diff --git a/lib/Analysis/ScalarEvolution.cpp b/lib/Analysis/ScalarEvolution.cpp
index 39bf95b92d9..08de6213e22 100644
--- a/lib/Analysis/ScalarEvolution.cpp
+++ b/lib/Analysis/ScalarEvolution.cpp
@@ -5744,6 +5744,16 @@ ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr) {
       getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
     return ExitLimit(Exact, Exact, /*MustExit=*/false);
   }
+
+  // If Step is a power of two that evenly divides Start we know that the loop
+  // will always terminate.  Start may not be a constant so we just have the
+  // number of trailing zeros available.  This is safe even in presence of
+  // overflow as the recurrence will overflow to exactly 0.
+  const APInt &StepV = StepC->getValue()->getValue();
+  if (StepV.isPowerOf2() &&
+      GetMinTrailingZeros(getNegativeSCEV(Start)) >= StepV.countTrailingZeros())
+    return getUDivExactExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
+
   // Then, try to solve the above equation provided that Start is constant.
   if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
     return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
diff --git a/test/Analysis/ScalarEvolution/trip-count-pow2.ll b/test/Analysis/ScalarEvolution/trip-count-pow2.ll
new file mode 100644
index 00000000000..2c5b72e49da
--- /dev/null
+++ b/test/Analysis/ScalarEvolution/trip-count-pow2.ll
@@ -0,0 +1,53 @@
+; RUN: opt < %s -scalar-evolution -analyze | FileCheck %s
+
+define void @test1(i32 %n) {
+entry:
+  %s = mul i32 %n, 96
+  br label %loop
+loop:
+  %i = phi i32 [ 0, %entry ], [ %i.next, %loop ]
+  %i.next = add i32 %i, 32
+  %t = icmp ne i32 %i.next, %s
+  br i1 %t, label %loop, label %exit
+exit:
+  ret void
+
+; CHECK-LABEL: @test1
+; CHECK: Loop %loop: backedge-taken count is ((-32 + (96 * %n)) /u 32)
+; CHECK: Loop %loop: max backedge-taken count is ((-32 + (96 * %n)) /u 32)
+}
+
+; PR19183
+define i32 @test2(i32 %n) {
+entry:
+  %s = and i32 %n, -32
+  br label %loop
+loop:
+  %i = phi i32 [ 0, %entry ], [ %i.next, %loop ]
+  %i.next = add i32 %i, 32
+  %t = icmp ne i32 %i.next, %s
+  br i1 %t, label %loop, label %exit
+exit:
+  ret i32 %i
+
+; CHECK-LABEL: @test2
+; CHECK: Loop %loop: backedge-taken count is ((-32 + (32 * (%n /u 32))) /u 32)
+; CHECK: Loop %loop: max backedge-taken count is ((-32 + (32 * (%n /u 32))) /u 32)
+}
+
+define void @test3(i32 %n) {
+entry:
+  %s = mul i32 %n, 96
+  br label %loop
+loop:
+  %i = phi i32 [ 0, %entry ], [ %i.next, %loop ]
+  %i.next = add i32 %i, 96
+  %t = icmp ne i32 %i.next, %s
+  br i1 %t, label %loop, label %exit
+exit:
+  ret void
+
+; CHECK-LABEL: @test3
+; CHECK: Loop %loop: Unpredictable backedge-taken count.
+; CHECK: Loop %loop: Unpredictable max backedge-taken count.
+}