Use the built-in float datatypes to implement geometric types

This patch makes the geometric operators and functions use the exported
function of the float4/float8 datatypes.  The main reason of doing so is
to check for underflow and overflow, and to handle NaNs consciously.

The float datatypes consider NaNs values to be equal and greater than
all non-NaN values.  This change considers NaNs equal only for equality
operators.  The placement operators, contains, overlaps, left/right of
etc. continue to return false when NaNs are involved.  We don't need
to worry about them being considered greater than any-NaN because there
aren't any basic comparison operators like less/greater than for the
geometric datatypes.

The changes may be summarised as:

* Check for underflow, overflow and division by zero
* Consider NaN values to be equal
* Return NULL when the distance is NaN for all closest point operators
* Favour not-NaN over NaN where it makes sense

The patch also replaces all occurrences of "double" as "float8".  They
are the same, but were used inconsistently in the same file.

Author: Emre Hasegeli
Reviewed-by: Kyotaro Horiguchi, Tomas Vondra

Discussion: https://www.postgresql.org/message-id/CAE2gYzxF7-5djV6-cEvqQu-fNsnt%3DEqbOURx7ZDg%2BVv6ZMTWbg%40mail.gmail.com

src/backend/access/gist/gistproc.c

@@ -55,7 +55,7 @@ rt_box_union(BOX *n, const BOX *a, const BOX *b)
  * Size of a BOX for penalty-calculation purposes.
  * The result can be +Infinity, but not NaN.
  */
-static double
+static float8
 size_box(const BOX *box)
 {
 	/*
@@ -76,20 +76,21 @@ size_box(const BOX *box)
 	 */
 	if (isnan(box->high.x) || isnan(box->high.y))
 		return get_float8_infinity();
-	return (box->high.x - box->low.x) * (box->high.y - box->low.y);
+	return float8_mul(float8_mi(box->high.x, box->low.x),
+					  float8_mi(box->high.y, box->low.y));
 }
 
 /*
  * Return amount by which the union of the two boxes is larger than
  * the original BOX's area.  The result can be +Infinity, but not NaN.
  */
-static double
+static float8
 box_penalty(const BOX *original, const BOX *new)
 {
 	BOX			unionbox;
 
 	rt_box_union(&unionbox, original, new);
-	return size_box(&unionbox) - size_box(original);
+	return float8_mi(size_box(&unionbox), size_box(original));
 }
 
 /*
@@ -263,7 +264,7 @@ typedef struct
 	/* Index of entry in the initial array */
 	int			index;
 	/* Delta between penalties of entry insertion into different groups */
-	double		delta;
+	float8		delta;
 } CommonEntry;
 
 /*
@@ -279,13 +280,13 @@ typedef struct
 
 	bool		first;			/* true if no split was selected yet */
 
-	double		leftUpper;		/* upper bound of left interval */
-	double		rightLower;		/* lower bound of right interval */
+	float8		leftUpper;		/* upper bound of left interval */
+	float8		rightLower;		/* lower bound of right interval */
 
 	float4		ratio;
 	float4		overlap;
 	int			dim;			/* axis of this split */
-	double		range;			/* width of general MBR projection to the
+	float8		range;			/* width of general MBR projection to the
 								 * selected axis */
 } ConsiderSplitContext;
 
@@ -294,7 +295,7 @@ typedef struct
  */
 typedef struct
 {
-	double		lower,
+	float8		lower,
 				upper;
 } SplitInterval;
 
@@ -304,7 +305,7 @@ typedef struct
 static int
 interval_cmp_lower(const void *i1, const void *i2)
 {
-	double		lower1 = ((const SplitInterval *) i1)->lower,
+	float8		lower1 = ((const SplitInterval *) i1)->lower,
 				lower2 = ((const SplitInterval *) i2)->lower;
 
 	return float8_cmp_internal(lower1, lower2);
@@ -316,7 +317,7 @@ interval_cmp_lower(const void *i1, const void *i2)
 static int
 interval_cmp_upper(const void *i1, const void *i2)
 {
-	double		upper1 = ((const SplitInterval *) i1)->upper,
+	float8		upper1 = ((const SplitInterval *) i1)->upper,
 				upper2 = ((const SplitInterval *) i2)->upper;
 
 	return float8_cmp_internal(upper1, upper2);
@@ -339,14 +340,14 @@ non_negative(float val)
  */
 static inline void
 g_box_consider_split(ConsiderSplitContext *context, int dimNum,
-					 double rightLower, int minLeftCount,
-					 double leftUpper, int maxLeftCount)
+					 float8 rightLower, int minLeftCount,
+					 float8 leftUpper, int maxLeftCount)
 {
 	int			leftCount,
 				rightCount;
 	float4		ratio,
 				overlap;
-	double		range;
+	float8		range;
 
 	/*
 	 * Calculate entries distribution ratio assuming most uniform distribution
@@ -369,8 +370,7 @@ g_box_consider_split(ConsiderSplitContext *context, int dimNum,
 	 * Ratio of split - quotient between size of lesser group and total
 	 * entries count.
 	 */
-	ratio = ((float4) Min(leftCount, rightCount)) /
-		((float4) context->entriesCount);
+	ratio = float4_div(Min(leftCount, rightCount), context->entriesCount);
 
 	if (ratio > LIMIT_RATIO)
 	{
@@ -384,11 +384,13 @@ g_box_consider_split(ConsiderSplitContext *context, int dimNum,
 		 * or less range with same overlap.
 		 */
 		if (dimNum == 0)
-			range = context->boundingBox.high.x - context->boundingBox.low.x;
+			range = float8_mi(context->boundingBox.high.x,
+							  context->boundingBox.low.x);
 		else
-			range = context->boundingBox.high.y - context->boundingBox.low.y;
+			range = float8_mi(context->boundingBox.high.y,
+							  context->boundingBox.low.y);
 
-		overlap = (leftUpper - rightLower) / range;
+		overlap = float8_div(float8_mi(leftUpper, rightLower), range);
 
 		/* If there is no previous selection, select this */
 		if (context->first)
@@ -444,20 +446,14 @@ g_box_consider_split(ConsiderSplitContext *context, int dimNum,
 
 /*
  * Compare common entries by their deltas.
- * (We assume the deltas can't be NaN.)
  */
 static int
 common_entry_cmp(const void *i1, const void *i2)
 {
-	double		delta1 = ((const CommonEntry *) i1)->delta,
+	float8		delta1 = ((const CommonEntry *) i1)->delta,
 				delta2 = ((const CommonEntry *) i2)->delta;
 
-	if (delta1 < delta2)
-		return -1;
-	else if (delta1 > delta2)
-		return 1;
-	else
-		return 0;
+	return float8_cmp_internal(delta1, delta2);
 }
 
 /*
@@ -531,7 +527,7 @@ gist_box_picksplit(PG_FUNCTION_ARGS)
 	context.first = true;		/* nothing selected yet */
 	for (dim = 0; dim < 2; dim++)
 	{
-		double		leftUpper,
+		float8		leftUpper,
 					rightLower;
 		int			i1,
 					i2;
@@ -728,7 +724,7 @@ gist_box_picksplit(PG_FUNCTION_ARGS)
 	 */
 	for (i = FirstOffsetNumber; i <= maxoff; i = OffsetNumberNext(i))
 	{
-		double		lower,
+		float8		lower,
 					upper;
 
 		/*
@@ -783,7 +779,7 @@ gist_box_picksplit(PG_FUNCTION_ARGS)
 		 * Calculate minimum number of entries that must be placed in both
 		 * groups, to reach LIMIT_RATIO.
 		 */
-		int			m = ceil(LIMIT_RATIO * (double) nentries);
+		int			m = ceil(LIMIT_RATIO * nentries);
 
 		/*
 		 * Calculate delta between penalties of join "common entries" to
@@ -792,8 +788,8 @@ gist_box_picksplit(PG_FUNCTION_ARGS)
 		for (i = 0; i < commonEntriesCount; i++)
 		{
 			box = DatumGetBoxP(entryvec->vector[commonEntries[i].index].key);
-			commonEntries[i].delta = Abs(box_penalty(leftBox, box) -
-										 box_penalty(rightBox, box));
+			commonEntries[i].delta = Abs(float8_mi(box_penalty(leftBox, box),
+												   box_penalty(rightBox, box)));
 		}
 
 		/*
@@ -1107,10 +1103,10 @@ gist_circle_compress(PG_FUNCTION_ARGS)
 		BOX		   *r;
 
 		r = (BOX *) palloc(sizeof(BOX));
-		r->high.x = in->center.x + in->radius;
-		r->low.x = in->center.x - in->radius;
-		r->high.y = in->center.y + in->radius;
-		r->low.y = in->center.y - in->radius;
+		r->high.x = float8_pl(in->center.x, in->radius);
+		r->low.x = float8_mi(in->center.x, in->radius);
+		r->high.y = float8_pl(in->center.y, in->radius);
+		r->low.y = float8_mi(in->center.y, in->radius);
 
 		retval = (GISTENTRY *) palloc(sizeof(GISTENTRY));
 		gistentryinit(*retval, PointerGetDatum(r),
@@ -1148,10 +1144,10 @@ gist_circle_consistent(PG_FUNCTION_ARGS)
 	 * rtree_internal_consistent even at leaf nodes.  (This works in part
 	 * because the index entries are bounding boxes not circles.)
 	 */
-	bbox.high.x = query->center.x + query->radius;
-	bbox.low.x = query->center.x - query->radius;
-	bbox.high.y = query->center.y + query->radius;
-	bbox.low.y = query->center.y - query->radius;
+	bbox.high.x = float8_pl(query->center.x, query->radius);
+	bbox.low.x = float8_mi(query->center.x, query->radius);
+	bbox.high.y = float8_pl(query->center.y, query->radius);
+	bbox.low.y = float8_mi(query->center.y, query->radius);
 
 	result = rtree_internal_consistent(DatumGetBoxP(entry->key),
 									   &bbox, strategy);
@@ -1216,10 +1212,10 @@ gist_point_fetch(PG_FUNCTION_ARGS)
 	DatumGetFloat8(DirectFunctionCall2(point_distance, \
 									   PointPGetDatum(p1), PointPGetDatum(p2)))
 
-static double
+static float8
 computeDistance(bool isLeaf, BOX *box, Point *point)
 {
-	double		result = 0.0;
+	float8		result = 0.0;
 
 	if (isLeaf)
 	{
@@ -1237,9 +1233,9 @@ computeDistance(bool isLeaf, BOX *box, Point *point)
 		/* point is over or below box */
 		Assert(box->low.y <= box->high.y);
 		if (point->y > box->high.y)
-			result = point->y - box->high.y;
+			result = float8_mi(point->y, box->high.y);
 		else if (point->y < box->low.y)
-			result = box->low.y - point->y;
+			result = float8_mi(box->low.y, point->y);
 		else
 			elog(ERROR, "inconsistent point values");
 	}
@@ -1248,9 +1244,9 @@ computeDistance(bool isLeaf, BOX *box, Point *point)
 		/* point is to left or right of box */
 		Assert(box->low.x <= box->high.x);
 		if (point->x > box->high.x)
-			result = point->x - box->high.x;
+			result = float8_mi(point->x, box->high.x);
 		else if (point->x < box->low.x)
-			result = box->low.x - point->x;
+			result = float8_mi(box->low.x, point->x);
 		else
 			elog(ERROR, "inconsistent point values");
 	}
@@ -1258,7 +1254,7 @@ computeDistance(bool isLeaf, BOX *box, Point *point)
 	{
 		/* closest point will be a vertex */
 		Point		p;
-		double		subresult;
+		float8		subresult;
 
 		result = point_point_distance(point, &box->low);
 
@@ -1449,7 +1445,7 @@ gist_point_distance(PG_FUNCTION_ARGS)
 {
 	GISTENTRY  *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
 	StrategyNumber strategy = (StrategyNumber) PG_GETARG_UINT16(2);
-	double		distance;
+	float8		distance;
 	StrategyNumber strategyGroup = strategy / GeoStrategyNumberOffset;
 
 	switch (strategyGroup)
@@ -1478,11 +1474,11 @@ gist_point_distance(PG_FUNCTION_ARGS)
  * This is a lower bound estimate of distance from point to indexed geometric
  * type.
  */
-static double
+static float8
 gist_bbox_distance(GISTENTRY *entry, Datum query,
 				   StrategyNumber strategy, bool *recheck)
 {
-	double		distance;
+	float8		distance;
 	StrategyNumber strategyGroup = strategy / GeoStrategyNumberOffset;
 
 	/* Bounding box distance is always inexact. */
@@ -1512,7 +1508,7 @@ gist_circle_distance(PG_FUNCTION_ARGS)
 
 	/* Oid subtype = PG_GETARG_OID(3); */
 	bool	   *recheck = (bool *) PG_GETARG_POINTER(4);
-	double		distance;
+	float8		distance;
 
 	distance = gist_bbox_distance(entry, query, strategy, recheck);
 
@@ -1528,7 +1524,7 @@ gist_poly_distance(PG_FUNCTION_ARGS)
 
 	/* Oid subtype = PG_GETARG_OID(3); */
 	bool	   *recheck = (bool *) PG_GETARG_POINTER(4);
-	double		distance;
+	float8		distance;
 
 	distance = gist_bbox_distance(entry, query, strategy, recheck);
 

src/backend/utils/adt/geo_spgist.c

@@ -84,14 +84,14 @@
  * Comparator for qsort
  *
  * We don't need to use the floating point macros in here, because this
- * is going only going to be used in a place to effect the performance
+ * is only going to be used in a place to effect the performance
  * of the index, not the correctness.
  */
 static int
 compareDoubles(const void *a, const void *b)
 {
-	double		x = *(double *) a;
-	double		y = *(double *) b;
+	float8		x = *(float8 *) a;
+	float8		y = *(float8 *) b;
 
 	if (x == y)
 		return 0;
@@ -100,8 +100,8 @@ compareDoubles(const void *a, const void *b)
 
 typedef struct
 {
-	double		low;
-	double		high;
+	float8		low;
+	float8		high;
 } Range;
 
 typedef struct
@@ -175,7 +175,7 @@ static RectBox *
 initRectBox(void)
 {
 	RectBox    *rect_box = (RectBox *) palloc(sizeof(RectBox));
-	double		infinity = get_float8_infinity();
+	float8		infinity = get_float8_infinity();
 
 	rect_box->range_box_x.left.low = -infinity;
 	rect_box->range_box_x.left.high = infinity;
@@ -418,10 +418,10 @@ spg_box_quad_picksplit(PG_FUNCTION_ARGS)
 	BOX		   *centroid;
 	int			median,
 				i;
-	double	   *lowXs = palloc(sizeof(double) * in->nTuples);
-	double	   *highXs = palloc(sizeof(double) * in->nTuples);
-	double	   *lowYs = palloc(sizeof(double) * in->nTuples);
-	double	   *highYs = palloc(sizeof(double) * in->nTuples);
+	float8	   *lowXs = palloc(sizeof(float8) * in->nTuples);
+	float8	   *highXs = palloc(sizeof(float8) * in->nTuples);
+	float8	   *lowYs = palloc(sizeof(float8) * in->nTuples);
+	float8	   *highYs = palloc(sizeof(float8) * in->nTuples);
 
 	/* Calculate median of all 4D coordinates */
 	for (i = 0; i < in->nTuples; i++)
@@ -434,10 +434,10 @@ spg_box_quad_picksplit(PG_FUNCTION_ARGS)
 		highYs[i] = box->high.y;
 	}
 
-	qsort(lowXs, in->nTuples, sizeof(double), compareDoubles);
-	qsort(highXs, in->nTuples, sizeof(double), compareDoubles);
-	qsort(lowYs, in->nTuples, sizeof(double), compareDoubles);
-	qsort(highYs, in->nTuples, sizeof(double), compareDoubles);
+	qsort(lowXs, in->nTuples, sizeof(float8), compareDoubles);
+	qsort(highXs, in->nTuples, sizeof(float8), compareDoubles);
+	qsort(lowYs, in->nTuples, sizeof(float8), compareDoubles);
+	qsort(highYs, in->nTuples, sizeof(float8), compareDoubles);
 
 	median = in->nTuples / 2;
 

src/include/utils/geo_decls.h

@@ -8,9 +8,6 @@
  *
  * src/include/utils/geo_decls.h
  *
- * NOTE
- *	  These routines do *not* use the float types from adt/.
- *
  *	  XXX These routines were not written by a numerical analyst.
  *
  *	  XXX I have made some attempt to flesh out the operators
@@ -21,14 +18,14 @@
 #ifndef GEO_DECLS_H
 #define GEO_DECLS_H
 
-#include <math.h>
-
 #include "fmgr.h"
 
 /*--------------------------------------------------------------------
  * Useful floating point utilities and constants.
- *-------------------------------------------------------------------*/
-
+ *-------------------------------------------------------------------
+ *
+ * XXX: They are not NaN-aware.
+ */
 
 #define EPSILON					1.0E-06
 
@@ -57,7 +54,7 @@
  *-------------------------------------------------------------------*/
 typedef struct
 {
-	double		x,
+	float8		x,
 				y;
 } Point;
 
@@ -89,7 +86,7 @@ typedef struct
  *-------------------------------------------------------------------*/
 typedef struct
 {
-	double		A,
+	float8		A,
 				B,
 				C;
 } LINE;
@@ -124,7 +121,7 @@ typedef struct
 typedef struct
 {
 	Point		center;
-	double		radius;
+	float8		radius;
 } CIRCLE;
 
 /*
@@ -178,6 +175,6 @@ typedef struct
  * in geo_ops.c
  */
 
-extern double pg_hypot(double x, double y);
+extern float8 pg_hypot(float8 x, float8 y);
 
 #endif							/* GEO_DECLS_H */