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[RISCV][CostModel] Estimate cost of llvm.vector.reduce.fmaximum/fminimum #80697

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arcbbb merged 3 commits into from
Mar 25, 2024
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[RISCV][CostModel] Estimate cost of llvm.vector.reduce.fmaximum/fminimum #80697

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[RISCV][CostModel] Estimate cost of llvm.vector.reduce.fmaximum/fminimum
arcbbb Feb 5, 2024
00bd3c2
Address comments
arcbbb Mar 20, 2024
145c3bb
Use getScalarSizeInBits
arcbbb Mar 21, 2024
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36 changes: 17 additions & 19 deletions llvm/lib/Target/RISCV/RISCVTargetTransformInfo.cpp
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Expand Up @@ -1002,50 +1002,48 @@ RISCVTTIImpl::getMinMaxReductionCost(Intrinsic::ID IID, VectorType *Ty,
}

if (IID == Intrinsic::maximum || IID == Intrinsic::minimum) {
SmallVector<unsigned, 5> SplitOps;
SmallVector<unsigned, 3> Opcodes;
InstructionCost ExtraCost = 0;
switch (IID) {
case Intrinsic::maximum:
if (FMF.noNaNs()) {
SplitOps = {RISCV::VFMAX_VV};
Opcodes = {RISCV::VFREDMAX_VS, RISCV::VFMV_F_S};
} else {
SplitOps = {RISCV::VMFEQ_VV, RISCV::VMERGE_VVM, RISCV::VMFEQ_VV,
RISCV::VMERGE_VVM, RISCV::VFMAX_VV};
Opcodes = {RISCV::VMFNE_VV, RISCV::VCPOP_M, RISCV::VFREDMAX_VS,
RISCV::VFMV_F_S};
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@preames preames Mar 15, 2024

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You're missing the cost of the scalar select here.

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@arcbbb arcbbb Mar 20, 2024

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Fixed with getCFInstrCost.

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@lukel97 lukel97 Mar 21, 2024

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Worth noting that we assume branches are predicted so getCFInstrCost(Instruction::Br, CostKind) will return 0 for throughput

// Cost of Canonical Nan
// Cost of Canonical Nan + branch
// lui a0, 523264
// fmv.w.x fa0, a0
ExtraCost = 2;
Type *DstTy = Ty->getScalarType();
const unsigned EltTyBits = DL.getTypeSizeInBits(DstTy);
Type *SrcTy = IntegerType::getIntNTy(DstTy->getContext(), EltTyBits);
ExtraCost = 1 +
getCastInstrCost(Instruction::UIToFP, DstTy, SrcTy,
TTI::CastContextHint::None, CostKind) +
getCFInstrCost(Instruction::Br, CostKind);
}
break;

case Intrinsic::minimum:
if (FMF.noNaNs()) {
SplitOps = {RISCV::VFMIN_VV};
Opcodes = {RISCV::VFREDMIN_VS, RISCV::VFMV_F_S};
} else {
SplitOps = {RISCV::VMFEQ_VV, RISCV::VMERGE_VVM, RISCV::VMFEQ_VV,
RISCV::VMERGE_VVM, RISCV::VFMIN_VV};
Opcodes = {RISCV::VMFNE_VV, RISCV::VCPOP_M, RISCV::VFREDMIN_VS,
RISCV::VFMV_F_S};
// Cost of Canonical Nan
// Cost of Canonical Nan + branch
// lui a0, 523264
// fmv.w.x fa0, a0
ExtraCost = 2;
Type *DstTy = Ty->getScalarType();
const unsigned EltTyBits = DL.getTypeSizeInBits(DstTy);
Comment on lines +1036 to +1037
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@lukel97 lukel97 Mar 21, 2024

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Nit, I think Ty->getScalarSizeInBits() does the same thing

Type *SrcTy = IntegerType::getIntNTy(DstTy->getContext(), EltTyBits);
ExtraCost = 1 +
getCastInstrCost(Instruction::UIToFP, DstTy, SrcTy,
TTI::CastContextHint::None, CostKind) +
getCFInstrCost(Instruction::Br, CostKind);
}
break;
}
// Add a cost for data larger than LMUL8
InstructionCost SplitCost =
(LT.first > 1)
? (LT.first - 1) *
getRISCVInstructionCost(SplitOps, LT.second, CostKind)
: 0;
return ExtraCost + SplitCost +
getRISCVInstructionCost(Opcodes, LT.second, CostKind);
return ExtraCost + getRISCVInstructionCost(Opcodes, LT.second, CostKind);
}

// IR Reduction is composed by two vmv and one rvv reduction instruction.
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38 changes: 19 additions & 19 deletions llvm/test/Analysis/CostModel/RISCV/reduce-fmaximum.ll
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Expand Up @@ -12,31 +12,31 @@ define float @reduce_fmaximum_f32(float %arg) {
; CHECK-NEXT: Cost Model: Found an estimated cost of 10 for instruction: %V16 = call float @llvm.vector.reduce.fmaximum.v16f32(<16 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 13 for instruction: %V32 = call float @llvm.vector.reduce.fmaximum.v32f32(<32 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 18 for instruction: %V64 = call float @llvm.vector.reduce.fmaximum.v64f32(<64 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 58 for instruction: %V128 = call float @llvm.vector.reduce.fmaximum.v128f32(<128 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 18 for instruction: %V128 = call float @llvm.vector.reduce.fmaximum.v128f32(<128 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 2 for instruction: %1 = call fast float @llvm.vector.reduce.fmaximum.v2f32(<2 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 3 for instruction: %2 = call fast float @llvm.vector.reduce.fmaximum.v4f32(<4 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 4 for instruction: %3 = call fast float @llvm.vector.reduce.fmaximum.v8f32(<8 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 5 for instruction: %4 = call fast float @llvm.vector.reduce.fmaximum.v16f32(<16 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %5 = call fast float @llvm.vector.reduce.fmaximum.v32f32(<32 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %6 = call fast float @llvm.vector.reduce.fmaximum.v64f32(<64 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 15 for instruction: %7 = call fast float @llvm.vector.reduce.fmaximum.v128f32(<128 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %7 = call fast float @llvm.vector.reduce.fmaximum.v128f32(<128 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 0 for instruction: ret float undef
;
; SIZE-LABEL: 'reduce_fmaximum_f32'
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V2 = call float @llvm.vector.reduce.fmaximum.v2f32(<2 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V4 = call float @llvm.vector.reduce.fmaximum.v4f32(<4 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V8 = call float @llvm.vector.reduce.fmaximum.v8f32(<8 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V16 = call float @llvm.vector.reduce.fmaximum.v16f32(<16 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V32 = call float @llvm.vector.reduce.fmaximum.v32f32(<32 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V64 = call float @llvm.vector.reduce.fmaximum.v64f32(<64 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 11 for instruction: %V128 = call float @llvm.vector.reduce.fmaximum.v128f32(<128 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V2 = call float @llvm.vector.reduce.fmaximum.v2f32(<2 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V4 = call float @llvm.vector.reduce.fmaximum.v4f32(<4 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V8 = call float @llvm.vector.reduce.fmaximum.v8f32(<8 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V16 = call float @llvm.vector.reduce.fmaximum.v16f32(<16 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V32 = call float @llvm.vector.reduce.fmaximum.v32f32(<32 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V64 = call float @llvm.vector.reduce.fmaximum.v64f32(<64 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V128 = call float @llvm.vector.reduce.fmaximum.v128f32(<128 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 2 for instruction: %1 = call fast float @llvm.vector.reduce.fmaximum.v2f32(<2 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 2 for instruction: %2 = call fast float @llvm.vector.reduce.fmaximum.v4f32(<4 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 2 for instruction: %3 = call fast float @llvm.vector.reduce.fmaximum.v8f32(<8 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 2 for instruction: %4 = call fast float @llvm.vector.reduce.fmaximum.v16f32(<16 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 2 for instruction: %5 = call fast float @llvm.vector.reduce.fmaximum.v32f32(<32 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 2 for instruction: %6 = call fast float @llvm.vector.reduce.fmaximum.v64f32(<64 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 3 for instruction: %7 = call fast float @llvm.vector.reduce.fmaximum.v128f32(<128 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 2 for instruction: %7 = call fast float @llvm.vector.reduce.fmaximum.v128f32(<128 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 1 for instruction: ret float undef
;
%V2 = call float @llvm.vector.reduce.fmaximum.v2f32(<2 x float> undef)
Expand Down Expand Up @@ -70,28 +70,28 @@ define double @reduce_fmaximum_f64(double %arg) {
; CHECK-NEXT: Cost Model: Found an estimated cost of 9 for instruction: %V8 = call double @llvm.vector.reduce.fmaximum.v8f64(<8 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 12 for instruction: %V16 = call double @llvm.vector.reduce.fmaximum.v16f64(<16 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 17 for instruction: %V32 = call double @llvm.vector.reduce.fmaximum.v32f64(<32 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 57 for instruction: %V64 = call double @llvm.vector.reduce.fmaximum.v64f64(<64 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 17 for instruction: %V64 = call double @llvm.vector.reduce.fmaximum.v64f64(<64 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 2 for instruction: %1 = call fast double @llvm.vector.reduce.fmaximum.v2f64(<2 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 3 for instruction: %2 = call fast double @llvm.vector.reduce.fmaximum.v4f64(<4 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 4 for instruction: %3 = call fast double @llvm.vector.reduce.fmaximum.v8f64(<8 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 5 for instruction: %4 = call fast double @llvm.vector.reduce.fmaximum.v16f64(<16 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %5 = call fast double @llvm.vector.reduce.fmaximum.v32f64(<32 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 14 for instruction: %6 = call fast double @llvm.vector.reduce.fmaximum.v64f64(<64 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %6 = call fast double @llvm.vector.reduce.fmaximum.v64f64(<64 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 0 for instruction: ret double undef
;
; SIZE-LABEL: 'reduce_fmaximum_f64'
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V2 = call double @llvm.vector.reduce.fmaximum.v2f64(<2 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V4 = call double @llvm.vector.reduce.fmaximum.v4f64(<4 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V8 = call double @llvm.vector.reduce.fmaximum.v8f64(<8 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V16 = call double @llvm.vector.reduce.fmaximum.v16f64(<16 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V32 = call double @llvm.vector.reduce.fmaximum.v32f64(<32 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 11 for instruction: %V64 = call double @llvm.vector.reduce.fmaximum.v64f64(<64 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V2 = call double @llvm.vector.reduce.fmaximum.v2f64(<2 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V4 = call double @llvm.vector.reduce.fmaximum.v4f64(<4 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V8 = call double @llvm.vector.reduce.fmaximum.v8f64(<8 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V16 = call double @llvm.vector.reduce.fmaximum.v16f64(<16 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V32 = call double @llvm.vector.reduce.fmaximum.v32f64(<32 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V64 = call double @llvm.vector.reduce.fmaximum.v64f64(<64 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 2 for instruction: %1 = call fast double @llvm.vector.reduce.fmaximum.v2f64(<2 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 2 for instruction: %2 = call fast double @llvm.vector.reduce.fmaximum.v4f64(<4 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 2 for instruction: %3 = call fast double @llvm.vector.reduce.fmaximum.v8f64(<8 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 2 for instruction: %4 = call fast double @llvm.vector.reduce.fmaximum.v16f64(<16 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 2 for instruction: %5 = call fast double @llvm.vector.reduce.fmaximum.v32f64(<32 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 3 for instruction: %6 = call fast double @llvm.vector.reduce.fmaximum.v64f64(<64 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 2 for instruction: %6 = call fast double @llvm.vector.reduce.fmaximum.v64f64(<64 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 1 for instruction: ret double undef
;
%V2 = call double @llvm.vector.reduce.fmaximum.v2f64(<2 x double> undef)
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30 changes: 15 additions & 15 deletions llvm/test/Analysis/CostModel/RISCV/reduce-fminimum.ll
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Expand Up @@ -12,17 +12,17 @@ define float @reduce_fmaximum_f32(float %arg) {
; CHECK-NEXT: Cost Model: Found an estimated cost of 10 for instruction: %V16 = call float @llvm.vector.reduce.fminimum.v16f32(<16 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 13 for instruction: %V32 = call float @llvm.vector.reduce.fminimum.v32f32(<32 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 18 for instruction: %V64 = call float @llvm.vector.reduce.fminimum.v64f32(<64 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 58 for instruction: %V128 = call float @llvm.vector.reduce.fminimum.v128f32(<128 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 18 for instruction: %V128 = call float @llvm.vector.reduce.fminimum.v128f32(<128 x float> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 0 for instruction: ret float undef
;
; SIZE-LABEL: 'reduce_fmaximum_f32'
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V2 = call float @llvm.vector.reduce.fminimum.v2f32(<2 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V4 = call float @llvm.vector.reduce.fminimum.v4f32(<4 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V8 = call float @llvm.vector.reduce.fminimum.v8f32(<8 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V16 = call float @llvm.vector.reduce.fminimum.v16f32(<16 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V32 = call float @llvm.vector.reduce.fminimum.v32f32(<32 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V64 = call float @llvm.vector.reduce.fminimum.v64f32(<64 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 11 for instruction: %V128 = call float @llvm.vector.reduce.fminimum.v128f32(<128 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V2 = call float @llvm.vector.reduce.fminimum.v2f32(<2 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V4 = call float @llvm.vector.reduce.fminimum.v4f32(<4 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V8 = call float @llvm.vector.reduce.fminimum.v8f32(<8 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V16 = call float @llvm.vector.reduce.fminimum.v16f32(<16 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V32 = call float @llvm.vector.reduce.fminimum.v32f32(<32 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V64 = call float @llvm.vector.reduce.fminimum.v64f32(<64 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V128 = call float @llvm.vector.reduce.fminimum.v128f32(<128 x float> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 1 for instruction: ret float undef
;
%V2 = call float @llvm.vector.reduce.fminimum.v2f32(<2 x float> undef)
Expand All @@ -49,16 +49,16 @@ define double @reduce_fmaximum_f64(double %arg) {
; CHECK-NEXT: Cost Model: Found an estimated cost of 9 for instruction: %V8 = call double @llvm.vector.reduce.fminimum.v8f64(<8 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 12 for instruction: %V16 = call double @llvm.vector.reduce.fminimum.v16f64(<16 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 17 for instruction: %V32 = call double @llvm.vector.reduce.fminimum.v32f64(<32 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 57 for instruction: %V64 = call double @llvm.vector.reduce.fminimum.v64f64(<64 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 17 for instruction: %V64 = call double @llvm.vector.reduce.fminimum.v64f64(<64 x double> undef)
; CHECK-NEXT: Cost Model: Found an estimated cost of 0 for instruction: ret double undef
;
; SIZE-LABEL: 'reduce_fmaximum_f64'
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V2 = call double @llvm.vector.reduce.fminimum.v2f64(<2 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V4 = call double @llvm.vector.reduce.fminimum.v4f64(<4 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V8 = call double @llvm.vector.reduce.fminimum.v8f64(<8 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V16 = call double @llvm.vector.reduce.fminimum.v16f64(<16 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 6 for instruction: %V32 = call double @llvm.vector.reduce.fminimum.v32f64(<32 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 11 for instruction: %V64 = call double @llvm.vector.reduce.fminimum.v64f64(<64 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V2 = call double @llvm.vector.reduce.fminimum.v2f64(<2 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V4 = call double @llvm.vector.reduce.fminimum.v4f64(<4 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V8 = call double @llvm.vector.reduce.fminimum.v8f64(<8 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V16 = call double @llvm.vector.reduce.fminimum.v16f64(<16 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V32 = call double @llvm.vector.reduce.fminimum.v32f64(<32 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 7 for instruction: %V64 = call double @llvm.vector.reduce.fminimum.v64f64(<64 x double> undef)
; SIZE-NEXT: Cost Model: Found an estimated cost of 1 for instruction: ret double undef
;
%V2 = call double @llvm.vector.reduce.fminimum.v2f64(<2 x double> undef)
Expand Down