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         if (!pos)
 858                 goto error;
 859         /* We have to be careful because dropping equalities may reorder them */
 860         dropped = 0;
 861         for (j = bmap->n_div - 1; j >= 0; --j) {
 862                 for (i = 0; i < bmap->n_eq; ++i)
 863                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 864                                 break;
 865                 if (i < bmap->n_eq) {
 866                         bmap = isl_basic_map_drop_div(bmap, j);
 867                         isl_basic_map_drop_equality(bmap, i);
 868                         ++dropped;
 869                 }
 870         }
 871         pos[0] = 0;
 872         needed = 0;
 873         for (i = 1; i < T->n_row; ++i) {
 874                 if (isl_int_is_one(T->row[i][i]))
 875                         pos[i] = i;
 876                 else
 877                         needed++;
 878         }
 879         if (needed > dropped) {
 880                 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
 881                                 needed, needed, 0);
 882                 if (!bmap)
 883                         goto error;
 884         }
 885         for (i = 1; i < T->n_row; ++i) {
 886                 if (isl_int_is_one(T->row[i][i]))
 887                         continue;
 888                 k = isl_basic_map_alloc_div(bmap);
 889                 pos[i] = 1 + total + k;
 890                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 891                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 892                 if (C2)
 893                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 894                 else
 895                         isl_int_set_si(bmap->div[k][1 + i], 1);
 896                 for (j = 0; j < i; ++j) {
 897                         if (isl_int_is_zero(T->row[i][j]))
 898                                 continue;
 899                         if (pos[j] < T->n_row && C2)
 900                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 901                                                 C2->row[pos[j]], 1 + total);
 902                         else
 903                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 904                                                                 T->row[i][j]);
 905                 }
 906                 j = isl_basic_map_alloc_equality(bmap);
 907                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 908                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 909         }
 910         free(pos);
 911         isl_mat_free(C2);
 912         isl_mat_free(T);
 913
 914         if (progress)
 915                 *progress = 1;
 916 done:
 917         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 918
 919         return bmap;
 920 error:
 921         isl_mat_free(C);
 922         isl_mat_free(C2);
 923         isl_mat_free(T);
 924         return bmap;
 925 }
 926
 927 static struct isl_basic_map *set_div_from_lower_bound(
 928         struct isl_basic_map *bmap, int div, int ineq)
 929 {
 930         unsigned total = 1 + isl_dim_total(bmap->dim);
 931
 932         isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
 933         isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
 934         isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
 935         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
 936         isl_int_set_si(bmap->div[div][1 + total + div], 0);
 937
 938         return bmap;
 939 }
 940
 941 /* Check whether it is ok to define a div based on an inequality.
 942  * To avoid the introduction of circular definitions of divs, we
 943  * do not allow such a definition if the resulting expression would refer to
 944  * any other undefined divs or if any known div is defined in
 945  * terms of the unknown div.
 946  */
 947 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
 948         int div, int ineq)
 949 {
 950         int j;
 951         unsigned total = 1 + isl_dim_total(bmap->dim);
 952
 953         /* Not defined in terms of unknown divs */
 954         for (j = 0; j < bmap->n_div; ++j) {
 955                 if (div == j)
 956                         continue;
 957                 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
 958                         continue;
 959                 if (isl_int_is_zero(bmap->div[j][0]))
 960                         return 0;
 961         }
 962
 963         /* No other div defined in terms of this one => avoid loops */
 964         for (j = 0; j < bmap->n_div; ++j) {
 965                 if (div == j)
 966                         continue;
 967                 if (isl_int_is_zero(bmap->div[j][0]))
 968                         continue;
 969                 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
 970                         return 0;
 971         }
 972
 973         return 1;
 974 }
 975
 976 /* Given two constraints "k" and "l" that are opposite to each other,
 977  * except for the constant term, check if we can use them
 978  * to obtain an expression for one of the hitherto unknown divs.
 979  * "sum" is the sum of the constant terms of the constraints.
 980  * If this sum is strictly smaller than the coefficient of one
 981  * of the divs, then this pair can be used define the div.
 982  * To avoid the introduction of circular definitions of divs, we
 983  * do not use the pair if the resulting expression would refer to
 984  * any other undefined divs or if any known div is defined in
 985  * terms of the unknown div.
 986  */
 987 static struct isl_basic_map *check_for_div_constraints(
 988         struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
 989 {
 990         int i;
 991         unsigned total = 1 + isl_dim_total(bmap->dim);
 992
 993         for (i = 0; i < bmap->n_div; ++i) {
 994                 if (!isl_int_is_zero(bmap->div[i][0]))
 995                         continue;
 996                 if (isl_int_is_zero(bmap->ineq[k][total + i]))
 997                         continue;
 998                 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
 999                         continue;
1000                 if (!ok_to_set_div_from_bound(bmap, i, k))
1001                         break;
1002                 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1003                         bmap = set_div_from_lower_bound(bmap, i, k);
1004                 else
1005                         bmap = set_div_from_lower_bound(bmap, i, l);
1006                 if (progress)
1007                         *progress = 1;
1008                 break;
1009         }
1010         return bmap;
1011 }
1012
1013 static struct isl_basic_map *remove_duplicate_constraints(
1014         struct isl_basic_map *bmap, int *progress)
1015 {
1016         unsigned int size;
1017         isl_int ***index;
1018         int k, l, h;
1019         int bits;
1020         unsigned total = isl_basic_map_total_dim(bmap);
1021         isl_int sum;
1022
1023         if (!bmap || bmap->n_ineq <= 1)
1024                 return bmap;
1025
1026         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1027         bits = ffs(size) - 1;
1028         index = isl_calloc_array(ctx, isl_int **, size);
1029         if (!index)
1030                 return bmap;
1031
1032         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1033         for (k = 1; k < bmap->n_ineq; ++k) {
1034                 h = hash_index(index, size, bits, bmap, k);
1035                 if (!index[h]) {
1036                         index[h] = &bmap->ineq[k];
1037                         continue;
1038                 }
1039                 if (progress)
1040                         *progress = 1;
1041                 l = index[h] - &bmap->ineq[0];
1042                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1043                         swap_inequality(bmap, k, l);
1044                 isl_basic_map_drop_inequality(bmap, k);
1045                 --k;
1046         }
1047         isl_int_init(sum);
1048         for (k = 0; k < bmap->n_ineq-1; ++k) {
1049                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1050                 h = hash_index(index, size, bits, bmap, k);
1051                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1052                 if (!index[h])
1053                         continue;
1054                 l = index[h] - &bmap->ineq[0];
1055                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1056                 if (isl_int_is_pos(sum)) {
1057                         bmap = check_for_div_constraints(bmap, k, l, sum,
1058                                                          progress);
1059                         continue;
1060                 }
1061                 if (isl_int_is_zero(sum)) {
1062                         /* We need to break out of the loop after these
1063                          * changes since the contents of the hash
1064                          * will no longer be valid.
1065                          * Plus, we probably we want to regauss first.
1066                          */
1067                         if (progress)
1068                                 *progress = 1;
1069                         isl_basic_map_drop_inequality(bmap, l);
1070                         isl_basic_map_inequality_to_equality(bmap, k);
1071                 } else
1072                         bmap = isl_basic_map_set_to_empty(bmap);
1073                 break;
1074         }
1075         isl_int_clear(sum);
1076
1077         free(index);
1078         return bmap;
1079 }
1080
1081
1082 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1083 {
1084         int progress = 1;
1085         if (!bmap)
1086                 return NULL;
1087         while (progress) {
1088                 progress = 0;
1089                 bmap = isl_basic_map_normalize_constraints(bmap);
1090                 bmap = remove_duplicate_divs(bmap, &progress);
1091                 bmap = eliminate_divs_eq(bmap, &progress);
1092                 bmap = eliminate_divs_ineq(bmap, &progress);
1093                 bmap = isl_basic_map_gauss(bmap, &progress);
1094                 /* requires equalities in normal form */
1095                 bmap = normalize_divs(bmap, &progress);
1096                 bmap = remove_duplicate_constraints(bmap, &progress);
1097         }
1098         return bmap;
1099 }
1100
1101 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1102 {
1103         return (struct isl_basic_set *)
1104                 isl_basic_map_simplify((struct isl_basic_map *)bset);
1105 }
1106
1107
1108 /* If the only constraints a div d=floor(f/m)
1109  * appears in are its two defining constraints
1110  *
1111  *      f - m d >=0
1112  *      -(f - (m - 1)) + m d >= 0
1113  *
1114  * then it can safely be removed.
1115  */
1116 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1117 {
1118         int i;
1119         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1120
1121         for (i = 0; i < bmap->n_eq; ++i)
1122                 if (!isl_int_is_zero(bmap->eq[i][pos]))
1123                         return 0;
1124
1125         for (i = 0; i < bmap->n_ineq; ++i) {
1126                 if (isl_int_is_zero(bmap->ineq[i][pos]))
1127                         continue;
1128                 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1129                         int neg;
1130                         isl_int_sub(bmap->div[div][1],
1131                                         bmap->div[div][1], bmap->div[div][0]);
1132                         isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1133                         neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
1134                         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1135                         isl_int_add(bmap->div[div][1],
1136                                         bmap->div[div][1], bmap->div[div][0]);
1137                         if (!neg)
1138                                 return 0;
1139                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1140                                                     bmap->n_div-div-1) != -1)
1141                                 return 0;
1142                 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1143                         if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
1144                                 return 0;
1145                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1146                                                     bmap->n_div-div-1) != -1)
1147                                 return 0;
1148                 } else
1149                         return 0;
1150         }
1151
1152         for (i = 0; i < bmap->n_div; ++i)
1153                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1154                         return 0;
1155
1156         return 1;
1157 }
1158
1159 /*
1160  * Remove divs that don't occur in any of the constraints or other divs.
1161  * These can arise when dropping some of the variables in a quast
1162  * returned by piplib.
1163  */
1164 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1165 {
1166         int i;
1167
1168         if (!bmap)
1169                 return NULL;
1170
1171         for (i = bmap->n_div-1; i >= 0; --i) {
1172                 if (!div_is_redundant(bmap, i))
1173                         continue;
1174                 bmap = isl_basic_map_drop_div(bmap, i);
1175         }
1176         return bmap;
1177 }
1178
1179 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1180 {
1181         bmap = remove_redundant_divs(bmap);
1182         if (!bmap)
1183                 return NULL;
1184         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1185         return bmap;
1186 }
1187
1188 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1189 {
1190         return (struct isl_basic_set *)
1191                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1192 }
1193
1194 struct isl_set *isl_set_finalize(struct isl_set *set)
1195 {
1196         int i;
1197
1198         if (!set)
1199                 return NULL;
1200         for (i = 0; i < set->n; ++i) {
1201                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1202                 if (!set->p[i])
1203                         goto error;
1204         }
1205         return set;
1206 error:
1207         isl_set_free(set);
1208         return NULL;
1209 }
1210
1211 struct isl_map *isl_map_finalize(struct isl_map *map)
1212 {
1213         int i;
1214
1215         if (!map)
1216                 return NULL;
1217         for (i = 0; i < map->n; ++i) {
1218                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1219                 if (!map->p[i])
1220                         goto error;
1221         }
1222         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1223         return map;
1224 error:
1225         isl_map_free(map);
1226         return NULL;
1227 }
1228
1229
1230 /* Remove definition of any div that is defined in terms of the given variable.
1231  * The div itself is not removed.  Functions such as
1232  * eliminate_divs_ineq depend on the other divs remaining in place.
1233  */
1234 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1235                                                                         int pos)
1236 {
1237         int i;
1238
1239         for (i = 0; i < bmap->n_div; ++i) {
1240                 if (isl_int_is_zero(bmap->div[i][0]))
1241                         continue;
1242                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1243                         continue;
1244                 isl_int_set_si(bmap->div[i][0], 0);
1245         }
1246         return bmap;
1247 }
1248
1249 /* Eliminate the specified variables from the constraints using
1250  * Fourier-Motzkin.  The variables themselves are not removed.
1251  */
1252 struct isl_basic_map *isl_basic_map_eliminate_vars(
1253         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1254 {
1255         int d;
1256         int i, j, k;
1257         unsigned total;
1258
1259         if (n == 0)
1260                 return bmap;
1261         if (!bmap)
1262                 return NULL;
1263         total = isl_basic_map_total_dim(bmap);
1264
1265         bmap = isl_basic_map_cow(bmap);
1266         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1267                 bmap = remove_dependent_vars(bmap, d);
1268
1269         for (d = pos + n - 1;
1270              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1271                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1272         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1273                 int n_lower, n_upper;
1274                 if (!bmap)
1275                         return NULL;
1276                 for (i = 0; i < bmap->n_eq; ++i) {
1277                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1278                                 continue;
1279                         eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1280                         isl_basic_map_drop_equality(bmap, i);
1281                         break;
1282                 }
1283                 if (i < bmap->n_eq)
1284                         continue;
1285                 n_lower = 0;
1286                 n_upper = 0;
1287                 for (i = 0; i < bmap->n_ineq; ++i) {
1288                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1289                                 n_lower++;
1290                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1291                                 n_upper++;
1292                 }
1293                 bmap = isl_basic_map_extend_constraints(bmap,
1294                                 0, n_lower * n_upper);
1295                 if (!bmap)
1296                         goto error;
1297                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1298                         int last;
1299                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1300                                 continue;
1301                         last = -1;
1302                         for (j = 0; j < i; ++j) {
1303                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1304                                         continue;
1305                                 last = j;
1306                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1307                                     isl_int_sgn(bmap->ineq[j][1+d]))
1308                                         continue;
1309                                 k = isl_basic_map_alloc_inequality(bmap);
1310                                 if (k < 0)
1311                                         goto error;
1312                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1313                                                 1+total);
1314                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1315                                                 1+d, 1+total, NULL);
1316                         }
1317                         isl_basic_map_drop_inequality(bmap, i);
1318                         i = last + 1;
1319                 }
1320                 if (n_lower > 0 && n_upper > 0) {
1321                         bmap = isl_basic_map_normalize_constraints(bmap);
1322                         bmap = remove_duplicate_constraints(bmap, NULL);
1323                         bmap = isl_basic_map_gauss(bmap, NULL);
1324                         bmap = isl_basic_map_convex_hull(bmap);
1325                         if (!bmap)
1326                                 goto error;
1327                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1328                                 break;
1329                 }
1330         }
1331         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1332         return bmap;
1333 error:
1334         isl_basic_map_free(bmap);
1335         return NULL;
1336 }
1337
1338 struct isl_basic_set *isl_basic_set_eliminate_vars(
1339         struct isl_basic_set *bset, unsigned pos, unsigned n)
1340 {
1341         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1342                         (struct isl_basic_map *)bset, pos, n);
1343 }
1344
1345 /* Don't assume equalities are in order, because align_divs
1346  * may have changed the order of the divs.
1347  */
1348 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1349 {
1350         int d, i;
1351         unsigned total;
1352
1353         total = isl_dim_total(bmap->dim);
1354         for (d = 0; d < total; ++d)
1355                 elim[d] = -1;
1356         for (i = 0; i < bmap->n_eq; ++i) {
1357                 for (d = total - 1; d >= 0; --d) {
1358                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1359                                 continue;
1360                         elim[d] = i;
1361                         break;
1362                 }
1363         }
1364 }
1365
1366 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1367 {
1368         compute_elimination_index((struct isl_basic_map *)bset, elim);
1369 }
1370
1371 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1372         struct isl_basic_map *bmap, int *elim)
1373 {
1374         int d;
1375         int copied = 0;
1376         unsigned total;
1377
1378         total = isl_dim_total(bmap->dim);
1379         for (d = total - 1; d >= 0; --d) {
1380                 if (isl_int_is_zero(src[1+d]))
1381                         continue;
1382                 if (elim[d] == -1)
1383                         continue;
1384                 if (!copied) {
1385                         isl_seq_cpy(dst, src, 1 + total);
1386                         copied = 1;
1387                 }
1388                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1389         }
1390         return copied;
1391 }
1392
1393 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1394         struct isl_basic_set *bset, int *elim)
1395 {
1396         return reduced_using_equalities(dst, src,
1397                                         (struct isl_basic_map *)bset, elim);
1398 }
1399
1400 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1401         struct isl_basic_set *bset, struct isl_basic_set *context)
1402 {
1403         int i;
1404         int *elim;
1405
1406         if (!bset || !context)
1407                 goto error;
1408
1409         if (context->n_eq == 0) {
1410                 isl_basic_set_free(context);
1411                 return bset;
1412         }
1413
1414         bset = isl_basic_set_cow(bset);
1415         if (!bset)
1416                 goto error;
1417
1418         elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1419         if (!elim)
1420                 goto error;
1421         set_compute_elimination_index(context, elim);
1422         for (i = 0; i < bset->n_eq; ++i)
1423                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1424                                                         context, elim);
1425         for (i = 0; i < bset->n_ineq; ++i)
1426                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1427                                                         context, elim);
1428         isl_basic_set_free(context);
1429         free(elim);
1430         bset = isl_basic_set_simplify(bset);
1431         bset = isl_basic_set_finalize(bset);
1432         return bset;
1433 error:
1434         isl_basic_set_free(bset);
1435         isl_basic_set_free(context);
1436         return NULL;
1437 }
1438
1439 static struct isl_basic_set *remove_shifted_constraints(
1440         struct isl_basic_set *bset, struct isl_basic_set *context)
1441 {
1442         unsigned int size;
1443         isl_int ***index;
1444         int bits;
1445         int k, h, l;
1446
1447         if (!bset)
1448                 return NULL;
1449
1450         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1451         bits = ffs(size) - 1;
1452         index = isl_calloc_array(ctx, isl_int **, size);
1453         if (!index)
1454                 return bset;
1455
1456         for (k = 0; k < context->n_ineq; ++k) {
1457                 h = set_hash_index(index, size, bits, context, k);
1458                 index[h] = &context->ineq[k];
1459         }
1460         for (k = 0; k < bset->n_ineq; ++k) {
1461                 h = set_hash_index(index, size, bits, bset, k);
1462                 if (!index[h])
1463                         continue;
1464                 l = index[h] - &context->ineq[0];
1465                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1466                         continue;
1467                 bset = isl_basic_set_cow(bset);
1468                 if (!bset)
1469                         goto error;
1470                 isl_basic_set_drop_inequality(bset, k);
1471                 --k;
1472         }
1473         free(index);
1474         return bset;
1475 error:
1476         free(index);
1477         return bset;
1478 }
1479
1480 /* Tighten (decrease) the constant terms of the inequalities based
1481  * on the equalities, without removing any integer points.
1482  * For example, if there is an equality
1483  *
1484  *              i = 3 * j
1485  *
1486  * and an inequality
1487  *
1488  *              i >= 1
1489  *
1490  * then we want to replace the inequality by
1491  *
1492  *              i >= 3
1493  *
1494  * We do this by computing a variable compression and translating
1495  * the constraints to the compressed space.
1496  * If any constraint has coefficients (except the contant term)
1497  * with a common factor "f", then we can replace the constant term "c"
1498  * by
1499  *
1500  *              f * floor(c/f)
1501  *
1502  * That is, we add
1503  *
1504  *              f * floor(c/f) - c = -fract(c/f)
1505  *
1506  * and we can add the same value to the original constraint.
1507  *
1508  * In the example, the compressed space only contains "j",
1509  * and the inequality translates to
1510  *
1511  *              3 * j - 1 >= 0
1512  *
1513  * We add -fract(-1/3) = -2 to the original constraint to obtain
1514  *
1515  *              i - 3 >= 0
1516  */
1517 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1518         struct isl_basic_set *bset)
1519 {
1520         int i;
1521         unsigned total;
1522         struct isl_mat *B, *C;
1523         isl_int gcd;
1524
1525         if (!bset)
1526                 return NULL;
1527
1528         if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1529                 return bset;
1530
1531         if (!bset->n_ineq)
1532                 return bset;
1533
1534         bset = isl_basic_set_cow(bset);
1535         if (!bset)
1536                 return NULL;
1537
1538         total = isl_basic_set_total_dim(bset);
1539         B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1540         C = isl_mat_variable_compression(B, NULL);
1541         if (!C)
1542                 return bset;
1543         if (C->n_col == 0) {
1544                 isl_mat_free(C);
1545                 return isl_basic_set_set_to_empty(bset);
1546         }
1547         B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1548                                                 0, bset->n_ineq, 0, 1 + total);
1549         C = isl_mat_product(B, C);
1550         if (!C)
1551                 return bset;
1552
1553         isl_int_init(gcd);
1554         for (i = 0; i < bset->n_ineq; ++i) {
1555                 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1556                 if (isl_int_is_one(gcd))
1557                         continue;
1558                 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1559                 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1560         }
1561         isl_int_clear(gcd);
1562
1563         isl_mat_free(C);
1564
1565         return bset;
1566 }
1567
1568 /* Remove all information from bset that is redundant in the context
1569  * of context.  Both bset and context are assumed to be full-dimensional.
1570  *
1571  * We first * remove the inequalities from "bset"
1572  * that are obviously redundant with respect to some inequality in "context".
1573  *
1574  * If there are any inequalities left, we construct a tableau for
1575  * the context and then add the inequalities of "bset".
1576  * Before adding these inequalities, we freeze all constraints such that
1577  * they won't be considered redundant in terms of the constraints of "bset".
1578  * Then we detect all redundant constraints (among the
1579  * constraints that weren't frozen), first by checking for redundancy in the
1580  * the tableau and then by checking if replacing a constraint by its negation
1581  * would lead to an empty set.  This last step is fairly expensive
1582  * and could be optimized by more reuse of the tableau.
1583  * Finally, we update bset according to the results.
1584  */
1585 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1586         __isl_take isl_basic_set *context)
1587 {
1588         int i, k;
1589         isl_basic_set *combined = NULL;
1590         struct isl_tab *tab = NULL;
1591         unsigned context_ineq;
1592         unsigned total;
1593
1594         if (!bset || !context)
1595                 goto error;
1596
1597         if (isl_basic_set_is_universe(bset)) {
1598                 isl_basic_set_free(context);
1599                 return bset;
1600         }
1601
1602         if (isl_basic_set_is_universe(context)) {
1603                 isl_basic_set_free(context);
1604                 return bset;
1605         }
1606
1607         bset = remove_shifted_constraints(bset, context);
1608         if (!bset)
1609                 goto error;
1610         if (bset->n_ineq == 0)
1611                 goto done;
1612
1613         context_ineq = context->n_ineq;
1614         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1615         combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1616         tab = isl_tab_from_basic_set(combined);
1617         for (i = 0; i < context_ineq; ++i)
1618                 if (isl_tab_freeze_constraint(tab, i) < 0)
1619                         goto error;
1620         tab = isl_tab_extend(tab, bset->n_ineq);
1621         for (i = 0; i < bset->n_ineq; ++i)
1622                 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1623                         goto error;
1624         bset = isl_basic_set_add_constraints(combined, bset, 0);
1625         combined = NULL;
1626         if (!bset)
1627                 goto error;
1628         if (isl_tab_detect_redundant(tab) < 0)
1629                 goto error;
1630         total = isl_basic_set_total_dim(bset);
1631         for (i = context_ineq; i < bset->n_ineq; ++i) {
1632                 int is_empty;
1633                 if (tab->con[i].is_redundant)
1634                         continue;
1635                 tab->con[i].is_redundant = 1;
1636                 combined = isl_basic_set_dup(bset);
1637                 combined = isl_basic_set_update_from_tab(combined, tab);
1638                 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1639                 k = isl_basic_set_alloc_inequality(combined);
1640                 if (k < 0)
1641                         goto error;
1642                 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1643                 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1644                 is_empty = isl_basic_set_is_empty(combined);
1645                 if (is_empty < 0)
1646                         goto error;
1647                 isl_basic_set_free(combined);
1648                 combined = NULL;
1649                 if (!is_empty)
1650                         tab->con[i].is_redundant = 0;
1651         }
1652         for (i = 0; i < context_ineq; ++i)
1653                 tab->con[i].is_redundant = 1;
1654         bset = isl_basic_set_update_from_tab(bset, tab);
1655         if (bset) {
1656                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1657                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1658         }
1659
1660         isl_tab_free(tab);
1661 done:
1662         bset = isl_basic_set_simplify(bset);
1663         bset = isl_basic_set_finalize(bset);
1664         isl_basic_set_free(context);
1665         return bset;
1666 error:
1667         isl_tab_free(tab);
1668         isl_basic_set_free(combined);
1669         isl_basic_set_free(context);
1670         isl_basic_set_free(bset);
1671         return NULL;
1672 }
1673
1674 /* Remove all information from bset that is redundant in the context
1675  * of context.  In particular, equalities that are linear combinations
1676  * of those in context are removed.  Then the inequalities that are
1677  * redundant in the context of the equalities and inequalities of
1678  * context are removed.
1679  *
1680  * We first compute the integer affine hull of the intersection,
1681  * compute the gist inside this affine hull and then add back
1682  * those equalities that are not implied by the context.
1683  */
1684 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1685         __isl_take isl_basic_set *context)
1686 {
1687         isl_mat *eq;
1688         isl_mat *T, *T2;
1689         isl_basic_set *aff;
1690         isl_basic_set *aff_context;
1691         unsigned total;
1692
1693         if (!bset || !context)
1694                 goto error;
1695
1696         bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1697         if (isl_basic_set_fast_is_empty(bset)) {
1698                 isl_basic_set_free(context);
1699                 return bset;
1700         }
1701         aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1702         if (!aff)
1703                 goto error;
1704         if (isl_basic_set_fast_is_empty(aff)) {
1705                 isl_basic_set_free(aff);
1706                 isl_basic_set_free(context);
1707                 return bset;
1708         }
1709         if (aff->n_eq == 0) {
1710                 isl_basic_set_free(aff);
1711                 return uset_gist_full(bset, context);
1712         }
1713         total = isl_basic_set_total_dim(bset);
1714         eq = isl_mat_sub_alloc(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1715         eq = isl_mat_cow(eq);
1716         T = isl_mat_variable_compression(eq, &T2);
1717         if (T && T->n_col == 0) {
1718                 isl_mat_free(T);
1719                 isl_mat_free(T2);
1720                 isl_basic_set_free(context);
1721                 isl_basic_set_free(aff);
1722                 return isl_basic_set_set_to_empty(bset);
1723         }
1724
1725         aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1726
1727         bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1728         context = isl_basic_set_preimage(context, T);
1729
1730         bset = uset_gist_full(bset, context);
1731         bset = isl_basic_set_preimage(bset, T2);
1732         bset = isl_basic_set_intersect(bset, aff);
1733         bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1734
1735         if (bset) {
1736                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1737                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1738         }
1739
1740         return bset;
1741 error:
1742         isl_basic_set_free(bset);
1743         isl_basic_set_free(context);
1744         return NULL;
1745 }
1746
1747 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1748  * We simply add the equalities in context to bmap and then do a regular
1749  * div normalizations.  Better results can be obtained by normalizing
1750  * only the divs in bmap than do not also appear in context.
1751  * We need to be careful to reduce the divs using the equalities
1752  * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1753  * spurious constraints.
1754  */
1755 static struct isl_basic_map *normalize_divs_in_context(
1756         struct isl_basic_map *bmap, struct isl_basic_map *context)
1757 {
1758         int i;
1759         unsigned total_context;
1760         int div_eq;
1761
1762         div_eq = n_pure_div_eq(bmap);
1763         if (div_eq == 0)
1764                 return bmap;
1765
1766         if (context->n_div > 0)
1767                 bmap = isl_basic_map_align_divs(bmap, context);
1768
1769         total_context = isl_basic_map_total_dim(context);
1770         bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1771         for (i = 0; i < context->n_eq; ++i) {
1772                 int k;
1773                 k = isl_basic_map_alloc_equality(bmap);
1774                 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1775                 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1776                                 isl_basic_map_total_dim(bmap) - total_context);
1777         }
1778         bmap = isl_basic_map_gauss(bmap, NULL);
1779         bmap = normalize_divs(bmap, NULL);
1780         bmap = isl_basic_map_gauss(bmap, NULL);
1781         return bmap;
1782 }
1783
1784 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1785         struct isl_basic_map *context)
1786 {
1787         struct isl_basic_set *bset;
1788
1789         if (!bmap || !context)
1790                 goto error;
1791
1792         if (isl_basic_map_is_universe(context)) {
1793                 isl_basic_map_free(context);
1794                 return bmap;
1795         }
1796         if (isl_basic_map_is_universe(bmap)) {
1797                 isl_basic_map_free(context);
1798                 return bmap;
1799         }
1800         if (isl_basic_map_fast_is_empty(context)) {
1801                 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1802                 isl_basic_map_free(context);
1803                 isl_basic_map_free(bmap);
1804                 return isl_basic_map_universe(dim);
1805         }
1806         if (isl_basic_map_fast_is_empty(bmap)) {
1807                 isl_basic_map_free(context);
1808                 return bmap;
1809         }
1810
1811         bmap = isl_basic_map_convex_hull(bmap);
1812         context = isl_basic_map_convex_hull(context);
1813
1814         if (context->n_eq)
1815                 bmap = normalize_divs_in_context(bmap, context);
1816
1817         context = isl_basic_map_align_divs(context, bmap);
1818         bmap = isl_basic_map_align_divs(bmap, context);
1819
1820         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1821                          isl_basic_map_underlying_set(context));
1822
1823         return isl_basic_map_overlying_set(bset, bmap);
1824 error:
1825         isl_basic_map_free(bmap);
1826         isl_basic_map_free(context);
1827         return NULL;
1828 }
1829
1830 /*
1831  * Assumes context has no implicit divs.
1832  */
1833 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1834         __isl_take isl_basic_map *context)
1835 {
1836         int i;
1837
1838         if (!map || !context)
1839                 goto error;;
1840
1841         if (isl_basic_map_is_universe(context)) {
1842                 isl_basic_map_free(context);
1843                 return map;
1844         }
1845         if (isl_basic_map_fast_is_empty(context)) {
1846                 struct isl_dim *dim = isl_dim_copy(map->dim);
1847                 isl_basic_map_free(context);
1848                 isl_map_free(map);
1849                 return isl_map_universe(dim);
1850         }
1851
1852         context = isl_basic_map_convex_hull(context);
1853         map = isl_map_cow(map);
1854         if (!map || !context)
1855                 goto error;;
1856         isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1857         map = isl_map_compute_divs(map);
1858         for (i = 0; i < map->n; ++i)
1859                 context = isl_basic_map_align_divs(context, map->p[i]);
1860         for (i = 0; i < map->n; ++i) {
1861                 map->p[i] = isl_basic_map_gist(map->p[i],
1862                                                 isl_basic_map_copy(context));
1863                 if (!map->p[i])
1864                         goto error;
1865         }
1866         isl_basic_map_free(context);
1867         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1868         return map;
1869 error:
1870         isl_map_free(map);
1871         isl_basic_map_free(context);
1872         return NULL;
1873 }
1874
1875 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1876         __isl_take isl_map *context)
1877 {
1878         return isl_map_gist_basic_map(map, isl_map_convex_hull(context));
1879 }
1880
1881 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1882                                                 struct isl_basic_set *context)
1883 {
1884         return (struct isl_basic_set *)isl_basic_map_gist(
1885                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1886 }
1887
1888 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1889         __isl_take isl_basic_set *context)
1890 {
1891         return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1892                                         (struct isl_basic_map *)context);
1893 }
1894
1895 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1896         __isl_take isl_set *context)
1897 {
1898         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1899                                         (struct isl_map *)context);
1900 }
1901
1902 /* Quick check to see if two basic maps are disjoint.
1903  * In particular, we reduce the equalities and inequalities of
1904  * one basic map in the context of the equalities of the other
1905  * basic map and check if we get a contradiction.
1906  */
1907 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1908         struct isl_basic_map *bmap2)
1909 {
1910         struct isl_vec *v = NULL;
1911         int *elim = NULL;
1912         unsigned total;
1913         int i;
1914
1915         if (!bmap1 || !bmap2)
1916                 return -1;
1917         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1918                         return -1);
1919         if (bmap1->n_div || bmap2->n_div)
1920                 return 0;
1921         if (!bmap1->n_eq && !bmap2->n_eq)
1922                 return 0;
1923
1924         total = isl_dim_total(bmap1->dim);
1925         if (total == 0)
1926                 return 0;
1927         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1928         if (!v)
1929                 goto error;
1930         elim = isl_alloc_array(bmap1->ctx, int, total);
1931         if (!elim)
1932                 goto error;
1933         compute_elimination_index(bmap1, elim);
1934         for (i = 0; i < bmap2->n_eq; ++i) {
1935                 int reduced;
1936                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1937                                                         bmap1, elim);
1938                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1939                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1940                         goto disjoint;
1941         }
1942         for (i = 0; i < bmap2->n_ineq; ++i) {
1943                 int reduced;
1944                 reduced = reduced_using_equalities(v->block.data,
1945                                                 bmap2->ineq[i], bmap1, elim);
1946                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1947                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1948                         goto disjoint;
1949         }
1950         compute_elimination_index(bmap2, elim);
1951         for (i = 0; i < bmap1->n_ineq; ++i) {
1952                 int reduced;
1953                 reduced = reduced_using_equalities(v->block.data,
1954                                                 bmap1->ineq[i], bmap2, elim);
1955                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1956                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1957                         goto disjoint;
1958         }
1959         isl_vec_free(v);
1960         free(elim);
1961         return 0;
1962 disjoint:
1963         isl_vec_free(v);
1964         free(elim);
1965         return 1;
1966 error:
1967         isl_vec_free(v);
1968         free(elim);
1969         return -1;
1970 }
1971
1972 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1973         struct isl_basic_set *bset2)
1974 {
1975         return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1976                                               (struct isl_basic_map *)bset2);
1977 }
1978
1979 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1980 {
1981         int i, j;
1982
1983         if (!map1 || !map2)
1984                 return -1;
1985
1986         if (isl_map_fast_is_equal(map1, map2))
1987                 return 0;
1988
1989         for (i = 0; i < map1->n; ++i) {
1990                 for (j = 0; j < map2->n; ++j) {
1991                         int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1992                                                                map2->p[j]);
1993                         if (d != 1)
1994                                 return d;
1995                 }
1996         }
1997         return 1;
1998 }
1999
2000 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
2001 {
2002         return isl_map_fast_is_disjoint((struct isl_map *)set1,
2003                                         (struct isl_map *)set2);
2004 }
2005
2006 /* Check if we can combine a given div with lower bound l and upper
2007  * bound u with some other div and if so return that other div.
2008  * Otherwise return -1.
2009  *
2010  * We first check that
2011  *      - the bounds are opposites of each other (except for the constant
2012  *        term)
2013  *      - the bounds do not reference any other div
2014  *      - no div is defined in terms of this div
2015  *
2016  * Let m be the size of the range allowed on the div by the bounds.
2017  * That is, the bounds are of the form
2018  *
2019  *      e <= a <= e + m - 1
2020  *
2021  * with e some expression in the other variables.
2022  * We look for another div b such that no third div is defined in terms
2023  * of this second div b and such that in any constraint that contains
2024  * a (except for the given lower and upper bound), also contains b
2025  * with a coefficient that is m times that of b.
2026  * That is, all constraints (execpt for the lower and upper bound)
2027  * are of the form
2028  *
2029  *      e + f (a + m b) >= 0
2030  *
2031  * If so, we return b so that "a + m b" can be replaced by
2032  * a single div "c = a + m b".
2033  */
2034 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2035         unsigned div, unsigned l, unsigned u)
2036 {
2037         int i, j;
2038         unsigned dim;
2039         int coalesce = -1;
2040
2041         if (bmap->n_div <= 1)
2042                 return -1;
2043         dim = isl_dim_total(bmap->dim);
2044         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2045                 return -1;
2046         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2047                                    bmap->n_div - div - 1) != -1)
2048                 return -1;
2049         if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2050                             dim + bmap->n_div))
2051                 return -1;
2052
2053         for (i = 0; i < bmap->n_div; ++i) {
2054                 if (isl_int_is_zero(bmap->div[i][0]))
2055                         continue;
2056                 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2057                         return -1;
2058         }
2059
2060         isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2061         if (isl_int_is_neg(bmap->ineq[l][0])) {
2062                 isl_int_sub(bmap->ineq[l][0],
2063                             bmap->ineq[l][0], bmap->ineq[u][0]);
2064                 bmap = isl_basic_map_copy(bmap);
2065                 bmap = isl_basic_map_set_to_empty(bmap);
2066                 isl_basic_map_free(bmap);
2067                 return -1;
2068         }
2069         isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2070         for (i = 0; i < bmap->n_div; ++i) {
2071                 if (i == div)
2072                         continue;
2073                 if (!pairs[i])
2074                         continue;
2075                 for (j = 0; j < bmap->n_div; ++j) {
2076                         if (isl_int_is_zero(bmap->div[j][0]))
2077                                 continue;
2078                         if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2079                                 break;
2080                 }
2081                 if (j < bmap->n_div)
2082                         continue;
2083                 for (j = 0; j < bmap->n_ineq; ++j) {
2084                         int valid;
2085                         if (j == l || j == u)
2086                                 continue;
2087                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2088                                 continue;
2089                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2090                                 break;
2091                         isl_int_mul(bmap->ineq[j][1 + dim + div],
2092                                     bmap->ineq[j][1 + dim + div],
2093                                     bmap->ineq[l][0]);
2094                         valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2095                                            bmap->ineq[j][1 + dim + i]);
2096                         isl_int_divexact(bmap->ineq[j][1 + dim + div],
2097                                          bmap->ineq[j][1 + dim + div],
2098                                          bmap->ineq[l][0]);
2099                         if (!valid)
2100                                 break;
2101                 }
2102                 if (j < bmap->n_ineq)
2103                         continue;
2104                 coalesce = i;
2105                 break;
2106         }
2107         isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2108         isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2109         return coalesce;
2110 }
2111
2112 /* Given a lower and an upper bound on div i, construct an inequality
2113  * that when nonnegative ensures that this pair of bounds always allows
2114  * for an integer value of the given div.
2115  * The lower bound is inequality l, while the upper bound is inequality u.
2116  * The constructed inequality is stored in ineq.
2117  * g, fl, fu are temporary scalars.
2118  *
2119  * Let the upper bound be
2120  *
2121  *      -n_u a + e_u >= 0
2122  *
2123  * and the lower bound
2124  *
2125  *      n_l a + e_l >= 0
2126  *
2127  * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2128  * We have
2129  *
2130  *      - f_u e_l <= f_u f_l g a <= f_l e_u
2131  *
2132  * Since all variables are integer valued, this is equivalent to
2133  *
2134  *      - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2135  *
2136  * If this interval is at least f_u f_l g, then it contains at least
2137  * one integer value for a.
2138  * That is, the test constraint is
2139  *
2140  *      f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2141  */
2142 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2143         int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2144 {
2145         unsigned dim;
2146         dim = isl_dim_total(bmap->dim);
2147
2148         isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2149         isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2150         isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2151         isl_int_neg(fu, fu);
2152         isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2153                         1 + dim + bmap->n_div);
2154         isl_int_add(ineq[0], ineq[0], fl);
2155         isl_int_add(ineq[0], ineq[0], fu);
2156         isl_int_sub_ui(ineq[0], ineq[0], 1);
2157         isl_int_mul(g, g, fl);
2158         isl_int_mul(g, g, fu);
2159         isl_int_sub(ineq[0], ineq[0], g);
2160 }
2161
2162 /* Remove more kinds of divs that are not strictly needed.
2163  * In particular, if all pairs of lower and upper bounds on a div
2164  * are such that they allow at least one integer value of the div,
2165  * the we can eliminate the div using Fourier-Motzkin without
2166  * introducing any spurious solutions.
2167  */
2168 static struct isl_basic_map *drop_more_redundant_divs(
2169         struct isl_basic_map *bmap, int *pairs, int n)
2170 {
2171         struct isl_tab *tab = NULL;
2172         struct isl_vec *vec = NULL;
2173         unsigned dim;
2174         int remove = -1;
2175         isl_int g, fl, fu;
2176
2177         isl_int_init(g);
2178         isl_int_init(fl);
2179         isl_int_init(fu);
2180
2181         if (!bmap)
2182                 goto error;
2183
2184         dim = isl_dim_total(bmap->dim);
2185         vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2186         if (!vec)
2187                 goto error;
2188
2189         tab = isl_tab_from_basic_map(bmap);
2190
2191         while (n > 0) {
2192                 int i, l, u;
2193                 int best = -1;
2194                 enum isl_lp_result res;
2195
2196                 for (i = 0; i < bmap->n_div; ++i) {
2197                         if (!pairs[i])
2198                                 continue;
2199                         if (best >= 0 && pairs[best] <= pairs[i])
2200                                 continue;
2201                         best = i;
2202                 }
2203
2204                 i = best;
2205                 for (l = 0; l < bmap->n_ineq; ++l) {
2206                         if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2207                                 continue;
2208                         for (u = 0; u < bmap->n_ineq; ++u) {
2209                                 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2210                                         continue;
2211                                 construct_test_ineq(bmap, i, l, u,
2212                                                     vec->el, g, fl, fu);
2213                                 res = isl_tab_min(tab, vec->el,
2214                                                   bmap->ctx->one, &g, NULL, 0);
2215                                 if (res == isl_lp_error)
2216                                         goto error;
2217                                 if (res == isl_lp_empty) {
2218                                         bmap = isl_basic_map_set_to_empty(bmap);
2219                                         break;
2220                                 }
2221                                 if (res != isl_lp_ok || isl_int_is_neg(g))
2222                                         break;
2223                         }
2224                         if (u < bmap->n_ineq)
2225                                 break;
2226                 }
2227                 if (l == bmap->n_ineq) {
2228                         remove = i;
2229                         break;
2230                 }
2231                 pairs[i] = 0;
2232                 --n;
2233         }
2234
2235         isl_tab_free(tab);
2236         isl_vec_free(vec);
2237
2238         isl_int_clear(g);
2239         isl_int_clear(fl);
2240         isl_int_clear(fu);
2241
2242         free(pairs);
2243
2244         if (remove < 0)
2245                 return bmap;
2246
2247         bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
2248         return isl_basic_map_drop_redundant_divs(bmap);
2249 error:
2250         free(pairs);
2251         isl_basic_map_free(bmap);
2252         isl_tab_free(tab);
2253         isl_vec_free(vec);
2254         isl_int_clear(g);
2255         isl_int_clear(fl);
2256         isl_int_clear(fu);
2257         return NULL;
2258 }
2259
2260 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2261  * and the upper bound u, div1 always occurs together with div2 in the form
2262  * (div1 + m div2), where m is the constant range on the variable div1
2263  * allowed by l and u, replace the pair div1 and div2 by a single
2264  * div that is equal to div1 + m div2.
2265  *
2266  * The new div will appear in the location that contains div2.
2267  * We need to modify all constraints that contain
2268  * div2 = (div - div1) / m
2269  * (If a constraint does not contain div2, it will also not contain div1.)
2270  * If the constraint also contains div1, then we know they appear
2271  * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2272  * i.e., the coefficient of div is f.
2273  *
2274  * Otherwise, we first need to introduce div1 into the constraint.
2275  * Let the l be
2276  *
2277  *      div1 + f >=0
2278  *
2279  * and u
2280  *
2281  *      -div1 + f' >= 0
2282  *
2283  * A lower bound on div2
2284  *
2285  *      n div2 + t >= 0
2286  *
2287  * can be replaced by
2288  *
2289  *      (n * (m div 2 + div1) + m t + n f)/g >= 0
2290  *
2291  * with g = gcd(m,n).
2292  * An upper bound
2293  *
2294  *      -n div2 + t >= 0
2295  *
2296  * can be replaced by
2297  *
2298  *      (-n * (m div2 + div1) + m t + n f')/g >= 0
2299  *
2300  * These constraint are those that we would obtain from eliminating
2301  * div1 using Fourier-Motzkin.
2302  *
2303  * After all constraints have been modified, we drop the lower and upper
2304  * bound and then drop div1.
2305  */
2306 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2307         unsigned div1, unsigned div2, unsigned l, unsigned u)
2308 {
2309         isl_int a;
2310         isl_int b;
2311         isl_int m;
2312         unsigned dim, total;
2313         int i;
2314
2315         dim = isl_dim_total(bmap->dim);
2316         total = 1 + dim + bmap->n_div;
2317
2318         isl_int_init(a);
2319         isl_int_init(b);
2320         isl_int_init(m);
2321         isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2322         isl_int_add_ui(m, m, 1);
2323
2324         for (i = 0; i < bmap->n_ineq; ++i) {
2325                 if (i == l || i == u)
2326                         continue;
2327                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2328                         continue;
2329                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2330                         isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2331                         isl_int_divexact(a, m, b);
2332                         isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2333                         if (isl_int_is_pos(b)) {
2334                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2335                                                 b, bmap->ineq[l], total);
2336                         } else {
2337                                 isl_int_neg(b, b);
2338                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2339                                                 b, bmap->ineq[u], total);
2340                         }
2341                 }
2342                 isl_int_set(bmap->ineq[i][1 + dim + div2],
2343                             bmap->ineq[i][1 + dim + div1]);
2344                 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2345         }
2346
2347         isl_int_clear(a);
2348         isl_int_clear(b);
2349         isl_int_clear(m);
2350         if (l > u) {
2351                 isl_basic_map_drop_inequality(bmap, l);
2352                 isl_basic_map_drop_inequality(bmap, u);
2353         } else {
2354                 isl_basic_map_drop_inequality(bmap, u);
2355                 isl_basic_map_drop_inequality(bmap, l);
2356         }
2357         bmap = isl_basic_map_drop_div(bmap, div1);
2358         return bmap;
2359 }
2360
2361 /* First check if we can coalesce any pair of divs and
2362  * then continue with dropping more redundant divs.
2363  *
2364  * We loop over all pairs of lower and upper bounds on a div
2365  * with coefficient 1 and -1, respectively, check if there
2366  * is any other div "c" with which we can coalesce the div
2367  * and if so, perform the coalescing.
2368  */
2369 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2370         struct isl_basic_map *bmap, int *pairs, int n)
2371 {
2372         int i, l, u;
2373         unsigned dim;
2374
2375         dim = isl_dim_total(bmap->dim);
2376
2377         for (i = 0; i < bmap->n_div; ++i) {
2378                 if (!pairs[i])
2379                         continue;
2380                 for (l = 0; l < bmap->n_ineq; ++l) {
2381                         if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2382                                 continue;
2383                         for (u = 0; u < bmap->n_ineq; ++u) {
2384                                 int c;
2385
2386                                 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2387                                         continue;
2388                                 c = div_find_coalesce(bmap, pairs, i, l, u);
2389                                 if (c < 0)
2390                                         continue;
2391                                 free(pairs);
2392                                 bmap = coalesce_divs(bmap, i, c, l, u);
2393                                 return isl_basic_map_drop_redundant_divs(bmap);
2394                         }
2395                 }
2396         }
2397
2398         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2399                 return bmap;
2400
2401         return drop_more_redundant_divs(bmap, pairs, n);
2402 }
2403
2404 /* Remove divs that are not strictly needed.
2405  * In particular, if a div only occurs positively (or negatively)
2406  * in constraints, then it can simply be dropped.
2407  * Also, if a div occurs only occurs in two constraints and if moreover
2408  * those two constraints are opposite to each other, except for the constant
2409  * term and if the sum of the constant terms is such that for any value
2410  * of the other values, there is always at least one integer value of the
2411  * div, i.e., if one plus this sum is greater than or equal to
2412  * the (absolute value) of the coefficent of the div in the constraints,
2413  * then we can also simply drop the div.
2414  *
2415  * If any divs are left after these simple checks then we move on
2416  * to more complicated cases in drop_more_redundant_divs.
2417  */
2418 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2419         struct isl_basic_map *bmap)
2420 {
2421         int i, j;
2422         unsigned off;
2423         int *pairs = NULL;
2424         int n = 0;
2425
2426         if (!bmap)
2427                 goto error;
2428
2429         off = isl_dim_total(bmap->dim);
2430         pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2431         if (!pairs)
2432                 goto error;
2433
2434         for (i = 0; i < bmap->n_div; ++i) {
2435                 int pos, neg;
2436                 int last_pos, last_neg;
2437                 int redundant;
2438                 int defined;
2439
2440                 defined = !isl_int_is_zero(bmap->div[i][0]);
2441                 for (j = 0; j < bmap->n_eq; ++j)
2442                         if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2443                                 break;
2444                 if (j < bmap->n_eq)
2445                         continue;
2446                 ++n;
2447                 pos = neg = 0;
2448                 for (j = 0; j < bmap->n_ineq; ++j) {
2449                         if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2450                                 last_pos = j;
2451                                 ++pos;
2452                         }
2453                         if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2454                                 last_neg = j;
2455                                 ++neg;
2456                         }
2457                 }
2458                 pairs[i] = pos * neg;
2459                 if (pairs[i] == 0) {
2460                         for (j = bmap->n_ineq - 1; j >= 0; --j)
2461                                 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2462                                         isl_basic_map_drop_inequality(bmap, j);
2463                         bmap = isl_basic_map_drop_div(bmap, i);
2464                         free(pairs);
2465                         return isl_basic_map_drop_redundant_divs(bmap);
2466                 }
2467                 if (pairs[i] != 1)
2468                         continue;
2469                 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2470                                     bmap->ineq[last_neg] + 1,
2471                                     off + bmap->n_div))
2472                         continue;
2473
2474                 isl_int_add(bmap->ineq[last_pos][0],
2475                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2476                 isl_int_add_ui(bmap->ineq[last_pos][0],
2477                                bmap->ineq[last_pos][0], 1);
2478                 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2479                                 bmap->ineq[last_pos][1+off+i]);
2480                 isl_int_sub_ui(bmap->ineq[last_pos][0],
2481                                bmap->ineq[last_pos][0], 1);
2482                 isl_int_sub(bmap->ineq[last_pos][0],
2483                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2484                 if (!redundant) {
2485                         if (defined ||
2486                             !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2487                                 pairs[i] = 0;
2488                                 --n;
2489                                 continue;
2490                         }
2491                         bmap = set_div_from_lower_bound(bmap, i, last_pos);
2492                         bmap = isl_basic_map_simplify(bmap);
2493                         free(pairs);
2494                         return isl_basic_map_drop_redundant_divs(bmap);
2495                 }
2496                 if (last_pos > last_neg) {
2497                         isl_basic_map_drop_inequality(bmap, last_pos);
2498                         isl_basic_map_drop_inequality(bmap, last_neg);
2499                 } else {
2500                         isl_basic_map_drop_inequality(bmap, last_neg);
2501                         isl_basic_map_drop_inequality(bmap, last_pos);
2502                 }
2503                 bmap = isl_basic_map_drop_div(bmap, i);
2504                 free(pairs);
2505                 return isl_basic_map_drop_redundant_divs(bmap);
2506         }
2507
2508         if (n > 0)
2509                 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2510
2511         free(pairs);
2512         return bmap;
2513 error:
2514         free(pairs);
2515         isl_basic_map_free(bmap);
2516         return NULL;
2517 }
2518
2519 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2520         struct isl_basic_set *bset)
2521 {
2522         return (struct isl_basic_set *)
2523             isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2524 }
2525
2526 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2527 {
2528         int i;
2529
2530         if (!map)
2531                 return NULL;
2532         for (i = 0; i < map->n; ++i) {
2533                 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2534                 if (!map->p[i])
2535                         goto error;
2536         }
2537         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2538         return map;
2539 error:
2540         isl_map_free(map);
2541         return NULL;
2542 }
2543
2544 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2545 {
2546         return (struct isl_set *)
2547             isl_map_drop_redundant_divs((struct isl_map *)set);
2548 }