diff --git a/src/opt/mpi/include/rrange.cc.h b/src/opt/mpi/include/rrange.cc.h
index 8efabf5..41cf1f4 100644
--- a/src/opt/mpi/include/rrange.cc.h
+++ b/src/opt/mpi/include/rrange.cc.h
@@ -227,7 +227,29 @@ namespace CNORXZ
 	template <class IndexI, class IndexK>
 	RIndex<IndexI,IndexK>& RIndex<IndexI,IndexK>::at(const MetaType& metaPos)
 	{
-	    CXZ_ERROR("not implemented");
+	    //VCHECK(toString(metaPos));
+	    //VCHECK(toString(mI->meta()));
+	    mI->at(metaPos);
+	    //VCHECK(toString(mI->meta()));
+	    const size_t lex = mI->lex();
+	    //VCHECK(lex);
+	    Vector<size_t> lexs(mK->lmax().val());
+	    MPI_Allgather(&lex, 1, MPI_UNSIGNED_LONG, lexs.data(), 1, MPI_UNSIGNED_LONG,
+			  MPI_COMM_WORLD);
+	    VCHECK(toString(lexs));
+	    SizeT root = 0;
+	    VCHECK(mI->lmax().val());
+	    for(; root != lexs.size() and lexs[root] == mI->lmax().val(); ++root) {}
+	    if(root == lexs.size()){ // metaPos not in rrange
+		*this = lmax().val();
+		assert(0);
+	    }
+	    else {
+		*mK = root;
+		*mI = lexs[root];
+		VCHECK(lexs[root]);
+		(*this)();
+	    }
 	    return *this;
 	}
 
@@ -277,6 +299,42 @@ namespace CNORXZ
 	    return _this->local()->xpr( _this->local() );
 	}
 
+	template <class IndexI, class IndexK>
+	RIndex<IndexI,IndexK>& RIndex<IndexI,IndexK>::operator()()
+	{
+	    if constexpr(has_static_sub<IndexI>::value){
+		constexpr SizeT NI = index_dim<IndexI>::value;
+		IB::mPos = iter<0,NI>
+		    ([&](auto i) {
+			return mK->pack()[i]->lex() * mK->lexFormat()[i].val() *
+			    mI->lexFormat()[i].val() * mI->pack()[i]->lmax().val() +
+			    mI->pack()[i]->lex() * mI->lexFormat()[i].val() *
+			    mK->lexFormat()[i].val();
+		    }, [](const auto&... e) { return (e + ...); });
+	    }
+	    else if constexpr( has_static_sub<IndexK>::value){
+		constexpr SizeT NI = index_dim<IndexK>::value;
+		IB::mPos = iter<0,NI>
+		    ([&](auto i) {
+			return mK->pack()[i]->lex() * mK->lexFormat()[i].val() *
+			    mI->lexFormat()[i].val() * mI->pack()[i]->lmax().val() +
+			    mI->pack()[i]->lex() * mI->lexFormat()[i].val() *
+			    mK->lexFormat()[i].val();
+		    }, [](const auto&... e) { return (e + ...); });
+	    }
+	    else {
+		const SizeT NI = mI->dim();
+		IB::mPos = 0;
+		for(SizeT i = 0; i != NI; ++i){
+		    IB::mPos += mK->pack()[i]->lex() * mK->lexFormat()[i].val() *
+			mI->lexFormat()[i].val() * mI->pack()[i]->lmax().val() +
+			mI->pack()[i]->lex() * mI->lexFormat()[i].val() *
+			mK->lexFormat()[i].val();
+		}
+	    }
+	    return *this;
+	}
+
 	template <class IndexI, class IndexK>
 	SizeT RIndex<IndexI,IndexK>::rank() const
 	{
@@ -365,7 +423,7 @@ namespace CNORXZ
 	template <class RangeI, class RangeK>
 	SizeT RRange<RangeI,RangeK>::dim() const
 	{
-	    return mGeom->dim() + mLocal->dim();
+	    return 2;
 	}
 	
 	template <class RangeI, class RangeK>
@@ -439,8 +497,23 @@ namespace CNORXZ
 	{
 	    return Vector<Uuid> { mLocal->id(), mGeom->id() };
 	}
-	
+
+	/*============================+
+	 |    non-member functions    |
+	 +============================*/
+
     } // namespace mpi
+
+    template <class RangeI, class RangeK>
+    Sptr<mpi::RRange<RangeI,RangeK>> RangeCast<mpi::RRange<RangeI,RangeK>>::func(const RangePtr& r)
+    {
+	CXZ_ASSERT(r->dim() == 2, "expected RRange");
+	Sptr<RangeI> loc = rangeCast<RangeI>(r->sub(1));
+	Sptr<RangeK> geom = rangeCast<RangeK>(r->sub(0));
+	return std::dynamic_pointer_cast<mpi::RRange<RangeI,RangeK>>
+	    ( mpi::RRangeFactory( loc, geom ).create() );
+    }
+	
 } // namespace CNORXZ
 
 #endif
diff --git a/src/opt/mpi/include/rrange.h b/src/opt/mpi/include/rrange.h
index 2f636cf..3aa0767 100644
--- a/src/opt/mpi/include/rrange.h
+++ b/src/opt/mpi/include/rrange.h
@@ -136,6 +136,9 @@ namespace CNORXZ
 	    /** @copydoc IndexInterface::xpr() */
 	    decltype(auto) xpr(const Sptr<RIndex<IndexI,IndexK>>& _this) const;
 
+	    /** Update index position according to the sub-indices. */
+	    RIndex& operator()();
+	    
 	    /** Get the current rank. */
 	    SizeT rank() const;
 
@@ -254,8 +257,15 @@ namespace CNORXZ
 	    @param geom Rank geometry.
 	*/
 	RangePtr rrange(const RangePtr& global, const RangePtr& geom);
-	
+
     } // namespace mpi
+
+    template <class RangeI, class RangeK>
+    struct RangeCast<mpi::RRange<RangeI,RangeK>>
+    {
+	static Sptr<mpi::RRange<RangeI,RangeK>> func(const RangePtr& r);
+    };
+	
 } // namespace CNORXZ
 
 #endif
diff --git a/src/opt/mpi/tests/rrange_unit_test.cc b/src/opt/mpi/tests/rrange_unit_test.cc
index 6f2b6ce..b7f4e2e 100644
--- a/src/opt/mpi/tests/rrange_unit_test.cc
+++ b/src/opt/mpi/tests/rrange_unit_test.cc
@@ -119,6 +119,43 @@ namespace
 	    EXPECT_EQ(s1 ,s2);
 	}
     }
+
+    TEST_F(RRange_Test, Global2)
+    {
+	typedef UIndex<Int> UI;
+	typedef MIndex<UI,UI,UI,UI> LocI;
+	typedef MIndex<CIndex,CIndex,CIndex,CIndex> RankI;
+	RIndex<LocI,RankI> rgi(mRRange);
+	LocI gi(mGRange);
+	for(SizeT c = 0; gi.lex() != gi.lmax().val(); ++gi, ++rgi, ++c) {
+	    const String s1 = gi.stringMeta();
+	    const String s2 = rgi.stringMeta();
+	    EXPECT_EQ(rgi.lex(), c);
+	    EXPECT_EQ(s1 ,s2);
+	}
+	rgi = 0;
+	gi = 0;
+	auto xi = gi;
+	gi = 10;
+	xi.at( gi.meta() );
+	EXPECT_EQ( xi.lex(), gi.lex() );
+	//VCHECK(toString(rgi.local()->meta()));
+	VCHECK(rgi.local()->at( gi.meta() ).lex());
+	/*
+	auto j = rgi;
+	for(auto i = rgi; i.lex() != i.lmax().val(); ++i){
+	    j.at( i.meta() );
+	    if(getRankNumber() == 0){
+		EXPECT_EQ(i.lex(), j.lex());
+		EXPECT_EQ(i.rank(), j.rank());
+		EXPECT_EQ(i.local()->lex(), j.local()->lex());
+	    }
+	    if(i.lex() == 50) {
+		break;
+	    }
+	}
+	*/
+    }
     
 }