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1/*2 * Copyright 2008-2009 Katholieke Universiteit Leuven3 * Copyright 2010 INRIA Saclay4 * Copyright 2012-2013 Ecole Normale Superieure5 * Copyright 2014 INRIA Rocquencourt6 * Copyright 2016 INRIA Paris7 * Copyright 2020 Cerebras Systems8 *9 * Use of this software is governed by the MIT license10 *11 * Written by Sven Verdoolaege, K.U.Leuven, Departement12 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium13 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,14 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France 15 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France16 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,17 * B.P. 105 - 78153 Le Chesnay, France18 * and Centre de Recherche Inria de Paris, 2 rue Simone Iff - Voie DQ12,19 * CS 42112, 75589 Paris Cedex 12, France20 * and Cerebras Systems, 175 S San Antonio Rd, Los Altos, CA, USA21 */22 23#include <isl_ctx_private.h>24#include "isl_map_private.h"25#include <isl_seq.h>26#include <isl/options.h>27#include "isl_tab.h"28#include <isl_mat_private.h>29#include <isl_local_space_private.h>30#include <isl_val_private.h>31#include <isl_vec_private.h>32#include <isl_aff_private.h>33#include <isl_equalities.h>34#include <isl_constraint_private.h>35 36#include <set_to_map.c>37#include <set_from_map.c>38 39#define STATUS_ERROR -140#define STATUS_REDUNDANT 141#define STATUS_VALID 242#define STATUS_SEPARATE 343#define STATUS_CUT 444#define STATUS_ADJ_EQ 545#define STATUS_ADJ_INEQ 646 47static int status_in(isl_int *ineq, struct isl_tab *tab)48{49 enum isl_ineq_type type = isl_tab_ineq_type(tab, ineq);50 switch (type) {51 default:52 case isl_ineq_error: return STATUS_ERROR;53 case isl_ineq_redundant: return STATUS_VALID;54 case isl_ineq_separate: return STATUS_SEPARATE;55 case isl_ineq_cut: return STATUS_CUT;56 case isl_ineq_adj_eq: return STATUS_ADJ_EQ;57 case isl_ineq_adj_ineq: return STATUS_ADJ_INEQ;58 }59}60 61/* Compute the position of the equalities of basic map "bmap_i"62 * with respect to the basic map represented by "tab_j".63 * The resulting array has twice as many entries as the number64 * of equalities corresponding to the two inequalities to which65 * each equality corresponds.66 */67static int *eq_status_in(__isl_keep isl_basic_map *bmap_i,68 struct isl_tab *tab_j)69{70 int k, l;71 int *eq;72 isl_size dim;73 74 dim = isl_basic_map_dim(bmap_i, isl_dim_all);75 if (dim < 0)76 return NULL;77 78 eq = isl_calloc_array(bmap_i->ctx, int, 2 * bmap_i->n_eq);79 if (!eq)80 return NULL;81 82 for (k = 0; k < bmap_i->n_eq; ++k) {83 for (l = 0; l < 2; ++l) {84 isl_seq_neg(bmap_i->eq[k], bmap_i->eq[k], 1+dim);85 eq[2 * k + l] = status_in(bmap_i->eq[k], tab_j);86 if (eq[2 * k + l] == STATUS_ERROR)87 goto error;88 }89 }90 91 return eq;92error:93 free(eq);94 return NULL;95}96 97/* Compute the position of the inequalities of basic map "bmap_i"98 * (also represented by "tab_i", if not NULL) with respect to the basic map99 * represented by "tab_j".100 */101static int *ineq_status_in(__isl_keep isl_basic_map *bmap_i,102 struct isl_tab *tab_i, struct isl_tab *tab_j)103{104 int k;105 unsigned n_eq = bmap_i->n_eq;106 int *ineq = isl_calloc_array(bmap_i->ctx, int, bmap_i->n_ineq);107 108 if (!ineq)109 return NULL;110 111 for (k = 0; k < bmap_i->n_ineq; ++k) {112 if (tab_i && isl_tab_is_redundant(tab_i, n_eq + k)) {113 ineq[k] = STATUS_REDUNDANT;114 continue;115 }116 ineq[k] = status_in(bmap_i->ineq[k], tab_j);117 if (ineq[k] == STATUS_ERROR)118 goto error;119 if (ineq[k] == STATUS_SEPARATE)120 break;121 }122 123 return ineq;124error:125 free(ineq);126 return NULL;127}128 129static int any(int *con, unsigned len, int status)130{131 int i;132 133 for (i = 0; i < len ; ++i)134 if (con[i] == status)135 return 1;136 return 0;137}138 139/* Return the first position of "status" in the list "con" of length "len".140 * Return -1 if there is no such entry.141 */142static int find(int *con, unsigned len, int status)143{144 int i;145 146 for (i = 0; i < len ; ++i)147 if (con[i] == status)148 return i;149 return -1;150}151 152static int count(int *con, unsigned len, int status)153{154 int i;155 int c = 0;156 157 for (i = 0; i < len ; ++i)158 if (con[i] == status)159 c++;160 return c;161}162 163static int all(int *con, unsigned len, int status)164{165 int i;166 167 for (i = 0; i < len ; ++i) {168 if (con[i] == STATUS_REDUNDANT)169 continue;170 if (con[i] != status)171 return 0;172 }173 return 1;174}175 176/* Internal information associated to a basic map in a map177 * that is to be coalesced by isl_map_coalesce.178 *179 * "bmap" is the basic map itself (or NULL if "removed" is set)180 * "tab" is the corresponding tableau (or NULL if "removed" is set)181 * "hull_hash" identifies the affine space in which "bmap" lives.182 * "modified" is set if this basic map may not be identical183 * to any of the basic maps in the input.184 * "removed" is set if this basic map has been removed from the map185 * "simplify" is set if this basic map may have some unknown integer186 * divisions that were not present in the input basic maps. The basic187 * map should then be simplified such that we may be able to find188 * a definition among the constraints.189 *190 * "eq" and "ineq" are only set if we are currently trying to coalesce191 * this basic map with another basic map, in which case they represent192 * the position of the inequalities of this basic map with respect to193 * the other basic map. The number of elements in the "eq" array194 * is twice the number of equalities in the "bmap", corresponding195 * to the two inequalities that make up each equality.196 */197struct isl_coalesce_info {198 isl_basic_map *bmap;199 struct isl_tab *tab;200 uint32_t hull_hash;201 int modified;202 int removed;203 int simplify;204 int *eq;205 int *ineq;206};207 208/* Is there any (half of an) equality constraint in the description209 * of the basic map represented by "info" that210 * has position "status" with respect to the other basic map?211 */212static int any_eq(struct isl_coalesce_info *info, int status)213{214 isl_size n_eq;215 216 n_eq = isl_basic_map_n_equality(info->bmap);217 return any(info->eq, 2 * n_eq, status);218}219 220/* Is there any inequality constraint in the description221 * of the basic map represented by "info" that222 * has position "status" with respect to the other basic map?223 */224static int any_ineq(struct isl_coalesce_info *info, int status)225{226 isl_size n_ineq;227 228 n_ineq = isl_basic_map_n_inequality(info->bmap);229 return any(info->ineq, n_ineq, status);230}231 232/* Return the position of the first half on an equality constraint233 * in the description of the basic map represented by "info" that234 * has position "status" with respect to the other basic map.235 * The returned value is twice the position of the equality constraint236 * plus zero for the negative half and plus one for the positive half.237 * Return -1 if there is no such entry.238 */239static int find_eq(struct isl_coalesce_info *info, int status)240{241 isl_size n_eq;242 243 n_eq = isl_basic_map_n_equality(info->bmap);244 return find(info->eq, 2 * n_eq, status);245}246 247/* Return the position of the first inequality constraint in the description248 * of the basic map represented by "info" that249 * has position "status" with respect to the other basic map.250 * Return -1 if there is no such entry.251 */252static int find_ineq(struct isl_coalesce_info *info, int status)253{254 isl_size n_ineq;255 256 n_ineq = isl_basic_map_n_inequality(info->bmap);257 return find(info->ineq, n_ineq, status);258}259 260/* Return the number of (halves of) equality constraints in the description261 * of the basic map represented by "info" that262 * have position "status" with respect to the other basic map.263 */264static int count_eq(struct isl_coalesce_info *info, int status)265{266 isl_size n_eq;267 268 n_eq = isl_basic_map_n_equality(info->bmap);269 return count(info->eq, 2 * n_eq, status);270}271 272/* Return the number of inequality constraints in the description273 * of the basic map represented by "info" that274 * have position "status" with respect to the other basic map.275 */276static int count_ineq(struct isl_coalesce_info *info, int status)277{278 isl_size n_ineq;279 280 n_ineq = isl_basic_map_n_inequality(info->bmap);281 return count(info->ineq, n_ineq, status);282}283 284/* Are all non-redundant constraints of the basic map represented by "info"285 * either valid or cut constraints with respect to the other basic map?286 */287static int all_valid_or_cut(struct isl_coalesce_info *info)288{289 int i;290 291 for (i = 0; i < 2 * info->bmap->n_eq; ++i) {292 if (info->eq[i] == STATUS_REDUNDANT)293 continue;294 if (info->eq[i] == STATUS_VALID)295 continue;296 if (info->eq[i] == STATUS_CUT)297 continue;298 return 0;299 }300 301 for (i = 0; i < info->bmap->n_ineq; ++i) {302 if (info->ineq[i] == STATUS_REDUNDANT)303 continue;304 if (info->ineq[i] == STATUS_VALID)305 continue;306 if (info->ineq[i] == STATUS_CUT)307 continue;308 return 0;309 }310 311 return 1;312}313 314/* Compute the hash of the (apparent) affine hull of info->bmap (with315 * the existentially quantified variables removed) and store it316 * in info->hash.317 */318static int coalesce_info_set_hull_hash(struct isl_coalesce_info *info)319{320 isl_basic_map *hull;321 isl_size n_div;322 323 hull = isl_basic_map_copy(info->bmap);324 hull = isl_basic_map_plain_affine_hull(hull);325 n_div = isl_basic_map_dim(hull, isl_dim_div);326 if (n_div < 0)327 hull = isl_basic_map_free(hull);328 hull = isl_basic_map_drop_constraints_involving_dims(hull,329 isl_dim_div, 0, n_div);330 info->hull_hash = isl_basic_map_get_hash(hull);331 isl_basic_map_free(hull);332 333 return hull ? 0 : -1;334}335 336/* Free all the allocated memory in an array337 * of "n" isl_coalesce_info elements.338 */339static void clear_coalesce_info(int n, struct isl_coalesce_info *info)340{341 int i;342 343 if (!info)344 return;345 346 for (i = 0; i < n; ++i) {347 isl_basic_map_free(info[i].bmap);348 isl_tab_free(info[i].tab);349 }350 351 free(info);352}353 354/* Clear the memory associated to "info".355 */356static void clear(struct isl_coalesce_info *info)357{358 info->bmap = isl_basic_map_free(info->bmap);359 isl_tab_free(info->tab);360 info->tab = NULL;361}362 363/* Drop the basic map represented by "info".364 * That is, clear the memory associated to the entry and365 * mark it as having been removed.366 */367static void drop(struct isl_coalesce_info *info)368{369 clear(info);370 info->removed = 1;371}372 373/* Exchange the information in "info1" with that in "info2".374 */375static void exchange(struct isl_coalesce_info *info1,376 struct isl_coalesce_info *info2)377{378 struct isl_coalesce_info info;379 380 info = *info1;381 *info1 = *info2;382 *info2 = info;383}384 385/* This type represents the kind of change that has been performed386 * while trying to coalesce two basic maps.387 *388 * isl_change_none: nothing was changed389 * isl_change_drop_first: the first basic map was removed390 * isl_change_drop_second: the second basic map was removed391 * isl_change_fuse: the two basic maps were replaced by a new basic map.392 */393enum isl_change {394 isl_change_error = -1,395 isl_change_none = 0,396 isl_change_drop_first,397 isl_change_drop_second,398 isl_change_fuse,399};400 401/* Update "change" based on an interchange of the first and the second402 * basic map. That is, interchange isl_change_drop_first and403 * isl_change_drop_second.404 */405static enum isl_change invert_change(enum isl_change change)406{407 switch (change) {408 case isl_change_error:409 return isl_change_error;410 case isl_change_none:411 return isl_change_none;412 case isl_change_drop_first:413 return isl_change_drop_second;414 case isl_change_drop_second:415 return isl_change_drop_first;416 case isl_change_fuse:417 return isl_change_fuse;418 }419 420 return isl_change_error;421}422 423/* Add the valid constraints of the basic map represented by "info"424 * to "bmap". "len" is the size of the constraints.425 * If only one of the pair of inequalities that make up an equality426 * is valid, then add that inequality.427 */428static __isl_give isl_basic_map *add_valid_constraints(429 __isl_take isl_basic_map *bmap, struct isl_coalesce_info *info,430 unsigned len)431{432 int k, l;433 434 if (!bmap)435 return NULL;436 437 for (k = 0; k < info->bmap->n_eq; ++k) {438 if (info->eq[2 * k] == STATUS_VALID &&439 info->eq[2 * k + 1] == STATUS_VALID) {440 l = isl_basic_map_alloc_equality(bmap);441 if (l < 0)442 return isl_basic_map_free(bmap);443 isl_seq_cpy(bmap->eq[l], info->bmap->eq[k], len);444 } else if (info->eq[2 * k] == STATUS_VALID) {445 l = isl_basic_map_alloc_inequality(bmap);446 if (l < 0)447 return isl_basic_map_free(bmap);448 isl_seq_neg(bmap->ineq[l], info->bmap->eq[k], len);449 } else if (info->eq[2 * k + 1] == STATUS_VALID) {450 l = isl_basic_map_alloc_inequality(bmap);451 if (l < 0)452 return isl_basic_map_free(bmap);453 isl_seq_cpy(bmap->ineq[l], info->bmap->eq[k], len);454 }455 }456 457 for (k = 0; k < info->bmap->n_ineq; ++k) {458 if (info->ineq[k] != STATUS_VALID)459 continue;460 l = isl_basic_map_alloc_inequality(bmap);461 if (l < 0)462 return isl_basic_map_free(bmap);463 isl_seq_cpy(bmap->ineq[l], info->bmap->ineq[k], len);464 }465 466 return bmap;467}468 469/* Is "bmap" defined by a number of (non-redundant) constraints that470 * is greater than the number of constraints of basic maps i and j combined?471 * Equalities are counted as two inequalities.472 */473static int number_of_constraints_increases(int i, int j,474 struct isl_coalesce_info *info,475 __isl_keep isl_basic_map *bmap, struct isl_tab *tab)476{477 int k, n_old, n_new;478 479 n_old = 2 * info[i].bmap->n_eq + info[i].bmap->n_ineq;480 n_old += 2 * info[j].bmap->n_eq + info[j].bmap->n_ineq;481 482 n_new = 2 * bmap->n_eq;483 for (k = 0; k < bmap->n_ineq; ++k)484 if (!isl_tab_is_redundant(tab, bmap->n_eq + k))485 ++n_new;486 487 return n_new > n_old;488}489 490/* Replace the pair of basic maps i and j by the basic map bounded491 * by the valid constraints in both basic maps and the constraints492 * in extra (if not NULL).493 * Place the fused basic map in the position that is the smallest of i and j.494 *495 * If "detect_equalities" is set, then look for equalities encoded496 * as pairs of inequalities.497 * If "check_number" is set, then the original basic maps are only498 * replaced if the total number of constraints does not increase.499 * While the number of integer divisions in the two basic maps500 * is assumed to be the same, the actual definitions may be different.501 * We only copy the definition from one of the basic maps if it is502 * the same as that of the other basic map. Otherwise, we mark503 * the integer division as unknown and simplify the basic map504 * in an attempt to recover the integer division definition.505 * If any extra constraints get introduced, then these may506 * involve integer divisions with a unit coefficient.507 * Eliminate those that do not appear with any other coefficient508 * in other constraints, to ensure they get eliminated completely,509 * improving the chances of further coalescing.510 */511static enum isl_change fuse(int i, int j, struct isl_coalesce_info *info,512 __isl_keep isl_mat *extra, int detect_equalities, int check_number)513{514 int k, l;515 struct isl_basic_map *fused = NULL;516 struct isl_tab *fused_tab = NULL;517 isl_size total = isl_basic_map_dim(info[i].bmap, isl_dim_all);518 unsigned extra_rows = extra ? extra->n_row : 0;519 unsigned n_eq, n_ineq;520 int simplify = 0;521 522 if (total < 0)523 return isl_change_error;524 if (j < i)525 return fuse(j, i, info, extra, detect_equalities, check_number);526 527 n_eq = info[i].bmap->n_eq + info[j].bmap->n_eq;528 n_ineq = info[i].bmap->n_ineq + info[j].bmap->n_ineq;529 fused = isl_basic_map_alloc_space(isl_space_copy(info[i].bmap->dim),530 info[i].bmap->n_div, n_eq, n_eq + n_ineq + extra_rows);531 fused = add_valid_constraints(fused, &info[i], 1 + total);532 fused = add_valid_constraints(fused, &info[j], 1 + total);533 if (!fused)534 goto error;535 if (ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_RATIONAL) &&536 ISL_F_ISSET(info[j].bmap, ISL_BASIC_MAP_RATIONAL))537 ISL_F_SET(fused, ISL_BASIC_MAP_RATIONAL);538 539 for (k = 0; k < info[i].bmap->n_div; ++k) {540 int l = isl_basic_map_alloc_div(fused);541 if (l < 0)542 goto error;543 if (isl_seq_eq(info[i].bmap->div[k], info[j].bmap->div[k],544 1 + 1 + total)) {545 isl_seq_cpy(fused->div[l], info[i].bmap->div[k],546 1 + 1 + total);547 } else {548 isl_int_set_si(fused->div[l][0], 0);549 simplify = 1;550 }551 }552 553 for (k = 0; k < extra_rows; ++k) {554 l = isl_basic_map_alloc_inequality(fused);555 if (l < 0)556 goto error;557 isl_seq_cpy(fused->ineq[l], extra->row[k], 1 + total);558 }559 560 if (detect_equalities)561 fused = isl_basic_map_detect_inequality_pairs(fused, NULL);562 fused = isl_basic_map_gauss(fused, NULL);563 if (simplify || info[j].simplify) {564 fused = isl_basic_map_simplify(fused);565 info[i].simplify = 0;566 } else if (extra_rows > 0) {567 fused = isl_basic_map_eliminate_pure_unit_divs(fused);568 }569 fused = isl_basic_map_finalize(fused);570 571 fused_tab = isl_tab_from_basic_map(fused, 0);572 if (isl_tab_detect_redundant(fused_tab) < 0)573 goto error;574 575 if (check_number &&576 number_of_constraints_increases(i, j, info, fused, fused_tab)) {577 isl_tab_free(fused_tab);578 isl_basic_map_free(fused);579 return isl_change_none;580 }581 582 clear(&info[i]);583 info[i].bmap = fused;584 info[i].tab = fused_tab;585 info[i].modified = 1;586 drop(&info[j]);587 588 return isl_change_fuse;589error:590 isl_tab_free(fused_tab);591 isl_basic_map_free(fused);592 return isl_change_error;593}594 595/* Given a pair of basic maps i and j such that all constraints are either596 * "valid" or "cut", check if the facets corresponding to the "cut"597 * constraints of i lie entirely within basic map j.598 * If so, replace the pair by the basic map consisting of the valid599 * constraints in both basic maps.600 * Checking whether the facet lies entirely within basic map j601 * is performed by checking whether the constraints of basic map j602 * are valid for the facet. These tests are performed on a rational603 * tableau to avoid the theoretical possibility that a constraint604 * that was considered to be a cut constraint for the entire basic map i605 * happens to be considered to be a valid constraint for the facet,606 * even though it cuts off the same rational points.607 *608 * To see that we are not introducing any extra points, call the609 * two basic maps A and B and the resulting map U and let x610 * be an element of U \setminus ( A \cup B ).611 * A line connecting x with an element of A \cup B meets a facet F612 * of either A or B. Assume it is a facet of B and let c_1 be613 * the corresponding facet constraint. We have c_1(x) < 0 and614 * so c_1 is a cut constraint. This implies that there is some615 * (possibly rational) point x' satisfying the constraints of A616 * and the opposite of c_1 as otherwise c_1 would have been marked617 * valid for A. The line connecting x and x' meets a facet of A618 * in a (possibly rational) point that also violates c_1, but this619 * is impossible since all cut constraints of B are valid for all620 * cut facets of A.621 * In case F is a facet of A rather than B, then we can apply the622 * above reasoning to find a facet of B separating x from A \cup B first.623 */624static enum isl_change check_facets(int i, int j,625 struct isl_coalesce_info *info)626{627 int k, l;628 struct isl_tab_undo *snap, *snap2;629 unsigned n_eq = info[i].bmap->n_eq;630 631 snap = isl_tab_snap(info[i].tab);632 if (isl_tab_mark_rational(info[i].tab) < 0)633 return isl_change_error;634 snap2 = isl_tab_snap(info[i].tab);635 636 for (k = 0; k < info[i].bmap->n_ineq; ++k) {637 if (info[i].ineq[k] != STATUS_CUT)638 continue;639 if (isl_tab_select_facet(info[i].tab, n_eq + k) < 0)640 return isl_change_error;641 for (l = 0; l < info[j].bmap->n_ineq; ++l) {642 int stat;643 if (info[j].ineq[l] != STATUS_CUT)644 continue;645 stat = status_in(info[j].bmap->ineq[l], info[i].tab);646 if (stat < 0)647 return isl_change_error;648 if (stat != STATUS_VALID)649 break;650 }651 if (isl_tab_rollback(info[i].tab, snap2) < 0)652 return isl_change_error;653 if (l < info[j].bmap->n_ineq)654 break;655 }656 657 if (k < info[i].bmap->n_ineq) {658 if (isl_tab_rollback(info[i].tab, snap) < 0)659 return isl_change_error;660 return isl_change_none;661 }662 return fuse(i, j, info, NULL, 0, 0);663}664 665/* Check if info->bmap contains the basic map represented666 * by the tableau "tab".667 * For each equality, we check both the constraint itself668 * (as an inequality) and its negation. Make sure the669 * equality is returned to its original state before returning.670 */671static isl_bool contains(struct isl_coalesce_info *info, struct isl_tab *tab)672{673 int k;674 isl_size dim;675 isl_basic_map *bmap = info->bmap;676 677 dim = isl_basic_map_dim(bmap, isl_dim_all);678 if (dim < 0)679 return isl_bool_error;680 for (k = 0; k < bmap->n_eq; ++k) {681 int stat;682 isl_seq_neg(bmap->eq[k], bmap->eq[k], 1 + dim);683 stat = status_in(bmap->eq[k], tab);684 isl_seq_neg(bmap->eq[k], bmap->eq[k], 1 + dim);685 if (stat < 0)686 return isl_bool_error;687 if (stat != STATUS_VALID)688 return isl_bool_false;689 stat = status_in(bmap->eq[k], tab);690 if (stat < 0)691 return isl_bool_error;692 if (stat != STATUS_VALID)693 return isl_bool_false;694 }695 696 for (k = 0; k < bmap->n_ineq; ++k) {697 int stat;698 if (info->ineq[k] == STATUS_REDUNDANT)699 continue;700 stat = status_in(bmap->ineq[k], tab);701 if (stat < 0)702 return isl_bool_error;703 if (stat != STATUS_VALID)704 return isl_bool_false;705 }706 return isl_bool_true;707}708 709/* Basic map "i" has an inequality "k" that is adjacent710 * to some inequality of basic map "j". All the other inequalities711 * are valid for "j".712 * If not NULL, then "extra" contains extra wrapping constraints that are valid713 * for both "i" and "j".714 * Check if basic map "j" forms an extension of basic map "i",715 * taking into account the extra constraints, if any.716 *717 * Note that this function is only called if some of the equalities or718 * inequalities of basic map "j" do cut basic map "i". The function is719 * correct even if there are no such cut constraints, but in that case720 * the additional checks performed by this function are overkill.721 *722 * In particular, we replace constraint k, say f >= 0, by constraint723 * f <= -1, add the inequalities of "j" that are valid for "i",724 * as well as the "extra" constraints, if any,725 * and check if the result is a subset of basic map "j".726 * To improve the chances of the subset relation being detected,727 * any variable that only attains a single integer value728 * in the tableau of "i" is first fixed to that value.729 * If the result is a subset, then we know that this result is exactly equal730 * to basic map "j" since all its constraints are valid for basic map "j".731 * By combining the valid constraints of "i" (all equalities and all732 * inequalities except "k"), the valid constraints of "j" and733 * the "extra" constraints, if any, we therefore734 * obtain a basic map that is equal to their union.735 * In this case, there is no need to perform a rollback of the tableau736 * since it is going to be destroyed in fuse().737 *738 *739 * |\__ |\__740 * | \__ | \__741 * | \_ => | \__742 * |_______| _ |_________\743 *744 *745 * |\ |\746 * | \ | \747 * | \ | \748 * | | | \749 * | ||\ => | \750 * | || \ | \751 * | || | | |752 * |__||_/ |_____/753 *754 *755 * _______ _______756 * | | __ | \__757 * | ||__| => | __|758 * |_______| |_______/759 */760static enum isl_change is_adj_ineq_extension_with_wraps(int i, int j, int k,761 struct isl_coalesce_info *info, __isl_keep isl_mat *extra)762{763 struct isl_tab_undo *snap;764 isl_size n_eq_i, n_ineq_j, n_extra;765 isl_size total = isl_basic_map_dim(info[i].bmap, isl_dim_all);766 isl_stat r;767 isl_bool super;768 769 if (total < 0)770 return isl_change_error;771 772 n_eq_i = isl_basic_map_n_equality(info[i].bmap);773 n_ineq_j = isl_basic_map_n_inequality(info[j].bmap);774 n_extra = isl_mat_rows(extra);775 if (n_eq_i < 0 || n_ineq_j < 0 || n_extra < 0)776 return isl_change_error;777 778 if (isl_tab_extend_cons(info[i].tab, 1 + n_ineq_j + n_extra) < 0)779 return isl_change_error;780 781 snap = isl_tab_snap(info[i].tab);782 783 if (isl_tab_unrestrict(info[i].tab, n_eq_i + k) < 0)784 return isl_change_error;785 786 isl_seq_neg(info[i].bmap->ineq[k], info[i].bmap->ineq[k], 1 + total);787 isl_int_sub_ui(info[i].bmap->ineq[k][0], info[i].bmap->ineq[k][0], 1);788 r = isl_tab_add_ineq(info[i].tab, info[i].bmap->ineq[k]);789 isl_seq_neg(info[i].bmap->ineq[k], info[i].bmap->ineq[k], 1 + total);790 isl_int_sub_ui(info[i].bmap->ineq[k][0], info[i].bmap->ineq[k][0], 1);791 if (r < 0)792 return isl_change_error;793 794 for (k = 0; k < n_ineq_j; ++k) {795 if (info[j].ineq[k] != STATUS_VALID)796 continue;797 if (isl_tab_add_ineq(info[i].tab, info[j].bmap->ineq[k]) < 0)798 return isl_change_error;799 }800 for (k = 0; k < n_extra; ++k) {801 if (isl_tab_add_ineq(info[i].tab, extra->row[k]) < 0)802 return isl_change_error;803 }804 if (isl_tab_detect_constants(info[i].tab) < 0)805 return isl_change_error;806 807 super = contains(&info[j], info[i].tab);808 if (super < 0)809 return isl_change_error;810 if (super)811 return fuse(i, j, info, extra, 0, 0);812 813 if (isl_tab_rollback(info[i].tab, snap) < 0)814 return isl_change_error;815 816 return isl_change_none;817}818 819/* Given an affine transformation matrix "T", does row "row" represent820 * anything other than a unit vector (possibly shifted by a constant)821 * that is not involved in any of the other rows?822 *823 * That is, if a constraint involves the variable corresponding to824 * the row, then could its preimage by "T" have any coefficients825 * that are different from those in the original constraint?826 */827static int not_unique_unit_row(__isl_keep isl_mat *T, int row)828{829 int i, j;830 int len = T->n_col - 1;831 832 i = isl_seq_first_non_zero(T->row[row] + 1, len);833 if (i < 0)834 return 1;835 if (!isl_int_is_one(T->row[row][1 + i]) &&836 !isl_int_is_negone(T->row[row][1 + i]))837 return 1;838 839 j = isl_seq_first_non_zero(T->row[row] + 1 + i + 1, len - (i + 1));840 if (j >= 0)841 return 1;842 843 for (j = 1; j < T->n_row; ++j) {844 if (j == row)845 continue;846 if (!isl_int_is_zero(T->row[j][1 + i]))847 return 1;848 }849 850 return 0;851}852 853/* Does inequality constraint "ineq" of "bmap" involve any of854 * the variables marked in "affected"?855 * "total" is the total number of variables, i.e., the number856 * of entries in "affected".857 */858static isl_bool is_affected(__isl_keep isl_basic_map *bmap, int ineq,859 int *affected, int total)860{861 int i;862 863 for (i = 0; i < total; ++i) {864 if (!affected[i])865 continue;866 if (!isl_int_is_zero(bmap->ineq[ineq][1 + i]))867 return isl_bool_true;868 }869 870 return isl_bool_false;871}872 873/* Given the compressed version of inequality constraint "ineq"874 * of info->bmap in "v", check if the constraint can be tightened,875 * where the compression is based on an equality constraint valid876 * for info->tab.877 * If so, add the tightened version of the inequality constraint878 * to info->tab. "v" may be modified by this function.879 *880 * That is, if the compressed constraint is of the form881 *882 * m f() + c >= 0883 *884 * with 0 < c < m, then it is equivalent to885 *886 * f() >= 0887 *888 * This means that c can also be subtracted from the original,889 * uncompressed constraint without affecting the integer points890 * in info->tab. Add this tightened constraint as an extra row891 * to info->tab to make this information explicitly available.892 */893static __isl_give isl_vec *try_tightening(struct isl_coalesce_info *info,894 int ineq, __isl_take isl_vec *v)895{896 isl_ctx *ctx;897 isl_stat r;898 899 if (!v)900 return NULL;901 902 ctx = isl_vec_get_ctx(v);903 isl_seq_gcd(v->el + 1, v->size - 1, &ctx->normalize_gcd);904 if (isl_int_is_zero(ctx->normalize_gcd) ||905 isl_int_is_one(ctx->normalize_gcd)) {906 return v;907 }908 909 v = isl_vec_cow(v);910 if (!v)911 return NULL;912 913 isl_int_fdiv_r(v->el[0], v->el[0], ctx->normalize_gcd);914 if (isl_int_is_zero(v->el[0]))915 return v;916 917 if (isl_tab_extend_cons(info->tab, 1) < 0)918 return isl_vec_free(v);919 920 isl_int_sub(info->bmap->ineq[ineq][0],921 info->bmap->ineq[ineq][0], v->el[0]);922 r = isl_tab_add_ineq(info->tab, info->bmap->ineq[ineq]);923 isl_int_add(info->bmap->ineq[ineq][0],924 info->bmap->ineq[ineq][0], v->el[0]);925 926 if (r < 0)927 return isl_vec_free(v);928 929 return v;930}931 932/* Tighten the (non-redundant) constraints on the facet represented933 * by info->tab.934 * In particular, on input, info->tab represents the result935 * of relaxing the "n" inequality constraints of info->bmap in "relaxed"936 * by one, i.e., replacing f_i >= 0 by f_i + 1 >= 0, and then937 * replacing the one at index "l" by the corresponding equality,938 * i.e., f_k + 1 = 0, with k = relaxed[l].939 *940 * Compute a variable compression from the equality constraint f_k + 1 = 0941 * and use it to tighten the other constraints of info->bmap942 * (that is, all constraints that have not been relaxed),943 * updating info->tab (and leaving info->bmap untouched).944 * The compression handles essentially two cases, one where a variable945 * is assigned a fixed value and can therefore be eliminated, and one946 * where one variable is a shifted multiple of some other variable and947 * can therefore be replaced by that multiple.948 * Gaussian elimination would also work for the first case, but for949 * the second case, the effectiveness would depend on the order950 * of the variables.951 * After compression, some of the constraints may have coefficients952 * with a common divisor. If this divisor does not divide the constant953 * term, then the constraint can be tightened.954 * The tightening is performed on the tableau info->tab by introducing955 * extra (temporary) constraints.956 *957 * Only constraints that are possibly affected by the compression are958 * considered. In particular, if the constraint only involves variables959 * that are directly mapped to a distinct set of other variables, then960 * no common divisor can be introduced and no tightening can occur.961 *962 * It is important to only consider the non-redundant constraints963 * since the facet constraint has been relaxed prior to the call964 * to this function, meaning that the constraints that were redundant965 * prior to the relaxation may no longer be redundant.966 * These constraints will be ignored in the fused result, so967 * the fusion detection should not exploit them.968 */969static isl_stat tighten_on_relaxed_facet(struct isl_coalesce_info *info,970 int n, int *relaxed, int l)971{972 isl_size total;973 isl_ctx *ctx;974 isl_vec *v = NULL;975 isl_mat *T;976 int i;977 int k;978 int *affected;979 980 k = relaxed[l];981 ctx = isl_basic_map_get_ctx(info->bmap);982 total = isl_basic_map_dim(info->bmap, isl_dim_all);983 if (total < 0)984 return isl_stat_error;985 isl_int_add_ui(info->bmap->ineq[k][0], info->bmap->ineq[k][0], 1);986 T = isl_mat_sub_alloc6(ctx, info->bmap->ineq, k, 1, 0, 1 + total);987 T = isl_mat_variable_compression(T, NULL);988 isl_int_sub_ui(info->bmap->ineq[k][0], info->bmap->ineq[k][0], 1);989 if (!T)990 return isl_stat_error;991 if (T->n_col == 0) {992 isl_mat_free(T);993 return isl_stat_ok;994 }995 996 affected = isl_alloc_array(ctx, int, total);997 if (!affected)998 goto error;999 1000 for (i = 0; i < total; ++i)1001 affected[i] = not_unique_unit_row(T, 1 + i);1002 1003 for (i = 0; i < info->bmap->n_ineq; ++i) {1004 isl_bool handle;1005 if (any(relaxed, n, i))1006 continue;1007 if (info->ineq[i] == STATUS_REDUNDANT)1008 continue;1009 handle = is_affected(info->bmap, i, affected, total);1010 if (handle < 0)1011 goto error;1012 if (!handle)1013 continue;1014 v = isl_vec_alloc(ctx, 1 + total);1015 if (!v)1016 goto error;1017 isl_seq_cpy(v->el, info->bmap->ineq[i], 1 + total);1018 v = isl_vec_mat_product(v, isl_mat_copy(T));1019 v = try_tightening(info, i, v);1020 isl_vec_free(v);1021 if (!v)1022 goto error;1023 }1024 1025 isl_mat_free(T);1026 free(affected);1027 return isl_stat_ok;1028error:1029 isl_mat_free(T);1030 free(affected);1031 return isl_stat_error;1032}1033 1034/* Replace the basic maps "i" and "j" by an extension of "i"1035 * along the "n" inequality constraints in "relax" by one.1036 * The tableau info[i].tab has already been extended.1037 * Extend info[i].bmap accordingly by relaxing all constraints in "relax"1038 * by one.1039 * Each integer division that does not have exactly the same1040 * definition in "i" and "j" is marked unknown and the basic map1041 * is scheduled to be simplified in an attempt to recover1042 * the integer division definition.1043 * Place the extension in the position that is the smallest of i and j.1044 */1045static enum isl_change extend(int i, int j, int n, int *relax,1046 struct isl_coalesce_info *info)1047{1048 int l;1049 isl_size total;1050 1051 info[i].bmap = isl_basic_map_cow(info[i].bmap);1052 total = isl_basic_map_dim(info[i].bmap, isl_dim_all);1053 if (total < 0)1054 return isl_change_error;1055 for (l = 0; l < info[i].bmap->n_div; ++l)1056 if (!isl_seq_eq(info[i].bmap->div[l],1057 info[j].bmap->div[l], 1 + 1 + total)) {1058 isl_int_set_si(info[i].bmap->div[l][0], 0);1059 info[i].simplify = 1;1060 }1061 for (l = 0; l < n; ++l)1062 isl_int_add_ui(info[i].bmap->ineq[relax[l]][0],1063 info[i].bmap->ineq[relax[l]][0], 1);1064 ISL_F_CLR(info[i].bmap, ISL_BASIC_MAP_NO_REDUNDANT);1065 ISL_F_SET(info[i].bmap, ISL_BASIC_MAP_FINAL);1066 drop(&info[j]);1067 info[i].modified = 1;1068 if (j < i)1069 exchange(&info[i], &info[j]);1070 return isl_change_fuse;1071}1072 1073/* Basic map "i" has "n" inequality constraints (collected in "relax")1074 * that are such that they include basic map "j" if they are relaxed1075 * by one. All the other inequalities are valid for "j".1076 * Check if basic map "j" forms an extension of basic map "i".1077 *1078 * In particular, relax the constraints in "relax", compute the corresponding1079 * facets one by one and check whether each of these is included1080 * in the other basic map.1081 * Before testing for inclusion, the constraints on each facet1082 * are tightened to increase the chance of an inclusion being detected.1083 * (Adding the valid constraints of "j" to the tableau of "i", as is done1084 * in is_adj_ineq_extension, may further increase those chances, but this1085 * is not currently done.)1086 * If each facet is included, we know that relaxing the constraints extends1087 * the basic map with exactly the other basic map (we already know that this1088 * other basic map is included in the extension, because all other1089 * inequality constraints are valid of "j") and we can replace the1090 * two basic maps by this extension.1091 *1092 * If any of the relaxed constraints turn out to be redundant, then bail out.1093 * isl_tab_select_facet refuses to handle such constraints. It may be1094 * possible to handle them anyway by making a distinction between1095 * redundant constraints with a corresponding facet that still intersects1096 * the set (allowing isl_tab_select_facet to handle them) and1097 * those where the facet does not intersect the set (which can be ignored1098 * because the empty facet is trivially included in the other disjunct).1099 * However, relaxed constraints that turn out to be redundant should1100 * be fairly rare and no such instance has been reported where1101 * coalescing would be successful.1102 * ____ _____1103 * / || / |1104 * / || / |1105 * \ || => \ |1106 * \ || \ |1107 * \___|| \____|1108 *1109 *1110 * \ |\1111 * |\\ | \1112 * | \\ | \1113 * | | => | /1114 * | / | /1115 * |/ |/1116 */1117static enum isl_change is_relaxed_extension(int i, int j, int n, int *relax,1118 struct isl_coalesce_info *info)1119{1120 int l;1121 isl_bool super;1122 struct isl_tab_undo *snap, *snap2;1123 unsigned n_eq = info[i].bmap->n_eq;1124 1125 for (l = 0; l < n; ++l)1126 if (isl_tab_is_equality(info[i].tab, n_eq + relax[l]))1127 return isl_change_none;1128 1129 snap = isl_tab_snap(info[i].tab);1130 for (l = 0; l < n; ++l)1131 if (isl_tab_relax(info[i].tab, n_eq + relax[l]) < 0)1132 return isl_change_error;1133 for (l = 0; l < n; ++l) {1134 if (!isl_tab_is_redundant(info[i].tab, n_eq + relax[l]))1135 continue;1136 if (isl_tab_rollback(info[i].tab, snap) < 0)1137 return isl_change_error;1138 return isl_change_none;1139 }1140 snap2 = isl_tab_snap(info[i].tab);1141 for (l = 0; l < n; ++l) {1142 if (isl_tab_rollback(info[i].tab, snap2) < 0)1143 return isl_change_error;1144 if (isl_tab_select_facet(info[i].tab, n_eq + relax[l]) < 0)1145 return isl_change_error;1146 if (tighten_on_relaxed_facet(&info[i], n, relax, l) < 0)1147 return isl_change_error;1148 super = contains(&info[j], info[i].tab);1149 if (super < 0)1150 return isl_change_error;1151 if (super)1152 continue;1153 if (isl_tab_rollback(info[i].tab, snap) < 0)1154 return isl_change_error;1155 return isl_change_none;1156 }1157 1158 if (isl_tab_rollback(info[i].tab, snap2) < 0)1159 return isl_change_error;1160 return extend(i, j, n, relax, info);1161}1162 1163/* Data structure that keeps track of the wrapping constraints1164 * and of information to bound the coefficients of those constraints.1165 *1166 * "failed" is set if wrapping has failed.1167 * bound is set if we want to apply a bound on the coefficients1168 * mat contains the wrapping constraints1169 * max is the bound on the coefficients (if bound is set)1170 */1171struct isl_wraps {1172 int failed;1173 int bound;1174 isl_mat *mat;1175 isl_int max;1176};1177 1178/* Update wraps->max to be greater than or equal to the coefficients1179 * in the equalities and inequalities of info->bmap that can be removed1180 * if we end up applying wrapping.1181 */1182static isl_stat wraps_update_max(struct isl_wraps *wraps,1183 struct isl_coalesce_info *info)1184{1185 int k;1186 isl_int max_k;1187 isl_size total = isl_basic_map_dim(info->bmap, isl_dim_all);1188 1189 if (total < 0)1190 return isl_stat_error;1191 isl_int_init(max_k);1192 1193 for (k = 0; k < info->bmap->n_eq; ++k) {1194 if (info->eq[2 * k] == STATUS_VALID &&1195 info->eq[2 * k + 1] == STATUS_VALID)1196 continue;1197 isl_seq_abs_max(info->bmap->eq[k] + 1, total, &max_k);1198 if (isl_int_abs_gt(max_k, wraps->max))1199 isl_int_set(wraps->max, max_k);1200 }1201 1202 for (k = 0; k < info->bmap->n_ineq; ++k) {1203 if (info->ineq[k] == STATUS_VALID ||1204 info->ineq[k] == STATUS_REDUNDANT)1205 continue;1206 isl_seq_abs_max(info->bmap->ineq[k] + 1, total, &max_k);1207 if (isl_int_abs_gt(max_k, wraps->max))1208 isl_int_set(wraps->max, max_k);1209 }1210 1211 isl_int_clear(max_k);1212 1213 return isl_stat_ok;1214}1215 1216/* Initialize the isl_wraps data structure.1217 * If we want to bound the coefficients of the wrapping constraints,1218 * we set wraps->max to the largest coefficient1219 * in the equalities and inequalities that can be removed if we end up1220 * applying wrapping.1221 */1222static isl_stat wraps_init(struct isl_wraps *wraps, __isl_take isl_mat *mat,1223 struct isl_coalesce_info *info, int i, int j)1224{1225 isl_ctx *ctx;1226 1227 wraps->failed = 0;1228 wraps->bound = 0;1229 wraps->mat = mat;1230 if (!mat)1231 return isl_stat_error;1232 wraps->mat->n_row = 0;1233 ctx = isl_mat_get_ctx(mat);1234 wraps->bound = isl_options_get_coalesce_bounded_wrapping(ctx);1235 if (!wraps->bound)1236 return isl_stat_ok;1237 isl_int_init(wraps->max);1238 isl_int_set_si(wraps->max, 0);1239 if (wraps_update_max(wraps, &info[i]) < 0)1240 return isl_stat_error;1241 if (wraps_update_max(wraps, &info[j]) < 0)1242 return isl_stat_error;1243 1244 return isl_stat_ok;1245}1246 1247/* Free the contents of the isl_wraps data structure.1248 */1249static void wraps_free(struct isl_wraps *wraps)1250{1251 isl_mat_free(wraps->mat);1252 if (wraps->bound)1253 isl_int_clear(wraps->max);1254}1255 1256/* Mark the wrapping as failed.1257 */1258static isl_stat wraps_mark_failed(struct isl_wraps *wraps)1259{1260 wraps->failed = 1;1261 return isl_stat_ok;1262}1263 1264/* Is the wrapping constraint in row "row" allowed?1265 *1266 * If wraps->bound is set, we check that none of the coefficients1267 * is greater than wraps->max.1268 */1269static int allow_wrap(struct isl_wraps *wraps, int row)1270{1271 int i;1272 1273 if (!wraps->bound)1274 return 1;1275 1276 for (i = 1; i < wraps->mat->n_col; ++i)1277 if (isl_int_abs_gt(wraps->mat->row[row][i], wraps->max))1278 return 0;1279 1280 return 1;1281}1282 1283/* Wrap "ineq" (or its opposite if "negate" is set) around "bound"1284 * to include "set" and add the result in position "w" of "wraps".1285 * "len" is the total number of coefficients in "bound" and "ineq".1286 * Return 1 on success, 0 on failure and -1 on error.1287 * Wrapping can fail if the result of wrapping is equal to "bound"1288 * or if we want to bound the sizes of the coefficients and1289 * the wrapped constraint does not satisfy this bound.1290 */1291static int add_wrap(struct isl_wraps *wraps, int w, isl_int *bound,1292 isl_int *ineq, unsigned len, __isl_keep isl_set *set, int negate)1293{1294 isl_seq_cpy(wraps->mat->row[w], bound, len);1295 if (negate) {1296 isl_seq_neg(wraps->mat->row[w + 1], ineq, len);1297 ineq = wraps->mat->row[w + 1];1298 }1299 if (!isl_set_wrap_facet(set, wraps->mat->row[w], ineq))1300 return -1;1301 if (isl_seq_eq(wraps->mat->row[w], bound, len))1302 return 0;1303 if (!allow_wrap(wraps, w))1304 return 0;1305 return 1;1306}1307 1308/* This function has two modes of operations.1309 *1310 * If "add_valid" is set, then all the constraints of info->bmap1311 * (except the opposite of "bound") are valid for the other basic map.1312 * In this case, attempts are made to wrap some of these valid constraints1313 * to more tightly fit around "set". Only successful wrappings are recorded1314 * and failed wrappings are ignored.1315 *1316 * If "add_valid" is not set, then some of the constraints of info->bmap1317 * are not valid for the other basic map, and only those are considered1318 * for wrapping. In this case all attempted wrappings need to succeed.1319 * Otherwise "wraps" is marked as failed.1320 * Note that the constraints that are valid for the other basic map1321 * will be added to the combined basic map by default, so there is1322 * no need to wrap them.1323 * The caller wrap_in_facets even relies on this function not wrapping1324 * any constraints that are already valid.1325 *1326 * Only consider constraints that are not redundant (as determined1327 * by info->tab) and that are valid or invalid depending on "add_valid".1328 * Wrap each constraint around "bound" such that it includes the whole1329 * set "set" and append the resulting constraint to "wraps".1330 * "wraps" is assumed to have been pre-allocated to the appropriate size.1331 * wraps->n_row is the number of actual wrapped constraints that have1332 * been added.1333 * If any of the wrapping problems results in a constraint that is1334 * identical to "bound", then this means that "set" is unbounded in such1335 * a way that no wrapping is possible.1336 * Similarly, if we want to bound the coefficients of the wrapping1337 * constraints and a newly added wrapping constraint does not1338 * satisfy the bound, then the wrapping is considered to have failed.1339 * Note though that "wraps" is only marked failed if "add_valid" is not set.1340 */1341static isl_stat add_selected_wraps(struct isl_wraps *wraps,1342 struct isl_coalesce_info *info, isl_int *bound, __isl_keep isl_set *set,1343 int add_valid)1344{1345 int l, m;1346 int w;1347 int added;1348 isl_basic_map *bmap = info->bmap;1349 isl_size total = isl_basic_map_dim(bmap, isl_dim_all);1350 unsigned len = 1 + total;1351 1352 if (total < 0)1353 return isl_stat_error;1354 1355 w = wraps->mat->n_row;1356 1357 for (l = 0; l < bmap->n_ineq; ++l) {1358 int is_valid = info->ineq[l] == STATUS_VALID;1359 if ((!add_valid && is_valid) ||1360 info->ineq[l] == STATUS_REDUNDANT)1361 continue;1362 if (isl_seq_is_neg(bound, bmap->ineq[l], len))1363 continue;1364 if (isl_seq_eq(bound, bmap->ineq[l], len))1365 continue;1366 if (isl_tab_is_redundant(info->tab, bmap->n_eq + l))1367 continue;1368 1369 added = add_wrap(wraps, w, bound, bmap->ineq[l], len, set, 0);1370 if (added < 0)1371 return isl_stat_error;1372 if (!added && !is_valid)1373 goto unbounded;1374 if (added)1375 ++w;1376 }1377 for (l = 0; l < bmap->n_eq; ++l) {1378 if (isl_seq_is_neg(bound, bmap->eq[l], len))1379 continue;1380 if (isl_seq_eq(bound, bmap->eq[l], len))1381 continue;1382 1383 for (m = 0; m < 2; ++m) {1384 if (info->eq[2 * l + m] == STATUS_VALID)1385 continue;1386 added = add_wrap(wraps, w, bound, bmap->eq[l], len,1387 set, !m);1388 if (added < 0)1389 return isl_stat_error;1390 if (!added)1391 goto unbounded;1392 ++w;1393 }1394 }1395 1396 wraps->mat->n_row = w;1397 return isl_stat_ok;1398unbounded:1399 return wraps_mark_failed(wraps);1400}1401 1402/* For each constraint in info->bmap that is not redundant (as determined1403 * by info->tab) and that is not a valid constraint for the other basic map,1404 * wrap the constraint around "bound" such that it includes the whole1405 * set "set" and append the resulting constraint to "wraps".1406 * Note that the constraints that are valid for the other basic map1407 * will be added to the combined basic map by default, so there is1408 * no need to wrap them.1409 * The caller wrap_in_facets even relies on this function not wrapping1410 * any constraints that are already valid.1411 * "wraps" is assumed to have been pre-allocated to the appropriate size.1412 * wraps->n_row is the number of actual wrapped constraints that have1413 * been added.1414 * If any of the wrapping problems results in a constraint that is1415 * identical to "bound", then this means that "set" is unbounded in such1416 * a way that no wrapping is possible. If this happens then "wraps"1417 * is marked as failed.1418 * Similarly, if we want to bound the coefficients of the wrapping1419 * constraints and a newly added wrapping constraint does not1420 * satisfy the bound, then "wraps" is also marked as failed.1421 */1422static isl_stat add_wraps(struct isl_wraps *wraps,1423 struct isl_coalesce_info *info, isl_int *bound, __isl_keep isl_set *set)1424{1425 return add_selected_wraps(wraps, info, bound, set, 0);1426}1427 1428/* Check if the constraints in "wraps" from "first" until the last1429 * are all valid for the basic set represented by "tab",1430 * dropping the invalid constraints if "keep" is set and1431 * marking the wrapping as failed if "keep" is not set and1432 * any constraint turns out to be invalid.1433 */1434static isl_stat check_wraps(struct isl_wraps *wraps, int first,1435 struct isl_tab *tab, int keep)1436{1437 int i;1438 1439 for (i = wraps->mat->n_row - 1; i >= first; --i) {1440 enum isl_ineq_type type;1441 type = isl_tab_ineq_type(tab, wraps->mat->row[i]);1442 if (type == isl_ineq_error)1443 return isl_stat_error;1444 if (type == isl_ineq_redundant)1445 continue;1446 if (!keep)1447 return wraps_mark_failed(wraps);1448 wraps->mat = isl_mat_drop_rows(wraps->mat, i, 1);1449 if (!wraps->mat)1450 return isl_stat_error;1451 }1452 1453 return isl_stat_ok;1454}1455 1456/* Return a set that corresponds to the non-redundant constraints1457 * (as recorded in tab) of bmap.1458 *1459 * It's important to remove the redundant constraints as some1460 * of the other constraints may have been modified after the1461 * constraints were marked redundant.1462 * In particular, a constraint may have been relaxed.1463 * Redundant constraints are ignored when a constraint is relaxed1464 * and should therefore continue to be ignored ever after.1465 * Otherwise, the relaxation might be thwarted by some of1466 * these constraints.1467 *1468 * Update the underlying set to ensure that the dimension doesn't change.1469 * Otherwise the integer divisions could get dropped if the tab1470 * turns out to be empty.1471 */1472static __isl_give isl_set *set_from_updated_bmap(__isl_keep isl_basic_map *bmap,1473 struct isl_tab *tab)1474{1475 isl_basic_set *bset;1476 1477 bmap = isl_basic_map_copy(bmap);1478 bset = isl_basic_map_underlying_set(bmap);1479 bset = isl_basic_set_cow(bset);1480 bset = isl_basic_set_update_from_tab(bset, tab);1481 return isl_set_from_basic_set(bset);1482}1483 1484/* Does "info" have any cut constraints that are redundant?1485 */1486static isl_bool has_redundant_cuts(struct isl_coalesce_info *info)1487{1488 int l;1489 isl_size n_eq, n_ineq;1490 1491 n_eq = isl_basic_map_n_equality(info->bmap);1492 n_ineq = isl_basic_map_n_inequality(info->bmap);1493 if (n_eq < 0 || n_ineq < 0)1494 return isl_bool_error;1495 for (l = 0; l < n_ineq; ++l) {1496 int red;1497 1498 if (info->ineq[l] != STATUS_CUT)1499 continue;1500 red = isl_tab_is_redundant(info->tab, n_eq + l);1501 if (red < 0)1502 return isl_bool_error;1503 if (red)1504 return isl_bool_true;1505 }1506 1507 return isl_bool_false;1508}1509 1510/* Wrap some constraints of info->bmap that bound the facet defined1511 * by inequality "k" around (the opposite of) this inequality to1512 * include "set". "bound" may be used to store the negated inequality.1513 *1514 * If "add_valid" is set, then all ridges are already valid and1515 * the purpose is to wrap "set" more tightly. In this case,1516 * wrapping doesn't fail, although it is possible that no constraint1517 * gets wrapped.1518 *1519 * If "add_valid" is not set, then some of the ridges are cut constraints1520 * and only those are wrapped around "set".1521 *1522 * Since the wrapped constraints are not guaranteed to contain the whole1523 * of info->bmap, we check them in check_wraps.1524 * If any of the wrapped constraints turn out to be invalid, then1525 * check_wraps will mark "wraps" as failed if "add_valid" is not set.1526 * If "add_valid" is set, then the offending constraints are1527 * simply removed.1528 *1529 * If the facet turns out to be empty, then no wrapping can be performed.1530 * This is considered a failure, unless "add_valid" is set.1531 *1532 * If any of the cut constraints of info->bmap turn out1533 * to be redundant with respect to other constraints1534 * then these will neither be wrapped nor added directly to the result.1535 * The result may therefore not be correct.1536 * Skip wrapping and mark "wraps" as failed in this case.1537 */1538static isl_stat add_selected_wraps_around_facet(struct isl_wraps *wraps,1539 struct isl_coalesce_info *info, int k, isl_int *bound,1540 __isl_keep isl_set *set, int add_valid)1541{1542 isl_bool nowrap;1543 struct isl_tab_undo *snap;1544 int n;1545 isl_size total = isl_basic_map_dim(info->bmap, isl_dim_all);1546 1547 if (total < 0)1548 return isl_stat_error;1549 1550 snap = isl_tab_snap(info->tab);1551 1552 if (isl_tab_select_facet(info->tab, info->bmap->n_eq + k) < 0)1553 return isl_stat_error;1554 if (isl_tab_detect_redundant(info->tab) < 0)1555 return isl_stat_error;1556 if (info->tab->empty) {1557 if (isl_tab_rollback(info->tab, snap) < 0)1558 return isl_stat_error;1559 if (!add_valid)1560 return wraps_mark_failed(wraps);1561 return isl_stat_ok;1562 }1563 nowrap = has_redundant_cuts(info);1564 if (nowrap < 0)1565 return isl_stat_error;1566 1567 n = wraps->mat->n_row;1568 if (!nowrap) {1569 isl_seq_neg(bound, info->bmap->ineq[k], 1 + total);1570 1571 if (add_selected_wraps(wraps, info, bound, set, add_valid) < 0)1572 return isl_stat_error;1573 }1574 1575 if (isl_tab_rollback(info->tab, snap) < 0)1576 return isl_stat_error;1577 if (nowrap)1578 return wraps_mark_failed(wraps);1579 if (check_wraps(wraps, n, info->tab, add_valid) < 0)1580 return isl_stat_error;1581 1582 return isl_stat_ok;1583}1584 1585/* Wrap the constraints of info->bmap that bound the facet defined1586 * by inequality "k" around (the opposite of) this inequality to1587 * include "set". "bound" may be used to store the negated inequality.1588 * If any of the wrapped constraints turn out to be invalid for info->bmap1589 * itself, then mark "wraps" as failed.1590 */1591static isl_stat add_wraps_around_facet(struct isl_wraps *wraps,1592 struct isl_coalesce_info *info, int k, isl_int *bound,1593 __isl_keep isl_set *set)1594{1595 return add_selected_wraps_around_facet(wraps, info, k, bound, set, 0);1596}1597 1598/* Wrap the (valid) constraints of info->bmap that bound the facet defined1599 * by inequality "k" around (the opposite of) this inequality to1600 * include "set" more tightly.1601 * "bound" may be used to store the negated inequality.1602 * Remove any wrapping constraints that turn out to be invalid1603 * for info->bmap itself.1604 */1605static isl_stat add_valid_wraps_around_facet(struct isl_wraps *wraps,1606 struct isl_coalesce_info *info, int k, isl_int *bound,1607 __isl_keep isl_set *set)1608{1609 return add_selected_wraps_around_facet(wraps, info, k, bound, set, 1);1610}1611 1612/* Basic map "i" has an inequality (say "k") that is adjacent1613 * to some inequality of basic map "j". All the other inequalities1614 * are valid for "j".1615 * Check if basic map "j" forms an extension of basic map "i".1616 *1617 * Note that this function is only called if some of the equalities or1618 * inequalities of basic map "j" do cut basic map "i". The function is1619 * correct even if there are no such cut constraints, but in that case1620 * the additional checks performed by this function are overkill.1621 *1622 * First try and wrap the ridges of "k" around "j".1623 * Note that those ridges are already valid for "j",1624 * but the wrapped versions may wrap "j" more tightly,1625 * increasing the chances of "j" being detected as an extension of "i"1626 */1627static enum isl_change is_adj_ineq_extension(int i, int j,1628 struct isl_coalesce_info *info)1629{1630 int k;1631 enum isl_change change;1632 isl_size total;1633 isl_size n_eq_i, n_ineq_i;1634 struct isl_wraps wraps;1635 isl_ctx *ctx;1636 isl_mat *mat;1637 isl_vec *bound;1638 isl_set *set_j;1639 isl_stat r;1640 1641 k = find_ineq(&info[i], STATUS_ADJ_INEQ);1642 if (k < 0)1643 isl_die(isl_basic_map_get_ctx(info[i].bmap), isl_error_internal,1644 "info[i].ineq should have exactly one STATUS_ADJ_INEQ",1645 return isl_change_error);1646 1647 total = isl_basic_map_dim(info[i].bmap, isl_dim_all);1648 n_eq_i = isl_basic_map_n_equality(info[i].bmap);1649 n_ineq_i = isl_basic_map_n_inequality(info[i].bmap);1650 if (total < 0 || n_eq_i < 0 || n_ineq_i < 0)1651 return isl_change_error;1652 1653 set_j = set_from_updated_bmap(info[j].bmap, info[j].tab);1654 ctx = isl_basic_map_get_ctx(info[i].bmap);1655 bound = isl_vec_alloc(ctx, 1 + total);1656 mat = isl_mat_alloc(ctx, 2 * n_eq_i + n_ineq_i, 1 + total);1657 if (wraps_init(&wraps, mat, info, i, j) < 0)1658 goto error;1659 if (!bound || !set_j)1660 goto error;1661 r = add_valid_wraps_around_facet(&wraps, &info[i], k, bound->el, set_j);1662 if (r < 0)1663 goto error;1664 1665 change = is_adj_ineq_extension_with_wraps(i, j, k, info, wraps.mat);1666 1667 wraps_free(&wraps);1668 isl_vec_free(bound);1669 isl_set_free(set_j);1670 1671 return change;1672error:1673 wraps_free(&wraps);1674 isl_vec_free(bound);1675 isl_set_free(set_j);1676 return isl_change_error;1677}1678 1679/* Both basic maps have at least one inequality with and adjacent1680 * (but opposite) inequality in the other basic map.1681 * Check that there are no cut constraints and that there is only1682 * a single pair of adjacent inequalities.1683 * If so, we can replace the pair by a single basic map described1684 * by all but the pair of adjacent inequalities.1685 * Any additional points introduced lie strictly between the two1686 * adjacent hyperplanes and can therefore be integral.1687 *1688 * ____ _____1689 * / ||\ / \1690 * / || \ / \1691 * \ || \ => \ \1692 * \ || / \ /1693 * \___||_/ \_____/1694 *1695 * The test for a single pair of adjacent inequalities is important1696 * for avoiding the combination of two basic maps like the following1697 *1698 * /|1699 * / |1700 * /__|1701 * _____1702 * | |1703 * | |1704 * |___|1705 *1706 * If there are some cut constraints on one side, then we may1707 * still be able to fuse the two basic maps, but we need to perform1708 * some additional checks in is_adj_ineq_extension.1709 */1710static enum isl_change check_adj_ineq(int i, int j,1711 struct isl_coalesce_info *info)1712{1713 int count_i, count_j;1714 int cut_i, cut_j;1715 1716 count_i = count_ineq(&info[i], STATUS_ADJ_INEQ);1717 count_j = count_ineq(&info[j], STATUS_ADJ_INEQ);1718 1719 if (count_i != 1 && count_j != 1)1720 return isl_change_none;1721 1722 cut_i = any_eq(&info[i], STATUS_CUT) || any_ineq(&info[i], STATUS_CUT);1723 cut_j = any_eq(&info[j], STATUS_CUT) || any_ineq(&info[j], STATUS_CUT);1724 1725 if (!cut_i && !cut_j && count_i == 1 && count_j == 1)1726 return fuse(i, j, info, NULL, 0, 0);1727 1728 if (count_i == 1 && !cut_i)1729 return is_adj_ineq_extension(i, j, info);1730 1731 if (count_j == 1 && !cut_j)1732 return is_adj_ineq_extension(j, i, info);1733 1734 return isl_change_none;1735}1736 1737/* Given a basic set i with a constraint k that is adjacent to1738 * basic set j, check if we can wrap1739 * both the facet corresponding to k (if "wrap_facet" is set) and basic map j1740 * (always) around their ridges to include the other set.1741 * If so, replace the pair of basic sets by their union.1742 *1743 * All constraints of i (except k) are assumed to be valid or1744 * cut constraints for j.1745 * Wrapping the cut constraints to include basic map j may result1746 * in constraints that are no longer valid of basic map i1747 * we have to check that the resulting wrapping constraints are valid for i.1748 * If "wrap_facet" is not set, then all constraints of i (except k)1749 * are assumed to be valid for j.1750 * ____ _____1751 * / | / \1752 * / || / |1753 * \ || => \ |1754 * \ || \ |1755 * \___|| \____|1756 *1757 */1758static enum isl_change can_wrap_in_facet(int i, int j, int k,1759 struct isl_coalesce_info *info, int wrap_facet)1760{1761 enum isl_change change = isl_change_none;1762 struct isl_wraps wraps;1763 isl_ctx *ctx;1764 isl_mat *mat;1765 struct isl_set *set_i = NULL;1766 struct isl_set *set_j = NULL;1767 struct isl_vec *bound = NULL;1768 isl_size total = isl_basic_map_dim(info[i].bmap, isl_dim_all);1769 1770 if (total < 0)1771 return isl_change_error;1772 set_i = set_from_updated_bmap(info[i].bmap, info[i].tab);1773 set_j = set_from_updated_bmap(info[j].bmap, info[j].tab);1774 ctx = isl_basic_map_get_ctx(info[i].bmap);1775 mat = isl_mat_alloc(ctx, 2 * (info[i].bmap->n_eq + info[j].bmap->n_eq) +1776 info[i].bmap->n_ineq + info[j].bmap->n_ineq,1777 1 + total);1778 if (wraps_init(&wraps, mat, info, i, j) < 0)1779 goto error;1780 bound = isl_vec_alloc(ctx, 1 + total);1781 if (!set_i || !set_j || !bound)1782 goto error;1783 1784 isl_seq_cpy(bound->el, info[i].bmap->ineq[k], 1 + total);1785 isl_int_add_ui(bound->el[0], bound->el[0], 1);1786 isl_seq_normalize(ctx, bound->el, 1 + total);1787 1788 isl_seq_cpy(wraps.mat->row[0], bound->el, 1 + total);1789 wraps.mat->n_row = 1;1790 1791 if (add_wraps(&wraps, &info[j], bound->el, set_i) < 0)1792 goto error;1793 if (wraps.failed)1794 goto unbounded;1795 1796 if (wrap_facet) {1797 if (add_wraps_around_facet(&wraps, &info[i], k,1798 bound->el, set_j) < 0)1799 goto error;1800 if (wraps.failed)1801 goto unbounded;1802 }1803 1804 change = fuse(i, j, info, wraps.mat, 0, 0);1805 1806unbounded:1807 wraps_free(&wraps);1808 1809 isl_set_free(set_i);1810 isl_set_free(set_j);1811 1812 isl_vec_free(bound);1813 1814 return change;1815error:1816 wraps_free(&wraps);1817 isl_vec_free(bound);1818 isl_set_free(set_i);1819 isl_set_free(set_j);1820 return isl_change_error;1821}1822 1823/* Given a cut constraint t(x) >= 0 of basic map i, stored in row "w"1824 * of wrap.mat, replace it by its relaxed version t(x) + 1 >= 0, and1825 * add wrapping constraints to wrap.mat for all constraints1826 * of basic map j that bound the part of basic map j that sticks out1827 * of the cut constraint.1828 * "set_i" is the underlying set of basic map i.1829 * If any wrapping fails, then wraps->mat.n_row is reset to zero.1830 *1831 * In particular, we first intersect basic map j with t(x) + 1 = 0.1832 * If the result is empty, then t(x) >= 0 was actually a valid constraint1833 * (with respect to the integer points), so we add t(x) >= 0 instead.1834 * Otherwise, we wrap the constraints of basic map j that are not1835 * redundant in this intersection and that are not already valid1836 * for basic map i over basic map i.1837 * Note that it is sufficient to wrap the constraints to include1838 * basic map i, because we will only wrap the constraints that do1839 * not include basic map i already. The wrapped constraint will1840 * therefore be more relaxed compared to the original constraint.1841 * Since the original constraint is valid for basic map j, so is1842 * the wrapped constraint.1843 */1844static isl_stat wrap_in_facet(struct isl_wraps *wraps, int w,1845 struct isl_coalesce_info *info_j, __isl_keep isl_set *set_i,1846 struct isl_tab_undo *snap)1847{1848 isl_int_add_ui(wraps->mat->row[w][0], wraps->mat->row[w][0], 1);1849 if (isl_tab_add_eq(info_j->tab, wraps->mat->row[w]) < 0)1850 return isl_stat_error;1851 if (isl_tab_detect_redundant(info_j->tab) < 0)1852 return isl_stat_error;1853 1854 if (info_j->tab->empty)1855 isl_int_sub_ui(wraps->mat->row[w][0], wraps->mat->row[w][0], 1);1856 else if (add_wraps(wraps, info_j, wraps->mat->row[w], set_i) < 0)1857 return isl_stat_error;1858 1859 if (isl_tab_rollback(info_j->tab, snap) < 0)1860 return isl_stat_error;1861 1862 return isl_stat_ok;1863}1864 1865/* Given a pair of basic maps i and j such that j sticks out1866 * of i at n cut constraints, each time by at most one,1867 * try to compute wrapping constraints and replace the two1868 * basic maps by a single basic map.1869 * The other constraints of i are assumed to be valid for j.1870 * "set_i" is the underlying set of basic map i.1871 * "wraps" has been initialized to be of the right size.1872 *1873 * For each cut constraint t(x) >= 0 of i, we add the relaxed version1874 * t(x) + 1 >= 0, along with wrapping constraints for all constraints1875 * of basic map j that bound the part of basic map j that sticks out1876 * of the cut constraint.1877 *1878 * If any wrapping fails, i.e., if we cannot wrap to touch1879 * the union, then we give up.1880 * Otherwise, the pair of basic maps is replaced by their union.1881 */1882static enum isl_change try_wrap_in_facets(int i, int j,1883 struct isl_coalesce_info *info, struct isl_wraps *wraps,1884 __isl_keep isl_set *set_i)1885{1886 int k, l, w;1887 isl_size total;1888 struct isl_tab_undo *snap;1889 1890 total = isl_basic_map_dim(info[i].bmap, isl_dim_all);1891 if (total < 0)1892 return isl_change_error;1893 1894 snap = isl_tab_snap(info[j].tab);1895 1896 for (k = 0; k < info[i].bmap->n_eq; ++k) {1897 for (l = 0; l < 2; ++l) {1898 if (info[i].eq[2 * k + l] != STATUS_CUT)1899 continue;1900 w = wraps->mat->n_row++;1901 if (l == 0)1902 isl_seq_neg(wraps->mat->row[w],1903 info[i].bmap->eq[k], 1 + total);1904 else1905 isl_seq_cpy(wraps->mat->row[w],1906 info[i].bmap->eq[k], 1 + total);1907 if (wrap_in_facet(wraps, w, &info[j], set_i, snap) < 0)1908 return isl_change_error;1909 1910 if (wraps->failed)1911 return isl_change_none;1912 }1913 }1914 1915 for (k = 0; k < info[i].bmap->n_ineq; ++k) {1916 if (info[i].ineq[k] != STATUS_CUT)1917 continue;1918 w = wraps->mat->n_row++;1919 isl_seq_cpy(wraps->mat->row[w],1920 info[i].bmap->ineq[k], 1 + total);1921 if (wrap_in_facet(wraps, w, &info[j], set_i, snap) < 0)1922 return isl_change_error;1923 1924 if (wraps->failed)1925 return isl_change_none;1926 }1927 1928 return fuse(i, j, info, wraps->mat, 0, 1);1929}1930 1931/* Given a pair of basic maps i and j such that j sticks out1932 * of i at n cut constraints, each time by at most one,1933 * try to compute wrapping constraints and replace the two1934 * basic maps by a single basic map.1935 * The other constraints of i are assumed to be valid for j.1936 *1937 * The core computation is performed by try_wrap_in_facets.1938 * This function simply extracts an underlying set representation1939 * of basic map i and initializes the data structure for keeping1940 * track of wrapping constraints.1941 */1942static enum isl_change wrap_in_facets(int i, int j, int n,1943 struct isl_coalesce_info *info)1944{1945 enum isl_change change = isl_change_none;1946 struct isl_wraps wraps;1947 isl_ctx *ctx;1948 isl_mat *mat;1949 isl_set *set_i = NULL;1950 isl_size total = isl_basic_map_dim(info[i].bmap, isl_dim_all);1951 int max_wrap;1952 1953 if (total < 0)1954 return isl_change_error;1955 if (isl_tab_extend_cons(info[j].tab, 1) < 0)1956 return isl_change_error;1957 1958 max_wrap = 1 + 2 * info[j].bmap->n_eq + info[j].bmap->n_ineq;1959 max_wrap *= n;1960 1961 set_i = set_from_updated_bmap(info[i].bmap, info[i].tab);1962 ctx = isl_basic_map_get_ctx(info[i].bmap);1963 mat = isl_mat_alloc(ctx, max_wrap, 1 + total);1964 if (wraps_init(&wraps, mat, info, i, j) < 0)1965 goto error;1966 if (!set_i)1967 goto error;1968 1969 change = try_wrap_in_facets(i, j, info, &wraps, set_i);1970 1971 wraps_free(&wraps);1972 isl_set_free(set_i);1973 1974 return change;1975error:1976 wraps_free(&wraps);1977 isl_set_free(set_i);1978 return isl_change_error;1979}1980 1981/* Return the effect of inequality "ineq" on the tableau "tab",1982 * after relaxing the constant term of "ineq" by one.1983 */1984static enum isl_ineq_type type_of_relaxed(struct isl_tab *tab, isl_int *ineq)1985{1986 enum isl_ineq_type type;1987 1988 isl_int_add_ui(ineq[0], ineq[0], 1);1989 type = isl_tab_ineq_type(tab, ineq);1990 isl_int_sub_ui(ineq[0], ineq[0], 1);1991 1992 return type;1993}1994 1995/* Given two basic sets i and j,1996 * check if relaxing all the cut constraints of i by one turns1997 * them into valid constraint for j and check if we can wrap in1998 * the bits that are sticking out.1999 * If so, replace the pair by their union.2000 *2001 * We first check if all relaxed cut inequalities of i are valid for j2002 * and then try to wrap in the intersections of the relaxed cut inequalities2003 * with j.2004 *2005 * During this wrapping, we consider the points of j that lie at a distance2006 * of exactly 1 from i. In particular, we ignore the points that lie in2007 * between this lower-dimensional space and the basic map i.2008 * We can therefore only apply this to integer maps.2009 * ____ _____2010 * / ___|_ / \2011 * / | | / |2012 * \ | | => \ |2013 * \|____| \ |2014 * \___| \____/2015 *2016 * _____ ______2017 * | ____|_ | \2018 * | | | | |2019 * | | | => | |2020 * |_| | | |2021 * |_____| \______|2022 *2023 * _______2024 * | |2025 * | |\ |2026 * | | \ |2027 * | | \ |2028 * | | \|2029 * | | \2030 * | |_____\2031 * | |2032 * |_______|2033 *2034 * Wrapping can fail if the result of wrapping one of the facets2035 * around its edges does not produce any new facet constraint.2036 * In particular, this happens when we try to wrap in unbounded sets.2037 *2038 * _______________________________________________________________________2039 * |2040 * | ___2041 * | | |2042 * |_| |_________________________________________________________________2043 * |___|2044 *2045 * The following is not an acceptable result of coalescing the above two2046 * sets as it includes extra integer points.2047 * _______________________________________________________________________2048 * |2049 * | 2050 * | 2051 * |2052 * \______________________________________________________________________2053 */2054static enum isl_change can_wrap_in_set(int i, int j,2055 struct isl_coalesce_info *info)2056{2057 int k, l;2058 int n;2059 isl_size total;2060 2061 if (ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_RATIONAL) ||2062 ISL_F_ISSET(info[j].bmap, ISL_BASIC_MAP_RATIONAL))2063 return isl_change_none;2064 2065 n = count_eq(&info[i], STATUS_CUT) + count_ineq(&info[i], STATUS_CUT);2066 if (n == 0)2067 return isl_change_none;2068 2069 total = isl_basic_map_dim(info[i].bmap, isl_dim_all);2070 if (total < 0)2071 return isl_change_error;2072 for (k = 0; k < info[i].bmap->n_eq; ++k) {2073 for (l = 0; l < 2; ++l) {2074 enum isl_ineq_type type;2075 2076 if (info[i].eq[2 * k + l] != STATUS_CUT)2077 continue;2078 2079 if (l == 0)2080 isl_seq_neg(info[i].bmap->eq[k],2081 info[i].bmap->eq[k], 1 + total);2082 type = type_of_relaxed(info[j].tab,2083 info[i].bmap->eq[k]);2084 if (l == 0)2085 isl_seq_neg(info[i].bmap->eq[k],2086 info[i].bmap->eq[k], 1 + total);2087 if (type == isl_ineq_error)2088 return isl_change_error;2089 if (type != isl_ineq_redundant)2090 return isl_change_none;2091 }2092 }2093 2094 for (k = 0; k < info[i].bmap->n_ineq; ++k) {2095 enum isl_ineq_type type;2096 2097 if (info[i].ineq[k] != STATUS_CUT)2098 continue;2099 2100 type = type_of_relaxed(info[j].tab, info[i].bmap->ineq[k]);2101 if (type == isl_ineq_error)2102 return isl_change_error;2103 if (type != isl_ineq_redundant)2104 return isl_change_none;2105 }2106 2107 return wrap_in_facets(i, j, n, info);2108}2109 2110/* Check if either i or j has only cut constraints that can2111 * be used to wrap in (a facet of) the other basic set.2112 * if so, replace the pair by their union.2113 */2114static enum isl_change check_wrap(int i, int j, struct isl_coalesce_info *info)2115{2116 enum isl_change change = isl_change_none;2117 2118 change = can_wrap_in_set(i, j, info);2119 if (change != isl_change_none)2120 return change;2121 2122 change = can_wrap_in_set(j, i, info);2123 return change;2124}2125 2126/* Check if all inequality constraints of "i" that cut "j" cease2127 * to be cut constraints if they are relaxed by one.2128 * If so, collect the cut constraints in "list".2129 * The caller is responsible for allocating "list".2130 */2131static isl_bool all_cut_by_one(int i, int j, struct isl_coalesce_info *info,2132 int *list)2133{2134 int l, n;2135 2136 n = 0;2137 for (l = 0; l < info[i].bmap->n_ineq; ++l) {2138 enum isl_ineq_type type;2139 2140 if (info[i].ineq[l] != STATUS_CUT)2141 continue;2142 type = type_of_relaxed(info[j].tab, info[i].bmap->ineq[l]);2143 if (type == isl_ineq_error)2144 return isl_bool_error;2145 if (type != isl_ineq_redundant)2146 return isl_bool_false;2147 list[n++] = l;2148 }2149 2150 return isl_bool_true;2151}2152 2153/* Given two basic maps such that "j" has at least one equality constraint2154 * that is adjacent to an inequality constraint of "i" and such that "i" has2155 * exactly one inequality constraint that is adjacent to an equality2156 * constraint of "j", check whether "i" can be extended to include "j" or2157 * whether "j" can be wrapped into "i".2158 * All remaining constraints of "i" and "j" are assumed to be valid2159 * or cut constraints of the other basic map.2160 * However, none of the equality constraints of "i" are cut constraints.2161 *2162 * If "i" has any "cut" inequality constraints, then check if relaxing2163 * each of them by one is sufficient for them to become valid.2164 * If so, check if the inequality constraint adjacent to an equality2165 * constraint of "j" along with all these cut constraints2166 * can be relaxed by one to contain exactly "j".2167 * Otherwise, or if this fails, check if "j" can be wrapped into "i".2168 */2169static enum isl_change check_single_adj_eq(int i, int j,2170 struct isl_coalesce_info *info)2171{2172 enum isl_change change = isl_change_none;2173 int k;2174 int n_cut;2175 int *relax;2176 isl_ctx *ctx;2177 isl_bool try_relax;2178 2179 n_cut = count_ineq(&info[i], STATUS_CUT);2180 2181 k = find_ineq(&info[i], STATUS_ADJ_EQ);2182 2183 if (n_cut > 0) {2184 ctx = isl_basic_map_get_ctx(info[i].bmap);2185 relax = isl_calloc_array(ctx, int, 1 + n_cut);2186 if (!relax)2187 return isl_change_error;2188 relax[0] = k;2189 try_relax = all_cut_by_one(i, j, info, relax + 1);2190 if (try_relax < 0)2191 change = isl_change_error;2192 } else {2193 try_relax = isl_bool_true;2194 relax = &k;2195 }2196 if (try_relax && change == isl_change_none)2197 change = is_relaxed_extension(i, j, 1 + n_cut, relax, info);2198 if (n_cut > 0)2199 free(relax);2200 if (change != isl_change_none)2201 return change;2202 2203 change = can_wrap_in_facet(i, j, k, info, n_cut > 0);2204 2205 return change;2206}2207 2208/* At least one of the basic maps has an equality that is adjacent2209 * to an inequality. Make sure that only one of the basic maps has2210 * such an equality and that the other basic map has exactly one2211 * inequality adjacent to an equality.2212 * If the other basic map does not have such an inequality, then2213 * check if all its constraints are either valid or cut constraints2214 * and, if so, try wrapping in the first map into the second.2215 * Otherwise, try to extend one basic map with the other or2216 * wrap one basic map in the other.2217 */2218static enum isl_change check_adj_eq(int i, int j,2219 struct isl_coalesce_info *info)2220{2221 if (any_eq(&info[i], STATUS_ADJ_INEQ) &&2222 any_eq(&info[j], STATUS_ADJ_INEQ))2223 /* ADJ EQ TOO MANY */2224 return isl_change_none;2225 2226 if (any_eq(&info[i], STATUS_ADJ_INEQ))2227 return check_adj_eq(j, i, info);2228 2229 /* j has an equality adjacent to an inequality in i */2230 2231 if (count_ineq(&info[i], STATUS_ADJ_EQ) != 1) {2232 if (all_valid_or_cut(&info[i]))2233 return can_wrap_in_set(i, j, info);2234 return isl_change_none;2235 }2236 if (any_eq(&info[i], STATUS_CUT))2237 return isl_change_none;2238 if (any_ineq(&info[j], STATUS_ADJ_EQ) ||2239 any_ineq(&info[i], STATUS_ADJ_INEQ) ||2240 any_ineq(&info[j], STATUS_ADJ_INEQ))2241 /* ADJ EQ TOO MANY */2242 return isl_change_none;2243 2244 return check_single_adj_eq(i, j, info);2245}2246 2247/* Disjunct "j" lies on a hyperplane that is adjacent to disjunct "i".2248 * In particular, disjunct "i" has an inequality constraint that is adjacent2249 * to a (combination of) equality constraint(s) of disjunct "j",2250 * but disjunct "j" has no explicit equality constraint adjacent2251 * to an inequality constraint of disjunct "i".2252 *2253 * Disjunct "i" is already known not to have any equality constraints2254 * that are adjacent to an equality or inequality constraint.2255 * Check that, other than the inequality constraint mentioned above,2256 * all other constraints of disjunct "i" are valid for disjunct "j".2257 * If so, try and wrap in disjunct "j".2258 */2259static enum isl_change check_ineq_adj_eq(int i, int j,2260 struct isl_coalesce_info *info)2261{2262 int k;2263 2264 if (any_eq(&info[i], STATUS_CUT))2265 return isl_change_none;2266 if (any_ineq(&info[i], STATUS_CUT))2267 return isl_change_none;2268 if (any_ineq(&info[i], STATUS_ADJ_INEQ))2269 return isl_change_none;2270 if (count_ineq(&info[i], STATUS_ADJ_EQ) != 1)2271 return isl_change_none;2272 2273 k = find_ineq(&info[i], STATUS_ADJ_EQ);2274 2275 return can_wrap_in_facet(i, j, k, info, 0);2276}2277 2278/* The two basic maps lie on adjacent hyperplanes. In particular,2279 * basic map "i" has an equality that lies parallel to basic map "j".2280 * Check if we can wrap the facets around the parallel hyperplanes2281 * to include the other set.2282 *2283 * We perform basically the same operations as can_wrap_in_facet,2284 * except that we don't need to select a facet of one of the sets.2285 * _2286 * \\ \\2287 * \\ => \\2288 * \ \|2289 *2290 * If there is more than one equality of "i" adjacent to an equality of "j",2291 * then the result will satisfy one or more equalities that are a linear2292 * combination of these equalities. These will be encoded as pairs2293 * of inequalities in the wrapping constraints and need to be made2294 * explicit.2295 */2296static enum isl_change check_eq_adj_eq(int i, int j,2297 struct isl_coalesce_info *info)2298{2299 int k;2300 enum isl_change change = isl_change_none;2301 int detect_equalities = 0;2302 struct isl_wraps wraps;2303 isl_ctx *ctx;2304 isl_mat *mat;2305 struct isl_set *set_i = NULL;2306 struct isl_set *set_j = NULL;2307 struct isl_vec *bound = NULL;2308 isl_size total = isl_basic_map_dim(info[i].bmap, isl_dim_all);2309 2310 if (total < 0)2311 return isl_change_error;2312 if (count_eq(&info[i], STATUS_ADJ_EQ) != 1)2313 detect_equalities = 1;2314 2315 k = find_eq(&info[i], STATUS_ADJ_EQ);2316 2317 set_i = set_from_updated_bmap(info[i].bmap, info[i].tab);2318 set_j = set_from_updated_bmap(info[j].bmap, info[j].tab);2319 ctx = isl_basic_map_get_ctx(info[i].bmap);2320 mat = isl_mat_alloc(ctx, 2 * (info[i].bmap->n_eq + info[j].bmap->n_eq) +2321 info[i].bmap->n_ineq + info[j].bmap->n_ineq,2322 1 + total);2323 if (wraps_init(&wraps, mat, info, i, j) < 0)2324 goto error;2325 bound = isl_vec_alloc(ctx, 1 + total);2326 if (!set_i || !set_j || !bound)2327 goto error;2328 2329 if (k % 2 == 0)2330 isl_seq_neg(bound->el, info[i].bmap->eq[k / 2], 1 + total);2331 else2332 isl_seq_cpy(bound->el, info[i].bmap->eq[k / 2], 1 + total);2333 isl_int_add_ui(bound->el[0], bound->el[0], 1);2334 2335 isl_seq_cpy(wraps.mat->row[0], bound->el, 1 + total);2336 wraps.mat->n_row = 1;2337 2338 if (add_wraps(&wraps, &info[j], bound->el, set_i) < 0)2339 goto error;2340 if (wraps.failed)2341 goto unbounded;2342 2343 isl_int_sub_ui(bound->el[0], bound->el[0], 1);2344 isl_seq_neg(bound->el, bound->el, 1 + total);2345 2346 isl_seq_cpy(wraps.mat->row[wraps.mat->n_row], bound->el, 1 + total);2347 wraps.mat->n_row++;2348 2349 if (add_wraps(&wraps, &info[i], bound->el, set_j) < 0)2350 goto error;2351 if (wraps.failed)2352 goto unbounded;2353 2354 change = fuse(i, j, info, wraps.mat, detect_equalities, 0);2355 2356 if (0) {2357error: change = isl_change_error;2358 }2359unbounded:2360 2361 wraps_free(&wraps);2362 isl_set_free(set_i);2363 isl_set_free(set_j);2364 isl_vec_free(bound);2365 2366 return change;2367}2368 2369/* Initialize the "eq" and "ineq" fields of "info".2370 */2371static void init_status(struct isl_coalesce_info *info)2372{2373 info->eq = info->ineq = NULL;2374}2375 2376/* Set info->eq to the positions of the equalities of info->bmap2377 * with respect to the basic map represented by "tab".2378 * If info->eq has already been computed, then do not compute it again.2379 */2380static void set_eq_status_in(struct isl_coalesce_info *info,2381 struct isl_tab *tab)2382{2383 if (info->eq)2384 return;2385 info->eq = eq_status_in(info->bmap, tab);2386}2387 2388/* Set info->ineq to the positions of the inequalities of info->bmap2389 * with respect to the basic map represented by "tab".2390 * If info->ineq has already been computed, then do not compute it again.2391 */2392static void set_ineq_status_in(struct isl_coalesce_info *info,2393 struct isl_tab *tab)2394{2395 if (info->ineq)2396 return;2397 info->ineq = ineq_status_in(info->bmap, info->tab, tab);2398}2399 2400/* Free the memory allocated by the "eq" and "ineq" fields of "info".2401 * This function assumes that init_status has been called on "info" first,2402 * after which the "eq" and "ineq" fields may or may not have been2403 * assigned a newly allocated array.2404 */2405static void clear_status(struct isl_coalesce_info *info)2406{2407 free(info->eq);2408 free(info->ineq);2409}2410 2411/* Are all inequality constraints of the basic map represented by "info"2412 * valid for the other basic map, except for a single constraint2413 * that is adjacent to an inequality constraint of the other basic map?2414 */2415static int all_ineq_valid_or_single_adj_ineq(struct isl_coalesce_info *info)2416{2417 int i;2418 int k = -1;2419 2420 for (i = 0; i < info->bmap->n_ineq; ++i) {2421 if (info->ineq[i] == STATUS_REDUNDANT)2422 continue;2423 if (info->ineq[i] == STATUS_VALID)2424 continue;2425 if (info->ineq[i] != STATUS_ADJ_INEQ)2426 return 0;2427 if (k != -1)2428 return 0;2429 k = i;2430 }2431 2432 return k != -1;2433}2434 2435/* Basic map "i" has one or more equality constraints that separate it2436 * from basic map "j". Check if it happens to be an extension2437 * of basic map "j".2438 * In particular, check that all constraints of "j" are valid for "i",2439 * except for one inequality constraint that is adjacent2440 * to an inequality constraints of "i".2441 * If so, check for "i" being an extension of "j" by calling2442 * is_adj_ineq_extension.2443 *2444 * Clean up the memory allocated for keeping track of the status2445 * of the constraints before returning.2446 */2447static enum isl_change separating_equality(int i, int j,2448 struct isl_coalesce_info *info)2449{2450 enum isl_change change = isl_change_none;2451 2452 if (all(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_VALID) &&2453 all_ineq_valid_or_single_adj_ineq(&info[j]))2454 change = is_adj_ineq_extension(j, i, info);2455 2456 clear_status(&info[i]);2457 clear_status(&info[j]);2458 return change;2459}2460 2461/* Check if the union of the given pair of basic maps2462 * can be represented by a single basic map.2463 * If so, replace the pair by the single basic map and return2464 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.2465 * Otherwise, return isl_change_none.2466 * The two basic maps are assumed to live in the same local space.2467 * The "eq" and "ineq" fields of info[i] and info[j] are assumed2468 * to have been initialized by the caller, either to NULL or2469 * to valid information.2470 *2471 * We first check the effect of each constraint of one basic map2472 * on the other basic map.2473 * The constraint may be2474 * redundant the constraint is redundant in its own2475 * basic map and should be ignore and removed2476 * in the end2477 * valid all (integer) points of the other basic map2478 * satisfy the constraint2479 * separate no (integer) point of the other basic map2480 * satisfies the constraint2481 * cut some but not all points of the other basic map2482 * satisfy the constraint2483 * adj_eq the given constraint is adjacent (on the outside)2484 * to an equality of the other basic map2485 * adj_ineq the given constraint is adjacent (on the outside)2486 * to an inequality of the other basic map2487 *2488 * We consider seven cases in which we can replace the pair by a single2489 * basic map. We ignore all "redundant" constraints.2490 *2491 * 1. all constraints of one basic map are valid2492 * => the other basic map is a subset and can be removed2493 *2494 * 2. all constraints of both basic maps are either "valid" or "cut"2495 * and the facets corresponding to the "cut" constraints2496 * of one of the basic maps lies entirely inside the other basic map2497 * => the pair can be replaced by a basic map consisting2498 * of the valid constraints in both basic maps2499 *2500 * 3. there is a single pair of adjacent inequalities2501 * (all other constraints are "valid")2502 * => the pair can be replaced by a basic map consisting2503 * of the valid constraints in both basic maps2504 *2505 * 4. one basic map has a single adjacent inequality, while the other2506 * constraints are "valid". The other basic map has some2507 * "cut" constraints, but replacing the adjacent inequality by2508 * its opposite and adding the valid constraints of the other2509 * basic map results in a subset of the other basic map2510 * => the pair can be replaced by a basic map consisting2511 * of the valid constraints in both basic maps2512 *2513 * 5. there is a single adjacent pair of an inequality and an equality,2514 * the other constraints of the basic map containing the inequality are2515 * "valid". Moreover, if the inequality the basic map is relaxed2516 * and then turned into an equality, then resulting facet lies2517 * entirely inside the other basic map2518 * => the pair can be replaced by the basic map containing2519 * the inequality, with the inequality relaxed.2520 *2521 * 6. there is a single inequality adjacent to an equality,2522 * the other constraints of the basic map containing the inequality are2523 * "valid". Moreover, the facets corresponding to both2524 * the inequality and the equality can be wrapped around their2525 * ridges to include the other basic map2526 * => the pair can be replaced by a basic map consisting2527 * of the valid constraints in both basic maps together2528 * with all wrapping constraints2529 *2530 * 7. one of the basic maps extends beyond the other by at most one.2531 * Moreover, the facets corresponding to the cut constraints and2532 * the pieces of the other basic map at offset one from these cut2533 * constraints can be wrapped around their ridges to include2534 * the union of the two basic maps2535 * => the pair can be replaced by a basic map consisting2536 * of the valid constraints in both basic maps together2537 * with all wrapping constraints2538 *2539 * 8. the two basic maps live in adjacent hyperplanes. In principle2540 * such sets can always be combined through wrapping, but we impose2541 * that there is only one such pair, to avoid overeager coalescing.2542 *2543 * Throughout the computation, we maintain a collection of tableaus2544 * corresponding to the basic maps. When the basic maps are dropped2545 * or combined, the tableaus are modified accordingly.2546 */2547static enum isl_change coalesce_local_pair_reuse(int i, int j,2548 struct isl_coalesce_info *info)2549{2550 enum isl_change change = isl_change_none;2551 2552 set_ineq_status_in(&info[i], info[j].tab);2553 if (info[i].bmap->n_ineq && !info[i].ineq)2554 goto error;2555 if (any_ineq(&info[i], STATUS_ERROR))2556 goto error;2557 if (any_ineq(&info[i], STATUS_SEPARATE))2558 goto done;2559 2560 set_ineq_status_in(&info[j], info[i].tab);2561 if (info[j].bmap->n_ineq && !info[j].ineq)2562 goto error;2563 if (any_ineq(&info[j], STATUS_ERROR))2564 goto error;2565 if (any_ineq(&info[j], STATUS_SEPARATE))2566 goto done;2567 2568 set_eq_status_in(&info[i], info[j].tab);2569 if (info[i].bmap->n_eq && !info[i].eq)2570 goto error;2571 if (any_eq(&info[i], STATUS_ERROR))2572 goto error;2573 2574 set_eq_status_in(&info[j], info[i].tab);2575 if (info[j].bmap->n_eq && !info[j].eq)2576 goto error;2577 if (any_eq(&info[j], STATUS_ERROR))2578 goto error;2579 2580 if (any_eq(&info[i], STATUS_SEPARATE))2581 return separating_equality(i, j, info);2582 if (any_eq(&info[j], STATUS_SEPARATE))2583 return separating_equality(j, i, info);2584 2585 if (all(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_VALID) &&2586 all(info[i].ineq, info[i].bmap->n_ineq, STATUS_VALID)) {2587 drop(&info[j]);2588 change = isl_change_drop_second;2589 } else if (all(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_VALID) &&2590 all(info[j].ineq, info[j].bmap->n_ineq, STATUS_VALID)) {2591 drop(&info[i]);2592 change = isl_change_drop_first;2593 } else if (any_eq(&info[i], STATUS_ADJ_EQ)) {2594 change = check_eq_adj_eq(i, j, info);2595 } else if (any_eq(&info[j], STATUS_ADJ_EQ)) {2596 change = check_eq_adj_eq(j, i, info);2597 } else if (any_eq(&info[i], STATUS_ADJ_INEQ) ||2598 any_eq(&info[j], STATUS_ADJ_INEQ)) {2599 change = check_adj_eq(i, j, info);2600 } else if (any_ineq(&info[i], STATUS_ADJ_EQ)) {2601 change = check_ineq_adj_eq(i, j, info);2602 } else if (any_ineq(&info[j], STATUS_ADJ_EQ)) {2603 change = check_ineq_adj_eq(j, i, info);2604 } else if (any_ineq(&info[i], STATUS_ADJ_INEQ) ||2605 any_ineq(&info[j], STATUS_ADJ_INEQ)) {2606 change = check_adj_ineq(i, j, info);2607 } else {2608 if (!any_eq(&info[i], STATUS_CUT) &&2609 !any_eq(&info[j], STATUS_CUT))2610 change = check_facets(i, j, info);2611 if (change == isl_change_none)2612 change = check_wrap(i, j, info);2613 }2614 2615done:2616 clear_status(&info[i]);2617 clear_status(&info[j]);2618 return change;2619error:2620 clear_status(&info[i]);2621 clear_status(&info[j]);2622 return isl_change_error;2623}2624 2625/* Check if the union of the given pair of basic maps2626 * can be represented by a single basic map.2627 * If so, replace the pair by the single basic map and return2628 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.2629 * Otherwise, return isl_change_none.2630 * The two basic maps are assumed to live in the same local space.2631 */2632static enum isl_change coalesce_local_pair(int i, int j,2633 struct isl_coalesce_info *info)2634{2635 init_status(&info[i]);2636 init_status(&info[j]);2637 return coalesce_local_pair_reuse(i, j, info);2638}2639 2640/* Shift the integer division at position "div" of the basic map2641 * represented by "info" by "shift".2642 *2643 * That is, if the integer division has the form2644 *2645 * floor(f(x)/d)2646 *2647 * then replace it by2648 *2649 * floor((f(x) + shift * d)/d) - shift2650 */2651static isl_stat shift_div(struct isl_coalesce_info *info, int div,2652 isl_int shift)2653{2654 isl_size total, n_div;2655 2656 info->bmap = isl_basic_map_shift_div(info->bmap, div, 0, shift);2657 if (!info->bmap)2658 return isl_stat_error;2659 2660 total = isl_basic_map_dim(info->bmap, isl_dim_all);2661 n_div = isl_basic_map_dim(info->bmap, isl_dim_div);2662 if (total < 0 || n_div < 0)2663 return isl_stat_error;2664 total -= n_div;2665 if (isl_tab_shift_var(info->tab, total + div, shift) < 0)2666 return isl_stat_error;2667 2668 return isl_stat_ok;2669}2670 2671/* If the integer division at position "div" is defined by an equality,2672 * i.e., a stride constraint, then change the integer division expression2673 * to have a constant term equal to zero.2674 *2675 * Let the equality constraint be2676 *2677 * c + f + m a = 02678 *2679 * The integer division expression is then typically of the form2680 *2681 * a = floor((-f - c')/m)2682 *2683 * The integer division is first shifted by t = floor(c/m),2684 * turning the equality constraint into2685 *2686 * c - m floor(c/m) + f + m a' = 02687 *2688 * i.e.,2689 *2690 * (c mod m) + f + m a' = 02691 *2692 * That is,2693 *2694 * a' = (-f - (c mod m))/m = floor((-f)/m)2695 *2696 * because a' is an integer and 0 <= (c mod m) < m.2697 * The constant term of a' can therefore be zeroed out,2698 * but only if the integer division expression is of the expected form.2699 */2700static isl_stat normalize_stride_div(struct isl_coalesce_info *info, int div)2701{2702 isl_bool defined, valid;2703 isl_stat r;2704 isl_constraint *c;2705 isl_int shift, stride;2706 2707 defined = isl_basic_map_has_defining_equality(info->bmap, isl_dim_div,2708 div, &c);2709 if (defined < 0)2710 return isl_stat_error;2711 if (!defined)2712 return isl_stat_ok;2713 if (!c)2714 return isl_stat_error;2715 valid = isl_constraint_is_div_equality(c, div);2716 isl_int_init(shift);2717 isl_int_init(stride);2718 isl_constraint_get_constant(c, &shift);2719 isl_constraint_get_coefficient(c, isl_dim_div, div, &stride);2720 isl_int_fdiv_q(shift, shift, stride);2721 r = shift_div(info, div, shift);2722 isl_int_clear(stride);2723 isl_int_clear(shift);2724 isl_constraint_free(c);2725 if (r < 0 || valid < 0)2726 return isl_stat_error;2727 if (!valid)2728 return isl_stat_ok;2729 info->bmap = isl_basic_map_set_div_expr_constant_num_si_inplace(2730 info->bmap, div, 0);2731 if (!info->bmap)2732 return isl_stat_error;2733 return isl_stat_ok;2734}2735 2736/* The basic maps represented by "info1" and "info2" are known2737 * to have the same number of integer divisions.2738 * Check if pairs of integer divisions are equal to each other2739 * despite the fact that they differ by a rational constant.2740 *2741 * In particular, look for any pair of integer divisions that2742 * only differ in their constant terms.2743 * If either of these integer divisions is defined2744 * by stride constraints, then modify it to have a zero constant term.2745 * If both are defined by stride constraints then in the end they will have2746 * the same (zero) constant term.2747 */2748static isl_stat harmonize_stride_divs(struct isl_coalesce_info *info1,2749 struct isl_coalesce_info *info2)2750{2751 int i;2752 isl_size n;2753 2754 n = isl_basic_map_dim(info1->bmap, isl_dim_div);2755 if (n < 0)2756 return isl_stat_error;2757 for (i = 0; i < n; ++i) {2758 isl_bool known, harmonize;2759 2760 known = isl_basic_map_div_is_known(info1->bmap, i);2761 if (known >= 0 && known)2762 known = isl_basic_map_div_is_known(info2->bmap, i);2763 if (known < 0)2764 return isl_stat_error;2765 if (!known)2766 continue;2767 harmonize = isl_basic_map_equal_div_expr_except_constant(2768 info1->bmap, i, info2->bmap, i);2769 if (harmonize < 0)2770 return isl_stat_error;2771 if (!harmonize)2772 continue;2773 if (normalize_stride_div(info1, i) < 0)2774 return isl_stat_error;2775 if (normalize_stride_div(info2, i) < 0)2776 return isl_stat_error;2777 }2778 2779 return isl_stat_ok;2780}2781 2782/* If "shift" is an integer constant, then shift the integer division2783 * at position "div" of the basic map represented by "info" by "shift".2784 * If "shift" is not an integer constant, then do nothing.2785 * If "shift" is equal to zero, then no shift needs to be performed either.2786 *2787 * That is, if the integer division has the form2788 *2789 * floor(f(x)/d)2790 *2791 * then replace it by2792 *2793 * floor((f(x) + shift * d)/d) - shift2794 */2795static isl_stat shift_if_cst_int(struct isl_coalesce_info *info, int div,2796 __isl_keep isl_aff *shift)2797{2798 isl_bool cst;2799 isl_stat r;2800 isl_int d;2801 isl_val *c;2802 2803 cst = isl_aff_is_cst(shift);2804 if (cst < 0 || !cst)2805 return cst < 0 ? isl_stat_error : isl_stat_ok;2806 2807 c = isl_aff_get_constant_val(shift);2808 cst = isl_val_is_int(c);2809 if (cst >= 0 && cst)2810 cst = isl_bool_not(isl_val_is_zero(c));2811 if (cst < 0 || !cst) {2812 isl_val_free(c);2813 return cst < 0 ? isl_stat_error : isl_stat_ok;2814 }2815 2816 isl_int_init(d);2817 r = isl_val_get_num_isl_int(c, &d);2818 if (r >= 0)2819 r = shift_div(info, div, d);2820 isl_int_clear(d);2821 2822 isl_val_free(c);2823 2824 return r;2825}2826 2827/* Check if some of the divs in the basic map represented by "info1"2828 * are shifts of the corresponding divs in the basic map represented2829 * by "info2", taking into account the equality constraints "eq1" of "info1"2830 * and "eq2" of "info2". If so, align them with those of "info2".2831 * "info1" and "info2" are assumed to have the same number2832 * of integer divisions.2833 *2834 * An integer division is considered to be a shift of another integer2835 * division if, after simplification with respect to the equality2836 * constraints of the other basic map, one is equal to the other2837 * plus a constant.2838 *2839 * In particular, for each pair of integer divisions, if both are known,2840 * have the same denominator and are not already equal to each other,2841 * simplify each with respect to the equality constraints2842 * of the other basic map. If the difference is an integer constant,2843 * then move this difference outside.2844 * That is, if, after simplification, one integer division is of the form2845 *2846 * floor((f(x) + c_1)/d)2847 *2848 * while the other is of the form2849 *2850 * floor((f(x) + c_2)/d)2851 *2852 * and n = (c_2 - c_1)/d is an integer, then replace the first2853 * integer division by2854 *2855 * floor((f_1(x) + c_1 + n * d)/d) - n,2856 *2857 * where floor((f_1(x) + c_1 + n * d)/d) = floor((f2(x) + c_2)/d)2858 * after simplification with respect to the equality constraints.2859 */2860static isl_stat harmonize_divs_with_hulls(struct isl_coalesce_info *info1,2861 struct isl_coalesce_info *info2, __isl_keep isl_basic_set *eq1,2862 __isl_keep isl_basic_set *eq2)2863{2864 int i;2865 isl_size total;2866 isl_local_space *ls1, *ls2;2867 2868 total = isl_basic_map_dim(info1->bmap, isl_dim_all);2869 if (total < 0)2870 return isl_stat_error;2871 ls1 = isl_local_space_wrap(isl_basic_map_get_local_space(info1->bmap));2872 ls2 = isl_local_space_wrap(isl_basic_map_get_local_space(info2->bmap));2873 for (i = 0; i < info1->bmap->n_div; ++i) {2874 isl_stat r;2875 isl_aff *div1, *div2;2876 2877 if (!isl_local_space_div_is_known(ls1, i) ||2878 !isl_local_space_div_is_known(ls2, i))2879 continue;2880 if (isl_int_ne(info1->bmap->div[i][0], info2->bmap->div[i][0]))2881 continue;2882 if (isl_seq_eq(info1->bmap->div[i] + 1,2883 info2->bmap->div[i] + 1, 1 + total))2884 continue;2885 div1 = isl_local_space_get_div(ls1, i);2886 div2 = isl_local_space_get_div(ls2, i);2887 div1 = isl_aff_substitute_equalities(div1,2888 isl_basic_set_copy(eq2));2889 div2 = isl_aff_substitute_equalities(div2,2890 isl_basic_set_copy(eq1));2891 div2 = isl_aff_sub(div2, div1);2892 r = shift_if_cst_int(info1, i, div2);2893 isl_aff_free(div2);2894 if (r < 0)2895 break;2896 }2897 isl_local_space_free(ls1);2898 isl_local_space_free(ls2);2899 2900 if (i < info1->bmap->n_div)2901 return isl_stat_error;2902 return isl_stat_ok;2903}2904 2905/* Check if some of the divs in the basic map represented by "info1"2906 * are shifts of the corresponding divs in the basic map represented2907 * by "info2". If so, align them with those of "info2".2908 * Only do this if "info1" and "info2" have the same number2909 * of integer divisions.2910 *2911 * An integer division is considered to be a shift of another integer2912 * division if, after simplification with respect to the equality2913 * constraints of the other basic map, one is equal to the other2914 * plus a constant.2915 *2916 * First check if pairs of integer divisions are equal to each other2917 * despite the fact that they differ by a rational constant.2918 * If so, try and arrange for them to have the same constant term.2919 *2920 * Then, extract the equality constraints and continue with2921 * harmonize_divs_with_hulls.2922 *2923 * If the equality constraints of both basic maps are the same,2924 * then there is no need to perform any shifting since2925 * the coefficients of the integer divisions should have been2926 * reduced in the same way.2927 */2928static isl_stat harmonize_divs(struct isl_coalesce_info *info1,2929 struct isl_coalesce_info *info2)2930{2931 isl_bool equal;2932 isl_basic_map *bmap1, *bmap2;2933 isl_basic_set *eq1, *eq2;2934 isl_stat r;2935 2936 if (!info1->bmap || !info2->bmap)2937 return isl_stat_error;2938 2939 if (info1->bmap->n_div != info2->bmap->n_div)2940 return isl_stat_ok;2941 if (info1->bmap->n_div == 0)2942 return isl_stat_ok;2943 2944 if (harmonize_stride_divs(info1, info2) < 0)2945 return isl_stat_error;2946 2947 bmap1 = isl_basic_map_copy(info1->bmap);2948 bmap2 = isl_basic_map_copy(info2->bmap);2949 eq1 = isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap1));2950 eq2 = isl_basic_map_wrap(isl_basic_map_plain_affine_hull(bmap2));2951 equal = isl_basic_set_plain_is_equal(eq1, eq2);2952 if (equal < 0)2953 r = isl_stat_error;2954 else if (equal)2955 r = isl_stat_ok;2956 else2957 r = harmonize_divs_with_hulls(info1, info2, eq1, eq2);2958 isl_basic_set_free(eq1);2959 isl_basic_set_free(eq2);2960 2961 return r;2962}2963 2964/* Do the two basic maps live in the same local space, i.e.,2965 * do they have the same (known) divs?2966 * If either basic map has any unknown divs, then we can only assume2967 * that they do not live in the same local space.2968 */2969static isl_bool same_divs(__isl_keep isl_basic_map *bmap1,2970 __isl_keep isl_basic_map *bmap2)2971{2972 int i;2973 isl_bool known;2974 isl_size total;2975 2976 if (!bmap1 || !bmap2)2977 return isl_bool_error;2978 if (bmap1->n_div != bmap2->n_div)2979 return isl_bool_false;2980 2981 if (bmap1->n_div == 0)2982 return isl_bool_true;2983 2984 known = isl_basic_map_divs_known(bmap1);2985 if (known < 0 || !known)2986 return known;2987 known = isl_basic_map_divs_known(bmap2);2988 if (known < 0 || !known)2989 return known;2990 2991 total = isl_basic_map_dim(bmap1, isl_dim_all);2992 if (total < 0)2993 return isl_bool_error;2994 for (i = 0; i < bmap1->n_div; ++i)2995 if (!isl_seq_eq(bmap1->div[i], bmap2->div[i], 2 + total))2996 return isl_bool_false;2997 2998 return isl_bool_true;2999}3000 3001/* Assuming that "tab" contains the equality constraints and3002 * the initial inequality constraints of "bmap", copy the remaining3003 * inequality constraints of "bmap" to "Tab".3004 */3005static isl_stat copy_ineq(struct isl_tab *tab, __isl_keep isl_basic_map *bmap)3006{3007 int i, n_ineq;3008 3009 if (!bmap)3010 return isl_stat_error;3011 3012 n_ineq = tab->n_con - tab->n_eq;3013 for (i = n_ineq; i < bmap->n_ineq; ++i)3014 if (isl_tab_add_ineq(tab, bmap->ineq[i]) < 0)3015 return isl_stat_error;3016 3017 return isl_stat_ok;3018}3019 3020/* Description of an integer division that is added3021 * during an expansion.3022 * "pos" is the position of the corresponding variable.3023 * "cst" indicates whether this integer division has a fixed value.3024 * "val" contains the fixed value, if the value is fixed.3025 */3026struct isl_expanded {3027 int pos;3028 isl_bool cst;3029 isl_int val;3030};3031 3032/* For each of the "n" integer division variables "expanded",3033 * if the variable has a fixed value, then add two inequality3034 * constraints expressing the fixed value.3035 * Otherwise, add the corresponding div constraints.3036 * The caller is responsible for removing the div constraints3037 * that it added for all these "n" integer divisions.3038 *3039 * The div constraints and the pair of inequality constraints3040 * forcing the fixed value cannot both be added for a given variable3041 * as the combination may render some of the original constraints redundant.3042 * These would then be ignored during the coalescing detection,3043 * while they could remain in the fused result.3044 *3045 * The two added inequality constraints are3046 *3047 * -a + v >= 03048 * a - v >= 03049 *3050 * with "a" the variable and "v" its fixed value.3051 * The facet corresponding to one of these two constraints is selected3052 * in the tableau to ensure that the pair of inequality constraints3053 * is treated as an equality constraint.3054 *3055 * The information in info->ineq is thrown away because it was3056 * computed in terms of div constraints, while some of those3057 * have now been replaced by these pairs of inequality constraints.3058 */3059static isl_stat fix_constant_divs(struct isl_coalesce_info *info,3060 int n, struct isl_expanded *expanded)3061{3062 unsigned o_div;3063 int i;3064 isl_vec *ineq;3065 3066 o_div = isl_basic_map_offset(info->bmap, isl_dim_div) - 1;3067 ineq = isl_vec_alloc(isl_tab_get_ctx(info->tab), 1 + info->tab->n_var);3068 if (!ineq)3069 return isl_stat_error;3070 isl_seq_clr(ineq->el + 1, info->tab->n_var);3071 3072 for (i = 0; i < n; ++i) {3073 if (!expanded[i].cst) {3074 info->bmap = isl_basic_map_extend_constraints(3075 info->bmap, 0, 2);3076 info->bmap = isl_basic_map_add_div_constraints(3077 info->bmap, expanded[i].pos - o_div);3078 } else {3079 isl_int_set_si(ineq->el[1 + expanded[i].pos], -1);3080 isl_int_set(ineq->el[0], expanded[i].val);3081 info->bmap = isl_basic_map_add_ineq(info->bmap,3082 ineq->el);3083 isl_int_set_si(ineq->el[1 + expanded[i].pos], 1);3084 isl_int_neg(ineq->el[0], expanded[i].val);3085 info->bmap = isl_basic_map_add_ineq(info->bmap,3086 ineq->el);3087 isl_int_set_si(ineq->el[1 + expanded[i].pos], 0);3088 }3089 if (copy_ineq(info->tab, info->bmap) < 0)3090 break;3091 if (expanded[i].cst &&3092 isl_tab_select_facet(info->tab, info->tab->n_con - 1) < 0)3093 break;3094 }3095 3096 isl_vec_free(ineq);3097 3098 clear_status(info);3099 init_status(info);3100 3101 return i < n ? isl_stat_error : isl_stat_ok;3102}3103 3104/* Insert the "n" integer division variables "expanded"3105 * into info->tab and info->bmap and3106 * update info->ineq with respect to the redundant constraints3107 * in the resulting tableau.3108 * "bmap" contains the result of this insertion in info->bmap,3109 * while info->bmap is the original version3110 * of "bmap", i.e., the one that corresponds to the current3111 * state of info->tab. The number of constraints in info->bmap3112 * is assumed to be the same as the number of constraints3113 * in info->tab. This is required to be able to detect3114 * the extra constraints in "bmap".3115 *3116 * In particular, introduce extra variables corresponding3117 * to the extra integer divisions and add the div constraints3118 * that were added to "bmap" after info->tab was created3119 * from info->bmap.3120 * Furthermore, check if these extra integer divisions happen3121 * to attain a fixed integer value in info->tab.3122 * If so, replace the corresponding div constraints by pairs3123 * of inequality constraints that fix these3124 * integer divisions to their single integer values.3125 * Replace info->bmap by "bmap" to match the changes to info->tab.3126 * info->ineq was computed without a tableau and therefore3127 * does not take into account the redundant constraints3128 * in the tableau. Mark them here.3129 * There is no need to check the newly added div constraints3130 * since they cannot be redundant.3131 * The redundancy check is not performed when constants have been discovered3132 * since info->ineq is completely thrown away in this case.3133 */3134static isl_stat tab_insert_divs(struct isl_coalesce_info *info,3135 int n, struct isl_expanded *expanded, __isl_take isl_basic_map *bmap)3136{3137 int i, n_ineq;3138 unsigned n_eq;3139 struct isl_tab_undo *snap;3140 int any;3141 3142 if (!bmap)3143 return isl_stat_error;3144 if (info->bmap->n_eq + info->bmap->n_ineq != info->tab->n_con)3145 isl_die(isl_basic_map_get_ctx(bmap), isl_error_internal,3146 "original tableau does not correspond "3147 "to original basic map", goto error);3148 3149 if (isl_tab_extend_vars(info->tab, n) < 0)3150 goto error;3151 if (isl_tab_extend_cons(info->tab, 2 * n) < 0)3152 goto error;3153 3154 for (i = 0; i < n; ++i) {3155 if (isl_tab_insert_var(info->tab, expanded[i].pos) < 0)3156 goto error;3157 }3158 3159 snap = isl_tab_snap(info->tab);3160 3161 n_ineq = info->tab->n_con - info->tab->n_eq;3162 if (copy_ineq(info->tab, bmap) < 0)3163 goto error;3164 3165 isl_basic_map_free(info->bmap);3166 info->bmap = bmap;3167 3168 any = 0;3169 for (i = 0; i < n; ++i) {3170 expanded[i].cst = isl_tab_is_constant(info->tab,3171 expanded[i].pos, &expanded[i].val);3172 if (expanded[i].cst < 0)3173 return isl_stat_error;3174 if (expanded[i].cst)3175 any = 1;3176 }3177 3178 if (any) {3179 if (isl_tab_rollback(info->tab, snap) < 0)3180 return isl_stat_error;3181 info->bmap = isl_basic_map_cow(info->bmap);3182 info->bmap = isl_basic_map_free_inequality(info->bmap, 2 * n);3183 if (!info->bmap)3184 return isl_stat_error;3185 3186 return fix_constant_divs(info, n, expanded);3187 }3188 3189 n_eq = info->bmap->n_eq;3190 for (i = 0; i < n_ineq; ++i) {3191 if (isl_tab_is_redundant(info->tab, n_eq + i))3192 info->ineq[i] = STATUS_REDUNDANT;3193 }3194 3195 return isl_stat_ok;3196error:3197 isl_basic_map_free(bmap);3198 return isl_stat_error;3199}3200 3201/* Expand info->tab and info->bmap in the same way "bmap" was expanded3202 * in isl_basic_map_expand_divs using the expansion "exp" and3203 * update info->ineq with respect to the redundant constraints3204 * in the resulting tableau. info->bmap is the original version3205 * of "bmap", i.e., the one that corresponds to the current3206 * state of info->tab. The number of constraints in info->bmap3207 * is assumed to be the same as the number of constraints3208 * in info->tab. This is required to be able to detect3209 * the extra constraints in "bmap".3210 *3211 * Extract the positions where extra local variables are introduced3212 * from "exp" and call tab_insert_divs.3213 */3214static isl_stat expand_tab(struct isl_coalesce_info *info, int *exp,3215 __isl_take isl_basic_map *bmap)3216{3217 isl_ctx *ctx;3218 struct isl_expanded *expanded;3219 int i, j, k, n;3220 int extra_var;3221 isl_size total, n_div;3222 unsigned pos;3223 isl_stat r;3224 3225 total = isl_basic_map_dim(bmap, isl_dim_all);3226 n_div = isl_basic_map_dim(bmap, isl_dim_div);3227 if (total < 0 || n_div < 0)3228 return isl_stat_error;3229 pos = total - n_div;3230 extra_var = total - info->tab->n_var;3231 n = n_div - extra_var;3232 3233 ctx = isl_basic_map_get_ctx(bmap);3234 expanded = isl_calloc_array(ctx, struct isl_expanded, extra_var);3235 if (extra_var && !expanded)3236 goto error;3237 3238 i = 0;3239 k = 0;3240 for (j = 0; j < n_div; ++j) {3241 if (i < n && exp[i] == j) {3242 ++i;3243 continue;3244 }3245 expanded[k++].pos = pos + j;3246 }3247 3248 for (k = 0; k < extra_var; ++k)3249 isl_int_init(expanded[k].val);3250 3251 r = tab_insert_divs(info, extra_var, expanded, bmap);3252 3253 for (k = 0; k < extra_var; ++k)3254 isl_int_clear(expanded[k].val);3255 free(expanded);3256 3257 return r;3258error:3259 isl_basic_map_free(bmap);3260 return isl_stat_error;3261}3262 3263/* Check if the union of the basic maps represented by info[i] and info[j]3264 * can be represented by a single basic map,3265 * after expanding the divs of info[i] to match those of info[j].3266 * If so, replace the pair by the single basic map and return3267 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.3268 * Otherwise, return isl_change_none.3269 *3270 * The caller has already checked for info[j] being a subset of info[i].3271 * If some of the divs of info[j] are unknown, then the expanded info[i]3272 * will not have the corresponding div constraints. The other patterns3273 * therefore cannot apply. Skip the computation in this case.3274 *3275 * The expansion is performed using the divs "div" and expansion "exp"3276 * computed by the caller.3277 * info[i].bmap has already been expanded and the result is passed in3278 * as "bmap".3279 * The "eq" and "ineq" fields of info[i] reflect the status of3280 * the constraints of the expanded "bmap" with respect to info[j].tab.3281 * However, inequality constraints that are redundant in info[i].tab3282 * have not yet been marked as such because no tableau was available.3283 *3284 * Replace info[i].bmap by "bmap" and expand info[i].tab as well,3285 * updating info[i].ineq with respect to the redundant constraints.3286 * Then try and coalesce the expanded info[i] with info[j],3287 * reusing the information in info[i].eq and info[i].ineq.3288 * If this does not result in any coalescing or if it results in info[j]3289 * getting dropped (which should not happen in practice, since the case3290 * of info[j] being a subset of info[i] has already been checked by3291 * the caller), then revert info[i] to its original state.3292 */3293static enum isl_change coalesce_expand_tab_divs(__isl_take isl_basic_map *bmap,3294 int i, int j, struct isl_coalesce_info *info, __isl_keep isl_mat *div,3295 int *exp)3296{3297 isl_bool known;3298 isl_basic_map *bmap_i;3299 struct isl_tab_undo *snap;3300 enum isl_change change = isl_change_none;3301 3302 known = isl_basic_map_divs_known(info[j].bmap);3303 if (known < 0 || !known) {3304 clear_status(&info[i]);3305 isl_basic_map_free(bmap);3306 return known < 0 ? isl_change_error : isl_change_none;3307 }3308 3309 bmap_i = isl_basic_map_copy(info[i].bmap);3310 snap = isl_tab_snap(info[i].tab);3311 if (expand_tab(&info[i], exp, bmap) < 0)3312 change = isl_change_error;3313 3314 init_status(&info[j]);3315 if (change == isl_change_none)3316 change = coalesce_local_pair_reuse(i, j, info);3317 else3318 clear_status(&info[i]);3319 if (change != isl_change_none && change != isl_change_drop_second) {3320 isl_basic_map_free(bmap_i);3321 } else {3322 isl_basic_map_free(info[i].bmap);3323 info[i].bmap = bmap_i;3324 3325 if (isl_tab_rollback(info[i].tab, snap) < 0)3326 change = isl_change_error;3327 }3328 3329 return change;3330}3331 3332/* Check if the union of "bmap" and the basic map represented by info[j]3333 * can be represented by a single basic map,3334 * after expanding the divs of "bmap" to match those of info[j].3335 * If so, replace the pair by the single basic map and return3336 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.3337 * Otherwise, return isl_change_none.3338 *3339 * In particular, check if the expanded "bmap" contains the basic map3340 * represented by the tableau info[j].tab.3341 * The expansion is performed using the divs "div" and expansion "exp"3342 * computed by the caller.3343 * Then we check if all constraints of the expanded "bmap" are valid for3344 * info[j].tab.3345 *3346 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.3347 * In this case, the positions of the constraints of info[i].bmap3348 * with respect to the basic map represented by info[j] are stored3349 * in info[i].3350 *3351 * If the expanded "bmap" does not contain the basic map3352 * represented by the tableau info[j].tab and if "i" is not -1,3353 * i.e., if the original "bmap" is info[i].bmap, then expand info[i].tab3354 * as well and check if that results in coalescing.3355 */3356static enum isl_change coalesce_with_expanded_divs(3357 __isl_keep isl_basic_map *bmap, int i, int j,3358 struct isl_coalesce_info *info, __isl_keep isl_mat *div, int *exp)3359{3360 enum isl_change change = isl_change_none;3361 struct isl_coalesce_info info_local, *info_i;3362 3363 info_i = i >= 0 ? &info[i] : &info_local;3364 init_status(info_i);3365 bmap = isl_basic_map_copy(bmap);3366 bmap = isl_basic_map_expand_divs(bmap, isl_mat_copy(div), exp);3367 bmap = isl_basic_map_mark_final(bmap);3368 3369 if (!bmap)3370 goto error;3371 3372 info_local.bmap = bmap;3373 info_i->eq = eq_status_in(bmap, info[j].tab);3374 if (bmap->n_eq && !info_i->eq)3375 goto error;3376 if (any_eq(info_i, STATUS_ERROR))3377 goto error;3378 if (any_eq(info_i, STATUS_SEPARATE))3379 goto done;3380 3381 info_i->ineq = ineq_status_in(bmap, NULL, info[j].tab);3382 if (bmap->n_ineq && !info_i->ineq)3383 goto error;3384 if (any_ineq(info_i, STATUS_ERROR))3385 goto error;3386 if (any_ineq(info_i, STATUS_SEPARATE))3387 goto done;3388 3389 if (all(info_i->eq, 2 * bmap->n_eq, STATUS_VALID) &&3390 all(info_i->ineq, bmap->n_ineq, STATUS_VALID)) {3391 drop(&info[j]);3392 change = isl_change_drop_second;3393 }3394 3395 if (change == isl_change_none && i != -1)3396 return coalesce_expand_tab_divs(bmap, i, j, info, div, exp);3397 3398done:3399 isl_basic_map_free(bmap);3400 clear_status(info_i);3401 return change;3402error:3403 isl_basic_map_free(bmap);3404 clear_status(info_i);3405 return isl_change_error;3406}3407 3408/* Check if the union of "bmap_i" and the basic map represented by info[j]3409 * can be represented by a single basic map,3410 * after aligning the divs of "bmap_i" to match those of info[j].3411 * If so, replace the pair by the single basic map and return3412 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.3413 * Otherwise, return isl_change_none.3414 *3415 * In particular, check if "bmap_i" contains the basic map represented by3416 * info[j] after aligning the divs of "bmap_i" to those of info[j].3417 * Note that this can only succeed if the number of divs of "bmap_i"3418 * is smaller than (or equal to) the number of divs of info[j].3419 *3420 * We first check if the divs of "bmap_i" are all known and form a subset3421 * of those of info[j].bmap. If so, we pass control over to3422 * coalesce_with_expanded_divs.3423 *3424 * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.3425 */3426static enum isl_change coalesce_after_aligning_divs(3427 __isl_keep isl_basic_map *bmap_i, int i, int j,3428 struct isl_coalesce_info *info)3429{3430 isl_bool known;3431 isl_mat *div_i, *div_j, *div;3432 int *exp1 = NULL;3433 int *exp2 = NULL;3434 isl_ctx *ctx;3435 enum isl_change change;3436 3437 known = isl_basic_map_divs_known(bmap_i);3438 if (known < 0)3439 return isl_change_error;3440 if (!known)3441 return isl_change_none;3442 3443 ctx = isl_basic_map_get_ctx(bmap_i);3444 3445 div_i = isl_basic_map_get_divs(bmap_i);3446 div_j = isl_basic_map_get_divs(info[j].bmap);3447 3448 if (!div_i || !div_j)3449 goto error;3450 3451 exp1 = isl_alloc_array(ctx, int, div_i->n_row);3452 exp2 = isl_alloc_array(ctx, int, div_j->n_row);3453 if ((div_i->n_row && !exp1) || (div_j->n_row && !exp2))3454 goto error;3455 3456 div = isl_merge_divs(div_i, div_j, exp1, exp2);3457 if (!div)3458 goto error;3459 3460 if (div->n_row == div_j->n_row)3461 change = coalesce_with_expanded_divs(bmap_i,3462 i, j, info, div, exp1);3463 else3464 change = isl_change_none;3465 3466 isl_mat_free(div);3467 3468 isl_mat_free(div_i);3469 isl_mat_free(div_j);3470 3471 free(exp2);3472 free(exp1);3473 3474 return change;3475error:3476 isl_mat_free(div_i);3477 isl_mat_free(div_j);3478 free(exp1);3479 free(exp2);3480 return isl_change_error;3481}3482 3483/* Check if basic map "j" is a subset of basic map "i" after3484 * exploiting the extra equalities of "j" to simplify the divs of "i".3485 * If so, remove basic map "j" and return isl_change_drop_second.3486 *3487 * If "j" does not have any equalities or if they are the same3488 * as those of "i", then we cannot exploit them to simplify the divs.3489 * Similarly, if there are no divs in "i", then they cannot be simplified.3490 * If, on the other hand, the affine hulls of "i" and "j" do not intersect,3491 * then "j" cannot be a subset of "i".3492 *3493 * Otherwise, we intersect "i" with the affine hull of "j" and then3494 * check if "j" is a subset of the result after aligning the divs.3495 * If so, then "j" is definitely a subset of "i" and can be removed.3496 * Note that if after intersection with the affine hull of "j".3497 * "i" still has more divs than "j", then there is no way we can3498 * align the divs of "i" to those of "j".3499 */3500static enum isl_change coalesce_subset_with_equalities(int i, int j,3501 struct isl_coalesce_info *info)3502{3503 isl_basic_map *hull_i, *hull_j, *bmap_i;3504 int equal, empty;3505 enum isl_change change;3506 3507 if (info[j].bmap->n_eq == 0)3508 return isl_change_none;3509 if (info[i].bmap->n_div == 0)3510 return isl_change_none;3511 3512 hull_i = isl_basic_map_copy(info[i].bmap);3513 hull_i = isl_basic_map_plain_affine_hull(hull_i);3514 hull_j = isl_basic_map_copy(info[j].bmap);3515 hull_j = isl_basic_map_plain_affine_hull(hull_j);3516 3517 hull_j = isl_basic_map_intersect(hull_j, isl_basic_map_copy(hull_i));3518 equal = isl_basic_map_plain_is_equal(hull_i, hull_j);3519 empty = isl_basic_map_plain_is_empty(hull_j);3520 isl_basic_map_free(hull_i);3521 3522 if (equal < 0 || equal || empty < 0 || empty) {3523 isl_basic_map_free(hull_j);3524 if (equal < 0 || empty < 0)3525 return isl_change_error;3526 return isl_change_none;3527 }3528 3529 bmap_i = isl_basic_map_copy(info[i].bmap);3530 bmap_i = isl_basic_map_intersect(bmap_i, hull_j);3531 if (!bmap_i)3532 return isl_change_error;3533 3534 if (bmap_i->n_div > info[j].bmap->n_div) {3535 isl_basic_map_free(bmap_i);3536 return isl_change_none;3537 }3538 3539 change = coalesce_after_aligning_divs(bmap_i, -1, j, info);3540 3541 isl_basic_map_free(bmap_i);3542 3543 return change;3544}3545 3546/* Check if the union of the basic maps represented by info[i] and info[j]3547 * can be represented by a single basic map, by aligning or equating3548 * their integer divisions.3549 * If so, replace the pair by the single basic map and return3550 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.3551 * Otherwise, return isl_change_none.3552 *3553 * Note that we only perform any test if the number of divs is different3554 * in the two basic maps. In case the number of divs is the same,3555 * we have already established that the divs are different3556 * in the two basic maps.3557 * In particular, if the number of divs of basic map i is smaller than3558 * the number of divs of basic map j, then we check if j is a subset of i3559 * and vice versa.3560 */3561static enum isl_change coalesce_divs(int i, int j,3562 struct isl_coalesce_info *info)3563{3564 enum isl_change change = isl_change_none;3565 3566 if (info[i].bmap->n_div < info[j].bmap->n_div)3567 change = coalesce_after_aligning_divs(info[i].bmap, i, j, info);3568 if (change != isl_change_none)3569 return change;3570 3571 if (info[j].bmap->n_div < info[i].bmap->n_div)3572 change = coalesce_after_aligning_divs(info[j].bmap, j, i, info);3573 if (change != isl_change_none)3574 return invert_change(change);3575 3576 change = coalesce_subset_with_equalities(i, j, info);3577 if (change != isl_change_none)3578 return change;3579 3580 change = coalesce_subset_with_equalities(j, i, info);3581 if (change != isl_change_none)3582 return invert_change(change);3583 3584 return isl_change_none;3585}3586 3587/* Does "bmap" involve any divs that themselves refer to divs?3588 */3589static isl_bool has_nested_div(__isl_keep isl_basic_map *bmap)3590{3591 int i;3592 isl_size total;3593 isl_size n_div;3594 3595 total = isl_basic_map_dim(bmap, isl_dim_all);3596 n_div = isl_basic_map_dim(bmap, isl_dim_div);3597 if (total < 0 || n_div < 0)3598 return isl_bool_error;3599 total -= n_div;3600 3601 for (i = 0; i < n_div; ++i)3602 if (isl_seq_first_non_zero(bmap->div[i] + 2 + total,3603 n_div) != -1)3604 return isl_bool_true;3605 3606 return isl_bool_false;3607}3608 3609/* Return a list of affine expressions, one for each integer division3610 * in "bmap_i". For each integer division that also appears in "bmap_j",3611 * the affine expression is set to NaN. The number of NaNs in the list3612 * is equal to the number of integer divisions in "bmap_j".3613 * For the other integer divisions of "bmap_i", the corresponding3614 * element in the list is a purely affine expression equal to the integer3615 * division in "hull".3616 * If no such list can be constructed, then the number of elements3617 * in the returned list is smaller than the number of integer divisions3618 * in "bmap_i".3619 * The integer division of "bmap_i" and "bmap_j" are assumed to be known and3620 * not contain any nested divs.3621 */3622static __isl_give isl_aff_list *set_up_substitutions(3623 __isl_keep isl_basic_map *bmap_i, __isl_keep isl_basic_map *bmap_j,3624 __isl_take isl_basic_map *hull)3625{3626 isl_size n_div_i, n_div_j, total;3627 isl_ctx *ctx;3628 isl_local_space *ls;3629 isl_basic_set *wrap_hull;3630 isl_aff *aff_nan;3631 isl_aff_list *list;3632 int i, j;3633 3634 n_div_i = isl_basic_map_dim(bmap_i, isl_dim_div);3635 n_div_j = isl_basic_map_dim(bmap_j, isl_dim_div);3636 total = isl_basic_map_dim(bmap_i, isl_dim_all);3637 if (!hull || n_div_i < 0 || n_div_j < 0 || total < 0)3638 return NULL;3639 3640 ctx = isl_basic_map_get_ctx(hull);3641 total -= n_div_i;3642 3643 ls = isl_basic_map_get_local_space(bmap_i);3644 ls = isl_local_space_wrap(ls);3645 wrap_hull = isl_basic_map_wrap(hull);3646 3647 aff_nan = isl_aff_nan_on_domain(isl_local_space_copy(ls));3648 list = isl_aff_list_alloc(ctx, n_div_i);3649 3650 j = 0;3651 for (i = 0; i < n_div_i; ++i) {3652 isl_aff *aff;3653 isl_size n_div;3654 3655 if (j < n_div_j &&3656 isl_basic_map_equal_div_expr_part(bmap_i, i, bmap_j, j,3657 0, 2 + total)) {3658 ++j;3659 list = isl_aff_list_add(list, isl_aff_copy(aff_nan));3660 continue;3661 }3662 if (n_div_i - i <= n_div_j - j)3663 break;3664 3665 aff = isl_local_space_get_div(ls, i);3666 aff = isl_aff_substitute_equalities(aff,3667 isl_basic_set_copy(wrap_hull));3668 aff = isl_aff_floor(aff);3669 n_div = isl_aff_dim(aff, isl_dim_div);3670 if (n_div < 0)3671 goto error;3672 if (n_div != 0) {3673 isl_aff_free(aff);3674 break;3675 }3676 3677 list = isl_aff_list_add(list, aff);3678 }3679 3680 isl_aff_free(aff_nan);3681 isl_local_space_free(ls);3682 isl_basic_set_free(wrap_hull);3683 3684 return list;3685error:3686 isl_aff_free(aff_nan);3687 isl_local_space_free(ls);3688 isl_basic_set_free(wrap_hull);3689 isl_aff_list_free(list);3690 return NULL;3691}3692 3693/* Add variables to info->bmap and info->tab corresponding to the elements3694 * in "list" that are not set to NaN.3695 * "extra_var" is the number of these elements.3696 * "dim" is the offset in the variables of "tab" where we should3697 * start considering the elements in "list".3698 * When this function returns, the total number of variables in "tab"3699 * is equal to "dim" plus the number of elements in "list".3700 *3701 * The newly added existentially quantified variables are not given3702 * an explicit representation because the corresponding div constraints3703 * do not appear in info->bmap. These constraints are not added3704 * to info->bmap because for internal consistency, they would need to3705 * be added to info->tab as well, where they could combine with the equality3706 * that is added later to result in constraints that do not hold3707 * in the original input.3708 */3709static isl_stat add_sub_vars(struct isl_coalesce_info *info,3710 __isl_keep isl_aff_list *list, int dim, int extra_var)3711{3712 int i, j, d;3713 isl_size n;3714 3715 info->bmap = isl_basic_map_cow(info->bmap);3716 info->bmap = isl_basic_map_extend(info->bmap, extra_var, 0, 0);3717 n = isl_aff_list_n_aff(list);3718 if (!info->bmap || n < 0)3719 return isl_stat_error;3720 for (i = 0; i < n; ++i) {3721 int is_nan;3722 isl_aff *aff;3723 3724 aff = isl_aff_list_get_aff(list, i);3725 is_nan = isl_aff_is_nan(aff);3726 isl_aff_free(aff);3727 if (is_nan < 0)3728 return isl_stat_error;3729 if (is_nan)3730 continue;3731 3732 if (isl_tab_insert_var(info->tab, dim + i) < 0)3733 return isl_stat_error;3734 d = isl_basic_map_alloc_div(info->bmap);3735 if (d < 0)3736 return isl_stat_error;3737 info->bmap = isl_basic_map_mark_div_unknown(info->bmap, d);3738 for (j = d; j > i; --j)3739 info->bmap = isl_basic_map_swap_div(info->bmap,3740 j - 1, j);3741 if (!info->bmap)3742 return isl_stat_error;3743 }3744 3745 return isl_stat_ok;3746}3747 3748/* For each element in "list" that is not set to NaN, fix the corresponding3749 * variable in "tab" to the purely affine expression defined by the element.3750 * "dim" is the offset in the variables of "tab" where we should3751 * start considering the elements in "list".3752 *3753 * This function assumes that a sufficient number of rows and3754 * elements in the constraint array are available in the tableau.3755 */3756static isl_stat add_sub_equalities(struct isl_tab *tab,3757 __isl_keep isl_aff_list *list, int dim)3758{3759 int i;3760 isl_size n;3761 isl_ctx *ctx;3762 isl_vec *sub;3763 isl_aff *aff;3764 3765 n = isl_aff_list_n_aff(list);3766 if (n < 0)3767 return isl_stat_error;3768 3769 ctx = isl_tab_get_ctx(tab);3770 sub = isl_vec_alloc(ctx, 1 + dim + n);3771 if (!sub)3772 return isl_stat_error;3773 isl_seq_clr(sub->el + 1 + dim, n);3774 3775 for (i = 0; i < n; ++i) {3776 aff = isl_aff_list_get_aff(list, i);3777 if (!aff)3778 goto error;3779 if (isl_aff_is_nan(aff)) {3780 isl_aff_free(aff);3781 continue;3782 }3783 isl_seq_cpy(sub->el, aff->v->el + 1, 1 + dim);3784 isl_int_neg(sub->el[1 + dim + i], aff->v->el[0]);3785 if (isl_tab_add_eq(tab, sub->el) < 0)3786 goto error;3787 isl_int_set_si(sub->el[1 + dim + i], 0);3788 isl_aff_free(aff);3789 }3790 3791 isl_vec_free(sub);3792 return isl_stat_ok;3793error:3794 isl_aff_free(aff);3795 isl_vec_free(sub);3796 return isl_stat_error;3797}3798 3799/* Add variables to info->tab and info->bmap corresponding to the elements3800 * in "list" that are not set to NaN. The value of the added variable3801 * in info->tab is fixed to the purely affine expression defined by the element.3802 * "dim" is the offset in the variables of info->tab where we should3803 * start considering the elements in "list".3804 * When this function returns, the total number of variables in info->tab3805 * is equal to "dim" plus the number of elements in "list".3806 */3807static isl_stat add_subs(struct isl_coalesce_info *info,3808 __isl_keep isl_aff_list *list, int dim)3809{3810 int extra_var;3811 isl_size n;3812 3813 n = isl_aff_list_n_aff(list);3814 if (n < 0)3815 return isl_stat_error;3816 3817 extra_var = n - (info->tab->n_var - dim);3818 3819 if (isl_tab_extend_vars(info->tab, extra_var) < 0)3820 return isl_stat_error;3821 if (isl_tab_extend_cons(info->tab, 2 * extra_var) < 0)3822 return isl_stat_error;3823 if (add_sub_vars(info, list, dim, extra_var) < 0)3824 return isl_stat_error;3825 3826 return add_sub_equalities(info->tab, list, dim);3827}3828 3829/* Coalesce basic map "j" into basic map "i" after adding the extra integer3830 * divisions in "i" but not in "j" to basic map "j", with values3831 * specified by "list". The total number of elements in "list"3832 * is equal to the number of integer divisions in "i", while the number3833 * of NaN elements in the list is equal to the number of integer divisions3834 * in "j".3835 *3836 * If no coalescing can be performed, then we need to revert basic map "j"3837 * to its original state. We do the same if basic map "i" gets dropped3838 * during the coalescing, even though this should not happen in practice3839 * since we have already checked for "j" being a subset of "i"3840 * before we reach this stage.3841 */3842static enum isl_change coalesce_with_subs(int i, int j,3843 struct isl_coalesce_info *info, __isl_keep isl_aff_list *list)3844{3845 isl_basic_map *bmap_j;3846 struct isl_tab_undo *snap;3847 isl_size dim, n_div;3848 enum isl_change change;3849 3850 bmap_j = isl_basic_map_copy(info[j].bmap);3851 snap = isl_tab_snap(info[j].tab);3852 3853 dim = isl_basic_map_dim(bmap_j, isl_dim_all);3854 n_div = isl_basic_map_dim(bmap_j, isl_dim_div);3855 if (dim < 0 || n_div < 0)3856 goto error;3857 dim -= n_div;3858 if (add_subs(&info[j], list, dim) < 0)3859 goto error;3860 3861 change = coalesce_local_pair(i, j, info);3862 if (change != isl_change_none && change != isl_change_drop_first) {3863 isl_basic_map_free(bmap_j);3864 } else {3865 isl_basic_map_free(info[j].bmap);3866 info[j].bmap = bmap_j;3867 3868 if (isl_tab_rollback(info[j].tab, snap) < 0)3869 return isl_change_error;3870 }3871 3872 return change;3873error:3874 isl_basic_map_free(bmap_j);3875 return isl_change_error;3876}3877 3878/* Check if we can coalesce basic map "j" into basic map "i" after copying3879 * those extra integer divisions in "i" that can be simplified away3880 * using the extra equalities in "j".3881 * All divs are assumed to be known and not contain any nested divs.3882 *3883 * We first check if there are any extra equalities in "j" that we3884 * can exploit. Then we check if every integer division in "i"3885 * either already appears in "j" or can be simplified using the3886 * extra equalities to a purely affine expression.3887 * If these tests succeed, then we try to coalesce the two basic maps3888 * by introducing extra dimensions in "j" corresponding to3889 * the extra integer divisions "i" fixed to the corresponding3890 * purely affine expression.3891 */3892static enum isl_change check_coalesce_into_eq(int i, int j,3893 struct isl_coalesce_info *info)3894{3895 isl_size n_div_i, n_div_j, n;3896 isl_basic_map *hull_i, *hull_j;3897 isl_bool equal, empty;3898 isl_aff_list *list;3899 enum isl_change change;3900 3901 n_div_i = isl_basic_map_dim(info[i].bmap, isl_dim_div);3902 n_div_j = isl_basic_map_dim(info[j].bmap, isl_dim_div);3903 if (n_div_i < 0 || n_div_j < 0)3904 return isl_change_error;3905 if (n_div_i <= n_div_j)3906 return isl_change_none;3907 if (info[j].bmap->n_eq == 0)3908 return isl_change_none;3909 3910 hull_i = isl_basic_map_copy(info[i].bmap);3911 hull_i = isl_basic_map_plain_affine_hull(hull_i);3912 hull_j = isl_basic_map_copy(info[j].bmap);3913 hull_j = isl_basic_map_plain_affine_hull(hull_j);3914 3915 hull_j = isl_basic_map_intersect(hull_j, isl_basic_map_copy(hull_i));3916 equal = isl_basic_map_plain_is_equal(hull_i, hull_j);3917 empty = isl_basic_map_plain_is_empty(hull_j);3918 isl_basic_map_free(hull_i);3919 3920 if (equal < 0 || empty < 0)3921 goto error;3922 if (equal || empty) {3923 isl_basic_map_free(hull_j);3924 return isl_change_none;3925 }3926 3927 list = set_up_substitutions(info[i].bmap, info[j].bmap, hull_j);3928 if (!list)3929 return isl_change_error;3930 n = isl_aff_list_n_aff(list);3931 if (n < 0)3932 change = isl_change_error;3933 else if (n < n_div_i)3934 change = isl_change_none;3935 else3936 change = coalesce_with_subs(i, j, info, list);3937 3938 isl_aff_list_free(list);3939 3940 return change;3941error:3942 isl_basic_map_free(hull_j);3943 return isl_change_error;3944}3945 3946/* Check if we can coalesce basic maps "i" and "j" after copying3947 * those extra integer divisions in one of the basic maps that can3948 * be simplified away using the extra equalities in the other basic map.3949 * We require all divs to be known in both basic maps.3950 * Furthermore, to simplify the comparison of div expressions,3951 * we do not allow any nested integer divisions.3952 */3953static enum isl_change check_coalesce_eq(int i, int j,3954 struct isl_coalesce_info *info)3955{3956 isl_bool known, nested;3957 enum isl_change change;3958 3959 known = isl_basic_map_divs_known(info[i].bmap);3960 if (known < 0 || !known)3961 return known < 0 ? isl_change_error : isl_change_none;3962 known = isl_basic_map_divs_known(info[j].bmap);3963 if (known < 0 || !known)3964 return known < 0 ? isl_change_error : isl_change_none;3965 nested = has_nested_div(info[i].bmap);3966 if (nested < 0 || nested)3967 return nested < 0 ? isl_change_error : isl_change_none;3968 nested = has_nested_div(info[j].bmap);3969 if (nested < 0 || nested)3970 return nested < 0 ? isl_change_error : isl_change_none;3971 3972 change = check_coalesce_into_eq(i, j, info);3973 if (change != isl_change_none)3974 return change;3975 change = check_coalesce_into_eq(j, i, info);3976 if (change != isl_change_none)3977 return invert_change(change);3978 3979 return isl_change_none;3980}3981 3982/* Check if the union of the given pair of basic maps3983 * can be represented by a single basic map.3984 * If so, replace the pair by the single basic map and return3985 * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.3986 * Otherwise, return isl_change_none.3987 *3988 * We first check if the two basic maps live in the same local space,3989 * after aligning the divs that differ by only an integer constant.3990 * If so, we do the complete check. Otherwise, we check if they have3991 * the same number of integer divisions and can be coalesced, if one is3992 * an obvious subset of the other or if the extra integer divisions3993 * of one basic map can be simplified away using the extra equalities3994 * of the other basic map.3995 *3996 * Note that trying to coalesce pairs of disjuncts with the same3997 * number, but different local variables may drop the explicit3998 * representation of some of these local variables.3999 * This operation is therefore not performed when4000 * the "coalesce_preserve_locals" option is set.4001 */4002static enum isl_change coalesce_pair(int i, int j,4003 struct isl_coalesce_info *info)4004{4005 int preserve;4006 isl_bool same;4007 enum isl_change change;4008 isl_ctx *ctx;4009 4010 if (harmonize_divs(&info[i], &info[j]) < 0)4011 return isl_change_error;4012 same = same_divs(info[i].bmap, info[j].bmap);4013 if (same < 0)4014 return isl_change_error;4015 if (same)4016 return coalesce_local_pair(i, j, info);4017 4018 ctx = isl_basic_map_get_ctx(info[i].bmap);4019 preserve = isl_options_get_coalesce_preserve_locals(ctx);4020 if (!preserve && info[i].bmap->n_div == info[j].bmap->n_div) {4021 change = coalesce_local_pair(i, j, info);4022 if (change != isl_change_none)4023 return change;4024 }4025 4026 change = coalesce_divs(i, j, info);4027 if (change != isl_change_none)4028 return change;4029 4030 return check_coalesce_eq(i, j, info);4031}4032 4033/* Return the maximum of "a" and "b".4034 */4035static int isl_max(int a, int b)4036{4037 return a > b ? a : b;4038}4039 4040/* Pairwise coalesce the basic maps in the range [start1, end1[ of "info"4041 * with those in the range [start2, end2[, skipping basic maps4042 * that have been removed (either before or within this function).4043 *4044 * For each basic map i in the first range, we check if it can be coalesced4045 * with respect to any previously considered basic map j in the second range.4046 * If i gets dropped (because it was a subset of some j), then4047 * we can move on to the next basic map.4048 * If j gets dropped, we need to continue checking against the other4049 * previously considered basic maps.4050 * If the two basic maps got fused, then we recheck the fused basic map4051 * against the previously considered basic maps, starting at i + 14052 * (even if start2 is greater than i + 1).4053 */4054static int coalesce_range(isl_ctx *ctx, struct isl_coalesce_info *info,4055 int start1, int end1, int start2, int end2)4056{4057 int i, j;4058 4059 for (i = end1 - 1; i >= start1; --i) {4060 if (info[i].removed)4061 continue;4062 for (j = isl_max(i + 1, start2); j < end2; ++j) {4063 enum isl_change changed;4064 4065 if (info[j].removed)4066 continue;4067 if (info[i].removed)4068 isl_die(ctx, isl_error_internal,4069 "basic map unexpectedly removed",4070 return -1);4071 changed = coalesce_pair(i, j, info);4072 switch (changed) {4073 case isl_change_error:4074 return -1;4075 case isl_change_none:4076 case isl_change_drop_second:4077 continue;4078 case isl_change_drop_first:4079 j = end2;4080 break;4081 case isl_change_fuse:4082 j = i;4083 break;4084 }4085 }4086 }4087 4088 return 0;4089}4090 4091/* Pairwise coalesce the basic maps described by the "n" elements of "info".4092 *4093 * We consider groups of basic maps that live in the same apparent4094 * affine hull and we first coalesce within such a group before we4095 * coalesce the elements in the group with elements of previously4096 * considered groups. If a fuse happens during the second phase,4097 * then we also reconsider the elements within the group.4098 */4099static int coalesce(isl_ctx *ctx, int n, struct isl_coalesce_info *info)4100{4101 int start, end;4102 4103 for (end = n; end > 0; end = start) {4104 start = end - 1;4105 while (start >= 1 &&4106 info[start - 1].hull_hash == info[start].hull_hash)4107 start--;4108 if (coalesce_range(ctx, info, start, end, start, end) < 0)4109 return -1;4110 if (coalesce_range(ctx, info, start, end, end, n) < 0)4111 return -1;4112 }4113 4114 return 0;4115}4116 4117/* Update the basic maps in "map" based on the information in "info".4118 * In particular, remove the basic maps that have been marked removed and4119 * update the others based on the information in the corresponding tableau.4120 * Since we detected implicit equalities without calling4121 * isl_basic_map_gauss, we need to do it now.4122 * Also call isl_basic_map_simplify if we may have lost the definition4123 * of one or more integer divisions.4124 * If a basic map is still equal to the one from which the corresponding "info"4125 * entry was created, then redundant constraint and4126 * implicit equality constraint detection have been performed4127 * on the corresponding tableau and the basic map can be marked as such.4128 */4129static __isl_give isl_map *update_basic_maps(__isl_take isl_map *map,4130 int n, struct isl_coalesce_info *info)4131{4132 int i;4133 4134 if (!map)4135 return NULL;4136 4137 for (i = n - 1; i >= 0; --i) {4138 if (info[i].removed) {4139 isl_basic_map_free(map->p[i]);4140 if (i != map->n - 1)4141 map->p[i] = map->p[map->n - 1];4142 map->n--;4143 continue;4144 }4145 4146 info[i].bmap = isl_basic_map_update_from_tab(info[i].bmap,4147 info[i].tab);4148 info[i].bmap = isl_basic_map_gauss(info[i].bmap, NULL);4149 if (info[i].simplify)4150 info[i].bmap = isl_basic_map_simplify(info[i].bmap);4151 info[i].bmap = isl_basic_map_finalize(info[i].bmap);4152 if (!info[i].bmap)4153 return isl_map_free(map);4154 if (!info[i].modified) {4155 ISL_F_SET(info[i].bmap, ISL_BASIC_MAP_NO_IMPLICIT);4156 ISL_F_SET(info[i].bmap, ISL_BASIC_MAP_NO_REDUNDANT);4157 }4158 isl_basic_map_free(map->p[i]);4159 map->p[i] = info[i].bmap;4160 info[i].bmap = NULL;4161 }4162 4163 return map;4164}4165 4166/* For each pair of basic maps in the map, check if the union of the two4167 * can be represented by a single basic map.4168 * If so, replace the pair by the single basic map and start over.4169 *4170 * We factor out any (hidden) common factor from the constraint4171 * coefficients to improve the detection of adjacent constraints.4172 * Note that this function does not call isl_basic_map_gauss,4173 * but it does make sure that only a single copy of the basic map4174 * is affected. This means that isl_basic_map_gauss may have4175 * to be called at the end of the computation (in update_basic_maps)4176 * on this single copy to ensure that4177 * the basic maps are not left in an unexpected state.4178 *4179 * Since we are constructing the tableaus of the basic maps anyway,4180 * we exploit them to detect implicit equalities and redundant constraints.4181 * This also helps the coalescing as it can ignore the redundant constraints.4182 * In order to avoid confusion, we make all implicit equalities explicit4183 * in the basic maps. If the basic map only has a single reference4184 * (this happens in particular if it was modified by4185 * isl_basic_map_reduce_coefficients), then isl_basic_map_gauss4186 * does not get called on the result. The call to4187 * isl_basic_map_gauss in update_basic_maps resolves this as well.4188 * For each basic map, we also compute the hash of the apparent affine hull4189 * for use in coalesce.4190 */4191__isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map)4192{4193 int i;4194 unsigned n;4195 isl_ctx *ctx;4196 struct isl_coalesce_info *info = NULL;4197 4198 map = isl_map_remove_empty_parts(map);4199 if (!map)4200 return NULL;4201 4202 if (map->n <= 1)4203 return map;4204 4205 ctx = isl_map_get_ctx(map);4206 map = isl_map_sort_divs(map);4207 map = isl_map_cow(map);4208 4209 if (!map)4210 return NULL;4211 4212 n = map->n;4213 4214 info = isl_calloc_array(map->ctx, struct isl_coalesce_info, n);4215 if (!info)4216 goto error;4217 4218 for (i = 0; i < map->n; ++i) {4219 map->p[i] = isl_basic_map_reduce_coefficients(map->p[i]);4220 if (!map->p[i])4221 goto error;4222 info[i].bmap = isl_basic_map_copy(map->p[i]);4223 info[i].tab = isl_tab_from_basic_map(info[i].bmap, 0);4224 if (!info[i].tab)4225 goto error;4226 if (!ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_NO_IMPLICIT))4227 if (isl_tab_detect_implicit_equalities(info[i].tab) < 0)4228 goto error;4229 info[i].bmap = isl_tab_make_equalities_explicit(info[i].tab,4230 info[i].bmap);4231 if (!info[i].bmap)4232 goto error;4233 if (!ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_NO_REDUNDANT))4234 if (isl_tab_detect_redundant(info[i].tab) < 0)4235 goto error;4236 if (coalesce_info_set_hull_hash(&info[i]) < 0)4237 goto error;4238 }4239 for (i = map->n - 1; i >= 0; --i)4240 if (info[i].tab->empty)4241 drop(&info[i]);4242 4243 if (coalesce(ctx, n, info) < 0)4244 goto error;4245 4246 map = update_basic_maps(map, n, info);4247 4248 clear_coalesce_info(n, info);4249 4250 return map;4251error:4252 clear_coalesce_info(n, info);4253 isl_map_free(map);4254 return NULL;4255}4256 4257/* For each pair of basic sets in the set, check if the union of the two4258 * can be represented by a single basic set.4259 * If so, replace the pair by the single basic set and start over.4260 */4261__isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set)4262{4263 return set_from_map(isl_map_coalesce(set_to_map(set)));4264}4265