Index: lib/Target/AMDGPU/AMDGPURegisterBankInfo.cpp
===================================================================
--- lib/Target/AMDGPU/AMDGPURegisterBankInfo.cpp
+++ lib/Target/AMDGPU/AMDGPURegisterBankInfo.cpp
@@ -192,7 +192,8 @@
     Operands[I] = AMDGPU::getValueMapping(AMDGPU::VGPRRegBankID, SizeI);
   }
 
-  unsigned MappingID = 0;
+  // getInstrMapping's default mapping uses ID 1, so start at 2.
+  unsigned MappingID = 2;
   for (const auto &Entry : Table) {
     for (unsigned I = 0; I < NumOps; ++I) {
       int OpIdx = RegSrcOpIdx[I];
@@ -337,6 +338,17 @@
 
   InstructionMappings AltMappings;
   switch (MI.getOpcode()) {
+  case TargetOpcode::G_CONSTANT:
+  case TargetOpcode::G_FCONSTANT:
+  case TargetOpcode::G_FRAME_INDEX:
+  case TargetOpcode::G_GLOBAL_VALUE: {
+    static const OpRegBankEntry<1> Table[2] = {
+      { { AMDGPU::VGPRRegBankID }, 1 },
+      { { AMDGPU::SGPRRegBankID }, 1 }
+    };
+
+    return addMappingFromTable<1>(MI, MRI, { 0 }, Table);
+  }
   case TargetOpcode::G_AND:
   case TargetOpcode::G_OR:
   case TargetOpcode::G_XOR: {
Index: test/CodeGen/AMDGPU/GlobalISel/regbankselect-constant.mir
===================================================================
--- /dev/null
+++ test/CodeGen/AMDGPU/GlobalISel/regbankselect-constant.mir
@@ -0,0 +1,34 @@
+# NOTE: Assertions have been autogenerated by utils/update_mir_test_checks.py
+# RUN: llc -march=amdgcn -mcpu=hawaii -run-pass=regbankselect -regbankselect-fast -verify-machineinstrs -o - %s | FileCheck %s
+# RUN: llc -march=amdgcn -mcpu=hawaii -run-pass=regbankselect -regbankselect-greedy -verify-machineinstrs -o - %s | FileCheck %s
+
+# FIXME: The constant bank should have been chosen as VGPR
+---
+name: test_constant_s32_vgpr_use
+legalized:       true
+body: |
+  bb.0:
+    liveins: $vgpr0_vgpr1
+    ; CHECK-LABEL: name: test_constant_s32_vgpr_use
+    ; CHECK: [[COPY:%[0-9]+]]:vgpr(p1) = COPY $vgpr0_vgpr1
+    ; CHECK: [[C:%[0-9]+]]:sgpr(s32) = G_CONSTANT i32 1
+    ; CHECK: [[COPY1:%[0-9]+]]:vgpr(s32) = COPY [[C]](s32)
+    ; CHECK: G_STORE [[COPY1]](s32), [[COPY]](p1) :: (store 4)
+    %0:_(p1) = COPY $vgpr0_vgpr1
+    %1:_(s32) = G_CONSTANT i32 1
+    G_STORE %1, %0 :: (store 4)
+
+...
+
+---
+name: test_constant_s32_sgpr_use
+legalized:       true
+body: |
+  bb.0:
+    ; CHECK-LABEL: name: test_constant_s32_sgpr_use
+    ; CHECK: [[C:%[0-9]+]]:sgpr(s32) = G_CONSTANT i32 1
+    ; CHECK: G_INTRINSIC_W_SIDE_EFFECTS intrinsic(@llvm.amdgcn.s.sendmsg), 0, [[C]](s32)
+    %0:_(s32) = G_CONSTANT i32 1
+    G_INTRINSIC_W_SIDE_EFFECTS intrinsic(@llvm.amdgcn.s.sendmsg), 0, %0
+
+...