src/main/java/org/apache/sysml/hops/rewrite/RewriteIndexingVectorization.java - systemds - Git at Google

 /*
  * Licensed to the Apache Software Foundation (ASF) under one
  * or more contributor license agreements.  See the NOTICE file
  * distributed with this work for additional information
  * regarding copyright ownership.  The ASF licenses this file
  * to you under the Apache License, Version 2.0 (the
  * "License"); you may not use this file except in compliance
  * with the License.  You may obtain a copy of the License at
  *
  *   http://www.apache.org/licenses/LICENSE-2.0
  *
  * Unless required by applicable law or agreed to in writing,
  * software distributed under the License is distributed on an
  * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
  * KIND, either express or implied.  See the License for the
  * specific language governing permissions and limitations
  * under the License.
  */

 package org.apache.sysml.hops.rewrite;

 import java.util.ArrayList;

 import org.apache.commons.logging.Log;
 import org.apache.commons.logging.LogFactory;
 import org.apache.sysml.hops.Hop;
 import org.apache.sysml.hops.HopsException;
 import org.apache.sysml.hops.IndexingOp;
 import org.apache.sysml.hops.LeftIndexingOp;
 import org.apache.sysml.hops.LiteralOp;

 /**
  * Rule: Indexing vectorization. This rewrite rule set simplifies
  * multiple right / left indexing accesses within a DAG into row/column
  * index accesses, which is beneficial for two reasons: (1) it is an
  * enabler for later row/column partitioning, and (2) it reduces the number
  * of operations over potentially large data (i.e., prevents unnecessary MR
  * operations and reduces pressure on the buffer pool due to copy on write
  * on left indexing).
  *
  */
 public class RewriteIndexingVectorization extends HopRewriteRule
 {

 	private static final Log LOG = LogFactory.getLog(RewriteIndexingVectorization.class.getName());

 	@Override
 	public ArrayList<Hop> rewriteHopDAGs(ArrayList<Hop> roots, ProgramRewriteStatus state)
 		throws HopsException
 	{
 		if( roots == null )
 			return roots;

 		for( Hop h : roots )
 			rule_IndexingVectorization( h );

 		return roots;
 	}

 	@Override
 	public Hop rewriteHopDAG(Hop root, ProgramRewriteStatus state)
 		throws HopsException
 	{
 		if( root == null )
 			return root;

 		rule_IndexingVectorization( root );

 		return root;
 	}


 	/**
 	 *
 	 * @param hop
 	 * @param descendFirst
 	 * @throws HopsException
 	 */
 	private void rule_IndexingVectorization( Hop hop )
 		throws HopsException
 	{
 		if(hop.getVisited() == Hop.VisitStatus.DONE)
 			return;

 		//recursively process children
 		for( int i=0; i<hop.getInput().size(); i++)
 		{
 			Hop hi = hop.getInput().get(i);

 			//apply indexing vectorization rewrites
 			//MB: disabled right indexing rewrite because (1) piggybacked in MR anyway, (2) usually
 			//not too much overhead, and (3) makes literal replacement more difficult
 			//vectorizeRightIndexing( hi ); //e.g., multiple rightindexing X[i,1], X[i,3] -> X[i,];
 			vectorizeLeftIndexing( hi );  //e.g., multiple left indexing X[i,1], X[i,3] -> X[i,];

 			//process childs recursively after rewrites
 			rule_IndexingVectorization( hi );
 		}

 		hop.setVisited(Hop.VisitStatus.DONE);
 	}

 	/**
 	 * Note: unnecessary row or column indexing then later removed via
 	 * dynamic rewrites
 	 *
 	 * @param hop
 	 * @throws HopsException
 	 */
 	@SuppressWarnings("unused")
 	private void vectorizeRightIndexing( Hop hop )
 		throws HopsException
 	{
 		if( hop instanceof IndexingOp ) //right indexing
 		{
 			IndexingOp ihop0 = (IndexingOp) hop;
 			boolean isSingleRow = ihop0.getRowLowerEqualsUpper();
 			boolean isSingleCol = ihop0.getColLowerEqualsUpper();
 			boolean appliedRow = false;

 			//search for multiple indexing in same row
 			if( isSingleRow && isSingleCol ){
 				Hop input = ihop0.getInput().get(0);
 				//find candidate set
 				//dependence on common subexpression elimination to find equal input / row expression
 				ArrayList<Hop> ihops = new ArrayList<Hop>();
 				ihops.add(ihop0);
 				for( Hop c : input.getParent() ){
 					if( c != ihop0 && c instanceof IndexingOp && c.getInput().get(0) == input
 					   && ((IndexingOp) c).getRowLowerEqualsUpper()
 					   && c.getInput().get(1)==ihop0.getInput().get(1) )
 					{
 						ihops.add( c );
 					}
 				}
 				//apply rewrite if found candidates
 				if( ihops.size() > 1 ){
 					//new row indexing operator
 					IndexingOp newRix = new IndexingOp("tmp", input.getDataType(), input.getValueType(), input,
 							            ihop0.getInput().get(1), ihop0.getInput().get(1), new LiteralOp(1),
 							            HopRewriteUtils.createValueHop(input, false), true, false);
 					HopRewriteUtils.setOutputParameters(newRix, -1, -1, input.getRowsInBlock(), input.getColsInBlock(), -1);
 					newRix.refreshSizeInformation();
 					//rewire current operator and all candidates
 					for( Hop c : ihops ) {
 						HopRewriteUtils.removeChildReference(c, input); //input data
 						HopRewriteUtils.addChildReference(c, newRix, 0);
 						HopRewriteUtils.removeChildReferenceByPos(c, c.getInput().get(1),1); //row lower expr
 						HopRewriteUtils.addChildReference(c, new LiteralOp(1), 1);
 						HopRewriteUtils.removeChildReferenceByPos(c, c.getInput().get(2),2); //row upper expr
 						HopRewriteUtils.addChildReference(c, new LiteralOp(1), 2);
 						c.refreshSizeInformation();
 					}

 					appliedRow = true;
 					LOG.debug("Applied vectorizeRightIndexingRow");
 				}
 			}

 			//search for multiple indexing in same col
 			if( isSingleRow && isSingleCol && !appliedRow ){
 				Hop input = ihop0.getInput().get(0);
 				//find candidate set
 				//dependence on common subexpression elimination to find equal input / row expression
 				ArrayList<Hop> ihops = new ArrayList<Hop>();
 				ihops.add(ihop0);
 				for( Hop c : input.getParent() ){
 					if( c != ihop0 && c instanceof IndexingOp && c.getInput().get(0) == input
 					   && ((IndexingOp) c).getColLowerEqualsUpper()
 					   && c.getInput().get(3)==ihop0.getInput().get(3) )
 					{
 						ihops.add( c );
 					}
 				}
 				//apply rewrite if found candidates
 				if( ihops.size() > 1 ){
 					//new row indexing operator
 					IndexingOp newRix = new IndexingOp("tmp", input.getDataType(), input.getValueType(), input,
 							         new LiteralOp(1), HopRewriteUtils.createValueHop(input, true),
 				                    ihop0.getInput().get(3), ihop0.getInput().get(3), false, true);
 					HopRewriteUtils.setOutputParameters(newRix, -1, -1, input.getRowsInBlock(), input.getColsInBlock(), -1);
 					newRix.refreshSizeInformation();
 					//rewire current operator and all candidates
 					for( Hop c : ihops ) {
 						HopRewriteUtils.removeChildReference(c, input); //input data
 						HopRewriteUtils.addChildReference(c, newRix, 0);
 						HopRewriteUtils.removeChildReferenceByPos(c, c.getInput().get(3),3); //col lower expr
 						HopRewriteUtils.addChildReference(c, new LiteralOp(1), 3);
 						HopRewriteUtils.removeChildReferenceByPos(c, c.getInput().get(4),4); //col upper expr
 						HopRewriteUtils.addChildReference(c, new LiteralOp(1), 4);
 						c.refreshSizeInformation();
 					}

 					LOG.debug("Applied vectorizeRightIndexingCol");
 				}
 			}
 		}
 	}

 	/**
 	 *
 	 * @param hop
 	 * @throws HopsException
 	 */
 	@SuppressWarnings("unchecked")
 	private void vectorizeLeftIndexing( Hop hop )
 		throws HopsException
 	{
 		if( hop instanceof LeftIndexingOp ) //left indexing
 		{
 			LeftIndexingOp ihop0 = (LeftIndexingOp) hop;
 			boolean isSingleRow = ihop0.getRowLowerEqualsUpper();
 			boolean isSingleCol = ihop0.getColLowerEqualsUpper();
 			boolean appliedRow = false;

 			if( isSingleRow && isSingleCol )
 			{
 				//collect simple chains (w/o multiple consumers) of left indexing ops
 				ArrayList<Hop> ihops = new ArrayList<Hop>();
 				ihops.add(ihop0);
 				Hop current = ihop0;
 				while( current.getInput().get(0) instanceof LeftIndexingOp ) {
 					LeftIndexingOp tmp = (LeftIndexingOp) current.getInput().get(0);
 					if(    tmp.getParent().size()>1  //multiple consumers, i.e., not a simple chain
 						|| !((LeftIndexingOp) tmp).getRowLowerEqualsUpper() //row merge not applicable
 						|| tmp.getInput().get(2) != ihop0.getInput().get(2) //not the same row
 						|| tmp.getInput().get(0).getDim2() <= 1 ) //target is single column or unknown
 					{
 						break;
 					}
 					ihops.add( tmp );
 					current = tmp;
 				}

 				//apply rewrite if found candidates
 				if( ihops.size() > 1 ){
 					Hop input = current.getInput().get(0);
 					Hop rowExpr = ihop0.getInput().get(2); //keep before reset

 					//new row indexing operator
 					IndexingOp newRix = new IndexingOp("tmp1", input.getDataType(), input.getValueType(), input,
 							            rowExpr, rowExpr, new LiteralOp(1),
 							            HopRewriteUtils.createValueHop(input, false), true, false);
 					HopRewriteUtils.setOutputParameters(newRix, -1, -1, input.getRowsInBlock(), input.getColsInBlock(), -1);
 					newRix.refreshSizeInformation();

 					//rewrite bottom left indexing operator
 					HopRewriteUtils.removeChildReference(current, input); //input data
 					HopRewriteUtils.addChildReference(current, newRix, 0);

 					//reset row index all candidates and refresh sizes (bottom-up)
 					for( int i=ihops.size()-1; i>=0; i-- ) {
 						Hop c = ihops.get(i);
 						HopRewriteUtils.removeChildReferenceByPos(c, c.getInput().get(2), 2); //row lower expr
 						HopRewriteUtils.addChildReference(c, new LiteralOp(1), 2);
 						HopRewriteUtils.removeChildReferenceByPos(c, c.getInput().get(3), 3); //row upper expr
 						HopRewriteUtils.addChildReference(c, new LiteralOp(1), 3);
 						((LeftIndexingOp)c).setRowLowerEqualsUpper(true);
 						c.refreshSizeInformation();
 					}

 					//new row left indexing operator (for all parents, only intermediates are guaranteed to have 1 parent)
 					//(note: it's important to clone the parent list before creating newLix on top of ihop0)
 					ArrayList<Hop> ihop0parents = (ArrayList<Hop>) ihop0.getParent().clone();
 					ArrayList<Integer> ihop0parentsPos = new ArrayList<Integer>();
 					for( Hop parent : ihop0parents ) {
 						int posp = HopRewriteUtils.getChildReferencePos(parent, ihop0);
 						HopRewriteUtils.removeChildReferenceByPos(parent, ihop0, posp); //input data
 						ihop0parentsPos.add(posp);
 					}

 					LeftIndexingOp newLix = new LeftIndexingOp("tmp2", input.getDataType(), input.getValueType(), input, ihop0,
 													rowExpr, rowExpr, new LiteralOp(1),
 													HopRewriteUtils.createValueHop(input, false), true, false);
 					HopRewriteUtils.setOutputParameters(newLix, -1, -1, input.getRowsInBlock(), input.getColsInBlock(), -1);
 					newLix.refreshSizeInformation();

 					for( int i=0; i<ihop0parentsPos.size(); i++ ) {
 						Hop parent = ihop0parents.get(i);
 						int posp = ihop0parentsPos.get(i);
 						HopRewriteUtils.addChildReference(parent, newLix, posp);
 					}

 					appliedRow = true;
 					LOG.debug("Applied vectorizeLeftIndexingRow");
 				}
 			}

 			if( isSingleRow && isSingleCol && !appliedRow )
 			{

 				//collect simple chains (w/o multiple consumers) of left indexing ops
 				ArrayList<Hop> ihops = new ArrayList<Hop>();
 				ihops.add(ihop0);
 				Hop current = ihop0;
 				while( current.getInput().get(0) instanceof LeftIndexingOp ) {
 					LeftIndexingOp tmp = (LeftIndexingOp) current.getInput().get(0);
 					if(    tmp.getParent().size()>1  //multiple consumers, i.e., not a simple chain
 						|| !((LeftIndexingOp) tmp).getColLowerEqualsUpper() //row merge not applicable
 						|| tmp.getInput().get(4) != ihop0.getInput().get(4)  //not the same col
 						|| tmp.getInput().get(0).getDim1() <= 1 )  //target is single row or unknown
 					{
 						break;
 					}
 					ihops.add( tmp );
 					current = tmp;
 				}

 				//apply rewrite if found candidates
 				if( ihops.size() > 1 ){
 					Hop input = current.getInput().get(0);
 					Hop colExpr = ihop0.getInput().get(4); //keep before reset

 					//new row indexing operator
 					IndexingOp newRix = new IndexingOp("tmp1", input.getDataType(), input.getValueType(), input,
 							        new LiteralOp(1), HopRewriteUtils.createValueHop(input, true),
 									colExpr, colExpr, false, true);
 					HopRewriteUtils.setOutputParameters(newRix, -1, -1, input.getRowsInBlock(), input.getColsInBlock(), -1);
 					newRix.refreshSizeInformation();

 					//rewrite bottom left indexing operator
 					HopRewriteUtils.removeChildReference(current, input); //input data
 					HopRewriteUtils.addChildReference(current, newRix, 0);

 					//reset col index all candidates and refresh sizes (bottom-up)
 					for( int i=ihops.size()-1; i>=0; i-- ) {
 						Hop c = ihops.get(i);
 						HopRewriteUtils.removeChildReferenceByPos(c, c.getInput().get(4), 4); //col lower expr
 						HopRewriteUtils.addChildReference(c, new LiteralOp(1), 4);
 						HopRewriteUtils.removeChildReferenceByPos(c, c.getInput().get(5), 5); //col upper expr
 						HopRewriteUtils.addChildReference(c, new LiteralOp(1), 5);
 						((LeftIndexingOp)c).setColLowerEqualsUpper(true);
 						c.refreshSizeInformation();
 					}

 					//new row left indexing operator (for all parents, only intermediates are guaranteed to have 1 parent)
 					//(note: it's important to clone the parent list before creating newLix on top of ihop0)
 					ArrayList<Hop> ihop0parents = (ArrayList<Hop>) ihop0.getParent().clone();
 					ArrayList<Integer> ihop0parentsPos = new ArrayList<Integer>();
 					for( Hop parent : ihop0parents ) {
 						int posp = HopRewriteUtils.getChildReferencePos(parent, ihop0);
 						HopRewriteUtils.removeChildReferenceByPos(parent, ihop0, posp); //input data
 						ihop0parentsPos.add(posp);
 					}

 					LeftIndexingOp newLix = new LeftIndexingOp("tmp2", input.getDataType(), input.getValueType(), input, ihop0,
 							                        new LiteralOp(1), HopRewriteUtils.createValueHop(input, true),
 													colExpr, colExpr, false, true);
 					HopRewriteUtils.setOutputParameters(newLix, -1, -1, input.getRowsInBlock(), input.getColsInBlock(), -1);
 					newLix.refreshSizeInformation();

 					for( int i=0; i<ihop0parentsPos.size(); i++ ) {
 						Hop parent = ihop0parents.get(i);
 						int posp = ihop0parentsPos.get(i);
 						HopRewriteUtils.addChildReference(parent, newLix, posp);
 					}

 					appliedRow = true;
 					LOG.debug("Applied vectorizeLeftIndexingCol");
 				}
 			}
 		}
 	}
 }
	/*
	* Licensed to the Apache Software Foundation (ASF) under one
	* or more contributor license agreements. See the NOTICE file
	* distributed with this work for additional information
	* regarding copyright ownership. The ASF licenses this file
	* to you under the Apache License, Version 2.0 (the
	* "License"); you may not use this file except in compliance
	* with the License. You may obtain a copy of the License at
	*
	* http://www.apache.org/licenses/LICENSE-2.0
	*
	* Unless required by applicable law or agreed to in writing,
	* software distributed under the License is distributed on an
	* "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
	* KIND, either express or implied. See the License for the
	* specific language governing permissions and limitations
	* under the License.
	*/

	package org.apache.sysml.hops.rewrite;

	import java.util.ArrayList;

	import org.apache.commons.logging.Log;
	import org.apache.commons.logging.LogFactory;
	import org.apache.sysml.hops.Hop;
	import org.apache.sysml.hops.HopsException;
	import org.apache.sysml.hops.IndexingOp;
	import org.apache.sysml.hops.LeftIndexingOp;
	import org.apache.sysml.hops.LiteralOp;

	/**
	* Rule: Indexing vectorization. This rewrite rule set simplifies
	* multiple right / left indexing accesses within a DAG into row/column
	* index accesses, which is beneficial for two reasons: (1) it is an
	* enabler for later row/column partitioning, and (2) it reduces the number
	* of operations over potentially large data (i.e., prevents unnecessary MR
	* operations and reduces pressure on the buffer pool due to copy on write
	* on left indexing).
	*
	*/
	public class RewriteIndexingVectorization extends HopRewriteRule
	{

	private static final Log LOG = LogFactory.getLog(RewriteIndexingVectorization.class.getName());

	@Override
	public ArrayList<Hop> rewriteHopDAGs(ArrayList<Hop> roots, ProgramRewriteStatus state)
	throws HopsException
	{
	if( roots == null )
	return roots;

	for( Hop h : roots )
	rule_IndexingVectorization( h );

	return roots;
	}

	@Override
	public Hop rewriteHopDAG(Hop root, ProgramRewriteStatus state)
	throws HopsException
	{
	if( root == null )
	return root;

	rule_IndexingVectorization( root );

	return root;
	}


	/**
	*
	* @param hop
	* @param descendFirst
	* @throws HopsException
	*/
	private void rule_IndexingVectorization( Hop hop )
	throws HopsException
	{
	if(hop.getVisited() == Hop.VisitStatus.DONE)
	return;

	//recursively process children
	for( int i=0; i<hop.getInput().size(); i++)
	{
	Hop hi = hop.getInput().get(i);

	//apply indexing vectorization rewrites
	//MB: disabled right indexing rewrite because (1) piggybacked in MR anyway, (2) usually
	//not too much overhead, and (3) makes literal replacement more difficult
	//vectorizeRightIndexing( hi ); //e.g., multiple rightindexing X[i,1], X[i,3] -> X[i,];
	vectorizeLeftIndexing( hi ); //e.g., multiple left indexing X[i,1], X[i,3] -> X[i,];

	//process childs recursively after rewrites
	rule_IndexingVectorization( hi );
	}

	hop.setVisited(Hop.VisitStatus.DONE);
	}

	/**
	* Note: unnecessary row or column indexing then later removed via
	* dynamic rewrites
	*
	* @param hop
	* @throws HopsException
	*/
	@SuppressWarnings("unused")
	private void vectorizeRightIndexing( Hop hop )
	throws HopsException
	{
	if( hop instanceof IndexingOp ) //right indexing
	{
	IndexingOp ihop0 = (IndexingOp) hop;
	boolean isSingleRow = ihop0.getRowLowerEqualsUpper();
	boolean isSingleCol = ihop0.getColLowerEqualsUpper();
	boolean appliedRow = false;

	//search for multiple indexing in same row
	if( isSingleRow && isSingleCol ){
	Hop input = ihop0.getInput().get(0);
	//find candidate set
	//dependence on common subexpression elimination to find equal input / row expression
	ArrayList<Hop> ihops = new ArrayList<Hop>();
	ihops.add(ihop0);
	for( Hop c : input.getParent() ){
	if( c != ihop0 && c instanceof IndexingOp && c.getInput().get(0) == input
	&& ((IndexingOp) c).getRowLowerEqualsUpper()
	&& c.getInput().get(1)==ihop0.getInput().get(1) )
	{
	ihops.add( c );
	}
	}
	//apply rewrite if found candidates
	if( ihops.size() > 1 ){
	//new row indexing operator
	IndexingOp newRix = new IndexingOp("tmp", input.getDataType(), input.getValueType(), input,
	ihop0.getInput().get(1), ihop0.getInput().get(1), new LiteralOp(1),
	HopRewriteUtils.createValueHop(input, false), true, false);
	HopRewriteUtils.setOutputParameters(newRix, -1, -1, input.getRowsInBlock(), input.getColsInBlock(), -1);
	newRix.refreshSizeInformation();
	//rewire current operator and all candidates
	for( Hop c : ihops ) {
	HopRewriteUtils.removeChildReference(c, input); //input data
	HopRewriteUtils.addChildReference(c, newRix, 0);
	HopRewriteUtils.removeChildReferenceByPos(c, c.getInput().get(1),1); //row lower expr
	HopRewriteUtils.addChildReference(c, new LiteralOp(1), 1);
	HopRewriteUtils.removeChildReferenceByPos(c, c.getInput().get(2),2); //row upper expr
	HopRewriteUtils.addChildReference(c, new LiteralOp(1), 2);
	c.refreshSizeInformation();
	}

	appliedRow = true;
	LOG.debug("Applied vectorizeRightIndexingRow");
	}
	}

	//search for multiple indexing in same col
	if( isSingleRow && isSingleCol && !appliedRow ){
	Hop input = ihop0.getInput().get(0);
	//find candidate set
	//dependence on common subexpression elimination to find equal input / row expression
	ArrayList<Hop> ihops = new ArrayList<Hop>();
	ihops.add(ihop0);
	for( Hop c : input.getParent() ){
	if( c != ihop0 && c instanceof IndexingOp && c.getInput().get(0) == input
	&& ((IndexingOp) c).getColLowerEqualsUpper()
	&& c.getInput().get(3)==ihop0.getInput().get(3) )
	{
	ihops.add( c );
	}
	}
	//apply rewrite if found candidates
	if( ihops.size() > 1 ){
	//new row indexing operator
	IndexingOp newRix = new IndexingOp("tmp", input.getDataType(), input.getValueType(), input,
	new LiteralOp(1), HopRewriteUtils.createValueHop(input, true),
	ihop0.getInput().get(3), ihop0.getInput().get(3), false, true);
	HopRewriteUtils.setOutputParameters(newRix, -1, -1, input.getRowsInBlock(), input.getColsInBlock(), -1);
	newRix.refreshSizeInformation();
	//rewire current operator and all candidates
	for( Hop c : ihops ) {
	HopRewriteUtils.removeChildReference(c, input); //input data
	HopRewriteUtils.addChildReference(c, newRix, 0);
	HopRewriteUtils.removeChildReferenceByPos(c, c.getInput().get(3),3); //col lower expr
	HopRewriteUtils.addChildReference(c, new LiteralOp(1), 3);
	HopRewriteUtils.removeChildReferenceByPos(c, c.getInput().get(4),4); //col upper expr
	HopRewriteUtils.addChildReference(c, new LiteralOp(1), 4);
	c.refreshSizeInformation();
	}

	LOG.debug("Applied vectorizeRightIndexingCol");
	}
	}
	}
	}

	/**
	*
	* @param hop
	* @throws HopsException
	*/
	@SuppressWarnings("unchecked")
	private void vectorizeLeftIndexing( Hop hop )
	throws HopsException
	{
	if( hop instanceof LeftIndexingOp ) //left indexing
	{
	LeftIndexingOp ihop0 = (LeftIndexingOp) hop;
	boolean isSingleRow = ihop0.getRowLowerEqualsUpper();
	boolean isSingleCol = ihop0.getColLowerEqualsUpper();
	boolean appliedRow = false;

	if( isSingleRow && isSingleCol )
	{
	//collect simple chains (w/o multiple consumers) of left indexing ops
	ArrayList<Hop> ihops = new ArrayList<Hop>();
	ihops.add(ihop0);
	Hop current = ihop0;
	while( current.getInput().get(0) instanceof LeftIndexingOp ) {
	LeftIndexingOp tmp = (LeftIndexingOp) current.getInput().get(0);
	if( tmp.getParent().size()>1 //multiple consumers, i.e., not a simple chain
	\|\| !((LeftIndexingOp) tmp).getRowLowerEqualsUpper() //row merge not applicable
	\|\| tmp.getInput().get(2) != ihop0.getInput().get(2) //not the same row
	\|\| tmp.getInput().get(0).getDim2() <= 1 ) //target is single column or unknown
	{
	break;
	}
	ihops.add( tmp );
	current = tmp;
	}

	//apply rewrite if found candidates
	if( ihops.size() > 1 ){
	Hop input = current.getInput().get(0);
	Hop rowExpr = ihop0.getInput().get(2); //keep before reset

	//new row indexing operator
	IndexingOp newRix = new IndexingOp("tmp1", input.getDataType(), input.getValueType(), input,
	rowExpr, rowExpr, new LiteralOp(1),
	HopRewriteUtils.createValueHop(input, false), true, false);
	HopRewriteUtils.setOutputParameters(newRix, -1, -1, input.getRowsInBlock(), input.getColsInBlock(), -1);
	newRix.refreshSizeInformation();

	//rewrite bottom left indexing operator
	HopRewriteUtils.removeChildReference(current, input); //input data
	HopRewriteUtils.addChildReference(current, newRix, 0);

	//reset row index all candidates and refresh sizes (bottom-up)
	for( int i=ihops.size()-1; i>=0; i-- ) {
	Hop c = ihops.get(i);
	HopRewriteUtils.removeChildReferenceByPos(c, c.getInput().get(2), 2); //row lower expr
	HopRewriteUtils.addChildReference(c, new LiteralOp(1), 2);
	HopRewriteUtils.removeChildReferenceByPos(c, c.getInput().get(3), 3); //row upper expr
	HopRewriteUtils.addChildReference(c, new LiteralOp(1), 3);
	((LeftIndexingOp)c).setRowLowerEqualsUpper(true);
	c.refreshSizeInformation();
	}

	//new row left indexing operator (for all parents, only intermediates are guaranteed to have 1 parent)
	//(note: it's important to clone the parent list before creating newLix on top of ihop0)
	ArrayList<Hop> ihop0parents = (ArrayList<Hop>) ihop0.getParent().clone();
	ArrayList<Integer> ihop0parentsPos = new ArrayList<Integer>();
	for( Hop parent : ihop0parents ) {
	int posp = HopRewriteUtils.getChildReferencePos(parent, ihop0);
	HopRewriteUtils.removeChildReferenceByPos(parent, ihop0, posp); //input data
	ihop0parentsPos.add(posp);
	}

	LeftIndexingOp newLix = new LeftIndexingOp("tmp2", input.getDataType(), input.getValueType(), input, ihop0,
	rowExpr, rowExpr, new LiteralOp(1),
	HopRewriteUtils.createValueHop(input, false), true, false);
	HopRewriteUtils.setOutputParameters(newLix, -1, -1, input.getRowsInBlock(), input.getColsInBlock(), -1);
	newLix.refreshSizeInformation();

	for( int i=0; i<ihop0parentsPos.size(); i++ ) {
	Hop parent = ihop0parents.get(i);
	int posp = ihop0parentsPos.get(i);
	HopRewriteUtils.addChildReference(parent, newLix, posp);
	}

	appliedRow = true;
	LOG.debug("Applied vectorizeLeftIndexingRow");
	}
	}

	if( isSingleRow && isSingleCol && !appliedRow )
	{

	//collect simple chains (w/o multiple consumers) of left indexing ops
	ArrayList<Hop> ihops = new ArrayList<Hop>();
	ihops.add(ihop0);
	Hop current = ihop0;
	while( current.getInput().get(0) instanceof LeftIndexingOp ) {
	LeftIndexingOp tmp = (LeftIndexingOp) current.getInput().get(0);
	if( tmp.getParent().size()>1 //multiple consumers, i.e., not a simple chain
	\|\| !((LeftIndexingOp) tmp).getColLowerEqualsUpper() //row merge not applicable
	\|\| tmp.getInput().get(4) != ihop0.getInput().get(4) //not the same col
	\|\| tmp.getInput().get(0).getDim1() <= 1 ) //target is single row or unknown
	{
	break;
	}
	ihops.add( tmp );
	current = tmp;
	}

	//apply rewrite if found candidates
	if( ihops.size() > 1 ){
	Hop input = current.getInput().get(0);
	Hop colExpr = ihop0.getInput().get(4); //keep before reset

	//new row indexing operator
	IndexingOp newRix = new IndexingOp("tmp1", input.getDataType(), input.getValueType(), input,
	new LiteralOp(1), HopRewriteUtils.createValueHop(input, true),
	colExpr, colExpr, false, true);
	HopRewriteUtils.setOutputParameters(newRix, -1, -1, input.getRowsInBlock(), input.getColsInBlock(), -1);
	newRix.refreshSizeInformation();

	//rewrite bottom left indexing operator
	HopRewriteUtils.removeChildReference(current, input); //input data
	HopRewriteUtils.addChildReference(current, newRix, 0);

	//reset col index all candidates and refresh sizes (bottom-up)
	for( int i=ihops.size()-1; i>=0; i-- ) {
	Hop c = ihops.get(i);
	HopRewriteUtils.removeChildReferenceByPos(c, c.getInput().get(4), 4); //col lower expr
	HopRewriteUtils.addChildReference(c, new LiteralOp(1), 4);
	HopRewriteUtils.removeChildReferenceByPos(c, c.getInput().get(5), 5); //col upper expr
	HopRewriteUtils.addChildReference(c, new LiteralOp(1), 5);
	((LeftIndexingOp)c).setColLowerEqualsUpper(true);
	c.refreshSizeInformation();
	}

	//new row left indexing operator (for all parents, only intermediates are guaranteed to have 1 parent)
	//(note: it's important to clone the parent list before creating newLix on top of ihop0)
	ArrayList<Hop> ihop0parents = (ArrayList<Hop>) ihop0.getParent().clone();
	ArrayList<Integer> ihop0parentsPos = new ArrayList<Integer>();
	for( Hop parent : ihop0parents ) {
	int posp = HopRewriteUtils.getChildReferencePos(parent, ihop0);
	HopRewriteUtils.removeChildReferenceByPos(parent, ihop0, posp); //input data
	ihop0parentsPos.add(posp);
	}

	LeftIndexingOp newLix = new LeftIndexingOp("tmp2", input.getDataType(), input.getValueType(), input, ihop0,
	new LiteralOp(1), HopRewriteUtils.createValueHop(input, true),
	colExpr, colExpr, false, true);
	HopRewriteUtils.setOutputParameters(newLix, -1, -1, input.getRowsInBlock(), input.getColsInBlock(), -1);
	newLix.refreshSizeInformation();

	for( int i=0; i<ihop0parentsPos.size(); i++ ) {
	Hop parent = ihop0parents.get(i);
	int posp = ihop0parentsPos.get(i);
	HopRewriteUtils.addChildReference(parent, newLix, posp);
	}

	appliedRow = true;
	LOG.debug("Applied vectorizeLeftIndexingCol");
	}
	}
	}
	}
	}