Index: llvm/lib/Analysis/ScalarEvolution.cpp
===================================================================
--- llvm/lib/Analysis/ScalarEvolution.cpp
+++ llvm/lib/Analysis/ScalarEvolution.cpp
@@ -5696,6 +5696,7 @@
   switch (BO->getOpcode()) {
   default:
     return CR;
+  case Instruction::AShr:
   case Instruction::LShr:
   case Instruction::Shl:
     break;
@@ -5725,6 +5726,27 @@
   switch (BO->getOpcode()) {
   default:
     llvm_unreachable("filtered out above");
+  case Instruction::AShr: {
+    // For each ashr, three cases:
+    //   shift = 0 => unchanged value
+    //   saturation => 0 or -1
+    //   other => a value closer to zero (of the same sign)
+    // Thus, the end value is closer to zero than the start.
+    auto KnownEnd = KnownBits::ashr(KnownStart,
+                                    KnownBits::makeConstant(TotalShift));
+    if (KnownStart.isNonNegative()) {
+      // Analogous to lshr (simply not yet canonicalized)
+      auto R = ConstantRange::getNonEmpty(KnownEnd.getMinValue(),
+                                          KnownStart.getMaxValue() + 1);
+      CR = CR.intersectWith(R);
+    } else if (KnownStart.isNegative()) {
+      // End >=u Start && End <=s Start
+      auto R = ConstantRange::getNonEmpty(KnownStart.getMinValue(),
+                                          KnownEnd.getMaxValue() + 1);
+      CR = CR.intersectWith(R);
+    }
+    break;
+  }
   case Instruction::LShr: {
     // For each lshr, three cases:
     //   shift = 0 => unchanged value
Index: llvm/test/Analysis/ScalarEvolution/shift-recurrences.ll
===================================================================
--- llvm/test/Analysis/ScalarEvolution/shift-recurrences.ll
+++ llvm/test/Analysis/ScalarEvolution/shift-recurrences.ll
@@ -503,7 +503,7 @@
 ; 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.ashr = phi i64 [ 1023, %entry ], [ %iv.ashr.next, %loop ]
-; CHECK-NEXT:    --> %iv.ashr U: [0,1024) S: [0,1024) Exits: 63 LoopDispositions: { %loop: Variant }
+; CHECK-NEXT:    --> %iv.ashr 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.ashr.next = ashr i64 %iv.ashr, 1
@@ -534,7 +534,7 @@
 ; 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.ashr = phi i8 [ -128, %entry ], [ %iv.ashr.next, %loop ]
-; CHECK-NEXT:    --> %iv.ashr U: [-128,0) S: [-128,0) Exits: -8 LoopDispositions: { %loop: Variant }
+; CHECK-NEXT:    --> %iv.ashr U: [-128,-7) S: [-128,-7) Exits: -8 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.ashr.next = ashr i8 %iv.ashr, 1
@@ -599,11 +599,11 @@
 ; 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.ashr = phi i64 [ 1023, %entry ], [ %iv.ashr.next, %loop ]
-; CHECK-NEXT:    --> %iv.ashr U: [0,1024) S: [0,1024) Exits: 1023 LoopDispositions: { %loop: Variant }
+; CHECK-NEXT:    --> %iv.ashr 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.ashr.next = ashr i64 %iv.ashr, 0
-; CHECK-NEXT:    --> %iv.ashr U: [0,1024) S: [0,1024) Exits: 1023 LoopDispositions: { %loop: Variant }
+; CHECK-NEXT:    --> %iv.ashr U: [1023,1024) S: [1023,1024) Exits: 1023 LoopDispositions: { %loop: Variant }
 ; CHECK-NEXT:  Determining loop execution counts for: @test_ashr_zero_shift
 ; CHECK-NEXT:  Loop %loop: backedge-taken count is 4
 ; CHECK-NEXT:  Loop %loop: max backedge-taken count is 4