Index: lib/Analysis/BasicAliasAnalysis.cpp
===================================================================
--- lib/Analysis/BasicAliasAnalysis.cpp
+++ lib/Analysis/BasicAliasAnalysis.cpp
@@ -254,7 +254,10 @@
     Value *Result = GetLinearExpression(CastOp, Scale, Offset, Extension,
                                         DL, Depth+1, AT, DT);
     Scale = Scale.zext(OldWidth);
-    Offset = Offset.zext(OldWidth);
+
+    // We have to sign-extend even if Extension == EK_ZeroExt as we can't
+    // decompose a sign extension (i.e. zext(x - 1) != zext(x) - zext(-1)).
+    Offset = Offset.sext(OldWidth);
 
     return Result;
   }
@@ -1055,8 +1058,35 @@
   // Grab the least significant bit set in any of the scales.
   if (!GEP1VariableIndices.empty()) {
     uint64_t Modulo = 0;
-    for (unsigned i = 0, e = GEP1VariableIndices.size(); i != e; ++i)
+    bool AllPositive = true;
+    for (unsigned i = 0, e = GEP1VariableIndices.size(); i != e; ++i) {
+      const Value *V = GEP1VariableIndices[i].V;
       Modulo |= (uint64_t)GEP1VariableIndices[i].Scale;
+
+      bool SignKnownZero, SignKnownOne;
+      ComputeSignBit(
+        const_cast<Value *>(V),
+        SignKnownZero, SignKnownOne,
+        DL, 0, AT, nullptr, DT);
+
+      // Zero-extension widens the variable, and so forces the sign
+      // bit to zero.
+      bool IsZExt = GEP1VariableIndices[i].Extension == EK_ZeroExt;
+      SignKnownZero |= IsZExt;
+      SignKnownOne &= !IsZExt;
+
+      // If the variable's been begins with a zero then we know it's
+      // positive, regardless of whether the value is signed or
+      // unsigned.
+      int64_t Scale = GEP1VariableIndices[i].Scale;
+      AllPositive &= 
+        (SignKnownZero && Scale >= 0) ||
+        (SignKnownOne && Scale < 0);
+
+      // If the Value is currently positive but could change in a cycle,
+      // then we can't guarantee it'll always br positive.
+      AllPositive &= isValueEqualInPotentialCycles(V, V);
+    }
     Modulo = Modulo ^ (Modulo & (Modulo - 1));
 
     // We can compute the difference between the two addresses
@@ -1066,6 +1096,12 @@
     if (V1Size != UnknownSize && V2Size != UnknownSize &&
         ModOffset >= V2Size && V1Size <= Modulo - ModOffset)
       return NoAlias;
+
+    // If we know all the variables are positive, then GEP1 >= GEP1BasePtr.
+    // If GEP1BasePtr > V2 (GEP1BaseOffset > 0) then we know the pointers
+    // don't alias if V2Size can fit in the gap between V2 and GEP1BasePtr.
+    if (AllPositive && GEP1BaseOffset > 0 && V2Size <= (uint64_t) GEP1BaseOffset)
+      return NoAlias;
   }
 
   // Statically, we can see that the base objects are the same, but the
Index: test/Analysis/BasicAA/phi-aa.ll
===================================================================
--- test/Analysis/BasicAA/phi-aa.ll
+++ test/Analysis/BasicAA/phi-aa.ll
@@ -39,6 +39,7 @@
 
 ; CHECK-LABEL: pr18068
 ; CHECK: MayAlias: i32* %0, i32* %arrayidx5
+; CHECK: NoAlias: i32* %arrayidx13, i32* %arrayidx5
 
 define i32 @pr18068(i32* %jj7, i32* %j) {
 entry:
Index: test/Analysis/BasicAA/zext.ll
===================================================================
--- /dev/null
+++ test/Analysis/BasicAA/zext.ll
@@ -0,0 +1,87 @@
+; RUN: opt < %s -basicaa -aa-eval -print-all-alias-modref-info -disable-output 2>&1 | FileCheck %s
+target datalayout = "e-p:64:64:64-i1:8:8-i8:8:8-i16:16:16-i32:32:32-i64:64:64-f32:32:32-f64:64:64-v64:64:64-v128:128:128-a0:0:64-s0:64:64-f80:128:128-n8:16:32:64-S128"
+target triple = "x86_64-unknown-linux-gnu"
+
+; CHECK-LABEL: test_with_zext
+; CHECK:  NoAlias: i8* %a, i8* %b
+
+define void @test_with_zext() {
+  %1 = tail call i8* @malloc(i64 120)
+  %a = getelementptr inbounds i8* %1, i64 8
+  %2 = getelementptr inbounds i8* %1, i64 16
+  %3 = zext i32 3 to i64
+  %b = getelementptr inbounds i8* %2, i64 %3
+  ret void
+}
+
+; CHECK-LABEL: test_with_lshr
+; CHECK:  NoAlias: i8* %a, i8* %b
+
+define void @test_with_lshr(i64 %i) {
+  %1 = tail call i8* @malloc(i64 120)
+  %a = getelementptr inbounds i8* %1, i64 8
+  %2 = getelementptr inbounds i8* %1, i64 16
+  %3 = lshr i64 %i, 2
+  %b = getelementptr inbounds i8* %2, i64 %3
+  ret void
+}
+
+; CHECK-LABEL: test_with_a_loop
+; CHECK:  NoAlias: i8* %a, i8* %b
+
+define void @test_with_a_loop() {
+  %1 = tail call i8* @malloc(i64 120)
+  %a = getelementptr inbounds i8* %1, i64 8
+  %2 = getelementptr inbounds i8* %1, i64 16
+  br label %for.loop
+
+for.loop:
+  %i = phi i32 [ 0, %0 ], [ %i.next, %for.loop ]
+  %3 = zext i32 %i to i64
+  %b = getelementptr inbounds i8* %2, i64 %3
+  %i.next = add nuw nsw i32 %i, 1
+  %4 = icmp eq i32 %i.next, 10
+  br i1 %4, label %for.loop.exit, label %for.loop
+
+for.loop.exit:
+  ret void
+}
+
+; CHECK-LABEL: test_sign_extension
+; CHECK:  PartialAlias: i64* %b.i64, i8* %a
+
+define void @test_sign_extension(i32 %p) {
+  %1 = tail call i8* @malloc(i64 120)
+  %p.64 = zext i32 %p to i64
+  %a = getelementptr inbounds i8* %1, i64 %p.64
+  %p.minus1 = add i32 %p, -1
+  %p.minus1.64 = zext i32 %p.minus1 to i64
+  %b.i8 = getelementptr inbounds i8* %1, i64 %p.minus1.64
+  %b.i64 = bitcast i8* %b.i8 to i64*
+  ret void
+}
+
+; CHECK-LABEL: test_fe_tools
+; CHECK:  PartialAlias: i32* %a, i32* %b
+
+define void @test_fe_tools([8 x i32]* %values) {
+  br label %reorder
+
+for.loop:
+  %i = phi i32 [ 0, %reorder ], [ %i.next, %for.loop ]
+  %idxprom = zext i32 %i to i64
+  %b = getelementptr inbounds [8 x i32]* %values, i64 0, i64 %idxprom
+  %i.next = add nuw nsw i32 %i, 1
+  %1 = icmp eq i32 %i.next, 10
+  br i1 %1, label %for.loop.exit, label %for.loop
+
+reorder:
+  %a = getelementptr inbounds [8 x i32]* %values, i64 0, i64 1
+  br label %for.loop
+
+for.loop.exit:
+  ret void
+}
+
+; Function Attrs: nounwind
+declare noalias i8* @malloc(i64)