diff --git a/clang/include/clang/AST/ASTContext.h b/clang/include/clang/AST/ASTContext.h
--- a/clang/include/clang/AST/ASTContext.h
+++ b/clang/include/clang/AST/ASTContext.h
@@ -1114,7 +1114,7 @@
       SatUnsignedLongFractTy;
   CanQualType HalfTy; // [OpenCL 6.1.1.1], ARM NEON
   CanQualType BFloat16Ty;
-  CanQualType Float16Ty; // C11 extension ISO/IEC TS 18661-3
+  CanQualType Float16Ty, Float16ComplexTy; // C11 extension ISO/IEC TS 18661-3
   CanQualType VoidPtrTy, NullPtrTy;
   CanQualType DependentTy, OverloadTy, BoundMemberTy, UnknownAnyTy;
   CanQualType BuiltinFnTy;
diff --git a/clang/lib/AST/ASTContext.cpp b/clang/lib/AST/ASTContext.cpp
--- a/clang/lib/AST/ASTContext.cpp
+++ b/clang/lib/AST/ASTContext.cpp
@@ -1327,6 +1327,7 @@
 
   // C11 extension ISO/IEC TS 18661-3
   InitBuiltinType(Float16Ty,           BuiltinType::Float16);
+  InitBuiltinType(Float16ComplexTy,    BuiltinType::Float16);
 
   // ISO/IEC JTC1 SC22 WG14 N1169 Extension
   InitBuiltinType(ShortAccumTy,            BuiltinType::ShortAccum);
@@ -6807,9 +6808,10 @@
   FloatingRank EltRank = getFloatingRank(Size);
   if (Domain->isComplexType()) {
     switch (EltRank) {
-    case BFloat16Rank: llvm_unreachable("Complex bfloat16 is not supported");
-    case Float16Rank:
+    case BFloat16Rank:
+      llvm_unreachable("Complex bfloat16 is not supported");
     case HalfRank: llvm_unreachable("Complex half is not supported");
+    case Float16Rank:    return getComplexType(Float16Ty);
     case Ibm128Rank:     return getComplexType(Ibm128Ty);
     case FloatRank:      return getComplexType(FloatTy);
     case DoubleRank:     return getComplexType(DoubleTy);
diff --git a/clang/test/CodeGen/aarch64-complex-half-math.c b/clang/test/CodeGen/aarch64-complex-half-math.c
new file mode 100644
--- /dev/null
+++ b/clang/test/CodeGen/aarch64-complex-half-math.c
@@ -0,0 +1,145 @@
+// RUN: %clang_cc1 %s -O1 -emit-llvm -triple aarch64-unknown-unknown -ffast-math -o - | FileCheck %s --check-prefix=AARCH64
+
+_Float16 _Complex add_float_rr(_Float16 a, _Float16 b) {
+  // AARCH64-LABEL: @add_float_rr(
+  // AARCH64: fadd reassoc nnan ninf nsz arcp afn half
+  // AARCH64-NOT: fadd
+  // AARCH64: ret { half, half }
+  return a + b;
+}
+_Float16 _Complex add_float_cr(_Float16 _Complex a, _Float16 b) {
+  // AARCH64-LABEL: @add_float_cr(
+  // AARCH64: fadd reassoc nnan ninf nsz arcp afn half
+  // AARCH64-NOT: fadd
+  // AARCH64: ret { half, half }
+  return a + b;
+}
+_Float16 _Complex add_float_rc(_Float16 a, _Float16 _Complex b) {
+  // AARCH64-LABEL: @add_float_rc(
+  // AARCH64: fadd reassoc nnan ninf nsz arcp afn half
+  // AARCH64-NOT: fadd
+  // AARCH64: ret { half, half }
+  return a + b;
+}
+_Float16 _Complex add_float_cc(_Float16 _Complex a, _Float16 _Complex b) {
+  // AARCH64-LABEL: @add_float_cc(
+  // AARCH64: fadd reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fadd reassoc nnan ninf nsz arcp afn half
+  // AARCH64-NOT: fadd
+  // AARCH64: ret { half, half }
+  return a + b;
+}
+
+_Float16 _Complex sub_float_rr(_Float16 a, _Float16 b) {
+  // AARCH64-LABEL: @sub_float_rr(
+  // AARCH64: fsub reassoc nnan ninf nsz arcp afn half
+  // AARCH64-NOT: fsub
+  // AARCH64: ret { half, half }
+  return a - b;
+}
+_Float16 _Complex sub_float_cr(_Float16 _Complex a, _Float16 b) {
+  // AARCH64-LABEL: @sub_float_cr(
+  // AARCH64: fsub reassoc nnan ninf nsz arcp afn half
+  // AARCH64-NOT: fsub
+  // AARCH64: ret { half, half }
+  return a - b;
+}
+_Float16 _Complex sub_float_rc(_Float16 a, _Float16 _Complex b) {
+  // AARCH64-LABEL: @sub_float_rc(
+  // AARCH64: fsub reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fneg reassoc nnan ninf nsz arcp afn half
+  // AARCH64-NOT: fsub
+  // AARCH64: ret { half, half }
+  return a - b;
+}
+_Float16 _Complex sub_float_cc(_Float16 _Complex a, _Float16 _Complex b) {
+  // AARCH64-LABEL: @sub_float_cc(
+  // AARCH64: fsub reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fsub reassoc nnan ninf nsz arcp afn half
+  // AARCH64-NOT: fsub
+  // AARCH64: ret { half, half }
+  return a - b;
+}
+
+_Float16 _Complex mul_float_rr(_Float16 a, _Float16 b) {
+  // AARCH64-LABEL: @mul_float_rr(
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64-NOT: fmul
+  // AARCH64: ret { half, half }
+  return a * b;
+}
+_Float16 _Complex mul_float_cr(_Float16 _Complex a, _Float16 b) {
+  // AARCH64-LABEL: @mul_float_cr(
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64-NOT: fmul
+  // AARCH64: ret { half, half }
+  return a * b;
+}
+_Float16 _Complex mul_float_rc(_Float16 a, _Float16 _Complex b) {
+  // AARCH64-LABEL: @mul_float_rc(
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64-NOT: fmul
+  // AARCH64: ret { half, half }
+  return a * b;
+}
+_Float16 _Complex mul_float_cc(_Float16 _Complex a, _Float16 _Complex b) {
+  // AARCH64-LABEL: @mul_float_cc(
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fadd reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fsub reassoc nnan ninf nsz arcp afn half
+  // AARCH64-NOT: fmul
+  // AARCH64: ret { half, half }
+  return a * b;
+}
+
+_Float16 _Complex div_float_rr(_Float16 a, _Float16 b) {
+  // AARCH64-LABEL: @div_float_rr(
+  // AARCH64: fdiv reassoc nnan ninf nsz arcp afn half
+  // AARCH64-NOT: fdiv reassoc nnan ninf nsz arcp afn half
+  // AARCH64: ret { half, half }
+  return a / b;
+}
+_Float16 _Complex div_float_cr(_Float16 _Complex a, _Float16 b) {
+  // AARCH64-LABEL: @div_float_cr(
+  // AARCH64: fdiv reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fdiv reassoc nnan ninf nsz arcp afn half
+  // AARCH64-NOT: fdiv reassoc nnan ninf nsz arcp afn half
+  // AARCH64: ret { half, half }
+  return a / b;
+}
+_Float16 _Complex div_float_rc(_Float16 a, _Float16 _Complex b) {
+  // AARCH64-LABEL: @div_float_rc(
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fadd reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fneg reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fdiv reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fdiv reassoc nnan ninf nsz arcp afn half
+  // AARCH64-NOT: fdiv reassoc nnan ninf nsz arcp afn half
+  // AARCH64: ret { half, half }
+  return a / b;
+}
+_Float16 _Complex div_float_cc(_Float16 _Complex a, _Float16 _Complex b) {
+  // AARCH64-LABEL: @div_float_cc(
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fadd reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fadd reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fmul reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fsub reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fdiv reassoc nnan ninf nsz arcp afn half
+  // AARCH64: fdiv reassoc nnan ninf nsz arcp afn half
+  // AARCH64-NOT: fdiv reassoc nnan ninf nsz arcp afn half
+  // AARCH64: ret { half, half }
+  return a / b;
+}