r219557 - [complex] Teach Clang to preserve different-type operands to arithmetic
Chandler Carruth
chandlerc at gmail.com
Fri Oct 10 17:57:19 PDT 2014
Author: chandlerc
Date: Fri Oct 10 19:57:18 2014
New Revision: 219557
URL: http://llvm.org/viewvc/llvm-project?rev=219557&view=rev
Log:
[complex] Teach Clang to preserve different-type operands to arithmetic
operators where one type is a C complex type, and to emit both the
efficient and correct implementation for complex arithmetic according to
C11 Annex G using this extra information.
For both multiply and divide the old code was writing a long-hand
reduced version of the math without any of the special handling of inf
and NaN recommended by the standard here. Instead of putting more
complexity here, this change does what GCC does which is to emit
a libcall for the fully general case.
However, the old code also failed to do the proper minimization of the
set of operations when there was a mixed complex and real operation. In
those cases, C provides a spec for much more minimal operations that are
valid. Clang now emits the exact suggested operations. This change isn't
*just* about performance though, without minimizing these operations, we
again lose the correct handling of infinities and NaNs. It is critical
that this happen in the frontend based on assymetric type operands to
complex math operations.
The performance implications of this change aren't trivial either. I've
run a set of benchmarks in Eigen, an open source mathematics library
that makes heavy use of complex. While a few have slowed down due to the
libcall being introduce, most sped up and some by a huge amount: up to
100% and 140%.
In order to make all of this work, also match the algorithm in the
constant evaluator to the one in the runtime library. Currently it is
a broken port of the simplifications from C's Annex G to the long-hand
formulation of the algorithm.
Splitting this patch up is very hard because none of this works without
the AST change to preserve non-complex operands. Sorry for the enormous
change.
Follow-up changes will include support for sinking the libcalls onto
cold paths in common cases and fastmath improvements to allow more
aggressive backend folding.
Differential Revision: http://reviews.llvm.org/D5698
Added:
cfe/trunk/test/CodeGen/complex-math.c
cfe/trunk/test/SemaCXX/complex-folding.cpp
Modified:
cfe/trunk/lib/AST/ExprConstant.cpp
cfe/trunk/lib/CodeGen/CGExprComplex.cpp
cfe/trunk/lib/Sema/SemaExpr.cpp
Modified: cfe/trunk/lib/AST/ExprConstant.cpp
URL: http://llvm.org/viewvc/llvm-project/cfe/trunk/lib/AST/ExprConstant.cpp?rev=219557&r1=219556&r2=219557&view=diff
==============================================================================
--- cfe/trunk/lib/AST/ExprConstant.cpp (original)
+++ cfe/trunk/lib/AST/ExprConstant.cpp Fri Oct 10 19:57:18 2014
@@ -7874,24 +7874,49 @@ bool ComplexExprEvaluator::VisitBinaryOp
if (E->isPtrMemOp() || E->isAssignmentOp() || E->getOpcode() == BO_Comma)
return ExprEvaluatorBaseTy::VisitBinaryOperator(E);
- bool LHSOK = Visit(E->getLHS());
+ // Track whether the LHS or RHS is real at the type system level. When this is
+ // the case we can simplify our evaluation strategy.
+ bool LHSReal = false, RHSReal = false;
+
+ bool LHSOK;
+ if (E->getLHS()->getType()->isRealFloatingType()) {
+ LHSReal = true;
+ APFloat &Real = Result.FloatReal;
+ LHSOK = EvaluateFloat(E->getLHS(), Real, Info);
+ if (LHSOK) {
+ Result.makeComplexFloat();
+ Result.FloatImag = APFloat(Real.getSemantics());
+ }
+ } else {
+ LHSOK = Visit(E->getLHS());
+ }
if (!LHSOK && !Info.keepEvaluatingAfterFailure())
return false;
ComplexValue RHS;
- if (!EvaluateComplex(E->getRHS(), RHS, Info) || !LHSOK)
+ if (E->getRHS()->getType()->isRealFloatingType()) {
+ RHSReal = true;
+ APFloat &Real = RHS.FloatReal;
+ if (!EvaluateFloat(E->getRHS(), Real, Info) || !LHSOK)
+ return false;
+ RHS.makeComplexFloat();
+ RHS.FloatImag = APFloat(Real.getSemantics());
+ } else if (!EvaluateComplex(E->getRHS(), RHS, Info) || !LHSOK)
return false;
- assert(Result.isComplexFloat() == RHS.isComplexFloat() &&
- "Invalid operands to binary operator.");
+ assert(!(LHSReal && RHSReal) &&
+ "Cannot have both operands of a complex operation be real.");
switch (E->getOpcode()) {
default: return Error(E);
case BO_Add:
if (Result.isComplexFloat()) {
Result.getComplexFloatReal().add(RHS.getComplexFloatReal(),
APFloat::rmNearestTiesToEven);
- Result.getComplexFloatImag().add(RHS.getComplexFloatImag(),
- APFloat::rmNearestTiesToEven);
+ if (LHSReal)
+ Result.getComplexFloatImag() = RHS.getComplexFloatImag();
+ else if (!RHSReal)
+ Result.getComplexFloatImag().add(RHS.getComplexFloatImag(),
+ APFloat::rmNearestTiesToEven);
} else {
Result.getComplexIntReal() += RHS.getComplexIntReal();
Result.getComplexIntImag() += RHS.getComplexIntImag();
@@ -7901,8 +7926,13 @@ bool ComplexExprEvaluator::VisitBinaryOp
if (Result.isComplexFloat()) {
Result.getComplexFloatReal().subtract(RHS.getComplexFloatReal(),
APFloat::rmNearestTiesToEven);
- Result.getComplexFloatImag().subtract(RHS.getComplexFloatImag(),
- APFloat::rmNearestTiesToEven);
+ if (LHSReal) {
+ Result.getComplexFloatImag() = RHS.getComplexFloatImag();
+ Result.getComplexFloatImag().changeSign();
+ } else if (!RHSReal) {
+ Result.getComplexFloatImag().subtract(RHS.getComplexFloatImag(),
+ APFloat::rmNearestTiesToEven);
+ }
} else {
Result.getComplexIntReal() -= RHS.getComplexIntReal();
Result.getComplexIntImag() -= RHS.getComplexIntImag();
@@ -7910,25 +7940,75 @@ bool ComplexExprEvaluator::VisitBinaryOp
break;
case BO_Mul:
if (Result.isComplexFloat()) {
+ // This is an implementation of complex multiplication according to the
+ // constraints laid out in C11 Annex G. The implemantion uses the
+ // following naming scheme:
+ // (a + ib) * (c + id)
ComplexValue LHS = Result;
- APFloat &LHS_r = LHS.getComplexFloatReal();
- APFloat &LHS_i = LHS.getComplexFloatImag();
- APFloat &RHS_r = RHS.getComplexFloatReal();
- APFloat &RHS_i = RHS.getComplexFloatImag();
-
- APFloat Tmp = LHS_r;
- Tmp.multiply(RHS_r, APFloat::rmNearestTiesToEven);
- Result.getComplexFloatReal() = Tmp;
- Tmp = LHS_i;
- Tmp.multiply(RHS_i, APFloat::rmNearestTiesToEven);
- Result.getComplexFloatReal().subtract(Tmp, APFloat::rmNearestTiesToEven);
-
- Tmp = LHS_r;
- Tmp.multiply(RHS_i, APFloat::rmNearestTiesToEven);
- Result.getComplexFloatImag() = Tmp;
- Tmp = LHS_i;
- Tmp.multiply(RHS_r, APFloat::rmNearestTiesToEven);
- Result.getComplexFloatImag().add(Tmp, APFloat::rmNearestTiesToEven);
+ APFloat &A = LHS.getComplexFloatReal();
+ APFloat &B = LHS.getComplexFloatImag();
+ APFloat &C = RHS.getComplexFloatReal();
+ APFloat &D = RHS.getComplexFloatImag();
+ APFloat &ResR = Result.getComplexFloatReal();
+ APFloat &ResI = Result.getComplexFloatImag();
+ if (LHSReal) {
+ assert(!RHSReal && "Cannot have two real operands for a complex op!");
+ ResR = A * C;
+ ResI = A * D;
+ } else if (RHSReal) {
+ ResR = C * A;
+ ResI = C * B;
+ } else {
+ // In the fully general case, we need to handle NaNs and infinities
+ // robustly.
+ APFloat AC = A * C;
+ APFloat BD = B * D;
+ APFloat AD = A * D;
+ APFloat BC = B * C;
+ ResR = AC - BD;
+ ResI = AD + BC;
+ if (ResR.isNaN() && ResI.isNaN()) {
+ bool Recalc = false;
+ if (A.isInfinity() || B.isInfinity()) {
+ A = APFloat::copySign(
+ APFloat(A.getSemantics(), A.isInfinity() ? 1 : 0), A);
+ B = APFloat::copySign(
+ APFloat(B.getSemantics(), B.isInfinity() ? 1 : 0), B);
+ if (C.isNaN())
+ C = APFloat::copySign(APFloat(C.getSemantics()), C);
+ if (D.isNaN())
+ D = APFloat::copySign(APFloat(D.getSemantics()), D);
+ Recalc = true;
+ }
+ if (C.isInfinity() || D.isInfinity()) {
+ C = APFloat::copySign(
+ APFloat(C.getSemantics(), C.isInfinity() ? 1 : 0), C);
+ D = APFloat::copySign(
+ APFloat(D.getSemantics(), D.isInfinity() ? 1 : 0), D);
+ if (A.isNaN())
+ A = APFloat::copySign(APFloat(A.getSemantics()), A);
+ if (B.isNaN())
+ B = APFloat::copySign(APFloat(B.getSemantics()), B);
+ Recalc = true;
+ }
+ if (!Recalc && (AC.isInfinity() || BD.isInfinity() ||
+ AD.isInfinity() || BC.isInfinity())) {
+ if (A.isNaN())
+ A = APFloat::copySign(APFloat(A.getSemantics()), A);
+ if (B.isNaN())
+ B = APFloat::copySign(APFloat(B.getSemantics()), B);
+ if (C.isNaN())
+ C = APFloat::copySign(APFloat(C.getSemantics()), C);
+ if (D.isNaN())
+ D = APFloat::copySign(APFloat(D.getSemantics()), D);
+ Recalc = true;
+ }
+ if (Recalc) {
+ ResR = APFloat::getInf(A.getSemantics()) * (A * C - B * D);
+ ResI = APFloat::getInf(A.getSemantics()) * (A * D + B * C);
+ }
+ }
+ }
} else {
ComplexValue LHS = Result;
Result.getComplexIntReal() =
@@ -7941,33 +8021,57 @@ bool ComplexExprEvaluator::VisitBinaryOp
break;
case BO_Div:
if (Result.isComplexFloat()) {
+ // This is an implementation of complex division according to the
+ // constraints laid out in C11 Annex G. The implemantion uses the
+ // following naming scheme:
+ // (a + ib) / (c + id)
ComplexValue LHS = Result;
- APFloat &LHS_r = LHS.getComplexFloatReal();
- APFloat &LHS_i = LHS.getComplexFloatImag();
- APFloat &RHS_r = RHS.getComplexFloatReal();
- APFloat &RHS_i = RHS.getComplexFloatImag();
- APFloat &Res_r = Result.getComplexFloatReal();
- APFloat &Res_i = Result.getComplexFloatImag();
-
- APFloat Den = RHS_r;
- Den.multiply(RHS_r, APFloat::rmNearestTiesToEven);
- APFloat Tmp = RHS_i;
- Tmp.multiply(RHS_i, APFloat::rmNearestTiesToEven);
- Den.add(Tmp, APFloat::rmNearestTiesToEven);
-
- Res_r = LHS_r;
- Res_r.multiply(RHS_r, APFloat::rmNearestTiesToEven);
- Tmp = LHS_i;
- Tmp.multiply(RHS_i, APFloat::rmNearestTiesToEven);
- Res_r.add(Tmp, APFloat::rmNearestTiesToEven);
- Res_r.divide(Den, APFloat::rmNearestTiesToEven);
-
- Res_i = LHS_i;
- Res_i.multiply(RHS_r, APFloat::rmNearestTiesToEven);
- Tmp = LHS_r;
- Tmp.multiply(RHS_i, APFloat::rmNearestTiesToEven);
- Res_i.subtract(Tmp, APFloat::rmNearestTiesToEven);
- Res_i.divide(Den, APFloat::rmNearestTiesToEven);
+ APFloat &A = LHS.getComplexFloatReal();
+ APFloat &B = LHS.getComplexFloatImag();
+ APFloat &C = RHS.getComplexFloatReal();
+ APFloat &D = RHS.getComplexFloatImag();
+ APFloat &ResR = Result.getComplexFloatReal();
+ APFloat &ResI = Result.getComplexFloatImag();
+ if (RHSReal) {
+ ResR = A / C;
+ ResI = B / C;
+ } else {
+ if (LHSReal) {
+ // No real optimizations we can do here, stub out with zero.
+ B = APFloat::getZero(A.getSemantics());
+ }
+ int DenomLogB = 0;
+ APFloat MaxCD = maxnum(abs(C), abs(D));
+ if (MaxCD.isFinite()) {
+ DenomLogB = ilogb(MaxCD);
+ C = scalbn(C, -DenomLogB);
+ D = scalbn(D, -DenomLogB);
+ }
+ APFloat Denom = C * C + D * D;
+ ResR = scalbn((A * C + B * D) / Denom, -DenomLogB);
+ ResI = scalbn((B * C - A * D) / Denom, -DenomLogB);
+ if (ResR.isNaN() && ResI.isNaN()) {
+ if (Denom.isPosZero() && (!A.isNaN() || !B.isNaN())) {
+ ResR = APFloat::getInf(ResR.getSemantics(), C.isNegative()) * A;
+ ResI = APFloat::getInf(ResR.getSemantics(), C.isNegative()) * B;
+ } else if ((A.isInfinity() || B.isInfinity()) && C.isFinite() &&
+ D.isFinite()) {
+ A = APFloat::copySign(
+ APFloat(A.getSemantics(), A.isInfinity() ? 1 : 0), A);
+ B = APFloat::copySign(
+ APFloat(B.getSemantics(), B.isInfinity() ? 1 : 0), B);
+ ResR = APFloat::getInf(ResR.getSemantics()) * (A * C + B * D);
+ ResI = APFloat::getInf(ResI.getSemantics()) * (B * C - A * D);
+ } else if (MaxCD.isInfinity() && A.isFinite() && B.isFinite()) {
+ C = APFloat::copySign(
+ APFloat(C.getSemantics(), C.isInfinity() ? 1 : 0), C);
+ D = APFloat::copySign(
+ APFloat(D.getSemantics(), D.isInfinity() ? 1 : 0), D);
+ ResR = APFloat::getZero(ResR.getSemantics()) * (A * C + B * D);
+ ResI = APFloat::getZero(ResI.getSemantics()) * (B * C - A * D);
+ }
+ }
+ }
} else {
if (RHS.getComplexIntReal() == 0 && RHS.getComplexIntImag() == 0)
return Error(E, diag::note_expr_divide_by_zero);
Modified: cfe/trunk/lib/CodeGen/CGExprComplex.cpp
URL: http://llvm.org/viewvc/llvm-project/cfe/trunk/lib/CodeGen/CGExprComplex.cpp?rev=219557&r1=219556&r2=219557&view=diff
==============================================================================
--- cfe/trunk/lib/CodeGen/CGExprComplex.cpp (original)
+++ cfe/trunk/lib/CodeGen/CGExprComplex.cpp Fri Oct 10 19:57:18 2014
@@ -230,6 +230,9 @@ public:
ComplexPairTy EmitBinMul(const BinOpInfo &Op);
ComplexPairTy EmitBinDiv(const BinOpInfo &Op);
+ ComplexPairTy EmitComplexBinOpLibCall(StringRef LibCallName,
+ const BinOpInfo &Op);
+
ComplexPairTy VisitBinAdd(const BinaryOperator *E) {
return EmitBinAdd(EmitBinOps(E));
}
@@ -528,9 +531,15 @@ ComplexPairTy ComplexExprEmitter::EmitBi
if (Op.LHS.first->getType()->isFloatingPointTy()) {
ResR = Builder.CreateFAdd(Op.LHS.first, Op.RHS.first, "add.r");
- ResI = Builder.CreateFAdd(Op.LHS.second, Op.RHS.second, "add.i");
+ if (Op.LHS.second && Op.RHS.second)
+ ResI = Builder.CreateFAdd(Op.LHS.second, Op.RHS.second, "add.i");
+ else
+ ResI = Op.LHS.second ? Op.LHS.second : Op.RHS.second;
+ assert(ResI && "Only one operand may be real!");
} else {
ResR = Builder.CreateAdd(Op.LHS.first, Op.RHS.first, "add.r");
+ assert(Op.LHS.second && Op.RHS.second &&
+ "Both operands of integer complex operators must be complex!");
ResI = Builder.CreateAdd(Op.LHS.second, Op.RHS.second, "add.i");
}
return ComplexPairTy(ResR, ResI);
@@ -539,63 +548,159 @@ ComplexPairTy ComplexExprEmitter::EmitBi
ComplexPairTy ComplexExprEmitter::EmitBinSub(const BinOpInfo &Op) {
llvm::Value *ResR, *ResI;
if (Op.LHS.first->getType()->isFloatingPointTy()) {
- ResR = Builder.CreateFSub(Op.LHS.first, Op.RHS.first, "sub.r");
- ResI = Builder.CreateFSub(Op.LHS.second, Op.RHS.second, "sub.i");
+ ResR = Builder.CreateFSub(Op.LHS.first, Op.RHS.first, "sub.r");
+ if (Op.LHS.second && Op.RHS.second)
+ ResI = Builder.CreateFSub(Op.LHS.second, Op.RHS.second, "sub.i");
+ else
+ ResI = Op.LHS.second ? Op.LHS.second
+ : Builder.CreateFNeg(Op.RHS.second, "sub.i");
+ assert(ResI && "Only one operand may be real!");
} else {
- ResR = Builder.CreateSub(Op.LHS.first, Op.RHS.first, "sub.r");
+ ResR = Builder.CreateSub(Op.LHS.first, Op.RHS.first, "sub.r");
+ assert(Op.LHS.second && Op.RHS.second &&
+ "Both operands of integer complex operators must be complex!");
ResI = Builder.CreateSub(Op.LHS.second, Op.RHS.second, "sub.i");
}
return ComplexPairTy(ResR, ResI);
}
+/// \brief Emit a libcall for a binary operation on complex types.
+ComplexPairTy ComplexExprEmitter::EmitComplexBinOpLibCall(StringRef LibCallName,
+ const BinOpInfo &Op) {
+ CallArgList Args;
+ Args.add(RValue::get(Op.LHS.first),
+ Op.Ty->castAs<ComplexType>()->getElementType());
+ Args.add(RValue::get(Op.LHS.second),
+ Op.Ty->castAs<ComplexType>()->getElementType());
+ Args.add(RValue::get(Op.RHS.first),
+ Op.Ty->castAs<ComplexType>()->getElementType());
+ Args.add(RValue::get(Op.RHS.second),
+ Op.Ty->castAs<ComplexType>()->getElementType());
+
+ // We *must* use the full CG function call building logic here because the
+ // complex type has special ABI handling.
+ const CGFunctionInfo &FuncInfo = CGF.CGM.getTypes().arrangeFreeFunctionCall(
+ Op.Ty, Args, FunctionType::ExtInfo(), RequiredArgs::All);
+ llvm::FunctionType *FTy = CGF.CGM.getTypes().GetFunctionType(FuncInfo);
+ llvm::Constant *Func = CGF.CGM.CreateRuntimeFunction(FTy, LibCallName);
+
+ llvm::Value *ArgVals[] = {Op.LHS.first, Op.LHS.second, Op.RHS.first,
+ Op.RHS.second};
+ llvm::Value *Result = CGF.EmitRuntimeCall(Func, ArgVals);
+
+ llvm::Value *ResR, *ResI;
+ if (Result->getType()->isVectorTy()) {
+ ResR = CGF.Builder.CreateExtractElement(Result, CGF.Builder.getInt32(0));
+ ResI = CGF.Builder.CreateExtractElement(Result, CGF.Builder.getInt32(1));
+ } else {
+ assert(Result->getType()->isAggregateType() &&
+ "Only vector and aggregate libcall returns are supported!");
+ unsigned ResRIndices[] = {0};
+ ResR = CGF.Builder.CreateExtractValue(Result, ResRIndices);
+ unsigned ResIIndices[] = {1};
+ ResI = CGF.Builder.CreateExtractValue(Result, ResIIndices);
+ }
+ return ComplexPairTy(ResR, ResI);
+}
+// See C11 Annex G.5.1 for the semantics of multiplicative operators on complex
+// typed values.
ComplexPairTy ComplexExprEmitter::EmitBinMul(const BinOpInfo &Op) {
using llvm::Value;
Value *ResR, *ResI;
if (Op.LHS.first->getType()->isFloatingPointTy()) {
- Value *ResRl = Builder.CreateFMul(Op.LHS.first, Op.RHS.first, "mul.rl");
- Value *ResRr = Builder.CreateFMul(Op.LHS.second, Op.RHS.second,"mul.rr");
- ResR = Builder.CreateFSub(ResRl, ResRr, "mul.r");
-
- Value *ResIl = Builder.CreateFMul(Op.LHS.second, Op.RHS.first, "mul.il");
- Value *ResIr = Builder.CreateFMul(Op.LHS.first, Op.RHS.second, "mul.ir");
- ResI = Builder.CreateFAdd(ResIl, ResIr, "mul.i");
+ // The general formulation is:
+ // (a + ib) * (c + id) = (a * c - b * d) + i(a * d + b * c)
+ //
+ // But we can fold away components which would be zero due to a real
+ // operand according to C11 Annex G.5.1p2.
+ // FIXME: C11 also provides for imaginary types which would allow folding
+ // still more of this within the type system.
+
+ if (Op.LHS.second && Op.RHS.second) {
+ // If both operands are complex, delegate to a libcall which works to
+ // prevent underflow and overflow.
+ StringRef LibCallName;
+ switch (Op.LHS.first->getType()->getTypeID()) {
+ default:
+ llvm_unreachable("Unsupported floating point type!");
+ case llvm::Type::HalfTyID:
+ return EmitComplexBinOpLibCall("__mulhc3", Op);
+ case llvm::Type::FloatTyID:
+ return EmitComplexBinOpLibCall("__mulsc3", Op);
+ case llvm::Type::DoubleTyID:
+ return EmitComplexBinOpLibCall("__muldc3", Op);
+ case llvm::Type::X86_FP80TyID:
+ return EmitComplexBinOpLibCall("__mulxc3", Op);
+ }
+ }
+ assert((Op.LHS.second || Op.RHS.second) &&
+ "At least one operand must be complex!");
+
+ // If either of the operands is a real rather than a complex, the
+ // imaginary component is ignored when computing the real component of the
+ // result.
+ ResR = Builder.CreateFMul(Op.LHS.first, Op.RHS.first, "mul.rl");
+
+ ResI = Op.LHS.second
+ ? Builder.CreateFMul(Op.LHS.second, Op.RHS.first, "mul.il")
+ : Builder.CreateFMul(Op.LHS.first, Op.RHS.second, "mul.ir");
} else {
+ assert(Op.LHS.second && Op.RHS.second &&
+ "Both operands of integer complex operators must be complex!");
Value *ResRl = Builder.CreateMul(Op.LHS.first, Op.RHS.first, "mul.rl");
- Value *ResRr = Builder.CreateMul(Op.LHS.second, Op.RHS.second,"mul.rr");
- ResR = Builder.CreateSub(ResRl, ResRr, "mul.r");
+ Value *ResRr = Builder.CreateMul(Op.LHS.second, Op.RHS.second, "mul.rr");
+ ResR = Builder.CreateSub(ResRl, ResRr, "mul.r");
Value *ResIl = Builder.CreateMul(Op.LHS.second, Op.RHS.first, "mul.il");
Value *ResIr = Builder.CreateMul(Op.LHS.first, Op.RHS.second, "mul.ir");
- ResI = Builder.CreateAdd(ResIl, ResIr, "mul.i");
+ ResI = Builder.CreateAdd(ResIl, ResIr, "mul.i");
}
return ComplexPairTy(ResR, ResI);
}
+// See C11 Annex G.5.1 for the semantics of multiplicative operators on complex
+// typed values.
ComplexPairTy ComplexExprEmitter::EmitBinDiv(const BinOpInfo &Op) {
llvm::Value *LHSr = Op.LHS.first, *LHSi = Op.LHS.second;
llvm::Value *RHSr = Op.RHS.first, *RHSi = Op.RHS.second;
llvm::Value *DSTr, *DSTi;
- if (Op.LHS.first->getType()->isFloatingPointTy()) {
- // (a+ib) / (c+id) = ((ac+bd)/(cc+dd)) + i((bc-ad)/(cc+dd))
- llvm::Value *Tmp1 = Builder.CreateFMul(LHSr, RHSr); // a*c
- llvm::Value *Tmp2 = Builder.CreateFMul(LHSi, RHSi); // b*d
- llvm::Value *Tmp3 = Builder.CreateFAdd(Tmp1, Tmp2); // ac+bd
-
- llvm::Value *Tmp4 = Builder.CreateFMul(RHSr, RHSr); // c*c
- llvm::Value *Tmp5 = Builder.CreateFMul(RHSi, RHSi); // d*d
- llvm::Value *Tmp6 = Builder.CreateFAdd(Tmp4, Tmp5); // cc+dd
-
- llvm::Value *Tmp7 = Builder.CreateFMul(LHSi, RHSr); // b*c
- llvm::Value *Tmp8 = Builder.CreateFMul(LHSr, RHSi); // a*d
- llvm::Value *Tmp9 = Builder.CreateFSub(Tmp7, Tmp8); // bc-ad
+ if (LHSr->getType()->isFloatingPointTy()) {
+ // If we have a complex operand on the RHS, we delegate to a libcall to
+ // handle all of the complexities and minimize underflow/overflow cases.
+ //
+ // FIXME: We would be able to avoid the libcall in many places if we
+ // supported imaginary types in addition to complex types.
+ if (RHSi) {
+ BinOpInfo LibCallOp = Op;
+ // If LHS was a real, supply a null imaginary part.
+ if (!LHSi)
+ LibCallOp.LHS.second = llvm::Constant::getNullValue(LHSr->getType());
+
+ StringRef LibCallName;
+ switch (LHSr->getType()->getTypeID()) {
+ default:
+ llvm_unreachable("Unsupported floating point type!");
+ case llvm::Type::HalfTyID:
+ return EmitComplexBinOpLibCall("__divhc3", LibCallOp);
+ case llvm::Type::FloatTyID:
+ return EmitComplexBinOpLibCall("__divsc3", LibCallOp);
+ case llvm::Type::DoubleTyID:
+ return EmitComplexBinOpLibCall("__divdc3", LibCallOp);
+ case llvm::Type::X86_FP80TyID:
+ return EmitComplexBinOpLibCall("__divxc3", LibCallOp);
+ }
+ }
+ assert(LHSi && "Can have at most one non-complex operand!");
- DSTr = Builder.CreateFDiv(Tmp3, Tmp6);
- DSTi = Builder.CreateFDiv(Tmp9, Tmp6);
+ DSTr = Builder.CreateFDiv(LHSr, RHSr);
+ DSTi = Builder.CreateFDiv(LHSi, RHSr);
} else {
+ assert(Op.LHS.second && Op.RHS.second &&
+ "Both operands of integer complex operators must be complex!");
// (a+ib) / (c+id) = ((ac+bd)/(cc+dd)) + i((bc-ad)/(cc+dd))
llvm::Value *Tmp1 = Builder.CreateMul(LHSr, RHSr); // a*c
llvm::Value *Tmp2 = Builder.CreateMul(LHSi, RHSi); // b*d
@@ -626,8 +731,15 @@ ComplexExprEmitter::EmitBinOps(const Bin
TestAndClearIgnoreReal();
TestAndClearIgnoreImag();
BinOpInfo Ops;
- Ops.LHS = Visit(E->getLHS());
- Ops.RHS = Visit(E->getRHS());
+ if (E->getLHS()->getType()->isRealFloatingType())
+ Ops.LHS = ComplexPairTy(CGF.EmitScalarExpr(E->getLHS()), nullptr);
+ else
+ Ops.LHS = Visit(E->getLHS());
+ if (E->getRHS()->getType()->isRealFloatingType())
+ Ops.RHS = ComplexPairTy(CGF.EmitScalarExpr(E->getRHS()), nullptr);
+ else
+ Ops.RHS = Visit(E->getRHS());
+
Ops.Ty = E->getType();
return Ops;
}
@@ -647,12 +759,19 @@ EmitCompoundAssignLValue(const CompoundA
// __block variables need to have the rhs evaluated first, plus this should
// improve codegen a little.
OpInfo.Ty = E->getComputationResultType();
+ QualType ComplexElementTy = cast<ComplexType>(OpInfo.Ty)->getElementType();
// The RHS should have been converted to the computation type.
- assert(OpInfo.Ty->isAnyComplexType());
- assert(CGF.getContext().hasSameUnqualifiedType(OpInfo.Ty,
- E->getRHS()->getType()));
- OpInfo.RHS = Visit(E->getRHS());
+ if (E->getRHS()->getType()->isRealFloatingType()) {
+ assert(
+ CGF.getContext()
+ .hasSameUnqualifiedType(ComplexElementTy, E->getRHS()->getType()));
+ OpInfo.RHS = ComplexPairTy(CGF.EmitScalarExpr(E->getRHS()), nullptr);
+ } else {
+ assert(CGF.getContext()
+ .hasSameUnqualifiedType(OpInfo.Ty, E->getRHS()->getType()));
+ OpInfo.RHS = Visit(E->getRHS());
+ }
LValue LHS = CGF.EmitLValue(E->getLHS());
@@ -662,7 +781,15 @@ EmitCompoundAssignLValue(const CompoundA
OpInfo.LHS = EmitComplexToComplexCast(LHSVal, LHSTy, OpInfo.Ty);
} else {
llvm::Value *LHSVal = CGF.EmitLoadOfScalar(LHS, E->getExprLoc());
- OpInfo.LHS = EmitScalarToComplexCast(LHSVal, LHSTy, OpInfo.Ty);
+ // For floating point real operands we can directly pass the scalar form
+ // to the binary operator emission and potentially get more efficient code.
+ if (LHSTy->isRealFloatingType()) {
+ if (!CGF.getContext().hasSameUnqualifiedType(ComplexElementTy, LHSTy))
+ LHSVal = CGF.EmitScalarConversion(LHSVal, LHSTy, ComplexElementTy);
+ OpInfo.LHS = ComplexPairTy(LHSVal, nullptr);
+ } else {
+ OpInfo.LHS = EmitScalarToComplexCast(LHSVal, LHSTy, OpInfo.Ty);
+ }
}
// Expand the binary operator.
Modified: cfe/trunk/lib/Sema/SemaExpr.cpp
URL: http://llvm.org/viewvc/llvm-project/cfe/trunk/lib/Sema/SemaExpr.cpp?rev=219557&r1=219556&r2=219557&view=diff
==============================================================================
--- cfe/trunk/lib/Sema/SemaExpr.cpp (original)
+++ cfe/trunk/lib/Sema/SemaExpr.cpp Fri Oct 10 19:57:18 2014
@@ -938,68 +938,6 @@ static bool handleIntegerToComplexFloatC
return false;
}
-/// \brief Takes two complex float types and converts them to the same type.
-/// Helper function of UsualArithmeticConversions()
-static QualType
-handleComplexFloatToComplexFloatConverstion(Sema &S, ExprResult &LHS,
- ExprResult &RHS, QualType LHSType,
- QualType RHSType,
- bool IsCompAssign) {
- int order = S.Context.getFloatingTypeOrder(LHSType, RHSType);
-
- if (order < 0) {
- // _Complex float -> _Complex double
- if (!IsCompAssign)
- LHS = S.ImpCastExprToType(LHS.get(), RHSType, CK_FloatingComplexCast);
- return RHSType;
- }
- if (order > 0)
- // _Complex float -> _Complex double
- RHS = S.ImpCastExprToType(RHS.get(), LHSType, CK_FloatingComplexCast);
- return LHSType;
-}
-
-/// \brief Converts otherExpr to complex float and promotes complexExpr if
-/// necessary. Helper function of UsualArithmeticConversions()
-static QualType handleOtherComplexFloatConversion(Sema &S,
- ExprResult &ComplexExpr,
- ExprResult &OtherExpr,
- QualType ComplexTy,
- QualType OtherTy,
- bool ConvertComplexExpr,
- bool ConvertOtherExpr) {
- int order = S.Context.getFloatingTypeOrder(ComplexTy, OtherTy);
-
- // If just the complexExpr is complex, the otherExpr needs to be converted,
- // and the complexExpr might need to be promoted.
- if (order > 0) { // complexExpr is wider
- // float -> _Complex double
- if (ConvertOtherExpr) {
- QualType fp = cast<ComplexType>(ComplexTy)->getElementType();
- OtherExpr = S.ImpCastExprToType(OtherExpr.get(), fp, CK_FloatingCast);
- OtherExpr = S.ImpCastExprToType(OtherExpr.get(), ComplexTy,
- CK_FloatingRealToComplex);
- }
- return ComplexTy;
- }
-
- // otherTy is at least as wide. Find its corresponding complex type.
- QualType result = (order == 0 ? ComplexTy :
- S.Context.getComplexType(OtherTy));
-
- // double -> _Complex double
- if (ConvertOtherExpr)
- OtherExpr = S.ImpCastExprToType(OtherExpr.get(), result,
- CK_FloatingRealToComplex);
-
- // _Complex float -> _Complex double
- if (ConvertComplexExpr && order < 0)
- ComplexExpr = S.ImpCastExprToType(ComplexExpr.get(), result,
- CK_FloatingComplexCast);
-
- return result;
-}
-
/// \brief Handle arithmetic conversion with complex types. Helper function of
/// UsualArithmeticConversions()
static QualType handleComplexFloatConversion(Sema &S, ExprResult &LHS,
@@ -1025,26 +963,35 @@ static QualType handleComplexFloatConver
// when combining a "long double" with a "double _Complex", the
// "double _Complex" is promoted to "long double _Complex".
- bool LHSComplexFloat = LHSType->isComplexType();
- bool RHSComplexFloat = RHSType->isComplexType();
+ // Compute the rank of the two types, regardless of whether they are complex.
+ int Order = S.Context.getFloatingTypeOrder(LHSType, RHSType);
- // If both are complex, just cast to the more precise type.
- if (LHSComplexFloat && RHSComplexFloat)
- return handleComplexFloatToComplexFloatConverstion(S, LHS, RHS,
- LHSType, RHSType,
- IsCompAssign);
-
- // If only one operand is complex, promote it if necessary and convert the
- // other operand to complex.
- if (LHSComplexFloat)
- return handleOtherComplexFloatConversion(
- S, LHS, RHS, LHSType, RHSType, /*convertComplexExpr*/!IsCompAssign,
- /*convertOtherExpr*/ true);
-
- assert(RHSComplexFloat);
- return handleOtherComplexFloatConversion(
- S, RHS, LHS, RHSType, LHSType, /*convertComplexExpr*/true,
- /*convertOtherExpr*/ !IsCompAssign);
+ auto *LHSComplexType = dyn_cast<ComplexType>(LHSType);
+ auto *RHSComplexType = dyn_cast<ComplexType>(RHSType);
+ QualType LHSElementType =
+ LHSComplexType ? LHSComplexType->getElementType() : LHSType;
+ QualType RHSElementType =
+ RHSComplexType ? RHSComplexType->getElementType() : RHSType;
+
+ QualType ResultType = S.Context.getComplexType(LHSElementType);
+ if (Order < 0) {
+ // Promote the precision of the LHS if not an assignment.
+ ResultType = S.Context.getComplexType(RHSElementType);
+ if (!IsCompAssign) {
+ if (LHSComplexType)
+ LHS =
+ S.ImpCastExprToType(LHS.get(), ResultType, CK_FloatingComplexCast);
+ else
+ LHS = S.ImpCastExprToType(LHS.get(), RHSElementType, CK_FloatingCast);
+ }
+ } else if (Order > 0) {
+ // Promote the precision of the RHS.
+ if (RHSComplexType)
+ RHS = S.ImpCastExprToType(RHS.get(), ResultType, CK_FloatingComplexCast);
+ else
+ RHS = S.ImpCastExprToType(RHS.get(), LHSElementType, CK_FloatingCast);
+ }
+ return ResultType;
}
/// \brief Hande arithmetic conversion from integer to float. Helper function
Added: cfe/trunk/test/CodeGen/complex-math.c
URL: http://llvm.org/viewvc/llvm-project/cfe/trunk/test/CodeGen/complex-math.c?rev=219557&view=auto
==============================================================================
--- cfe/trunk/test/CodeGen/complex-math.c (added)
+++ cfe/trunk/test/CodeGen/complex-math.c Fri Oct 10 19:57:18 2014
@@ -0,0 +1,367 @@
+// RUN: %clang_cc1 %s -O1 -emit-llvm -triple x86_64-unknown-unknown -o - | FileCheck %s --check-prefix=X86
+
+float _Complex add_float_rr(float a, float b) {
+ // X86-LABEL: @add_float_rr(
+ // X86: fadd
+ // X86-NOT: fadd
+ // X86: ret
+ return a + b;
+}
+float _Complex add_float_cr(float _Complex a, float b) {
+ // X86-LABEL: @add_float_cr(
+ // X86: fadd
+ // X86-NOT: fadd
+ // X86: ret
+ return a + b;
+}
+float _Complex add_float_rc(float a, float _Complex b) {
+ // X86-LABEL: @add_float_rc(
+ // X86: fadd
+ // X86-NOT: fadd
+ // X86: ret
+ return a + b;
+}
+float _Complex add_float_cc(float _Complex a, float _Complex b) {
+ // X86-LABEL: @add_float_cc(
+ // X86: fadd
+ // X86: fadd
+ // X86-NOT: fadd
+ // X86: ret
+ return a + b;
+}
+
+float _Complex sub_float_rr(float a, float b) {
+ // X86-LABEL: @sub_float_rr(
+ // X86: fsub
+ // X86-NOT: fsub
+ // X86: ret
+ return a - b;
+}
+float _Complex sub_float_cr(float _Complex a, float b) {
+ // X86-LABEL: @sub_float_cr(
+ // X86: fsub
+ // X86-NOT: fsub
+ // X86: ret
+ return a - b;
+}
+float _Complex sub_float_rc(float a, float _Complex b) {
+ // X86-LABEL: @sub_float_rc(
+ // X86: fsub
+ // X86: fsub float -0.{{0+}}e+00,
+ // X86-NOT: fsub
+ // X86: ret
+ return a - b;
+}
+float _Complex sub_float_cc(float _Complex a, float _Complex b) {
+ // X86-LABEL: @sub_float_cc(
+ // X86: fsub
+ // X86: fsub
+ // X86-NOT: fsub
+ // X86: ret
+ return a - b;
+}
+
+float _Complex mul_float_rr(float a, float b) {
+ // X86-LABEL: @mul_float_rr(
+ // X86: fmul
+ // X86-NOT: fmul
+ // X86: ret
+ return a * b;
+}
+float _Complex mul_float_cr(float _Complex a, float b) {
+ // X86-LABEL: @mul_float_cr(
+ // X86: fmul
+ // X86: fmul
+ // X86-NOT: fmul
+ // X86: ret
+ return a * b;
+}
+float _Complex mul_float_rc(float a, float _Complex b) {
+ // X86-LABEL: @mul_float_rc(
+ // X86: fmul
+ // X86: fmul
+ // X86-NOT: fmul
+ // X86: ret
+ return a * b;
+}
+float _Complex mul_float_cc(float _Complex a, float _Complex b) {
+ // X86-LABEL: @mul_float_cc(
+ // X86-NOT: fmul
+ // X86: call <2 x float> @__mulsc3(
+ // X86: ret
+ return a * b;
+}
+
+float _Complex div_float_rr(float a, float b) {
+ // X86-LABEL: @div_float_rr(
+ // X86: fdiv
+ // X86-NOT: fdiv
+ // X86: ret
+ return a / b;
+}
+float _Complex div_float_cr(float _Complex a, float b) {
+ // X86-LABEL: @div_float_cr(
+ // X86: fdiv
+ // X86: fdiv
+ // X86-NOT: fdiv
+ // X86: ret
+ return a / b;
+}
+float _Complex div_float_rc(float a, float _Complex b) {
+ // X86-LABEL: @div_float_rc(
+ // X86-NOT: fdiv
+ // X86: call <2 x float> @__divsc3(
+ // X86: ret
+ return a / b;
+}
+float _Complex div_float_cc(float _Complex a, float _Complex b) {
+ // X86-LABEL: @div_float_cc(
+ // X86-NOT: fdiv
+ // X86: call <2 x float> @__divsc3(
+ // X86: ret
+ return a / b;
+}
+
+double _Complex add_double_rr(double a, double b) {
+ // X86-LABEL: @add_double_rr(
+ // X86: fadd
+ // X86-NOT: fadd
+ // X86: ret
+ return a + b;
+}
+double _Complex add_double_cr(double _Complex a, double b) {
+ // X86-LABEL: @add_double_cr(
+ // X86: fadd
+ // X86-NOT: fadd
+ // X86: ret
+ return a + b;
+}
+double _Complex add_double_rc(double a, double _Complex b) {
+ // X86-LABEL: @add_double_rc(
+ // X86: fadd
+ // X86-NOT: fadd
+ // X86: ret
+ return a + b;
+}
+double _Complex add_double_cc(double _Complex a, double _Complex b) {
+ // X86-LABEL: @add_double_cc(
+ // X86: fadd
+ // X86: fadd
+ // X86-NOT: fadd
+ // X86: ret
+ return a + b;
+}
+
+double _Complex sub_double_rr(double a, double b) {
+ // X86-LABEL: @sub_double_rr(
+ // X86: fsub
+ // X86-NOT: fsub
+ // X86: ret
+ return a - b;
+}
+double _Complex sub_double_cr(double _Complex a, double b) {
+ // X86-LABEL: @sub_double_cr(
+ // X86: fsub
+ // X86-NOT: fsub
+ // X86: ret
+ return a - b;
+}
+double _Complex sub_double_rc(double a, double _Complex b) {
+ // X86-LABEL: @sub_double_rc(
+ // X86: fsub
+ // X86: fsub double -0.{{0+}}e+00,
+ // X86-NOT: fsub
+ // X86: ret
+ return a - b;
+}
+double _Complex sub_double_cc(double _Complex a, double _Complex b) {
+ // X86-LABEL: @sub_double_cc(
+ // X86: fsub
+ // X86: fsub
+ // X86-NOT: fsub
+ // X86: ret
+ return a - b;
+}
+
+double _Complex mul_double_rr(double a, double b) {
+ // X86-LABEL: @mul_double_rr(
+ // X86: fmul
+ // X86-NOT: fmul
+ // X86: ret
+ return a * b;
+}
+double _Complex mul_double_cr(double _Complex a, double b) {
+ // X86-LABEL: @mul_double_cr(
+ // X86: fmul
+ // X86: fmul
+ // X86-NOT: fmul
+ // X86: ret
+ return a * b;
+}
+double _Complex mul_double_rc(double a, double _Complex b) {
+ // X86-LABEL: @mul_double_rc(
+ // X86: fmul
+ // X86: fmul
+ // X86-NOT: fmul
+ // X86: ret
+ return a * b;
+}
+double _Complex mul_double_cc(double _Complex a, double _Complex b) {
+ // X86-LABEL: @mul_double_cc(
+ // X86-NOT: fmul
+ // X86: call { double, double } @__muldc3(
+ // X86: ret
+ return a * b;
+}
+
+double _Complex div_double_rr(double a, double b) {
+ // X86-LABEL: @div_double_rr(
+ // X86: fdiv
+ // X86-NOT: fdiv
+ // X86: ret
+ return a / b;
+}
+double _Complex div_double_cr(double _Complex a, double b) {
+ // X86-LABEL: @div_double_cr(
+ // X86: fdiv
+ // X86: fdiv
+ // X86-NOT: fdiv
+ // X86: ret
+ return a / b;
+}
+double _Complex div_double_rc(double a, double _Complex b) {
+ // X86-LABEL: @div_double_rc(
+ // X86-NOT: fdiv
+ // X86: call { double, double } @__divdc3(
+ // X86: ret
+ return a / b;
+}
+double _Complex div_double_cc(double _Complex a, double _Complex b) {
+ // X86-LABEL: @div_double_cc(
+ // X86-NOT: fdiv
+ // X86: call { double, double } @__divdc3(
+ // X86: ret
+ return a / b;
+}
+
+long double _Complex add_long_double_rr(long double a, long double b) {
+ // X86-LABEL: @add_long_double_rr(
+ // X86: fadd
+ // X86-NOT: fadd
+ // X86: ret
+ return a + b;
+}
+long double _Complex add_long_double_cr(long double _Complex a, long double b) {
+ // X86-LABEL: @add_long_double_cr(
+ // X86: fadd
+ // X86-NOT: fadd
+ // X86: ret
+ return a + b;
+}
+long double _Complex add_long_double_rc(long double a, long double _Complex b) {
+ // X86-LABEL: @add_long_double_rc(
+ // X86: fadd
+ // X86-NOT: fadd
+ // X86: ret
+ return a + b;
+}
+long double _Complex add_long_double_cc(long double _Complex a, long double _Complex b) {
+ // X86-LABEL: @add_long_double_cc(
+ // X86: fadd
+ // X86: fadd
+ // X86-NOT: fadd
+ // X86: ret
+ return a + b;
+}
+
+long double _Complex sub_long_double_rr(long double a, long double b) {
+ // X86-LABEL: @sub_long_double_rr(
+ // X86: fsub
+ // X86-NOT: fsub
+ // X86: ret
+ return a - b;
+}
+long double _Complex sub_long_double_cr(long double _Complex a, long double b) {
+ // X86-LABEL: @sub_long_double_cr(
+ // X86: fsub
+ // X86-NOT: fsub
+ // X86: ret
+ return a - b;
+}
+long double _Complex sub_long_double_rc(long double a, long double _Complex b) {
+ // X86-LABEL: @sub_long_double_rc(
+ // X86: fsub
+ // X86: fsub x86_fp80 0xK8{{0+}},
+ // X86-NOT: fsub
+ // X86: ret
+ return a - b;
+}
+long double _Complex sub_long_double_cc(long double _Complex a, long double _Complex b) {
+ // X86-LABEL: @sub_long_double_cc(
+ // X86: fsub
+ // X86: fsub
+ // X86-NOT: fsub
+ // X86: ret
+ return a - b;
+}
+
+long double _Complex mul_long_double_rr(long double a, long double b) {
+ // X86-LABEL: @mul_long_double_rr(
+ // X86: fmul
+ // X86-NOT: fmul
+ // X86: ret
+ return a * b;
+}
+long double _Complex mul_long_double_cr(long double _Complex a, long double b) {
+ // X86-LABEL: @mul_long_double_cr(
+ // X86: fmul
+ // X86: fmul
+ // X86-NOT: fmul
+ // X86: ret
+ return a * b;
+}
+long double _Complex mul_long_double_rc(long double a, long double _Complex b) {
+ // X86-LABEL: @mul_long_double_rc(
+ // X86: fmul
+ // X86: fmul
+ // X86-NOT: fmul
+ // X86: ret
+ return a * b;
+}
+long double _Complex mul_long_double_cc(long double _Complex a, long double _Complex b) {
+ // X86-LABEL: @mul_long_double_cc(
+ // X86-NOT: fmul
+ // X86: call { x86_fp80, x86_fp80 } @__mulxc3(
+ // X86: ret
+ return a * b;
+}
+
+long double _Complex div_long_double_rr(long double a, long double b) {
+ // X86-LABEL: @div_long_double_rr(
+ // X86: fdiv
+ // X86-NOT: fdiv
+ // X86: ret
+ return a / b;
+}
+long double _Complex div_long_double_cr(long double _Complex a, long double b) {
+ // X86-LABEL: @div_long_double_cr(
+ // X86: fdiv
+ // X86: fdiv
+ // X86-NOT: fdiv
+ // X86: ret
+ return a / b;
+}
+long double _Complex div_long_double_rc(long double a, long double _Complex b) {
+ // X86-LABEL: @div_long_double_rc(
+ // X86-NOT: fdiv
+ // X86: call { x86_fp80, x86_fp80 } @__divxc3(
+ // X86: ret
+ return a / b;
+}
+long double _Complex div_long_double_cc(long double _Complex a, long double _Complex b) {
+ // X86-LABEL: @div_long_double_cc(
+ // X86-NOT: fdiv
+ // X86: call { x86_fp80, x86_fp80 } @__divxc3(
+ // X86: ret
+ return a / b;
+}
Added: cfe/trunk/test/SemaCXX/complex-folding.cpp
URL: http://llvm.org/viewvc/llvm-project/cfe/trunk/test/SemaCXX/complex-folding.cpp?rev=219557&view=auto
==============================================================================
--- cfe/trunk/test/SemaCXX/complex-folding.cpp (added)
+++ cfe/trunk/test/SemaCXX/complex-folding.cpp Fri Oct 10 19:57:18 2014
@@ -0,0 +1,82 @@
+// RUN: %clang_cc1 %s -std=c++1z -fsyntax-only -verify
+//
+// Test the constant folding of builtin complex numbers.
+
+static_assert((0.0 + 0.0j) == (0.0 + 0.0j));
+
+// Walk around the complex plane stepping between angular differences and
+// equality.
+static_assert((1.0 + 0.0j) == (0.0 + 0.0j)); // expected-error {{static_assert}}
+static_assert((1.0 + 0.0j) == (1.0 + 0.0j));
+static_assert((1.0 + 1.0j) == (1.0 + 0.0j)); // expected-error {{static_assert}}
+static_assert((1.0 + 1.0j) == (1.0 + 1.0j));
+static_assert((0.0 + 1.0j) == (1.0 + 1.0j)); // expected-error {{static_assert}}
+static_assert((0.0 + 1.0j) == (0.0 + 1.0j));
+static_assert((-1.0 + 1.0j) == (0.0 + 1.0j)); // expected-error {{static_assert}}
+static_assert((-1.0 + 1.0j) == (-1.0 + 1.0j));
+static_assert((-1.0 + 0.0j) == (-1.0 + 1.0j)); // expected-error {{static_assert}}
+static_assert((-1.0 + 0.0j) == (-1.0 + 0.0j));
+static_assert((-1.0 - 1.0j) == (-1.0 + 0.0j)); // expected-error {{static_assert}}
+static_assert((-1.0 - 1.0j) == (-1.0 - 1.0j));
+static_assert((0.0 - 1.0j) == (-1.0 - 1.0j)); // expected-error {{static_assert}}
+static_assert((0.0 - 1.0j) == (0.0 - 1.0j));
+static_assert((1.0 - 1.0j) == (0.0 - 1.0j)); // expected-error {{static_assert}}
+static_assert((1.0 - 1.0j) == (1.0 - 1.0j));
+
+// Test basic mathematical folding of both complex and real operands.
+static_assert(((1.0 + 0.5j) + (0.25 - 0.75j)) == (1.25 - 0.25j));
+static_assert(((1.0 + 0.5j) + 0.25) == (1.25 + 0.5j));
+static_assert((1.0 + (0.25 - 0.75j)) == (1.25 - 0.75j));
+
+static_assert(((1.0 + 0.5j) - (0.25 - 0.75j)) == (0.75 + 1.25j));
+static_assert(((1.0 + 0.5j) - 0.25) == (0.75 + 0.5j));
+static_assert((1.0 - (0.25 - 0.75j)) == (0.75 + 0.75j));
+
+static_assert(((1.25 + 0.5j) * (0.25 - 0.75j)) == (0.6875 - 0.8125j));
+static_assert(((1.25 + 0.5j) * 0.25) == (0.3125 + 0.125j));
+static_assert((1.25 * (0.25 - 0.75j)) == (0.3125 - 0.9375j));
+
+static_assert(((1.25 + 0.5j) / (0.25 - 0.75j)) == (-0.1 + 1.7j));
+static_assert(((1.25 + 0.5j) / 0.25) == (5.0 + 2.0j));
+static_assert((1.25 / (0.25 - 0.75j)) == (0.5 + 1.5j));
+
+// Test that infinities are preserved, don't turn into NaNs, and do form zeros
+// when the divisor.
+static_assert(__builtin_isinf_sign(__real__((__builtin_inf() + 1.0j) * 1.0)) == 1);
+static_assert(__builtin_isinf_sign(__imag__((1.0 + __builtin_inf() * 1.0j) * 1.0)) == 1);
+static_assert(__builtin_isinf_sign(__real__(1.0 * (__builtin_inf() + 1.0j))) == 1);
+static_assert(__builtin_isinf_sign(__imag__(1.0 * (1.0 + __builtin_inf() * 1.0j))) == 1);
+
+static_assert(__builtin_isinf_sign(__real__((__builtin_inf() + 1.0j) * (1.0 + 1.0j))) == 1);
+static_assert(__builtin_isinf_sign(__real__((1.0 + 1.0j) * (__builtin_inf() + 1.0j))) == 1);
+static_assert(__builtin_isinf_sign(__real__((__builtin_inf() + 1.0j) * (__builtin_inf() + 1.0j))) == 1);
+
+static_assert(__builtin_isinf_sign(__real__((1.0 + __builtin_inf() * 1.0j) * (1.0 + 1.0j))) == -1);
+static_assert(__builtin_isinf_sign(__imag__((1.0 + __builtin_inf() * 1.0j) * (1.0 + 1.0j))) == 1);
+static_assert(__builtin_isinf_sign(__real__((1.0 + 1.0j) * (1.0 + __builtin_inf() * 1.0j))) == -1);
+static_assert(__builtin_isinf_sign(__imag__((1.0 + 1.0j) * (1.0 + __builtin_inf() * 1.0j))) == 1);
+
+static_assert(__builtin_isinf_sign(__real__((1.0 + __builtin_inf() * 1.0j) * (1.0 + __builtin_inf() * 1.0j))) == -1);
+static_assert(__builtin_isinf_sign(__real__((__builtin_inf() + __builtin_inf() * 1.0j) * (__builtin_inf() + __builtin_inf() * 1.0j))) == -1);
+
+static_assert(__builtin_isinf_sign(__real__((__builtin_inf() + 1.0j) / (1.0 + 1.0j))) == 1);
+static_assert(__builtin_isinf_sign(__imag__(1.0 + (__builtin_inf() * 1.0j) / (1.0 + 1.0j))) == 1);
+static_assert(__builtin_isinf_sign(__imag__((__builtin_inf() + __builtin_inf() * 1.0j) / (1.0 + 1.0j))) == 1);
+static_assert(__builtin_isinf_sign(__real__((__builtin_inf() + 1.0j) / 1.0)) == 1);
+static_assert(__builtin_isinf_sign(__imag__(1.0 + (__builtin_inf() * 1.0j) / 1.0)) == 1);
+static_assert(__builtin_isinf_sign(__imag__((__builtin_inf() + __builtin_inf() * 1.0j) / 1.0)) == 1);
+
+static_assert(((1.0 + 1.0j) / (__builtin_inf() + 1.0j)) == (0.0 + 0.0j));
+static_assert(((1.0 + 1.0j) / (1.0 + __builtin_inf() * 1.0j)) == (0.0 + 0.0j));
+static_assert(((1.0 + 1.0j) / (__builtin_inf() + __builtin_inf() * 1.0j)) == (0.0 + 0.0j));
+static_assert(((1.0 + 1.0j) / __builtin_inf()) == (0.0 + 0.0j));
+
+static_assert(__builtin_isinf_sign(__real__((1.0 + 1.0j) / (0.0 + 0.0j))) == 1);
+static_assert(__builtin_isinf_sign(__real__((1.0 + 1.0j) / 0.0)) == 1);
+
+static_assert(__builtin_isinf_sign(__real__((__builtin_inf() + 1.0j) / (0.0 + 0.0j))) == 1);
+static_assert(__builtin_isinf_sign(__imag__((1.0 + __builtin_inf() * 1.0j) / (0.0 + 0.0j))) == 1);
+static_assert(__builtin_isinf_sign(__imag__((__builtin_inf() + __builtin_inf() * 1.0j) / (0.0 + 0.0j))) == 1);
+static_assert(__builtin_isinf_sign(__real__((__builtin_inf() + 1.0j) / 0.0)) == 1);
+static_assert(__builtin_isinf_sign(__imag__((1.0 + __builtin_inf() * 1.0j) / 0.0)) == 1);
+static_assert(__builtin_isinf_sign(__imag__((__builtin_inf() + __builtin_inf() * 1.0j) / 0.0)) == 1);
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