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Rewrite the planner's handling of materialized plan types so that there is
authorTom Lane <tgl@sss.pgh.pa.us>
Sat, 12 Sep 2009 22:12:09 +0000 (22:12 +0000)
committerTom Lane <tgl@sss.pgh.pa.us>
Sat, 12 Sep 2009 22:12:09 +0000 (22:12 +0000)
an explicit model of rescan costs being different from first-time costs.
The costing of Material nodes in particular now has some visible relationship
to the actual runtime behavior, where before it was essentially fantasy.
This also fixes up a couple of places where different materialized plan types
were treated differently for no very good reason (probably just oversights).

A couple of the regression tests are affected, because the planner now chooses
to put the other relation on the inside of a nestloop-with-materialize.
So far as I can see both changes are sane, and the planner is now more
consistently following the expectation that it should prefer to materialize
the smaller of two relations.

Per a recent discussion with Robert Haas.

12 files changed:
src/backend/executor/execAmi.c patch | blob | blame | history
src/backend/optimizer/path/costsize.c patch | blob | blame | history
src/backend/optimizer/path/joinpath.c patch | blob | blame | history
src/backend/optimizer/plan/createplan.c patch | blob | blame | history
src/backend/optimizer/plan/subselect.c patch | blob | blame | history
src/backend/optimizer/util/pathnode.c patch | blob | blame | history
src/include/executor/executor.h patch | blob | blame | history
src/include/optimizer/cost.h patch | blob | blame | history
src/test/regress/expected/geometry.out patch | blob | blame | history
src/test/regress/expected/geometry_1.out patch | blob | blame | history
src/test/regress/expected/geometry_2.out patch | blob | blame | history
src/test/regress/expected/join.out patch | blob | blame | history

diff --git a/src/backend/executor/execAmi.c b/src/backend/executor/execAmi.c
index 25f350f273681f6aaeffe70ce4322c004f26eb6b..2fecb462ab2e9d30f07ecf889b503b6382ac6158 100644 (file)
--- a/src/backend/executor/execAmi.c
+++ b/src/backend/executor/execAmi.c
@@ -496,3 +496,30 @@ IndexSupportsBackwardScan(Oid indexid)
 
        return result;
 }
+
+/*
+ * ExecMaterializesOutput - does a plan type materialize its output?
+ *
+ * Returns true if the plan node type is one that automatically materializes
+ * its output (typically by keeping it in a tuplestore).  For such plans,
+ * a rescan without any parameter change will have zero startup cost and
+ * very low per-tuple cost.
+ */
+bool
+ExecMaterializesOutput(NodeTag plantype)
+{
+       switch (plantype)
+       {
+               case T_Material:
+               case T_FunctionScan:
+               case T_CteScan:
+               case T_WorkTableScan:
+               case T_Sort:
+                       return true;
+
+               default:
+                       break;
+       }
+
+       return false;
+}
diff --git a/src/backend/optimizer/path/costsize.c b/src/backend/optimizer/path/costsize.c
index fcbb8cabad833e966c64ced91ff739519f199517..c9c5025c593291a43555612b0fd85d4287dae50c 100644 (file)
--- a/src/backend/optimizer/path/costsize.c
+++ b/src/backend/optimizer/path/costsize.c
@@ -63,6 +63,7 @@
 
 #include <math.h>
 
+#include "executor/executor.h"
 #include "executor/nodeHash.h"
 #include "miscadmin.h"
 #include "nodes/nodeFuncs.h"
@@ -119,6 +120,8 @@ typedef struct
 static MergeScanSelCache *cached_scansel(PlannerInfo *root,
                           RestrictInfo *rinfo,
                           PathKey *pathkey);
+static void cost_rescan(PlannerInfo *root, Path *path,
+                       Cost *rescan_startup_cost, Cost *rescan_total_cost);
 static bool cost_qual_eval_walker(Node *node, cost_qual_eval_context *context);
 static bool adjust_semi_join(PlannerInfo *root, JoinPath *path,
                                 SpecialJoinInfo *sjinfo,
@@ -895,15 +898,26 @@ cost_functionscan(Path *path, PlannerInfo *root, RelOptInfo *baserel)
        rte = planner_rt_fetch(baserel->relid, root);
        Assert(rte->rtekind == RTE_FUNCTION);
 
-       /* Estimate costs of executing the function expression */
+       /*
+        * Estimate costs of executing the function expression.
+        *
+        * Currently, nodeFunctionscan.c always executes the function to
+        * completion before returning any rows, and caches the results in a
+        * tuplestore.  So the function eval cost is all startup cost, and
+        * per-row costs are minimal.
+        *
+        * XXX in principle we ought to charge tuplestore spill costs if the
+        * number of rows is large.  However, given how phony our rowcount
+        * estimates for functions tend to be, there's not a lot of point
+        * in that refinement right now.
+        */
        cost_qual_eval_node(&exprcost, rte->funcexpr, root);
 
-       startup_cost += exprcost.startup;
-       cpu_per_tuple = exprcost.per_tuple;
+       startup_cost += exprcost.startup + exprcost.per_tuple;
 
        /* Add scanning CPU costs */
        startup_cost += baserel->baserestrictcost.startup;
-       cpu_per_tuple += cpu_tuple_cost + baserel->baserestrictcost.per_tuple;
+       cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost.per_tuple;
        run_cost += cpu_per_tuple * baserel->tuples;
 
        path->startup_cost = startup_cost;
@@ -1176,41 +1190,44 @@ sort_exceeds_work_mem(Sort *sort)
  *
  * If the total volume of data to materialize exceeds work_mem, we will need
  * to write it to disk, so the cost is much higher in that case.
+ *
+ * Note that here we are estimating the costs for the first scan of the
+ * relation, so the materialization is all overhead --- any savings will
+ * occur only on rescan, which is estimated in cost_rescan.
  */
 void
 cost_material(Path *path,
-                         Cost input_cost, double tuples, int width)
+                         Cost input_startup_cost, Cost input_total_cost,
+                         double tuples, int width)
 {
-       Cost            startup_cost = input_cost;
-       Cost            run_cost = 0;
+       Cost            startup_cost = input_startup_cost;
+       Cost            run_cost = input_total_cost - input_startup_cost;
        double          nbytes = relation_byte_size(tuples, width);
        long            work_mem_bytes = work_mem * 1024L;
 
-       /* disk costs */
+       /*
+        * Whether spilling or not, charge 2x cpu_tuple_cost per tuple to reflect
+        * bookkeeping overhead.  (This rate must be more than cpu_tuple_cost;
+        * if it is exactly the same then there will be a cost tie between
+        * nestloop with A outer, materialized B inner and nestloop with B outer,
+        * materialized A inner.  The extra cost ensures we'll prefer
+        * materializing the smaller rel.)
+        */
+       run_cost += 2 * cpu_tuple_cost * tuples;
+
+       /*
+        * If we will spill to disk, charge at the rate of seq_page_cost per page.
+        * This cost is assumed to be evenly spread through the plan run phase,
+        * which isn't exactly accurate but our cost model doesn't allow for
+        * nonuniform costs within the run phase.
+        */
        if (nbytes > work_mem_bytes)
        {
                double          npages = ceil(nbytes / BLCKSZ);
 
-               /* We'll write during startup and read during retrieval */
-               startup_cost += seq_page_cost * npages;
                run_cost += seq_page_cost * npages;
        }
 
-       /*
-        * Charge a very small amount per inserted tuple, to reflect bookkeeping
-        * costs.  We use cpu_tuple_cost/10 for this.  This is needed to break the
-        * tie that would otherwise exist between nestloop with A outer,
-        * materialized B inner and nestloop with B outer, materialized A inner.
-        * The extra cost ensures we'll prefer materializing the smaller rel.
-        */
-       startup_cost += cpu_tuple_cost * 0.1 * tuples;
-
-       /*
-        * Also charge a small amount per extracted tuple.      We use cpu_tuple_cost
-        * so that it doesn't appear worthwhile to materialize a bare seqscan.
-        */
-       run_cost += cpu_tuple_cost * tuples;
-
        path->startup_cost = startup_cost;
        path->total_cost = startup_cost + run_cost;
 }
@@ -1400,7 +1417,10 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo)
        Path       *inner_path = path->innerjoinpath;
        Cost            startup_cost = 0;
        Cost            run_cost = 0;
+       Cost            inner_rescan_start_cost;
+       Cost            inner_rescan_total_cost;
        Cost            inner_run_cost;
+       Cost            inner_rescan_run_cost;
        Cost            cpu_per_tuple;
        QualCost        restrict_qual_cost;
        double          outer_path_rows = PATH_ROWS(outer_path);
@@ -1413,32 +1433,26 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo)
        if (!enable_nestloop)
                startup_cost += disable_cost;
 
+       /* estimate costs to rescan the inner relation */
+       cost_rescan(root, inner_path,
+                               &inner_rescan_start_cost,
+                               &inner_rescan_total_cost);
+
        /* cost of source data */
 
        /*
         * NOTE: clearly, we must pay both outer and inner paths' startup_cost
         * before we can start returning tuples, so the join's startup cost is
-        * their sum.  What's not so clear is whether the inner path's
-        * startup_cost must be paid again on each rescan of the inner path. This
-        * is not true if the inner path is materialized or is a hashjoin, but
-        * probably is true otherwise.
+        * their sum.  We'll also pay the inner path's rescan startup cost
+        * multiple times.
         */
        startup_cost += outer_path->startup_cost + inner_path->startup_cost;
        run_cost += outer_path->total_cost - outer_path->startup_cost;
-       if (IsA(inner_path, MaterialPath) ||
-               IsA(inner_path, HashPath))
-       {
-               /* charge only run cost for each iteration of inner path */
-       }
-       else
-       {
-               /*
-                * charge startup cost for each iteration of inner path, except we
-                * already charged the first startup_cost in our own startup
-                */
-               run_cost += (outer_path_rows - 1) * inner_path->startup_cost;
-       }
+       if (outer_path_rows > 1)
+               run_cost += (outer_path_rows - 1) * inner_rescan_start_cost;
+
        inner_run_cost = inner_path->total_cost - inner_path->startup_cost;
+       inner_rescan_run_cost = inner_rescan_total_cost - inner_rescan_start_cost;
 
        if (adjust_semi_join(root, path, sjinfo,
                                                 &outer_match_frac,
@@ -1458,12 +1472,22 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo)
                 * that fraction.  (If we used a larger fuzz factor, we'd have to
                 * clamp inner_scan_frac to at most 1.0; but since match_count is at
                 * least 1, no such clamp is needed now.)
+                *
+                * A complicating factor is that rescans may be cheaper than first
+                * scans.  If we never scan all the way to the end of the inner rel,
+                * it might be (depending on the plan type) that we'd never pay the
+                * whole inner first-scan run cost.  However it is difficult to
+                * estimate whether that will happen, so be conservative and always
+                * charge the whole first-scan cost once.
                 */
+               run_cost += inner_run_cost;
+
                outer_matched_rows = rint(outer_path_rows * outer_match_frac);
                inner_scan_frac = 2.0 / (match_count + 1.0);
 
-               /* Add inner run cost for outer tuples having matches */
-               run_cost += outer_matched_rows * inner_run_cost * inner_scan_frac;
+               /* Add inner run cost for additional outer tuples having matches */
+               if (outer_matched_rows > 1)
+                       run_cost += (outer_matched_rows - 1) * inner_rescan_run_cost * inner_scan_frac;
 
                /* Compute number of tuples processed (not number emitted!) */
                ntuples = outer_matched_rows * inner_path_rows * inner_scan_frac;
@@ -1479,13 +1503,16 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo)
                if (indexed_join_quals)
                {
                        run_cost += (outer_path_rows - outer_matched_rows) *
-                               inner_run_cost / inner_path_rows;
-                       /* We won't be evaluating any quals at all for these rows */
+                               inner_rescan_run_cost / inner_path_rows;
+                       /*
+                        * We won't be evaluating any quals at all for these rows,
+                        * so don't add them to ntuples.
+                        */
                }
                else
                {
                        run_cost += (outer_path_rows - outer_matched_rows) *
-                               inner_run_cost;
+                               inner_rescan_run_cost;
                        ntuples += (outer_path_rows - outer_matched_rows) *
                                inner_path_rows;
                }
@@ -1493,7 +1520,9 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo)
        else
        {
                /* Normal case; we'll scan whole input rel for each outer row */
-               run_cost += outer_path_rows * inner_run_cost;
+               run_cost += inner_run_cost;
+               if (outer_path_rows > 1)
+                       run_cost += (outer_path_rows - 1) * inner_rescan_run_cost;
 
                /* Compute number of tuples processed (not number emitted!) */
                ntuples = outer_path_rows * inner_path_rows;
@@ -2190,13 +2219,13 @@ cost_subplan(PlannerInfo *root, SubPlan *subplan, Plan *plan)
 
                /*
                 * Also account for subplan's startup cost. If the subplan is
-                * uncorrelated or undirect correlated, AND its topmost node is a Sort
-                * or Material node, assume that we'll only need to pay its startup
-                * cost once; otherwise assume we pay the startup cost every time.
+                * uncorrelated or undirect correlated, AND its topmost node is one
+                * that materializes its output, assume that we'll only need to pay
+                * its startup cost once; otherwise assume we pay the startup cost
+                * every time.
                 */
                if (subplan->parParam == NIL &&
-                       (IsA(plan, Sort) ||
-                        IsA(plan, Material)))
+                       ExecMaterializesOutput(nodeTag(plan)))
                        sp_cost.startup += plan->startup_cost;
                else
                        sp_cost.per_tuple += plan->startup_cost;
@@ -2207,6 +2236,81 @@ cost_subplan(PlannerInfo *root, SubPlan *subplan, Plan *plan)
 }
 
 
+/*
+ * cost_rescan
+ *             Given a finished Path, estimate the costs of rescanning it after
+ *             having done so the first time.  For some Path types a rescan is
+ *             cheaper than an original scan (if no parameters change), and this
+ *             function embodies knowledge about that.  The default is to return
+ *             the same costs stored in the Path.  (Note that the cost estimates
+ *             actually stored in Paths are always for first scans.)
+ *
+ * This function is not currently intended to model effects such as rescans
+ * being cheaper due to disk block caching; what we are concerned with is
+ * plan types wherein the executor caches results explicitly, or doesn't
+ * redo startup calculations, etc.
+ */
+static void
+cost_rescan(PlannerInfo *root, Path *path,
+                       Cost *rescan_startup_cost,              /* output parameters */
+                       Cost *rescan_total_cost)
+{
+       switch (path->pathtype)
+       {
+               case T_FunctionScan:
+                       /*
+                        * Currently, nodeFunctionscan.c always executes the function
+                        * to completion before returning any rows, and caches the
+                        * results in a tuplestore.  So the function eval cost is
+                        * all startup cost and isn't paid over again on rescans.
+                        * However, all run costs will be paid over again.
+                        */
+                       *rescan_startup_cost = 0;
+                       *rescan_total_cost = path->total_cost - path->startup_cost;
+                       break;
+               case T_HashJoin:
+                       /*
+                        * Assume that all of the startup cost represents hash table
+                        * building, which we won't have to do over.
+                        */
+                       *rescan_startup_cost = 0;
+                       *rescan_total_cost = path->total_cost - path->startup_cost;
+                       break;
+               case T_Material:
+               case T_CteScan:
+               case T_WorkTableScan:
+               case T_Sort:
+                       {
+                               /*
+                                * These plan types materialize their final result in a
+                                * tuplestore or tuplesort object.  So the rescan cost is only
+                                * cpu_tuple_cost per tuple, unless the result is large enough
+                                * to spill to disk.
+                                */
+                               Cost    run_cost = cpu_tuple_cost * path->parent->rows;
+                               double  nbytes = relation_byte_size(path->parent->rows,
+                                                                                                       path->parent->width);
+                               long    work_mem_bytes = work_mem * 1024L;
+
+                               if (nbytes > work_mem_bytes)
+                               {
+                                       /* It will spill, so account for re-read cost */
+                                       double          npages = ceil(nbytes / BLCKSZ);
+
+                                       run_cost += seq_page_cost * npages;
+                               }
+                               *rescan_startup_cost = 0;
+                               *rescan_total_cost = run_cost;
+                       }
+                       break;
+               default:
+                       *rescan_startup_cost = path->startup_cost;
+                       *rescan_total_cost = path->total_cost;
+                       break;
+       }
+}
+
+
 /*
  * cost_qual_eval
  *             Estimate the CPU costs of evaluating a WHERE clause.
diff --git a/src/backend/optimizer/path/joinpath.c b/src/backend/optimizer/path/joinpath.c
index 8e5767d17e016049c670de5c5b6e8607ee379820..ef13110fb926b5341a3a6405a8b81a66a17a2f97 100644 (file)
--- a/src/backend/optimizer/path/joinpath.c
+++ b/src/backend/optimizer/path/joinpath.c
@@ -16,6 +16,7 @@
 
 #include <math.h>
 
+#include "executor/executor.h"
 #include "optimizer/cost.h"
 #include "optimizer/pathnode.h"
 #include "optimizer/paths.h"
@@ -405,18 +406,10 @@ match_unsorted_outer(PlannerInfo *root,
        else if (nestjoinOK)
        {
                /*
-                * If the cheapest inner path is a join or seqscan, we should consider
-                * materializing it.  (This is a heuristic: we could consider it
-                * always, but for inner indexscans it's probably a waste of time.)
-                * Also skip it if the inner path materializes its output anyway.
+                * Consider materializing the cheapest inner path, unless it is one
+                * that materializes its output anyway.
                 */
-               if (!(inner_cheapest_total->pathtype == T_IndexScan ||
-                         inner_cheapest_total->pathtype == T_BitmapHeapScan ||
-                         inner_cheapest_total->pathtype == T_TidScan ||
-                         inner_cheapest_total->pathtype == T_Material ||
-                         inner_cheapest_total->pathtype == T_FunctionScan ||
-                         inner_cheapest_total->pathtype == T_CteScan ||
-                         inner_cheapest_total->pathtype == T_WorkTableScan))
+               if (!ExecMaterializesOutput(inner_cheapest_total->pathtype))
                        matpath = (Path *)
                                create_material_path(innerrel, inner_cheapest_total);
 
diff --git a/src/backend/optimizer/plan/createplan.c b/src/backend/optimizer/plan/createplan.c
index 6e5c2519c7980ddcf89196748cd9cb905879550b..ccea2e8e09adfc0d2907a10aade598822d417516 100644 (file)
--- a/src/backend/optimizer/plan/createplan.c
+++ b/src/backend/optimizer/plan/createplan.c
@@ -3266,6 +3266,7 @@ materialize_finished_plan(Plan *subplan)
 
        /* Set cost data */
        cost_material(&matpath,
+                                 subplan->startup_cost,
                                  subplan->total_cost,
                                  subplan->plan_rows,
                                  subplan->plan_width);
diff --git a/src/backend/optimizer/plan/subselect.c b/src/backend/optimizer/plan/subselect.c
index 92e9d6e44125b4ab6bebd1fdedd48c84cf4523df..5ba22541c9869399e70635347caffc6a235765b7 100644 (file)
--- a/src/backend/optimizer/plan/subselect.c
+++ b/src/backend/optimizer/plan/subselect.c
@@ -15,6 +15,7 @@
 
 #include "catalog/pg_operator.h"
 #include "catalog/pg_type.h"
+#include "executor/executor.h"
 #include "miscadmin.h"
 #include "nodes/makefuncs.h"
 #include "nodes/nodeFuncs.h"
@@ -564,33 +565,16 @@ build_subplan(PlannerInfo *root, Plan *plan, List *rtable,
                        splan->useHashTable = true;
 
                /*
-                * Otherwise, we have the option to tack a MATERIAL node onto the top
+                * Otherwise, we have the option to tack a Material node onto the top
                 * of the subplan, to reduce the cost of reading it repeatedly.  This
                 * is pointless for a direct-correlated subplan, since we'd have to
                 * recompute its results each time anyway.      For uncorrelated/undirect
-                * correlated subplans, we add MATERIAL unless the subplan's top plan
+                * correlated subplans, we add Material unless the subplan's top plan
                 * node would materialize its output anyway.
                 */
-               else if (splan->parParam == NIL)
-               {
-                       bool            use_material;
-
-                       switch (nodeTag(plan))
-                       {
-                               case T_Material:
-                               case T_FunctionScan:
-                               case T_CteScan:
-                               case T_WorkTableScan:
-                               case T_Sort:
-                                       use_material = false;
-                                       break;
-                               default:
-                                       use_material = true;
-                                       break;
-                       }
-                       if (use_material)
-                               plan = materialize_finished_plan(plan);
-               }
+               else if (splan->parParam == NIL &&
+                                !ExecMaterializesOutput(nodeTag(plan)))
+                       plan = materialize_finished_plan(plan);
 
                result = (Node *) splan;
                isInitPlan = false;
diff --git a/src/backend/optimizer/util/pathnode.c b/src/backend/optimizer/util/pathnode.c
index b7c3d3c4e2ae6ebae1ef278985f5b2e1dec4ddf3..e80f4cf1743e1de269f707145a1c0059b5bbc750 100644 (file)
--- a/src/backend/optimizer/util/pathnode.c
+++ b/src/backend/optimizer/util/pathnode.c
@@ -711,6 +711,7 @@ create_material_path(RelOptInfo *rel, Path *subpath)
        pathnode->subpath = subpath;
 
        cost_material(&pathnode->path,
+                                 subpath->startup_cost,
                                  subpath->total_cost,
                                  rel->rows,
                                  rel->width);
@@ -1424,7 +1425,8 @@ create_mergejoin_path(PlannerInfo *root,
                 * cost_mergejoin will avoid choosing anyway).  Therefore
                 * cost_material's cost estimate is bogus and we should charge just
                 * cpu_tuple_cost per tuple.  (Keep this estimate in sync with similar
-                * ones in cost_mergejoin and create_mergejoin_plan.)
+                * ones in cost_mergejoin and create_mergejoin_plan; also see
+                * cost_rescan.)
                 */
                mpath->startup_cost = inner_path->startup_cost;
                mpath->total_cost = inner_path->total_cost;
diff --git a/src/include/executor/executor.h b/src/include/executor/executor.h
index a80d18ae739d1f90393f455ad82f849858aa360f..bdd19badb12721aee62df499f991f3773c077973 100644 (file)
--- a/src/include/executor/executor.h
+++ b/src/include/executor/executor.h
@@ -83,6 +83,7 @@ extern void ExecMarkPos(PlanState *node);
 extern void ExecRestrPos(PlanState *node);
 extern bool ExecSupportsMarkRestore(NodeTag plantype);
 extern bool ExecSupportsBackwardScan(Plan *node);
+extern bool ExecMaterializesOutput(NodeTag plantype);
 
 /*
  * prototypes from functions in execCurrent.c
diff --git a/src/include/optimizer/cost.h b/src/include/optimizer/cost.h
index 11be226fe4b7b5af93e1aff45c03e1ba1a84efce..511170952749f5bb630ad12559e9af0f024b4331 100644 (file)
--- a/src/include/optimizer/cost.h
+++ b/src/include/optimizer/cost.h
@@ -86,7 +86,8 @@ extern void cost_sort(Path *path, PlannerInfo *root,
                  double limit_tuples);
 extern bool sort_exceeds_work_mem(Sort *sort);
 extern void cost_material(Path *path,
-                         Cost input_cost, double tuples, int width);
+                         Cost input_startup_cost, Cost input_total_cost,
+                         double tuples, int width);
 extern void cost_agg(Path *path, PlannerInfo *root,
                 AggStrategy aggstrategy, int numAggs,
                 int numGroupCols, double numGroups,
diff --git a/src/test/regress/expected/geometry.out b/src/test/regress/expected/geometry.out
index 6910e54ec661796d254902098346508c8776e61a..81237252eb77b3c0e09922f019cfbd4fb188d0d5 100644 (file)
--- a/src/test/regress/expected/geometry.out
+++ b/src/test/regress/expected/geometry.out
@@ -260,24 +260,24 @@ SELECT '' AS twenty, b.f1 / p.f1 AS rotation
  twenty |                               rotation                               
 --------+----------------------------------------------------------------------
         | (0,-0),(-0.2,-0.2)
-        | (-0.1,-0.1),(-0.3,-0.3)
-        | (-0.25,-0.25),(-0.25,-0.35)
-        | (-0.3,-0.3),(-0.3,-0.3)
         | (0.08,-0),(0,-0.56)
-        | (0.12,-0.28),(0.04,-0.84)
-        | (0.26,-0.7),(0.1,-0.82)
-        | (0.12,-0.84),(0.12,-0.84)
         | (0.0651176557644,0),(0,-0.0483449262493)
-        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
-        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
-        | (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
         | (-0,0.0828402366864),(-0.201183431953,0)
-        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
-        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
-        | (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
         | (0.2,0),(0,0)
+        | (-0.1,-0.1),(-0.3,-0.3)
+        | (0.12,-0.28),(0.04,-0.84)
+        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
+        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
         | (0.3,0),(0.1,0)
+        | (-0.25,-0.25),(-0.25,-0.35)
+        | (0.26,-0.7),(0.1,-0.82)
+        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
+        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
         | (0.3,0.05),(0.25,0)
+        | (-0.3,-0.3),(-0.3,-0.3)
+        | (0.12,-0.84),(0.12,-0.84)
+        | (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
+        | (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
         | (0.3,0),(0.3,0)
 (20 rows)
 
diff --git a/src/test/regress/expected/geometry_1.out b/src/test/regress/expected/geometry_1.out
index 0e014925257aac965d074677696752a77fae412c..684ccd716838862eab6f8190803ebe126930050e 100644 (file)
--- a/src/test/regress/expected/geometry_1.out
+++ b/src/test/regress/expected/geometry_1.out
@@ -260,24 +260,24 @@ SELECT '' AS twenty, b.f1 / p.f1 AS rotation
  twenty |                               rotation                               
 --------+----------------------------------------------------------------------
         | (0,0),(-0.2,-0.2)
-        | (-0.1,-0.1),(-0.3,-0.3)
-        | (-0.25,-0.25),(-0.25,-0.35)
-        | (-0.3,-0.3),(-0.3,-0.3)
         | (0.08,0),(0,-0.56)
-        | (0.12,-0.28),(0.04,-0.84)
-        | (0.26,-0.7),(0.1,-0.82)
-        | (0.12,-0.84),(0.12,-0.84)
         | (0.0651176557644,0),(0,-0.0483449262493)
-        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
-        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
-        | (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
         | (0,0.0828402366864),(-0.201183431953,0)
-        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
-        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
-        | (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
         | (0.2,0),(0,0)
+        | (-0.1,-0.1),(-0.3,-0.3)
+        | (0.12,-0.28),(0.04,-0.84)
+        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
+        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
         | (0.3,0),(0.1,0)
+        | (-0.25,-0.25),(-0.25,-0.35)
+        | (0.26,-0.7),(0.1,-0.82)
+        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
+        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
         | (0.3,0.05),(0.25,0)
+        | (-0.3,-0.3),(-0.3,-0.3)
+        | (0.12,-0.84),(0.12,-0.84)
+        | (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
+        | (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
         | (0.3,0),(0.3,0)
 (20 rows)
 
diff --git a/src/test/regress/expected/geometry_2.out b/src/test/regress/expected/geometry_2.out
index 7787dab06185c6e79d9a6150651e2a6990f52946..658dba48aa50bd5c17d70d6eae0c8cb5cd152f6e 100644 (file)
--- a/src/test/regress/expected/geometry_2.out
+++ b/src/test/regress/expected/geometry_2.out
@@ -260,24 +260,24 @@ SELECT '' AS twenty, b.f1 / p.f1 AS rotation
  twenty |                               rotation                               
 --------+----------------------------------------------------------------------
         | (0,-0),(-0.2,-0.2)
-        | (-0.1,-0.1),(-0.3,-0.3)
-        | (-0.25,-0.25),(-0.25,-0.35)
-        | (-0.3,-0.3),(-0.3,-0.3)
         | (0.08,-0),(0,-0.56)
-        | (0.12,-0.28),(0.04,-0.84)
-        | (0.26,-0.7),(0.1,-0.82)
-        | (0.12,-0.84),(0.12,-0.84)
         | (0.0651176557644,0),(0,-0.0483449262493)
-        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
-        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
-        | (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
         | (-0,0.0828402366864),(-0.201183431953,0)
-        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
-        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
-        | (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
         | (0.2,0),(0,0)
+        | (-0.1,-0.1),(-0.3,-0.3)
+        | (0.12,-0.28),(0.04,-0.84)
+        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
+        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
         | (0.3,0),(0.1,0)
+        | (-0.25,-0.25),(-0.25,-0.35)
+        | (0.26,-0.7),(0.1,-0.82)
+        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
+        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
         | (0.3,0.05),(0.25,0)
+        | (-0.3,-0.3),(-0.3,-0.3)
+        | (0.12,-0.84),(0.12,-0.84)
+        | (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
+        | (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
         | (0.3,0),(0.3,0)
 (20 rows)
 
diff --git a/src/test/regress/expected/join.out b/src/test/regress/expected/join.out
index dd9bf9c43f0d59713e885f00d511d57744798e55..0dc3e56960374cbbe326d10decf961c9281a82f5 100644 (file)
--- a/src/test/regress/expected/join.out
+++ b/src/test/regress/expected/join.out
@@ -662,895 +662,895 @@ SELECT '' AS "xxx", *
  xxx | i | j |   t   | i | k  | i | k  
 -----+---+---+-------+---+----+---+----
      | 1 | 4 | one   | 1 | -1 | 1 | -1
-     | 2 | 3 | two   | 1 | -1 | 1 | -1
-     | 3 | 2 | three | 1 | -1 | 1 | -1
-     | 4 | 1 | four  | 1 | -1 | 1 | -1
-     | 5 | 0 | five  | 1 | -1 | 1 | -1
-     | 6 | 6 | six   | 1 | -1 | 1 | -1
-     | 7 | 7 | seven | 1 | -1 | 1 | -1
-     | 8 | 8 | eight | 1 | -1 | 1 | -1
-     | 0 |   | zero  | 1 | -1 | 1 | -1
-     |   |   | null  | 1 | -1 | 1 | -1
-     |   | 0 | zero  | 1 | -1 | 1 | -1
-     | 1 | 4 | one   | 1 | -1 | 2 |  2
-     | 2 | 3 | two   | 1 | -1 | 2 |  2
-     | 3 | 2 | three | 1 | -1 | 2 |  2
-     | 4 | 1 | four  | 1 | -1 | 2 |  2
-     | 5 | 0 | five  | 1 | -1 | 2 |  2
-     | 6 | 6 | six   | 1 | -1 | 2 |  2
-     | 7 | 7 | seven | 1 | -1 | 2 |  2
-     | 8 | 8 | eight | 1 | -1 | 2 |  2
-     | 0 |   | zero  | 1 | -1 | 2 |  2
-     |   |   | null  | 1 | -1 | 2 |  2
-     |   | 0 | zero  | 1 | -1 | 2 |  2
-     | 1 | 4 | one   | 1 | -1 | 3 | -3
-     | 2 | 3 | two   | 1 | -1 | 3 | -3
-     | 3 | 2 | three | 1 | -1 | 3 | -3
-     | 4 | 1 | four  | 1 | -1 | 3 | -3
-     | 5 | 0 | five  | 1 | -1 | 3 | -3
-     | 6 | 6 | six   | 1 | -1 | 3 | -3
-     | 7 | 7 | seven | 1 | -1 | 3 | -3
-     | 8 | 8 | eight | 1 | -1 | 3 | -3
-     | 0 |   | zero  | 1 | -1 | 3 | -3
-     |   |   | null  | 1 | -1 | 3 | -3
-     |   | 0 | zero  | 1 | -1 | 3 | -3
-     | 1 | 4 | one   | 1 | -1 | 2 |  4
-     | 2 | 3 | two   | 1 | -1 | 2 |  4
-     | 3 | 2 | three | 1 | -1 | 2 |  4
-     | 4 | 1 | four  | 1 | -1 | 2 |  4
-     | 5 | 0 | five  | 1 | -1 | 2 |  4
-     | 6 | 6 | six   | 1 | -1 | 2 |  4
-     | 7 | 7 | seven | 1 | -1 | 2 |  4
-     | 8 | 8 | eight | 1 | -1 | 2 |  4
-     | 0 |   | zero  | 1 | -1 | 2 |  4
-     |   |   | null  | 1 | -1 | 2 |  4
-     |   | 0 | zero  | 1 | -1 | 2 |  4
-     | 1 | 4 | one   | 1 | -1 | 5 | -5
-     | 2 | 3 | two   | 1 | -1 | 5 | -5
-     | 3 | 2 | three | 1 | -1 | 5 | -5
-     | 4 | 1 | four  | 1 | -1 | 5 | -5
-     | 5 | 0 | five  | 1 | -1 | 5 | -5
-     | 6 | 6 | six   | 1 | -1 | 5 | -5
-     | 7 | 7 | seven | 1 | -1 | 5 | -5
-     | 8 | 8 | eight | 1 | -1 | 5 | -5
-     | 0 |   | zero  | 1 | -1 | 5 | -5
-     |   |   | null  | 1 | -1 | 5 | -5
-     |   | 0 | zero  | 1 | -1 | 5 | -5
-     | 1 | 4 | one   | 1 | -1 | 5 | -5
-     | 2 | 3 | two   | 1 | -1 | 5 | -5
-     | 3 | 2 | three | 1 | -1 | 5 | -5
-     | 4 | 1 | four  | 1 | -1 | 5 | -5
-     | 5 | 0 | five  | 1 | -1 | 5 | -5
-     | 6 | 6 | six   | 1 | -1 | 5 | -5
-     | 7 | 7 | seven | 1 | -1 | 5 | -5
-     | 8 | 8 | eight | 1 | -1 | 5 | -5
-     | 0 |   | zero  | 1 | -1 | 5 | -5
-     |   |   | null  | 1 | -1 | 5 | -5
-     |   | 0 | zero  | 1 | -1 | 5 | -5
-     | 1 | 4 | one   | 1 | -1 | 0 |   
-     | 2 | 3 | two   | 1 | -1 | 0 |   
-     | 3 | 2 | three | 1 | -1 | 0 |   
-     | 4 | 1 | four  | 1 | -1 | 0 |   
-     | 5 | 0 | five  | 1 | -1 | 0 |   
-     | 6 | 6 | six   | 1 | -1 | 0 |   
-     | 7 | 7 | seven | 1 | -1 | 0 |   
-     | 8 | 8 | eight | 1 | -1 | 0 |   
-     | 0 |   | zero  | 1 | -1 | 0 |   
-     |   |   | null  | 1 | -1 | 0 |   
-     |   | 0 | zero  | 1 | -1 | 0 |   
-     | 1 | 4 | one   | 1 | -1 |   |   
-     | 2 | 3 | two   | 1 | -1 |   |   
-     | 3 | 2 | three | 1 | -1 |   |   
-     | 4 | 1 | four  | 1 | -1 |   |   
-     | 5 | 0 | five  | 1 | -1 |   |   
-     | 6 | 6 | six   | 1 | -1 |   |   
-     | 7 | 7 | seven | 1 | -1 |   |   
-     | 8 | 8 | eight | 1 | -1 |   |   
-     | 0 |   | zero  | 1 | -1 |   |   
-     |   |   | null  | 1 | -1 |   |   
-     |   | 0 | zero  | 1 | -1 |   |   
-     | 1 | 4 | one   | 1 | -1 |   |  0
-     | 2 | 3 | two   | 1 | -1 |   |  0
-     | 3 | 2 | three | 1 | -1 |   |  0
-     | 4 | 1 | four  | 1 | -1 |   |  0
-     | 5 | 0 | five  | 1 | -1 |   |  0
-     | 6 | 6 | six   | 1 | -1 |   |  0
-     | 7 | 7 | seven | 1 | -1 |   |  0
-     | 8 | 8 | eight | 1 | -1 |   |  0
-     | 0 |   | zero  | 1 | -1 |   |  0
-     |   |   | null  | 1 | -1 |   |  0
-     |   | 0 | zero  | 1 | -1 |   |  0
-     | 1 | 4 | one   | 2 |  2 | 1 | -1
-     | 2 | 3 | two   | 2 |  2 | 1 | -1
-     | 3 | 2 | three | 2 |  2 | 1 | -1
-     | 4 | 1 | four  | 2 |  2 | 1 | -1
-     | 5 | 0 | five  | 2 |  2 | 1 | -1
-     | 6 | 6 | six   | 2 |  2 | 1 | -1
-     | 7 | 7 | seven | 2 |  2 | 1 | -1
-     | 8 | 8 | eight | 2 |  2 | 1 | -1
-     | 0 |   | zero  | 2 |  2 | 1 | -1
-     |   |   | null  | 2 |  2 | 1 | -1
-     |   | 0 | zero  | 2 |  2 | 1 | -1
-     | 1 | 4 | one   | 2 |  2 | 2 |  2
-     | 2 | 3 | two   | 2 |  2 | 2 |  2
-     | 3 | 2 | three | 2 |  2 | 2 |  2
-     | 4 | 1 | four  | 2 |  2 | 2 |  2
-     | 5 | 0 | five  | 2 |  2 | 2 |  2
-     | 6 | 6 | six   | 2 |  2 | 2 |  2
-     | 7 | 7 | seven | 2 |  2 | 2 |  2
-     | 8 | 8 | eight | 2 |  2 | 2 |  2
-     | 0 |   | zero  | 2 |  2 | 2 |  2
-     |   |   | null  | 2 |  2 | 2 |  2
-     |   | 0 | zero  | 2 |  2 | 2 |  2
-     | 1 | 4 | one   | 2 |  2 | 3 | -3
-     | 2 | 3 | two   | 2 |  2 | 3 | -3
-     | 3 | 2 | three | 2 |  2 | 3 | -3
-     | 4 | 1 | four  | 2 |  2 | 3 | -3
-     | 5 | 0 | five  | 2 |  2 | 3 | -3
-     | 6 | 6 | six   | 2 |  2 | 3 | -3
-     | 7 | 7 | seven | 2 |  2 | 3 | -3
-     | 8 | 8 | eight | 2 |  2 | 3 | -3
-     | 0 |   | zero  | 2 |  2 | 3 | -3
-     |   |   | null  | 2 |  2 | 3 | -3
-     |   | 0 | zero  | 2 |  2 | 3 | -3
-     | 1 | 4 | one   | 2 |  2 | 2 |  4
-     | 2 | 3 | two   | 2 |  2 | 2 |  4
-     | 3 | 2 | three | 2 |  2 | 2 |  4
-     | 4 | 1 | four  | 2 |  2 | 2 |  4
-     | 5 | 0 | five  | 2 |  2 | 2 |  4
-     | 6 | 6 | six   | 2 |  2 | 2 |  4
-     | 7 | 7 | seven | 2 |  2 | 2 |  4
-     | 8 | 8 | eight | 2 |  2 | 2 |  4
-     | 0 |   | zero  | 2 |  2 | 2 |  4
-     |   |   | null  | 2 |  2 | 2 |  4
-     |   | 0 | zero  | 2 |  2 | 2 |  4
-     | 1 | 4 | one   | 2 |  2 | 5 | -5
-     | 2 | 3 | two   | 2 |  2 | 5 | -5
-     | 3 | 2 | three | 2 |  2 | 5 | -5
-     | 4 | 1 | four  | 2 |  2 | 5 | -5
-     | 5 | 0 | five  | 2 |  2 | 5 | -5
-     | 6 | 6 | six   | 2 |  2 | 5 | -5
-     | 7 | 7 | seven | 2 |  2 | 5 | -5
-     | 8 | 8 | eight | 2 |  2 | 5 | -5
-     | 0 |   | zero  | 2 |  2 | 5 | -5
-     |   |   | null  | 2 |  2 | 5 | -5
-     |   | 0 | zero  | 2 |  2 | 5 | -5
-     | 1 | 4 | one   | 2 |  2 | 5 | -5
-     | 2 | 3 | two   | 2 |  2 | 5 | -5
-     | 3 | 2 | three | 2 |  2 | 5 | -5
-     | 4 | 1 | four  | 2 |  2 | 5 | -5
-     | 5 | 0 | five  | 2 |  2 | 5 | -5
-     | 6 | 6 | six   | 2 |  2 | 5 | -5
-     | 7 | 7 | seven | 2 |  2 | 5 | -5
-     | 8 | 8 | eight | 2 |  2 | 5 | -5
-     | 0 |   | zero  | 2 |  2 | 5 | -5
-     |   |   | null  | 2 |  2 | 5 | -5
-     |   | 0 | zero  | 2 |  2 | 5 | -5
-     | 1 | 4 | one   | 2 |  2 | 0 |   
-     | 2 | 3 | two   | 2 |  2 | 0 |   
-     | 3 | 2 | three | 2 |  2 | 0 |   
-     | 4 | 1 | four  | 2 |  2 | 0 |   
-     | 5 | 0 | five  | 2 |  2 | 0 |   
-     | 6 | 6 | six   | 2 |  2 | 0 |   
-     | 7 | 7 | seven | 2 |  2 | 0 |   
-     | 8 | 8 | eight | 2 |  2 | 0 |   
-     | 0 |   | zero  | 2 |  2 | 0 |   
-     |   |   | null  | 2 |  2 | 0 |   
-     |   | 0 | zero  | 2 |  2 | 0 |   
-     | 1 | 4 | one   | 2 |  2 |   |   
-     | 2 | 3 | two   | 2 |  2 |   |   
-     | 3 | 2 | three | 2 |  2 |   |   
-     | 4 | 1 | four  | 2 |  2 |   |   
-     | 5 | 0 | five  | 2 |  2 |   |   
-     | 6 | 6 | six   | 2 |  2 |   |   
-     | 7 | 7 | seven | 2 |  2 |   |   
-     | 8 | 8 | eight | 2 |  2 |   |   
-     | 0 |   | zero  | 2 |  2 |   |   
-     |   |   | null  | 2 |  2 |   |   
-     |   | 0 | zero  | 2 |  2 |   |   
-     | 1 | 4 | one   | 2 |  2 |   |  0
-     | 2 | 3 | two   | 2 |  2 |   |  0
-     | 3 | 2 | three | 2 |  2 |   |  0
-     | 4 | 1 | four  | 2 |  2 |   |  0
-     | 5 | 0 | five  | 2 |  2 |   |  0
-     | 6 | 6 | six   | 2 |  2 |   |  0
-     | 7 | 7 | seven | 2 |  2 |   |  0
-     | 8 | 8 | eight | 2 |  2 |   |  0
-     | 0 |   | zero  | 2 |  2 |   |  0
-     |   |   | null  | 2 |  2 |   |  0
-     |   | 0 | zero  | 2 |  2 |   |  0
-     | 1 | 4 | one   | 3 | -3 | 1 | -1
-     | 2 | 3 | two   | 3 | -3 | 1 | -1
-     | 3 | 2 | three | 3 | -3 | 1 | -1
-     | 4 | 1 | four  | 3 | -3 | 1 | -1
-     | 5 | 0 | five  | 3 | -3 | 1 | -1
-     | 6 | 6 | six   | 3 | -3 | 1 | -1
-     | 7 | 7 | seven | 3 | -3 | 1 | -1
-     | 8 | 8 | eight | 3 | -3 | 1 | -1
-     | 0 |   | zero  | 3 | -3 | 1 | -1
-     |   |   | null  | 3 | -3 | 1 | -1
-     |   | 0 | zero  | 3 | -3 | 1 | -1
-     | 1 | 4 | one   | 3 | -3 | 2 |  2
-     | 2 | 3 | two   | 3 | -3 | 2 |  2
-     | 3 | 2 | three | 3 | -3 | 2 |  2
-     | 4 | 1 | four  | 3 | -3 | 2 |  2
-     | 5 | 0 | five  | 3 | -3 | 2 |  2
-     | 6 | 6 | six   | 3 | -3 | 2 |  2
-     | 7 | 7 | seven | 3 | -3 | 2 |  2
-     | 8 | 8 | eight | 3 | -3 | 2 |  2
-     | 0 |   | zero  | 3 | -3 | 2 |  2
-     |   |   | null  | 3 | -3 | 2 |  2
-     |   | 0 | zero  | 3 | -3 | 2 |  2
-     | 1 | 4 | one   | 3 | -3 | 3 | -3
-     | 2 | 3 | two   | 3 | -3 | 3 | -3
-     | 3 | 2 | three | 3 | -3 | 3 | -3
-     | 4 | 1 | four  | 3 | -3 | 3 | -3
-     | 5 | 0 | five  | 3 | -3 | 3 | -3
-     | 6 | 6 | six   | 3 | -3 | 3 | -3
-     | 7 | 7 | seven | 3 | -3 | 3 | -3
-     | 8 | 8 | eight | 3 | -3 | 3 | -3
-     | 0 |   | zero  | 3 | -3 | 3 | -3
-     |   |   | null  | 3 | -3 | 3 | -3
-     |   | 0 | zero  | 3 | -3 | 3 | -3
-     | 1 | 4 | one   | 3 | -3 | 2 |  4
-     | 2 | 3 | two   | 3 | -3 | 2 |  4
-     | 3 | 2 | three | 3 | -3 | 2 |  4
-     | 4 | 1 | four  | 3 | -3 | 2 |  4
-     | 5 | 0 | five  | 3 | -3 | 2 |  4
-     | 6 | 6 | six   | 3 | -3 | 2 |  4
-     | 7 | 7 | seven | 3 | -3 | 2 |  4
-     | 8 | 8 | eight | 3 | -3 | 2 |  4
-     | 0 |   | zero  | 3 | -3 | 2 |  4
-     |   |   | null  | 3 | -3 | 2 |  4
-     |   | 0 | zero  | 3 | -3 | 2 |  4
-     | 1 | 4 | one   | 3 | -3 | 5 | -5
-     | 2 | 3 | two   | 3 | -3 | 5 | -5
-     | 3 | 2 | three | 3 | -3 | 5 | -5
-     | 4 | 1 | four  | 3 | -3 | 5 | -5
-     | 5 | 0 | five  | 3 | -3 | 5 | -5
-     | 6 | 6 | six   | 3 | -3 | 5 | -5
-     | 7 | 7 | seven | 3 | -3 | 5 | -5
-     | 8 | 8 | eight | 3 | -3 | 5 | -5
-     | 0 |   | zero  | 3 | -3 | 5 | -5
-     |   |   | null  | 3 | -3 | 5 | -5
-     |   | 0 | zero  | 3 | -3 | 5 | -5
-     | 1 | 4 | one   | 3 | -3 | 5 | -5
-     | 2 | 3 | two   | 3 | -3 | 5 | -5
-     | 3 | 2 | three | 3 | -3 | 5 | -5
-     | 4 | 1 | four  | 3 | -3 | 5 | -5
-     | 5 | 0 | five  | 3 | -3 | 5 | -5
-     | 6 | 6 | six   | 3 | -3 | 5 | -5
-     | 7 | 7 | seven | 3 | -3 | 5 | -5
-     | 8 | 8 | eight | 3 | -3 | 5 | -5
-     | 0 |   | zero  | 3 | -3 | 5 | -5
-     |   |   | null  | 3 | -3 | 5 | -5
-     |   | 0 | zero  | 3 | -3 | 5 | -5
-     | 1 | 4 | one   | 3 | -3 | 0 |   
-     | 2 | 3 | two   | 3 | -3 | 0 |   
-     | 3 | 2 | three | 3 | -3 | 0 |   
-     | 4 | 1 | four  | 3 | -3 | 0 |   
-     | 5 | 0 | five  | 3 | -3 | 0 |   
-     | 6 | 6 | six   | 3 | -3 | 0 |   
-     | 7 | 7 | seven | 3 | -3 | 0 |   
-     | 8 | 8 | eight | 3 | -3 | 0 |   
-     | 0 |   | zero  | 3 | -3 | 0 |   
-     |   |   | null  | 3 | -3 | 0 |   
-     |   | 0 | zero  | 3 | -3 | 0 |   
-     | 1 | 4 | one   | 3 | -3 |   |   
-     | 2 | 3 | two   | 3 | -3 |   |   
-     | 3 | 2 | three | 3 | -3 |   |   
-     | 4 | 1 | four  | 3 | -3 |   |   
-     | 5 | 0 | five  | 3 | -3 |   |   
-     | 6 | 6 | six   | 3 | -3 |   |   
-     | 7 | 7 | seven | 3 | -3 |   |   
-     | 8 | 8 | eight | 3 | -3 |   |   
-     | 0 |   | zero  | 3 | -3 |   |   
-     |   |   | null  | 3 | -3 |   |   
-     |   | 0 | zero  | 3 | -3 |   |   
-     | 1 | 4 | one   | 3 | -3 |   |  0
-     | 2 | 3 | two   | 3 | -3 |   |  0
-     | 3 | 2 | three | 3 | -3 |   |  0
-     | 4 | 1 | four  | 3 | -3 |   |  0
-     | 5 | 0 | five  | 3 | -3 |   |  0
-     | 6 | 6 | six   | 3 | -3 |   |  0
-     | 7 | 7 | seven | 3 | -3 |   |  0
-     | 8 | 8 | eight | 3 | -3 |   |  0
-     | 0 |   | zero  | 3 | -3 |   |  0
-     |   |   | null  | 3 | -3 |   |  0
-     |   | 0 | zero  | 3 | -3 |   |  0
-     | 1 | 4 | one   | 2 |  4 | 1 | -1
-     | 2 | 3 | two   | 2 |  4 | 1 | -1
-     | 3 | 2 | three | 2 |  4 | 1 | -1
-     | 4 | 1 | four  | 2 |  4 | 1 | -1
-     | 5 | 0 | five  | 2 |  4 | 1 | -1
-     | 6 | 6 | six   | 2 |  4 | 1 | -1
-     | 7 | 7 | seven | 2 |  4 | 1 | -1
-     | 8 | 8 | eight | 2 |  4 | 1 | -1
-     | 0 |   | zero  | 2 |  4 | 1 | -1
-     |   |   | null  | 2 |  4 | 1 | -1
-     |   | 0 | zero  | 2 |  4 | 1 | -1
-     | 1 | 4 | one   | 2 |  4 | 2 |  2
-     | 2 | 3 | two   | 2 |  4 | 2 |  2
-     | 3 | 2 | three | 2 |  4 | 2 |  2
-     | 4 | 1 | four  | 2 |  4 | 2 |  2
-     | 5 | 0 | five  | 2 |  4 | 2 |  2
-     | 6 | 6 | six   | 2 |  4 | 2 |  2
-     | 7 | 7 | seven | 2 |  4 | 2 |  2
-     | 8 | 8 | eight | 2 |  4 | 2 |  2
-     | 0 |   | zero  | 2 |  4 | 2 |  2
-     |   |   | null  | 2 |  4 | 2 |  2
-     |   | 0 | zero  | 2 |  4 | 2 |  2
-     | 1 | 4 | one   | 2 |  4 | 3 | -3
-     | 2 | 3 | two   | 2 |  4 | 3 | -3
-     | 3 | 2 | three | 2 |  4 | 3 | -3
-     | 4 | 1 | four  | 2 |  4 | 3 | -3
-     | 5 | 0 | five  | 2 |  4 | 3 | -3
-     | 6 | 6 | six   | 2 |  4 | 3 | -3
-     | 7 | 7 | seven | 2 |  4 | 3 | -3
-     | 8 | 8 | eight | 2 |  4 | 3 | -3
-     | 0 |   | zero  | 2 |  4 | 3 | -3
-     |   |   | null  | 2 |  4 | 3 | -3
-     |   | 0 | zero  | 2 |  4 | 3 | -3
-     | 1 | 4 | one   | 2 |  4 | 2 |  4
-     | 2 | 3 | two   | 2 |  4 | 2 |  4
-     | 3 | 2 | three | 2 |  4 | 2 |  4
-     | 4 | 1 | four  | 2 |  4 | 2 |  4
-     | 5 | 0 | five  | 2 |  4 | 2 |  4
-     | 6 | 6 | six   | 2 |  4 | 2 |  4
-     | 7 | 7 | seven | 2 |  4 | 2 |  4
-     | 8 | 8 | eight | 2 |  4 | 2 |  4
-     | 0 |   | zero  | 2 |  4 | 2 |  4
-     |   |   | null  | 2 |  4 | 2 |  4
-     |   | 0 | zero  | 2 |  4 | 2 |  4
-     | 1 | 4 | one   | 2 |  4 | 5 | -5
-     | 2 | 3 | two   | 2 |  4 | 5 | -5
-     | 3 | 2 | three | 2 |  4 | 5 | -5
-     | 4 | 1 | four  | 2 |  4 | 5 | -5
-     | 5 | 0 | five  | 2 |  4 | 5 | -5
-     | 6 | 6 | six   | 2 |  4 | 5 | -5
-     | 7 | 7 | seven | 2 |  4 | 5 | -5
-     | 8 | 8 | eight | 2 |  4 | 5 | -5
-     | 0 |   | zero  | 2 |  4 | 5 | -5
-     |   |   | null  | 2 |  4 | 5 | -5
-     |   | 0 | zero  | 2 |  4 | 5 | -5
-     | 1 | 4 | one   | 2 |  4 | 5 | -5
-     | 2 | 3 | two   | 2 |  4 | 5 | -5
-     | 3 | 2 | three | 2 |  4 | 5 | -5
-     | 4 | 1 | four  | 2 |  4 | 5 | -5
-     | 5 | 0 | five  | 2 |  4 | 5 | -5
-     | 6 | 6 | six   | 2 |  4 | 5 | -5
-     | 7 | 7 | seven | 2 |  4 | 5 | -5
-     | 8 | 8 | eight | 2 |  4 | 5 | -5
-     | 0 |   | zero  | 2 |  4 | 5 | -5
-     |   |   | null  | 2 |  4 | 5 | -5
-     |   | 0 | zero  | 2 |  4 | 5 | -5
-     | 1 | 4 | one   | 2 |  4 | 0 |   
-     | 2 | 3 | two   | 2 |  4 | 0 |   
-     | 3 | 2 | three | 2 |  4 | 0 |   
-     | 4 | 1 | four  | 2 |  4 | 0 |   
-     | 5 | 0 | five  | 2 |  4 | 0 |   
-     | 6 | 6 | six   | 2 |  4 | 0 |   
-     | 7 | 7 | seven | 2 |  4 | 0 |   
-     | 8 | 8 | eight | 2 |  4 | 0 |   
-     | 0 |   | zero  | 2 |  4 | 0 |   
-     |   |   | null  | 2 |  4 | 0 |   
-     |   | 0 | zero  | 2 |  4 | 0 |   
-     | 1 | 4 | one   | 2 |  4 |   |   
-     | 2 | 3 | two   | 2 |  4 |   |   
-     | 3 | 2 | three | 2 |  4 |   |   
-     | 4 | 1 | four  | 2 |  4 |   |   
-     | 5 | 0 | five  | 2 |  4 |   |   
-     | 6 | 6 | six   | 2 |  4 |   |   
-     | 7 | 7 | seven | 2 |  4 |   |   
-     | 8 | 8 | eight | 2 |  4 |   |   
-     | 0 |   | zero  | 2 |  4 |   |   
-     |   |   | null  | 2 |  4 |   |   
-     |   | 0 | zero  | 2 |  4 |   |   
-     | 1 | 4 | one   | 2 |  4 |   |  0
-     | 2 | 3 | two   | 2 |  4 |   |  0
-     | 3 | 2 | three | 2 |  4 |   |  0
-     | 4 | 1 | four  | 2 |  4 |   |  0
-     | 5 | 0 | five  | 2 |  4 |   |  0
-     | 6 | 6 | six   | 2 |  4 |   |  0
-     | 7 | 7 | seven | 2 |  4 |   |  0
-     | 8 | 8 | eight | 2 |  4 |   |  0
-     | 0 |   | zero  | 2 |  4 |   |  0
-     |   |   | null  | 2 |  4 |   |  0
-     |   | 0 | zero  | 2 |  4 |   |  0
-     | 1 | 4 | one   | 5 | -5 | 1 | -1
-     | 2 | 3 | two   | 5 | -5 | 1 | -1
-     | 3 | 2 | three | 5 | -5 | 1 | -1
-     | 4 | 1 | four  | 5 | -5 | 1 | -1
-     | 5 | 0 | five  | 5 | -5 | 1 | -1
-     | 6 | 6 | six   | 5 | -5 | 1 | -1
-     | 7 | 7 | seven | 5 | -5 | 1 | -1
-     | 8 | 8 | eight | 5 | -5 | 1 | -1
-     | 0 |   | zero  | 5 | -5 | 1 | -1
-     |   |   | null  | 5 | -5 | 1 | -1
-     |   | 0 | zero  | 5 | -5 | 1 | -1
-     | 1 | 4 | one   | 5 | -5 | 2 |  2
-     | 2 | 3 | two   | 5 | -5 | 2 |  2
-     | 3 | 2 | three | 5 | -5 | 2 |  2
-     | 4 | 1 | four  | 5 | -5 | 2 |  2
-     | 5 | 0 | five  | 5 | -5 | 2 |  2
-     | 6 | 6 | six   | 5 | -5 | 2 |  2
-     | 7 | 7 | seven | 5 | -5 | 2 |  2
-     | 8 | 8 | eight | 5 | -5 | 2 |  2
-     | 0 |   | zero  | 5 | -5 | 2 |  2
-     |   |   | null  | 5 | -5 | 2 |  2
-     |   | 0 | zero  | 5 | -5 | 2 |  2
-     | 1 | 4 | one   | 5 | -5 | 3 | -3
-     | 2 | 3 | two   | 5 | -5 | 3 | -3
-     | 3 | 2 | three | 5 | -5 | 3 | -3
-     | 4 | 1 | four  | 5 | -5 | 3 | -3
-     | 5 | 0 | five  | 5 | -5 | 3 | -3
-     | 6 | 6 | six   | 5 | -5 | 3 | -3
-     | 7 | 7 | seven | 5 | -5 | 3 | -3
-     | 8 | 8 | eight | 5 | -5 | 3 | -3
-     | 0 |   | zero  | 5 | -5 | 3 | -3
-     |   |   | null  | 5 | -5 | 3 | -3
-     |   | 0 | zero  | 5 | -5 | 3 | -3
-     | 1 | 4 | one   | 5 | -5 | 2 |  4
-     | 2 | 3 | two   | 5 | -5 | 2 |  4
-     | 3 | 2 | three | 5 | -5 | 2 |  4
-     | 4 | 1 | four  | 5 | -5 | 2 |  4
-     | 5 | 0 | five  | 5 | -5 | 2 |  4
-     | 6 | 6 | six   | 5 | -5 | 2 |  4
-     | 7 | 7 | seven | 5 | -5 | 2 |  4
-     | 8 | 8 | eight | 5 | -5 | 2 |  4
-     | 0 |   | zero  | 5 | -5 | 2 |  4
-     |   |   | null  | 5 | -5 | 2 |  4
-     |   | 0 | zero  | 5 | -5 | 2 |  4
-     | 1 | 4 | one   | 5 | -5 | 5 | -5
-     | 2 | 3 | two   | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 0 |   | zero  | 5 | -5 | 5 | -5
-     |   |   | null  | 5 | -5 | 5 | -5
-     |   | 0 | zero  | 5 | -5 | 5 | -5
-     | 1 | 4 | one   | 5 | -5 | 5 | -5
-     | 2 | 3 | two   | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 0 |   | zero  | 5 | -5 | 5 | -5
-     |   |   | null  | 5 | -5 | 5 | -5
-     |   | 0 | zero  | 5 | -5 | 5 | -5
-     | 1 | 4 | one   | 5 | -5 | 0 |   
-     | 2 | 3 | two   | 5 | -5 | 0 |   
-     | 3 | 2 | three | 5 | -5 | 0 |   
-     | 4 | 1 | four  | 5 | -5 | 0 |   
-     | 5 | 0 | five  | 5 | -5 | 0 |   
-     | 6 | 6 | six   | 5 | -5 | 0 |   
-     | 7 | 7 | seven | 5 | -5 | 0 |   
-     | 8 | 8 | eight | 5 | -5 | 0 |   
-     | 0 |   | zero  | 5 | -5 | 0 |   
-     |   |   | null  | 5 | -5 | 0 |   
-     |   | 0 | zero  | 5 | -5 | 0 |   
-     | 1 | 4 | one   | 5 | -5 |   |   
-     | 2 | 3 | two   | 5 | -5 |   |   
-     | 3 | 2 | three | 5 | -5 |   |   
-     | 4 | 1 | four  | 5 | -5 |   |   
-     | 5 | 0 | five  | 5 | -5 |   |   
-     | 6 | 6 | six   | 5 | -5 |   |   
-     | 7 | 7 | seven | 5 | -5 |   |   
-     | 8 | 8 | eight | 5 | -5 |   |   
-     | 0 |   | zero  | 5 | -5 |   |   
-     |   |   | null  | 5 | -5 |   |   
-     |   | 0 | zero  | 5 | -5 |   |   
-     | 1 | 4 | one   | 5 | -5 |   |  0
-     | 2 | 3 | two   | 5 | -5 |   |  0
-     | 3 | 2 | three | 5 | -5 |   |  0
-     | 4 | 1 | four  | 5 | -5 |   |  0
-     | 5 | 0 | five  | 5 | -5 |   |  0
-     | 6 | 6 | six   | 5 | -5 |   |  0
-     | 7 | 7 | seven | 5 | -5 |   |  0
-     | 8 | 8 | eight | 5 | -5 |   |  0
-     | 0 |   | zero  | 5 | -5 |   |  0
-     |   |   | null  | 5 | -5 |   |  0
-     |   | 0 | zero  | 5 | -5 |   |  0
-     | 1 | 4 | one   | 5 | -5 | 1 | -1
-     | 2 | 3 | two   | 5 | -5 | 1 | -1
-     | 3 | 2 | three | 5 | -5 | 1 | -1
-     | 4 | 1 | four  | 5 | -5 | 1 | -1
-     | 5 | 0 | five  | 5 | -5 | 1 | -1
-     | 6 | 6 | six   | 5 | -5 | 1 | -1
-     | 7 | 7 | seven | 5 | -5 | 1 | -1
-     | 8 | 8 | eight | 5 | -5 | 1 | -1
-     | 0 |   | zero  | 5 | -5 | 1 | -1
-     |   |   | null  | 5 | -5 | 1 | -1
-     |   | 0 | zero  | 5 | -5 | 1 | -1
-     | 1 | 4 | one   | 5 | -5 | 2 |  2
-     | 2 | 3 | two   | 5 | -5 | 2 |  2
-     | 3 | 2 | three | 5 | -5 | 2 |  2
-     | 4 | 1 | four  | 5 | -5 | 2 |  2
-     | 5 | 0 | five  | 5 | -5 | 2 |  2
-     | 6 | 6 | six   | 5 | -5 | 2 |  2
-     | 7 | 7 | seven | 5 | -5 | 2 |  2
-     | 8 | 8 | eight | 5 | -5 | 2 |  2
-     | 0 |   | zero  | 5 | -5 | 2 |  2
-     |   |   | null  | 5 | -5 | 2 |  2
-     |   | 0 | zero  | 5 | -5 | 2 |  2
-     | 1 | 4 | one   | 5 | -5 | 3 | -3
-     | 2 | 3 | two   | 5 | -5 | 3 | -3
-     | 3 | 2 | three | 5 | -5 | 3 | -3
-     | 4 | 1 | four  | 5 | -5 | 3 | -3
-     | 5 | 0 | five  | 5 | -5 | 3 | -3
-     | 6 | 6 | six   | 5 | -5 | 3 | -3
-     | 7 | 7 | seven | 5 | -5 | 3 | -3
-     | 8 | 8 | eight | 5 | -5 | 3 | -3
-     | 0 |   | zero  | 5 | -5 | 3 | -3
-     |   |   | null  | 5 | -5 | 3 | -3
-     |   | 0 | zero  | 5 | -5 | 3 | -3
-     | 1 | 4 | one   | 5 | -5 | 2 |  4
-     | 2 | 3 | two   | 5 | -5 | 2 |  4
-     | 3 | 2 | three | 5 | -5 | 2 |  4
-     | 4 | 1 | four  | 5 | -5 | 2 |  4
-     | 5 | 0 | five  | 5 | -5 | 2 |  4
-     | 6 | 6 | six   | 5 | -5 | 2 |  4
-     | 7 | 7 | seven | 5 | -5 | 2 |  4
-     | 8 | 8 | eight | 5 | -5 | 2 |  4
-     | 0 |   | zero  | 5 | -5 | 2 |  4
-     |   |   | null  | 5 | -5 | 2 |  4
-     |   | 0 | zero  | 5 | -5 | 2 |  4
-     | 1 | 4 | one   | 5 | -5 | 5 | -5
-     | 2 | 3 | two   | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 0 |   | zero  | 5 | -5 | 5 | -5
-     |   |   | null  | 5 | -5 | 5 | -5
-     |   | 0 | zero  | 5 | -5 | 5 | -5
-     | 1 | 4 | one   | 5 | -5 | 5 | -5
-     | 2 | 3 | two   | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 0 |   | zero  | 5 | -5 | 5 | -5
-     |   |   | null  | 5 | -5 | 5 | -5
-     |   | 0 | zero  | 5 | -5 | 5 | -5
-     | 1 | 4 | one   | 5 | -5 | 0 |   
-     | 2 | 3 | two   | 5 | -5 | 0 |   
-     | 3 | 2 | three | 5 | -5 | 0 |   
-     | 4 | 1 | four  | 5 | -5 | 0 |   
-     | 5 | 0 | five  | 5 | -5 | 0 |   
-     | 6 | 6 | six   | 5 | -5 | 0 |   
-     | 7 | 7 | seven | 5 | -5 | 0 |   
-     | 8 | 8 | eight | 5 | -5 | 0 |   
-     | 0 |   | zero  | 5 | -5 | 0 |   
-     |   |   | null  | 5 | -5 | 0 |   
-     |   | 0 | zero  | 5 | -5 | 0 |   
-     | 1 | 4 | one   | 5 | -5 |   |   
-     | 2 | 3 | two   | 5 | -5 |   |   
-     | 3 | 2 | three | 5 | -5 |   |   
-     | 4 | 1 | four  | 5 | -5 |   |   
-     | 5 | 0 | five  | 5 | -5 |   |   
-     | 6 | 6 | six   | 5 | -5 |   |   
-     | 7 | 7 | seven | 5 | -5 |   |   
-     | 8 | 8 | eight | 5 | -5 |   |   
-     | 0 |   | zero  | 5 | -5 |   |   
-     |   |   | null  | 5 | -5 |   |   
-     |   | 0 | zero  | 5 | -5 |   |   
-     | 1 | 4 | one   | 5 | -5 |   |  0
-     | 2 | 3 | two   | 5 | -5 |   |  0
-     | 3 | 2 | three | 5 | -5 |   |  0
-     | 4 | 1 | four  | 5 | -5 |   |  0
-     | 5 | 0 | five  | 5 | -5 |   |  0
-     | 6 | 6 | six   | 5 | -5 |   |  0
-     | 7 | 7 | seven | 5 | -5 |   |  0
-     | 8 | 8 | eight | 5 | -5 |   |  0
-     | 0 |   | zero  | 5 | -5 |   |  0
-     |   |   | null  | 5 | -5 |   |  0
-     |   | 0 | zero  | 5 | -5 |   |  0
+     | 1 | 4 | one   | 2 |  2 | 1 | -1
+     | 1 | 4 | one   | 3 | -3 | 1 | -1
+     | 1 | 4 | one   | 2 |  4 | 1 | -1
+     | 1 | 4 | one   | 5 | -5 | 1 | -1
+     | 1 | 4 | one   | 5 | -5 | 1 | -1
      | 1 | 4 | one   | 0 |    | 1 | -1
-     | 2 | 3 | two   | 0 |    | 1 | -1
-     | 3 | 2 | three | 0 |    | 1 | -1
-     | 4 | 1 | four  | 0 |    | 1 | -1
-     | 5 | 0 | five  | 0 |    | 1 | -1
-     | 6 | 6 | six   | 0 |    | 1 | -1
-     | 7 | 7 | seven | 0 |    | 1 | -1
-     | 8 | 8 | eight | 0 |    | 1 | -1
-     | 0 |   | zero  | 0 |    | 1 | -1
-     |   |   | null  | 0 |    | 1 | -1
-     |   | 0 | zero  | 0 |    | 1 | -1
-     | 1 | 4 | one   | 0 |    | 2 |  2
-     | 2 | 3 | two   | 0 |    | 2 |  2
-     | 3 | 2 | three | 0 |    | 2 |  2
-     | 4 | 1 | four  | 0 |    | 2 |  2
-     | 5 | 0 | five  | 0 |    | 2 |  2
-     | 6 | 6 | six   | 0 |    | 2 |  2
-     | 7 | 7 | seven | 0 |    | 2 |  2
-     | 8 | 8 | eight | 0 |    | 2 |  2
-     | 0 |   | zero  | 0 |    | 2 |  2
-     |   |   | null  | 0 |    | 2 |  2
-     |   | 0 | zero  | 0 |    | 2 |  2
-     | 1 | 4 | one   | 0 |    | 3 | -3
-     | 2 | 3 | two   | 0 |    | 3 | -3
-     | 3 | 2 | three | 0 |    | 3 | -3
-     | 4 | 1 | four  | 0 |    | 3 | -3
-     | 5 | 0 | five  | 0 |    | 3 | -3
-     | 6 | 6 | six   | 0 |    | 3 | -3
-     | 7 | 7 | seven | 0 |    | 3 | -3
-     | 8 | 8 | eight | 0 |    | 3 | -3
-     | 0 |   | zero  | 0 |    | 3 | -3
-     |   |   | null  | 0 |    | 3 | -3
-     |   | 0 | zero  | 0 |    | 3 | -3
-     | 1 | 4 | one   | 0 |    | 2 |  4
-     | 2 | 3 | two   | 0 |    | 2 |  4
-     | 3 | 2 | three | 0 |    | 2 |  4
-     | 4 | 1 | four  | 0 |    | 2 |  4
-     | 5 | 0 | five  | 0 |    | 2 |  4
-     | 6 | 6 | six   | 0 |    | 2 |  4
-     | 7 | 7 | seven | 0 |    | 2 |  4
-     | 8 | 8 | eight | 0 |    | 2 |  4
-     | 0 |   | zero  | 0 |    | 2 |  4
-     |   |   | null  | 0 |    | 2 |  4
-     |   | 0 | zero  | 0 |    | 2 |  4
-     | 1 | 4 | one   | 0 |    | 5 | -5
-     | 2 | 3 | two   | 0 |    | 5 | -5
-     | 3 | 2 | three | 0 |    | 5 | -5
-     | 4 | 1 | four  | 0 |    | 5 | -5
-     | 5 | 0 | five  | 0 |    | 5 | -5
-     | 6 | 6 | six   | 0 |    | 5 | -5
-     | 7 | 7 | seven | 0 |    | 5 | -5
-     | 8 | 8 | eight | 0 |    | 5 | -5
-     | 0 |   | zero  | 0 |    | 5 | -5
-     |   |   | null  | 0 |    | 5 | -5
-     |   | 0 | zero  | 0 |    | 5 | -5
-     | 1 | 4 | one   | 0 |    | 5 | -5
-     | 2 | 3 | two   | 0 |    | 5 | -5
-     | 3 | 2 | three | 0 |    | 5 | -5
-     | 4 | 1 | four  | 0 |    | 5 | -5
-     | 5 | 0 | five  | 0 |    | 5 | -5
-     | 6 | 6 | six   | 0 |    | 5 | -5
-     | 7 | 7 | seven | 0 |    | 5 | -5
-     | 8 | 8 | eight | 0 |    | 5 | -5
-     | 0 |   | zero  | 0 |    | 5 | -5
-     |   |   | null  | 0 |    | 5 | -5
-     |   | 0 | zero  | 0 |    | 5 | -5
-     | 1 | 4 | one   | 0 |    | 0 |   
-     | 2 | 3 | two   | 0 |    | 0 |   
-     | 3 | 2 | three | 0 |    | 0 |   
-     | 4 | 1 | four  | 0 |    | 0 |   
-     | 5 | 0 | five  | 0 |    | 0 |   
-     | 6 | 6 | six   | 0 |    | 0 |   
-     | 7 | 7 | seven | 0 |    | 0 |   
-     | 8 | 8 | eight | 0 |    | 0 |   
-     | 0 |   | zero  | 0 |    | 0 |   
-     |   |   | null  | 0 |    | 0 |   
-     |   | 0 | zero  | 0 |    | 0 |   
-     | 1 | 4 | one   | 0 |    |   |   
-     | 2 | 3 | two   | 0 |    |   |   
-     | 3 | 2 | three | 0 |    |   |   
-     | 4 | 1 | four  | 0 |    |   |   
-     | 5 | 0 | five  | 0 |    |   |   
-     | 6 | 6 | six   | 0 |    |   |   
-     | 7 | 7 | seven | 0 |    |   |   
-     | 8 | 8 | eight | 0 |    |   |   
-     | 0 |   | zero  | 0 |    |   |   
-     |   |   | null  | 0 |    |   |   
-     |   | 0 | zero  | 0 |    |   |   
-     | 1 | 4 | one   | 0 |    |   |  0
-     | 2 | 3 | two   | 0 |    |   |  0
-     | 3 | 2 | three | 0 |    |   |  0
-     | 4 | 1 | four  | 0 |    |   |  0
-     | 5 | 0 | five  | 0 |    |   |  0
-     | 6 | 6 | six   | 0 |    |   |  0
-     | 7 | 7 | seven | 0 |    |   |  0
-     | 8 | 8 | eight | 0 |    |   |  0
-     | 0 |   | zero  | 0 |    |   |  0
-     |   |   | null  | 0 |    |   |  0
-     |   | 0 | zero  | 0 |    |   |  0
      | 1 | 4 | one   |   |    | 1 | -1
-     | 2 | 3 | two   |   |    | 1 | -1
-     | 3 | 2 | three |   |    | 1 | -1
-     | 4 | 1 | four  |   |    | 1 | -1
-     | 5 | 0 | five  |   |    | 1 | -1
-     | 6 | 6 | six   |   |    | 1 | -1
-     | 7 | 7 | seven |   |    | 1 | -1
-     | 8 | 8 | eight |   |    | 1 | -1
-     | 0 |   | zero  |   |    | 1 | -1
-     |   |   | null  |   |    | 1 | -1
-     |   | 0 | zero  |   |    | 1 | -1
-     | 1 | 4 | one   |   |    | 2 |  2
-     | 2 | 3 | two   |   |    | 2 |  2
-     | 3 | 2 | three |   |    | 2 |  2
-     | 4 | 1 | four  |   |    | 2 |  2
-     | 5 | 0 | five  |   |    | 2 |  2
-     | 6 | 6 | six   |   |    | 2 |  2
-     | 7 | 7 | seven |   |    | 2 |  2
-     | 8 | 8 | eight |   |    | 2 |  2
-     | 0 |   | zero  |   |    | 2 |  2
-     |   |   | null  |   |    | 2 |  2
-     |   | 0 | zero  |   |    | 2 |  2
-     | 1 | 4 | one   |   |    | 3 | -3
-     | 2 | 3 | two   |   |    | 3 | -3
-     | 3 | 2 | three |   |    | 3 | -3
-     | 4 | 1 | four  |   |    | 3 | -3
-     | 5 | 0 | five  |   |    | 3 | -3
-     | 6 | 6 | six   |   |    | 3 | -3
-     | 7 | 7 | seven |   |    | 3 | -3
-     | 8 | 8 | eight |   |    | 3 | -3
-     | 0 |   | zero  |   |    | 3 | -3
-     |   |   | null  |   |    | 3 | -3
-     |   | 0 | zero  |   |    | 3 | -3
-     | 1 | 4 | one   |   |    | 2 |  4
-     | 2 | 3 | two   |   |    | 2 |  4
-     | 3 | 2 | three |   |    | 2 |  4
-     | 4 | 1 | four  |   |    | 2 |  4
-     | 5 | 0 | five  |   |    | 2 |  4
-     | 6 | 6 | six   |   |    | 2 |  4
-     | 7 | 7 | seven |   |    | 2 |  4
-     | 8 | 8 | eight |   |    | 2 |  4
-     | 0 |   | zero  |   |    | 2 |  4
-     |   |   | null  |   |    | 2 |  4
-     |   | 0 | zero  |   |    | 2 |  4
-     | 1 | 4 | one   |   |    | 5 | -5
-     | 2 | 3 | two   |   |    | 5 | -5
-     | 3 | 2 | three |   |    | 5 | -5
-     | 4 | 1 | four  |   |    | 5 | -5
-     | 5 | 0 | five  |   |    | 5 | -5
-     | 6 | 6 | six   |   |    | 5 | -5
-     | 7 | 7 | seven |   |    | 5 | -5
-     | 8 | 8 | eight |   |    | 5 | -5
-     | 0 |   | zero  |   |    | 5 | -5
-     |   |   | null  |   |    | 5 | -5
-     |   | 0 | zero  |   |    | 5 | -5
-     | 1 | 4 | one   |   |    | 5 | -5
-     | 2 | 3 | two   |   |    | 5 | -5
-     | 3 | 2 | three |   |    | 5 | -5
-     | 4 | 1 | four  |   |    | 5 | -5
-     | 5 | 0 | five  |   |    | 5 | -5
-     | 6 | 6 | six   |   |    | 5 | -5
-     | 7 | 7 | seven |   |    | 5 | -5
-     | 8 | 8 | eight |   |    | 5 | -5
-     | 0 |   | zero  |   |    | 5 | -5
-     |   |   | null  |   |    | 5 | -5
-     |   | 0 | zero  |   |    | 5 | -5
-     | 1 | 4 | one   |   |    | 0 |   
-     | 2 | 3 | two   |   |    | 0 |   
-     | 3 | 2 | three |   |    | 0 |   
-     | 4 | 1 | four  |   |    | 0 |   
-     | 5 | 0 | five  |   |    | 0 |   
-     | 6 | 6 | six   |   |    | 0 |   
-     | 7 | 7 | seven |   |    | 0 |   
-     | 8 | 8 | eight |   |    | 0 |   
-     | 0 |   | zero  |   |    | 0 |   
-     |   |   | null  |   |    | 0 |   
-     |   | 0 | zero  |   |    | 0 |   
-     | 1 | 4 | one   |   |    |   |   
-     | 2 | 3 | two   |   |    |   |   
-     | 3 | 2 | three |   |    |   |   
-     | 4 | 1 | four  |   |    |   |   
-     | 5 | 0 | five  |   |    |   |   
-     | 6 | 6 | six   |   |    |   |   
-     | 7 | 7 | seven |   |    |   |   
-     | 8 | 8 | eight |   |    |   |   
-     | 0 |   | zero  |   |    |   |   
-     |   |   | null  |   |    |   |   
-     |   | 0 | zero  |   |    |   |   
-     | 1 | 4 | one   |   |    |   |  0
-     | 2 | 3 | two   |   |    |   |  0
-     | 3 | 2 | three |   |    |   |  0
-     | 4 | 1 | four  |   |    |   |  0
-     | 5 | 0 | five  |   |    |   |  0
-     | 6 | 6 | six   |   |    |   |  0
-     | 7 | 7 | seven |   |    |   |  0
-     | 8 | 8 | eight |   |    |   |  0
-     | 0 |   | zero  |   |    |   |  0
-     |   |   | null  |   |    |   |  0
-     |   | 0 | zero  |   |    |   |  0
      | 1 | 4 | one   |   |  0 | 1 | -1
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      | 6 | 6 | six   |   |  0 | 1 | -1
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      | 7 | 7 | seven |   |  0 | 1 | -1
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      | 8 | 8 | eight |   |  0 | 1 | -1
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      | 0 |   | zero  |   |  0 | 1 | -1
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+     |   |   | null  | 2 |  4 | 1 | -1
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      |   |   | null  |   |  0 | 1 | -1
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      |   | 0 | zero  |   |  0 | 1 | -1
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+     | 1 | 4 | one   | 3 | -3 | 2 |  2
+     | 1 | 4 | one   | 2 |  4 | 2 |  2
+     | 1 | 4 | one   | 5 | -5 | 2 |  2
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+     | 1 | 4 | one   | 0 |    | 2 |  2
+     | 1 | 4 | one   |   |    | 2 |  2
      | 1 | 4 | one   |   |  0 | 2 |  2
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+     | 2 | 3 | two   | 5 | -5 | 2 |  2
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+     | 2 | 3 | two   | 0 |    | 2 |  2
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      | 2 | 3 | two   |   |  0 | 2 |  2
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+     | 3 | 2 | three | 5 | -5 | 2 |  2
+     | 3 | 2 | three | 0 |    | 2 |  2
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      | 3 | 2 | three |   |  0 | 2 |  2
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+     | 4 | 1 | four  | 3 | -3 | 2 |  2
+     | 4 | 1 | four  | 2 |  4 | 2 |  2
+     | 4 | 1 | four  | 5 | -5 | 2 |  2
+     | 4 | 1 | four  | 5 | -5 | 2 |  2
+     | 4 | 1 | four  | 0 |    | 2 |  2
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      | 4 | 1 | four  |   |  0 | 2 |  2
+     | 5 | 0 | five  | 1 | -1 | 2 |  2
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+     | 5 | 0 | five  | 5 | -5 | 2 |  2
+     | 5 | 0 | five  | 5 | -5 | 2 |  2
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      | 5 | 0 | five  |   |  0 | 2 |  2
+     | 6 | 6 | six   | 1 | -1 | 2 |  2
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+     | 6 | 6 | six   | 3 | -3 | 2 |  2
+     | 6 | 6 | six   | 2 |  4 | 2 |  2
+     | 6 | 6 | six   | 5 | -5 | 2 |  2
+     | 6 | 6 | six   | 5 | -5 | 2 |  2
+     | 6 | 6 | six   | 0 |    | 2 |  2
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      | 6 | 6 | six   |   |  0 | 2 |  2
+     | 7 | 7 | seven | 1 | -1 | 2 |  2
+     | 7 | 7 | seven | 2 |  2 | 2 |  2
+     | 7 | 7 | seven | 3 | -3 | 2 |  2
+     | 7 | 7 | seven | 2 |  4 | 2 |  2
+     | 7 | 7 | seven | 5 | -5 | 2 |  2
+     | 7 | 7 | seven | 5 | -5 | 2 |  2
+     | 7 | 7 | seven | 0 |    | 2 |  2
+     | 7 | 7 | seven |   |    | 2 |  2
      | 7 | 7 | seven |   |  0 | 2 |  2
+     | 8 | 8 | eight | 1 | -1 | 2 |  2
+     | 8 | 8 | eight | 2 |  2 | 2 |  2
+     | 8 | 8 | eight | 3 | -3 | 2 |  2
+     | 8 | 8 | eight | 2 |  4 | 2 |  2
+     | 8 | 8 | eight | 5 | -5 | 2 |  2
+     | 8 | 8 | eight | 5 | -5 | 2 |  2
+     | 8 | 8 | eight | 0 |    | 2 |  2
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      | 8 | 8 | eight |   |  0 | 2 |  2
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      | 0 |   | zero  |   |  0 | 2 |  2
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+     |   |   | null  | 3 | -3 | 2 |  2
+     |   |   | null  | 2 |  4 | 2 |  2
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      |   |   | null  |   |  0 | 2 |  2
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      |   | 0 | zero  |   |  0 | 2 |  2
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+     | 1 | 4 | one   | 5 | -5 | 3 | -3
+     | 1 | 4 | one   | 0 |    | 3 | -3
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      | 1 | 4 | one   |   |  0 | 3 | -3
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+     | 2 | 3 | two   | 2 |  4 | 3 | -3
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+     | 2 | 3 | two   | 0 |    | 3 | -3
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      | 2 | 3 | two   |   |  0 | 3 | -3
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+     | 3 | 2 | three | 2 |  4 | 3 | -3
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+     | 3 | 2 | three | 5 | -5 | 3 | -3
+     | 3 | 2 | three | 0 |    | 3 | -3
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      | 3 | 2 | three |   |  0 | 3 | -3
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+     | 4 | 1 | four  | 2 |  2 | 3 | -3
+     | 4 | 1 | four  | 3 | -3 | 3 | -3
+     | 4 | 1 | four  | 2 |  4 | 3 | -3
+     | 4 | 1 | four  | 5 | -5 | 3 | -3
+     | 4 | 1 | four  | 5 | -5 | 3 | -3
+     | 4 | 1 | four  | 0 |    | 3 | -3
+     | 4 | 1 | four  |   |    | 3 | -3
      | 4 | 1 | four  |   |  0 | 3 | -3
+     | 5 | 0 | five  | 1 | -1 | 3 | -3
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 (891 rows)
 
Simon's dev repository