Index: llvm/lib/Transforms/Scalar/CorrelatedValuePropagation.cpp
===================================================================
--- llvm/lib/Transforms/Scalar/CorrelatedValuePropagation.cpp
+++ llvm/lib/Transforms/Scalar/CorrelatedValuePropagation.cpp
@@ -58,6 +58,7 @@
 STATISTIC(NumReturns,   "Number of return values propagated");
 STATISTIC(NumDeadCases, "Number of switch cases removed");
 STATISTIC(NumSDivs,     "Number of sdiv converted to udiv");
+STATISTIC(NumUDivs,     "Number of udivs whose width was decreased");
 STATISTIC(NumAShrs,     "Number of ashr converted to lshr");
 STATISTIC(NumSRems,     "Number of srem converted to urem");
 STATISTIC(NumOverflows, "Number of overflow checks removed");
@@ -432,6 +433,45 @@
   return true;
 }
 
+/// Try to shrink a udiv/urem's width down to the smallest power of two that's
+/// sufficient to contain its operands.
+static bool processUDivOrURem(BinaryOperator *SDI, LazyValueInfo *LVI) {
+  assert(SDI->getOpcode() == Instruction::UDiv ||
+         SDI->getOpcode() == Instruction::URem);
+  if (SDI->getType()->isVectorTy())
+    return false;
+
+  // Find the smallest power of two bitwidth that's sufficient to hold SDI's
+  // operands.
+  auto OrigWidth = SDI->getType()->getIntegerBitWidth();
+  ConstantRange R(OrigWidth, /*isFullset=*/false);
+  for (Value *Operand : SDI->operands()) {
+    R = R.unionWith(LVI->getConstantRange(Operand, SDI->getParent()));
+  }
+  // Don't shrink below 8 bits wide.
+  unsigned NewWidth = std::max<unsigned>(
+      PowerOf2Ceil((R.getUnsignedMax() + 1).ceilLogBase2()), 8);
+  if (NewWidth == OrigWidth)
+    return false;
+
+  ++NumUDivs;
+  auto *TruncTy = Type::getIntNTy(SDI->getContext(), NewWidth);
+  auto *LHS = CastInst::Create(Instruction::Trunc, SDI->getOperand(0), TruncTy,
+                               SDI->getName() + ".lhs.trunc", SDI);
+  auto *RHS = CastInst::Create(Instruction::Trunc, SDI->getOperand(1), TruncTy,
+                               SDI->getName() + ".rhs.trunc", SDI);
+  auto *BO =
+      BinaryOperator::Create(SDI->getOpcode(), LHS, RHS, SDI->getName(), SDI);
+  auto *Zext = CastInst::Create(Instruction::ZExt, BO, SDI->getType(),
+                                SDI->getName() + ".zext", SDI);
+  if (BO->getOpcode() == Instruction::UDiv)
+    BO->setIsExact(SDI->isExact());
+
+  SDI->replaceAllUsesWith(Zext);
+  SDI->eraseFromParent();
+  return true;
+}
+
 static bool processSRem(BinaryOperator *SDI, LazyValueInfo *LVI) {
   if (SDI->getType()->isVectorTy() || !hasPositiveOperands(SDI, LVI))
     return false;
@@ -441,6 +481,10 @@
                                         SDI->getName(), SDI);
   SDI->replaceAllUsesWith(BO);
   SDI->eraseFromParent();
+
+  // Try to process our new urem.
+  processUDivOrURem(BO, LVI);
+
   return true;
 }
 
@@ -460,6 +504,9 @@
   SDI->replaceAllUsesWith(BO);
   SDI->eraseFromParent();
 
+  // Try to simplify our new udiv.
+  processUDivOrURem(BO, LVI);
+
   return true;
 }
 
@@ -595,6 +642,10 @@
       case Instruction::SDiv:
         BBChanged |= processSDiv(cast<BinaryOperator>(II), LVI);
         break;
+      case Instruction::UDiv:
+      case Instruction::URem:
+        BBChanged |= processUDivOrURem(cast<BinaryOperator>(II), LVI);
+        break;
       case Instruction::AShr:
         BBChanged |= processAShr(cast<BinaryOperator>(II), LVI);
         break;
Index: llvm/test/Transforms/CorrelatedValuePropagation/udiv.ll
===================================================================
--- /dev/null
+++ llvm/test/Transforms/CorrelatedValuePropagation/udiv.ll
@@ -0,0 +1,73 @@
+; RUN: opt < %s -correlated-propagation -S | FileCheck %s
+
+; CHECK-LABEL: @test1(
+define void @test1(i32 %n) {
+entry:
+  %cmp = icmp ule i32 %n, 65535
+  br i1 %cmp, label %bb, label %exit
+
+bb:
+; CHECK: udiv i16
+  %div = udiv i32 %n, 100
+  br label %exit
+
+exit:
+  ret void
+}
+
+; CHECK-LABEL: @test2(
+define void @test2(i32 %n) {
+entry:
+  %cmp = icmp ule i32 %n, 65536
+  br i1 %cmp, label %bb, label %exit
+
+bb:
+; CHECK: udiv i32 %n, 100
+  %div = udiv i32 %n, 100
+  br label %exit
+
+exit:
+  ret void
+}
+
+; CHECK-LABEL: @test3(
+define void @test3(i32 %m, i32 %n) {
+entry:
+  %cmp1 = icmp ult i32 %m, 65535
+  %cmp2 = icmp ult i32 %n, 65535
+  %cmp = and i1 %cmp1, %cmp2
+  br i1 %cmp, label %bb, label %exit
+
+bb:
+; CHECK: udiv i16
+  %div = udiv i32 %m, %n
+  br label %exit
+
+exit:
+  ret void
+}
+
+; CHECK-LABEL: @test4(
+define void @test4(i32 %m, i32 %n) {
+entry:
+  %cmp1 = icmp ult i32 %m, 65535
+  %cmp2 = icmp ule i32 %n, 65536
+  %cmp = and i1 %cmp1, %cmp2
+  br i1 %cmp, label %bb, label %exit
+
+bb:
+; CHECK: udiv i32 %m, %n
+  %div = udiv i32 %m, %n
+  br label %exit
+
+exit:
+  ret void
+}
+
+; CHECK-LABEL: @test5
+define void @test5(i32 %n) {
+  %trunc = and i32 %n, 65535
+  ; CHECK: udiv i16
+  %div = udiv i32 %trunc, 42
+  ret void
+}
Index: llvm/test/Transforms/CorrelatedValuePropagation/urem.ll
===================================================================
--- /dev/null
+++ llvm/test/Transforms/CorrelatedValuePropagation/urem.ll
@@ -0,0 +1,81 @@
+; RUN: opt < %s -correlated-propagation -S | FileCheck %s
+
+; CHECK-LABEL: @test1(
+define void @test1(i32 %n) {
+entry:
+  %cmp = icmp ule i32 %n, 65535
+  br i1 %cmp, label %bb, label %exit
+
+bb:
+; CHECK: urem i16
+  %div = urem i32 %n, 100
+  br label %exit
+
+exit:
+  ret void
+}
+
+; CHECK-LABEL: @test2(
+define void @test2(i32 %n) {
+entry:
+  %cmp = icmp ule i32 %n, 65536
+  br i1 %cmp, label %bb, label %exit
+
+bb:
+; CHECK: urem i32 %n, 100
+  %div = urem i32 %n, 100
+  br label %exit
+
+exit:
+  ret void
+}
+
+; CHECK-LABEL: @test3(
+define void @test3(i32 %m, i32 %n) {
+entry:
+  %cmp1 = icmp ult i32 %m, 65535
+  %cmp2 = icmp ult i32 %n, 65535
+  %cmp = and i1 %cmp1, %cmp2
+  br i1 %cmp, label %bb, label %exit
+
+bb:
+; CHECK: urem i16
+  %div = urem i32 %m, %n
+  br label %exit
+
+exit:
+  ret void
+}
+
+; CHECK-LABEL: @test4(
+define void @test4(i32 %m, i32 %n) {
+entry:
+  %cmp1 = icmp ult i32 %m, 65535
+  %cmp2 = icmp ule i32 %n, 65536
+  %cmp = and i1 %cmp1, %cmp2
+  br i1 %cmp, label %bb, label %exit
+
+bb:
+; CHECK: urem i32 %m, %n
+  %div = urem i32 %m, %n
+  br label %exit
+
+exit:
+  ret void
+}
+
+; CHECK-LABEL: @test5
+define void @test5(i32 %n) {
+  %trunc = and i32 %n, 63
+  ; CHECK: urem i8
+  %div = urem i32 %trunc, 42
+  ret void
+}
+
+; CHECK-LABEL: @test6
+define void @test6(i32 %n) {
+  %trunc = and i32 %n, 63
+  ; CHECK: urem i8
+  %div = srem i32 %trunc, 42
+  ret void
+}