diff --git a/llvm/include/llvm/CodeGen/GlobalISel/CombinerHelper.h b/llvm/include/llvm/CodeGen/GlobalISel/CombinerHelper.h
--- a/llvm/include/llvm/CodeGen/GlobalISel/CombinerHelper.h
+++ b/llvm/include/llvm/CodeGen/GlobalISel/CombinerHelper.h
@@ -190,6 +190,19 @@
   bool applyCombineShiftToUnmerge(MachineInstr &MI, const unsigned &ShiftVal);
   bool tryCombineShiftToUnmerge(MachineInstr &MI, unsigned TargetShiftAmount);
 
+  /// Return true if any explicit use operand on \p MI is defined by a
+  /// G_IMPLICIT_DEF.
+  bool matchAnyExplicitUseIsUndef(MachineInstr &MI);
+
+  /// Replace an instruction with a G_FCONSTANT with value \p C.
+  bool replaceInstWithFConstant(MachineInstr &MI, double C);
+
+  /// Replace an instruction with a G_CONSTANT with value \p C.
+  bool replaceInstWithConstant(MachineInstr &MI, int64_t C);
+
+  /// Replace an instruction with a G_IMPLICIT_DEF.
+  bool replaceInstWithUndef(MachineInstr &MI);
+
   /// Try to transform \p MI by using all of the above
   /// combine functions. Returns true if changed.
   bool tryCombine(MachineInstr &MI);
diff --git a/llvm/include/llvm/Target/GlobalISel/Combine.td b/llvm/include/llvm/Target/GlobalISel/Combine.td
--- a/llvm/include/llvm/Target/GlobalISel/Combine.td
+++ b/llvm/include/llvm/Target/GlobalISel/Combine.td
@@ -142,7 +142,34 @@
          [{ return Helper.matchCombineMulToShl(*${mi}, ${matchinfo}); }]),
   (apply [{ Helper.applyCombineMulToShl(*${mi}, ${matchinfo}); }])>;
 
+// [us]itofp(undef) = 0, because the result value is bounded.
+def undef_to_fp_zero : GICombineRule<
+  (defs root:$root),
+  (match (wip_match_opcode G_UITOFP, G_SITOFP):$root,
+         [{ return Helper.matchAnyExplicitUseIsUndef(*${root}); }]),
+  (apply [{ Helper.replaceInstWithFConstant(*${root}, 0.0); }])>;
+
+def undef_to_int_zero: GICombineRule<
+  (defs root:$root),
+  (match (wip_match_opcode G_AND, G_MUL):$root,
+         [{ return Helper.matchAnyExplicitUseIsUndef(*${root}); }]),
+  (apply [{ Helper.replaceInstWithConstant(*${root}, 0); }])>;
+
+def undef_to_negative_one: GICombineRule<
+  (defs root:$root),
+  (match (wip_match_opcode G_OR):$root,
+         [{ return Helper.matchAnyExplicitUseIsUndef(*${root}); }]),
+  (apply [{ Helper.replaceInstWithConstant(*${root}, -1); }])>;
+
+def propagate_undef: GICombineRule<
+  (defs root:$root),
+  (match (wip_match_opcode G_ADD, G_FPTOSI, G_FPTOUI, G_SUB, G_XOR):$root,
+         [{ return Helper.matchAnyExplicitUseIsUndef(*${root}); }]),
+  (apply [{ Helper.replaceInstWithUndef(*${root}); }])>;
+
+def undef_combines : GICombineGroup<[undef_to_fp_zero, undef_to_int_zero,
+                                     undef_to_negative_one, propagate_undef]>;
+
 def trivial_combines : GICombineGroup<[copy_prop, mul_to_shl]>;
 def all_combines : GICombineGroup<[trivial_combines, ptr_add_immed_chain,
-    combines_for_extload, combine_indexed_load_store]>;
-
+    combines_for_extload, combine_indexed_load_store, undef_combines]>;
diff --git a/llvm/lib/CodeGen/GlobalISel/CombinerHelper.cpp b/llvm/lib/CodeGen/GlobalISel/CombinerHelper.cpp
--- a/llvm/lib/CodeGen/GlobalISel/CombinerHelper.cpp
+++ b/llvm/lib/CodeGen/GlobalISel/CombinerHelper.cpp
@@ -1483,6 +1483,37 @@
   return false;
 }
 
+bool CombinerHelper::matchAnyExplicitUseIsUndef(MachineInstr &MI) {
+  return any_of(MI.explicit_uses(), [this](const MachineOperand &MO) {
+    return MO.isReg() &&
+           getOpcodeDef(TargetOpcode::G_IMPLICIT_DEF, MO.getReg(), MRI);
+  });
+}
+
+bool CombinerHelper::replaceInstWithFConstant(MachineInstr &MI, double C) {
+  assert(MI.getNumDefs() == 1 && "Expected only one def?");
+  Builder.setInstr(MI);
+  Builder.buildFConstant(MI.getOperand(0), C);
+  MI.eraseFromParent();
+  return true;
+}
+
+bool CombinerHelper::replaceInstWithConstant(MachineInstr &MI, int64_t C) {
+  assert(MI.getNumDefs() == 1 && "Expected only one def?");
+  Builder.setInstr(MI);
+  Builder.buildConstant(MI.getOperand(0), C);
+  MI.eraseFromParent();
+  return true;
+}
+
+bool CombinerHelper::replaceInstWithUndef(MachineInstr &MI) {
+  assert(MI.getNumDefs() == 1 && "Expected only one def?");
+  Builder.setInstr(MI);
+  Builder.buildUndef(MI.getOperand(0));
+  MI.eraseFromParent();
+  return true;
+}
+
 bool CombinerHelper::tryCombine(MachineInstr &MI) {
   if (tryCombineCopy(MI))
     return true;
diff --git a/llvm/test/CodeGen/AArch64/GlobalISel/arm64-fallback.ll b/llvm/test/CodeGen/AArch64/GlobalISel/arm64-fallback.ll
--- a/llvm/test/CodeGen/AArch64/GlobalISel/arm64-fallback.ll
+++ b/llvm/test/CodeGen/AArch64/GlobalISel/arm64-fallback.ll
@@ -167,16 +167,6 @@
   ret void
 }
 
-; FALLBACK-WITH-REPORT-ERR: remark: <unknown>:0:0: cannot select: %{{[0-9]+}}:gpr64(s64), %{{[0-9]+}}:gpr(s1) = G_UADDE %{{[0-9]+}}:gpr, %{{[0-9]+}}:gpr, %{{[0-9]+}}:gpr (in function: nonpow2_store_narrowing)
-; FALLBACK-WITH-REPORT-ERR: warning: Instruction selection used fallback path for nonpow2_store_narrowing
-; FALLBACK-WITH-REPORT-OUT-LABEL: nonpow2_store_narrowing:
-define void @nonpow2_store_narrowing(i96* %c) {
-  %a = add i128 undef, undef
-  %b = trunc i128 %a to i96
-  store i96 %b, i96* %c
-  ret void
-}
-
 ; Currently can't handle vector lengths that aren't an exact multiple of
 ; natively supported vector lengths. Test that the fall-back works for those.
 ; FALLBACK-WITH-REPORT-ERR-G_IMPLICIT_DEF-LEGALIZABLE: (FIXME: this is what is expected once we can legalize non-pow-of-2 G_IMPLICIT_DEF) remark: <unknown>:0:0: unable to legalize instruction: %1:_(<7 x s64>) = G_ADD %0, %0 (in function: nonpow2_vector_add_fewerelements
diff --git a/llvm/test/CodeGen/AArch64/GlobalISel/prelegalizercombiner-undef.mir b/llvm/test/CodeGen/AArch64/GlobalISel/prelegalizercombiner-undef.mir
new file mode 100644
--- /dev/null
+++ b/llvm/test/CodeGen/AArch64/GlobalISel/prelegalizercombiner-undef.mir
@@ -0,0 +1,168 @@
+# NOTE: Assertions have been autogenerated by utils/update_mir_test_checks.py
+# RUN: llc -mtriple aarch64 -run-pass=aarch64-prelegalizer-combiner -verify-machineinstrs %s -o - | FileCheck %s
+
+name:            uitofp_to_zero
+alignment:       4
+tracksRegLiveness: true
+body:             |
+  bb.0:
+    ; CHECK-LABEL: name: uitofp_to_zero
+    ; CHECK: [[C:%[0-9]+]]:_(s32) = G_FCONSTANT float 0.000000e+00
+    ; CHECK: $s0 = COPY [[C]](s32)
+    ; CHECK: RET_ReallyLR implicit $s0
+    %0:_(s32) = G_IMPLICIT_DEF
+    %1:_(s32) = G_UITOFP %0(s32)
+    $s0 = COPY %1(s32)
+    RET_ReallyLR implicit $s0
+
+...
+---
+name:            sitofp_to_zero
+alignment:       4
+tracksRegLiveness: true
+body:             |
+  bb.0:
+    ; CHECK-LABEL: name: sitofp_to_zero
+    ; CHECK: [[C:%[0-9]+]]:_(s32) = G_FCONSTANT float 0.000000e+00
+    ; CHECK: $s0 = COPY [[C]](s32)
+    ; CHECK: RET_ReallyLR implicit $s0
+    %0:_(s32) = G_IMPLICIT_DEF
+    %1:_(s32) = G_SITOFP %0(s32)
+    $s0 = COPY %1(s32)
+    RET_ReallyLR implicit $s0
+
+...
+---
+name:            and_to_zero
+alignment:       4
+tracksRegLiveness: true
+body:             |
+  bb.0:
+    ; CHECK-LABEL: name: and_to_zero
+    ; CHECK: [[C:%[0-9]+]]:_(s32) = G_CONSTANT i32 0
+    ; CHECK: $w0 = COPY [[C]](s32)
+    ; CHECK: RET_ReallyLR implicit $w0
+    %0:_(s32) = G_CONSTANT i32 10
+    %1:_(s32) = G_IMPLICIT_DEF
+    %2:_(s32) = G_AND %0, %1
+    $w0 = COPY %2(s32)
+    RET_ReallyLR implicit $w0
+
+...
+---
+name:            mul_to_zero
+alignment:       4
+tracksRegLiveness: true
+body:             |
+  bb.0:
+    ; CHECK-LABEL: name: mul_to_zero
+    ; CHECK: [[C:%[0-9]+]]:_(s32) = G_CONSTANT i32 0
+    ; CHECK: $w0 = COPY [[C]](s32)
+    ; CHECK: RET_ReallyLR implicit $w0
+    %0:_(s32) = G_CONSTANT i32 10
+    %1:_(s32) = G_IMPLICIT_DEF
+    %2:_(s32) = G_MUL %0, %1
+    $w0 = COPY %2(s32)
+    RET_ReallyLR implicit $w0
+
+...
+---
+name:            or_to_negative_one
+alignment:       4
+tracksRegLiveness: true
+body:             |
+  bb.0:
+    ; CHECK-LABEL: name: or_to_negative_one
+    ; CHECK: [[C:%[0-9]+]]:_(s32) = G_CONSTANT i32 -1
+    ; CHECK: $w0 = COPY [[C]](s32)
+    ; CHECK: RET_ReallyLR implicit $w0
+    %0:_(s32) = G_CONSTANT i32 10
+    %1:_(s32) = G_IMPLICIT_DEF
+    %2:_(s32) = G_OR %0, %1
+    $w0 = COPY %2(s32)
+    RET_ReallyLR implicit $w0
+
+...
+---
+name:            xor_to_undef
+alignment:       4
+tracksRegLiveness: true
+body:             |
+  bb.0:
+    ; CHECK-LABEL: name: xor_to_undef
+    ; CHECK: [[DEF:%[0-9]+]]:_(s32) = G_IMPLICIT_DEF
+    ; CHECK: $w0 = COPY [[DEF]](s32)
+    ; CHECK: RET_ReallyLR implicit $w0
+    %0:_(s32) = G_CONSTANT i32 10
+    %1:_(s32) = G_IMPLICIT_DEF
+    %2:_(s32) = G_XOR %0, %1
+    $w0 = COPY %2(s32)
+    RET_ReallyLR implicit $w0
+
+...
+---
+name:            add_to_undef
+alignment:       4
+tracksRegLiveness: true
+body:             |
+  bb.0:
+    ; CHECK-LABEL: name: add_to_undef
+    ; CHECK: [[DEF:%[0-9]+]]:_(s32) = G_IMPLICIT_DEF
+    ; CHECK: $w0 = COPY [[DEF]](s32)
+    ; CHECK: RET_ReallyLR implicit $w0
+    %0:_(s32) = G_CONSTANT i32 10
+    %1:_(s32) = G_IMPLICIT_DEF
+    %2:_(s32) = G_ADD %0, %1
+    $w0 = COPY %2(s32)
+    RET_ReallyLR implicit $w0
+
+...
+---
+name:            sub_to_undef
+alignment:       4
+tracksRegLiveness: true
+body:             |
+  bb.0:
+    ; CHECK-LABEL: name: sub_to_undef
+    ; CHECK: [[DEF:%[0-9]+]]:_(s32) = G_IMPLICIT_DEF
+    ; CHECK: $w0 = COPY [[DEF]](s32)
+    ; CHECK: RET_ReallyLR implicit $w0
+    %0:_(s32) = G_CONSTANT i32 10
+    %1:_(s32) = G_IMPLICIT_DEF
+    %2:_(s32) = G_SUB %0, %1
+    $w0 = COPY %2(s32)
+    RET_ReallyLR implicit $w0
+
+...
+---
+name:            fptoui_to_undef
+alignment:       4
+tracksRegLiveness: true
+body:             |
+  bb.0:
+    ; CHECK-LABEL: name: fptoui_to_undef
+    ; CHECK: [[DEF:%[0-9]+]]:_(s32) = G_IMPLICIT_DEF
+    ; CHECK: $w0 = COPY [[DEF]](s32)
+    ; CHECK: RET_ReallyLR implicit $w0
+    %0:_(s32) = G_IMPLICIT_DEF
+    %1:_(s32) = G_FPTOUI %0(s32)
+    $w0 = COPY %1(s32)
+    RET_ReallyLR implicit $w0
+
+...
+---
+name:            fptosi_to_undef
+alignment:       4
+tracksRegLiveness: true
+body:             |
+  bb.0:
+    ; CHECK-LABEL: name: fptosi_to_undef
+    ; CHECK: [[DEF:%[0-9]+]]:_(s32) = G_IMPLICIT_DEF
+    ; CHECK: $w0 = COPY [[DEF]](s32)
+    ; CHECK: RET_ReallyLR implicit $w0
+    %0:_(s32) = G_IMPLICIT_DEF
+    %1:_(s32) = G_FPTOSI %0(s32)
+    $w0 = COPY %1(s32)
+    RET_ReallyLR implicit $w0
+
+...