull set.
 665     return getFull();
 666   };
 667 }
 668
 669 ConstantRange ConstantRange::zeroExtend(uint32_t DstTySize) const {
 670   if (isEmptySet()) return getEmpty(DstTySize);
 671
 672   unsigned SrcTySize = getBitWidth();
 673   assert(SrcTySize < DstTySize && "Not a value extension");
 674   if (isFullSet() || isUpperWrapped()) {
 675     // Change into [0, 1 << src bit width)
 676     APInt LowerExt(DstTySize, 0);
 677     if (!Upper) // special case: [X, 0) -- not really wrapping around
 678       LowerExt = Lower.zext(DstTySize);
 679     return ConstantRange(std::move(LowerExt),
 680                          APInt::getOneBitSet(DstTySize, SrcTySize));
 681   }
 682
 683   return ConstantRange(Lower.zext(DstTySize), Upper.zext(DstTySize));
 684 }
 685
 686 ConstantRange ConstantRange::signExtend(uint32_t DstTySize) const {
 687   if (isEmptySet()) return getEmpty(DstTySize);
 688
 689   unsigned SrcTySize = getBitWidth();
 690   assert(SrcTySize < DstTySize && "Not a value extension");
 691
 692   // special case: [X, INT_MIN) -- not really wrapping around
 693   if (Upper.isMinSignedValue())
 694     return ConstantRange(Lower.sext(DstTySize), Upper.zext(DstTySize));
 695
 696   if (isFullSet() || isSignWrappedSet()) {
 697     return ConstantRange(APInt::getHighBitsSet(DstTySize,DstTySize-SrcTySize+1),
 698                          APInt::getLowBitsSet(DstTySize, SrcTySize-1) + 1);
 699   }
 700
 701   return ConstantRange(Lower.sext(DstTySize), Upper.sext(DstTySize));
 702 }
 703
 704 ConstantRange ConstantRange::truncate(uint32_t DstTySize) const {
 705   assert(getBitWidth() > DstTySize && "Not a value truncation");
 706   if (isEmptySet())
 707     return getEmpty(DstTySize);
 708   if (isFullSet())
 709     return getFull(DstTySize);
 710
 711   APInt LowerDiv(Lower), UpperDiv(Upper);
 712   ConstantRange Union(DstTySize, /*isFullSet=*/false);
 713
 714   // Analyze wrapped sets in their two parts: [0, Upper) \/ [Lower, MaxValue]
 715   // We use the non-wrapped set code to analyze the [Lower, MaxValue) part, and
 716   // then we do the union with [MaxValue, Upper)
 717   if (isUpperWrapped()) {
 718     // If Upper is greater than or equal to MaxValue(DstTy), it covers the whole
 719     // truncated range.
 720     if (Upper.getActiveBits() > DstTySize ||
 721         Upper.countTrailingOnes() == DstTySize)
 722       return getFull(DstTySize);
 723
 724     Union = ConstantRange(APInt::getMaxValue(DstTySize),Upper.trunc(DstTySize));
 725     UpperDiv.setAllBits();
 726
 727     // Union covers the MaxValue case, so return if the remaining range is just
 728     // MaxValue(DstTy).
 729     if (LowerDiv == UpperDiv)
 730       return Union;
 731   }
 732
 733   // Chop off the most significant bits that are past the destination bitwidth.
 734   if (LowerDiv.getActiveBits() > DstTySize) {
 735     // Mask to just the signficant bits and subtract from LowerDiv/UpperDiv.
 736     APInt Adjust = LowerDiv & APInt::getBitsSetFrom(getBitWidth(), DstTySize);
 737     LowerDiv -= Adjust;
 738     UpperDiv -= Adjust;
 739   }
 740
 741   unsigned UpperDivWidth = UpperDiv.getActiveBits();
 742   if (UpperDivWidth <= DstTySize)
 743     return ConstantRange(LowerDiv.trunc(DstTySize),
 744                          UpperDiv.trunc(DstTySize)).unionWith(Union);
 745
 746   // The truncated value wraps around. Check if we can do better than fullset.
 747   if (UpperDivWidth == DstTySize + 1) {
 748     // Clear the MSB so that UpperDiv wraps around.
 749     UpperDiv.clearBit(DstTySize);
 750     if (UpperDiv.ult(LowerDiv))
 751       return ConstantRange(LowerDiv.trunc(DstTySize),
 752                            UpperDiv.trunc(DstTySize)).unionWith(Union);
 753   }
 754
 755   return getFull(DstTySize);
 756 }
 757
 758 ConstantRange ConstantRange::zextOrTrunc(uint32_t DstTySize) const {
 759   unsigned SrcTySize = getBitWidth();
 760   if (SrcTySize > DstTySize)
 761     return truncate(DstTySize);
 762   if (SrcTySize < DstTySize)
 763     return zeroExtend(DstTySize);
 764   return *this;
 765 }
 766
 767 ConstantRange ConstantRange::sextOrTrunc(uint32_t DstTySize) const {
 768   unsigned SrcTySize = getBitWidth();
 769   if (SrcTySize > DstTySize)
 770     return truncate(DstTySize);
 771   if (SrcTySize < DstTySize)
 772     return signExtend(DstTySize);
 773   return *this;
 774 }
 775
 776 ConstantRange ConstantRange::binaryOp(Instruction::BinaryOps BinOp,
 777                                       const ConstantRange &Other) const {
 778   assert(Instruction::isBinaryOp(BinOp) && "Binary operators only!");
 779
 780   switch (BinOp) {
 781   case Instruction::Add:
 782     return add(Other);
 783   case Instruction::Sub:
 784     return sub(Other);
 785   case Instruction::Mul:
 786     return multiply(Other);
 787   case Instruction::UDiv:
 788     return udiv(Other);
 789   case Instruction::SDiv:
 790     return sdiv(Other);
 791   case Instruction::URem:
 792     return urem(Other);
 793   case Instruction::SRem:
 794     return srem(Other);
 795   case Instruction::Shl:
 796     return shl(Other);
 797   case Instruction::LShr:
 798     return lshr(Other);
 799   case Instruction::AShr:
 800     return ashr(Other);
 801   case Instruction::And:
 802     return binaryAnd(Other);
 803   case Instruction::Or:
 804     return binaryOr(Other);
 805   // Note: floating point operations applied to abstract ranges are just
 806   // ideal integer operations with a lossy representation
 807   case Instruction::FAdd:
 808     return add(Other);
 809   case Instruction::FSub:
 810     return sub(Other);
 811   case Instruction::FMul:
 812     return multiply(Other);
 813   default:
 814     // Conservatively return getFull set.
 815     return getFull();
 816   }
 817 }
 818
 819 ConstantRange
 820 ConstantRange::add(const ConstantRange &Other) const {
 821   if (isEmptySet() || Other.isEmptySet())
 822     return getEmpty();
 823   if (isFullSet() || Other.isFullSet())
 824     return getFull();
 825
 826   APInt NewLower = getLower() + Other.getLower();
 827   APInt NewUpper = getUpper() + Other.getUpper() - 1;
 828   if (NewLower == NewUpper)
 829     return getFull();
 830
 831   ConstantRange X = ConstantRange(std::move(NewLower), std::move(NewUpper));
 832   if (X.isSizeStrictlySmallerThan(*this) ||
 833       X.isSizeStrictlySmallerThan(Other))
 834     // We've wrapped, therefore, full set.
 835     return getFull();
 836   return X;
 837 }
 838
 839 ConstantRange ConstantRange::addWithNoWrap(const ConstantRange &Other,
 840                                            unsigned NoWrapKind,
 841                                            PreferredRangeType RangeType) const {
 842   // Calculate the range for "X + Y" which is guaranteed not to wrap(overflow).
 843   // (X is from this, and Y is from Other)
 844   if (isEmptySet() || Other.isEmptySet())
 845     return getEmpty();
 846   if (isFullSet() && Other.isFullSet())
 847     return getFull();
 848
 849   using OBO = OverflowingBinaryOperator;
 850   ConstantRange Result = add(Other);
 851
 852   auto addWithNoUnsignedWrap = [this](const ConstantRange &Other) {
 853     APInt LMin = getUnsignedMin(), LMax = getUnsignedMax();
 854     APInt RMin = Other.getUnsignedMin(), RMax = Other.getUnsignedMax();
 855     bool Overflow;
 856     APInt NewMin = LMin.uadd_ov(RMin, Overflow);
 857     if (Overflow)
 858       return getEmpty();
 859     APInt NewMax = LMax.uadd_sat(RMax);
 860     return getNonEmpty(std::move(NewMin), std::move(NewMax) + 1);
 861   };
 862
 863   auto addWithNoSignedWrap = [this](const ConstantRange &Other) {
 864     APInt LMin = getSignedMin(), LMax = getSignedMax();
 865     APInt RMin = Other.getSignedMin(), RMax = Other.getSignedMax();
 866     if (LMin.isNonNegative()) {
 867       bool Overflow;
 868       APInt Temp = LMin.sadd_ov(RMin, Overflow);
 869       if (Overflow)
 870         return getEmpty();
 871     }
 872     if (LMax.isNegative()) {
 873       bool Overflow;
 874       APInt Temp = LMax.sadd_ov(RMax, Overflow);
 875       if (Overflow)
 876         return getEmpty();
 877     }
 878     APInt NewMin = LMin.sadd_sat(RMin);
 879     APInt NewMax = LMax.sadd_sat(RMax);
 880     return getNonEmpty(std::move(NewMin), std::move(NewMax) + 1);
 881   };
 882
 883   if (NoWrapKind & OBO::NoSignedWrap)
 884     Result = Result.intersectWith(addWithNoSignedWrap(Other), RangeType);
 885   if (NoWrapKind & OBO::NoUnsignedWrap)
 886     Result = Result.intersectWith(addWithNoUnsignedWrap(Other), RangeType);
 887   return Result;
 888 }
 889
 890 ConstantRange
 891 ConstantRange::sub(const ConstantRange &Other) const {
 892   if (isEmptySet() || Other.isEmptySet())
 893     return getEmpty();
 894   if (isFullSet() || Other.isFullSet())
 895     return getFull();
 896
 897   APInt NewLower = getLower() - Other.getUpper() + 1;
 898   APInt NewUpper = getUpper() - Other.getLower();
 899   if (NewLower == NewUpper)
 900     return getFull();
 901
 902   ConstantRange X = ConstantRange(std::move(NewLower), std::move(NewUpper));
 903   if (X.isSizeStrictlySmallerThan(*this) ||
 904       X.isSizeStrictlySmallerThan(Other))
 905     // We've wrapped, therefore, full set.
 906     return getFull();
 907   return X;
 908 }
 909
 910 ConstantRange
 911 ConstantRange::multiply(const ConstantRange &Other) const {
 912   // TODO: If either operand is a single element and the multiply is known to
 913   // be non-wrapping, round the result min and max value to the appropriate
 914   // multiple of that element. If wrapping is possible, at least adjust the
 915   // range according to the greatest power-of-two factor of the single element.
 916
 917   if (isEmptySet() || Other.isEmptySet())
 918     return getEmpty();
 919
 920   // Multiplication is signedness-independent. However different ranges can be
 921   // obtained depending on how the input ranges are treated. These different
 922   // ranges are all conservatively correct, but one might be better than the
 923   // other. We calculate two ranges; one treating the inputs as unsigned
 924   // and the other signed, then return the smallest of these ranges.
 925
 926   // Unsigned range first.
 927   APInt this_min = getUnsignedMin().zext(getBitWidth() * 2);
 928   APInt this_max = getUnsignedMax().zext(getBitWidth() * 2);
 929   APInt Other_min = Other.getUnsignedMin().zext(getBitWidth() * 2);
 930   APInt Other_max = Other.getUnsignedMax().zext(getBitWidth() * 2);
 931
 932   ConstantRange Result_zext = ConstantRange(this_min * Other_min,
 933                                             this_max * Other_max + 1);
 934   ConstantRange UR = Result_zext.truncate(getBitWidth());
 935
 936   // If the unsigned range doesn't wrap, and isn't negative then it's a range
 937   // from one positive number to another which is as good as we can generate.
 938   // In this case, skip the extra work of generating signed ranges which aren't
 939   // going to be better than this range.
 940   if (!UR.isUpperWrapped() &&
 941       (UR.getUpper().isNonNegative() || UR.getUpper().isMinSignedValue()))
 942     return UR;
 943
 944   // Now the signed range. Because we could be dealing with negative numbers
 945   // here, the lower bound is the smallest of the cartesian product of the
 946   // lower and upper ranges; for example:
 947   //   [-1,4) * [-2,3) = min(-1*-2, -1*2, 3*-2, 3*2) = -6.
 948   // Similarly for the upper bound, swapping min for max.
 949
 950   this_min = getSignedMin().sext(getBitWidth() * 2);
 951   this_max = getSignedMax().sext(getBitWidth() * 2);
 952   Other_min = Other.getSignedMin().sext(getBitWidth() * 2);
 953   Other_max = Other.getSignedMax().sext(getBitWidth() * 2);
 954
 955   auto L = {this_min * Other_min, this_min * Other_max,
 956             this_max * Other_min, this_max * Other_max};
 957   auto Compare = [](const APInt &A, const APInt &B) { return A.slt(B); };
 958   ConstantRange Result_sext(std::min(L, Compare), std::max(L, Compare) + 1);
 959   ConstantRange SR = Result_sext.truncate(getBitWidth());
 960
 961   return UR.isSizeStrictlySmallerThan(SR) ? UR : SR;
 962 }
 963
 964 ConstantRange
 965 ConstantRange::smax(const ConstantRange &Other) const {
 966   // X smax Y is: range(smax(X_smin, Y_smin),
 967   //                    smax(X_smax, Y_smax))
 968   if (isEmptySet() || Other.isEmptySet())
 969     return getEmpty();
 970   APInt NewL = APIntOps::smax(getSignedMin(), Other.getSignedMin());
 971   APInt NewU = APIntOps::smax(getSignedMax(), Other.getSignedMax()) + 1;
 972   return getNonEmpty(std::move(NewL), std::move(NewU));
 973 }
 974
 975 ConstantRange
 976 ConstantRange::umax(const ConstantRange &Other) const {
 977   // X umax Y is: range(umax(X_umin, Y_umin),
 978   //                    umax(X_umax, Y_umax))
 979   if (isEmptySet() || Other.isEmptySet())
 980     return getEmpty();
 981   APInt NewL = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
 982   APInt NewU = APIntOps::umax(getUnsignedMax(), Other.getUnsignedMax()) + 1;
 983   return getNonEmpty(std::move(NewL), std::move(NewU));
 984 }
 985
 986 ConstantRange
 987 ConstantRange::smin(const ConstantRange &Other) const {
 988   // X smin Y is: range(smin(X_smin, Y_smin),
 989   //                    smin(X_smax, Y_smax))
 990   if (isEmptySet() || Other.isEmptySet())
 991     return getEmpty();
 992   APInt NewL = APIntOps::smin(getSignedMin(), Other.getSignedMin());
 993   APInt NewU = APIntOps::smin(getSignedMax(), Other.getSignedMax()) + 1;
 994   return getNonEmpty(std::move(NewL), std::move(NewU));
 995 }
 996
 997 ConstantRange
 998 ConstantRange::umin(const ConstantRange &Other) const {
 999   // X umin Y is: range(umin(X_umin, Y_umin),
1000   //                    umin(X_umax, Y_umax))
1001   if (isEmptySet() || Other.isEmptySet())
1002     return getEmpty();
1003   APInt NewL = APIntOps::umin(getUnsignedMin(), Other.getUnsignedMin());
1004   APInt NewU = APIntOps::umin(getUnsignedMax(), Other.getUnsignedMax()) + 1;
1005   return getNonEmpty(std::move(NewL), std::move(NewU));
1006 }
1007
1008 ConstantRange
1009 ConstantRange::udiv(const ConstantRange &RHS) const {
1010   if (isEmptySet() || RHS.isEmptySet() || RHS.getUnsignedMax().isNullValue())
1011     return getEmpty();
1012
1013   APInt Lower = getUnsignedMin().udiv(RHS.getUnsignedMax());
1014
1015   APInt RHS_umin = RHS.getUnsignedMin();
1016   if (RHS_umin.isNullValue()) {
1017     // We want the lowest value in RHS excluding zero. Usually that would be 1
1018     // except for a range in the form of [X, 1) in which case it would be X.
1019     if (RHS.getUpper() == 1)
1020       RHS_umin = RHS.getLower();
1021     else
1022       RHS_umin = 1;
1023   }
1024
1025   APInt Upper = getUnsignedMax().udiv(RHS_umin) + 1;
1026   return getNonEmpty(std::move(Lower), std::move(Upper));
1027 }
1028
1029 ConstantRange ConstantRange::sdiv(const ConstantRange &RHS) const {
1030   // We split up the LHS and RHS into positive and negative components
1031   // and then also compute the positive and negative components of the result
1032   // separately by combining division results with the appropriate signs.
1033   APInt Zero = APInt::getNullValue(getBitWidth());
1034   APInt SignedMin = APInt::getSignedMinValue(getBitWidth());
1035   ConstantRange PosFilter(APInt(getBitWidth(), 1), SignedMin);
1036   ConstantRange NegFilter(SignedMin, Zero);
1037   ConstantRange PosL = intersectWith(PosFilter);
1038   ConstantRange NegL = intersectWith(NegFilter);
1039   ConstantRange PosR = RHS.intersectWith(PosFilter);
1040   ConstantRange NegR = RHS.intersectWith(NegFilter);
1041
1042   ConstantRange PosRes = getEmpty();
1043   if (!PosL.isEmptySet() && !PosR.isEmptySet())
1044     // pos / pos = pos.
1045     PosRes = ConstantRange(PosL.Lower.sdiv(PosR.Upper - 1),
1046                            (PosL.Upper - 1).sdiv(PosR.Lower) + 1);
1047
1048   if (!NegL.isEmptySet() && !NegR.isEmptySet()) {
1049     // neg / neg = pos.
1050     //
1051     // We need to deal with one tricky case here: SignedMin / -1 is UB on the
1052     // IR level, so we'll want to exclude this case when calculating bounds.
1053     // (For APInts the operation is well-defined and yields SignedMin.) We
1054     // handle this by dropping either SignedMin from the LHS or -1 from the RHS.
1055     APInt Lo = (NegL.Upper - 1).sdiv(NegR.Lower);
1056     if (NegL.Lower.isMinSignedValue() && NegR.Upper.isNullValue()) {
1057       // Remove -1 from the LHS. Skip if it's the only element, as this would
1058       // leave us with an empty set.
1059       if (!NegR.Lower.isAllOnesValue()) {
1060         APInt AdjNegRUpper;
1061         if (RHS.Lower.isAllOnesValue())
1062           // Negative part of [-1, X] without -1 is [SignedMin, X].
1063           AdjNegRUpper = RHS.Upper;
1064         else
1065           // [X, -1] without -1 is [X, -2].
1066           AdjNegRUpper = NegR.Upper - 1;
1067
1068         PosRes = PosRes.unionWith(
1069             ConstantRange(Lo, NegL.Lower.sdiv(AdjNegRUpper - 1) + 1));
1070       }
1071
1072       // Remove SignedMin from the RHS. Skip if it's the only element, as this
1073       // would leave us with an empty set.
1074       if (NegL.Upper != SignedMin + 1) {
1075         APInt AdjNegLLower;
1076         if (Upper == SignedMin + 1)
1077           // Negative part of [X, SignedMin] without SignedMin is [X, -1].
1078           AdjNegLLower = Lower;
1079         else
1080           // [SignedMin, X] without SignedMin is [SignedMin + 1, X].
1081           AdjNegLLower = NegL.Lower + 1;
1082
1083         PosRes = PosRes.unionWith(
1084             ConstantRange(std::move(Lo),
1085                           AdjNegLLower.sdiv(NegR.Upper - 1) + 1));
1086       }
1087     } else {
1088       PosRes = PosRes.unionWith(
1089           ConstantRange(std::move(Lo), NegL.Lower.sdiv(NegR.Upper - 1) + 1));
1090     }
1091   }
1092
1093   ConstantRange NegRes = getEmpty();
1094   if (!PosL.isEmptySet() && !NegR.isEmptySet())
1095     // pos / neg = neg.
1096     NegRes = ConstantRange((PosL.Upper - 1).sdiv(NegR.Upper - 1),
1097                            PosL.Lower.sdiv(NegR.Lower) + 1);
1098
1099   if (!NegL.isEmptySet() && !PosR.isEmptySet())
1100     // neg / pos = neg.
1101     NegRes = NegRes.unionWith(
1102         ConstantRange(NegL.Lower.sdiv(PosR.Lower),
1103                       (NegL.Upper - 1).sdiv(PosR.Upper - 1) + 1));
1104
1105   // Prefer a non-wrapping signed range here.
1106   ConstantRange Res = NegRes.unionWith(PosRes, PreferredRangeType::Signed);
1107
1108   // Preserve the zero that we dropped when splitting the LHS by sign.
1109   if (contains(Zero) && (!PosR.isEmptySet() || !NegR.isEmptySet()))
1110     Res = Res.unionWith(ConstantRange(Zero));
1111   return Res;
1112 }
1113
1114 ConstantRange ConstantRange::urem(const ConstantRange &RHS) const {
1115   if (isEmptySet() || RHS.isEmptySet() || RHS.getUnsignedMax().isNullValue())
1116     return getEmpty();
1117
1118   // L % R for L < R is L.
1119   if (getUnsignedMax().ult(RHS.getUnsignedMin()))
1120     return *this;
1121
1122   // L % R is <= L and < R.
1123   APInt Upper = APIntOps::umin(getUnsignedMax(), RHS.getUnsignedMax() - 1) + 1;
1124   return getNonEmpty(APInt::getNullValue(getBitWidth()), std::move(Upper));
1125 }
1126
1127 ConstantRange ConstantRange::srem(const ConstantRange &RHS) const {
1128   if (isEmptySet() || RHS.isEmptySet())
1129     return getEmpty();
1130
1131   ConstantRange AbsRHS = RHS.abs();
1132   APInt MinAbsRHS = AbsRHS.getUnsignedMin();
1133   APInt MaxAbsRHS = AbsRHS.getUnsignedMax();
1134
1135   // Modulus by zero is UB.
1136   if (MaxAbsRHS.isNullValue())
1137     return getEmpty();
1138
1139   if (MinAbsRHS.isNullValue())
1140     ++MinAbsRHS;
1141
1142   APInt MinLHS = getSignedMin(), MaxLHS = getSignedMax();
1143
1144   if (MinLHS.isNonNegative()) {
1145     // L % R for L < R is L.
1146     if (MaxLHS.ult(MinAbsRHS))
1147       return *this;
1148
1149     // L % R is <= L and < R.
1150     APInt Upper = APIntOps::umin(MaxLHS, MaxAbsRHS - 1) + 1;
1151     return ConstantRange(APInt::getNullValue(getBitWidth()), std::move(Upper));
1152   }
1153
1154   // Same basic logic as above, but the result is negative.
1155   if (MaxLHS.isNegative()) {
1156     if (MinLHS.ugt(-MinAbsRHS))
1157       return *this;
1158
1159     APInt Lower = APIntOps::umax(MinLHS, -MaxAbsRHS + 1);
1160     return ConstantRange(std::move(Lower), APInt(getBitWidth(), 1));
1161   }
1162
1163   // LHS range crosses zero.
1164   APInt Lower = APIntOps::umax(MinLHS, -MaxAbsRHS + 1);
1165   APInt Upper = APIntOps::umin(MaxLHS, MaxAbsRHS - 1) + 1;
1166   return ConstantRange(std::move(Lower), std::move(Upper));
1167 }
1168
1169 ConstantRange
1170 ConstantRange::binaryAnd(const ConstantRange &Other) const {
1171   if (isEmptySet() || Other.isEmptySet())
1172     return getEmpty();
1173
1174   // TODO: replace this with something less conservative
1175
1176   APInt umin = APIntOps::umin(Other.getUnsignedMax(), getUnsignedMax());
1177   return getNonEmpty(APInt::getNullValue(getBitWidth()), std::move(umin) + 1);
1178 }
1179
1180 ConstantRange
1181 ConstantRange::binaryOr(const ConstantRange &Other) const {
1182   if (isEmptySet() || Other.isEmptySet())
1183     return getEmpty();
1184
1185   // TODO: replace this with something less conservative
1186
1187   APInt umax = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
1188   return getNonEmpty(std::move(umax), APInt::getNullValue(getBitWidth()));
1189 }
1190
1191 ConstantRange
1192 ConstantRange::shl(const ConstantRange &Other) const {
1193   if (isEmptySet() || Other.isEmptySet())
1194     return getEmpty();
1195
1196   APInt max = getUnsignedMax();
1197   APInt Other_umax = Other.getUnsignedMax();
1198
1199   // If we are shifting by maximum amount of
1200   // zero return return the original range.
1201   if (Other_umax.isNullValue())
1202     return *this;
1203   // there's overflow!
1204   if (Other_umax.ugt(max.countLeadingZeros()))
1205     return getFull();
1206
1207   // FIXME: implement the other tricky cases
1208
1209   APInt min = getUnsignedMin();
1210   min <<= Other.getUnsignedMin();
1211   max <<= Other_umax;
1212
1213   return ConstantRange(std::move(min), std::move(max) + 1);
1214 }
1215
1216 ConstantRange
1217 ConstantRange::lshr(const ConstantRange &Other) const {
1218   if (isEmptySet() || Other.isEmptySet())
1219     return getEmpty();
1220
1221   APInt max = getUnsignedMax().lshr(Other.getUnsignedMin()) + 1;
1222   APInt min = getUnsignedMin().lshr(Other.getUnsignedMax());
1223   return getNonEmpty(std::move(min), std::move(max));
1224 }
1225
1226 ConstantRange
1227 ConstantRange::ashr(const ConstantRange &Other) const {
1228   if (isEmptySet() || Other.isEmptySet())
1229     return getEmpty();
1230
1231   // May straddle zero, so handle both positive and negative cases.
1232   // 'PosMax' is the upper bound of the result of the ashr
1233   // operation, when Upper of the LHS of ashr is a non-negative.
1234   // number. Since ashr of a non-negative number will result in a
1235   // smaller number, the Upper value of LHS is shifted right with
1236   // the minimum value of 'Other' instead of the maximum value.
1237   APInt PosMax = getSignedMax().ashr(Other.getUnsignedMin()) + 1;
1238
1239   // 'PosMin' is the lower bound of the result of the ashr
1240   // operation, when Lower of the LHS is a non-negative number.
1241   // Since ashr of a non-negative number will result in a smaller
1242   // number, the Lower value of LHS is shifted right with the
1243   // maximum value of 'Other'.
1244   APInt PosMin = getSignedMin().ashr(Other.getUnsignedMax());
1245
1246   // 'NegMax' is the upper bound of the result of the ashr
1247   // operation, when Upper of the LHS of ashr is a negative number.
1248   // Since 'ashr' of a negative number will result in a bigger
1249   // number, the Upper value of LHS is shifted right with the
1250   // maximum value of 'Other'.
1251   APInt NegMax = getSignedMax().ashr(Other.getUnsignedMax()) + 1;
1252
1253   // 'NegMin' is the lower bound of the result of the ashr
1254   // operation, when Lower of the LHS of ashr is a negative number.
1255   // Since 'ashr' of a negative number will result in a bigger
1256   // number, the Lower value of LHS is shifted right with the
1257   // minimum value of 'Other'.
1258   APInt NegMin = getSignedMin().ashr(Other.getUnsignedMin());
1259
1260   APInt max, min;
1261   if (getSignedMin().isNonNegative()) {
1262     // Upper and Lower of LHS are non-negative.
1263     min = PosMin;
1264     max = PosMax;
1265   } else if (getSignedMax().isNegative()) {
1266     // Upper and Lower of LHS are negative.
1267     min = NegMin;
1268     max = NegMax;
1269   } else {
1270     // Upper is non-negative and Lower is negative.
1271     min = NegMin;
1272     max = PosMax;
1273   }
1274   return getNonEmpty(std::move(min), std::move(max));
1275 }
1276
1277 ConstantRange ConstantRange::uadd_sat(const ConstantRange &Other) const {
1278   if (isEmptySet() || Other.isEmptySet())
1279     return getEmpty();
1280
1281   APInt NewL = getUnsignedMin().uadd_sat(Other.getUnsignedMin());
1282   APInt NewU = getUnsignedMax().uadd_sat(Other.getUnsignedMax()) + 1;
1283   return getNonEmpty(std::move(NewL), std::move(NewU));
1284 }
1285
1286 ConstantRange ConstantRange::sadd_sat(const ConstantRange &Other) const {
1287   if (isEmptySet() || Other.isEmptySet())
1288     return getEmpty();
1289
1290   APInt NewL = getSignedMin().sadd_sat(Other.getSignedMin());
1291   APInt NewU = getSignedMax().sadd_sat(Other.getSignedMax()) + 1;
1292   return getNonEmpty(std::move(NewL), std::move(NewU));
1293 }
1294
1295 ConstantRange ConstantRange::usub_sat(const ConstantRange &Other) const {
1296   if (isEmptySet() || Other.isEmptySet())
1297     return getEmpty();
1298
1299   APInt NewL = getUnsignedMin().usub_sat(Other.getUnsignedMax());
1300   APInt NewU = getUnsignedMax().usub_sat(Other.getUnsignedMin()) + 1;
1301   return getNonEmpty(std::move(NewL), std::move(NewU));
1302 }
1303
1304 ConstantRange ConstantRange::ssub_sat(const ConstantRange &Other) const {
1305   if (isEmptySet() || Other.isEmptySet())
1306     return getEmpty();
1307
1308   APInt NewL = getSignedMin().ssub_sat(Other.getSignedMax());
1309   APInt NewU = getSignedMax().ssub_sat(Other.getSignedMin()) + 1;
1310   return getNonEmpty(std::move(NewL), std::move(NewU));
1311 }
1312
1313 ConstantRange ConstantRange::inverse() const {
1314   if (isFullSet())
1315     return getEmpty();
1316   if (isEmptySet())
1317     return getFull();
1318   return ConstantRange(Upper, Lower);
1319 }
1320
1321 ConstantRange ConstantRange::abs() const {
1322   if (isEmptySet())
1323     return getEmpty();
1324
1325   if (isSignWrappedSet()) {
1326     APInt Lo;
1327     // Check whether the range crosses zero.
1328     if (Upper.isStrictlyPositive() || !Lower.isStrictlyPositive())
1329       Lo = APInt::getNullValue(getBitWidth());
1330     else
1331       Lo = APIntOps::umin(Lower, -Upper + 1);
1332
1333     // SignedMin is included in the result range.
1334     return ConstantRange(Lo, APInt::getSignedMinValue(getBitWidth()) + 1);
1335   }
1336
1337   APInt SMin = getSignedMin(), SMax = getSignedMax();
1338
1339   // All non-negative.
1340   if (SMin.isNonNegative())
1341     return *this;
1342
1343   // All negative.
1344   if (SMax.isNegative())
1345     return ConstantRange(-SMax, -SMin + 1);
1346
1347   // Range crosses zero.
1348   return ConstantRange(APInt::getNullValue(getBitWidth()),
1349                        APIntOps::umax(-SMin, SMax) + 1);
1350 }
1351
1352 ConstantRange::OverflowResult ConstantRange::unsignedAddMayOverflow(
1353     const ConstantRange &Other) const {
1354   if (isEmptySet() || Other.isEmptySet())
1355     return OverflowResult::MayOverflow;
1356
1357   APInt Min = getUnsignedMin(), Max = getUnsignedMax();
1358   APInt OtherMin = Other.getUnsignedMin(), OtherMax = Other.getUnsignedMax();
1359
1360   // a u+ b overflows high iff a u> ~b.
1361   if (Min.ugt(~OtherMin))
1362     return OverflowResult::AlwaysOverflowsHigh;
1363   if (Max.ugt(~OtherMax))
1364     return OverflowResult::MayOverflow;
1365   return OverflowResult::NeverOverflows;
1366 }
1367
1368 ConstantRange::OverflowResult ConstantRange::signedAddMayOverflow(
1369     const ConstantRange &Other) const {
1370   if (isEmptySet() || Other.isEmptySet())
1371     return OverflowResult::MayOverflow;
1372
1373   APInt Min = getSignedMin(), Max = getSignedMax();
1374   APInt OtherMin = Other.getSignedMin(), OtherMax = Other.getSignedMax();
1375
1376   APInt SignedMin = APInt::getSignedMinValue(getBitWidth());
1377   APInt SignedMax = APInt::getSignedMaxValue(getBitWidth());
1378
1379   // a s+ b overflows high iff a s>=0 && b s>= 0 && a s> smax - b.
1380   // a s+ b overflows low iff a s< 0 && b s< 0 && a s< smin - b.
1381   if (Min.isNonNegative() && OtherMin.isNonNegative() &&
1382       Min.sgt(SignedMax - OtherMin))
1383     return OverflowResult::AlwaysOverflowsHigh;
1384   if (Max.isNegative() && OtherMax.isNegative() &&
1385       Max.slt(SignedMin - OtherMax))
1386     return OverflowResult::AlwaysOverflowsLow;
1387
1388   if (Max.isNonNegative() && OtherMax.isNonNegative() &&
1389       Max.sgt(SignedMax - OtherMax))
1390     return OverflowResult::MayOverflow;
1391   if (Min.isNegative() && OtherMin.isNegative() &&
1392       Min.slt(SignedMin - OtherMin))
1393     return OverflowResult::MayOverflow;
1394
1395   return OverflowResult::NeverOverflows;
1396 }
1397
1398 ConstantRange::OverflowResult ConstantRange::unsignedSubMayOverflow(
1399     const ConstantRange &Other) const {
1400   if (isEmptySet() || Other.isEmptySet())
1401     return OverflowResult::MayOverflow;
1402
1403   APInt Min = getUnsignedMin(), Max = getUnsignedMax();
1404   APInt OtherMin = Other.getUnsignedMin(), OtherMax = Other.getUnsignedMax();
1405
1406   // a u- b overflows low iff a u< b.
1407   if (Max.ult(OtherMin))
1408     return OverflowResult::AlwaysOverflowsLow;
1409   if (Min.ult(OtherMax))
1410     return OverflowResult::MayOverflow;
1411   return OverflowResult::NeverOverflows;
1412 }
1413
1414 ConstantRange::OverflowResult ConstantRange::signedSubMayOverflow(
1415     const ConstantRange &Other) const {
1416   if (isEmptySet() || Other.isEmptySet())
1417     return OverflowResult::MayOverflow;
1418
1419   APInt Min = getSignedMin(), Max = getSignedMax();
1420   APInt OtherMin = Other.getSignedMin(), OtherMax = Other.getSignedMax();
1421
1422   APInt SignedMin = APInt::getSignedMinValue(getBitWidth());
1423   APInt SignedMax = APInt::getSignedMaxValue(getBitWidth());
1424
1425   // a s- b overflows high iff a s>=0 && b s< 0 && a s> smax + b.
1426   // a s- b overflows low iff a s< 0 && b s>= 0 && a s< smin + b.
1427   if (Min.isNonNegative() && OtherMax.isNegative() &&
1428       Min.sgt(SignedMax + OtherMax))
1429     return OverflowResult::AlwaysOverflowsHigh;
1430   if (Max.isNegative() && OtherMin.isNonNegative() &&
1431       Max.slt(SignedMin + OtherMin))
1432     return OverflowResult::AlwaysOverflowsLow;
1433
1434   if (Max.isNonNegative() && OtherMin.isNegative() &&
1435       Max.sgt(SignedMax + OtherMin))
1436     return OverflowResult::MayOverflow;
1437   if (Min.isNegative() && OtherMax.isNonNegative() &&
1438       Min.slt(SignedMin + OtherMax))
1439     return OverflowResult::MayOverflow;
1440
1441   return OverflowResult::NeverOverflows;
1442 }
1443
1444 ConstantRange::OverflowResult ConstantRange::unsignedMulMayOverflow(
1445     const ConstantRange &Other) const {
1446   if (isEmptySet() || Other.isEmptySet())
1447     return OverflowResult::MayOverflow;
1448
1449   APInt Min = getUnsignedMin(), Max = getUnsignedMax();
1450   APInt OtherMin = Other.getUnsignedMin(), OtherMax = Other.getUnsignedMax();
1451   bool Overflow;
1452
1453   (void) Min.umul_ov(OtherMin, Overflow);
1454   if (Overflow)
1455     return OverflowResult::AlwaysOverflowsHigh;
1456
1457   (void) Max.umul_ov(OtherMax, Overflow);
1458   if (Overflow)
1459     return OverflowResult::MayOverflow;
1460
1461   return OverflowResult::NeverOverflows;
1462 }
1463
1464 void ConstantRange::print(raw_ostream &OS) const {
1465   if (isFullSet())
1466     OS << "full-set";
1467   else if (isEmptySet())
1468     OS << "empty-set";
1469   else
1470     OS << "[" << Lower << "," << Upper << ")";
1471 }
1472
1473 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
1474 LLVM_DUMP_METHOD void ConstantRange::dump() const {
1475   print(dbgs());
1476 }
1477 #endif
1478
1479 ConstantRange llvm::getConstantRangeFromMetadata(const MDNode &Ranges) {
1480   const unsigned NumRanges = Ranges.getNumOperands() / 2;
1481   assert(NumRanges >= 1 && "Must have at least one range!");
1482   assert(Ranges.getNumOperands() % 2 == 0 && "Must be a sequence of pairs");
1483
1484   auto *FirstLow = mdconst::extract<ConstantInt>(Ranges.getOperand(0));
1485   auto *FirstHigh = mdconst::extract<ConstantInt>(Ranges.getOperand(1));
1486
1487   ConstantRange CR(FirstLow->getValue(), FirstHigh->getValue());
1488
1489   for (unsigned i = 1; i < NumRanges; ++i) {
1490     auto *Low = mdconst::extract<ConstantInt>(Ranges.getOperand(2 * i + 0));
1491     auto *High = mdconst::extract<ConstantInt>(Ranges.getOperand(2 * i + 1));
1492
1493     // Note: unionWith will potentially create a range that contains values not
1494     // contained in any of the original N ranges.
1495     CR = CR.unionWith(ConstantRange(Low->getValue(), High->getValue()));
1496   }
1497
1498   return CR;
1499 }