[fir] Add complex operations conversion from FIR LLVM IR

This patch add conversion for primitive operations on complex types.
- fir.addc
- fir.subc
- fir.mulc
- fir.divc
- fir.negc

This adds also the type conversion for !fir.complex<KIND> type.

This patch is part of the upstreaming effort from fir-dev branch.

Reviewed By: rovka

Differential Revision: https://reviews.llvm.org/D113434

Co-authored-by: Jean Perier <jperier@nvidia.com>
Co-authored-by: Eric Schweitz <eschweitz@nvidia.com>

flang/lib/Optimizer/CodeGen/CodeGen.cpp

@@ -14,6 +14,7 @@
 #include "PassDetail.h"
 #include "flang/Optimizer/Dialect/FIROps.h"
 #include "flang/Optimizer/Dialect/FIRType.h"
+#include "flang/Optimizer/Support/FIRContext.h"
 #include "mlir/Conversion/ArithmeticToLLVM/ArithmeticToLLVM.h"
 #include "mlir/Conversion/LLVMCommon/Pattern.h"
 #include "mlir/Conversion/LLVMCommon/TypeConverter.h"
@@ -487,6 +488,175 @@ struct InsertOnRangeOpConversion
     return success();
   }
 };
+
+static mlir::Type getComplexEleTy(mlir::Type complex) {
+  if (auto cc = complex.dyn_cast<mlir::ComplexType>())
+    return cc.getElementType();
+  return complex.cast<fir::ComplexType>().getElementType();
+}
+
+//
+// Primitive operations on Complex types
+//
+
+/// Generate inline code for complex addition/subtraction
+template <typename LLVMOP, typename OPTY>
+mlir::LLVM::InsertValueOp complexSum(OPTY sumop, mlir::ValueRange opnds,
+                                     mlir::ConversionPatternRewriter &rewriter,
+                                     fir::LLVMTypeConverter &lowering) {
+  mlir::Value a = opnds[0];
+  mlir::Value b = opnds[1];
+  auto loc = sumop.getLoc();
+  auto ctx = sumop.getContext();
+  auto c0 = mlir::ArrayAttr::get(ctx, rewriter.getI32IntegerAttr(0));
+  auto c1 = mlir::ArrayAttr::get(ctx, rewriter.getI32IntegerAttr(1));
+  mlir::Type eleTy = lowering.convertType(getComplexEleTy(sumop.getType()));
+  mlir::Type ty = lowering.convertType(sumop.getType());
+  auto x0 = rewriter.create<mlir::LLVM::ExtractValueOp>(loc, eleTy, a, c0);
+  auto y0 = rewriter.create<mlir::LLVM::ExtractValueOp>(loc, eleTy, a, c1);
+  auto x1 = rewriter.create<mlir::LLVM::ExtractValueOp>(loc, eleTy, b, c0);
+  auto y1 = rewriter.create<mlir::LLVM::ExtractValueOp>(loc, eleTy, b, c1);
+  auto rx = rewriter.create<LLVMOP>(loc, eleTy, x0, x1);
+  auto ry = rewriter.create<LLVMOP>(loc, eleTy, y0, y1);
+  auto r0 = rewriter.create<mlir::LLVM::UndefOp>(loc, ty);
+  auto r1 = rewriter.create<mlir::LLVM::InsertValueOp>(loc, ty, r0, rx, c0);
+  return rewriter.create<mlir::LLVM::InsertValueOp>(loc, ty, r1, ry, c1);
+}
+
+struct AddcOpConversion : public FIROpConversion<fir::AddcOp> {
+  using FIROpConversion::FIROpConversion;
+
+  mlir::LogicalResult
+  matchAndRewrite(fir::AddcOp addc, OpAdaptor adaptor,
+                  mlir::ConversionPatternRewriter &rewriter) const override {
+    // given: (x + iy) + (x' + iy')
+    // result: (x + x') + i(y + y')
+    auto r = complexSum<mlir::LLVM::FAddOp>(addc, adaptor.getOperands(),
+                                            rewriter, lowerTy());
+    rewriter.replaceOp(addc, r.getResult());
+    return success();
+  }
+};
+
+struct SubcOpConversion : public FIROpConversion<fir::SubcOp> {
+  using FIROpConversion::FIROpConversion;
+
+  mlir::LogicalResult
+  matchAndRewrite(fir::SubcOp subc, OpAdaptor adaptor,
+                  mlir::ConversionPatternRewriter &rewriter) const override {
+    // given: (x + iy) - (x' + iy')
+    // result: (x - x') + i(y - y')
+    auto r = complexSum<mlir::LLVM::FSubOp>(subc, adaptor.getOperands(),
+                                            rewriter, lowerTy());
+    rewriter.replaceOp(subc, r.getResult());
+    return success();
+  }
+};
+
+/// Inlined complex multiply
+struct MulcOpConversion : public FIROpConversion<fir::MulcOp> {
+  using FIROpConversion::FIROpConversion;
+
+  mlir::LogicalResult
+  matchAndRewrite(fir::MulcOp mulc, OpAdaptor adaptor,
+                  mlir::ConversionPatternRewriter &rewriter) const override {
+    // TODO: Can we use a call to __muldc3 ?
+    // given: (x + iy) * (x' + iy')
+    // result: (xx'-yy')+i(xy'+yx')
+    mlir::Value a = adaptor.getOperands()[0];
+    mlir::Value b = adaptor.getOperands()[1];
+    auto loc = mulc.getLoc();
+    auto *ctx = mulc.getContext();
+    auto c0 = mlir::ArrayAttr::get(ctx, rewriter.getI32IntegerAttr(0));
+    auto c1 = mlir::ArrayAttr::get(ctx, rewriter.getI32IntegerAttr(1));
+    mlir::Type eleTy = convertType(getComplexEleTy(mulc.getType()));
+    mlir::Type ty = convertType(mulc.getType());
+    auto x0 = rewriter.create<mlir::LLVM::ExtractValueOp>(loc, eleTy, a, c0);
+    auto y0 = rewriter.create<mlir::LLVM::ExtractValueOp>(loc, eleTy, a, c1);
+    auto x1 = rewriter.create<mlir::LLVM::ExtractValueOp>(loc, eleTy, b, c0);
+    auto y1 = rewriter.create<mlir::LLVM::ExtractValueOp>(loc, eleTy, b, c1);
+    auto xx = rewriter.create<mlir::LLVM::FMulOp>(loc, eleTy, x0, x1);
+    auto yx = rewriter.create<mlir::LLVM::FMulOp>(loc, eleTy, y0, x1);
+    auto xy = rewriter.create<mlir::LLVM::FMulOp>(loc, eleTy, x0, y1);
+    auto ri = rewriter.create<mlir::LLVM::FAddOp>(loc, eleTy, xy, yx);
+    auto yy = rewriter.create<mlir::LLVM::FMulOp>(loc, eleTy, y0, y1);
+    auto rr = rewriter.create<mlir::LLVM::FSubOp>(loc, eleTy, xx, yy);
+    auto ra = rewriter.create<mlir::LLVM::UndefOp>(loc, ty);
+    auto r1 = rewriter.create<mlir::LLVM::InsertValueOp>(loc, ty, ra, rr, c0);
+    auto r0 = rewriter.create<mlir::LLVM::InsertValueOp>(loc, ty, r1, ri, c1);
+    rewriter.replaceOp(mulc, r0.getResult());
+    return success();
+  }
+};
+
+/// Inlined complex division
+struct DivcOpConversion : public FIROpConversion<fir::DivcOp> {
+  using FIROpConversion::FIROpConversion;
+
+  mlir::LogicalResult
+  matchAndRewrite(fir::DivcOp divc, OpAdaptor adaptor,
+                  mlir::ConversionPatternRewriter &rewriter) const override {
+    // TODO: Can we use a call to __divdc3 instead?
+    // Just generate inline code for now.
+    // given: (x + iy) / (x' + iy')
+    // result: ((xx'+yy')/d) + i((yx'-xy')/d) where d = x'x' + y'y'
+    mlir::Value a = adaptor.getOperands()[0];
+    mlir::Value b = adaptor.getOperands()[1];
+    auto loc = divc.getLoc();
+    auto *ctx = divc.getContext();
+    auto c0 = mlir::ArrayAttr::get(ctx, rewriter.getI32IntegerAttr(0));
+    auto c1 = mlir::ArrayAttr::get(ctx, rewriter.getI32IntegerAttr(1));
+    mlir::Type eleTy = convertType(getComplexEleTy(divc.getType()));
+    mlir::Type ty = convertType(divc.getType());
+    auto x0 = rewriter.create<mlir::LLVM::ExtractValueOp>(loc, eleTy, a, c0);
+    auto y0 = rewriter.create<mlir::LLVM::ExtractValueOp>(loc, eleTy, a, c1);
+    auto x1 = rewriter.create<mlir::LLVM::ExtractValueOp>(loc, eleTy, b, c0);
+    auto y1 = rewriter.create<mlir::LLVM::ExtractValueOp>(loc, eleTy, b, c1);
+    auto xx = rewriter.create<mlir::LLVM::FMulOp>(loc, eleTy, x0, x1);
+    auto x1x1 = rewriter.create<mlir::LLVM::FMulOp>(loc, eleTy, x1, x1);
+    auto yx = rewriter.create<mlir::LLVM::FMulOp>(loc, eleTy, y0, x1);
+    auto xy = rewriter.create<mlir::LLVM::FMulOp>(loc, eleTy, x0, y1);
+    auto yy = rewriter.create<mlir::LLVM::FMulOp>(loc, eleTy, y0, y1);
+    auto y1y1 = rewriter.create<mlir::LLVM::FMulOp>(loc, eleTy, y1, y1);
+    auto d = rewriter.create<mlir::LLVM::FAddOp>(loc, eleTy, x1x1, y1y1);
+    auto rrn = rewriter.create<mlir::LLVM::FAddOp>(loc, eleTy, xx, yy);
+    auto rin = rewriter.create<mlir::LLVM::FSubOp>(loc, eleTy, yx, xy);
+    auto rr = rewriter.create<mlir::LLVM::FDivOp>(loc, eleTy, rrn, d);
+    auto ri = rewriter.create<mlir::LLVM::FDivOp>(loc, eleTy, rin, d);
+    auto ra = rewriter.create<mlir::LLVM::UndefOp>(loc, ty);
+    auto r1 = rewriter.create<mlir::LLVM::InsertValueOp>(loc, ty, ra, rr, c0);
+    auto r0 = rewriter.create<mlir::LLVM::InsertValueOp>(loc, ty, r1, ri, c1);
+    rewriter.replaceOp(divc, r0.getResult());
+    return success();
+  }
+};
+
+/// Inlined complex negation
+struct NegcOpConversion : public FIROpConversion<fir::NegcOp> {
+  using FIROpConversion::FIROpConversion;
+
+  mlir::LogicalResult
+  matchAndRewrite(fir::NegcOp neg, OpAdaptor adaptor,
+                  mlir::ConversionPatternRewriter &rewriter) const override {
+    // given: -(x + iy)
+    // result: -x - iy
+    auto *ctxt = neg.getContext();
+    auto eleTy = convertType(getComplexEleTy(neg.getType()));
+    auto ty = convertType(neg.getType());
+    auto loc = neg.getLoc();
+    mlir::Value o0 = adaptor.getOperands()[0];
+    auto c0 = mlir::ArrayAttr::get(ctxt, rewriter.getI32IntegerAttr(0));
+    auto c1 = mlir::ArrayAttr::get(ctxt, rewriter.getI32IntegerAttr(1));
+    auto rp = rewriter.create<mlir::LLVM::ExtractValueOp>(loc, eleTy, o0, c0);
+    auto ip = rewriter.create<mlir::LLVM::ExtractValueOp>(loc, eleTy, o0, c1);
+    auto nrp = rewriter.create<mlir::LLVM::FNegOp>(loc, eleTy, rp);
+    auto nip = rewriter.create<mlir::LLVM::FNegOp>(loc, eleTy, ip);
+    auto r = rewriter.create<mlir::LLVM::InsertValueOp>(loc, ty, o0, nrp, c0);
+    rewriter.replaceOpWithNewOp<mlir::LLVM::InsertValueOp>(neg, ty, r, nip, c1);
+    return success();
+  }
+};
+
 } // namespace
 
 namespace {
@@ -504,12 +674,13 @@ public:
     auto *context = getModule().getContext();
     fir::LLVMTypeConverter typeConverter{getModule()};
     mlir::OwningRewritePatternList pattern(context);
-    pattern.insert<
+    pattern.insert<AddcOpConversion, AddrOfOpConversion, CallOpConversion,
-        AddrOfOpConversion, CallOpConversion, ExtractValueOpConversion,
+                   DivcOpConversion, ExtractValueOpConversion,
-        HasValueOpConversion, GlobalOpConversion, InsertOnRangeOpConversion,
+                   HasValueOpConversion, GlobalOpConversion,
-        InsertValueOpConversion, SelectOpConversion, SelectRankOpConversion,
+                   InsertOnRangeOpConversion, InsertValueOpConversion,
-        UndefOpConversion, UnreachableOpConversion, ZeroOpConversion>(
+                   NegcOpConversion, MulcOpConversion, SelectOpConversion,
-        typeConverter);
+                   SelectRankOpConversion, SubcOpConversion, UndefOpConversion,
+                   UnreachableOpConversion, ZeroOpConversion>(typeConverter);
     mlir::populateStdToLLVMConversionPatterns(typeConverter, pattern);
     mlir::arith::populateArithmeticToLLVMConversionPatterns(typeConverter,
                                                             pattern);

flang/lib/Optimizer/CodeGen/Target.cpp

@@ -35,6 +35,13 @@ struct GenericTarget : public CodeGenSpecifics {
   using CodeGenSpecifics::CodeGenSpecifics;
   using AT = CodeGenSpecifics::Attributes;
 
+  mlir::Type complexMemoryType(mlir::Type eleTy) const override {
+    assert(fir::isa_real(eleTy));
+    // { t, t }   struct of 2 eleTy
+    mlir::TypeRange range = {eleTy, eleTy};
+    return mlir::TupleType::get(eleTy.getContext(), range);
+  }
+
   Marshalling boxcharArgumentType(mlir::Type eleTy, bool sret) const override {
     CodeGenSpecifics::Marshalling marshal;
     auto idxTy = mlir::IntegerType::get(eleTy.getContext(), S::defaultWidth);

flang/lib/Optimizer/CodeGen/Target.h

@@ -65,6 +65,9 @@ public:
   CodeGenSpecifics() = delete;
   virtual ~CodeGenSpecifics() {}
 
+  /// Type presentation of a `complex<ele>` type value in memory.
+  virtual mlir::Type complexMemoryType(mlir::Type eleTy) const = 0;
+
   /// Type representation of a `complex<eleTy>` type argument when passed by
   /// value. An argument value may need to be passed as a (safe) reference
   /// argument.

flang/lib/Optimizer/CodeGen/TypeConverter.h

@@ -14,6 +14,7 @@
 #define FORTRAN_OPTIMIZER_CODEGEN_TYPECONVERTER_H
 
 #include "DescriptorModel.h"
+#include "Target.h"
 #include "flang/Lower/Todo.h" // remove when TODO's are done
 #include "flang/Optimizer/Support/FIRContext.h"
 #include "flang/Optimizer/Support/KindMapping.h"
@@ -28,7 +29,10 @@ class LLVMTypeConverter : public mlir::LLVMTypeConverter {
 public:
   LLVMTypeConverter(mlir::ModuleOp module)
       : mlir::LLVMTypeConverter(module.getContext()),
-        kindMapping(getKindMapping(module)) {
+        kindMapping(getKindMapping(module)),
+        specifics(CodeGenSpecifics::get(module.getContext(),
+                                        getTargetTriple(module),
+                                        getKindMapping(module))) {
     LLVM_DEBUG(llvm::dbgs() << "FIR type converter\n");
 
     // Each conversion should return a value of type mlir::Type.
@@ -39,6 +43,10 @@ public:
     });
     addConversion(
         [&](fir::RecordType derived) { return convertRecordType(derived); });
+    addConversion(
+        [&](fir::ComplexType cmplx) { return convertComplexType(cmplx); });
+    addConversion(
+        [&](fir::RealType real) { return convertRealType(real.getFKind()); });
     addConversion(
         [&](fir::ReferenceType ref) { return convertPointerLike(ref); });
     addConversion(
@@ -140,6 +148,24 @@ public:
                                                /*isPacked=*/false));
   }
 
+  // Use the target specifics to figure out how to map complex to LLVM IR. The
+  // use of complex values in function signatures is handled before conversion
+  // to LLVM IR dialect here.
+  //
+  // fir.complex<T> | std.complex<T>    --> llvm<"{t,t}">
+  template <typename C>
+  mlir::Type convertComplexType(C cmplx) {
+    LLVM_DEBUG(llvm::dbgs() << "type convert: " << cmplx << '\n');
+    auto eleTy = cmplx.getElementType();
+    return convertType(specifics->complexMemoryType(eleTy));
+  }
+
+  // convert a front-end kind value to either a std or LLVM IR dialect type
+  // fir.real<n>  -->  llvm.anyfloat  where anyfloat is a kind mapping
+  mlir::Type convertRealType(fir::KindTy kind) {
+    return fromRealTypeID(kindMapping.getRealTypeID(kind), kind);
+  }
+
   template <typename A>
   mlir::Type convertPointerLike(A &ty) {
     mlir::Type eleTy = ty.getEleTy();
@@ -187,8 +213,33 @@ public:
     return mlir::LLVM::LLVMPointerType::get(baseTy);
   }
 
+  /// Convert llvm::Type::TypeID to mlir::Type
+  mlir::Type fromRealTypeID(llvm::Type::TypeID typeID, fir::KindTy kind) {
+    switch (typeID) {
+    case llvm::Type::TypeID::HalfTyID:
+      return mlir::FloatType::getF16(&getContext());
+    case llvm::Type::TypeID::BFloatTyID:
+      return mlir::FloatType::getBF16(&getContext());
+    case llvm::Type::TypeID::FloatTyID:
+      return mlir::FloatType::getF32(&getContext());
+    case llvm::Type::TypeID::DoubleTyID:
+      return mlir::FloatType::getF64(&getContext());
+    case llvm::Type::TypeID::X86_FP80TyID:
+      return mlir::FloatType::getF80(&getContext());
+    case llvm::Type::TypeID::FP128TyID:
+      return mlir::FloatType::getF128(&getContext());
+    default:
+      emitError(UnknownLoc::get(&getContext()))
+          << "unsupported type: !fir.real<" << kind << ">";
+      return {};
+    }
+  }
+
+  KindMapping &getKindMap() { return kindMapping; }
+
 private:
   KindMapping kindMapping;
+  std::unique_ptr<CodeGenSpecifics> specifics;
 };
 
 } // namespace fir

flang/test/Fir/convert-to-llvm.fir

@@ -376,3 +376,137 @@ func @test_call_return_val() -> i32 {
 // CHECK-NEXT:    %0 = llvm.call @dummy_return_val() : () -> i32
 // CHECK-NEXT:    llvm.return %0 : i32
 // CHECK-NEXT:  }
+
+// -----
+
+// Test FIR complex addition conversion
+// given: (x + iy) + (x' + iy')
+// result: (x + x') + i(y + y')
+
+func @fir_complex_add(%a: !fir.complex<16>, %b: !fir.complex<16>) -> !fir.complex<16> {
+  %c = fir.addc %a, %b : !fir.complex<16>
+  return %c : !fir.complex<16>
+}
+
+// CHECK-LABEL: llvm.func @fir_complex_add(
+// CHECK-SAME:                             %[[ARG0:.*]]: !llvm.struct<(f128, f128)>, 
+// CHECK-SAME:                             %[[ARG1:.*]]: !llvm.struct<(f128, f128)>) -> !llvm.struct<(f128, f128)> {
+// CHECK:         %[[X0:.*]] = llvm.extractvalue %[[ARG0]][0 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[Y0:.*]] = llvm.extractvalue %[[ARG0]][1 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[X1:.*]] = llvm.extractvalue %[[ARG1]][0 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[Y1:.*]] = llvm.extractvalue %[[ARG1]][1 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[ADD_X0_X1:.*]] = llvm.fadd %[[X0]], %[[X1]]  : f128
+// CHECK:         %[[ADD_Y0_Y1:.*]] = llvm.fadd %[[Y0]], %[[Y1]]  : f128
+// CHECK:         %{{.*}} = llvm.mlir.undef : !llvm.struct<(f128, f128)>
+// CHECK:         %{{.*}} = llvm.insertvalue %[[ADD_X0_X1]], %{{.*}}[0 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %{{.*}} = llvm.insertvalue %[[ADD_Y0_Y1]], %{{.*}}[1 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         llvm.return %{{.*}} : !llvm.struct<(f128, f128)>
+
+// -----
+
+// Test FIR complex substraction conversion
+// given: (x + iy) - (x' + iy')
+// result: (x - x') + i(y - y')
+
+func @fir_complex_sub(%a: !fir.complex<16>, %b: !fir.complex<16>) -> !fir.complex<16> {
+  %c = fir.subc %a, %b : !fir.complex<16>
+  return %c : !fir.complex<16>
+}
+
+// CHECK-LABEL: llvm.func @fir_complex_sub(
+// CHECK-SAME:                             %[[ARG0:.*]]: !llvm.struct<(f128, f128)>, 
+// CHECK-SAME:                             %[[ARG1:.*]]: !llvm.struct<(f128, f128)>) -> !llvm.struct<(f128, f128)> {
+// CHECK:         %[[X0:.*]] = llvm.extractvalue %[[ARG0]][0 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[Y0:.*]] = llvm.extractvalue %[[ARG0]][1 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[X1:.*]] = llvm.extractvalue %[[ARG1]][0 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[Y1:.*]] = llvm.extractvalue %[[ARG1]][1 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[SUB_X0_X1:.*]] = llvm.fsub %[[X0]], %[[X1]]  : f128
+// CHECK:         %[[SUB_Y0_Y1:.*]] = llvm.fsub %[[Y0]], %[[Y1]]  : f128
+// CHECK:         %{{.*}} = llvm.mlir.undef : !llvm.struct<(f128, f128)>
+// CHECK:         %{{.*}} = llvm.insertvalue %[[SUB_X0_X1]], %{{.*}}[0 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %{{.*}} = llvm.insertvalue %[[SUB_Y0_Y1]], %{{.*}}[1 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         llvm.return %{{.*}} : !llvm.struct<(f128, f128)>
+
+// -----
+
+// Test FIR complex multiply conversion
+// given: (x + iy) * (x' + iy')
+// result: (xx'-yy')+i(xy'+yx')
+
+func @fir_complex_mul(%a: !fir.complex<16>, %b: !fir.complex<16>) -> !fir.complex<16> {
+  %c = fir.mulc %a, %b : !fir.complex<16>
+  return %c : !fir.complex<16>
+}
+
+// CHECK-LABEL: llvm.func @fir_complex_mul(
+// CHECK-SAME:                             %[[ARG0:.*]]: !llvm.struct<(f128, f128)>, 
+// CHECK-SAME:                             %[[ARG1:.*]]: !llvm.struct<(f128, f128)>) -> !llvm.struct<(f128, f128)> {
+// CHECK:         %[[X0:.*]] = llvm.extractvalue %[[ARG0]][0 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[Y0:.*]] = llvm.extractvalue %[[ARG0]][1 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[X1:.*]] = llvm.extractvalue %[[ARG1]][0 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[Y1:.*]] = llvm.extractvalue %[[ARG1]][1 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[MUL_X0_X1:.*]] = llvm.fmul %[[X0]], %[[X1]]  : f128
+// CHECK:         %[[MUL_Y0_X1:.*]] = llvm.fmul %[[Y0]], %[[X1]]  : f128
+// CHECK:         %[[MUL_X0_Y1:.*]] = llvm.fmul %[[X0]], %[[Y1]]  : f128
+// CHECK:         %[[ADD:.*]] = llvm.fadd %[[MUL_X0_Y1]], %[[MUL_Y0_X1]]  : f128
+// CHECK:         %[[MUL_Y0_Y1:.*]] = llvm.fmul %[[Y0]], %[[Y1]]  : f128
+// CHECK:         %[[SUB:.*]] = llvm.fsub %[[MUL_X0_X1]], %[[MUL_Y0_Y1]]  : f128
+// CHECK:         %{{.*}} = llvm.mlir.undef : !llvm.struct<(f128, f128)>
+// CHECK:         %{{.*}} = llvm.insertvalue %[[SUB]], %{{.*}}[0 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %{{.*}} = llvm.insertvalue %[[ADD]], %{{.*}}[1 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         llvm.return %{{.*}} : !llvm.struct<(f128, f128)>
+
+// -----
+
+// Test FIR complex division conversion
+// given: (x + iy) / (x' + iy')
+// result: ((xx'+yy')/d) + i((yx'-xy')/d) where d = x'x' + y'y'
+
+func @fir_complex_div(%a: !fir.complex<16>, %b: !fir.complex<16>) -> !fir.complex<16> {
+  %c = fir.divc %a, %b : !fir.complex<16>
+  return %c : !fir.complex<16>
+}
+
+// CHECK-LABEL: llvm.func @fir_complex_div(
+// CHECK-SAME:                             %[[ARG0:.*]]: !llvm.struct<(f128, f128)>, 
+// CHECK-SAME:                             %[[ARG1:.*]]: !llvm.struct<(f128, f128)>) -> !llvm.struct<(f128, f128)> {
+// CHECK:         %[[X0:.*]] = llvm.extractvalue %[[ARG0]][0 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[Y0:.*]] = llvm.extractvalue %[[ARG0]][1 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[X1:.*]] = llvm.extractvalue %[[ARG1]][0 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[Y1:.*]] = llvm.extractvalue %[[ARG1]][1 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[MUL_X0_X1:.*]] = llvm.fmul %[[X0]], %[[X1]]  : f128
+// CHECK:         %[[MUL_X1_X1:.*]] = llvm.fmul %[[X1]], %[[X1]]  : f128
+// CHECK:         %[[MUL_Y0_X1:.*]] = llvm.fmul %[[Y0]], %[[X1]]  : f128
+// CHECK:         %[[MUL_X0_Y1:.*]] = llvm.fmul %[[X0]], %[[Y1]]  : f128
+// CHECK:         %[[MUL_Y0_Y1:.*]] = llvm.fmul %[[Y0]], %[[Y1]]  : f128
+// CHECK:         %[[MUL_Y1_Y1:.*]] = llvm.fmul %[[Y1]], %[[Y1]]  : f128
+// CHECK:         %[[ADD_X1X1_Y1Y1:.*]] = llvm.fadd %[[MUL_X1_X1]], %[[MUL_Y1_Y1]]  : f128
+// CHECK:         %[[ADD_X0X1_Y0Y1:.*]] = llvm.fadd %[[MUL_X0_X1]], %[[MUL_Y0_Y1]]  : f128
+// CHECK:         %[[SUB_Y0X1_X0Y1:.*]] = llvm.fsub %[[MUL_Y0_X1]], %[[MUL_X0_Y1]]  : f128
+// CHECK:         %[[DIV0:.*]] = llvm.fdiv %[[ADD_X0X1_Y0Y1]], %[[ADD_X1X1_Y1Y1]]  : f128
+// CHECK:         %[[DIV1:.*]] = llvm.fdiv %[[SUB_Y0X1_X0Y1]], %[[ADD_X1X1_Y1Y1]]  : f128
+// CHECK:         %{{.*}} = llvm.mlir.undef : !llvm.struct<(f128, f128)>
+// CHECK:         %{{.*}} = llvm.insertvalue %[[DIV0]], %{{.*}}[0 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %{{.*}} = llvm.insertvalue %[[DIV1]], %{{.*}}[1 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         llvm.return %{{.*}} : !llvm.struct<(f128, f128)>
+
+// -----
+
+// Test FIR complex negation conversion
+// given: -(x + iy)
+// result: -x - iy
+
+func @fir_complex_neg(%a: !fir.complex<16>) -> !fir.complex<16> {
+  %c = fir.negc %a : !fir.complex<16>
+  return %c : !fir.complex<16>
+}
+
+// CHECK-LABEL: llvm.func @fir_complex_neg(
+// CHECK-SAME:                             %[[ARG0:.*]]: !llvm.struct<(f128, f128)>) -> !llvm.struct<(f128, f128)> {
+// CHECK:         %[[X:.*]] = llvm.extractvalue %[[ARG0]][0 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[Y:.*]] = llvm.extractvalue %[[ARG0]][1 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %[[NEGX:.*]] = llvm.fneg %[[X]]  : f128
+// CHECK:         %[[NEGY:.*]] = llvm.fneg %[[Y]]  : f128
+// CHECK:         %{{.*}} = llvm.insertvalue %[[NEGX]], %{{.*}}[0 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         %{{.*}} = llvm.insertvalue %[[NEGY]], %{{.*}}[1 : i32] : !llvm.struct<(f128, f128)>
+// CHECK:         llvm.return %{{.*}} : !llvm.struct<(f128, f128)>

flang/test/Fir/types-to-llvm.fir

@@ -72,3 +72,31 @@ func private @foo3(%arg0: !fir.logical<8>)
 func private @foo4(%arg0: !fir.logical<16>)
 // CHECK-LABEL: foo4
 // CHECK-SAME: i128
+
+// -----
+
+// Test `!fir.complex<KIND>` conversion.
+
+func private @foo0(%arg0: !fir.complex<2>)
+// CHECK-LABEL: foo0
+// CHECK-SAME: !llvm.struct<(f16, f16)>)
+
+func private @foo1(%arg0: !fir.complex<3>)
+// CHECK-LABEL: foo1
+// CHECK-SAME: !llvm.struct<(bf16, bf16)>)
+
+func private @foo2(%arg0: !fir.complex<4>)
+// CHECK-LABEL: foo2
+// CHECK-SAME: !llvm.struct<(f32, f32)>)
+
+func private @foo3(%arg0: !fir.complex<8>)
+// CHECK-LABEL: foo3
+// CHECK-SAME: !llvm.struct<(f64, f64)>)
+
+func private @foo4(%arg0: !fir.complex<10>)
+// CHECK-LABEL: foo4
+// CHECK-SAME: !llvm.struct<(f80, f80)>)
+
+func private @foo5(%arg0: !fir.complex<16>)
+// CHECK-LABEL: foo5
+// CHECK-SAME: !llvm.struct<(f128, f128)>)