Many hyperlinks are disabled.
Use anonymous login
to enable hyperlinks.
Overview
Comment: | Allow WHERE terms to be pushed down into sub-queries that contain window functions, provided that the WHERE term is made up of entirely of constants and copies of expressions found in the PARTITION BY clauses of all window functions in the sub-query. |
---|---|
Downloads: | Tarball | ZIP archive | SQL archive |
Timelines: | family | ancestors | descendants | both | trunk |
Files: | files | file ages | folders |
SHA3-256: |
20689468100aed264877111367b42837 |
User & Date: | dan 2021-02-23 15:53:22 |
Context
2021-02-23
| ||
16:40 | When a sub-transaction is released, if no pages required by containing sub-transactions were journaled, truncate the statement journal. This prevents out of control statement journal growth in some cases. See forum thread e78ffd751185a67e for context. (check-in: 23ca2389 user: dan tags: trunk) | |
15:53 | Allow WHERE terms to be pushed down into sub-queries that contain window functions, provided that the WHERE term is made up of entirely of constants and copies of expressions found in the PARTITION BY clauses of all window functions in the sub-query. (check-in: 20689468 user: dan tags: trunk) | |
15:36 | Further tests for the push-down optimization with window functions. (Closed-Leaf check-in: 4b089f70 user: dan tags: window-functions-pushdown) | |
2021-02-22
| ||
19:57 | Add a few simple test cases for MATERIALIZED and NOT MATERIALIZED. (check-in: 64878124 user: drh tags: trunk) | |
Changes
Changes to src/select.c.
︙ | ︙ | |||
4485 4486 4487 4488 4489 4490 4491 4492 4493 4494 4495 4496 4497 4498 | sqlite3DbFree(x.pParse->db, x.apExpr); nChng += x.nChng; } }while( x.nChng ); return nChng; } #if !defined(SQLITE_OMIT_SUBQUERY) || !defined(SQLITE_OMIT_VIEW) /* ** Make copies of relevant WHERE clause terms of the outer query into ** the WHERE clause of subquery. Example: ** ** SELECT * FROM (SELECT a AS x, c-d AS y FROM t1) WHERE x=5 AND y=10; ** | > > > > > > > > > > > > > > > > > > > > > > > > > > > > > | 4485 4486 4487 4488 4489 4490 4491 4492 4493 4494 4495 4496 4497 4498 4499 4500 4501 4502 4503 4504 4505 4506 4507 4508 4509 4510 4511 4512 4513 4514 4515 4516 4517 4518 4519 4520 4521 4522 4523 4524 4525 4526 4527 | sqlite3DbFree(x.pParse->db, x.apExpr); nChng += x.nChng; } }while( x.nChng ); return nChng; } #if !defined(SQLITE_OMIT_SUBQUERY) || !defined(SQLITE_OMIT_VIEW) # if !defined(SQLITE_OMIT_WINDOWFUNC) /* ** This function is called to determine whether or not it is safe to ** push WHERE clause expression pExpr down to FROM clause sub-query ** pSubq, which contains at least one window function. Return 1 ** if it is safe and the expression should be pushed down, or 0 ** otherwise. ** ** It is only safe to push the expression down if it consists only ** of constants and copies of expressions that appear in the PARTITION ** BY clause of all window function used by the sub-query. It is safe ** to filter out entire partitions, but not rows within partitions, as ** this may change the results of the window functions. ** ** At the time this function is called it is guaranteed that ** ** * the sub-query uses only one distinct window frame, and ** * that the window frame has a PARTITION BY clase. */ static int pushDownWindowCheck(Parse *pParse, Select *pSubq, Expr *pExpr){ assert( pSubq->pWin->pPartition ); assert( (pSubq->selFlags & SF_MultiPart)==0 ); assert( pSubq->pPrior==0 ); return sqlite3ExprIsConstantOrGroupBy(pParse, pExpr, pSubq->pWin->pPartition); } # endif /* SQLITE_OMIT_WINDOWFUNC */ #endif /* !defined(SQLITE_OMIT_SUBQUERY) || !defined(SQLITE_OMIT_VIEW) */ #if !defined(SQLITE_OMIT_SUBQUERY) || !defined(SQLITE_OMIT_VIEW) /* ** Make copies of relevant WHERE clause terms of the outer query into ** the WHERE clause of subquery. Example: ** ** SELECT * FROM (SELECT a AS x, c-d AS y FROM t1) WHERE x=5 AND y=10; ** |
︙ | ︙ | |||
4532 4533 4534 4535 4536 4537 4538 | ** JOIN (SELECT 1 AS b2 UNION ALL SELECT 2) AS bb ON (a1=b2) ** LEFT JOIN (SELECT 8 AS c3 UNION ALL SELECT 9) AS cc ON (b2=2); ** ** The correct answer is three rows: (1,1,NULL),(2,2,8),(2,2,9). ** But if the (b2=2) term were to be pushed down into the bb subquery, ** then the (1,1,NULL) row would be suppressed. ** | | | > | > > > > > > > > > > < | > > | | > > > | 4561 4562 4563 4564 4565 4566 4567 4568 4569 4570 4571 4572 4573 4574 4575 4576 4577 4578 4579 4580 4581 4582 4583 4584 4585 4586 4587 4588 4589 4590 4591 4592 4593 4594 4595 4596 4597 4598 4599 4600 4601 4602 4603 4604 4605 4606 4607 4608 4609 4610 4611 4612 4613 4614 4615 4616 | ** JOIN (SELECT 1 AS b2 UNION ALL SELECT 2) AS bb ON (a1=b2) ** LEFT JOIN (SELECT 8 AS c3 UNION ALL SELECT 9) AS cc ON (b2=2); ** ** The correct answer is three rows: (1,1,NULL),(2,2,8),(2,2,9). ** But if the (b2=2) term were to be pushed down into the bb subquery, ** then the (1,1,NULL) row would be suppressed. ** ** (6) Window functions make things tricky as changes to the WHERE clause ** of the inner query could change the window over which window ** functions are calculated. Therefore, do not attempt the optimization ** if: ** ** (6a) The inner query uses multiple incompatible window partitions. ** ** (6b) The inner query is a compound and uses window-functions. ** ** (6c) The WHERE clause does not consist entirely of constants and ** copies of expressions found in the PARTITION BY clause of ** all window-functions used by the sub-query. It is safe to ** filter out entire partitions, as this does not change the ** window over which any window-function is calculated. ** ** (7) The inner query is a Common Table Expression (CTE) that should ** be materialized. (This restriction is implemented in the calling ** routine.) ** ** Return 0 if no changes are made and non-zero if one or more WHERE clause ** terms are duplicated into the subquery. */ static int pushDownWhereTerms( Parse *pParse, /* Parse context (for malloc() and error reporting) */ Select *pSubq, /* The subquery whose WHERE clause is to be augmented */ Expr *pWhere, /* The WHERE clause of the outer query */ int iCursor, /* Cursor number of the subquery */ int isLeftJoin /* True if pSubq is the right term of a LEFT JOIN */ ){ Expr *pNew; int nChng = 0; if( pWhere==0 ) return 0; if( pSubq->selFlags & (SF_Recursive|SF_MultiPart) ) return 0; #ifndef SQLITE_OMIT_WINDOWFUNC if( pSubq->pPrior ){ Select *pSel; for(pSel=pSubq; pSel; pSel=pSel->pPrior){ if( pSel->pWin ) return 0; /* restriction (6b) */ } }else{ if( pSubq->pWin && pSubq->pWin->pPartition==0 ) return 0; } #endif #ifdef SQLITE_DEBUG /* Only the first term of a compound can have a WITH clause. But make ** sure no other terms are marked SF_Recursive in case something changes ** in the future. |
︙ | ︙ | |||
4605 4606 4607 4608 4609 4610 4611 4612 4613 4614 4615 4616 4617 4618 | unsetJoinExpr(pNew, -1); x.pParse = pParse; x.iTable = iCursor; x.iNewTable = iCursor; x.isLeftJoin = 0; x.pEList = pSubq->pEList; pNew = substExpr(&x, pNew); if( pSubq->selFlags & SF_Aggregate ){ pSubq->pHaving = sqlite3ExprAnd(pParse, pSubq->pHaving, pNew); }else{ pSubq->pWhere = sqlite3ExprAnd(pParse, pSubq->pWhere, pNew); } pSubq = pSubq->pPrior; } | > > > > > > > > | 4649 4650 4651 4652 4653 4654 4655 4656 4657 4658 4659 4660 4661 4662 4663 4664 4665 4666 4667 4668 4669 4670 | unsetJoinExpr(pNew, -1); x.pParse = pParse; x.iTable = iCursor; x.iNewTable = iCursor; x.isLeftJoin = 0; x.pEList = pSubq->pEList; pNew = substExpr(&x, pNew); #ifndef SQLITE_OMIT_WINDOWFUNC if( pSubq->pWin && 0==pushDownWindowCheck(pParse, pSubq, pNew) ){ /* Restriction 6c has prevented push-down in this case */ sqlite3ExprDelete(pParse->db, pNew); nChng--; break; } #endif if( pSubq->selFlags & SF_Aggregate ){ pSubq->pHaving = sqlite3ExprAnd(pParse, pSubq->pHaving, pNew); }else{ pSubq->pWhere = sqlite3ExprAnd(pParse, pSubq->pWhere, pNew); } pSubq = pSubq->pPrior; } |
︙ | ︙ |
Changes to src/sqliteInt.h.
︙ | ︙ | |||
3200 3201 3202 3203 3204 3205 3206 3207 3208 3209 3210 3211 3212 3213 | #define SF_ComplexResult 0x0040000 /* Result contains subquery or function */ #define SF_WhereBegin 0x0080000 /* Really a WhereBegin() call. Debug Only */ #define SF_WinRewrite 0x0100000 /* Window function rewrite accomplished */ #define SF_View 0x0200000 /* SELECT statement is a view */ #define SF_NoopOrderBy 0x0400000 /* ORDER BY is ignored for this query */ #define SF_UpdateFrom 0x0800000 /* Statement is an UPDATE...FROM */ #define SF_PushDown 0x1000000 /* SELECT has be modified by push-down opt */ /* ** The results of a SELECT can be distributed in several ways, as defined ** by one of the following macros. The "SRT" prefix means "SELECT Result ** Type". ** ** SRT_Union Store results as a key in a temporary index | > | 3200 3201 3202 3203 3204 3205 3206 3207 3208 3209 3210 3211 3212 3213 3214 | #define SF_ComplexResult 0x0040000 /* Result contains subquery or function */ #define SF_WhereBegin 0x0080000 /* Really a WhereBegin() call. Debug Only */ #define SF_WinRewrite 0x0100000 /* Window function rewrite accomplished */ #define SF_View 0x0200000 /* SELECT statement is a view */ #define SF_NoopOrderBy 0x0400000 /* ORDER BY is ignored for this query */ #define SF_UpdateFrom 0x0800000 /* Statement is an UPDATE...FROM */ #define SF_PushDown 0x1000000 /* SELECT has be modified by push-down opt */ #define SF_MultiPart 0x2000000 /* Has multiple incompatible PARTITIONs */ /* ** The results of a SELECT can be distributed in several ways, as defined ** by one of the following macros. The "SRT" prefix means "SELECT Result ** Type". ** ** SRT_Union Store results as a key in a temporary index |
︙ | ︙ |
Changes to src/window.c.
︙ | ︙ | |||
1300 1301 1302 1303 1304 1305 1306 | /* ** Possibly link window pWin into the list at pSel->pWin (window functions ** to be processed as part of SELECT statement pSel). The window is linked ** in if either (a) there are no other windows already linked to this ** SELECT, or (b) the windows already linked use a compatible window frame. */ void sqlite3WindowLink(Select *pSel, Window *pWin){ | | | < | | | | | | > > > > > | 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 | /* ** Possibly link window pWin into the list at pSel->pWin (window functions ** to be processed as part of SELECT statement pSel). The window is linked ** in if either (a) there are no other windows already linked to this ** SELECT, or (b) the windows already linked use a compatible window frame. */ void sqlite3WindowLink(Select *pSel, Window *pWin){ if( pSel ){ if( 0==pSel->pWin || 0==sqlite3WindowCompare(0, pSel->pWin, pWin, 0) ){ pWin->pNextWin = pSel->pWin; if( pSel->pWin ){ pSel->pWin->ppThis = &pWin->pNextWin; } pSel->pWin = pWin; pWin->ppThis = &pSel->pWin; }else{ if( sqlite3ExprListCompare(pWin->pPartition, pSel->pWin->pPartition,-1) ){ pSel->selFlags |= SF_MultiPart; } } } } /* ** Return 0 if the two window objects are identical, 1 if they are ** different, or 2 if it cannot be determined if the objects are identical ** or not. Identical window objects can be processed in a single scan. |
︙ | ︙ |
Changes to test/windowfault.test.
︙ | ︙ | |||
242 243 244 245 246 247 248 249 250 251 252 253 254 255 | ) ) } } -test { faultsim_test_result {0 {}} } reset_db do_execsql_test 11.0 { DROP TABLE IF EXISTS t0; CREATE TABLE t0(c0 INTEGER UNIQUE); INSERT INTO t0 VALUES(0); } {} | > | | > > > > > > > > > > > > > > > > > | 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 | ) ) } } -test { faultsim_test_result {0 {}} } #------------------------------------------------------------------------- reset_db do_execsql_test 11.0 { DROP TABLE IF EXISTS t0; CREATE TABLE t0(c0 INTEGER UNIQUE); INSERT INTO t0 VALUES(0); } {} do_faultsim_test 11.1 -faults oom* -prep { } -body { execsql { SELECT * FROM t0 WHERE (0, t0.c0) IN (SELECT DENSE_RANK() OVER(), LAG(0) OVER() FROM t0); } } -test { faultsim_test_result {0 {}} } do_faultsim_test 11.2 -faults oom* -prep { } -body { execsql { VALUES(false),(current_date collate binary) intersect values(count() not like group_concat(cast(cast(0e00 as text) as integer) <= NULL || 0.4e-0 || 0x8 & true ) over () collate rtrim); } } -test { faultsim_test_result {0 {}} } #------------------------------------------------------------------------- reset_db do_execsql_test 12.0 { CREATE TABLE t1(a, b, c); } {} do_faultsim_test 12 -faults oom* -prep { } -body { execsql { WITH v(a, b, row_number) AS ( SELECT a, b, row_number() OVER (PARTITION BY a ORDER BY b) FROM t1 ) SELECT * FROM v WHERE a=2 } } -test { faultsim_test_result {0 {}} } finish_test |
Added test/windowpushd.test.
> > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 | # 2021 February 23 # # The author disclaims copyright to this source code. In place of # a legal notice, here is a blessing: # # May you do good and not evil. # May you find forgiveness for yourself and forgive others. # May you share freely, never taking more than you give. # #*********************************************************************** # This file implements regression tests for SQLite library. The # focus of this file is testing the push-down optimization when # WHERE constraints are pushed down into a sub-query that uses # window functions. # set testdir [file dirname $argv0] source $testdir/tester.tcl set testprefix windowpushd do_execsql_test 1.0 { CREATE TABLE t1(id INTEGER PRIMARY KEY, grp_id); CREATE INDEX i1 ON t1(grp_id); CREATE VIEW lll AS SELECT row_number() OVER (PARTITION BY grp_id), grp_id, id FROM t1 } do_execsql_test 1.1 { INSERT INTO t1 VALUES (1, 2), (2, 3), (3, 3), (4, 1), (5, 1), (6, 1), (7, 1), (8, 1), (9, 3), (10, 3), (11, 2), (12, 3), (13, 3), (14, 2), (15, 1), (16, 2), (17, 1), (18, 2), (19, 3), (20, 2) } do_execsql_test 1.2 { SELECT * FROM lll } { 1 1 4 2 1 5 3 1 6 4 1 7 5 1 8 6 1 15 7 1 17 1 2 1 2 2 11 3 2 14 4 2 16 5 2 18 6 2 20 1 3 2 2 3 3 3 3 9 4 3 10 5 3 12 6 3 13 7 3 19 } do_execsql_test 1.3 { SELECT * FROM lll WHERE grp_id=2 } { 1 2 1 2 2 11 3 2 14 4 2 16 5 2 18 6 2 20 } do_eqp_test 1.4 { SELECT * FROM lll WHERE grp_id=2 } {SEARCH TABLE t1 USING COVERING INDEX i1 (grp_id=?)} #------------------------------------------------------------------------- reset_db do_execsql_test 2.0 { CREATE TABLE t1(a, b, c, d); INSERT INTO t1 VALUES('A', 'C', 1, 0.1); INSERT INTO t1 VALUES('A', 'D', 2, 0.2); INSERT INTO t1 VALUES('A', 'E', 3, 0.3); INSERT INTO t1 VALUES('A', 'C', 4, 0.4); INSERT INTO t1 VALUES('B', 'D', 5, 0.5); INSERT INTO t1 VALUES('B', 'E', 6, 0.6); INSERT INTO t1 VALUES('B', 'C', 7, 0.7); INSERT INTO t1 VALUES('B', 'D', 8, 0.8); INSERT INTO t1 VALUES('C', 'E', 9, 0.9); INSERT INTO t1 VALUES('C', 'C', 10, 1.0); INSERT INTO t1 VALUES('C', 'D', 11, 1.1); INSERT INTO t1 VALUES('C', 'E', 12, 1.2); CREATE INDEX i1 ON t1(a); CREATE INDEX i2 ON t1(b); CREATE VIEW v1 AS SELECT a, c, max(c) OVER (PARTITION BY a) FROM t1; CREATE VIEW v2 AS SELECT a, c, max(c) OVER (PARTITION BY a), row_number() OVER () FROM t1; CREATE VIEW v3 AS SELECT b, d, max(d) OVER (PARTITION BY b), row_number() OVER (PARTITION BY b) FROM t1; CREATE TABLE t2(x, y, z); INSERT INTO t2 VALUES('W', 3, 1); INSERT INTO t2 VALUES('W', 2, 2); INSERT INTO t2 VALUES('X', 1, 4); INSERT INTO t2 VALUES('X', 5, 7); INSERT INTO t2 VALUES('Y', 1, 9); INSERT INTO t2 VALUES('Y', 4, 2); INSERT INTO t2 VALUES('Z', 3, 3); INSERT INTO t2 VALUES('Z', 3, 4); } foreach tn {0 1} { optimization_control db push-down $tn do_execsql_test 2.$tn.1.1 { SELECT * FROM v1; } { A 1 4 A 2 4 A 3 4 A 4 4 B 5 8 B 6 8 B 7 8 B 8 8 C 9 12 C 10 12 C 11 12 C 12 12 } do_execsql_test 2.$tn.1.2 { SELECT * FROM v1 WHERE a IN ('A', 'B'); } { A 1 4 A 2 4 A 3 4 A 4 4 B 5 8 B 6 8 B 7 8 B 8 8 } do_execsql_test 2.$tn.1.3 { SELECT * FROM v1 WHERE a IS 'C' } { C 9 12 C 10 12 C 11 12 C 12 12 } if {$tn==1} { do_eqp_test 2.$tn.1.4 { SELECT * FROM v1 WHERE a IN ('A', 'B'); } {USING INDEX i1 (a=?)} do_eqp_test 2.$tn.1.5 { SELECT * FROM v1 WHERE a = 'c' COLLATE nocase } {USING INDEX i1} } do_execsql_test 2.$tn.2.1 { SELECT * FROM v2; } { A 1 4 1 A 2 4 2 A 3 4 3 A 4 4 4 B 5 8 5 B 6 8 6 B 7 8 7 B 8 8 8 C 9 12 9 C 10 12 10 C 11 12 11 C 12 12 12 } do_execsql_test 2.$tn.2.2 { SELECT * FROM v2 WHERE a = 'C'; } { C 9 12 9 C 10 12 10 C 11 12 11 C 12 12 12 } do_execsql_test 2.$tn.3.1 { SELECT * FROM v3; } { C 0.1 1.0 1 C 0.4 1.0 2 C 0.7 1.0 3 C 1.0 1.0 4 D 0.2 1.1 1 D 0.5 1.1 2 D 0.8 1.1 3 D 1.1 1.1 4 E 0.3 1.2 1 E 0.6 1.2 2 E 0.9 1.2 3 E 1.2 1.2 4 } do_execsql_test 2.$tn.3.2 { SELECT * FROM v3 WHERE b<'E' } { C 0.1 1.0 1 C 0.4 1.0 2 C 0.7 1.0 3 C 1.0 1.0 4 D 0.2 1.1 1 D 0.5 1.1 2 D 0.8 1.1 3 D 1.1 1.1 4 } if {$tn==1} { do_eqp_test 2.$tn.3.3 { SELECT * FROM v3 WHERE b='E' } {SEARCH TABLE t1 USING INDEX i2 (b=?)} do_eqp_test 2.$tn.3.4 { SELECT * FROM v3 WHERE b>'C' } {SEARCH TABLE t1 USING INDEX i2 (b>?)} } do_execsql_test 2.$tn.3.5 { SELECT * FROM v3 WHERE d<0.55; } { C 0.1 1.0 1 C 0.4 1.0 2 D 0.2 1.1 1 D 0.5 1.1 2 E 0.3 1.2 1 } if {$tn==1} { do_eqp_test 2.$tn.3.6 { SELECT * FROM v3 WHERE d<0.55 } {SCAN TABLE t1 USING INDEX i2} } do_execsql_test 2.$tn.4.1 { SELECT * FROM ( SELECT x, sum(y) AS s, max(z) AS m FROM t2 GROUP BY x ) } { W 5 2 X 6 7 Y 5 9 Z 6 4 } do_execsql_test 2.$tn.4.1 { SELECT * FROM ( SELECT x, sum(y) AS s, max(z) AS m, max( max(z) ) OVER (PARTITION BY sum(y) ROWS BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING ) FROM t2 GROUP BY x ) } { W 5 2 9 Y 5 9 9 X 6 7 7 Z 6 4 7 } do_execsql_test 2.$tn.4.2 { SELECT * FROM ( SELECT x, sum(y) AS s, max(z) AS m, max( max(z) ) OVER (PARTITION BY sum(y) ROWS BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING ) FROM t2 GROUP BY x ) WHERE s=6 } { X 6 7 7 Z 6 4 7 } do_execsql_test 2.$tn.4.3 { SELECT * FROM ( SELECT x, sum(y) AS s, max(z) AS m, max( max(z) ) OVER (PARTITION BY sum(y) ROWS BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING ) FROM t2 GROUP BY x ) WHERE s<6 } { W 5 2 9 Y 5 9 9 } } finish_test |