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 #include <isl_dim_private.h>
  16
  17 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
  18 {
  19         isl_int *t = bmap->eq[a];
  20         bmap->eq[a] = bmap->eq[b];
  21         bmap->eq[b] = t;
  22 }
  23
  24 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
  25 {
  26         if (a != b) {
  27                 isl_int *t = bmap->ineq[a];
  28                 bmap->ineq[a] = bmap->ineq[b];
  29                 bmap->ineq[b] = t;
  30         }
  31 }
  32
  33 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
  34 {
  35         swap_inequality((struct isl_basic_map *)bset, a, b);
  36 }
  37
  38 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
  39 {
  40         isl_seq_cpy(c, c + n, rem);
  41         isl_seq_clr(c + rem, n);
  42 }
  43
  44 /* Drop n dimensions starting at first.
  45  *
  46  * In principle, this frees up some extra variables as the number
  47  * of columns remains constant, but we would have to extend
  48  * the div array too as the number of rows in this array is assumed
  49  * to be equal to extra.
  50  */
  51 struct isl_basic_set *isl_basic_set_drop_dims(
  52                 struct isl_basic_set *bset, unsigned first, unsigned n)
  53 {
  54         int i;
  55
  56         if (!bset)
  57                 goto error;
  58
  59         isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
  60
  61         if (n == 0 && !isl_dim_get_tuple_name(bset->dim, isl_dim_set))
  62                 return bset;
  63
  64         bset = isl_basic_set_cow(bset);
  65         if (!bset)
  66                 return NULL;
  67
  68         for (i = 0; i < bset->n_eq; ++i)
  69                 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
  70                                      (bset->dim->n_out-first-n)+bset->extra);
  71
  72         for (i = 0; i < bset->n_ineq; ++i)
  73                 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
  74                                      (bset->dim->n_out-first-n)+bset->extra);
  75
  76         for (i = 0; i < bset->n_div; ++i)
  77                 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
  78                                      (bset->dim->n_out-first-n)+bset->extra);
  79
  80         bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
  81         if (!bset->dim)
  82                 goto error;
  83
  84         ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
  85         bset = isl_basic_set_simplify(bset);
  86         return isl_basic_set_finalize(bset);
  87 error:
  88         isl_basic_set_free(bset);
  89         return NULL;
  90 }
  91
  92 struct isl_set *isl_set_drop_dims(
  93                 struct isl_set *set, unsigned first, unsigned n)
  94 {
  95         int i;
  96
  97         if (!set)
  98                 goto error;
  99
 100         isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
 101
 102         if (n == 0 && !isl_dim_get_tuple_name(set->dim, isl_dim_set))
 103                 return set;
 104         set = isl_set_cow(set);
 105         if (!set)
 106                 goto error;
 107         set->dim = isl_dim_drop_outputs(set->dim, first, n);
 108         if (!set->dim)
 109                 goto error;
 110
 111         for (i = 0; i < set->n; ++i) {
 112                 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
 113                 if (!set->p[i])
 114                         goto error;
 115         }
 116
 117         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 118         return set;
 119 error:
 120         isl_set_free(set);
 121         return NULL;
 122 }
 123
 124 /* Move "n" divs starting at "first" to the end of the list of divs.
 125  */
 126 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
 127         unsigned first, unsigned n)
 128 {
 129         isl_int **div;
 130         int i;
 131
 132         if (first + n == bmap->n_div)
 133                 return bmap;
 134
 135         div = isl_alloc_array(bmap->ctx, isl_int *, n);
 136         if (!div)
 137                 goto error;
 138         for (i = 0; i < n; ++i)
 139                 div[i] = bmap->div[first + i];
 140         for (i = 0; i < bmap->n_div - first - n; ++i)
 141                 bmap->div[first + i] = bmap->div[first + n + i];
 142         for (i = 0; i < n; ++i)
 143                 bmap->div[bmap->n_div - n + i] = div[i];
 144         free(div);
 145         return bmap;
 146 error:
 147         isl_basic_map_free(bmap);
 148         return NULL;
 149 }
 150
 151 /* Drop "n" dimensions of type "type" starting at "first".
 152  *
 153  * In principle, this frees up some extra variables as the number
 154  * of columns remains constant, but we would have to extend
 155  * the div array too as the number of rows in this array is assumed
 156  * to be equal to extra.
 157  */
 158 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
 159         enum isl_dim_type type, unsigned first, unsigned n)
 160 {
 161         int i;
 162         unsigned dim;
 163         unsigned offset;
 164         unsigned left;
 165
 166         if (!bmap)
 167                 goto error;
 168
 169         dim = isl_basic_map_dim(bmap, type);
 170         isl_assert(bmap->ctx, first + n <= dim, goto error);
 171
 172         if (n == 0 && !isl_dim_get_tuple_name(bmap->dim, type))
 173                 return bmap;
 174
 175         bmap = isl_basic_map_cow(bmap);
 176         if (!bmap)
 177                 return NULL;
 178
 179         offset = isl_basic_map_offset(bmap, type) + first;
 180         left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
 181         for (i = 0; i < bmap->n_eq; ++i)
 182                 constraint_drop_vars(bmap->eq[i]+offset, n, left);
 183
 184         for (i = 0; i < bmap->n_ineq; ++i)
 185                 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
 186
 187         for (i = 0; i < bmap->n_div; ++i)
 188                 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
 189
 190         if (type == isl_dim_div) {
 191                 bmap = move_divs_last(bmap, first, n);
 192                 if (!bmap)
 193                         goto error;
 194                 isl_basic_map_free_div(bmap, n);
 195         } else
 196                 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
 197         if (!bmap->dim)
 198                 goto error;
 199
 200         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 201         bmap = isl_basic_map_simplify(bmap);
 202         return isl_basic_map_finalize(bmap);
 203 error:
 204         isl_basic_map_free(bmap);
 205         return NULL;
 206 }
 207
 208 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
 209         enum isl_dim_type type, unsigned first, unsigned n)
 210 {
 211         return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
 212                                                         type, first, n);
 213 }
 214
 215 struct isl_basic_map *isl_basic_map_drop_inputs(
 216                 struct isl_basic_map *bmap, unsigned first, unsigned n)
 217 {
 218         return isl_basic_map_drop(bmap, isl_dim_in, first, n);
 219 }
 220
 221 struct isl_map *isl_map_drop(struct isl_map *map,
 222         enum isl_dim_type type, unsigned first, unsigned n)
 223 {
 224         int i;
 225
 226         if (!map)
 227                 goto error;
 228
 229         isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
 230
 231         if (n == 0 && !isl_dim_get_tuple_name(map->dim, type))
 232                 return map;
 233         map = isl_map_cow(map);
 234         if (!map)
 235                 goto error;
 236         map->dim = isl_dim_drop(map->dim, type, first, n);
 237         if (!map->dim)
 238                 goto error;
 239
 240         for (i = 0; i < map->n; ++i) {
 241                 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
 242                 if (!map->p[i])
 243                         goto error;
 244         }
 245         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
 246
 247         return map;
 248 error:
 249         isl_map_free(map);
 250         return NULL;
 251 }
 252
 253 struct isl_set *isl_set_drop(struct isl_set *set,
 254         enum isl_dim_type type, unsigned first, unsigned n)
 255 {
 256         return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
 257 }
 258
 259 struct isl_map *isl_map_drop_inputs(
 260                 struct isl_map *map, unsigned first, unsigned n)
 261 {
 262         return isl_map_drop(map, isl_dim_in, first, n);
 263 }
 264
 265 /*
 266  * We don't cow, as the div is assumed to be redundant.
 267  */
 268 static struct isl_basic_map *isl_basic_map_drop_div(
 269                 struct isl_basic_map *bmap, unsigned div)
 270 {
 271         int i;
 272         unsigned pos;
 273
 274         if (!bmap)
 275                 goto error;
 276
 277         pos = 1 + isl_dim_total(bmap->dim) + div;
 278
 279         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
 280
 281         for (i = 0; i < bmap->n_eq; ++i)
 282                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
 283
 284         for (i = 0; i < bmap->n_ineq; ++i) {
 285                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
 286                         isl_basic_map_drop_inequality(bmap, i);
 287                         --i;
 288                         continue;
 289                 }
 290                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
 291         }
 292
 293         for (i = 0; i < bmap->n_div; ++i)
 294                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
 295
 296         if (div != bmap->n_div - 1) {
 297                 int j;
 298                 isl_int *t = bmap->div[div];
 299
 300                 for (j = div; j < bmap->n_div - 1; ++j)
 301                         bmap->div[j] = bmap->div[j+1];
 302
 303                 bmap->div[bmap->n_div - 1] = t;
 304         }
 305         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 306         isl_basic_map_free_div(bmap, 1);
 307
 308         return bmap;
 309 error:
 310         isl_basic_map_free(bmap);
 311         return NULL;
 312 }
 313
 314 struct isl_basic_map *isl_basic_map_normalize_constraints(
 315         struct isl_basic_map *bmap)
 316 {
 317         int i;
 318         isl_int gcd;
 319         unsigned total = isl_basic_map_total_dim(bmap);
 320
 321         if (!bmap)
 322                 return NULL;
 323
 324         isl_int_init(gcd);
 325         for (i = bmap->n_eq - 1; i >= 0; --i) {
 326                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
 327                 if (isl_int_is_zero(gcd)) {
 328                         if (!isl_int_is_zero(bmap->eq[i][0])) {
 329                                 bmap = isl_basic_map_set_to_empty(bmap);
 330                                 break;
 331                         }
 332                         isl_basic_map_drop_equality(bmap, i);
 333                         continue;
 334                 }
 335                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 336                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
 337                 if (isl_int_is_one(gcd))
 338                         continue;
 339                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
 340                         bmap = isl_basic_map_set_to_empty(bmap);
 341                         break;
 342                 }
 343                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
 344         }
 345
 346         for (i = bmap->n_ineq - 1; i >= 0; --i) {
 347                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
 348                 if (isl_int_is_zero(gcd)) {
 349                         if (isl_int_is_neg(bmap->ineq[i][0])) {
 350                                 bmap = isl_basic_map_set_to_empty(bmap);
 351                                 break;
 352                         }
 353                         isl_basic_map_drop_inequality(bmap, i);
 354                         continue;
 355                 }
 356                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 357                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
 358                 if (isl_int_is_one(gcd))
 359                         continue;
 360                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
 361                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
 362         }
 363         isl_int_clear(gcd);
 364
 365         return bmap;
 366 }
 367
 368 struct isl_basic_set *isl_basic_set_normalize_constraints(
 369         struct isl_basic_set *bset)
 370 {
 371         return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
 372                 (struct isl_basic_map *)bset);
 373 }
 374
 375 /* Assumes divs have been ordered if keep_divs is set.
 376  */
 377 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
 378         unsigned pos, isl_int *eq, int keep_divs, int *progress)
 379 {
 380         unsigned total;
 381         int k;
 382         int last_div;
 383
 384         total = isl_basic_map_total_dim(bmap);
 385         last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
 386                                                 bmap->n_div);
 387         for (k = 0; k < bmap->n_eq; ++k) {
 388                 if (bmap->eq[k] == eq)
 389                         continue;
 390                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
 391                         continue;
 392                 if (progress)
 393                         *progress = 1;
 394                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
 395         }
 396
 397         for (k = 0; k < bmap->n_ineq; ++k) {
 398                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
 399                         continue;
 400                 if (progress)
 401                         *progress = 1;
 402                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
 403                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 404         }
 405
 406         for (k = 0; k < bmap->n_div; ++k) {
 407                 if (isl_int_is_zero(bmap->div[k][0]))
 408                         continue;
 409                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
 410                         continue;
 411                 if (progress)
 412                         *progress = 1;
 413                 /* We need to be careful about circular definitions,
 414                  * so for now we just remove the definition of div k
 415                  * if the equality contains any divs.
 416                  * If keep_divs is set, then the divs have been ordered
 417                  * and we can keep the definition as long as the result
 418                  * is still ordered.
 419                  */
 420                 if (last_div == -1 || (keep_divs && last_div < k))
 421                         isl_seq_elim(bmap->div[k]+1, eq,
 422                                         1+pos, 1+total, &bmap->div[k][0]);
 423                 else
 424                         isl_seq_clr(bmap->div[k], 1 + total);
 425                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 426         }
 427 }
 428
 429 /* Assumes divs have been ordered if keep_divs is set.
 430  */
 431 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
 432         unsigned div, int keep_divs)
 433 {
 434         unsigned pos = isl_dim_total(bmap->dim) + div;
 435
 436         eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
 437
 438         isl_basic_map_drop_div(bmap, div);
 439 }
 440
 441 /* Check if elimination of div "div" using equality "eq" would not
 442  * result in a div depending on a later div.
 443  */
 444 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
 445         unsigned div)
 446 {
 447         int k;
 448         int last_div;
 449         unsigned pos = isl_dim_total(bmap->dim) + div;
 450
 451         last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
 452                                                 bmap->n_div);
 453         if (last_div < 0 || last_div <= div)
 454                 return 1;
 455
 456         for (k = 0; k <= last_div; ++k) {
 457                 if (isl_int_is_zero(bmap->div[k][0]))
 458                         return 1;
 459                 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
 460                         return 0;
 461         }
 462
 463         return 1;
 464 }
 465
 466 /* Elimininate divs based on equalities
 467  */
 468 static struct isl_basic_map *eliminate_divs_eq(
 469                 struct isl_basic_map *bmap, int *progress)
 470 {
 471         int d;
 472         int i;
 473         int modified = 0;
 474         unsigned off;
 475
 476         bmap = isl_basic_map_order_divs(bmap);
 477
 478         if (!bmap)
 479                 return NULL;
 480
 481         off = 1 + isl_dim_total(bmap->dim);
 482
 483         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 484                 for (i = 0; i < bmap->n_eq; ++i) {
 485                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
 486                             !isl_int_is_negone(bmap->eq[i][off + d]))
 487                                 continue;
 488                         if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
 489                                 continue;
 490                         modified = 1;
 491                         *progress = 1;
 492                         eliminate_div(bmap, bmap->eq[i], d, 1);
 493                         isl_basic_map_drop_equality(bmap, i);
 494                         break;
 495                 }
 496         }
 497         if (modified)
 498                 return eliminate_divs_eq(bmap, progress);
 499         return bmap;
 500 }
 501
 502 /* Elimininate divs based on inequalities
 503  */
 504 static struct isl_basic_map *eliminate_divs_ineq(
 505                 struct isl_basic_map *bmap, int *progress)
 506 {
 507         int d;
 508         int i;
 509         unsigned off;
 510         struct isl_ctx *ctx;
 511
 512         if (!bmap)
 513                 return NULL;
 514
 515         ctx = bmap->ctx;
 516         off = 1 + isl_dim_total(bmap->dim);
 517
 518         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 519                 for (i = 0; i < bmap->n_eq; ++i)
 520                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
 521                                 break;
 522                 if (i < bmap->n_eq)
 523                         continue;
 524                 for (i = 0; i < bmap->n_ineq; ++i)
 525                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
 526                                 break;
 527                 if (i < bmap->n_ineq)
 528                         continue;
 529                 *progress = 1;
 530                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
 531                 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 532                         break;
 533                 bmap = isl_basic_map_drop_div(bmap, d);
 534                 if (!bmap)
 535                         break;
 536         }
 537         return bmap;
 538 }
 539
 540 struct isl_basic_map *isl_basic_map_gauss(
 541         struct isl_basic_map *bmap, int *progress)
 542 {
 543         int k;
 544         int done;
 545         int last_var;
 546         unsigned total_var;
 547         unsigned total;
 548
 549         bmap = isl_basic_map_order_divs(bmap);
 550
 551         if (!bmap)
 552                 return NULL;
 553
 554         total = isl_basic_map_total_dim(bmap);
 555         total_var = total - bmap->n_div;
 556
 557         last_var = total - 1;
 558         for (done = 0; done < bmap->n_eq; ++done) {
 559                 for (; last_var >= 0; --last_var) {
 560                         for (k = done; k < bmap->n_eq; ++k)
 561                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
 562                                         break;
 563                         if (k < bmap->n_eq)
 564                                 break;
 565                 }
 566                 if (last_var < 0)
 567                         break;
 568                 if (k != done)
 569                         swap_equality(bmap, k, done);
 570                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 571                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 572
 573                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
 574                                                 progress);
 575
 576                 if (last_var >= total_var &&
 577                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
 578                         unsigned div = last_var - total_var;
 579                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
 580                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 581                         isl_int_set(bmap->div[div][0],
 582                                     bmap->eq[done][1+last_var]);
 583                         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 584                 }
 585         }
 586         if (done == bmap->n_eq)
 587                 return bmap;
 588         for (k = done; k < bmap->n_eq; ++k) {
 589                 if (isl_int_is_zero(bmap->eq[k][0]))
 590                         continue;
 591                 return isl_basic_map_set_to_empty(bmap);
 592         }
 593         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
 594         return bmap;
 595 }
 596
 597 struct isl_basic_set *isl_basic_set_gauss(
 598         struct isl_basic_set *bset, int *progress)
 599 {
 600         return (struct isl_basic_set*)isl_basic_map_gauss(
 601                         (struct isl_basic_map *)bset, progress);
 602 }
 603
 604
 605 static unsigned int round_up(unsigned int v)
 606 {
 607         int old_v = v;
 608
 609         while (v) {
 610                 old_v = v;
 611                 v ^= v & -v;
 612         }
 613         return old_v << 1;
 614 }
 615
 616 static int hash_index(isl_int ***index, unsigned int size, int bits,
 617                         struct isl_basic_map *bmap, int k)
 618 {
 619         int h;
 620         unsigned total = isl_basic_map_total_dim(bmap);
 621         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
 622         for (h = hash; index[h]; h = (h+1) % size)
 623                 if (&bmap->ineq[k] != index[h] &&
 624                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
 625                         break;
 626         return h;
 627 }
 628
 629 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
 630                           struct isl_basic_set *bset, int k)
 631 {
 632         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
 633 }
 634
 635 /* If we can eliminate more than one div, then we need to make
 636  * sure we do it from last div to first div, in order not to
 637  * change the position of the other divs that still need to
 638  * be removed.
 639  */
 640 static struct isl_basic_map *remove_duplicate_divs(
 641         struct isl_basic_map *bmap, int *progress)
 642 {
 643         unsigned int size;
 644         int *index;
 645         int *elim_for;
 646         int k, l, h;
 647         int bits;
 648         struct isl_blk eq;
 649         unsigned total_var;
 650         unsigned total;
 651         struct isl_ctx *ctx;
 652
 653         if (!bmap || bmap->n_div <= 1)
 654                 return bmap;
 655
 656         total_var = isl_dim_total(bmap->dim);
 657         total = total_var + bmap->n_div;
 658
 659         ctx = bmap->ctx;
 660         for (k = bmap->n_div - 1; k >= 0; --k)
 661                 if (!isl_int_is_zero(bmap->div[k][0]))
 662                         break;
 663         if (k <= 0)
 664                 return bmap;
 665
 666         elim_for = isl_calloc_array(ctx, int, bmap->n_div);
 667         size = round_up(4 * bmap->n_div / 3 - 1);
 668         bits = ffs(size) - 1;
 669         index = isl_calloc_array(ctx, int, size);
 670         if (!index)
 671                 return bmap;
 672         eq = isl_blk_alloc(ctx, 1+total);
 673         if (isl_blk_is_error(eq))
 674                 goto out;
 675
 676         isl_seq_clr(eq.data, 1+total);
 677         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
 678         for (--k; k >= 0; --k) {
 679                 uint32_t hash;
 680
 681                 if (isl_int_is_zero(bmap->div[k][0]))
 682                         continue;
 683
 684                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
 685                 for (h = hash; index[h]; h = (h+1) % size)
 686                         if (isl_seq_eq(bmap->div[k],
 687                                        bmap->div[index[h]-1], 2+total))
 688                                 break;
 689                 if (index[h]) {
 690                         *progress = 1;
 691                         l = index[h] - 1;
 692                         elim_for[l] = k + 1;
 693                 }
 694                 index[h] = k+1;
 695         }
 696         for (l = bmap->n_div - 1; l >= 0; --l) {
 697                 if (!elim_for[l])
 698                         continue;
 699                 k = elim_for[l] - 1;
 700                 isl_int_set_si(eq.data[1+total_var+k], -1);
 701                 isl_int_set_si(eq.data[1+total_var+l], 1);
 702                 eliminate_div(bmap, eq.data, l, 0);
 703                 isl_int_set_si(eq.data[1+total_var+k], 0);
 704                 isl_int_set_si(eq.data[1+total_var+l], 0);
 705         }
 706
 707         isl_blk_free(ctx, eq);
 708 out:
 709         free(index);
 710         free(elim_for);
 711         return bmap;
 712 }
 713
 714 static int n_pure_div_eq(struct isl_basic_map *bmap)
 715 {
 716         int i, j;
 717         unsigned total;
 718
 719         total = isl_dim_total(bmap->dim);
 720         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 721                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 722                         --j;
 723                 if (j < 0)
 724                         break;
 725                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 726                         return 0;
 727         }
 728         return i;
 729 }
 730
 731 /* Normalize divs that appear in equalities.
 732  *
 733  * In particular, we assume that bmap contains some equalities
 734  * of the form
 735  *
 736  *      a x = m * e_i
 737  *
 738  * and we want to replace the set of e_i by a minimal set and
 739  * such that the new e_i have a canonical representation in terms
 740  * of the vector x.
 741  * If any of the equalities involves more than one divs, then
 742  * we currently simply bail out.
 743  *
 744  * Let us first additionally assume that all equalities involve
 745  * a div.  The equalities then express modulo constraints on the
 746  * remaining variables and we can use "parameter compression"
 747  * to find a minimal set of constraints.  The result is a transformation
 748  *
 749  *      x = T(x') = x_0 + G x'
 750  *
 751  * with G a lower-triangular matrix with all elements below the diagonal
 752  * non-negative and smaller than the diagonal element on the same row.
 753  * We first normalize x_0 by making the same property hold in the affine
 754  * T matrix.
 755  * The rows i of G with a 1 on the diagonal do not impose any modulo
 756  * constraint and simply express x_i = x'_i.
 757  * For each of the remaining rows i, we introduce a div and a corresponding
 758  * equality.  In particular
 759  *
 760  *      g_ii e_j = x_i - g_i(x')
 761  *
 762  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 763  * corresponding div (if g_kk != 1).
 764  *
 765  * If there are any equalities not involving any div, then we
 766  * first apply a variable compression on the variables x:
 767  *
 768  *      x = C x''       x'' = C_2 x
 769  *
 770  * and perform the above parameter compression on A C instead of on A.
 771  * The resulting compression is then of the form
 772  *
 773  *      x'' = T(x') = x_0 + G x'
 774  *
 775  * and in constructing the new divs and the corresponding equalities,
 776  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 777  * by the corresponding row from C_2.
 778  */
 779 static struct isl_basic_map *normalize_divs(
 780         struct isl_basic_map *bmap, int *progress)
 781 {
 782         int i, j, k;
 783         int total;
 784         int div_eq;
 785         struct isl_mat *B;
 786         struct isl_vec *d;
 787         struct isl_mat *T = NULL;
 788         struct isl_mat *C = NULL;
 789         struct isl_mat *C2 = NULL;
 790         isl_int v;
 791         int *pos;
 792         int dropped, needed;
 793
 794         if (!bmap)
 795                 return NULL;
 796
 797         if (bmap->n_div == 0)
 798                 return bmap;
 799
 800         if (bmap->n_eq == 0)
 801                 return bmap;
 802
 803         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 804                 return bmap;
 805
 806         total = isl_dim_total(bmap->dim);
 807         div_eq = n_pure_div_eq(bmap);
 808         if (div_eq == 0)
 809                 return bmap;
 810
 811         if (div_eq < bmap->n_eq) {
 812                 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
 813                                         bmap->n_eq - div_eq, 0, 1 + total);
 814                 C = isl_mat_variable_compression(B, &C2);
 815                 if (!C || !C2)
 816                         goto error;
 817                 if (C->n_col == 0) {
 818                         bmap = isl_basic_map_set_to_empty(bmap);
 819                         isl_mat_free(C);
 820                         isl_mat_free(C2);
 821                         goto done;
 822                 }
 823         }
 824
 825         d = isl_vec_alloc(bmap->ctx, div_eq);
 826         if (!d)
 827                 goto error;
 828         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 829                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 830                         --j;
 831                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 832         }
 833         B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 834
 835         if (C) {
 836                 B = isl_mat_product(B, C);
 837                 C = NULL;
 838         }
 839
 840         T = isl_mat_parameter_compression(B, d);
 841         if (!T)
 842                 goto error;
 843         if (T->n_col == 0) {
 844                 bmap = isl_basic_map_set_to_empty(bmap);
 845                 isl_mat_free(C2);
 846                 isl_mat_free(T);
 847                 goto done;
 848         }
 849         isl_int_init(v);
 850         for (i = 0; i < T->n_row - 1; ++i) {
 851                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 852                 if (isl_int_is_zero(v))
 853                         continue;
 854                 isl_mat_col_submul(T, 0, v, 1 + i);
 855         }
 856         isl_int_clear(v);
 857         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 858         if (!pos)
 859                 goto error;
 860         /* We have to be careful because dropping equalities may reorder them */
 861         dropped = 0;
 862         for (j = bmap->n_div - 1; j >= 0; --j) {
 863                 for (i = 0; i < bmap->n_eq; ++i)
 864                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 865                                 break;
 866                 if (i < bmap->n_eq) {
 867                         bmap = isl_basic_map_drop_div(bmap, j);
 868                         isl_basic_map_drop_equality(bmap, i);
 869                         ++dropped;
 870                 }
 871         }
 872         pos[0] = 0;
 873         needed = 0;
 874         for (i = 1; i < T->n_row; ++i) {
 875                 if (isl_int_is_one(T->row[i][i]))
 876                         pos[i] = i;
 877                 else
 878                         needed++;
 879         }
 880         if (needed > dropped) {
 881                 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
 882                                 needed, needed, 0);
 883                 if (!bmap)
 884                         goto error;
 885         }
 886         for (i = 1; i < T->n_row; ++i) {
 887                 if (isl_int_is_one(T->row[i][i]))
 888                         continue;
 889                 k = isl_basic_map_alloc_div(bmap);
 890                 pos[i] = 1 + total + k;
 891                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 892                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 893                 if (C2)
 894                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 895                 else
 896                         isl_int_set_si(bmap->div[k][1 + i], 1);
 897                 for (j = 0; j < i; ++j) {
 898                         if (isl_int_is_zero(T->row[i][j]))
 899                                 continue;
 900                         if (pos[j] < T->n_row && C2)
 901                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 902                                                 C2->row[pos[j]], 1 + total);
 903                         else
 904                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 905                                                                 T->row[i][j]);
 906                 }
 907                 j = isl_basic_map_alloc_equality(bmap);
 908                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 909                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 910         }
 911         free(pos);
 912         isl_mat_free(C2);
 913         isl_mat_free(T);
 914
 915         if (progress)
 916                 *progress = 1;
 917 done:
 918         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 919
 920         return bmap;
 921 error:
 922         isl_mat_free(C);
 923         isl_mat_free(C2);
 924         isl_mat_free(T);
 925         return bmap;
 926 }
 927
 928 static struct isl_basic_map *set_div_from_lower_bound(
 929         struct isl_basic_map *bmap, int div, int ineq)
 930 {
 931         unsigned total = 1 + isl_dim_total(bmap->dim);
 932
 933         isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
 934         isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
 935         isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
 936         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
 937         isl_int_set_si(bmap->div[div][1 + total + div], 0);
 938
 939         return bmap;
 940 }
 941
 942 /* Check whether it is ok to define a div based on an inequality.
 943  * To avoid the introduction of circular definitions of divs, we
 944  * do not allow such a definition if the resulting expression would refer to
 945  * any other undefined divs or if any known div is defined in
 946  * terms of the unknown div.
 947  */
 948 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
 949         int div, int ineq)
 950 {
 951         int j;
 952         unsigned total = 1 + isl_dim_total(bmap->dim);
 953
 954         /* Not defined in terms of unknown divs */
 955         for (j = 0; j < bmap->n_div; ++j) {
 956                 if (div == j)
 957                         continue;
 958                 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
 959                         continue;
 960                 if (isl_int_is_zero(bmap->div[j][0]))
 961                         return 0;
 962         }
 963
 964         /* No other div defined in terms of this one => avoid loops */
 965         for (j = 0; j < bmap->n_div; ++j) {
 966                 if (div == j)
 967                         continue;
 968                 if (isl_int_is_zero(bmap->div[j][0]))
 969                         continue;
 970                 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
 971                         return 0;
 972         }
 973
 974         return 1;
 975 }
 976
 977 /* Given two constraints "k" and "l" that are opposite to each other,
 978  * except for the constant term, check if we can use them
 979  * to obtain an expression for one of the hitherto unknown divs.
 980  * "sum" is the sum of the constant terms of the constraints.
 981  * If this sum is strictly smaller than the coefficient of one
 982  * of the divs, then this pair can be used define the div.
 983  * To avoid the introduction of circular definitions of divs, we
 984  * do not use the pair if the resulting expression would refer to
 985  * any other undefined divs or if any known div is defined in
 986  * terms of the unknown div.
 987  */
 988 static struct isl_basic_map *check_for_div_constraints(
 989         struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
 990 {
 991         int i;
 992         unsigned total = 1 + isl_dim_total(bmap->dim);
 993
 994         for (i = 0; i < bmap->n_div; ++i) {
 995                 if (!isl_int_is_zero(bmap->div[i][0]))
 996                         continue;
 997                 if (isl_int_is_zero(bmap->ineq[k][total + i]))
 998                         continue;
 999                 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1000                         continue;
1001                 if (!ok_to_set_div_from_bound(bmap, i, k))
1002                         break;
1003                 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1004                         bmap = set_div_from_lower_bound(bmap, i, k);
1005                 else
1006                         bmap = set_div_from_lower_bound(bmap, i, l);
1007                 if (progress)
1008                         *progress = 1;
1009                 break;
1010         }
1011         return bmap;
1012 }
1013
1014 static struct isl_basic_map *remove_duplicate_constraints(
1015         struct isl_basic_map *bmap, int *progress)
1016 {
1017         unsigned int size;
1018         isl_int ***index;
1019         int k, l, h;
1020         int bits;
1021         unsigned total = isl_basic_map_total_dim(bmap);
1022         isl_int sum;
1023
1024         if (!bmap || bmap->n_ineq <= 1)
1025                 return bmap;
1026
1027         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1028         bits = ffs(size) - 1;
1029         index = isl_calloc_array(ctx, isl_int **, size);
1030         if (!index)
1031                 return bmap;
1032
1033         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1034         for (k = 1; k < bmap->n_ineq; ++k) {
1035                 h = hash_index(index, size, bits, bmap, k);
1036                 if (!index[h]) {
1037                         index[h] = &bmap->ineq[k];
1038                         continue;
1039                 }
1040                 if (progress)
1041                         *progress = 1;
1042                 l = index[h] - &bmap->ineq[0];
1043                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1044                         swap_inequality(bmap, k, l);
1045                 isl_basic_map_drop_inequality(bmap, k);
1046                 --k;
1047         }
1048         isl_int_init(sum);
1049         for (k = 0; k < bmap->n_ineq-1; ++k) {
1050                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1051                 h = hash_index(index, size, bits, bmap, k);
1052                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1053                 if (!index[h])
1054                         continue;
1055                 l = index[h] - &bmap->ineq[0];
1056                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1057                 if (isl_int_is_pos(sum)) {
1058                         bmap = check_for_div_constraints(bmap, k, l, sum,
1059                                                          progress);
1060                         continue;
1061                 }
1062                 if (isl_int_is_zero(sum)) {
1063                         /* We need to break out of the loop after these
1064                          * changes since the contents of the hash
1065                          * will no longer be valid.
1066                          * Plus, we probably we want to regauss first.
1067                          */
1068                         if (progress)
1069                                 *progress = 1;
1070                         isl_basic_map_drop_inequality(bmap, l);
1071                         isl_basic_map_inequality_to_equality(bmap, k);
1072                 } else
1073                         bmap = isl_basic_map_set_to_empty(bmap);
1074                 break;
1075         }
1076         isl_int_clear(sum);
1077
1078         free(index);
1079         return bmap;
1080 }
1081
1082
1083 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1084 {
1085         int progress = 1;
1086         if (!bmap)
1087                 return NULL;
1088         while (progress) {
1089                 progress = 0;
1090                 bmap = isl_basic_map_normalize_constraints(bmap);
1091                 bmap = remove_duplicate_divs(bmap, &progress);
1092                 bmap = eliminate_divs_eq(bmap, &progress);
1093                 bmap = eliminate_divs_ineq(bmap, &progress);
1094                 bmap = isl_basic_map_gauss(bmap, &progress);
1095                 /* requires equalities in normal form */
1096                 bmap = normalize_divs(bmap, &progress);
1097                 bmap = remove_duplicate_constraints(bmap, &progress);
1098         }
1099         return bmap;
1100 }
1101
1102 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1103 {
1104         return (struct isl_basic_set *)
1105                 isl_basic_map_simplify((struct isl_basic_map *)bset);
1106 }
1107
1108
1109 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1110         isl_int *constraint, unsigned div)
1111 {
1112         unsigned pos;
1113
1114         if (!bmap)
1115                 return -1;
1116
1117         pos = 1 + isl_dim_total(bmap->dim) + div;
1118
1119         if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1120                 int neg;
1121                 isl_int_sub(bmap->div[div][1],
1122                                 bmap->div[div][1], bmap->div[div][0]);
1123                 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1124                 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1125                 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1126                 isl_int_add(bmap->div[div][1],
1127                                 bmap->div[div][1], bmap->div[div][0]);
1128                 if (!neg)
1129                         return 0;
1130                 if (isl_seq_first_non_zero(constraint+pos+1,
1131                                             bmap->n_div-div-1) != -1)
1132                         return 0;
1133         } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1134                 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1135                         return 0;
1136                 if (isl_seq_first_non_zero(constraint+pos+1,
1137                                             bmap->n_div-div-1) != -1)
1138                         return 0;
1139         } else
1140                 return 0;
1141
1142         return 1;
1143 }
1144
1145
1146 /* If the only constraints a div d=floor(f/m)
1147  * appears in are its two defining constraints
1148  *
1149  *      f - m d >=0
1150  *      -(f - (m - 1)) + m d >= 0
1151  *
1152  * then it can safely be removed.
1153  */
1154 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1155 {
1156         int i;
1157         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1158
1159         for (i = 0; i < bmap->n_eq; ++i)
1160                 if (!isl_int_is_zero(bmap->eq[i][pos]))
1161                         return 0;
1162
1163         for (i = 0; i < bmap->n_ineq; ++i) {
1164                 if (isl_int_is_zero(bmap->ineq[i][pos]))
1165                         continue;
1166                 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1167                         return 0;
1168         }
1169
1170         for (i = 0; i < bmap->n_div; ++i)
1171                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1172                         return 0;
1173
1174         return 1;
1175 }
1176
1177 /*
1178  * Remove divs that don't occur in any of the constraints or other divs.
1179  * These can arise when dropping some of the variables in a quast
1180  * returned by piplib.
1181  */
1182 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1183 {
1184         int i;
1185
1186         if (!bmap)
1187                 return NULL;
1188
1189         for (i = bmap->n_div-1; i >= 0; --i) {
1190                 if (!div_is_redundant(bmap, i))
1191                         continue;
1192                 bmap = isl_basic_map_drop_div(bmap, i);
1193         }
1194         return bmap;
1195 }
1196
1197 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1198 {
1199         bmap = remove_redundant_divs(bmap);
1200         if (!bmap)
1201                 return NULL;
1202         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1203         return bmap;
1204 }
1205
1206 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1207 {
1208         return (struct isl_basic_set *)
1209                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1210 }
1211
1212 struct isl_set *isl_set_finalize(struct isl_set *set)
1213 {
1214         int i;
1215
1216         if (!set)
1217                 return NULL;
1218         for (i = 0; i < set->n; ++i) {
1219                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1220                 if (!set->p[i])
1221                         goto error;
1222         }
1223         return set;
1224 error:
1225         isl_set_free(set);
1226         return NULL;
1227 }
1228
1229 struct isl_map *isl_map_finalize(struct isl_map *map)
1230 {
1231         int i;
1232
1233         if (!map)
1234                 return NULL;
1235         for (i = 0; i < map->n; ++i) {
1236                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1237                 if (!map->p[i])
1238                         goto error;
1239         }
1240         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1241         return map;
1242 error:
1243         isl_map_free(map);
1244         return NULL;
1245 }
1246
1247
1248 /* Remove definition of any div that is defined in terms of the given variable.
1249  * The div itself is not removed.  Functions such as
1250  * eliminate_divs_ineq depend on the other divs remaining in place.
1251  */
1252 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1253                                                                         int pos)
1254 {
1255         int i;
1256
1257         for (i = 0; i < bmap->n_div; ++i) {
1258                 if (isl_int_is_zero(bmap->div[i][0]))
1259                         continue;
1260                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1261                         continue;
1262                 isl_int_set_si(bmap->div[i][0], 0);
1263         }
1264         return bmap;
1265 }
1266
1267 /* Eliminate the specified variables from the constraints using
1268  * Fourier-Motzkin.  The variables themselves are not removed.
1269  */
1270 struct isl_basic_map *isl_basic_map_eliminate_vars(
1271         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1272 {
1273         int d;
1274         int i, j, k;
1275         unsigned total;
1276
1277         if (n == 0)
1278                 return bmap;
1279         if (!bmap)
1280                 return NULL;
1281         total = isl_basic_map_total_dim(bmap);
1282
1283         bmap = isl_basic_map_cow(bmap);
1284         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1285                 bmap = remove_dependent_vars(bmap, d);
1286
1287         for (d = pos + n - 1;
1288              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1289                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1290         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1291                 int n_lower, n_upper;
1292                 if (!bmap)
1293                         return NULL;
1294                 for (i = 0; i < bmap->n_eq; ++i) {
1295                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1296                                 continue;
1297                         eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1298                         isl_basic_map_drop_equality(bmap, i);
1299                         break;
1300                 }
1301                 if (i < bmap->n_eq)
1302                         continue;
1303                 n_lower = 0;
1304                 n_upper = 0;
1305                 for (i = 0; i < bmap->n_ineq; ++i) {
1306                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1307                                 n_lower++;
1308                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1309                                 n_upper++;
1310                 }
1311                 bmap = isl_basic_map_extend_constraints(bmap,
1312                                 0, n_lower * n_upper);
1313                 if (!bmap)
1314                         goto error;
1315                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1316                         int last;
1317                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1318                                 continue;
1319                         last = -1;
1320                         for (j = 0; j < i; ++j) {
1321                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1322                                         continue;
1323                                 last = j;
1324                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1325                                     isl_int_sgn(bmap->ineq[j][1+d]))
1326                                         continue;
1327                                 k = isl_basic_map_alloc_inequality(bmap);
1328                                 if (k < 0)
1329                                         goto error;
1330                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1331                                                 1+total);
1332                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1333                                                 1+d, 1+total, NULL);
1334                         }
1335                         isl_basic_map_drop_inequality(bmap, i);
1336                         i = last + 1;
1337                 }
1338                 if (n_lower > 0 && n_upper > 0) {
1339                         bmap = isl_basic_map_normalize_constraints(bmap);
1340                         bmap = remove_duplicate_constraints(bmap, NULL);
1341                         bmap = isl_basic_map_gauss(bmap, NULL);
1342                         bmap = isl_basic_map_remove_redundancies(bmap);
1343                         if (!bmap)
1344                                 goto error;
1345                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1346                                 break;
1347                 }
1348         }
1349         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1350         return bmap;
1351 error:
1352         isl_basic_map_free(bmap);
1353         return NULL;
1354 }
1355
1356 struct isl_basic_set *isl_basic_set_eliminate_vars(
1357         struct isl_basic_set *bset, unsigned pos, unsigned n)
1358 {
1359         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1360                         (struct isl_basic_map *)bset, pos, n);
1361 }
1362
1363 /* Don't assume equalities are in order, because align_divs
1364  * may have changed the order of the divs.
1365  */
1366 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1367 {
1368         int d, i;
1369         unsigned total;
1370
1371         total = isl_dim_total(bmap->dim);
1372         for (d = 0; d < total; ++d)
1373                 elim[d] = -1;
1374         for (i = 0; i < bmap->n_eq; ++i) {
1375                 for (d = total - 1; d >= 0; --d) {
1376                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1377                                 continue;
1378                         elim[d] = i;
1379                         break;
1380                 }
1381         }
1382 }
1383
1384 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1385 {
1386         compute_elimination_index((struct isl_basic_map *)bset, elim);
1387 }
1388
1389 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1390         struct isl_basic_map *bmap, int *elim)
1391 {
1392         int d;
1393         int copied = 0;
1394         unsigned total;
1395
1396         total = isl_dim_total(bmap->dim);
1397         for (d = total - 1; d >= 0; --d) {
1398                 if (isl_int_is_zero(src[1+d]))
1399                         continue;
1400                 if (elim[d] == -1)
1401                         continue;
1402                 if (!copied) {
1403                         isl_seq_cpy(dst, src, 1 + total);
1404                         copied = 1;
1405                 }
1406                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1407         }
1408         return copied;
1409 }
1410
1411 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1412         struct isl_basic_set *bset, int *elim)
1413 {
1414         return reduced_using_equalities(dst, src,
1415                                         (struct isl_basic_map *)bset, elim);
1416 }
1417
1418 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1419         struct isl_basic_set *bset, struct isl_basic_set *context)
1420 {
1421         int i;
1422         int *elim;
1423
1424         if (!bset || !context)
1425                 goto error;
1426
1427         if (context->n_eq == 0) {
1428                 isl_basic_set_free(context);
1429                 return bset;
1430         }
1431
1432         bset = isl_basic_set_cow(bset);
1433         if (!bset)
1434                 goto error;
1435
1436         elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1437         if (!elim)
1438                 goto error;
1439         set_compute_elimination_index(context, elim);
1440         for (i = 0; i < bset->n_eq; ++i)
1441                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1442                                                         context, elim);
1443         for (i = 0; i < bset->n_ineq; ++i)
1444                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1445                                                         context, elim);
1446         isl_basic_set_free(context);
1447         free(elim);
1448         bset = isl_basic_set_simplify(bset);
1449         bset = isl_basic_set_finalize(bset);
1450         return bset;
1451 error:
1452         isl_basic_set_free(bset);
1453         isl_basic_set_free(context);
1454         return NULL;
1455 }
1456
1457 static struct isl_basic_set *remove_shifted_constraints(
1458         struct isl_basic_set *bset, struct isl_basic_set *context)
1459 {
1460         unsigned int size;
1461         isl_int ***index;
1462         int bits;
1463         int k, h, l;
1464
1465         if (!bset)
1466                 return NULL;
1467
1468         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1469         bits = ffs(size) - 1;
1470         index = isl_calloc_array(ctx, isl_int **, size);
1471         if (!index)
1472                 return bset;
1473
1474         for (k = 0; k < context->n_ineq; ++k) {
1475                 h = set_hash_index(index, size, bits, context, k);
1476                 index[h] = &context->ineq[k];
1477         }
1478         for (k = 0; k < bset->n_ineq; ++k) {
1479                 h = set_hash_index(index, size, bits, bset, k);
1480                 if (!index[h])
1481                         continue;
1482                 l = index[h] - &context->ineq[0];
1483                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1484                         continue;
1485                 bset = isl_basic_set_cow(bset);
1486                 if (!bset)
1487                         goto error;
1488                 isl_basic_set_drop_inequality(bset, k);
1489                 --k;
1490         }
1491         free(index);
1492         return bset;
1493 error:
1494         free(index);
1495         return bset;
1496 }
1497
1498 /* Tighten (decrease) the constant terms of the inequalities based
1499  * on the equalities, without removing any integer points.
1500  * For example, if there is an equality
1501  *
1502  *              i = 3 * j
1503  *
1504  * and an inequality
1505  *
1506  *              i >= 1
1507  *
1508  * then we want to replace the inequality by
1509  *
1510  *              i >= 3
1511  *
1512  * We do this by computing a variable compression and translating
1513  * the constraints to the compressed space.
1514  * If any constraint has coefficients (except the contant term)
1515  * with a common factor "f", then we can replace the constant term "c"
1516  * by
1517  *
1518  *              f * floor(c/f)
1519  *
1520  * That is, we add
1521  *
1522  *              f * floor(c/f) - c = -fract(c/f)
1523  *
1524  * and we can add the same value to the original constraint.
1525  *
1526  * In the example, the compressed space only contains "j",
1527  * and the inequality translates to
1528  *
1529  *              3 * j - 1 >= 0
1530  *
1531  * We add -fract(-1/3) = -2 to the original constraint to obtain
1532  *
1533  *              i - 3 >= 0
1534  */
1535 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1536         struct isl_basic_set *bset)
1537 {
1538         int i;
1539         unsigned total;
1540         struct isl_mat *B, *C;
1541         isl_int gcd;
1542
1543         if (!bset)
1544                 return NULL;
1545
1546         if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1547                 return bset;
1548
1549         if (!bset->n_ineq)
1550                 return bset;
1551
1552         bset = isl_basic_set_cow(bset);
1553         if (!bset)
1554                 return NULL;
1555
1556         total = isl_basic_set_total_dim(bset);
1557         B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1558         C = isl_mat_variable_compression(B, NULL);
1559         if (!C)
1560                 return bset;
1561         if (C->n_col == 0) {
1562                 isl_mat_free(C);
1563                 return isl_basic_set_set_to_empty(bset);
1564         }
1565         B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1566                                                 0, bset->n_ineq, 0, 1 + total);
1567         C = isl_mat_product(B, C);
1568         if (!C)
1569                 return bset;
1570
1571         isl_int_init(gcd);
1572         for (i = 0; i < bset->n_ineq; ++i) {
1573                 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1574                 if (isl_int_is_one(gcd))
1575                         continue;
1576                 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1577                 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1578         }
1579         isl_int_clear(gcd);
1580
1581         isl_mat_free(C);
1582
1583         return bset;
1584 }
1585
1586 /* Remove all information from bset that is redundant in the context
1587  * of context.  Both bset and context are assumed to be full-dimensional.
1588  *
1589  * We first * remove the inequalities from "bset"
1590  * that are obviously redundant with respect to some inequality in "context".
1591  *
1592  * If there are any inequalities left, we construct a tableau for
1593  * the context and then add the inequalities of "bset".
1594  * Before adding these inequalities, we freeze all constraints such that
1595  * they won't be considered redundant in terms of the constraints of "bset".
1596  * Then we detect all redundant constraints (among the
1597  * constraints that weren't frozen), first by checking for redundancy in the
1598  * the tableau and then by checking if replacing a constraint by its negation
1599  * would lead to an empty set.  This last step is fairly expensive
1600  * and could be optimized by more reuse of the tableau.
1601  * Finally, we update bset according to the results.
1602  */
1603 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1604         __isl_take isl_basic_set *context)
1605 {
1606         int i, k;
1607         isl_basic_set *combined = NULL;
1608         struct isl_tab *tab = NULL;
1609         unsigned context_ineq;
1610         unsigned total;
1611
1612         if (!bset || !context)
1613                 goto error;
1614
1615         if (isl_basic_set_is_universe(bset)) {
1616                 isl_basic_set_free(context);
1617                 return bset;
1618         }
1619
1620         if (isl_basic_set_is_universe(context)) {
1621                 isl_basic_set_free(context);
1622                 return bset;
1623         }
1624
1625         bset = remove_shifted_constraints(bset, context);
1626         if (!bset)
1627                 goto error;
1628         if (bset->n_ineq == 0)
1629                 goto done;
1630
1631         context_ineq = context->n_ineq;
1632         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1633         combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1634         tab = isl_tab_from_basic_set(combined);
1635         for (i = 0; i < context_ineq; ++i)
1636                 if (isl_tab_freeze_constraint(tab, i) < 0)
1637                         goto error;
1638         tab = isl_tab_extend(tab, bset->n_ineq);
1639         for (i = 0; i < bset->n_ineq; ++i)
1640                 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1641                         goto error;
1642         bset = isl_basic_set_add_constraints(combined, bset, 0);
1643         combined = NULL;
1644         if (!bset)
1645                 goto error;
1646         if (isl_tab_detect_redundant(tab) < 0)
1647                 goto error;
1648         total = isl_basic_set_total_dim(bset);
1649         for (i = context_ineq; i < bset->n_ineq; ++i) {
1650                 int is_empty;
1651                 if (tab->con[i].is_redundant)
1652                         continue;
1653                 tab->con[i].is_redundant = 1;
1654                 combined = isl_basic_set_dup(bset);
1655                 combined = isl_basic_set_update_from_tab(combined, tab);
1656                 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1657                 k = isl_basic_set_alloc_inequality(combined);
1658                 if (k < 0)
1659                         goto error;
1660                 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1661                 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1662                 is_empty = isl_basic_set_is_empty(combined);
1663                 if (is_empty < 0)
1664                         goto error;
1665                 isl_basic_set_free(combined);
1666                 combined = NULL;
1667                 if (!is_empty)
1668                         tab->con[i].is_redundant = 0;
1669         }
1670         for (i = 0; i < context_ineq; ++i)
1671                 tab->con[i].is_redundant = 1;
1672         bset = isl_basic_set_update_from_tab(bset, tab);
1673         if (bset) {
1674                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1675                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1676         }
1677
1678         isl_tab_free(tab);
1679 done:
1680         bset = isl_basic_set_simplify(bset);
1681         bset = isl_basic_set_finalize(bset);
1682         isl_basic_set_free(context);
1683         return bset;
1684 error:
1685         isl_tab_free(tab);
1686         isl_basic_set_free(combined);
1687         isl_basic_set_free(context);
1688         isl_basic_set_free(bset);
1689         return NULL;
1690 }
1691
1692 /* Remove all information from bset that is redundant in the context
1693  * of context.  In particular, equalities that are linear combinations
1694  * of those in context are removed.  Then the inequalities that are
1695  * redundant in the context of the equalities and inequalities of
1696  * context are removed.
1697  *
1698  * We first compute the integer affine hull of the intersection,
1699  * compute the gist inside this affine hull and then add back
1700  * those equalities that are not implied by the context.
1701  */
1702 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1703         __isl_take isl_basic_set *context)
1704 {
1705         isl_mat *eq;
1706         isl_mat *T, *T2;
1707         isl_basic_set *aff;
1708         isl_basic_set *aff_context;
1709         unsigned total;
1710
1711         if (!bset || !context)
1712                 goto error;
1713
1714         bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1715         if (isl_basic_set_fast_is_empty(bset)) {
1716                 isl_basic_set_free(context);
1717                 return bset;
1718         }
1719         aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1720         if (!aff)
1721                 goto error;
1722         if (isl_basic_set_fast_is_empty(aff)) {
1723                 isl_basic_set_free(aff);
1724                 isl_basic_set_free(context);
1725                 return bset;
1726         }
1727         if (aff->n_eq == 0) {
1728                 isl_basic_set_free(aff);
1729                 return uset_gist_full(bset, context);
1730         }
1731         total = isl_basic_set_total_dim(bset);
1732         eq = isl_mat_sub_alloc(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1733         eq = isl_mat_cow(eq);
1734         T = isl_mat_variable_compression(eq, &T2);
1735         if (T && T->n_col == 0) {
1736                 isl_mat_free(T);
1737                 isl_mat_free(T2);
1738                 isl_basic_set_free(context);
1739                 isl_basic_set_free(aff);
1740                 return isl_basic_set_set_to_empty(bset);
1741         }
1742
1743         aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1744
1745         bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1746         context = isl_basic_set_preimage(context, T);
1747
1748         bset = uset_gist_full(bset, context);
1749         bset = isl_basic_set_preimage(bset, T2);
1750         bset = isl_basic_set_intersect(bset, aff);
1751         bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1752
1753         if (bset) {
1754                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1755                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1756         }
1757
1758         return bset;
1759 error:
1760         isl_basic_set_free(bset);
1761         isl_basic_set_free(context);
1762         return NULL;
1763 }
1764
1765 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1766  * We simply add the equalities in context to bmap and then do a regular
1767  * div normalizations.  Better results can be obtained by normalizing
1768  * only the divs in bmap than do not also appear in context.
1769  * We need to be careful to reduce the divs using the equalities
1770  * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1771  * spurious constraints.
1772  */
1773 static struct isl_basic_map *normalize_divs_in_context(
1774         struct isl_basic_map *bmap, struct isl_basic_map *context)
1775 {
1776         int i;
1777         unsigned total_context;
1778         int div_eq;
1779
1780         div_eq = n_pure_div_eq(bmap);
1781         if (div_eq == 0)
1782                 return bmap;
1783
1784         if (context->n_div > 0)
1785                 bmap = isl_basic_map_align_divs(bmap, context);
1786
1787         total_context = isl_basic_map_total_dim(context);
1788         bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1789         for (i = 0; i < context->n_eq; ++i) {
1790                 int k;
1791                 k = isl_basic_map_alloc_equality(bmap);
1792                 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1793                 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1794                                 isl_basic_map_total_dim(bmap) - total_context);
1795         }
1796         bmap = isl_basic_map_gauss(bmap, NULL);
1797         bmap = normalize_divs(bmap, NULL);
1798         bmap = isl_basic_map_gauss(bmap, NULL);
1799         return bmap;
1800 }
1801
1802 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1803         struct isl_basic_map *context)
1804 {
1805         struct isl_basic_set *bset;
1806
1807         if (!bmap || !context)
1808                 goto error;
1809
1810         if (isl_basic_map_is_universe(bmap)) {
1811                 isl_basic_map_free(context);
1812                 return bmap;
1813         }
1814         if (isl_basic_map_fast_is_empty(context)) {
1815                 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1816                 isl_basic_map_free(context);
1817                 isl_basic_map_free(bmap);
1818                 return isl_basic_map_universe(dim);
1819         }
1820         if (isl_basic_map_fast_is_empty(bmap)) {
1821                 isl_basic_map_free(context);
1822                 return bmap;
1823         }
1824
1825         bmap = isl_basic_map_remove_redundancies(bmap);
1826         context = isl_basic_map_remove_redundancies(context);
1827
1828         if (context->n_eq)
1829                 bmap = normalize_divs_in_context(bmap, context);
1830
1831         context = isl_basic_map_align_divs(context, bmap);
1832         bmap = isl_basic_map_align_divs(bmap, context);
1833
1834         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1835                          isl_basic_map_underlying_set(context));
1836
1837         return isl_basic_map_overlying_set(bset, bmap);
1838 error:
1839         isl_basic_map_free(bmap);
1840         isl_basic_map_free(context);
1841         return NULL;
1842 }
1843
1844 /*
1845  * Assumes context has no implicit divs.
1846  */
1847 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1848         __isl_take isl_basic_map *context)
1849 {
1850         int i;
1851
1852         if (!map || !context)
1853                 goto error;;
1854
1855         if (isl_basic_map_fast_is_empty(context)) {
1856                 struct isl_dim *dim = isl_dim_copy(map->dim);
1857                 isl_basic_map_free(context);
1858                 isl_map_free(map);
1859                 return isl_map_universe(dim);
1860         }
1861
1862         context = isl_basic_map_remove_redundancies(context);
1863         map = isl_map_cow(map);
1864         if (!map || !context)
1865                 goto error;;
1866         isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1867         map = isl_map_compute_divs(map);
1868         for (i = 0; i < map->n; ++i)
1869                 context = isl_basic_map_align_divs(context, map->p[i]);
1870         for (i = 0; i < map->n; ++i) {
1871                 map->p[i] = isl_basic_map_gist(map->p[i],
1872                                                 isl_basic_map_copy(context));
1873                 if (!map->p[i])
1874                         goto error;
1875         }
1876         isl_basic_map_free(context);
1877         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1878         return map;
1879 error:
1880         isl_map_free(map);
1881         isl_basic_map_free(context);
1882         return NULL;
1883 }
1884
1885 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1886         __isl_take isl_map *context)
1887 {
1888         return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1889 }
1890
1891 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1892                                                 struct isl_basic_set *context)
1893 {
1894         return (struct isl_basic_set *)isl_basic_map_gist(
1895                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1896 }
1897
1898 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1899         __isl_take isl_basic_set *context)
1900 {
1901         return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1902                                         (struct isl_basic_map *)context);
1903 }
1904
1905 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1906         __isl_take isl_set *context)
1907 {
1908         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1909                                         (struct isl_map *)context);
1910 }
1911
1912 /* Quick check to see if two basic maps are disjoint.
1913  * In particular, we reduce the equalities and inequalities of
1914  * one basic map in the context of the equalities of the other
1915  * basic map and check if we get a contradiction.
1916  */
1917 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1918         struct isl_basic_map *bmap2)
1919 {
1920         struct isl_vec *v = NULL;
1921         int *elim = NULL;
1922         unsigned total;
1923         int i;
1924
1925         if (!bmap1 || !bmap2)
1926                 return -1;
1927         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1928                         return -1);
1929         if (bmap1->n_div || bmap2->n_div)
1930                 return 0;
1931         if (!bmap1->n_eq && !bmap2->n_eq)
1932                 return 0;
1933
1934         total = isl_dim_total(bmap1->dim);
1935         if (total == 0)
1936                 return 0;
1937         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1938         if (!v)
1939                 goto error;
1940         elim = isl_alloc_array(bmap1->ctx, int, total);
1941         if (!elim)
1942                 goto error;
1943         compute_elimination_index(bmap1, elim);
1944         for (i = 0; i < bmap2->n_eq; ++i) {
1945                 int reduced;
1946                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1947                                                         bmap1, elim);
1948                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1949                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1950                         goto disjoint;
1951         }
1952         for (i = 0; i < bmap2->n_ineq; ++i) {
1953                 int reduced;
1954                 reduced = reduced_using_equalities(v->block.data,
1955                                                 bmap2->ineq[i], bmap1, elim);
1956                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1957                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1958                         goto disjoint;
1959         }
1960         compute_elimination_index(bmap2, elim);
1961         for (i = 0; i < bmap1->n_ineq; ++i) {
1962                 int reduced;
1963                 reduced = reduced_using_equalities(v->block.data,
1964                                                 bmap1->ineq[i], bmap2, elim);
1965                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1966                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1967                         goto disjoint;
1968         }
1969         isl_vec_free(v);
1970         free(elim);
1971         return 0;
1972 disjoint:
1973         isl_vec_free(v);
1974         free(elim);
1975         return 1;
1976 error:
1977         isl_vec_free(v);
1978         free(elim);
1979         return -1;
1980 }
1981
1982 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1983         struct isl_basic_set *bset2)
1984 {
1985         return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1986                                               (struct isl_basic_map *)bset2);
1987 }
1988
1989 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1990 {
1991         int i, j;
1992
1993         if (!map1 || !map2)
1994                 return -1;
1995
1996         if (isl_map_fast_is_equal(map1, map2))
1997                 return 0;
1998
1999         for (i = 0; i < map1->n; ++i) {
2000                 for (j = 0; j < map2->n; ++j) {
2001                         int d = isl_basic_map_fast_is_disjoint(map1->p[i],
2002                                                                map2->p[j]);
2003                         if (d != 1)
2004                                 return d;
2005                 }
2006         }
2007         return 1;
2008 }
2009
2010 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
2011 {
2012         return isl_map_fast_is_disjoint((struct isl_map *)set1,
2013                                         (struct isl_map *)set2);
2014 }
2015
2016 /* Check if we can combine a given div with lower bound l and upper
2017  * bound u with some other div and if so return that other div.
2018  * Otherwise return -1.
2019  *
2020  * We first check that
2021  *      - the bounds are opposites of each other (except for the constant
2022  *        term)
2023  *      - the bounds do not reference any other div
2024  *      - no div is defined in terms of this div
2025  *
2026  * Let m be the size of the range allowed on the div by the bounds.
2027  * That is, the bounds are of the form
2028  *
2029  *      e <= a <= e + m - 1
2030  *
2031  * with e some expression in the other variables.
2032  * We look for another div b such that no third div is defined in terms
2033  * of this second div b and such that in any constraint that contains
2034  * a (except for the given lower and upper bound), also contains b
2035  * with a coefficient that is m times that of b.
2036  * That is, all constraints (execpt for the lower and upper bound)
2037  * are of the form
2038  *
2039  *      e + f (a + m b) >= 0
2040  *
2041  * If so, we return b so that "a + m b" can be replaced by
2042  * a single div "c = a + m b".
2043  */
2044 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2045         unsigned div, unsigned l, unsigned u)
2046 {
2047         int i, j;
2048         unsigned dim;
2049         int coalesce = -1;
2050
2051         if (bmap->n_div <= 1)
2052                 return -1;
2053         dim = isl_dim_total(bmap->dim);
2054         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2055                 return -1;
2056         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2057                                    bmap->n_div - div - 1) != -1)
2058                 return -1;
2059         if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2060                             dim + bmap->n_div))
2061                 return -1;
2062
2063         for (i = 0; i < bmap->n_div; ++i) {
2064                 if (isl_int_is_zero(bmap->div[i][0]))
2065                         continue;
2066                 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2067                         return -1;
2068         }
2069
2070         isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2071         if (isl_int_is_neg(bmap->ineq[l][0])) {
2072                 isl_int_sub(bmap->ineq[l][0],
2073                             bmap->ineq[l][0], bmap->ineq[u][0]);
2074                 bmap = isl_basic_map_copy(bmap);
2075                 bmap = isl_basic_map_set_to_empty(bmap);
2076                 isl_basic_map_free(bmap);
2077                 return -1;
2078         }
2079         isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2080         for (i = 0; i < bmap->n_div; ++i) {
2081                 if (i == div)
2082                         continue;
2083                 if (!pairs[i])
2084                         continue;
2085                 for (j = 0; j < bmap->n_div; ++j) {
2086                         if (isl_int_is_zero(bmap->div[j][0]))
2087                                 continue;
2088                         if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2089                                 break;
2090                 }
2091                 if (j < bmap->n_div)
2092                         continue;
2093                 for (j = 0; j < bmap->n_ineq; ++j) {
2094                         int valid;
2095                         if (j == l || j == u)
2096                                 continue;
2097                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2098                                 continue;
2099                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2100                                 break;
2101                         isl_int_mul(bmap->ineq[j][1 + dim + div],
2102                                     bmap->ineq[j][1 + dim + div],
2103                                     bmap->ineq[l][0]);
2104                         valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2105                                            bmap->ineq[j][1 + dim + i]);
2106                         isl_int_divexact(bmap->ineq[j][1 + dim + div],
2107                                          bmap->ineq[j][1 + dim + div],
2108                                          bmap->ineq[l][0]);
2109                         if (!valid)
2110                                 break;
2111                 }
2112                 if (j < bmap->n_ineq)
2113                         continue;
2114                 coalesce = i;
2115                 break;
2116         }
2117         isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2118         isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2119         return coalesce;
2120 }
2121
2122 /* Given a lower and an upper bound on div i, construct an inequality
2123  * that when nonnegative ensures that this pair of bounds always allows
2124  * for an integer value of the given div.
2125  * The lower bound is inequality l, while the upper bound is inequality u.
2126  * The constructed inequality is stored in ineq.
2127  * g, fl, fu are temporary scalars.
2128  *
2129  * Let the upper bound be
2130  *
2131  *      -n_u a + e_u >= 0
2132  *
2133  * and the lower bound
2134  *
2135  *      n_l a + e_l >= 0
2136  *
2137  * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2138  * We have
2139  *
2140  *      - f_u e_l <= f_u f_l g a <= f_l e_u
2141  *
2142  * Since all variables are integer valued, this is equivalent to
2143  *
2144  *      - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2145  *
2146  * If this interval is at least f_u f_l g, then it contains at least
2147  * one integer value for a.
2148  * That is, the test constraint is
2149  *
2150  *      f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2151  */
2152 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2153         int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2154 {
2155         unsigned dim;
2156         dim = isl_dim_total(bmap->dim);
2157
2158         isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2159         isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2160         isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2161         isl_int_neg(fu, fu);
2162         isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2163                         1 + dim + bmap->n_div);
2164         isl_int_add(ineq[0], ineq[0], fl);
2165         isl_int_add(ineq[0], ineq[0], fu);
2166         isl_int_sub_ui(ineq[0], ineq[0], 1);
2167         isl_int_mul(g, g, fl);
2168         isl_int_mul(g, g, fu);
2169         isl_int_sub(ineq[0], ineq[0], g);
2170 }
2171
2172 /* Remove more kinds of divs that are not strictly needed.
2173  * In particular, if all pairs of lower and upper bounds on a div
2174  * are such that they allow at least one integer value of the div,
2175  * the we can eliminate the div using Fourier-Motzkin without
2176  * introducing any spurious solutions.
2177  */
2178 static struct isl_basic_map *drop_more_redundant_divs(
2179         struct isl_basic_map *bmap, int *pairs, int n)
2180 {
2181         struct isl_tab *tab = NULL;
2182         struct isl_vec *vec = NULL;
2183         unsigned dim;
2184         int remove = -1;
2185         isl_int g, fl, fu;
2186
2187         isl_int_init(g);
2188         isl_int_init(fl);
2189         isl_int_init(fu);
2190
2191         if (!bmap)
2192                 goto error;
2193
2194         dim = isl_dim_total(bmap->dim);
2195         vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2196         if (!vec)
2197                 goto error;
2198
2199         tab = isl_tab_from_basic_map(bmap);
2200
2201         while (n > 0) {
2202                 int i, l, u;
2203                 int best = -1;
2204                 enum isl_lp_result res;
2205
2206                 for (i = 0; i < bmap->n_div; ++i) {
2207                         if (!pairs[i])
2208                                 continue;
2209                         if (best >= 0 && pairs[best] <= pairs[i])
2210                                 continue;
2211                         best = i;
2212                 }
2213
2214                 i = best;
2215                 for (l = 0; l < bmap->n_ineq; ++l) {
2216                         if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2217                                 continue;
2218                         for (u = 0; u < bmap->n_ineq; ++u) {
2219                                 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2220                                         continue;
2221                                 construct_test_ineq(bmap, i, l, u,
2222                                                     vec->el, g, fl, fu);
2223                                 res = isl_tab_min(tab, vec->el,
2224                                                   bmap->ctx->one, &g, NULL, 0);
2225                                 if (res == isl_lp_error)
2226                                         goto error;
2227                                 if (res == isl_lp_empty) {
2228                                         bmap = isl_basic_map_set_to_empty(bmap);
2229                                         break;
2230                                 }
2231                                 if (res != isl_lp_ok || isl_int_is_neg(g))
2232                                         break;
2233                         }
2234                         if (u < bmap->n_ineq)
2235                                 break;
2236                 }
2237                 if (l == bmap->n_ineq) {
2238                         remove = i;
2239                         break;
2240                 }
2241                 pairs[i] = 0;
2242                 --n;
2243         }
2244
2245         isl_tab_free(tab);
2246         isl_vec_free(vec);
2247
2248         isl_int_clear(g);
2249         isl_int_clear(fl);
2250         isl_int_clear(fu);
2251
2252         free(pairs);
2253
2254         if (remove < 0)
2255                 return bmap;
2256
2257         bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
2258         return isl_basic_map_drop_redundant_divs(bmap);
2259 error:
2260         free(pairs);
2261         isl_basic_map_free(bmap);
2262         isl_tab_free(tab);
2263         isl_vec_free(vec);
2264         isl_int_clear(g);
2265         isl_int_clear(fl);
2266         isl_int_clear(fu);
2267         return NULL;
2268 }
2269
2270 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2271  * and the upper bound u, div1 always occurs together with div2 in the form
2272  * (div1 + m div2), where m is the constant range on the variable div1
2273  * allowed by l and u, replace the pair div1 and div2 by a single
2274  * div that is equal to div1 + m div2.
2275  *
2276  * The new div will appear in the location that contains div2.
2277  * We need to modify all constraints that contain
2278  * div2 = (div - div1) / m
2279  * (If a constraint does not contain div2, it will also not contain div1.)
2280  * If the constraint also contains div1, then we know they appear
2281  * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2282  * i.e., the coefficient of div is f.
2283  *
2284  * Otherwise, we first need to introduce div1 into the constraint.
2285  * Let the l be
2286  *
2287  *      div1 + f >=0
2288  *
2289  * and u
2290  *
2291  *      -div1 + f' >= 0
2292  *
2293  * A lower bound on div2
2294  *
2295  *      n div2 + t >= 0
2296  *
2297  * can be replaced by
2298  *
2299  *      (n * (m div 2 + div1) + m t + n f)/g >= 0
2300  *
2301  * with g = gcd(m,n).
2302  * An upper bound
2303  *
2304  *      -n div2 + t >= 0
2305  *
2306  * can be replaced by
2307  *
2308  *      (-n * (m div2 + div1) + m t + n f')/g >= 0
2309  *
2310  * These constraint are those that we would obtain from eliminating
2311  * div1 using Fourier-Motzkin.
2312  *
2313  * After all constraints have been modified, we drop the lower and upper
2314  * bound and then drop div1.
2315  */
2316 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2317         unsigned div1, unsigned div2, unsigned l, unsigned u)
2318 {
2319         isl_int a;
2320         isl_int b;
2321         isl_int m;
2322         unsigned dim, total;
2323         int i;
2324
2325         dim = isl_dim_total(bmap->dim);
2326         total = 1 + dim + bmap->n_div;
2327
2328         isl_int_init(a);
2329         isl_int_init(b);
2330         isl_int_init(m);
2331         isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2332         isl_int_add_ui(m, m, 1);
2333
2334         for (i = 0; i < bmap->n_ineq; ++i) {
2335                 if (i == l || i == u)
2336                         continue;
2337                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2338                         continue;
2339                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2340                         isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2341                         isl_int_divexact(a, m, b);
2342                         isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2343                         if (isl_int_is_pos(b)) {
2344                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2345                                                 b, bmap->ineq[l], total);
2346                         } else {
2347                                 isl_int_neg(b, b);
2348                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2349                                                 b, bmap->ineq[u], total);
2350                         }
2351                 }
2352                 isl_int_set(bmap->ineq[i][1 + dim + div2],
2353                             bmap->ineq[i][1 + dim + div1]);
2354                 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2355         }
2356
2357         isl_int_clear(a);
2358         isl_int_clear(b);
2359         isl_int_clear(m);
2360         if (l > u) {
2361                 isl_basic_map_drop_inequality(bmap, l);
2362                 isl_basic_map_drop_inequality(bmap, u);
2363         } else {
2364                 isl_basic_map_drop_inequality(bmap, u);
2365                 isl_basic_map_drop_inequality(bmap, l);
2366         }
2367         bmap = isl_basic_map_drop_div(bmap, div1);
2368         return bmap;
2369 }
2370
2371 /* First check if we can coalesce any pair of divs and
2372  * then continue with dropping more redundant divs.
2373  *
2374  * We loop over all pairs of lower and upper bounds on a div
2375  * with coefficient 1 and -1, respectively, check if there
2376  * is any other div "c" with which we can coalesce the div
2377  * and if so, perform the coalescing.
2378  */
2379 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2380         struct isl_basic_map *bmap, int *pairs, int n)
2381 {
2382         int i, l, u;
2383         unsigned dim;
2384
2385         dim = isl_dim_total(bmap->dim);
2386
2387         for (i = 0; i < bmap->n_div; ++i) {
2388                 if (!pairs[i])
2389                         continue;
2390                 for (l = 0; l < bmap->n_ineq; ++l) {
2391                         if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2392                                 continue;
2393                         for (u = 0; u < bmap->n_ineq; ++u) {
2394                                 int c;
2395
2396                                 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2397                                         continue;
2398                                 c = div_find_coalesce(bmap, pairs, i, l, u);
2399                                 if (c < 0)
2400                                         continue;
2401                                 free(pairs);
2402                                 bmap = coalesce_divs(bmap, i, c, l, u);
2403                                 return isl_basic_map_drop_redundant_divs(bmap);
2404                         }
2405                 }
2406         }
2407
2408         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2409                 return bmap;
2410
2411         return drop_more_redundant_divs(bmap, pairs, n);
2412 }
2413
2414 /* Remove divs that are not strictly needed.
2415  * In particular, if a div only occurs positively (or negatively)
2416  * in constraints, then it can simply be dropped.
2417  * Also, if a div occurs only occurs in two constraints and if moreover
2418  * those two constraints are opposite to each other, except for the constant
2419  * term and if the sum of the constant terms is such that for any value
2420  * of the other values, there is always at least one integer value of the
2421  * div, i.e., if one plus this sum is greater than or equal to
2422  * the (absolute value) of the coefficent of the div in the constraints,
2423  * then we can also simply drop the div.
2424  *
2425  * If any divs are left after these simple checks then we move on
2426  * to more complicated cases in drop_more_redundant_divs.
2427  */
2428 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2429         struct isl_basic_map *bmap)
2430 {
2431         int i, j;
2432         unsigned off;
2433         int *pairs = NULL;
2434         int n = 0;
2435
2436         if (!bmap)
2437                 goto error;
2438
2439         off = isl_dim_total(bmap->dim);
2440         pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2441         if (!pairs)
2442                 goto error;
2443
2444         for (i = 0; i < bmap->n_div; ++i) {
2445                 int pos, neg;
2446                 int last_pos, last_neg;
2447                 int redundant;
2448                 int defined;
2449
2450                 defined = !isl_int_is_zero(bmap->div[i][0]);
2451                 for (j = 0; j < bmap->n_eq; ++j)
2452                         if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2453                                 break;
2454                 if (j < bmap->n_eq)
2455                         continue;
2456                 ++n;
2457                 pos = neg = 0;
2458                 for (j = 0; j < bmap->n_ineq; ++j) {
2459                         if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2460                                 last_pos = j;
2461                                 ++pos;
2462                         }
2463                         if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2464                                 last_neg = j;
2465                                 ++neg;
2466                         }
2467                 }
2468                 pairs[i] = pos * neg;
2469                 if (pairs[i] == 0) {
2470                         for (j = bmap->n_ineq - 1; j >= 0; --j)
2471                                 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2472                                         isl_basic_map_drop_inequality(bmap, j);
2473                         bmap = isl_basic_map_drop_div(bmap, i);
2474                         free(pairs);
2475                         return isl_basic_map_drop_redundant_divs(bmap);
2476                 }
2477                 if (pairs[i] != 1)
2478                         continue;
2479                 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2480                                     bmap->ineq[last_neg] + 1,
2481                                     off + bmap->n_div))
2482                         continue;
2483
2484                 isl_int_add(bmap->ineq[last_pos][0],
2485                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2486                 isl_int_add_ui(bmap->ineq[last_pos][0],
2487                                bmap->ineq[last_pos][0], 1);
2488                 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2489                                 bmap->ineq[last_pos][1+off+i]);
2490                 isl_int_sub_ui(bmap->ineq[last_pos][0],
2491                                bmap->ineq[last_pos][0], 1);
2492                 isl_int_sub(bmap->ineq[last_pos][0],
2493                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2494                 if (!redundant) {
2495                         if (defined ||
2496                             !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2497                                 pairs[i] = 0;
2498                                 --n;
2499                                 continue;
2500                         }
2501                         bmap = set_div_from_lower_bound(bmap, i, last_pos);
2502                         bmap = isl_basic_map_simplify(bmap);
2503                         free(pairs);
2504                         return isl_basic_map_drop_redundant_divs(bmap);
2505                 }
2506                 if (last_pos > last_neg) {
2507                         isl_basic_map_drop_inequality(bmap, last_pos);
2508                         isl_basic_map_drop_inequality(bmap, last_neg);
2509                 } else {
2510                         isl_basic_map_drop_inequality(bmap, last_neg);
2511                         isl_basic_map_drop_inequality(bmap, last_pos);
2512                 }
2513                 bmap = isl_basic_map_drop_div(bmap, i);
2514                 free(pairs);
2515                 return isl_basic_map_drop_redundant_divs(bmap);
2516         }
2517
2518         if (n > 0)
2519                 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2520
2521         free(pairs);
2522         return bmap;
2523 error:
2524         free(pairs);
2525         isl_basic_map_free(bmap);
2526         return NULL;
2527 }
2528
2529 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2530         struct isl_basic_set *bset)
2531 {
2532         return (struct isl_basic_set *)
2533             isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2534 }
2535
2536 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2537 {
2538         int i;
2539
2540         if (!map)
2541                 return NULL;
2542         for (i = 0; i < map->n; ++i) {
2543                 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2544                 if (!map->p[i])
2545                         goto error;
2546         }
2547         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2548         return map;
2549 error:
2550         isl_map_free(map);
2551         return NULL;
2552 }
2553
2554 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2555 {
2556         return (struct isl_set *)
2557             isl_map_drop_redundant_divs((struct isl_map *)set);
2558 }