Index: lib/Analysis/ScalarEvolution.cpp
===================================================================
--- lib/Analysis/ScalarEvolution.cpp
+++ lib/Analysis/ScalarEvolution.cpp
@@ -5952,6 +5952,24 @@
     return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
 
   case Instruction::SExt:
+    if (auto BO = MatchBinaryOp(U->getOperand(0), DT)) {
+      // The NSW flag of a subtract does not always survive the conversion to
+      // A + (-1)*B.  By pushing sign extension onto its operands we are much
+      // more likely to preserve NSW and allow later AddRec optimisations.
+      //
+      // NOTE: This is effectively duplicating this logic from getSignExtend:
+      //   sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
+      // but by that point the NSW information has potentially been lost.
+      if (BO->Opcode == Instruction::Sub && BO->Op) {
+        SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
+        if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
+          Type *Ty = U->getType();
+          auto *V1 = getSignExtendExpr(getSCEV(BO->LHS), Ty);
+          auto *V2 = getSignExtendExpr(getSCEV(BO->RHS), Ty);
+          return getMinusSCEV(V1, V2, SCEV::FlagNSW);
+        }
+      }
+    }
     return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
 
   case Instruction::BitCast:
Index: test/Analysis/ScalarEvolution/flags-from-poison.ll
===================================================================
--- test/Analysis/ScalarEvolution/flags-from-poison.ll
+++ test/Analysis/ScalarEvolution/flags-from-poison.ll
@@ -609,7 +609,7 @@
   %index32 = sub nsw i32 %i, %sub
 
 ; CHECK: %index64 =
-; CHECK: --> {(sext i32 (-1 * %sub) to i64),+,1}<nsw>
+; CHECK: --> {(-1 * (sext i32 %sub to i64))<nsw>,+,1}<nsw
   %index64 = sext i32 %index32 to i64
 
   %ptr = getelementptr inbounds float, float* %input, i64 %index64
Index: test/Transforms/LoopStrengthReduce/sext-ind-var.ll
===================================================================
--- test/Transforms/LoopStrengthReduce/sext-ind-var.ll
+++ test/Transforms/LoopStrengthReduce/sext-ind-var.ll
@@ -47,8 +47,7 @@
 ;
 define float @testsub(float* %input, i32 %offset, i32 %numIterations) {
 ; CHECK-LABEL: @testsub
-; CHECK: sub i32 0, %offset
-; CHECK: sext i32
+; CHECK: sext i32 %offset to i64
 ; CHECK: loop:
 ; CHECK-DAG: phi float*
 ; CHECK-DAG: phi i32