Index: llvm/lib/Analysis/ScalarEvolution.cpp
===================================================================
--- llvm/lib/Analysis/ScalarEvolution.cpp
+++ llvm/lib/Analysis/ScalarEvolution.cpp
@@ -2205,19 +2205,32 @@
 
   SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
 
-  if (SignOrUnsignWrap != SignOrUnsignMask && Type == scAddExpr &&
-      Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) {
+  if (SignOrUnsignWrap != SignOrUnsignMask &&
+      (Type == scAddExpr || Type == scMulExpr) && Ops.size() == 2 &&
+      isa<SCEVConstant>(Ops[0])) {
 
-    // (A + C) --> (A + C)<nsw> if the addition does not sign overflow
-    // (A + C) --> (A + C)<nuw> if the addition does not unsign overflow
+    auto Opcode = [&] {
+      switch (Type) {
+      case scAddExpr:
+        return Instruction::Add;
+      case scMulExpr:
+        return Instruction::Mul;
+      default:
+        llvm_unreachable("Unexpected SCEV op.");
+      }
+    }();
 
     const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
+
+    // (A <opcode> C) --> (A <opcode> C)<nsw> if the op doesn't sign overflow.
     if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
       auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
-          Instruction::Add, C, OBO::NoSignedWrap);
+          Opcode, C, OBO::NoSignedWrap);
       if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
         Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
     }
+
+    // (A <opcode> C) --> (A <opcode> C)<nuw> if the op doesn't unsign overflow.
     if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
       auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
           Instruction::Add, C, OBO::NoUnsignedWrap);
Index: llvm/test/Analysis/Delinearization/a.ll
===================================================================
--- llvm/test/Analysis/Delinearization/a.ll
+++ llvm/test/Analysis/Delinearization/a.ll
@@ -10,7 +10,7 @@
 ; AddRec: {{{(28 + (4 * (-4 + (3 * %m)) * %o) + %A),+,(8 * %m * %o)}<%for.i>,+,(12 * %o)}<%for.j>,+,20}<%for.k>
 ; CHECK: Base offset: %A
 ; CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of 4 bytes.
-; CHECK: ArrayRef[{3,+,2}<%for.i>][{-4,+,3}<nw><%for.j>][{7,+,5}<nw><%for.k>]
+; CHECK: ArrayRef[{3,+,2}<nw><%for.i>][{-4,+,3}<nw><%for.j>][{7,+,5}<nw><%for.k>]
 
 define void @foo(i64 %n, i64 %m, i64 %o, i32* nocapture %A) #0 {
 entry:
Index: llvm/test/Analysis/ScalarEvolution/sext-mul.ll
===================================================================
--- llvm/test/Analysis/ScalarEvolution/sext-mul.ll
+++ llvm/test/Analysis/ScalarEvolution/sext-mul.ll
@@ -1,7 +1,7 @@
 ; RUN: opt < %s -analyze -scalar-evolution | FileCheck %s
 
 ; CHECK: %tmp9 = shl i64 %tmp8, 33
-; CHECK-NEXT: --> {{.*}} Exits: (-8589934592 + (8589934592 * (zext i32 %arg2 to i64)))
+; CHECK-NEXT: --> {{.*}} Exits: (-8589934592 + (8589934592 * (zext i32 %arg2 to i64))<nuw>)
 ; CHECK: %tmp10 = ashr exact i64 %tmp9, 32
 ; CHECK-NEXT: --> {{.*}} Exits: (sext i32 (-2 + (2 * %arg2)) to i64)
 ; CHECK: %tmp11 = getelementptr inbounds i32, i32* %arg, i64 %tmp10
@@ -48,9 +48,9 @@
 }
 
 ; CHECK: %t10 = ashr exact i128 %t9, 1
-; CHECK-NEXT: --> {{.*}} Exits: (sext i127 (-633825300114114700748351602688 + (633825300114114700748351602688 * (zext i32 %arg5 to i127))) to i128)
+; CHECK-NEXT: --> {{.*}} Exits: (sext i127 (-633825300114114700748351602688 + (633825300114114700748351602688 * (zext i32 %arg5 to i127))<nuw>) to i128)
 ; CHECK: %t14 = or i128 %t10, 1
-; CHECK-NEXT: --> {{.*}} Exits: (1 + (sext i127 (-633825300114114700748351602688 + (633825300114114700748351602688 * (zext i32 %arg5 to i127))) to i128))<nsw>
+; CHECK-NEXT: --> {{.*}} Exits: (1 + (sext i127 (-633825300114114700748351602688 + (633825300114114700748351602688 * (zext i32 %arg5 to i127))<nuw>) to i128))<nsw>
 ; CHECK: Loop %bb7: backedge-taken count is (-1 + (zext i32 %arg5 to i128))<nsw>
 ; CHECK-NEXT: Loop %bb7: max backedge-taken count is -1
 ; CHECK-NEXT: Loop %bb7: Predicated backedge-taken count is (-1 + (zext i32 %arg5 to i128))<nsw>
Index: llvm/test/Transforms/IndVarSimplify/2011-09-10-widen-nsw.ll
===================================================================
--- llvm/test/Transforms/IndVarSimplify/2011-09-10-widen-nsw.ll
+++ llvm/test/Transforms/IndVarSimplify/2011-09-10-widen-nsw.ll
@@ -20,7 +20,7 @@
 ; CHECK: add nuw nsw i64 %indvars.iv, 1
 ; CHECK: sub nsw i64 %indvars.iv, 2
 ; CHECK: sub nsw i64 4, %indvars.iv
-; CHECK: mul nsw i64 %indvars.iv, 8
+; CHECK: mul nuw nsw i64 %indvars.iv, 8
 for.body170:                                      ; preds = %for.body170, %for.body153
   %i2.19 = phi i32 [ %add249, %for.body170 ], [ 0, %for.body153 ]