Updated SparsevecInnerProduct [skip ci]

src/bitutils.c

@@ -169,7 +169,7 @@ BitJaccardDistanceAvx512Popcount(uint32 bytes, unsigned char *ax, unsigned char
 #endif
 
 TARGET_XSAVE static bool
-SupportsAvx512Popcount(void)
+SupportsAvx512Popcount()
 {
 	unsigned int exx[4] = {0, 0, 0, 0};
 

src/hnsw.c

@@ -13,7 +13,6 @@
 #include "hnsw.h"
 #include "miscadmin.h"
 #include "nodes/pg_list.h"
-#include "storage/lwlock.h"
 #include "utils/float.h"
 #include "utils/guc.h"
 #include "utils/relcache.h"

src/hnsw.h

@@ -10,10 +10,6 @@
 #include "lib/pairingheap.h"
 #include "nodes/execnodes.h"
 #include "port.h"				/* for random() */
-#include "storage/bufpage.h"
-#include "storage/condition_variable.h"
-#include "storage/lwlock.h"
-#include "storage/s_lock.h"
 #include "utils/relptr.h"
 #include "utils/sampling.h"
 #include "vector.h"
@@ -372,13 +368,6 @@ typedef union
 	ItemPointerData indextid;
 }			HnswUnvisited;
 
-typedef struct HnswReadStreamData
-{
-	HnswUnvisited *unvisited;
-	int			unvisitedLength;
-	int			visited;
-}			HnswReadStreamData;
-
 typedef struct HnswScanOpaqueData
 {
 	const		HnswTypeInfo *typeInfo;
@@ -434,13 +423,13 @@ bool		HnswCheckNorm(HnswSupport * support, Datum value);
 Buffer		HnswNewBuffer(Relation index, ForkNumber forkNum);
 void		HnswInitPage(Buffer buf, Page page);
 void		HnswInit(void);
-List	   *HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation index, HnswSupport * support, int m, bool inserting, HnswElement skipElement, visited_hash * v, pairingheap **discarded, bool initVisited, int64 *tuples, bool maintenance);
+List	   *HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation index, HnswSupport * support, int m, bool inserting, HnswElement skipElement, visited_hash * v, pairingheap **discarded, bool initVisited, int64 *tuples);
 HnswElement HnswGetEntryPoint(Relation index);
 void		HnswGetMetaPageInfo(Relation index, int *m, HnswElement * entryPoint);
 void	   *HnswAlloc(HnswAllocator * allocator, Size size);
 HnswElement HnswInitElement(char *base, ItemPointer tid, int m, double ml, int maxLevel, HnswAllocator * alloc);
 HnswElement HnswInitElementFromBlock(BlockNumber blkno, OffsetNumber offno);
-void		HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint, Relation index, HnswSupport * support, int m, int efConstruction, bool existing, bool maintenance);
+void		HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint, Relation index, HnswSupport * support, int m, int efConstruction, bool existing);
 HnswSearchCandidate *HnswEntryCandidate(char *base, HnswElement entryPoint, HnswQuery * q, Relation index, HnswSupport * support, bool loadVec);
 void		HnswUpdateMetaPage(Relation index, int updateEntry, HnswElement entryPoint, BlockNumber insertPage, ForkNumber forkNum, bool building);
 void		HnswSetNeighborTuple(char *base, HnswNeighborTuple ntup, HnswElement e, int m);

src/hnswbuild.c

@@ -54,7 +54,6 @@
 #include "nodes/execnodes.h"
 #include "optimizer/optimizer.h"
 #include "storage/bufmgr.h"
-#include "storage/condition_variable.h"
 #include "tcop/tcopprot.h"
 #include "utils/datum.h"
 #include "utils/memutils.h"
@@ -470,7 +469,7 @@ InsertTupleInMemory(HnswBuildState * buildstate, HnswElement element)
 	}
 
 	/* Find neighbors for element */
-	HnswFindElementNeighbors(base, element, entryPoint, NULL, support, m, efConstruction, false, true);
+	HnswFindElementNeighbors(base, element, entryPoint, NULL, support, m, efConstruction, false);
 
 	/* Update graph in memory */
 	UpdateGraphInMemory(support, element, m, entryPoint, buildstate);
@@ -803,11 +802,7 @@ HnswParallelScanAndInsert(Relation heapRel, Relation indexRel, HnswShared * hnsw
 	buildstate.hnswarea = hnswarea;
 	InitAllocator(&buildstate.allocator, &HnswSharedMemoryAlloc, &buildstate);
 	scan = table_beginscan_parallel(heapRel,
-									ParallelTableScanFromHnswShared(hnswshared)
+									ParallelTableScanFromHnswShared(hnswshared));
-#if PG_VERSION_NUM >= 190000
-									,SO_NONE
-#endif
-		);
 	reltuples = table_index_build_scan(heapRel, indexRel, indexInfo,
 									   true, progress, BuildCallback,
 									   (void *) &buildstate, scan);

src/hnswinsert.c

@@ -6,7 +6,6 @@
 #include "nodes/execnodes.h"
 #include "storage/bufmgr.h"
 #include "storage/lmgr.h"
-#include "storage/lwlock.h"
 #include "utils/datum.h"
 #include "utils/memutils.h"
 #include "utils/rel.h"
@@ -731,7 +730,7 @@ HnswInsertTupleOnDisk(Relation index, HnswSupport * support, Datum value, ItemPo
 	}
 
 	/* Find neighbors for element */
-	HnswFindElementNeighbors(base, element, entryPoint, index, support, m, efConstruction, false, building);
+	HnswFindElementNeighbors(base, element, entryPoint, index, support, m, efConstruction, false);
 
 	/* Update graph on disk */
 	UpdateGraphOnDisk(index, support, element, m, entryPoint, building);

src/hnswscan.c

@@ -48,11 +48,11 @@ GetScanItems(IndexScanDesc scan, Datum value)
 
 	for (int lc = entryPoint->level; lc >= 1; lc--)
 	{
-		w = HnswSearchLayer(base, q, ep, 1, lc, index, support, m, false, NULL, NULL, NULL, true, NULL, false);
+		w = HnswSearchLayer(base, q, ep, 1, lc, index, support, m, false, NULL, NULL, NULL, true, NULL);
 		ep = w;
 	}
 
-	return HnswSearchLayer(base, q, ep, hnsw_ef_search, 0, index, support, m, false, NULL, &so->v, hnsw_iterative_scan != HNSW_ITERATIVE_SCAN_OFF ? &so->discarded : NULL, true, &so->tuples, false);
+	return HnswSearchLayer(base, q, ep, hnsw_ef_search, 0, index, support, m, false, NULL, &so->v, hnsw_iterative_scan != HNSW_ITERATIVE_SCAN_OFF ? &so->discarded : NULL, true, &so->tuples);
 }
 
 /*
@@ -83,7 +83,7 @@ ResumeScanItems(IndexScanDesc scan)
 		ep = lappend(ep, sc);
 	}
 
-	return HnswSearchLayer(base, &so->q, ep, batch_size, 0, index, &so->support, so->m, false, NULL, &so->v, &so->discarded, false, &so->tuples, false);
+	return HnswSearchLayer(base, &so->q, ep, batch_size, 0, index, &so->support, so->m, false, NULL, &so->v, &so->discarded, false, &so->tuples);
 }
 
 /*

src/hnswutils.c

@@ -21,10 +21,6 @@
 #include "varatt.h"
 #endif
 
-#if PG_VERSION_NUM >= 190000
-#include "storage/read_stream.h"
-#endif
-
 #if PG_VERSION_NUM < 170000
 static inline uint64
 murmurhash64(uint64 data)
@@ -535,12 +531,14 @@ HnswGetDistance(Datum a, Datum b, HnswSupport * support)
  * Load an element and optionally get its distance from q
  */
 static void
-HnswLoadElementImpl(Buffer buf, OffsetNumber offno, double *distance, HnswQuery * q, Relation index, HnswSupport * support, bool loadVec, double *maxDistance, HnswElement * element)
+HnswLoadElementImpl(BlockNumber blkno, OffsetNumber offno, double *distance, HnswQuery * q, Relation index, HnswSupport * support, bool loadVec, double *maxDistance, HnswElement * element)
 {
+	Buffer		buf;
 	Page		page;
 	HnswElementTuple etup;
 
 	/* Read vector */
+	buf = ReadBuffer(index, blkno);
 	LockBuffer(buf, BUFFER_LOCK_SHARE);
 	page = BufferGetPage(buf);
 
@@ -561,7 +559,7 @@ HnswLoadElementImpl(Buffer buf, OffsetNumber offno, double *distance, HnswQuery
 	if (distance == NULL || maxDistance == NULL || *distance < *maxDistance)
 	{
 		if (*element == NULL)
-			*element = HnswInitElementFromBlock(BufferGetBlockNumber(buf), offno);
+			*element = HnswInitElementFromBlock(blkno, offno);
 
 		HnswLoadElementFromTuple(*element, etup, true, loadVec);
 	}
@@ -575,9 +573,7 @@ HnswLoadElementImpl(Buffer buf, OffsetNumber offno, double *distance, HnswQuery
 void
 HnswLoadElement(HnswElement element, double *distance, HnswQuery * q, Relation index, HnswSupport * support, bool loadVec, double *maxDistance)
 {
-	Buffer		buf = ReadBuffer(index, element->blkno);
+	HnswLoadElementImpl(element->blkno, element->offno, distance, q, index, support, loadVec, maxDistance, &element);
-
-	HnswLoadElementImpl(buf, element->offno, distance, q, index, support, loadVec, maxDistance, &element);
 }
 
 /*
@@ -817,31 +813,11 @@ HnswLoadUnvisitedFromDisk(HnswElement element, HnswUnvisited * unvisited, int *u
 	}
 }
 
-#if PG_VERSION_NUM >= 190000
-/*
- * Get next block number for read stream
- */
-static BlockNumber
-HnswReadStreamNextBlock(ReadStream *stream, void *callback_private_data, void *per_buffer_data)
-{
-	HnswReadStreamData *streamData = callback_private_data;
-	OffsetNumber *offno = per_buffer_data;
-	HnswUnvisited *uv;
-
-	if (streamData->visited == streamData->unvisitedLength)
-		return InvalidBlockNumber;
-
-	uv = &streamData->unvisited[streamData->visited++];
-	*offno = ItemPointerGetOffsetNumber(&uv->indextid);
-	return ItemPointerGetBlockNumber(&uv->indextid);
-}
-#endif
-
 /*
  * Algorithm 2 from paper
  */
 List *
-HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation index, HnswSupport * support, int m, bool inserting, HnswElement skipElement, visited_hash * v, pairingheap **discarded, bool initVisited, int64 *tuples, bool maintenance)
+HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation index, HnswSupport * support, int m, bool inserting, HnswElement skipElement, visited_hash * v, pairingheap **discarded, bool initVisited, int64 *tuples)
 {
 	List	   *w = NIL;
 	pairingheap *C = pairingheap_allocate(CompareNearestCandidates, NULL);
@@ -856,21 +832,6 @@ HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation in
 	int			unvisitedLength;
 	bool		inMemory = index == NULL;
 
-#if PG_VERSION_NUM >= 190000
-	HnswReadStreamData streamData;
-	ReadStream *stream = NULL;
-
-	if (!inMemory)
-	{
-		int			flags = READ_STREAM_USE_BATCHING;
-
-		if (maintenance)
-			flags |= READ_STREAM_MAINTENANCE;
-
-		stream = read_stream_begin_relation(flags, NULL, index, MAIN_FORKNUM, HnswReadStreamNextBlock, &streamData, sizeof(OffsetNumber));
-	}
-#endif
-
 	if (v == NULL)
 	{
 		v = &vh;
@@ -933,23 +894,13 @@ HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation in
 		if (inMemory)
 			HnswLoadUnvisitedFromMemory(base, cElement, unvisited, &unvisitedLength, v, lc, localNeighborhood, neighborhoodSize);
 		else
-		{
 			HnswLoadUnvisitedFromDisk(cElement, unvisited, &unvisitedLength, v, index, m, lm, lc);
 
-#if PG_VERSION_NUM >= 190000
-			read_stream_resume(stream);
-
-			streamData.unvisited = unvisited;
-			streamData.unvisitedLength = unvisitedLength;
-			streamData.visited = 0;
-#endif
-		}
-
 		/* OK to count elements instead of tuples */
 		if (tuples != NULL)
 			(*tuples) += unvisitedLength;
 
-		for (int i = 0;; i++)
+		for (int i = 0; i < unvisitedLength; i++)
 		{
 			HnswElement eElement;
 			HnswSearchCandidate *e;
@@ -960,40 +911,18 @@ HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation in
 
 			if (inMemory)
 			{
-				if (i == unvisitedLength)
-					break;
-
 				eElement = unvisited[i].element;
 				eDistance = GetElementDistance(base, eElement, q, support);
 			}
 			else
 			{
-				Buffer		buf;
+				ItemPointer indextid = &unvisited[i].indextid;
-				OffsetNumber offno;
+				BlockNumber blkno = ItemPointerGetBlockNumber(indextid);
-
+				OffsetNumber offno = ItemPointerGetOffsetNumber(indextid);
-#if PG_VERSION_NUM >= 190000
-				void	   *offnoPtr;
-
-				buf = read_stream_next_buffer(stream, &offnoPtr);
-
-				if (!BufferIsValid(buf))
-					break;
-
-				offno = *((OffsetNumber *) offnoPtr);
-#else
-				ItemPointer indextid;
-
-				if (i == unvisitedLength)
-					break;
-
-				indextid = &unvisited[i].indextid;
-				buf = ReadBuffer(index, ItemPointerGetBlockNumber(indextid));
-				offno = ItemPointerGetOffsetNumber(indextid);
-#endif
 
 				/* Avoid any allocations if not adding */
 				eElement = NULL;
-				HnswLoadElementImpl(buf, offno, &eDistance, q, index, support, inserting, alwaysAdd || discarded != NULL ? NULL : &f->distance, &eElement);
+				HnswLoadElementImpl(blkno, offno, &eDistance, q, index, support, inserting, alwaysAdd || discarded != NULL ? NULL : &f->distance, &eElement);
 
 				if (eElement == NULL)
 					continue;
@@ -1049,11 +978,6 @@ HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation in
 		w = lappend(w, sc);
 	}
 
-#if PG_VERSION_NUM >= 190000
-	if (!inMemory)
-		read_stream_end(stream);
-#endif
-
 	return w;
 }
 
@@ -1349,7 +1273,7 @@ PrecomputeHash(char *base, HnswElement element)
  * Algorithm 1 from paper
  */
 void
-HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint, Relation index, HnswSupport * support, int m, int efConstruction, bool existing, bool maintenance)
+HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint, Relation index, HnswSupport * support, int m, int efConstruction, bool existing)
 {
 	List	   *ep;
 	List	   *w;
@@ -1376,7 +1300,7 @@ HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint
 	/* 1st phase: greedy search to insert level */
 	for (int lc = entryLevel; lc >= level + 1; lc--)
 	{
-		w = HnswSearchLayer(base, &q, ep, 1, lc, index, support, m, true, skipElement, NULL, NULL, true, NULL, maintenance);
+		w = HnswSearchLayer(base, &q, ep, 1, lc, index, support, m, true, skipElement, NULL, NULL, true, NULL);
 		ep = w;
 	}
 
@@ -1395,7 +1319,7 @@ HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint
 		List	   *lw = NIL;
 		ListCell   *lc2;
 
-		w = HnswSearchLayer(base, &q, ep, efConstruction, lc, index, support, m, true, skipElement, NULL, NULL, true, NULL, maintenance);
+		w = HnswSearchLayer(base, &q, ep, efConstruction, lc, index, support, m, true, skipElement, NULL, NULL, true, NULL);
 
 		/* Convert search candidates to candidates */
 		foreach(lc2, w)

src/hnswvacuum.c

@@ -218,7 +218,7 @@ RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element, HnswEleme
 	element->heaptidsLength = 0;
 
 	/* Find neighbors for element, skipping itself */
-	HnswFindElementNeighbors(base, element, entryPoint, index, support, m, efConstruction, true, true);
+	HnswFindElementNeighbors(base, element, entryPoint, index, support, m, efConstruction, true);
 
 	/* Zero memory for each element */
 	MemSet(ntup, 0, HNSW_TUPLE_ALLOC_SIZE);

src/ivfbuild.c

@@ -22,7 +22,6 @@
 #include "nodes/execnodes.h"
 #include "optimizer/optimizer.h"
 #include "storage/bufmgr.h"
-#include "storage/condition_variable.h"
 #include "tcop/tcopprot.h"
 #include "utils/memutils.h"
 #include "utils/rel.h"
@@ -63,13 +62,15 @@ AddSample(Datum *values, IvfflatBuildState * buildstate)
 	Datum		value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
 
 	/*
-	 * Check with KMEANS_NORM_PROC that the value can be normalized since
+	 * Normalize with KMEANS_NORM_PROC since spherical distance function
-	 * spherical distance function expects unit vectors
+	 * expects unit vectors
 	 */
 	if (buildstate->kmeansnormprocinfo != NULL)
 	{
 		if (!IvfflatCheckNorm(buildstate->kmeansnormprocinfo, buildstate->collation, value))
 			return;
+
+		value = IvfflatNormValue(buildstate->typeInfo, buildstate->collation, value);
 	}
 
 	if (samples->length < targsamples)
@@ -80,7 +81,7 @@ AddSample(Datum *values, IvfflatBuildState * buildstate)
 	else
 	{
 		if (buildstate->rowstoskip < 0)
-			buildstate->rowstoskip = reservoir_get_next_S(&buildstate->rstate, buildstate->samplerows, targsamples);
+			buildstate->rowstoskip = reservoir_get_next_S(&buildstate->rstate, samples->length, targsamples);
 
 		if (buildstate->rowstoskip <= 0)
 		{
@@ -96,9 +97,6 @@ AddSample(Datum *values, IvfflatBuildState * buildstate)
 
 		buildstate->rowstoskip -= 1;
 	}
-
-	/* Increment after reservoir_get_next_S */
-	buildstate->samplerows += 1;
 }
 
 /*
@@ -135,7 +133,6 @@ SampleRows(IvfflatBuildState * buildstate)
 	int			targsamples = buildstate->samples->maxlen;
 	BlockNumber totalblocks = RelationGetNumberOfBlocks(buildstate->heap);
 
-	buildstate->samplerows = 0;
 	buildstate->rowstoskip = -1;
 
 	BlockSampler_Init(&buildstate->bs, totalblocks, targsamples, RandomInt());
@@ -148,21 +145,6 @@ SampleRows(IvfflatBuildState * buildstate)
 		table_index_build_range_scan(buildstate->heap, buildstate->index, buildstate->indexInfo,
 									 false, true, false, targblock, 1, SampleCallback, (void *) buildstate, NULL);
 	}
-
-	/* Normalize if needed */
-	if (buildstate->kmeansnormprocinfo != NULL)
-	{
-		VectorArray samples = buildstate->samples;
-
-		for (int i = 0; i < samples->length; i++)
-		{
-			Datum		value = PointerGetDatum(VectorArrayGet(samples, i));
-			Datum		normValue = IvfflatNormValue(buildstate->typeInfo, buildstate->collation, value);
-
-			VectorArraySet(samples, i, DatumGetPointer(normValue));
-			pfree(DatumGetPointer(normValue));
-		}
-	}
 }
 
 /*
@@ -392,9 +374,6 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 	TupleDescInitEntry(buildstate->sortdesc, (AttrNumber) 1, "list", INT4OID, -1, 0);
 	TupleDescInitEntry(buildstate->sortdesc, (AttrNumber) 2, "tid", TIDOID, -1, 0);
 	TupleDescInitEntry(buildstate->sortdesc, (AttrNumber) 3, "vector", TupleDescAttr(buildstate->tupdesc, 0)->atttypid, -1, 0);
-#if PG_VERSION_NUM >= 190000
-	TupleDescFinalize(buildstate->sortdesc);
-#endif
 
 	buildstate->slot = MakeSingleTupleTableSlot(buildstate->sortdesc, &TTSOpsVirtual);
 
@@ -456,7 +435,7 @@ ComputeCenters(IvfflatBuildState * buildstate)
 	buildstate->samples = VectorArrayInit(numSamples, buildstate->dimensions, buildstate->centers->itemsize);
 	if (buildstate->heap != NULL)
 	{
-		IvfflatBench("sample rows", SampleRows(buildstate));
+		SampleRows(buildstate);
 
 		if (buildstate->samples->length < buildstate->lists)
 		{
@@ -671,11 +650,7 @@ IvfflatParallelScanAndSort(IvfflatSpool * ivfspool, IvfflatShared * ivfshared, S
 	ivfspool->sortstate = InitBuildSortState(buildstate.sortdesc, sortmem, coordinate);
 	buildstate.sortstate = ivfspool->sortstate;
 	scan = table_beginscan_parallel(ivfspool->heap,
-									ParallelTableScanFromIvfflatShared(ivfshared)
+									ParallelTableScanFromIvfflatShared(ivfshared));
-#if PG_VERSION_NUM >= 190000
-									,SO_NONE
-#endif
-		);
 	reltuples = table_index_build_scan(ivfspool->heap, ivfspool->index, indexInfo,
 									   true, progress, BuildCallback,
 									   (void *) &buildstate, scan);

src/ivfflat.h

@@ -9,7 +9,6 @@
 #include "lib/pairingheap.h"
 #include "nodes/execnodes.h"
 #include "port.h"				/* for random() */
-#include "storage/condition_variable.h"
 #include "utils/sampling.h"
 #include "utils/tuplesort.h"
 #include "vector.h"
@@ -214,8 +213,7 @@ typedef struct IvfflatBuildState
 	/* Sampling */
 	BlockSamplerData bs;
 	ReservoirStateData rstate;
-	double		samplerows;
+	int			rowstoskip;
-	double		rowstoskip;
 
 	/* Sorting */
 	Tuplesortstate *sortstate;

src/ivfscan.c

@@ -298,9 +298,6 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	so->tupdesc = CreateTemplateTupleDesc(2);
 	TupleDescInitEntry(so->tupdesc, (AttrNumber) 1, "distance", FLOAT8OID, -1, 0);
 	TupleDescInitEntry(so->tupdesc, (AttrNumber) 2, "heaptid", TIDOID, -1, 0);
-#if PG_VERSION_NUM >= 190000
-	TupleDescFinalize(so->tupdesc);
-#endif
 
 	/* Prep sort */
 	so->sortstate = InitScanSortState(so->tupdesc);

src/sparsevec.c

@@ -895,28 +895,24 @@ SparsevecInnerProduct(SparseVector * a, SparseVector * b)
 	float	   *ax = SPARSEVEC_VALUES(a);
 	float	   *bx = SPARSEVEC_VALUES(b);
 	float		distance = 0.0;
-	int			bpos = 0;
+	int			i = 0;
+	int			j = 0;
 
-	for (int i = 0; i < a->nnz; i++)
+	while (i < a->nnz && j < b->nnz)
 	{
 		int			ai = a->indices[i];
-
-		for (int j = bpos; j < b->nnz; j++)
-		{
 		int			bi = b->indices[j];
 
-			/* Only update when the same index */
 		if (ai == bi)
+		{
 			distance += ax[i] * bx[j];
-
+			i++;
-			/* Update start for next iteration */
+			j++;
-			if (ai >= bi)
-				bpos = j + 1;
-
-			/* Found or passed it */
-			if (bi >= ai)
-				break;
 		}
+		else if (ai < bi)
+			i++;
+		else
+			j++;
 	}
 
 	return distance;