Index: llvm/lib/Transforms/InstCombine/InstCombineSelect.cpp
===================================================================
--- llvm/lib/Transforms/InstCombine/InstCombineSelect.cpp
+++ llvm/lib/Transforms/InstCombine/InstCombineSelect.cpp
@@ -2584,6 +2584,41 @@
   return nullptr;
 }
 
+/// Tries to reduce a pattern that arises when calculating the remainder of the
+/// Euclidean division. When the divisor is a power of two and is guaranteed not
+/// to be negative, a signed remainder can be folded with a bitwise and.
+///
+/// (x % n) < 0 ? (x % n) + n : (x % n)
+///    -> x & (n - 1)
+static Instruction *foldSelectWithSRem(SelectInst &SI) {
+  Value *CondVal = SI.getCondition();
+  Value *TrueVal = SI.getTrueValue();
+  Value *FalseVal = SI.getFalseValue();
+
+  ICmpInst::Predicate Pred;
+  Value *Op, *Rem, *CmpCond;
+
+  // We are matching a quite specific pattern here:
+  // %rem = srem i32 %x, %n
+  // %cnd = icmp slt i32 %rem, 0
+  // %add = add nsw i32 %rem, %n
+  // %sel = select i1 %cnd, i32 %add, i32 %rem
+  const APInt *I0, *I1;
+  if (!(match(TrueVal, m_Add(m_Value(Rem), m_Power2(I0))) &&
+        match(Rem, m_SRem(m_Value(Op), m_Power2(I1))) && FalseVal == Rem &&
+        I0 == I1))
+    return nullptr;
+
+  // Signed comparisons have been canonicalized into a ICMP_SLT at this point,
+  // we can safely check this type of comparison.
+  if (!(match(CondVal, m_ICmp(Pred, m_Value(CmpCond), m_Zero())) &&
+        Pred == ICmpInst::ICMP_SLT && CmpCond == Rem))
+    return nullptr;
+
+  Value *Mask = ConstantInt::get(Rem->getType(), I0->getZExtValue() - 1);
+  return BinaryOperator::CreateAnd(Op, Mask);
+}
+
 static Value *foldSelectWithFrozenICmp(SelectInst &Sel, InstCombiner::BuilderTy &Builder) {
   FreezeInst *FI = dyn_cast<FreezeInst>(Sel.getCondition());
   if (!FI)
@@ -3616,6 +3651,9 @@
   if (Instruction *I = foldVectorSelect(SI))
     return I;
 
+  if (Instruction *I = foldSelectWithSRem(SI))
+    return I;
+
   // If we can compute the condition, there's no need for a select.
   // Like the above fold, we are attempting to reduce compile-time cost by
   // putting this fold here with limitations rather than in InstSimplify.
Index: llvm/test/Transforms/InstCombine/select-divrem.ll
===================================================================
--- llvm/test/Transforms/InstCombine/select-divrem.ll
+++ llvm/test/Transforms/InstCombine/select-divrem.ll
@@ -213,3 +213,27 @@
   %sel = select i1 %b, i5 %r2, i5 %r1
   ret i5 %sel
 }
+
+define i32 @rem_euclid_1(i32 %0) {
+; CHECK-LABEL: @rem_euclid_1(
+; CHECK-NEXT:    [[SEL:%.*]] = and i32 [[TMP0:%.*]], 7
+; CHECK-NEXT:    ret i32 [[SEL]]
+;
+  %rem = srem i32 %0, 8
+  %cond = icmp slt i32 %rem, 0
+  %add = add nsw i32 %rem, 8
+  %sel = select i1 %cond, i32 %add, i32 %rem
+  ret i32 %sel
+}
+
+define i32 @rem_euclid_2(i32 %0) {
+; CHECK-LABEL: @rem_euclid_2(
+; CHECK-NEXT:    [[SEL:%.*]] = and i32 [[TMP0:%.*]], 7
+; CHECK-NEXT:    ret i32 [[SEL]]
+;
+  %rem = srem i32 %0, 8
+  %cond = icmp sgt i32 %rem, -1
+  %add = add nsw i32 %rem, 8
+  %sel = select i1 %cond, i32 %rem, i32 %add
+  ret i32 %sel
+}