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 }
 274
 275 ConstantRange ConstantRange::makeExactNoWrapRegion(Instruction::BinaryOps BinOp,
 276                                                    const APInt &Other,
 277                                                    unsigned NoWrapKind) {
 278   // makeGuaranteedNoWrapRegion() is exact for single-element ranges, as
 279   // "for all" and "for any" coincide in this case.
 280   return makeGuaranteedNoWrapRegion(BinOp, ConstantRange(Other), NoWrapKind);
 281 }
 282
 283 bool ConstantRange::isFullSet() const {
 284   return Lower == Upper && Lower.isMaxValue();
 285 }
 286
 287 bool ConstantRange::isEmptySet() const {
 288   return Lower == Upper && Lower.isMinValue();
 289 }
 290
 291 bool ConstantRange::isWrappedSet() const {
 292   return Lower.ugt(Upper) && !Upper.isNullValue();
 293 }
 294
 295 bool ConstantRange::isUpperWrapped() const {
 296   return Lower.ugt(Upper);
 297 }
 298
 299 bool ConstantRange::isSignWrappedSet() const {
 300   return Lower.sgt(Upper) && !Upper.isMinSignedValue();
 301 }
 302
 303 bool ConstantRange::isUpperSignWrapped() const {
 304   return Lower.sgt(Upper);
 305 }
 306
 307 bool
 308 ConstantRange::isSizeStrictlySmallerThan(const ConstantRange &Other) const {
 309   assert(getBitWidth() == Other.getBitWidth());
 310   if (isFullSet())
 311     return false;
 312   if (Other.isFullSet())
 313     return true;
 314   return (Upper - Lower).ult(Other.Upper - Other.Lower);
 315 }
 316
 317 bool
 318 ConstantRange::isSizeLargerThan(uint64_t MaxSize) const {
 319   assert(MaxSize && "MaxSize can't be 0.");
 320   // If this a full set, we need special handling to avoid needing an extra bit
 321   // to represent the size.
 322   if (isFullSet())
 323     return APInt::getMaxValue(getBitWidth()).ugt(MaxSize - 1);
 324
 325   return (Upper - Lower).ugt(MaxSize);
 326 }
 327
 328 bool ConstantRange::isAllNegative() const {
 329   // Empty set is all negative, full set is not.
 330   if (isEmptySet())
 331     return true;
 332   if (isFullSet())
 333     return false;
 334
 335   return !isUpperSignWrapped() && !Upper.isStrictlyPositive();
 336 }
 337
 338 bool ConstantRange::isAllNonNegative() const {
 339   // Empty and full set are automatically treated correctly.
 340   return !isSignWrappedSet() && Lower.isNonNegative();
 341 }
 342
 343 APInt ConstantRange::getUnsignedMax() const {
 344   if (isFullSet() || isUpperWrapped())
 345     return APInt::getMaxValue(getBitWidth());
 346   return getUpper() - 1;
 347 }
 348
 349 APInt ConstantRange::getUnsignedMin() const {
 350   if (isFullSet() || isWrappedSet())
 351     return APInt::getMinValue(getBitWidth());
 352   return getLower();
 353 }
 354
 355 APInt ConstantRange::getSignedMax() const {
 356   if (isFullSet() || isUpperSignWrapped())
 357     return APInt::getSignedMaxValue(getBitWidth());
 358   return getUpper() - 1;
 359 }
 360
 361 APInt ConstantRange::getSignedMin() const {
 362   if (isFullSet() || isSignWrappedSet())
 363     return APInt::getSignedMinValue(getBitWidth());
 364   return getLower();
 365 }
 366
 367 bool ConstantRange::contains(const APInt &V) const {
 368   if (Lower == Upper)
 369     return isFullSet();
 370
 371   if (!isUpperWrapped())
 372     return Lower.ule(V) && V.ult(Upper);
 373   return Lower.ule(V) || V.ult(Upper);
 374 }
 375
 376 bool ConstantRange::contains(const ConstantRange &Other) const {
 377   if (isFullSet() || Other.isEmptySet()) return true;
 378   if (isEmptySet() || Other.isFullSet()) return false;
 379
 380   if (!isUpperWrapped()) {
 381     if (Other.isUpperWrapped())
 382       return false;
 383
 384     return Lower.ule(Other.getLower()) && Other.getUpper().ule(Upper);
 385   }
 386
 387   if (!Other.isUpperWrapped())
 388     return Other.getUpper().ule(Upper) ||
 389            Lower.ule(Other.getLower());
 390
 391   return Other.getUpper().ule(Upper) && Lower.ule(Other.getLower());
 392 }
 393
 394 ConstantRange ConstantRange::subtract(const APInt &Val) const {
 395   assert(Val.getBitWidth() == getBitWidth() && "Wrong bit width");
 396   // If the set is empty or full, don't modify the endpoints.
 397   if (Lower == Upper)
 398     return *this;
 399   return ConstantRange(Lower - Val, Upper - Val);
 400 }
 401
 402 ConstantRange ConstantRange::difference(const ConstantRange &CR) const {
 403   return intersectWith(CR.inverse());
 404 }
 405
 406 static ConstantRange getPreferredRange(
 407     const ConstantRange &CR1, const ConstantRange &CR2,
 408     ConstantRange::PreferredRangeType Type) {
 409   if (Type == ConstantRange::Unsigned) {
 410     if (!CR1.isWrappedSet() && CR2.isWrappedSet())
 411       return CR1;
 412     if (CR1.isWrappedSet() && !CR2.isWrappedSet())
 413       return CR2;
 414   } else if (Type == ConstantRange::Signed) {
 415     if (!CR1.isSignWrappedSet() && CR2.isSignWrappedSet())
 416       return CR1;
 417     if (CR1.isSignWrappedSet() && !CR2.isSignWrappedSet())
 418       return CR2;
 419   }
 420
 421   if (CR1.isSizeStrictlySmallerThan(CR2))
 422     return CR1;
 423   return CR2;
 424 }
 425
 426 ConstantRange ConstantRange::intersectWith(const ConstantRange &CR,
 427                                            PreferredRangeType Type) const {
 428   assert(getBitWidth() == CR.getBitWidth() &&
 429          "ConstantRange types don't agree!");
 430
 431   // Handle common cases.
 432   if (   isEmptySet() || CR.isFullSet()) return *this;
 433   if (CR.isEmptySet() ||    isFullSet()) return CR;
 434
 435   if (!isUpperWrapped() && CR.isUpperWrapped())
 436     return CR.intersectWith(*this, Type);
 437
 438   if (!isUpperWrapped() && !CR.isUpperWrapped()) {
 439     if (Lower.ult(CR.Lower)) {
 440       // L---U       : this
 441       //       L---U : CR
 442       if (Upper.ule(CR.Lower))
 443         return getEmpty();
 444
 445       // L---U       : this
 446       //   L---U     : CR
 447       if (Upper.ult(CR.Upper))
 448         return ConstantRange(CR.Lower, Upper);
 449
 450       // L-------U   : this
 451       //   L---U     : CR
 452       return CR;
 453     }
 454     //   L---U     : this
 455     // L-------U   : CR
 456     if (Upper.ult(CR.Upper))
 457       return *this;
 458
 459     //   L-----U   : this
 460     // L-----U     : CR
 461     if (Lower.ult(CR.Upper))
 462       return ConstantRange(Lower, CR.Upper);
 463
 464     //       L---U : this
 465     // L---U       : CR
 466     return getEmpty();
 467   }
 468
 469   if (isUpperWrapped() && !CR.isUpperWrapped()) {
 470     if (CR.Lower.ult(Upper)) {
 471       // ------U   L--- : this
 472       //  L--U          : CR
 473       if (CR.Upper.ult(Upper))
 474         return CR;
 475
 476       // ------U   L--- : this
 477       //  L------U      : CR
 478       if (CR.Upper.ule(Lower))
 479         return ConstantRange(CR.Lower, Upper);
 480
 481       // ------U   L--- : this
 482       //  L----------U  : CR
 483       return getPreferredRange(*this, CR, Type);
 484     }
 485     if (CR.Lower.ult(Lower)) {
 486       // --U      L---- : this
 487       //     L--U       : CR
 488       if (CR.Upper.ule(Lower))
 489         return getEmpty();
 490
 491       // --U      L---- : this
 492       //     L------U   : CR
 493       return ConstantRange(Lower, CR.Upper);
 494     }
 495
 496     // --U  L------ : this
 497     //        L--U  : CR
 498     return CR;
 499   }
 500
 501   if (CR.Upper.ult(Upper)) {
 502     // ------U L-- : this
 503     // --U L------ : CR
 504     if (CR.Lower.ult(Upper))
 505       return getPreferredRange(*this, CR, Type);
 506
 507     // ----U   L-- : this
 508     // --U   L---- : CR
 509     if (CR.Lower.ult(Lower))
 510       return ConstantRange(Lower, CR.Upper);
 511
 512     // ----U L---- : this
 513     // --U     L-- : CR
 514     return CR;
 515   }
 516   if (CR.Upper.ule(Lower)) {
 517     // --U     L-- : this
 518     // ----U L---- : CR
 519     if (CR.Lower.ult(Lower))
 520       return *this;
 521
 522     // --U   L---- : this
 523     // ----U   L-- : CR
 524     return ConstantRange(CR.Lower, Upper);
 525   }
 526
 527   // --U L------ : this
 528   // ------U L-- : CR
 529   return getPreferredRange(*this, CR, Type);
 530 }
 531
 532 ConstantRange ConstantRange::unionWith(const ConstantRange &CR,
 533                                        PreferredRangeType Type) const {
 534   assert(getBitWidth() == CR.getBitWidth() &&
 535          "ConstantRange types don't agree!");
 536
 537   if (   isFullSet() || CR.isEmptySet()) return *this;
 538   if (CR.isFullSet() ||    isEmptySet()) return CR;
 539
 540   if (!isUpperWrapped() && CR.isUpperWrapped())
 541     return CR.unionWith(*this, Type);
 542
 543   if (!isUpperWrapped() && !CR.isUpperWrapped()) {
 544     //        L---U  and  L---U        : this
 545     //  L---U                   L---U  : CR
 546     // result in one of
 547     //  L---------U
 548     // -----U L-----
 549     if (CR.Upper.ult(Lower) || Upper.ult(CR.Lower))
 550       return getPreferredRange(
 551           ConstantRange(Lower, CR.Upper), ConstantRange(CR.Lower, Upper), Type);
 552
 553     APInt L = CR.Lower.ult(Lower) ? CR.Lower : Lower;
 554     APInt U = (CR.Upper - 1).ugt(Upper - 1) ? CR.Upper : Upper;
 555
 556     if (L.isNullValue() && U.isNullValue())
 557       return getFull();
 558
 559     return ConstantRange(std::move(L), std::move(U));
 560   }
 561
 562   if (!CR.isUpperWrapped()) {
 563     // ------U   L-----  and  ------U   L----- : this
 564     //   L--U                            L--U  : CR
 565     if (CR.Upper.ule(Upper) || CR.Lower.uge(Lower))
 566       return *this;
 567
 568     // ------U   L----- : this
 569     //    L---------U   : CR
 570     if (CR.Lower.ule(Upper) && Lower.ule(CR.Upper))
 571       return getFull();
 572
 573     // ----U       L---- : this
 574     //       L---U       : CR
 575     // results in one of
 576     // ----------U L----
 577     // ----U L----------
 578     if (Upper.ult(CR.Lower) && CR.Upper.ult(Lower))
 579       return getPreferredRange(
 580           ConstantRange(Lower, CR.Upper), ConstantRange(CR.Lower, Upper), Type);
 581
 582     // ----U     L----- : this
 583     //        L----U    : CR
 584     if (Upper.ult(CR.Lower) && Lower.ule(CR.Upper))
 585       return ConstantRange(CR.Lower, Upper);
 586
 587     // ------U    L---- : this
 588     //    L-----U       : CR
 589     assert(CR.Lower.ule(Upper) && CR.Upper.ult(Lower) &&
 590            "ConstantRange::unionWith missed a case with one range wrapped");
 591     return ConstantRange(Lower, CR.Upper);
 592   }
 593
 594   // ------U    L----  and  ------U    L---- : this
 595   // -U  L-----------  and  ------------U  L : CR
 596   if (CR.Lower.ule(Upper) || Lower.ule(CR.Upper))
 597     return getFull();
 598
 599   APInt L = CR.Lower.ult(Lower) ? CR.Lower : Lower;
 600   APInt U = CR.Upper.ugt(Upper) ? CR.Upper : Upper;
 601
 602   return ConstantRange(std::move(L), std::move(U));
 603 }
 604
 605 ConstantRange ConstantRange::castOp(Instruction::CastOps CastOp,
 606                                     uint32_t ResultBitWidth) const {
 607   switch (CastOp) {
 608   default:
 609     llvm_unreachable("unsupported cast type");
 610   case Instruction::Trunc:
 611     return truncate(ResultBitWidth);
 612   case Instruction::SExt:
 613     return signExtend(ResultBitWidth);
 614   case Instruction::ZExt:
 615     return zeroExtend(ResultBitWidth);
 616   case Instruction::BitCast:
 617     return *this;
 618   case Instruction::FPToUI:
 619   case Instruction::FPToSI:
 620     if (getBitWidth() == ResultBitWidth)
 621       return *this;
 622     else
 623       return getFull();
 624   case Instruction::UIToFP: {
 625     // TODO: use input range if available
 626     auto BW = getBitWidth();
 627     APInt Min = APInt::getMinValue(BW).zextOrSelf(ResultBitWidth);
 628     APInt Max = APInt::getMaxValue(BW).zextOrSelf(ResultBitWidth);
 629     return ConstantRange(std::move(Min), std::move(Max));
 630   }
 631   case Instruction::SIToFP: {
 632     // TODO: use input range if available
 633     auto BW = getBitWidth();
 634     APInt SMin = APInt::getSignedMinValue(BW).sextOrSelf(ResultBitWidth);
 635     APInt SMax = APInt::getSignedMaxValue(BW).sextOrSelf(ResultBitWidth);
 636     return ConstantRange(std::move(SMin), std::move(SMax));
 637   }
 638   case Instruction::FPTrunc:
 639   case Instruction::FPExt:
 640   case Instruction::IntToPtr:
 641   case Instruction::PtrToInt:
 642   case Instruction::AddrSpaceCast:
 643     // Conservatively return getFull set.
 644     return getFull();
 645   };
 646 }
 647
 648 ConstantRange ConstantRange::zeroExtend(uint32_t DstTySize) const {
 649   if (isEmptySet()) return getEmpty(DstTySize);
 650
 651   unsigned SrcTySize = getBitWidth();
 652   assert(SrcTySize < DstTySize && "Not a value extension");
 653   if (isFullSet() || isUpperWrapped()) {
 654     // Change into [0, 1 << src bit width)
 655     APInt LowerExt(DstTySize, 0);
 656     if (!Upper) // special case: [X, 0) -- not really wrapping around
 657       LowerExt = Lower.zext(DstTySize);
 658     return ConstantRange(std::move(LowerExt),
 659                          APInt::getOneBitSet(DstTySize, SrcTySize));
 660   }
 661
 662   return ConstantRange(Lower.zext(DstTySize), Upper.zext(DstTySize));
 663 }
 664
 665 ConstantRange ConstantRange::signExtend(uint32_t DstTySize) const {
 666   if (isEmptySet()) return getEmpty(DstTySize);
 667
 668   unsigned SrcTySize = getBitWidth();
 669   assert(SrcTySize < DstTySize && "Not a value extension");
 670
 671   // special case: [X, INT_MIN) -- not really wrapping around
 672   if (Upper.isMinSignedValue())
 673     return ConstantRange(Lower.sext(DstTySize), Upper.zext(DstTySize));
 674
 675   if (isFullSet() || isSignWrappedSet()) {
 676     return ConstantRange(APInt::getHighBitsSet(DstTySize,DstTySize-SrcTySize+1),
 677                          APInt::getLowBitsSet(DstTySize, SrcTySize-1) + 1);
 678   }
 679
 680   return ConstantRange(Lower.sext(DstTySize), Upper.sext(DstTySize));
 681 }
 682
 683 ConstantRange ConstantRange::truncate(uint32_t DstTySize) const {
 684   assert(getBitWidth() > DstTySize && "Not a value truncation");
 685   if (isEmptySet())
 686     return getEmpty(DstTySize);
 687   if (isFullSet())
 688     return getFull(DstTySize);
 689
 690   APInt LowerDiv(Lower), UpperDiv(Upper);
 691   ConstantRange Union(DstTySize, /*isFullSet=*/false);
 692
 693   // Analyze wrapped sets in their two parts: [0, Upper) \/ [Lower, MaxValue]
 694   // We use the non-wrapped set code to analyze the [Lower, MaxValue) part, and
 695   // then we do the union with [MaxValue, Upper)
 696   if (isUpperWrapped()) {
 697     // If Upper is greater than or equal to MaxValue(DstTy), it covers the whole
 698     // truncated range.
 699     if (Upper.getActiveBits() > DstTySize ||
 700         Upper.countTrailingOnes() == DstTySize)
 701       return getFull(DstTySize);
 702
 703     Union = ConstantRange(APInt::getMaxValue(DstTySize),Upper.trunc(DstTySize));
 704     UpperDiv.setAllBits();
 705
 706     // Union covers the MaxValue case, so return if the remaining range is just
 707     // MaxValue(DstTy).
 708     if (LowerDiv == UpperDiv)
 709       return Union;
 710   }
 711
 712   // Chop off the most significant bits that are past the destination bitwidth.
 713   if (LowerDiv.getActiveBits() > DstTySize) {
 714     // Mask to just the signficant bits and subtract from LowerDiv/UpperDiv.
 715     APInt Adjust = LowerDiv & APInt::getBitsSetFrom(getBitWidth(), DstTySize);
 716     LowerDiv -= Adjust;
 717     UpperDiv -= Adjust;
 718   }
 719
 720   unsigned UpperDivWidth = UpperDiv.getActiveBits();
 721   if (UpperDivWidth <= DstTySize)
 722     return ConstantRange(LowerDiv.trunc(DstTySize),
 723                          UpperDiv.trunc(DstTySize)).unionWith(Union);
 724
 725   // The truncated value wraps around. Check if we can do better than fullset.
 726   if (UpperDivWidth == DstTySize + 1) {
 727     // Clear the MSB so that UpperDiv wraps around.
 728     UpperDiv.clearBit(DstTySize);
 729     if (UpperDiv.ult(LowerDiv))
 730       return ConstantRange(LowerDiv.trunc(DstTySize),
 731                            UpperDiv.trunc(DstTySize)).unionWith(Union);
 732   }
 733
 734   return getFull(DstTySize);
 735 }
 736
 737 ConstantRange ConstantRange::zextOrTrunc(uint32_t DstTySize) const {
 738   unsigned SrcTySize = getBitWidth();
 739   if (SrcTySize > DstTySize)
 740     return truncate(DstTySize);
 741   if (SrcTySize < DstTySize)
 742     return zeroExtend(DstTySize);
 743   return *this;
 744 }
 745
 746 ConstantRange ConstantRange::sextOrTrunc(uint32_t DstTySize) const {
 747   unsigned SrcTySize = getBitWidth();
 748   if (SrcTySize > DstTySize)
 749     return truncate(DstTySize);
 750   if (SrcTySize < DstTySize)
 751     return signExtend(DstTySize);
 752   return *this;
 753 }
 754
 755 ConstantRange ConstantRange::binaryOp(Instruction::BinaryOps BinOp,
 756                                       const ConstantRange &Other) const {
 757   assert(Instruction::isBinaryOp(BinOp) && "Binary operators only!");
 758
 759   switch (BinOp) {
 760   case Instruction::Add:
 761     return add(Other);
 762   case Instruction::Sub:
 763     return sub(Other);
 764   case Instruction::Mul:
 765     return multiply(Other);
 766   case Instruction::UDiv:
 767     return udiv(Other);
 768   case Instruction::SDiv:
 769     return sdiv(Other);
 770   case Instruction::URem:
 771     return urem(Other);
 772   case Instruction::SRem:
 773     return srem(Other);
 774   case Instruction::Shl:
 775     return shl(Other);
 776   case Instruction::LShr:
 777     return lshr(Other);
 778   case Instruction::AShr:
 779     return ashr(Other);
 780   case Instruction::And:
 781     return binaryAnd(Other);
 782   case Instruction::Or:
 783     return binaryOr(Other);
 784   // Note: floating point operations applied to abstract ranges are just
 785   // ideal integer operations with a lossy representation
 786   case Instruction::FAdd:
 787     return add(Other);
 788   case Instruction::FSub:
 789     return sub(Other);
 790   case Instruction::FMul:
 791     return multiply(Other);
 792   default:
 793     // Conservatively return getFull set.
 794     return getFull();
 795   }
 796 }
 797
 798 ConstantRange
 799 ConstantRange::add(const ConstantRange &Other) const {
 800   if (isEmptySet() || Other.isEmptySet())
 801     return getEmpty();
 802   if (isFullSet() || Other.isFullSet())
 803     return getFull();
 804
 805   APInt NewLower = getLower() + Other.getLower();
 806   APInt NewUpper = getUpper() + Other.getUpper() - 1;
 807   if (NewLower == NewUpper)
 808     return getFull();
 809
 810   ConstantRange X = ConstantRange(std::move(NewLower), std::move(NewUpper));
 811   if (X.isSizeStrictlySmallerThan(*this) ||
 812       X.isSizeStrictlySmallerThan(Other))
 813     // We've wrapped, therefore, full set.
 814     return getFull();
 815   return X;
 816 }
 817
 818 ConstantRange ConstantRange::addWithNoWrap(const ConstantRange &Other,
 819                                            unsigned NoWrapKind,
 820                                            PreferredRangeType RangeType) const {
 821   // Calculate the range for "X + Y" which is guaranteed not to wrap(overflow).
 822   // (X is from this, and Y is from Other)
 823   if (isEmptySet() || Other.isEmptySet())
 824     return getEmpty();
 825   if (isFullSet() && Other.isFullSet())
 826     return getFull();
 827
 828   using OBO = OverflowingBinaryOperator;
 829   ConstantRange Result = add(Other);
 830
 831   auto addWithNoUnsignedWrap = [this](const ConstantRange &Other) {
 832     APInt LMin = getUnsignedMin(), LMax = getUnsignedMax();
 833     APInt RMin = Other.getUnsignedMin(), RMax = Other.getUnsignedMax();
 834     bool Overflow;
 835     APInt NewMin = LMin.uadd_ov(RMin, Overflow);
 836     if (Overflow)
 837       return getEmpty();
 838     APInt NewMax = LMax.uadd_sat(RMax);
 839     return getNonEmpty(std::move(NewMin), std::move(NewMax) + 1);
 840   };
 841
 842   auto addWithNoSignedWrap = [this](const ConstantRange &Other) {
 843     APInt LMin = getSignedMin(), LMax = getSignedMax();
 844     APInt RMin = Other.getSignedMin(), RMax = Other.getSignedMax();
 845     if (LMin.isNonNegative()) {
 846       bool Overflow;
 847       APInt Temp = LMin.sadd_ov(RMin, Overflow);
 848       if (Overflow)
 849         return getEmpty();
 850     }
 851     if (LMax.isNegative()) {
 852       bool Overflow;
 853       APInt Temp = LMax.sadd_ov(RMax, Overflow);
 854       if (Overflow)
 855         return getEmpty();
 856     }
 857     APInt NewMin = LMin.sadd_sat(RMin);
 858     APInt NewMax = LMax.sadd_sat(RMax);
 859     return getNonEmpty(std::move(NewMin), std::move(NewMax) + 1);
 860   };
 861
 862   if (NoWrapKind & OBO::NoSignedWrap)
 863     Result = Result.intersectWith(addWithNoSignedWrap(Other), RangeType);
 864   if (NoWrapKind & OBO::NoUnsignedWrap)
 865     Result = Result.intersectWith(addWithNoUnsignedWrap(Other), RangeType);
 866   return Result;
 867 }
 868
 869 ConstantRange
 870 ConstantRange::sub(const ConstantRange &Other) const {
 871   if (isEmptySet() || Other.isEmptySet())
 872     return getEmpty();
 873   if (isFullSet() || Other.isFullSet())
 874     return getFull();
 875
 876   APInt NewLower = getLower() - Other.getUpper() + 1;
 877   APInt NewUpper = getUpper() - Other.getLower();
 878   if (NewLower == NewUpper)
 879     return getFull();
 880
 881   ConstantRange X = ConstantRange(std::move(NewLower), std::move(NewUpper));
 882   if (X.isSizeStrictlySmallerThan(*this) ||
 883       X.isSizeStrictlySmallerThan(Other))
 884     // We've wrapped, therefore, full set.
 885     return getFull();
 886   return X;
 887 }
 888
 889 ConstantRange
 890 ConstantRange::multiply(const ConstantRange &Other) const {
 891   // TODO: If either operand is a single element and the multiply is known to
 892   // be non-wrapping, round the result min and max value to the appropriate
 893   // multiple of that element. If wrapping is possible, at least adjust the
 894   // range according to the greatest power-of-two factor of the single element.
 895
 896   if (isEmptySet() || Other.isEmptySet())
 897     return getEmpty();
 898
 899   // Multiplication is signedness-independent. However different ranges can be
 900   // obtained depending on how the input ranges are treated. These different
 901   // ranges are all conservatively correct, but one might be better than the
 902   // other. We calculate two ranges; one treating the inputs as unsigned
 903   // and the other signed, then return the smallest of these ranges.
 904
 905   // Unsigned range first.
 906   APInt this_min = getUnsignedMin().zext(getBitWidth() * 2);
 907   APInt this_max = getUnsignedMax().zext(getBitWidth() * 2);
 908   APInt Other_min = Other.getUnsignedMin().zext(getBitWidth() * 2);
 909   APInt Other_max = Other.getUnsignedMax().zext(getBitWidth() * 2);
 910
 911   ConstantRange Result_zext = ConstantRange(this_min * Other_min,
 912                                             this_max * Other_max + 1);
 913   ConstantRange UR = Result_zext.truncate(getBitWidth());
 914
 915   // If the unsigned range doesn't wrap, and isn't negative then it's a range
 916   // from one positive number to another which is as good as we can generate.
 917   // In this case, skip the extra work of generating signed ranges which aren't
 918   // going to be better than this range.
 919   if (!UR.isUpperWrapped() &&
 920       (UR.getUpper().isNonNegative() || UR.getUpper().isMinSignedValue()))
 921     return UR;
 922
 923   // Now the signed range. Because we could be dealing with negative numbers
 924   // here, the lower bound is the smallest of the cartesian product of the
 925   // lower and upper ranges; for example:
 926   //   [-1,4) * [-2,3) = min(-1*-2, -1*2, 3*-2, 3*2) = -6.
 927   // Similarly for the upper bound, swapping min for max.
 928
 929   this_min = getSignedMin().sext(getBitWidth() * 2);
 930   this_max = getSignedMax().sext(getBitWidth() * 2);
 931   Other_min = Other.getSignedMin().sext(getBitWidth() * 2);
 932   Other_max = Other.getSignedMax().sext(getBitWidth() * 2);
 933
 934   auto L = {this_min * Other_min, this_min * Other_max,
 935             this_max * Other_min, this_max * Other_max};
 936   auto Compare = [](const APInt &A, const APInt &B) { return A.slt(B); };
 937   ConstantRange Result_sext(std::min(L, Compare), std::max(L, Compare) + 1);
 938   ConstantRange SR = Result_sext.truncate(getBitWidth());
 939
 940   return UR.isSizeStrictlySmallerThan(SR) ? UR : SR;
 941 }
 942
 943 ConstantRange
 944 ConstantRange::smax(const ConstantRange &Other) const {
 945   // X smax Y is: range(smax(X_smin, Y_smin),
 946   //                    smax(X_smax, Y_smax))
 947   if (isEmptySet() || Other.isEmptySet())
 948     return getEmpty();
 949   APInt NewL = APIntOps::smax(getSignedMin(), Other.getSignedMin());
 950   APInt NewU = APIntOps::smax(getSignedMax(), Other.getSignedMax()) + 1;
 951   return getNonEmpty(std::move(NewL), std::move(NewU));
 952 }
 953
 954 ConstantRange
 955 ConstantRange::umax(const ConstantRange &Other) const {
 956   // X umax Y is: range(umax(X_umin, Y_umin),
 957   //                    umax(X_umax, Y_umax))
 958   if (isEmptySet() || Other.isEmptySet())
 959     return getEmpty();
 960   APInt NewL = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
 961   APInt NewU = APIntOps::umax(getUnsignedMax(), Other.getUnsignedMax()) + 1;
 962   return getNonEmpty(std::move(NewL), std::move(NewU));
 963 }
 964
 965 ConstantRange
 966 ConstantRange::smin(const ConstantRange &Other) const {
 967   // X smin Y is: range(smin(X_smin, Y_smin),
 968   //                    smin(X_smax, Y_smax))
 969   if (isEmptySet() || Other.isEmptySet())
 970     return getEmpty();
 971   APInt NewL = APIntOps::smin(getSignedMin(), Other.getSignedMin());
 972   APInt NewU = APIntOps::smin(getSignedMax(), Other.getSignedMax()) + 1;
 973   return getNonEmpty(std::move(NewL), std::move(NewU));
 974 }
 975
 976 ConstantRange
 977 ConstantRange::umin(const ConstantRange &Other) const {
 978   // X umin Y is: range(umin(X_umin, Y_umin),
 979   //                    umin(X_umax, Y_umax))
 980   if (isEmptySet() || Other.isEmptySet())
 981     return getEmpty();
 982   APInt NewL = APIntOps::umin(getUnsignedMin(), Other.getUnsignedMin());
 983   APInt NewU = APIntOps::umin(getUnsignedMax(), Other.getUnsignedMax()) + 1;
 984   return getNonEmpty(std::move(NewL), std::move(NewU));
 985 }
 986
 987 ConstantRange
 988 ConstantRange::udiv(const ConstantRange &RHS) const {
 989   if (isEmptySet() || RHS.isEmptySet() || RHS.getUnsignedMax().isNullValue())
 990     return getEmpty();
 991
 992   APInt Lower = getUnsignedMin().udiv(RHS.getUnsignedMax());
 993
 994   APInt RHS_umin = RHS.getUnsignedMin();
 995   if (RHS_umin.isNullValue()) {
 996     // We want the lowest value in RHS excluding zero. Usually that would be 1
 997     // except for a range in the form of [X, 1) in which case it would be X.
 998     if (RHS.getUpper() == 1)
 999       RHS_umin = RHS.getLower();
1000     else
1001       RHS_umin = 1;
1002   }
1003
1004   APInt Upper = getUnsignedMax().udiv(RHS_umin) + 1;
1005   return getNonEmpty(std::move(Lower), std::move(Upper));
1006 }
1007
1008 ConstantRange ConstantRange::sdiv(const ConstantRange &RHS) const {
1009   // We split up the LHS and RHS into positive and negative components
1010   // and then also compute the positive and negative components of the result
1011   // separately by combining division results with the appropriate signs.
1012   APInt Zero = APInt::getNullValue(getBitWidth());
1013   APInt SignedMin = APInt::getSignedMinValue(getBitWidth());
1014   ConstantRange PosFilter(APInt(getBitWidth(), 1), SignedMin);
1015   ConstantRange NegFilter(SignedMin, Zero);
1016   ConstantRange PosL = intersectWith(PosFilter);
1017   ConstantRange NegL = intersectWith(NegFilter);
1018   ConstantRange PosR = RHS.intersectWith(PosFilter);
1019   ConstantRange NegR = RHS.intersectWith(NegFilter);
1020
1021   ConstantRange PosRes = getEmpty();
1022   if (!PosL.isEmptySet() && !PosR.isEmptySet())
1023     // pos / pos = pos.
1024     PosRes = ConstantRange(PosL.Lower.sdiv(PosR.Upper - 1),
1025                            (PosL.Upper - 1).sdiv(PosR.Lower) + 1);
1026
1027   if (!NegL.isEmptySet() && !NegR.isEmptySet()) {
1028     // neg / neg = pos.
1029     //
1030     // We need to deal with one tricky case here: SignedMin / -1 is UB on the
1031     // IR level, so we'll want to exclude this case when calculating bounds.
1032     // (For APInts the operation is well-defined and yields SignedMin.) We
1033     // handle this by dropping either SignedMin from the LHS or -1 from the RHS.
1034     APInt Lo = (NegL.Upper - 1).sdiv(NegR.Lower);
1035     if (NegL.Lower.isMinSignedValue() && NegR.Upper.isNullValue()) {
1036       // Remove -1 from the LHS. Skip if it's the only element, as this would
1037       // leave us with an empty set.
1038       if (!NegR.Lower.isAllOnesValue()) {
1039         APInt AdjNegRUpper;
1040         if (RHS.Lower.isAllOnesValue())
1041           // Negative part of [-1, X] without -1 is [SignedMin, X].
1042           AdjNegRUpper = RHS.Upper;
1043         else
1044           // [X, -1] without -1 is [X, -2].
1045           AdjNegRUpper = NegR.Upper - 1;
1046
1047         PosRes = PosRes.unionWith(
1048             ConstantRange(Lo, NegL.Lower.sdiv(AdjNegRUpper - 1) + 1));
1049       }
1050
1051       // Remove SignedMin from the RHS. Skip if it's the only element, as this
1052       // would leave us with an empty set.
1053       if (NegL.Upper != SignedMin + 1) {
1054         APInt AdjNegLLower;
1055         if (Upper == SignedMin + 1)
1056           // Negative part of [X, SignedMin] without SignedMin is [X, -1].
1057           AdjNegLLower = Lower;
1058         else
1059           // [SignedMin, X] without SignedMin is [SignedMin + 1, X].
1060           AdjNegLLower = NegL.Lower + 1;
1061
1062         PosRes = PosRes.unionWith(
1063             ConstantRange(std::move(Lo),
1064                           AdjNegLLower.sdiv(NegR.Upper - 1) + 1));
1065       }
1066     } else {
1067       PosRes = PosRes.unionWith(
1068           ConstantRange(std::move(Lo), NegL.Lower.sdiv(NegR.Upper - 1) + 1));
1069     }
1070   }
1071
1072   ConstantRange NegRes = getEmpty();
1073   if (!PosL.isEmptySet() && !NegR.isEmptySet())
1074     // pos / neg = neg.
1075     NegRes = ConstantRange((PosL.Upper - 1).sdiv(NegR.Upper - 1),
1076                            PosL.Lower.sdiv(NegR.Lower) + 1);
1077
1078   if (!NegL.isEmptySet() && !PosR.isEmptySet())
1079     // neg / pos = neg.
1080     NegRes = NegRes.unionWith(
1081         ConstantRange(NegL.Lower.sdiv(PosR.Lower),
1082                       (NegL.Upper - 1).sdiv(PosR.Upper - 1) + 1));
1083
1084   // Prefer a non-wrapping signed range here.
1085   ConstantRange Res = NegRes.unionWith(PosRes, PreferredRangeType::Signed);
1086
1087   // Preserve the zero that we dropped when splitting the LHS by sign.
1088   if (contains(Zero) && (!PosR.isEmptySet() || !NegR.isEmptySet()))
1089     Res = Res.unionWith(ConstantRange(Zero));
1090   return Res;
1091 }
1092
1093 ConstantRange ConstantRange::urem(const ConstantRange &RHS) const {
1094   if (isEmptySet() || RHS.isEmptySet() || RHS.getUnsignedMax().isNullValue())
1095     return getEmpty();
1096
1097   // L % R for L < R is L.
1098   if (getUnsignedMax().ult(RHS.getUnsignedMin()))
1099     return *this;
1100
1101   // L % R is <= L and < R.
1102   APInt Upper = APIntOps::umin(getUnsignedMax(), RHS.getUnsignedMax() - 1) + 1;
1103   return getNonEmpty(APInt::getNullValue(getBitWidth()), std::move(Upper));
1104 }
1105
1106 ConstantRange ConstantRange::srem(const ConstantRange &RHS) const {
1107   if (isEmptySet() || RHS.isEmptySet())
1108     return getEmpty();
1109
1110   ConstantRange AbsRHS = RHS.abs();
1111   APInt MinAbsRHS = AbsRHS.getUnsignedMin();
1112   APInt MaxAbsRHS = AbsRHS.getUnsignedMax();
1113
1114   // Modulus by zero is UB.
1115   if (MaxAbsRHS.isNullValue())
1116     return getEmpty();
1117
1118   if (MinAbsRHS.isNullValue())
1119     ++MinAbsRHS;
1120
1121   APInt MinLHS = getSignedMin(), MaxLHS = getSignedMax();
1122
1123   if (MinLHS.isNonNegative()) {
1124     // L % R for L < R is L.
1125     if (MaxLHS.ult(MinAbsRHS))
1126       return *this;
1127
1128     // L % R is <= L and < R.
1129     APInt Upper = APIntOps::umin(MaxLHS, MaxAbsRHS - 1) + 1;
1130     return ConstantRange(APInt::getNullValue(getBitWidth()), std::move(Upper));
1131   }
1132
1133   // Same basic logic as above, but the result is negative.
1134   if (MaxLHS.isNegative()) {
1135     if (MinLHS.ugt(-MinAbsRHS))
1136       return *this;
1137
1138     APInt Lower = APIntOps::umax(MinLHS, -MaxAbsRHS + 1);
1139     return ConstantRange(std::move(Lower), APInt(getBitWidth(), 1));
1140   }
1141
1142   // LHS range crosses zero.
1143   APInt Lower = APIntOps::umax(MinLHS, -MaxAbsRHS + 1);
1144   APInt Upper = APIntOps::umin(MaxLHS, MaxAbsRHS - 1) + 1;
1145   return ConstantRange(std::move(Lower), std::move(Upper));
1146 }
1147
1148 ConstantRange
1149 ConstantRange::binaryAnd(const ConstantRange &Other) const {
1150   if (isEmptySet() || Other.isEmptySet())
1151     return getEmpty();
1152
1153   // TODO: replace this with something less conservative
1154
1155   APInt umin = APIntOps::umin(Other.getUnsignedMax(), getUnsignedMax());
1156   return getNonEmpty(APInt::getNullValue(getBitWidth()), std::move(umin) + 1);
1157 }
1158
1159 ConstantRange
1160 ConstantRange::binaryOr(const ConstantRange &Other) const {
1161   if (isEmptySet() || Other.isEmptySet())
1162     return getEmpty();
1163
1164   // TODO: replace this with something less conservative
1165
1166   APInt umax = APIntOps::umax(getUnsignedMin(), Other.getUnsignedMin());
1167   return getNonEmpty(std::move(umax), APInt::getNullValue(getBitWidth()));
1168 }
1169
1170 ConstantRange
1171 ConstantRange::shl(const ConstantRange &Other) const {
1172   if (isEmptySet() || Other.isEmptySet())
1173     return getEmpty();
1174
1175   APInt max = getUnsignedMax();
1176   APInt Other_umax = Other.getUnsignedMax();
1177
1178   // If we are shifting by maximum amount of
1179   // zero return return the original range.
1180   if (Other_umax.isNullValue())
1181     return *this;
1182   // there's overflow!
1183   if (Other_umax.ugt(max.countLeadingZeros()))
1184     return getFull();
1185
1186   // FIXME: implement the other tricky cases
1187
1188   APInt min = getUnsignedMin();
1189   min <<= Other.getUnsignedMin();
1190   max <<= Other_umax;
1191
1192   return ConstantRange(std::move(min), std::move(max) + 1);
1193 }
1194
1195 ConstantRange
1196 ConstantRange::lshr(const ConstantRange &Other) const {
1197   if (isEmptySet() || Other.isEmptySet())
1198     return getEmpty();
1199
1200   APInt max = getUnsignedMax().lshr(Other.getUnsignedMin()) + 1;
1201   APInt min = getUnsignedMin().lshr(Other.getUnsignedMax());
1202   return getNonEmpty(std::move(min), std::move(max));
1203 }
1204
1205 ConstantRange
1206 ConstantRange::ashr(const ConstantRange &Other) const {
1207   if (isEmptySet() || Other.isEmptySet())
1208     return getEmpty();
1209
1210   // May straddle zero, so handle both positive and negative cases.
1211   // 'PosMax' is the upper bound of the result of the ashr
1212   // operation, when Upper of the LHS of ashr is a non-negative.
1213   // number. Since ashr of a non-negative number will result in a
1214   // smaller number, the Upper value of LHS is shifted right with
1215   // the minimum value of 'Other' instead of the maximum value.
1216   APInt PosMax = getSignedMax().ashr(Other.getUnsignedMin()) + 1;
1217
1218   // 'PosMin' is the lower bound of the result of the ashr
1219   // operation, when Lower of the LHS is a non-negative number.
1220   // Since ashr of a non-negative number will result in a smaller
1221   // number, the Lower value of LHS is shifted right with the
1222   // maximum value of 'Other'.
1223   APInt PosMin = getSignedMin().ashr(Other.getUnsignedMax());
1224
1225   // 'NegMax' is the upper bound of the result of the ashr
1226   // operation, when Upper of the LHS of ashr is a negative number.
1227   // Since 'ashr' of a negative number will result in a bigger
1228   // number, the Upper value of LHS is shifted right with the
1229   // maximum value of 'Other'.
1230   APInt NegMax = getSignedMax().ashr(Other.getUnsignedMax()) + 1;
1231
1232   // 'NegMin' is the lower bound of the result of the ashr
1233   // operation, when Lower of the LHS of ashr is a negative number.
1234   // Since 'ashr' of a negative number will result in a bigger
1235   // number, the Lower value of LHS is shifted right with the
1236   // minimum value of 'Other'.
1237   APInt NegMin = getSignedMin().ashr(Other.getUnsignedMin());
1238
1239   APInt max, min;
1240   if (getSignedMin().isNonNegative()) {
1241     // Upper and Lower of LHS are non-negative.
1242     min = PosMin;
1243     max = PosMax;
1244   } else if (getSignedMax().isNegative()) {
1245     // Upper and Lower of LHS are negative.
1246     min = NegMin;
1247     max = NegMax;
1248   } else {
1249     // Upper is non-negative and Lower is negative.
1250     min = NegMin;
1251     max = PosMax;
1252   }
1253   return getNonEmpty(std::move(min), std::move(max));
1254 }
1255
1256 ConstantRange ConstantRange::uadd_sat(const ConstantRange &Other) const {
1257   if (isEmptySet() || Other.isEmptySet())
1258     return getEmpty();
1259
1260   APInt NewL = getUnsignedMin().uadd_sat(Other.getUnsignedMin());
1261   APInt NewU = getUnsignedMax().uadd_sat(Other.getUnsignedMax()) + 1;
1262   return getNonEmpty(std::move(NewL), std::move(NewU));
1263 }
1264
1265 ConstantRange ConstantRange::sadd_sat(const ConstantRange &Other) const {
1266   if (isEmptySet() || Other.isEmptySet())
1267     return getEmpty();
1268
1269   APInt NewL = getSignedMin().sadd_sat(Other.getSignedMin());
1270   APInt NewU = getSignedMax().sadd_sat(Other.getSignedMax()) + 1;
1271   return getNonEmpty(std::move(NewL), std::move(NewU));
1272 }
1273
1274 ConstantRange ConstantRange::usub_sat(const ConstantRange &Other) const {
1275   if (isEmptySet() || Other.isEmptySet())
1276     return getEmpty();
1277
1278   APInt NewL = getUnsignedMin().usub_sat(Other.getUnsignedMax());
1279   APInt NewU = getUnsignedMax().usub_sat(Other.getUnsignedMin()) + 1;
1280   return getNonEmpty(std::move(NewL), std::move(NewU));
1281 }
1282
1283 ConstantRange ConstantRange::ssub_sat(const ConstantRange &Other) const {
1284   if (isEmptySet() || Other.isEmptySet())
1285     return getEmpty();
1286
1287   APInt NewL = getSignedMin().ssub_sat(Other.getSignedMax());
1288   APInt NewU = getSignedMax().ssub_sat(Other.getSignedMin()) + 1;
1289   return getNonEmpty(std::move(NewL), std::move(NewU));
1290 }
1291
1292 ConstantRange ConstantRange::inverse() const {
1293   if (isFullSet())
1294     return getEmpty();
1295   if (isEmptySet())
1296     return getFull();
1297   return ConstantRange(Upper, Lower);
1298 }
1299
1300 ConstantRange ConstantRange::abs() const {
1301   if (isEmptySet())
1302     return getEmpty();
1303
1304   if (isSignWrappedSet()) {
1305     APInt Lo;
1306     // Check whether the range crosses zero.
1307     if (Upper.isStrictlyPositive() || !Lower.isStrictlyPositive())
1308       Lo = APInt::getNullValue(getBitWidth());
1309     else
1310       Lo = APIntOps::umin(Lower, -Upper + 1);
1311
1312     // SignedMin is included in the result range.
1313     return ConstantRange(Lo, APInt::getSignedMinValue(getBitWidth()) + 1);
1314   }
1315
1316   APInt SMin = getSignedMin(), SMax = getSignedMax();
1317
1318   // All non-negative.
1319   if (SMin.isNonNegative())
1320     return *this;
1321
1322   // All negative.
1323   if (SMax.isNegative())
1324     return ConstantRange(-SMax, -SMin + 1);
1325
1326   // Range crosses zero.
1327   return ConstantRange(APInt::getNullValue(getBitWidth()),
1328                        APIntOps::umax(-SMin, SMax) + 1);
1329 }
1330
1331 ConstantRange::OverflowResult ConstantRange::unsignedAddMayOverflow(
1332     const ConstantRange &Other) const {
1333   if (isEmptySet() || Other.isEmptySet())
1334     return OverflowResult::MayOverflow;
1335
1336   APInt Min = getUnsignedMin(), Max = getUnsignedMax();
1337   APInt OtherMin = Other.getUnsignedMin(), OtherMax = Other.getUnsignedMax();
1338
1339   // a u+ b overflows high iff a u> ~b.
1340   if (Min.ugt(~OtherMin))
1341     return OverflowResult::AlwaysOverflowsHigh;
1342   if (Max.ugt(~OtherMax))
1343     return OverflowResult::MayOverflow;
1344   return OverflowResult::NeverOverflows;
1345 }
1346
1347 ConstantRange::OverflowResult ConstantRange::signedAddMayOverflow(
1348     const ConstantRange &Other) const {
1349   if (isEmptySet() || Other.isEmptySet())
1350     return OverflowResult::MayOverflow;
1351
1352   APInt Min = getSignedMin(), Max = getSignedMax();
1353   APInt OtherMin = Other.getSignedMin(), OtherMax = Other.getSignedMax();
1354
1355   APInt SignedMin = APInt::getSignedMinValue(getBitWidth());
1356   APInt SignedMax = APInt::getSignedMaxValue(getBitWidth());
1357
1358   // a s+ b overflows high iff a s>=0 && b s>= 0 && a s> smax - b.
1359   // a s+ b overflows low iff a s< 0 && b s< 0 && a s< smin - b.
1360   if (Min.isNonNegative() && OtherMin.isNonNegative() &&
1361       Min.sgt(SignedMax - OtherMin))
1362     return OverflowResult::AlwaysOverflowsHigh;
1363   if (Max.isNegative() && OtherMax.isNegative() &&
1364       Max.slt(SignedMin - OtherMax))
1365     return OverflowResult::AlwaysOverflowsLow;
1366
1367   if (Max.isNonNegative() && OtherMax.isNonNegative() &&
1368       Max.sgt(SignedMax - OtherMax))
1369     return OverflowResult::MayOverflow;
1370   if (Min.isNegative() && OtherMin.isNegative() &&
1371       Min.slt(SignedMin - OtherMin))
1372     return OverflowResult::MayOverflow;
1373
1374   return OverflowResult::NeverOverflows;
1375 }
1376
1377 ConstantRange::OverflowResult ConstantRange::unsignedSubMayOverflow(
1378     const ConstantRange &Other) const {
1379   if (isEmptySet() || Other.isEmptySet())
1380     return OverflowResult::MayOverflow;
1381
1382   APInt Min = getUnsignedMin(), Max = getUnsignedMax();
1383   APInt OtherMin = Other.getUnsignedMin(), OtherMax = Other.getUnsignedMax();
1384
1385   // a u- b overflows low iff a u< b.
1386   if (Max.ult(OtherMin))
1387     return OverflowResult::AlwaysOverflowsLow;
1388   if (Min.ult(OtherMax))
1389     return OverflowResult::MayOverflow;
1390   return OverflowResult::NeverOverflows;
1391 }
1392
1393 ConstantRange::OverflowResult ConstantRange::signedSubMayOverflow(
1394     const ConstantRange &Other) const {
1395   if (isEmptySet() || Other.isEmptySet())
1396     return OverflowResult::MayOverflow;
1397
1398   APInt Min = getSignedMin(), Max = getSignedMax();
1399   APInt OtherMin = Other.getSignedMin(), OtherMax = Other.getSignedMax();
1400
1401   APInt SignedMin = APInt::getSignedMinValue(getBitWidth());
1402   APInt SignedMax = APInt::getSignedMaxValue(getBitWidth());
1403
1404   // a s- b overflows high iff a s>=0 && b s< 0 && a s> smax + b.
1405   // a s- b overflows low iff a s< 0 && b s>= 0 && a s< smin + b.
1406   if (Min.isNonNegative() && OtherMax.isNegative() &&
1407       Min.sgt(SignedMax + OtherMax))
1408     return OverflowResult::AlwaysOverflowsHigh;
1409   if (Max.isNegative() && OtherMin.isNonNegative() &&
1410       Max.slt(SignedMin + OtherMin))
1411     return OverflowResult::AlwaysOverflowsLow;
1412
1413   if (Max.isNonNegative() && OtherMin.isNegative() &&
1414       Max.sgt(SignedMax + OtherMin))
1415     return OverflowResult::MayOverflow;
1416   if (Min.isNegative() && OtherMax.isNonNegative() &&
1417       Min.slt(SignedMin + OtherMax))
1418     return OverflowResult::MayOverflow;
1419
1420   return OverflowResult::NeverOverflows;
1421 }
1422
1423 ConstantRange::OverflowResult ConstantRange::unsignedMulMayOverflow(
1424     const ConstantRange &Other) const {
1425   if (isEmptySet() || Other.isEmptySet())
1426     return OverflowResult::MayOverflow;
1427
1428   APInt Min = getUnsignedMin(), Max = getUnsignedMax();
1429   APInt OtherMin = Other.getUnsignedMin(), OtherMax = Other.getUnsignedMax();
1430   bool Overflow;
1431
1432   (void) Min.umul_ov(OtherMin, Overflow);
1433   if (Overflow)
1434     return OverflowResult::AlwaysOverflowsHigh;
1435
1436   (void) Max.umul_ov(OtherMax, Overflow);
1437   if (Overflow)
1438     return OverflowResult::MayOverflow;
1439
1440   return OverflowResult::NeverOverflows;
1441 }
1442
1443 void ConstantRange::print(raw_ostream &OS) const {
1444   if (isFullSet())
1445     OS << "full-set";
1446   else if (isEmptySet())
1447     OS << "empty-set";
1448   else
1449     OS << "[" << Lower << "," << Upper << ")";
1450 }
1451
1452 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
1453 LLVM_DUMP_METHOD void ConstantRange::dump() const {
1454   print(dbgs());
1455 }
1456 #endif
1457
1458 ConstantRange llvm::getConstantRangeFromMetadata(const MDNode &Ranges) {
1459   const unsigned NumRanges = Ranges.getNumOperands() / 2;
1460   assert(NumRanges >= 1 && "Must have at least one range!");
1461   assert(Ranges.getNumOperands() % 2 == 0 && "Must be a sequence of pairs");
1462
1463   auto *FirstLow = mdconst::extract<ConstantInt>(Ranges.getOperand(0));
1464   auto *FirstHigh = mdconst::extract<ConstantInt>(Ranges.getOperand(1));
1465
1466   ConstantRange CR(FirstLow->getValue(), FirstHigh->getValue());
1467
1468   for (unsigned i = 1; i < NumRanges; ++i) {
1469     auto *Low = mdconst::extract<ConstantInt>(Ranges.getOperand(2 * i + 0));
1470     auto *High = mdconst::extract<ConstantInt>(Ranges.getOperand(2 * i + 1));
1471
1472     // Note: unionWith will potentially create a range that contains values not
1473     // contained in any of the original N ranges.
1474     CR = CR.unionWith(ConstantRange(Low->getValue(), High->getValue()));
1475   }
1476
1477   return CR;
1478 }