[ConstantRange] Add sdiv() support

The implementation is conceptually simple: We separate the LHS and
RHS into positive and negative components and then also compute the
positive and negative components of the result, taking into account
that e.g. only pos/pos and neg/neg will give a positive result.

However, there's one significant complication: SignedMin / -1 is UB
for sdiv, and we can't just ignore it, because the APInt result of
SignedMin would break the sign segregation. Instead we drop SignedMin
or -1 from the corresponding ranges, taking into account some edge
cases with wrapped ranges.

Because of the sign segregation, the implementation ends up being
nearly fully precise even for wrapped ranges (the remaining
imprecision is due to ranges that are both signed and unsigned
wrapping and are divided by a trivial divisor like 1). This means
that the testing cannot just check the signed envelope as we
usually do. Instead we collect all possible results in a bitvector
and construct a better sign wrapped range (than the full envelope).

Differential Revision: https://reviews.llvm.org/D61238

llvm-svn: 362430

include/llvm/IR/ConstantRange.h

@@ -364,6 +364,13 @@ public:
   /// \p Other.
   ConstantRange udiv(const ConstantRange &Other) const;
 
+  /// Return a new range representing the possible values resulting
+  /// from a signed division of a value in this range and a value in
+  /// \p Other. Division by zero and division of SignedMin by -1 are considered
+  /// undefined behavior, in line with IR, and do not contribute towards the
+  /// result.
+  ConstantRange sdiv(const ConstantRange &Other) const;
+
   /// Return a new range representing the possible values resulting
   /// from an unsigned remainder operation of a value in this range and a
   /// value in \p Other.

lib/IR/ConstantRange.cpp

@@ -765,6 +765,8 @@ ConstantRange ConstantRange::binaryOp(Instruction::BinaryOps BinOp,
     return multiply(Other);
   case Instruction::UDiv:
     return udiv(Other);
+  case Instruction::SDiv:
+    return sdiv(Other);
   case Instruction::URem:
     return urem(Other);
   case Instruction::SRem:
@@ -962,6 +964,91 @@ ConstantRange::udiv(const ConstantRange &RHS) const {
   return getNonEmpty(std::move(Lower), std::move(Upper));
 }
 
+ConstantRange ConstantRange::sdiv(const ConstantRange &RHS) const {
+  // We split up the LHS and RHS into positive and negative components
+  // and then also compute the positive and negative components of the result
+  // separately by combining division results with the appropriate signs.
+  APInt Zero = APInt::getNullValue(getBitWidth());
+  APInt SignedMin = APInt::getSignedMinValue(getBitWidth());
+  ConstantRange PosFilter(APInt(getBitWidth(), 1), SignedMin);
+  ConstantRange NegFilter(SignedMin, Zero);
+  ConstantRange PosL = intersectWith(PosFilter);
+  ConstantRange NegL = intersectWith(NegFilter);
+  ConstantRange PosR = RHS.intersectWith(PosFilter);
+  ConstantRange NegR = RHS.intersectWith(NegFilter);
+
+  ConstantRange PosRes = getEmpty();
+  if (!PosL.isEmptySet() && !PosR.isEmptySet())
+    // pos / pos = pos.
+    PosRes = ConstantRange(PosL.Lower.sdiv(PosR.Upper - 1),
+                           (PosL.Upper - 1).sdiv(PosR.Lower) + 1);
+
+  if (!NegL.isEmptySet() && !NegR.isEmptySet()) {
+    // neg / neg = pos.
+    //
+    // We need to deal with one tricky case here: SignedMin / -1 is UB on the
+    // IR level, so we'll want to exclude this case when calculating bounds.
+    // (For APInts the operation is well-defined and yields SignedMin.) We
+    // handle this by dropping either SignedMin from the LHS or -1 from the RHS.
+    APInt Lo = (NegL.Upper - 1).sdiv(NegR.Lower);
+    if (NegL.Lower.isMinSignedValue() && NegR.Upper.isNullValue()) {
+      // Remove -1 from the LHS. Skip if it's the only element, as this would
+      // leave us with an empty set.
+      if (!NegR.Lower.isAllOnesValue()) {
+        APInt AdjNegRUpper;
+        if (RHS.Lower.isAllOnesValue())
+          // Negative part of [-1, X] without -1 is [SignedMin, X].
+          AdjNegRUpper = RHS.Upper;
+        else
+          // [X, -1] without -1 is [X, -2].
+          AdjNegRUpper = NegR.Upper - 1;
+
+        PosRes = PosRes.unionWith(
+            ConstantRange(Lo, NegL.Lower.sdiv(AdjNegRUpper - 1) + 1));
+      }
+
+      // Remove SignedMin from the RHS. Skip if it's the only element, as this
+      // would leave us with an empty set.
+      if (NegL.Upper != SignedMin + 1) {
+        APInt AdjNegLLower;
+        if (Upper == SignedMin + 1)
+          // Negative part of [X, SignedMin] without SignedMin is [X, -1].
+          AdjNegLLower = Lower;
+        else
+          // [SignedMin, X] without SignedMin is [SignedMin + 1, X].
+          AdjNegLLower = NegL.Lower + 1;
+
+        PosRes = PosRes.unionWith(
+            ConstantRange(std::move(Lo),
+                          AdjNegLLower.sdiv(NegR.Upper - 1) + 1));
+      }
+    } else {
+      PosRes = PosRes.unionWith(
+          ConstantRange(std::move(Lo), NegL.Lower.sdiv(NegR.Upper - 1) + 1));
+    }
+  }
+
+  ConstantRange NegRes = getEmpty();
+  if (!PosL.isEmptySet() && !NegR.isEmptySet())
+    // pos / neg = neg.
+    NegRes = ConstantRange((PosL.Upper - 1).sdiv(NegR.Upper - 1),
+                           PosL.Lower.sdiv(NegR.Lower) + 1);
+
+  if (!NegL.isEmptySet() && !PosR.isEmptySet())
+    // neg / pos = neg.
+    NegRes = NegRes.unionWith(
+        ConstantRange(NegL.Lower.sdiv(PosR.Lower),
+                      (NegL.Upper - 1).sdiv(PosR.Upper - 1) + 1));
+
+  // Prefer a non-wrapping signed range here.
+  ConstantRange Res = NegRes.unionWith(PosRes, PreferredRangeType::Signed);
+
+  // Preserve the zero that we dropped when splitting the LHS by sign.
+  if (contains(Zero) && (!PosR.isEmptySet() || !NegR.isEmptySet()))
+    Res = Res.unionWith(ConstantRange(Zero));
+  return Res;
+}
+
 ConstantRange ConstantRange::urem(const ConstantRange &RHS) const {
   if (isEmptySet() || RHS.isEmptySet() || RHS.getUnsignedMax().isNullValue())
     return getEmpty();

unittests/IR/ConstantRangeTest.cpp

@@ -6,6 +6,7 @@
 //
 //===----------------------------------------------------------------------===//
 
+#include "llvm/ADT/BitVector.h"
 #include "llvm/IR/ConstantRange.h"
 #include "llvm/IR/Instructions.h"
 #include "llvm/IR/Operator.h"
@@ -844,6 +845,63 @@ TEST_F(ConstantRangeTest, UDiv) {
             ConstantRange(APInt(16, 0), APInt(16, 99)));
 }
 
+TEST_F(ConstantRangeTest, SDiv) {
+  unsigned Bits = 4;
+  EnumerateTwoConstantRanges(Bits, [&](const ConstantRange &CR1,
+                                       const ConstantRange &CR2) {
+    // Collect possible results in a bit vector. We store the signed value plus
+    // a bias to make it unsigned.
+    int Bias = 1 << (Bits - 1);
+    BitVector Results(1 << Bits);
+    ForeachNumInConstantRange(CR1, [&](const APInt &N1) {
+      ForeachNumInConstantRange(CR2, [&](const APInt &N2) {
+        // Division by zero is UB.
+        if (N2 == 0)
+          return;
+
+        // SignedMin / -1 is UB.
+        if (N1.isMinSignedValue() && N2.isAllOnesValue())
+          return;
+
+        APInt N = N1.sdiv(N2);
+        Results.set(N.getSExtValue() + Bias);
+      });
+    });
+
+    ConstantRange CR = CR1.sdiv(CR2);
+    if (Results.none()) {
+      EXPECT_TRUE(CR.isEmptySet());
+      return;
+    }
+
+    // If there is a non-full signed envelope, that should be the result.
+    APInt SMin(Bits, Results.find_first() - Bias);
+    APInt SMax(Bits, Results.find_last() - Bias);
+    ConstantRange Envelope = ConstantRange::getNonEmpty(SMin, SMax + 1);
+    if (!Envelope.isFullSet()) {
+      EXPECT_EQ(Envelope, CR);
+      return;
+    }
+
+    // If the signed envelope is a full set, try to find a smaller sign wrapped
+    // set that is separated in negative and positive components (or one which
+    // can also additionally contain zero).
+    int LastNeg = Results.find_last_in(0, Bias) - Bias;
+    int LastPos = Results.find_next(Bias) - Bias;
+    if (Results[Bias]) {
+      if (LastNeg == -1)
+        ++LastNeg;
+      else if (LastPos == 1)
+        --LastPos;
+    }
+
+    APInt WMax(Bits, LastNeg);
+    APInt WMin(Bits, LastPos);
+    ConstantRange Wrapped = ConstantRange::getNonEmpty(WMin, WMax + 1);
+    EXPECT_EQ(Wrapped, CR);
+  });
+}
+
 TEST_F(ConstantRangeTest, URem) {
   EXPECT_EQ(Full.urem(Empty), Empty);
   EXPECT_EQ(Empty.urem(Full), Empty);