[KnownBits] Improve KnownBits::udiv

We can more precisely determine the upper bits doing `MaxNum /
MinDenum` as opposed to only using the MSB.

As well, if the `exact` flag is set, we can sometimes determine some
of the low-bits.

Differential Revision: https://reviews.llvm.org/D150094

llvm/include/llvm/Support/KnownBits.h

@@ -347,7 +347,8 @@ struct KnownBits {
                         bool Exact = false);
 
   /// Compute known bits for udiv(LHS, RHS).
-  static KnownBits udiv(const KnownBits &LHS, const KnownBits &RHS);
+  static KnownBits udiv(const KnownBits &LHS, const KnownBits &RHS,
+                        bool Exact = false);
 
   /// Compute known bits for urem(LHS, RHS).
   static KnownBits urem(const KnownBits &LHS, const KnownBits &RHS);

llvm/lib/Support/KnownBits.cpp

@@ -540,7 +540,7 @@ KnownBits KnownBits::sdiv(const KnownBits &LHS, const KnownBits &RHS,
                           bool Exact) {
   // Equivilent of `udiv`. We must have caught this before it was folded.
   if (LHS.isNonNegative() && RHS.isNonNegative())
-    return udiv(LHS, RHS);
+    return udiv(LHS, RHS, Exact);
 
   unsigned BitWidth = LHS.getBitWidth();
   assert(!LHS.hasConflict() && !RHS.hasConflict() && "Bad inputs");
@@ -604,21 +604,33 @@ KnownBits KnownBits::sdiv(const KnownBits &LHS, const KnownBits &RHS,
   return Known;
 }
 
-KnownBits KnownBits::udiv(const KnownBits &LHS, const KnownBits &RHS) {
+KnownBits KnownBits::udiv(const KnownBits &LHS, const KnownBits &RHS,
+                          bool Exact) {
   unsigned BitWidth = LHS.getBitWidth();
   assert(!LHS.hasConflict() && !RHS.hasConflict());
   KnownBits Known(BitWidth);
 
-  // For the purposes of computing leading zeros we can conservatively
-  // treat a udiv as a logical right shift by the power of 2 known to
-  // be less than the denominator.
-  unsigned LeadZ = LHS.countMinLeadingZeros();
-  unsigned RHSMaxLeadingZeros = RHS.countMaxLeadingZeros();
+  // We can figure out the minimum number of upper zero bits by doing
+  // MaxNumerator / MinDenominator. If the Numerator gets smaller or Denominator
+  // gets larger, the number of upper zero bits increases.
+  APInt MinDenum = RHS.getMinValue();
+  APInt MaxNum = LHS.getMaxValue();
+  APInt MaxRes = MinDenum.isZero() ? MaxNum : MaxNum.udiv(MinDenum);
 
-  if (RHSMaxLeadingZeros != BitWidth)
-    LeadZ = std::min(BitWidth, LeadZ + BitWidth - RHSMaxLeadingZeros - 1);
+  unsigned LeadZ = MaxRes.countLeadingZeros();
 
   Known.Zero.setHighBits(LeadZ);
+  if (Exact) {
+    // Odd / Odd -> Odd
+    if (LHS.One[0] && RHS.One[0])
+      Known.One.setBit(0);
+    // Even / Odd -> Even
+    else if (LHS.Zero[0] && RHS.One[0])
+      Known.Zero.setBit(0);
+    // Odd / Even -> impossible
+    // Even / Even -> unknown
+  }
+
   return Known;
 }
 

llvm/test/Analysis/ValueTracking/knownbits-div.ll

@@ -185,12 +185,7 @@ define i1 @sdiv_exact_even_even_fail_unknown2(i8 %x, i8 %y) {
 
 define i1 @udiv_high_bits(i8 %x, i8 %y) {
 ; CHECK-LABEL: @udiv_high_bits(
-; CHECK-NEXT:    [[NUM:%.*]] = and i8 [[X:%.*]], -127
-; CHECK-NEXT:    [[DENUM:%.*]] = or i8 [[Y:%.*]], 31
-; CHECK-NEXT:    [[DIV:%.*]] = udiv i8 [[NUM]], [[DENUM]]
-; CHECK-NEXT:    [[AND:%.*]] = and i8 [[DIV]], 8
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[AND]], 8
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %num = and i8 %x, 129
   %denum = or i8 %y, 31

llvm/unittests/Support/KnownBitsTest.cpp

@@ -249,6 +249,16 @@ TEST(KnownBitsTest, BinaryExhaustive) {
         return N1.udiv(N2);
       },
       checkCorrectnessOnlyBinary);
+  testBinaryOpExhaustive(
+      [](const KnownBits &Known1, const KnownBits &Known2) {
+        return KnownBits::udiv(Known1, Known2, /*Exact*/ true);
+      },
+      [](const APInt &N1, const APInt &N2) -> std::optional<APInt> {
+        if (N2.isZero() || !N1.urem(N2).isZero())
+          return std::nullopt;
+        return N1.udiv(N2);
+      },
+      checkCorrectnessOnlyBinary);
   testBinaryOpExhaustive(
       [](const KnownBits &Known1, const KnownBits &Known2) {
         return KnownBits::sdiv(Known1, Known2);