[MLIR] Add complex numbers to standard dialect

[frgossen]

Summary

Add CreateComplexOp, ReOp, and ImOp to the standard dialect.
This is the first step to support complex numbers.

[pifon2a]

awesome! thanks!

mlir/include/mlir/Dialect/StandardOps/IR/Ops.td

1541

verifier is already included in Std_Op, you don't have to add it here.

mlir/lib/Conversion/StandardToLLVM/StandardToLLVM.cpp

197

const can be omitted in LLVM codebase.

1314

auto loc = op->getLoc(); and reuse it 3 times?

[bondhugula]

mlir/include/mlir/Conversion/StandardToLLVM/ConvertStandardToLLVM.h

161

These comments should all be triple /// I believe.

mlir/include/mlir/Dialect/StandardOps/IR/Ops.td

1525

Please document the operands.

1937

Please document the operands.

mlir/lib/Dialect/StandardOps/IR/Ops.cpp

1905

dyn_cast -> cast

[bondhugula]

mlir/test/mlir-cpu-runner/complex_numbers.mlir

6

CHECK-LABEL to prevent things from matching past this.

21

CHECK-LABEL here please.

[frgossen]

Document operands, small changes.

[frgossen]

mlir/test/mlir-cpu-runner/complex_numbers.mlir

6

I double-checked the output of mlir-opt %s -convert-std-to-llvm | mlir-cpu-runner -e create_and_extract_real -entry-point-result=f32 and it is no more than the result of the computation, i.e. 1.200000e+00.
Because the two functions are compiled and executed separately, I believe matching past things is not an issue here and I don't see how I can use CHECK-LABEL in a useful way.
Do let me know if there is a more elegant way to write this test.

21

See above.

[ftynse]

Looks good in general! I have some advice on the op syntax, feel free to argue against it.

mlir/include/mlir/Dialect/StandardOps/IR/Ops.td

1013

Could we use a full word for the name, $complex. We generate functions with this name, it's more readable but reasonably short

1016

Do we want to support "mixed" types, e.g. f32, f64 -> complex<f64>? If not, I would just keep the type($cplx) here.

1530

This example looks wrong: the spec below says there is only one operand

1538

I think complex<X> -> X is quite redundant here, keeping just the complex type should suffice.

1943

Same as above

mlir/lib/Conversion/StandardToLLVM/StandardToLLVM.cpp

197

I think you can just call convertType(type.getElementType()) and let it be dispatched for you.

1299

We tend to use the kRealIdxInCpxNumStruct style for constants.

1312

Could you rather derive a new ComplexStructBuilder from `StructBuilder and use it here? Look at MemRefDescriptor for an example.

mlir/lib/Dialect/StandardOps/IR/Ops.cpp

1230

Could you please add a test for this? test/IR/invalid-ops.mlir sounds like the right file (although the file itself is misplaced)

mlir/test/Conversion/StandardToLLVM/convert-to-llvmir.mlir

78

You don't need an explicit label for the entry block in MLIR functions (and most other operations)

mlir/test/mlir-cpu-runner/complex_numbers.mlir

2

I think the conversion is straightforward enough to trust the individual components and drop this test. The -runner tests are intended to check that the runner itself works, your patch does not alter it in any way.

[frgossen]

Thanks for the many helpful comments.
There is one comment for which I'd like clarification.

mlir/include/mlir/Dialect/StandardOps/IR/Ops.td

1016

I would love to have only type($cplx) here.
The reason for the current format is that tablegen complained when I dropped the other types.
I can fix this with a hand-written parser and printer but before I do that I want to ask if this is also possible with the assemblyFormat thingy.
What is the elegant way to do this?

[ftynse]

mlir/include/mlir/Dialect/StandardOps/IR/Ops.td

1016

Indeed, auto-generated printer and parser needs a way to resolve _all_ types and cannot do so in this case. Sometimes, it can rely on the traits like SameOperandAndResultTypes, but not here. Ideally, we would have some way of specifying "type deduction rules"... Until that exists, you will need printer and parser functions. To make life easier, you can just take those generated by mlir-tblgen today and amend them a bit to deduce the types.

[rriddle]

mlir/include/mlir/Conversion/StandardToLLVM/ConvertStandardToLLVM.h

18

Please use forward declarations instead of includes in header files when you can.

mlir/include/mlir/Dialect/StandardOps/IR/Ops.td

996

Same comment as below.

1016

You can do that with TypesMatchWith, it was intended for this purpose..

1518

Don't provide a syntax if you have the declarative assembly(assemblyFormat). It is included automatically in the docs.

1931

Same here.

mlir/lib/Dialect/StandardOps/IR/Ops.cpp

1228

You should be able to verify this in tablegen with TypesMatchWith.

1649

Same comment as the other verifier.

1905

Same here.

[frgossen]

Simplified assembly format, introduced ComplexStructBuilder.

[frgossen]

mlir/include/mlir/Dialect/StandardOps/IR/Ops.td

1013

Also changed $imag to $imaginary.

1016

Nice. Thanks!

[ftynse]

Thanks!

mlir/include/mlir/Dialect/StandardOps/EDSC/Intrinsics.h

34

Nit: let's use std_re to be consistent with the assembly spelling.

mlir/test/IR/invalid-ops.mlir

1236 ↗

(On Diff #261766)

Nit: let's not hardcode SSA value names in checks, I think it's fine to shorten the expected-error message to expects different type than prior uses: 'f32' vs 'f64'

[frgossen]

Nits

[frgossen]

Address nits.

[frgossen]

Apply clang tidy suggestions

mlir/include/mlir/Conversion/StandardToLLVM/ConvertStandardToLLVM.h

 // converts Standard ops and types and provides hooks for dialect-specific
 // extensions to the conversion.
 //
 //===----------------------------------------------------------------------===//
 
 #ifndef MLIR_CONVERSION_STANDARDTOLLVM_CONVERTSTANDARDTOLLVM_H
 #define MLIR_CONVERSION_STANDARDTOLLVM_CONVERTSTANDARDTOLLVM_H
 
+#include "mlir/IR/StandardTypes.h"
 #include "mlir/Transforms/DialectConversion.h"
 
 namespace llvm {
 class IntegerType;
 class LLVMContext;
 class Module;
 class Type;
 } // namespace llvm
private:
   // Convert an integer type `i*` to `!llvm<"i*">`.
   Type convertIntegerType(IntegerType type);
 
   // Convert a floating point type: `f16` to `!llvm.half`, `f32` to
   // `!llvm.float` and `f64` to `!llvm.double`.  `bf16` is not supported
   // by LLVM.
   Type convertFloatType(FloatType type);
 
+  // Convert complex number type: `complex<f16>` to `!llvm<"{ half, half }">`,
+  // `complex<f32>` to `!llvm<"{ float, float }">`, and `complex<f64>` to
+  // `!llvm<"{ double, double }">`. `complex<bf16>` is not supported.
+  Type convertComplexType(ComplexType type);
+
   /// Convert a memref type into an LLVM type that captures the relevant data.
   Type convertMemRefType(MemRefType type);
 
   /// Convert a memref type into a list of non-aggregate LLVM IR types that
   /// contain all the relevant data. In particular, the list will contain:
   /// - two pointers to the memref element type, followed by
   /// - an integer offset, followed by
   /// - one integer size per dimension of the memref, followed by
public:
   matchAndRewrite(Operation *op, ArrayRef<Value> operands,
                   ConversionPatternRewriter &rewriter) const override {
     return LLVM::detail::oneToOneRewrite(op, TargetOp::getOperationName(),
                                          operands, this->typeConverter,
                                          rewriter);
   }
 };
 
-/// Basic lowering implementation for rewriting from Ops to LLVM Dialect Ops
-/// with one result. This supports higher-dimensional vector types.
+/// Basic lowering implementation to rewrite Ops with just one result to the
+/// LLVM Dialect. This supports higher-dimensional vector types.
 template <typename SourceOp, typename TargetOp>
 class VectorConvertToLLVMPattern : public ConvertOpToLLVMPattern<SourceOp> {
 public:
   using ConvertOpToLLVMPattern<SourceOp>::ConvertOpToLLVMPattern;
   using Super = VectorConvertToLLVMPattern<SourceOp, TargetOp>;
 
   LogicalResult
   matchAndRewrite(Operation *op, ArrayRef<Value> operands,

mlir/include/mlir/Dialect/StandardOps/EDSC/Intrinsics.h

 
 namespace mlir {
 namespace edsc {
 namespace intrinsics {
 
 using std_addf = ValueBuilder<AddFOp>;
 using std_alloc = ValueBuilder<AllocOp>;
 using std_call = OperationBuilder<CallOp>;
+using std_create_complex = ValueBuilder<CreateComplexOp>;
 using std_constant = ValueBuilder<ConstantOp>;
 using std_constant_float = ValueBuilder<ConstantFloatOp>;
 using std_constant_index = ValueBuilder<ConstantIndexOp>;
 using std_constant_int = ValueBuilder<ConstantIntOp>;
 using std_dealloc = OperationBuilder<DeallocOp>;
 using std_dim = ValueBuilder<DimOp>;
 using std_extract_element = ValueBuilder<ExtractElementOp>;
+using std_im = ValueBuilder<ImOp>;
 using std_index_cast = ValueBuilder<IndexCastOp>;
 using std_muli = ValueBuilder<MulIOp>;
 using std_mulf = ValueBuilder<MulFOp>;
 using std_memref_cast = ValueBuilder<MemRefCastOp>;
+using std_real = ValueBuilder<ReOp>;
 using std_ret = OperationBuilder<ReturnOp>;
 using std_select = ValueBuilder<SelectOp>;
 using std_load = ValueBuilder<LoadOp>;
 using std_store = OperationBuilder<StoreOp>;
 using std_subi = ValueBuilder<SubIOp>;
 using std_sub_view = ValueBuilder<SubViewOp>;
 using std_tanh = ValueBuilder<TanhOp>;
 using std_tensor_load = ValueBuilder<TensorLoadOp>;

mlir/include/mlir/Dialect/StandardOps/IR/Ops.td

def CmpIOp : Std_Op<"cmpi",
   let verifier = [{ return success(); }];
 
   let hasFolder = 1;
 
   let assemblyFormat = "$predicate `,` $lhs `,` $rhs attr-dict `:` type($lhs)";
 }
 
 //===----------------------------------------------------------------------===//
+// CreateComplexOp
+//===----------------------------------------------------------------------===//
+
+def CreateComplexOp : Std_Op<"create_complex", [NoSideEffect]> {
+  let summary = "creates a complex number";
+  let description = [{
+    Syntax:
+
+    ```
+    operation ::= ssa-id `=` `std.create_complex` ssa-use `,` ssa-use `:` type
+    ```
+
+    The `create_complex` operation creates a complex number from two
+    floating-point operands, the real and the imaginary part.
+
+    Example:
+
+    ```mlir
+    %a = create_complex %b, %c : f32, f32 -> complex<f32>
+    ```
+  }];
+
+  let arguments = (ins AnyFloat:$real, AnyFloat:$imag);
+  let results = (outs Complex<AnyFloat>:$cplx);
+
+  let assemblyFormat = [{
+    $real `,` $imag attr-dict `:` type($real) `,` type($imag) `->` type($cplx)
+  }];
+
+  let verifier = [{ return ::verify(*this); }];
+}
+
+//===----------------------------------------------------------------------===//
 // CondBranchOp
 //===----------------------------------------------------------------------===//
 
 def CondBranchOp : Std_Op<"cond_br",
     [AttrSizedOperandSegments, DeclareOpInterfaceMethods<BranchOpInterface>,
      NoSideEffect, Terminator]> {
   let summary = "conditional branch operation";
   let description = [{
let extraClassDeclaration = [{
     /// the operation.
     static bool areCastCompatible(Type a, Type b);
   }];
 
   let hasFolder = 0;
 }
 
 //===----------------------------------------------------------------------===//
+// ImOp
+//===----------------------------------------------------------------------===//
+
+def ImOp : Std_Op<"im", [NoSideEffect]> {
+  let summary = "extracts the imaginary part of a complex number";
+  let description = [{
+    Syntax:
+
+    ```
+    operation ::= ssa-id `=` `std.im` ssa-use `:` type
+    ```
+
+    The `im` operation extracts the imaginary part of a complex number as a
+    floating-point value.
+
+    Example:
+
+    ```mlir
+    %a = im %b, %c : complex<f32> -> f32
+    ```
+  }];
+
+  let arguments = (ins Complex<AnyFloat>:$cplx);
+  let results = (outs AnyFloat:$imag);
+
+  let assemblyFormat = [{
+    $cplx attr-dict `:` type($cplx) `->` type($imag)
+  }];
+
+  let verifier = [{ return ::verify(*this); }];
+}
+
+//===----------------------------------------------------------------------===//
 // IndexCastOp
 //===----------------------------------------------------------------------===//
 
 def IndexCastOp : CastOp<"index_cast">, Arguments<(ins AnyType:$in)> {
   let summary = "cast between index and integer types";
   let description = [{
     Casts between integer scalars and 'index' scalars. Index is an integer of
     platform-specific bit width. If casting to a wider integer, the value is
"OpBuilder &builder, OperationState &result, Value tensor", [{
       build(builder, result, indexType, tensor);
     }]>];
 
   let hasFolder = 1;
   let assemblyFormat = "operands attr-dict `:` type(operands)";
 }
 
 //===----------------------------------------------------------------------===//
+// ReOp
+//===----------------------------------------------------------------------===//
+
+def ReOp : Std_Op<"re", [NoSideEffect]> {
+  let summary = "extracts the real part of a complex number";
+  let description = [{
+    Syntax:
+
+    ```
+    operation ::= ssa-id `=` `std.re` ssa-use `:` type
+    ```
+
+    The `re` operation extracts the real part of a complex number as a
+    floating-point value.
+
+    Example:
+
+    ```mlir
+    %a = re %b, %c : complex<f32> -> f32
+    ```
+  }];
+
+  let arguments = (ins Complex<AnyFloat>:$cplx);
+  let results = (outs AnyFloat:$real);
+
+  let assemblyFormat = [{
+    $cplx attr-dict `:` type($cplx) `->` type($real)
+  }];
+
+  let verifier = [{ return ::verify(*this); }];
+}
+
+//===----------------------------------------------------------------------===//
 // RemFOp
 //===----------------------------------------------------------------------===//
 
 def RemFOp : FloatArithmeticOp<"remf"> {
   let summary = "floating point division remainder operation";
 }
 
 //===----------------------------------------------------------------------===//

mlir/lib/Conversion/StandardToLLVM/StandardToLLVM.cpp

: llvmDialect(ctx->getRegisteredDialect<LLVM::LLVMDialect>()),
       customizations(customs) {
   assert(llvmDialect && "LLVM IR dialect is not registered");
   module = &llvmDialect->getLLVMModule();
   if (customizations.indexBitwidth == kDeriveIndexBitwidthFromDataLayout)
     customizations.indexBitwidth =
         module->getDataLayout().getPointerSizeInBits();
 
   // Register conversions for the standard types.
+  addConversion([&](ComplexType type) { return convertComplexType(type); });
   addConversion([&](FloatType type) { return convertFloatType(type); });
   addConversion([&](FunctionType type) { return convertFunctionType(type); });
   addConversion([&](IndexType type) { return convertIndexType(type); });
   addConversion([&](IntegerType type) { return convertIntegerType(type); });
   addConversion([&](MemRefType type) { return convertMemRefType(type); });
   addConversion(
       [&](UnrankedMemRefType type) { return convertUnrankedMemRefType(type); });
   addConversion([&](VectorType type) { return convertVectorType(type); });
case mlir::StandardTypes::BF16: {
     return emitError(UnknownLoc::get(mlirContext), "unsupported type: BF16"),
            Type();
   }
   default:
     llvm_unreachable("non-float type in convertFloatType");
   }
 }
 
+Type LLVMTypeConverter::convertComplexType(ComplexType type) {
+  const FloatType elementType = type.getElementType().dyn_cast<FloatType>();
+  const LLVM::LLVMType llvmElementType =
+      convertFloatType(elementType).dyn_cast<LLVM::LLVMType>();
+  return LLVM::LLVMType::getStructTy(llvmDialect,
+                                     {llvmElementType, llvmElementType});
+}
+
 // Except for signatures, MLIR function types are converted into LLVM
 // pointer-to-function types.
 Type LLVMTypeConverter::convertFunctionType(FunctionType type) {
   SignatureConversion conversion(type.getNumInputs());
   LLVM::LLVMType converted =
       convertFunctionSignature(type, /*isVariadic=*/false, conversion);
   return converted.getPointerTo();
 }

 using UnsignedDivIOpLowering =
     VectorConvertToLLVMPattern<UnsignedDivIOp, LLVM::UDivOp>;
 using UnsignedRemIOpLowering =
     VectorConvertToLLVMPattern<UnsignedRemIOp, LLVM::URemOp>;
 using UnsignedShiftRightOpLowering =
     OneToOneConvertToLLVMPattern<UnsignedShiftRightOp, LLVM::LShrOp>;
 using XOrOpLowering = VectorConvertToLLVMPattern<XOrOp, LLVM::XOrOp>;
 
+// Lowerings for operations on complex numbers, `CreateComplexOp`, `ReOp`, and
+// `ImOp`.
+
+const int REAL_IDX_IN_CPLX_NUM_STRUCT = 0;
+const int IMAG_IDX_IN_CPLX_NUM_STRUCT = 1;
+
+struct CreateComplexOpLowering
+    : public ConvertOpToLLVMPattern<CreateComplexOp> {
+  using ConvertOpToLLVMPattern<CreateComplexOp>::ConvertOpToLLVMPattern;
+
+  LogicalResult
+  matchAndRewrite(Operation *op, ArrayRef<Value> operands,
+                  ConversionPatternRewriter &rewriter) const override {
+    auto complexOp = cast<CreateComplexOp>(op);
+    OperandAdaptor<CreateComplexOp> transformed(operands);
+
+    // Pack real and imaginary part into one structure.
+    auto packedType = typeConverter.convertType(complexOp.getType());
+    Value packed = rewriter.create<LLVM::UndefOp>(op->getLoc(), packedType);
+    packed = rewriter.create<LLVM::InsertValueOp>(
+        op->getLoc(), packedType, packed, transformed.real(),
+        rewriter.getI64ArrayAttr(REAL_IDX_IN_CPLX_NUM_STRUCT));
+    packed = rewriter.create<LLVM::InsertValueOp>(
+        op->getLoc(), packedType, packed, transformed.imag(),
+        rewriter.getI64ArrayAttr(IMAG_IDX_IN_CPLX_NUM_STRUCT));
+
+    rewriter.replaceOp(op, packed);
+    return success();
+  }
+};
+
+struct ReOpLowering : public ConvertOpToLLVMPattern<ReOp> {
+  using ConvertOpToLLVMPattern<ReOp>::ConvertOpToLLVMPattern;
+
+  LogicalResult
+  matchAndRewrite(Operation *op, ArrayRef<Value> operands,
+                  ConversionPatternRewriter &rewriter) const override {
+    auto reOp = cast<ReOp>(op);
+    OperandAdaptor<ReOp> transformed(operands);
+
+    // Extract real part from packed structure.
+    auto reType = typeConverter.convertType(reOp.getType());
+    rewriter.replaceOpWithNewOp<LLVM::ExtractValueOp>(
+        op, reType, transformed.cplx(),
+        rewriter.getI64ArrayAttr(REAL_IDX_IN_CPLX_NUM_STRUCT));
+
+    return success();
+  }
+};
+
+struct ImOpLowering : public ConvertOpToLLVMPattern<ImOp> {
+  using ConvertOpToLLVMPattern<ImOp>::ConvertOpToLLVMPattern;
+
+  LogicalResult
+  matchAndRewrite(Operation *op, ArrayRef<Value> operands,
+                  ConversionPatternRewriter &rewriter) const override {
+    auto imOp = cast<ImOp>(op);
+    OperandAdaptor<ImOp> transformed(operands);
+
+    // Extract imaginary part from packed structure.
+    auto imType = typeConverter.convertType(imOp.getType());
+    rewriter.replaceOpWithNewOp<LLVM::ExtractValueOp>(
+        op, imType, transformed.cplx(),
+        rewriter.getI64ArrayAttr(IMAG_IDX_IN_CPLX_NUM_STRUCT));
+
+    return success();
+  }
+};
+
 // Check if the MemRefType `type` is supported by the lowering. We currently
 // only support memrefs with identity maps.
 static bool isSupportedMemRefType(MemRefType type) {
   return type.getAffineMaps().empty() ||
          llvm::all_of(type.getAffineMaps(),
                       [](AffineMap map) { return map.isIdentity(); });
 }
 
patterns.insert<
       CallOpLowering,
       CeilFOpLowering,
       CmpFOpLowering,
       CmpIOpLowering,
       CondBranchOpLowering,
       CopySignOpLowering,
       CosOpLowering,
       ConstLLVMOpLowering,
+      CreateComplexOpLowering,
       DialectCastOpLowering,
       DivFOpLowering,
       ExpOpLowering,
       Exp2OpLowering,
       GenericAtomicRMWOpLowering,
       LogOpLowering,
       Log10OpLowering,
       Log2OpLowering,
       FPExtLowering,
       FPTruncLowering,
+      ImOpLowering,
       IndexCastOpLowering,
       MulFOpLowering,
       MulIOpLowering,
       NegFOpLowering,
       OrOpLowering,
       PrefetchOpLowering,
+      ReOpLowering, 
       RemFOpLowering,
       ReturnOpLowering,
       RsqrtOpLowering,
       SIToFPLowering,
       SelectOpLowering,
       ShiftLeftOpLowering,
       SignExtendIOpLowering,
       SignedDivIOpLowering,

mlir/lib/Dialect/StandardOps/IR/Ops.cpp

 
 void ConstantIndexOp::build(OpBuilder &builder, OperationState &result,
                             int64_t value) {
   Type type = builder.getIndexType();
   ConstantOp::build(builder, result, type, builder.getIntegerAttr(type, value));
 }
 
 //===----------------------------------------------------------------------===//
+// CreateComplexOp
+//===----------------------------------------------------------------------===//
+
+static LogicalResult verify(CreateComplexOp op) {
+  auto elementType = op.getType().dyn_cast<ComplexType>().getElementType();
+  if (op.real().getType() != elementType || op.imag().getType() != elementType)
+    return op.emitOpError(
+        "expected two operand types and complex element type to be the same");
+  return success();
+}
+
+//===----------------------------------------------------------------------===//
 // DeallocOp
 //===----------------------------------------------------------------------===//
 namespace {
 /// Fold Dealloc operations that are deallocating an AllocOp that is only used
 /// by other Dealloc operations.
 struct SimplifyDeadDealloc : public OpRewritePattern<DeallocOp> {
   using OpRewritePattern<DeallocOp>::OpRewritePattern;
 
bool FPTruncOp::areCastCompatible(Type a, Type b) {
   if (auto va = a.dyn_cast<VectorType>())
     if (auto vb = b.dyn_cast<VectorType>())
       return va.getShape().equals(vb.getShape()) &&
              areCastCompatible(va.getElementType(), vb.getElementType());
   return false;
 }
 
 //===----------------------------------------------------------------------===//
+// ImOp
+//===----------------------------------------------------------------------===//
+
+static LogicalResult verify(ImOp op) {
+  const auto &complexElementType =
+      op.cplx().getType().dyn_cast<ComplexType>().getElementType();
+  if (complexElementType != op.imag().getType())
+    return op.emitOpError(
+        "expected result type and complex element type to be the same");
+  return success();
+}
+
+//===----------------------------------------------------------------------===//
 // IndexCastOp
 //===----------------------------------------------------------------------===//
 
 // Index cast is applicable from index to integer and backwards.
 bool IndexCastOp::areCastCompatible(Type a, Type b) {
   return (a.isIndex() && b.isSignlessInteger()) ||
          (a.isSignlessInteger() && b.isIndex());
 }
OpFoldResult RankOp::fold(ArrayRef<Attribute> operands) {
   // Constant fold rank when the rank of the tensor is known.
   auto type = getOperand().getType();
   if (auto tensorType = type.dyn_cast<RankedTensorType>())
     return IntegerAttr::get(IndexType::get(getContext()), tensorType.getRank());
   return IntegerAttr();
 }
 
 //===----------------------------------------------------------------------===//
+// ReOp
+//===----------------------------------------------------------------------===//
+
+static LogicalResult verify(ReOp op) {
+  const auto &complexElementType =
+      op.cplx().getType().dyn_cast<ComplexType>().getElementType();
+  if (complexElementType != op.real().getType())
+    return op.emitOpError(
+        "expected result type and complex element type to be the same");
+  return success();
+}
+
+//===----------------------------------------------------------------------===//
 // ReturnOp
 //===----------------------------------------------------------------------===//
 
 static LogicalResult verify(ReturnOp op) {
   auto function = cast<FuncOp>(op.getParentOp());
 
   // The operand number and types must match the function signature.
   const auto &results = function.getType().getResults();

mlir/test/Conversion/StandardToLLVM/convert-to-llvmir.mlir

^bb3: // pred: ^bb2
   br ^bb2(%2 : index)
 
 // CHECK:      ^bb4:  // pred: ^bb2
 // CHECK-NEXT:  llvm.return
 ^bb4: // pred: ^bb2
   return
 }
 
+// CHECK-LABEL: llvm.func @complex_numbers()
+// CHECK-NEXT:    %[[REAL0:.*]] = llvm.mlir.constant(1.200000e+00 : f32) : !llvm.float
+// CHECK-NEXT:    %[[IMAG0:.*]] = llvm.mlir.constant(3.400000e+00 : f32) : !llvm.float
+// CHECK-NEXT:    %[[CPLX0:.*]] = llvm.mlir.undef : !llvm<"{ float, float }">
+// CHECK-NEXT:    %[[CPLX1:.*]] = llvm.insertvalue %[[REAL0]], %[[CPLX0]][0] : !llvm<"{ float, float }">
+// CHECK-NEXT:    %[[CPLX2:.*]] = llvm.insertvalue %[[IMAG0]], %[[CPLX1]][1] : !llvm<"{ float, float }">
+// CHECK-NEXT:    %[[REAL1:.*]] = llvm.extractvalue %[[CPLX2:.*]][0] : !llvm<"{ float, float }">
+// CHECK-NEXT:    %[[IMAG1:.*]] = llvm.extractvalue %[[CPLX2:.*]][1] : !llvm<"{ float, float }">
+// CHECK-NEXT:    llvm.return
+func @complex_numbers() {
+^bb0:
+  %real0 = constant 1.2 : f32
+  %imag0 = constant 3.4 : f32
+  %cplx2 = create_complex %real0, %imag0 : f32, f32 -> complex<f32>
+  %real1 = re %cplx2 : complex<f32> -> f32
+  %imag1 = im %cplx2 : complex<f32> -> f32
+  return
+}
+
 // CHECK-LABEL: func @simple_caller() {
 // CHECK-NEXT:  llvm.call @simple_loop() : () -> ()
 // CHECK-NEXT:  llvm.return
 // CHECK-NEXT: }
 func @simple_caller() {
 ^bb0:
   call @simple_loop() : () -> ()
   return

 ^bb12:  // pred: ^bb2
   return
 }
 
 // CHECK-LABEL: func @get_i64() -> !llvm.i64
 func @get_i64() -> (i64)
 // CHECK-LABEL: func @get_f32() -> !llvm.float
 func @get_f32() -> (f32)
+// CHECK-LABEL: func @get_c16() -> !llvm<"{ half, half }">
+func @get_c16() -> (complex<f16>)
+// CHECK-LABEL: func @get_c32() -> !llvm<"{ float, float }">
+func @get_c32() -> (complex<f32>)
+// CHECK-LABEL: func @get_c64() -> !llvm<"{ double, double }">
+func @get_c64() -> (complex<f64>)
 // CHECK-LABEL: func @get_memref() -> !llvm<"{ float*, float*, i64, [4 x i64], [4 x i64] }">
 // CHECK32-LABEL: func @get_memref() -> !llvm<"{ float*, float*, i32, [4 x i32], [4 x i32] }">
 func @get_memref() -> (memref<42x?x10x?xf32>)
 
 // CHECK-LABEL: func @multireturn() -> !llvm<"{ i64, float, { float*, float*, i64, [4 x i64], [4 x i64] } }"> {
 // CHECK32-LABEL: func @multireturn() -> !llvm<"{ i64, float, { float*, float*, i32, [4 x i32], [4 x i32] } }"> {
 func @multireturn() -> (i64, f32, memref<42x?x10x?xf32>) {
 ^bb0:

mlir/test/IR/core-ops.mlir

^bb42(%t: tensor<4x4x?xf32>, %f: f32, %i: i32, %idx : index, %j: i64, %half: f16):
   %i5 = subi %i4, %i4 : i32
 
   // CHECK: %12 = mulf %2, %2 : f32
   %f6 = mulf %f2, %f2 : f32
 
   // CHECK: %13 = muli %4, %4 : i32
   %i6 = muli %i2, %i2 : i32
 
+  // CHECK: %[[C0:.*]] = create_complex %[[F2:.*]], %[[F2]] : f32, f32 -> complex<f32>
+  %c0 = "std.create_complex"(%f2, %f2) : (f32, f32) -> complex<f32>
+
+  // CHECK: %[[C1:.*]] = create_complex %[[F2]], %[[F2]] : f32, f32 -> complex<f32>
+  %c1 = create_complex %f2, %f2 : f32, f32 -> complex<f32>
+
+  // CHECK: %[[REAL0:.*]] = re %[[CPLX0:.*]] : complex<f32> -> f32
+  %real0 = "std.re"(%c0) : (complex<f32>) -> f32
+
+  // CHECK: %[[REAL1:.*]] = re %[[CPLX0]] : complex<f32> -> f32
+  %real1 = re %c0 : complex<f32> -> f32
+
+  // CHECK: %[[IMAG0:.*]] = im %[[CPLX0]] : complex<f32> -> f32
+  %imag0 = "std.im"(%c0) : (complex<f32>) -> f32
+
+  // CHECK: %[[IMAG1:.*]] = im %[[CPLX0]] : complex<f32> -> f32
+  %imag1 = im %c0 : complex<f32> -> f32
+
   // CHECK: %c42_i32 = constant 42 : i32
   %x = "std.constant"(){value = 42 : i32} : () -> i32
 
   // CHECK: %c42_i32_0 = constant 42 : i32
   %7 = constant 42 : i32
 
   // CHECK: %c43 = constant {crazy = "std.foo"} 43 : index
   %8 = constant {crazy = "std.foo"} 43: index

mlir/test/mlir-cpu-runner/complex_numbers.mlir

+// RUN: mlir-opt %s -convert-std-to-llvm \
+// RUN: | mlir-cpu-runner -e create_and_extract_real -entry-point-result=f32 \
+// RUN: | FileCheck -check-prefix=CHECK_REAL %s
+
+// Create complex number and extracit real part.
+func @create_and_extract_real() -> f32 {
+  %real = constant 1.2 : f32
+  %imag = constant 2.3 : f32
+  %cplx = create_complex %real, %imag : f32, f32 -> complex<f32>
+  %result = re %cplx : complex<f32> -> f32
+  return %result : f32
+}
+// CHECK_REAL: 1.200000e+00
+
+
+
+// RUN: mlir-opt %s -convert-std-to-llvm \
+// RUN: | mlir-cpu-runner -e create_and_extract_imag -entry-point-result=f32 \
+// RUN: | FileCheck -check-prefix=CHECK_IMAG %s
+
+// Create complex number and extract imaginary part.
+func @create_and_extract_imag() -> f32 {
+  %real = constant 1.2 : f32
+  %imag = constant 2.3 : f32
+  %cplx = create_complex %real, %imag : f32, f32 -> complex<f32>
+  %result = im %cplx : complex<f32> -> f32
+  return %result : f32
+}
+// CHECK_IMAG: 2.300000e+00