diff --git a/llvm/lib/Transforms/InstCombine/InstCombineCompares.cpp b/llvm/lib/Transforms/InstCombine/InstCombineCompares.cpp
index 6737b50405ee2..c6f317a668cfe 100644
--- a/llvm/lib/Transforms/InstCombine/InstCombineCompares.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineCompares.cpp
@@ -5120,6 +5120,18 @@ static Instruction *foldICmpXorXX(ICmpInst &I, const SimplifyQuery &Q,
   return nullptr;
 }
 
+/// Return true if X is a multiple of C.
+/// TODO: Handle non-power-of-2 factors.
+static bool isMultipleOf(Value *X, const APInt &C, const SimplifyQuery &Q) {
+  if (C.isOne())
+    return true;
+
+  if (!C.isPowerOf2())
+    return false;
+
+  return MaskedValueIsZero(X, C - 1, Q);
+}
+
 /// Try to fold icmp (binop), X or icmp X, (binop).
 /// TODO: A large part of this logic is duplicated in InstSimplify's
 /// simplifyICmpWithBinOp(). We should be able to share that and avoid the code
@@ -5278,66 +5290,62 @@ Instruction *InstCombinerImpl::foldICmpBinOp(ICmpInst &I,
     return new ICmpInst(Pred, Y, Z);
   }
 
-  // icmp slt (A + -1), Op1 -> icmp sle A, Op1
-  if (A && NoOp0WrapProblem && Pred == CmpInst::ICMP_SLT &&
-      match(B, m_AllOnes()))
-    return new ICmpInst(CmpInst::ICMP_SLE, A, Op1);
-
-  // icmp sge (A + -1), Op1 -> icmp sgt A, Op1
-  if (A && NoOp0WrapProblem && Pred == CmpInst::ICMP_SGE &&
-      match(B, m_AllOnes()))
-    return new ICmpInst(CmpInst::ICMP_SGT, A, Op1);
-
-  // icmp sle (A + 1), Op1 -> icmp slt A, Op1
-  if (A && NoOp0WrapProblem && Pred == CmpInst::ICMP_SLE && match(B, m_One()))
-    return new ICmpInst(CmpInst::ICMP_SLT, A, Op1);
-
-  // icmp sgt (A + 1), Op1 -> icmp sge A, Op1
-  if (A && NoOp0WrapProblem && Pred == CmpInst::ICMP_SGT && match(B, m_One()))
-    return new ICmpInst(CmpInst::ICMP_SGE, A, Op1);
+  if (ICmpInst::isRelational(Pred)) {
+    // Return if both X and Y is divisible by Z/-Z.
+    // TODO: Generalize to check if (X - Y) is divisible by Z/-Z.
+    auto ShareCommonDivisor = [&Q](Value *X, Value *Y, Value *Z,
+                                   bool IsNegative) -> bool {
+      const APInt *OffsetC;
+      if (!match(Z, m_APInt(OffsetC)))
+        return false;
 
-  // icmp sgt Op0, (C + -1) -> icmp sge Op0, C
-  if (C && NoOp1WrapProblem && Pred == CmpInst::ICMP_SGT &&
-      match(D, m_AllOnes()))
-    return new ICmpInst(CmpInst::ICMP_SGE, Op0, C);
+      // Fast path for Z == 1/-1.
+      if (IsNegative ? OffsetC->isAllOnes() : OffsetC->isOne())
+        return true;
 
-  // icmp sle Op0, (C + -1) -> icmp slt Op0, C
-  if (C && NoOp1WrapProblem && Pred == CmpInst::ICMP_SLE &&
-      match(D, m_AllOnes()))
-    return new ICmpInst(CmpInst::ICMP_SLT, Op0, C);
+      APInt C = *OffsetC;
+      if (IsNegative)
+        C.negate();
+      // Note: -INT_MIN is also negative.
+      if (!C.isStrictlyPositive())
+        return false;
 
-  // icmp sge Op0, (C + 1) -> icmp sgt Op0, C
-  if (C && NoOp1WrapProblem && Pred == CmpInst::ICMP_SGE && match(D, m_One()))
-    return new ICmpInst(CmpInst::ICMP_SGT, Op0, C);
+      return isMultipleOf(X, C, Q) && isMultipleOf(Y, C, Q);
+    };
 
-  // icmp slt Op0, (C + 1) -> icmp sle Op0, C
-  if (C && NoOp1WrapProblem && Pred == CmpInst::ICMP_SLT && match(D, m_One()))
-    return new ICmpInst(CmpInst::ICMP_SLE, Op0, C);
+    // TODO: The subtraction-related identities shown below also hold, but
+    // canonicalization from (X -nuw 1) to (X + -1) means that the combinations
+    // wouldn't happen even if they were implemented.
+    //
+    // icmp ult (A - 1), Op1 -> icmp ule A, Op1
+    // icmp uge (A - 1), Op1 -> icmp ugt A, Op1
+    // icmp ugt Op0, (C - 1) -> icmp uge Op0, C
+    // icmp ule Op0, (C - 1) -> icmp ult Op0, C
+
+    // icmp slt (A + -1), Op1 -> icmp sle A, Op1
+    // icmp sge (A + -1), Op1 -> icmp sgt A, Op1
+    // icmp sle (A + 1), Op1 -> icmp slt A, Op1
+    // icmp sgt (A + 1), Op1 -> icmp sge A, Op1
+    // icmp ule (A + 1), Op0 -> icmp ult A, Op1
+    // icmp ugt (A + 1), Op0 -> icmp uge A, Op1
+    if (A && NoOp0WrapProblem &&
+        ShareCommonDivisor(A, Op1, B,
+                           ICmpInst::isLT(Pred) || ICmpInst::isGE(Pred)))
+      return new ICmpInst(ICmpInst::getFlippedStrictnessPredicate(Pred), A,
+                          Op1);
 
-  // TODO: The subtraction-related identities shown below also hold, but
-  // canonicalization from (X -nuw 1) to (X + -1) means that the combinations
-  // wouldn't happen even if they were implemented.
-  //
-  // icmp ult (A - 1), Op1 -> icmp ule A, Op1
-  // icmp uge (A - 1), Op1 -> icmp ugt A, Op1
-  // icmp ugt Op0, (C - 1) -> icmp uge Op0, C
-  // icmp ule Op0, (C - 1) -> icmp ult Op0, C
-
-  // icmp ule (A + 1), Op0 -> icmp ult A, Op1
-  if (A && NoOp0WrapProblem && Pred == CmpInst::ICMP_ULE && match(B, m_One()))
-    return new ICmpInst(CmpInst::ICMP_ULT, A, Op1);
-
-  // icmp ugt (A + 1), Op0 -> icmp uge A, Op1
-  if (A && NoOp0WrapProblem && Pred == CmpInst::ICMP_UGT && match(B, m_One()))
-    return new ICmpInst(CmpInst::ICMP_UGE, A, Op1);
-
-  // icmp uge Op0, (C + 1) -> icmp ugt Op0, C
-  if (C && NoOp1WrapProblem && Pred == CmpInst::ICMP_UGE && match(D, m_One()))
-    return new ICmpInst(CmpInst::ICMP_UGT, Op0, C);
-
-  // icmp ult Op0, (C + 1) -> icmp ule Op0, C
-  if (C && NoOp1WrapProblem && Pred == CmpInst::ICMP_ULT && match(D, m_One()))
-    return new ICmpInst(CmpInst::ICMP_ULE, Op0, C);
+    // icmp sgt Op0, (C + -1) -> icmp sge Op0, C
+    // icmp sle Op0, (C + -1) -> icmp slt Op0, C
+    // icmp sge Op0, (C + 1) -> icmp sgt Op0, C
+    // icmp slt Op0, (C + 1) -> icmp sle Op0, C
+    // icmp uge Op0, (C + 1) -> icmp ugt Op0, C
+    // icmp ult Op0, (C + 1) -> icmp ule Op0, C
+    if (C && NoOp1WrapProblem &&
+        ShareCommonDivisor(Op0, C, D,
+                           ICmpInst::isGT(Pred) || ICmpInst::isLE(Pred)))
+      return new ICmpInst(ICmpInst::getFlippedStrictnessPredicate(Pred), Op0,
+                          C);
+  }
 
   // if C1 has greater magnitude than C2:
   //  icmp (A + C1), (C + C2) -> icmp (A + C3), C
diff --git a/llvm/test/Transforms/InstCombine/icmp.ll b/llvm/test/Transforms/InstCombine/icmp.ll
index 365c17b35a468..a090f9c4d2614 100644
--- a/llvm/test/Transforms/InstCombine/icmp.ll
+++ b/llvm/test/Transforms/InstCombine/icmp.ll
@@ -1900,6 +1900,108 @@ define i1 @icmp_add1_sle(i32 %x, i32 %y) {
   ret i1 %cmp
 }
 
+define i1 @icmp_slt_offset_with_common_divisor(i64 %x, i64 %y) {
+; CHECK-LABEL: @icmp_slt_offset_with_common_divisor(
+; CHECK-NEXT:    [[SHLX:%.*]] = shl i64 [[X:%.*]], 4
+; CHECK-NEXT:    [[SHLY:%.*]] = shl i64 [[Y:%.*]], 4
+; CHECK-NEXT:    [[CMP:%.*]] = icmp sle i64 [[SHLX]], [[SHLY]]
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %shlx = shl i64 %x, 4
+  %shly = shl i64 %y, 4
+  %shlx_offset = add nsw i64 %shlx, -16
+  %cmp = icmp slt i64 %shlx_offset, %shly
+  ret i1 %cmp
+}
+
+define i1 @icmp_slt_offset_with_smaller_common_divisor(i64 %x, i64 %y) {
+; CHECK-LABEL: @icmp_slt_offset_with_smaller_common_divisor(
+; CHECK-NEXT:    [[SHLX:%.*]] = shl i64 [[X:%.*]], 4
+; CHECK-NEXT:    [[SHLY:%.*]] = shl i64 [[Y:%.*]], 4
+; CHECK-NEXT:    [[CMP:%.*]] = icmp sle i64 [[SHLX]], [[SHLY]]
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %shlx = shl i64 %x, 4
+  %shly = shl i64 %y, 4
+  %shlx_offset = add nsw i64 %shlx, -8
+  %cmp = icmp slt i64 %shlx_offset, %shly
+  ret i1 %cmp
+}
+
+define i1 @icmp_sle_offset_with_common_divisor(i64 %x, i64 %y) {
+; CHECK-LABEL: @icmp_sle_offset_with_common_divisor(
+; CHECK-NEXT:    [[SHLX:%.*]] = shl i64 [[X:%.*]], 4
+; CHECK-NEXT:    [[SHLY:%.*]] = shl i64 [[Y:%.*]], 4
+; CHECK-NEXT:    [[CMP:%.*]] = icmp slt i64 [[SHLX]], [[SHLY]]
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %shlx = shl i64 %x, 4
+  %shly = shl i64 %y, 4
+  %shlx_offset = add nsw i64 %shlx, 16
+  %cmp = icmp sle i64 %shlx_offset, %shly
+  ret i1 %cmp
+}
+
+define i1 @icmp_ule_offset_with_common_divisor(i64 %x, i64 %y) {
+; CHECK-LABEL: @icmp_ule_offset_with_common_divisor(
+; CHECK-NEXT:    [[SHLX:%.*]] = shl i64 [[X:%.*]], 4
+; CHECK-NEXT:    [[SHLY:%.*]] = shl i64 [[Y:%.*]], 4
+; CHECK-NEXT:    [[CMP:%.*]] = icmp ult i64 [[SHLX]], [[SHLY]]
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %shlx = shl i64 %x, 4
+  %shly = shl i64 %y, 4
+  %shlx_offset = add nuw i64 %shlx, 16
+  %cmp = icmp ule i64 %shlx_offset, %shly
+  ret i1 %cmp
+}
+
+; TODO: Handle non-power-of-2 divisors
+define i1 @icmp_ule_offset_with_common_non_pow2_divisor(i64 %x, i64 %y) {
+; CHECK-LABEL: @icmp_ule_offset_with_common_non_pow2_divisor(
+; CHECK-NEXT:    [[MULX:%.*]] = mul nuw i64 [[X:%.*]], 7
+; CHECK-NEXT:    [[MULY:%.*]] = mul nuw i64 [[Y:%.*]], 7
+; CHECK-NEXT:    [[MULX_OFFSET:%.*]] = add nuw i64 [[MULX]], 7
+; CHECK-NEXT:    [[CMP:%.*]] = icmp ule i64 [[MULX_OFFSET]], [[MULY]]
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %mulx = mul nuw i64 %x, 7
+  %muly = mul nuw i64 %y, 7
+  %mulx_offset = add nuw i64 %mulx, 7
+  %cmp = icmp ule i64 %mulx_offset, %muly
+  ret i1 %cmp
+}
+
+define i1 @neg_icmp_slt_offset_without_common_divisor(i64 %x, i64 %y) {
+; CHECK-LABEL: @neg_icmp_slt_offset_without_common_divisor(
+; CHECK-NEXT:    [[SHLX:%.*]] = shl i64 [[X:%.*]], 4
+; CHECK-NEXT:    [[SHLY:%.*]] = shl i64 [[Y:%.*]], 4
+; CHECK-NEXT:    [[SHLX_OFFSET:%.*]] = add nsw i64 [[SHLX]], -32
+; CHECK-NEXT:    [[CMP:%.*]] = icmp slt i64 [[SHLX_OFFSET]], [[SHLY]]
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %shlx = shl i64 %x, 4
+  %shly = shl i64 %y, 4
+  %shlx_offset = add nsw i64 %shlx, -32
+  %cmp = icmp slt i64 %shlx_offset, %shly
+  ret i1 %cmp
+}
+
+define i1 @neg_icmp_slt_offset_with_wrong_sign(i64 %x, i64 %y) {
+; CHECK-LABEL: @neg_icmp_slt_offset_with_wrong_sign(
+; CHECK-NEXT:    [[SHLX:%.*]] = shl i64 [[X:%.*]], 4
+; CHECK-NEXT:    [[SHLY:%.*]] = shl i64 [[Y:%.*]], 4
+; CHECK-NEXT:    [[SHLX_OFFSET:%.*]] = add nsw i64 [[SHLX]], 16
+; CHECK-NEXT:    [[CMP:%.*]] = icmp slt i64 [[SHLX_OFFSET]], [[SHLY]]
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %shlx = shl i64 %x, 4
+  %shly = shl i64 %y, 4
+  %shlx_offset = add nsw i64 %shlx, 16
+  %cmp = icmp slt i64 %shlx_offset, %shly
+  ret i1 %cmp
+}
+
 define i1 @icmp_add20_sge_add57(i32 %x, i32 %y) {
 ; CHECK-LABEL: @icmp_add20_sge_add57(
 ; CHECK-NEXT:    [[TMP1:%.*]] = add nsw i32 [[Y:%.*]], 37