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