LCOV - code coverage report
Current view: top level - monetdb5/modules/kernel - algebra.c (source / functions) Hit Total Coverage
Test: coverage.info Lines: 761 993 76.6 %
Date: 2024-10-03 20:03:20 Functions: 67 82 81.7 %

          Line data    Source code
       1             : /*
       2             :  * SPDX-License-Identifier: MPL-2.0
       3             :  *
       4             :  * This Source Code Form is subject to the terms of the Mozilla Public
       5             :  * License, v. 2.0.  If a copy of the MPL was not distributed with this
       6             :  * file, You can obtain one at http://mozilla.org/MPL/2.0/.
       7             :  *
       8             :  * Copyright 2024 MonetDB Foundation;
       9             :  * Copyright August 2008 - 2023 MonetDB B.V.;
      10             :  * Copyright 1997 - July 2008 CWI.
      11             :  */
      12             : 
      13             : /*
      14             :  * (c) Peter Boncz, Martin Kersten, Niels Nes, Sjoerd Mullender
      15             :  * BAT Algebra
      16             :  * This modules contains the most common algebraic BAT manipulation
      17             :  * commands. We call them algebra, because all operations take
      18             :  * values as parameters, and produce new result values, but
      19             :  * do not modify their parameters.
      20             :  *
      21             :  * Unlike the previous Monet versions, we reduce the number
      22             :  * of functions returning a BAT reference. This was previously needed
      23             :  * to simplify recursive bat-expression and manage reference counts.
      24             :  * In the current version we return only a BAT identifier when a new
      25             :  * bat is being created.
      26             :  *
      27             :  * All parameters to the modules are passed by reference.
      28             :  * In particular, this means that
      29             :  * string values are passed to the module layer as (str *)
      30             :  * and we have to de-reference them before entering the gdk library.
      31             :  * This calls for knowledge on the underlying BAT typs`s
      32             :  */
      33             : #define derefStr(b, v)                                                  \
      34             :         do {                                                                            \
      35             :                 int _tpe= ATOMstorage((b)->ttype);           \
      36             :                 if (_tpe >= TYPE_str) {                                      \
      37             :                         if ((v) == 0 || *(str*) (v) == 0)       \
      38             :                                 (v) = (str) str_nil;                    \
      39             :                         else                                                            \
      40             :                                 (v) = *(str *) (v);                             \
      41             :                 }                                                                               \
      42             :         } while (0)
      43             : 
      44             : #include "monetdb_config.h"
      45             : #include "algebra.h"
      46             : 
      47             : /*
      48             :  * Command Implementations in C
      49             :  * This module contains just a wrapper implementations; since all described
      50             :  * operations are part of the GDK kernel.
      51             :  *
      52             :  * BAT sum operation
      53             :  * The sum aggregate only works for int and float fields.
      54             :  * The routines below assumes that the caller knows what type
      55             :  * is large enough to prevent overflow.
      56             :  */
      57             : 
      58             : static gdk_return
      59        2388 : CMDgen_group(BAT **result, BAT *gids, BAT *cnts)
      60             : {
      61        2388 :         BUN j;
      62        2388 :         BATiter gi = bat_iterator(gids);
      63        2388 :         BAT *r = COLnew(0, TYPE_oid, gi.count * 2, TRANSIENT);
      64             : 
      65        2388 :         if (r == NULL) {
      66           0 :                 bat_iterator_end(&gi);
      67           0 :                 return GDK_FAIL;
      68             :         }
      69        2388 :         BATiter ci = bat_iterator(cnts);
      70        2388 :         if (gi.type == TYPE_void) {
      71        1049 :                 oid id = gi.tseq;
      72        1049 :                 lng *cnt = (lng *) ci.base;
      73       96195 :                 for (j = 0; j < gi.count; j++) {
      74       95146 :                         lng i, sz = cnt[j];
      75      190236 :                         for (i = 0; i < sz; i++) {
      76       95090 :                                 if (BUNappend(r, &id, false) != GDK_SUCCEED) {
      77           0 :                                         BBPreclaim(r);
      78           0 :                                         bat_iterator_end(&ci);
      79           0 :                                         bat_iterator_end(&gi);
      80           0 :                                         return GDK_FAIL;
      81             :                                 }
      82             :                         }
      83       95146 :                         id ++;
      84             :                 }
      85             :         } else {
      86        1339 :                 oid *id = (oid *) gi.base;
      87        1339 :                 lng *cnt = (lng *) ci.base;
      88      140494 :                 for (j = 0; j < gi.count; j++) {
      89      139155 :                         lng i, sz = cnt[j];
      90      274814 :                         for (i = 0; i < sz; i++) {
      91      135659 :                                 if (BUNappend(r, id, false) != GDK_SUCCEED) {
      92           0 :                                         BBPreclaim(r);
      93           0 :                                         bat_iterator_end(&ci);
      94           0 :                                         bat_iterator_end(&gi);
      95           0 :                                         return GDK_FAIL;
      96             :                                 }
      97             :                         }
      98      139155 :                         id ++;
      99             :                 }
     100             :         }
     101        2388 :         bat_iterator_end(&ci);
     102        2388 :         r->tkey = false;
     103        2388 :         r->tseqbase = oid_nil;
     104        2388 :         r->tsorted = gi.sorted;
     105        2388 :         r->trevsorted = gi.revsorted;
     106        2388 :         r->tnonil = gi.nonil;
     107        2388 :         bat_iterator_end(&gi);
     108        2388 :         *result = r;
     109        2388 :         return GDK_SUCCEED;
     110             : }
     111             : 
     112             : 
     113             : static gdk_return
     114           6 : slice(BAT **retval, BAT *b, lng start, lng end)
     115             : {
     116             :         /* the internal BATslice requires exclusive end */
     117           6 :         if (start < 0) {
     118           0 :                 GDKerror("start position of slice should >= 0\n");
     119           0 :                 return GDK_FAIL;
     120             :         }
     121           6 :         if (is_lng_nil(end))
     122           3 :                 end = BATcount(b);
     123             : 
     124           6 :         return (*retval = BATslice(b, (BUN) start, (BUN) end + 1)) ? GDK_SUCCEED : GDK_FAIL;
     125             : }
     126             : 
     127             : /*
     128             :  *
     129             :  * The remainder of this file contains the wrapper around the V4 code base
     130             :  * The BAT identifiers passed through this module may indicate
     131             :  * that the 'reverse' view applies. This should be taken into
     132             :  * account while resolving them.
     133             :  *
     134             :  * The sum aggregate only works for int and float fields.
     135             :  * The routines below assumes that the caller knows what type
     136             :  * is large enough to prevent overflow.
     137             :  */
     138             : 
     139             : static str
     140         722 : ALGminany_skipnil(ptr result, const bat *bid, const bit *skipnil)
     141             : {
     142         722 :         BAT *b;
     143         722 :         ptr p;
     144         722 :         str msg = MAL_SUCCEED;
     145             : 
     146         722 :         if (result == NULL || (b = BATdescriptor(*bid)) == NULL)
     147           0 :                 throw(MAL, "algebra.min", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     148             : 
     149         722 :         if (!ATOMlinear(b->ttype)) {
     150           0 :                 msg = createException(MAL, "algebra.min",
     151             :                                                           "atom '%s' cannot be ordered linearly",
     152             :                                                           ATOMname(b->ttype));
     153             :         } else {
     154         722 :                 if (ATOMextern(b->ttype)) {
     155          34 :                         *(ptr *) result = p = BATmin_skipnil(b, NULL, *skipnil);
     156             :                 } else {
     157         688 :                         p = BATmin_skipnil(b, result, *skipnil);
     158         688 :                         if (p != result)
     159           0 :                                 msg = createException(MAL, "algebra.min",
     160             :                                                                           SQLSTATE(HY002) "INTERNAL ERROR");
     161             :                 }
     162         722 :                 if (msg == MAL_SUCCEED && p == NULL)
     163           0 :                         msg = createException(MAL, "algebra.min", GDK_EXCEPTION);
     164             :         }
     165         722 :         BBPunfix(b->batCacheid);
     166         722 :         return msg;
     167             : }
     168             : 
     169             : static str
     170         722 : ALGminany(ptr result, const bat *bid)
     171             : {
     172         722 :         bit skipnil = TRUE;
     173         722 :         return ALGminany_skipnil(result, bid, &skipnil);
     174             : }
     175             : 
     176             : static str
     177         596 : ALGmaxany_skipnil(ptr result, const bat *bid, const bit *skipnil)
     178             : {
     179         596 :         BAT *b;
     180         596 :         ptr p;
     181         596 :         str msg = MAL_SUCCEED;
     182             : 
     183         596 :         if (result == NULL || (b = BATdescriptor(*bid)) == NULL)
     184           0 :                 throw(MAL, "algebra.max", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     185             : 
     186         596 :         if (!ATOMlinear(b->ttype)) {
     187           0 :                 msg = createException(MAL, "algebra.max",
     188             :                                                           "atom '%s' cannot be ordered linearly",
     189             :                                                           ATOMname(b->ttype));
     190             :         } else {
     191         596 :                 if (ATOMextern(b->ttype)) {
     192          48 :                         *(ptr *) result = p = BATmax_skipnil(b, NULL, *skipnil);
     193             :                 } else {
     194         548 :                         p = BATmax_skipnil(b, result, *skipnil);
     195         548 :                         if (p != result)
     196           0 :                                 msg = createException(MAL, "algebra.max",
     197             :                                                                           SQLSTATE(HY002) "INTERNAL ERROR");
     198             :                 }
     199         596 :                 if (msg == MAL_SUCCEED && p == NULL)
     200           0 :                         msg = createException(MAL, "algebra.max", GDK_EXCEPTION);
     201             :         }
     202         596 :         BBPunfix(b->batCacheid);
     203         596 :         return msg;
     204             : }
     205             : 
     206             : static str
     207         596 : ALGmaxany(ptr result, const bat *bid)
     208             : {
     209         596 :         bit skipnil = TRUE;
     210         596 :         return ALGmaxany_skipnil(result, bid, &skipnil);
     211             : }
     212             : 
     213             : static str
     214        2388 : ALGgroupby(bat *res, const bat *gids, const bat *cnts)
     215             : {
     216        2388 :         BAT *bn, *g, *c;
     217             : 
     218        2388 :         g = BATdescriptor(*gids);
     219        2388 :         if (g == NULL) {
     220           0 :                 throw(MAL, "algebra.groupby", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     221             :         }
     222        2388 :         c = BATdescriptor(*cnts);
     223        2388 :         if (c == NULL) {
     224           0 :                 BBPunfix(g->batCacheid);
     225           0 :                 throw(MAL, "algebra.groupby", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     226             :         }
     227        2388 :         if (CMDgen_group(&bn, g, c) != GDK_SUCCEED) {
     228           0 :                 BBPunfix(g->batCacheid);
     229           0 :                 BBPunfix(c->batCacheid);
     230           0 :                 throw(MAL, "algebra.groupby", GDK_EXCEPTION);
     231             :         }
     232        2388 :         *res = bn->batCacheid;
     233        2388 :         BBPkeepref(bn);
     234        2388 :         BBPunfix(g->batCacheid);
     235        2388 :         BBPunfix(c->batCacheid);
     236        2388 :         return MAL_SUCCEED;
     237             : }
     238             : 
     239             : static str
     240           1 : ALGcard(lng *result, const bat *bid)
     241             : {
     242           1 :         BAT *b, *en;
     243             : 
     244           1 :         if ((b = BATdescriptor(*bid)) == NULL) {
     245           0 :                 throw(MAL, "algebra.card", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     246             :         }
     247           1 :         en = BATunique(b, NULL);
     248           1 :         BBPunfix(b->batCacheid);
     249           1 :         if (en == NULL) {
     250           0 :                 throw(MAL, "algebra.card", GDK_EXCEPTION);
     251             :         }
     252           1 :         struct canditer ci;
     253           1 :         canditer_init(&ci, NULL, en);
     254           1 :         *result = (lng) ci.ncand;
     255           1 :         BBPunfix(en->batCacheid);
     256           1 :         return MAL_SUCCEED;
     257             : }
     258             : 
     259             : static str
     260       87145 : ALGselect2(bat *result, const bat *bid, const bat *sid, const void *low,
     261             :                    const void *high, const bit *li, const bit *hi, const bit *anti)
     262             : {
     263       87145 :         BAT *b, *s = NULL, *bn;
     264       87145 :         const void *nilptr;
     265             : 
     266       87145 :         if ((*li != 0 && *li != 1) ||
     267       87145 :                 (*hi != 0 && *hi != 1) || (*anti != 0 && *anti != 1)) {
     268           0 :                 throw(MAL, "algebra.select", ILLEGAL_ARGUMENT);
     269             :         }
     270       87145 :         if ((b = BATdescriptor(*bid)) == NULL) {
     271           0 :                 throw(MAL, "algebra.select", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     272             :         }
     273       87141 :         if (sid && !is_bat_nil(*sid) && (s = BATdescriptor(*sid)) == NULL) {
     274           0 :                 BBPunfix(b->batCacheid);
     275           0 :                 throw(MAL, "algebra.select", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     276             :         }
     277       87139 :         derefStr(b, low);
     278       87139 :         derefStr(b, high);
     279       87139 :         nilptr = ATOMnilptr(b->ttype);
     280      174129 :         if (*li == 1 && *hi == 1 && nilptr != NULL &&
     281      109709 :                 ATOMcmp(b->ttype, low, nilptr) == 0 &&
     282       22724 :                 ATOMcmp(b->ttype, high, nilptr) == 0) {
     283             :                 /* special case: equi-select for NIL */
     284       87144 :                 high = NULL;
     285             :         }
     286       87144 :         bn = BATselect(b, s, low, high, *li, *hi, *anti);
     287       87141 :         BBPunfix(b->batCacheid);
     288       87136 :         BBPreclaim(s);
     289       87134 :         if (bn == NULL)
     290           0 :                 throw(MAL, "algebra.select", GDK_EXCEPTION);
     291       87134 :         *result = bn->batCacheid;
     292       87134 :         BBPkeepref(bn);
     293       87134 :         return MAL_SUCCEED;
     294             : }
     295             : 
     296             : static str
     297        3961 : ALGselect2nil(bat *result, const bat *bid, const bat *sid, const void *low,
     298             :                           const void *high, const bit *li, const bit *hi, const bit *anti,
     299             :                           const bit *unknown)
     300             : {
     301        3961 :         BAT *b, *s = NULL, *bn;
     302        3961 :         bit nanti = *anti, nli = *li, nhi = *hi;
     303             : 
     304        3961 :         if (!*unknown)
     305           0 :                 return ALGselect2(result, bid, sid, low, high, li, hi, anti);
     306             : 
     307        3961 :         if ((nli != 0 && nli != 1) ||
     308        3961 :                 (nhi != 0 && nhi != 1) || (nanti != 0 && nanti != 1)) {
     309           0 :                 throw(MAL, "algebra.select", ILLEGAL_ARGUMENT);
     310             :         }
     311        3961 :         if ((b = BATdescriptor(*bid)) == NULL) {
     312           0 :                 throw(MAL, "algebra.select", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     313             :         }
     314        3961 :         if (sid && !is_bat_nil(*sid) && (s = BATdescriptor(*sid)) == NULL) {
     315           0 :                 BBPunfix(b->batCacheid);
     316           0 :                 throw(MAL, "algebra.select", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     317             :         }
     318        3961 :         derefStr(b, low);
     319        3961 :         derefStr(b, high);
     320             :         /* here we don't need open ended parts with nil */
     321        3961 :         if (!nanti) {
     322         883 :                 const void *nilptr = ATOMnilptr(b->ttype);
     323         883 :                 if (nilptr) {
     324         883 :                         if (nli == 1 && ATOMcmp(b->ttype, low, nilptr) == 0) {
     325          16 :                                 low = high;
     326          16 :                                 nli = 0;
     327             :                         }
     328         884 :                         if (nhi == 1 && ATOMcmp(b->ttype, high, nilptr) == 0) {
     329          18 :                                 high = low;
     330          18 :                                 nhi = 0;
     331             :                         }
     332         885 :                         if (ATOMcmp(b->ttype, low, high) == 0 && ATOMcmp(b->ttype, high, nilptr) == 0)    /* ugh sql nil != nil */
     333        3961 :                                 nanti = 1;
     334             :                 }
     335             :         }
     336             : 
     337        3961 :         bn = BATselect(b, s, low, high, nli, nhi, nanti);
     338        3961 :         BBPunfix(b->batCacheid);
     339        3961 :         BBPreclaim(s);
     340        3960 :         if (bn == NULL)
     341           0 :                 throw(MAL, "algebra.select", GDK_EXCEPTION);
     342        3960 :         *result = bn->batCacheid;
     343        3960 :         BBPkeepref(bn);
     344        3960 :         return MAL_SUCCEED;
     345             : }
     346             : 
     347             : static str
     348       60612 : ALGselect1(bat *result, const bat *bid, const void *low, const void *high,
     349             :                    const bit *li, const bit *hi, const bit *anti)
     350             : {
     351       60612 :         return ALGselect2(result, bid, NULL, low, high, li, hi, anti);
     352             : }
     353             : 
     354             : static str
     355         272 : ALGselect1nil(bat *result, const bat *bid, const void *low, const void *high,
     356             :                           const bit *li, const bit *hi, const bit *anti, const bit *unknown)
     357             : {
     358         272 :         return ALGselect2nil(result, bid, NULL, low, high, li, hi, anti, unknown);
     359             : }
     360             : 
     361             : static str
     362      300419 : ALGthetaselect2(bat *result, const bat *bid, const bat *sid, const void *val,
     363             :                                 const char **op)
     364             : {
     365      300419 :         BAT *b, *s = NULL, *bn;
     366             : 
     367      300419 :         if ((b = BATdescriptor(*bid)) == NULL) {
     368           0 :                 throw(MAL, "algebra.thetaselect",
     369             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     370             :         }
     371      300412 :         if (sid && !is_bat_nil(*sid) && (s = BATdescriptor(*sid)) == NULL) {
     372           0 :                 BBPunfix(b->batCacheid);
     373           0 :                 throw(MAL, "algebra.thetaselect",
     374             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     375             :         }
     376      300414 :         derefStr(b, val);
     377      300414 :         bn = BATthetaselect(b, s, val, *op);
     378      300395 :         BBPunfix(b->batCacheid);
     379      300394 :         BBPreclaim(s);
     380      300386 :         if (bn == NULL)
     381           0 :                 throw(MAL, "algebra.select", GDK_EXCEPTION);
     382      300386 :         *result = bn->batCacheid;
     383      300386 :         BBPkeepref(bn);
     384      300386 :         return MAL_SUCCEED;
     385             : }
     386             : 
     387             : static str
     388         396 : ALGmarkselect(bat *r1, bat *r2, const bat *gid, const bat *mid, const bat *pid, const bit *Any)
     389             : {
     390         396 :         BAT *g = BATdescriptor(*gid); /* oid */
     391         396 :         BAT *m = BATdescriptor(*mid); /* bit, true: match, false: empty set, nil: nil on left */
     392         396 :         BAT *p = BATdescriptor(*pid); /* bit */
     393         396 :         BAT *res1 = NULL, *res2 = NULL;
     394         396 :         bit any = *Any; /* any or normal comparison semantics */
     395             : 
     396         396 :         if (!g || !m || !p) {
     397           0 :                 if (g) BBPreclaim(g);
     398           0 :                 if (m) BBPreclaim(m);
     399           0 :                 if (p) BBPreclaim(p);
     400           0 :                 throw(MAL, "algebra.markselect", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     401             :         }
     402         396 :         BUN nr = BATcount(g), q = 0;
     403             : 
     404         396 :         if ((res1 = COLnew(0, TYPE_oid, nr, TRANSIENT)) == NULL || (res2 = COLnew(0, TYPE_bit, nr, TRANSIENT)) == NULL) {
     405             :                 BBPreclaim(g);
     406           0 :                 BBPreclaim(m);
     407           0 :                 BBPreclaim(p);
     408           0 :                 if (res1) BBPreclaim(res1);
     409           0 :                 throw(MAL, "algebra.markselect", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     410             :         }
     411         396 :         assert(g->tsorted);
     412         396 :         oid *ri1 = Tloc(res1, 0);
     413         396 :         bit *ri2 = Tloc(res2, 0);
     414         396 :         bit *mi = Tloc(m, 0);
     415         396 :         bit *pi = Tloc(p, 0);
     416         396 :         oid cur = oid_nil;
     417             : 
     418         396 :         if (g->ttype == TYPE_void) { /* void case ? */
     419          31 :                 oid c = g->hseqbase;
     420         127 :                 for (BUN n = 0; n < nr; n++, c++) {
     421          96 :                         ri1[q] = c;
     422          96 :                         ri2[q] = FALSE;
     423          96 :                         if (pi[n] == TRUE && mi[n] == TRUE)
     424           7 :                                 ri2[q] = TRUE;
     425          89 :                         else if ((mi[n] == bit_nil && pi[n] != bit_nil && !any) || (mi[n] != FALSE && pi[n] == bit_nil && any))
     426           7 :                                 ri2[q] = bit_nil;
     427          96 :                         q++;
     428             :                 }
     429             :         } else {
     430         365 :                 oid *gi = Tloc(g, 0);
     431         365 :                 oid c = g->hseqbase;
     432         365 :                 if (nr)
     433         365 :                         cur = gi[0];
     434             :                 bit m = FALSE;
     435             :                 bool has_nil = false;
     436      332661 :                 for (BUN n = 0; n < nr; n++, c++) {
     437      332296 :                         if (c && cur != gi[n]) {
     438       57735 :                                 ri1[q] = c-1;
     439       57735 :                                 ri2[q] = (m == TRUE)?TRUE:(has_nil)?bit_nil:FALSE;
     440       57735 :                                 q++;
     441       57735 :                                 cur = gi[n];
     442       57735 :                                 m = FALSE;
     443       57735 :                                 has_nil = false;
     444             :                         }
     445      332296 :                         if (m == TRUE)
     446      191843 :                                 continue;
     447             : 
     448      140453 :                         if (pi[n] == TRUE && mi[n] == TRUE)
     449             :                                 m = TRUE;
     450      133526 :                         else if ((mi[n] == bit_nil && pi[n] != bit_nil && !any) || (mi[n] != FALSE && pi[n] == bit_nil && any))
     451      332296 :                                 has_nil = true;
     452             :                 }
     453         365 :                 if (nr) {
     454         365 :                         ri1[q] = c-1;
     455         365 :                         ri2[q] = (m == TRUE)?TRUE:(has_nil)?bit_nil:FALSE;
     456             :                 }
     457         365 :                 q++;
     458             :         }
     459         396 :         BATsetcount(res1, q);
     460         396 :         BATsetcount(res2, q);
     461         396 :         res1->tsorted = true;
     462         396 :         res1->tkey = true;
     463         396 :         res1->trevsorted = false;
     464         396 :         res2->tsorted = false;
     465         396 :         res2->trevsorted = false;
     466         396 :         res1->tnil = false;
     467         396 :         res1->tnonil = true;
     468         396 :         res2->tnonil = false;
     469         396 :         res2->tkey = false;
     470             : 
     471         396 :         BBPreclaim(g);
     472         396 :         BBPreclaim(m);
     473         396 :         BBPreclaim(p);
     474             : 
     475         396 :         BBPkeepref(res1);
     476         396 :         BBPkeepref(res2);
     477         396 :         *r1 = res1->batCacheid;
     478         396 :         *r2 = res2->batCacheid;
     479         396 :         return MAL_SUCCEED;
     480             : }
     481             : 
     482             : static str
     483          38 : ALGouterselect(bat *r1, bat *r2, const bat *gid, const bat *mid, const bat *pid, const bit *Any)
     484             : {
     485          38 :         BAT *g = BATdescriptor(*gid); /* oid */
     486          38 :         BAT *m = BATdescriptor(*mid); /* bit, true: match, false: empty set, nil: nil on left */
     487          38 :         BAT *p = BATdescriptor(*pid); /* bit */
     488          38 :         BAT *res1 = NULL, *res2 = NULL;
     489          38 :         bit any = *Any; /* any or normal comparison semantics */
     490             : 
     491          38 :         if (!g || !m || !p) {
     492           0 :                 if (g) BBPreclaim(g);
     493           0 :                 if (m) BBPreclaim(m);
     494           0 :                 if (p) BBPreclaim(p);
     495           0 :                 throw(MAL, "algebra.outerselect", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     496             :         }
     497          38 :         BUN nr = BATcount(g), q = 0;
     498             : 
     499          38 :         if ((res1 = COLnew(0, TYPE_oid, nr, TRANSIENT)) == NULL || (res2 = COLnew(0, TYPE_bit, nr, TRANSIENT)) == NULL) {
     500             :                 BBPreclaim(g);
     501           0 :                 BBPreclaim(m);
     502           0 :                 BBPreclaim(p);
     503           0 :                 if (res1) BBPreclaim(res1);
     504           0 :                 throw(MAL, "algebra.outerselect", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     505             :         }
     506          38 :         assert(g->tsorted);
     507          38 :         oid *ri1 = Tloc(res1, 0);
     508          38 :         bit *ri2 = Tloc(res2, 0);
     509          38 :         bit *mi = Tloc(m, 0);
     510          38 :         bit *pi = Tloc(p, 0);
     511          38 :         oid cur = oid_nil;
     512             : 
     513          38 :         if (g->ttype == TYPE_void) { /* void case ? */
     514          12 :                 oid c = g->hseqbase;
     515         101 :                 for (BUN n = 0; n < nr; n++, c++) {
     516          89 :                         ri1[q] = c;
     517         161 :                         ri2[q] = (any && (mi[n] == bit_nil || pi[n] == bit_nil))?bit_nil:(mi[n] == TRUE && pi[n] == TRUE)?TRUE:FALSE;
     518          89 :                         q++;
     519             :                 }
     520             :         } else {
     521          26 :                 oid *gi = Tloc(g, 0);
     522          26 :                 oid c = g->hseqbase;
     523          26 :                 if (nr)
     524          26 :                         cur = gi[0];
     525             :                 bool used = false;
     526         602 :                 for (BUN n = 0; n < nr; n++, c++) {
     527         576 :                         if (c && cur != gi[n]) {
     528         159 :                                 if (!used) {
     529           3 :                                         ri1[q] = c-1;
     530           3 :                                         ri2[q] = false;
     531           3 :                                         q++;
     532             :                                 }
     533         159 :                                 used = false;
     534         159 :                                 cur = gi[n];
     535             :                         }
     536         576 :                         if (mi[n] == TRUE && pi[n] == TRUE) {
     537         322 :                                 ri1[q] = c;
     538         322 :                                 ri2[q] = TRUE;
     539         322 :                                 used = true;
     540         322 :                                 q++;
     541         254 :                         } else if (mi[n] == FALSE) { /* empty */
     542          55 :                                 ri1[q] = c;
     543          55 :                                 ri2[q] = FALSE;
     544          55 :                                 used = true;
     545          55 :                                 q++;
     546         199 :                         } else if (any && (mi[n] == bit_nil /* ie has nil */ || pi[n] == bit_nil)) {
     547           6 :                                 ri1[q] = c;
     548           6 :                                 ri2[q] = bit_nil;
     549           6 :                                 used = true;
     550           6 :                                 q++;
     551             :                         }
     552             :                 }
     553          26 :                 if (nr && !used) {
     554           1 :                         ri1[q] = c-1;
     555           1 :                         ri2[q] = FALSE;
     556           1 :                         q++;
     557             :                 }
     558             :         }
     559          38 :         BATsetcount(res1, q);
     560          38 :         BATsetcount(res2, q);
     561          38 :         res1->tsorted = true;
     562          38 :         res1->tkey = true;
     563          38 :         res1->trevsorted = false;
     564          38 :         res2->tsorted = false;
     565          38 :         res2->trevsorted = false;
     566          38 :         res1->tnil = false;
     567          38 :         res1->tnonil = true;
     568          38 :         res2->tnonil = false;
     569          38 :         res2->tkey = false;
     570             : 
     571          38 :         BBPreclaim(g);
     572          38 :         BBPreclaim(m);
     573          38 :         BBPreclaim(p);
     574             : 
     575          38 :         BBPkeepref(res1);
     576          38 :         BBPkeepref(res2);
     577          38 :         *r1 = res1->batCacheid;
     578          38 :         *r2 = res2->batCacheid;
     579          38 :         return MAL_SUCCEED;
     580             : }
     581             : 
     582             : 
     583             : static str
     584        1540 : ALGselectNotNil(bat *result, const bat *bid)
     585             : {
     586        1540 :         BAT *b;
     587             : 
     588        1540 :         if ((b = BATdescriptor(*bid)) == NULL)
     589           0 :                 throw(MAL, "algebra.selectNotNil",
     590             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     591             : 
     592        1540 :         MT_lock_set(&b->theaplock);
     593        1540 :         bool bnonil = b->tnonil || b->ttype == TYPE_msk;
     594        1540 :         MT_lock_unset(&b->theaplock);
     595        1540 :         if (!bnonil) {
     596          97 :                 BAT *s;
     597          97 :                 s = BATselect(b, NULL, ATOMnilptr(b->ttype), NULL, true, true, true);
     598          97 :                 if (s) {
     599          97 :                         BAT *bn = BATproject(s, b);
     600          97 :                         BBPunfix(s->batCacheid);
     601          97 :                         if (bn) {
     602          97 :                                 BBPunfix(b->batCacheid);
     603          97 :                                 *result = bn->batCacheid;
     604          97 :                                 BBPkeepref(bn);
     605          97 :                                 return MAL_SUCCEED;
     606             :                         }
     607             :                 }
     608           0 :                 BBPunfix(b->batCacheid);
     609           0 :                 throw(MAL, "algebra.selectNotNil", GDK_EXCEPTION);
     610             :         }
     611             :         /* just pass on the result */
     612        1443 :         *result = b->batCacheid;
     613        1443 :         BBPkeepref(b);
     614        1443 :         return MAL_SUCCEED;
     615             : }
     616             : 
     617             : static str
     618      290590 : do_join(bat *r1, bat *r2, bat *r3, const bat *lid, const bat *rid, const bat *r2id, const bat *slid, const bat *srid, int op, const void *c1, const void *c2, bool li, bool hi, bool anti, bool symmetric,      /* these two only for rangejoin */
     619             :                 const bit *nil_matches, const bit *not_in, const bit *max_one,
     620             :                 const lng *estimate,
     621             :                 gdk_return (*joinfunc)(BAT **, BAT **, BAT *, BAT *, BAT *, BAT *,
     622             :                                                            bool, BUN),
     623             :                 gdk_return (*semifunc)(BAT **, BAT **, BAT *, BAT *, BAT *, BAT *,
     624             :                                                           bool, bool, BUN),
     625             :                 gdk_return (*markfunc)(BAT **, BAT **, BAT **,
     626             :                                                            BAT *, BAT *, BAT *, BAT *, BUN),
     627             :                 gdk_return (*thetafunc)(BAT **, BAT **, BAT *, BAT *, BAT *, BAT *,
     628             :                                                            int, bool, BUN),
     629             :                 gdk_return (*bandfunc)(BAT **, BAT **, BAT *, BAT *, BAT *, BAT *,
     630             :                                                           const void *, const void *, bool, bool, BUN),
     631             :                 gdk_return (*rangefunc)(BAT **, BAT **, BAT *, BAT *, BAT *,
     632             :                                                            BAT *, BAT *, bool, bool, bool, bool, BUN),
     633             :                 BAT * (*difffunc)(BAT *, BAT *, BAT *, BAT *, bool, bool, BUN),
     634             :                 BAT * (*interfunc)(BAT *, BAT *, BAT *, BAT *, bool, bool, BUN),
     635             :                 const char *funcname)
     636             : {
     637      290590 :         BAT *left = NULL, *right = NULL, *right2 = NULL;
     638      290590 :         BAT *candleft = NULL, *candright = NULL;
     639      290590 :         BAT *result1 = NULL, *result2 = NULL, *result3 = NULL;
     640      290590 :         BUN est;
     641      290590 :         const char *err = SQLSTATE(HY002) RUNTIME_OBJECT_MISSING;
     642             : 
     643      290590 :         assert(r2id == NULL || rangefunc != NULL);
     644             : 
     645      290590 :         if ((left = BATdescriptor(*lid)) == NULL)
     646           0 :                 goto fail;
     647      290586 :         if ((right = BATdescriptor(*rid)) == NULL)
     648           0 :                 goto fail;
     649      290582 :         if (slid && !is_bat_nil(*slid) && (candleft = BATdescriptor(*slid)) == NULL)
     650           0 :                 goto fail;
     651      290582 :         if (srid && !is_bat_nil(*srid)
     652           0 :                 && (candright = BATdescriptor(*srid)) == NULL)
     653           0 :                 goto fail;
     654      290582 :         if (estimate == NULL || *estimate < 0 || is_lng_nil(*estimate)
     655           0 :                 || *estimate > (lng) BUN_MAX)
     656             :                 est = BUN_NONE;
     657             :         else
     658           0 :                 est = (BUN) *estimate;
     659             : 
     660      290582 :         err = NULL;                                     /* most likely error now is GDK_EXCEPTION */
     661             : 
     662      290582 :         if (thetafunc) {
     663       16831 :                 assert(joinfunc == NULL);
     664       16831 :                 assert(semifunc == NULL);
     665       16831 :                 assert(markfunc == NULL);
     666       16831 :                 assert(bandfunc == NULL);
     667       16831 :                 assert(rangefunc == NULL);
     668       16831 :                 assert(difffunc == NULL);
     669       16831 :                 assert(interfunc == NULL);
     670       16831 :                 if ((*thetafunc)
     671             :                         (&result1, r2 ? &result2 : NULL, left, right, candleft, candright,
     672       16831 :                          op, *nil_matches, est) != GDK_SUCCEED)
     673           0 :                         goto fail;
     674      273751 :         } else if (joinfunc) {
     675      193016 :                 assert(semifunc == NULL);
     676      193016 :                 assert(markfunc == NULL);
     677      193016 :                 assert(bandfunc == NULL);
     678      193016 :                 assert(rangefunc == NULL);
     679      193016 :                 assert(difffunc == NULL);
     680      193016 :                 assert(interfunc == NULL);
     681      193016 :                 if ((*joinfunc)
     682             :                         (&result1, r2 ? &result2 : NULL, left, right, candleft, candright,
     683      193016 :                          *nil_matches, est) != GDK_SUCCEED)
     684           1 :                         goto fail;
     685       80735 :         } else if (semifunc) {
     686         331 :                 assert(markfunc == NULL);
     687         331 :                 assert(bandfunc == NULL);
     688         331 :                 assert(rangefunc == NULL);
     689         331 :                 assert(difffunc == NULL);
     690         331 :                 assert(interfunc == NULL);
     691         331 :                 if ((*semifunc)
     692             :                         (&result1, r2 ? &result2 : NULL, left, right, candleft, candright,
     693         331 :                          *nil_matches, *max_one, est) != GDK_SUCCEED)
     694          42 :                         goto fail;
     695       80404 :         } else if (markfunc) {
     696        3313 :                 assert(bandfunc == NULL);
     697        3313 :                 assert(rangefunc == NULL);
     698        3313 :                 assert(difffunc == NULL);
     699        3313 :                 assert(interfunc == NULL);
     700        6621 :                 if ((*markfunc) (&result1, r2 ? &result2 : NULL, &result3,
     701             :                                                  left, right, candleft, candright, est) != GDK_SUCCEED)
     702           0 :                         goto fail;
     703       77091 :         } else if (bandfunc) {
     704           0 :                 assert(rangefunc == NULL);
     705           0 :                 assert(difffunc == NULL);
     706           0 :                 assert(interfunc == NULL);
     707           0 :                 if ((*bandfunc)
     708             :                         (&result1, r2 ? &result2 : NULL, left, right, candleft, candright,
     709             :                          c1, c2, li, hi, est) != GDK_SUCCEED)
     710           0 :                         goto fail;
     711       77091 :         } else if (rangefunc) {
     712         129 :                 assert(difffunc == NULL);
     713         129 :                 assert(interfunc == NULL);
     714         129 :                 if ((right2 = BATdescriptor(*r2id)) == NULL) {
     715           0 :                         err = SQLSTATE(HY002) RUNTIME_OBJECT_MISSING;
     716           0 :                         goto fail;
     717             :                 }
     718         152 :                 if ((*rangefunc)
     719             :                         (&result1, r2 ? &result2 : NULL, left, right, right2, candleft,
     720             :                          candright, li, hi, anti, symmetric, est) != GDK_SUCCEED)
     721           0 :                         goto fail;
     722         129 :                 BBPunfix(right2->batCacheid);
     723       76962 :         } else if (difffunc) {
     724       71196 :                 assert(r2 == NULL);
     725       71196 :                 assert(interfunc == NULL);
     726       71196 :                 if ((result1 = (*difffunc) (left, right, candleft, candright,
     727       71196 :                                                                         *nil_matches, *not_in, est)) == NULL)
     728           0 :                         goto fail;
     729             :         } else {
     730        5766 :                 assert(r2 == NULL);
     731        5766 :                 if ((result1 = (*interfunc) (left, right, candleft, candright,
     732        5766 :                                                                          *nil_matches, *max_one, est)) == NULL)
     733           1 :                         goto fail;
     734             :         }
     735      290509 :         *r1 = result1->batCacheid;
     736      290509 :         BBPkeepref(result1);
     737      290439 :         if (r2) {
     738      173693 :                 *r2 = result2->batCacheid;
     739      173693 :                 BBPkeepref(result2);
     740             :         }
     741      290398 :         if (r3) {
     742        3313 :                 *r3 = result3->batCacheid;
     743        3313 :                 BBPkeepref(result3);
     744             :         }
     745      290398 :         BBPunfix(left->batCacheid);
     746      290442 :         BBPunfix(right->batCacheid);
     747      290478 :         BBPreclaim(candleft);
     748      290479 :         BBPreclaim(candright);
     749             :         return MAL_SUCCEED;
     750             : 
     751          44 :   fail:
     752          44 :         BBPreclaim(left);
     753          44 :         BBPreclaim(right);
     754          44 :         BBPreclaim(right2);
     755          44 :         BBPreclaim(candleft);
     756          44 :         BBPreclaim(candright);
     757          44 :         if (err == NULL)
     758          44 :                 throw(MAL, funcname, GDK_EXCEPTION);
     759           0 :         throw(MAL, funcname, "%s", err);
     760             : }
     761             : 
     762             : static str
     763      168444 : ALGjoin(bat *r1, bat *r2, const bat *lid, const bat *rid, const bat *slid,
     764             :                 const bat *srid, const bit *nil_matches, const lng *estimate)
     765             : {
     766      168444 :         return do_join(r1, r2, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     767             :                                    false, false, false, false, nil_matches, NULL, NULL,
     768             :                                    estimate, BATjoin, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
     769             :                                    "algebra.join");
     770             : }
     771             : 
     772             : static str
     773       23933 : ALGjoin1(bat *r1, const bat *lid, const bat *rid, const bat *slid,
     774             :                  const bat *srid, const bit *nil_matches, const lng *estimate)
     775             : {
     776       23933 :         return do_join(r1, NULL, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     777             :                                    false, false, false, false, nil_matches, NULL, NULL,
     778             :                                    estimate, BATjoin, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
     779             :                                    "algebra.join");
     780             : }
     781             : 
     782             : static str
     783         645 : ALGleftjoin(bat *r1, bat *r2, const bat *lid, const bat *rid, const bat *slid,
     784             :                         const bat *srid, const bit *nil_matches, const lng *estimate)
     785             : {
     786         645 :         return do_join(r1, r2, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     787             :                                    false, false, false, false, nil_matches, NULL, NULL,
     788             :                                    estimate, BATleftjoin, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
     789             :                                    "algebra.leftjoin");
     790             : }
     791             : 
     792             : static str
     793           0 : ALGleftjoin1(bat *r1, const bat *lid, const bat *rid, const bat *slid,
     794             :                          const bat *srid, const bit *nil_matches, const lng *estimate)
     795             : {
     796           0 :         return do_join(r1, NULL, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     797             :                                    false, false, false, false, nil_matches, NULL, NULL,
     798             :                                    estimate, BATleftjoin, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
     799             :                                    "algebra.leftjoin");
     800             : }
     801             : 
     802             : static str
     803         122 : ALGouterjoin(bat *r1, bat *r2, const bat *lid, const bat *rid, const bat *slid,
     804             :                          const bat *srid, const bit *nil_matches, const bit *match_one,
     805             :                          const lng *estimate)
     806             : {
     807         122 :         return do_join(r1, r2, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     808             :                                    false, false, false, false, nil_matches, NULL, match_one,
     809             :                                    estimate, NULL, BATouterjoin, NULL, NULL, NULL, NULL, NULL, NULL,
     810             :                                    "algebra.outerjoin");
     811             : }
     812             : 
     813             : static str
     814           0 : ALGouterjoin1(bat *r1, const bat *lid, const bat *rid, const bat *slid,
     815             :                           const bat *srid, const bit *nil_matches, const bit *match_one,
     816             :                           const lng *estimate)
     817             : {
     818           0 :         return do_join(r1, NULL, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     819             :                                    false, false, false, false, nil_matches, NULL, match_one,
     820             :                                    estimate, NULL, BATouterjoin, NULL, NULL, NULL, NULL, NULL, NULL,
     821             :                                    "algebra.outerjoin");
     822             : }
     823             : 
     824             : static str
     825         209 : ALGsemijoin(bat *r1, bat *r2, const bat *lid, const bat *rid, const bat *slid,
     826             :                         const bat *srid, const bit *nil_matches, const bit *max_one,
     827             :                         const lng *estimate)
     828             : {
     829         209 :         return do_join(r1, r2, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     830             :                                    false, false, false, false, nil_matches, NULL, max_one,
     831             :                                    estimate, NULL, BATsemijoin, NULL, NULL, NULL, NULL, NULL, NULL,
     832             :                                    "algebra.semijoin");
     833             : }
     834             : 
     835             : static str
     836        3308 : ALGmark2join(bat *r1, bat *r3, const bat *lid, const bat *rid,
     837             :                          const bat *slid, const bat *srid, const lng *estimate)
     838             : {
     839        3308 :         return do_join(r1, NULL, r3, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     840             :                                    false, false, false, false, NULL, NULL, NULL,
     841             :                                    estimate, NULL, NULL, BATmarkjoin, NULL, NULL, NULL, NULL, NULL,
     842             :                                    "algebra.markjoin");
     843             : }
     844             : 
     845             : static str
     846           5 : ALGmark3join(bat *r1, bat *r2, bat *r3, const bat *lid, const bat *rid,
     847             :                          const bat *slid, const bat *srid, const lng *estimate)
     848             : {
     849           5 :         return do_join(r1, r2, r3, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     850             :                                    false, false, false, false, NULL, NULL, NULL,
     851             :                                    estimate, NULL, NULL, BATmarkjoin, NULL, NULL, NULL, NULL, NULL,
     852             :                                    "algebra.markjoin");
     853             : }
     854             : 
     855             : static str
     856        4293 : ALGthetajoin(bat *r1, bat *r2, const bat *lid, const bat *rid, const bat *slid,
     857             :                          const bat *srid, const int *op, const bit *nil_matches,
     858             :                          const lng *estimate)
     859             : {
     860        4293 :         return do_join(r1, r2, NULL, lid, rid, NULL, slid, srid, *op, NULL, NULL,
     861             :                                    false, false, false, false, nil_matches, NULL, NULL,
     862             :                                    estimate, NULL, NULL, NULL, BATthetajoin, NULL, NULL, NULL, NULL,
     863             :                                    "algebra.thetajoin");
     864             : }
     865             : 
     866             : static str
     867       12538 : ALGthetajoin1(bat *r1, const bat *lid, const bat *rid, const bat *slid,
     868             :                           const bat *srid, const int *op, const bit *nil_matches,
     869             :                           const lng *estimate)
     870             : {
     871       12538 :         return do_join(r1, NULL, NULL, lid, rid, NULL, slid, srid, *op, NULL, NULL,
     872             :                                    false, false, false, false, nil_matches, NULL, NULL,
     873             :                                    estimate, NULL, NULL, NULL, BATthetajoin, NULL, NULL, NULL, NULL,
     874             :                                    "algebra.thetajoin");
     875             : }
     876             : 
     877             : static str
     878           0 : ALGbandjoin(bat *r1, bat *r2, const bat *lid, const bat *rid, const bat *slid,
     879             :                         const bat *srid, const void *c1, const void *c2, const bit *li,
     880             :                         const bit *hi, const lng *estimate)
     881             : {
     882           0 :         return do_join(r1, r2, NULL, lid, rid, NULL, slid, srid, 0, c1, c2,
     883           0 :                                    *li, *hi, false, false, NULL, NULL, NULL, estimate,
     884             :                                    NULL, NULL, NULL, NULL, BATbandjoin, NULL, NULL, NULL,
     885             :                                    "algebra.bandjoin");
     886             : }
     887             : 
     888             : static str
     889           0 : ALGbandjoin1(bat *r1, const bat *lid, const bat *rid, const bat *slid,
     890             :                          const bat *srid, const void *c1, const void *c2, const bit *li,
     891             :                          const bit *hi, const lng *estimate)
     892             : {
     893           0 :         return do_join(r1, NULL, NULL, lid, rid, NULL, slid, srid, 0, c1, c2,
     894           0 :                                    *li, *hi, false, false, NULL, NULL, NULL, estimate,
     895             :                                    NULL, NULL, NULL, NULL, BATbandjoin, NULL, NULL, NULL,
     896             :                                    "algebra.bandjoin");
     897             : }
     898             : 
     899             : static str
     900         106 : ALGrangejoin(bat *r1, bat *r2, const bat *lid, const bat *rlid, const bat *rhid,
     901             :                          const bat *slid, const bat *srid, const bit *li, const bit *hi,
     902             :                          const bit *anti, const bit *symmetric, const lng *estimate)
     903             : {
     904         212 :         return do_join(r1, r2, NULL, lid, rlid, rhid, slid, srid, 0, NULL, NULL,
     905         106 :                                    *li, *hi, *anti, *symmetric, NULL, NULL, NULL, estimate,
     906             :                                    NULL, NULL, NULL, NULL, NULL, BATrangejoin, NULL, NULL,
     907             :                                    "algebra.rangejoin");
     908             : }
     909             : 
     910             : static str
     911          23 : ALGrangejoin1(bat *r1, const bat *lid, const bat *rlid, const bat *rhid,
     912             :                           const bat *slid, const bat *srid, const bit *li, const bit *hi,
     913             :                           const bit *anti, const bit *symmetric, const lng *estimate)
     914             : {
     915          46 :         return do_join(r1, NULL, NULL, lid, rlid, rhid, slid, srid, 0, NULL, NULL,
     916          23 :                                    *li, *hi, *anti, *symmetric, NULL, NULL, NULL, estimate,
     917             :                                    NULL, NULL, NULL, NULL, NULL, BATrangejoin, NULL, NULL,
     918             :                                    "algebra.rangejoin");
     919             : }
     920             : 
     921             : static str
     922       71197 : ALGdifference(bat *r1, const bat *lid, const bat *rid, const bat *slid,
     923             :                           const bat *srid, const bit *nil_matches, const bit *not_in,
     924             :                           const lng *estimate)
     925             : {
     926       71197 :         return do_join(r1, NULL, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     927             :                                    false, false, false, false, nil_matches, not_in, NULL,
     928             :                                    estimate, NULL, NULL, NULL, NULL, NULL, NULL, BATdiff, NULL,
     929             :                                    "algebra.difference");
     930             : }
     931             : 
     932             : static str
     933        5766 : ALGintersect(bat *r1, const bat *lid, const bat *rid, const bat *slid,
     934             :                          const bat *srid, const bit *nil_matches, const bit *max_one,
     935             :                          const lng *estimate)
     936             : {
     937        5766 :         return do_join(r1, NULL, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     938             :                                    false, false, false, false, nil_matches, NULL, max_one,
     939             :                                    estimate, NULL, NULL, NULL, NULL, NULL, NULL, NULL, BATintersect,
     940             :                                    "algebra.intersect");
     941             : }
     942             : 
     943             : /* algebra.firstn(b:bat[:any],
     944             :  *                [ s:bat[:oid],
     945             :  *                [ g:bat[:oid], ] ]
     946             :  *                n:lng,
     947             :  *                asc:bit,
     948             :  *                nilslast:bit,
     949             :  *                distinct:bit)
     950             :  * returns :bat[:oid] [ , :bat[:oid] ]
     951             :  */
     952             : static str
     953        1208 : ALGfirstn(Client cntxt, MalBlkPtr mb, MalStkPtr stk, InstrPtr pci)
     954             : {
     955        1208 :         bat *ret1, *ret2 = NULL;
     956        1208 :         bat bid, sid, gid;
     957        1208 :         BAT *b, *s = NULL, *g = NULL;
     958        1208 :         BAT *bn = NULL, *gn = NULL;
     959        1208 :         lng n;
     960        1208 :         bit asc, nilslast, distinct;
     961        1208 :         gdk_return rc;
     962             : 
     963        1208 :         (void) cntxt;
     964        1208 :         (void) mb;
     965             : 
     966        1208 :         assert(pci->retc == 1 || pci->retc == 2);
     967        1208 :         assert(pci->argc - pci->retc >= 5 && pci->argc - pci->retc <= 7);
     968             : 
     969        1208 :         n = *getArgReference_lng(stk, pci, pci->argc - 4);
     970        1208 :         if (n < 0)
     971           0 :                 throw(MAL, "algebra.firstn", ILLEGAL_ARGUMENT);
     972        1208 :         if (n > (lng) BUN_MAX)
     973             :                 n = BUN_MAX;
     974        1208 :         ret1 = getArgReference_bat(stk, pci, 0);
     975        1208 :         if (pci->retc == 2)
     976         458 :                 ret2 = getArgReference_bat(stk, pci, 1);
     977        1208 :         bid = *getArgReference_bat(stk, pci, pci->retc);
     978        1208 :         if ((b = BATdescriptor(bid)) == NULL)
     979           0 :                 throw(MAL, "algebra.firstn", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     980        1208 :         if (pci->argc - pci->retc > 5) {
     981        1208 :                 sid = *getArgReference_bat(stk, pci, pci->retc + 1);
     982        1208 :                 if (!is_bat_nil(sid) && (s = BATdescriptor(sid)) == NULL) {
     983           0 :                         BBPunfix(bid);
     984           0 :                         throw(MAL, "algebra.firstn",
     985             :                                   SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     986             :                 }
     987        1208 :                 if (pci->argc - pci->retc > 6) {
     988        1208 :                         gid = *getArgReference_bat(stk, pci, pci->retc + 2);
     989        1208 :                         if (!is_bat_nil(gid) && (g = BATdescriptor(gid)) == NULL) {
     990           0 :                                 BBPunfix(bid);
     991           0 :                                 BBPunfix(sid);
     992           0 :                                 throw(MAL, "algebra.firstn",
     993             :                                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     994             :                         }
     995             :                 }
     996             :         }
     997        1208 :         asc = *getArgReference_bit(stk, pci, pci->argc - 3);
     998        1208 :         nilslast = *getArgReference_bit(stk, pci, pci->argc - 2);
     999        1208 :         distinct = *getArgReference_bit(stk, pci, pci->argc - 1);
    1000        1958 :         rc = BATfirstn(&bn, ret2 ? &gn : NULL, b, s, g, (BUN) n, asc, nilslast,
    1001             :                                    distinct);
    1002        1207 :         BBPunfix(b->batCacheid);
    1003        1208 :         BBPreclaim(s);
    1004        1208 :         BBPreclaim(g);
    1005        1208 :         if (rc != GDK_SUCCEED)
    1006           0 :                 throw(MAL, "algebra.firstn", GDK_EXCEPTION);
    1007        1208 :         *ret1 = bn->batCacheid;
    1008        1208 :         BBPkeepref(bn);
    1009        1208 :         if (ret2) {
    1010         458 :                 *ret2 = gn->batCacheid;
    1011         458 :                 BBPkeepref(gn);
    1012             :         }
    1013             :         return MAL_SUCCEED;
    1014             : }
    1015             : 
    1016             : static str
    1017           9 : ALGunary(bat *result, const bat *bid, BAT *(*func)(BAT *), const char *name)
    1018             : {
    1019           9 :         BAT *b, *bn;
    1020             : 
    1021           9 :         if ((b = BATdescriptor(*bid)) == NULL) {
    1022           0 :                 throw(MAL, name, SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1023             :         }
    1024           9 :         bn = (*func) (b);
    1025           9 :         BBPunfix(b->batCacheid);
    1026           9 :         if (bn == NULL)
    1027           0 :                 throw(MAL, name, GDK_EXCEPTION);
    1028           9 :         *result = bn->batCacheid;
    1029           9 :         BBPkeepref(bn);
    1030           9 :         return MAL_SUCCEED;
    1031             : }
    1032             : 
    1033             : static inline BAT *
    1034           9 : BATwcopy(BAT *b)
    1035             : {
    1036           9 :         return COLcopy(b, b->ttype, true, TRANSIENT);
    1037             : }
    1038             : 
    1039             : static str
    1040           9 : ALGcopy(bat *result, const bat *bid)
    1041             : {
    1042           9 :         return ALGunary(result, bid, BATwcopy, "algebra.copy");
    1043             : }
    1044             : 
    1045             : static str
    1046          74 : ALGunique(bat *result, const bat *bid, const bat *sid)
    1047             : {
    1048          74 :         BAT *b, *s = NULL, *bn = NULL;
    1049             : 
    1050          74 :         if ((b = BATdescriptor(*bid)) == NULL) {
    1051           0 :                 throw(MAL, "algebra.unique", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1052             :         }
    1053          74 :         if (sid && !is_bat_nil(*sid) && (s = BATdescriptor(*sid)) == NULL) {
    1054           0 :                 BBPunfix(b->batCacheid);
    1055           0 :                 throw(MAL, "algebra.unique", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1056             :         }
    1057          74 :         bn = BATunique(b, s);
    1058          74 :         BBPunfix(b->batCacheid);
    1059          74 :         BBPreclaim(s);
    1060          74 :         if (bn == NULL)
    1061           0 :                 throw(MAL, "algebra.unique", GDK_EXCEPTION);
    1062          74 :         *result = bn->batCacheid;
    1063          74 :         BBPkeepref(bn);
    1064          74 :         return MAL_SUCCEED;
    1065             : }
    1066             : 
    1067             : static str
    1068       26503 : ALGcrossproduct(bat *l, bat *r, const bat *left, const bat *right,
    1069             :                                 const bat *slid, const bat *srid, const bit *max_one)
    1070             : {
    1071       26503 :         BAT *L, *R, *bn1, *bn2 = NULL;
    1072       26503 :         BAT *sl = NULL, *sr = NULL;
    1073       26503 :         gdk_return ret;
    1074             : 
    1075       26503 :         L = BATdescriptor(*left);
    1076       26503 :         R = BATdescriptor(*right);
    1077       26504 :         if (L == NULL || R == NULL) {
    1078           0 :                 BBPreclaim(L);
    1079           0 :                 BBPreclaim(R);
    1080           0 :                 throw(MAL, "algebra.crossproduct",
    1081             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1082             :         }
    1083       26504 :         if ((slid && !is_bat_nil(*slid) && (sl = BATdescriptor(*slid)) == NULL) ||
    1084           0 :                 (srid && !is_bat_nil(*srid) && (sr = BATdescriptor(*srid)) == NULL)) {
    1085           0 :                 BBPunfix(L->batCacheid);
    1086           0 :                 BBPunfix(R->batCacheid);
    1087           0 :                 BBPreclaim(sl);
    1088             :                 /* sr == NULL, so no need to unfix */
    1089           0 :                 throw(MAL, "algebra.crossproduct",
    1090             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1091             :         }
    1092       27874 :         ret = BATsubcross(&bn1, r ? &bn2 : NULL, L, R, sl, sr,
    1093       26504 :                                           max_one && !is_bit_nil(*max_one) && *max_one);
    1094       26491 :         BBPunfix(L->batCacheid);
    1095       26503 :         BBPunfix(R->batCacheid);
    1096       26503 :         BBPreclaim(sl);
    1097       26503 :         BBPreclaim(sr);
    1098       26503 :         if (ret != GDK_SUCCEED)
    1099          77 :                 throw(MAL, "algebra.crossproduct", GDK_EXCEPTION);
    1100       26426 :         *l = bn1->batCacheid;
    1101       26426 :         BBPkeepref(bn1);
    1102       26423 :         if (r) {
    1103       25061 :                 *r = bn2->batCacheid;
    1104       25061 :                 BBPkeepref(bn2);
    1105             :         }
    1106             :         return MAL_SUCCEED;
    1107             : }
    1108             : 
    1109             : static str
    1110        1370 : ALGcrossproduct1(bat *l, const bat *left, const bat *right, const bit *max_one)
    1111             : {
    1112        1370 :         return ALGcrossproduct(l, NULL, left, right, NULL, NULL, max_one);
    1113             : }
    1114             : 
    1115             : static str
    1116       25133 : ALGcrossproduct2(bat *l, bat *r, const bat *left, const bat *right,
    1117             :                                  const bit *max_one)
    1118             : {
    1119       25133 :         return ALGcrossproduct(l, r, left, right, NULL, NULL, max_one);
    1120             : }
    1121             : 
    1122             : static str
    1123           0 : ALGcrossproduct3(bat *l, bat *r, const bat *left, const bat *right,
    1124             :                                  const bat *sl, const bat *sr, const bit *max_one)
    1125             : {
    1126           0 :         return ALGcrossproduct(l, r, left, right, sl, sr, max_one);
    1127             : }
    1128             : 
    1129             : static str
    1130           0 : ALGcrossproduct4(bat *l, const bat *left, const bat *right, const bat *sl,
    1131             :                                  const bat *sr, const bit *max_one)
    1132             : {
    1133           0 :         return ALGcrossproduct(l, NULL, left, right, sl, sr, max_one);
    1134             : }
    1135             : 
    1136             : static str
    1137         425 : ALGoutercrossproduct3(bat *l, bat *r, const bat *left, const bat *right, const bat *slid, const bat *srid, const bit *max_one)
    1138             : {
    1139         425 :         BAT *L, *R, *bn1, *bn2 = NULL;
    1140         425 :         BAT *sl = NULL, *sr = NULL;
    1141         425 :         gdk_return ret;
    1142             : 
    1143         425 :         L = BATdescriptor(*left);
    1144         425 :         R = BATdescriptor(*right);
    1145         425 :         if (L == NULL || R == NULL) {
    1146           0 :                 BBPreclaim(L);
    1147           0 :                 BBPreclaim(R);
    1148           0 :                 throw(MAL, "algebra.crossproduct", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1149             :         }
    1150         425 :         if ((slid && !is_bat_nil(*slid) && (sl = BATdescriptor(*slid)) == NULL) ||
    1151         425 :                 (srid && !is_bat_nil(*srid) && (sr = BATdescriptor(*srid)) == NULL)) {
    1152           0 :                 BBPunfix(L->batCacheid);
    1153           0 :                 BBPunfix(R->batCacheid);
    1154           0 :                 BBPreclaim(sl);
    1155             :                 /* sr == NULL, so no need to unfix */
    1156           0 :                 throw(MAL, "algebra.crossproduct", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1157             :         }
    1158         425 :         ret = BAToutercross(&bn1, r ? &bn2 : NULL, L, R, sl, sr,
    1159         425 :                                           max_one && !is_bit_nil(*max_one) && *max_one);
    1160         425 :         BBPunfix(L->batCacheid);
    1161         425 :         BBPunfix(R->batCacheid);
    1162         425 :         BBPreclaim(sl);
    1163         425 :         BBPreclaim(sr);
    1164         425 :         if (ret != GDK_SUCCEED)
    1165           0 :                 throw(MAL, "algebra.crossproduct", GDK_EXCEPTION);
    1166         425 :         *l = bn1->batCacheid;
    1167         425 :         BBPkeepref(bn1);
    1168         425 :         if (r) {
    1169         425 :                 *r = bn2->batCacheid;
    1170         425 :                 BBPkeepref(bn2);
    1171             :         }
    1172             :         return MAL_SUCCEED;
    1173             : }
    1174             : 
    1175             : static str
    1176     1084317 : ALGprojection2(bat *result, const bat *lid, const bat *r1id, const bat *r2id)
    1177             : {
    1178     1084317 :         BAT *l, *r1, *r2 = NULL, *bn;
    1179             : 
    1180     1084317 :         if ((l = BATdescriptor(*lid)) == NULL) {
    1181           0 :                 throw(MAL, "algebra.projection",
    1182             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1183             :         }
    1184     1084256 :         if ((r1 = BATdescriptor(*r1id)) == NULL) {
    1185           0 :                 BBPunfix(l->batCacheid);
    1186           0 :                 throw(MAL, "algebra.projection",
    1187             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1188             :         }
    1189     1084191 :         if (r2id && !is_bat_nil(*r2id) && (r2 = BATdescriptor(*r2id)) == NULL) {
    1190           0 :                 BBPunfix(l->batCacheid);
    1191           0 :                 BBPunfix(r1->batCacheid);
    1192           0 :                 throw(MAL, "algebra.projection",
    1193             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1194             :         }
    1195     1084191 :         bn = BATproject2(l, r1, r2);
    1196     1083771 :         BBPunfix(l->batCacheid);
    1197     1084121 :         BBPunfix(r1->batCacheid);
    1198     1084089 :         BBPreclaim(r2);
    1199     1084090 :         if (bn == NULL)
    1200           0 :                 throw(MAL, "algebra.projection", GDK_EXCEPTION);
    1201     1084090 :         *result = bn->batCacheid;
    1202     1084090 :         BBPkeepref(bn);
    1203     1084090 :         return MAL_SUCCEED;
    1204             : }
    1205             : 
    1206             : str
    1207     1084302 : ALGprojection(bat *result, const bat *lid, const bat *rid)
    1208             : {
    1209     1084302 :         return ALGprojection2(result, lid, rid, NULL);
    1210             : }
    1211             : 
    1212             : static str
    1213       23804 : ALGsort33(bat *result, bat *norder, bat *ngroup, const bat *bid,
    1214             :                   const bat *order, const bat *group, const bit *reverse,
    1215             :                   const bit *nilslast, const bit *stable)
    1216             : {
    1217       23804 :         BAT *bn = NULL, *on = NULL, *gn = NULL;
    1218       23804 :         BAT *b = NULL, *o = NULL, *g = NULL;
    1219             : 
    1220       23804 :         if ((b = BATdescriptor(*bid)) == NULL)
    1221           0 :                 throw(MAL, "algebra.sort", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1222       23804 :         if (order && !is_bat_nil(*order) && (o = BATdescriptor(*order)) == NULL) {
    1223           0 :                 BBPunfix(b->batCacheid);
    1224           0 :                 throw(MAL, "algebra.sort", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1225             :         }
    1226       23804 :         if (group &&!is_bat_nil(*group) && (g = BATdescriptor(*group)) == NULL) {
    1227           0 :                 BBPreclaim(o);
    1228           0 :                 BBPunfix(b->batCacheid);
    1229           0 :                 throw(MAL, "algebra.sort", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1230             :         }
    1231       27403 :         if (BATsort(result ? &bn : NULL,
    1232             :                                 norder ? &on : NULL,
    1233             :                                 ngroup ? &gn : NULL,
    1234       23804 :                                 b, o, g, *reverse, *nilslast, *stable) != GDK_SUCCEED) {
    1235           0 :                 BBPreclaim(o);
    1236           0 :                 BBPreclaim(g);
    1237           0 :                 BBPunfix(b->batCacheid);
    1238           0 :                 throw(MAL, "algebra.sort", GDK_EXCEPTION);
    1239             :         }
    1240       23804 :         BBPunfix(b->batCacheid);
    1241       23804 :         BBPreclaim(o);
    1242       23804 :         BBPreclaim(g);
    1243       23804 :         if (result) {
    1244       23804 :                 *result = bn->batCacheid;
    1245       23804 :                 BBPkeepref(bn);
    1246             :         }
    1247       23804 :         if (norder) {
    1248       20205 :                 *norder = on->batCacheid;
    1249       20205 :                 BBPkeepref(on);
    1250             :         }
    1251       23804 :         if (ngroup) {
    1252       13509 :                 *ngroup = gn->batCacheid;
    1253       13509 :                 BBPkeepref(gn);
    1254             :         }
    1255             :         return MAL_SUCCEED;
    1256             : }
    1257             : 
    1258             : static str
    1259        4036 : ALGsort32(bat *result, bat *norder, const bat *bid, const bat *order,
    1260             :                   const bat *group, const bit *reverse, const bit *nilslast,
    1261             :                   const bit *stable)
    1262             : {
    1263        4036 :         return ALGsort33(result, norder, NULL, bid, order, group, reverse, nilslast,
    1264             :                                          stable);
    1265             : }
    1266             : 
    1267             : static str
    1268        1958 : ALGsort31(bat *result, const bat *bid, const bat *order, const bat *group,
    1269             :                   const bit *reverse, const bit *nilslast, const bit *stable)
    1270             : {
    1271        1958 :         return ALGsort33(result, NULL, NULL, bid, order, group, reverse, nilslast,
    1272             :                                          stable);
    1273             : }
    1274             : 
    1275             : static str
    1276           0 : ALGsort23(bat *result, bat *norder, bat *ngroup, const bat *bid,
    1277             :                   const bat *order, const bit *reverse, const bit *nilslast,
    1278             :                   const bit *stable)
    1279             : {
    1280           0 :         return ALGsort33(result, norder, ngroup, bid, order, NULL, reverse,
    1281             :                                          nilslast, stable);
    1282             : }
    1283             : 
    1284             : static str
    1285           0 : ALGsort22(bat *result, bat *norder, const bat *bid, const bat *order,
    1286             :                   const bit *reverse, const bit *nilslast, const bit *stable)
    1287             : {
    1288           0 :         return ALGsort33(result, norder, NULL, bid, order, NULL, reverse, nilslast,
    1289             :                                          stable);
    1290             : }
    1291             : 
    1292             : static str
    1293           0 : ALGsort21(bat *result, const bat *bid, const bat *order, const bit *reverse,
    1294             :                   const bit *nilslast, const bit *stable)
    1295             : {
    1296           0 :         return ALGsort33(result, NULL, NULL, bid, order, NULL, reverse, nilslast,
    1297             :                                          stable);
    1298             : }
    1299             : 
    1300             : static str
    1301        6249 : ALGsort13(bat *result, bat *norder, bat *ngroup, const bat *bid,
    1302             :                   const bit *reverse, const bit *nilslast, const bit *stable)
    1303             : {
    1304        6249 :         return ALGsort33(result, norder, ngroup, bid, NULL, NULL, reverse, nilslast,
    1305             :                                          stable);
    1306             : }
    1307             : 
    1308             : static str
    1309        2660 : ALGsort12(bat *result, bat *norder, const bat *bid, const bit *reverse,
    1310             :                   const bit *nilslast, const bit *stable)
    1311             : {
    1312        2660 :         return ALGsort33(result, norder, NULL, bid, NULL, NULL, reverse, nilslast,
    1313             :                                          stable);
    1314             : }
    1315             : 
    1316             : static str
    1317        1641 : ALGsort11(bat *result, const bat *bid, const bit *reverse, const bit *nilslast,
    1318             :                   const bit *stable)
    1319             : {
    1320        1641 :         return ALGsort33(result, NULL, NULL, bid, NULL, NULL, reverse, nilslast,
    1321             :                                          stable);
    1322             : }
    1323             : 
    1324             : static str
    1325       69528 : ALGcountCND_nil(lng *result, const bat *bid, const bat *cnd,
    1326             :                                 const bit *ignore_nils)
    1327             : {
    1328       69528 :         BAT *b, *s = NULL;
    1329             : 
    1330       69528 :         if ((b = BATdescriptor(*bid)) == NULL) {
    1331           0 :                 throw(MAL, "aggr.count", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1332             :         }
    1333       69528 :         if (cnd && !is_bat_nil(*cnd) && (s = BATdescriptor(*cnd)) == NULL) {
    1334           0 :                 BBPunfix(b->batCacheid);
    1335           0 :                 throw(MAL, "aggr.count", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1336             :         }
    1337       69528 :         if (b->ttype == TYPE_msk || mask_cand(b)) {
    1338          30 :                 BATsum(result, TYPE_lng, b, s, *ignore_nils, false);
    1339       69498 :         } else if (*ignore_nils) {
    1340        1723 :                 *result = (lng) BATcount_no_nil(b, s);
    1341             :         } else {
    1342       67775 :                 struct canditer ci;
    1343       67775 :                 canditer_init(&ci, b, s);
    1344       67774 :                 *result = (lng) ci.ncand;
    1345             :         }
    1346       69527 :         BBPreclaim(s);
    1347       69527 :         BBPunfix(b->batCacheid);
    1348       69527 :         return MAL_SUCCEED;
    1349             : }
    1350             : 
    1351             : static str
    1352        1723 : ALGcount_nil(lng *result, const bat *bid, const bit *ignore_nils)
    1353             : {
    1354        1723 :         return ALGcountCND_nil(result, bid, NULL, ignore_nils);
    1355             : }
    1356             : 
    1357             : static str
    1358           0 : ALGcountCND_bat(lng *result, const bat *bid, const bat *cnd)
    1359             : {
    1360           0 :         return ALGcountCND_nil(result, bid, cnd, &(bit) { 0 });
    1361             : }
    1362             : 
    1363             : static str
    1364       67805 : ALGcount_bat(lng *result, const bat *bid)
    1365             : {
    1366       67805 :         return ALGcountCND_nil(result, bid, NULL, &(bit) { 0 });
    1367             : }
    1368             : 
    1369             : static str
    1370           0 : ALGcountCND_no_nil(lng *result, const bat *bid, const bat *cnd)
    1371             : {
    1372           0 :         return ALGcountCND_nil(result, bid, cnd, &(bit) { 1 });
    1373             : }
    1374             : 
    1375             : static str
    1376           0 : ALGcount_no_nil(lng *result, const bat *bid)
    1377             : {
    1378           0 :         return ALGcountCND_nil(result, bid, NULL, &(bit) { 1 });
    1379             : }
    1380             : 
    1381             : static str
    1382           6 : ALGslice(bat *ret, const bat *bid, const lng *start, const lng *end)
    1383             : {
    1384           6 :         BAT *b, *bn = NULL;
    1385             : 
    1386           6 :         if ((b = BATdescriptor(*bid)) == NULL) {
    1387           0 :                 throw(MAL, "algebra.slice", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1388             :         }
    1389           6 :         if (slice(&bn, b, *start, *end) == GDK_SUCCEED) {
    1390           6 :                 *ret = bn->batCacheid;
    1391           6 :                 BBPkeepref(bn);
    1392           6 :                 BBPunfix(b->batCacheid);
    1393           6 :                 return MAL_SUCCEED;
    1394             :         }
    1395           0 :         BBPunfix(b->batCacheid);
    1396           0 :         throw(MAL, "algebra.slice", GDK_EXCEPTION);
    1397             : }
    1398             : 
    1399             : static str
    1400           1 : ALGslice_int(bat *ret, const bat *bid, const int *start, const int *end)
    1401             : {
    1402           1 :         lng s = *start;
    1403           1 :         lng e = (is_int_nil(*end) ? lng_nil : *end);
    1404             : 
    1405           1 :         return ALGslice(ret, bid, &s, &e);
    1406             : }
    1407             : 
    1408             : static str
    1409           0 : ALGslice_lng(bat *ret, const bat *bid, const lng *start, const lng *end)
    1410             : {
    1411           0 :         lng s = *start;
    1412           0 :         lng e = *end;
    1413             : 
    1414           0 :         return ALGslice(ret, bid, &s, &e);
    1415             : }
    1416             : 
    1417             : /* carve out a slice based on the OIDs */
    1418             : /* beware that BATs may have different OID bases */
    1419             : static str
    1420           5 : ALGslice_oid(bat *ret, const bat *bid, const oid *start, const oid *end)
    1421             : {
    1422           5 :         lng s = (lng) (is_oid_nil(*start) ? 0 : (lng) *start);
    1423           5 :         lng e = (is_oid_nil(*end) ? lng_nil : (lng) *end);
    1424             : 
    1425           5 :         return ALGslice(ret, bid, &s, &e);
    1426             : }
    1427             : 
    1428             : static str
    1429       17138 : ALGsubslice_lng(bat *ret, const bat *bid, const lng *start, const lng *end)
    1430             : {
    1431       17138 :         BAT *b, *bn;
    1432       17138 :         BUN s, e;
    1433             : 
    1434       17138 :         if (*start < 0 || (*end < 0 && !is_lng_nil(*end)))
    1435           0 :                 throw(MAL, "algebra.subslice", ILLEGAL_ARGUMENT);
    1436       17138 :         if ((b = BBPquickdesc(*bid)) == NULL)
    1437           0 :                 throw(MAL, "algebra.subslice", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1438       17138 :         s = (BUN) *start;
    1439       17138 :         if (s > BATcount(b))
    1440             :                 s = BATcount(b);
    1441       17138 :         e = is_lng_nil(*end) ? BATcount(b) : (BUN) *end + 1;
    1442       17138 :         if (e > BATcount(b))
    1443             :                 e = BATcount(b);
    1444       17138 :         if (e < s)
    1445             :                 e = s;
    1446       17138 :         bn = BATdense(0, b->hseqbase + s, e - s);
    1447       17138 :         if (bn == NULL)
    1448           0 :                 throw(MAL, "algebra.subslice", SQLSTATE(HY013) MAL_MALLOC_FAIL);
    1449       17138 :         *ret = bn->batCacheid;
    1450       17138 :         BBPkeepref(bn);
    1451       17138 :         return MAL_SUCCEED;
    1452             : }
    1453             : 
    1454             : /*
    1455             :  * BUN Get/Fetch
    1456             :  */
    1457             : 
    1458             : static str
    1459       88510 : doALGfetch(ptr ret, BAT *b, BUN pos)
    1460             : {
    1461       88510 :         assert(pos <= BUN_MAX);
    1462       88510 :         BATiter bi = bat_iterator(b);
    1463       88510 :         if (ATOMextern(b->ttype)) {
    1464         190 :                 ptr _src = BUNtail(bi, pos);
    1465         190 :                 size_t _len = ATOMlen(b->ttype, _src);
    1466         190 :                 ptr _dst = GDKmalloc(_len);
    1467         190 :                 if (_dst == NULL) {
    1468           0 :                         bat_iterator_end(&bi);
    1469           0 :                         throw(MAL, "doAlgFetch", SQLSTATE(HY013) MAL_MALLOC_FAIL);
    1470             :                 }
    1471         190 :                 memcpy(_dst, _src, _len);
    1472         190 :                 *(ptr *) ret = _dst;
    1473             :         } else {
    1474       88320 :                 size_t _s = ATOMsize(ATOMtype(b->ttype));
    1475       88320 :                 if (b->ttype == TYPE_void) {
    1476           0 :                         *(oid *) ret = b->tseqbase;
    1477           0 :                         if (!is_oid_nil(b->tseqbase))
    1478           0 :                                 *(oid *) ret += pos;
    1479       88320 :                 } else if (_s == 4) {
    1480       88233 :                         *(int *) ret = ((int *) bi.base)[pos];
    1481             :                 } else if (_s == 1) {
    1482          11 :                         *(bte *) ret = ((bte *) bi.base)[pos];
    1483             :                 } else if (_s == 2) {
    1484           1 :                         *(sht *) ret = ((sht *) bi.base)[pos];
    1485             :                 } else if (_s == 8) {
    1486          75 :                         *(lng *) ret = ((lng *) bi.base)[pos];
    1487             : #ifdef HAVE_HGE
    1488             :                 } else if (_s == 16) {
    1489           0 :                         *(hge *) ret = ((hge *) bi.base)[pos];
    1490             : #endif
    1491             :                 } else {
    1492           0 :                         memcpy(ret, (const char *) bi.base + (pos << bi.shift), _s);
    1493             :                 }
    1494             :         }
    1495       88510 :         bat_iterator_end(&bi);
    1496       88510 :         return MAL_SUCCEED;
    1497             : }
    1498             : 
    1499             : static str
    1500       88512 : ALGfetch(ptr ret, const bat *bid, const lng *pos)
    1501             : {
    1502       88512 :         BAT *b;
    1503       88512 :         str msg;
    1504             : 
    1505       88512 :         if ((b = BATdescriptor(*bid)) == NULL) {
    1506           0 :                 throw(MAL, "algebra.fetch", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1507             :         }
    1508       88512 :         if (*pos < (lng) 0) {
    1509           0 :                 BBPunfix(b->batCacheid);
    1510           0 :                 throw(MAL, "algebra.fetch",
    1511             :                           ILLEGAL_ARGUMENT ": row index to fetch must be non negative\n");
    1512             :         }
    1513       88512 :         if (BATcount(b) == 0) {
    1514           2 :                 BBPunfix(b->batCacheid);
    1515           2 :                 throw(MAL, "algebra.fetch",
    1516             :                           ILLEGAL_ARGUMENT
    1517             :                           ": cannot fetch a single row from an empty input\n");
    1518             :         }
    1519       88510 :         if (*pos >= (lng) BATcount(b)) {
    1520           0 :                 BBPunfix(b->batCacheid);
    1521           0 :                 throw(MAL, "algebra.fetch",
    1522             :                           ILLEGAL_ARGUMENT ": row index to fetch is out of range\n");
    1523             :         }
    1524       88510 :         msg = doALGfetch(ret, b, (BUN) *pos);
    1525       88510 :         BBPunfix(b->batCacheid);
    1526       88510 :         return msg;
    1527             : }
    1528             : 
    1529             : str
    1530       88512 : ALGfetchoid(ptr ret, const bat *bid, const oid *pos)
    1531             : {
    1532       88512 :         lng o = *pos;
    1533             : 
    1534       88512 :         return ALGfetch(ret, bid, &o);
    1535             : }
    1536             : 
    1537             : static str
    1538           0 : ALGexist(bit *ret, const bat *bid, const void *val)
    1539             : {
    1540           0 :         BAT *b;
    1541           0 :         BUN q;
    1542             : 
    1543           0 :         if ((b = BATdescriptor(*bid)) == NULL) {
    1544           0 :                 throw(MAL, "algebra.exist", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1545             :         }
    1546           0 :         derefStr(b, val);
    1547           0 :         q = BUNfnd(b, val);
    1548           0 :         *ret = (q != BUN_NONE);
    1549           0 :         BBPunfix(b->batCacheid);
    1550           0 :         return MAL_SUCCEED;
    1551             : }
    1552             : 
    1553             : static str
    1554           9 : ALGfind(oid *ret, const bat *bid, ptr val)
    1555             : {
    1556           9 :         BAT *b;
    1557           9 :         BUN q;
    1558           9 :         str msg = MAL_SUCCEED;
    1559             : 
    1560           9 :         if ((b = BATdescriptor(*bid)) == NULL) {
    1561           0 :                 throw(MAL, "algebra.find", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1562             :         }
    1563           9 :         derefStr(b, val);
    1564           9 :         q = BUNfnd(b, val);
    1565             : 
    1566           9 :         if (q == BUN_NONE) {
    1567           3 :                 *ret = oid_nil;
    1568             :         } else
    1569           6 :                 *ret = (oid) q;
    1570           9 :         BBPunfix(b->batCacheid);
    1571           9 :         return msg;
    1572             : }
    1573             : 
    1574             : 
    1575             : static str
    1576      141899 : ALGprojecttail(Client cntxt, MalBlkPtr mb, MalStkPtr stk, InstrPtr pci)
    1577             : {
    1578      141899 :         bat *ret = getArgReference_bat(stk, pci, 0);
    1579      141899 :         bat bid = *getArgReference_bat(stk, pci, 1);
    1580      141899 :         const ValRecord *v = &stk->stk[getArg(pci, 2)];
    1581      141899 :         BAT *b, *bn;
    1582             : 
    1583      141899 :         (void) cntxt;
    1584      141899 :         (void) mb;
    1585      141899 :         if (isaBatType(getArgType(mb, pci, 2)))
    1586           0 :                 throw(MAL, "algebra.project", "Scalar value expected");
    1587      141899 :         if ((b = BBPquickdesc(bid)) == NULL)
    1588           0 :                 throw(MAL, "algebra.project", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1589      141885 :         bn = BATconstant(b->hseqbase, v->vtype, VALptr(v), BATcount(b), TRANSIENT);
    1590      141884 :         if (bn == NULL) {
    1591           0 :                 *ret = bat_nil;
    1592           0 :                 throw(MAL, "algebra.project", SQLSTATE(HY013) MAL_MALLOC_FAIL);
    1593             :         }
    1594      141884 :         *ret = bn->batCacheid;
    1595      141884 :         BBPkeepref(bn);
    1596      141884 :         return MAL_SUCCEED;
    1597             : }
    1598             : 
    1599             : 
    1600             : static str
    1601           0 : ALGreuse(bat *ret, const bat *bid)
    1602             : {
    1603           0 :         BAT *b, *bn;
    1604           0 :         if ((b = BATdescriptor(*bid)) == NULL)
    1605           0 :                 throw(MAL, "algebra.reuse", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1606             : 
    1607           0 :         if (!b->batTransient || b->batRestricted != BAT_WRITE) {
    1608           0 :                 if (ATOMvarsized(b->ttype)) {
    1609           0 :                         bn = BATwcopy(b);
    1610           0 :                         if (bn == NULL) {
    1611           0 :                                 BBPunfix(b->batCacheid);
    1612           0 :                                 throw(MAL, "algebra.reuse", SQLSTATE(HY013) MAL_MALLOC_FAIL);
    1613             :                         }
    1614             :                 } else {
    1615           0 :                         bn = COLnew(b->hseqbase, b->ttype, BATcount(b), TRANSIENT);
    1616           0 :                         if (bn == NULL) {
    1617           0 :                                 BBPunfix(b->batCacheid);
    1618           0 :                                 throw(MAL, "algebra.reuse", SQLSTATE(HY013) MAL_MALLOC_FAIL);
    1619             :                         }
    1620           0 :                         BATsetcount(bn, BATcount(b));
    1621           0 :                         bn->tsorted = false;
    1622           0 :                         bn->trevsorted = false;
    1623           0 :                         BATkey(bn, false);
    1624             :                 }
    1625           0 :                 *ret = bn->batCacheid;
    1626           0 :                 BBPkeepref(bn);
    1627           0 :                 BBPunfix(b->batCacheid);
    1628             :         } else
    1629           0 :                 BBPkeepref(b);
    1630             :         return MAL_SUCCEED;
    1631             : }
    1632             : 
    1633             : /*
    1634             :  * BAT standard deviation
    1635             :  */
    1636             : static str
    1637           7 : ALGstdev(dbl *res, const bat *bid)
    1638             : {
    1639           7 :         BAT *b;
    1640           7 :         dbl stdev;
    1641             : 
    1642           7 :         if ((b = BATdescriptor(*bid)) == NULL)
    1643           0 :                 throw(MAL, "aggr.stdev", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1644           7 :         stdev = BATcalcstdev_sample(NULL, b);
    1645           7 :         BBPunfix(b->batCacheid);
    1646           7 :         if (is_dbl_nil(stdev) && GDKerrbuf && GDKerrbuf[0])
    1647           0 :                 throw(MAL, "aggr.stdev", GDK_EXCEPTION);
    1648           7 :         *res = stdev;
    1649           7 :         return MAL_SUCCEED;
    1650             : }
    1651             : 
    1652             : static str
    1653          13 : ALGstdevp(dbl *res, const bat *bid)
    1654             : {
    1655          13 :         BAT *b;
    1656          13 :         dbl stdev;
    1657             : 
    1658          13 :         if ((b = BATdescriptor(*bid)) == NULL)
    1659           0 :                 throw(MAL, "aggr.stdevp", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1660          13 :         stdev = BATcalcstdev_population(NULL, b);
    1661          13 :         BBPunfix(b->batCacheid);
    1662          13 :         if (is_dbl_nil(stdev) && GDKerrbuf && GDKerrbuf[0])
    1663           1 :                 throw(MAL, "aggr.stdevp", GDK_EXCEPTION);
    1664          12 :         *res = stdev;
    1665          12 :         return MAL_SUCCEED;
    1666             : }
    1667             : 
    1668             : /*
    1669             :  * BAT variance
    1670             :  */
    1671             : static str
    1672           2 : ALGvariance(dbl *res, const bat *bid)
    1673             : {
    1674           2 :         BAT *b;
    1675           2 :         dbl variance;
    1676             : 
    1677           2 :         if ((b = BATdescriptor(*bid)) == NULL)
    1678           0 :                 throw(MAL, "aggr.variance", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1679           2 :         variance = BATcalcvariance_sample(NULL, b);
    1680           2 :         BBPunfix(b->batCacheid);
    1681           2 :         if (is_dbl_nil(variance) && GDKerrbuf && GDKerrbuf[0])
    1682           0 :                 throw(MAL, "aggr.variance", GDK_EXCEPTION);
    1683           2 :         *res = variance;
    1684           2 :         return MAL_SUCCEED;
    1685             : }
    1686             : 
    1687             : static str
    1688           5 : ALGvariancep(dbl *res, const bat *bid)
    1689             : {
    1690           5 :         BAT *b;
    1691           5 :         dbl variance;
    1692             : 
    1693           5 :         if ((b = BATdescriptor(*bid)) == NULL)
    1694           0 :                 throw(MAL, "aggr.variancep", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1695           5 :         variance = BATcalcvariance_population(NULL, b);
    1696           5 :         BBPunfix(b->batCacheid);
    1697           5 :         if (is_dbl_nil(variance) && GDKerrbuf && GDKerrbuf[0])
    1698           1 :                 throw(MAL, "aggr.variancep", GDK_EXCEPTION);
    1699           4 :         *res = variance;
    1700           4 :         return MAL_SUCCEED;
    1701             : }
    1702             : 
    1703             : /*
    1704             :  * BAT covariance
    1705             :  */
    1706             : static str
    1707           5 : ALGcovariance(dbl *res, const bat *bid1, const bat *bid2)
    1708             : {
    1709           5 :         BAT *b1, *b2;
    1710           5 :         dbl covariance;
    1711             : 
    1712           5 :         if ((b1 = BATdescriptor(*bid1)) == NULL)
    1713           0 :                 throw(MAL, "aggr.covariance", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1714           5 :         if ((b2 = BATdescriptor(*bid2)) == NULL) {
    1715           0 :                 BBPunfix(b1->batCacheid);
    1716           0 :                 throw(MAL, "aggr.covariance", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1717             :         }
    1718             : 
    1719           5 :         covariance = BATcalccovariance_sample(b1, b2);
    1720           5 :         BBPunfix(b1->batCacheid);
    1721           5 :         BBPunfix(b2->batCacheid);
    1722           5 :         if (is_dbl_nil(covariance) && GDKerrbuf && GDKerrbuf[0])
    1723           0 :                 throw(MAL, "aggr.covariance", GDK_EXCEPTION);
    1724           5 :         *res = covariance;
    1725           5 :         return MAL_SUCCEED;
    1726             : }
    1727             : 
    1728             : static str
    1729           9 : ALGcovariancep(dbl *res, const bat *bid1, const bat *bid2)
    1730             : {
    1731           9 :         BAT *b1, *b2;
    1732           9 :         dbl covariance;
    1733             : 
    1734           9 :         if ((b1 = BATdescriptor(*bid1)) == NULL)
    1735           0 :                 throw(MAL, "aggr.covariancep", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1736           9 :         if ((b2 = BATdescriptor(*bid2)) == NULL) {
    1737           0 :                 BBPunfix(b1->batCacheid);
    1738           0 :                 throw(MAL, "aggr.covariancep", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1739             :         }
    1740             : 
    1741           9 :         covariance = BATcalccovariance_population(b1, b2);
    1742           9 :         BBPunfix(b1->batCacheid);
    1743           9 :         BBPunfix(b2->batCacheid);
    1744           9 :         if (is_dbl_nil(covariance) && GDKerrbuf && GDKerrbuf[0])
    1745           1 :                 throw(MAL, "aggr.covariancep", GDK_EXCEPTION);
    1746           8 :         *res = covariance;
    1747           8 :         return MAL_SUCCEED;
    1748             : }
    1749             : 
    1750             : /*
    1751             :  * BAT correlation
    1752             :  */
    1753             : static str
    1754          19 : ALGcorr(dbl *res, const bat *bid1, const bat *bid2)
    1755             : {
    1756          19 :         BAT *b1, *b2;
    1757          19 :         dbl covariance;
    1758             : 
    1759          19 :         if ((b1 = BATdescriptor(*bid1)) == NULL)
    1760           0 :                 throw(MAL, "aggr.corr", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1761          19 :         if ((b2 = BATdescriptor(*bid2)) == NULL) {
    1762           0 :                 BBPunfix(b1->batCacheid);
    1763           0 :                 throw(MAL, "aggr.corr", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1764             :         }
    1765             : 
    1766          19 :         covariance = BATcalccorrelation(b1, b2);
    1767          19 :         BBPunfix(b1->batCacheid);
    1768          19 :         BBPunfix(b2->batCacheid);
    1769          19 :         if (is_dbl_nil(covariance) && GDKerrbuf && GDKerrbuf[0])
    1770           1 :                 throw(MAL, "aggr.corr", GDK_EXCEPTION);
    1771          18 :         *res = covariance;
    1772          18 :         return MAL_SUCCEED;
    1773             : }
    1774             : 
    1775             : #include "mel.h"
    1776             : mel_func algebra_init_funcs[] = {
    1777             :  command("algebra", "groupby", ALGgroupby, false, "Produces a new BAT with groups identified by the head column. The result contains tail times the head value, ie the tail contains the result group sizes.", args(1,3, batarg("",oid),batarg("gids",oid),batarg("cnts",lng))),
    1778             :  command("algebra", "find", ALGfind, false, "Returns the index position of a value.  If no such BUN exists return OID-nil.", args(1,3, arg("",oid),batargany("b",1),argany("t",1))),
    1779             :  command("algebra", "fetch", ALGfetchoid, false, "Returns the value of the BUN at x-th position with 0 <= x < b.count", args(1,3, argany("",1),batargany("b",1),arg("x",oid))),
    1780             :  pattern("algebra", "project", ALGprojecttail, false, "Fill the tail with a constant", args(1,3, batargany("",2),batargany("b",1),argany("v",2))),
    1781             :  command("algebra", "projection", ALGprojection, false, "Project left input onto right input.", args(1,3, batargany("",1),batarg("left",oid),batargany("right",1))),
    1782             :  command("algebra", "projection", ALGprojection2, false, "Project left input onto right inputs which should be consecutive.", args(1,4, batargany("",1),batarg("left",oid),batargany("right1",1),batargany("right2",1))),
    1783             :  command("algebra", "copy", ALGcopy, false, "Returns physical copy of a BAT.", args(1,2, batargany("",1),batargany("b",1))),
    1784             :  command("algebra", "exist", ALGexist, false, "Returns whether 'val' occurs in b.", args(1,3, arg("",bit),batargany("b",1),argany("val",1))),
    1785             :  command("algebra", "select", ALGselect1, false, "Select all head values for which the tail value is in range.\nInput is a dense-headed BAT, output is a dense-headed BAT with in\nthe tail the head value of the input BAT for which the tail value\nis between the values low and high (inclusive if li respectively\nhi is set).  The output BAT is sorted on the tail value.  If low\nor high is nil, the boundary is not considered (effectively - and\n+ infinity).  If anti is set, the result is the complement.  Nil\nvalues in the tail are never matched, unless low=nil, high=nil,\nli=1, hi=1, anti=0.  All non-nil values are returned if low=nil,\nhigh=nil, and li, hi are not both 1, or anti=1.\nNote that the output is suitable as second input for the other\nversion of this function.", args(1,7, batarg("",oid),batargany("b",1),argany("low",1),argany("high",1),arg("li",bit),arg("hi",bit),arg("anti",bit))),
    1786             :  command("algebra", "select", ALGselect2, false, "Select all head values of the first input BAT for which the tail value\nis in range and for which the head value occurs in the tail of the\nsecond input BAT.\nThe first input is a dense-headed BAT, the second input is a\ndense-headed BAT with sorted tail, output is a dense-headed BAT\nwith in the tail the head value of the input BAT for which the\ntail value is between the values low and high (inclusive if li\nrespectively hi is set).  The output BAT is sorted on the tail\nvalue.  If low or high is nil, the boundary is not considered\n(effectively - and + infinity).  If anti is set, the result is the\ncomplement.  Nil values in the tail are never matched, unless\nlow=nil, high=nil, li=1, hi=1, anti=0.  All non-nil values are\nreturned if low=nil, high=nil, and li, hi are not both 1, or anti=1.\nNote that the output is suitable as second input for this\nfunction.", args(1,8, batarg("",oid),batargany("b",1),batarg("s",oid),argany("low",1),argany("high",1),arg("li",bit),arg("hi",bit),arg("anti",bit))),
    1787             :  command("algebra", "select", ALGselect1nil, false, "With unknown set, each nil != nil", args(1,8, batarg("",oid),batargany("b",1),argany("low",1),argany("high",1),arg("li",bit),arg("hi",bit),arg("anti",bit),arg("unknown",bit))),
    1788             :  command("algebra", "select", ALGselect2nil, false, "With unknown set, each nil != nil", args(1,9, batarg("",oid),batargany("b",1),batarg("s",oid),argany("low",1),argany("high",1),arg("li",bit),arg("hi",bit),arg("anti",bit),arg("unknown",bit))),
    1789             :  command("algebra", "thetaselect", ALGthetaselect2, false, "Select all head values of the first input BAT for which the tail value\nobeys the relation value OP VAL and for which the head value occurs in\nthe tail of the second input BAT.\nInput is a dense-headed BAT, output is a dense-headed BAT with in\nthe tail the head value of the input BAT for which the\nrelationship holds.  The output BAT is sorted on the tail value.", args(1,5, batarg("",oid),batargany("b",1),batarg("s",oid),argany("val",1),arg("op",str))),
    1790             :  command("algebra", "markselect", ALGmarkselect, false, "Group on group-ids, return aggregated anyequal or allnotequal", args(2,6, batarg("",oid), batarg("", bit), batarg("gid",oid), batarg("m", bit), batarg("p", bit), arg("any", bit))),
    1791             :  command("algebra", "outerselect", ALGouterselect, false, "Per input lid return at least one row, if none of the predicates (p) hold, return a nil, else 'all' true cases.", args(2,6, batarg("",oid), batarg("", bit), batarg("lid", oid), batarg("rid", bit), batarg("predicate", bit), arg("any", bit))),
    1792             :  command("algebra", "selectNotNil", ALGselectNotNil, false, "Select all not-nil values", args(1,2, batargany("",1),batargany("b",1))),
    1793             :  command("algebra", "sort", ALGsort11, false, "Returns a copy of the BAT sorted on tail values.\nThe order is descending if the reverse bit is set.\nThis is a stable sort if the stable bit is set.", args(1,5, batargany("",1),batargany("b",1),arg("reverse",bit),arg("nilslast",bit),arg("stable",bit))),
    1794             :  command("algebra", "sort", ALGsort12, false, "Returns a copy of the BAT sorted on tail values and a BAT that\nspecifies how the input was reordered.\nThe order is descending if the reverse bit is set.\nThis is a stable sort if the stable bit is set.", args(2,6, batargany("",1),batarg("",oid),batargany("b",1),arg("reverse",bit),arg("nilslast",bit),arg("stable",bit))),
    1795             :  command("algebra", "sort", ALGsort13, false, "Returns a copy of the BAT sorted on tail values, a BAT that specifies\nhow the input was reordered, and a BAT with group information.\nThe order is descending if the reverse bit is set.\nThis is a stable sort if the stable bit is set.", args(3,7, batargany("",1),batarg("",oid),batarg("",oid),batargany("b",1),arg("reverse",bit),arg("nilslast",bit),arg("stable",bit))),
    1796             :  command("algebra", "sort", ALGsort21, false, "Returns a copy of the BAT sorted on tail values.\nThe order is descending if the reverse bit is set.\nThis is a stable sort if the stable bit is set.", args(1,6, batargany("",1),batargany("b",1),batarg("o",oid),arg("reverse",bit),arg("nilslast",bit),arg("stable",bit))),
    1797             :  command("algebra", "sort", ALGsort22, false, "Returns a copy of the BAT sorted on tail values and a BAT that\nspecifies how the input was reordered.\nThe order is descending if the reverse bit is set.\nThis is a stable sort if the stable bit is set.", args(2,7, batargany("",1),batarg("",oid),batargany("b",1),batarg("o",oid),arg("reverse",bit),arg("nilslast",bit),arg("stable",bit))),
    1798             :  command("algebra", "sort", ALGsort23, false, "Returns a copy of the BAT sorted on tail values, a BAT that specifies\nhow the input was reordered, and a BAT with group information.\nThe order is descending if the reverse bit is set.\nThis is a stable sort if the stable bit is set.", args(3,8, batargany("",1),batarg("",oid),batarg("",oid),batargany("b",1),batarg("o",oid),arg("reverse",bit),arg("nilslast",bit),arg("stable",bit))),
    1799             :  command("algebra", "sort", ALGsort31, false, "Returns a copy of the BAT sorted on tail values.\nThe order is descending if the reverse bit is set.\nThis is a stable sort if the stable bit is set.", args(1,7, batargany("",1),batargany("b",1),batarg("o",oid),batarg("g",oid),arg("reverse",bit),arg("nilslast",bit),arg("stable",bit))),
    1800             :  command("algebra", "sort", ALGsort32, false, "Returns a copy of the BAT sorted on tail values and a BAT that\nspecifies how the input was reordered.\nThe order is descending if the reverse bit is set.\nThis is a stable sort if the stable bit is set.", args(2,8, batargany("",1),batarg("",oid),batargany("b",1),batarg("o",oid),batarg("g",oid),arg("reverse",bit),arg("nilslast",bit),arg("stable",bit))),
    1801             :  command("algebra", "sort", ALGsort33, false, "Returns a copy of the BAT sorted on tail values, a BAT that specifies\nhow the input was reordered, and a BAT with group information.\nThe order is descending if the reverse bit is set.\nThis is a stable sort if the stable bit is set.", args(3,9, batargany("",1),batarg("",oid),batarg("",oid),batargany("b",1),batarg("o",oid),batarg("g",oid),arg("reverse",bit),arg("nilslast",bit),arg("stable",bit))),
    1802             :  command("algebra", "unique", ALGunique, false, "Select all unique values from the tail of the first input.\nInput is a dense-headed BAT, the second input is a\ndense-headed BAT with sorted tail, output is a dense-headed\nBAT with in the tail the head value of the input BAT that was\nselected.  The output BAT is sorted on the tail value.  The\nsecond input BAT is a list of candidates.", args(1,3, batarg("",oid),batargany("b",1),batarg("s",oid))),
    1803             :  command("algebra", "crossproduct", ALGcrossproduct2, false, "Returns 2 columns with all BUNs, consisting of the head-oids\nfrom 'left' and 'right' for which there are BUNs in 'left'\nand 'right' with equal tails", args(2,5, batarg("l",oid),batarg("r",oid),batargany("left",1),batargany("right",2),arg("max_one",bit))),
    1804             :  command("algebra", "crossproduct", ALGcrossproduct1, false, "Compute the cross product of both input bats; but only produce left output", args(1,4, batarg("",oid),batargany("left",1),batargany("right",2),arg("max_one",bit))),
    1805             :  command("algebra", "crossproduct", ALGcrossproduct3, false, "Compute the cross product of both input bats", args(2,7, batarg("l",oid),batarg("r",oid),batargany("left",1),batargany("right",2),batarg("sl",oid),batarg("sr",oid),arg("max_one",bit))),
    1806             :  command("algebra", "crossproduct", ALGcrossproduct4, false, "Compute the cross product of both input bats; but only produce left output", args(1,6, batarg("",oid),batargany("left",1),batargany("right",2),batarg("sl",oid),batarg("sr",oid),arg("max_one",bit))),
    1807             :  command("algebra", "outercrossproduct", ALGoutercrossproduct3, false, "Compute the outer cross product of both input bats", args(2,7, batarg("l",oid),batarg("r",oid),batargany("left",1),batargany("right",2),batarg("sl",oid),batarg("sr",oid),arg("max_one",bit))),
    1808             :  command("algebra", "join", ALGjoin, false, "Join", args(2,8, batarg("",oid),batarg("",oid),batargany("l",1),batargany("r",1),batarg("sl",oid),batarg("sr",oid),arg("nil_matches",bit),arg("estimate",lng))),
    1809             :  command("algebra", "join", ALGjoin1, false, "Join; only produce left output", args(1,7, batarg("",oid),batargany("l",1),batargany("r",1),batarg("sl",oid),batarg("sr",oid),arg("nil_matches",bit),arg("estimate",lng))),
    1810             :  command("algebra", "leftjoin", ALGleftjoin, false, "Left join with candidate lists", args(2,8, batarg("",oid),batarg("",oid),batargany("l",1),batargany("r",1),batarg("sl",oid),batarg("sr",oid),arg("nil_matches",bit),arg("estimate",lng))),
    1811             :  command("algebra", "leftjoin", ALGleftjoin1, false, "Left join with candidate lists; only produce left output", args(1,7, batarg("",oid),batargany("l",1),batargany("r",1),batarg("sl",oid),batarg("sr",oid),arg("nil_matches",bit),arg("estimate",lng))),
    1812             :  command("algebra", "outerjoin", ALGouterjoin, false, "Left outer join with candidate lists", args(2,9, batarg("",oid),batarg("",oid),batargany("l",1),batargany("r",1),batarg("sl",oid),batarg("sr",oid),arg("nil_matches",bit),arg("match_one",bit),arg("estimate",lng))),
    1813             :  command("algebra", "outerjoin", ALGouterjoin1, false, "Left outer join with candidate lists; only produce left output", args(1,8,batarg("",oid),batargany("l",1),batargany("r",1),batarg("sl",oid),batarg("sr",oid),arg("nil_matches",bit),arg("match_one",bit),arg("estimate",lng))),
    1814             :  command("algebra", "semijoin", ALGsemijoin, false, "Semi join with candidate lists", args(2,9, batarg("",oid),batarg("",oid),batargany("l",1),batargany("r",1),batarg("sl",oid),batarg("sr",oid),arg("nil_matches",bit),arg("max_one",bit),arg("estimate",lng))),
    1815             :  command("algebra", "markjoin", ALGmark2join, false, "Mark join with candidate lists", args(2,7, batarg("",oid),batarg("",bit),batargany("l",1),batargany("r",1),batarg("sl",oid),batarg("sr",oid),arg("estimate",lng))),
    1816             :  command("algebra", "markjoin", ALGmark3join, false, "Mark join with candidate lists", args(3,8, batarg("",oid),batarg("",oid),batarg("",bit),batargany("l",1),batargany("r",1),batarg("sl",oid),batarg("sr",oid),arg("estimate",lng))),
    1817             :  command("algebra", "thetajoin", ALGthetajoin, false, "Theta join with candidate lists", args(2,9, batarg("",oid),batarg("",oid),batargany("l",1),batargany("r",1),batarg("sl",oid),batarg("sr",oid),arg("op",int),arg("nil_matches",bit),arg("estimate",lng))),
    1818             :  command("algebra", "thetajoin", ALGthetajoin1, false, "Theta join with candidate lists; only produce left output", args(1,8, batarg("",oid),batargany("l",1),batargany("r",1),batarg("sl",oid),batarg("sr",oid),arg("op",int),arg("nil_matches",bit),arg("estimate",lng))),
    1819             :  command("algebra", "bandjoin", ALGbandjoin, false, "Band join: values in l and r match if r - c1 <[=] l <[=] r + c2", args(2,11, batarg("",oid),batarg("",oid),batargany("l",1),batargany("r",1),batarg("sl",oid),batarg("sr",oid),argany("c1",1),argany("c2",1),arg("li",bit),arg("hi",bit),arg("estimate",lng))),
    1820             :  command("algebra", "bandjoin", ALGbandjoin1, false, "Band join: values in l and r match if r - c1 <[=] l <[=] r + c2; only produce left output", args(1,10, batarg("",oid),batargany("l",1),batargany("r",1),batarg("sl",oid),batarg("sr",oid),argany("c1",1),argany("c2",1),arg("li",bit),arg("hi",bit),arg("estimate",lng))),
    1821             :  command("algebra", "rangejoin", ALGrangejoin, false, "Range join: values in l and r1/r2 match if r1 <[=] l <[=] r2", args(2,12, batarg("",oid),batarg("",oid),batargany("l",1),batargany("r1",1),batargany("r2",1),batarg("sl",oid),batarg("sr",oid),arg("li",bit),arg("hi",bit),arg("anti",bit),arg("symmetric",bit),arg("estimate",lng))),
    1822             :  command("algebra", "rangejoin", ALGrangejoin1, false, "Range join: values in l and r1/r2 match if r1 <[=] l <[=] r2; only produce left output", args(1,11,batarg("",oid),batargany("l",1),batargany("r1",1),batargany("r2",1),batarg("sl",oid),batarg("sr",oid),arg("li",bit),arg("hi",bit),arg("anti",bit),arg("symmetric",bit),arg("estimate",lng))),
    1823             :  command("algebra", "difference", ALGdifference, false, "Difference of l and r with candidate lists", args(1,8, batarg("",oid),batargany("l",1),batargany("r",1),batarg("sl",oid),batarg("sr",oid),arg("nil_matches",bit),arg("nil_clears",bit),arg("estimate",lng))),
    1824             :  command("algebra", "intersect", ALGintersect, false, "Intersection of l and r with candidate lists (i.e. half of semi-join)", args(1,8, batarg("",oid),batargany("l",1),batargany("r",1),batarg("sl",oid),batarg("sr",oid),arg("nil_matches",bit),arg("max_one",bit),arg("estimate",lng))),
    1825             :  pattern("algebra", "firstn", ALGfirstn, false, "Calculate first N values of B with candidate list S", args(1,8, batarg("",oid),batargany("b",0),batarg("s",oid),batarg("g",oid),arg("n",lng),arg("asc",bit),arg("nilslast",bit),arg("distinct",bit))),
    1826             :  pattern("algebra", "firstn", ALGfirstn, false, "Calculate first N values of B with candidate list S", args(2,9, batarg("",oid),batarg("",oid),batargany("b",0),batarg("s",oid),batarg("g",oid),arg("n",lng),arg("asc",bit),arg("nilslast",bit),arg("distinct",bit))),
    1827             :  command("algebra", "reuse", ALGreuse, false, "Reuse a temporary BAT if you can. Otherwise,\nallocate enough storage to accept result of an\noperation (not involving the heap)", args(1,2, batargany("",1),batargany("b",1))),
    1828             :  command("algebra", "slice", ALGslice_oid, false, "Return the slice based on head oid x till y (exclusive).", args(1,4, batargany("",1),batargany("b",1),arg("x",oid),arg("y",oid))),
    1829             :  command("algebra", "slice", ALGslice_int, false, "Return the slice with the BUNs at position x till y.", args(1,4, batargany("",1),batargany("b",1),arg("x",int),arg("y",int))),
    1830             :  command("algebra", "slice", ALGslice_lng, false, "Return the slice with the BUNs at position x till y.", args(1,4, batargany("",1),batargany("b",1),arg("x",lng),arg("y",lng))),
    1831             :  command("algebra", "subslice", ALGsubslice_lng, false, "Return the oids of the slice with the BUNs at position x till y.", args(1,4, batarg("",oid),batargany("b",1),arg("x",lng),arg("y",lng))),
    1832             :  command("aggr", "count", ALGcount_bat, false, "Return the current size (in number of elements) in a BAT.", args(1,2, arg("",lng),batargany("b",0))),
    1833             :  command("aggr", "count", ALGcount_nil, false, "Return the number of elements currently in a BAT ignores\nBUNs with nil-tail iff ignore_nils==TRUE.", args(1,3, arg("",lng),batargany("b",0),arg("ignore_nils",bit))),
    1834             :  command("aggr", "count_no_nil", ALGcount_no_nil, false, "Return the number of elements currently\nin a BAT ignoring BUNs with nil-tail", args(1,2, arg("",lng),batargany("b",2))),
    1835             :  command("aggr", "count", ALGcountCND_bat, false, "Return the current size (in number of elements) in a BAT.", args(1,3, arg("",lng),batargany("b",0),batarg("cnd",oid))),
    1836             :  command("aggr", "count", ALGcountCND_nil, false, "Return the number of elements currently in a BAT ignores\nBUNs with nil-tail iff ignore_nils==TRUE.", args(1,4, arg("",lng),batargany("b",0),batarg("cnd",oid),arg("ignore_nils",bit))),
    1837             :  command("aggr", "count_no_nil", ALGcountCND_no_nil, false, "Return the number of elements currently\nin a BAT ignoring BUNs with nil-tail", args(1,3, arg("",lng),batargany("b",2),batarg("cnd",oid))),
    1838             :  command("aggr", "cardinality", ALGcard, false, "Return the cardinality of the BAT tail values.", args(1,2, arg("",lng),batargany("b",2))),
    1839             :  command("aggr", "min", ALGminany, false, "Return the lowest tail value or nil.", args(1,2, argany("",2),batargany("b",2))),
    1840             :  command("aggr", "min", ALGminany_skipnil, false, "Return the lowest tail value or nil.", args(1,3, argany("",2),batargany("b",2),arg("skipnil",bit))),
    1841             :  command("aggr", "max", ALGmaxany, false, "Return the highest tail value or nil.", args(1,2, argany("",2),batargany("b",2))),
    1842             :  command("aggr", "max", ALGmaxany_skipnil, false, "Return the highest tail value or nil.", args(1,3, argany("",2),batargany("b",2),arg("skipnil",bit))),
    1843             :  command("aggr", "stdev", ALGstdev, false, "Gives the standard deviation of all tail values", args(1,2, arg("",dbl),batargany("b",2))),
    1844             :  command("aggr", "stdevp", ALGstdevp, false, "Gives the standard deviation of all tail values", args(1,2, arg("",dbl),batargany("b",2))),
    1845             :  command("aggr", "variance", ALGvariance, false, "Gives the variance of all tail values", args(1,2, arg("",dbl),batargany("b",2))),
    1846             :  command("aggr", "variancep", ALGvariancep, false, "Gives the variance of all tail values", args(1,2, arg("",dbl),batargany("b",2))),
    1847             :  command("aggr", "covariance", ALGcovariance, false, "Gives the covariance of all tail values", args(1,3, arg("",dbl),batargany("b1",2),batargany("b2",2))),
    1848             :  command("aggr", "covariancep", ALGcovariancep, false, "Gives the covariance of all tail values", args(1,3, arg("",dbl),batargany("b1",2),batargany("b2",2))),
    1849             :  command("aggr", "corr", ALGcorr, false, "Gives the correlation of all tail values", args(1,3, arg("",dbl),batargany("b1",2),batargany("b2",2))),
    1850             :  // sql
    1851             :  command("aggr", "exist", ALGexist, false, "", args(1,3, arg("",bit),batargany("b",2),argany("h",1))),
    1852             :  { .imp=NULL }
    1853             : };
    1854             : #include "mal_import.h"
    1855             : #ifdef _MSC_VER
    1856             : #undef read
    1857             : #pragma section(".CRT$XCU",read)
    1858             : #endif
    1859         320 : LIB_STARTUP_FUNC(init_algebra_mal)
    1860         320 : { mal_module("algebra", NULL, algebra_init_funcs); }

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