diff --git a/llvm/lib/Analysis/ScalarEvolution.cpp b/llvm/lib/Analysis/ScalarEvolution.cpp
--- a/llvm/lib/Analysis/ScalarEvolution.cpp
+++ b/llvm/lib/Analysis/ScalarEvolution.cpp
@@ -5696,6 +5696,7 @@
   switch (BO->getOpcode()) {
   default:
     return CR;
+  case Instruction::LShr:
   case Instruction::Shl:
     break;
   };
@@ -5724,6 +5725,19 @@
   switch (BO->getOpcode()) {
   default:
     llvm_unreachable("filtered out above");
+  case Instruction::LShr: {
+    // For each lshr, three cases:
+    //   shift = 0 => unchanged value
+    //   saturation => 0
+    //   other => a smaller positive number
+    // Thus, the low end of the unsigned range is the last value produced.
+    auto KnownEnd = KnownBits::lshr(KnownStart,
+                                    KnownBits::makeConstant(TotalShift));
+    auto R = ConstantRange::getNonEmpty(KnownEnd.getMinValue(),
+                                        KnownStart.getMaxValue() + 1);
+    CR = CR.intersectWith(R);
+    break;
+  }
   case Instruction::Shl: {
     // Iff no bits are shifted out, value increases on every shift.
     auto KnownEnd = KnownBits::shl(KnownStart,
diff --git a/llvm/test/Analysis/ScalarEvolution/shift-recurrences.ll b/llvm/test/Analysis/ScalarEvolution/shift-recurrences.ll
--- a/llvm/test/Analysis/ScalarEvolution/shift-recurrences.ll
+++ b/llvm/test/Analysis/ScalarEvolution/shift-recurrences.ll
@@ -630,11 +630,11 @@
 ; CHECK-NEXT:    %iv = phi i64 [ 0, %entry ], [ %iv.next, %loop ]
 ; CHECK-NEXT:    --> {0,+,1}<%loop> U: [0,5) S: [0,5) Exits: 4 LoopDispositions: { %loop: Computable }
 ; CHECK-NEXT:    %iv.lshr = phi i64 [ 1023, %entry ], [ %iv.lshr.next, %loop ]
-; CHECK-NEXT:    --> %iv.lshr U: [0,1024) S: [0,1024) Exits: 63 LoopDispositions: { %loop: Variant }
+; CHECK-NEXT:    --> %iv.lshr U: [63,1024) S: [63,1024) Exits: 63 LoopDispositions: { %loop: Variant }
 ; CHECK-NEXT:    %iv.next = add i64 %iv, 1
 ; CHECK-NEXT:    --> {1,+,1}<%loop> U: [1,6) S: [1,6) Exits: 5 LoopDispositions: { %loop: Computable }
 ; CHECK-NEXT:    %iv.lshr.next = lshr i64 %iv.lshr, 1
-; CHECK-NEXT:    --> (%iv.lshr /u 2) U: [0,512) S: [0,512) Exits: 31 LoopDispositions: { %loop: Variant }
+; CHECK-NEXT:    --> (%iv.lshr /u 2) U: [31,512) S: [31,512) Exits: 31 LoopDispositions: { %loop: Variant }
 ; CHECK-NEXT:  Determining loop execution counts for: @test_lshr_tc_positive
 ; CHECK-NEXT:  Loop %loop: backedge-taken count is 4
 ; CHECK-NEXT:  Loop %loop: max backedge-taken count is 4
@@ -661,11 +661,11 @@
 ; CHECK-NEXT:    %iv = phi i64 [ 0, %entry ], [ %iv.next, %loop ]
 ; CHECK-NEXT:    --> {0,+,1}<%loop> U: [0,5) S: [0,5) Exits: 4 LoopDispositions: { %loop: Computable }
 ; CHECK-NEXT:    %iv.lshr = phi i8 [ -1, %entry ], [ %iv.lshr.next, %loop ]
-; CHECK-NEXT:    --> %iv.lshr U: [-1,-128) S: [-1,-128) Exits: 15 LoopDispositions: { %loop: Variant }
+; CHECK-NEXT:    --> %iv.lshr U: [15,0) S: [-1,-128) Exits: 15 LoopDispositions: { %loop: Variant }
 ; CHECK-NEXT:    %iv.next = add i64 %iv, 1
 ; CHECK-NEXT:    --> {1,+,1}<%loop> U: [1,6) S: [1,6) Exits: 5 LoopDispositions: { %loop: Computable }
 ; CHECK-NEXT:    %iv.lshr.next = lshr i8 %iv.lshr, 1
-; CHECK-NEXT:    --> (%iv.lshr /u 2) U: [0,-128) S: [0,-128) Exits: 7 LoopDispositions: { %loop: Variant }
+; CHECK-NEXT:    --> (%iv.lshr /u 2) U: [7,-128) S: [7,-128) Exits: 7 LoopDispositions: { %loop: Variant }
 ; CHECK-NEXT:  Determining loop execution counts for: @test_lshr_tc_negative
 ; CHECK-NEXT:  Loop %loop: backedge-taken count is 4
 ; CHECK-NEXT:  Loop %loop: max backedge-taken count is 4
@@ -726,11 +726,11 @@
 ; CHECK-NEXT:    %iv = phi i64 [ 0, %entry ], [ %iv.next, %loop ]
 ; CHECK-NEXT:    --> {0,+,1}<%loop> U: [0,5) S: [0,5) Exits: 4 LoopDispositions: { %loop: Computable }
 ; CHECK-NEXT:    %iv.lshr = phi i64 [ 1023, %entry ], [ %iv.lshr.next, %loop ]
-; CHECK-NEXT:    --> %iv.lshr U: [0,1024) S: [0,1024) Exits: 1023 LoopDispositions: { %loop: Variant }
+; CHECK-NEXT:    --> %iv.lshr U: [1023,1024) S: [1023,1024) Exits: 1023 LoopDispositions: { %loop: Variant }
 ; CHECK-NEXT:    %iv.next = add i64 %iv, 1
 ; CHECK-NEXT:    --> {1,+,1}<%loop> U: [1,6) S: [1,6) Exits: 5 LoopDispositions: { %loop: Computable }
 ; CHECK-NEXT:    %iv.lshr.next = lshr i64 %iv.lshr, 0
-; CHECK-NEXT:    --> %iv.lshr U: [0,1024) S: [0,1024) Exits: 1023 LoopDispositions: { %loop: Variant }
+; CHECK-NEXT:    --> %iv.lshr U: [1023,1024) S: [1023,1024) Exits: 1023 LoopDispositions: { %loop: Variant }
 ; CHECK-NEXT:  Determining loop execution counts for: @test_lshr_zero_shift
 ; CHECK-NEXT:  Loop %loop: backedge-taken count is 4
 ; CHECK-NEXT:  Loop %loop: max backedge-taken count is 4
@@ -758,11 +758,11 @@
 ; CHECK-NEXT:    %iv = phi i64 [ 0, %entry ], [ %iv.next, %loop ]
 ; CHECK-NEXT:    --> {0,+,1}<%loop> U: [0,5) S: [0,5) Exits: 4 LoopDispositions: { %loop: Computable }
 ; CHECK-NEXT:    %iv.lshr = phi i64 [ 1024, %entry ], [ %iv.lshr.next, %loop ]
-; CHECK-NEXT:    --> %iv.lshr U: [0,1025) S: [0,1025) Exits: 4 LoopDispositions: { %loop: Variant }
+; CHECK-NEXT:    --> %iv.lshr U: [4,1025) S: [4,1025) Exits: 4 LoopDispositions: { %loop: Variant }
 ; CHECK-NEXT:    %iv.next = add i64 %iv, 1
 ; CHECK-NEXT:    --> {1,+,1}<%loop> U: [1,6) S: [1,6) Exits: 5 LoopDispositions: { %loop: Computable }
 ; CHECK-NEXT:    %iv.lshr.next = lshr i64 %iv.lshr, 2
-; CHECK-NEXT:    --> (%iv.lshr /u 4) U: [0,512) S: [0,512) Exits: 1 LoopDispositions: { %loop: Variant }
+; CHECK-NEXT:    --> (%iv.lshr /u 4) U: [1,257) S: [1,257) Exits: 1 LoopDispositions: { %loop: Variant }
 ; CHECK-NEXT:  Determining loop execution counts for: @test_lshr_power_of_2_start
 ; CHECK-NEXT:  Loop %loop: backedge-taken count is 4
 ; CHECK-NEXT:  Loop %loop: max backedge-taken count is 4
@@ -790,11 +790,11 @@
 ; CHECK-NEXT:    %iv = phi i64 [ 0, %entry ], [ %iv.next, %loop ]
 ; CHECK-NEXT:    --> {0,+,1}<%loop> U: [0,5) S: [0,5) Exits: 4 LoopDispositions: { %loop: Computable }
 ; CHECK-NEXT:    %iv.lshr = phi i64 [ 957, %entry ], [ %iv.lshr.next, %loop ]
-; CHECK-NEXT:    --> %iv.lshr U: [0,958) S: [0,958) Exits: 3 LoopDispositions: { %loop: Variant }
+; CHECK-NEXT:    --> %iv.lshr U: [3,958) S: [3,958) Exits: 3 LoopDispositions: { %loop: Variant }
 ; CHECK-NEXT:    %iv.next = add i64 %iv, 1
 ; CHECK-NEXT:    --> {1,+,1}<%loop> U: [1,6) S: [1,6) Exits: 5 LoopDispositions: { %loop: Computable }
 ; CHECK-NEXT:    %iv.lshr.next = lshr i64 %iv.lshr, 2
-; CHECK-NEXT:    --> (%iv.lshr /u 4) U: [0,256) S: [0,256) Exits: 0 LoopDispositions: { %loop: Variant }
+; CHECK-NEXT:    --> (%iv.lshr /u 4) U: [0,240) S: [0,240) Exits: 0 LoopDispositions: { %loop: Variant }
 ; CHECK-NEXT:  Determining loop execution counts for: @test_lshr_arbitrary_start
 ; CHECK-NEXT:  Loop %loop: backedge-taken count is 4
 ; CHECK-NEXT:  Loop %loop: max backedge-taken count is 4
@@ -821,11 +821,11 @@
 ; CHECK-NEXT:    %iv = phi i64 [ 0, %entry ], [ %iv.next, %loop ]
 ; CHECK-NEXT:    --> {0,+,1}<%loop> U: [0,5) S: [0,5) Exits: 4 LoopDispositions: { %loop: Computable }
 ; CHECK-NEXT:    %iv.lshr = phi i64 [ 1025, %entry ], [ %iv.lshr.next, %loop ]
-; CHECK-NEXT:    --> %iv.lshr U: [0,1026) S: [0,1026) Exits: 4 LoopDispositions: { %loop: Variant }
+; CHECK-NEXT:    --> %iv.lshr U: [4,1026) S: [4,1026) Exits: 4 LoopDispositions: { %loop: Variant }
 ; CHECK-NEXT:    %iv.next = add i64 %iv, 1
 ; CHECK-NEXT:    --> {1,+,1}<%loop> U: [1,6) S: [1,6) Exits: 5 LoopDispositions: { %loop: Computable }
 ; CHECK-NEXT:    %iv.lshr.next = lshr i64 %iv.lshr, 2
-; CHECK-NEXT:    --> (%iv.lshr /u 4) U: [0,512) S: [0,512) Exits: 1 LoopDispositions: { %loop: Variant }
+; CHECK-NEXT:    --> (%iv.lshr /u 4) U: [1,257) S: [1,257) Exits: 1 LoopDispositions: { %loop: Variant }
 ; CHECK-NEXT:  Determining loop execution counts for: @test_lshr_start_power_of_2_plus_one
 ; CHECK-NEXT:  Loop %loop: backedge-taken count is 4
 ; CHECK-NEXT:  Loop %loop: max backedge-taken count is 4