From 0197e7db6e71bf3a6c8b860affba4de9fb59cda2 Mon Sep 17 00:00:00 2001
From: Christian Zimmermann <christian.zimmermann@ur.de>
Date: Sun, 6 Nov 2022 22:58:46 +0100
Subject: [PATCH] more on MIndex + operator << for PosTypes

---
 src/include/operation/op_types.cc.h |   1 +
 src/include/ranges/mrange.cc.h      | 232 ++++++++++++++++++----------
 src/include/ranges/mrange.h         |  57 ++++++-
 src/include/ranges/urange.cc.h      |  14 --
 src/include/ranges/urange.h         |   3 -
 src/include/xpr/pos_type.cc.h       |  45 +++++-
 src/include/xpr/pos_type.h          |  31 +++-
 7 files changed, 265 insertions(+), 118 deletions(-)

diff --git a/src/include/operation/op_types.cc.h b/src/include/operation/op_types.cc.h
index 0146c2e..344710a 100644
--- a/src/include/operation/op_types.cc.h
+++ b/src/include/operation/op_types.cc.h
@@ -264,6 +264,7 @@ namespace CNORXZ
     template <class F, class... Ops>
     constexpr decltype(auto) Operation<F,Ops...>::rootSteps(const IndexId<I>& id) const
     {
+	// !!!
 	return mOps.rootSteps(id);
     }
 
diff --git a/src/include/ranges/mrange.cc.h b/src/include/ranges/mrange.cc.h
index 37691ac..7648e7c 100644
--- a/src/include/ranges/mrange.cc.h
+++ b/src/include/ranges/mrange.cc.h
@@ -32,6 +32,13 @@ namespace CNORXZ
     {
 	return f( g(std::get<Is>(mIPack))... );
     }
+    
+    template <class... Indices>
+    template <class G, class F, SizeT... Is>
+    constexpr decltype(auto) MIndex<Indices...>::accumulate2i(const G& g, const F& f, std::index_sequence<Is...> is) const
+    {
+	return f( g(std::get<Is>(mIPack), std::get<Is>(mBlockSizes))... );
+    }
 
     template <class... Indices>
     template <SizeT B, SizeT E, class G, class F>
@@ -40,25 +47,127 @@ namespace CNORXZ
 	return accumulatei(g, f, mkIndexSequence<B,E>())
     }
 
+    template <class... Indices>
+    template <SizeT B, SizeT E, class G, class F>
+    constexpr decltype(auto) MIndex<Indices...>::accumulate2(const G& g, const F& f) const
+    {
+	return accumulate2i(g, f, mkIndexSequence<B,E>())
+    }
+
     template <class... Indices>
     template <SizeT... Is>
-    constexpr decltype(auto) mkIPack(SizeT pos, std::index_sequence<Is...> is) const
+    constexpr decltype(auto) MIndex<Indices...>::mkIPack(SizeT pos, std::index_sequence<Is...> is) const
     {
 	static_assert(sizeof...(Is) == sizeof...(Indices),
 		      "sequence size does not match number of indices");
 	return std::make_tuple( std::make_shared<Indices>( mRange->sub(Is) )... );
+				//, (pos / std::get<Is>(mBlockSizes) ) %  )... );
     }
     
     template <class... Indices>
     template <SizeT... Is>
-    constexpr decltype(auto) mkBlockSizes(std::index_sequence<Is...> is) const
+    inline void MIndex<Indices...>::setIPack(std::index_sequence<Is...> is) const
+    {
+	( (std::get<Is>(mIPack) = (IB::mPos / std::get<Is>(mBlockSize)) % std::get<Is>(mIPack)->max() ),... );
+    }
+    
+    template <class... Indices>
+    template <SizeT... Is>
+    constexpr decltype(auto) MIndex<Indices...>::mkBlockSizes(std::index_sequence<Is...> is) const
     {
 	static_assert(sizeof...(Is) == sizeof...(Indices)-1,
 		      "set lowest block size manually");
-	return Arr<SizeT,sizeof...(Indices)>
-	    { accumulate<Is,sizeof...(Indices)>( [](const auto& i) { return i->max(); },
-						 [](const auto&... as) { return (as * ...); } ),
-	      1 };
+	return std::make_tuple
+	    ( accumulate<Is,sizeof...(Indices)>
+	      ( [](const auto& i) { return i->max(); },
+		[](const auto&... as) { return (as * ...); } )...,
+	      SPos<1>() );
+    }
+
+    template <class... Indices>
+    template <SizeT... Is>
+    constexpr decltype(auto) MIndex<Indices...>::mkPos(std::index_sequence<Is...> is) const
+    {
+	return ( (std::get<Is>(mIPack)*std::get<Is>(mBlockSizes)) + ... );
+    }
+
+    template <class... Indices>
+    template <SizeT I>
+    inline void MIndex<Indices...>::up()
+    {
+	auto& i = std::get<I>(mIPack);
+	if constexpr(I != 0){
+	    if(i->pos() == i->max()-1){
+		IB::mPos -= std::get<I>(mBlockSize) * i->pos();
+		(*i) = 0;
+		upi<N-1>();
+		return;
+	    }
+	}
+	IB::mPos += std::get<I>(mBlockSize);
+	++(*i);
+    }
+
+    template <class... Indices>
+    template <SizeT I>
+    inline void MIndex<Indices...>::down()
+    {
+	auto& i = std::get<I>(mIPack);
+	if constexpr(I != 0){
+	    if(i->pos() == 0){
+		(*i) = i->max()-1;
+		IB::mPos += std::get<I>(mBlockSize) * i->pos();
+		downi<N-1>();
+		return;
+	    }
+	}
+	IB::mPos -= std::get<I>(mBlockSize);
+	--(*i);
+    }
+
+    template <class... Indices>
+    template <SizeT... Is>
+    inline String MIndex<Indices...>::mkStringMeta(std::index_sequence<Is...> is) const
+    {
+	const String blim = "[";
+	const String elim = "]";
+	const String dlim = ",";
+	static_assert(sizeof...(Is) == sizeof...(Indices)-1,
+		      "set last position outside the index pack");
+	if constexpr(sizeof...(Is) == 0){
+	    return blim + std::get<0>(mIPack)->stringMeta() + elim;
+	}
+	else {
+	    return blim +
+		( ( std::get<Is>(mIPack)->stringMeta() + dlim ) + ... +
+		  std::get<sizeof...(Indices)-1>(mIPack)->stringMeta() )
+		+ elim;
+	}
+    }
+
+    template <class... Indices>
+    template <SizeT... Is>
+    inline typename MIndex<Indices...>::MetaType MIndex<Indices...>::mkMeta(std::index_sequence<Is...> is) const
+    {
+	return std::make_tuple( std::get<Is>(mIPack)->meta()... );
+    }
+    
+    template <class... Indices>
+    template <SizeT I, class Xpr, class F>
+    constexpr decltype(auto) MIndex<Indices...>::mkIFor(const Xpr& xpr, F&& f) const
+    {
+	if constexpr(I == sizeof..(Indices)-1){
+	    return std::get<I>(mIPack)->ifor(xpr,f);
+	}
+	else {
+	    return std::get<I>(mIPack)->ifor( mkIFor<I+1>( xpr, f ), f );
+	}
+    }
+
+    template <SizeT... Is>
+    inline void ati(const MetaType& meta, std::index_sequence<Is...> is) const
+    {
+	( std::get<Is>(mIPack)->at( std::get<Is>(meta) ), ... );
     }
 
     /**************
@@ -68,18 +177,19 @@ namespace CNORXZ
     template <class... Indices>
     template <class MRange>
     MIndex<Indices...>::MIndex(const Sptr<MRange>& range, SizeT pos) :
-	IndexInterface<MIndex<Indices...>,Tuple<typename Indices::MetaType...>>(pos),
+	IndexInterface<MIndex<Indices...>,Tuple<typename Indices::MetaType...>>(0),
 	mIPack(mkIPack(IB::mPos, std::make_index_sequence<sizeof...(Indices)>{})),
 	mBlockSizes(mkBlockSizes(IB::mPos), std::make_index_sequence<sizeof...(Indices)>{}),
-	mRange(range)
-    {}
+	mRange(range),
+    {
+	(*this) = pos;
+    }
 
     template <class... Indices>
     MIndex<Indices...>& MIndex<Indices...>::operator()(const Sptr<MIndex>& mi)
     {
-	sfor_pn<0,sizeof...(Indices)>
-	    ( [&](auto i) { std::get<i>(mIPack) = std::get<i>(indices); return 0; } );
-	RangeHelper::setIndexPack<sizeof...(Indices)-1>(mIPack, IB::mPos);
+	mIPack = mi.mIPack;
+	IB::mPos = mkPos(std::make_index_sequence<sizeof...(Indices)>{});
 	return *this;
     }
 
@@ -87,78 +197,47 @@ namespace CNORXZ
     MIndex<Indices...>& MIndex<Indices...>::operator=(SizeT pos)
     {
 	IB::mPos = pos;
-	RangeHelper::setIndexPack<sizeof...(Indices)-1>(mIPack, pos);
+	setIPack(std::make_index_sequence<sizeof...(Indices)>{});
 	return *this;
     }
 
     template <class... Indices>
     MIndex<Indices...>& MIndex<Indices...>::operator++()
     {
-	sfor_m<sizeof...(Indices),0>
-	    ( [&](auto i) {
-		auto& si = *std::get<i>( mIPack );
-		if(si.last() and i != 0) { si = 0; return true; }
-		else { ++si; return false; }
-		return false;
-	    } );
-	++IB::mPos;
+	// End state is defined by high-index being end while all other indices are zero
+	auto& i0 = std::get<0>(mIPack);
+	if(i0->pos() != i0->max()){
+	    up<sizeof...(Indices)-1>();
+	}
 	return *this;
     }
 
     template <class... Indices>
     MIndex<Indices...>& MIndex<Indices...>::operator--()
     {
-	sfor_m<sizeof...(Indices),0>
-	    ( [&](auto i) {
-		auto& si = *std::get<i>( mIPack );
-		if(si.first() and i != 0) { si = si.max()-1; return true; }
-		else { --si; return false; }
-		return false;
-	    } );
-	--IB::mPos;
+	if(IB::mPos != 0){
+	    down<sizeof...(Indices)-1>();
+	}
 	return *this;
     }
 
-
-    template <class... Indices>
-    int MIndex<Indices...>::pp(PtrId idxPtrNum)
-    {
-	const int tmp = RangeHelper::ppx<sizeof...(Indices)-1>(mIPack, mBlockSizes, idxPtrNum);
-	IB::mPos += tmp;
-	return tmp;
-    }
-
-    template <class... Indices>
-    int MIndex<Indices...>::mm(PtrId idxPtrNum)
-    {
-	const int tmp = RangeHelper::mmx<sizeof...(Indices)-1>(mIPack, mBlockSizes, idxPtrNum);
-	IB::mPos -= tmp;
-	return tmp;
-    }
-
     template <class... Indices>
     String MIndex<Indices...>::stringMeta() const
     {
-	return std::dynamic_pointer_cast<RangeType>( IB::mRangePtr )->stringMeta(IB::mPos);
+	return mkStringMeta(std::make_index_sequence<sizeof...(Indices)-1>{});
     }
     
     template <class... Indices>
     typename MIndex<Indices...>::MetaType MIndex<Indices...>::meta() const
     {
-	MetaType metaTuple;
-	sfor_pn<0,sizeof...(Indices)>
-	    ( [&](auto i) { std::get<i>(metaTuple) = std::get<i>(mIPack)->meta(); return 0; } );
-	return metaTuple;
+	return mkMeta(std::make_index_sequence<sizeof...(Indices)>{});
     }
 
     template <class... Indices>
     MIndex<Indices...>& MIndex<Indices...>::at(const MetaType& metaPos)
     {
-	sfor_pn<0,sizeof...(Indices)>
-	    ( [&](auto i) { std::get<i>(mIPack)->at( std::get<i>(metaPos) ); return 0; } );
-	IB::mPos = sfor_m<sizeof...(Indices),0>
-	    ( [&](auto i) { return std::get<i>(mIPack); },
-	      [&](auto a, auto b) {return a->pos() + b*a->max();}, 0 );
+	ati(metaPos, std::make_index_sequence<sizeof...(Indices)>{});
+	IB::mPos = mkPos(std::make_index_sequence<sizeof...(Indices)>{});
 	return *this;
     }
 
@@ -176,22 +255,19 @@ namespace CNORXZ
     }
 
     template <class... Indices>	
-    SizeT MIndex<Indices...>::getStepSize(SizeT n)
+    template <SizeT I>
+    decltype(auto) MIndex<Indices...>::stepSize(const IndexId<I>& id) const;
     {
-	if(n >= sizeof...(Indices)){
-	    assert(0);
-	    // throw !!
-	}
-	return mBlockSizes[n+1];
+	return accumulate2( [](const auto& i, const auto& b) { return i->stepSize(id) * b },
+			    [](const auto&... ss) { return ( ss + ... ); });
     }
-    /*
-    template <class... Indices>
-    template <class Exprs>
-    auto MIndex<Indices...>::ifor(SizeT step, Exprs exs) const
+
+    template <class... Indices>	
+    template <class Xpr, class F>
+    constexpr decltype(auto) MIndex<Indices...>::ifor(const Xpr& xpr, F&& f) const
     {
-	return RangeHelper::mkFor<0>(step, mIPack, mBlockSizes, exs);
+	return mkIFor<0>(xpr, f);
     }
-    */
     
     /*********************
      *   MRangeFactory   *
@@ -256,19 +332,7 @@ namespace CNORXZ
     template <class... Ranges>
     String MRange<Ranges...>::stringMeta(SizeT pos) const
     {
-	
-    }
-
-    template <class... Ranges>
-    IndexType MRange<Ranges...>::begin() const
-    {
-	
-    }
-    
-    template <class... Ranges>
-    IndexType MRange<Ranges...>::end() const
-    {
-
+	return (begin()+pos).stringMeta();
     }
 
     template <class... Ranges>
@@ -280,14 +344,14 @@ namespace CNORXZ
     template <class... Ranges>
     const MetaType MRange<Ranges...>::get(SizeT pos) const
     {
-	
+	return (begin()+pos)->meta();
     }
 
     template <class... Ranges>
     SizeT MRange<Ranges...>::getMeta(const MetaType& metaPos) const
     {
-	assert(0);
-	//return RangeHelper::getMeta<sizeof...(Ranges)-1>(mSpace,metaPos);
+	auto i = begin();
+	return i.at(metaPos).pos();
     }
 
     /************************
diff --git a/src/include/ranges/mrange.h b/src/include/ranges/mrange.h
index 1a7cb3a..074a074 100644
--- a/src/include/ranges/mrange.h
+++ b/src/include/ranges/mrange.h
@@ -52,9 +52,6 @@ namespace CNORXZ
 	SizeT operator*() const;
 	SizeT operator->() const;
 
-	int pp(PtrId idxPtrNum);
-	int mm(PtrId idxPtrNum);
-
 	SizeT dim();
 	Sptr<RangeType> range();
 
@@ -66,13 +63,15 @@ namespace CNORXZ
 	MIndex& at(const MetaType& metaPos);
 
 	template <class Xpr, class F>
-	decltype(auto) ifor(const Xpr& xpr, F&& f) const;
+	constexpr decltype(auto) ifor(const Xpr& xpr, F&& f) const;
 
     private:
 	MIndex() = default;
 	
 	IndexPack mIPack;
-	Arr<SizeT,sizeof...(Indices)> mBlockSizes;
+	//Arr<SizeT,sizeof...(Indices)> mBlockSizes;
+	typedef decltype(mkBlockSizes(std::make_index_sequence<sizeof...(Indices)-1>{})) BlockTuple;
+	BlockTuple mBlockSizes;
 	Sptr<RangeType> mRange;
 
 	// shift to utils:
@@ -87,16 +86,64 @@ namespace CNORXZ
 	template <class G, class F, SizeT... Is>
 	constexpr decltype(auto) accumulatei(const G& g, const F& f, std::index_sequence<Is...> is) const;
 
+	template <class G, class F, SizeT... Is>
+	constexpr decltype(auto) accumulate2i(const G& g, const F& f, std::index_sequence<Is...> is) const;
+
 	template <SizeT B, SizeT E, class G, class F>
 	constexpr decltype(auto) accumulate(const G& g, const F& f) const;
 
+	template <SizeT B, SizeT E, class G, class F>
+	constexpr decltype(auto) accumulate2(const G& g, const F& f) const;
+
 	template <SizeT... Is>
 	constexpr decltype(auto) mkIPack(SizeT pos, std::index_sequence<Is...> is) const;
 
+	template <SizeT... Is>
+	inline void setIPack(std::index_sequence<Is...> is) const;
+
 	template <SizeT... Is>
 	constexpr decltype(auto) mkBlockSizes(std::index_sequence<Is...> is) const;
+
+	template <SizeT... Is>
+	constexpr decltype(auto) mkPos(std::index_sequence<Is...> is) const;
+
+	template <SizeT I>
+	inline void up();
+
+	template <SizeT I>
+	inline void down();
+
+	template <SizeT... Is>
+	inline String mkStringMeta(std::index_sequence<Is...> is) const;
+
+	template <SizeT... Is>
+	inline MetaType mkMeta(std::index_sequence<Is...> is) const;
+
+	template <SizeT I, class Xpr, class F>
+	constexpr decltype(auto) mkIFor(const Xpr& xpr, F&& f) const;
+
+	template <SizeT... Is>
+	inline void ati(const MetaType& meta, std::index_sequence<Is...> is) const;
     };
 
+    // modified blockSizes; to be used for Slices; can be created from MIndices
+    template <class MIndexType, class BlockType>
+    class GMIndex : public MIndexType
+    {
+    public:
+	// override everything that modyfies IB::mPos or uses mBlockSizes!!!
+	
+	constexpr GMIndex(const MIndexType& mi, const BlockType& b);
+	
+	template <class Xpr, class F>
+	constexpr decltype(auto) ifor(const Xpr& xpr, F&& f) const;
+
+    private:
+	BlockType mBlockSizes;
+
+	template <SizeT... Is>
+	constexpr decltype(auto) mkPos(std::index_sequence<Is...> is) const;
+    };
 
     // NOT THREAD SAVE
     template <class... Ranges>
diff --git a/src/include/ranges/urange.cc.h b/src/include/ranges/urange.cc.h
index 746da68..897e836 100644
--- a/src/include/ranges/urange.cc.h
+++ b/src/include/ranges/urange.cc.h
@@ -92,20 +92,6 @@ namespace CNORXZ
 	return mMetaPtr + IB::mPos;
     }
 	
-    template <typename MetaType>
-    Int UIndex<MetaType>::pp(PtrId idxPtrNum)
-    {
-	++(*this);
-	return 1;
-    }
-
-    template <typename MetaType>
-    Int UIndex<MetaType>::mm(PtrId idxPtrNum)
-    {
-	--(*this);
-	return 1;
-    }
-
     template <typename MetaType>
     String UIndex<MetaType>::stringMeta() const
     {
diff --git a/src/include/ranges/urange.h b/src/include/ranges/urange.h
index 939665c..4798c56 100644
--- a/src/include/ranges/urange.h
+++ b/src/include/ranges/urange.h
@@ -35,9 +35,6 @@ namespace CNORXZ
 	const MetaType& operator*() const;
 	const MetaType* operator->() const;
 	
-	Int pp(PtrId idxPtrNum);
-	Int mm(PtrId idxPtrNum);
-
 	SizeT dim() const; // = 1
 	Sptr<RangeType> range() const;
 
diff --git a/src/include/xpr/pos_type.cc.h b/src/include/xpr/pos_type.cc.h
index c635180..db8c28d 100644
--- a/src/include/xpr/pos_type.cc.h
+++ b/src/include/xpr/pos_type.cc.h
@@ -65,11 +65,18 @@ namespace CNORXZ
 
     template <SizeT N>
     template <class PosT>
-    constexpr auto SPos<N>::extend(const PosT& a) const
+    constexpr decltype(auto) SPos<N>::extend(const PosT& a) const
     {
 	return MPos<SPos<N>,PosT>(*this,a);
     }
 
+    template <SizeT N>
+    template <class PosT>
+    constexpr decltype(auto) SPos<N>::operator<<(const PosT& a) const
+    {
+	return extend(a);
+    }
+
     template <SizeT N>
     constexpr SPos<N>::operator UPos() const
     {
@@ -121,11 +128,17 @@ namespace CNORXZ
     }
 	
     template <class PosT>
-    constexpr auto UPos::extend(const PosT& p1) const
+    constexpr decltype(auto) UPos::extend(const PosT& p1) const
     {
 	return MPos<UPos,PosT>(*this, p1);
     }
 
+    template <class PosT>
+    constexpr decltype(auto) UPos::operator<<(const PosT& a) const
+    {
+	return extend(a);
+    }
+    
     /************
      *   FPos   *
      ************/
@@ -160,12 +173,18 @@ namespace CNORXZ
 	return UPos(mExt * mMap[a.val()]);
     }
 
-    template <class PosT1>
-    constexpr auto FPos::extend(const PosT1& a) const
+    template <class PosT>
+    constexpr decltype(auto) FPos::extend(const PosT& a) const
     {
 	return MPos<FPos,PosT1>(*this,a);
     }
 
+    template <class PosT>
+    constexpr decltype(auto) FPos::operator<<(const PosT& a) const
+    {
+	return extend(a);
+    }
+
     /*************
      *   SFPos   *
      *************/
@@ -228,11 +247,18 @@ namespace CNORXZ
 
     template <SizeT N, SizeT... Ms>
     template <class PosT>
-    constexpr auto SFPos<N,Ms...>::extend(const PosT& a) const
+    constexpr decltype(auto) SFPos<N,Ms...>::extend(const PosT& a) const
     {
 	return MPos<SFPos<N,Ms...>,PosT>(*this,a);
     }
 
+    template <SizeT N, SizeT... Ms>
+    template <class PosT>
+    constexpr decltype(auto) SFPos<N,Ms...>::operator<<(const PosT& a) const
+    {
+	return extend(a);
+    }
+
     template <SizeT N, SizeT... Ms>
     constexpr SFPos<N,Ms...>::operator FPos() const
     {
@@ -317,12 +343,19 @@ namespace CNORXZ
 	
     template <class BPosT, class NPosT>
     template <class PosT>
-    constexpr auto MPos<BPosT,NPosT>::extend(const PosT& a) const
+    constexpr decltype(auto) MPos<BPosT,NPosT>::extend(const PosT& a) const
     {
 	typedef decltype(mNext.extend(a)) ONPosT;
 	return MPos<BPosT,ONPosT>(*this, mNext.extend(a));
     }
 
+    template <class BPosT, class NPosT>
+    template <class PosT>
+    constexpr decltype(auto) MPos<BPosT,NPosT>::operator<<(const PosT& a) const
+    {
+	return extend(a);
+    }
+    
     /************
      *   DPos   *
      ************/
diff --git a/src/include/xpr/pos_type.h b/src/include/xpr/pos_type.h
index 152fbd4..de1e367 100644
--- a/src/include/xpr/pos_type.h
+++ b/src/include/xpr/pos_type.h
@@ -30,8 +30,11 @@ namespace CNORXZ
 	constexpr auto operator()(const UPos& a) const;
 	
 	template <class PosT>
-	constexpr auto extend(const PosT& a) const;
+	constexpr decltype(auto) extend(const PosT& a) const;
 
+	template <class PosT>
+	constexpr decltype(auto) operator<<(const PosT& a) const;
+	
 	explicit constexpr operator UPos() const;
     };
 
@@ -61,8 +64,10 @@ namespace CNORXZ
 	constexpr UPos operator()(const PosT& a) const;
 
         template <class PosT>
-        constexpr auto extend(const PosT& a) const;
+        constexpr decltype(auto) extend(const PosT& a) const;
 
+	template <class PosT>
+	constexpr decltype(auto) operator<<(const PosT& a) const;
     };
 
     class FPos
@@ -88,9 +93,11 @@ namespace CNORXZ
 	template <class PosT>
 	constexpr UPos operator()(const PosT& a) const;
 
-	template <class PosT1>
-	constexpr auto extend(const PosT1& a) const;
+	template <class PosT>
+	constexpr decltype(auto) extend(const PosT& a) const;
 
+	template <class PosT>
+	constexpr decltype(auto) operator<<(const PosT& a) const;
     };
 
     template <SizeT N, SizeT... Ms>
@@ -116,7 +123,10 @@ namespace CNORXZ
 	constexpr auto operator()(const UPos& a) const;
 
 	template <class PosT>
-	constexpr auto extend(const PosT& a) const;
+	constexpr decltype(auto) extend(const PosT& a) const;
+
+	template <class PosT>
+	constexpr decltype(auto) operator<<(const PosT& a) const;
 
 	explicit constexpr operator FPos() const;
     };
@@ -151,7 +161,10 @@ namespace CNORXZ
 	constexpr auto operator()(const PosT& a) const;
 	
 	template <class PosT>
-	constexpr auto extend(const PosT& a) const;
+	constexpr decltype(auto) extend(const PosT& a) const;
+
+	template <class PosT>
+	constexpr decltype(auto) operator<<(const PosT& a) const;
     };
 
     // treat as scalar pos!!!
@@ -188,6 +201,9 @@ namespace CNORXZ
 	
 	template <class PosT>
 	inline decltype(auto) extend(const PosT& a) const;
+
+	template <class PosT>
+	inline decltype(auto) operator<<(const PosT& a) const;
     };
 
     class DPosRef
@@ -219,6 +235,9 @@ namespace CNORXZ
 	
 	template <class PosT>
 	inline decltype(auto) extend(const PosT& a) const;
+
+	template <class PosT>
+	inline decltype(auto) operator<<(const PosT& a) const;
     };
 
     // for common call of extension vector elements