From 2f5f29f577ae7cc21b2ae5473cea7f0d5ff35997 Mon Sep 17 00:00:00 2001
From: Christian Zimmermann <christian.zimmermann@ur.de>
Date: Sun, 20 Nov 2022 23:18:58 +0100
Subject: [PATCH] mrange: different members for blockSizes and lexBlockSizes

---
 src/include/base/types.h        |   7 +-
 src/include/ranges/crange.cc.h  |   2 +-
 src/include/ranges/crange.h     |   4 +-
 src/include/ranges/dindex.h     |   4 +-
 src/include/ranges/index_base.h |   4 +-
 src/include/ranges/mrange.cc.h  | 282 ++++++++++++++++++++------------
 src/include/ranges/mrange.h     |  90 +++++-----
 src/include/ranges/urange.cc.h  |  10 +-
 src/include/ranges/urange.h     |   4 +-
 src/include/ranges/xindex.cc.h  |   8 +-
 src/include/ranges/xindex.h     |   8 +-
 src/include/ranges/yrange.h     |   8 +-
 src/include/xpr/pos_type.cc.h   |  34 +++-
 src/include/xpr/pos_type.h      |  11 ++
 src/lib/ranges/crange.cc        |   8 +-
 src/lib/ranges/dindex.cc        |   4 +-
 src/lib/ranges/yrange.cc        |  39 ++---
 src/tests/range_unit_test.cc    |  12 +-
 18 files changed, 326 insertions(+), 213 deletions(-)

diff --git a/src/include/base/types.h b/src/include/base/types.h
index 57d9b4e..74601db 100644
--- a/src/include/base/types.h
+++ b/src/include/base/types.h
@@ -82,6 +82,9 @@ namespace CNORXZ
 	B = (mutable) Array
 	F = Functional, Map,...
      ***/
+
+    // default template parameter
+    class None {};
     
     // definition: base/dtype.h
     class DType;
@@ -174,8 +177,8 @@ namespace CNORXZ
     class MRange; // multi range
 
     // definition: ranges/mrange.h
-    template <class... Indices>
-    class MIndex;
+    template <class BlockType, class... Indices>
+    class GMIndex;
 
     // definition: ranges/xindex.h
     class XIndexBase; // dynamic index wrapper
diff --git a/src/include/ranges/crange.cc.h b/src/include/ranges/crange.cc.h
index 63b344e..c078f22 100644
--- a/src/include/ranges/crange.cc.h
+++ b/src/include/ranges/crange.cc.h
@@ -9,7 +9,7 @@ namespace CNORXZ
     template <class Xpr, class F>
     decltype(auto) CIndex::ifor(const Xpr& xpr, F&& f) const
     {
-	return For<0,Xpr,F>(this->pmax(), this->id(), xpr, std::forward<F>(f));
+	return For<0,Xpr,F>(this->pmax().val(), this->id(), xpr, std::forward<F>(f));
     }
 }
 
diff --git a/src/include/ranges/crange.h b/src/include/ranges/crange.h
index eb49167..b74cf6a 100644
--- a/src/include/ranges/crange.h
+++ b/src/include/ranges/crange.h
@@ -28,8 +28,8 @@ namespace CNORXZ
 	CIndex& operator-=(Int n);
 
 	SizeT lex() const;
-	SizeT pmax() const;
-	SizeT lmax() const;
+	UPos pmax() const;
+	UPos lmax() const;
 	IndexId<0> id() const;
 	
 	SizeT operator*() const;
diff --git a/src/include/ranges/dindex.h b/src/include/ranges/dindex.h
index 16e42c3..be0e785 100644
--- a/src/include/ranges/dindex.h
+++ b/src/include/ranges/dindex.h
@@ -33,8 +33,8 @@ namespace CNORXZ
 	DIndex& operator-=(Int n);
 
 	SizeT lex() const;
-	SizeT pmax() const;
-	SizeT lmax() const;
+	UPos pmax() const;
+	UPos lmax() const;
 	IndexId<0> id() const;
 	
 	DType operator*() const;
diff --git a/src/include/ranges/index_base.h b/src/include/ranges/index_base.h
index 6e2fe8c..de56d77 100644
--- a/src/include/ranges/index_base.h
+++ b/src/include/ranges/index_base.h
@@ -30,8 +30,8 @@ namespace CNORXZ
 	
 	SizeT pos() const; // 'memory' pos
 	SizeT lex() const { return THIS().lex(); } // lexicographic pos
-	SizeT pmax() const { return THIS().pmax(); } // memory pos max
-	SizeT lmax() const { return THIS().lmax(); } // lexicographic pos max
+	SizeT pmax() const { return static_cast<SizeT>(THIS().pmax()); } // memory pos max
+	SizeT lmax() const { return static_cast<SizeT>(THIS().lmax()); } // lexicographic pos max
 	PtrId ptrId() const;
 	decltype(auto) id() const { return THIS().id(); }
 
diff --git a/src/include/ranges/mrange.cc.h b/src/include/ranges/mrange.cc.h
index 48fc971..4f5664d 100644
--- a/src/include/ranges/mrange.cc.h
+++ b/src/include/ranges/mrange.cc.h
@@ -6,13 +6,13 @@
 
 namespace CNORXZ
 {
-    /***********************
-     *   MIndex (private)  *
-     ***********************/
+    /************************
+     *   GMIndex (private)  *
+     ************************/
 
-    template <class... Indices>
+    template <class BlockType, class... Indices>
     template <SizeT... Is>
-    constexpr decltype(auto) MIndex<Indices...>::mkIPack(Isq<Is...> is) const
+    constexpr decltype(auto) GMIndex<BlockType,Indices...>::mkIPack(Isq<Is...> is) const
     {
 	static_assert(sizeof...(Is) == NI,
 		      "sequence sioze does not match number of indices");
@@ -20,56 +20,88 @@ namespace CNORXZ
 		    "subranges not available" );
 	return std::make_tuple( std::make_shared<Indices>( mRange->sub(Is) )... );
     }
-    
-    template <class... Indices>
+
+    template <class BlockType, class... Indices>
+    constexpr decltype(auto) GMIndex<BlockType,Indices...>::mkLMax(const IndexPack& ipack)
+    {
+	return iter<0,NI>( [&](auto i) { return std::get<i>(ipack)->lmax(); },
+			   [](auto... e) { return (e * ...); });
+    }
+
+    template <class BlockType, class... Indices>
+    constexpr decltype(auto) GMIndex<BlockType,Indices...>::mkPMax(const IndexPack& ipack, const BlockType& blockSizes)
+    {
+	if constexpr(std::is_same<BlockType,None>::value){
+	    return mkLMax(ipack);
+	}
+	else {
+	    return iter<0,NI>
+		( [&](auto i)
+		{ return (std::get<i>(ipack)->pmax() - SPos<1>()) * std::get<i>(blockSizes); },
+		    [](auto... e) { return (e + ...); }) + SPos<1>();
+	}
+    }
+
+    template <class BlockType, class... Indices>
     template <SizeT... Is>
-    constexpr decltype(auto) MIndex<Indices...>::mkBlockSizes(const IndexPack& ipack, Isq<Is...> is)
+    constexpr decltype(auto) GMIndex<BlockType,Indices...>::mkLexBlockSizes(const IndexPack& ipack, Isq<Is...> is)
     {
 	return std::make_tuple
 	    ( iter<Is,NI>
-	      // replace UPos by SPos where possible !!!
-	      ( [&](auto i) { return UPos(std::get<i>(ipack)->pmax()); },
+	      ( [&](auto i) { return std::get<i>(ipack)->pmax(); },
 		[&](const auto&... as) { return (as * ...); } )...,
 	      SPos<1>() );
     }
 
-    template <class... Indices>
+    template <class BlockType, class... Indices>
     template <SizeT I>
-    inline void MIndex<Indices...>::up()
+    inline void GMIndex<BlockType,Indices...>::up()
     {
 	auto& i = std::get<I>(mIPack);
 	if constexpr(I != 0){
-	    if(i->lex() == i->lmax()-1){
-		IB::mPos -= std::get<I>(mBlockSizes).val() * i->pos();
+	    if(i->lex() == i->lmax().val()-1){
+		IB::mPos -= std::get<I>(blockSizes()).val() * i->pos();
+		if constexpr(not std::is_same<BlockType,None>::value){
+		    mLex -= std::get<I>(lexBlockSizes()).val() * i->lex();
+		}
 		(*i) = 0;
 		up<I-1>();
 		return;
 	    }
 	}
-	IB::mPos += std::get<I>(mBlockSizes).val();
+	IB::mPos += std::get<I>(blockSizes()).val();
+	if constexpr(not std::is_same<BlockType,None>::value){
+	    mLex += std::get<I>(lexBlockSizes()).val();
+	}
 	++(*i);
     }
 
-    template <class... Indices>
+    template <class BlockType, class... Indices>
     template <SizeT I>
-    inline void MIndex<Indices...>::down()
+    inline void GMIndex<BlockType,Indices...>::down()
     {
 	auto& i = std::get<I>(mIPack);
 	if constexpr(I != 0){
 	    if(i->lex() == 0){
-		(*i) = i->lmax()-1;
-		IB::mPos += std::get<I>(mBlockSizes).val() * i->pos();
+		(*i) = i->lmax().val()-1;
+		IB::mPos += std::get<I>(blockSizes()).val() * i->pos();
+		if constexpr(not std::is_same<BlockType,None>::value){
+		    mLex += std::get<I>(lexBlockSizes()).val() * i->lex();
+		}
 		down<I-1>();
 		return;
 	    }
 	}
-	IB::mPos -= std::get<I>(mBlockSizes).val();
+	IB::mPos -= std::get<I>(blockSizes()).val();
+	if constexpr(not std::is_same<BlockType,None>::value){
+	    mLex -= std::get<I>(lexBlockSizes()).val();
+	}
 	--(*i);
     }
 
-    template <class... Indices>
+    template <class BlockType, class... Indices>
     template <SizeT I, class Xpr, class F>
-    constexpr decltype(auto) MIndex<Indices...>::mkIFor(const Xpr& xpr, F&& f) const
+    constexpr decltype(auto) GMIndex<BlockType,Indices...>::mkIFor(const Xpr& xpr, F&& f) const
     {
 	if constexpr(I == sizeof...(Indices)-1){
 	    return std::get<I>(mIPack)->ifor(xpr,f);
@@ -79,169 +111,202 @@ namespace CNORXZ
 	}
     }
 
-    /**************
-     *   MIndex   *
-     **************/
+    /***************
+     *   GMIndex   *
+     ***************/
 
-    template <class... Indices>
-    MIndex<Indices...>::MIndex(const MIndex& i) :
-	IndexInterface<MIndex<Indices...>,Tuple<typename Indices::MetaType...>>(0),
+    template <class BlockType, class... Indices>
+    constexpr GMIndex<BlockType,Indices...>::GMIndex(const GMIndex& i) :
+	IndexInterface<GMIndex<BlockType,Indices...>,Tuple<typename Indices::MetaType...>>(0),
 	mRange(rangeCast<RangeType>(i.range())),
 	mIPack(mkIPack(Isqr<0,NI>{})),
-	mBlockSizes(mkBlockSizes(mIPack,Isqr<0,NI-1>{}))
+	mLexBlockSizes(mkLexBlockSizes(mIPack,Isqr<0,NI-1>{})),
+	mBlockSizes(i.mBlockSizes),
+	mLMax(mkLMax(mIPack)),
+	mPMax(mkPMax(mIPack,mBlockSizes))
     {
-	mPMax = iter<0,NI>( [&](auto i) { return std::get<i>(mIPack)->pmax(); },
-			    [](auto... e) { return (e * ...); });
 	*this = i.pos();
     }
 
-    template <class... Indices>
-    MIndex<Indices...>& MIndex<Indices...>::operator=(const MIndex& i)
+    template <class BlockType, class... Indices>
+    constexpr GMIndex<BlockType,Indices...>& GMIndex<BlockType,Indices...>::operator=(const GMIndex& i)
     {
-	IndexInterface<MIndex<Indices...>,Tuple<typename Indices::MetaType...>>::operator=(0);
+	IndexInterface<GMIndex<BlockType,Indices...>,Tuple<typename Indices::MetaType...>>::operator=(0);
 	mRange = rangeCast<RangeType>(i.range());
 	mIPack = mkIPack(Isqr<0,NI>{});
-	mBlockSizes = mkBlockSizes(mIPack,Isqr<0,NI-1>{});
-	mPMax = iter<0,NI>( [&](auto i) { return std::get<i>(mIPack)->pmax(); },
-			    [](auto... e) { return (e * ...); });
+	mLexBlockSizes = mkLexBlockSizes(mIPack,Isqr<0,NI-1>{});
+	mBlockSizes = i.mBlockSizes;
+	mLMax = mkLMax(mIPack);
+	mPMax = mkPMax(mIPack,mBlockSizes);
 	return *this = i.pos();
     }
 
-    template <class... Indices>
-    MIndex<Indices...>::MIndex(const RangePtr& range, SizeT lexpos) :
-	IndexInterface<MIndex<Indices...>,Tuple<typename Indices::MetaType...>>(0),
+    template <class BlockType, class... Indices>
+    constexpr GMIndex<BlockType,Indices...>::GMIndex(const RangePtr& range, SizeT lexpos) :
+	IndexInterface<GMIndex<BlockType,Indices...>,Tuple<typename Indices::MetaType...>>(0),
 	mRange(rangeCast<RangeType>(range)),
 	mIPack(mkIPack(Isqr<0,NI>{})),
-	mBlockSizes(mkBlockSizes(mIPack,Isqr<0,NI-1>{}))
+	mLexBlockSizes(mkLexBlockSizes(mIPack,Isqr<0,NI-1>{})),
+	mBlockSizes(),
+	mLMax(mkLMax(mIPack)),
+	mPMax(mkPMax(mIPack,mBlockSizes))
     {
-	mPMax = iter<0,NI>( [&](auto i) { return std::get<i>(mIPack)->pmax(); },
-			    [](auto... e) { return (e * ...); });
 	*this = lexpos;
     }
 
-    template <class... Indices>
-    MIndex<Indices...>& MIndex<Indices...>::operator=(SizeT lexpos)
+    template <class BlockType, class... Indices>
+    constexpr GMIndex<BlockType,Indices...>::GMIndex(const RangePtr& range, const BlockType& blockSizes, SizeT lexpos) :
+	IndexInterface<GMIndex<BlockType,Indices...>,Tuple<typename Indices::MetaType...>>(0),
+	mRange(rangeCast<RangeType>(range)),
+	mIPack(mkIPack(Isqr<0,NI>{})),
+	mLexBlockSizes(mkLexBlockSizes(mIPack,Isqr<0,NI-1>{})),
+	mBlockSizes(blockSizes),
+	mLMax(mkLMax(mIPack)),
+	mPMax(mkPMax(mIPack,mBlockSizes))
     {
-	// Adapt in GMIndex
-	IB::mPos = lexpos;
-	iter<0,NI>( [&](auto i) { *std::get<i>(mIPack) = (IB::mPos / std::get<i>(mBlockSizes).val()) % std::get<i>(mIPack)->pmax(); }, NoF{} );
+	*this = lexpos;
+    }
+
+    template <class BlockType, class... Indices>
+    GMIndex<BlockType,Indices...>& GMIndex<BlockType,Indices...>::operator=(SizeT lexpos)
+    {
+	if(lexpos >= lmax().val()){
+	    if constexpr(not std::is_same<BlockType,None>::value){ mLex = lmax().val(); }
+	    IB::mPos = pmax().val();
+	    return *this;
+	}
+	if constexpr(not std::is_same<BlockType,None>::value){ mLex = lexpos; }
+	IB::mPos = iter<0,NI>( [&](auto i) {
+	    *std::get<i>(mIPack) = (lex() / std::get<i>(lexBlockSizes()).val()) % std::get<i>(mIPack)->lmax().val();
+	    return std::get<i>(blockSizes()).val() * std::get<i>(mIPack)->pos();
+	}, [](const auto&... e) { return (e + ...); } );
 	return *this;
     }
 
-    template <class... Indices>
-    MIndex<Indices...>& MIndex<Indices...>::operator++()
+    template <class BlockType, class... Indices>
+    GMIndex<BlockType,Indices...>& GMIndex<BlockType,Indices...>::operator++()
     {
-	// End state is defined by high-index being end while all other indices are zero
-	if(lex() != lmax()){
+	if(lex() == lmax().val()-1){
+	    return *this = lmax().val();
+	}
+	if(lex() != lmax().val()){
 	    up<NI-1>();
 	}
 	return *this;
     }
 
-    template <class... Indices>
-    MIndex<Indices...>& MIndex<Indices...>::operator--()
+    template <class BlockType, class... Indices>
+    GMIndex<BlockType,Indices...>& GMIndex<BlockType,Indices...>::operator--()
     {
+	if(lex() == lmax().val()){
+	    return *this = lmax().val()-1;
+	}
 	if(lex() != 0){
 	    down<NI-1>();
 	}
 	return *this;
     }
 
-    template <class... Indices>
-    MIndex<Indices...> MIndex<Indices...>::operator+(Int n) const
+    template <class BlockType, class... Indices>
+    GMIndex<BlockType,Indices...> GMIndex<BlockType,Indices...>::operator+(Int n) const
     {
-	MIndex o(*this);
+	GMIndex o(*this);
 	return o += n;
     }
 
-    template <class... Indices>
-    MIndex<Indices...> MIndex<Indices...>::operator-(Int n) const
+    template <class BlockType, class... Indices>
+    GMIndex<BlockType,Indices...> GMIndex<BlockType,Indices...>::operator-(Int n) const
     {
-	MIndex o(*this);
+	GMIndex o(*this);
 	return o -= n;
     }
 
-    template <class... Indices>
-    MIndex<Indices...>& MIndex<Indices...>::operator+=(Int n)
+    template <class BlockType, class... Indices>
+    GMIndex<BlockType,Indices...>& GMIndex<BlockType,Indices...>::operator+=(Int n)
     {
 	if(-n > static_cast<long int>(lex())){
 	    (*this) = 0;
 	}
 	const SizeT p = lex() + n;
-	if(p > lmax()){
-	    (*this) = lmax();
+	if(p > lmax().val()){
+	    (*this) = lmax().val();
 	}
 	(*this) = p;
 	return *this;
     }
 
-    template <class... Indices>
-    MIndex<Indices...>& MIndex<Indices...>::operator-=(Int n)
+    template <class BlockType, class... Indices>
+    GMIndex<BlockType,Indices...>& GMIndex<BlockType,Indices...>::operator-=(Int n)
     {
 	if(n > static_cast<long int>(lex())){
 	    (*this) = 0;
 	}
 	const SizeT p = lex() + n;
-	if(p > lmax()){
-	    (*this) = lmax();
+	if(p > lmax().val()){
+	    (*this) = lmax().val();
 	}
 	(*this) = p;
 	return *this;
     }
 
-    template <class... Indices>
-    SizeT MIndex<Indices...>::lex() const
+    template <class BlockType, class... Indices>
+    SizeT GMIndex<BlockType,Indices...>::lex() const
     {
-	return IB::mPos;
+	if constexpr(std::is_same<BlockType,None>::value){
+	    return IB::mPos;
+	}
+	else {
+	    return mLex;
+	}
     }
     
-    template <class... Indices>
-    SizeT MIndex<Indices...>::pmax() const
+    template <class BlockType, class... Indices>
+    constexpr decltype(auto) GMIndex<BlockType,Indices...>::pmax() const
     {
 	return mPMax;
     }
 
-    template <class... Indices>
-    SizeT MIndex<Indices...>::lmax() const
+    template <class BlockType, class... Indices>
+    constexpr decltype(auto) GMIndex<BlockType,Indices...>::lmax() const
     {
 	return mPMax;
     }
 
-    template <class... Indices>
-    IndexId<0> MIndex<Indices...>::id() const
+    template <class BlockType, class... Indices>
+    IndexId<0> GMIndex<BlockType,Indices...>::id() const
     {
 	return IndexId<0>(this->ptrId());
     }
 
-    template <class... Indices>
-    typename MIndex<Indices...>::MetaType MIndex<Indices...>::operator*() const
+    template <class BlockType, class... Indices>
+    typename GMIndex<BlockType,Indices...>::MetaType GMIndex<BlockType,Indices...>::operator*() const
     {
 	return meta();
     }
     
-    template <class... Indices>	
-    SizeT MIndex<Indices...>::dim() const
+    template <class BlockType, class... Indices>	
+    constexpr SizeT GMIndex<BlockType,Indices...>::dim() const
     {
 	return NI;
     }	
 
-    template <class... Indices>	
-    Sptr<typename MIndex<Indices...>::RangeType> MIndex<Indices...>::range() const
+    template <class BlockType, class... Indices>	
+    Sptr<typename GMIndex<BlockType,Indices...>::RangeType> GMIndex<BlockType,Indices...>::range() const
     {
 	return mRange;
     }
 
-    template <class... Indices>	
+    template <class BlockType, class... Indices>	
     template <SizeT I>
-    decltype(auto) MIndex<Indices...>::stepSize(const IndexId<I>& id) const
+    decltype(auto) GMIndex<BlockType,Indices...>::stepSize(const IndexId<I>& id) const
     {
 	return iter<0,NI>
-	    ( [&](auto i) { return std::get<i>(mIPack)->stepSize(id) * std::get<i>(mBlockSizes); },
+	    ( [&](auto i) { return std::get<i>(mIPack)->stepSize(id) * std::get<i>(blockSizes()); },
 	      [](const auto&... ss) { return ( ss + ... ); });
     }
 
-    template <class... Indices>
-    String MIndex<Indices...>::stringMeta() const
+    template <class BlockType, class... Indices>
+    String GMIndex<BlockType,Indices...>::stringMeta() const
     {
 	const String blim = "(";
 	const String elim = ")";
@@ -253,50 +318,61 @@ namespace CNORXZ
 	      } );
     }
     
-    template <class... Indices>
-    typename MIndex<Indices...>::MetaType MIndex<Indices...>::meta() const
+    template <class BlockType, class... Indices>
+    typename GMIndex<BlockType,Indices...>::MetaType GMIndex<BlockType,Indices...>::meta() const
     {
 	return iter<0,NI>( [&](auto i) { return std::get<i>(mIPack)->meta(); },
 			   [](const auto&... xs) { return std::make_tuple(xs...); } );
     }
 
-    template <class... Indices>
-    MIndex<Indices...>& MIndex<Indices...>::at(const MetaType& metaPos)
+    template <class BlockType, class... Indices>
+    GMIndex<BlockType,Indices...>& GMIndex<BlockType,Indices...>::at(const MetaType& metaPos)
     {
 	iter<0,NI>( [&](auto i) { std::get<i>(mIPack)->at( std::get<i>(metaPos) ); }, NoF {} );
 	IB::mPos = iter<0,NI>
-	    ( [&](auto i) { return std::get<i>(mIPack)->pos()*std::get<i>(mBlockSizes).val(); },
+	    ( [&](auto i) { return std::get<i>(mIPack)->pos()*std::get<i>(blockSizes()).val(); },
 	      [](const auto&... xs) { return (xs + ...); });
 	return *this;
     }
 
-    template <class... Indices>	
+    template <class BlockType, class... Indices>	
     template <class Xpr, class F>
-    constexpr decltype(auto) MIndex<Indices...>::ifor(const Xpr& xpr, F&& f) const
+    constexpr decltype(auto) GMIndex<BlockType,Indices...>::ifor(const Xpr& xpr, F&& f) const
     {
 	return mkIFor<0>(xpr, f);
     }
 
-    template <class... Indices>
-    MIndex<Indices...>& MIndex<Indices...>::operator()(const Sptr<MIndex>& mi)
+    template <class BlockType, class... Indices>
+    GMIndex<BlockType,Indices...>& GMIndex<BlockType,Indices...>::operator()(const Sptr<GMIndex>& mi)
     {
 	mIPack = mi.mIPack;
 	IB::mPos = iter<0,NI>
-	    ( [&](auto i) { return std::get<i>(mIPack)->pos()*std::get<i>(mBlockSizes).val(); },
+	    ( [&](auto i) { return std::get<i>(mIPack)->pos()*std::get<i>(blockSizes()).val(); },
 	      [](const auto&... xs) { return (xs + ...); });
 	return *this;
     }
 
-    template <class... Indices>
-    const typename MIndex<Indices...>::IndexPack& MIndex<Indices...>::pack() const
+    template <class BlockType, class... Indices>
+    const typename GMIndex<BlockType,Indices...>::IndexPack& GMIndex<BlockType,Indices...>::pack() const
     {
 	return mIPack;
     }
 
-    template <class... Indices>
-    const auto& MIndex<Indices...>::blockSizes() const
+    template <class BlockType, class... Indices>
+    const auto& GMIndex<BlockType,Indices...>::blockSizes() const
     {
-	return mBlockSizes;
+	if constexpr(std::is_same<BlockType,None>::value){
+	    return mLexBlockSizes;
+	}
+	else {
+	    return mBlockSizes;
+	}
+    }
+
+    template <class BlockType, class... Indices>
+    const auto& GMIndex<BlockType,Indices...>::lexBlockSizes() const
+    {
+	return mLexBlockSizes;
     }
 
     
diff --git a/src/include/ranges/mrange.h b/src/include/ranges/mrange.h
index 5ad50cd..6c051b0 100644
--- a/src/include/ranges/mrange.h
+++ b/src/include/ranges/mrange.h
@@ -11,14 +11,14 @@
 namespace CNORXZ
 {
     
-    template <class... Indices>
-    class MIndex : public IndexInterface<MIndex<Indices...>,
-					 Tuple<typename Indices::MetaType...> >
+    template <class BlockType, class... Indices>
+    class GMIndex : public IndexInterface<GMIndex<BlockType,Indices...>,
+					  Tuple<typename Indices::MetaType...> >
     {
     public:
 	
-	typedef IndexInterface<MIndex<Indices...>,
-			       Tuple<typename Indices::MetaType...> > IB;
+	typedef IndexInterface<GMIndex<BlockType,Indices...>,
+			       Tuple<typename Indices::MetaType...>> IB;
 	typedef Tuple<Sptr<Indices>...> IndexPack;
 	typedef Tuple<typename Indices::MetaType...> MetaType;
 	typedef MRange<typename Indices::RangeType...> RangeType;
@@ -26,31 +26,32 @@ namespace CNORXZ
 
 	// NO DEFAULT HERE !!!
 	// ( have to assign sub-indices (ptr!) correctly )
-	MIndex() = default;
-	MIndex(MIndex&& i) = default;
-	MIndex& operator=(MIndex&& i) = default;
+	constexpr GMIndex() = default;
+	constexpr GMIndex(GMIndex&& i) = default;
+	constexpr GMIndex& operator=(GMIndex&& i) = default;
 
-	MIndex(const MIndex& i);
-	MIndex& operator=(const MIndex& i);
+	constexpr GMIndex(const GMIndex& i);
+	constexpr GMIndex& operator=(const GMIndex& i);
 
-	MIndex(const RangePtr& range, SizeT lexpos = 0);
+	constexpr GMIndex(const RangePtr& range, SizeT lexpos = 0);
+	constexpr GMIndex(const RangePtr& range, const BlockType& blockSizes, SizeT lexpos = 0);
 
-	MIndex& operator=(SizeT pos);
-	MIndex& operator++();
-	MIndex& operator--();
-	MIndex operator+(Int n) const;
-	MIndex operator-(Int n) const;
-	MIndex& operator+=(Int n);
-	MIndex& operator-=(Int n);
+	GMIndex& operator=(SizeT pos);
+	GMIndex& operator++();
+	GMIndex& operator--();
+	GMIndex operator+(Int n) const;
+	GMIndex operator-(Int n) const;
+	GMIndex& operator+=(Int n);
+	GMIndex& operator-=(Int n);
 
 	SizeT lex() const;
-	SizeT pmax() const;
-	SizeT lmax() const;
+	constexpr decltype(auto) pmax() const;
+	constexpr decltype(auto) lmax() const;
 	IndexId<0> id() const;
 
 	MetaType operator*() const;
-
-	SizeT dim() const;
+	
+	constexpr SizeT dim() const;
 	Sptr<RangeType> range() const;
 
 	template <SizeT I>
@@ -58,20 +59,25 @@ namespace CNORXZ
 	
 	String stringMeta() const;
 	MetaType meta() const;
-	MIndex& at(const MetaType& metaPos);
+	GMIndex& at(const MetaType& metaPos);
 	
 	template <class Xpr, class F>
 	constexpr decltype(auto) ifor(const Xpr& xpr, F&& f) const;
 
 	// replace sub-index instances; only use if you know what you are doing!
-	MIndex& operator()(const Sptr<MIndex>& mi);
+	GMIndex& operator()(const Sptr<GMIndex>& mi);
 
 	const IndexPack& pack() const;
 	const auto& blockSizes() const;
+	const auto& lexBlockSizes() const;
 
     private:
 	template <SizeT... Is>
-	static constexpr decltype(auto) mkBlockSizes(const IndexPack& ipack, Isq<Is...> is);
+	static constexpr decltype(auto) mkLexBlockSizes(const IndexPack& ipack, Isq<Is...> is);
+
+	static constexpr decltype(auto) mkLMax(const IndexPack& ipack);
+
+	static constexpr decltype(auto) mkPMax(const IndexPack& ipack, const BlockType& blockSizes);
 
 	template <SizeT... Is>
 	constexpr decltype(auto) mkIPack(Isq<Is...> is) const;
@@ -87,31 +93,19 @@ namespace CNORXZ
 
 	Sptr<RangeType> mRange;
 	IndexPack mIPack;
-	typedef RemoveRef<decltype(mkBlockSizes(mIPack,Isqr<0,NI-1>{}))> BlockTuple;
-	BlockTuple mBlockSizes;
-	SizeT mPMax = 0; // = LMax here, add new variable in GMIndex!
+	typedef RemoveRef<decltype(mkLexBlockSizes(mIPack,Isqr<0,NI-1>{}))> LexBlockType;
+	LexBlockType mLexBlockSizes;
+	BlockType mBlockSizes;
+	SizeT mLex;
+	typedef RemoveRef<decltype(mkLMax(mIPack))> LMaxT;
+	LMaxT mLMax;
+	typedef RemoveRef<decltype(mkPMax(mIPack,mBlockSizes))> PMaxT;
+	PMaxT mPMax;
     };
 
-    // 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 mLexBlockSizes;
-
-	template <SizeT... Is>
-	constexpr decltype(auto) mkPos(Isq<Is...> is) const;
-    };
-
-    // NOT THREAD SAVE
+    template <class... Indices>
+    using MIndex = GMIndex<None,Indices...>;
+    
     template <class... Ranges>
     class MRangeFactory : public RangeFactoryBase
     {
diff --git a/src/include/ranges/urange.cc.h b/src/include/ranges/urange.cc.h
index 5243d17..ae8405f 100644
--- a/src/include/ranges/urange.cc.h
+++ b/src/include/ranges/urange.cc.h
@@ -75,15 +75,15 @@ namespace CNORXZ
     }
     
     template <typename MetaType>
-    SizeT UIndex<MetaType>::pmax() const
+    UPos UIndex<MetaType>::pmax() const
     {
-	return mRangePtr->size();
+	return UPos(mRangePtr->size());
     }
 
     template <typename MetaType>
-    SizeT UIndex<MetaType>::lmax() const
+    UPos UIndex<MetaType>::lmax() const
     {
-	return mRangePtr->size();
+	return UPos(mRangePtr->size());
     }
 
     template <typename MetaType>
@@ -140,7 +140,7 @@ namespace CNORXZ
     template <class Xpr, class F>
     decltype(auto) UIndex<MetaType>::ifor(const Xpr& xpr, F&& f) const
     {
-	return For<0,Xpr,F>(this->pmax(), this->id(), xpr, std::forward<F>(f));
+	return For<0,Xpr,F>(this->pmax().val(), this->id(), xpr, std::forward<F>(f));
     }
     
     /**********************
diff --git a/src/include/ranges/urange.h b/src/include/ranges/urange.h
index 44c0245..904d87e 100644
--- a/src/include/ranges/urange.h
+++ b/src/include/ranges/urange.h
@@ -31,8 +31,8 @@ namespace CNORXZ
 	UIndex& operator-=(Int n);
 
 	SizeT lex() const;
-	SizeT pmax() const;
-	SizeT lmax() const;
+	UPos pmax() const;
+	UPos lmax() const;
 	IndexId<0> id() const;
 	
 	const MetaT& operator*() const;
diff --git a/src/include/ranges/xindex.cc.h b/src/include/ranges/xindex.cc.h
index 07c2c4c..c0c829f 100644
--- a/src/include/ranges/xindex.cc.h
+++ b/src/include/ranges/xindex.cc.h
@@ -86,15 +86,15 @@ namespace CNORXZ
     }
 
     template <class Index, typename Meta>
-    SizeT XIndex<Index,Meta>::pmax() const
+    UPos XIndex<Index,Meta>::pmax() const
     {
-	return mI->pmax();
+	return UPos(mI->pmax());
     }
 
     template <class Index, typename Meta>
-    SizeT XIndex<Index,Meta>::lmax() const
+    UPos XIndex<Index,Meta>::lmax() const
     {
-	return mI->lmax();
+	return UPos(mI->lmax());
     }
 
     template <class Index, typename Meta>
diff --git a/src/include/ranges/xindex.h b/src/include/ranges/xindex.h
index e615754..f8f1837 100644
--- a/src/include/ranges/xindex.h
+++ b/src/include/ranges/xindex.h
@@ -26,8 +26,8 @@ namespace CNORXZ
 	virtual XIndexBase& operator-=(Int n) = 0;
 
 	virtual SizeT lex() const = 0;
-	virtual SizeT pmax() const = 0;
-	virtual SizeT lmax() const = 0;
+	virtual UPos pmax() const = 0;
+	virtual UPos lmax() const = 0;
 	virtual IndexId<0> id() const = 0;
 	
 	virtual DType operator*() const = 0;
@@ -74,8 +74,8 @@ namespace CNORXZ
 	virtual XIndex& operator-=(Int n) override final;
 
 	virtual SizeT lex() const override final;
-	virtual SizeT pmax() const override final;
-	virtual SizeT lmax() const override final;
+	virtual UPos pmax() const override final;
+	virtual UPos lmax() const override final;
 	virtual IndexId<0> id() const override final;
 	
 	virtual DType operator*() const override final;
diff --git a/src/include/ranges/yrange.h b/src/include/ranges/yrange.h
index a5551a3..61599dc 100644
--- a/src/include/ranges/yrange.h
+++ b/src/include/ranges/yrange.h
@@ -35,8 +35,8 @@ namespace CNORXZ
 	YIndex& operator-=(Int n);
 
 	SizeT lex() const;
-	SizeT pmax() const;
-	SizeT lmax() const;
+	UPos pmax() const;
+	UPos lmax() const;
 	IndexId<0> id() const;
 	
 	DType operator*() const;
@@ -69,8 +69,8 @@ namespace CNORXZ
 	Vector<SizeT> mBlockSizes; // dim() elements only!!!
 	Vector<SizeT> mLexBlockSizes; // dim() elements only!!!
 	SizeT mLex = 0;
-	SizeT mPMax = 0;
-	SizeT mLMax = 0;
+	UPos mPMax = 0;
+	UPos mLMax = 0;
     };
 
     class YRangeFactory : public RangeFactoryBase
diff --git a/src/include/xpr/pos_type.cc.h b/src/include/xpr/pos_type.cc.h
index d675474..40dffa5 100644
--- a/src/include/xpr/pos_type.cc.h
+++ b/src/include/xpr/pos_type.cc.h
@@ -83,6 +83,12 @@ namespace CNORXZ
 	return UPos(N);
     }
 
+    template <SizeT N>
+    constexpr SPos<N>::operator SizeT() const
+    {
+	return val();
+    }
+
     /************
      *   UPos   *
      ************/
@@ -138,7 +144,12 @@ namespace CNORXZ
     {
 	return extend(a);
     }
-    
+
+    constexpr UPos::operator SizeT() const
+    {
+	return val();
+    }
+
     /************
      *   FPos   *
      ************/
@@ -185,6 +196,11 @@ namespace CNORXZ
 	return extend(a);
     }
 
+    constexpr FPos::operator SizeT() const
+    {
+	return val();
+    }
+
     /*************
      *   SFPos   *
      *************/
@@ -265,6 +281,12 @@ namespace CNORXZ
 	return FPos(N, &sMs[0]);
     }
 
+    template <SizeT N, SizeT... Ms>
+    constexpr SFPos<N,Ms...>::operator SizeT() const
+    {
+	return val();
+    }
+
     /************
      *   MPos   *
      ************/
@@ -456,6 +478,11 @@ namespace CNORXZ
 	return MPos<DPos,PosT>(*this,a);
     }
 
+    inline DPos::operator SizeT() const
+    {
+	return val();
+    }
+
     /***************
      *   DPosRef   *
      ***************/
@@ -531,6 +558,11 @@ namespace CNORXZ
 	//return DPos(mP->vextend( a ));
 	return MPos<DPos,PosT>(*this,a);
     }
+
+    inline DPosRef::operator SizeT() const
+    {
+	return val();
+    }
     
     /************
      *   EPos   *
diff --git a/src/include/xpr/pos_type.h b/src/include/xpr/pos_type.h
index de1e367..cac728f 100644
--- a/src/include/xpr/pos_type.h
+++ b/src/include/xpr/pos_type.h
@@ -36,6 +36,7 @@ namespace CNORXZ
 	constexpr decltype(auto) operator<<(const PosT& a) const;
 	
 	explicit constexpr operator UPos() const;
+	explicit constexpr operator SizeT() const;
     };
 
     class UPos
@@ -68,6 +69,8 @@ namespace CNORXZ
 
 	template <class PosT>
 	constexpr decltype(auto) operator<<(const PosT& a) const;
+
+	explicit constexpr operator SizeT() const;
     };
 
     class FPos
@@ -98,6 +101,8 @@ namespace CNORXZ
 
 	template <class PosT>
 	constexpr decltype(auto) operator<<(const PosT& a) const;
+
+	explicit constexpr operator SizeT() const;
     };
 
     template <SizeT N, SizeT... Ms>
@@ -129,6 +134,8 @@ namespace CNORXZ
 	constexpr decltype(auto) operator<<(const PosT& a) const;
 
 	explicit constexpr operator FPos() const;
+
+	explicit constexpr operator SizeT() const;
     };
 
     template <class BPosT, class NPosT>
@@ -204,6 +211,8 @@ namespace CNORXZ
 
 	template <class PosT>
 	inline decltype(auto) operator<<(const PosT& a) const;
+
+	explicit inline operator SizeT() const;
     };
 
     class DPosRef
@@ -238,6 +247,8 @@ namespace CNORXZ
 
 	template <class PosT>
 	inline decltype(auto) operator<<(const PosT& a) const;
+
+	explicit inline operator SizeT() const;
     };
 
     // for common call of extension vector elements
diff --git a/src/lib/ranges/crange.cc b/src/lib/ranges/crange.cc
index 6be9932..9f3dc03 100644
--- a/src/lib/ranges/crange.cc
+++ b/src/lib/ranges/crange.cc
@@ -56,14 +56,14 @@ namespace CNORXZ
 	return IB::mPos;
     }
     
-    SizeT CIndex::lmax() const
+    UPos CIndex::lmax() const
     {
-	return mRangePtr->size();
+	return UPos(mRangePtr->size());
     }
 
-    SizeT CIndex::pmax() const
+    UPos CIndex::pmax() const
     {
-	return mRangePtr->size();
+	return UPos(mRangePtr->size());
     }
 
     IndexId<0> CIndex::id() const
diff --git a/src/lib/ranges/dindex.cc b/src/lib/ranges/dindex.cc
index cb83a12..5aa2f9d 100644
--- a/src/lib/ranges/dindex.cc
+++ b/src/lib/ranges/dindex.cc
@@ -87,12 +87,12 @@ namespace CNORXZ
 	return mI->lex();
     }
     
-    SizeT DIndex::pmax() const
+    UPos DIndex::pmax() const
     {
 	return mI->pmax();
     }
     
-    SizeT DIndex::lmax() const
+    UPos DIndex::lmax() const
     {
 	return mI->lmax();
     }
diff --git a/src/lib/ranges/yrange.cc b/src/lib/ranges/yrange.cc
index dde2762..1000f71 100644
--- a/src/lib/ranges/yrange.cc
+++ b/src/lib/ranges/yrange.cc
@@ -25,7 +25,7 @@ namespace CNORXZ
 	for(SizeT i = o.size(); i != 0; --i){
 	    const SizeT j = i-1;
 	    o[j] = b;
-	    b *= mIs[j]->pmax();
+	    b *= mIs[j]->pmax().val();
 	}
 	return o;
     }
@@ -37,7 +37,7 @@ namespace CNORXZ
 	for(SizeT i = o.size(); i != 0; --i){
 	    const SizeT j = i-1;
 	    o[j] = b;
-	    b *= mIs[j]->lmax();
+	    b *= mIs[j]->lmax().val();
 	}
 	return o;
     }
@@ -47,7 +47,7 @@ namespace CNORXZ
 	auto& idx = mIs[i];
 	// it is guaranteed that the last accessible position 
 	// is one less than the max position (=end)
-	if(i != 0 and idx->lex() == idx->lmax()-1){
+	if(i != 0 and idx->lex() == idx->lmax().val()-1){
 	    IB::mPos -= mBlockSizes[i] * idx->pos();
 	    mLex -= mLexBlockSizes[i] * idx->lex();
 	    (*idx) = 0;
@@ -63,7 +63,7 @@ namespace CNORXZ
     {
 	auto& idx = mIs[i];
 	if(i != 0 and idx->pos() == 0){
-	    (*idx) = idx->lmax()-1;
+	    (*idx) = idx->lmax().val()-1;
 	    IB::mPos += mBlockSizes[i] * idx->pos();
 	    mLex += mLexBlockSizes[i] * idx->lex();
 	    down(i-1);
@@ -89,7 +89,7 @@ namespace CNORXZ
     {
 	SizeT o = 0;
 	for(SizeT i = 0; i != mIs.size(); ++i){
-	    o += (mIs[i]->pmax()-1) * mBlockSizes[i];
+	    o += (mIs[i]->pmax().val()-1) * mBlockSizes[i];
 	}
 	return o+1;
     }
@@ -97,7 +97,7 @@ namespace CNORXZ
     inline SizeT YIndex::mkLMax() const
     {
 	return std::accumulate(mIs.begin(), mIs.end(),1,
-			       [](const auto& res, const auto& el) { return res * el->lmax(); } );
+			       [](const auto& res, const auto& el) { return res * el->lmax().val(); } );
     }
     
     
@@ -143,15 +143,15 @@ namespace CNORXZ
 
     YIndex& YIndex::operator=(SizeT lexpos)
     {
-	if(lexpos >= lmax()){
-	    mLex = lmax();
-	    IB::mPos = pmax();
+	if(lexpos >= lmax().val()){
+	    mLex = lmax().val();
+	    IB::mPos = pmax().val();
 	    return *this;
 	}
 	mLex = lexpos;
 	IB::mPos = 0;
 	for(SizeT i = 0; i != mIs.size(); ++i){
-	    *mIs[i] = (lex() / mLexBlockSizes[i]) % mIs[i]->lmax();
+	    *mIs[i] = (lex() / mLexBlockSizes[i]) % mIs[i]->lmax().val();
 	    IB::mPos += mBlockSizes[i] * mIs[i]->pos();
 	}
 	return *this;
@@ -159,22 +159,19 @@ namespace CNORXZ
     
     YIndex& YIndex::operator++()
     {
-	auto& i0 = mIs[0];
-	if(i0->lex() != i0->lmax()){
-	    up(mIs.size()-1);
+	if(lex() == lmax().val()-1){
+	    return *this = lmax().val();
 	}
-	// no else! up() changes i0!
-	if(i0->lex() == i0->lmax()){
-	    IB::mPos = pmax();
+	if(lex() != lmax().val()){
+	    up(mIs.size()-1);
 	}
 	return *this;
     }
     
     YIndex& YIndex::operator--()
     {
-	auto& i0 = mIs[0];
-	if(i0->lex() == i0->lmax()){
-	    IB::mPos = mBlockSizes[0] * i0->pmax();
+	if(lex() == lmax().val()){
+	    return *this = lmax().val()-1;
 	}
 	if(lex() != 0){
 	    down(mIs.size()-1);
@@ -215,12 +212,12 @@ namespace CNORXZ
 	return mLex;
     }
     
-    SizeT YIndex::pmax() const
+    UPos YIndex::pmax() const
     {
 	return mPMax;
     }
 
-    SizeT YIndex::lmax() const
+    UPos YIndex::lmax() const
     {
 	return mLMax;
     }
diff --git a/src/tests/range_unit_test.cc b/src/tests/range_unit_test.cc
index 9cc4748..99042ca 100644
--- a/src/tests/range_unit_test.cc
+++ b/src/tests/range_unit_test.cc
@@ -231,8 +231,8 @@ namespace
 	auto yrx = std::dynamic_pointer_cast<YRange>(yr);
 	auto yi = yrx->begin();
 
-	EXPECT_EQ(yi.pmax(), yr->size());
-	EXPECT_EQ(yi.lmax(), yr->size());
+	EXPECT_EQ(yi.pmax().val(), yr->size());
+	EXPECT_EQ(yi.lmax().val(), yr->size());
 	EXPECT_EQ(yi.range(), yr);
 	EXPECT_EQ(yi.range(), yrx);
 	EXPECT_EQ(yi.dim(), 2u);
@@ -258,11 +258,11 @@ namespace
 		EXPECT_EQ(b.stringMeta(), toString(mmj));
 	    }
 	}
-	yi += yi.lmax() + 10;
-	EXPECT_EQ(yi.lex(), yi.lmax());
-	EXPECT_EQ(yi.pos(), yi.pmax());
+	yi += yi.lmax().val() + 10;
+	EXPECT_EQ(yi.lex(), yi.lmax().val());
+	EXPECT_EQ(yi.pos(), yi.pmax().val());
 
-	yi -= yi.lmax() + 20;
+	yi -= yi.lmax().val() + 20;
 	EXPECT_EQ(yi.lex(), 0u);
 	EXPECT_EQ(yi.pos(), 0u);
     }