LCOV - code coverage report
Current view: top level - monetdb5/modules/kernel - algebra.c (source / functions) Hit Total Coverage
Test: coverage.info Lines: 762 993 76.7 %
Date: 2024-12-19 20:05:57 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         480 : ALGmaxany_skipnil(ptr result, const bat *bid, const bit *skipnil)
     178             : {
     179         480 :         BAT *b;
     180         480 :         ptr p;
     181         480 :         str msg = MAL_SUCCEED;
     182             : 
     183         480 :         if (result == NULL || (b = BATdescriptor(*bid)) == NULL)
     184           0 :                 throw(MAL, "algebra.max", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     185             : 
     186         480 :         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         480 :                 if (ATOMextern(b->ttype)) {
     192          48 :                         *(ptr *) result = p = BATmax_skipnil(b, NULL, *skipnil);
     193             :                 } else {
     194         432 :                         p = BATmax_skipnil(b, result, *skipnil);
     195         432 :                         if (p != result)
     196           0 :                                 msg = createException(MAL, "algebra.max",
     197             :                                                                           SQLSTATE(HY002) "INTERNAL ERROR");
     198             :                 }
     199         480 :                 if (msg == MAL_SUCCEED && p == NULL)
     200           0 :                         msg = createException(MAL, "algebra.max", GDK_EXCEPTION);
     201             :         }
     202         480 :         BBPunfix(b->batCacheid);
     203         480 :         return msg;
     204             : }
     205             : 
     206             : static str
     207         480 : ALGmaxany(ptr result, const bat *bid)
     208             : {
     209         480 :         bit skipnil = TRUE;
     210         480 :         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       89154 : 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       89154 :         BAT *b, *s = NULL, *bn;
     264       89154 :         const void *nilptr;
     265             : 
     266       89154 :         if ((*li != 0 && *li != 1) ||
     267       89154 :                 (*hi != 0 && *hi != 1) || (*anti != 0 && *anti != 1)) {
     268           1 :                 throw(MAL, "algebra.select", ILLEGAL_ARGUMENT);
     269             :         }
     270       89153 :         if ((b = BATdescriptor(*bid)) == NULL) {
     271           0 :                 throw(MAL, "algebra.select", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     272             :         }
     273       89157 :         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       89155 :         derefStr(b, low);
     278       89155 :         derefStr(b, high);
     279       89155 :         nilptr = ATOMnilptr(b->ttype);
     280      178158 :         if (*li == 1 && *hi == 1 && nilptr != NULL &&
     281      111806 :                 ATOMcmp(b->ttype, low, nilptr) == 0 &&
     282       22806 :                 ATOMcmp(b->ttype, high, nilptr) == 0) {
     283             :                 /* special case: equi-select for NIL */
     284       89156 :                 high = NULL;
     285             :         }
     286       89156 :         bn = BATselect(b, s, low, high, *li, *hi, *anti);
     287       89156 :         BBPunfix(b->batCacheid);
     288       89157 :         BBPreclaim(s);
     289       89155 :         if (bn == NULL)
     290           0 :                 throw(MAL, "algebra.select", GDK_EXCEPTION);
     291       89155 :         *result = bn->batCacheid;
     292       89155 :         BBPkeepref(bn);
     293       89155 :         return MAL_SUCCEED;
     294             : }
     295             : 
     296             : static str
     297        3964 : 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        3964 :         BAT *b, *s = NULL, *bn;
     302        3964 :         bit nanti = *anti, nli = *li, nhi = *hi;
     303             : 
     304        3964 :         if (!*unknown)
     305           0 :                 return ALGselect2(result, bid, sid, low, high, li, hi, anti);
     306             : 
     307        3964 :         if ((nli != 0 && nli != 1) ||
     308        3964 :                 (nhi != 0 && nhi != 1) || (nanti != 0 && nanti != 1)) {
     309           0 :                 throw(MAL, "algebra.select", ILLEGAL_ARGUMENT);
     310             :         }
     311        3964 :         if ((b = BATdescriptor(*bid)) == NULL) {
     312           0 :                 throw(MAL, "algebra.select", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     313             :         }
     314        3964 :         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        3964 :         derefStr(b, low);
     319        3964 :         derefStr(b, high);
     320             :         /* here we don't need open ended parts with nil */
     321        3964 :         if (!nanti) {
     322         886 :                 const void *nilptr = ATOMnilptr(b->ttype);
     323         886 :                 if (nilptr) {
     324         886 :                         if (nli == 1 && ATOMcmp(b->ttype, low, nilptr) == 0) {
     325          16 :                                 low = high;
     326          16 :                                 nli = 0;
     327             :                         }
     328         886 :                         if (nhi == 1 && ATOMcmp(b->ttype, high, nilptr) == 0) {
     329          18 :                                 high = low;
     330          18 :                                 nhi = 0;
     331             :                         }
     332         886 :                         if (ATOMcmp(b->ttype, low, high) == 0 && ATOMcmp(b->ttype, high, nilptr) == 0)    /* ugh sql nil != nil */
     333        3964 :                                 nanti = 1;
     334             :                 }
     335             :         }
     336             : 
     337        3964 :         bn = BATselect(b, s, low, high, nli, nhi, nanti);
     338        3964 :         BBPunfix(b->batCacheid);
     339        3964 :         BBPreclaim(s);
     340        3964 :         if (bn == NULL)
     341           0 :                 throw(MAL, "algebra.select", GDK_EXCEPTION);
     342        3964 :         *result = bn->batCacheid;
     343        3964 :         BBPkeepref(bn);
     344        3964 :         return MAL_SUCCEED;
     345             : }
     346             : 
     347             : static str
     348       62592 : ALGselect1(bat *result, const bat *bid, const void *low, const void *high,
     349             :                    const bit *li, const bit *hi, const bit *anti)
     350             : {
     351       62592 :         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      338654 : ALGthetaselect2(bat *result, const bat *bid, const bat *sid, const void *val,
     363             :                                 const char **op)
     364             : {
     365      338654 :         BAT *b, *s = NULL, *bn;
     366             : 
     367      338654 :         if ((b = BATdescriptor(*bid)) == NULL) {
     368           0 :                 throw(MAL, "algebra.thetaselect",
     369             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     370             :         }
     371      338652 :         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      338640 :         derefStr(b, val);
     377      338640 :         bn = BATthetaselect(b, s, val, *op);
     378      338625 :         BBPunfix(b->batCacheid);
     379      338651 :         BBPreclaim(s);
     380      338639 :         if (bn == NULL)
     381           0 :                 throw(MAL, "algebra.select", GDK_EXCEPTION);
     382      338639 :         *result = bn->batCacheid;
     383      338639 :         BBPkeepref(bn);
     384      338639 :         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        1588 : ALGselectNotNil(bat *result, const bat *bid)
     585             : {
     586        1588 :         BAT *b;
     587             : 
     588        1588 :         if ((b = BATdescriptor(*bid)) == NULL)
     589           0 :                 throw(MAL, "algebra.selectNotNil",
     590             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     591             : 
     592        1588 :         MT_lock_set(&b->theaplock);
     593        1588 :         bool bnonil = b->tnonil || b->ttype == TYPE_msk;
     594        1588 :         MT_lock_unset(&b->theaplock);
     595        1588 :         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        1491 :         *result = b->batCacheid;
     613        1491 :         BBPkeepref(b);
     614        1491 :         return MAL_SUCCEED;
     615             : }
     616             : 
     617             : static str
     618      342681 : 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      342681 :         BAT *left = NULL, *right = NULL, *right2 = NULL;
     638      342681 :         BAT *candleft = NULL, *candright = NULL;
     639      342681 :         BAT *result1 = NULL, *result2 = NULL, *result3 = NULL;
     640      342681 :         BUN est;
     641      342681 :         const char *err = SQLSTATE(HY002) RUNTIME_OBJECT_MISSING;
     642             : 
     643      342681 :         assert(r2id == NULL || rangefunc != NULL);
     644             : 
     645      342681 :         if ((left = BATdescriptor(*lid)) == NULL)
     646           0 :                 goto fail;
     647      342672 :         if ((right = BATdescriptor(*rid)) == NULL)
     648           0 :                 goto fail;
     649      342661 :         if (slid && !is_bat_nil(*slid) && (candleft = BATdescriptor(*slid)) == NULL)
     650           0 :                 goto fail;
     651      342661 :         if (srid && !is_bat_nil(*srid)
     652           0 :                 && (candright = BATdescriptor(*srid)) == NULL)
     653           0 :                 goto fail;
     654      342661 :         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      342661 :         err = NULL;                                     /* most likely error now is GDK_EXCEPTION */
     661             : 
     662      342661 :         if (thetafunc) {
     663       16833 :                 assert(joinfunc == NULL);
     664       16833 :                 assert(semifunc == NULL);
     665       16833 :                 assert(markfunc == NULL);
     666       16833 :                 assert(bandfunc == NULL);
     667       16833 :                 assert(rangefunc == NULL);
     668       16833 :                 assert(difffunc == NULL);
     669       16833 :                 assert(interfunc == NULL);
     670       16833 :                 if ((*thetafunc)
     671             :                         (&result1, r2 ? &result2 : NULL, left, right, candleft, candright,
     672       16833 :                          op, *nil_matches, est) != GDK_SUCCEED)
     673           0 :                         goto fail;
     674      325828 :         } else if (joinfunc) {
     675      217538 :                 assert(semifunc == NULL);
     676      217538 :                 assert(markfunc == NULL);
     677      217538 :                 assert(bandfunc == NULL);
     678      217538 :                 assert(rangefunc == NULL);
     679      217538 :                 assert(difffunc == NULL);
     680      217538 :                 assert(interfunc == NULL);
     681      217538 :                 if ((*joinfunc)
     682             :                         (&result1, r2 ? &result2 : NULL, left, right, candleft, candright,
     683      217538 :                          *nil_matches, est) != GDK_SUCCEED)
     684           1 :                         goto fail;
     685      108290 :         } else if (semifunc) {
     686         332 :                 assert(markfunc == NULL);
     687         332 :                 assert(bandfunc == NULL);
     688         332 :                 assert(rangefunc == NULL);
     689         332 :                 assert(difffunc == NULL);
     690         332 :                 assert(interfunc == NULL);
     691         332 :                 if ((*semifunc)
     692             :                         (&result1, r2 ? &result2 : NULL, left, right, candleft, candright,
     693         332 :                          *nil_matches, *max_one, est) != GDK_SUCCEED)
     694          42 :                         goto fail;
     695      107958 :         } else if (markfunc) {
     696        9686 :                 assert(bandfunc == NULL);
     697        9686 :                 assert(rangefunc == NULL);
     698        9686 :                 assert(difffunc == NULL);
     699        9686 :                 assert(interfunc == NULL);
     700       19367 :                 if ((*markfunc) (&result1, r2 ? &result2 : NULL, &result3,
     701             :                                                  left, right, candleft, candright, est) != GDK_SUCCEED)
     702           0 :                         goto fail;
     703       98272 :         } 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       98272 :         } 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       98143 :         } else if (difffunc) {
     724       92158 :                 assert(r2 == NULL);
     725       92158 :                 assert(interfunc == NULL);
     726       92154 :                 if ((result1 = (*difffunc) (left, right, candleft, candright,
     727       92158 :                                                                         *nil_matches, *not_in, est)) == NULL)
     728           0 :                         goto fail;
     729             :         } else {
     730        5985 :                 assert(r2 == NULL);
     731        5985 :                 if ((result1 = (*interfunc) (left, right, candleft, candright,
     732        5985 :                                                                          *nil_matches, *max_one, est)) == NULL)
     733           1 :                         goto fail;
     734             :         }
     735      342601 :         *r1 = result1->batCacheid;
     736      342601 :         BBPkeepref(result1);
     737      342610 :         if (r2) {
     738      195690 :                 *r2 = result2->batCacheid;
     739      195690 :                 BBPkeepref(result2);
     740             :         }
     741      342593 :         if (r3) {
     742        9686 :                 *r3 = result3->batCacheid;
     743        9686 :                 BBPkeepref(result3);
     744             :         }
     745      342593 :         BBPunfix(left->batCacheid);
     746      342611 :         BBPunfix(right->batCacheid);
     747      342612 :         BBPreclaim(candleft);
     748      342612 :         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      190363 : 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      190363 :         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       26538 : 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       26538 :         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         123 : 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         123 :         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        9680 : ALGmark2join(bat *r1, bat *r3, const bat *lid, const bat *rid,
     837             :                          const bat *slid, const bat *srid, const lng *estimate)
     838             : {
     839        9680 :         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        4298 : 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        4298 :         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       92162 : 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       92162 :         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        5985 : 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        5985 :         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        1269 : ALGfirstn(Client cntxt, MalBlkPtr mb, MalStkPtr stk, InstrPtr pci)
     954             : {
     955        1269 :         bat *ret1, *ret2 = NULL;
     956        1269 :         bat bid, sid, gid;
     957        1269 :         BAT *b, *s = NULL, *g = NULL;
     958        1269 :         BAT *bn = NULL, *gn = NULL;
     959        1269 :         lng n;
     960        1269 :         bit asc, nilslast, distinct;
     961        1269 :         gdk_return rc;
     962             : 
     963        1269 :         (void) cntxt;
     964        1269 :         (void) mb;
     965             : 
     966        1269 :         assert(pci->retc == 1 || pci->retc == 2);
     967        1269 :         assert(pci->argc - pci->retc >= 5 && pci->argc - pci->retc <= 7);
     968             : 
     969        1269 :         n = *getArgReference_lng(stk, pci, pci->argc - 4);
     970        1269 :         if (n < 0)
     971           0 :                 throw(MAL, "algebra.firstn", ILLEGAL_ARGUMENT);
     972        1269 :         if (n > (lng) BUN_MAX)
     973             :                 n = BUN_MAX;
     974        1269 :         ret1 = getArgReference_bat(stk, pci, 0);
     975        1269 :         if (pci->retc == 2)
     976         510 :                 ret2 = getArgReference_bat(stk, pci, 1);
     977        1269 :         bid = *getArgReference_bat(stk, pci, pci->retc);
     978        1269 :         if ((b = BATdescriptor(bid)) == NULL)
     979           0 :                 throw(MAL, "algebra.firstn", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     980        1269 :         if (pci->argc - pci->retc > 5) {
     981        1269 :                 sid = *getArgReference_bat(stk, pci, pci->retc + 1);
     982        1269 :                 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        1269 :                 if (pci->argc - pci->retc > 6) {
     988        1269 :                         gid = *getArgReference_bat(stk, pci, pci->retc + 2);
     989        1269 :                         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        1269 :         asc = *getArgReference_bit(stk, pci, pci->argc - 3);
     998        1269 :         nilslast = *getArgReference_bit(stk, pci, pci->argc - 2);
     999        1269 :         distinct = *getArgReference_bit(stk, pci, pci->argc - 1);
    1000        2028 :         rc = BATfirstn(&bn, ret2 ? &gn : NULL, b, s, g, (BUN) n, asc, nilslast,
    1001             :                                    distinct);
    1002        1269 :         BBPunfix(b->batCacheid);
    1003        1268 :         BBPreclaim(s);
    1004        1269 :         BBPreclaim(g);
    1005        1269 :         if (rc != GDK_SUCCEED)
    1006           0 :                 throw(MAL, "algebra.firstn", GDK_EXCEPTION);
    1007        1269 :         *ret1 = bn->batCacheid;
    1008        1269 :         BBPkeepref(bn);
    1009        1269 :         if (ret2) {
    1010         510 :                 *ret2 = gn->batCacheid;
    1011         510 :                 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       26749 : ALGcrossproduct(bat *l, bat *r, const bat *left, const bat *right,
    1069             :                                 const bat *slid, const bat *srid, const bit *max_one)
    1070             : {
    1071       26749 :         BAT *L, *R, *bn1, *bn2 = NULL;
    1072       26749 :         BAT *sl = NULL, *sr = NULL;
    1073       26749 :         gdk_return ret;
    1074             : 
    1075       26749 :         L = BATdescriptor(*left);
    1076       26751 :         R = BATdescriptor(*right);
    1077       26751 :         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       26751 :         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       28138 :         ret = BATsubcross(&bn1, r ? &bn2 : NULL, L, R, sl, sr,
    1093       26751 :                                           max_one && !is_bit_nil(*max_one) && *max_one);
    1094       26743 :         BBPunfix(L->batCacheid);
    1095       26750 :         BBPunfix(R->batCacheid);
    1096       26751 :         BBPreclaim(sl);
    1097       26751 :         BBPreclaim(sr);
    1098       26751 :         if (ret != GDK_SUCCEED)
    1099          77 :                 throw(MAL, "algebra.crossproduct", GDK_EXCEPTION);
    1100       26674 :         *l = bn1->batCacheid;
    1101       26674 :         BBPkeepref(bn1);
    1102       26671 :         if (r) {
    1103       25291 :                 *r = bn2->batCacheid;
    1104       25291 :                 BBPkeepref(bn2);
    1105             :         }
    1106             :         return MAL_SUCCEED;
    1107             : }
    1108             : 
    1109             : static str
    1110        1387 : ALGcrossproduct1(bat *l, const bat *left, const bat *right, const bit *max_one)
    1111             : {
    1112        1387 :         return ALGcrossproduct(l, NULL, left, right, NULL, NULL, max_one);
    1113             : }
    1114             : 
    1115             : static str
    1116       25362 : ALGcrossproduct2(bat *l, bat *r, const bat *left, const bat *right,
    1117             :                                  const bit *max_one)
    1118             : {
    1119       25362 :         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     1193500 : ALGprojection2(bat *result, const bat *lid, const bat *r1id, const bat *r2id)
    1177             : {
    1178     1193500 :         BAT *l, *r1, *r2 = NULL, *bn;
    1179             : 
    1180     1193500 :         if ((l = BATdescriptor(*lid)) == NULL) {
    1181           0 :                 throw(MAL, "algebra.projection",
    1182             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1183             :         }
    1184     1193460 :         if ((r1 = BATdescriptor(*r1id)) == NULL) {
    1185           0 :                 BBPunfix(l->batCacheid);
    1186           0 :                 throw(MAL, "algebra.projection",
    1187             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1188             :         }
    1189     1193326 :         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     1193326 :         bn = BATproject2(l, r1, r2);
    1196     1192990 :         BBPunfix(l->batCacheid);
    1197     1193419 :         BBPunfix(r1->batCacheid);
    1198     1193378 :         BBPreclaim(r2);
    1199     1193385 :         if (bn == NULL)
    1200           0 :                 throw(MAL, "algebra.projection", GDK_EXCEPTION);
    1201     1193385 :         *result = bn->batCacheid;
    1202     1193385 :         BBPkeepref(bn);
    1203     1193385 :         return MAL_SUCCEED;
    1204             : }
    1205             : 
    1206             : str
    1207     1193489 : ALGprojection(bat *result, const bat *lid, const bat *rid)
    1208             : {
    1209     1193489 :         return ALGprojection2(result, lid, rid, NULL);
    1210             : }
    1211             : 
    1212             : static str
    1213       24130 : 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       24130 :         BAT *bn = NULL, *on = NULL, *gn = NULL;
    1218       24130 :         BAT *b = NULL, *o = NULL, *g = NULL;
    1219             : 
    1220       24130 :         if ((b = BATdescriptor(*bid)) == NULL)
    1221           0 :                 throw(MAL, "algebra.sort", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1222       24130 :         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       24130 :         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       27858 :         if (BATsort(result ? &bn : NULL,
    1232             :                                 norder ? &on : NULL,
    1233             :                                 ngroup ? &gn : NULL,
    1234       24130 :                                 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       24130 :         BBPunfix(b->batCacheid);
    1241       24130 :         BBPreclaim(o);
    1242       24130 :         BBPreclaim(g);
    1243       24130 :         if (result) {
    1244       24130 :                 *result = bn->batCacheid;
    1245       24130 :                 BBPkeepref(bn);
    1246             :         }
    1247       24130 :         if (norder) {
    1248       20402 :                 *norder = on->batCacheid;
    1249       20402 :                 BBPkeepref(on);
    1250             :         }
    1251       24130 :         if (ngroup) {
    1252       13701 :                 *ngroup = gn->batCacheid;
    1253       13701 :                 BBPkeepref(gn);
    1254             :         }
    1255             :         return MAL_SUCCEED;
    1256             : }
    1257             : 
    1258             : static str
    1259        4100 : 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        4100 :         return ALGsort33(result, norder, NULL, bid, order, group, reverse, nilslast,
    1264             :                                          stable);
    1265             : }
    1266             : 
    1267             : static str
    1268        2085 : ALGsort31(bat *result, const bat *bid, const bat *order, const bat *group,
    1269             :                   const bit *reverse, const bit *nilslast, const bit *stable)
    1270             : {
    1271        2085 :         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        6440 : ALGsort13(bat *result, bat *norder, bat *ngroup, const bat *bid,
    1302             :                   const bit *reverse, const bit *nilslast, const bit *stable)
    1303             : {
    1304        6440 :         return ALGsort33(result, norder, ngroup, bid, NULL, NULL, reverse, nilslast,
    1305             :                                          stable);
    1306             : }
    1307             : 
    1308             : static str
    1309        2601 : ALGsort12(bat *result, bat *norder, const bat *bid, const bit *reverse,
    1310             :                   const bit *nilslast, const bit *stable)
    1311             : {
    1312        2601 :         return ALGsort33(result, norder, NULL, bid, NULL, NULL, reverse, nilslast,
    1313             :                                          stable);
    1314             : }
    1315             : 
    1316             : static str
    1317        1643 : ALGsort11(bat *result, const bat *bid, const bit *reverse, const bit *nilslast,
    1318             :                   const bit *stable)
    1319             : {
    1320        1643 :         return ALGsort33(result, NULL, NULL, bid, NULL, NULL, reverse, nilslast,
    1321             :                                          stable);
    1322             : }
    1323             : 
    1324             : static str
    1325       69577 : ALGcountCND_nil(lng *result, const bat *bid, const bat *cnd,
    1326             :                                 const bit *ignore_nils)
    1327             : {
    1328       69577 :         BAT *b, *s = NULL;
    1329             : 
    1330       69577 :         if ((b = BATdescriptor(*bid)) == NULL) {
    1331           0 :                 throw(MAL, "aggr.count", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1332             :         }
    1333       69576 :         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       69576 :         if (b->ttype == TYPE_msk || mask_cand(b)) {
    1338          30 :                 BATsum(result, TYPE_lng, b, s, *ignore_nils, false);
    1339       69546 :         } else if (*ignore_nils) {
    1340        1723 :                 *result = (lng) BATcount_no_nil(b, s);
    1341             :         } else {
    1342       67823 :                 struct canditer ci;
    1343       67823 :                 canditer_init(&ci, b, s);
    1344       67824 :                 *result = (lng) ci.ncand;
    1345             :         }
    1346       69577 :         BBPreclaim(s);
    1347       69577 :         BBPunfix(b->batCacheid);
    1348       69577 :         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       67854 : ALGcount_bat(lng *result, const bat *bid)
    1365             : {
    1366       67854 :         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       17160 : ALGsubslice_lng(bat *ret, const bat *bid, const lng *start, const lng *end)
    1430             : {
    1431       17160 :         BAT *b, *bn;
    1432       17160 :         BUN s, e;
    1433             : 
    1434       17160 :         if (*start < 0 || (*end < 0 && !is_lng_nil(*end)))
    1435           0 :                 throw(MAL, "algebra.subslice", ILLEGAL_ARGUMENT);
    1436       17160 :         if ((b = BBPquickdesc(*bid)) == NULL)
    1437           0 :                 throw(MAL, "algebra.subslice", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1438       17160 :         s = (BUN) *start;
    1439       17160 :         if (s > BATcount(b))
    1440             :                 s = BATcount(b);
    1441       17160 :         e = is_lng_nil(*end) ? BATcount(b) : (BUN) *end + 1;
    1442       17160 :         if (e > BATcount(b))
    1443             :                 e = BATcount(b);
    1444       17160 :         if (e < s)
    1445             :                 e = s;
    1446       17160 :         bn = BATdense(0, b->hseqbase + s, e - s);
    1447       17160 :         if (bn == NULL)
    1448           0 :                 throw(MAL, "algebra.subslice", SQLSTATE(HY013) MAL_MALLOC_FAIL);
    1449       17160 :         *ret = bn->batCacheid;
    1450       17160 :         BBPkeepref(bn);
    1451       17160 :         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      178609 : ALGprojecttail(Client cntxt, MalBlkPtr mb, MalStkPtr stk, InstrPtr pci)
    1577             : {
    1578      178609 :         bat *ret = getArgReference_bat(stk, pci, 0);
    1579      178609 :         bat bid = *getArgReference_bat(stk, pci, 1);
    1580      178609 :         const ValRecord *v = &stk->stk[getArg(pci, 2)];
    1581      178609 :         BAT *b, *bn;
    1582             : 
    1583      178609 :         (void) cntxt;
    1584      178609 :         (void) mb;
    1585      178609 :         if (isaBatType(getArgType(mb, pci, 2)))
    1586           0 :                 throw(MAL, "algebra.project", "Scalar value expected");
    1587      178609 :         if ((b = BBPquickdesc(bid)) == NULL)
    1588           0 :                 throw(MAL, "algebra.project", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1589      178604 :         bn = BATconstant(b->hseqbase, v->vtype, VALptr(v), BATcount(b), TRANSIENT);
    1590      178608 :         if (bn == NULL) {
    1591           0 :                 *ret = bat_nil;
    1592           0 :                 throw(MAL, "algebra.project", SQLSTATE(HY013) MAL_MALLOC_FAIL);
    1593             :         }
    1594      178608 :         *ret = bn->batCacheid;
    1595      178608 :         BBPkeepref(bn);
    1596      178608 :         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         325 : LIB_STARTUP_FUNC(init_algebra_mal)
    1860         325 : { mal_module("algebra", NULL, algebra_init_funcs); }

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