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 int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set *bset,
1150         isl_int *constraint, unsigned div)
1151 {
1152         return isl_basic_map_is_div_constraint(bset, constraint, div);
1153 }
1154
1155
1156 /* If the only constraints a div d=floor(f/m)
1157  * appears in are its two defining constraints
1158  *
1159  *      f - m d >=0
1160  *      -(f - (m - 1)) + m d >= 0
1161  *
1162  * then it can safely be removed.
1163  */
1164 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1165 {
1166         int i;
1167         unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1168
1169         for (i = 0; i < bmap->n_eq; ++i)
1170                 if (!isl_int_is_zero(bmap->eq[i][pos]))
1171                         return 0;
1172
1173         for (i = 0; i < bmap->n_ineq; ++i) {
1174                 if (isl_int_is_zero(bmap->ineq[i][pos]))
1175                         continue;
1176                 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1177                         return 0;
1178         }
1179
1180         for (i = 0; i < bmap->n_div; ++i)
1181                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1182                         return 0;
1183
1184         return 1;
1185 }
1186
1187 /*
1188  * Remove divs that don't occur in any of the constraints or other divs.
1189  * These can arise when dropping some of the variables in a quast
1190  * returned by piplib.
1191  */
1192 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1193 {
1194         int i;
1195
1196         if (!bmap)
1197                 return NULL;
1198
1199         for (i = bmap->n_div-1; i >= 0; --i) {
1200                 if (!div_is_redundant(bmap, i))
1201                         continue;
1202                 bmap = isl_basic_map_drop_div(bmap, i);
1203         }
1204         return bmap;
1205 }
1206
1207 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1208 {
1209         bmap = remove_redundant_divs(bmap);
1210         if (!bmap)
1211                 return NULL;
1212         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1213         return bmap;
1214 }
1215
1216 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1217 {
1218         return (struct isl_basic_set *)
1219                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1220 }
1221
1222 struct isl_set *isl_set_finalize(struct isl_set *set)
1223 {
1224         int i;
1225
1226         if (!set)
1227                 return NULL;
1228         for (i = 0; i < set->n; ++i) {
1229                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1230                 if (!set->p[i])
1231                         goto error;
1232         }
1233         return set;
1234 error:
1235         isl_set_free(set);
1236         return NULL;
1237 }
1238
1239 struct isl_map *isl_map_finalize(struct isl_map *map)
1240 {
1241         int i;
1242
1243         if (!map)
1244                 return NULL;
1245         for (i = 0; i < map->n; ++i) {
1246                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1247                 if (!map->p[i])
1248                         goto error;
1249         }
1250         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1251         return map;
1252 error:
1253         isl_map_free(map);
1254         return NULL;
1255 }
1256
1257
1258 /* Remove definition of any div that is defined in terms of the given variable.
1259  * The div itself is not removed.  Functions such as
1260  * eliminate_divs_ineq depend on the other divs remaining in place.
1261  */
1262 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1263                                                                         int pos)
1264 {
1265         int i;
1266
1267         for (i = 0; i < bmap->n_div; ++i) {
1268                 if (isl_int_is_zero(bmap->div[i][0]))
1269                         continue;
1270                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1271                         continue;
1272                 isl_int_set_si(bmap->div[i][0], 0);
1273         }
1274         return bmap;
1275 }
1276
1277 /* Eliminate the specified variables from the constraints using
1278  * Fourier-Motzkin.  The variables themselves are not removed.
1279  */
1280 struct isl_basic_map *isl_basic_map_eliminate_vars(
1281         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1282 {
1283         int d;
1284         int i, j, k;
1285         unsigned total;
1286         int need_gauss = 0;
1287
1288         if (n == 0)
1289                 return bmap;
1290         if (!bmap)
1291                 return NULL;
1292         total = isl_basic_map_total_dim(bmap);
1293
1294         bmap = isl_basic_map_cow(bmap);
1295         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1296                 bmap = remove_dependent_vars(bmap, d);
1297
1298         for (d = pos + n - 1;
1299              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1300                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1301         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1302                 int n_lower, n_upper;
1303                 if (!bmap)
1304                         return NULL;
1305                 for (i = 0; i < bmap->n_eq; ++i) {
1306                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1307                                 continue;
1308                         eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1309                         isl_basic_map_drop_equality(bmap, i);
1310                         need_gauss = 1;
1311                         break;
1312                 }
1313                 if (i < bmap->n_eq)
1314                         continue;
1315                 n_lower = 0;
1316                 n_upper = 0;
1317                 for (i = 0; i < bmap->n_ineq; ++i) {
1318                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1319                                 n_lower++;
1320                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1321                                 n_upper++;
1322                 }
1323                 bmap = isl_basic_map_extend_constraints(bmap,
1324                                 0, n_lower * n_upper);
1325                 if (!bmap)
1326                         goto error;
1327                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1328                         int last;
1329                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1330                                 continue;
1331                         last = -1;
1332                         for (j = 0; j < i; ++j) {
1333                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1334                                         continue;
1335                                 last = j;
1336                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1337                                     isl_int_sgn(bmap->ineq[j][1+d]))
1338                                         continue;
1339                                 k = isl_basic_map_alloc_inequality(bmap);
1340                                 if (k < 0)
1341                                         goto error;
1342                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1343                                                 1+total);
1344                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1345                                                 1+d, 1+total, NULL);
1346                         }
1347                         isl_basic_map_drop_inequality(bmap, i);
1348                         i = last + 1;
1349                 }
1350                 if (n_lower > 0 && n_upper > 0) {
1351                         bmap = isl_basic_map_normalize_constraints(bmap);
1352                         bmap = remove_duplicate_constraints(bmap, NULL, 0);
1353                         bmap = isl_basic_map_gauss(bmap, NULL);
1354                         bmap = isl_basic_map_remove_redundancies(bmap);
1355                         need_gauss = 0;
1356                         if (!bmap)
1357                                 goto error;
1358                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1359                                 break;
1360                 }
1361         }
1362         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1363         if (need_gauss)
1364                 bmap = isl_basic_map_gauss(bmap, NULL);
1365         return bmap;
1366 error:
1367         isl_basic_map_free(bmap);
1368         return NULL;
1369 }
1370
1371 struct isl_basic_set *isl_basic_set_eliminate_vars(
1372         struct isl_basic_set *bset, unsigned pos, unsigned n)
1373 {
1374         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1375                         (struct isl_basic_map *)bset, pos, n);
1376 }
1377
1378 /* Eliminate the specified n dimensions starting at first from the
1379  * constraints, without removing the dimensions from the space.
1380  * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1381  * Otherwise, they are projected out and the original space is restored.
1382  */
1383 __isl_give isl_basic_map *isl_basic_map_eliminate(
1384         __isl_take isl_basic_map *bmap,
1385         enum isl_dim_type type, unsigned first, unsigned n)
1386 {
1387         isl_space *space;
1388
1389         if (!bmap)
1390                 return NULL;
1391         if (n == 0)
1392                 return bmap;
1393
1394         if (first + n > isl_basic_map_dim(bmap, type))
1395                 isl_die(bmap->ctx, isl_error_invalid,
1396                         "index out of bounds", goto error);
1397
1398         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
1399                 first += isl_basic_map_offset(bmap, type) - 1;
1400                 bmap = isl_basic_map_eliminate_vars(bmap, first, n);
1401                 return isl_basic_map_finalize(bmap);
1402         }
1403
1404         space = isl_basic_map_get_space(bmap);
1405         bmap = isl_basic_map_project_out(bmap, type, first, n);
1406         bmap = isl_basic_map_insert(bmap, type, first, n);
1407         bmap = isl_basic_map_reset_space(bmap, space);
1408         return bmap;
1409 error:
1410         isl_basic_map_free(bmap);
1411         return NULL;
1412 }
1413
1414 /* Don't assume equalities are in order, because align_divs
1415  * may have changed the order of the divs.
1416  */
1417 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1418 {
1419         int d, i;
1420         unsigned total;
1421
1422         total = isl_space_dim(bmap->dim, isl_dim_all);
1423         for (d = 0; d < total; ++d)
1424                 elim[d] = -1;
1425         for (i = 0; i < bmap->n_eq; ++i) {
1426                 for (d = total - 1; d >= 0; --d) {
1427                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1428                                 continue;
1429                         elim[d] = i;
1430                         break;
1431                 }
1432         }
1433 }
1434
1435 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1436 {
1437         compute_elimination_index((struct isl_basic_map *)bset, elim);
1438 }
1439
1440 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1441         struct isl_basic_map *bmap, int *elim)
1442 {
1443         int d;
1444         int copied = 0;
1445         unsigned total;
1446
1447         total = isl_space_dim(bmap->dim, isl_dim_all);
1448         for (d = total - 1; d >= 0; --d) {
1449                 if (isl_int_is_zero(src[1+d]))
1450                         continue;
1451                 if (elim[d] == -1)
1452                         continue;
1453                 if (!copied) {
1454                         isl_seq_cpy(dst, src, 1 + total);
1455                         copied = 1;
1456                 }
1457                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1458         }
1459         return copied;
1460 }
1461
1462 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1463         struct isl_basic_set *bset, int *elim)
1464 {
1465         return reduced_using_equalities(dst, src,
1466                                         (struct isl_basic_map *)bset, elim);
1467 }
1468
1469 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1470         struct isl_basic_set *bset, struct isl_basic_set *context)
1471 {
1472         int i;
1473         int *elim;
1474
1475         if (!bset || !context)
1476                 goto error;
1477
1478         if (context->n_eq == 0) {
1479                 isl_basic_set_free(context);
1480                 return bset;
1481         }
1482
1483         bset = isl_basic_set_cow(bset);
1484         if (!bset)
1485                 goto error;
1486
1487         elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1488         if (!elim)
1489                 goto error;
1490         set_compute_elimination_index(context, elim);
1491         for (i = 0; i < bset->n_eq; ++i)
1492                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1493                                                         context, elim);
1494         for (i = 0; i < bset->n_ineq; ++i)
1495                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1496                                                         context, elim);
1497         isl_basic_set_free(context);
1498         free(elim);
1499         bset = isl_basic_set_simplify(bset);
1500         bset = isl_basic_set_finalize(bset);
1501         return bset;
1502 error:
1503         isl_basic_set_free(bset);
1504         isl_basic_set_free(context);
1505         return NULL;
1506 }
1507
1508 static struct isl_basic_set *remove_shifted_constraints(
1509         struct isl_basic_set *bset, struct isl_basic_set *context)
1510 {
1511         unsigned int size;
1512         isl_int ***index;
1513         int bits;
1514         int k, h, l;
1515         isl_ctx *ctx;
1516
1517         if (!bset)
1518                 return NULL;
1519
1520         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1521         bits = ffs(size) - 1;
1522         ctx = isl_basic_set_get_ctx(bset);
1523         index = isl_calloc_array(ctx, isl_int **, size);
1524         if (!index)
1525                 return bset;
1526
1527         for (k = 0; k < context->n_ineq; ++k) {
1528                 h = set_hash_index(index, size, bits, context, k);
1529                 index[h] = &context->ineq[k];
1530         }
1531         for (k = 0; k < bset->n_ineq; ++k) {
1532                 h = set_hash_index(index, size, bits, bset, k);
1533                 if (!index[h])
1534                         continue;
1535                 l = index[h] - &context->ineq[0];
1536                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1537                         continue;
1538                 bset = isl_basic_set_cow(bset);
1539                 if (!bset)
1540                         goto error;
1541                 isl_basic_set_drop_inequality(bset, k);
1542                 --k;
1543         }
1544         free(index);
1545         return bset;
1546 error:
1547         free(index);
1548         return bset;
1549 }
1550
1551 /* Remove all information from bset that is redundant in the context
1552  * of context.  Both bset and context are assumed to be full-dimensional.
1553  *
1554  * We first * remove the inequalities from "bset"
1555  * that are obviously redundant with respect to some inequality in "context".
1556  *
1557  * If there are any inequalities left, we construct a tableau for
1558  * the context and then add the inequalities of "bset".
1559  * Before adding these inequalities, we freeze all constraints such that
1560  * they won't be considered redundant in terms of the constraints of "bset".
1561  * Then we detect all redundant constraints (among the
1562  * constraints that weren't frozen), first by checking for redundancy in the
1563  * the tableau and then by checking if replacing a constraint by its negation
1564  * would lead to an empty set.  This last step is fairly expensive
1565  * and could be optimized by more reuse of the tableau.
1566  * Finally, we update bset according to the results.
1567  */
1568 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1569         __isl_take isl_basic_set *context)
1570 {
1571         int i, k;
1572         isl_basic_set *combined = NULL;
1573         struct isl_tab *tab = NULL;
1574         unsigned context_ineq;
1575         unsigned total;
1576
1577         if (!bset || !context)
1578                 goto error;
1579
1580         if (isl_basic_set_is_universe(bset)) {
1581                 isl_basic_set_free(context);
1582                 return bset;
1583         }
1584
1585         if (isl_basic_set_is_universe(context)) {
1586                 isl_basic_set_free(context);
1587                 return bset;
1588         }
1589
1590         bset = remove_shifted_constraints(bset, context);
1591         if (!bset)
1592                 goto error;
1593         if (bset->n_ineq == 0)
1594                 goto done;
1595
1596         context_ineq = context->n_ineq;
1597         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1598         combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1599         tab = isl_tab_from_basic_set(combined, 0);
1600         for (i = 0; i < context_ineq; ++i)
1601                 if (isl_tab_freeze_constraint(tab, i) < 0)
1602                         goto error;
1603         tab = isl_tab_extend(tab, bset->n_ineq);
1604         for (i = 0; i < bset->n_ineq; ++i)
1605                 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1606                         goto error;
1607         bset = isl_basic_set_add_constraints(combined, bset, 0);
1608         combined = NULL;
1609         if (!bset)
1610                 goto error;
1611         if (isl_tab_detect_redundant(tab) < 0)
1612                 goto error;
1613         total = isl_basic_set_total_dim(bset);
1614         for (i = context_ineq; i < bset->n_ineq; ++i) {
1615                 int is_empty;
1616                 if (tab->con[i].is_redundant)
1617                         continue;
1618                 tab->con[i].is_redundant = 1;
1619                 combined = isl_basic_set_dup(bset);
1620                 combined = isl_basic_set_update_from_tab(combined, tab);
1621                 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1622                 k = isl_basic_set_alloc_inequality(combined);
1623                 if (k < 0)
1624                         goto error;
1625                 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1626                 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1627                 is_empty = isl_basic_set_is_empty(combined);
1628                 if (is_empty < 0)
1629                         goto error;
1630                 isl_basic_set_free(combined);
1631                 combined = NULL;
1632                 if (!is_empty)
1633                         tab->con[i].is_redundant = 0;
1634         }
1635         for (i = 0; i < context_ineq; ++i)
1636                 tab->con[i].is_redundant = 1;
1637         bset = isl_basic_set_update_from_tab(bset, tab);
1638         if (bset) {
1639                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1640                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1641         }
1642
1643         isl_tab_free(tab);
1644 done:
1645         bset = isl_basic_set_simplify(bset);
1646         bset = isl_basic_set_finalize(bset);
1647         isl_basic_set_free(context);
1648         return bset;
1649 error:
1650         isl_tab_free(tab);
1651         isl_basic_set_free(combined);
1652         isl_basic_set_free(context);
1653         isl_basic_set_free(bset);
1654         return NULL;
1655 }
1656
1657 /* Remove all information from bset that is redundant in the context
1658  * of context.  In particular, equalities that are linear combinations
1659  * of those in context are removed.  Then the inequalities that are
1660  * redundant in the context of the equalities and inequalities of
1661  * context are removed.
1662  *
1663  * We first compute the integer affine hull of the intersection,
1664  * compute the gist inside this affine hull and then add back
1665  * those equalities that are not implied by the context.
1666  *
1667  * If two constraints are mutually redundant, then uset_gist_full
1668  * will remove the second of those constraints.  We therefore first
1669  * sort the constraints so that constraints not involving existentially
1670  * quantified variables are given precedence over those that do.
1671  * We have to perform this sorting before the variable compression,
1672  * because that may effect the order of the variables.
1673  */
1674 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1675         __isl_take isl_basic_set *context)
1676 {
1677         isl_mat *eq;
1678         isl_mat *T, *T2;
1679         isl_basic_set *aff;
1680         isl_basic_set *aff_context;
1681         unsigned total;
1682
1683         if (!bset || !context)
1684                 goto error;
1685
1686         bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1687         if (isl_basic_set_plain_is_empty(bset)) {
1688                 isl_basic_set_free(context);
1689                 return bset;
1690         }
1691         bset = isl_basic_set_sort_constraints(bset);
1692         aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1693         if (!aff)
1694                 goto error;
1695         if (isl_basic_set_plain_is_empty(aff)) {
1696                 isl_basic_set_free(aff);
1697                 isl_basic_set_free(context);
1698                 return bset;
1699         }
1700         if (aff->n_eq == 0) {
1701                 isl_basic_set_free(aff);
1702                 return uset_gist_full(bset, context);
1703         }
1704         total = isl_basic_set_total_dim(bset);
1705         eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1706         eq = isl_mat_cow(eq);
1707         T = isl_mat_variable_compression(eq, &T2);
1708         if (T && T->n_col == 0) {
1709                 isl_mat_free(T);
1710                 isl_mat_free(T2);
1711                 isl_basic_set_free(context);
1712                 isl_basic_set_free(aff);
1713                 return isl_basic_set_set_to_empty(bset);
1714         }
1715
1716         aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1717
1718         bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1719         context = isl_basic_set_preimage(context, T);
1720
1721         bset = uset_gist_full(bset, context);
1722         bset = isl_basic_set_preimage(bset, T2);
1723         bset = isl_basic_set_intersect(bset, aff);
1724         bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1725
1726         if (bset) {
1727                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1728                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1729         }
1730
1731         return bset;
1732 error:
1733         isl_basic_set_free(bset);
1734         isl_basic_set_free(context);
1735         return NULL;
1736 }
1737
1738 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1739  * We simply add the equalities in context to bmap and then do a regular
1740  * div normalizations.  Better results can be obtained by normalizing
1741  * only the divs in bmap than do not also appear in context.
1742  * We need to be careful to reduce the divs using the equalities
1743  * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1744  * spurious constraints.
1745  */
1746 static struct isl_basic_map *normalize_divs_in_context(
1747         struct isl_basic_map *bmap, struct isl_basic_map *context)
1748 {
1749         int i;
1750         unsigned total_context;
1751         int div_eq;
1752
1753         div_eq = n_pure_div_eq(bmap);
1754         if (div_eq == 0)
1755                 return bmap;
1756
1757         if (context->n_div > 0)
1758                 bmap = isl_basic_map_align_divs(bmap, context);
1759
1760         total_context = isl_basic_map_total_dim(context);
1761         bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1762         for (i = 0; i < context->n_eq; ++i) {
1763                 int k;
1764                 k = isl_basic_map_alloc_equality(bmap);
1765                 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1766                 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1767                                 isl_basic_map_total_dim(bmap) - total_context);
1768         }
1769         bmap = isl_basic_map_gauss(bmap, NULL);
1770         bmap = normalize_divs(bmap, NULL);
1771         bmap = isl_basic_map_gauss(bmap, NULL);
1772         return bmap;
1773 }
1774
1775 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1776         struct isl_basic_map *context)
1777 {
1778         struct isl_basic_set *bset;
1779
1780         if (!bmap || !context)
1781                 goto error;
1782
1783         if (isl_basic_map_is_universe(bmap)) {
1784                 isl_basic_map_free(context);
1785                 return bmap;
1786         }
1787         if (isl_basic_map_plain_is_empty(context)) {
1788                 isl_basic_map_free(bmap);
1789                 return context;
1790         }
1791         if (isl_basic_map_plain_is_empty(bmap)) {
1792                 isl_basic_map_free(context);
1793                 return bmap;
1794         }
1795
1796         bmap = isl_basic_map_remove_redundancies(bmap);
1797         context = isl_basic_map_remove_redundancies(context);
1798
1799         if (context->n_eq)
1800                 bmap = normalize_divs_in_context(bmap, context);
1801
1802         context = isl_basic_map_align_divs(context, bmap);
1803         bmap = isl_basic_map_align_divs(bmap, context);
1804
1805         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1806                          isl_basic_map_underlying_set(context));
1807
1808         return isl_basic_map_overlying_set(bset, bmap);
1809 error:
1810         isl_basic_map_free(bmap);
1811         isl_basic_map_free(context);
1812         return NULL;
1813 }
1814
1815 /*
1816  * Assumes context has no implicit divs.
1817  */
1818 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1819         __isl_take isl_basic_map *context)
1820 {
1821         int i;
1822
1823         if (!map || !context)
1824                 goto error;;
1825
1826         if (isl_basic_map_plain_is_empty(context)) {
1827                 isl_map_free(map);
1828                 return isl_map_from_basic_map(context);
1829         }
1830
1831         context = isl_basic_map_remove_redundancies(context);
1832         map = isl_map_cow(map);
1833         if (!map || !context)
1834                 goto error;;
1835         isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error);
1836         map = isl_map_compute_divs(map);
1837         for (i = 0; i < map->n; ++i)
1838                 context = isl_basic_map_align_divs(context, map->p[i]);
1839         for (i = map->n - 1; i >= 0; --i) {
1840                 map->p[i] = isl_basic_map_gist(map->p[i],
1841                                                 isl_basic_map_copy(context));
1842                 if (!map->p[i])
1843                         goto error;
1844                 if (isl_basic_map_plain_is_empty(map->p[i])) {
1845                         isl_basic_map_free(map->p[i]);
1846                         if (i != map->n - 1)
1847                                 map->p[i] = map->p[map->n - 1];
1848                         map->n--;
1849                 }
1850         }
1851         isl_basic_map_free(context);
1852         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1853         return map;
1854 error:
1855         isl_map_free(map);
1856         isl_basic_map_free(context);
1857         return NULL;
1858 }
1859
1860 static __isl_give isl_map *map_gist(__isl_take isl_map *map,
1861         __isl_take isl_map *context)
1862 {
1863         context = isl_map_compute_divs(context);
1864         return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1865 }
1866
1867 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1868         __isl_take isl_map *context)
1869 {
1870         return isl_map_align_params_map_map_and(map, context, &map_gist);
1871 }
1872
1873 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1874                                                 struct isl_basic_set *context)
1875 {
1876         return (struct isl_basic_set *)isl_basic_map_gist(
1877                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1878 }
1879
1880 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1881         __isl_take isl_basic_set *context)
1882 {
1883         return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1884                                         (struct isl_basic_map *)context);
1885 }
1886
1887 __isl_give isl_set *isl_set_gist_params_basic_set(__isl_take isl_set *set,
1888         __isl_take isl_basic_set *context)
1889 {
1890         isl_space *space = isl_set_get_space(set);
1891         isl_basic_set *dom_context = isl_basic_set_universe(space);
1892         dom_context = isl_basic_set_intersect_params(dom_context, context);
1893         return isl_set_gist_basic_set(set, dom_context);
1894 }
1895
1896 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1897         __isl_take isl_set *context)
1898 {
1899         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1900                                         (struct isl_map *)context);
1901 }
1902
1903 __isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map,
1904         __isl_take isl_set *context)
1905 {
1906         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
1907         map_context = isl_map_intersect_domain(map_context, context);
1908         return isl_map_gist(map, map_context);
1909 }
1910
1911 __isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map,
1912         __isl_take isl_set *context)
1913 {
1914         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
1915         map_context = isl_map_intersect_range(map_context, context);
1916         return isl_map_gist(map, map_context);
1917 }
1918
1919 __isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
1920         __isl_take isl_set *context)
1921 {
1922         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
1923         map_context = isl_map_intersect_params(map_context, context);
1924         return isl_map_gist(map, map_context);
1925 }
1926
1927 __isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set,
1928         __isl_take isl_set *context)
1929 {
1930         return isl_map_gist_params(set, context);
1931 }
1932
1933 /* Quick check to see if two basic maps are disjoint.
1934  * In particular, we reduce the equalities and inequalities of
1935  * one basic map in the context of the equalities of the other
1936  * basic map and check if we get a contradiction.
1937  */
1938 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
1939         __isl_keep isl_basic_map *bmap2)
1940 {
1941         struct isl_vec *v = NULL;
1942         int *elim = NULL;
1943         unsigned total;
1944         int i;
1945
1946         if (!bmap1 || !bmap2)
1947                 return -1;
1948         isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
1949                         return -1);
1950         if (bmap1->n_div || bmap2->n_div)
1951                 return 0;
1952         if (!bmap1->n_eq && !bmap2->n_eq)
1953                 return 0;
1954
1955         total = isl_space_dim(bmap1->dim, isl_dim_all);
1956         if (total == 0)
1957                 return 0;
1958         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1959         if (!v)
1960                 goto error;
1961         elim = isl_alloc_array(bmap1->ctx, int, total);
1962         if (!elim)
1963                 goto error;
1964         compute_elimination_index(bmap1, elim);
1965         for (i = 0; i < bmap2->n_eq; ++i) {
1966                 int reduced;
1967                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1968                                                         bmap1, elim);
1969                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1970                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1971                         goto disjoint;
1972         }
1973         for (i = 0; i < bmap2->n_ineq; ++i) {
1974                 int reduced;
1975                 reduced = reduced_using_equalities(v->block.data,
1976                                                 bmap2->ineq[i], bmap1, elim);
1977                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1978                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1979                         goto disjoint;
1980         }
1981         compute_elimination_index(bmap2, elim);
1982         for (i = 0; i < bmap1->n_ineq; ++i) {
1983                 int reduced;
1984                 reduced = reduced_using_equalities(v->block.data,
1985                                                 bmap1->ineq[i], bmap2, elim);
1986                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1987                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1988                         goto disjoint;
1989         }
1990         isl_vec_free(v);
1991         free(elim);
1992         return 0;
1993 disjoint:
1994         isl_vec_free(v);
1995         free(elim);
1996         return 1;
1997 error:
1998         isl_vec_free(v);
1999         free(elim);
2000         return -1;
2001 }
2002
2003 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
2004         __isl_keep isl_basic_set *bset2)
2005 {
2006         return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
2007                                               (struct isl_basic_map *)bset2);
2008 }
2009
2010 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
2011         __isl_keep isl_map *map2)
2012 {
2013         int i, j;
2014
2015         if (!map1 || !map2)
2016                 return -1;
2017
2018         if (isl_map_plain_is_equal(map1, map2))
2019                 return 0;
2020
2021         for (i = 0; i < map1->n; ++i) {
2022                 for (j = 0; j < map2->n; ++j) {
2023                         int d = isl_basic_map_plain_is_disjoint(map1->p[i],
2024                                                                map2->p[j]);
2025                         if (d != 1)
2026                                 return d;
2027                 }
2028         }
2029         return 1;
2030 }
2031
2032 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2033         __isl_keep isl_set *set2)
2034 {
2035         return isl_map_plain_is_disjoint((struct isl_map *)set1,
2036                                         (struct isl_map *)set2);
2037 }
2038
2039 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
2040 {
2041         return isl_set_plain_is_disjoint(set1, set2);
2042 }
2043
2044 /* Check if we can combine a given div with lower bound l and upper
2045  * bound u with some other div and if so return that other div.
2046  * Otherwise return -1.
2047  *
2048  * We first check that
2049  *      - the bounds are opposites of each other (except for the constant
2050  *        term)
2051  *      - the bounds do not reference any other div
2052  *      - no div is defined in terms of this div
2053  *
2054  * Let m be the size of the range allowed on the div by the bounds.
2055  * That is, the bounds are of the form
2056  *
2057  *      e <= a <= e + m - 1
2058  *
2059  * with e some expression in the other variables.
2060  * We look for another div b such that no third div is defined in terms
2061  * of this second div b and such that in any constraint that contains
2062  * a (except for the given lower and upper bound), also contains b
2063  * with a coefficient that is m times that of b.
2064  * That is, all constraints (execpt for the lower and upper bound)
2065  * are of the form
2066  *
2067  *      e + f (a + m b) >= 0
2068  *
2069  * If so, we return b so that "a + m b" can be replaced by
2070  * a single div "c = a + m b".
2071  */
2072 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2073         unsigned div, unsigned l, unsigned u)
2074 {
2075         int i, j;
2076         unsigned dim;
2077         int coalesce = -1;
2078
2079         if (bmap->n_div <= 1)
2080                 return -1;
2081         dim = isl_space_dim(bmap->dim, isl_dim_all);
2082         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2083                 return -1;
2084         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2085                                    bmap->n_div - div - 1) != -1)
2086                 return -1;
2087         if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2088                             dim + bmap->n_div))
2089                 return -1;
2090
2091         for (i = 0; i < bmap->n_div; ++i) {
2092                 if (isl_int_is_zero(bmap->div[i][0]))
2093                         continue;
2094                 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2095                         return -1;
2096         }
2097
2098         isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2099         if (isl_int_is_neg(bmap->ineq[l][0])) {
2100                 isl_int_sub(bmap->ineq[l][0],
2101                             bmap->ineq[l][0], bmap->ineq[u][0]);
2102                 bmap = isl_basic_map_copy(bmap);
2103                 bmap = isl_basic_map_set_to_empty(bmap);
2104                 isl_basic_map_free(bmap);
2105                 return -1;
2106         }
2107         isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2108         for (i = 0; i < bmap->n_div; ++i) {
2109                 if (i == div)
2110                         continue;
2111                 if (!pairs[i])
2112                         continue;
2113                 for (j = 0; j < bmap->n_div; ++j) {
2114                         if (isl_int_is_zero(bmap->div[j][0]))
2115                                 continue;
2116                         if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2117                                 break;
2118                 }
2119                 if (j < bmap->n_div)
2120                         continue;
2121                 for (j = 0; j < bmap->n_ineq; ++j) {
2122                         int valid;
2123                         if (j == l || j == u)
2124                                 continue;
2125                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2126                                 continue;
2127                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2128                                 break;
2129                         isl_int_mul(bmap->ineq[j][1 + dim + div],
2130                                     bmap->ineq[j][1 + dim + div],
2131                                     bmap->ineq[l][0]);
2132                         valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2133                                            bmap->ineq[j][1 + dim + i]);
2134                         isl_int_divexact(bmap->ineq[j][1 + dim + div],
2135                                          bmap->ineq[j][1 + dim + div],
2136                                          bmap->ineq[l][0]);
2137                         if (!valid)
2138                                 break;
2139                 }
2140                 if (j < bmap->n_ineq)
2141                         continue;
2142                 coalesce = i;
2143                 break;
2144         }
2145         isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2146         isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2147         return coalesce;
2148 }
2149
2150 /* Given a lower and an upper bound on div i, construct an inequality
2151  * that when nonnegative ensures that this pair of bounds always allows
2152  * for an integer value of the given div.
2153  * The lower bound is inequality l, while the upper bound is inequality u.
2154  * The constructed inequality is stored in ineq.
2155  * g, fl, fu are temporary scalars.
2156  *
2157  * Let the upper bound be
2158  *
2159  *      -n_u a + e_u >= 0
2160  *
2161  * and the lower bound
2162  *
2163  *      n_l a + e_l >= 0
2164  *
2165  * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2166  * We have
2167  *
2168  *      - f_u e_l <= f_u f_l g a <= f_l e_u
2169  *
2170  * Since all variables are integer valued, this is equivalent to
2171  *
2172  *      - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2173  *
2174  * If this interval is at least f_u f_l g, then it contains at least
2175  * one integer value for a.
2176  * That is, the test constraint is
2177  *
2178  *      f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2179  */
2180 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2181         int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2182 {
2183         unsigned dim;
2184         dim = isl_space_dim(bmap->dim, isl_dim_all);
2185
2186         isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2187         isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2188         isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2189         isl_int_neg(fu, fu);
2190         isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2191                         1 + dim + bmap->n_div);
2192         isl_int_add(ineq[0], ineq[0], fl);
2193         isl_int_add(ineq[0], ineq[0], fu);
2194         isl_int_sub_ui(ineq[0], ineq[0], 1);
2195         isl_int_mul(g, g, fl);
2196         isl_int_mul(g, g, fu);
2197         isl_int_sub(ineq[0], ineq[0], g);
2198 }
2199
2200 /* Remove more kinds of divs that are not strictly needed.
2201  * In particular, if all pairs of lower and upper bounds on a div
2202  * are such that they allow at least one integer value of the div,
2203  * the we can eliminate the div using Fourier-Motzkin without
2204  * introducing any spurious solutions.
2205  */
2206 static struct isl_basic_map *drop_more_redundant_divs(
2207         struct isl_basic_map *bmap, int *pairs, int n)
2208 {
2209         struct isl_tab *tab = NULL;
2210         struct isl_vec *vec = NULL;
2211         unsigned dim;
2212         int remove = -1;
2213         isl_int g, fl, fu;
2214
2215         isl_int_init(g);
2216         isl_int_init(fl);
2217         isl_int_init(fu);
2218
2219         if (!bmap)
2220                 goto error;
2221
2222         dim = isl_space_dim(bmap->dim, isl_dim_all);
2223         vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2224         if (!vec)
2225                 goto error;
2226
2227         tab = isl_tab_from_basic_map(bmap, 0);
2228
2229         while (n > 0) {
2230                 int i, l, u;
2231                 int best = -1;
2232                 enum isl_lp_result res;
2233
2234                 for (i = 0; i < bmap->n_div; ++i) {
2235                         if (!pairs[i])
2236                                 continue;
2237                         if (best >= 0 && pairs[best] <= pairs[i])
2238                                 continue;
2239                         best = i;
2240                 }
2241
2242                 i = best;
2243                 for (l = 0; l < bmap->n_ineq; ++l) {
2244                         if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2245                                 continue;
2246                         for (u = 0; u < bmap->n_ineq; ++u) {
2247                                 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2248                                         continue;
2249                                 construct_test_ineq(bmap, i, l, u,
2250                                                     vec->el, g, fl, fu);
2251                                 res = isl_tab_min(tab, vec->el,
2252                                                   bmap->ctx->one, &g, NULL, 0);
2253                                 if (res == isl_lp_error)
2254                                         goto error;
2255                                 if (res == isl_lp_empty) {
2256                                         bmap = isl_basic_map_set_to_empty(bmap);
2257                                         break;
2258                                 }
2259                                 if (res != isl_lp_ok || isl_int_is_neg(g))
2260                                         break;
2261                         }
2262                         if (u < bmap->n_ineq)
2263                                 break;
2264                 }
2265                 if (l == bmap->n_ineq) {
2266                         remove = i;
2267                         break;
2268                 }
2269                 pairs[i] = 0;
2270                 --n;
2271         }
2272
2273         isl_tab_free(tab);
2274         isl_vec_free(vec);
2275
2276         isl_int_clear(g);
2277         isl_int_clear(fl);
2278         isl_int_clear(fu);
2279
2280         free(pairs);
2281
2282         if (remove < 0)
2283                 return bmap;
2284
2285         bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2286         return isl_basic_map_drop_redundant_divs(bmap);
2287 error:
2288         free(pairs);
2289         isl_basic_map_free(bmap);
2290         isl_tab_free(tab);
2291         isl_vec_free(vec);
2292         isl_int_clear(g);
2293         isl_int_clear(fl);
2294         isl_int_clear(fu);
2295         return NULL;
2296 }
2297
2298 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2299  * and the upper bound u, div1 always occurs together with div2 in the form
2300  * (div1 + m div2), where m is the constant range on the variable div1
2301  * allowed by l and u, replace the pair div1 and div2 by a single
2302  * div that is equal to div1 + m div2.
2303  *
2304  * The new div will appear in the location that contains div2.
2305  * We need to modify all constraints that contain
2306  * div2 = (div - div1) / m
2307  * (If a constraint does not contain div2, it will also not contain div1.)
2308  * If the constraint also contains div1, then we know they appear
2309  * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2310  * i.e., the coefficient of div is f.
2311  *
2312  * Otherwise, we first need to introduce div1 into the constraint.
2313  * Let the l be
2314  *
2315  *      div1 + f >=0
2316  *
2317  * and u
2318  *
2319  *      -div1 + f' >= 0
2320  *
2321  * A lower bound on div2
2322  *
2323  *      n div2 + t >= 0
2324  *
2325  * can be replaced by
2326  *
2327  *      (n * (m div 2 + div1) + m t + n f)/g >= 0
2328  *
2329  * with g = gcd(m,n).
2330  * An upper bound
2331  *
2332  *      -n div2 + t >= 0
2333  *
2334  * can be replaced by
2335  *
2336  *      (-n * (m div2 + div1) + m t + n f')/g >= 0
2337  *
2338  * These constraint are those that we would obtain from eliminating
2339  * div1 using Fourier-Motzkin.
2340  *
2341  * After all constraints have been modified, we drop the lower and upper
2342  * bound and then drop div1.
2343  */
2344 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2345         unsigned div1, unsigned div2, unsigned l, unsigned u)
2346 {
2347         isl_int a;
2348         isl_int b;
2349         isl_int m;
2350         unsigned dim, total;
2351         int i;
2352
2353         dim = isl_space_dim(bmap->dim, isl_dim_all);
2354         total = 1 + dim + bmap->n_div;
2355
2356         isl_int_init(a);
2357         isl_int_init(b);
2358         isl_int_init(m);
2359         isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2360         isl_int_add_ui(m, m, 1);
2361
2362         for (i = 0; i < bmap->n_ineq; ++i) {
2363                 if (i == l || i == u)
2364                         continue;
2365                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2366                         continue;
2367                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2368                         isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2369                         isl_int_divexact(a, m, b);
2370                         isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2371                         if (isl_int_is_pos(b)) {
2372                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2373                                                 b, bmap->ineq[l], total);
2374                         } else {
2375                                 isl_int_neg(b, b);
2376                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2377                                                 b, bmap->ineq[u], total);
2378                         }
2379                 }
2380                 isl_int_set(bmap->ineq[i][1 + dim + div2],
2381                             bmap->ineq[i][1 + dim + div1]);
2382                 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2383         }
2384
2385         isl_int_clear(a);
2386         isl_int_clear(b);
2387         isl_int_clear(m);
2388         if (l > u) {
2389                 isl_basic_map_drop_inequality(bmap, l);
2390                 isl_basic_map_drop_inequality(bmap, u);
2391         } else {
2392                 isl_basic_map_drop_inequality(bmap, u);
2393                 isl_basic_map_drop_inequality(bmap, l);
2394         }
2395         bmap = isl_basic_map_drop_div(bmap, div1);
2396         return bmap;
2397 }
2398
2399 /* First check if we can coalesce any pair of divs and
2400  * then continue with dropping more redundant divs.
2401  *
2402  * We loop over all pairs of lower and upper bounds on a div
2403  * with coefficient 1 and -1, respectively, check if there
2404  * is any other div "c" with which we can coalesce the div
2405  * and if so, perform the coalescing.
2406  */
2407 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2408         struct isl_basic_map *bmap, int *pairs, int n)
2409 {
2410         int i, l, u;
2411         unsigned dim;
2412
2413         dim = isl_space_dim(bmap->dim, isl_dim_all);
2414
2415         for (i = 0; i < bmap->n_div; ++i) {
2416                 if (!pairs[i])
2417                         continue;
2418                 for (l = 0; l < bmap->n_ineq; ++l) {
2419                         if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2420                                 continue;
2421                         for (u = 0; u < bmap->n_ineq; ++u) {
2422                                 int c;
2423
2424                                 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2425                                         continue;
2426                                 c = div_find_coalesce(bmap, pairs, i, l, u);
2427                                 if (c < 0)
2428                                         continue;
2429                                 free(pairs);
2430                                 bmap = coalesce_divs(bmap, i, c, l, u);
2431                                 return isl_basic_map_drop_redundant_divs(bmap);
2432                         }
2433                 }
2434         }
2435
2436         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2437                 return bmap;
2438
2439         return drop_more_redundant_divs(bmap, pairs, n);
2440 }
2441
2442 /* Remove divs that are not strictly needed.
2443  * In particular, if a div only occurs positively (or negatively)
2444  * in constraints, then it can simply be dropped.
2445  * Also, if a div occurs only occurs in two constraints and if moreover
2446  * those two constraints are opposite to each other, except for the constant
2447  * term and if the sum of the constant terms is such that for any value
2448  * of the other values, there is always at least one integer value of the
2449  * div, i.e., if one plus this sum is greater than or equal to
2450  * the (absolute value) of the coefficent of the div in the constraints,
2451  * then we can also simply drop the div.
2452  *
2453  * If any divs are left after these simple checks then we move on
2454  * to more complicated cases in drop_more_redundant_divs.
2455  */
2456 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2457         struct isl_basic_map *bmap)
2458 {
2459         int i, j;
2460         unsigned off;
2461         int *pairs = NULL;
2462         int n = 0;
2463
2464         if (!bmap)
2465                 goto error;
2466
2467         off = isl_space_dim(bmap->dim, isl_dim_all);
2468         pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2469         if (!pairs)
2470                 goto error;
2471
2472         for (i = 0; i < bmap->n_div; ++i) {
2473                 int pos, neg;
2474                 int last_pos, last_neg;
2475                 int redundant;
2476                 int defined;
2477
2478                 defined = !isl_int_is_zero(bmap->div[i][0]);
2479                 for (j = 0; j < bmap->n_eq; ++j)
2480                         if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2481                                 break;
2482                 if (j < bmap->n_eq)
2483                         continue;
2484                 ++n;
2485                 pos = neg = 0;
2486                 for (j = 0; j < bmap->n_ineq; ++j) {
2487                         if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2488                                 last_pos = j;
2489                                 ++pos;
2490                         }
2491                         if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2492                                 last_neg = j;
2493                                 ++neg;
2494                         }
2495                 }
2496                 pairs[i] = pos * neg;
2497                 if (pairs[i] == 0) {
2498                         for (j = bmap->n_ineq - 1; j >= 0; --j)
2499                                 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2500                                         isl_basic_map_drop_inequality(bmap, j);
2501                         bmap = isl_basic_map_drop_div(bmap, i);
2502                         free(pairs);
2503                         return isl_basic_map_drop_redundant_divs(bmap);
2504                 }
2505                 if (pairs[i] != 1)
2506                         continue;
2507                 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2508                                     bmap->ineq[last_neg] + 1,
2509                                     off + bmap->n_div))
2510                         continue;
2511
2512                 isl_int_add(bmap->ineq[last_pos][0],
2513                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2514                 isl_int_add_ui(bmap->ineq[last_pos][0],
2515                                bmap->ineq[last_pos][0], 1);
2516                 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2517                                 bmap->ineq[last_pos][1+off+i]);
2518                 isl_int_sub_ui(bmap->ineq[last_pos][0],
2519                                bmap->ineq[last_pos][0], 1);
2520                 isl_int_sub(bmap->ineq[last_pos][0],
2521                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2522                 if (!redundant) {
2523                         if (defined ||
2524                             !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2525                                 pairs[i] = 0;
2526                                 --n;
2527                                 continue;
2528                         }
2529                         bmap = set_div_from_lower_bound(bmap, i, last_pos);
2530                         bmap = isl_basic_map_simplify(bmap);
2531                         free(pairs);
2532                         return isl_basic_map_drop_redundant_divs(bmap);
2533                 }
2534                 if (last_pos > last_neg) {
2535                         isl_basic_map_drop_inequality(bmap, last_pos);
2536                         isl_basic_map_drop_inequality(bmap, last_neg);
2537                 } else {
2538                         isl_basic_map_drop_inequality(bmap, last_neg);
2539                         isl_basic_map_drop_inequality(bmap, last_pos);
2540                 }
2541                 bmap = isl_basic_map_drop_div(bmap, i);
2542                 free(pairs);
2543                 return isl_basic_map_drop_redundant_divs(bmap);
2544         }
2545
2546         if (n > 0)
2547                 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2548
2549         free(pairs);
2550         return bmap;
2551 error:
2552         free(pairs);
2553         isl_basic_map_free(bmap);
2554         return NULL;
2555 }
2556
2557 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2558         struct isl_basic_set *bset)
2559 {
2560         return (struct isl_basic_set *)
2561             isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2562 }
2563
2564 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2565 {
2566         int i;
2567
2568         if (!map)
2569                 return NULL;
2570         for (i = 0; i < map->n; ++i) {
2571                 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2572                 if (!map->p[i])
2573                         goto error;
2574         }
2575         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2576         return map;
2577 error:
2578         isl_map_free(map);
2579         return NULL;
2580 }
2581
2582 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2583 {
2584         return (struct isl_set *)
2585             isl_map_drop_redundant_divs((struct isl_map *)set);
2586 }