isl_map_simplify.c

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  *
   4  * Use of this software is governed by the GNU LGPLv2.1 license
   5  *
   6  * Written by Sven Verdoolaege, K.U.Leuven, Departement
   7  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
   8  */
   9
  10 #include <strings.h>
  11 #include <isl_ctx_private.h>
  12 #include <isl_map_private.h>
  13 #include "isl_equalities.h"
  14 #include <isl/map.h>
  15 #include <isl/seq.h>
  16 #include "isl_tab.h"
  17 #include <isl_space_private.h>
  18 #include <isl_mat_private.h>
  19
  20 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
  21 {
  22         isl_int *t = bmap->eq[a];
  23         bmap->eq[a] = bmap->eq[b];
  24         bmap->eq[b] = t;
  25 }
  26
  27 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
  28 {
  29         if (a != b) {
  30                 isl_int *t = bmap->ineq[a];
  31                 bmap->ineq[a] = bmap->ineq[b];
  32                 bmap->ineq[b] = t;
  33         }
  34 }
  35
  36 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
  37 {
  38         isl_seq_cpy(c, c + n, rem);
  39         isl_seq_clr(c + rem, n);
  40 }
  41
  42 /* Drop n dimensions starting at first.
  43  *
  44  * In principle, this frees up some extra variables as the number
  45  * of columns remains constant, but we would have to extend
  46  * the div array too as the number of rows in this array is assumed
  47  * to be equal to extra.
  48  */
  49 struct isl_basic_set *isl_basic_set_drop_dims(
  50                 struct isl_basic_set *bset, unsigned first, unsigned n)
  51 {
  52         int i;
  53
  54         if (!bset)
  55                 goto error;
  56
  57         isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
  58
  59         if (n == 0 && !isl_space_get_tuple_name(bset->dim, isl_dim_set))
  60                 return bset;
  61
  62         bset = isl_basic_set_cow(bset);
  63         if (!bset)
  64                 return NULL;
  65
  66         for (i = 0; i < bset->n_eq; ++i)
  67                 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
  68                                      (bset->dim->n_out-first-n)+bset->extra);
  69
  70         for (i = 0; i < bset->n_ineq; ++i)
  71                 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
  72                                      (bset->dim->n_out-first-n)+bset->extra);
  73
  74         for (i = 0; i < bset->n_div; ++i)
  75                 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
  76                                      (bset->dim->n_out-first-n)+bset->extra);
  77
  78         bset->dim = isl_space_drop_outputs(bset->dim, first, n);
  79         if (!bset->dim)
  80                 goto error;
  81
  82         ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
  83         bset = isl_basic_set_simplify(bset);
  84         return isl_basic_set_finalize(bset);
  85 error:
  86         isl_basic_set_free(bset);
  87         return NULL;
  88 }
  89
  90 struct isl_set *isl_set_drop_dims(
  91                 struct isl_set *set, unsigned first, unsigned n)
  92 {
  93         int i;
  94
  95         if (!set)
  96                 goto error;
  97
  98         isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
  99
 100         if (n == 0 && !isl_space_get_tuple_name(set->dim, isl_dim_set))
 101                 return set;
 102         set = isl_set_cow(set);
 103         if (!set)
 104                 goto error;
 105         set->dim = isl_space_drop_outputs(set->dim, first, n);
 106         if (!set->dim)
 107                 goto error;
 108
 109         for (i = 0; i < set->n; ++i) {
 110                 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
 111                 if (!set->p[i])
 112                         goto error;
 113         }
 114
 115         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 116         return set;
 117 error:
 118         isl_set_free(set);
 119         return NULL;
 120 }
 121
 122 /* Move "n" divs starting at "first" to the end of the list of divs.
 123  */
 124 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
 125         unsigned first, unsigned n)
 126 {
 127         isl_int **div;
 128         int i;
 129
 130         if (first + n == bmap->n_div)
 131                 return bmap;
 132
 133         div = isl_alloc_array(bmap->ctx, isl_int *, n);
 134         if (!div)
 135                 goto error;
 136         for (i = 0; i < n; ++i)
 137                 div[i] = bmap->div[first + i];
 138         for (i = 0; i < bmap->n_div - first - n; ++i)
 139                 bmap->div[first + i] = bmap->div[first + n + i];
 140         for (i = 0; i < n; ++i)
 141                 bmap->div[bmap->n_div - n + i] = div[i];
 142         free(div);
 143         return bmap;
 144 error:
 145         isl_basic_map_free(bmap);
 146         return NULL;
 147 }
 148
 149 /* Drop "n" dimensions of type "type" starting at "first".
 150  *
 151  * In principle, this frees up some extra variables as the number
 152  * of columns remains constant, but we would have to extend
 153  * the div array too as the number of rows in this array is assumed
 154  * to be equal to extra.
 155  */
 156 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
 157         enum isl_dim_type type, unsigned first, unsigned n)
 158 {
 159         int i;
 160         unsigned dim;
 161         unsigned offset;
 162         unsigned left;
 163
 164         if (!bmap)
 165                 goto error;
 166
 167         dim = isl_basic_map_dim(bmap, type);
 168         isl_assert(bmap->ctx, first + n <= dim, goto error);
 169
 170         if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
 171                 return bmap;
 172
 173         bmap = isl_basic_map_cow(bmap);
 174         if (!bmap)
 175                 return NULL;
 176
 177         offset = isl_basic_map_offset(bmap, type) + first;
 178         left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
 179         for (i = 0; i < bmap->n_eq; ++i)
 180                 constraint_drop_vars(bmap->eq[i]+offset, n, left);
 181
 182         for (i = 0; i < bmap->n_ineq; ++i)
 183                 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
 184
 185         for (i = 0; i < bmap->n_div; ++i)
 186                 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
 187
 188         if (type == isl_dim_div) {
 189                 bmap = move_divs_last(bmap, first, n);
 190                 if (!bmap)
 191                         goto error;
 192                 isl_basic_map_free_div(bmap, n);
 193         } else
 194                 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
 195         if (!bmap->dim)
 196                 goto error;
 197
 198         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 199         bmap = isl_basic_map_simplify(bmap);
 200         return isl_basic_map_finalize(bmap);
 201 error:
 202         isl_basic_map_free(bmap);
 203         return NULL;
 204 }
 205
 206 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
 207         enum isl_dim_type type, unsigned first, unsigned n)
 208 {
 209         return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
 210                                                         type, first, n);
 211 }
 212
 213 struct isl_basic_map *isl_basic_map_drop_inputs(
 214                 struct isl_basic_map *bmap, unsigned first, unsigned n)
 215 {
 216         return isl_basic_map_drop(bmap, isl_dim_in, first, n);
 217 }
 218
 219 struct isl_map *isl_map_drop(struct isl_map *map,
 220         enum isl_dim_type type, unsigned first, unsigned n)
 221 {
 222         int i;
 223
 224         if (!map)
 225                 goto error;
 226
 227         isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
 228
 229         if (n == 0 && !isl_space_get_tuple_name(map->dim, type))
 230                 return map;
 231         map = isl_map_cow(map);
 232         if (!map)
 233                 goto error;
 234         map->dim = isl_space_drop_dims(map->dim, type, first, n);
 235         if (!map->dim)
 236                 goto error;
 237
 238         for (i = 0; i < map->n; ++i) {
 239                 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
 240                 if (!map->p[i])
 241                         goto error;
 242         }
 243         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
 244
 245         return map;
 246 error:
 247         isl_map_free(map);
 248         return NULL;
 249 }
 250
 251 struct isl_set *isl_set_drop(struct isl_set *set,
 252         enum isl_dim_type type, unsigned first, unsigned n)
 253 {
 254         return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
 255 }
 256
 257 struct isl_map *isl_map_drop_inputs(
 258                 struct isl_map *map, unsigned first, unsigned n)
 259 {
 260         return isl_map_drop(map, isl_dim_in, first, n);
 261 }
 262
 263 /*
 264  * We don't cow, as the div is assumed to be redundant.
 265  */
 266 static struct isl_basic_map *isl_basic_map_drop_div(
 267                 struct isl_basic_map *bmap, unsigned div)
 268 {
 269         int i;
 270         unsigned pos;
 271
 272         if (!bmap)
 273                 goto error;
 274
 275         pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
 276
 277         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
 278
 279         for (i = 0; i < bmap->n_eq; ++i)
 280                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
 281
 282         for (i = 0; i < bmap->n_ineq; ++i) {
 283                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
 284                         isl_basic_map_drop_inequality(bmap, i);
 285                         --i;
 286                         continue;
 287                 }
 288                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
 289         }
 290
 291         for (i = 0; i < bmap->n_div; ++i)
 292                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
 293
 294         if (div != bmap->n_div - 1) {
 295                 int j;
 296                 isl_int *t = bmap->div[div];
 297
 298                 for (j = div; j < bmap->n_div - 1; ++j)
 299                         bmap->div[j] = bmap->div[j+1];
 300
 301                 bmap->div[bmap->n_div - 1] = t;
 302         }
 303         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 304         isl_basic_map_free_div(bmap, 1);
 305
 306         return bmap;
 307 error:
 308         isl_basic_map_free(bmap);
 309         return NULL;
 310 }
 311
 312 struct isl_basic_map *isl_basic_map_normalize_constraints(
 313         struct isl_basic_map *bmap)
 314 {
 315         int i;
 316         isl_int gcd;
 317         unsigned total = isl_basic_map_total_dim(bmap);
 318
 319         if (!bmap)
 320                 return NULL;
 321
 322         isl_int_init(gcd);
 323         for (i = bmap->n_eq - 1; i >= 0; --i) {
 324                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
 325                 if (isl_int_is_zero(gcd)) {
 326                         if (!isl_int_is_zero(bmap->eq[i][0])) {
 327                                 bmap = isl_basic_map_set_to_empty(bmap);
 328                                 break;
 329                         }
 330                         isl_basic_map_drop_equality(bmap, i);
 331                         continue;
 332                 }
 333                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 334                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
 335                 if (isl_int_is_one(gcd))
 336                         continue;
 337                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
 338                         bmap = isl_basic_map_set_to_empty(bmap);
 339                         break;
 340                 }
 341                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
 342         }
 343
 344         for (i = bmap->n_ineq - 1; i >= 0; --i) {
 345                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
 346                 if (isl_int_is_zero(gcd)) {
 347                         if (isl_int_is_neg(bmap->ineq[i][0])) {
 348                                 bmap = isl_basic_map_set_to_empty(bmap);
 349                                 break;
 350                         }
 351                         isl_basic_map_drop_inequality(bmap, i);
 352                         continue;
 353                 }
 354                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 355                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
 356                 if (isl_int_is_one(gcd))
 357                         continue;
 358                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
 359                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
 360         }
 361         isl_int_clear(gcd);
 362
 363         return bmap;
 364 }
 365
 366 struct isl_basic_set *isl_basic_set_normalize_constraints(
 367         struct isl_basic_set *bset)
 368 {
 369         return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
 370                 (struct isl_basic_map *)bset);
 371 }
 372
 373 /* Assumes divs have been ordered if keep_divs is set.
 374  */
 375 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
 376         unsigned pos, isl_int *eq, int keep_divs, int *progress)
 377 {
 378         unsigned total;
 379         unsigned space_total;
 380         int k;
 381         int last_div;
 382
 383         total = isl_basic_map_total_dim(bmap);
 384         space_total = isl_space_dim(bmap->dim, isl_dim_all);
 385         last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
 386         for (k = 0; k < bmap->n_eq; ++k) {
 387                 if (bmap->eq[k] == eq)
 388                         continue;
 389                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
 390                         continue;
 391                 if (progress)
 392                         *progress = 1;
 393                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
 394                 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
 395         }
 396
 397         for (k = 0; k < bmap->n_ineq; ++k) {
 398                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
 399                         continue;
 400                 if (progress)
 401                         *progress = 1;
 402                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
 403                 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
 404                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 405         }
 406
 407         for (k = 0; k < bmap->n_div; ++k) {
 408                 if (isl_int_is_zero(bmap->div[k][0]))
 409                         continue;
 410                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
 411                         continue;
 412                 if (progress)
 413                         *progress = 1;
 414                 /* We need to be careful about circular definitions,
 415                  * so for now we just remove the definition of div k
 416                  * if the equality contains any divs.
 417                  * If keep_divs is set, then the divs have been ordered
 418                  * and we can keep the definition as long as the result
 419                  * is still ordered.
 420                  */
 421                 if (last_div == -1 || (keep_divs && last_div < k))
 422                         isl_seq_elim(bmap->div[k]+1, eq,
 423                                         1+pos, 1+total, &bmap->div[k][0]);
 424                 else
 425                         isl_seq_clr(bmap->div[k], 1 + total);
 426                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 427         }
 428 }
 429
 430 /* Assumes divs have been ordered if keep_divs is set.
 431  */
 432 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
 433         unsigned div, int keep_divs)
 434 {
 435         unsigned pos = isl_space_dim(bmap->dim, isl_dim_all) + div;
 436
 437         eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
 438
 439         isl_basic_map_drop_div(bmap, div);
 440 }
 441
 442 /* Check if elimination of div "div" using equality "eq" would not
 443  * result in a div depending on a later div.
 444  */
 445 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
 446         unsigned div)
 447 {
 448         int k;
 449         int last_div;
 450         unsigned space_total = isl_space_dim(bmap->dim, isl_dim_all);
 451         unsigned pos = space_total + div;
 452
 453         last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
 454         if (last_div < 0 || last_div <= div)
 455                 return 1;
 456
 457         for (k = 0; k <= last_div; ++k) {
 458                 if (isl_int_is_zero(bmap->div[k][0]))
 459                         return 1;
 460                 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
 461                         return 0;
 462         }
 463
 464         return 1;
 465 }
 466
 467 /* Elimininate divs based on equalities
 468  */
 469 static struct isl_basic_map *eliminate_divs_eq(
 470                 struct isl_basic_map *bmap, int *progress)
 471 {
 472         int d;
 473         int i;
 474         int modified = 0;
 475         unsigned off;
 476
 477         bmap = isl_basic_map_order_divs(bmap);
 478
 479         if (!bmap)
 480                 return NULL;
 481
 482         off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 483
 484         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 485                 for (i = 0; i < bmap->n_eq; ++i) {
 486                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
 487                             !isl_int_is_negone(bmap->eq[i][off + d]))
 488                                 continue;
 489                         if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
 490                                 continue;
 491                         modified = 1;
 492                         *progress = 1;
 493                         eliminate_div(bmap, bmap->eq[i], d, 1);
 494                         isl_basic_map_drop_equality(bmap, i);
 495                         break;
 496                 }
 497         }
 498         if (modified)
 499                 return eliminate_divs_eq(bmap, progress);
 500         return bmap;
 501 }
 502
 503 /* Elimininate divs based on inequalities
 504  */
 505 static struct isl_basic_map *eliminate_divs_ineq(
 506                 struct isl_basic_map *bmap, int *progress)
 507 {
 508         int d;
 509         int i;
 510         unsigned off;
 511         struct isl_ctx *ctx;
 512
 513         if (!bmap)
 514                 return NULL;
 515
 516         ctx = bmap->ctx;
 517         off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 518
 519         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 520                 for (i = 0; i < bmap->n_eq; ++i)
 521                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
 522                                 break;
 523                 if (i < bmap->n_eq)
 524                         continue;
 525                 for (i = 0; i < bmap->n_ineq; ++i)
 526                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
 527                                 break;
 528                 if (i < bmap->n_ineq)
 529                         continue;
 530                 *progress = 1;
 531                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
 532                 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 533                         break;
 534                 bmap = isl_basic_map_drop_div(bmap, d);
 535                 if (!bmap)
 536                         break;
 537         }
 538         return bmap;
 539 }
 540
 541 struct isl_basic_map *isl_basic_map_gauss(
 542         struct isl_basic_map *bmap, int *progress)
 543 {
 544         int k;
 545         int done;
 546         int last_var;
 547         unsigned total_var;
 548         unsigned total;
 549
 550         bmap = isl_basic_map_order_divs(bmap);
 551
 552         if (!bmap)
 553                 return NULL;
 554
 555         total = isl_basic_map_total_dim(bmap);
 556         total_var = total - bmap->n_div;
 557
 558         last_var = total - 1;
 559         for (done = 0; done < bmap->n_eq; ++done) {
 560                 for (; last_var >= 0; --last_var) {
 561                         for (k = done; k < bmap->n_eq; ++k)
 562                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
 563                                         break;
 564                         if (k < bmap->n_eq)
 565                                 break;
 566                 }
 567                 if (last_var < 0)
 568                         break;
 569                 if (k != done)
 570                         swap_equality(bmap, k, done);
 571                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 572                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 573
 574                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
 575                                                 progress);
 576
 577                 if (last_var >= total_var &&
 578                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
 579                         unsigned div = last_var - total_var;
 580                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
 581                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 582                         isl_int_set(bmap->div[div][0],
 583                                     bmap->eq[done][1+last_var]);
 584                         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 585                 }
 586         }
 587         if (done == bmap->n_eq)
 588                 return bmap;
 589         for (k = done; k < bmap->n_eq; ++k) {
 590                 if (isl_int_is_zero(bmap->eq[k][0]))
 591                         continue;
 592                 return isl_basic_map_set_to_empty(bmap);
 593         }
 594         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
 595         return bmap;
 596 }
 597
 598 struct isl_basic_set *isl_basic_set_gauss(
 599         struct isl_basic_set *bset, int *progress)
 600 {
 601         return (struct isl_basic_set*)isl_basic_map_gauss(
 602                         (struct isl_basic_map *)bset, progress);
 603 }
 604
 605
 606 static unsigned int round_up(unsigned int v)
 607 {
 608         int old_v = v;
 609
 610         while (v) {
 611                 old_v = v;
 612                 v ^= v & -v;
 613         }
 614         return old_v << 1;
 615 }
 616
 617 static int hash_index(isl_int ***index, unsigned int size, int bits,
 618                         struct isl_basic_map *bmap, int k)
 619 {
 620         int h;
 621         unsigned total = isl_basic_map_total_dim(bmap);
 622         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
 623         for (h = hash; index[h]; h = (h+1) % size)
 624                 if (&bmap->ineq[k] != index[h] &&
 625                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
 626                         break;
 627         return h;
 628 }
 629
 630 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
 631                           struct isl_basic_set *bset, int k)
 632 {
 633         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
 634 }
 635
 636 /* If we can eliminate more than one div, then we need to make
 637  * sure we do it from last div to first div, in order not to
 638  * change the position of the other divs that still need to
 639  * be removed.
 640  */
 641 static struct isl_basic_map *remove_duplicate_divs(
 642         struct isl_basic_map *bmap, int *progress)
 643 {
 644         unsigned int size;
 645         int *index;
 646         int *elim_for;
 647         int k, l, h;
 648         int bits;
 649         struct isl_blk eq;
 650         unsigned total_var;
 651         unsigned total;
 652         struct isl_ctx *ctx;
 653
 654         if (!bmap || bmap->n_div <= 1)
 655                 return bmap;
 656
 657         total_var = isl_space_dim(bmap->dim, isl_dim_all);
 658         total = total_var + bmap->n_div;
 659
 660         ctx = bmap->ctx;
 661         for (k = bmap->n_div - 1; k >= 0; --k)
 662                 if (!isl_int_is_zero(bmap->div[k][0]))
 663                         break;
 664         if (k <= 0)
 665                 return bmap;
 666
 667         elim_for = isl_calloc_array(ctx, int, bmap->n_div);
 668         size = round_up(4 * bmap->n_div / 3 - 1);
 669         bits = ffs(size) - 1;
 670         index = isl_calloc_array(ctx, int, size);
 671         if (!index)
 672                 return bmap;
 673         eq = isl_blk_alloc(ctx, 1+total);
 674         if (isl_blk_is_error(eq))
 675                 goto out;
 676
 677         isl_seq_clr(eq.data, 1+total);
 678         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
 679         for (--k; k >= 0; --k) {
 680                 uint32_t hash;
 681
 682                 if (isl_int_is_zero(bmap->div[k][0]))
 683                         continue;
 684
 685                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
 686                 for (h = hash; index[h]; h = (h+1) % size)
 687                         if (isl_seq_eq(bmap->div[k],
 688                                        bmap->div[index[h]-1], 2+total))
 689                                 break;
 690                 if (index[h]) {
 691                         *progress = 1;
 692                         l = index[h] - 1;
 693                         elim_for[l] = k + 1;
 694                 }
 695                 index[h] = k+1;
 696         }
 697         for (l = bmap->n_div - 1; l >= 0; --l) {
 698                 if (!elim_for[l])
 699                         continue;
 700                 k = elim_for[l] - 1;
 701                 isl_int_set_si(eq.data[1+total_var+k], -1);
 702                 isl_int_set_si(eq.data[1+total_var+l], 1);
 703                 eliminate_div(bmap, eq.data, l, 0);
 704                 isl_int_set_si(eq.data[1+total_var+k], 0);
 705                 isl_int_set_si(eq.data[1+total_var+l], 0);
 706         }
 707
 708         isl_blk_free(ctx, eq);
 709 out:
 710         free(index);
 711         free(elim_for);
 712         return bmap;
 713 }
 714
 715 static int n_pure_div_eq(struct isl_basic_map *bmap)
 716 {
 717         int i, j;
 718         unsigned total;
 719
 720         total = isl_space_dim(bmap->dim, isl_dim_all);
 721         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 722                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 723                         --j;
 724                 if (j < 0)
 725                         break;
 726                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 727                         return 0;
 728         }
 729         return i;
 730 }
 731
 732 /* Normalize divs that appear in equalities.
 733  *
 734  * In particular, we assume that bmap contains some equalities
 735  * of the form
 736  *
 737  *      a x = m * e_i
 738  *
 739  * and we want to replace the set of e_i by a minimal set and
 740  * such that the new e_i have a canonical representation in terms
 741  * of the vector x.
 742  * If any of the equalities involves more than one divs, then
 743  * we currently simply bail out.
 744  *
 745  * Let us first additionally assume that all equalities involve
 746  * a div.  The equalities then express modulo constraints on the
 747  * remaining variables and we can use "parameter compression"
 748  * to find a minimal set of constraints.  The result is a transformation
 749  *
 750  *      x = T(x') = x_0 + G x'
 751  *
 752  * with G a lower-triangular matrix with all elements below the diagonal
 753  * non-negative and smaller than the diagonal element on the same row.
 754  * We first normalize x_0 by making the same property hold in the affine
 755  * T matrix.
 756  * The rows i of G with a 1 on the diagonal do not impose any modulo
 757  * constraint and simply express x_i = x'_i.
 758  * For each of the remaining rows i, we introduce a div and a corresponding
 759  * equality.  In particular
 760  *
 761  *      g_ii e_j = x_i - g_i(x')
 762  *
 763  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 764  * corresponding div (if g_kk != 1).
 765  *
 766  * If there are any equalities not involving any div, then we
 767  * first apply a variable compression on the variables x:
 768  *
 769  *      x = C x''       x'' = C_2 x
 770  *
 771  * and perform the above parameter compression on A C instead of on A.
 772  * The resulting compression is then of the form
 773  *
 774  *      x'' = T(x') = x_0 + G x'
 775  *
 776  * and in constructing the new divs and the corresponding equalities,
 777  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 778  * by the corresponding row from C_2.
 779  */
 780 static struct isl_basic_map *normalize_divs(
 781         struct isl_basic_map *bmap, int *progress)
 782 {
 783         int i, j, k;
 784         int total;
 785         int div_eq;
 786         struct isl_mat *B;
 787         struct isl_vec *d;
 788         struct isl_mat *T = NULL;
 789         struct isl_mat *C = NULL;
 790         struct isl_mat *C2 = NULL;
 791         isl_int v;
 792         int *pos;
 793         int dropped, needed;
 794
 795         if (!bmap)
 796                 return NULL;
 797
 798         if (bmap->n_div == 0)
 799                 return bmap;
 800
 801         if (bmap->n_eq == 0)
 802                 return bmap;
 803
 804         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 805                 return bmap;
 806
 807         total = isl_space_dim(bmap->dim, isl_dim_all);
 808         div_eq = n_pure_div_eq(bmap);
 809         if (div_eq == 0)
 810                 return bmap;
 811
 812         if (div_eq < bmap->n_eq) {
 813                 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
 814                                         bmap->n_eq - div_eq, 0, 1 + total);
 815                 C = isl_mat_variable_compression(B, &C2);
 816                 if (!C || !C2)
 817                         goto error;
 818                 if (C->n_col == 0) {
 819                         bmap = isl_basic_map_set_to_empty(bmap);
 820                         isl_mat_free(C);
 821                         isl_mat_free(C2);
 822                         goto done;
 823                 }
 824         }
 825
 826         d = isl_vec_alloc(bmap->ctx, div_eq);
 827         if (!d)
 828                 goto error;
 829         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 830                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 831                         --j;
 832                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 833         }
 834         B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 835
 836         if (C) {
 837                 B = isl_mat_product(B, C);
 838                 C = NULL;
 839         }
 840
 841         T = isl_mat_parameter_compression(B, d);
 842         if (!T)
 843                 goto error;
 844         if (T->n_col == 0) {
 845                 bmap = isl_basic_map_set_to_empty(bmap);
 846                 isl_mat_free(C2);
 847                 isl_mat_free(T);
 848                 goto done;
 849         }
 850         isl_int_init(v);
 851         for (i = 0; i < T->n_row - 1; ++i) {
 852                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 853                 if (isl_int_is_zero(v))
 854                         continue;
 855                 isl_mat_col_submul(T, 0, v, 1 + i);
 856         }
 857         isl_int_clear(v);
 858         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 859         if (!pos)
 860                 goto error;
 861         /* We have to be careful because dropping equalities may reorder them */
 862         dropped = 0;
 863         for (j = bmap->n_div - 1; j >= 0; --j) {
 864                 for (i = 0; i < bmap->n_eq; ++i)
 865                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 866                                 break;
 867                 if (i < bmap->n_eq) {
 868                         bmap = isl_basic_map_drop_div(bmap, j);
 869                         isl_basic_map_drop_equality(bmap, i);
 870                         ++dropped;
 871                 }
 872         }
 873         pos[0] = 0;
 874         needed = 0;
 875         for (i = 1; i < T->n_row; ++i) {
 876                 if (isl_int_is_one(T->row[i][i]))
 877                         pos[i] = i;
 878                 else
 879                         needed++;
 880         }
 881         if (needed > dropped) {
 882                 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
 883                                 needed, needed, 0);
 884                 if (!bmap)
 885                         goto error;
 886         }
 887         for (i = 1; i < T->n_row; ++i) {
 888                 if (isl_int_is_one(T->row[i][i]))
 889                         continue;
 890                 k = isl_basic_map_alloc_div(bmap);
 891                 pos[i] = 1 + total + k;
 892                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 893                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 894                 if (C2)
 895                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 896                 else
 897                         isl_int_set_si(bmap->div[k][1 + i], 1);
 898                 for (j = 0; j < i; ++j) {
 899                         if (isl_int_is_zero(T->row[i][j]))
 900                                 continue;
 901                         if (pos[j] < T->n_row && C2)
 902                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 903                                                 C2->row[pos[j]], 1 + total);
 904                         else
 905                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 906                                                                 T->row[i][j]);
 907                 }
 908                 j = isl_basic_map_alloc_equality(bmap);
 909                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 910                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 911         }
 912         free(pos);
 913         isl_mat_free(C2);
 914         isl_mat_free(T);
 915
 916         if (progress)
 917                 *progress = 1;
 918 done:
 919         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 920
 921         return bmap;
 922 error:
 923         isl_mat_free(C);
 924         isl_mat_free(C2);
 925         isl_mat_free(T);
 926         return bmap;
 927 }
 928
 929 static struct isl_basic_map *set_div_from_lower_bound(
 930         struct isl_basic_map *bmap, int div, int ineq)
 931 {
 932         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 933
 934         isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
 935         isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
 936         isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
 937         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
 938         isl_int_set_si(bmap->div[div][1 + total + div], 0);
 939
 940         return bmap;
 941 }
 942
 943 /* Check whether it is ok to define a div based on an inequality.
 944  * To avoid the introduction of circular definitions of divs, we
 945  * do not allow such a definition if the resulting expression would refer to
 946  * any other undefined divs or if any known div is defined in
 947  * terms of the unknown div.
 948  */
 949 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
 950         int div, int ineq)
 951 {
 952         int j;
 953         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 954
 955         /* Not defined in terms of unknown divs */
 956         for (j = 0; j < bmap->n_div; ++j) {
 957                 if (div == j)
 958                         continue;
 959                 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
 960                         continue;
 961                 if (isl_int_is_zero(bmap->div[j][0]))
 962                         return 0;
 963         }
 964
 965         /* No other div defined in terms of this one => avoid loops */
 966         for (j = 0; j < bmap->n_div; ++j) {
 967                 if (div == j)
 968                         continue;
 969                 if (isl_int_is_zero(bmap->div[j][0]))
 970                         continue;
 971                 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
 972                         return 0;
 973         }
 974
 975         return 1;
 976 }
 977
 978 /* Given two constraints "k" and "l" that are opposite to each other,
 979  * except for the constant term, check if we can use them
 980  * to obtain an expression for one of the hitherto unknown divs.
 981  * "sum" is the sum of the constant terms of the constraints.
 982  * If this sum is strictly smaller than the coefficient of one
 983  * of the divs, then this pair can be used define the div.
 984  * To avoid the introduction of circular definitions of divs, we
 985  * do not use the pair if the resulting expression would refer to
 986  * any other undefined divs or if any known div is defined in
 987  * terms of the unknown div.
 988  */
 989 static struct isl_basic_map *check_for_div_constraints(
 990         struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
 991 {
 992         int i;
 993         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 994
 995         for (i = 0; i < bmap->n_div; ++i) {
 996                 if (!isl_int_is_zero(bmap->div[i][0]))
 997                         continue;
 998                 if (isl_int_is_zero(bmap->ineq[k][total + i]))
 999                         continue;
1000                 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1001                         continue;
1002                 if (!ok_to_set_div_from_bound(bmap, i, k))
1003                         break;
1004                 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1005                         bmap = set_div_from_lower_bound(bmap, i, k);
1006                 else
1007                         bmap = set_div_from_lower_bound(bmap, i, l);
1008                 if (progress)
1009                         *progress = 1;
1010                 break;
1011         }
1012         return bmap;
1013 }
1014
1015 static struct isl_basic_map *remove_duplicate_constraints(
1016         struct isl_basic_map *bmap, int *progress, int detect_divs)
1017 {
1018         unsigned int size;
1019         isl_int ***index;
1020         int k, l, h;
1021         int bits;
1022         unsigned total = isl_basic_map_total_dim(bmap);
1023         isl_int sum;
1024         isl_ctx *ctx;
1025
1026         if (!bmap || bmap->n_ineq <= 1)
1027                 return bmap;
1028
1029         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1030         bits = ffs(size) - 1;
1031         ctx = isl_basic_map_get_ctx(bmap);
1032         index = isl_calloc_array(ctx, isl_int **, size);
1033         if (!index)
1034                 return bmap;
1035
1036         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1037         for (k = 1; k < bmap->n_ineq; ++k) {
1038                 h = hash_index(index, size, bits, bmap, k);
1039                 if (!index[h]) {
1040                         index[h] = &bmap->ineq[k];
1041                         continue;
1042                 }
1043                 if (progress)
1044                         *progress = 1;
1045                 l = index[h] - &bmap->ineq[0];
1046                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1047                         swap_inequality(bmap, k, l);
1048                 isl_basic_map_drop_inequality(bmap, k);
1049                 --k;
1050         }
1051         isl_int_init(sum);
1052         for (k = 0; k < bmap->n_ineq-1; ++k) {
1053                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1054                 h = hash_index(index, size, bits, bmap, k);
1055                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1056                 if (!index[h])
1057                         continue;
1058                 l = index[h] - &bmap->ineq[0];
1059                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1060                 if (isl_int_is_pos(sum)) {
1061                         if (detect_divs)
1062                                 bmap = check_for_div_constraints(bmap, k, l,
1063                                                                  sum, progress);
1064                         continue;
1065                 }
1066                 if (isl_int_is_zero(sum)) {
1067                         /* We need to break out of the loop after these
1068                          * changes since the contents of the hash
1069                          * will no longer be valid.
1070                          * Plus, we probably we want to regauss first.
1071                          */
1072                         if (progress)
1073                                 *progress = 1;
1074                         isl_basic_map_drop_inequality(bmap, l);
1075                         isl_basic_map_inequality_to_equality(bmap, k);
1076                 } else
1077                         bmap = isl_basic_map_set_to_empty(bmap);
1078                 break;
1079         }
1080         isl_int_clear(sum);
1081
1082         free(index);
1083         return bmap;
1084 }
1085
1086
1087 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1088 {
1089         int progress = 1;
1090         if (!bmap)
1091                 return NULL;
1092         while (progress) {
1093                 progress = 0;
1094                 bmap = isl_basic_map_normalize_constraints(bmap);
1095                 bmap = remove_duplicate_divs(bmap, &progress);
1096                 bmap = eliminate_divs_eq(bmap, &progress);
1097                 bmap = eliminate_divs_ineq(bmap, &progress);
1098                 bmap = isl_basic_map_gauss(bmap, &progress);
1099                 /* requires equalities in normal form */
1100                 bmap = normalize_divs(bmap, &progress);
1101                 bmap = remove_duplicate_constraints(bmap, &progress, 1);
1102         }
1103         return bmap;
1104 }
1105
1106 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1107 {
1108         return (struct isl_basic_set *)
1109                 isl_basic_map_simplify((struct isl_basic_map *)bset);
1110 }
1111
1112
1113 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1114         isl_int *constraint, unsigned div)
1115 {
1116         unsigned pos;
1117
1118         if (!bmap)
1119                 return -1;
1120
1121         pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1122
1123         if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1124                 int neg;
1125                 isl_int_sub(bmap->div[div][1],
1126                                 bmap->div[div][1], bmap->div[div][0]);
1127                 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1128                 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1129                 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1130                 isl_int_add(bmap->div[div][1],
1131                                 bmap->div[div][1], bmap->div[div][0]);
1132                 if (!neg)
1133                         return 0;
1134                 if (isl_seq_first_non_zero(constraint+pos+1,
1135                                             bmap->n_div-div-1) != -1)
1136                         return 0;
1137         } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1138                 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1139                         return 0;
1140                 if (isl_seq_first_non_zero(constraint+pos+1,
1141                                             bmap->n_div-div-1) != -1)
1142                         return 0;
1143         } else
1144                 return 0;
1145
1146         return 1;
1147 }
1148
1149
1150 /* If the only constraints a div d=floor(f/m)
1151  * appears in are its two defining constraints
1152  *
1153  *      f - m d >=0
1154  *      -(f - (m - 1)) + m d >= 0
1155  *
1156  * then it can safely be removed.
1157  */
1158 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1159 {
1160         int i;
1161         unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1162
1163         for (i = 0; i < bmap->n_eq; ++i)
1164                 if (!isl_int_is_zero(bmap->eq[i][pos]))
1165                         return 0;
1166
1167         for (i = 0; i < bmap->n_ineq; ++i) {
1168                 if (isl_int_is_zero(bmap->ineq[i][pos]))
1169                         continue;
1170                 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1171                         return 0;
1172         }
1173
1174         for (i = 0; i < bmap->n_div; ++i)
1175                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1176                         return 0;
1177
1178         return 1;
1179 }
1180
1181 /*
1182  * Remove divs that don't occur in any of the constraints or other divs.
1183  * These can arise when dropping some of the variables in a quast
1184  * returned by piplib.
1185  */
1186 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1187 {
1188         int i;
1189
1190         if (!bmap)
1191                 return NULL;
1192
1193         for (i = bmap->n_div-1; i >= 0; --i) {
1194                 if (!div_is_redundant(bmap, i))
1195                         continue;
1196                 bmap = isl_basic_map_drop_div(bmap, i);
1197         }
1198         return bmap;
1199 }
1200
1201 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1202 {
1203         bmap = remove_redundant_divs(bmap);
1204         if (!bmap)
1205                 return NULL;
1206         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1207         return bmap;
1208 }
1209
1210 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1211 {
1212         return (struct isl_basic_set *)
1213                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1214 }
1215
1216 struct isl_set *isl_set_finalize(struct isl_set *set)
1217 {
1218         int i;
1219
1220         if (!set)
1221                 return NULL;
1222         for (i = 0; i < set->n; ++i) {
1223                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1224                 if (!set->p[i])
1225                         goto error;
1226         }
1227         return set;
1228 error:
1229         isl_set_free(set);
1230         return NULL;
1231 }
1232
1233 struct isl_map *isl_map_finalize(struct isl_map *map)
1234 {
1235         int i;
1236
1237         if (!map)
1238                 return NULL;
1239         for (i = 0; i < map->n; ++i) {
1240                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1241                 if (!map->p[i])
1242                         goto error;
1243         }
1244         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1245         return map;
1246 error:
1247         isl_map_free(map);
1248         return NULL;
1249 }
1250
1251
1252 /* Remove definition of any div that is defined in terms of the given variable.
1253  * The div itself is not removed.  Functions such as
1254  * eliminate_divs_ineq depend on the other divs remaining in place.
1255  */
1256 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1257                                                                         int pos)
1258 {
1259         int i;
1260
1261         for (i = 0; i < bmap->n_div; ++i) {
1262                 if (isl_int_is_zero(bmap->div[i][0]))
1263                         continue;
1264                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1265                         continue;
1266                 isl_int_set_si(bmap->div[i][0], 0);
1267         }
1268         return bmap;
1269 }
1270
1271 /* Eliminate the specified variables from the constraints using
1272  * Fourier-Motzkin.  The variables themselves are not removed.
1273  */
1274 struct isl_basic_map *isl_basic_map_eliminate_vars(
1275         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1276 {
1277         int d;
1278         int i, j, k;
1279         unsigned total;
1280         int need_gauss = 0;
1281
1282         if (n == 0)
1283                 return bmap;
1284         if (!bmap)
1285                 return NULL;
1286         total = isl_basic_map_total_dim(bmap);
1287
1288         bmap = isl_basic_map_cow(bmap);
1289         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1290                 bmap = remove_dependent_vars(bmap, d);
1291
1292         for (d = pos + n - 1;
1293              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1294                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1295         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1296                 int n_lower, n_upper;
1297                 if (!bmap)
1298                         return NULL;
1299                 for (i = 0; i < bmap->n_eq; ++i) {
1300                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1301                                 continue;
1302                         eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1303                         isl_basic_map_drop_equality(bmap, i);
1304                         need_gauss = 1;
1305                         break;
1306                 }
1307                 if (i < bmap->n_eq)
1308                         continue;
1309                 n_lower = 0;
1310                 n_upper = 0;
1311                 for (i = 0; i < bmap->n_ineq; ++i) {
1312                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1313                                 n_lower++;
1314                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1315                                 n_upper++;
1316                 }
1317                 bmap = isl_basic_map_extend_constraints(bmap,
1318                                 0, n_lower * n_upper);
1319                 if (!bmap)
1320                         goto error;
1321                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1322                         int last;
1323                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1324                                 continue;
1325                         last = -1;
1326                         for (j = 0; j < i; ++j) {
1327                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1328                                         continue;
1329                                 last = j;
1330                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1331                                     isl_int_sgn(bmap->ineq[j][1+d]))
1332                                         continue;
1333                                 k = isl_basic_map_alloc_inequality(bmap);
1334                                 if (k < 0)
1335                                         goto error;
1336                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1337                                                 1+total);
1338                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1339                                                 1+d, 1+total, NULL);
1340                         }
1341                         isl_basic_map_drop_inequality(bmap, i);
1342                         i = last + 1;
1343                 }
1344                 if (n_lower > 0 && n_upper > 0) {
1345                         bmap = isl_basic_map_normalize_constraints(bmap);
1346                         bmap = remove_duplicate_constraints(bmap, NULL, 0);
1347                         bmap = isl_basic_map_gauss(bmap, NULL);
1348                         bmap = isl_basic_map_remove_redundancies(bmap);
1349                         need_gauss = 0;
1350                         if (!bmap)
1351                                 goto error;
1352                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1353                                 break;
1354                 }
1355         }
1356         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1357         if (need_gauss)
1358                 bmap = isl_basic_map_gauss(bmap, NULL);
1359         return bmap;
1360 error:
1361         isl_basic_map_free(bmap);
1362         return NULL;
1363 }
1364
1365 struct isl_basic_set *isl_basic_set_eliminate_vars(
1366         struct isl_basic_set *bset, unsigned pos, unsigned n)
1367 {
1368         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1369                         (struct isl_basic_map *)bset, pos, n);
1370 }
1371
1372 /* Eliminate the specified n dimensions starting at first from the
1373  * constraints using Fourier-Motzkin.  The dimensions themselves
1374  * are not removed.
1375  */
1376 __isl_give isl_basic_map *isl_basic_map_eliminate(
1377         __isl_take isl_basic_map *bmap,
1378         enum isl_dim_type type, unsigned first, unsigned n)
1379 {
1380         if (!bmap)
1381                 return NULL;
1382         if (n == 0)
1383                 return bmap;
1384
1385         if (first + n > isl_basic_map_dim(bmap, type))
1386                 isl_die(bmap->ctx, isl_error_invalid,
1387                         "index out of bounds", goto error);
1388
1389         first += isl_basic_map_offset(bmap, type) - 1;
1390         return isl_basic_map_eliminate_vars(bmap, first, n);
1391 error:
1392         isl_basic_map_free(bmap);
1393         return NULL;
1394 }
1395
1396 /* Don't assume equalities are in order, because align_divs
1397  * may have changed the order of the divs.
1398  */
1399 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1400 {
1401         int d, i;
1402         unsigned total;
1403
1404         total = isl_space_dim(bmap->dim, isl_dim_all);
1405         for (d = 0; d < total; ++d)
1406                 elim[d] = -1;
1407         for (i = 0; i < bmap->n_eq; ++i) {
1408                 for (d = total - 1; d >= 0; --d) {
1409                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1410                                 continue;
1411                         elim[d] = i;
1412                         break;
1413                 }
1414         }
1415 }
1416
1417 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1418 {
1419         compute_elimination_index((struct isl_basic_map *)bset, elim);
1420 }
1421
1422 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1423         struct isl_basic_map *bmap, int *elim)
1424 {
1425         int d;
1426         int copied = 0;
1427         unsigned total;
1428
1429         total = isl_space_dim(bmap->dim, isl_dim_all);
1430         for (d = total - 1; d >= 0; --d) {
1431                 if (isl_int_is_zero(src[1+d]))
1432                         continue;
1433                 if (elim[d] == -1)
1434                         continue;
1435                 if (!copied) {
1436                         isl_seq_cpy(dst, src, 1 + total);
1437                         copied = 1;
1438                 }
1439                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1440         }
1441         return copied;
1442 }
1443
1444 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1445         struct isl_basic_set *bset, int *elim)
1446 {
1447         return reduced_using_equalities(dst, src,
1448                                         (struct isl_basic_map *)bset, elim);
1449 }
1450
1451 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1452         struct isl_basic_set *bset, struct isl_basic_set *context)
1453 {
1454         int i;
1455         int *elim;
1456
1457         if (!bset || !context)
1458                 goto error;
1459
1460         if (context->n_eq == 0) {
1461                 isl_basic_set_free(context);
1462                 return bset;
1463         }
1464
1465         bset = isl_basic_set_cow(bset);
1466         if (!bset)
1467                 goto error;
1468
1469         elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1470         if (!elim)
1471                 goto error;
1472         set_compute_elimination_index(context, elim);
1473         for (i = 0; i < bset->n_eq; ++i)
1474                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1475                                                         context, elim);
1476         for (i = 0; i < bset->n_ineq; ++i)
1477                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1478                                                         context, elim);
1479         isl_basic_set_free(context);
1480         free(elim);
1481         bset = isl_basic_set_simplify(bset);
1482         bset = isl_basic_set_finalize(bset);
1483         return bset;
1484 error:
1485         isl_basic_set_free(bset);
1486         isl_basic_set_free(context);
1487         return NULL;
1488 }
1489
1490 static struct isl_basic_set *remove_shifted_constraints(
1491         struct isl_basic_set *bset, struct isl_basic_set *context)
1492 {
1493         unsigned int size;
1494         isl_int ***index;
1495         int bits;
1496         int k, h, l;
1497         isl_ctx *ctx;
1498
1499         if (!bset)
1500                 return NULL;
1501
1502         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1503         bits = ffs(size) - 1;
1504         ctx = isl_basic_set_get_ctx(bset);
1505         index = isl_calloc_array(ctx, isl_int **, size);
1506         if (!index)
1507                 return bset;
1508
1509         for (k = 0; k < context->n_ineq; ++k) {
1510                 h = set_hash_index(index, size, bits, context, k);
1511                 index[h] = &context->ineq[k];
1512         }
1513         for (k = 0; k < bset->n_ineq; ++k) {
1514                 h = set_hash_index(index, size, bits, bset, k);
1515                 if (!index[h])
1516                         continue;
1517                 l = index[h] - &context->ineq[0];
1518                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1519                         continue;
1520                 bset = isl_basic_set_cow(bset);
1521                 if (!bset)
1522                         goto error;
1523                 isl_basic_set_drop_inequality(bset, k);
1524                 --k;
1525         }
1526         free(index);
1527         return bset;
1528 error:
1529         free(index);
1530         return bset;
1531 }
1532
1533 /* Remove all information from bset that is redundant in the context
1534  * of context.  Both bset and context are assumed to be full-dimensional.
1535  *
1536  * We first * remove the inequalities from "bset"
1537  * that are obviously redundant with respect to some inequality in "context".
1538  *
1539  * If there are any inequalities left, we construct a tableau for
1540  * the context and then add the inequalities of "bset".
1541  * Before adding these inequalities, we freeze all constraints such that
1542  * they won't be considered redundant in terms of the constraints of "bset".
1543  * Then we detect all redundant constraints (among the
1544  * constraints that weren't frozen), first by checking for redundancy in the
1545  * the tableau and then by checking if replacing a constraint by its negation
1546  * would lead to an empty set.  This last step is fairly expensive
1547  * and could be optimized by more reuse of the tableau.
1548  * Finally, we update bset according to the results.
1549  */
1550 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1551         __isl_take isl_basic_set *context)
1552 {
1553         int i, k;
1554         isl_basic_set *combined = NULL;
1555         struct isl_tab *tab = NULL;
1556         unsigned context_ineq;
1557         unsigned total;
1558
1559         if (!bset || !context)
1560                 goto error;
1561
1562         if (isl_basic_set_is_universe(bset)) {
1563                 isl_basic_set_free(context);
1564                 return bset;
1565         }
1566
1567         if (isl_basic_set_is_universe(context)) {
1568                 isl_basic_set_free(context);
1569                 return bset;
1570         }
1571
1572         bset = remove_shifted_constraints(bset, context);
1573         if (!bset)
1574                 goto error;
1575         if (bset->n_ineq == 0)
1576                 goto done;
1577
1578         context_ineq = context->n_ineq;
1579         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1580         combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1581         tab = isl_tab_from_basic_set(combined);
1582         for (i = 0; i < context_ineq; ++i)
1583                 if (isl_tab_freeze_constraint(tab, i) < 0)
1584                         goto error;
1585         tab = isl_tab_extend(tab, bset->n_ineq);
1586         for (i = 0; i < bset->n_ineq; ++i)
1587                 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1588                         goto error;
1589         bset = isl_basic_set_add_constraints(combined, bset, 0);
1590         combined = NULL;
1591         if (!bset)
1592                 goto error;
1593         if (isl_tab_detect_redundant(tab) < 0)
1594                 goto error;
1595         total = isl_basic_set_total_dim(bset);
1596         for (i = context_ineq; i < bset->n_ineq; ++i) {
1597                 int is_empty;
1598                 if (tab->con[i].is_redundant)
1599                         continue;
1600                 tab->con[i].is_redundant = 1;
1601                 combined = isl_basic_set_dup(bset);
1602                 combined = isl_basic_set_update_from_tab(combined, tab);
1603                 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1604                 k = isl_basic_set_alloc_inequality(combined);
1605                 if (k < 0)
1606                         goto error;
1607                 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1608                 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1609                 is_empty = isl_basic_set_is_empty(combined);
1610                 if (is_empty < 0)
1611                         goto error;
1612                 isl_basic_set_free(combined);
1613                 combined = NULL;
1614                 if (!is_empty)
1615                         tab->con[i].is_redundant = 0;
1616         }
1617         for (i = 0; i < context_ineq; ++i)
1618                 tab->con[i].is_redundant = 1;
1619         bset = isl_basic_set_update_from_tab(bset, tab);
1620         if (bset) {
1621                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1622                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1623         }
1624
1625         isl_tab_free(tab);
1626 done:
1627         bset = isl_basic_set_simplify(bset);
1628         bset = isl_basic_set_finalize(bset);
1629         isl_basic_set_free(context);
1630         return bset;
1631 error:
1632         isl_tab_free(tab);
1633         isl_basic_set_free(combined);
1634         isl_basic_set_free(context);
1635         isl_basic_set_free(bset);
1636         return NULL;
1637 }
1638
1639 /* Remove all information from bset that is redundant in the context
1640  * of context.  In particular, equalities that are linear combinations
1641  * of those in context are removed.  Then the inequalities that are
1642  * redundant in the context of the equalities and inequalities of
1643  * context are removed.
1644  *
1645  * We first compute the integer affine hull of the intersection,
1646  * compute the gist inside this affine hull and then add back
1647  * those equalities that are not implied by the context.
1648  *
1649  * If two constraints are mutually redundant, then uset_gist_full
1650  * will remove the second of those constraints.  We therefore first
1651  * sort the constraints so that constraints not involving existentially
1652  * quantified variables are given precedence over those that do.
1653  * We have to perform this sorting before the variable compression,
1654  * because that may effect the order of the variables.
1655  */
1656 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1657         __isl_take isl_basic_set *context)
1658 {
1659         isl_mat *eq;
1660         isl_mat *T, *T2;
1661         isl_basic_set *aff;
1662         isl_basic_set *aff_context;
1663         unsigned total;
1664
1665         if (!bset || !context)
1666                 goto error;
1667
1668         bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1669         if (isl_basic_set_plain_is_empty(bset)) {
1670                 isl_basic_set_free(context);
1671                 return bset;
1672         }
1673         bset = isl_basic_set_sort_constraints(bset);
1674         aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1675         if (!aff)
1676                 goto error;
1677         if (isl_basic_set_plain_is_empty(aff)) {
1678                 isl_basic_set_free(aff);
1679                 isl_basic_set_free(context);
1680                 return bset;
1681         }
1682         if (aff->n_eq == 0) {
1683                 isl_basic_set_free(aff);
1684                 return uset_gist_full(bset, context);
1685         }
1686         total = isl_basic_set_total_dim(bset);
1687         eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1688         eq = isl_mat_cow(eq);
1689         T = isl_mat_variable_compression(eq, &T2);
1690         if (T && T->n_col == 0) {
1691                 isl_mat_free(T);
1692                 isl_mat_free(T2);
1693                 isl_basic_set_free(context);
1694                 isl_basic_set_free(aff);
1695                 return isl_basic_set_set_to_empty(bset);
1696         }
1697
1698         aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1699
1700         bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1701         context = isl_basic_set_preimage(context, T);
1702
1703         bset = uset_gist_full(bset, context);
1704         bset = isl_basic_set_preimage(bset, T2);
1705         bset = isl_basic_set_intersect(bset, aff);
1706         bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1707
1708         if (bset) {
1709                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1710                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1711         }
1712
1713         return bset;
1714 error:
1715         isl_basic_set_free(bset);
1716         isl_basic_set_free(context);
1717         return NULL;
1718 }
1719
1720 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1721  * We simply add the equalities in context to bmap and then do a regular
1722  * div normalizations.  Better results can be obtained by normalizing
1723  * only the divs in bmap than do not also appear in context.
1724  * We need to be careful to reduce the divs using the equalities
1725  * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1726  * spurious constraints.
1727  */
1728 static struct isl_basic_map *normalize_divs_in_context(
1729         struct isl_basic_map *bmap, struct isl_basic_map *context)
1730 {
1731         int i;
1732         unsigned total_context;
1733         int div_eq;
1734
1735         div_eq = n_pure_div_eq(bmap);
1736         if (div_eq == 0)
1737                 return bmap;
1738
1739         if (context->n_div > 0)
1740                 bmap = isl_basic_map_align_divs(bmap, context);
1741
1742         total_context = isl_basic_map_total_dim(context);
1743         bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1744         for (i = 0; i < context->n_eq; ++i) {
1745                 int k;
1746                 k = isl_basic_map_alloc_equality(bmap);
1747                 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1748                 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1749                                 isl_basic_map_total_dim(bmap) - total_context);
1750         }
1751         bmap = isl_basic_map_gauss(bmap, NULL);
1752         bmap = normalize_divs(bmap, NULL);
1753         bmap = isl_basic_map_gauss(bmap, NULL);
1754         return bmap;
1755 }
1756
1757 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1758         struct isl_basic_map *context)
1759 {
1760         struct isl_basic_set *bset;
1761
1762         if (!bmap || !context)
1763                 goto error;
1764
1765         if (isl_basic_map_is_universe(bmap)) {
1766                 isl_basic_map_free(context);
1767                 return bmap;
1768         }
1769         if (isl_basic_map_plain_is_empty(context)) {
1770                 isl_space *dim = isl_space_copy(bmap->dim);
1771                 isl_basic_map_free(context);
1772                 isl_basic_map_free(bmap);
1773                 return isl_basic_map_universe(dim);
1774         }
1775         if (isl_basic_map_plain_is_empty(bmap)) {
1776                 isl_basic_map_free(context);
1777                 return bmap;
1778         }
1779
1780         bmap = isl_basic_map_remove_redundancies(bmap);
1781         context = isl_basic_map_remove_redundancies(context);
1782
1783         if (context->n_eq)
1784                 bmap = normalize_divs_in_context(bmap, context);
1785
1786         context = isl_basic_map_align_divs(context, bmap);
1787         bmap = isl_basic_map_align_divs(bmap, context);
1788
1789         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1790                          isl_basic_map_underlying_set(context));
1791
1792         return isl_basic_map_overlying_set(bset, bmap);
1793 error:
1794         isl_basic_map_free(bmap);
1795         isl_basic_map_free(context);
1796         return NULL;
1797 }
1798
1799 /*
1800  * Assumes context has no implicit divs.
1801  */
1802 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1803         __isl_take isl_basic_map *context)
1804 {
1805         int i;
1806
1807         if (!map || !context)
1808                 goto error;;
1809
1810         if (isl_basic_map_plain_is_empty(context)) {
1811                 isl_space *dim = isl_space_copy(map->dim);
1812                 isl_basic_map_free(context);
1813                 isl_map_free(map);
1814                 return isl_map_universe(dim);
1815         }
1816
1817         context = isl_basic_map_remove_redundancies(context);
1818         map = isl_map_cow(map);
1819         if (!map || !context)
1820                 goto error;;
1821         isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error);
1822         map = isl_map_compute_divs(map);
1823         for (i = 0; i < map->n; ++i)
1824                 context = isl_basic_map_align_divs(context, map->p[i]);
1825         for (i = map->n - 1; i >= 0; --i) {
1826                 map->p[i] = isl_basic_map_gist(map->p[i],
1827                                                 isl_basic_map_copy(context));
1828                 if (!map->p[i])
1829                         goto error;
1830                 if (isl_basic_map_plain_is_empty(map->p[i])) {
1831                         isl_basic_map_free(map->p[i]);
1832                         if (i != map->n - 1)
1833                                 map->p[i] = map->p[map->n - 1];
1834                         map->n--;
1835                 }
1836         }
1837         isl_basic_map_free(context);
1838         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1839         return map;
1840 error:
1841         isl_map_free(map);
1842         isl_basic_map_free(context);
1843         return NULL;
1844 }
1845
1846 static __isl_give isl_map *map_gist(__isl_take isl_map *map,
1847         __isl_take isl_map *context)
1848 {
1849         context = isl_map_compute_divs(context);
1850         return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1851 }
1852
1853 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1854         __isl_take isl_map *context)
1855 {
1856         return isl_map_align_params_map_map_and(map, context, &map_gist);
1857 }
1858
1859 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1860                                                 struct isl_basic_set *context)
1861 {
1862         return (struct isl_basic_set *)isl_basic_map_gist(
1863                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1864 }
1865
1866 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1867         __isl_take isl_basic_set *context)
1868 {
1869         return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1870                                         (struct isl_basic_map *)context);
1871 }
1872
1873 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1874         __isl_take isl_set *context)
1875 {
1876         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1877                                         (struct isl_map *)context);
1878 }
1879
1880 __isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
1881         __isl_take isl_set *context)
1882 {
1883         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
1884         map_context = isl_map_intersect_params(map_context, context);
1885         return isl_map_gist(map, map_context);
1886 }
1887
1888 __isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set,
1889         __isl_take isl_set *context)
1890 {
1891         return isl_map_gist_params(set, context);
1892 }
1893
1894 /* Quick check to see if two basic maps are disjoint.
1895  * In particular, we reduce the equalities and inequalities of
1896  * one basic map in the context of the equalities of the other
1897  * basic map and check if we get a contradiction.
1898  */
1899 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
1900         __isl_keep isl_basic_map *bmap2)
1901 {
1902         struct isl_vec *v = NULL;
1903         int *elim = NULL;
1904         unsigned total;
1905         int i;
1906
1907         if (!bmap1 || !bmap2)
1908                 return -1;
1909         isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
1910                         return -1);
1911         if (bmap1->n_div || bmap2->n_div)
1912                 return 0;
1913         if (!bmap1->n_eq && !bmap2->n_eq)
1914                 return 0;
1915
1916         total = isl_space_dim(bmap1->dim, isl_dim_all);
1917         if (total == 0)
1918                 return 0;
1919         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1920         if (!v)
1921                 goto error;
1922         elim = isl_alloc_array(bmap1->ctx, int, total);
1923         if (!elim)
1924                 goto error;
1925         compute_elimination_index(bmap1, elim);
1926         for (i = 0; i < bmap2->n_eq; ++i) {
1927                 int reduced;
1928                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1929                                                         bmap1, elim);
1930                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1931                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1932                         goto disjoint;
1933         }
1934         for (i = 0; i < bmap2->n_ineq; ++i) {
1935                 int reduced;
1936                 reduced = reduced_using_equalities(v->block.data,
1937                                                 bmap2->ineq[i], bmap1, elim);
1938                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1939                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1940                         goto disjoint;
1941         }
1942         compute_elimination_index(bmap2, elim);
1943         for (i = 0; i < bmap1->n_ineq; ++i) {
1944                 int reduced;
1945                 reduced = reduced_using_equalities(v->block.data,
1946                                                 bmap1->ineq[i], bmap2, elim);
1947                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1948                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1949                         goto disjoint;
1950         }
1951         isl_vec_free(v);
1952         free(elim);
1953         return 0;
1954 disjoint:
1955         isl_vec_free(v);
1956         free(elim);
1957         return 1;
1958 error:
1959         isl_vec_free(v);
1960         free(elim);
1961         return -1;
1962 }
1963
1964 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
1965         __isl_keep isl_basic_set *bset2)
1966 {
1967         return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
1968                                               (struct isl_basic_map *)bset2);
1969 }
1970
1971 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
1972         __isl_keep isl_map *map2)
1973 {
1974         int i, j;
1975
1976         if (!map1 || !map2)
1977                 return -1;
1978
1979         if (isl_map_plain_is_equal(map1, map2))
1980                 return 0;
1981
1982         for (i = 0; i < map1->n; ++i) {
1983                 for (j = 0; j < map2->n; ++j) {
1984                         int d = isl_basic_map_plain_is_disjoint(map1->p[i],
1985                                                                map2->p[j]);
1986                         if (d != 1)
1987                                 return d;
1988                 }
1989         }
1990         return 1;
1991 }
1992
1993 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1994         __isl_keep isl_set *set2)
1995 {
1996         return isl_map_plain_is_disjoint((struct isl_map *)set1,
1997                                         (struct isl_map *)set2);
1998 }
1999
2000 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
2001 {
2002         return isl_set_plain_is_disjoint(set1, set2);
2003 }
2004
2005 /* Check if we can combine a given div with lower bound l and upper
2006  * bound u with some other div and if so return that other div.
2007  * Otherwise return -1.
2008  *
2009  * We first check that
2010  *      - the bounds are opposites of each other (except for the constant
2011  *        term)
2012  *      - the bounds do not reference any other div
2013  *      - no div is defined in terms of this div
2014  *
2015  * Let m be the size of the range allowed on the div by the bounds.
2016  * That is, the bounds are of the form
2017  *
2018  *      e <= a <= e + m - 1
2019  *
2020  * with e some expression in the other variables.
2021  * We look for another div b such that no third div is defined in terms
2022  * of this second div b and such that in any constraint that contains
2023  * a (except for the given lower and upper bound), also contains b
2024  * with a coefficient that is m times that of b.
2025  * That is, all constraints (execpt for the lower and upper bound)
2026  * are of the form
2027  *
2028  *      e + f (a + m b) >= 0
2029  *
2030  * If so, we return b so that "a + m b" can be replaced by
2031  * a single div "c = a + m b".
2032  */
2033 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2034         unsigned div, unsigned l, unsigned u)
2035 {
2036         int i, j;
2037         unsigned dim;
2038         int coalesce = -1;
2039
2040         if (bmap->n_div <= 1)
2041                 return -1;
2042         dim = isl_space_dim(bmap->dim, isl_dim_all);
2043         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2044                 return -1;
2045         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2046                                    bmap->n_div - div - 1) != -1)
2047                 return -1;
2048         if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2049                             dim + bmap->n_div))
2050                 return -1;
2051
2052         for (i = 0; i < bmap->n_div; ++i) {
2053                 if (isl_int_is_zero(bmap->div[i][0]))
2054                         continue;
2055                 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2056                         return -1;
2057         }
2058
2059         isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2060         if (isl_int_is_neg(bmap->ineq[l][0])) {
2061                 isl_int_sub(bmap->ineq[l][0],
2062                             bmap->ineq[l][0], bmap->ineq[u][0]);
2063                 bmap = isl_basic_map_copy(bmap);
2064                 bmap = isl_basic_map_set_to_empty(bmap);
2065                 isl_basic_map_free(bmap);
2066                 return -1;
2067         }
2068         isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2069         for (i = 0; i < bmap->n_div; ++i) {
2070                 if (i == div)
2071                         continue;
2072                 if (!pairs[i])
2073                         continue;
2074                 for (j = 0; j < bmap->n_div; ++j) {
2075                         if (isl_int_is_zero(bmap->div[j][0]))
2076                                 continue;
2077                         if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2078                                 break;
2079                 }
2080                 if (j < bmap->n_div)
2081                         continue;
2082                 for (j = 0; j < bmap->n_ineq; ++j) {
2083                         int valid;
2084                         if (j == l || j == u)
2085                                 continue;
2086                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2087                                 continue;
2088                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2089                                 break;
2090                         isl_int_mul(bmap->ineq[j][1 + dim + div],
2091                                     bmap->ineq[j][1 + dim + div],
2092                                     bmap->ineq[l][0]);
2093                         valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2094                                            bmap->ineq[j][1 + dim + i]);
2095                         isl_int_divexact(bmap->ineq[j][1 + dim + div],
2096                                          bmap->ineq[j][1 + dim + div],
2097                                          bmap->ineq[l][0]);
2098                         if (!valid)
2099                                 break;
2100                 }
2101                 if (j < bmap->n_ineq)
2102                         continue;
2103                 coalesce = i;
2104                 break;
2105         }
2106         isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2107         isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2108         return coalesce;
2109 }
2110
2111 /* Given a lower and an upper bound on div i, construct an inequality
2112  * that when nonnegative ensures that this pair of bounds always allows
2113  * for an integer value of the given div.
2114  * The lower bound is inequality l, while the upper bound is inequality u.
2115  * The constructed inequality is stored in ineq.
2116  * g, fl, fu are temporary scalars.
2117  *
2118  * Let the upper bound be
2119  *
2120  *      -n_u a + e_u >= 0
2121  *
2122  * and the lower bound
2123  *
2124  *      n_l a + e_l >= 0
2125  *
2126  * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2127  * We have
2128  *
2129  *      - f_u e_l <= f_u f_l g a <= f_l e_u
2130  *
2131  * Since all variables are integer valued, this is equivalent to
2132  *
2133  *      - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2134  *
2135  * If this interval is at least f_u f_l g, then it contains at least
2136  * one integer value for a.
2137  * That is, the test constraint is
2138  *
2139  *      f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2140  */
2141 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2142         int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2143 {
2144         unsigned dim;
2145         dim = isl_space_dim(bmap->dim, isl_dim_all);
2146
2147         isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2148         isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2149         isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2150         isl_int_neg(fu, fu);
2151         isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2152                         1 + dim + bmap->n_div);
2153         isl_int_add(ineq[0], ineq[0], fl);
2154         isl_int_add(ineq[0], ineq[0], fu);
2155         isl_int_sub_ui(ineq[0], ineq[0], 1);
2156         isl_int_mul(g, g, fl);
2157         isl_int_mul(g, g, fu);
2158         isl_int_sub(ineq[0], ineq[0], g);
2159 }
2160
2161 /* Remove more kinds of divs that are not strictly needed.
2162  * In particular, if all pairs of lower and upper bounds on a div
2163  * are such that they allow at least one integer value of the div,
2164  * the we can eliminate the div using Fourier-Motzkin without
2165  * introducing any spurious solutions.
2166  */
2167 static struct isl_basic_map *drop_more_redundant_divs(
2168         struct isl_basic_map *bmap, int *pairs, int n)
2169 {
2170         struct isl_tab *tab = NULL;
2171         struct isl_vec *vec = NULL;
2172         unsigned dim;
2173         int remove = -1;
2174         isl_int g, fl, fu;
2175
2176         isl_int_init(g);
2177         isl_int_init(fl);
2178         isl_int_init(fu);
2179
2180         if (!bmap)
2181                 goto error;
2182
2183         dim = isl_space_dim(bmap->dim, isl_dim_all);
2184         vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2185         if (!vec)
2186                 goto error;
2187
2188         tab = isl_tab_from_basic_map(bmap);
2189
2190         while (n > 0) {
2191                 int i, l, u;
2192                 int best = -1;
2193                 enum isl_lp_result res;
2194
2195                 for (i = 0; i < bmap->n_div; ++i) {
2196                         if (!pairs[i])
2197                                 continue;
2198                         if (best >= 0 && pairs[best] <= pairs[i])
2199                                 continue;
2200                         best = i;
2201                 }
2202
2203                 i = best;
2204                 for (l = 0; l < bmap->n_ineq; ++l) {
2205                         if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2206                                 continue;
2207                         for (u = 0; u < bmap->n_ineq; ++u) {
2208                                 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2209                                         continue;
2210                                 construct_test_ineq(bmap, i, l, u,
2211                                                     vec->el, g, fl, fu);
2212                                 res = isl_tab_min(tab, vec->el,
2213                                                   bmap->ctx->one, &g, NULL, 0);
2214                                 if (res == isl_lp_error)
2215                                         goto error;
2216                                 if (res == isl_lp_empty) {
2217                                         bmap = isl_basic_map_set_to_empty(bmap);
2218                                         break;
2219                                 }
2220                                 if (res != isl_lp_ok || isl_int_is_neg(g))
2221                                         break;
2222                         }
2223                         if (u < bmap->n_ineq)
2224                                 break;
2225                 }
2226                 if (l == bmap->n_ineq) {
2227                         remove = i;
2228                         break;
2229                 }
2230                 pairs[i] = 0;
2231                 --n;
2232         }
2233
2234         isl_tab_free(tab);
2235         isl_vec_free(vec);
2236
2237         isl_int_clear(g);
2238         isl_int_clear(fl);
2239         isl_int_clear(fu);
2240
2241         free(pairs);
2242
2243         if (remove < 0)
2244                 return bmap;
2245
2246         bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2247         return isl_basic_map_drop_redundant_divs(bmap);
2248 error:
2249         free(pairs);
2250         isl_basic_map_free(bmap);
2251         isl_tab_free(tab);
2252         isl_vec_free(vec);
2253         isl_int_clear(g);
2254         isl_int_clear(fl);
2255         isl_int_clear(fu);
2256         return NULL;
2257 }
2258
2259 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2260  * and the upper bound u, div1 always occurs together with div2 in the form
2261  * (div1 + m div2), where m is the constant range on the variable div1
2262  * allowed by l and u, replace the pair div1 and div2 by a single
2263  * div that is equal to div1 + m div2.
2264  *
2265  * The new div will appear in the location that contains div2.
2266  * We need to modify all constraints that contain
2267  * div2 = (div - div1) / m
2268  * (If a constraint does not contain div2, it will also not contain div1.)
2269  * If the constraint also contains div1, then we know they appear
2270  * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2271  * i.e., the coefficient of div is f.
2272  *
2273  * Otherwise, we first need to introduce div1 into the constraint.
2274  * Let the l be
2275  *
2276  *      div1 + f >=0
2277  *
2278  * and u
2279  *
2280  *      -div1 + f' >= 0
2281  *
2282  * A lower bound on div2
2283  *
2284  *      n div2 + t >= 0
2285  *
2286  * can be replaced by
2287  *
2288  *      (n * (m div 2 + div1) + m t + n f)/g >= 0
2289  *
2290  * with g = gcd(m,n).
2291  * An upper bound
2292  *
2293  *      -n div2 + t >= 0
2294  *
2295  * can be replaced by
2296  *
2297  *      (-n * (m div2 + div1) + m t + n f')/g >= 0
2298  *
2299  * These constraint are those that we would obtain from eliminating
2300  * div1 using Fourier-Motzkin.
2301  *
2302  * After all constraints have been modified, we drop the lower and upper
2303  * bound and then drop div1.
2304  */
2305 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2306         unsigned div1, unsigned div2, unsigned l, unsigned u)
2307 {
2308         isl_int a;
2309         isl_int b;
2310         isl_int m;
2311         unsigned dim, total;
2312         int i;
2313
2314         dim = isl_space_dim(bmap->dim, isl_dim_all);
2315         total = 1 + dim + bmap->n_div;
2316
2317         isl_int_init(a);
2318         isl_int_init(b);
2319         isl_int_init(m);
2320         isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2321         isl_int_add_ui(m, m, 1);
2322
2323         for (i = 0; i < bmap->n_ineq; ++i) {
2324                 if (i == l || i == u)
2325                         continue;
2326                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2327                         continue;
2328                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2329                         isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2330                         isl_int_divexact(a, m, b);
2331                         isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2332                         if (isl_int_is_pos(b)) {
2333                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2334                                                 b, bmap->ineq[l], total);
2335                         } else {
2336                                 isl_int_neg(b, b);
2337                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2338                                                 b, bmap->ineq[u], total);
2339                         }
2340                 }
2341                 isl_int_set(bmap->ineq[i][1 + dim + div2],
2342                             bmap->ineq[i][1 + dim + div1]);
2343                 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2344         }
2345
2346         isl_int_clear(a);
2347         isl_int_clear(b);
2348         isl_int_clear(m);
2349         if (l > u) {
2350                 isl_basic_map_drop_inequality(bmap, l);
2351                 isl_basic_map_drop_inequality(bmap, u);
2352         } else {
2353                 isl_basic_map_drop_inequality(bmap, u);
2354                 isl_basic_map_drop_inequality(bmap, l);
2355         }
2356         bmap = isl_basic_map_drop_div(bmap, div1);
2357         return bmap;
2358 }
2359
2360 /* First check if we can coalesce any pair of divs and
2361  * then continue with dropping more redundant divs.
2362  *
2363  * We loop over all pairs of lower and upper bounds on a div
2364  * with coefficient 1 and -1, respectively, check if there
2365  * is any other div "c" with which we can coalesce the div
2366  * and if so, perform the coalescing.
2367  */
2368 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2369         struct isl_basic_map *bmap, int *pairs, int n)
2370 {
2371         int i, l, u;
2372         unsigned dim;
2373
2374         dim = isl_space_dim(bmap->dim, isl_dim_all);
2375
2376         for (i = 0; i < bmap->n_div; ++i) {
2377                 if (!pairs[i])
2378                         continue;
2379                 for (l = 0; l < bmap->n_ineq; ++l) {
2380                         if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2381                                 continue;
2382                         for (u = 0; u < bmap->n_ineq; ++u) {
2383                                 int c;
2384
2385                                 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2386                                         continue;
2387                                 c = div_find_coalesce(bmap, pairs, i, l, u);
2388                                 if (c < 0)
2389                                         continue;
2390                                 free(pairs);
2391                                 bmap = coalesce_divs(bmap, i, c, l, u);
2392                                 return isl_basic_map_drop_redundant_divs(bmap);
2393                         }
2394                 }
2395         }
2396
2397         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2398                 return bmap;
2399
2400         return drop_more_redundant_divs(bmap, pairs, n);
2401 }
2402
2403 /* Remove divs that are not strictly needed.
2404  * In particular, if a div only occurs positively (or negatively)
2405  * in constraints, then it can simply be dropped.
2406  * Also, if a div occurs only occurs in two constraints and if moreover
2407  * those two constraints are opposite to each other, except for the constant
2408  * term and if the sum of the constant terms is such that for any value
2409  * of the other values, there is always at least one integer value of the
2410  * div, i.e., if one plus this sum is greater than or equal to
2411  * the (absolute value) of the coefficent of the div in the constraints,
2412  * then we can also simply drop the div.
2413  *
2414  * If any divs are left after these simple checks then we move on
2415  * to more complicated cases in drop_more_redundant_divs.
2416  */
2417 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2418         struct isl_basic_map *bmap)
2419 {
2420         int i, j;
2421         unsigned off;
2422         int *pairs = NULL;
2423         int n = 0;
2424
2425         if (!bmap)
2426                 goto error;
2427
2428         off = isl_space_dim(bmap->dim, isl_dim_all);
2429         pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2430         if (!pairs)
2431                 goto error;
2432
2433         for (i = 0; i < bmap->n_div; ++i) {
2434                 int pos, neg;
2435                 int last_pos, last_neg;
2436                 int redundant;
2437                 int defined;
2438
2439                 defined = !isl_int_is_zero(bmap->div[i][0]);
2440                 for (j = 0; j < bmap->n_eq; ++j)
2441                         if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2442                                 break;
2443                 if (j < bmap->n_eq)
2444                         continue;
2445                 ++n;
2446                 pos = neg = 0;
2447                 for (j = 0; j < bmap->n_ineq; ++j) {
2448                         if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2449                                 last_pos = j;
2450                                 ++pos;
2451                         }
2452                         if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2453                                 last_neg = j;
2454                                 ++neg;
2455                         }
2456                 }
2457                 pairs[i] = pos * neg;
2458                 if (pairs[i] == 0) {
2459                         for (j = bmap->n_ineq - 1; j >= 0; --j)
2460                                 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2461                                         isl_basic_map_drop_inequality(bmap, j);
2462                         bmap = isl_basic_map_drop_div(bmap, i);
2463                         free(pairs);
2464                         return isl_basic_map_drop_redundant_divs(bmap);
2465                 }
2466                 if (pairs[i] != 1)
2467                         continue;
2468                 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2469                                     bmap->ineq[last_neg] + 1,
2470                                     off + bmap->n_div))
2471                         continue;
2472
2473                 isl_int_add(bmap->ineq[last_pos][0],
2474                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2475                 isl_int_add_ui(bmap->ineq[last_pos][0],
2476                                bmap->ineq[last_pos][0], 1);
2477                 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2478                                 bmap->ineq[last_pos][1+off+i]);
2479                 isl_int_sub_ui(bmap->ineq[last_pos][0],
2480                                bmap->ineq[last_pos][0], 1);
2481                 isl_int_sub(bmap->ineq[last_pos][0],
2482                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2483                 if (!redundant) {
2484                         if (defined ||
2485                             !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2486                                 pairs[i] = 0;
2487                                 --n;
2488                                 continue;
2489                         }
2490                         bmap = set_div_from_lower_bound(bmap, i, last_pos);
2491                         bmap = isl_basic_map_simplify(bmap);
2492                         free(pairs);
2493                         return isl_basic_map_drop_redundant_divs(bmap);
2494                 }
2495                 if (last_pos > last_neg) {
2496                         isl_basic_map_drop_inequality(bmap, last_pos);
2497                         isl_basic_map_drop_inequality(bmap, last_neg);
2498                 } else {
2499                         isl_basic_map_drop_inequality(bmap, last_neg);
2500                         isl_basic_map_drop_inequality(bmap, last_pos);
2501                 }
2502                 bmap = isl_basic_map_drop_div(bmap, i);
2503                 free(pairs);
2504                 return isl_basic_map_drop_redundant_divs(bmap);
2505         }
2506
2507         if (n > 0)
2508                 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2509
2510         free(pairs);
2511         return bmap;
2512 error:
2513         free(pairs);
2514         isl_basic_map_free(bmap);
2515         return NULL;
2516 }
2517
2518 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2519         struct isl_basic_set *bset)
2520 {
2521         return (struct isl_basic_set *)
2522             isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2523 }
2524
2525 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2526 {
2527         int i;
2528
2529         if (!map)
2530                 return NULL;
2531         for (i = 0; i < map->n; ++i) {
2532                 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2533                 if (!map->p[i])
2534                         goto error;
2535         }
2536         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2537         return map;
2538 error:
2539         isl_map_free(map);
2540         return NULL;
2541 }
2542
2543 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2544 {
2545         return (struct isl_set *)
2546             isl_map_drop_redundant_divs((struct isl_map *)set);
2547 }