Use the built-in float datatypes to implement geometric types
authorTomas Vondra <tomas.vondra@postgresql.org>
Thu, 16 Aug 2018 17:56:11 +0000 (19:56 +0200)
committerTomas Vondra <tomas.vondra@postgresql.org>
Thu, 16 Aug 2018 17:56:11 +0000 (19:56 +0200)
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
src/backend/utils/adt/geo_ops.c
src/backend/utils/adt/geo_spgist.c
src/include/utils/geo_decls.h

index d6ce5ccf6cc1fa966b8abb59b2c5521c7897c55c..c3383bd6da6de65190d427ae9c063a28c241931a 100644 (file)
@@ -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);
 
index bd8e21775db85f2887ab469dd44eb17ce443c985..13dc1ab6e6002e505df49560b19fe3bda52a4c38 100644 (file)
@@ -59,7 +59,7 @@ 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 int     lseg_crossing(float8 x, float8 y, float8 px, float8 py);
 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);
@@ -69,9 +69,9 @@ static float8 lseg_closept_lseg(Point *result, LSEG *l1, LSEG *l2);
 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 float8 box_ar(BOX *box);
+static float8 box_ht(BOX *box);
+static float8 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);
@@ -80,7 +80,7 @@ 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 float8 circle_ar(CIRCLE *circle);
 
 /* Routines for polygons */
 static void make_bound_box(POLYGON *poly);
@@ -91,10 +91,10 @@ static bool plist_same(int npts, Point *p1, Point *p2);
 static float8 dist_ppoly_internal(Point *pt, POLYGON *poly);
 
 /* Routines for encoding and decoding */
-static double single_decode(char *num, char **endptr_p,
+static float8 single_decode(char *num, char **endptr_p,
                          const char *type_name, const char *orig_string);
 static void single_encode(float8 x, StringInfo str);
-static void pair_decode(char *str, double *x, double *y, char **endptr_p,
+static void pair_decode(char *str, float8 *x, float8 *y, char **endptr_p,
                        const char *type_name, const char *orig_string);
 static void pair_encode(float8 x, float8 y, StringInfo str);
 static int     pair_count(char *s, char delim);
@@ -146,7 +146,7 @@ static char *path_encode(enum path_delim path_delim, int npts, Point *pt);
  *     and restore that order for text output - tgl 97/01/16
  */
 
-static double
+static float8
 single_decode(char *num, char **endptr_p,
                          const char *type_name, const char *orig_string)
 {
@@ -163,7 +163,7 @@ single_encode(float8 x, StringInfo str)
 }                                                              /* single_encode() */
 
 static void
-pair_decode(char *str, double *x, double *y, char **endptr_p,
+pair_decode(char *str, float8 *x, float8 *y, char **endptr_p,
                        const char *type_name, const char *orig_string)
 {
        bool            has_delim;
@@ -376,19 +376,19 @@ box_in(PG_FUNCTION_ARGS)
        char       *str = PG_GETARG_CSTRING(0);
        BOX                *box = (BOX *) palloc(sizeof(BOX));
        bool            isopen;
-       double          x,
+       float8          x,
                                y;
 
        path_decode(str, false, 2, &(box->high), &isopen, NULL, "box", str);
 
        /* reorder corners if necessary... */
-       if (box->high.x < box->low.x)
+       if (float8_lt(box->high.x, box->low.x))
        {
                x = box->high.x;
                box->high.x = box->low.x;
                box->low.x = x;
        }
-       if (box->high.y < box->low.y)
+       if (float8_lt(box->high.y, box->low.y))
        {
                y = box->high.y;
                box->high.y = box->low.y;
@@ -416,7 +416,7 @@ box_recv(PG_FUNCTION_ARGS)
 {
        StringInfo      buf = (StringInfo) PG_GETARG_POINTER(0);
        BOX                *box;
-       double          x,
+       float8          x,
                                y;
 
        box = (BOX *) palloc(sizeof(BOX));
@@ -427,13 +427,13 @@ box_recv(PG_FUNCTION_ARGS)
        box->low.y = pq_getmsgfloat8(buf);
 
        /* reorder corners if necessary... */
-       if (box->high.x < box->low.x)
+       if (float8_lt(box->high.x, box->low.x))
        {
                x = box->high.x;
                box->high.x = box->low.x;
                box->low.x = x;
        }
-       if (box->high.y < box->low.y)
+       if (float8_lt(box->high.y, box->low.y))
        {
                y = box->high.y;
                box->high.y = box->low.y;
@@ -466,7 +466,7 @@ box_send(PG_FUNCTION_ARGS)
 static inline void
 box_construct(BOX *result, Point *pt1, Point *pt2)
 {
-       if (pt1->x > pt2->x)
+       if (float8_gt(pt1->x, pt2->x))
        {
                result->high.x = pt1->x;
                result->low.x = pt2->x;
@@ -476,7 +476,7 @@ box_construct(BOX *result, Point *pt1, Point *pt2)
                result->high.x = pt2->x;
                result->low.x = pt1->x;
        }
-       if (pt1->y > pt2->y)
+       if (float8_gt(pt1->y, pt2->y))
        {
                result->high.y = pt1->y;
                result->low.y = pt2->y;
@@ -808,10 +808,10 @@ box_center(PG_FUNCTION_ARGS)
 
 /*             box_ar  -               returns the area of the box.
  */
-static double
+static float8
 box_ar(BOX *box)
 {
-       return box_wd(box) * box_ht(box);
+       return float8_mul(box_wd(box), box_ht(box));
 }
 
 
@@ -820,28 +820,28 @@ box_ar(BOX *box)
 static void
 box_cn(Point *center, BOX *box)
 {
-       center->x = (box->high.x + box->low.x) / 2.0;
-       center->y = (box->high.y + box->low.y) / 2.0;
+       center->x = float8_div(float8_pl(box->high.x, box->low.x), 2.0);
+       center->y = float8_div(float8_pl(box->high.y, box->low.y), 2.0);
 }
 
 
 /*             box_wd  -               returns the width (length) of the box
  *                                                               (horizontal magnitude).
  */
-static double
+static float8
 box_wd(BOX *box)
 {
-       return box->high.x - box->low.x;
+       return float8_mi(box->high.x, box->low.x);
 }
 
 
 /*             box_ht  -               returns the height of the box
  *                                                               (vertical magnitude).
  */
-static double
+static float8
 box_ht(BOX *box)
 {
-       return box->high.y - box->low.y;
+       return float8_mi(box->high.y, box->low.y);
 }
 
 
@@ -865,10 +865,10 @@ box_intersect(PG_FUNCTION_ARGS)
 
        result = (BOX *) palloc(sizeof(BOX));
 
-       result->high.x = Min(box1->high.x, box2->high.x);
-       result->low.x = Max(box1->low.x, box2->low.x);
-       result->high.y = Min(box1->high.y, box2->high.y);
-       result->low.y = Max(box1->low.y, box2->low.y);
+       result->high.x = float8_min(box1->high.x, box2->high.x);
+       result->low.x = float8_max(box1->low.x, box2->low.x);
+       result->high.y = float8_min(box1->high.y, box2->high.y);
+       result->low.y = float8_max(box1->low.y, box2->low.y);
 
        PG_RETURN_BOX_P(result);
 }
@@ -1014,8 +1014,8 @@ line_construct(LINE *result, Point *pt, float8 m)
        if (m == DBL_MAX)
        {
                /* vertical - use "x = C" */
-               result->A = -1;
-               result->B = 0;
+               result->A = -1.0;
+               result->B = 0.0;
                result->C = pt->x;
        }
        else
@@ -1023,7 +1023,7 @@ line_construct(LINE *result, Point *pt, float8 m)
                /* use "mx - y + yinter = 0" */
                result->A = m;
                result->B = -1.0;
-               result->C = pt->y - m * pt->x;
+               result->C = float8_mi(pt->y, float8_mul(m, pt->x));
                /* on some platforms, the preceding expression tends to produce -0 */
                if (result->C == 0.0)
                        result->C = 0.0;
@@ -1079,7 +1079,8 @@ line_perp(PG_FUNCTION_ARGS)
        else if (FPzero(l1->B))
                PG_RETURN_BOOL(FPzero(l2->A));
 
-       PG_RETURN_BOOL(FPeq(((l1->A * l2->B) / (l1->B * l2->A)), -1.0));
+       PG_RETURN_BOOL(FPeq(float8_div(float8_mul(l1->A, l2->B),
+                                                                  float8_mul(l1->B, l2->A)), -1.0));
 }
 
 Datum
@@ -1098,25 +1099,35 @@ line_horizontal(PG_FUNCTION_ARGS)
        PG_RETURN_BOOL(FPzero(line->A));
 }
 
+
+/*
+ * Check whether the two lines are the same
+ *
+ * We consider NaNs values to be equal to each other to let those lines
+ * to be found.
+ */
 Datum
 line_eq(PG_FUNCTION_ARGS)
 {
        LINE       *l1 = PG_GETARG_LINE_P(0);
        LINE       *l2 = PG_GETARG_LINE_P(1);
-       double          k;
-
-       if (!FPzero(l2->A))
-               k = l1->A / l2->A;
-       else if (!FPzero(l2->B))
-               k = l1->B / l2->B;
-       else if (!FPzero(l2->C))
-               k = l1->C / l2->C;
+       float8          ratio;
+
+       if (!FPzero(l2->A) && !isnan(l2->A))
+               ratio = float8_div(l1->A, l2->A);
+       else if (!FPzero(l2->B) && !isnan(l2->B))
+               ratio = float8_div(l1->B, l2->B);
+       else if (!FPzero(l2->C) && !isnan(l2->C))
+               ratio = float8_div(l1->C, l2->C);
        else
-               k = 1.0;
+               ratio = 1.0;
 
-       PG_RETURN_BOOL(FPeq(l1->A, k * l2->A) &&
-                                  FPeq(l1->B, k * l2->B) &&
-                                  FPeq(l1->C, k * l2->C));
+       PG_RETURN_BOOL((FPeq(l1->A, float8_mul(ratio, l2->A)) &&
+                                       FPeq(l1->B, float8_mul(ratio, l2->B)) &&
+                                       FPeq(l1->C, float8_mul(ratio, l2->C))) ||
+                                  (float8_eq(l1->A, l2->A) &&
+                                       float8_eq(l1->B, l2->B) &&
+                                       float8_eq(l1->C, l2->C)));
 }
 
 
@@ -1134,7 +1145,7 @@ line_invsl(LINE *line)
                return DBL_MAX;
        if (FPzero(line->B))
                return 0.0;
-       return line->B / line->A;
+       return float8_div(line->B, line->A);
 }
 
 
@@ -1152,7 +1163,7 @@ line_distance(PG_FUNCTION_ARGS)
        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));
+               PG_RETURN_FLOAT8(fabs(float8_mi(l1->C, l2->C)));
        point_construct(&tmp, 0.0, l1->C);
        result = line_closept_point(NULL, l2, &tmp);
        PG_RETURN_FLOAT8(result);
@@ -1185,11 +1196,15 @@ line_interpt(PG_FUNCTION_ARGS)
  * 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 the lines have NaN constants, we will return true, and the intersection
+ * point would have NaN coordinates.  We shouldn't return false in this case
+ * because that would mean the lines are parallel.
  */
 static bool
 line_interpt_line(Point *result, LINE *l1, LINE *l2)
 {
-       double          x,
+       float8          x,
                                y;
 
        if (FPzero(l1->B))                      /* l1 vertical? */
@@ -1198,20 +1213,20 @@ line_interpt_line(Point *result, LINE *l1, LINE *l2)
                        return false;
 
                x = l1->C;
-               y = (l2->A * x + l2->C);
+               y = float8_pl(float8_mul(l2->A, x), l2->C);
        }
        else if (FPzero(l2->B))         /* l2 vertical? */
        {
                x = l2->C;
-               y = (l1->A * x + l1->C);
+               y = float8_pl(float8_mul(l1->A, x), l1->C);
        }
        else
        {
-               if (FPeq(l2->A, l1->A * (l2->B / l1->B)))
+               if (FPeq(l2->A, float8_mul(l1->A, float8_div(l2->B, l1->B))))
                        return false;
 
-               x = (l1->C - l2->C) / (l2->A - l1->A);
-               y = (l1->A * x + l1->C);
+               x = float8_div(float8_mi(l1->C, l2->C), float8_mi(l2->A, l1->A));
+               y = float8_pl(float8_mul(l1->A, x), l1->C);
        }
 
        if (result != NULL)
@@ -1247,7 +1262,7 @@ Datum
 path_area(PG_FUNCTION_ARGS)
 {
        PATH       *path = PG_GETARG_PATH_P(0);
-       double          area = 0.0;
+       float8          area = 0.0;
        int                     i,
                                j;
 
@@ -1257,12 +1272,11 @@ path_area(PG_FUNCTION_ARGS)
        for (i = 0; i < path->npts; i++)
        {
                j = (i + 1) % path->npts;
-               area += path->p[i].x * path->p[j].y;
-               area -= path->p[i].y * path->p[j].x;
+               area = float8_pl(area, float8_mul(path->p[i].x, path->p[j].y));
+               area = float8_mi(area, float8_mul(path->p[i].y, path->p[j].x));
        }
 
-       area *= 0.5;
-       PG_RETURN_FLOAT8(area < 0.0 ? -area : area);
+       PG_RETURN_FLOAT8(float8_div(fabs(area), 2.0));
 }
 
 
@@ -1532,19 +1546,19 @@ path_inter(PG_FUNCTION_ARGS)
        b1.high.y = b1.low.y = p1->p[0].y;
        for (i = 1; i < p1->npts; i++)
        {
-               b1.high.x = Max(p1->p[i].x, b1.high.x);
-               b1.high.y = Max(p1->p[i].y, b1.high.y);
-               b1.low.x = Min(p1->p[i].x, b1.low.x);
-               b1.low.y = Min(p1->p[i].y, b1.low.y);
+               b1.high.x = float8_max(p1->p[i].x, b1.high.x);
+               b1.high.y = float8_max(p1->p[i].y, b1.high.y);
+               b1.low.x = float8_min(p1->p[i].x, b1.low.x);
+               b1.low.y = float8_min(p1->p[i].y, b1.low.y);
        }
        b2.high.x = b2.low.x = p2->p[0].x;
        b2.high.y = b2.low.y = p2->p[0].y;
        for (i = 1; i < p2->npts; i++)
        {
-               b2.high.x = Max(p2->p[i].x, b2.high.x);
-               b2.high.y = Max(p2->p[i].y, b2.high.y);
-               b2.low.x = Min(p2->p[i].x, b2.low.x);
-               b2.low.y = Min(p2->p[i].y, b2.low.y);
+               b2.high.x = float8_max(p2->p[i].x, b2.high.x);
+               b2.high.y = float8_max(p2->p[i].y, b2.high.y);
+               b2.low.x = float8_min(p2->p[i].x, b2.low.x);
+               b2.low.y = float8_min(p2->p[i].y, b2.low.y);
        }
        if (!box_ov(&b1, &b2))
                PG_RETURN_BOOL(false);
@@ -1634,7 +1648,7 @@ path_distance(PG_FUNCTION_ARGS)
                        statlseg_construct(&seg2, &p2->p[jprev], &p2->p[j]);
 
                        tmp = lseg_closept_lseg(NULL, &seg1, &seg2);
-                       if (!have_min || tmp < min)
+                       if (!have_min || float8_lt(tmp, min))
                        {
                                min = tmp;
                                have_min = true;
@@ -1673,7 +1687,7 @@ path_length(PG_FUNCTION_ARGS)
                        iprev = path->npts - 1; /* include the closure segment */
                }
 
-               result += point_dt(&path->p[iprev], &path->p[i]);
+               result = float8_pl(result, point_dt(&path->p[iprev], &path->p[i]));
        }
 
        PG_RETURN_FLOAT8(result);
@@ -1833,10 +1847,18 @@ point_ne(PG_FUNCTION_ARGS)
        PG_RETURN_BOOL(!point_eq_point(pt1, pt2));
 }
 
+
+/*
+ * Check whether the two points are the same
+ *
+ * We consider NaNs coordinates to be equal to each other to let those points
+ * to be found.
+ */
 static inline bool
 point_eq_point(Point *pt1, Point *pt2)
 {
-       return FPeq(pt1->x, pt2->x) && FPeq(pt1->y, pt2->y);
+       return ((FPeq(pt1->x, pt2->x) && FPeq(pt1->y, pt2->y)) ||
+                       (float8_eq(pt1->x, pt2->x) && float8_eq(pt1->y, pt2->y)));
 }
 
 
@@ -1856,7 +1878,7 @@ point_distance(PG_FUNCTION_ARGS)
 static inline float8
 point_dt(Point *pt1, Point *pt2)
 {
-       return HYPOT(pt1->x - pt2->x, pt1->y - pt2->y);
+       return HYPOT(float8_mi(pt1->x, pt2->x), float8_mi(pt1->y, pt2->y));
 }
 
 Datum
@@ -1881,7 +1903,7 @@ point_sl(Point *pt1, Point *pt2)
                return DBL_MAX;
        if (FPeq(pt1->y, pt2->y))
                return 0.0;
-       return (pt1->y - pt2->y) / (pt1->x - pt2->x);
+       return float8_div(float8_mi(pt1->y, pt2->y), float8_mi(pt1->x, pt2->x));
 }
 
 
@@ -1897,7 +1919,7 @@ point_invsl(Point *pt1, Point *pt2)
                return 0.0;
        if (FPeq(pt1->y, pt2->y))
                return DBL_MAX;
-       return (pt1->x - pt2->x) / (pt2->y - pt1->y);
+       return float8_div(float8_mi(pt1->x, pt2->x), float8_mi(pt2->y, pt1->y));
 }
 
 
@@ -2171,8 +2193,8 @@ lseg_center(PG_FUNCTION_ARGS)
 
        result = (Point *) palloc(sizeof(Point));
 
-       result->x = (lseg->p[0].x + lseg->p[1].x) / 2.0;
-       result->y = (lseg->p[0].y + lseg->p[1].y) / 2.0;
+       result->x = float8_div(float8_pl(lseg->p[0].x, lseg->p[1].x), 2.0);
+       result->y = float8_div(float8_pl(lseg->p[0].y, lseg->p[1].y), 2.0);
 
        PG_RETURN_POINT_P(result);
 }
@@ -2295,7 +2317,7 @@ dist_ppath(PG_FUNCTION_ARGS)
 
                statlseg_construct(&lseg, &path->p[iprev], &path->p[i]);
                tmp = lseg_closept_point(NULL, &lseg, pt);
-               if (!have_min || tmp < result)
+               if (!have_min || float8_lt(tmp, result))
                {
                        result = tmp;
                        have_min = true;
@@ -2325,19 +2347,14 @@ dist_sl(PG_FUNCTION_ARGS)
 {
        LSEG       *lseg = PG_GETARG_LSEG_P(0);
        LINE       *line = PG_GETARG_LINE_P(1);
-       float8          result,
-                               d2;
+       float8          result;
 
        if (lseg_interpt_line(NULL, lseg, line))
                result = 0.0;
        else
-       {
-               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;
-       }
+               result = float8_max(line_closept_point(NULL, line, &lseg->p[0]),
+                                                       line_closept_point(NULL, line, &lseg->p[1]));
 
        PG_RETURN_FLOAT8(result);
 }
@@ -2384,11 +2401,10 @@ dist_cpoly(PG_FUNCTION_ARGS)
        float8          result;
 
        /* calculate distance to center, and subtract radius */
-       result = dist_ppoly_internal(&circle->center, poly);
-
-       result -= circle->radius;
-       if (result < 0)
-               result = 0;
+       result = float8_mi(dist_ppoly_internal(&circle->center, poly),
+                                          circle->radius);
+       if (result < 0.0)
+               result = 0.0;
 
        PG_RETURN_FLOAT8(result);
 }
@@ -2414,7 +2430,7 @@ dist_polyp(PG_FUNCTION_ARGS)
        PG_RETURN_FLOAT8(dist_ppoly_internal(point, poly));
 }
 
-static double
+static float8
 dist_ppoly_internal(Point *pt, POLYGON *poly)
 {
        float8          result;
@@ -2440,7 +2456,7 @@ dist_ppoly_internal(Point *pt, POLYGON *poly)
                seg.p[1].x = poly->p[i + 1].x;
                seg.p[1].y = poly->p[i + 1].y;
                d = lseg_closept_point(NULL, &seg, pt);
-               if (d < result)
+               if (float8_lt(d, result))
                        result = d;
        }
 
@@ -2543,7 +2559,8 @@ close_pl(PG_FUNCTION_ARGS)
 
        result = (Point *) palloc(sizeof(Point));
 
-       line_closept_point(result, line, pt);
+       if (isnan(line_closept_point(result, line, pt)))
+               PG_RETURN_NULL();
 
        PG_RETURN_POINT_P(result);
 }
@@ -2600,8 +2617,8 @@ static float8
 lseg_closept_lseg(Point *result, LSEG *l1, LSEG *l2)
 {
        Point           point;
-       double          dist;
-       double          d;
+       float8          dist,
+                               d;
 
        d = lseg_closept_point(NULL, l1, &l2->p[0]);
        dist = d;
@@ -2609,20 +2626,20 @@ lseg_closept_lseg(Point *result, LSEG *l1, LSEG *l2)
                *result = l2->p[0];
 
        d = lseg_closept_point(NULL, l1, &l2->p[1]);
-       if (d < dist)
+       if (float8_lt(d, dist))
        {
                dist = d;
                if (result != NULL)
                        *result = l2->p[1];
        }
 
-       if (lseg_closept_point(&point, l2, &l1->p[0]) < dist)
+       if (float8_lt(lseg_closept_point(&point, l2, &l1->p[0]), dist))
                d = lseg_closept_point(result, l1, &point);
 
-       if (lseg_closept_point(&point, l2, &l1->p[1]) < dist)
+       if (float8_lt(lseg_closept_point(&point, l2, &l1->p[1]), dist))
                d = lseg_closept_point(result, l1, &point);
 
-       if (d < dist)
+       if (float8_lt(d, dist))
                dist = d;
 
        return dist;
@@ -2637,7 +2654,8 @@ close_lseg(PG_FUNCTION_ARGS)
 
        result = (Point *) palloc(sizeof(Point));
 
-       lseg_closept_lseg(result, l2, l1);
+       if (isnan(lseg_closept_lseg(result, l2, l1)))
+               PG_RETURN_NULL();
 
        PG_RETURN_POINT_P(result);
 }
@@ -2652,11 +2670,11 @@ close_lseg(PG_FUNCTION_ARGS)
 static float8
 box_closept_point(Point *result, BOX *box, Point *pt)
 {
-       LSEG            lseg;
+       float8          dist,
+                               d;
        Point           point,
                                closept;
-       double          dist,
-                               d;
+       LSEG            lseg;
 
        if (box_contain_point(box, pt))
        {
@@ -2674,7 +2692,7 @@ box_closept_point(Point *result, BOX *box, Point *pt)
 
        statlseg_construct(&lseg, &box->high, &point);
        d = lseg_closept_point(&closept, &lseg, pt);
-       if (d < dist)
+       if (float8_lt(d, dist))
        {
                dist = d;
                if (result != NULL)
@@ -2685,7 +2703,7 @@ box_closept_point(Point *result, BOX *box, Point *pt)
        point.y = box->low.y;
        statlseg_construct(&lseg, &box->low, &point);
        d = lseg_closept_point(&closept, &lseg, pt);
-       if (d < dist)
+       if (float8_lt(d, dist))
        {
                dist = d;
                if (result != NULL)
@@ -2694,7 +2712,7 @@ box_closept_point(Point *result, BOX *box, Point *pt)
 
        statlseg_construct(&lseg, &box->high, &point);
        d = lseg_closept_point(&closept, &lseg, pt);
-       if (d < dist)
+       if (float8_lt(d, dist))
        {
                dist = d;
                if (result != NULL)
@@ -2713,7 +2731,8 @@ close_pb(PG_FUNCTION_ARGS)
 
        result = (Point *) palloc(sizeof(Point));
 
-       box_closept_point(result, box, pt);
+       if (isnan(box_closept_point(result, box, pt)))
+               PG_RETURN_NULL();
 
        PG_RETURN_POINT_P(result);
 }
@@ -2745,7 +2764,7 @@ close_sl(PG_FUNCTION_ARGS)
 
        d1 = line_closept_point(NULL, line, &lseg->p[0]);
        d2 = line_closept_point(NULL, line, &lseg->p[1]);
-       if (d1 < d2)
+       if (float8_lt(d1, d2))
                *result = lseg->p[0];
        else
                *result = lseg->p[1];
@@ -2809,7 +2828,8 @@ close_ls(PG_FUNCTION_ARGS)
 
        result = (Point *) palloc(sizeof(Point));
 
-       lseg_closept_line(result, lseg, line);
+       if (isnan(lseg_closept_line(result, lseg, line)))
+               PG_RETURN_NULL();
 
        PG_RETURN_POINT_P(result);
 }
@@ -2824,11 +2844,11 @@ close_ls(PG_FUNCTION_ARGS)
 static float8
 box_closept_lseg(Point *result, BOX *box, LSEG *lseg)
 {
+       float8          dist,
+                               d;
        Point           point,
                                closept;
        LSEG            bseg;
-       double          dist,
-                               d;
 
        if (box_interpt_lseg(result, box, lseg))
                return 0.0;
@@ -2841,7 +2861,7 @@ box_closept_lseg(Point *result, BOX *box, LSEG *lseg)
 
        statlseg_construct(&bseg, &box->high, &point);
        d = lseg_closept_lseg(&closept, &bseg, lseg);
-       if (d < dist)
+       if (float8_lt(d, dist))
        {
                dist = d;
                if (result != NULL)
@@ -2852,7 +2872,7 @@ box_closept_lseg(Point *result, BOX *box, LSEG *lseg)
        point.y = box->low.y;
        statlseg_construct(&bseg, &box->low, &point);
        d = lseg_closept_lseg(&closept, &bseg, lseg);
-       if (d < dist)
+       if (float8_lt(d, dist))
        {
                dist = d;
                if (result != NULL)
@@ -2861,7 +2881,7 @@ box_closept_lseg(Point *result, BOX *box, LSEG *lseg)
 
        statlseg_construct(&bseg, &box->high, &point);
        d = lseg_closept_lseg(&closept, &bseg, lseg);
-       if (d < dist)
+       if (float8_lt(d, dist))
        {
                dist = d;
                if (result != NULL)
@@ -2880,7 +2900,8 @@ close_sb(PG_FUNCTION_ARGS)
 
        result = (Point *) palloc(sizeof(Point));
 
-       box_closept_lseg(result, box, lseg);
+       if (isnan(box_closept_lseg(result, box, lseg)))
+               PG_RETURN_NULL();
 
        PG_RETURN_POINT_P(result);
 }
@@ -2913,7 +2934,9 @@ close_lb(PG_FUNCTION_ARGS)
 static bool
 line_contain_point(LINE *line, Point *point)
 {
-       return FPzero(line->A * point->x + line->B * point->y + line->C);
+       return FPzero(float8_pl(float8_pl(float8_mul(line->A, point->x),
+                                                                         float8_mul(line->B, point->y)),
+                                                       line->C));
 }
 
 Datum
@@ -2994,7 +3017,7 @@ on_ppath(PG_FUNCTION_ARGS)
        PATH       *path = PG_GETARG_PATH_P(1);
        int                     i,
                                n;
-       double          a,
+       float8          a,
                                b;
 
        /*-- OPEN --*/
@@ -3005,8 +3028,7 @@ on_ppath(PG_FUNCTION_ARGS)
                for (i = 0; i < n; i++)
                {
                        b = point_dt(pt, &path->p[i + 1]);
-                       if (FPeq(a + b,
-                                        point_dt(&path->p[i], &path->p[i + 1])))
+                       if (FPeq(float8_pl(a, b), point_dt(&path->p[i], &path->p[i + 1])))
                                PG_RETURN_BOOL(true);
                        a = b;
                }
@@ -3092,10 +3114,10 @@ box_interpt_lseg(Point *result, BOX *box, LSEG *lseg)
        LSEG            bseg;
        Point           point;
 
-       lbox.low.x = Min(lseg->p[0].x, lseg->p[1].x);
-       lbox.low.y = Min(lseg->p[0].y, lseg->p[1].y);
-       lbox.high.x = Max(lseg->p[0].x, lseg->p[1].x);
-       lbox.high.y = Max(lseg->p[0].y, lseg->p[1].y);
+       lbox.low.x = float8_min(lseg->p[0].x, lseg->p[1].x);
+       lbox.low.y = float8_min(lseg->p[0].y, lseg->p[1].y);
+       lbox.high.x = float8_max(lseg->p[0].x, lseg->p[1].x);
+       lbox.high.y = float8_max(lseg->p[0].y, lseg->p[1].y);
 
        /* nothing close to overlap? then not going to intersect */
        if (!box_ov(&lbox, box))
@@ -3202,7 +3224,7 @@ static void
 make_bound_box(POLYGON *poly)
 {
        int                     i;
-       double          x1,
+       float8          x1,
                                y1,
                                x2,
                                y2;
@@ -3213,13 +3235,13 @@ make_bound_box(POLYGON *poly)
        y2 = y1 = poly->p[0].y;
        for (i = 1; i < poly->npts; i++)
        {
-               if (poly->p[i].x < x1)
+               if (float8_lt(poly->p[i].x, x1))
                        x1 = poly->p[i].x;
-               if (poly->p[i].x > x2)
+               if (float8_gt(poly->p[i].x, x2))
                        x2 = poly->p[i].x;
-               if (poly->p[i].y < y1)
+               if (float8_lt(poly->p[i].y, y1))
                        y1 = poly->p[i].y;
-               if (poly->p[i].y > y2)
+               if (float8_gt(poly->p[i].y, y2))
                        y2 = poly->p[i].y;
        }
 
@@ -3732,8 +3754,8 @@ lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start)
                 * if X-intersection wasn't found  then check central point of tested
                 * segment. In opposite case we already check all subsegments
                 */
-               p.x = (t.p[0].x + t.p[1].x) / 2.0;
-               p.y = (t.p[0].y + t.p[1].y) / 2.0;
+               p.x = float8_div(float8_pl(t.p[0].x, t.p[1].x), 2.0);
+               p.y = float8_div(float8_pl(t.p[0].y, t.p[1].y), 2.0);
 
                res = point_inside(&p, poly->npts, poly->p);
        }
@@ -3873,8 +3895,8 @@ static inline void
 point_add_point(Point *result, Point *pt1, Point *pt2)
 {
        point_construct(result,
-                                       pt1->x + pt2->x,
-                                       pt1->y + pt2->y);
+                                       float8_pl(pt1->x, pt2->x),
+                                       float8_pl(pt1->y, pt2->y));
 }
 
 Datum
@@ -3896,8 +3918,8 @@ static inline void
 point_sub_point(Point *result, Point *pt1, Point *pt2)
 {
        point_construct(result,
-                                       pt1->x - pt2->x,
-                                       pt1->y - pt2->y);
+                                       float8_mi(pt1->x, pt2->x),
+                                       float8_mi(pt1->y, pt2->y));
 }
 
 Datum
@@ -3919,8 +3941,10 @@ 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));
+                                       float8_mi(float8_mul(pt1->x, pt2->x),
+                                                         float8_mul(pt1->y, pt2->y)),
+                                       float8_pl(float8_mul(pt1->x, pt2->y),
+                                                         float8_mul(pt1->y, pt2->x)));
 }
 
 Datum
@@ -3941,18 +3965,15 @@ point_mul(PG_FUNCTION_ARGS)
 static inline void
 point_div_point(Point *result, Point *pt1, Point *pt2)
 {
-       double          div;
-
-       div = (pt2->x * pt2->x) + (pt2->y * pt2->y);
+       float8          div;
 
-       if (div == 0.0)
-               ereport(ERROR,
-                               (errcode(ERRCODE_DIVISION_BY_ZERO),
-                                errmsg("division by zero")));
+       div = float8_pl(float8_mul(pt2->x, pt2->x), float8_mul(pt2->y, pt2->y));
 
        point_construct(result,
-                                       ((pt1->x * pt2->x) + (pt1->y * pt2->y)) / div,
-                                       ((pt2->x * pt1->y) - (pt2->y * pt1->x)) / div);
+                                       float8_div(float8_pl(float8_mul(pt1->x, pt2->x),
+                                                                                float8_mul(pt1->y, pt2->y)), div),
+                                       float8_div(float8_mi(float8_mul(pt1->y, pt2->x),
+                                                                                float8_mul(pt1->x, pt2->y)), div));
 }
 
 Datum
@@ -4089,10 +4110,10 @@ boxes_bound_box(PG_FUNCTION_ARGS)
 
        container = (BOX *) palloc(sizeof(BOX));
 
-       container->high.x = Max(box1->high.x, box2->high.x);
-       container->low.x = Min(box1->low.x, box2->low.x);
-       container->high.y = Max(box1->high.y, box2->high.y);
-       container->low.y = Min(box1->low.y, box2->low.y);
+       container->high.x = float8_max(box1->high.x, box2->high.x);
+       container->low.x = float8_min(box1->low.x, box2->low.x);
+       container->high.y = float8_max(box1->high.y, box2->high.y);
+       container->low.y = float8_min(box1->low.y, box2->low.y);
 
        PG_RETURN_BOX_P(container);
 }
@@ -4412,7 +4433,8 @@ circle_in(PG_FUNCTION_ARGS)
                s++;
 
        circle->radius = single_decode(s, &s, "circle", str);
-       if (circle->radius < 0)
+       /* We have to accept NaN. */
+       if (circle->radius < 0.0)
                ereport(ERROR,
                                (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
                                 errmsg("invalid input syntax for type %s: \"%s\"",
@@ -4479,7 +4501,8 @@ circle_recv(PG_FUNCTION_ARGS)
        circle->center.y = pq_getmsgfloat8(buf);
        circle->radius = pq_getmsgfloat8(buf);
 
-       if (circle->radius < 0)
+       /* We have to accept NaN. */
+       if (circle->radius < 0.0)
                ereport(ERROR,
                                (errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
                                 errmsg("invalid radius in external \"circle\" value")));
@@ -4510,6 +4533,9 @@ circle_send(PG_FUNCTION_ARGS)
  *---------------------------------------------------------*/
 
 /*             circles identical?
+ *
+ * We consider NaNs values to be equal to each other to let those circles
+ * to be found.
  */
 Datum
 circle_same(PG_FUNCTION_ARGS)
@@ -4517,7 +4543,8 @@ circle_same(PG_FUNCTION_ARGS)
        CIRCLE     *circle1 = PG_GETARG_CIRCLE_P(0);
        CIRCLE     *circle2 = PG_GETARG_CIRCLE_P(1);
 
-       PG_RETURN_BOOL(FPeq(circle1->radius, circle2->radius) &&
+       PG_RETURN_BOOL(((isnan(circle1->radius) && isnan(circle1->radius)) ||
+                                       FPeq(circle1->radius, circle2->radius)) &&
                                   point_eq_point(&circle1->center, &circle2->center));
 }
 
@@ -4530,7 +4557,7 @@ circle_overlap(PG_FUNCTION_ARGS)
        CIRCLE     *circle2 = PG_GETARG_CIRCLE_P(1);
 
        PG_RETURN_BOOL(FPle(point_dt(&circle1->center, &circle2->center),
-                                               circle1->radius + circle2->radius));
+                                               float8_pl(circle1->radius, circle2->radius)));
 }
 
 /*             circle_overleft -               is the right edge of circle1 at or left of
@@ -4542,8 +4569,8 @@ circle_overleft(PG_FUNCTION_ARGS)
        CIRCLE     *circle1 = PG_GETARG_CIRCLE_P(0);
        CIRCLE     *circle2 = PG_GETARG_CIRCLE_P(1);
 
-       PG_RETURN_BOOL(FPle((circle1->center.x + circle1->radius),
-                                               (circle2->center.x + circle2->radius)));
+       PG_RETURN_BOOL(FPle(float8_pl(circle1->center.x, circle1->radius),
+                                               float8_pl(circle2->center.x, circle2->radius)));
 }
 
 /*             circle_left             -               is circle1 strictly left of circle2?
@@ -4554,8 +4581,8 @@ circle_left(PG_FUNCTION_ARGS)
        CIRCLE     *circle1 = PG_GETARG_CIRCLE_P(0);
        CIRCLE     *circle2 = PG_GETARG_CIRCLE_P(1);
 
-       PG_RETURN_BOOL(FPlt((circle1->center.x + circle1->radius),
-                                               (circle2->center.x - circle2->radius)));
+       PG_RETURN_BOOL(FPlt(float8_pl(circle1->center.x, circle1->radius),
+                                               float8_mi(circle2->center.x, circle2->radius)));
 }
 
 /*             circle_right    -               is circle1 strictly right of circle2?
@@ -4566,8 +4593,8 @@ circle_right(PG_FUNCTION_ARGS)
        CIRCLE     *circle1 = PG_GETARG_CIRCLE_P(0);
        CIRCLE     *circle2 = PG_GETARG_CIRCLE_P(1);
 
-       PG_RETURN_BOOL(FPgt((circle1->center.x - circle1->radius),
-                                               (circle2->center.x + circle2->radius)));
+       PG_RETURN_BOOL(FPgt(float8_mi(circle1->center.x, circle1->radius),
+                                               float8_pl(circle2->center.x, circle2->radius)));
 }
 
 /*             circle_overright        -       is the left edge of circle1 at or right of
@@ -4579,8 +4606,8 @@ circle_overright(PG_FUNCTION_ARGS)
        CIRCLE     *circle1 = PG_GETARG_CIRCLE_P(0);
        CIRCLE     *circle2 = PG_GETARG_CIRCLE_P(1);
 
-       PG_RETURN_BOOL(FPge((circle1->center.x - circle1->radius),
-                                               (circle2->center.x - circle2->radius)));
+       PG_RETURN_BOOL(FPge(float8_mi(circle1->center.x, circle1->radius),
+                                               float8_mi(circle2->center.x, circle2->radius)));
 }
 
 /*             circle_contained                -               is circle1 contained by circle2?
@@ -4592,7 +4619,7 @@ circle_contained(PG_FUNCTION_ARGS)
        CIRCLE     *circle2 = PG_GETARG_CIRCLE_P(1);
 
        PG_RETURN_BOOL(FPle(point_dt(&circle1->center, &circle2->center),
-                                               circle2->radius - circle1->radius));
+                                               float8_mi(circle2->radius, circle1->radius)));
 }
 
 /*             circle_contain  -               does circle1 contain circle2?
@@ -4604,7 +4631,7 @@ circle_contain(PG_FUNCTION_ARGS)
        CIRCLE     *circle2 = PG_GETARG_CIRCLE_P(1);
 
        PG_RETURN_BOOL(FPle(point_dt(&circle1->center, &circle2->center),
-                                               circle1->radius - circle2->radius));
+                                               float8_mi(circle1->radius, circle2->radius)));
 }
 
 
@@ -4616,8 +4643,8 @@ circle_below(PG_FUNCTION_ARGS)
        CIRCLE     *circle1 = PG_GETARG_CIRCLE_P(0);
        CIRCLE     *circle2 = PG_GETARG_CIRCLE_P(1);
 
-       PG_RETURN_BOOL(FPlt((circle1->center.y + circle1->radius),
-                                               (circle2->center.y - circle2->radius)));
+       PG_RETURN_BOOL(FPlt(float8_pl(circle1->center.y, circle1->radius),
+                                               float8_mi(circle2->center.y, circle2->radius)));
 }
 
 /*             circle_above    -               is circle1 strictly above circle2?
@@ -4628,8 +4655,8 @@ circle_above(PG_FUNCTION_ARGS)
        CIRCLE     *circle1 = PG_GETARG_CIRCLE_P(0);
        CIRCLE     *circle2 = PG_GETARG_CIRCLE_P(1);
 
-       PG_RETURN_BOOL(FPgt((circle1->center.y - circle1->radius),
-                                               (circle2->center.y + circle2->radius)));
+       PG_RETURN_BOOL(FPgt(float8_mi(circle1->center.y, circle1->radius),
+                                               float8_pl(circle2->center.y, circle2->radius)));
 }
 
 /*             circle_overbelow -              is the upper edge of circle1 at or below
@@ -4641,8 +4668,8 @@ circle_overbelow(PG_FUNCTION_ARGS)
        CIRCLE     *circle1 = PG_GETARG_CIRCLE_P(0);
        CIRCLE     *circle2 = PG_GETARG_CIRCLE_P(1);
 
-       PG_RETURN_BOOL(FPle((circle1->center.y + circle1->radius),
-                                               (circle2->center.y + circle2->radius)));
+       PG_RETURN_BOOL(FPle(float8_pl(circle1->center.y, circle1->radius),
+                                               float8_pl(circle2->center.y, circle2->radius)));
 }
 
 /*             circle_overabove        -       is the lower edge of circle1 at or above
@@ -4654,8 +4681,8 @@ circle_overabove(PG_FUNCTION_ARGS)
        CIRCLE     *circle1 = PG_GETARG_CIRCLE_P(0);
        CIRCLE     *circle2 = PG_GETARG_CIRCLE_P(1);
 
-       PG_RETURN_BOOL(FPge((circle1->center.y - circle1->radius),
-                                               (circle2->center.y - circle2->radius)));
+       PG_RETURN_BOOL(FPge(float8_mi(circle1->center.y, circle1->radius),
+                                               float8_mi(circle2->center.y, circle2->radius)));
 }
 
 
@@ -4768,7 +4795,7 @@ circle_mul_pt(PG_FUNCTION_ARGS)
        result = (CIRCLE *) palloc(sizeof(CIRCLE));
 
        point_mul_point(&result->center, &circle->center, point);
-       result->radius = circle->radius * HYPOT(point->x, point->y);
+       result->radius = float8_mul(circle->radius, HYPOT(point->x, point->y));
 
        PG_RETURN_CIRCLE_P(result);
 }
@@ -4783,7 +4810,7 @@ circle_div_pt(PG_FUNCTION_ARGS)
        result = (CIRCLE *) palloc(sizeof(CIRCLE));
 
        point_div_point(&result->center, &circle->center, point);
-       result->radius = circle->radius / HYPOT(point->x, point->y);
+       result->radius = float8_div(circle->radius, HYPOT(point->x, point->y));
 
        PG_RETURN_CIRCLE_P(result);
 }
@@ -4807,7 +4834,7 @@ circle_diameter(PG_FUNCTION_ARGS)
 {
        CIRCLE     *circle = PG_GETARG_CIRCLE_P(0);
 
-       PG_RETURN_FLOAT8(2 * circle->radius);
+       PG_RETURN_FLOAT8(float8_mul(circle->radius, 2.0));
 }
 
 
@@ -4832,10 +4859,11 @@ 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);
-       if (result < 0)
-               result = 0;
+       result = float8_mi(point_dt(&circle1->center, &circle2->center),
+                                          float8_pl(circle1->radius, circle2->radius));
+       if (result < 0.0)
+               result = 0.0;
+
        PG_RETURN_FLOAT8(result);
 }
 
@@ -4845,7 +4873,7 @@ circle_contain_pt(PG_FUNCTION_ARGS)
 {
        CIRCLE     *circle = PG_GETARG_CIRCLE_P(0);
        Point      *point = PG_GETARG_POINT_P(1);
-       double          d;
+       float8          d;
 
        d = point_dt(&circle->center, point);
        PG_RETURN_BOOL(d <= circle->radius);
@@ -4857,7 +4885,7 @@ pt_contained_circle(PG_FUNCTION_ARGS)
 {
        Point      *point = PG_GETARG_POINT_P(0);
        CIRCLE     *circle = PG_GETARG_CIRCLE_P(1);
-       double          d;
+       float8          d;
 
        d = point_dt(&circle->center, point);
        PG_RETURN_BOOL(d <= circle->radius);
@@ -4874,9 +4902,11 @@ dist_pc(PG_FUNCTION_ARGS)
        CIRCLE     *circle = PG_GETARG_CIRCLE_P(1);
        float8          result;
 
-       result = point_dt(point, &circle->center) - circle->radius;
-       if (result < 0)
-               result = 0;
+       result = float8_mi(point_dt(point, &circle->center),
+                                          circle->radius);
+       if (result < 0.0)
+               result = 0.0;
+
        PG_RETURN_FLOAT8(result);
 }
 
@@ -4890,9 +4920,10 @@ dist_cpoint(PG_FUNCTION_ARGS)
        Point      *point = PG_GETARG_POINT_P(1);
        float8          result;
 
-       result = point_dt(point, &circle->center) - circle->radius;
-       if (result < 0)
-               result = 0;
+       result = float8_mi(point_dt(point, &circle->center), circle->radius);
+       if (result < 0.0)
+               result = 0.0;
+
        PG_RETURN_FLOAT8(result);
 }
 
@@ -4914,10 +4945,10 @@ circle_center(PG_FUNCTION_ARGS)
 
 /*             circle_ar               -               returns the area of the circle.
  */
-static double
+static float8
 circle_ar(CIRCLE *circle)
 {
-       return M_PI * (circle->radius * circle->radius);
+       return float8_mul(float8_mul(circle->radius, circle->radius), M_PI);
 }
 
 
@@ -4946,16 +4977,16 @@ circle_box(PG_FUNCTION_ARGS)
 {
        CIRCLE     *circle = PG_GETARG_CIRCLE_P(0);
        BOX                *box;
-       double          delta;
+       float8          delta;
 
        box = (BOX *) palloc(sizeof(BOX));
 
-       delta = circle->radius / sqrt(2.0);
+       delta = float8_div(circle->radius, sqrt(2.0));
 
-       box->high.x = circle->center.x + delta;
-       box->low.x = circle->center.x - delta;
-       box->high.y = circle->center.y + delta;
-       box->low.y = circle->center.y - delta;
+       box->high.x = float8_pl(circle->center.x, delta);
+       box->low.x = float8_mi(circle->center.x, delta);
+       box->high.y = float8_pl(circle->center.y, delta);
+       box->low.y = float8_mi(circle->center.y, delta);
 
        PG_RETURN_BOX_P(box);
 }
@@ -4971,8 +5002,8 @@ box_circle(PG_FUNCTION_ARGS)
 
        circle = (CIRCLE *) palloc(sizeof(CIRCLE));
 
-       circle->center.x = (box->high.x + box->low.x) / 2;
-       circle->center.y = (box->high.y + box->low.y) / 2;
+       circle->center.x = float8_div(float8_pl(box->high.x, box->low.x), 2.0);
+       circle->center.y = float8_div(float8_pl(box->high.y, box->low.y), 2.0);
 
        circle->radius = point_dt(&circle->center, &box->high);
 
@@ -4989,8 +5020,8 @@ circle_poly(PG_FUNCTION_ARGS)
        int                     base_size,
                                size;
        int                     i;
-       double          angle;
-       double          anglestep;
+       float8          angle;
+       float8          anglestep;
 
        if (FPzero(circle->radius))
                ereport(ERROR,
@@ -5015,13 +5046,16 @@ circle_poly(PG_FUNCTION_ARGS)
        SET_VARSIZE(poly, size);
        poly->npts = npts;
 
-       anglestep = (2.0 * M_PI) / npts;
+       anglestep = float8_div(2.0 * M_PI, npts);
 
        for (i = 0; i < npts; i++)
        {
-               angle = i * anglestep;
-               poly->p[i].x = circle->center.x - (circle->radius * cos(angle));
-               poly->p[i].y = circle->center.y + (circle->radius * sin(angle));
+               angle = float8_mul(anglestep, i);
+
+               poly->p[i].x = float8_mi(circle->center.x,
+                                                                float8_mul(circle->radius, cos(angle)));
+               poly->p[i].y = float8_pl(circle->center.y,
+                                                                float8_mul(circle->radius, sin(angle)));
        }
 
        make_bound_box(poly);
@@ -5050,12 +5084,13 @@ poly_to_circle(CIRCLE *result, POLYGON *poly)
 
        for (i = 0; i < poly->npts; i++)
                point_add_point(&result->center, &result->center, &poly->p[i]);
-       result->center.x /= poly->npts;
-       result->center.y /= poly->npts;
+       result->center.x = float8_div(result->center.x, poly->npts);
+       result->center.y = float8_div(result->center.y, poly->npts);
 
        for (i = 0; i < poly->npts; i++)
-               result->radius += point_dt(&poly->p[i], &result->center);
-       result->radius /= poly->npts;
+               result->radius = float8_pl(result->radius,
+                                                                  point_dt(&poly->p[i], &result->center));
+       result->radius = float8_div(result->radius, poly->npts);
 }
 
 Datum
@@ -5094,12 +5129,12 @@ poly_circle(PG_FUNCTION_ARGS)
 static int
 point_inside(Point *p, int npts, Point *plist)
 {
-       double          x0,
+       float8          x0,
                                y0;
-       double          prev_x,
+       float8          prev_x,
                                prev_y;
        int                     i = 0;
-       double          x,
+       float8          x,
                                y;
        int                     cross,
                                total_cross = 0;
@@ -5107,8 +5142,8 @@ point_inside(Point *p, int npts, Point *plist)
        Assert(npts > 0);
 
        /* compute first polygon point relative to single point */
-       x0 = plist[0].x - p->x;
-       y0 = plist[0].y - p->y;
+       x0 = float8_mi(plist[0].x, p->x);
+       y0 = float8_mi(plist[0].y, p->y);
 
        prev_x = x0;
        prev_y = y0;
@@ -5116,8 +5151,8 @@ point_inside(Point *p, int npts, Point *plist)
        for (i = 1; i < npts; i++)
        {
                /* compute next polygon point relative to single point */
-               x = plist[i].x - p->x;
-               y = plist[i].y - p->y;
+               x = float8_mi(plist[i].x, p->x);
+               y = float8_mi(plist[i].y, p->y);
 
                /* compute previous to current point crossing */
                if ((cross = lseg_crossing(x, y, prev_x, prev_y)) == POINT_ON_POLYGON)
@@ -5149,9 +5184,9 @@ point_inside(Point *p, int npts, Point *plist)
  */
 
 static int
-lseg_crossing(double x, double y, double prev_x, double prev_y)
+lseg_crossing(float8 x, float8 y, float8 prev_x, float8 prev_y)
 {
-       double          z;
+       float8          z;
        int                     y_sign;
 
        if (FPzero(y))
@@ -5162,42 +5197,47 @@ lseg_crossing(double x, double y, double prev_x, double prev_y)
                {                                               /* x > 0 */
                        if (FPzero(prev_y)) /* y and prev_y are zero */
                                /* prev_x > 0? */
-                               return FPgt(prev_x, 0) ? 0 : POINT_ON_POLYGON;
-                       return FPlt(prev_y, 0) ? 1 : -1;
+                               return FPgt(prev_x, 0.0) ? 0 : POINT_ON_POLYGON;
+                       return FPlt(prev_y, 0.0) ? 1 : -1;
                }
                else
                {                                               /* x < 0, x not on positive X axis */
                        if (FPzero(prev_y))
                                /* prev_x < 0? */
-                               return FPlt(prev_x, 0) ? 0 : POINT_ON_POLYGON;
+                               return FPlt(prev_x, 0.0) ? 0 : POINT_ON_POLYGON;
                        return 0;
                }
        }
        else
        {                                                       /* y != 0 */
                /* compute y crossing direction from previous point */
-               y_sign = FPgt(y, 0) ? 1 : -1;
+               y_sign = FPgt(y, 0.0) ? 1 : -1;
 
                if (FPzero(prev_y))
                        /* previous point was on X axis, so new point is either off or on */
-                       return FPlt(prev_x, 0) ? 0 : y_sign;
-               else if (FPgt(y_sign * prev_y, 0))
+                       return FPlt(prev_x, 0.0) ? 0 : y_sign;
+               else if ((y_sign < 0 && FPlt(prev_y, 0.0)) ||
+                                (y_sign > 0 && FPgt(prev_y, 0.0)))
                        /* both above or below X axis */
                        return 0;                       /* same sign */
                else
                {                                               /* y and prev_y cross X-axis */
-                       if (FPge(x, 0) && FPgt(prev_x, 0))
+                       if (FPge(x, 0.0) && FPgt(prev_x, 0.0))
                                /* both non-negative so cross positive X-axis */
                                return 2 * y_sign;
-                       if (FPlt(x, 0) && FPle(prev_x, 0))
+                       if (FPlt(x, 0.0) && FPle(prev_x, 0.0))
                                /* both non-positive so do not cross positive X-axis */
                                return 0;
 
                        /* x and y cross axises, see URL above point_inside() */
-                       z = (x - prev_x) * y - (y - prev_y) * x;
+                       z = float8_mi(float8_mul(float8_mi(x, prev_x), y),
+                                                 float8_mul(float8_mi(y, prev_y), x));
                        if (FPzero(z))
                                return POINT_ON_POLYGON;
-                       return FPgt((y_sign * z), 0) ? 0 : 2 * y_sign;
+                       if ((y_sign < 0 && FPlt(z, 0.0)) ||
+                               (y_sign > 0 && FPgt(z, 0.0)))
+                               return 0;
+                       return 2 * y_sign;
                }
        }
 }
@@ -5265,10 +5305,11 @@ plist_same(int npts, Point *p1, Point *p2)
  * case of hypot(inf,nan) results in INF, and not NAN.
  *-----------------------------------------------------------------------
  */
-double
-pg_hypot(double x, double y)
+float8
+pg_hypot(float8 x, float8 y)
 {
-       double          yx;
+       float8          yx,
+                               result;
 
        /* Handle INF and NaN properly */
        if (isinf(x) || isinf(y))
@@ -5284,7 +5325,7 @@ pg_hypot(double x, double y)
        /* Swap x and y if needed to make x the larger one */
        if (x < y)
        {
-               double          temp = x;
+               float8          temp = x;
 
                x = y;
                y = temp;
@@ -5300,5 +5341,9 @@ pg_hypot(double x, double y)
 
        /* Determine the hypotenuse */
        yx = y / x;
-       return x * sqrt(1.0 + (yx * yx));
+       result = x * sqrt(1.0 + (yx * yx));
+
+       check_float8_val(result, false, false);
+
+       return result;
 }
index fea36f361ae8dbb5fa052aae804e2e4214a89a06..4aff973ef37bcb9b29a7be856a6cd50f40f0da2d 100644 (file)
  * 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;
 
index 0e066894cd1c343b16a5cb5a30e60592ac706ddb..9f8505804e8b579a8845fda75fb72cc068d2ac04 100644 (file)
@@ -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
 #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 */