Index: lib/Analysis/ValueTracking.cpp
===================================================================
--- lib/Analysis/ValueTracking.cpp
+++ lib/Analysis/ValueTracking.cpp
@@ -3214,6 +3214,8 @@
   switch (Inst->getOpcode()) {
   default:
     return true;
+  //TODO: Div, rem and shifts can probably be smarter about non-constant values,
+  //and use known bits.
   case Instruction::UDiv:
   case Instruction::URem: {
     // x / y is undefined if y == 0.
@@ -3241,6 +3243,20 @@
     // The numerator *might* be MinSignedValue.
     return false;
   }
+  case Instruction::AShr:
+  case Instruction::LShr:
+  case Instruction::Shl: {
+    // A shift is undefined if the second operand is equal or larger than
+    // the number of bits in the first operand.
+    const APInt *ShiftAmt;
+    unsigned BitWidth =
+        cast<IntegerType>(Inst->getOperand(0)->getType()->getScalarType())
+            ->getBitWidth();
+    if (!match(Inst->getOperand(1), m_APInt(ShiftAmt)))
+      return false;
+
+    return (ShiftAmt->getZExtValue() < BitWidth);
+  }
   case Instruction::Load: {
     const LoadInst *LI = cast<LoadInst>(Inst);
     if (!LI->isUnordered() ||
Index: test/Transforms/SimplifyCFG/speculat-shift.ll
===================================================================
--- test/Transforms/SimplifyCFG/speculat-shift.ll
+++ test/Transforms/SimplifyCFG/speculat-shift.ll
@@ -0,0 +1,146 @@
+; RUN: opt -S -simplifycfg < %s | FileCheck %s
+
+
+; CHECK-LABEL: @ashr_test_static_good(
+; CHECK: select i1 %cmp, i32 %shift, i32 0
+define i32 @ashr_test_static_good(i32 %a, i32 %b) {
+entry:
+  %cmp = icmp eq i32 %a, %b
+  br i1 %cmp, label %cond.true, label %cond.end
+
+cond.true:
+  %shift = ashr i32 %b, 1
+  br label %cond.end
+
+cond.end:
+  %cond = phi i32 [ %shift, %cond.true ], [ 0, %entry ]
+  ret i32 %cond
+}
+
+; CHECK-LABEL: @ashr_test_static_bad(
+; CHECK: %cond = phi i32 [ %shift, %cond.true ], [ 0, %entry ]
+define i32 @ashr_test_static_bad(i32 %a, i32 %b) {
+entry:
+  %cmp = icmp eq i32 %a, %b
+  br i1 %cmp, label %cond.true, label %cond.end
+
+cond.true:
+  %shift = ashr i32 %b, 40
+  br label %cond.end
+
+cond.end:
+  %cond = phi i32 [ %shift, %cond.true ], [ 0, %entry ]
+  ret i32 %cond
+}
+
+; CHECK-LABEL: @ashr_test_dynamic(
+; CHECK: %cond = phi i32 [ %shift, %cond.true ], [ 0, %entry ]
+define i32 @ashr_test_dynamic(i32 %a, i32 %b) {
+entry:
+  %cmp = icmp eq i32 %a, %b
+  br i1 %cmp, label %cond.true, label %cond.end
+
+cond.true:
+  %shift = ashr i32 %b, %a
+  br label %cond.end
+
+cond.end:
+  %cond = phi i32 [ %shift, %cond.true ], [ 0, %entry ]
+  ret i32 %cond
+}
+
+; CHECK-LABEL: @lshr_test_static_good(
+; CHECK: select i1 %cmp, i32 %shift, i32 0
+define i32 @lshr_test_static_good(i32 %a, i32 %b) {
+entry:
+  %cmp = icmp eq i32 %a, %b
+  br i1 %cmp, label %cond.true, label %cond.end
+
+cond.true:
+  %shift = lshr i32 %b, 1
+  br label %cond.end
+
+cond.end:
+  %cond = phi i32 [ %shift, %cond.true ], [ 0, %entry ]
+  ret i32 %cond
+}
+
+; CHECK-LABEL: @lshr_test_static_bad(
+; CHECK: %cond = phi i32 [ %shift, %cond.true ], [ 0, %entry ]
+define i32 @lshr_test_static_bad(i32 %a, i32 %b) {
+entry:
+  %cmp = icmp eq i32 %a, %b
+  br i1 %cmp, label %cond.true, label %cond.end
+
+cond.true:
+  %shift = lshr i32 %b, 40
+  br label %cond.end
+
+cond.end:
+  %cond = phi i32 [ %shift, %cond.true ], [ 0, %entry ]
+  ret i32 %cond
+}
+
+; CHECK-LABEL: @lshr_test_dynamic(
+; CHECK: %cond = phi i32 [ %shift, %cond.true ], [ 0, %entry ]
+define i32 @lshr_test_dynamic(i32 %a, i32 %b) {
+entry:
+  %cmp = icmp eq i32 %a, %b
+  br i1 %cmp, label %cond.true, label %cond.end
+
+cond.true:
+  %shift = lshr i32 %b, %a
+  br label %cond.end
+
+cond.end:
+  %cond = phi i32 [ %shift, %cond.true ], [ 0, %entry ]
+  ret i32 %cond
+}
+
+; CHECK-LABEL: @shl_test_static_good(
+; CHECK: select i1 %cmp, i32 %shift, i32 0
+define i32 @shl_test_static_good(i32 %a, i32 %b) {
+entry:
+  %cmp = icmp eq i32 %a, %b
+  br i1 %cmp, label %cond.true, label %cond.end
+
+cond.true:
+  %shift = shl i32 %b, 1
+  br label %cond.end
+
+cond.end:
+  %cond = phi i32 [ %shift, %cond.true ], [ 0, %entry ]
+  ret i32 %cond
+}
+
+; CHECK-LABEL: @shl_test_static_bad(
+; CHECK: %cond = phi i32 [ %shift, %cond.true ], [ 0, %entry ]
+define i32 @shl_test_static_bad(i32 %a, i32 %b) {
+entry:
+  %cmp = icmp eq i32 %a, %b
+  br i1 %cmp, label %cond.true, label %cond.end
+
+cond.true:
+  %shift = shl i32 %b, 40
+  br label %cond.end
+
+cond.end:
+  %cond = phi i32 [ %shift, %cond.true ], [ 0, %entry ]
+  ret i32 %cond
+}
+
+; CHECK-LABEL: @shl_test_dynamic(
+; CHECK: %cond = phi i32 [ %shift, %cond.true ], [ 0, %entry ]
+define i32 @shl_test_dynamic(i32 %a, i32 %b) {
+entry:
+  %cmp = icmp eq i32 %a, %b
+  br i1 %cmp, label %cond.true, label %cond.end
+
+cond.true:
+  %shift = shl i32 %b, %a
+  br label %cond.end
+
+cond.end:
+  %cond = phi i32 [ %shift, %cond.true ], [ 0, %entry ]
+  ret i32 %cond
+}