diff --git a/llvm/lib/Transforms/Instrumentation/HWAddressSanitizer.cpp b/llvm/lib/Transforms/Instrumentation/HWAddressSanitizer.cpp
--- a/llvm/lib/Transforms/Instrumentation/HWAddressSanitizer.cpp
+++ b/llvm/lib/Transforms/Instrumentation/HWAddressSanitizer.cpp
@@ -1585,11 +1585,14 @@
   Hasher.final(Hash);
   uint8_t Tag = Hash[0];
 
+  assert(TagMaskByte >= 16);
+
   for (GlobalVariable *GV : Globals) {
-    Tag &= TagMaskByte;
-    // Skip tag 0 in order to avoid collisions with untagged memory.
-    if (Tag == 0)
-      Tag = 1;
+    // Don't allow globals to be tagged with something that looks like a
+    // short-granule tag, otherwise we lose inter-granule overflow detection, as
+    // the fast path shadow-vs-address check succeeds.
+    if (Tag < 16 || Tag > TagMaskByte)
+      Tag = 16;
     instrumentGlobal(GV, Tag++);
   }
 }
diff --git a/llvm/test/Instrumentation/HWAddressSanitizer/X86/globals.ll b/llvm/test/Instrumentation/HWAddressSanitizer/X86/globals.ll
--- a/llvm/test/Instrumentation/HWAddressSanitizer/X86/globals.ll
+++ b/llvm/test/Instrumentation/HWAddressSanitizer/X86/globals.ll
@@ -7,19 +7,19 @@
 
 ; CHECK: @hwasan.dummy.global = private constant [0 x i8] zeroinitializer, section "hwasan_globals", comdat($hwasan.module_ctor), !associated [[NOTE:![0-9]+]]
 
-; CHECK: @four.hwasan = private global { i32, [12 x i8] } { i32 1, [12 x i8] c"\00\00\00\00\00\00\00\00\00\00\00," }, align 16
-; CHECK: @four.hwasan.descriptor = private constant { i32, i32 } { i32 trunc (i64 sub (i64 ptrtoint (ptr @four.hwasan to i64), i64 ptrtoint (ptr @four.hwasan.descriptor to i64)) to i32), i32 738197508 }, section "hwasan_globals", !associated [[FOUR:![0-9]+]]
+; CHECK: @four.hwasan = private global { i32, [12 x i8] } { i32 1, [12 x i8] c"\00\00\00\00\00\00\00\00\00\00\00\10" }, align 16
+; CHECK: @four.hwasan.descriptor = private constant { i32, i32 } { i32 trunc (i64 sub (i64 ptrtoint (ptr @four.hwasan to i64), i64 ptrtoint (ptr @four.hwasan.descriptor to i64)) to i32), i32 268435460 }, section "hwasan_globals", !associated [[FOUR:![0-9]+]]
 
 ; CHECK: @sixteen.hwasan = private global [16 x i8] zeroinitializer, align 16
-; CHECK: @sixteen.hwasan.descriptor = private constant { i32, i32 } { i32 trunc (i64 sub (i64 ptrtoint (ptr @sixteen.hwasan to i64), i64 ptrtoint (ptr @sixteen.hwasan.descriptor to i64)) to i32), i32 754974736 }, section "hwasan_globals", !associated [[SIXTEEN:![0-9]+]]
+; CHECK: @sixteen.hwasan.descriptor = private constant { i32, i32 } { i32 trunc (i64 sub (i64 ptrtoint (ptr @sixteen.hwasan to i64), i64 ptrtoint (ptr @sixteen.hwasan.descriptor to i64)) to i32), i32 285212688 }, section "hwasan_globals", !associated [[SIXTEEN:![0-9]+]]
 
 ; CHECK: @huge.hwasan = private global [16777232 x i8] zeroinitializer, align 16
-; CHECK: @huge.hwasan.descriptor = private constant { i32, i32 } { i32 trunc (i64 sub (i64 ptrtoint (ptr @huge.hwasan to i64), i64 ptrtoint (ptr @huge.hwasan.descriptor to i64)) to i32), i32 788529136 }, section "hwasan_globals", !associated [[HUGE:![0-9]+]]
-; CHECK: @huge.hwasan.descriptor.1 = private constant { i32, i32 } { i32 trunc (i64 add (i64 sub (i64 ptrtoint (ptr @huge.hwasan to i64), i64 ptrtoint (ptr @huge.hwasan.descriptor.1 to i64)), i64 16777200) to i32), i32 771751968 }, section "hwasan_globals", !associated [[HUGE]]
+; CHECK: @huge.hwasan.descriptor = private constant { i32, i32 } { i32 trunc (i64 sub (i64 ptrtoint (ptr @huge.hwasan to i64), i64 ptrtoint (ptr @huge.hwasan.descriptor to i64)) to i32), i32 318767088 }, section "hwasan_globals", !associated [[HUGE:![0-9]+]]
+; CHECK: @huge.hwasan.descriptor.1 = private constant { i32, i32 } { i32 trunc (i64 add (i64 sub (i64 ptrtoint (ptr @huge.hwasan to i64), i64 ptrtoint (ptr @huge.hwasan.descriptor.1 to i64)), i64 16777200) to i32), i32 301989920 }, section "hwasan_globals", !associated [[HUGE]]
 
-; CHECK: @four = alias i32, inttoptr (i64 add (i64 ptrtoint (ptr @four.hwasan to i64), i64 6341068275337658368) to ptr)
-; CHECK: @sixteen = alias [16 x i8], inttoptr (i64 add (i64 ptrtoint (ptr @sixteen.hwasan to i64), i64 6485183463413514240) to ptr)
-; CHECK: @huge = alias [16777232 x i8], inttoptr (i64 add (i64 ptrtoint (ptr @huge.hwasan to i64), i64 6629298651489370112) to ptr)
+; CHECK: @four = alias i32, inttoptr (i64 add (i64 ptrtoint (ptr @four.hwasan to i64), i64 2305843009213693952) to ptr)
+; CHECK: @sixteen = alias [16 x i8], inttoptr (i64 add (i64 ptrtoint (ptr @sixteen.hwasan to i64), i64 2449958197289549824) to ptr)
+; CHECK: @huge = alias [16777232 x i8], inttoptr (i64 add (i64 ptrtoint (ptr @huge.hwasan to i64), i64 2594073385365405696) to ptr)
 
 ; CHECK: [[NOTE]] = !{ptr @hwasan.note}
 ; CHECK: [[FOUR]] = !{ptr @four.hwasan}
diff --git a/llvm/test/Instrumentation/HWAddressSanitizer/globals-tag.ll b/llvm/test/Instrumentation/HWAddressSanitizer/globals-tag.ll
--- a/llvm/test/Instrumentation/HWAddressSanitizer/globals-tag.ll
+++ b/llvm/test/Instrumentation/HWAddressSanitizer/globals-tag.ll
@@ -35,21 +35,6 @@
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00~"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00$"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\000"
-; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\01"
-; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\02"
-; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\03"
-; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\04"
-; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\05"
-; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\06"
-; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\07"
-; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\08"
-; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\09"
-; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\0A"
-; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\0B"
-; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\0C"
-; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\0D"
-; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\0E"
-; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\0F"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\001"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\10"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\11"
@@ -185,20 +170,35 @@
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00e"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00E"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E0"
+; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E0"
+; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E1"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E1"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E2"
+; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E2"
+; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E3"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E3"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E4"
+; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E4"
+; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E5"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E5"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E6"
+; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E6"
+; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E7"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E7"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E8"
+; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E8"
+; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E9"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\E9"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\EA"
+; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\EA"
+; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\EB"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\EB"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\EC"
+; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\EC"
+; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\ED"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\ED"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\EE"
+; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\EE"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00\EF"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00f"
 ; CHECK-DAG: "\00\00\00\00\00\00\00\00\00\00\00F"