Fix contrib/seg's GiST picksplit method.

This patch replaces Guttman's generalized split method with a simple
sort-by-center-points algorithm.  Since the data is only one-dimensional
we don't really need the slow and none-too-stable Guttman method.

This is in part a bug fix, since seg has the same size_alpha versus
size_beta typo that was recently fixed in contrib/cube.  It seems
prudent to apply this rather aggressive fix only in HEAD, though.
Back branches will just get the typo fix.

Alexander Korotkov, reviewed by Yeb Havinga

contrib/seg/seg.c

@@ -33,6 +33,16 @@ extern void seg_scanner_finish(void);
 extern int	 seg_yydebug;
 */
 
+/*
+ * Auxiliary data structure for picksplit method.
+ */
+typedef struct
+{
+	float		center;
+	OffsetNumber index;
+	SEG		   *data;
+} gseg_picksplit_item;
+
 /*
 ** Input/Output routines
 */
@@ -292,152 +302,104 @@ gseg_penalty(GISTENTRY *origentry, GISTENTRY *newentry, float *result)
 	return (result);
 }
 
+/*
+ * Compare function for gseg_picksplit_item: sort by center.
+ */
+static int
+gseg_picksplit_item_cmp(const void *a, const void *b)
+{
+	const gseg_picksplit_item *i1 = (const gseg_picksplit_item *) a;
+	const gseg_picksplit_item *i2 = (const gseg_picksplit_item *) b;
 
+	if (i1->center < i2->center)
+		return -1;
+	else if (i1->center == i2->center)
+		return 0;
+	else
+		return 1;
+}
 
 /*
-** The GiST PickSplit method for segments
-** We use Guttman's poly time split algorithm
-*/
+ * The GiST PickSplit method for segments
+ *
+ * We used to use Guttman's split algorithm here, but since the data is 1-D
+ * it's easier and more robust to just sort the segments by center-point and
+ * split at the middle.
+ */
 GIST_SPLITVEC *
 gseg_picksplit(GistEntryVector *entryvec,
 			   GIST_SPLITVEC *v)
 {
-	OffsetNumber i,
-				j;
-	SEG		   *datum_alpha,
-			   *datum_beta;
+	int			i;
 	SEG		   *datum_l,
-			   *datum_r;
-	SEG		   *union_d,
-			   *union_dl,
-			   *union_dr;
-	SEG		   *inter_d;
-	bool		firsttime;
-	float		size_alpha,
-				size_beta,
-				size_union,
-				size_inter;
-	float		size_waste,
-				waste;
-	float		size_l,
-				size_r;
-	int			nbytes;
-	OffsetNumber seed_1 = 1,
-				seed_2 = 2;
+			   *datum_r,
+			   *seg;
+	gseg_picksplit_item *sort_items;
 	OffsetNumber *left,
 			   *right;
 	OffsetNumber maxoff;
+	OffsetNumber firstright;
 
 #ifdef GIST_DEBUG
 	fprintf(stderr, "picksplit\n");
 #endif
 
-	maxoff = entryvec->n - 2;
-	nbytes = (maxoff + 2) * sizeof(OffsetNumber);
-	v->spl_left = (OffsetNumber *) palloc(nbytes);
-	v->spl_right = (OffsetNumber *) palloc(nbytes);
-
-	firsttime = true;
-	waste = 0.0;
-
-	for (i = FirstOffsetNumber; i < maxoff; i = OffsetNumberNext(i))
-	{
-		datum_alpha = (SEG *) DatumGetPointer(entryvec->vector[i].key);
-		for (j = OffsetNumberNext(i); j <= maxoff; j = OffsetNumberNext(j))
-		{
-			datum_beta = (SEG *) DatumGetPointer(entryvec->vector[j].key);
-
-			/* compute the wasted space by unioning these guys */
-			/* size_waste = size_union - size_inter; */
-			union_d = seg_union(datum_alpha, datum_beta);
-			rt_seg_size(union_d, &size_union);
-			inter_d = seg_inter(datum_alpha, datum_beta);
-			rt_seg_size(inter_d, &size_inter);
-			size_waste = size_union - size_inter;
+	/* Valid items in entryvec->vector[] are indexed 1..maxoff */
+	maxoff = entryvec->n - 1;
 
 	/*
-			 * are these a more promising split that what we've already seen?
+	 * Prepare the auxiliary array and sort it.
 	 */
-			if (size_waste > waste || firsttime)
+	sort_items = (gseg_picksplit_item *)
+		palloc(maxoff * sizeof(gseg_picksplit_item));
+	for (i = 1; i <= maxoff; i++)
 	{
-				waste = size_waste;
-				seed_1 = i;
-				seed_2 = j;
-				firsttime = false;
-			}
-		}
+		seg = (SEG *) DatumGetPointer(entryvec->vector[i].key);
+		/* center calculation is done this way to avoid possible overflow */
+		sort_items[i - 1].center = seg->lower*0.5f + seg->upper*0.5f;
+		sort_items[i - 1].index = i;
+		sort_items[i - 1].data = seg;
 	}
+	qsort(sort_items, maxoff, sizeof(gseg_picksplit_item),
+		  gseg_picksplit_item_cmp);
+
+	/* sort items below "firstright" will go into the left side */
+	firstright = maxoff / 2;
 
+	v->spl_left = (OffsetNumber *) palloc(maxoff * sizeof(OffsetNumber));
+	v->spl_right = (OffsetNumber *) palloc(maxoff * sizeof(OffsetNumber));
 	left = v->spl_left;
 	v->spl_nleft = 0;
 	right = v->spl_right;
 	v->spl_nright = 0;
 
-	datum_alpha = (SEG *) DatumGetPointer(entryvec->vector[seed_1].key);
-	datum_l = seg_union(datum_alpha, datum_alpha);
-	rt_seg_size(datum_l, &size_l);
-	datum_beta = (SEG *) DatumGetPointer(entryvec->vector[seed_2].key);
-	datum_r = seg_union(datum_beta, datum_beta);
-	rt_seg_size(datum_r, &size_r);
-
 	/*
-	 * Now split up the regions between the two seeds.	An important property
-	 * of this split algorithm is that the split vector v has the indices of
-	 * items to be split in order in its left and right vectors.  We exploit
-	 * this property by doing a merge in the code that actually splits the
-	 * page.
-	 *
-	 * For efficiency, we also place the new index tuple in this loop. This is
-	 * handled at the very end, when we have placed all the existing tuples
-	 * and i == maxoff + 1.
+	 * Emit segments to the left output page, and compute its bounding box.
 	 */
-
-	maxoff = OffsetNumberNext(maxoff);
-	for (i = FirstOffsetNumber; i <= maxoff; i = OffsetNumberNext(i))
-	{
-		/*
-		 * If we've already decided where to place this item, just put it on
-		 * the right list.	Otherwise, we need to figure out which page needs
-		 * the least enlargement in order to store the item.
-		 */
-
-		if (i == seed_1)
-		{
-			*left++ = i;
+	datum_l = (SEG *) palloc(sizeof(SEG));
+	memcpy(datum_l, sort_items[0].data, sizeof(SEG));
+	*left++ = sort_items[0].index;
 	v->spl_nleft++;
-			continue;
-		}
-		else if (i == seed_2)
+	for (i = 1; i < firstright; i++)
 	{
-			*right++ = i;
-			v->spl_nright++;
-			continue;
-		}
-
-		/* okay, which page needs least enlargement? */
-		datum_alpha = (SEG *) DatumGetPointer(entryvec->vector[i].key);
-		union_dl = seg_union(datum_l, datum_alpha);
-		union_dr = seg_union(datum_r, datum_alpha);
-		rt_seg_size(union_dl, &size_alpha);
-		rt_seg_size(union_dr, &size_beta);
-
-		/* pick which page to add it to */
-		if (size_alpha - size_l < size_beta - size_r)
-		{
-			datum_l = union_dl;
-			size_l = size_alpha;
-			*left++ = i;
+		datum_l = seg_union(datum_l, sort_items[i].data);
+		*left++ = sort_items[i].index;
 		v->spl_nleft++;
 	}
-		else
+
+	/*
+	 * Likewise for the right page.
+	 */
+	datum_r = (SEG *) palloc(sizeof(SEG));
+	memcpy(datum_r, sort_items[firstright].data, sizeof(SEG));
+	*right++ = sort_items[firstright].index;
+	v->spl_nright++;
+	for (i = firstright + 1; i < maxoff; i++)
 	{
-			datum_r = union_dr;
-			size_r = size_alpha;
-			*right++ = i;
+		datum_r = seg_union(datum_r, sort_items[i].data);
+		*right++ = sort_items[i].index;
 		v->spl_nright++;
 	}
-	}
-	*left = *right = FirstOffsetNumber; /* sentinel value, see dosplit() */
 
 	v->spl_ldatum = PointerGetDatum(datum_l);
 	v->spl_rdatum = PointerGetDatum(datum_r);