LCOV - code coverage report
Current view: top level - monetdb5/modules/kernel - algebra.c (source / functions) Hit Total Coverage
Test: coverage.info Lines: 747 973 76.8 %
Date: 2024-10-04 20:04:04 Functions: 67 82 81.7 %

          Line data    Source code
       1             : /*
       2             :  * SPDX-License-Identifier: MPL-2.0
       3             :  *
       4             :  * This Source Code Form is subject to the terms of the Mozilla Public
       5             :  * License, v. 2.0.  If a copy of the MPL was not distributed with this
       6             :  * file, You can obtain one at http://mozilla.org/MPL/2.0/.
       7             :  *
       8             :  * Copyright 2024 MonetDB Foundation;
       9             :  * Copyright August 2008 - 2023 MonetDB B.V.;
      10             :  * Copyright 1997 - July 2008 CWI.
      11             :  */
      12             : 
      13             : /*
      14             :  * (c) Peter Boncz, Martin Kersten, Niels Nes, Sjoerd Mullender
      15             :  * BAT Algebra
      16             :  * This modules contains the most common algebraic BAT manipulation
      17             :  * commands. We call them algebra, because all operations take
      18             :  * values as parameters, and produce new result values, but
      19             :  * do not modify their parameters.
      20             :  *
      21             :  * Unlike the previous Monet versions, we reduce the number
      22             :  * of functions returning a BAT reference. This was previously needed
      23             :  * to simplify recursive bat-expression and manage reference counts.
      24             :  * In the current version we return only a BAT identifier when a new
      25             :  * bat is being created.
      26             :  *
      27             :  * All parameters to the modules are passed by reference.
      28             :  * In particular, this means that
      29             :  * string values are passed to the module layer as (str *)
      30             :  * and we have to de-reference them before entering the gdk library.
      31             :  * This calls for knowledge on the underlying BAT typs`s
      32             :  */
      33             : #define derefStr(b, v)                                                  \
      34             :         do {                                                                            \
      35             :                 int _tpe= ATOMstorage((b)->ttype);           \
      36             :                 if (_tpe >= TYPE_str) {                                      \
      37             :                         if ((v) == 0 || *(str*) (v) == 0)       \
      38             :                                 (v) = (str) str_nil;                    \
      39             :                         else                                                            \
      40             :                                 (v) = *(str *) (v);                             \
      41             :                 }                                                                               \
      42             :         } while (0)
      43             : 
      44             : #include "monetdb_config.h"
      45             : #include "algebra.h"
      46             : 
      47             : /*
      48             :  * Command Implementations in C
      49             :  * This module contains just a wrapper implementations; since all described
      50             :  * operations are part of the GDK kernel.
      51             :  *
      52             :  * BAT sum operation
      53             :  * The sum aggregate only works for int and float fields.
      54             :  * The routines below assumes that the caller knows what type
      55             :  * is large enough to prevent overflow.
      56             :  */
      57             : 
      58             : static gdk_return
      59        2388 : CMDgen_group(BAT **result, BAT *gids, BAT *cnts)
      60             : {
      61        2388 :         BUN j;
      62        2388 :         BATiter gi = bat_iterator(gids);
      63        2388 :         BAT *r = COLnew(0, TYPE_oid, gi.count * 2, TRANSIENT);
      64             : 
      65        2388 :         if (r == NULL) {
      66           0 :                 bat_iterator_end(&gi);
      67           0 :                 return GDK_FAIL;
      68             :         }
      69        2388 :         BATiter ci = bat_iterator(cnts);
      70        2388 :         if (gi.type == TYPE_void) {
      71        1049 :                 oid id = gi.tseq;
      72        1049 :                 lng *cnt = (lng *) ci.base;
      73       96195 :                 for (j = 0; j < gi.count; j++) {
      74       95146 :                         lng i, sz = cnt[j];
      75      190236 :                         for (i = 0; i < sz; i++) {
      76       95090 :                                 if (BUNappend(r, &id, false) != GDK_SUCCEED) {
      77           0 :                                         BBPreclaim(r);
      78           0 :                                         bat_iterator_end(&ci);
      79           0 :                                         bat_iterator_end(&gi);
      80           0 :                                         return GDK_FAIL;
      81             :                                 }
      82             :                         }
      83       95146 :                         id ++;
      84             :                 }
      85             :         } else {
      86        1339 :                 oid *id = (oid *) gi.base;
      87        1339 :                 lng *cnt = (lng *) ci.base;
      88      140494 :                 for (j = 0; j < gi.count; j++) {
      89      139155 :                         lng i, sz = cnt[j];
      90      274814 :                         for (i = 0; i < sz; i++) {
      91      135659 :                                 if (BUNappend(r, id, false) != GDK_SUCCEED) {
      92           0 :                                         BBPreclaim(r);
      93           0 :                                         bat_iterator_end(&ci);
      94           0 :                                         bat_iterator_end(&gi);
      95           0 :                                         return GDK_FAIL;
      96             :                                 }
      97             :                         }
      98      139155 :                         id ++;
      99             :                 }
     100             :         }
     101        2388 :         bat_iterator_end(&ci);
     102        2388 :         r->tkey = false;
     103        2388 :         r->tseqbase = oid_nil;
     104        2388 :         r->tsorted = gi.sorted;
     105        2388 :         r->trevsorted = gi.revsorted;
     106        2388 :         r->tnonil = gi.nonil;
     107        2388 :         bat_iterator_end(&gi);
     108        2388 :         *result = r;
     109        2388 :         return GDK_SUCCEED;
     110             : }
     111             : 
     112             : 
     113             : static gdk_return
     114           6 : slice(BAT **retval, BAT *b, lng start, lng end)
     115             : {
     116             :         /* the internal BATslice requires exclusive end */
     117           6 :         if (start < 0) {
     118           0 :                 GDKerror("start position of slice should >= 0\n");
     119           0 :                 return GDK_FAIL;
     120             :         }
     121           6 :         if (is_lng_nil(end))
     122           3 :                 end = BATcount(b);
     123             : 
     124           6 :         return (*retval = BATslice(b, (BUN) start, (BUN) end + 1)) ? GDK_SUCCEED : GDK_FAIL;
     125             : }
     126             : 
     127             : /*
     128             :  *
     129             :  * The remainder of this file contains the wrapper around the V4 code base
     130             :  * The BAT identifiers passed through this module may indicate
     131             :  * that the 'reverse' view applies. This should be taken into
     132             :  * account while resolving them.
     133             :  *
     134             :  * The sum aggregate only works for int and float fields.
     135             :  * The routines below assumes that the caller knows what type
     136             :  * is large enough to prevent overflow.
     137             :  */
     138             : 
     139             : static str
     140         722 : ALGminany_skipnil(ptr result, const bat *bid, const bit *skipnil)
     141             : {
     142         722 :         BAT *b;
     143         722 :         ptr p;
     144         722 :         str msg = MAL_SUCCEED;
     145             : 
     146         722 :         if (result == NULL || (b = BATdescriptor(*bid)) == NULL)
     147           0 :                 throw(MAL, "algebra.min", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     148             : 
     149         722 :         if (!ATOMlinear(b->ttype)) {
     150           0 :                 msg = createException(MAL, "algebra.min",
     151             :                                                           "atom '%s' cannot be ordered linearly",
     152             :                                                           ATOMname(b->ttype));
     153             :         } else {
     154         722 :                 if (ATOMextern(b->ttype)) {
     155          34 :                         *(ptr *) result = p = BATmin_skipnil(b, NULL, *skipnil);
     156             :                 } else {
     157         688 :                         p = BATmin_skipnil(b, result, *skipnil);
     158         688 :                         if (p != result)
     159           0 :                                 msg = createException(MAL, "algebra.min",
     160             :                                                                           SQLSTATE(HY002) "INTERNAL ERROR");
     161             :                 }
     162         722 :                 if (msg == MAL_SUCCEED && p == NULL)
     163           0 :                         msg = createException(MAL, "algebra.min", GDK_EXCEPTION);
     164             :         }
     165         722 :         BBPunfix(b->batCacheid);
     166         722 :         return msg;
     167             : }
     168             : 
     169             : static str
     170         722 : ALGminany(ptr result, const bat *bid)
     171             : {
     172         722 :         bit skipnil = TRUE;
     173         722 :         return ALGminany_skipnil(result, bid, &skipnil);
     174             : }
     175             : 
     176             : static str
     177         596 : ALGmaxany_skipnil(ptr result, const bat *bid, const bit *skipnil)
     178             : {
     179         596 :         BAT *b;
     180         596 :         ptr p;
     181         596 :         str msg = MAL_SUCCEED;
     182             : 
     183         596 :         if (result == NULL || (b = BATdescriptor(*bid)) == NULL)
     184           0 :                 throw(MAL, "algebra.max", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     185             : 
     186         596 :         if (!ATOMlinear(b->ttype)) {
     187           0 :                 msg = createException(MAL, "algebra.max",
     188             :                                                           "atom '%s' cannot be ordered linearly",
     189             :                                                           ATOMname(b->ttype));
     190             :         } else {
     191         596 :                 if (ATOMextern(b->ttype)) {
     192          48 :                         *(ptr *) result = p = BATmax_skipnil(b, NULL, *skipnil);
     193             :                 } else {
     194         548 :                         p = BATmax_skipnil(b, result, *skipnil);
     195         548 :                         if (p != result)
     196           0 :                                 msg = createException(MAL, "algebra.max",
     197             :                                                                           SQLSTATE(HY002) "INTERNAL ERROR");
     198             :                 }
     199         596 :                 if (msg == MAL_SUCCEED && p == NULL)
     200           0 :                         msg = createException(MAL, "algebra.max", GDK_EXCEPTION);
     201             :         }
     202         596 :         BBPunfix(b->batCacheid);
     203         596 :         return msg;
     204             : }
     205             : 
     206             : static str
     207         596 : ALGmaxany(ptr result, const bat *bid)
     208             : {
     209         596 :         bit skipnil = TRUE;
     210         596 :         return ALGmaxany_skipnil(result, bid, &skipnil);
     211             : }
     212             : 
     213             : static str
     214        2388 : ALGgroupby(bat *res, const bat *gids, const bat *cnts)
     215             : {
     216        2388 :         BAT *bn, *g, *c;
     217             : 
     218        2388 :         g = BATdescriptor(*gids);
     219        2388 :         if (g == NULL) {
     220           0 :                 throw(MAL, "algebra.groupby", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     221             :         }
     222        2388 :         c = BATdescriptor(*cnts);
     223        2388 :         if (c == NULL) {
     224           0 :                 BBPunfix(g->batCacheid);
     225           0 :                 throw(MAL, "algebra.groupby", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     226             :         }
     227        2388 :         if (CMDgen_group(&bn, g, c) != GDK_SUCCEED) {
     228           0 :                 BBPunfix(g->batCacheid);
     229           0 :                 BBPunfix(c->batCacheid);
     230           0 :                 throw(MAL, "algebra.groupby", GDK_EXCEPTION);
     231             :         }
     232        2388 :         *res = bn->batCacheid;
     233        2388 :         BBPkeepref(bn);
     234        2388 :         BBPunfix(g->batCacheid);
     235        2388 :         BBPunfix(c->batCacheid);
     236        2388 :         return MAL_SUCCEED;
     237             : }
     238             : 
     239             : static str
     240           1 : ALGcard(lng *result, const bat *bid)
     241             : {
     242           1 :         BAT *b, *en;
     243             : 
     244           1 :         if ((b = BATdescriptor(*bid)) == NULL) {
     245           0 :                 throw(MAL, "algebra.card", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     246             :         }
     247           1 :         en = BATunique(b, NULL);
     248           1 :         BBPunfix(b->batCacheid);
     249           1 :         if (en == NULL) {
     250           0 :                 throw(MAL, "algebra.card", GDK_EXCEPTION);
     251             :         }
     252           1 :         struct canditer ci;
     253           1 :         canditer_init(&ci, NULL, en);
     254           1 :         *result = (lng) ci.ncand;
     255           1 :         BBPunfix(en->batCacheid);
     256           1 :         return MAL_SUCCEED;
     257             : }
     258             : 
     259             : static str
     260       67593 : ALGselect2nil(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             :                           const bit *unknown)
     263             : {
     264       67593 :         BAT *b, *s = NULL, *bn;
     265             : 
     266       67593 :         if ((*li != 0 && *li != 1) ||
     267       67593 :                 (*hi != 0 && *hi != 1) || (*anti != 0 && *anti != 1)) {
     268           0 :                 throw(MAL, "algebra.select", ILLEGAL_ARGUMENT);
     269             :         }
     270             : 
     271       67593 :         if ((b = BATdescriptor(*bid)) == NULL) {
     272           0 :                 throw(MAL, "algebra.select", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     273             :         }
     274       67593 :         if (sid && !is_bat_nil(*sid) && (s = BATdescriptor(*sid)) == NULL) {
     275           0 :                 BBPunfix(b->batCacheid);
     276           0 :                 throw(MAL, "algebra.select", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     277             :         }
     278       67592 :         derefStr(b, low);
     279       67592 :         derefStr(b, high);
     280             : 
     281       67592 :         bool nanti = *anti, nli = *li, nhi = *hi;
     282             : 
     283             :         /* here we don't need open ended parts with nil */
     284       67592 :         if (!nanti && *unknown) {
     285         883 :                 const void *nilptr = ATOMnilptr(b->ttype);
     286         883 :                 if (nilptr) {
     287         883 :                         if (nli && ATOMcmp(b->ttype, low, nilptr) == 0) {
     288          16 :                                 low = high;
     289          16 :                                 nli = false;
     290             :                         }
     291         883 :                         if (nhi && ATOMcmp(b->ttype, high, nilptr) == 0) {
     292          18 :                                 high = low;
     293          18 :                                 nhi = false;
     294             :                         }
     295         883 :                         if (ATOMcmp(b->ttype, low, high) == 0 && ATOMcmp(b->ttype, high, nilptr) == 0)    /* ugh sql nil != nil */
     296          11 :                                 nanti = true;
     297             :                 }
     298       66709 :         } else if (!*unknown) {
     299       63628 :                 const void *nilptr = ATOMnilptr(b->ttype);
     300      127105 :                 if (nli && nhi && nilptr != NULL &&
     301       63499 :                         ATOMcmp(b->ttype, low, nilptr) == 0 &&
     302          24 :                         ATOMcmp(b->ttype, high, nilptr) == 0) {
     303             :                         /* special case: equi-select for NIL */
     304       67594 :                         high = NULL;
     305             :                 }
     306             :         }
     307             : 
     308       67594 :         bn = BATselect(b, s, low, high, nli, nhi, nanti, false);
     309       67592 :         BBPunfix(b->batCacheid);
     310       67586 :         BBPreclaim(s);
     311       67587 :         if (bn == NULL)
     312           0 :                 throw(MAL, "algebra.select", GDK_EXCEPTION);
     313       67587 :         *result = bn->batCacheid;
     314       67587 :         BBPkeepref(bn);
     315       67587 :         return MAL_SUCCEED;
     316             : }
     317             : 
     318             : static str
     319       20753 : ALGselect2(bat *result, const bat *bid, const bat *sid, const void *low,
     320             :                    const void *high, const bit *li, const bit *hi, const bit *anti)
     321             : {
     322       20753 :         return ALGselect2nil(result, bid, sid, low, high, li, hi, anti, &(bit){0});
     323             : }
     324             : 
     325             : static str
     326       42879 : ALGselect1(bat *result, const bat *bid, const void *low, const void *high,
     327             :                    const bit *li, const bit *hi, const bit *anti)
     328             : {
     329       42879 :         return ALGselect2nil(result, bid, NULL, low, high, li, hi, anti, &(bit){0});
     330             : }
     331             : 
     332             : static str
     333         272 : ALGselect1nil(bat *result, const bat *bid, const void *low, const void *high,
     334             :                           const bit *li, const bit *hi, const bit *anti, const bit *unknown)
     335             : {
     336         272 :         return ALGselect2nil(result, bid, NULL, low, high, li, hi, anti, unknown);
     337             : }
     338             : 
     339             : static str
     340      323539 : ALGthetaselect2(bat *result, const bat *bid, const bat *sid, const void *val,
     341             :                                 const char **op)
     342             : {
     343      323539 :         BAT *b, *s = NULL, *bn;
     344             : 
     345      323539 :         if ((b = BATdescriptor(*bid)) == NULL) {
     346           0 :                 throw(MAL, "algebra.thetaselect",
     347             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     348             :         }
     349      323525 :         if (sid && !is_bat_nil(*sid) && (s = BATdescriptor(*sid)) == NULL) {
     350           0 :                 BBPunfix(b->batCacheid);
     351           0 :                 throw(MAL, "algebra.thetaselect",
     352             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     353             :         }
     354      323505 :         derefStr(b, val);
     355      323505 :         bn = BATthetaselect(b, s, val, *op);
     356      323519 :         BBPunfix(b->batCacheid);
     357      323510 :         BBPreclaim(s);
     358      323513 :         if (bn == NULL)
     359           0 :                 throw(MAL, "algebra.select", GDK_EXCEPTION);
     360      323513 :         *result = bn->batCacheid;
     361      323513 :         BBPkeepref(bn);
     362      323513 :         return MAL_SUCCEED;
     363             : }
     364             : 
     365             : static str
     366         396 : ALGmarkselect(bat *r1, bat *r2, const bat *gid, const bat *mid, const bat *pid, const bit *Any)
     367             : {
     368         396 :         BAT *g = BATdescriptor(*gid); /* oid */
     369         396 :         BAT *m = BATdescriptor(*mid); /* bit, true: match, false: empty set, nil: nil on left */
     370         396 :         BAT *p = BATdescriptor(*pid); /* bit */
     371         396 :         BAT *res1 = NULL, *res2 = NULL;
     372         396 :         bit any = *Any; /* any or normal comparison semantics */
     373             : 
     374         396 :         if (!g || !m || !p) {
     375           0 :                 if (g) BBPreclaim(g);
     376           0 :                 if (m) BBPreclaim(m);
     377           0 :                 if (p) BBPreclaim(p);
     378           0 :                 throw(MAL, "algebra.markselect", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     379             :         }
     380         396 :         BUN nr = BATcount(g), q = 0;
     381             : 
     382         396 :         if ((res1 = COLnew(0, TYPE_oid, nr, TRANSIENT)) == NULL || (res2 = COLnew(0, TYPE_bit, nr, TRANSIENT)) == NULL) {
     383             :                 BBPreclaim(g);
     384           0 :                 BBPreclaim(m);
     385           0 :                 BBPreclaim(p);
     386           0 :                 if (res1) BBPreclaim(res1);
     387           0 :                 throw(MAL, "algebra.markselect", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     388             :         }
     389         396 :         assert(g->tsorted);
     390         396 :         oid *ri1 = Tloc(res1, 0);
     391         396 :         bit *ri2 = Tloc(res2, 0);
     392         396 :         bit *mi = Tloc(m, 0);
     393         396 :         bit *pi = Tloc(p, 0);
     394         396 :         oid cur = oid_nil;
     395             : 
     396         396 :         if (g->ttype == TYPE_void) { /* void case ? */
     397          31 :                 oid c = g->hseqbase;
     398         127 :                 for (BUN n = 0; n < nr; n++, c++) {
     399          96 :                         ri1[q] = c;
     400          96 :                         ri2[q] = FALSE;
     401          96 :                         if (pi[n] == TRUE && mi[n] == TRUE)
     402           7 :                                 ri2[q] = TRUE;
     403          89 :                         else if ((mi[n] == bit_nil && pi[n] != bit_nil && !any) || (mi[n] != FALSE && pi[n] == bit_nil && any))
     404           7 :                                 ri2[q] = bit_nil;
     405          96 :                         q++;
     406             :                 }
     407             :         } else {
     408         365 :                 oid *gi = Tloc(g, 0);
     409         365 :                 oid c = g->hseqbase;
     410         365 :                 if (nr)
     411         365 :                         cur = gi[0];
     412             :                 bit m = FALSE;
     413             :                 bool has_nil = false;
     414      332661 :                 for (BUN n = 0; n < nr; n++, c++) {
     415      332296 :                         if (c && cur != gi[n]) {
     416       57735 :                                 ri1[q] = c-1;
     417       57735 :                                 ri2[q] = (m == TRUE)?TRUE:(has_nil)?bit_nil:FALSE;
     418       57735 :                                 q++;
     419       57735 :                                 cur = gi[n];
     420       57735 :                                 m = FALSE;
     421       57735 :                                 has_nil = false;
     422             :                         }
     423      332296 :                         if (m == TRUE)
     424      191843 :                                 continue;
     425             : 
     426      140453 :                         if (pi[n] == TRUE && mi[n] == TRUE)
     427             :                                 m = TRUE;
     428      133526 :                         else if ((mi[n] == bit_nil && pi[n] != bit_nil && !any) || (mi[n] != FALSE && pi[n] == bit_nil && any))
     429      332296 :                                 has_nil = true;
     430             :                 }
     431         365 :                 if (nr) {
     432         365 :                         ri1[q] = c-1;
     433         365 :                         ri2[q] = (m == TRUE)?TRUE:(has_nil)?bit_nil:FALSE;
     434             :                 }
     435         365 :                 q++;
     436             :         }
     437         396 :         BATsetcount(res1, q);
     438         396 :         BATsetcount(res2, q);
     439         396 :         res1->tsorted = true;
     440         396 :         res1->tkey = true;
     441         396 :         res1->trevsorted = false;
     442         396 :         res2->tsorted = false;
     443         396 :         res2->trevsorted = false;
     444         396 :         res1->tnil = false;
     445         396 :         res1->tnonil = true;
     446         396 :         res2->tnonil = false;
     447         396 :         res2->tkey = false;
     448             : 
     449         396 :         BBPreclaim(g);
     450         396 :         BBPreclaim(m);
     451         396 :         BBPreclaim(p);
     452             : 
     453         396 :         BBPkeepref(res1);
     454         396 :         BBPkeepref(res2);
     455         396 :         *r1 = res1->batCacheid;
     456         396 :         *r2 = res2->batCacheid;
     457         396 :         return MAL_SUCCEED;
     458             : }
     459             : 
     460             : static str
     461          38 : ALGouterselect(bat *r1, bat *r2, const bat *gid, const bat *mid, const bat *pid, const bit *Any)
     462             : {
     463          38 :         BAT *g = BATdescriptor(*gid); /* oid */
     464          38 :         BAT *m = BATdescriptor(*mid); /* bit, true: match, false: empty set, nil: nil on left */
     465          38 :         BAT *p = BATdescriptor(*pid); /* bit */
     466          38 :         BAT *res1 = NULL, *res2 = NULL;
     467          38 :         bit any = *Any; /* any or normal comparison semantics */
     468             : 
     469          38 :         if (!g || !m || !p) {
     470           0 :                 if (g) BBPreclaim(g);
     471           0 :                 if (m) BBPreclaim(m);
     472           0 :                 if (p) BBPreclaim(p);
     473           0 :                 throw(MAL, "algebra.outerselect", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     474             :         }
     475          38 :         BUN nr = BATcount(g), q = 0;
     476             : 
     477          38 :         if ((res1 = COLnew(0, TYPE_oid, nr, TRANSIENT)) == NULL || (res2 = COLnew(0, TYPE_bit, nr, TRANSIENT)) == NULL) {
     478             :                 BBPreclaim(g);
     479           0 :                 BBPreclaim(m);
     480           0 :                 BBPreclaim(p);
     481           0 :                 if (res1) BBPreclaim(res1);
     482           0 :                 throw(MAL, "algebra.outerselect", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     483             :         }
     484          38 :         assert(g->tsorted);
     485          38 :         oid *ri1 = Tloc(res1, 0);
     486          38 :         bit *ri2 = Tloc(res2, 0);
     487          38 :         bit *mi = Tloc(m, 0);
     488          38 :         bit *pi = Tloc(p, 0);
     489          38 :         oid cur = oid_nil;
     490             : 
     491          38 :         if (g->ttype == TYPE_void) { /* void case ? */
     492          12 :                 oid c = g->hseqbase;
     493         101 :                 for (BUN n = 0; n < nr; n++, c++) {
     494          89 :                         ri1[q] = c;
     495         161 :                         ri2[q] = (any && (mi[n] == bit_nil || pi[n] == bit_nil))?bit_nil:(mi[n] == TRUE && pi[n] == TRUE)?TRUE:FALSE;
     496          89 :                         q++;
     497             :                 }
     498             :         } else {
     499          26 :                 oid *gi = Tloc(g, 0);
     500          26 :                 oid c = g->hseqbase;
     501          26 :                 if (nr)
     502          26 :                         cur = gi[0];
     503             :                 bool used = false;
     504         602 :                 for (BUN n = 0; n < nr; n++, c++) {
     505         576 :                         if (c && cur != gi[n]) {
     506         159 :                                 if (!used) {
     507           3 :                                         ri1[q] = c-1;
     508           3 :                                         ri2[q] = false;
     509           3 :                                         q++;
     510             :                                 }
     511         159 :                                 used = false;
     512         159 :                                 cur = gi[n];
     513             :                         }
     514         576 :                         if (mi[n] == TRUE && pi[n] == TRUE) {
     515         322 :                                 ri1[q] = c;
     516         322 :                                 ri2[q] = TRUE;
     517         322 :                                 used = true;
     518         322 :                                 q++;
     519         254 :                         } else if (mi[n] == FALSE) { /* empty */
     520          55 :                                 ri1[q] = c;
     521          55 :                                 ri2[q] = FALSE;
     522          55 :                                 used = true;
     523          55 :                                 q++;
     524         199 :                         } else if (any && (mi[n] == bit_nil /* ie has nil */ || pi[n] == bit_nil)) {
     525           6 :                                 ri1[q] = c;
     526           6 :                                 ri2[q] = bit_nil;
     527           6 :                                 used = true;
     528           6 :                                 q++;
     529             :                         }
     530             :                 }
     531          26 :                 if (nr && !used) {
     532           1 :                         ri1[q] = c-1;
     533           1 :                         ri2[q] = FALSE;
     534           1 :                         q++;
     535             :                 }
     536             :         }
     537          38 :         BATsetcount(res1, q);
     538          38 :         BATsetcount(res2, q);
     539          38 :         res1->tsorted = true;
     540          38 :         res1->tkey = true;
     541          38 :         res1->trevsorted = false;
     542          38 :         res2->tsorted = false;
     543          38 :         res2->trevsorted = false;
     544          38 :         res1->tnil = false;
     545          38 :         res1->tnonil = true;
     546          38 :         res2->tnonil = false;
     547          38 :         res2->tkey = false;
     548             : 
     549          38 :         BBPreclaim(g);
     550          38 :         BBPreclaim(m);
     551          38 :         BBPreclaim(p);
     552             : 
     553          38 :         BBPkeepref(res1);
     554          38 :         BBPkeepref(res2);
     555          38 :         *r1 = res1->batCacheid;
     556          38 :         *r2 = res2->batCacheid;
     557          38 :         return MAL_SUCCEED;
     558             : }
     559             : 
     560             : 
     561             : static str
     562        1540 : ALGselectNotNil(bat *result, const bat *bid)
     563             : {
     564        1540 :         BAT *b;
     565             : 
     566        1540 :         if ((b = BATdescriptor(*bid)) == NULL)
     567           0 :                 throw(MAL, "algebra.selectNotNil",
     568             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     569             : 
     570        1540 :         MT_lock_set(&b->theaplock);
     571        1540 :         bool bnonil = b->tnonil || b->ttype == TYPE_msk;
     572        1540 :         MT_lock_unset(&b->theaplock);
     573        1540 :         if (!bnonil) {
     574          97 :                 BAT *s;
     575          97 :                 s = BATselect(b, NULL, ATOMnilptr(b->ttype), NULL, true, true, true, false);
     576          97 :                 if (s) {
     577          97 :                         BAT *bn = BATproject(s, b);
     578          97 :                         BBPunfix(s->batCacheid);
     579          97 :                         if (bn) {
     580          97 :                                 BBPunfix(b->batCacheid);
     581          97 :                                 *result = bn->batCacheid;
     582          97 :                                 BBPkeepref(bn);
     583          97 :                                 return MAL_SUCCEED;
     584             :                         }
     585             :                 }
     586           0 :                 BBPunfix(b->batCacheid);
     587           0 :                 throw(MAL, "algebra.selectNotNil", GDK_EXCEPTION);
     588             :         }
     589             :         /* just pass on the result */
     590        1443 :         *result = b->batCacheid;
     591        1443 :         BBPkeepref(b);
     592        1443 :         return MAL_SUCCEED;
     593             : }
     594             : 
     595             : static str
     596      290705 : 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 */
     597             :                 const bit *nil_matches, const bit *not_in, const bit *max_one,
     598             :                 const lng *estimate,
     599             :                 gdk_return (*joinfunc)(BAT **, BAT **, BAT *, BAT *, BAT *, BAT *,
     600             :                                                            bool, BUN),
     601             :                 gdk_return (*semifunc)(BAT **, BAT **, BAT *, BAT *, BAT *, BAT *,
     602             :                                                           bool, bool, BUN),
     603             :                 gdk_return (*markfunc)(BAT **, BAT **, BAT **,
     604             :                                                            BAT *, BAT *, BAT *, BAT *, BUN),
     605             :                 gdk_return (*thetafunc)(BAT **, BAT **, BAT *, BAT *, BAT *, BAT *,
     606             :                                                            int, bool, BUN),
     607             :                 gdk_return (*bandfunc)(BAT **, BAT **, BAT *, BAT *, BAT *, BAT *,
     608             :                                                           const void *, const void *, bool, bool, BUN),
     609             :                 gdk_return (*rangefunc)(BAT **, BAT **, BAT *, BAT *, BAT *,
     610             :                                                            BAT *, BAT *, bool, bool, bool, bool, BUN),
     611             :                 BAT * (*difffunc)(BAT *, BAT *, BAT *, BAT *, bool, bool, BUN),
     612             :                 BAT * (*interfunc)(BAT *, BAT *, BAT *, BAT *, bool, bool, BUN),
     613             :                 const char *funcname)
     614             : {
     615      290705 :         BAT *left = NULL, *right = NULL, *right2 = NULL;
     616      290705 :         BAT *candleft = NULL, *candright = NULL;
     617      290705 :         BAT *result1 = NULL, *result2 = NULL, *result3 = NULL;
     618      290705 :         BUN est;
     619      290705 :         const char *err = SQLSTATE(HY002) RUNTIME_OBJECT_MISSING;
     620             : 
     621      290705 :         assert(r2id == NULL || rangefunc != NULL);
     622             : 
     623      290705 :         if ((left = BATdescriptor(*lid)) == NULL)
     624           0 :                 goto fail;
     625      290685 :         if ((right = BATdescriptor(*rid)) == NULL)
     626           0 :                 goto fail;
     627      290687 :         if (slid && !is_bat_nil(*slid) && (candleft = BATdescriptor(*slid)) == NULL)
     628           0 :                 goto fail;
     629      290687 :         if (srid && !is_bat_nil(*srid)
     630           0 :                 && (candright = BATdescriptor(*srid)) == NULL)
     631           0 :                 goto fail;
     632      290687 :         if (estimate == NULL || *estimate < 0 || is_lng_nil(*estimate)
     633           0 :                 || *estimate > (lng) BUN_MAX)
     634             :                 est = BUN_NONE;
     635             :         else
     636           0 :                 est = (BUN) *estimate;
     637             : 
     638      290687 :         err = NULL;                                     /* most likely error now is GDK_EXCEPTION */
     639             : 
     640      290687 :         if (thetafunc) {
     641       16827 :                 assert(joinfunc == NULL);
     642       16827 :                 assert(semifunc == NULL);
     643       16827 :                 assert(markfunc == NULL);
     644       16827 :                 assert(bandfunc == NULL);
     645       16827 :                 assert(rangefunc == NULL);
     646       16827 :                 assert(difffunc == NULL);
     647       16827 :                 assert(interfunc == NULL);
     648       16827 :                 if ((*thetafunc)
     649             :                         (&result1, r2 ? &result2 : NULL, left, right, candleft, candright,
     650       16827 :                          op, *nil_matches, est) != GDK_SUCCEED)
     651           0 :                         goto fail;
     652      273860 :         } else if (joinfunc) {
     653      193106 :                 assert(semifunc == NULL);
     654      193106 :                 assert(markfunc == NULL);
     655      193106 :                 assert(bandfunc == NULL);
     656      193106 :                 assert(rangefunc == NULL);
     657      193106 :                 assert(difffunc == NULL);
     658      193106 :                 assert(interfunc == NULL);
     659      193106 :                 if ((*joinfunc)
     660             :                         (&result1, r2 ? &result2 : NULL, left, right, candleft, candright,
     661      193106 :                          *nil_matches, est) != GDK_SUCCEED)
     662           1 :                         goto fail;
     663       80754 :         } else if (semifunc) {
     664         332 :                 assert(markfunc == NULL);
     665         332 :                 assert(bandfunc == NULL);
     666         332 :                 assert(rangefunc == NULL);
     667         332 :                 assert(difffunc == NULL);
     668         332 :                 assert(interfunc == NULL);
     669         332 :                 if ((*semifunc)
     670             :                         (&result1, r2 ? &result2 : NULL, left, right, candleft, candright,
     671         332 :                          *nil_matches, *max_one, est) != GDK_SUCCEED)
     672          42 :                         goto fail;
     673       80422 :         } else if (markfunc) {
     674        3318 :                 assert(bandfunc == NULL);
     675        3318 :                 assert(rangefunc == NULL);
     676        3318 :                 assert(difffunc == NULL);
     677        3318 :                 assert(interfunc == NULL);
     678        6631 :                 if ((*markfunc) (&result1, r2 ? &result2 : NULL, &result3,
     679             :                                                  left, right, candleft, candright, est) != GDK_SUCCEED)
     680           0 :                         goto fail;
     681       77104 :         } else if (bandfunc) {
     682           0 :                 assert(rangefunc == NULL);
     683           0 :                 assert(difffunc == NULL);
     684           0 :                 assert(interfunc == NULL);
     685           0 :                 if ((*bandfunc)
     686             :                         (&result1, r2 ? &result2 : NULL, left, right, candleft, candright,
     687             :                          c1, c2, li, hi, est) != GDK_SUCCEED)
     688           0 :                         goto fail;
     689       77104 :         } else if (rangefunc) {
     690         125 :                 assert(difffunc == NULL);
     691         125 :                 assert(interfunc == NULL);
     692         125 :                 if ((right2 = BATdescriptor(*r2id)) == NULL) {
     693           0 :                         err = SQLSTATE(HY002) RUNTIME_OBJECT_MISSING;
     694           0 :                         goto fail;
     695             :                 }
     696         148 :                 if ((*rangefunc)
     697             :                         (&result1, r2 ? &result2 : NULL, left, right, right2, candleft,
     698             :                          candright, li, hi, anti, symmetric, est) != GDK_SUCCEED)
     699           0 :                         goto fail;
     700         125 :                 BBPunfix(right2->batCacheid);
     701       76979 :         } else if (difffunc) {
     702       71239 :                 assert(r2 == NULL);
     703       71239 :                 assert(interfunc == NULL);
     704       71239 :                 if ((result1 = (*difffunc) (left, right, candleft, candright,
     705       71239 :                                                                         *nil_matches, *not_in, est)) == NULL)
     706           0 :                         goto fail;
     707             :         } else {
     708        5740 :                 assert(r2 == NULL);
     709        5741 :                 if ((result1 = (*interfunc) (left, right, candleft, candright,
     710        5740 :                                                                          *nil_matches, *max_one, est)) == NULL)
     711           1 :                         goto fail;
     712             :         }
     713      290627 :         *r1 = result1->batCacheid;
     714      290627 :         BBPkeepref(result1);
     715      290601 :         if (r2) {
     716      173854 :                 *r2 = result2->batCacheid;
     717      173854 :                 BBPkeepref(result2);
     718             :         }
     719      290586 :         if (r3) {
     720        3318 :                 *r3 = result3->batCacheid;
     721        3318 :                 BBPkeepref(result3);
     722             :         }
     723      290586 :         BBPunfix(left->batCacheid);
     724      290591 :         BBPunfix(right->batCacheid);
     725      290603 :         BBPreclaim(candleft);
     726      290603 :         BBPreclaim(candright);
     727             :         return MAL_SUCCEED;
     728             : 
     729          44 :   fail:
     730          44 :         BBPreclaim(left);
     731          44 :         BBPreclaim(right);
     732          44 :         BBPreclaim(right2);
     733          44 :         BBPreclaim(candleft);
     734          44 :         BBPreclaim(candright);
     735          44 :         if (err == NULL)
     736          44 :                 throw(MAL, funcname, GDK_EXCEPTION);
     737           0 :         throw(MAL, funcname, "%s", err);
     738             : }
     739             : 
     740             : static str
     741      168567 : ALGjoin(bat *r1, bat *r2, const bat *lid, const bat *rid, const bat *slid,
     742             :                 const bat *srid, const bit *nil_matches, const lng *estimate)
     743             : {
     744      168567 :         return do_join(r1, r2, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     745             :                                    false, false, false, false, nil_matches, NULL, NULL,
     746             :                                    estimate, BATjoin, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
     747             :                                    "algebra.join");
     748             : }
     749             : 
     750             : static str
     751       23906 : ALGjoin1(bat *r1, const bat *lid, const bat *rid, const bat *slid,
     752             :                  const bat *srid, const bit *nil_matches, const lng *estimate)
     753             : {
     754       23906 :         return do_join(r1, NULL, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     755             :                                    false, false, false, false, nil_matches, NULL, NULL,
     756             :                                    estimate, BATjoin, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
     757             :                                    "algebra.join");
     758             : }
     759             : 
     760             : static str
     761         645 : ALGleftjoin(bat *r1, bat *r2, const bat *lid, const bat *rid, const bat *slid,
     762             :                         const bat *srid, const bit *nil_matches, const lng *estimate)
     763             : {
     764         645 :         return do_join(r1, r2, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     765             :                                    false, false, false, false, nil_matches, NULL, NULL,
     766             :                                    estimate, BATleftjoin, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
     767             :                                    "algebra.leftjoin");
     768             : }
     769             : 
     770             : static str
     771           0 : ALGleftjoin1(bat *r1, const bat *lid, const bat *rid, const bat *slid,
     772             :                          const bat *srid, const bit *nil_matches, const lng *estimate)
     773             : {
     774           0 :         return do_join(r1, NULL, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     775             :                                    false, false, false, false, nil_matches, NULL, NULL,
     776             :                                    estimate, BATleftjoin, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
     777             :                                    "algebra.leftjoin");
     778             : }
     779             : 
     780             : static str
     781         123 : ALGouterjoin(bat *r1, bat *r2, const bat *lid, const bat *rid, const bat *slid,
     782             :                          const bat *srid, const bit *nil_matches, const bit *match_one,
     783             :                          const lng *estimate)
     784             : {
     785         123 :         return do_join(r1, r2, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     786             :                                    false, false, false, false, nil_matches, NULL, match_one,
     787             :                                    estimate, NULL, BATouterjoin, NULL, NULL, NULL, NULL, NULL, NULL,
     788             :                                    "algebra.outerjoin");
     789             : }
     790             : 
     791             : static str
     792           0 : ALGouterjoin1(bat *r1, const bat *lid, const bat *rid, const bat *slid,
     793             :                           const bat *srid, const bit *nil_matches, const bit *match_one,
     794             :                           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, match_one,
     798             :                                    estimate, NULL, BATouterjoin, NULL, NULL, NULL, NULL, NULL, NULL,
     799             :                                    "algebra.outerjoin");
     800             : }
     801             : 
     802             : static str
     803         209 : ALGsemijoin(bat *r1, bat *r2, const bat *lid, const bat *rid, const bat *slid,
     804             :                         const bat *srid, const bit *nil_matches, const bit *max_one,
     805             :                         const lng *estimate)
     806             : {
     807         209 :         return do_join(r1, r2, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     808             :                                    false, false, false, false, nil_matches, NULL, max_one,
     809             :                                    estimate, NULL, BATsemijoin, NULL, NULL, NULL, NULL, NULL, NULL,
     810             :                                    "algebra.semijoin");
     811             : }
     812             : 
     813             : static str
     814        3313 : ALGmark2join(bat *r1, bat *r3, const bat *lid, const bat *rid,
     815             :                          const bat *slid, const bat *srid, const lng *estimate)
     816             : {
     817        3313 :         return do_join(r1, NULL, r3, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     818             :                                    false, false, false, false, NULL, NULL, NULL,
     819             :                                    estimate, NULL, NULL, BATmarkjoin, NULL, NULL, NULL, NULL, NULL,
     820             :                                    "algebra.markjoin");
     821             : }
     822             : 
     823             : static str
     824           5 : ALGmark3join(bat *r1, bat *r2, bat *r3, const bat *lid, const bat *rid,
     825             :                          const bat *slid, const bat *srid, const lng *estimate)
     826             : {
     827           5 :         return do_join(r1, r2, r3, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     828             :                                    false, false, false, false, NULL, NULL, NULL,
     829             :                                    estimate, NULL, NULL, BATmarkjoin, NULL, NULL, NULL, NULL, NULL,
     830             :                                    "algebra.markjoin");
     831             : }
     832             : 
     833             : static str
     834        4293 : ALGthetajoin(bat *r1, bat *r2, const bat *lid, const bat *rid, const bat *slid,
     835             :                          const bat *srid, const int *op, const bit *nil_matches,
     836             :                          const lng *estimate)
     837             : {
     838        4293 :         return do_join(r1, r2, NULL, lid, rid, NULL, slid, srid, *op, NULL, NULL,
     839             :                                    false, false, false, false, nil_matches, NULL, NULL,
     840             :                                    estimate, NULL, NULL, NULL, BATthetajoin, NULL, NULL, NULL, NULL,
     841             :                                    "algebra.thetajoin");
     842             : }
     843             : 
     844             : static str
     845       12538 : ALGthetajoin1(bat *r1, const bat *lid, const bat *rid, const bat *slid,
     846             :                           const bat *srid, const int *op, const bit *nil_matches,
     847             :                           const lng *estimate)
     848             : {
     849       12538 :         return do_join(r1, NULL, NULL, lid, rid, NULL, slid, srid, *op, NULL, NULL,
     850             :                                    false, false, false, false, nil_matches, NULL, NULL,
     851             :                                    estimate, NULL, NULL, NULL, BATthetajoin, NULL, NULL, NULL, NULL,
     852             :                                    "algebra.thetajoin");
     853             : }
     854             : 
     855             : static str
     856           0 : ALGbandjoin(bat *r1, bat *r2, const bat *lid, const bat *rid, const bat *slid,
     857             :                         const bat *srid, const void *c1, const void *c2, const bit *li,
     858             :                         const bit *hi, const lng *estimate)
     859             : {
     860           0 :         return do_join(r1, r2, NULL, lid, rid, NULL, slid, srid, 0, c1, c2,
     861           0 :                                    *li, *hi, false, false, NULL, NULL, NULL, estimate,
     862             :                                    NULL, NULL, NULL, NULL, BATbandjoin, NULL, NULL, NULL,
     863             :                                    "algebra.bandjoin");
     864             : }
     865             : 
     866             : static str
     867           0 : ALGbandjoin1(bat *r1, const bat *lid, const bat *rid, const bat *slid,
     868             :                          const bat *srid, const void *c1, const void *c2, const bit *li,
     869             :                          const bit *hi, const lng *estimate)
     870             : {
     871           0 :         return do_join(r1, NULL, NULL, lid, rid, NULL, slid, srid, 0, c1, c2,
     872           0 :                                    *li, *hi, false, false, NULL, NULL, NULL, estimate,
     873             :                                    NULL, NULL, NULL, NULL, BATbandjoin, NULL, NULL, NULL,
     874             :                                    "algebra.bandjoin");
     875             : }
     876             : 
     877             : static str
     878         102 : ALGrangejoin(bat *r1, bat *r2, const bat *lid, const bat *rlid, const bat *rhid,
     879             :                          const bat *slid, const bat *srid, const bit *li, const bit *hi,
     880             :                          const bit *anti, const bit *symmetric, const lng *estimate)
     881             : {
     882         204 :         return do_join(r1, r2, NULL, lid, rlid, rhid, slid, srid, 0, NULL, NULL,
     883         102 :                                    *li, *hi, *anti, *symmetric, NULL, NULL, NULL, estimate,
     884             :                                    NULL, NULL, NULL, NULL, NULL, BATrangejoin, NULL, NULL,
     885             :                                    "algebra.rangejoin");
     886             : }
     887             : 
     888             : static str
     889          23 : ALGrangejoin1(bat *r1, const bat *lid, const bat *rlid, const bat *rhid,
     890             :                           const bat *slid, const bat *srid, const bit *li, const bit *hi,
     891             :                           const bit *anti, const bit *symmetric, const lng *estimate)
     892             : {
     893          46 :         return do_join(r1, NULL, NULL, lid, rlid, rhid, slid, srid, 0, NULL, NULL,
     894          23 :                                    *li, *hi, *anti, *symmetric, NULL, NULL, NULL, estimate,
     895             :                                    NULL, NULL, NULL, NULL, NULL, BATrangejoin, NULL, NULL,
     896             :                                    "algebra.rangejoin");
     897             : }
     898             : 
     899             : static str
     900       71241 : ALGdifference(bat *r1, const bat *lid, const bat *rid, const bat *slid,
     901             :                           const bat *srid, const bit *nil_matches, const bit *not_in,
     902             :                           const lng *estimate)
     903             : {
     904       71241 :         return do_join(r1, NULL, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     905             :                                    false, false, false, false, nil_matches, not_in, NULL,
     906             :                                    estimate, NULL, NULL, NULL, NULL, NULL, NULL, BATdiff, NULL,
     907             :                                    "algebra.difference");
     908             : }
     909             : 
     910             : static str
     911        5741 : ALGintersect(bat *r1, const bat *lid, const bat *rid, const bat *slid,
     912             :                          const bat *srid, const bit *nil_matches, const bit *max_one,
     913             :                          const lng *estimate)
     914             : {
     915        5741 :         return do_join(r1, NULL, NULL, lid, rid, NULL, slid, srid, 0, NULL, NULL,
     916             :                                    false, false, false, false, nil_matches, NULL, max_one,
     917             :                                    estimate, NULL, NULL, NULL, NULL, NULL, NULL, NULL, BATintersect,
     918             :                                    "algebra.intersect");
     919             : }
     920             : 
     921             : /* algebra.firstn(b:bat[:any],
     922             :  *                [ s:bat[:oid],
     923             :  *                [ g:bat[:oid], ] ]
     924             :  *                n:lng,
     925             :  *                asc:bit,
     926             :  *                nilslast:bit,
     927             :  *                distinct:bit)
     928             :  * returns :bat[:oid] [ , :bat[:oid] ]
     929             :  */
     930             : static str
     931        1208 : ALGfirstn(Client cntxt, MalBlkPtr mb, MalStkPtr stk, InstrPtr pci)
     932             : {
     933        1208 :         bat *ret1, *ret2 = NULL;
     934        1208 :         bat bid, sid, gid;
     935        1208 :         BAT *b, *s = NULL, *g = NULL;
     936        1208 :         BAT *bn = NULL, *gn = NULL;
     937        1208 :         lng n;
     938        1208 :         bit asc, nilslast, distinct;
     939        1208 :         gdk_return rc;
     940             : 
     941        1208 :         (void) cntxt;
     942        1208 :         (void) mb;
     943             : 
     944        1208 :         assert(pci->retc == 1 || pci->retc == 2);
     945        1208 :         assert(pci->argc - pci->retc >= 5 && pci->argc - pci->retc <= 7);
     946             : 
     947        1208 :         n = *getArgReference_lng(stk, pci, pci->argc - 4);
     948        1208 :         if (n < 0)
     949           0 :                 throw(MAL, "algebra.firstn", ILLEGAL_ARGUMENT);
     950        1208 :         if (n > (lng) BUN_MAX)
     951             :                 n = BUN_MAX;
     952        1208 :         ret1 = getArgReference_bat(stk, pci, 0);
     953        1208 :         if (pci->retc == 2)
     954         458 :                 ret2 = getArgReference_bat(stk, pci, 1);
     955        1208 :         bid = *getArgReference_bat(stk, pci, pci->retc);
     956        1208 :         if ((b = BATdescriptor(bid)) == NULL)
     957           0 :                 throw(MAL, "algebra.firstn", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     958        1208 :         if (pci->argc - pci->retc > 5) {
     959        1208 :                 sid = *getArgReference_bat(stk, pci, pci->retc + 1);
     960        1208 :                 if (!is_bat_nil(sid) && (s = BATdescriptor(sid)) == NULL) {
     961           0 :                         BBPunfix(bid);
     962           0 :                         throw(MAL, "algebra.firstn",
     963             :                                   SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     964             :                 }
     965        1208 :                 if (pci->argc - pci->retc > 6) {
     966        1208 :                         gid = *getArgReference_bat(stk, pci, pci->retc + 2);
     967        1208 :                         if (!is_bat_nil(gid) && (g = BATdescriptor(gid)) == NULL) {
     968           0 :                                 BBPunfix(bid);
     969           0 :                                 BBPunfix(sid);
     970           0 :                                 throw(MAL, "algebra.firstn",
     971             :                                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
     972             :                         }
     973             :                 }
     974             :         }
     975        1208 :         asc = *getArgReference_bit(stk, pci, pci->argc - 3);
     976        1208 :         nilslast = *getArgReference_bit(stk, pci, pci->argc - 2);
     977        1208 :         distinct = *getArgReference_bit(stk, pci, pci->argc - 1);
     978        1958 :         rc = BATfirstn(&bn, ret2 ? &gn : NULL, b, s, g, (BUN) n, asc, nilslast,
     979             :                                    distinct);
     980        1208 :         BBPunfix(b->batCacheid);
     981        1208 :         BBPreclaim(s);
     982        1208 :         BBPreclaim(g);
     983        1208 :         if (rc != GDK_SUCCEED)
     984           0 :                 throw(MAL, "algebra.firstn", GDK_EXCEPTION);
     985        1208 :         *ret1 = bn->batCacheid;
     986        1208 :         BBPkeepref(bn);
     987        1208 :         if (ret2) {
     988         458 :                 *ret2 = gn->batCacheid;
     989         458 :                 BBPkeepref(gn);
     990             :         }
     991             :         return MAL_SUCCEED;
     992             : }
     993             : 
     994             : static str
     995           9 : ALGunary(bat *result, const bat *bid, BAT *(*func)(BAT *), const char *name)
     996             : {
     997           9 :         BAT *b, *bn;
     998             : 
     999           9 :         if ((b = BATdescriptor(*bid)) == NULL) {
    1000           0 :                 throw(MAL, name, SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1001             :         }
    1002           9 :         bn = (*func) (b);
    1003           9 :         BBPunfix(b->batCacheid);
    1004           9 :         if (bn == NULL)
    1005           0 :                 throw(MAL, name, GDK_EXCEPTION);
    1006           9 :         *result = bn->batCacheid;
    1007           9 :         BBPkeepref(bn);
    1008           9 :         return MAL_SUCCEED;
    1009             : }
    1010             : 
    1011             : static inline BAT *
    1012           9 : BATwcopy(BAT *b)
    1013             : {
    1014           9 :         return COLcopy(b, b->ttype, true, TRANSIENT);
    1015             : }
    1016             : 
    1017             : static str
    1018           9 : ALGcopy(bat *result, const bat *bid)
    1019             : {
    1020           9 :         return ALGunary(result, bid, BATwcopy, "algebra.copy");
    1021             : }
    1022             : 
    1023             : static str
    1024          74 : ALGunique(bat *result, const bat *bid, const bat *sid)
    1025             : {
    1026          74 :         BAT *b, *s = NULL, *bn = NULL;
    1027             : 
    1028          74 :         if ((b = BATdescriptor(*bid)) == NULL) {
    1029           0 :                 throw(MAL, "algebra.unique", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1030             :         }
    1031          74 :         if (sid && !is_bat_nil(*sid) && (s = BATdescriptor(*sid)) == NULL) {
    1032           0 :                 BBPunfix(b->batCacheid);
    1033           0 :                 throw(MAL, "algebra.unique", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1034             :         }
    1035          74 :         bn = BATunique(b, s);
    1036          74 :         BBPunfix(b->batCacheid);
    1037          74 :         BBPreclaim(s);
    1038          74 :         if (bn == NULL)
    1039           0 :                 throw(MAL, "algebra.unique", GDK_EXCEPTION);
    1040          74 :         *result = bn->batCacheid;
    1041          74 :         BBPkeepref(bn);
    1042          74 :         return MAL_SUCCEED;
    1043             : }
    1044             : 
    1045             : static str
    1046       26514 : ALGcrossproduct(bat *l, bat *r, const bat *left, const bat *right,
    1047             :                                 const bat *slid, const bat *srid, const bit *max_one)
    1048             : {
    1049       26514 :         BAT *L, *R, *bn1, *bn2 = NULL;
    1050       26514 :         BAT *sl = NULL, *sr = NULL;
    1051       26514 :         gdk_return ret;
    1052             : 
    1053       26514 :         L = BATdescriptor(*left);
    1054       26514 :         R = BATdescriptor(*right);
    1055       26513 :         if (L == NULL || R == NULL) {
    1056           0 :                 BBPreclaim(L);
    1057           0 :                 BBPreclaim(R);
    1058           0 :                 throw(MAL, "algebra.crossproduct",
    1059             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1060             :         }
    1061       26513 :         if ((slid && !is_bat_nil(*slid) && (sl = BATdescriptor(*slid)) == NULL) ||
    1062           0 :                 (srid && !is_bat_nil(*srid) && (sr = BATdescriptor(*srid)) == NULL)) {
    1063           0 :                 BBPunfix(L->batCacheid);
    1064           0 :                 BBPunfix(R->batCacheid);
    1065           0 :                 BBPreclaim(sl);
    1066             :                 /* sr == NULL, so no need to unfix */
    1067           0 :                 throw(MAL, "algebra.crossproduct",
    1068             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1069             :         }
    1070       27885 :         ret = BATsubcross(&bn1, r ? &bn2 : NULL, L, R, sl, sr,
    1071       26513 :                                           max_one && !is_bit_nil(*max_one) && *max_one);
    1072       26506 :         BBPunfix(L->batCacheid);
    1073       26508 :         BBPunfix(R->batCacheid);
    1074       26507 :         BBPreclaim(sl);
    1075       26507 :         BBPreclaim(sr);
    1076       26507 :         if (ret != GDK_SUCCEED)
    1077          78 :                 throw(MAL, "algebra.crossproduct", GDK_EXCEPTION);
    1078       26429 :         *l = bn1->batCacheid;
    1079       26429 :         BBPkeepref(bn1);
    1080       26434 :         if (r) {
    1081       25070 :                 *r = bn2->batCacheid;
    1082       25070 :                 BBPkeepref(bn2);
    1083             :         }
    1084             :         return MAL_SUCCEED;
    1085             : }
    1086             : 
    1087             : static str
    1088        1372 : ALGcrossproduct1(bat *l, const bat *left, const bat *right, const bit *max_one)
    1089             : {
    1090        1372 :         return ALGcrossproduct(l, NULL, left, right, NULL, NULL, max_one);
    1091             : }
    1092             : 
    1093             : static str
    1094       25142 : ALGcrossproduct2(bat *l, bat *r, const bat *left, const bat *right,
    1095             :                                  const bit *max_one)
    1096             : {
    1097       25142 :         return ALGcrossproduct(l, r, left, right, NULL, NULL, max_one);
    1098             : }
    1099             : 
    1100             : static str
    1101           0 : ALGcrossproduct3(bat *l, bat *r, const bat *left, const bat *right,
    1102             :                                  const bat *sl, const bat *sr, const bit *max_one)
    1103             : {
    1104           0 :         return ALGcrossproduct(l, r, left, right, sl, sr, max_one);
    1105             : }
    1106             : 
    1107             : static str
    1108           0 : ALGcrossproduct4(bat *l, const bat *left, const bat *right, const bat *sl,
    1109             :                                  const bat *sr, const bit *max_one)
    1110             : {
    1111           0 :         return ALGcrossproduct(l, NULL, left, right, sl, sr, max_one);
    1112             : }
    1113             : 
    1114             : static str
    1115         425 : ALGoutercrossproduct3(bat *l, bat *r, const bat *left, const bat *right, const bat *slid, const bat *srid, const bit *max_one)
    1116             : {
    1117         425 :         BAT *L, *R, *bn1, *bn2 = NULL;
    1118         425 :         BAT *sl = NULL, *sr = NULL;
    1119         425 :         gdk_return ret;
    1120             : 
    1121         425 :         L = BATdescriptor(*left);
    1122         425 :         R = BATdescriptor(*right);
    1123         425 :         if (L == NULL || R == NULL) {
    1124           0 :                 BBPreclaim(L);
    1125           0 :                 BBPreclaim(R);
    1126           0 :                 throw(MAL, "algebra.crossproduct", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1127             :         }
    1128         425 :         if ((slid && !is_bat_nil(*slid) && (sl = BATdescriptor(*slid)) == NULL) ||
    1129         425 :                 (srid && !is_bat_nil(*srid) && (sr = BATdescriptor(*srid)) == NULL)) {
    1130           0 :                 BBPunfix(L->batCacheid);
    1131           0 :                 BBPunfix(R->batCacheid);
    1132           0 :                 BBPreclaim(sl);
    1133             :                 /* sr == NULL, so no need to unfix */
    1134           0 :                 throw(MAL, "algebra.crossproduct", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1135             :         }
    1136         425 :         ret = BAToutercross(&bn1, r ? &bn2 : NULL, L, R, sl, sr,
    1137         425 :                                           max_one && !is_bit_nil(*max_one) && *max_one);
    1138         425 :         BBPunfix(L->batCacheid);
    1139         425 :         BBPunfix(R->batCacheid);
    1140         425 :         BBPreclaim(sl);
    1141         425 :         BBPreclaim(sr);
    1142         425 :         if (ret != GDK_SUCCEED)
    1143           0 :                 throw(MAL, "algebra.crossproduct", GDK_EXCEPTION);
    1144         425 :         *l = bn1->batCacheid;
    1145         425 :         BBPkeepref(bn1);
    1146         425 :         if (r) {
    1147         425 :                 *r = bn2->batCacheid;
    1148         425 :                 BBPkeepref(bn2);
    1149             :         }
    1150             :         return MAL_SUCCEED;
    1151             : }
    1152             : 
    1153             : static str
    1154     1085054 : ALGprojection2(bat *result, const bat *lid, const bat *r1id, const bat *r2id)
    1155             : {
    1156     1085054 :         BAT *l, *r1, *r2 = NULL, *bn;
    1157             : 
    1158     1085054 :         if ((l = BATdescriptor(*lid)) == NULL) {
    1159           0 :                 throw(MAL, "algebra.projection",
    1160             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1161             :         }
    1162     1084991 :         if ((r1 = BATdescriptor(*r1id)) == NULL) {
    1163           0 :                 BBPunfix(l->batCacheid);
    1164           0 :                 throw(MAL, "algebra.projection",
    1165             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1166             :         }
    1167     1084881 :         if (r2id && !is_bat_nil(*r2id) && (r2 = BATdescriptor(*r2id)) == NULL) {
    1168           0 :                 BBPunfix(l->batCacheid);
    1169           0 :                 BBPunfix(r1->batCacheid);
    1170           0 :                 throw(MAL, "algebra.projection",
    1171             :                           SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1172             :         }
    1173     1084881 :         bn = BATproject2(l, r1, r2);
    1174     1084403 :         BBPunfix(l->batCacheid);
    1175     1084882 :         BBPunfix(r1->batCacheid);
    1176     1084813 :         BBPreclaim(r2);
    1177     1084818 :         if (bn == NULL)
    1178           0 :                 throw(MAL, "algebra.projection", GDK_EXCEPTION);
    1179     1084818 :         *result = bn->batCacheid;
    1180     1084818 :         BBPkeepref(bn);
    1181     1084818 :         return MAL_SUCCEED;
    1182             : }
    1183             : 
    1184             : str
    1185     1085053 : ALGprojection(bat *result, const bat *lid, const bat *rid)
    1186             : {
    1187     1085053 :         return ALGprojection2(result, lid, rid, NULL);
    1188             : }
    1189             : 
    1190             : static str
    1191       23804 : ALGsort33(bat *result, bat *norder, bat *ngroup, const bat *bid,
    1192             :                   const bat *order, const bat *group, const bit *reverse,
    1193             :                   const bit *nilslast, const bit *stable)
    1194             : {
    1195       23804 :         BAT *bn = NULL, *on = NULL, *gn = NULL;
    1196       23804 :         BAT *b = NULL, *o = NULL, *g = NULL;
    1197             : 
    1198       23804 :         if ((b = BATdescriptor(*bid)) == NULL)
    1199           0 :                 throw(MAL, "algebra.sort", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1200       23804 :         if (order && !is_bat_nil(*order) && (o = BATdescriptor(*order)) == NULL) {
    1201           0 :                 BBPunfix(b->batCacheid);
    1202           0 :                 throw(MAL, "algebra.sort", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1203             :         }
    1204       23804 :         if (group &&!is_bat_nil(*group) && (g = BATdescriptor(*group)) == NULL) {
    1205           0 :                 BBPreclaim(o);
    1206           0 :                 BBPunfix(b->batCacheid);
    1207           0 :                 throw(MAL, "algebra.sort", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1208             :         }
    1209       27403 :         if (BATsort(result ? &bn : NULL,
    1210             :                                 norder ? &on : NULL,
    1211             :                                 ngroup ? &gn : NULL,
    1212       23804 :                                 b, o, g, *reverse, *nilslast, *stable) != GDK_SUCCEED) {
    1213           0 :                 BBPreclaim(o);
    1214           0 :                 BBPreclaim(g);
    1215           0 :                 BBPunfix(b->batCacheid);
    1216           0 :                 throw(MAL, "algebra.sort", GDK_EXCEPTION);
    1217             :         }
    1218       23804 :         BBPunfix(b->batCacheid);
    1219       23804 :         BBPreclaim(o);
    1220       23804 :         BBPreclaim(g);
    1221       23804 :         if (result) {
    1222       23804 :                 *result = bn->batCacheid;
    1223       23804 :                 BBPkeepref(bn);
    1224             :         }
    1225       23804 :         if (norder) {
    1226       20205 :                 *norder = on->batCacheid;
    1227       20205 :                 BBPkeepref(on);
    1228             :         }
    1229       23804 :         if (ngroup) {
    1230       13509 :                 *ngroup = gn->batCacheid;
    1231       13509 :                 BBPkeepref(gn);
    1232             :         }
    1233             :         return MAL_SUCCEED;
    1234             : }
    1235             : 
    1236             : static str
    1237        4036 : ALGsort32(bat *result, bat *norder, const bat *bid, const bat *order,
    1238             :                   const bat *group, const bit *reverse, const bit *nilslast,
    1239             :                   const bit *stable)
    1240             : {
    1241        4036 :         return ALGsort33(result, norder, NULL, bid, order, group, reverse, nilslast,
    1242             :                                          stable);
    1243             : }
    1244             : 
    1245             : static str
    1246        1958 : ALGsort31(bat *result, const bat *bid, const bat *order, const bat *group,
    1247             :                   const bit *reverse, const bit *nilslast, const bit *stable)
    1248             : {
    1249        1958 :         return ALGsort33(result, NULL, NULL, bid, order, group, reverse, nilslast,
    1250             :                                          stable);
    1251             : }
    1252             : 
    1253             : static str
    1254           0 : ALGsort23(bat *result, bat *norder, bat *ngroup, const bat *bid,
    1255             :                   const bat *order, const bit *reverse, const bit *nilslast,
    1256             :                   const bit *stable)
    1257             : {
    1258           0 :         return ALGsort33(result, norder, ngroup, bid, order, NULL, reverse,
    1259             :                                          nilslast, stable);
    1260             : }
    1261             : 
    1262             : static str
    1263           0 : ALGsort22(bat *result, bat *norder, const bat *bid, const bat *order,
    1264             :                   const bit *reverse, const bit *nilslast, const bit *stable)
    1265             : {
    1266           0 :         return ALGsort33(result, norder, NULL, bid, order, NULL, reverse, nilslast,
    1267             :                                          stable);
    1268             : }
    1269             : 
    1270             : static str
    1271           0 : ALGsort21(bat *result, const bat *bid, const bat *order, const bit *reverse,
    1272             :                   const bit *nilslast, const bit *stable)
    1273             : {
    1274           0 :         return ALGsort33(result, NULL, NULL, bid, order, NULL, reverse, nilslast,
    1275             :                                          stable);
    1276             : }
    1277             : 
    1278             : static str
    1279        6249 : ALGsort13(bat *result, bat *norder, bat *ngroup, const bat *bid,
    1280             :                   const bit *reverse, const bit *nilslast, const bit *stable)
    1281             : {
    1282        6249 :         return ALGsort33(result, norder, ngroup, bid, NULL, NULL, reverse, nilslast,
    1283             :                                          stable);
    1284             : }
    1285             : 
    1286             : static str
    1287        2660 : ALGsort12(bat *result, bat *norder, const bat *bid, const bit *reverse,
    1288             :                   const bit *nilslast, const bit *stable)
    1289             : {
    1290        2660 :         return ALGsort33(result, norder, NULL, bid, NULL, NULL, reverse, nilslast,
    1291             :                                          stable);
    1292             : }
    1293             : 
    1294             : static str
    1295        1641 : ALGsort11(bat *result, const bat *bid, const bit *reverse, const bit *nilslast,
    1296             :                   const bit *stable)
    1297             : {
    1298        1641 :         return ALGsort33(result, NULL, NULL, bid, NULL, NULL, reverse, nilslast,
    1299             :                                          stable);
    1300             : }
    1301             : 
    1302             : static str
    1303       69623 : ALGcountCND_nil(lng *result, const bat *bid, const bat *cnd,
    1304             :                                 const bit *ignore_nils)
    1305             : {
    1306       69623 :         BAT *b, *s = NULL;
    1307             : 
    1308       69623 :         if ((b = BATdescriptor(*bid)) == NULL) {
    1309           0 :                 throw(MAL, "aggr.count", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1310             :         }
    1311       69621 :         if (cnd && !is_bat_nil(*cnd) && (s = BATdescriptor(*cnd)) == NULL) {
    1312           0 :                 BBPunfix(b->batCacheid);
    1313           0 :                 throw(MAL, "aggr.count", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1314             :         }
    1315       69621 :         if (b->ttype == TYPE_msk || mask_cand(b)) {
    1316          30 :                 BATsum(result, TYPE_lng, b, s, *ignore_nils, false);
    1317       69591 :         } else if (*ignore_nils) {
    1318        1723 :                 *result = (lng) BATcount_no_nil(b, s);
    1319             :         } else {
    1320       67868 :                 struct canditer ci;
    1321       67868 :                 canditer_init(&ci, b, s);
    1322       67870 :                 *result = (lng) ci.ncand;
    1323             :         }
    1324       69623 :         BBPreclaim(s);
    1325       69623 :         BBPunfix(b->batCacheid);
    1326       69623 :         return MAL_SUCCEED;
    1327             : }
    1328             : 
    1329             : static str
    1330        1723 : ALGcount_nil(lng *result, const bat *bid, const bit *ignore_nils)
    1331             : {
    1332        1723 :         return ALGcountCND_nil(result, bid, NULL, ignore_nils);
    1333             : }
    1334             : 
    1335             : static str
    1336           0 : ALGcountCND_bat(lng *result, const bat *bid, const bat *cnd)
    1337             : {
    1338           0 :         return ALGcountCND_nil(result, bid, cnd, &(bit) { 0 });
    1339             : }
    1340             : 
    1341             : static str
    1342       67900 : ALGcount_bat(lng *result, const bat *bid)
    1343             : {
    1344       67900 :         return ALGcountCND_nil(result, bid, NULL, &(bit) { 0 });
    1345             : }
    1346             : 
    1347             : static str
    1348           0 : ALGcountCND_no_nil(lng *result, const bat *bid, const bat *cnd)
    1349             : {
    1350           0 :         return ALGcountCND_nil(result, bid, cnd, &(bit) { 1 });
    1351             : }
    1352             : 
    1353             : static str
    1354           0 : ALGcount_no_nil(lng *result, const bat *bid)
    1355             : {
    1356           0 :         return ALGcountCND_nil(result, bid, NULL, &(bit) { 1 });
    1357             : }
    1358             : 
    1359             : static str
    1360           6 : ALGslice(bat *ret, const bat *bid, const lng *start, const lng *end)
    1361             : {
    1362           6 :         BAT *b, *bn = NULL;
    1363             : 
    1364           6 :         if ((b = BATdescriptor(*bid)) == NULL) {
    1365           0 :                 throw(MAL, "algebra.slice", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1366             :         }
    1367           6 :         if (slice(&bn, b, *start, *end) == GDK_SUCCEED) {
    1368           6 :                 *ret = bn->batCacheid;
    1369           6 :                 BBPkeepref(bn);
    1370           6 :                 BBPunfix(b->batCacheid);
    1371           6 :                 return MAL_SUCCEED;
    1372             :         }
    1373           0 :         BBPunfix(b->batCacheid);
    1374           0 :         throw(MAL, "algebra.slice", GDK_EXCEPTION);
    1375             : }
    1376             : 
    1377             : static str
    1378           1 : ALGslice_int(bat *ret, const bat *bid, const int *start, const int *end)
    1379             : {
    1380           1 :         lng s = *start;
    1381           1 :         lng e = (is_int_nil(*end) ? lng_nil : *end);
    1382             : 
    1383           1 :         return ALGslice(ret, bid, &s, &e);
    1384             : }
    1385             : 
    1386             : static str
    1387           0 : ALGslice_lng(bat *ret, const bat *bid, const lng *start, const lng *end)
    1388             : {
    1389           0 :         lng s = *start;
    1390           0 :         lng e = *end;
    1391             : 
    1392           0 :         return ALGslice(ret, bid, &s, &e);
    1393             : }
    1394             : 
    1395             : /* carve out a slice based on the OIDs */
    1396             : /* beware that BATs may have different OID bases */
    1397             : static str
    1398           5 : ALGslice_oid(bat *ret, const bat *bid, const oid *start, const oid *end)
    1399             : {
    1400           5 :         lng s = (lng) (is_oid_nil(*start) ? 0 : (lng) *start);
    1401           5 :         lng e = (is_oid_nil(*end) ? lng_nil : (lng) *end);
    1402             : 
    1403           5 :         return ALGslice(ret, bid, &s, &e);
    1404             : }
    1405             : 
    1406             : static str
    1407       17214 : ALGsubslice_lng(bat *ret, const bat *bid, const lng *start, const lng *end)
    1408             : {
    1409       17214 :         BAT *b, *bn;
    1410       17214 :         BUN s, e;
    1411             : 
    1412       17214 :         if (*start < 0 || (*end < 0 && !is_lng_nil(*end)))
    1413           0 :                 throw(MAL, "algebra.subslice", ILLEGAL_ARGUMENT);
    1414       17214 :         if ((b = BBPquickdesc(*bid)) == NULL)
    1415           0 :                 throw(MAL, "algebra.subslice", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1416       17214 :         s = (BUN) *start;
    1417       17214 :         if (s > BATcount(b))
    1418             :                 s = BATcount(b);
    1419       17214 :         e = is_lng_nil(*end) ? BATcount(b) : (BUN) *end + 1;
    1420       17214 :         if (e > BATcount(b))
    1421             :                 e = BATcount(b);
    1422       17214 :         if (e < s)
    1423             :                 e = s;
    1424       17214 :         bn = BATdense(0, b->hseqbase + s, e - s);
    1425       17214 :         if (bn == NULL)
    1426           0 :                 throw(MAL, "algebra.subslice", SQLSTATE(HY013) MAL_MALLOC_FAIL);
    1427       17214 :         *ret = bn->batCacheid;
    1428       17214 :         BBPkeepref(bn);
    1429       17214 :         return MAL_SUCCEED;
    1430             : }
    1431             : 
    1432             : /*
    1433             :  * BUN Get/Fetch
    1434             :  */
    1435             : 
    1436             : static str
    1437       88858 : doALGfetch(ptr ret, BAT *b, BUN pos)
    1438             : {
    1439       88858 :         assert(pos <= BUN_MAX);
    1440       88858 :         BATiter bi = bat_iterator(b);
    1441       88858 :         if (ATOMextern(b->ttype)) {
    1442         190 :                 ptr _src = BUNtail(bi, pos);
    1443         190 :                 size_t _len = ATOMlen(b->ttype, _src);
    1444         190 :                 ptr _dst = GDKmalloc(_len);
    1445         190 :                 if (_dst == NULL) {
    1446           0 :                         bat_iterator_end(&bi);
    1447           0 :                         throw(MAL, "doAlgFetch", SQLSTATE(HY013) MAL_MALLOC_FAIL);
    1448             :                 }
    1449         190 :                 memcpy(_dst, _src, _len);
    1450         190 :                 *(ptr *) ret = _dst;
    1451             :         } else {
    1452       88668 :                 size_t _s = ATOMsize(ATOMtype(b->ttype));
    1453       88668 :                 if (b->ttype == TYPE_void) {
    1454           0 :                         *(oid *) ret = b->tseqbase;
    1455           0 :                         if (!is_oid_nil(b->tseqbase))
    1456           0 :                                 *(oid *) ret += pos;
    1457       88668 :                 } else if (_s == 4) {
    1458       88581 :                         *(int *) ret = ((int *) bi.base)[pos];
    1459             :                 } else if (_s == 1) {
    1460          11 :                         *(bte *) ret = ((bte *) bi.base)[pos];
    1461             :                 } else if (_s == 2) {
    1462           1 :                         *(sht *) ret = ((sht *) bi.base)[pos];
    1463             :                 } else if (_s == 8) {
    1464          75 :                         *(lng *) ret = ((lng *) bi.base)[pos];
    1465             : #ifdef HAVE_HGE
    1466             :                 } else if (_s == 16) {
    1467           0 :                         *(hge *) ret = ((hge *) bi.base)[pos];
    1468             : #endif
    1469             :                 } else {
    1470           0 :                         memcpy(ret, (const char *) bi.base + (pos << bi.shift), _s);
    1471             :                 }
    1472             :         }
    1473       88858 :         bat_iterator_end(&bi);
    1474       88858 :         return MAL_SUCCEED;
    1475             : }
    1476             : 
    1477             : static str
    1478       88860 : ALGfetch(ptr ret, const bat *bid, const lng *pos)
    1479             : {
    1480       88860 :         BAT *b;
    1481       88860 :         str msg;
    1482             : 
    1483       88860 :         if ((b = BATdescriptor(*bid)) == NULL) {
    1484           0 :                 throw(MAL, "algebra.fetch", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1485             :         }
    1486       88860 :         if (*pos < (lng) 0) {
    1487           0 :                 BBPunfix(b->batCacheid);
    1488           0 :                 throw(MAL, "algebra.fetch",
    1489             :                           ILLEGAL_ARGUMENT ": row index to fetch must be non negative\n");
    1490             :         }
    1491       88860 :         if (BATcount(b) == 0) {
    1492           2 :                 BBPunfix(b->batCacheid);
    1493           2 :                 throw(MAL, "algebra.fetch",
    1494             :                           ILLEGAL_ARGUMENT
    1495             :                           ": cannot fetch a single row from an empty input\n");
    1496             :         }
    1497       88858 :         if (*pos >= (lng) BATcount(b)) {
    1498           0 :                 BBPunfix(b->batCacheid);
    1499           0 :                 throw(MAL, "algebra.fetch",
    1500             :                           ILLEGAL_ARGUMENT ": row index to fetch is out of range\n");
    1501             :         }
    1502       88858 :         msg = doALGfetch(ret, b, (BUN) *pos);
    1503       88858 :         BBPunfix(b->batCacheid);
    1504       88858 :         return msg;
    1505             : }
    1506             : 
    1507             : str
    1508       88860 : ALGfetchoid(ptr ret, const bat *bid, const oid *pos)
    1509             : {
    1510       88860 :         lng o = *pos;
    1511             : 
    1512       88860 :         return ALGfetch(ret, bid, &o);
    1513             : }
    1514             : 
    1515             : static str
    1516           0 : ALGexist(bit *ret, const bat *bid, const void *val)
    1517             : {
    1518           0 :         BAT *b;
    1519           0 :         BUN q;
    1520             : 
    1521           0 :         if ((b = BATdescriptor(*bid)) == NULL) {
    1522           0 :                 throw(MAL, "algebra.exist", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1523             :         }
    1524           0 :         derefStr(b, val);
    1525           0 :         q = BUNfnd(b, val);
    1526           0 :         *ret = (q != BUN_NONE);
    1527           0 :         BBPunfix(b->batCacheid);
    1528           0 :         return MAL_SUCCEED;
    1529             : }
    1530             : 
    1531             : static str
    1532           9 : ALGfind(oid *ret, const bat *bid, ptr val)
    1533             : {
    1534           9 :         BAT *b;
    1535           9 :         BUN q;
    1536           9 :         str msg = MAL_SUCCEED;
    1537             : 
    1538           9 :         if ((b = BATdescriptor(*bid)) == NULL) {
    1539           0 :                 throw(MAL, "algebra.find", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1540             :         }
    1541           9 :         derefStr(b, val);
    1542           9 :         q = BUNfnd(b, val);
    1543             : 
    1544           9 :         if (q == BUN_NONE) {
    1545           3 :                 *ret = oid_nil;
    1546             :         } else
    1547           6 :                 *ret = (oid) q;
    1548           9 :         BBPunfix(b->batCacheid);
    1549           9 :         return msg;
    1550             : }
    1551             : 
    1552             : 
    1553             : static str
    1554      141887 : ALGprojecttail(Client cntxt, MalBlkPtr mb, MalStkPtr stk, InstrPtr pci)
    1555             : {
    1556      141887 :         bat *ret = getArgReference_bat(stk, pci, 0);
    1557      141887 :         bat bid = *getArgReference_bat(stk, pci, 1);
    1558      141887 :         const ValRecord *v = &stk->stk[getArg(pci, 2)];
    1559      141887 :         BAT *b, *bn;
    1560             : 
    1561      141887 :         (void) cntxt;
    1562      141887 :         (void) mb;
    1563      141887 :         if (isaBatType(getArgType(mb, pci, 2)))
    1564           0 :                 throw(MAL, "algebra.project", "Scalar value expected");
    1565      141887 :         if ((b = BBPquickdesc(bid)) == NULL)
    1566           0 :                 throw(MAL, "algebra.project", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1567      141885 :         bn = BATconstant(b->hseqbase, v->vtype, VALptr(v), BATcount(b), TRANSIENT);
    1568      141884 :         if (bn == NULL) {
    1569           0 :                 *ret = bat_nil;
    1570           0 :                 throw(MAL, "algebra.project", SQLSTATE(HY013) MAL_MALLOC_FAIL);
    1571             :         }
    1572      141884 :         *ret = bn->batCacheid;
    1573      141884 :         BBPkeepref(bn);
    1574      141884 :         return MAL_SUCCEED;
    1575             : }
    1576             : 
    1577             : 
    1578             : static str
    1579           0 : ALGreuse(bat *ret, const bat *bid)
    1580             : {
    1581           0 :         BAT *b, *bn;
    1582           0 :         if ((b = BATdescriptor(*bid)) == NULL)
    1583           0 :                 throw(MAL, "algebra.reuse", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1584             : 
    1585           0 :         if (!b->batTransient || b->batRestricted != BAT_WRITE) {
    1586           0 :                 if (ATOMvarsized(b->ttype)) {
    1587           0 :                         bn = BATwcopy(b);
    1588           0 :                         if (bn == NULL) {
    1589           0 :                                 BBPunfix(b->batCacheid);
    1590           0 :                                 throw(MAL, "algebra.reuse", SQLSTATE(HY013) MAL_MALLOC_FAIL);
    1591             :                         }
    1592             :                 } else {
    1593           0 :                         bn = COLnew(b->hseqbase, b->ttype, BATcount(b), TRANSIENT);
    1594           0 :                         if (bn == NULL) {
    1595           0 :                                 BBPunfix(b->batCacheid);
    1596           0 :                                 throw(MAL, "algebra.reuse", SQLSTATE(HY013) MAL_MALLOC_FAIL);
    1597             :                         }
    1598           0 :                         BATsetcount(bn, BATcount(b));
    1599           0 :                         bn->tsorted = false;
    1600           0 :                         bn->trevsorted = false;
    1601           0 :                         BATkey(bn, false);
    1602             :                 }
    1603           0 :                 *ret = bn->batCacheid;
    1604           0 :                 BBPkeepref(bn);
    1605           0 :                 BBPunfix(b->batCacheid);
    1606             :         } else
    1607           0 :                 BBPkeepref(b);
    1608             :         return MAL_SUCCEED;
    1609             : }
    1610             : 
    1611             : /*
    1612             :  * BAT standard deviation
    1613             :  */
    1614             : static str
    1615           7 : ALGstdev(dbl *res, const bat *bid)
    1616             : {
    1617           7 :         BAT *b;
    1618           7 :         dbl stdev;
    1619             : 
    1620           7 :         if ((b = BATdescriptor(*bid)) == NULL)
    1621           0 :                 throw(MAL, "aggr.stdev", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1622           7 :         stdev = BATcalcstdev_sample(NULL, b);
    1623           7 :         BBPunfix(b->batCacheid);
    1624           7 :         if (is_dbl_nil(stdev) && GDKerrbuf && GDKerrbuf[0])
    1625           0 :                 throw(MAL, "aggr.stdev", GDK_EXCEPTION);
    1626           7 :         *res = stdev;
    1627           7 :         return MAL_SUCCEED;
    1628             : }
    1629             : 
    1630             : static str
    1631          13 : ALGstdevp(dbl *res, const bat *bid)
    1632             : {
    1633          13 :         BAT *b;
    1634          13 :         dbl stdev;
    1635             : 
    1636          13 :         if ((b = BATdescriptor(*bid)) == NULL)
    1637           0 :                 throw(MAL, "aggr.stdevp", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1638          13 :         stdev = BATcalcstdev_population(NULL, b);
    1639          13 :         BBPunfix(b->batCacheid);
    1640          13 :         if (is_dbl_nil(stdev) && GDKerrbuf && GDKerrbuf[0])
    1641           1 :                 throw(MAL, "aggr.stdevp", GDK_EXCEPTION);
    1642          12 :         *res = stdev;
    1643          12 :         return MAL_SUCCEED;
    1644             : }
    1645             : 
    1646             : /*
    1647             :  * BAT variance
    1648             :  */
    1649             : static str
    1650           2 : ALGvariance(dbl *res, const bat *bid)
    1651             : {
    1652           2 :         BAT *b;
    1653           2 :         dbl variance;
    1654             : 
    1655           2 :         if ((b = BATdescriptor(*bid)) == NULL)
    1656           0 :                 throw(MAL, "aggr.variance", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1657           2 :         variance = BATcalcvariance_sample(NULL, b);
    1658           2 :         BBPunfix(b->batCacheid);
    1659           2 :         if (is_dbl_nil(variance) && GDKerrbuf && GDKerrbuf[0])
    1660           0 :                 throw(MAL, "aggr.variance", GDK_EXCEPTION);
    1661           2 :         *res = variance;
    1662           2 :         return MAL_SUCCEED;
    1663             : }
    1664             : 
    1665             : static str
    1666           5 : ALGvariancep(dbl *res, const bat *bid)
    1667             : {
    1668           5 :         BAT *b;
    1669           5 :         dbl variance;
    1670             : 
    1671           5 :         if ((b = BATdescriptor(*bid)) == NULL)
    1672           0 :                 throw(MAL, "aggr.variancep", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1673           5 :         variance = BATcalcvariance_population(NULL, b);
    1674           5 :         BBPunfix(b->batCacheid);
    1675           5 :         if (is_dbl_nil(variance) && GDKerrbuf && GDKerrbuf[0])
    1676           1 :                 throw(MAL, "aggr.variancep", GDK_EXCEPTION);
    1677           4 :         *res = variance;
    1678           4 :         return MAL_SUCCEED;
    1679             : }
    1680             : 
    1681             : /*
    1682             :  * BAT covariance
    1683             :  */
    1684             : static str
    1685           5 : ALGcovariance(dbl *res, const bat *bid1, const bat *bid2)
    1686             : {
    1687           5 :         BAT *b1, *b2;
    1688           5 :         dbl covariance;
    1689             : 
    1690           5 :         if ((b1 = BATdescriptor(*bid1)) == NULL)
    1691           0 :                 throw(MAL, "aggr.covariance", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1692           5 :         if ((b2 = BATdescriptor(*bid2)) == NULL) {
    1693           0 :                 BBPunfix(b1->batCacheid);
    1694           0 :                 throw(MAL, "aggr.covariance", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1695             :         }
    1696             : 
    1697           5 :         covariance = BATcalccovariance_sample(b1, b2);
    1698           5 :         BBPunfix(b1->batCacheid);
    1699           5 :         BBPunfix(b2->batCacheid);
    1700           5 :         if (is_dbl_nil(covariance) && GDKerrbuf && GDKerrbuf[0])
    1701           0 :                 throw(MAL, "aggr.covariance", GDK_EXCEPTION);
    1702           5 :         *res = covariance;
    1703           5 :         return MAL_SUCCEED;
    1704             : }
    1705             : 
    1706             : static str
    1707           9 : ALGcovariancep(dbl *res, const bat *bid1, const bat *bid2)
    1708             : {
    1709           9 :         BAT *b1, *b2;
    1710           9 :         dbl covariance;
    1711             : 
    1712           9 :         if ((b1 = BATdescriptor(*bid1)) == NULL)
    1713           0 :                 throw(MAL, "aggr.covariancep", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1714           9 :         if ((b2 = BATdescriptor(*bid2)) == NULL) {
    1715           0 :                 BBPunfix(b1->batCacheid);
    1716           0 :                 throw(MAL, "aggr.covariancep", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1717             :         }
    1718             : 
    1719           9 :         covariance = BATcalccovariance_population(b1, b2);
    1720           9 :         BBPunfix(b1->batCacheid);
    1721           9 :         BBPunfix(b2->batCacheid);
    1722           9 :         if (is_dbl_nil(covariance) && GDKerrbuf && GDKerrbuf[0])
    1723           1 :                 throw(MAL, "aggr.covariancep", GDK_EXCEPTION);
    1724           8 :         *res = covariance;
    1725           8 :         return MAL_SUCCEED;
    1726             : }
    1727             : 
    1728             : /*
    1729             :  * BAT correlation
    1730             :  */
    1731             : static str
    1732          19 : ALGcorr(dbl *res, const bat *bid1, const bat *bid2)
    1733             : {
    1734          19 :         BAT *b1, *b2;
    1735          19 :         dbl covariance;
    1736             : 
    1737          19 :         if ((b1 = BATdescriptor(*bid1)) == NULL)
    1738           0 :                 throw(MAL, "aggr.corr", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1739          19 :         if ((b2 = BATdescriptor(*bid2)) == NULL) {
    1740           0 :                 BBPunfix(b1->batCacheid);
    1741           0 :                 throw(MAL, "aggr.corr", SQLSTATE(HY002) RUNTIME_OBJECT_MISSING);
    1742             :         }
    1743             : 
    1744          19 :         covariance = BATcalccorrelation(b1, b2);
    1745          19 :         BBPunfix(b1->batCacheid);
    1746          19 :         BBPunfix(b2->batCacheid);
    1747          19 :         if (is_dbl_nil(covariance) && GDKerrbuf && GDKerrbuf[0])
    1748           1 :                 throw(MAL, "aggr.corr", GDK_EXCEPTION);
    1749          18 :         *res = covariance;
    1750          18 :         return MAL_SUCCEED;
    1751             : }
    1752             : 
    1753             : #include "mel.h"
    1754             : mel_func algebra_init_funcs[] = {
    1755             :  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))),
    1756             :  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))),
    1757             :  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))),
    1758             :  pattern("algebra", "project", ALGprojecttail, false, "Fill the tail with a constant", args(1,3, batargany("",2),batargany("b",1),argany("v",2))),
    1759             :  command("algebra", "projection", ALGprojection, false, "Project left input onto right input.", args(1,3, batargany("",1),batarg("left",oid),batargany("right",1))),
    1760             :  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))),
    1761             :  command("algebra", "copy", ALGcopy, false, "Returns physical copy of a BAT.", args(1,2, batargany("",1),batargany("b",1))),
    1762             :  command("algebra", "exist", ALGexist, false, "Returns whether 'val' occurs in b.", args(1,3, arg("",bit),batargany("b",1),argany("val",1))),
    1763             :  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))),
    1764             :  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))),
    1765             :  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))),
    1766             :  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))),
    1767             :  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))),
    1768             :  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))),
    1769             :  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))),
    1770             :  command("algebra", "selectNotNil", ALGselectNotNil, false, "Select all not-nil values", args(1,2, batargany("",1),batargany("b",1))),
    1771             :  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))),
    1772             :  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))),
    1773             :  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))),
    1774             :  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))),
    1775             :  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))),
    1776             :  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))),
    1777             :  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))),
    1778             :  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))),
    1779             :  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))),
    1780             :  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))),
    1781             :  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))),
    1782             :  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))),
    1783             :  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))),
    1784             :  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))),
    1785             :  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))),
    1786             :  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))),
    1787             :  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))),
    1788             :  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))),
    1789             :  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))),
    1790             :  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))),
    1791             :  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))),
    1792             :  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))),
    1793             :  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))),
    1794             :  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))),
    1795             :  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))),
    1796             :  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))),
    1797             :  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))),
    1798             :  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))),
    1799             :  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))),
    1800             :  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))),
    1801             :  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))),
    1802             :  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))),
    1803             :  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))),
    1804             :  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))),
    1805             :  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))),
    1806             :  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))),
    1807             :  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))),
    1808             :  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))),
    1809             :  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))),
    1810             :  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))),
    1811             :  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))),
    1812             :  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))),
    1813             :  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))),
    1814             :  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))),
    1815             :  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))),
    1816             :  command("aggr", "cardinality", ALGcard, false, "Return the cardinality of the BAT tail values.", args(1,2, arg("",lng),batargany("b",2))),
    1817             :  command("aggr", "min", ALGminany, false, "Return the lowest tail value or nil.", args(1,2, argany("",2),batargany("b",2))),
    1818             :  command("aggr", "min", ALGminany_skipnil, false, "Return the lowest tail value or nil.", args(1,3, argany("",2),batargany("b",2),arg("skipnil",bit))),
    1819             :  command("aggr", "max", ALGmaxany, false, "Return the highest tail value or nil.", args(1,2, argany("",2),batargany("b",2))),
    1820             :  command("aggr", "max", ALGmaxany_skipnil, false, "Return the highest tail value or nil.", args(1,3, argany("",2),batargany("b",2),arg("skipnil",bit))),
    1821             :  command("aggr", "stdev", ALGstdev, false, "Gives the standard deviation of all tail values", args(1,2, arg("",dbl),batargany("b",2))),
    1822             :  command("aggr", "stdevp", ALGstdevp, false, "Gives the standard deviation of all tail values", args(1,2, arg("",dbl),batargany("b",2))),
    1823             :  command("aggr", "variance", ALGvariance, false, "Gives the variance of all tail values", args(1,2, arg("",dbl),batargany("b",2))),
    1824             :  command("aggr", "variancep", ALGvariancep, false, "Gives the variance of all tail values", args(1,2, arg("",dbl),batargany("b",2))),
    1825             :  command("aggr", "covariance", ALGcovariance, false, "Gives the covariance of all tail values", args(1,3, arg("",dbl),batargany("b1",2),batargany("b2",2))),
    1826             :  command("aggr", "covariancep", ALGcovariancep, false, "Gives the covariance of all tail values", args(1,3, arg("",dbl),batargany("b1",2),batargany("b2",2))),
    1827             :  command("aggr", "corr", ALGcorr, false, "Gives the correlation of all tail values", args(1,3, arg("",dbl),batargany("b1",2),batargany("b2",2))),
    1828             :  // sql
    1829             :  command("aggr", "exist", ALGexist, false, "", args(1,3, arg("",bit),batargany("b",2),argany("h",1))),
    1830             :  { .imp=NULL }
    1831             : };
    1832             : #include "mal_import.h"
    1833             : #ifdef _MSC_VER
    1834             : #undef read
    1835             : #pragma section(".CRT$XCU",read)
    1836             : #endif
    1837         323 : LIB_STARTUP_FUNC(init_algebra_mal)
    1838         323 : { mal_module("algebra", NULL, algebra_init_funcs); }

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