Refactor geometric functions and operators

The primary goal of this patch is to eliminate duplicate code and share
code between different geometric data types more often, to prepare the
ground for additional patches.  Until now the code reuse was limited,
probably because the simpler types (line and point) were implemented
after the more complex ones.

The changes are quite extensive and can be summarised as:

* Eliminate SQL-level function calls.
* Re-use more functions to implement others.
* Unify internal function names and signatures.
* Remove private functions from geo_decls.h.
* Replace should-not-happen checks with assertions.
* Add comments describe for various functions.
* Remove some unreachable code.
* Define delimiter symbols of line datatype like the other ones.
* Remove the GEODEBUG macro and printf() calls.
* Unify code style of a few oddly formatted lines.

While the goal was to cause minimal user-visible changes, it was not
possible to keep the original behavior in all cases - for example when
handling NaN values, or when reusing code makes the functions return
consistent results.

Author: Emre Hasegeli
Reviewed-by: Kyotaro Horiguchi, me

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

src/backend/utils/adt/geo_ops.c

@@ -38,24 +38,62 @@ enum path_delim
 	PATH_NONE, PATH_OPEN, PATH_CLOSED
 };
 
+/* Routines for points */
+static inline void point_construct(Point *result, float8 x, float8 y);
+static inline void point_add_point(Point *result, Point *pt1, Point *pt2);
+static inline void point_sub_point(Point *result, Point *pt1, Point *pt2);
+static inline void point_mul_point(Point *result, Point *pt1, Point *pt2);
+static inline void point_div_point(Point *result, Point *pt1, Point *pt2);
+static inline bool point_eq_point(Point *pt1, Point *pt2);
+static inline float8 point_dt(Point *pt1, Point *pt2);
+static inline float8 point_sl(Point *pt1, Point *pt2);
 static int	point_inside(Point *p, int npts, Point *plist);
+
+/* Routines for lines */
+static inline void line_construct(LINE *result, Point *pt, float8 m);
+static inline float8 line_invsl(LINE *line);
+static bool	line_interpt_line(Point *result, LINE *l1, LINE *l2);
+static bool line_contain_point(LINE *line, Point *point);
+static float8 line_closept_point(Point *result, LINE *line, Point *pt);
+
+/* Routines for line segments */
+static inline void statlseg_construct(LSEG *lseg, Point *pt1, Point *pt2);
+static inline float8 lseg_sl(LSEG *lseg);
+static inline float8 lseg_invsl(LSEG *lseg);
+static bool	lseg_interpt_line(Point *result, LSEG *lseg, LINE *line);
+static bool	lseg_interpt_lseg(Point *result, LSEG *l1, LSEG *l2);
 static int	lseg_crossing(double x, double y, double px, double py);
-static BOX *box_construct(double x1, double x2, double y1, double y2);
-static BOX *box_fill(BOX *result, double x1, double x2, double y1, double y2);
+static bool	lseg_contain_point(LSEG *lseg, Point *point);
+static float8 lseg_closept_point(Point *result, LSEG *lseg, Point *pt);
+static float8 lseg_closept_line(Point *result, LSEG *lseg, LINE *line);
+static float8 lseg_closept_lseg(Point *result, LSEG *l1, LSEG *l2);
+
+/* Routines for boxes */
+static inline void box_construct(BOX *result, Point *pt1, Point *pt2);
+static void box_cn(Point *center, BOX *box);
 static bool box_ov(BOX *box1, BOX *box2);
+static double box_ar(BOX *box);
 static double box_ht(BOX *box);
 static double box_wd(BOX *box);
+static bool box_contain_point(BOX *box, Point *point);
+static bool box_contain_box(BOX *box1, BOX *box2);
+static bool box_contain_lseg(BOX *box, LSEG *lseg);
+static bool box_interpt_lseg(Point *result, BOX *box, LSEG *lseg);
+static float8 box_closept_point(Point *result, BOX *box, Point *point);
+static float8 box_closept_lseg(Point *result, BOX *box, LSEG *lseg);
+
+/* Routines for circles */
 static double circle_ar(CIRCLE *circle);
-static CIRCLE *circle_copy(CIRCLE *circle);
-static LINE *line_construct_pm(Point *pt, double m);
-static void line_construct_pts(LINE *line, Point *pt1, Point *pt2);
-static bool lseg_intersect_internal(LSEG *l1, LSEG *l2);
-static double lseg_dt(LSEG *l1, LSEG *l2);
-static bool on_ps_internal(Point *pt, LSEG *lseg);
+
+/* Routines for polygons */
 static void make_bound_box(POLYGON *poly);
+static void poly_to_circle(CIRCLE *result, POLYGON *poly);
+static bool lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start);
+static bool poly_contain_poly(POLYGON *polya, POLYGON *polyb);
 static bool plist_same(int npts, Point *p1, Point *p2);
-static Point *point_construct(double x, double y);
-static Point *point_copy(Point *pt);
+static float8 dist_ppoly_internal(Point *pt, POLYGON *poly);
+
+/* Routines for encoding and decoding */
 static double single_decode(char *num, char **endptr_p,
 			  const char *type_name, const char *orig_string);
 static void single_encode(float8 x, StringInfo str);
@@ -67,17 +105,6 @@ static void path_decode(char *str, bool opentype, int npts, Point *p,
 			bool *isopen, char **endptr_p,
 			const char *type_name, const char *orig_string);
 static char *path_encode(enum path_delim path_delim, int npts, Point *pt);
-static void statlseg_construct(LSEG *lseg, Point *pt1, Point *pt2);
-static double box_ar(BOX *box);
-static void box_cn(Point *center, BOX *box);
-static Point *interpt_sl(LSEG *lseg, LINE *line);
-static bool has_interpt_sl(LSEG *lseg, LINE *line);
-static double dist_pl_internal(Point *pt, LINE *line);
-static double dist_ps_internal(Point *pt, LSEG *lseg);
-static Point *line_interpt_internal(LINE *l1, LINE *l2);
-static bool lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start);
-static Point *lseg_interpt_internal(LSEG *l1, LSEG *l2);
-static double dist_ppoly_internal(Point *pt, POLYGON *poly);
 
 
 /*
@@ -93,6 +120,8 @@ static double dist_ppoly_internal(Point *pt, POLYGON *poly);
 #define RDELIM_EP		']'
 #define LDELIM_C		'<'
 #define RDELIM_C		'>'
+#define LDELIM_L		'{'
+#define RDELIM_L		'}'
 
 
 /*
@@ -236,12 +265,9 @@ path_decode(char *str, bool opentype, int npts, Point *p,
 		p++;
 	}
 
-	while (isspace((unsigned char) *str))
-		str++;
 	while (depth > 0)
 	{
-		if ((*str == RDELIM)
-			|| ((*str == RDELIM_EP) && (*isopen) && (depth == 1)))
+		if (*str == RDELIM || (*str == RDELIM_EP && *isopen && depth == 1))
 		{
 			depth--;
 			str++;
@@ -440,55 +466,29 @@ box_send(PG_FUNCTION_ARGS)
 
 /*		box_construct	-		fill in a new box.
  */
-static BOX *
-box_construct(double x1, double x2, double y1, double y2)
-{
-	BOX		   *result = (BOX *) palloc(sizeof(BOX));
-
-	return box_fill(result, x1, x2, y1, y2);
-}
-
-
-/*		box_fill		-		fill in a given box struct
- */
-static BOX *
-box_fill(BOX *result, double x1, double x2, double y1, double y2)
+static inline void
+box_construct(BOX *result, Point *pt1, Point *pt2)
 {
-	if (x1 > x2)
+	if (pt1->x > pt2->x)
 	{
-		result->high.x = x1;
-		result->low.x = x2;
+		result->high.x = pt1->x;
+		result->low.x = pt2->x;
 	}
 	else
 	{
-		result->high.x = x2;
-		result->low.x = x1;
+		result->high.x = pt2->x;
+		result->low.x = pt1->x;
 	}
-	if (y1 > y2)
+	if (pt1->y > pt2->y)
 	{
-		result->high.y = y1;
-		result->low.y = y2;
+		result->high.y = pt1->y;
+		result->low.y = pt2->y;
 	}
 	else
 	{
-		result->high.y = y2;
-		result->low.y = y1;
+		result->high.y = pt2->y;
+		result->low.y = pt1->y;
 	}
-
-	return result;
-}
-
-
-/*		box_copy		-		copy a box
- */
-BOX *
-box_copy(BOX *box)
-{
-	BOX		   *result = (BOX *) palloc(sizeof(BOX));
-
-	memcpy((char *) result, (char *) box, sizeof(BOX));
-
-	return result;
 }
 
 
@@ -505,10 +505,8 @@ box_same(PG_FUNCTION_ARGS)
 	BOX		   *box1 = PG_GETARG_BOX_P(0);
 	BOX		   *box2 = PG_GETARG_BOX_P(1);
 
-	PG_RETURN_BOOL(FPeq(box1->high.x, box2->high.x) &&
-				   FPeq(box1->low.x, box2->low.x) &&
-				   FPeq(box1->high.y, box2->high.y) &&
-				   FPeq(box1->low.y, box2->low.y));
+	PG_RETURN_BOOL(point_eq_point(&box1->high, &box2->high) &&
+				   point_eq_point(&box1->low, &box2->low));
 }
 
 /*		box_overlap		-		does box1 overlap box2?
@@ -637,10 +635,7 @@ box_contained(PG_FUNCTION_ARGS)
 	BOX		   *box1 = PG_GETARG_BOX_P(0);
 	BOX		   *box2 = PG_GETARG_BOX_P(1);
 
-	PG_RETURN_BOOL(FPle(box1->high.x, box2->high.x) &&
-				   FPge(box1->low.x, box2->low.x) &&
-				   FPle(box1->high.y, box2->high.y) &&
-				   FPge(box1->low.y, box2->low.y));
+	PG_RETURN_BOOL(box_contain_box(box2, box1));
 }
 
 /*		box_contain		-		does box1 contain box2?
@@ -651,10 +646,19 @@ box_contain(PG_FUNCTION_ARGS)
 	BOX		   *box1 = PG_GETARG_BOX_P(0);
 	BOX		   *box2 = PG_GETARG_BOX_P(1);
 
-	PG_RETURN_BOOL(FPge(box1->high.x, box2->high.x) &&
+	PG_RETURN_BOOL(box_contain_box(box1, box2));
+}
+
+/*
+ * Check whether the box is in the box or on its border
+ */
+static bool
+box_contain_box(BOX *box1, BOX *box2)
+{
+	return FPge(box1->high.x, box2->high.x) &&
 		   FPle(box1->low.x, box2->low.x) &&
 		   FPge(box1->high.y, box2->high.y) &&
-				   FPle(box1->low.y, box2->low.y));
+		   FPle(box1->low.y, box2->low.y);
 }
 
 
@@ -757,7 +761,7 @@ box_width(PG_FUNCTION_ARGS)
 {
 	BOX		   *box = PG_GETARG_BOX_P(0);
 
-	PG_RETURN_FLOAT8(box->high.x - box->low.x);
+	PG_RETURN_FLOAT8(box_wd(box));
 }
 
 
@@ -769,7 +773,7 @@ box_height(PG_FUNCTION_ARGS)
 {
 	BOX		   *box = PG_GETARG_BOX_P(0);
 
-	PG_RETURN_FLOAT8(box->high.y - box->low.y);
+	PG_RETURN_FLOAT8(box_ht(box));
 }
 
 
@@ -787,7 +791,7 @@ box_distance(PG_FUNCTION_ARGS)
 	box_cn(&a, box1);
 	box_cn(&b, box2);
 
-	PG_RETURN_FLOAT8(HYPOT(a.x - b.x, a.y - b.y));
+	PG_RETURN_FLOAT8(point_dt(&a, &b));
 }
 
 
@@ -905,7 +909,7 @@ line_decode(char *s, const char *str, LINE *line)
 	if (*s++ != DELIM)
 		return false;
 	line->C = single_decode(s, &s, "line", str);
-	if (*s++ != '}')
+	if (*s++ != RDELIM_L)
 		return false;
 	while (isspace((unsigned char) *s))
 		s++;
@@ -926,7 +930,7 @@ line_in(PG_FUNCTION_ARGS)
 	s = str;
 	while (isspace((unsigned char) *s))
 		s++;
-	if (*s == '{')
+	if (*s == LDELIM_L)
 	{
 		if (!line_decode(s + 1, str, line))
 			ereport(ERROR,
@@ -940,12 +944,12 @@ line_in(PG_FUNCTION_ARGS)
 	}
 	else
 	{
-		path_decode(s, true, 2, &(lseg.p[0]), &isopen, NULL, "line", str);
-		if (FPeq(lseg.p[0].x, lseg.p[1].x) && FPeq(lseg.p[0].y, lseg.p[1].y))
+		path_decode(s, true, 2, &lseg.p[0], &isopen, NULL, "line", str);
+		if (point_eq_point(&lseg.p[0], &lseg.p[1]))
 			ereport(ERROR,
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 					 errmsg("invalid line specification: must be two distinct points")));
-		line_construct_pts(line, &lseg.p[0], &lseg.p[1]);
+		line_construct(line, &lseg.p[0], lseg_sl(&lseg));
 	}
 
 	PG_RETURN_LINE_P(line);
@@ -960,7 +964,8 @@ line_out(PG_FUNCTION_ARGS)
 	char	   *bstr = float8out_internal(line->B);
 	char	   *cstr = float8out_internal(line->C);
 
-	PG_RETURN_CSTRING(psprintf("{%s,%s,%s}", astr, bstr, cstr));
+	PG_RETURN_CSTRING(psprintf("%c%s%c%s%c%s%c", LDELIM_L, astr, DELIM, bstr,
+							   DELIM, cstr, RDELIM_L));
 }
 
 /*
@@ -1003,14 +1008,12 @@ line_send(PG_FUNCTION_ARGS)
  *		Internal form:	Ax+By+C=0
  *---------------------------------------------------------*/
 
-/* line_construct_pm()
- * point-slope
+/*
+ * Fill already-allocated LINE struct from the point and the slope
  */
-static LINE *
-line_construct_pm(Point *pt, double m)
+static inline void
+line_construct(LINE *result, Point *pt, float8 m)
 {
-	LINE	   *result = (LINE *) palloc(sizeof(LINE));
-
 	if (m == DBL_MAX)
 	{
 		/* vertical - use "x = C" */
@@ -1025,50 +1028,6 @@ line_construct_pm(Point *pt, double m)
 		result->B = -1.0;
 		result->C = pt->y - m * pt->x;
 	}
-
-	return result;
-}
-
-/*
- * Fill already-allocated LINE struct from two points on the line
- */
-static void
-line_construct_pts(LINE *line, Point *pt1, Point *pt2)
-{
-	if (FPeq(pt1->x, pt2->x))
-	{							/* vertical */
-		/* use "x = C" */
-		line->A = -1;
-		line->B = 0;
-		line->C = pt1->x;
-#ifdef GEODEBUG
-		printf("line_construct_pts- line is vertical\n");
-#endif
-	}
-	else if (FPeq(pt1->y, pt2->y))
-	{							/* horizontal */
-		/* use "y = C" */
-		line->A = 0;
-		line->B = -1;
-		line->C = pt1->y;
-#ifdef GEODEBUG
-		printf("line_construct_pts- line is horizontal\n");
-#endif
-	}
-	else
-	{
-		/* use "mx - y + yinter = 0" */
-		line->A = (pt2->y - pt1->y) / (pt2->x - pt1->x);
-		line->B = -1.0;
-		line->C = pt1->y - line->A * pt1->x;
-		/* on some platforms, the preceding expression tends to produce -0 */
-		if (line->C == 0.0)
-			line->C = 0.0;
-#ifdef GEODEBUG
-		printf("line_construct_pts- line is neither vertical nor horizontal (diffs x=%.*g, y=%.*g\n",
-			   DBL_DIG, (pt2->x - pt1->x), DBL_DIG, (pt2->y - pt1->y));
-#endif
-	}
 }
 
 /* line_construct_pp()
@@ -1081,7 +1040,8 @@ line_construct_pp(PG_FUNCTION_ARGS)
 	Point	   *pt2 = PG_GETARG_POINT_P(1);
 	LINE	   *result = (LINE *) palloc(sizeof(LINE));
 
-	line_construct_pts(result, pt1, pt2);
+	line_construct(result, pt1, point_sl(pt1, pt2));
+
 	PG_RETURN_LINE_P(result);
 }
 
@@ -1096,9 +1056,7 @@ line_intersect(PG_FUNCTION_ARGS)
 	LINE	   *l1 = PG_GETARG_LINE_P(0);
 	LINE	   *l2 = PG_GETARG_LINE_P(1);
 
-	PG_RETURN_BOOL(!DatumGetBool(DirectFunctionCall2(line_parallel,
-													 LinePGetDatum(l1),
-													 LinePGetDatum(l2))));
+	PG_RETURN_BOOL(line_interpt_line(NULL, l1, l2));
 }
 
 Datum
@@ -1107,10 +1065,7 @@ line_parallel(PG_FUNCTION_ARGS)
 	LINE	   *l1 = PG_GETARG_LINE_P(0);
 	LINE	   *l2 = PG_GETARG_LINE_P(1);
 
-	if (FPzero(l1->B))
-		PG_RETURN_BOOL(FPzero(l2->B));
-
-	PG_RETURN_BOOL(FPeq(l2->A, l1->A * (l2->B / l1->B)));
+	PG_RETURN_BOOL(!line_interpt_line(NULL, l1, l2));
 }
 
 Datum
@@ -1169,6 +1124,20 @@ line_eq(PG_FUNCTION_ARGS)
  *	Line arithmetic routines.
  *---------------------------------------------------------*/
 
+/*
+ * Return inverse slope of the line
+ */
+static inline float8
+line_invsl(LINE *line)
+{
+	if (FPzero(line->A))
+		return DBL_MAX;
+	if (FPzero(line->B))
+		return 0.0;
+	return line->B / line->A;
+}
+
+
 /* line_distance()
  * Distance between two lines.
  */
@@ -1178,16 +1147,14 @@ line_distance(PG_FUNCTION_ARGS)
 	LINE	   *l1 = PG_GETARG_LINE_P(0);
 	LINE	   *l2 = PG_GETARG_LINE_P(1);
 	float8		result;
-	Point	   *tmp;
+	Point		tmp;
 
-	if (!DatumGetBool(DirectFunctionCall2(line_parallel,
-										  LinePGetDatum(l1),
-										  LinePGetDatum(l2))))
+	if (line_interpt_line(NULL, l1, l2))	/* intersecting? */
 		PG_RETURN_FLOAT8(0.0);
 	if (FPzero(l1->B))			/* vertical? */
 		PG_RETURN_FLOAT8(fabs(l1->C - l2->C));
-	tmp = point_construct(0.0, l1->C);
-	result = dist_pl_internal(tmp, l2);
+	point_construct(&tmp, 0.0, l1->C);
+	result = line_closept_point(NULL, l2, &tmp);
 	PG_RETURN_FLOAT8(result);
 }
 
@@ -1201,9 +1168,9 @@ line_interpt(PG_FUNCTION_ARGS)
 	LINE	   *l2 = PG_GETARG_LINE_P(1);
 	Point	   *result;
 
-	result = line_interpt_internal(l1, l2);
+	result = (Point *) palloc(sizeof(Point));
 
-	if (result == NULL)
+	if (!line_interpt_line(result, l1, l2))
 		PG_RETURN_NULL();
 	PG_RETURN_POINT_P(result);
 }
@@ -1211,27 +1178,25 @@ line_interpt(PG_FUNCTION_ARGS)
 /*
  * Internal version of line_interpt
  *
- * returns a NULL pointer if no intersection point
+ * This returns true if two lines intersect (they do, if they are not
+ * parallel), false if they do not.  This also sets the intersection point
+ * to *result, if it is not NULL.
+ *
+ * NOTE: If the lines are identical then we will find they are parallel
+ * and report "no intersection".  This is a little weird, but since
+ * there's no *unique* intersection, maybe it's appropriate behavior.
  */
-static Point *
-line_interpt_internal(LINE *l1, LINE *l2)
+static bool
+line_interpt_line(Point *result, LINE *l1, LINE *l2)
 {
-	Point	   *result;
 	double		x,
 				y;
 
-	/*
-	 * NOTE: if the lines are identical then we will find they are parallel
-	 * and report "no intersection".  This is a little weird, but since
-	 * there's no *unique* intersection, maybe it's appropriate behavior.
-	 */
-	if (DatumGetBool(DirectFunctionCall2(line_parallel,
-										 LinePGetDatum(l1),
-										 LinePGetDatum(l2))))
-		return NULL;
-
 	if (FPzero(l1->B))			/* l1 vertical? */
 	{
+		if (FPzero(l2->B))		/* l2 vertical? */
+			return false;
+
 		x = l1->C;
 		y = (l2->A * x + l2->C);
 	}
@@ -1242,18 +1207,17 @@ line_interpt_internal(LINE *l1, LINE *l2)
 	}
 	else
 	{
+		if (FPeq(l2->A, l1->A * (l2->B / l1->B)))
+			return false;
+
 		x = (l1->C - l2->C) / (l2->A - l1->A);
 		y = (l1->A * x + l1->C);
 	}
-	result = point_construct(x, y);
 
-#ifdef GEODEBUG
-	printf("line_interpt- lines are A=%.*g, B=%.*g, C=%.*g, A=%.*g, B=%.*g, C=%.*g\n",
-		   DBL_DIG, l1->A, DBL_DIG, l1->B, DBL_DIG, l1->C, DBL_DIG, l2->A, DBL_DIG, l2->B, DBL_DIG, l2->C);
-	printf("line_interpt- lines intersect at (%.*g,%.*g)\n", DBL_DIG, x, DBL_DIG, y);
-#endif
+	if (result != NULL)
+		point_construct(result, x, y);
 
-	return result;
+	return true;
 }
 
 
@@ -1562,8 +1526,7 @@ path_inter(PG_FUNCTION_ARGS)
 	LSEG		seg1,
 				seg2;
 
-	if (p1->npts <= 0 || p2->npts <= 0)
-		PG_RETURN_BOOL(false);
+	Assert(p1->npts > 0 && p2->npts > 0);
 
 	b1.high.x = b1.low.x = p1->p[0].x;
 	b1.high.y = b1.low.y = p1->p[0].y;
@@ -1615,7 +1578,7 @@ path_inter(PG_FUNCTION_ARGS)
 
 			statlseg_construct(&seg1, &p1->p[iprev], &p1->p[i]);
 			statlseg_construct(&seg2, &p2->p[jprev], &p2->p[j]);
-			if (lseg_intersect_internal(&seg1, &seg2))
+			if (lseg_interpt_lseg(NULL, &seg1, &seg2))
 				PG_RETURN_BOOL(true);
 		}
 	}
@@ -1670,9 +1633,7 @@ path_distance(PG_FUNCTION_ARGS)
 			statlseg_construct(&seg1, &p1->p[iprev], &p1->p[i]);
 			statlseg_construct(&seg2, &p2->p[jprev], &p2->p[j]);
 
-			tmp = DatumGetFloat8(DirectFunctionCall2(lseg_distance,
-													 LsegPGetDatum(&seg1),
-													 LsegPGetDatum(&seg2)));
+			tmp = lseg_closept_lseg(NULL, &seg1, &seg2);
 			if (!have_min || tmp < min)
 			{
 				min = tmp;
@@ -1780,30 +1741,14 @@ point_send(PG_FUNCTION_ARGS)
 }
 
 
-static Point *
-point_construct(double x, double y)
+/*
+ * Initialize a point
+ */
+static inline void
+point_construct(Point *result, float8 x, float8 y)
 {
-	Point	   *result = (Point *) palloc(sizeof(Point));
-
 	result->x = x;
 	result->y = y;
-	return result;
-}
-
-
-static Point *
-point_copy(Point *pt)
-{
-	Point	   *result;
-
-	if (!PointerIsValid(pt))
-		return NULL;
-
-	result = (Point *) palloc(sizeof(Point));
-
-	result->x = pt->x;
-	result->y = pt->y;
-	return result;
 }
 
 
@@ -1876,7 +1821,7 @@ point_eq(PG_FUNCTION_ARGS)
 	Point	   *pt1 = PG_GETARG_POINT_P(0);
 	Point	   *pt2 = PG_GETARG_POINT_P(1);
 
-	PG_RETURN_BOOL(FPeq(pt1->x, pt2->x) && FPeq(pt1->y, pt2->y));
+	PG_RETURN_BOOL(point_eq_point(pt1, pt2));
 }
 
 Datum
@@ -1885,9 +1830,16 @@ point_ne(PG_FUNCTION_ARGS)
 	Point	   *pt1 = PG_GETARG_POINT_P(0);
 	Point	   *pt2 = PG_GETARG_POINT_P(1);
 
-	PG_RETURN_BOOL(FPne(pt1->x, pt2->x) || FPne(pt1->y, pt2->y));
+	PG_RETURN_BOOL(!point_eq_point(pt1, pt2));
+}
+
+static inline bool
+point_eq_point(Point *pt1, Point *pt2)
+{
+	return FPeq(pt1->x, pt2->x) && FPeq(pt1->y, pt2->y);
 }
 
+
 /*----------------------------------------------------------
  *	"Arithmetic" operators on points.
  *---------------------------------------------------------*/
@@ -1898,16 +1850,12 @@ point_distance(PG_FUNCTION_ARGS)
 	Point	   *pt1 = PG_GETARG_POINT_P(0);
 	Point	   *pt2 = PG_GETARG_POINT_P(1);
 
-	PG_RETURN_FLOAT8(HYPOT(pt1->x - pt2->x, pt1->y - pt2->y));
+	PG_RETURN_FLOAT8(point_dt(pt1, pt2));
 }
 
-double
+static inline float8
 point_dt(Point *pt1, Point *pt2)
 {
-#ifdef GEODEBUG
-	printf("point_dt- segment (%f,%f),(%f,%f) length is %f\n",
-		   pt1->x, pt1->y, pt2->x, pt2->y, HYPOT(pt1->x - pt2->x, pt1->y - pt2->y));
-#endif
 	return HYPOT(pt1->x - pt2->x, pt1->y - pt2->y);
 }
 
@@ -1921,12 +1869,35 @@ point_slope(PG_FUNCTION_ARGS)
 }
 
 
-double
+/*
+ * Return slope of two points
+ *
+ * Note that this function returns DBL_MAX when the points are the same.
+ */
+static inline float8
 point_sl(Point *pt1, Point *pt2)
 {
-	return (FPeq(pt1->x, pt2->x)
-			? (double) DBL_MAX
-			: (pt1->y - pt2->y) / (pt1->x - pt2->x));
+	if (FPeq(pt1->x, pt2->x))
+		return DBL_MAX;
+	if (FPeq(pt1->y, pt2->y))
+		return 0.0;
+	return (pt1->y - pt2->y) / (pt1->x - pt2->x);
+}
+
+
+/*
+ * Return inverse slope of two points
+ *
+ * Note that this function returns 0.0 when the points are the same.
+ */
+static inline float8
+point_invsl(Point *pt1, Point *pt2)
+{
+	if (FPeq(pt1->x, pt2->x))
+		return 0.0;
+	if (FPeq(pt1->y, pt2->y))
+		return DBL_MAX;
+	return (pt1->x - pt2->x) / (pt2->y - pt1->y);
 }
 
 
@@ -1952,7 +1923,7 @@ lseg_in(PG_FUNCTION_ARGS)
 	LSEG	   *lseg = (LSEG *) palloc(sizeof(LSEG));
 	bool		isopen;
 
-	path_decode(str, true, 2, &(lseg->p[0]), &isopen, NULL, "lseg", str);
+	path_decode(str, true, 2, &lseg->p[0], &isopen, NULL, "lseg", str);
 	PG_RETURN_LSEG_P(lseg);
 }
 
@@ -1962,7 +1933,7 @@ lseg_out(PG_FUNCTION_ARGS)
 {
 	LSEG	   *ls = PG_GETARG_LSEG_P(0);
 
-	PG_RETURN_CSTRING(path_encode(PATH_OPEN, 2, (Point *) &(ls->p[0])));
+	PG_RETURN_CSTRING(path_encode(PATH_OPEN, 2, &ls->p[0]));
 }
 
 /*
@@ -2012,16 +1983,13 @@ lseg_construct(PG_FUNCTION_ARGS)
 	Point	   *pt2 = PG_GETARG_POINT_P(1);
 	LSEG	   *result = (LSEG *) palloc(sizeof(LSEG));
 
-	result->p[0].x = pt1->x;
-	result->p[0].y = pt1->y;
-	result->p[1].x = pt2->x;
-	result->p[1].y = pt2->y;
+	statlseg_construct(result, pt1, pt2);
 
 	PG_RETURN_LSEG_P(result);
 }
 
 /* like lseg_construct, but assume space already allocated */
-static void
+static inline void
 statlseg_construct(LSEG *lseg, Point *pt1, Point *pt2)
 {
 	lseg->p[0].x = pt1->x;
@@ -2030,6 +1998,27 @@ statlseg_construct(LSEG *lseg, Point *pt1, Point *pt2)
 	lseg->p[1].y = pt2->y;
 }
 
+
+/*
+ * Return slope of the line segment
+ */
+static inline float8
+lseg_sl(LSEG *lseg)
+{
+	return point_sl(&lseg->p[0], &lseg->p[1]);
+}
+
+
+/*
+ * Return inverse slope of the line segment
+ */
+static inline float8
+lseg_invsl(LSEG *lseg)
+{
+	return point_invsl(&lseg->p[0], &lseg->p[1]);
+}
+
+
 Datum
 lseg_length(PG_FUNCTION_ARGS)
 {
@@ -2052,25 +2041,9 @@ lseg_intersect(PG_FUNCTION_ARGS)
 	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
 	LSEG	   *l2 = PG_GETARG_LSEG_P(1);
 
-	PG_RETURN_BOOL(lseg_intersect_internal(l1, l2));
+	PG_RETURN_BOOL(lseg_interpt_lseg(NULL, l1, l2));
 }
 
-static bool
-lseg_intersect_internal(LSEG *l1, LSEG *l2)
-{
-	LINE		ln;
-	Point	   *interpt;
-	bool		retval;
-
-	line_construct_pts(&ln, &l2->p[0], &l2->p[1]);
-	interpt = interpt_sl(l1, &ln);
-
-	if (interpt != NULL && on_ps_internal(interpt, l2))
-		retval = true;			/* interpt on l1 and l2 */
-	else
-		retval = false;
-	return retval;
-}
 
 Datum
 lseg_parallel(PG_FUNCTION_ARGS)
@@ -2078,39 +2051,19 @@ lseg_parallel(PG_FUNCTION_ARGS)
 	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
 	LSEG	   *l2 = PG_GETARG_LSEG_P(1);
 
-	PG_RETURN_BOOL(FPeq(point_sl(&l1->p[0], &l1->p[1]),
-						point_sl(&l2->p[0], &l2->p[1])));
+	PG_RETURN_BOOL(FPeq(lseg_sl(l1), lseg_sl(l2)));
 }
 
-/* lseg_perp()
+/*
  * Determine if two line segments are perpendicular.
- *
- * This code did not get the correct answer for
- *	'((0,0),(0,1))'::lseg ?-| '((0,0),(1,0))'::lseg
- * So, modified it to check explicitly for slope of vertical line
- *	returned by point_sl() and the results seem better.
- * - thomas 1998-01-31
  */
 Datum
 lseg_perp(PG_FUNCTION_ARGS)
 {
 	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
 	LSEG	   *l2 = PG_GETARG_LSEG_P(1);
-	double		m1,
-				m2;
-
-	m1 = point_sl(&(l1->p[0]), &(l1->p[1]));
-	m2 = point_sl(&(l2->p[0]), &(l2->p[1]));
 
-#ifdef GEODEBUG
-	printf("lseg_perp- slopes are %g and %g\n", m1, m2);
-#endif
-	if (FPzero(m1))
-		PG_RETURN_BOOL(FPeq(m2, DBL_MAX));
-	else if (FPzero(m2))
-		PG_RETURN_BOOL(FPeq(m1, DBL_MAX));
-
-	PG_RETURN_BOOL(FPeq(m1 / m2, -1.0));
+	PG_RETURN_BOOL(FPeq(lseg_sl(l1), lseg_invsl(l2)));
 }
 
 Datum
@@ -2136,10 +2089,8 @@ lseg_eq(PG_FUNCTION_ARGS)
 	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
 	LSEG	   *l2 = PG_GETARG_LSEG_P(1);
 
-	PG_RETURN_BOOL(FPeq(l1->p[0].x, l2->p[0].x) &&
-				   FPeq(l1->p[0].y, l2->p[0].y) &&
-				   FPeq(l1->p[1].x, l2->p[1].x) &&
-				   FPeq(l1->p[1].y, l2->p[1].y));
+	PG_RETURN_BOOL(point_eq_point(&l1->p[0], &l2->p[0]) &&
+				   point_eq_point(&l1->p[1], &l2->p[1]));
 }
 
 Datum
@@ -2148,10 +2099,8 @@ lseg_ne(PG_FUNCTION_ARGS)
 	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
 	LSEG	   *l2 = PG_GETARG_LSEG_P(1);
 
-	PG_RETURN_BOOL(!FPeq(l1->p[0].x, l2->p[0].x) ||
-				   !FPeq(l1->p[0].y, l2->p[0].y) ||
-				   !FPeq(l1->p[1].x, l2->p[1].x) ||
-				   !FPeq(l1->p[1].y, l2->p[1].y));
+	PG_RETURN_BOOL(!point_eq_point(&l1->p[0], &l2->p[0]) ||
+				   !point_eq_point(&l1->p[1], &l2->p[1]));
 }
 
 Datum
@@ -2210,33 +2159,7 @@ lseg_distance(PG_FUNCTION_ARGS)
 	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
 	LSEG	   *l2 = PG_GETARG_LSEG_P(1);
 
-	PG_RETURN_FLOAT8(lseg_dt(l1, l2));
-}
-
-/* lseg_dt()
- * Distance between two line segments.
- * Must check both sets of endpoints to ensure minimum distance is found.
- * - thomas 1998-02-01
- */
-static double
-lseg_dt(LSEG *l1, LSEG *l2)
-{
-	double		result,
-				d;
-
-	if (lseg_intersect_internal(l1, l2))
-		return 0.0;
-
-	d = dist_ps_internal(&l1->p[0], l2);
-	result = d;
-	d = dist_ps_internal(&l1->p[1], l2);
-	result = Min(result, d);
-	d = dist_ps_internal(&l2->p[0], l1);
-	result = Min(result, d);
-	d = dist_ps_internal(&l2->p[1], l1);
-	result = Min(result, d);
-
-	return result;
+	PG_RETURN_FLOAT8(lseg_closept_lseg(NULL, l1, l2));
 }
 
 
@@ -2254,57 +2177,38 @@ lseg_center(PG_FUNCTION_ARGS)
 	PG_RETURN_POINT_P(result);
 }
 
-static Point *
-lseg_interpt_internal(LSEG *l1, LSEG *l2)
-{
-	Point	   *result;
-	LINE		tmp1,
-				tmp2;
 
-	/*
-	 * Find the intersection of the appropriate lines, if any.
+/*
+ *		Find the intersection point of two segments (if any).
+ *
+ * This returns true if two line segments intersect, false if they do not.
+ * This also sets the intersection point to *result, if it is not NULL.
+ * This function is almost perfectly symmetric, even though it doesn't look
+ * like it.  See lseg_interpt_line() for the other half of it.
  */
-	line_construct_pts(&tmp1, &l1->p[0], &l1->p[1]);
-	line_construct_pts(&tmp2, &l2->p[0], &l2->p[1]);
-	result = line_interpt_internal(&tmp1, &tmp2);
-	if (!PointerIsValid(result))
-		return NULL;
+static bool
+lseg_interpt_lseg(Point *result, LSEG *l1, LSEG *l2)
+{
+	Point		interpt;
+	LINE		tmp;
 
-	/*
-	 * If the line intersection point isn't within l1 (or equivalently l2),
-	 * there is no valid segment intersection point at all.
-	 */
-	if (!on_ps_internal(result, l1) ||
-		!on_ps_internal(result, l2))
-	{
-		pfree(result);
-		return NULL;
-	}
+	line_construct(&tmp, &l2->p[0], lseg_sl(l2));
+	if (!lseg_interpt_line(&interpt, l1, &tmp))
+		return false;
 
 	/*
-	 * If there is an intersection, then check explicitly for matching
-	 * endpoints since there may be rounding effects with annoying lsb
-	 * residue. - tgl 1997-07-09
+	 * If the line intersection point isn't within l2, there is no valid
+	 * segment intersection point at all.
 	 */
-	if ((FPeq(l1->p[0].x, l2->p[0].x) && FPeq(l1->p[0].y, l2->p[0].y)) ||
-		(FPeq(l1->p[0].x, l2->p[1].x) && FPeq(l1->p[0].y, l2->p[1].y)))
-	{
-		result->x = l1->p[0].x;
-		result->y = l1->p[0].y;
-	}
-	else if ((FPeq(l1->p[1].x, l2->p[0].x) && FPeq(l1->p[1].y, l2->p[0].y)) ||
-			 (FPeq(l1->p[1].x, l2->p[1].x) && FPeq(l1->p[1].y, l2->p[1].y)))
-	{
-		result->x = l1->p[1].x;
-		result->y = l1->p[1].y;
-	}
+	if (!lseg_contain_point(l2, &interpt))
+		return false;
 
-	return result;
+	if (result != NULL)
+		*result = interpt;
+
+	return true;
 }
 
-/* lseg_interpt -
- *		Find the intersection point of two segments (if any).
- */
 Datum
 lseg_interpt(PG_FUNCTION_ARGS)
 {
@@ -2312,10 +2216,10 @@ lseg_interpt(PG_FUNCTION_ARGS)
 	LSEG	   *l2 = PG_GETARG_LSEG_P(1);
 	Point	   *result;
 
-	result = lseg_interpt_internal(l1, l2);
-	if (!PointerIsValid(result))
-		PG_RETURN_NULL();
+	result = (Point *) palloc(sizeof(Point));
 
+	if (!lseg_interpt_lseg(result, l1, l2))
+		PG_RETURN_NULL();
 	PG_RETURN_POINT_P(result);
 }
 
@@ -2340,15 +2244,9 @@ dist_pl(PG_FUNCTION_ARGS)
 	Point	   *pt = PG_GETARG_POINT_P(0);
 	LINE	   *line = PG_GETARG_LINE_P(1);
 
-	PG_RETURN_FLOAT8(dist_pl_internal(pt, line));
+	PG_RETURN_FLOAT8(line_closept_point(NULL, line, pt));
 }
 
-static double
-dist_pl_internal(Point *pt, LINE *line)
-{
-	return fabs((line->A * pt->x + line->B * pt->y + line->C) /
-				HYPOT(line->A, line->B));
-}
 
 /*
  * Distance from a point to a lseg
@@ -2359,60 +2257,7 @@ dist_ps(PG_FUNCTION_ARGS)
 	Point	   *pt = PG_GETARG_POINT_P(0);
 	LSEG	   *lseg = PG_GETARG_LSEG_P(1);
 
-	PG_RETURN_FLOAT8(dist_ps_internal(pt, lseg));
-}
-
-static double
-dist_ps_internal(Point *pt, LSEG *lseg)
-{
-	double		m;				/* slope of perp. */
-	LINE	   *ln;
-	double		result,
-				tmpdist;
-	Point	   *ip;
-
-	/*
-	 * Construct a line perpendicular to the input segment and through the
-	 * input point
-	 */
-	if (lseg->p[1].x == lseg->p[0].x)
-		m = 0;
-	else if (lseg->p[1].y == lseg->p[0].y)
-		m = (double) DBL_MAX;	/* slope is infinite */
-	else
-		m = (lseg->p[0].x - lseg->p[1].x) / (lseg->p[1].y - lseg->p[0].y);
-	ln = line_construct_pm(pt, m);
-
-#ifdef GEODEBUG
-	printf("dist_ps- line is A=%g B=%g C=%g from (point) slope (%f,%f) %g\n",
-		   ln->A, ln->B, ln->C, pt->x, pt->y, m);
-#endif
-
-	/*
-	 * Calculate distance to the line segment or to the nearest endpoint of
-	 * the segment.
-	 */
-
-	/* intersection is on the line segment? */
-	if ((ip = interpt_sl(lseg, ln)) != NULL)
-	{
-		/* yes, so use distance to the intersection point */
-		result = point_dt(pt, ip);
-#ifdef GEODEBUG
-		printf("dist_ps- distance is %f to intersection point is (%f,%f)\n",
-			   result, ip->x, ip->y);
-#endif
-	}
-	else
-	{
-		/* no, so use distance to the nearer endpoint */
-		result = point_dt(pt, &lseg->p[0]);
-		tmpdist = point_dt(pt, &lseg->p[1]);
-		if (tmpdist < result)
-			result = tmpdist;
-	}
-
-	return result;
+	PG_RETURN_FLOAT8(lseg_closept_point(NULL, lseg, pt));
 }
 
 /*
@@ -2429,21 +2274,10 @@ dist_ppath(PG_FUNCTION_ARGS)
 	int			i;
 	LSEG		lseg;
 
-	switch (path->npts)
-	{
-		case 0:
-			/* no points in path? then result is undefined... */
-			PG_RETURN_NULL();
-		case 1:
-			/* one point in path? then get distance between two points... */
-			result = point_dt(pt, &path->p[0]);
-			break;
-		default:
-			/* make sure the path makes sense... */
-			Assert(path->npts > 1);
+	Assert(path->npts > 0);
 
 	/*
-			 * the distance from a point to a path is the smallest distance
+	 * The distance from a point to a path is the smallest distance
 	 * from the point to any of its constituent segments.
 	 */
 	for (i = 0; i < path->npts; i++)
@@ -2456,19 +2290,18 @@ dist_ppath(PG_FUNCTION_ARGS)
 		{
 			if (!path->closed)
 				continue;
-					iprev = path->npts - 1; /* include the closure segment */
+			iprev = path->npts - 1; /* Include the closure segment */
 		}
 
 		statlseg_construct(&lseg, &path->p[iprev], &path->p[i]);
-				tmp = dist_ps_internal(pt, &lseg);
+		tmp = lseg_closept_point(NULL, &lseg, pt);
 		if (!have_min || tmp < result)
 		{
 			result = tmp;
 			have_min = true;
 		}
 	}
-			break;
-	}
+
 	PG_RETURN_FLOAT8(result);
 }
 
@@ -2480,15 +2313,8 @@ dist_pb(PG_FUNCTION_ARGS)
 {
 	Point	   *pt = PG_GETARG_POINT_P(0);
 	BOX		   *box = PG_GETARG_BOX_P(1);
-	float8		result;
-	Point	   *near;
-
-	near = DatumGetPointP(DirectFunctionCall2(close_pb,
-											  PointPGetDatum(pt),
-											  BoxPGetDatum(box)));
-	result = point_dt(near, pt);
 
-	PG_RETURN_FLOAT8(result);
+	PG_RETURN_FLOAT8(box_closept_point(NULL, box, pt));
 }
 
 /*
@@ -2502,12 +2328,12 @@ dist_sl(PG_FUNCTION_ARGS)
 	float8		result,
 				d2;
 
-	if (has_interpt_sl(lseg, line))
+	if (lseg_interpt_line(NULL, lseg, line))
 		result = 0.0;
 	else
 	{
-		result = dist_pl_internal(&lseg->p[0], line);
-		d2 = dist_pl_internal(&lseg->p[1], line);
+		result = line_closept_point(NULL, line, &lseg->p[0]);
+		d2 = line_closept_point(NULL, line, &lseg->p[1]);
 		/* XXX shouldn't we take the min not max? */
 		if (d2 > result)
 			result = d2;
@@ -2524,17 +2350,8 @@ dist_sb(PG_FUNCTION_ARGS)
 {
 	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
 	BOX		   *box = PG_GETARG_BOX_P(1);
-	Point	   *tmp;
-	Datum		result;
-
-	tmp = DatumGetPointP(DirectFunctionCall2(close_sb,
-											 LsegPGetDatum(lseg),
-											 BoxPGetDatum(box)));
-	result = DirectFunctionCall2(dist_pb,
-								 PointPGetDatum(tmp),
-								 BoxPGetDatum(box));
 
-	PG_RETURN_DATUM(result);
+	PG_RETURN_FLOAT8(box_closept_lseg(NULL, box, lseg));
 }
 
 /*
@@ -2584,11 +2401,8 @@ dist_ppoly(PG_FUNCTION_ARGS)
 {
 	Point	   *point = PG_GETARG_POINT_P(0);
 	POLYGON    *poly = PG_GETARG_POLYGON_P(1);
-	float8		result;
-
-	result = dist_ppoly_internal(point, poly);
 
-	PG_RETURN_FLOAT8(result);
+	PG_RETURN_FLOAT8(dist_ppoly_internal(point, poly));
 }
 
 Datum
@@ -2596,11 +2410,8 @@ dist_polyp(PG_FUNCTION_ARGS)
 {
 	POLYGON    *poly = PG_GETARG_POLYGON_P(0);
 	Point	   *point = PG_GETARG_POINT_P(1);
-	float8		result;
 
-	result = dist_ppoly_internal(point, poly);
-
-	PG_RETURN_FLOAT8(result);
+	PG_RETURN_FLOAT8(dist_ppoly_internal(point, poly));
 }
 
 static double
@@ -2624,19 +2435,19 @@ dist_ppoly_internal(Point *pt, POLYGON *poly)
 	seg.p[0].y = poly->p[0].y;
 	seg.p[1].x = poly->p[poly->npts - 1].x;
 	seg.p[1].y = poly->p[poly->npts - 1].y;
-	result = dist_ps_internal(pt, &seg);
+	result = lseg_closept_point(NULL, &seg, pt);
 #ifdef GEODEBUG
 	printf("dist_ppoly_internal- segment 0/n distance is %f\n", result);
 #endif
 
 	/* check distances for other segments */
-	for (i = 0; (i < poly->npts - 1); i++)
+	for (i = 0; i < poly->npts - 1; i++)
 	{
 		seg.p[0].x = poly->p[i].x;
 		seg.p[0].y = poly->p[i].y;
 		seg.p[1].x = poly->p[i + 1].x;
 		seg.p[1].y = poly->p[i + 1].y;
-		d = dist_ps_internal(pt, &seg);
+		d = lseg_closept_point(NULL, &seg, pt);
 #ifdef GEODEBUG
 		printf("dist_ppoly_internal- segment %d distance is %f\n", (i + 1), d);
 #endif
@@ -2655,49 +2466,51 @@ dist_ppoly_internal(Point *pt, POLYGON *poly)
  *				  lines and boxes, since there are typically two.
  *-------------------------------------------------------------------*/
 
-/* Get intersection point of lseg and line; returns NULL if no intersection */
-static Point *
-interpt_sl(LSEG *lseg, LINE *line)
+/*
+ * Check if the line segment intersects with the line
+ *
+ * This returns true if line segment intersects with line, false if they
+ * do not.  This also sets the intersection point to *result, if it is not
+ * NULL.
+ */
+static bool
+lseg_interpt_line(Point *result, LSEG *lseg, LINE *line)
 {
+	Point		interpt;
 	LINE		tmp;
-	Point	   *p;
-
-	line_construct_pts(&tmp, &lseg->p[0], &lseg->p[1]);
-	p = line_interpt_internal(&tmp, line);
-#ifdef GEODEBUG
-	printf("interpt_sl- segment is (%.*g %.*g) (%.*g %.*g)\n",
-		   DBL_DIG, lseg->p[0].x, DBL_DIG, lseg->p[0].y, DBL_DIG, lseg->p[1].x, DBL_DIG, lseg->p[1].y);
-	printf("interpt_sl- segment becomes line A=%.*g B=%.*g C=%.*g\n",
-		   DBL_DIG, tmp.A, DBL_DIG, tmp.B, DBL_DIG, tmp.C);
-#endif
-	if (PointerIsValid(p))
-	{
-#ifdef GEODEBUG
-		printf("interpt_sl- intersection point is (%.*g %.*g)\n", DBL_DIG, p->x, DBL_DIG, p->y);
-#endif
-		if (on_ps_internal(p, lseg))
-		{
-#ifdef GEODEBUG
-			printf("interpt_sl- intersection point is on segment\n");
-#endif
-		}
-		else
-			p = NULL;
-	}
 
-	return p;
-}
+	/*
+	 * First, we promote the line segment to a line, because we know how
+	 * to find the intersection point of two lines.  If they don't have
+	 * an intersection point, we are done.
+	 */
+	line_construct(&tmp, &lseg->p[0], lseg_sl(lseg));
+	if (!line_interpt_line(&interpt, &tmp, line))
+		return false;
 
-/* variant: just indicate if intersection point exists */
-static bool
-has_interpt_sl(LSEG *lseg, LINE *line)
-{
-	Point	   *tmp;
+	/*
+	 * Then, we check whether the intersection point is actually on the line
+	 * segment.
+	 */
+	if (!lseg_contain_point(lseg, &interpt))
+		return false;
+
+	if (result == NULL)
+		return true;
+
+	/*
+	 * If there is an intersection, then check explicitly for matching
+	 * endpoints since there may be rounding effects with annoying LSB
+	 * residue.
+	 */
+	if (point_eq_point(&lseg->p[0], &interpt))
+		*result = lseg->p[0];
+	else if (point_eq_point(&lseg->p[1], &interpt))
+		*result = lseg->p[1];
+	else
+		*result = interpt;
 
-	tmp = interpt_sl(lseg, line);
-	if (tmp)
 	return true;
-	return false;
 }
 
 /*---------------------------------------------------------------------
@@ -2705,277 +2518,217 @@ has_interpt_sl(LSEG *lseg, LINE *line)
  *				Point of closest proximity between objects.
  *-------------------------------------------------------------------*/
 
-/* close_pl -
+/*
  *		The intersection point of a perpendicular of the line
  *		through the point.
+ *
+ * This sets the closest point to the *result if it is not NULL and returns
+ * the distance to the closest point.
  */
+static float8
+line_closept_point(Point *result, LINE *line, Point *point)
+{
+	bool		retval;
+	Point       closept;
+	LINE		tmp;
+
+	/* We drop a perpendicular to find the intersection point. */
+	line_construct(&tmp, point, line_invsl(line));
+	retval = line_interpt_line(&closept, line, &tmp);
+	Assert(retval);		/* XXX: We need something better. */
+
+	if (result != NULL)
+		*result = closept;
+
+	/* Then we calculate the distance between the points. */
+	return point_dt(&closept, point);
+}
+
 Datum
 close_pl(PG_FUNCTION_ARGS)
 {
 	Point	   *pt = PG_GETARG_POINT_P(0);
 	LINE	   *line = PG_GETARG_LINE_P(1);
 	Point	   *result;
-	LINE	   *tmp;
-	double		invm;
 
 	result = (Point *) palloc(sizeof(Point));
 
-	if (FPzero(line->B))		/* vertical? */
-	{
-		result->x = line->C;
-		result->y = pt->y;
-		PG_RETURN_POINT_P(result);
-	}
-	if (FPzero(line->A))		/* horizontal? */
-	{
-		result->x = pt->x;
-		result->y = line->C;
-		PG_RETURN_POINT_P(result);
-	}
-	/* drop a perpendicular and find the intersection point */
+	line_closept_point(result, line, pt);
 
-	/* invert and flip the sign on the slope to get a perpendicular */
-	invm = line->B / line->A;
-	tmp = line_construct_pm(pt, invm);
-	result = line_interpt_internal(tmp, line);
-	Assert(result != NULL);
 	PG_RETURN_POINT_P(result);
 }
 
 
-/* close_ps()
+/*
  * Closest point on line segment to specified point.
- * Take the closest endpoint if the point is left, right,
- *	above, or below the segment, otherwise find the intersection
- *	point of the segment and its perpendicular through the point.
  *
- * Some tricky code here, relying on boolean expressions
- *	evaluating to only zero or one to use as an array index.
- *		bug fixes by gthaker@atl.lmco.com; May 1, 1998
+ * This sets the closest point to the *result if it is not NULL and returns
+ * the distance to the closest point.
  */
-Datum
-close_ps(PG_FUNCTION_ARGS)
+static float8
+lseg_closept_point(Point *result, LSEG *lseg, Point *pt)
 {
-	Point	   *pt = PG_GETARG_POINT_P(0);
-	LSEG	   *lseg = PG_GETARG_LSEG_P(1);
-	Point	   *result = NULL;
-	LINE	   *tmp;
-	double		invm;
-	int			xh,
-				yh;
-
-#ifdef GEODEBUG
-	printf("close_sp:pt->x %f pt->y %f\nlseg(0).x %f lseg(0).y %f  lseg(1).x %f lseg(1).y %f\n",
-		   pt->x, pt->y, lseg->p[0].x, lseg->p[0].y,
-		   lseg->p[1].x, lseg->p[1].y);
-#endif
+	Point		closept;
+	LINE		tmp;
 
-	/* xh (or yh) is the index of upper x( or y) end point of lseg */
-	/* !xh (or !yh) is the index of lower x( or y) end point of lseg */
-	xh = lseg->p[0].x < lseg->p[1].x;
-	yh = lseg->p[0].y < lseg->p[1].y;
+	/*
+	 * To find the closest point, we draw a perpendicular line from the point
+	 * to the line segment.
+	 */
+	line_construct(&tmp, pt, point_invsl(&lseg->p[0], &lseg->p[1]));
+	lseg_closept_line(&closept, lseg, &tmp);
 
-	if (FPeq(lseg->p[0].x, lseg->p[1].x))	/* vertical? */
-	{
-#ifdef GEODEBUG
-		printf("close_ps- segment is vertical\n");
-#endif
-		/* first check if point is below or above the entire lseg. */
-		if (pt->y < lseg->p[!yh].y)
-			result = point_copy(&lseg->p[!yh]); /* below the lseg */
-		else if (pt->y > lseg->p[yh].y)
-			result = point_copy(&lseg->p[yh]);	/* above the lseg */
 	if (result != NULL)
-			PG_RETURN_POINT_P(result);
+		*result = closept;
 
-		/* point lines along (to left or right) of the vertical lseg. */
+	return point_dt(&closept, pt);
+}
 
-		result = (Point *) palloc(sizeof(Point));
-		result->x = lseg->p[0].x;
-		result->y = pt->y;
-		PG_RETURN_POINT_P(result);
-	}
-	else if (FPeq(lseg->p[0].y, lseg->p[1].y))	/* horizontal? */
-	{
-#ifdef GEODEBUG
-		printf("close_ps- segment is horizontal\n");
-#endif
-		/* first check if point is left or right of the entire lseg. */
-		if (pt->x < lseg->p[!xh].x)
-			result = point_copy(&lseg->p[!xh]); /* left of the lseg */
-		else if (pt->x > lseg->p[xh].x)
-			result = point_copy(&lseg->p[xh]);	/* right of the lseg */
-		if (result != NULL)
-			PG_RETURN_POINT_P(result);
+Datum
+close_ps(PG_FUNCTION_ARGS)
+{
+	Point	   *pt = PG_GETARG_POINT_P(0);
+	LSEG	   *lseg = PG_GETARG_LSEG_P(1);
+	Point	   *result;
 
-		/* point lines along (at top or below) the horiz. lseg. */
 	result = (Point *) palloc(sizeof(Point));
-		result->x = pt->x;
-		result->y = lseg->p[0].y;
-		PG_RETURN_POINT_P(result);
-	}
-
-	/*
-	 * vert. and horiz. cases are down, now check if the closest point is one
-	 * of the end points or someplace on the lseg.
-	 */
-
-	invm = -1.0 / point_sl(&(lseg->p[0]), &(lseg->p[1]));
-	tmp = line_construct_pm(&lseg->p[!yh], invm);	/* lower edge of the
-													 * "band" */
-	if (pt->y < (tmp->A * pt->x + tmp->C))
-	{							/* we are below the lower edge */
-		result = point_copy(&lseg->p[!yh]); /* below the lseg, take lower end
-											 * pt */
-#ifdef GEODEBUG
-		printf("close_ps below: tmp A %f  B %f   C %f\n",
-			   tmp->A, tmp->B, tmp->C);
-#endif
-		PG_RETURN_POINT_P(result);
-	}
-	tmp = line_construct_pm(&lseg->p[yh], invm);	/* upper edge of the
-													 * "band" */
-	if (pt->y > (tmp->A * pt->x + tmp->C))
-	{							/* we are below the lower edge */
-		result = point_copy(&lseg->p[yh]);	/* above the lseg, take higher end
-											 * pt */
-#ifdef GEODEBUG
-		printf("close_ps above: tmp A %f  B %f   C %f\n",
-			   tmp->A, tmp->B, tmp->C);
-#endif
-		PG_RETURN_POINT_P(result);
-	}
-
-	/*
-	 * at this point the "normal" from point will hit lseg. The closest point
-	 * will be somewhere on the lseg
-	 */
-	tmp = line_construct_pm(pt, invm);
-#ifdef GEODEBUG
-	printf("close_ps- tmp A %f  B %f   C %f\n",
-		   tmp->A, tmp->B, tmp->C);
-#endif
-	result = interpt_sl(lseg, tmp);
 
-	/*
-	 * ordinarily we should always find an intersection point, but that could
-	 * fail in the presence of NaN coordinates, and perhaps even from simple
-	 * roundoff issues.  Return a SQL NULL if so.
-	 */
-	if (result == NULL)
+	if (isnan(lseg_closept_point(result, lseg, pt)))
 		PG_RETURN_NULL();
 
-#ifdef GEODEBUG
-	printf("close_ps- result.x %f  result.y %f\n", result->x, result->y);
-#endif
 	PG_RETURN_POINT_P(result);
 }
 
 
-/* close_lseg()
- * Closest point to l1 on l2.
+/*
+ * Closest point on line segment to line segment
+ *
+ * This sets the closest point to the *result if it is not NULL and returns
+ * the distance to the closest point.
  */
-Datum
-close_lseg(PG_FUNCTION_ARGS)
+static float8
+lseg_closept_lseg(Point *result, LSEG *l1, LSEG *l2)
 {
-	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
-	LSEG	   *l2 = PG_GETARG_LSEG_P(1);
-	Point	   *result = NULL;
 	Point		point;
 	double		dist;
 	double		d;
 
-	d = dist_ps_internal(&l1->p[0], l2);
+	d = lseg_closept_point(NULL, l1, &l2->p[0]);
 	dist = d;
-	memcpy(&point, &l1->p[0], sizeof(Point));
+	if (result != NULL)
+		*result = l2->p[0];
 
-	if ((d = dist_ps_internal(&l1->p[1], l2)) < dist)
+	d = lseg_closept_point(NULL, l1, &l2->p[1]);
+	if (d < dist)
 	{
 		dist = d;
-		memcpy(&point, &l1->p[1], sizeof(Point));
+		if (result != NULL)
+			*result = l2->p[1];
 	}
 
-	if (dist_ps_internal(&l2->p[0], l1) < dist)
-	{
-		result = DatumGetPointP(DirectFunctionCall2(close_ps,
-													PointPGetDatum(&l2->p[0]),
-													LsegPGetDatum(l1)));
-		memcpy(&point, result, sizeof(Point));
-		result = DatumGetPointP(DirectFunctionCall2(close_ps,
-													PointPGetDatum(&point),
-													LsegPGetDatum(l2)));
-	}
+	if (lseg_closept_point(&point, l2, &l1->p[0]) < dist)
+		d = lseg_closept_point(result, l1, &point);
 
-	if (dist_ps_internal(&l2->p[1], l1) < dist)
-	{
-		result = DatumGetPointP(DirectFunctionCall2(close_ps,
-													PointPGetDatum(&l2->p[1]),
-													LsegPGetDatum(l1)));
-		memcpy(&point, result, sizeof(Point));
-		result = DatumGetPointP(DirectFunctionCall2(close_ps,
-													PointPGetDatum(&point),
-													LsegPGetDatum(l2)));
-	}
+	if (lseg_closept_point(&point, l2, &l1->p[1]) < dist)
+		d = lseg_closept_point(result, l1, &point);
 
-	if (result == NULL)
-		result = point_copy(&point);
+	if (d < dist)
+		dist = d;
+
+	return dist;
+}
+
+Datum
+close_lseg(PG_FUNCTION_ARGS)
+{
+	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
+	LSEG	   *l2 = PG_GETARG_LSEG_P(1);
+	Point	   *result;
+
+	result = (Point *) palloc(sizeof(Point));
+
+	lseg_closept_lseg(result, l2, l1);
 
 	PG_RETURN_POINT_P(result);
 }
 
-/* close_pb()
+
+/*
  * Closest point on or in box to specified point.
+ *
+ * This sets the closest point to the *result if it is not NULL and returns
+ * the distance to the closest point.
  */
-Datum
-close_pb(PG_FUNCTION_ARGS)
+static float8
+box_closept_point(Point *result, BOX *box, Point *pt)
 {
-	Point	   *pt = PG_GETARG_POINT_P(0);
-	BOX		   *box = PG_GETARG_BOX_P(1);
-	LSEG		lseg,
-				seg;
-	Point		point;
+	LSEG		lseg;
+	Point		point,
+				closept;
 	double		dist,
 				d;
 
-	if (DatumGetBool(DirectFunctionCall2(on_pb,
-										 PointPGetDatum(pt),
-										 BoxPGetDatum(box))))
-		PG_RETURN_POINT_P(pt);
+	if (box_contain_point(box, pt))
+	{
+		if (result != NULL)
+			*result = *pt;
+
+		return 0.0;
+	}
 
 	/* pairwise check lseg distances */
 	point.x = box->low.x;
 	point.y = box->high.y;
 	statlseg_construct(&lseg, &box->low, &point);
-	dist = dist_ps_internal(pt, &lseg);
+	dist = lseg_closept_point(result, &lseg, pt);
 
-	statlseg_construct(&seg, &box->high, &point);
-	if ((d = dist_ps_internal(pt, &seg)) < dist)
+	statlseg_construct(&lseg, &box->high, &point);
+	d = lseg_closept_point(&closept, &lseg, pt);
+	if (d < dist)
 	{
 		dist = d;
-		memcpy(&lseg, &seg, sizeof(lseg));
+		if (result != NULL)
+			*result = closept;
 	}
 
 	point.x = box->high.x;
 	point.y = box->low.y;
-	statlseg_construct(&seg, &box->low, &point);
-	if ((d = dist_ps_internal(pt, &seg)) < dist)
+	statlseg_construct(&lseg, &box->low, &point);
+	d = lseg_closept_point(&closept, &lseg, pt);
+	if (d < dist)
 	{
 		dist = d;
-		memcpy(&lseg, &seg, sizeof(lseg));
+		if (result != NULL)
+			*result = closept;
 	}
 
-	statlseg_construct(&seg, &box->high, &point);
-	if ((d = dist_ps_internal(pt, &seg)) < dist)
+	statlseg_construct(&lseg, &box->high, &point);
+	d = lseg_closept_point(&closept, &lseg, pt);
+	if (d < dist)
 	{
 		dist = d;
-		memcpy(&lseg, &seg, sizeof(lseg));
+		if (result != NULL)
+			*result = closept;
 	}
 
-	PG_RETURN_DATUM(DirectFunctionCall2(close_ps,
-										PointPGetDatum(pt),
-										LsegPGetDatum(&lseg)));
+	return dist;
+}
+
+Datum
+close_pb(PG_FUNCTION_ARGS)
+{
+	Point	   *pt = PG_GETARG_POINT_P(0);
+	BOX		   *box = PG_GETARG_BOX_P(1);
+	Point	   *result;
+
+	result = (Point *) palloc(sizeof(Point));
+
+	box_closept_point(result, box, pt);
+
+	PG_RETURN_POINT_P(result);
 }
 
+
 /* close_sl()
  * Closest point on line to line segment.
  *
@@ -2995,16 +2748,17 @@ close_sl(PG_FUNCTION_ARGS)
 	float8		d1,
 				d2;
 
-	result = interpt_sl(lseg, line);
-	if (result)
+	result = (Point *) palloc(sizeof(Point));
+
+	if (lseg_interpt_line(result, lseg, line))
 		PG_RETURN_POINT_P(result);
 
-	d1 = dist_pl_internal(&lseg->p[0], line);
-	d2 = dist_pl_internal(&lseg->p[1], line);
+	d1 = line_closept_point(NULL, line, &lseg->p[0]);
+	d2 = line_closept_point(NULL, line, &lseg->p[1]);
 	if (d1 < d2)
-		result = point_copy(&lseg->p[0]);
+		*result = lseg->p[0];
 	else
-		result = point_copy(&lseg->p[1]);
+		*result = lseg->p[1];
 
 	PG_RETURN_POINT_P(result);
 #endif
@@ -3016,92 +2770,132 @@ close_sl(PG_FUNCTION_ARGS)
 	PG_RETURN_NULL();
 }
 
-/* close_ls()
+/*
  * Closest point on line segment to line.
+ *
+ * This sets the closest point to the *result if it is not NULL and returns
+ * the distance to the closest point.
+ *
+ * NOTE: When the lines are parallel, endpoints of one of the line segment
+ * are FPeq(), in presence of NaN or Infinitive coordinates, or perhaps =
+ * even because of simple roundoff issues, there may not be a single closest
+ * point.  We are likely to set the result to the second endpoint in these
+ * cases.
  */
+static float8
+lseg_closept_line(Point *result, LSEG *lseg, LINE *line)
+{
+	float8		dist1,
+				dist2;
+
+	if (lseg_interpt_line(result, lseg, line))
+		return 0.0;
+
+	dist1 = line_closept_point(NULL, line, &lseg->p[0]);
+	dist2 = line_closept_point(NULL, line, &lseg->p[1]);
+
+	if (dist1 < dist2)
+	{
+		if (result != NULL)
+			*result = lseg->p[0];
+
+		return dist1;
+	}
+	else
+	{
+		if (result != NULL)
+			*result = lseg->p[1];
+
+		return dist2;
+	}
+}
+
 Datum
 close_ls(PG_FUNCTION_ARGS)
 {
 	LINE	   *line = PG_GETARG_LINE_P(0);
 	LSEG	   *lseg = PG_GETARG_LSEG_P(1);
 	Point	   *result;
-	float8		d1,
-				d2;
 
-	result = interpt_sl(lseg, line);
-	if (result)
-		PG_RETURN_POINT_P(result);
+	result = (Point *) palloc(sizeof(Point));
 
-	d1 = dist_pl_internal(&lseg->p[0], line);
-	d2 = dist_pl_internal(&lseg->p[1], line);
-	if (d1 < d2)
-		result = point_copy(&lseg->p[0]);
-	else
-		result = point_copy(&lseg->p[1]);
+	lseg_closept_line(result, lseg, line);
 
 	PG_RETURN_POINT_P(result);
 }
 
-/* close_sb()
+
+/*
  * Closest point on or in box to line segment.
+ *
+ * This sets the closest point to the *result if it is not NULL and returns
+ * the distance to the closest point.
  */
-Datum
-close_sb(PG_FUNCTION_ARGS)
+static float8
+box_closept_lseg(Point *result, BOX *box, LSEG *lseg)
 {
-	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
-	BOX		   *box = PG_GETARG_BOX_P(1);
-	Point		point;
-	LSEG		bseg,
-				seg;
+	Point		point,
+				closept;
+	LSEG		bseg;
 	double		dist,
 				d;
 
-	/* segment intersects box? then just return closest point to center */
-	if (DatumGetBool(DirectFunctionCall2(inter_sb,
-										 LsegPGetDatum(lseg),
-										 BoxPGetDatum(box))))
-	{
-		box_cn(&point, box);
-		PG_RETURN_DATUM(DirectFunctionCall2(close_ps,
-											PointPGetDatum(&point),
-											LsegPGetDatum(lseg)));
-	}
+	if (box_interpt_lseg(result, box, lseg))
+		return 0.0;
 
 	/* pairwise check lseg distances */
 	point.x = box->low.x;
 	point.y = box->high.y;
 	statlseg_construct(&bseg, &box->low, &point);
-	dist = lseg_dt(lseg, &bseg);
+	dist = lseg_closept_lseg(result, &bseg, lseg);
 
-	statlseg_construct(&seg, &box->high, &point);
-	if ((d = lseg_dt(lseg, &seg)) < dist)
+	statlseg_construct(&bseg, &box->high, &point);
+	d = lseg_closept_lseg(&closept, &bseg, lseg);
+	if (d < dist)
 	{
 		dist = d;
-		memcpy(&bseg, &seg, sizeof(bseg));
+		if (result != NULL)
+			*result = closept;
 	}
 
 	point.x = box->high.x;
 	point.y = box->low.y;
-	statlseg_construct(&seg, &box->low, &point);
-	if ((d = lseg_dt(lseg, &seg)) < dist)
+	statlseg_construct(&bseg, &box->low, &point);
+	d = lseg_closept_lseg(&closept, &bseg, lseg);
+	if (d < dist)
 	{
 		dist = d;
-		memcpy(&bseg, &seg, sizeof(bseg));
+		if (result != NULL)
+			*result = closept;
 	}
 
-	statlseg_construct(&seg, &box->high, &point);
-	if ((d = lseg_dt(lseg, &seg)) < dist)
+	statlseg_construct(&bseg, &box->high, &point);
+	d = lseg_closept_lseg(&closept, &bseg, lseg);
+	if (d < dist)
 	{
 		dist = d;
-		memcpy(&bseg, &seg, sizeof(bseg));
+		if (result != NULL)
+			*result = closept;
 	}
 
-	/* OK, we now have the closest line segment on the box boundary */
-	PG_RETURN_DATUM(DirectFunctionCall2(close_lseg,
-										LsegPGetDatum(lseg),
-										LsegPGetDatum(&bseg)));
+	return dist;
 }
 
+Datum
+close_sb(PG_FUNCTION_ARGS)
+{
+	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
+	BOX		   *box = PG_GETARG_BOX_P(1);
+	Point	   *result;
+
+	result = (Point *) palloc(sizeof(Point));
+
+	box_closept_lseg(result, box, lseg);
+
+	PG_RETURN_POINT_P(result);
+}
+
+
 Datum
 close_lb(PG_FUNCTION_ARGS)
 {
@@ -3123,37 +2917,55 @@ close_lb(PG_FUNCTION_ARGS)
  *				Whether one object lies completely within another.
  *-------------------------------------------------------------------*/
 
-/* on_pl -
+/*
  *		Does the point satisfy the equation?
  */
+static bool
+line_contain_point(LINE *line, Point *point)
+{
+	return FPzero(line->A * point->x + line->B * point->y + line->C);
+}
+
 Datum
 on_pl(PG_FUNCTION_ARGS)
 {
 	Point	   *pt = PG_GETARG_POINT_P(0);
 	LINE	   *line = PG_GETARG_LINE_P(1);
 
-	PG_RETURN_BOOL(FPzero(line->A * pt->x + line->B * pt->y + line->C));
+	PG_RETURN_BOOL(line_contain_point(line, pt));
 }
 
 
-/* on_ps -
+/*
  *		Determine colinearity by detecting a triangle inequality.
  * This algorithm seems to behave nicely even with lsb residues - tgl 1997-07-09
  */
+static bool
+lseg_contain_point(LSEG *lseg, Point *pt)
+{
+	return FPeq(point_dt(pt, &lseg->p[0]) +
+				point_dt(pt, &lseg->p[1]),
+				point_dt(&lseg->p[0], &lseg->p[1]));
+}
+
 Datum
 on_ps(PG_FUNCTION_ARGS)
 {
 	Point	   *pt = PG_GETARG_POINT_P(0);
 	LSEG	   *lseg = PG_GETARG_LSEG_P(1);
 
-	PG_RETURN_BOOL(on_ps_internal(pt, lseg));
+	PG_RETURN_BOOL(lseg_contain_point(lseg, pt));
 }
 
+
+/*
+ * Check whether the point is in the box or on its border
+ */
 static bool
-on_ps_internal(Point *pt, LSEG *lseg)
+box_contain_point(BOX *box, Point *point)
 {
-	return FPeq(point_dt(pt, &lseg->p[0]) + point_dt(pt, &lseg->p[1]),
-				point_dt(&lseg->p[0], &lseg->p[1]));
+	return box->high.x >= point->x && box->low.x <= point->x &&
+		   box->high.y >= point->y && box->low.y <= point-> y;
 }
 
 Datum
@@ -3162,8 +2974,7 @@ on_pb(PG_FUNCTION_ARGS)
 	Point	   *pt = PG_GETARG_POINT_P(0);
 	BOX		   *box = PG_GETARG_BOX_P(1);
 
-	PG_RETURN_BOOL(pt->x <= box->high.x && pt->x >= box->low.x &&
-				   pt->y <= box->high.y && pt->y >= box->low.y);
+	PG_RETURN_BOOL(box_contain_point(box, pt));
 }
 
 Datum
@@ -3172,8 +2983,7 @@ box_contain_pt(PG_FUNCTION_ARGS)
 	BOX		   *box = PG_GETARG_BOX_P(0);
 	Point	   *pt = PG_GETARG_POINT_P(1);
 
-	PG_RETURN_BOOL(pt->x <= box->high.x && pt->x >= box->low.x &&
-				   pt->y <= box->high.y && pt->y >= box->low.y);
+	PG_RETURN_BOOL(box_contain_point(box, pt));
 }
 
 /* on_ppath -
@@ -3217,18 +3027,33 @@ on_ppath(PG_FUNCTION_ARGS)
 	PG_RETURN_BOOL(point_inside(pt, path->npts, path->p) != 0);
 }
 
+
+/*
+ * Check whether the line segment is on the line or close enough
+ *
+ * It is, if both of its points are on the line or close enough.
+ */
 Datum
 on_sl(PG_FUNCTION_ARGS)
 {
 	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
 	LINE	   *line = PG_GETARG_LINE_P(1);
 
-	PG_RETURN_BOOL(DatumGetBool(DirectFunctionCall2(on_pl,
-													PointPGetDatum(&lseg->p[0]),
-													LinePGetDatum(line))) &&
-				   DatumGetBool(DirectFunctionCall2(on_pl,
-													PointPGetDatum(&lseg->p[1]),
-													LinePGetDatum(line))));
+	PG_RETURN_BOOL(line_contain_point(line, &lseg->p[0]) &&
+				   line_contain_point(line, &lseg->p[1]));
+}
+
+
+/*
+ * Check whether the line segment is in the box or on its border
+ *
+ * It is, if both of its points are in the box or on its border.
+ */
+static bool
+box_contain_lseg(BOX *box, LSEG *lseg)
+{
+	return box_contain_point(box, &lseg->p[0]) &&
+		   box_contain_point(box, &lseg->p[1]);
 }
 
 Datum
@@ -3237,12 +3062,7 @@ on_sb(PG_FUNCTION_ARGS)
 	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
 	BOX		   *box = PG_GETARG_BOX_P(1);
 
-	PG_RETURN_BOOL(DatumGetBool(DirectFunctionCall2(on_pb,
-													PointPGetDatum(&lseg->p[0]),
-													BoxPGetDatum(box))) &&
-				   DatumGetBool(DirectFunctionCall2(on_pb,
-													PointPGetDatum(&lseg->p[1]),
-													BoxPGetDatum(box))));
+	PG_RETURN_BOOL(box_contain_lseg(box, lseg));
 }
 
 /*---------------------------------------------------------------------
@@ -3256,24 +3076,28 @@ inter_sl(PG_FUNCTION_ARGS)
 	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
 	LINE	   *line = PG_GETARG_LINE_P(1);
 
-	PG_RETURN_BOOL(has_interpt_sl(lseg, line));
+	PG_RETURN_BOOL(lseg_interpt_line(NULL, lseg, line));
 }
 
-/* inter_sb()
+
+/*
  * Do line segment and box intersect?
  *
  * Segment completely inside box counts as intersection.
  * If you want only segments crossing box boundaries,
  *	try converting box to path first.
  *
+ * This function also sets the *result to the closest point on the line
+ * segment to the center of the box when they overlap and the result is
+ * not NULL.  It is somewhat arbitrary, but maybe the best we can do as
+ * there are typically two points they intersect.
+ *
  * Optimize for non-intersection by checking for box intersection first.
  * - thomas 1998-01-30
  */
-Datum
-inter_sb(PG_FUNCTION_ARGS)
+static bool
+box_interpt_lseg(Point *result, BOX *box, LSEG *lseg)
 {
-	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
-	BOX		   *box = PG_GETARG_BOX_P(1);
 	BOX			lbox;
 	LSEG		bseg;
 	Point		point;
@@ -3285,42 +3109,54 @@ inter_sb(PG_FUNCTION_ARGS)
 
 	/* nothing close to overlap? then not going to intersect */
 	if (!box_ov(&lbox, box))
-		PG_RETURN_BOOL(false);
+		return false;
+
+	if (result != NULL)
+	{
+		box_cn(&point, box);
+		lseg_closept_point(result, lseg, &point);
+	}
 
 	/* an endpoint of segment is inside box? then clearly intersects */
-	if (DatumGetBool(DirectFunctionCall2(on_pb,
-										 PointPGetDatum(&lseg->p[0]),
-										 BoxPGetDatum(box))) ||
-		DatumGetBool(DirectFunctionCall2(on_pb,
-										 PointPGetDatum(&lseg->p[1]),
-										 BoxPGetDatum(box))))
-		PG_RETURN_BOOL(true);
+	if (box_contain_point(box, &lseg->p[0]) ||
+		box_contain_point(box, &lseg->p[1]))
+		return true;
 
 	/* pairwise check lseg intersections */
 	point.x = box->low.x;
 	point.y = box->high.y;
 	statlseg_construct(&bseg, &box->low, &point);
-	if (lseg_intersect_internal(&bseg, lseg))
-		PG_RETURN_BOOL(true);
+	if (lseg_interpt_lseg(NULL, &bseg, lseg))
+		return true;
 
 	statlseg_construct(&bseg, &box->high, &point);
-	if (lseg_intersect_internal(&bseg, lseg))
-		PG_RETURN_BOOL(true);
+	if (lseg_interpt_lseg(NULL, &bseg, lseg))
+		return true;
 
 	point.x = box->high.x;
 	point.y = box->low.y;
 	statlseg_construct(&bseg, &box->low, &point);
-	if (lseg_intersect_internal(&bseg, lseg))
-		PG_RETURN_BOOL(true);
+	if (lseg_interpt_lseg(NULL, &bseg, lseg))
+		return true;
 
 	statlseg_construct(&bseg, &box->high, &point);
-	if (lseg_intersect_internal(&bseg, lseg))
-		PG_RETURN_BOOL(true);
+	if (lseg_interpt_lseg(NULL, &bseg, lseg))
+		return true;
 
 	/* if we dropped through, no two segs intersected */
-	PG_RETURN_BOOL(false);
+	return false;
+}
+
+Datum
+inter_sb(PG_FUNCTION_ARGS)
+{
+	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
+	BOX		   *box = PG_GETARG_BOX_P(1);
+
+	PG_RETURN_BOOL(box_interpt_lseg(NULL, box, lseg));
 }
 
+
 /* inter_lb()
  * Do line and box intersect?
  */
@@ -3339,22 +3175,22 @@ inter_lb(PG_FUNCTION_ARGS)
 	p2.x = box->low.x;
 	p2.y = box->high.y;
 	statlseg_construct(&bseg, &p1, &p2);
-	if (has_interpt_sl(&bseg, line))
+	if (lseg_interpt_line(NULL, &bseg, line))
 		PG_RETURN_BOOL(true);
 	p1.x = box->high.x;
 	p1.y = box->high.y;
 	statlseg_construct(&bseg, &p1, &p2);
-	if (has_interpt_sl(&bseg, line))
+	if (lseg_interpt_line(NULL, &bseg, line))
 		PG_RETURN_BOOL(true);
 	p2.x = box->high.x;
 	p2.y = box->low.y;
 	statlseg_construct(&bseg, &p1, &p2);
-	if (has_interpt_sl(&bseg, line))
+	if (lseg_interpt_line(NULL, &bseg, line))
 		PG_RETURN_BOOL(true);
 	p1.x = box->low.x;
 	p1.y = box->low.y;
 	statlseg_construct(&bseg, &p1, &p2);
-	if (has_interpt_sl(&bseg, line))
+	if (lseg_interpt_line(NULL, &bseg, line))
 		PG_RETURN_BOOL(true);
 
 	/* if we dropped through, no intersection */
@@ -3381,9 +3217,9 @@ make_bound_box(POLYGON *poly)
 				x2,
 				y2;
 
-	if (poly->npts > 0)
-	{
-		x2 = x1 = poly->p[0].x;
+	Assert(poly->npts > 0);
+
+	x1 = x2 = poly->p[0].x;
 	y2 = y1 = poly->p[0].y;
 	for (i = 1; i < poly->npts; i++)
 	{
@@ -3397,12 +3233,10 @@ make_bound_box(POLYGON *poly)
 			y2 = poly->p[i].y;
 	}
 
-		box_fill(&(poly->boundbox), x1, x2, y1, y2);
-	}
-	else
-		ereport(ERROR,
-				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
-				 errmsg("cannot create bounding box for empty polygon")));
+	poly->boundbox.low.x = x1;
+	poly->boundbox.high.x = x2;
+	poly->boundbox.low.y = y1;
+	poly->boundbox.high.y = y2;
 }
 
 /*------------------------------------------------------------------
@@ -3746,9 +3580,10 @@ poly_overlap(PG_FUNCTION_ARGS)
 	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
 	bool		result;
 
+	Assert(polya->npts > 0 && polyb->npts > 0);
+
 	/* Quick check by bounding box */
-	result = (polya->npts > 0 && polyb->npts > 0 &&
-			  box_ov(&polya->boundbox, &polyb->boundbox)) ? true : false;
+	result = box_ov(&polya->boundbox, &polyb->boundbox);
 
 	/*
 	 * Brute-force algorithm - try to find intersected edges, if so then
@@ -3766,7 +3601,7 @@ poly_overlap(PG_FUNCTION_ARGS)
 		sa.p[0] = polya->p[polya->npts - 1];
 		result = false;
 
-		for (ia = 0; ia < polya->npts && result == false; ia++)
+		for (ia = 0; ia < polya->npts && !result; ia++)
 		{
 			/* Second point of polya's edge is a current one */
 			sa.p[1] = polya->p[ia];
@@ -3774,10 +3609,10 @@ poly_overlap(PG_FUNCTION_ARGS)
 			/* Init first of polyb's edge with last point */
 			sb.p[0] = polyb->p[polyb->npts - 1];
 
-			for (ib = 0; ib < polyb->npts && result == false; ib++)
+			for (ib = 0; ib < polyb->npts && !result; ib++)
 			{
 				sb.p[1] = polyb->p[ib];
-				result = lseg_intersect_internal(&sa, &sb);
+				result = lseg_interpt_lseg(NULL, &sa, &sb);
 				sb.p[0] = sb.p[1];
 			}
 
@@ -3787,10 +3622,9 @@ poly_overlap(PG_FUNCTION_ARGS)
 			sa.p[0] = sa.p[1];
 		}
 
-		if (result == false)
+		if (!result)
 		{
-			result = (point_inside(polya->p, polyb->npts, polyb->p)
-					  ||
+			result = (point_inside(polya->p, polyb->npts, polyb->p) ||
 					  point_inside(polyb->p, polya->npts, polya->p));
 		}
 	}
@@ -3824,22 +3658,21 @@ touched_lseg_inside_poly(Point *a, Point *b, LSEG *s, POLYGON *poly, int start)
 	t.p[0] = *a;
 	t.p[1] = *b;
 
-#define POINTEQ(pt1, pt2)	(FPeq((pt1)->x, (pt2)->x) && FPeq((pt1)->y, (pt2)->y))
-	if (POINTEQ(a, s->p))
+	if (point_eq_point(a, s->p))
 	{
-		if (on_ps_internal(s->p + 1, &t))
+		if (lseg_contain_point(&t, s->p + 1))
 			return lseg_inside_poly(b, s->p + 1, poly, start);
 	}
-	else if (POINTEQ(a, s->p + 1))
+	else if (point_eq_point(a, s->p + 1))
 	{
-		if (on_ps_internal(s->p, &t))
+		if (lseg_contain_point(&t, s->p))
 			return lseg_inside_poly(b, s->p, poly, start);
 	}
-	else if (on_ps_internal(s->p, &t))
+	else if (lseg_contain_point(&t, s->p))
 	{
 		return lseg_inside_poly(b, s->p, poly, start);
 	}
-	else if (on_ps_internal(s->p + 1, &t))
+	else if (lseg_contain_point(&t, s->p + 1))
 	{
 		return lseg_inside_poly(b, s->p + 1, poly, start);
 	}
@@ -3867,36 +3700,35 @@ lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start)
 
 	for (i = start; i < poly->npts && res; i++)
 	{
-		Point	   *interpt;
+		Point		interpt;
 
 		CHECK_FOR_INTERRUPTS();
 
 		s.p[1] = poly->p[i];
 
-		if (on_ps_internal(t.p, &s))
+		if (lseg_contain_point(&s, t.p))
 		{
-			if (on_ps_internal(t.p + 1, &s))
+			if (lseg_contain_point(&s, t.p + 1))
 				return true;	/* t is contained by s */
 
 			/* Y-cross */
 			res = touched_lseg_inside_poly(t.p, t.p + 1, &s, poly, i + 1);
 		}
-		else if (on_ps_internal(t.p + 1, &s))
+		else if (lseg_contain_point(&s, t.p + 1))
 		{
 			/* Y-cross */
 			res = touched_lseg_inside_poly(t.p + 1, t.p, &s, poly, i + 1);
 		}
-		else if ((interpt = lseg_interpt_internal(&t, &s)) != NULL)
+		else if (lseg_interpt_lseg(&interpt, &t, &s))
 		{
 			/*
 			 * segments are X-crossing, go to check each subsegment
 			 */
 
 			intersection = true;
-			res = lseg_inside_poly(t.p, interpt, poly, i + 1);
+			res = lseg_inside_poly(t.p, &interpt, poly, i + 1);
 			if (res)
-				res = lseg_inside_poly(t.p + 1, interpt, poly, i + 1);
-			pfree(interpt);
+				res = lseg_inside_poly(t.p + 1, &interpt, poly, i + 1);
 		}
 
 		s.p[0] = s.p[1];
@@ -3922,38 +3754,41 @@ lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start)
 /*-----------------------------------------------------------------
  * Determine if polygon A contains polygon B.
  *-----------------------------------------------------------------*/
-Datum
-poly_contain(PG_FUNCTION_ARGS)
+static bool
+poly_contain_poly(POLYGON *polya, POLYGON *polyb)
 {
-	POLYGON    *polya = PG_GETARG_POLYGON_P(0);
-	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
-	bool		result;
+	int			i;
+	LSEG		s;
+
+	Assert(polya->npts > 0 && polyb->npts > 0);
 
 	/*
 	 * Quick check to see if bounding box is contained.
 	 */
-	if (polya->npts > 0 && polyb->npts > 0 &&
-		DatumGetBool(DirectFunctionCall2(box_contain,
-										 BoxPGetDatum(&polya->boundbox),
-										 BoxPGetDatum(&polyb->boundbox))))
-	{
-		int			i;
-		LSEG		s;
+	if (!box_contain_box(&polya->boundbox, &polyb->boundbox))
+		return false;
 
 	s.p[0] = polyb->p[polyb->npts - 1];
-		result = true;
 
-		for (i = 0; i < polyb->npts && result; i++)
+	for (i = 0; i < polyb->npts; i++)
 	{
 		s.p[1] = polyb->p[i];
-			result = lseg_inside_poly(s.p, s.p + 1, polya, 0);
+		if (!lseg_inside_poly(s.p, s.p + 1, polya, 0))
+			return false;
 		s.p[0] = s.p[1];
 	}
-	}
-	else
-	{
-		result = false;
-	}
+
+	return true;
+}
+
+Datum
+poly_contain(PG_FUNCTION_ARGS)
+{
+	POLYGON    *polya = PG_GETARG_POLYGON_P(0);
+	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
+	bool		result;
+
+	result = poly_contain_poly(polya, polyb);
 
 	/*
 	 * Avoid leaking memory for toasted inputs ... needed for rtree indexes
@@ -3971,11 +3806,20 @@ poly_contain(PG_FUNCTION_ARGS)
 Datum
 poly_contained(PG_FUNCTION_ARGS)
 {
-	Datum		polya = PG_GETARG_DATUM(0);
-	Datum		polyb = PG_GETARG_DATUM(1);
+	POLYGON    *polya = PG_GETARG_POLYGON_P(0);
+	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
+	bool		result;
 
 	/* Just switch the arguments and pass it off to poly_contain */
-	PG_RETURN_DATUM(DirectFunctionCall2(poly_contain, polyb, polya));
+	result = poly_contain_poly(polyb, polya);
+
+	/*
+	 * Avoid leaking memory for toasted inputs ... needed for rtree indexes
+	 */
+	PG_FREE_IF_COPY(polya, 0);
+	PG_FREE_IF_COPY(polyb, 1);
+
+	PG_RETURN_BOOL(result);
 }
 
 
@@ -4025,8 +3869,22 @@ construct_point(PG_FUNCTION_ARGS)
 {
 	float8		x = PG_GETARG_FLOAT8(0);
 	float8		y = PG_GETARG_FLOAT8(1);
+	Point	   *result;
+
+	result = (Point *) palloc(sizeof(Point));
+
+	point_construct(result, x, y);
 
-	PG_RETURN_POINT_P(point_construct(x, y));
+	PG_RETURN_POINT_P(result);
+}
+
+
+static inline void
+point_add_point(Point *result, Point *pt1, Point *pt2)
+{
+	point_construct(result,
+					pt1->x + pt2->x,
+					pt1->y + pt2->y);
 }
 
 Datum
@@ -4038,12 +3896,20 @@ point_add(PG_FUNCTION_ARGS)
 
 	result = (Point *) palloc(sizeof(Point));
 
-	result->x = (p1->x + p2->x);
-	result->y = (p1->y + p2->y);
+	point_add_point(result, p1, p2);
 
 	PG_RETURN_POINT_P(result);
 }
 
+
+static inline void
+point_sub_point(Point *result, Point *pt1, Point *pt2)
+{
+	point_construct(result,
+					pt1->x - pt2->x,
+					pt1->y - pt2->y);
+}
+
 Datum
 point_sub(PG_FUNCTION_ARGS)
 {
@@ -4053,12 +3919,20 @@ point_sub(PG_FUNCTION_ARGS)
 
 	result = (Point *) palloc(sizeof(Point));
 
-	result->x = (p1->x - p2->x);
-	result->y = (p1->y - p2->y);
+	point_sub_point(result, p1, p2);
 
 	PG_RETURN_POINT_P(result);
 }
 
+
+static inline void
+point_mul_point(Point *result, Point *pt1, Point *pt2)
+{
+	point_construct(result,
+					(pt1->x * pt2->x) - (pt1->y * pt2->y),
+					(pt1->x * pt2->y) + (pt1->y * pt2->x));
+}
+
 Datum
 point_mul(PG_FUNCTION_ARGS)
 {
@@ -4068,31 +3942,39 @@ point_mul(PG_FUNCTION_ARGS)
 
 	result = (Point *) palloc(sizeof(Point));
 
-	result->x = (p1->x * p2->x) - (p1->y * p2->y);
-	result->y = (p1->x * p2->y) + (p1->y * p2->x);
+	point_mul_point(result, p1, p2);
 
 	PG_RETURN_POINT_P(result);
 }
 
-Datum
-point_div(PG_FUNCTION_ARGS)
+
+static inline void
+point_div_point(Point *result, Point *pt1, Point *pt2)
 {
-	Point	   *p1 = PG_GETARG_POINT_P(0);
-	Point	   *p2 = PG_GETARG_POINT_P(1);
-	Point	   *result;
 	double		div;
 
-	result = (Point *) palloc(sizeof(Point));
-
-	div = (p2->x * p2->x) + (p2->y * p2->y);
+	div = (pt2->x * pt2->x) + (pt2->y * pt2->y);
 
 	if (div == 0.0)
 		ereport(ERROR,
 				(errcode(ERRCODE_DIVISION_BY_ZERO),
 				 errmsg("division by zero")));
 
-	result->x = ((p1->x * p2->x) + (p1->y * p2->y)) / div;
-	result->y = ((p2->x * p1->y) - (p2->y * p1->x)) / div;
+	point_construct(result,
+					((pt1->x * pt2->x) + (pt1->y * pt2->y)) / div,
+					((pt2->x * pt1->y) - (pt2->y * pt1->x)) / div);
+}
+
+Datum
+point_div(PG_FUNCTION_ARGS)
+{
+	Point	   *p1 = PG_GETARG_POINT_P(0);
+	Point	   *p2 = PG_GETARG_POINT_P(1);
+	Point	   *result;
+
+	result = (Point *) palloc(sizeof(Point));
+
+	point_div_point(result, p1, p2);
 
 	PG_RETURN_POINT_P(result);
 }
@@ -4109,8 +3991,13 @@ points_box(PG_FUNCTION_ARGS)
 {
 	Point	   *p1 = PG_GETARG_POINT_P(0);
 	Point	   *p2 = PG_GETARG_POINT_P(1);
+	BOX		   *result;
+
+	result = (BOX *) palloc(sizeof(BOX));
+
+	box_construct(result, p1, p2);
 
-	PG_RETURN_BOX_P(box_construct(p1->x, p2->x, p1->y, p2->y));
+	PG_RETURN_BOX_P(result);
 }
 
 Datum
@@ -4118,11 +4005,14 @@ box_add(PG_FUNCTION_ARGS)
 {
 	BOX		   *box = PG_GETARG_BOX_P(0);
 	Point	   *p = PG_GETARG_POINT_P(1);
+	BOX		   *result;
+
+	result = (BOX *) palloc(sizeof(BOX));
+
+	point_add_point(&result->high, &box->high, p);
+	point_add_point(&result->low, &box->low, p);
 
-	PG_RETURN_BOX_P(box_construct((box->high.x + p->x),
-								  (box->low.x + p->x),
-								  (box->high.y + p->y),
-								  (box->low.y + p->y)));
+	PG_RETURN_BOX_P(result);
 }
 
 Datum
@@ -4130,11 +4020,14 @@ box_sub(PG_FUNCTION_ARGS)
 {
 	BOX		   *box = PG_GETARG_BOX_P(0);
 	Point	   *p = PG_GETARG_POINT_P(1);
+	BOX		   *result;
+
+	result = (BOX *) palloc(sizeof(BOX));
 
-	PG_RETURN_BOX_P(box_construct((box->high.x - p->x),
-								  (box->low.x - p->x),
-								  (box->high.y - p->y),
-								  (box->low.y - p->y)));
+	point_sub_point(&result->high, &box->high, p);
+	point_sub_point(&result->low, &box->low, p);
+
+	PG_RETURN_BOX_P(result);
 }
 
 Datum
@@ -4143,17 +4036,15 @@ box_mul(PG_FUNCTION_ARGS)
 	BOX		   *box = PG_GETARG_BOX_P(0);
 	Point	   *p = PG_GETARG_POINT_P(1);
 	BOX		   *result;
-	Point	   *high,
-			   *low;
+	Point		high,
+				low;
 
-	high = DatumGetPointP(DirectFunctionCall2(point_mul,
-											  PointPGetDatum(&box->high),
-											  PointPGetDatum(p)));
-	low = DatumGetPointP(DirectFunctionCall2(point_mul,
-											 PointPGetDatum(&box->low),
-											 PointPGetDatum(p)));
+	result = (BOX *) palloc(sizeof(BOX));
 
-	result = box_construct(high->x, low->x, high->y, low->y);
+	point_mul_point(&high, &box->high, p);
+	point_mul_point(&low, &box->low, p);
+
+	box_construct(result, &high, &low);
 
 	PG_RETURN_BOX_P(result);
 }
@@ -4164,17 +4055,15 @@ box_div(PG_FUNCTION_ARGS)
 	BOX		   *box = PG_GETARG_BOX_P(0);
 	Point	   *p = PG_GETARG_POINT_P(1);
 	BOX		   *result;
-	Point	   *high,
-			   *low;
+	Point		high,
+				low;
+
+	result = (BOX *) palloc(sizeof(BOX));
 
-	high = DatumGetPointP(DirectFunctionCall2(point_div,
-											  PointPGetDatum(&box->high),
-											  PointPGetDatum(p)));
-	low = DatumGetPointP(DirectFunctionCall2(point_div,
-											 PointPGetDatum(&box->low),
-											 PointPGetDatum(p)));
+	point_div_point(&high, &box->high, p);
+	point_div_point(&low, &box->low, p);
 
-	result = box_construct(high->x, low->x, high->y, low->y);
+	box_construct(result, &high, &low);
 
 	PG_RETURN_BOX_P(result);
 }
@@ -4284,10 +4173,7 @@ path_add_pt(PG_FUNCTION_ARGS)
 	int			i;
 
 	for (i = 0; i < path->npts; i++)
-	{
-		path->p[i].x += point->x;
-		path->p[i].y += point->y;
-	}
+		point_add_point(&path->p[i], &path->p[i], point);
 
 	PG_RETURN_PATH_P(path);
 }
@@ -4300,10 +4186,7 @@ path_sub_pt(PG_FUNCTION_ARGS)
 	int			i;
 
 	for (i = 0; i < path->npts; i++)
-	{
-		path->p[i].x -= point->x;
-		path->p[i].y -= point->y;
-	}
+		point_sub_point(&path->p[i], &path->p[i], point);
 
 	PG_RETURN_PATH_P(path);
 }
@@ -4316,17 +4199,10 @@ path_mul_pt(PG_FUNCTION_ARGS)
 {
 	PATH	   *path = PG_GETARG_PATH_P_COPY(0);
 	Point	   *point = PG_GETARG_POINT_P(1);
-	Point	   *p;
 	int			i;
 
 	for (i = 0; i < path->npts; i++)
-	{
-		p = DatumGetPointP(DirectFunctionCall2(point_mul,
-											   PointPGetDatum(&path->p[i]),
-											   PointPGetDatum(point)));
-		path->p[i].x = p->x;
-		path->p[i].y = p->y;
-	}
+		point_mul_point(&path->p[i], &path->p[i], point);
 
 	PG_RETURN_PATH_P(path);
 }
@@ -4336,17 +4212,10 @@ path_div_pt(PG_FUNCTION_ARGS)
 {
 	PATH	   *path = PG_GETARG_PATH_P_COPY(0);
 	Point	   *point = PG_GETARG_POINT_P(1);
-	Point	   *p;
 	int			i;
 
 	for (i = 0; i < path->npts; i++)
-	{
-		p = DatumGetPointP(DirectFunctionCall2(point_div,
-											   PointPGetDatum(&path->p[i]),
-											   PointPGetDatum(point)));
-		path->p[i].x = p->x;
-		path->p[i].y = p->y;
-	}
+		point_div_point(&path->p[i], &path->p[i], point);
 
 	PG_RETURN_PATH_P(path);
 }
@@ -4421,15 +4290,15 @@ Datum
 poly_center(PG_FUNCTION_ARGS)
 {
 	POLYGON    *poly = PG_GETARG_POLYGON_P(0);
-	Datum		result;
-	CIRCLE	   *circle;
+	Point	   *result;
+	CIRCLE		circle;
 
-	circle = DatumGetCircleP(DirectFunctionCall1(poly_circle,
-												 PolygonPGetDatum(poly)));
-	result = DirectFunctionCall1(circle_center,
-								 CirclePGetDatum(circle));
+	result = (Point *) palloc(sizeof(Point));
+
+	poly_to_circle(&circle, poly);
+	*result = circle.center;
 
-	PG_RETURN_DATUM(result);
+	PG_RETURN_POINT_P(result);
 }
 
 
@@ -4439,10 +4308,8 @@ poly_box(PG_FUNCTION_ARGS)
 	POLYGON    *poly = PG_GETARG_POLYGON_P(0);
 	BOX		   *box;
 
-	if (poly->npts < 1)
-		PG_RETURN_NULL();
-
-	box = box_copy(&poly->boundbox);
+	box = (BOX *) palloc(sizeof(BOX));
+	*box = poly->boundbox;
 
 	PG_RETURN_BOX_P(box);
 }
@@ -4474,8 +4341,7 @@ box_poly(PG_FUNCTION_ARGS)
 	poly->p[3].x = box->high.x;
 	poly->p[3].y = box->low.y;
 
-	box_fill(&poly->boundbox, box->high.x, box->low.x,
-			 box->high.y, box->low.y);
+	box_construct(&poly->boundbox, &box->high, &box->low);
 
 	PG_RETURN_POLYGON_P(poly);
 }
@@ -4564,8 +4430,7 @@ circle_in(PG_FUNCTION_ARGS)
 
 	while (depth > 0)
 	{
-		if ((*s == RDELIM)
-			|| ((*s == RDELIM_C) && (depth == 1)))
+		if ((*s == RDELIM) || ((*s == RDELIM_C) && (depth == 1)))
 		{
 			depth--;
 			s++;
@@ -4663,8 +4528,7 @@ circle_same(PG_FUNCTION_ARGS)
 	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);
 
 	PG_RETURN_BOOL(FPeq(circle1->radius, circle2->radius) &&
-				   FPeq(circle1->center.x, circle2->center.x) &&
-				   FPeq(circle1->center.y, circle2->center.y));
+				   point_eq_point(&circle1->center, &circle2->center));
 }
 
 /*		circle_overlap	-		does circle1 overlap circle2?
@@ -4737,7 +4601,8 @@ circle_contained(PG_FUNCTION_ARGS)
 	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
 	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);
 
-	PG_RETURN_BOOL(FPle((point_dt(&circle1->center, &circle2->center) + circle1->radius), circle2->radius));
+	PG_RETURN_BOOL(FPle(point_dt(&circle1->center, &circle2->center),
+						circle2->radius - circle1->radius));
 }
 
 /*		circle_contain	-		does circle1 contain circle2?
@@ -4748,7 +4613,8 @@ circle_contain(PG_FUNCTION_ARGS)
 	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
 	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);
 
-	PG_RETURN_BOOL(FPle((point_dt(&circle1->center, &circle2->center) + circle2->radius), circle1->radius));
+	PG_RETURN_BOOL(FPle(point_dt(&circle1->center, &circle2->center),
+						circle1->radius - circle2->radius));
 }
 
 
@@ -4865,20 +4731,6 @@ circle_ge(PG_FUNCTION_ARGS)
  *	"Arithmetic" operators on circles.
  *---------------------------------------------------------*/
 
-static CIRCLE *
-circle_copy(CIRCLE *circle)
-{
-	CIRCLE	   *result;
-
-	if (!PointerIsValid(circle))
-		return NULL;
-
-	result = (CIRCLE *) palloc(sizeof(CIRCLE));
-	memcpy((char *) result, (char *) circle, sizeof(CIRCLE));
-	return result;
-}
-
-
 /* circle_add_pt()
  * Translation operator.
  */
@@ -4889,10 +4741,10 @@ circle_add_pt(PG_FUNCTION_ARGS)
 	Point	   *point = PG_GETARG_POINT_P(1);
 	CIRCLE	   *result;
 
-	result = circle_copy(circle);
+	result = (CIRCLE *) palloc(sizeof(CIRCLE));
 
-	result->center.x += point->x;
-	result->center.y += point->y;
+	point_add_point(&result->center, &circle->center, point);
+	result->radius = circle->radius;
 
 	PG_RETURN_CIRCLE_P(result);
 }
@@ -4904,10 +4756,10 @@ circle_sub_pt(PG_FUNCTION_ARGS)
 	Point	   *point = PG_GETARG_POINT_P(1);
 	CIRCLE	   *result;
 
-	result = circle_copy(circle);
+	result = (CIRCLE *) palloc(sizeof(CIRCLE));
 
-	result->center.x -= point->x;
-	result->center.y -= point->y;
+	point_sub_point(&result->center, &circle->center, point);
+	result->radius = circle->radius;
 
 	PG_RETURN_CIRCLE_P(result);
 }
@@ -4922,16 +4774,11 @@ circle_mul_pt(PG_FUNCTION_ARGS)
 	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);
 	Point	   *point = PG_GETARG_POINT_P(1);
 	CIRCLE	   *result;
-	Point	   *p;
 
-	result = circle_copy(circle);
+	result = (CIRCLE *) palloc(sizeof(CIRCLE));
 
-	p = DatumGetPointP(DirectFunctionCall2(point_mul,
-										   PointPGetDatum(&circle->center),
-										   PointPGetDatum(point)));
-	result->center.x = p->x;
-	result->center.y = p->y;
-	result->radius *= HYPOT(point->x, point->y);
+	point_mul_point(&result->center, &circle->center, point);
+	result->radius = circle->radius * HYPOT(point->x, point->y);
 
 	PG_RETURN_CIRCLE_P(result);
 }
@@ -4942,16 +4789,11 @@ circle_div_pt(PG_FUNCTION_ARGS)
 	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);
 	Point	   *point = PG_GETARG_POINT_P(1);
 	CIRCLE	   *result;
-	Point	   *p;
 
-	result = circle_copy(circle);
+	result = (CIRCLE *) palloc(sizeof(CIRCLE));
 
-	p = DatumGetPointP(DirectFunctionCall2(point_div,
-										   PointPGetDatum(&circle->center),
-										   PointPGetDatum(point)));
-	result->center.x = p->x;
-	result->center.y = p->y;
-	result->radius /= HYPOT(point->x, point->y);
+	point_div_point(&result->center, &circle->center, point);
+	result->radius = circle->radius / HYPOT(point->x, point->y);
 
 	PG_RETURN_CIRCLE_P(result);
 }
@@ -5000,8 +4842,8 @@ circle_distance(PG_FUNCTION_ARGS)
 	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);
 	float8		result;
 
-	result = point_dt(&circle1->center, &circle2->center)
-		- (circle1->radius + circle2->radius);
+	result = point_dt(&circle1->center, &circle2->center) -
+		(circle1->radius + circle2->radius);
 	if (result < 0)
 		result = 0;
 	PG_RETURN_FLOAT8(result);
@@ -5197,42 +5039,46 @@ circle_poly(PG_FUNCTION_ARGS)
 	PG_RETURN_POLYGON_P(poly);
 }
 
-/*		poly_circle		- convert polygon to circle
+/*
+ * Convert polygon to circle
+ *
+ * The result must be preallocated.
  *
  * XXX This algorithm should use weighted means of line segments
  *	rather than straight average values of points - tgl 97/01/21.
  */
-Datum
-poly_circle(PG_FUNCTION_ARGS)
+static void
+poly_to_circle(CIRCLE *result, POLYGON *poly)
 {
-	POLYGON    *poly = PG_GETARG_POLYGON_P(0);
-	CIRCLE	   *circle;
 	int			i;
 
-	if (poly->npts < 1)
-		ereport(ERROR,
-				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
-				 errmsg("cannot convert empty polygon to circle")));
+	Assert(poly->npts > 0);
 
-	circle = (CIRCLE *) palloc(sizeof(CIRCLE));
-
-	circle->center.x = 0;
-	circle->center.y = 0;
-	circle->radius = 0;
+	result->center.x = 0;
+	result->center.y = 0;
+	result->radius = 0;
 
 	for (i = 0; i < poly->npts; i++)
-	{
-		circle->center.x += poly->p[i].x;
-		circle->center.y += poly->p[i].y;
-	}
-	circle->center.x /= poly->npts;
-	circle->center.y /= poly->npts;
+		point_add_point(&result->center, &result->center, &poly->p[i]);
+	result->center.x /= poly->npts;
+	result->center.y /= poly->npts;
 
 	for (i = 0; i < poly->npts; i++)
-		circle->radius += point_dt(&poly->p[i], &circle->center);
-	circle->radius /= poly->npts;
+		result->radius += point_dt(&poly->p[i], &result->center);
+	result->radius /= poly->npts;
+}
 
-	PG_RETURN_CIRCLE_P(circle);
+Datum
+poly_circle(PG_FUNCTION_ARGS)
+{
+	POLYGON    *poly = PG_GETARG_POLYGON_P(0);
+	CIRCLE	   *result;
+
+	result = (CIRCLE *) palloc(sizeof(CIRCLE));
+
+	poly_to_circle(result, poly);
+
+	PG_RETURN_CIRCLE_P(result);
 }
 
 
@@ -5268,8 +5114,7 @@ point_inside(Point *p, int npts, Point *plist)
 	int			cross,
 				total_cross = 0;
 
-	if (npts <= 0)
-		return 0;
+	Assert(npts > 0);
 
 	/* compute first polygon point relative to single point */
 	x0 = plist[0].x - p->x;
@@ -5378,8 +5223,7 @@ plist_same(int npts, Point *p1, Point *p2)
 	/* find match for first point */
 	for (i = 0; i < npts; i++)
 	{
-		if ((FPeq(p2[i].x, p1[0].x))
-			&& (FPeq(p2[i].y, p1[0].y)))
+		if (point_eq_point(&p2[i], &p1[0]))
 		{
 
 			/* match found? then look forward through remaining points */
@@ -5387,8 +5231,7 @@ plist_same(int npts, Point *p1, Point *p2)
 			{
 				if (j >= npts)
 					j = 0;
-				if ((!FPeq(p2[j].x, p1[ii].x))
-					|| (!FPeq(p2[j].y, p1[ii].y)))
+				if (!point_eq_point(&p2[j], &p1[ii]))
 				{
 #ifdef GEODEBUG
 					printf("plist_same- %d failed forward match with %d\n", j, ii);
@@ -5407,8 +5250,7 @@ plist_same(int npts, Point *p1, Point *p2)
 			{
 				if (j < 0)
 					j = (npts - 1);
-				if ((!FPeq(p2[j].x, p1[ii].x))
-					|| (!FPeq(p2[j].y, p1[ii].y)))
+				if (!point_eq_point(&p2[j], &p1[ii]))
 				{
 #ifdef GEODEBUG
 					printf("plist_same- %d failed reverse match with %d\n", j, ii);

src/backend/utils/adt/geo_spgist.c

@@ -793,7 +793,8 @@ spg_poly_quad_compress(PG_FUNCTION_ARGS)
 	POLYGON    *polygon = PG_GETARG_POLYGON_P(0);
 	BOX		   *box;
 
-	box = box_copy(&polygon->boundbox);
+	box = (BOX *) palloc(sizeof(BOX));
+	*box = polygon->boundbox;
 
 	PG_RETURN_BOX_P(box);
 }

src/include/utils/geo_decls.h

@@ -178,10 +178,6 @@ typedef struct
  * in geo_ops.c
  */
 
-/* private routines */
-extern double point_dt(Point *pt1, Point *pt2);
-extern double point_sl(Point *pt1, Point *pt2);
 extern double pg_hypot(double x, double y);
-extern BOX *box_copy(BOX *box);
 
 #endif							/* GEO_DECLS_H */

src/test/regress/regress.c

@@ -176,8 +176,13 @@ pt_in_widget(PG_FUNCTION_ARGS)
 {
 	Point	   *point = PG_GETARG_POINT_P(0);
 	WIDGET	   *widget = (WIDGET *) PG_GETARG_POINTER(1);
+	float8		distance;
 
-	PG_RETURN_BOOL(point_dt(point, &widget->center) < widget->radius);
+	distance = DatumGetFloat8(DirectFunctionCall2(point_distance,
+												  PointPGetDatum(point),
+											PointPGetDatum(&widget->center)));
+
+	PG_RETURN_BOOL(distance < widget->radius);
 }
 
 PG_FUNCTION_INFO_V1(reverse_name);