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