diff --git a/llvm/lib/Target/AArch64/AArch64ExpandPseudoInsts.cpp b/llvm/lib/Target/AArch64/AArch64ExpandPseudoInsts.cpp
--- a/llvm/lib/Target/AArch64/AArch64ExpandPseudoInsts.cpp
+++ b/llvm/lib/Target/AArch64/AArch64ExpandPseudoInsts.cpp
@@ -696,10 +696,12 @@
      return true;
    }
    case AArch64::TAGPstack: {
-     BuildMI(MBB, MBBI, MI.getDebugLoc(), TII->get(AArch64::ADDG))
+     int64_t Offset = MI.getOperand(2).getImm();
+     BuildMI(MBB, MBBI, MI.getDebugLoc(),
+             TII->get(Offset >= 0 ? AArch64::ADDG : AArch64::SUBG))
          .add(MI.getOperand(0))
          .add(MI.getOperand(1))
-         .add(MI.getOperand(2))
+         .addImm(std::abs(Offset))
          .add(MI.getOperand(4));
      MI.eraseFromParent();
      return true;
diff --git a/llvm/lib/Target/AArch64/AArch64InstrInfo.cpp b/llvm/lib/Target/AArch64/AArch64InstrInfo.cpp
--- a/llvm/lib/Target/AArch64/AArch64InstrInfo.cpp
+++ b/llvm/lib/Target/AArch64/AArch64InstrInfo.cpp
@@ -2188,12 +2188,19 @@
     MaxOffset = 4095;
     break;
   case AArch64::ADDG:
-  case AArch64::TAGPstack:
     Scale = 16;
     Width = 0;
     MinOffset = 0;
     MaxOffset = 63;
     break;
+  case AArch64::TAGPstack:
+    Scale = 16;
+    Width = 0;
+    // TAGP with a negative offset turns into SUBP, which has a maximum offset
+    // of 63 (not 64!).
+    MinOffset = -63;
+    MaxOffset = 63;
+    break;
   case AArch64::LDG:
   case AArch64::STGOffset:
   case AArch64::STZGOffset:
diff --git a/llvm/test/CodeGen/AArch64/addg_subg.mir b/llvm/test/CodeGen/AArch64/addg_subg.mir
new file mode 100644
--- /dev/null
+++ b/llvm/test/CodeGen/AArch64/addg_subg.mir
@@ -0,0 +1,37 @@
+# RUN: llc -mtriple=aarch64 -run-pass=prologepilog,aarch64-expand-pseudo %s -o - | FileCheck %s
+
+# CHECK: renamable $x8 = IRG $sp, $xzr
+
+# CHECK: renamable $x0 = ADDG $x8, 0, 0
+# CHECK: renamable $x0 = ADDG $x8, 5, 0
+# CHECK: renamable $x0 = ADDG $x8, 63, 0
+# CHECK: $[[R:x[0-9]+]] = ADDXri $x8, 16, 0
+# CHECK: renamable $x0 = ADDG killed $[[R]], 63, 0
+
+# CHECK: renamable $x0 = SUBG $x8, 5, 0
+# CHECK: renamable $x0 = SUBG $x8, 63, 0
+# CHECK: $[[R:x[0-9]+]] = SUBXri $x8, 16, 0
+# CHECK: renamable $x0 = SUBG killed $[[R]], 63, 0
+
+---
+name: subg
+stack:
+  - { id: 0, type: default, offset: 0, size: 16, alignment: 16,
+      stack-id: default, callee-saved-register: '', callee-saved-restored: true,
+      local-offset: -16, debug-info-variable: '', debug-info-expression: '',
+      debug-info-location: '' }
+body:             |
+  bb.0.entry:
+    renamable $x8 = IRGstack $sp, $xzr
+
+    renamable $x0 = TAGPstack %stack.0, 0, killed renamable $x8, 0
+    renamable $x0 = TAGPstack %stack.0, 5, killed renamable $x8, 0
+    renamable $x0 = TAGPstack %stack.0, 63, killed renamable $x8, 0
+    renamable $x0 = TAGPstack %stack.0, 64, killed renamable $x8, 0
+
+    renamable $x0 = TAGPstack %stack.0, -5, killed renamable $x8, 0
+    renamable $x0 = TAGPstack %stack.0, -63, killed renamable $x8, 0
+    renamable $x0 = TAGPstack %stack.0, -64, killed renamable $x8, 0
+    RET_ReallyLR
+
+...