isl_map_simplify.c

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  *
   4  * Use of this software is governed by the GNU LGPLv2.1 license
   5  *
   6  * Written by Sven Verdoolaege, K.U.Leuven, Departement
   7  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
   8  */
   9
  10 #include <strings.h>
  11 #include <isl_ctx_private.h>
  12 #include <isl_map_private.h>
  13 #include "isl_equalities.h"
  14 #include <isl/map.h>
  15 #include <isl/seq.h>
  16 #include "isl_tab.h"
  17 #include <isl_space_private.h>
  18 #include <isl_mat_private.h>
  19
  20 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
  21 {
  22         isl_int *t = bmap->eq[a];
  23         bmap->eq[a] = bmap->eq[b];
  24         bmap->eq[b] = t;
  25 }
  26
  27 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
  28 {
  29         if (a != b) {
  30                 isl_int *t = bmap->ineq[a];
  31                 bmap->ineq[a] = bmap->ineq[b];
  32                 bmap->ineq[b] = t;
  33         }
  34 }
  35
  36 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
  37 {
  38         isl_seq_cpy(c, c + n, rem);
  39         isl_seq_clr(c + rem, n);
  40 }
  41
  42 /* Drop n dimensions starting at first.
  43  *
  44  * In principle, this frees up some extra variables as the number
  45  * of columns remains constant, but we would have to extend
  46  * the div array too as the number of rows in this array is assumed
  47  * to be equal to extra.
  48  */
  49 struct isl_basic_set *isl_basic_set_drop_dims(
  50                 struct isl_basic_set *bset, unsigned first, unsigned n)
  51 {
  52         int i;
  53
  54         if (!bset)
  55                 goto error;
  56
  57         isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
  58
  59         if (n == 0 && !isl_space_get_tuple_name(bset->dim, isl_dim_set))
  60                 return bset;
  61
  62         bset = isl_basic_set_cow(bset);
  63         if (!bset)
  64                 return NULL;
  65
  66         for (i = 0; i < bset->n_eq; ++i)
  67                 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
  68                                      (bset->dim->n_out-first-n)+bset->extra);
  69
  70         for (i = 0; i < bset->n_ineq; ++i)
  71                 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
  72                                      (bset->dim->n_out-first-n)+bset->extra);
  73
  74         for (i = 0; i < bset->n_div; ++i)
  75                 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
  76                                      (bset->dim->n_out-first-n)+bset->extra);
  77
  78         bset->dim = isl_space_drop_outputs(bset->dim, first, n);
  79         if (!bset->dim)
  80                 goto error;
  81
  82         ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
  83         bset = isl_basic_set_simplify(bset);
  84         return isl_basic_set_finalize(bset);
  85 error:
  86         isl_basic_set_free(bset);
  87         return NULL;
  88 }
  89
  90 struct isl_set *isl_set_drop_dims(
  91                 struct isl_set *set, unsigned first, unsigned n)
  92 {
  93         int i;
  94
  95         if (!set)
  96                 goto error;
  97
  98         isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
  99
 100         if (n == 0 && !isl_space_get_tuple_name(set->dim, isl_dim_set))
 101                 return set;
 102         set = isl_set_cow(set);
 103         if (!set)
 104                 goto error;
 105         set->dim = isl_space_drop_outputs(set->dim, first, n);
 106         if (!set->dim)
 107                 goto error;
 108
 109         for (i = 0; i < set->n; ++i) {
 110                 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
 111                 if (!set->p[i])
 112                         goto error;
 113         }
 114
 115         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 116         return set;
 117 error:
 118         isl_set_free(set);
 119         return NULL;
 120 }
 121
 122 /* Move "n" divs starting at "first" to the end of the list of divs.
 123  */
 124 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
 125         unsigned first, unsigned n)
 126 {
 127         isl_int **div;
 128         int i;
 129
 130         if (first + n == bmap->n_div)
 131                 return bmap;
 132
 133         div = isl_alloc_array(bmap->ctx, isl_int *, n);
 134         if (!div)
 135                 goto error;
 136         for (i = 0; i < n; ++i)
 137                 div[i] = bmap->div[first + i];
 138         for (i = 0; i < bmap->n_div - first - n; ++i)
 139                 bmap->div[first + i] = bmap->div[first + n + i];
 140         for (i = 0; i < n; ++i)
 141                 bmap->div[bmap->n_div - n + i] = div[i];
 142         free(div);
 143         return bmap;
 144 error:
 145         isl_basic_map_free(bmap);
 146         return NULL;
 147 }
 148
 149 /* Drop "n" dimensions of type "type" starting at "first".
 150  *
 151  * In principle, this frees up some extra variables as the number
 152  * of columns remains constant, but we would have to extend
 153  * the div array too as the number of rows in this array is assumed
 154  * to be equal to extra.
 155  */
 156 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
 157         enum isl_dim_type type, unsigned first, unsigned n)
 158 {
 159         int i;
 160         unsigned dim;
 161         unsigned offset;
 162         unsigned left;
 163
 164         if (!bmap)
 165                 goto error;
 166
 167         dim = isl_basic_map_dim(bmap, type);
 168         isl_assert(bmap->ctx, first + n <= dim, goto error);
 169
 170         if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
 171                 return bmap;
 172
 173         bmap = isl_basic_map_cow(bmap);
 174         if (!bmap)
 175                 return NULL;
 176
 177         offset = isl_basic_map_offset(bmap, type) + first;
 178         left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
 179         for (i = 0; i < bmap->n_eq; ++i)
 180                 constraint_drop_vars(bmap->eq[i]+offset, n, left);
 181
 182         for (i = 0; i < bmap->n_ineq; ++i)
 183                 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
 184
 185         for (i = 0; i < bmap->n_div; ++i)
 186                 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
 187
 188         if (type == isl_dim_div) {
 189                 bmap = move_divs_last(bmap, first, n);
 190                 if (!bmap)
 191                         goto error;
 192                 isl_basic_map_free_div(bmap, n);
 193         } else
 194                 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
 195         if (!bmap->dim)
 196                 goto error;
 197
 198         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 199         bmap = isl_basic_map_simplify(bmap);
 200         return isl_basic_map_finalize(bmap);
 201 error:
 202         isl_basic_map_free(bmap);
 203         return NULL;
 204 }
 205
 206 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
 207         enum isl_dim_type type, unsigned first, unsigned n)
 208 {
 209         return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
 210                                                         type, first, n);
 211 }
 212
 213 struct isl_basic_map *isl_basic_map_drop_inputs(
 214                 struct isl_basic_map *bmap, unsigned first, unsigned n)
 215 {
 216         return isl_basic_map_drop(bmap, isl_dim_in, first, n);
 217 }
 218
 219 struct isl_map *isl_map_drop(struct isl_map *map,
 220         enum isl_dim_type type, unsigned first, unsigned n)
 221 {
 222         int i;
 223
 224         if (!map)
 225                 goto error;
 226
 227         isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
 228
 229         if (n == 0 && !isl_space_get_tuple_name(map->dim, type))
 230                 return map;
 231         map = isl_map_cow(map);
 232         if (!map)
 233                 goto error;
 234         map->dim = isl_space_drop_dims(map->dim, type, first, n);
 235         if (!map->dim)
 236                 goto error;
 237
 238         for (i = 0; i < map->n; ++i) {
 239                 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
 240                 if (!map->p[i])
 241                         goto error;
 242         }
 243         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
 244
 245         return map;
 246 error:
 247         isl_map_free(map);
 248         return NULL;
 249 }
 250
 251 struct isl_set *isl_set_drop(struct isl_set *set,
 252         enum isl_dim_type type, unsigned first, unsigned n)
 253 {
 254         return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
 255 }
 256
 257 struct isl_map *isl_map_drop_inputs(
 258                 struct isl_map *map, unsigned first, unsigned n)
 259 {
 260         return isl_map_drop(map, isl_dim_in, first, n);
 261 }
 262
 263 /*
 264  * We don't cow, as the div is assumed to be redundant.
 265  */
 266 static struct isl_basic_map *isl_basic_map_drop_div(
 267                 struct isl_basic_map *bmap, unsigned div)
 268 {
 269         int i;
 270         unsigned pos;
 271
 272         if (!bmap)
 273                 goto error;
 274
 275         pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
 276
 277         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
 278
 279         for (i = 0; i < bmap->n_eq; ++i)
 280                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
 281
 282         for (i = 0; i < bmap->n_ineq; ++i) {
 283                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
 284                         isl_basic_map_drop_inequality(bmap, i);
 285                         --i;
 286                         continue;
 287                 }
 288                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
 289         }
 290
 291         for (i = 0; i < bmap->n_div; ++i)
 292                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
 293
 294         if (div != bmap->n_div - 1) {
 295                 int j;
 296                 isl_int *t = bmap->div[div];
 297
 298                 for (j = div; j < bmap->n_div - 1; ++j)
 299                         bmap->div[j] = bmap->div[j+1];
 300
 301                 bmap->div[bmap->n_div - 1] = t;
 302         }
 303         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 304         isl_basic_map_free_div(bmap, 1);
 305
 306         return bmap;
 307 error:
 308         isl_basic_map_free(bmap);
 309         return NULL;
 310 }
 311
 312 struct isl_basic_map *isl_basic_map_normalize_constraints(
 313         struct isl_basic_map *bmap)
 314 {
 315         int i;
 316         isl_int gcd;
 317         unsigned total = isl_basic_map_total_dim(bmap);
 318
 319         if (!bmap)
 320                 return NULL;
 321
 322         isl_int_init(gcd);
 323         for (i = bmap->n_eq - 1; i >= 0; --i) {
 324                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
 325                 if (isl_int_is_zero(gcd)) {
 326                         if (!isl_int_is_zero(bmap->eq[i][0])) {
 327                                 bmap = isl_basic_map_set_to_empty(bmap);
 328                                 break;
 329                         }
 330                         isl_basic_map_drop_equality(bmap, i);
 331                         continue;
 332                 }
 333                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 334                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
 335                 if (isl_int_is_one(gcd))
 336                         continue;
 337                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
 338                         bmap = isl_basic_map_set_to_empty(bmap);
 339                         break;
 340                 }
 341                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
 342         }
 343
 344         for (i = bmap->n_ineq - 1; i >= 0; --i) {
 345                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
 346                 if (isl_int_is_zero(gcd)) {
 347                         if (isl_int_is_neg(bmap->ineq[i][0])) {
 348                                 bmap = isl_basic_map_set_to_empty(bmap);
 349                                 break;
 350                         }
 351                         isl_basic_map_drop_inequality(bmap, i);
 352                         continue;
 353                 }
 354                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 355                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
 356                 if (isl_int_is_one(gcd))
 357                         continue;
 358                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
 359                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
 360         }
 361         isl_int_clear(gcd);
 362
 363         return bmap;
 364 }
 365
 366 struct isl_basic_set *isl_basic_set_normalize_constraints(
 367         struct isl_basic_set *bset)
 368 {
 369         return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
 370                 (struct isl_basic_map *)bset);
 371 }
 372
 373 /* Assumes divs have been ordered if keep_divs is set.
 374  */
 375 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
 376         unsigned pos, isl_int *eq, int keep_divs, int *progress)
 377 {
 378         unsigned total;
 379         unsigned space_total;
 380         int k;
 381         int last_div;
 382
 383         total = isl_basic_map_total_dim(bmap);
 384         space_total = isl_space_dim(bmap->dim, isl_dim_all);
 385         last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
 386         for (k = 0; k < bmap->n_eq; ++k) {
 387                 if (bmap->eq[k] == eq)
 388                         continue;
 389                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
 390                         continue;
 391                 if (progress)
 392                         *progress = 1;
 393                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
 394                 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
 395         }
 396
 397         for (k = 0; k < bmap->n_ineq; ++k) {
 398                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
 399                         continue;
 400                 if (progress)
 401                         *progress = 1;
 402                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
 403                 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
 404                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 405         }
 406
 407         for (k = 0; k < bmap->n_div; ++k) {
 408                 if (isl_int_is_zero(bmap->div[k][0]))
 409                         continue;
 410                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
 411                         continue;
 412                 if (progress)
 413                         *progress = 1;
 414                 /* We need to be careful about circular definitions,
 415                  * so for now we just remove the definition of div k
 416                  * if the equality contains any divs.
 417                  * If keep_divs is set, then the divs have been ordered
 418                  * and we can keep the definition as long as the result
 419                  * is still ordered.
 420                  */
 421                 if (last_div == -1 || (keep_divs && last_div < k))
 422                         isl_seq_elim(bmap->div[k]+1, eq,
 423                                         1+pos, 1+total, &bmap->div[k][0]);
 424                 else
 425                         isl_seq_clr(bmap->div[k], 1 + total);
 426                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 427         }
 428 }
 429
 430 /* Assumes divs have been ordered if keep_divs is set.
 431  */
 432 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
 433         unsigned div, int keep_divs)
 434 {
 435         unsigned pos = isl_space_dim(bmap->dim, isl_dim_all) + div;
 436
 437         eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
 438
 439         isl_basic_map_drop_div(bmap, div);
 440 }
 441
 442 /* Check if elimination of div "div" using equality "eq" would not
 443  * result in a div depending on a later div.
 444  */
 445 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
 446         unsigned div)
 447 {
 448         int k;
 449         int last_div;
 450         unsigned space_total = isl_space_dim(bmap->dim, isl_dim_all);
 451         unsigned pos = space_total + div;
 452
 453         last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
 454         if (last_div < 0 || last_div <= div)
 455                 return 1;
 456
 457         for (k = 0; k <= last_div; ++k) {
 458                 if (isl_int_is_zero(bmap->div[k][0]))
 459                         return 1;
 460                 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
 461                         return 0;
 462         }
 463
 464         return 1;
 465 }
 466
 467 /* Elimininate divs based on equalities
 468  */
 469 static struct isl_basic_map *eliminate_divs_eq(
 470                 struct isl_basic_map *bmap, int *progress)
 471 {
 472         int d;
 473         int i;
 474         int modified = 0;
 475         unsigned off;
 476
 477         bmap = isl_basic_map_order_divs(bmap);
 478
 479         if (!bmap)
 480                 return NULL;
 481
 482         off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 483
 484         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 485                 for (i = 0; i < bmap->n_eq; ++i) {
 486                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
 487                             !isl_int_is_negone(bmap->eq[i][off + d]))
 488                                 continue;
 489                         if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
 490                                 continue;
 491                         modified = 1;
 492                         *progress = 1;
 493                         eliminate_div(bmap, bmap->eq[i], d, 1);
 494                         isl_basic_map_drop_equality(bmap, i);
 495                         break;
 496                 }
 497         }
 498         if (modified)
 499                 return eliminate_divs_eq(bmap, progress);
 500         return bmap;
 501 }
 502
 503 /* Elimininate divs based on inequalities
 504  */
 505 static struct isl_basic_map *eliminate_divs_ineq(
 506                 struct isl_basic_map *bmap, int *progress)
 507 {
 508         int d;
 509         int i;
 510         unsigned off;
 511         struct isl_ctx *ctx;
 512
 513         if (!bmap)
 514                 return NULL;
 515
 516         ctx = bmap->ctx;
 517         off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 518
 519         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 520                 for (i = 0; i < bmap->n_eq; ++i)
 521                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
 522                                 break;
 523                 if (i < bmap->n_eq)
 524                         continue;
 525                 for (i = 0; i < bmap->n_ineq; ++i)
 526                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
 527                                 break;
 528                 if (i < bmap->n_ineq)
 529                         continue;
 530                 *progress = 1;
 531                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
 532                 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 533                         break;
 534                 bmap = isl_basic_map_drop_div(bmap, d);
 535                 if (!bmap)
 536                         break;
 537         }
 538         return bmap;
 539 }
 540
 541 struct isl_basic_map *isl_basic_map_gauss(
 542         struct isl_basic_map *bmap, int *progress)
 543 {
 544         int k;
 545         int done;
 546         int last_var;
 547         unsigned total_var;
 548         unsigned total;
 549
 550         bmap = isl_basic_map_order_divs(bmap);
 551
 552         if (!bmap)
 553                 return NULL;
 554
 555         total = isl_basic_map_total_dim(bmap);
 556         total_var = total - bmap->n_div;
 557
 558         last_var = total - 1;
 559         for (done = 0; done < bmap->n_eq; ++done) {
 560                 for (; last_var >= 0; --last_var) {
 561                         for (k = done; k < bmap->n_eq; ++k)
 562                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
 563                                         break;
 564                         if (k < bmap->n_eq)
 565                                 break;
 566                 }
 567                 if (last_var < 0)
 568                         break;
 569                 if (k != done)
 570                         swap_equality(bmap, k, done);
 571                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 572                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 573
 574                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
 575                                                 progress);
 576
 577                 if (last_var >= total_var &&
 578                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
 579                         unsigned div = last_var - total_var;
 580                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
 581                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 582                         isl_int_set(bmap->div[div][0],
 583                                     bmap->eq[done][1+last_var]);
 584                         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 585                 }
 586         }
 587         if (done == bmap->n_eq)
 588                 return bmap;
 589         for (k = done; k < bmap->n_eq; ++k) {
 590                 if (isl_int_is_zero(bmap->eq[k][0]))
 591                         continue;
 592                 return isl_basic_map_set_to_empty(bmap);
 593         }
 594         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
 595         return bmap;
 596 }
 597
 598 struct isl_basic_set *isl_basic_set_gauss(
 599         struct isl_basic_set *bset, int *progress)
 600 {
 601         return (struct isl_basic_set*)isl_basic_map_gauss(
 602                         (struct isl_basic_map *)bset, progress);
 603 }
 604
 605
 606 static unsigned int round_up(unsigned int v)
 607 {
 608         int old_v = v;
 609
 610         while (v) {
 611                 old_v = v;
 612                 v ^= v & -v;
 613         }
 614         return old_v << 1;
 615 }
 616
 617 static int hash_index(isl_int ***index, unsigned int size, int bits,
 618                         struct isl_basic_map *bmap, int k)
 619 {
 620         int h;
 621         unsigned total = isl_basic_map_total_dim(bmap);
 622         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
 623         for (h = hash; index[h]; h = (h+1) % size)
 624                 if (&bmap->ineq[k] != index[h] &&
 625                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
 626                         break;
 627         return h;
 628 }
 629
 630 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
 631                           struct isl_basic_set *bset, int k)
 632 {
 633         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
 634 }
 635
 636 /* If we can eliminate more than one div, then we need to make
 637  * sure we do it from last div to first div, in order not to
 638  * change the position of the other divs that still need to
 639  * be removed.
 640  */
 641 static struct isl_basic_map *remove_duplicate_divs(
 642         struct isl_basic_map *bmap, int *progress)
 643 {
 644         unsigned int size;
 645         int *index;
 646         int *elim_for;
 647         int k, l, h;
 648         int bits;
 649         struct isl_blk eq;
 650         unsigned total_var;
 651         unsigned total;
 652         struct isl_ctx *ctx;
 653
 654         if (!bmap || bmap->n_div <= 1)
 655                 return bmap;
 656
 657         total_var = isl_space_dim(bmap->dim, isl_dim_all);
 658         total = total_var + bmap->n_div;
 659
 660         ctx = bmap->ctx;
 661         for (k = bmap->n_div - 1; k >= 0; --k)
 662                 if (!isl_int_is_zero(bmap->div[k][0]))
 663                         break;
 664         if (k <= 0)
 665                 return bmap;
 666
 667         elim_for = isl_calloc_array(ctx, int, bmap->n_div);
 668         size = round_up(4 * bmap->n_div / 3 - 1);
 669         bits = ffs(size) - 1;
 670         index = isl_calloc_array(ctx, int, size);
 671         if (!index)
 672                 return bmap;
 673         eq = isl_blk_alloc(ctx, 1+total);
 674         if (isl_blk_is_error(eq))
 675                 goto out;
 676
 677         isl_seq_clr(eq.data, 1+total);
 678         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
 679         for (--k; k >= 0; --k) {
 680                 uint32_t hash;
 681
 682                 if (isl_int_is_zero(bmap->div[k][0]))
 683                         continue;
 684
 685                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
 686                 for (h = hash; index[h]; h = (h+1) % size)
 687                         if (isl_seq_eq(bmap->div[k],
 688                                        bmap->div[index[h]-1], 2+total))
 689                                 break;
 690                 if (index[h]) {
 691                         *progress = 1;
 692                         l = index[h] - 1;
 693                         elim_for[l] = k + 1;
 694                 }
 695                 index[h] = k+1;
 696         }
 697         for (l = bmap->n_div - 1; l >= 0; --l) {
 698                 if (!elim_for[l])
 699                         continue;
 700                 k = elim_for[l] - 1;
 701                 isl_int_set_si(eq.data[1+total_var+k], -1);
 702                 isl_int_set_si(eq.data[1+total_var+l], 1);
 703                 eliminate_div(bmap, eq.data, l, 0);
 704                 isl_int_set_si(eq.data[1+total_var+k], 0);
 705                 isl_int_set_si(eq.data[1+total_var+l], 0);
 706         }
 707
 708         isl_blk_free(ctx, eq);
 709 out:
 710         free(index);
 711         free(elim_for);
 712         return bmap;
 713 }
 714
 715 static int n_pure_div_eq(struct isl_basic_map *bmap)
 716 {
 717         int i, j;
 718         unsigned total;
 719
 720         total = isl_space_dim(bmap->dim, isl_dim_all);
 721         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 722                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 723                         --j;
 724                 if (j < 0)
 725                         break;
 726                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 727                         return 0;
 728         }
 729         return i;
 730 }
 731
 732 /* Normalize divs that appear in equalities.
 733  *
 734  * In particular, we assume that bmap contains some equalities
 735  * of the form
 736  *
 737  *      a x = m * e_i
 738  *
 739  * and we want to replace the set of e_i by a minimal set and
 740  * such that the new e_i have a canonical representation in terms
 741  * of the vector x.
 742  * If any of the equalities involves more than one divs, then
 743  * we currently simply bail out.
 744  *
 745  * Let us first additionally assume that all equalities involve
 746  * a div.  The equalities then express modulo constraints on the
 747  * remaining variables and we can use "parameter compression"
 748  * to find a minimal set of constraints.  The result is a transformation
 749  *
 750  *      x = T(x') = x_0 + G x'
 751  *
 752  * with G a lower-triangular matrix with all elements below the diagonal
 753  * non-negative and smaller than the diagonal element on the same row.
 754  * We first normalize x_0 by making the same property hold in the affine
 755  * T matrix.
 756  * The rows i of G with a 1 on the diagonal do not impose any modulo
 757  * constraint and simply express x_i = x'_i.
 758  * For each of the remaining rows i, we introduce a div and a corresponding
 759  * equality.  In particular
 760  *
 761  *      g_ii e_j = x_i - g_i(x')
 762  *
 763  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 764  * corresponding div (if g_kk != 1).
 765  *
 766  * If there are any equalities not involving any div, then we
 767  * first apply a variable compression on the variables x:
 768  *
 769  *      x = C x''       x'' = C_2 x
 770  *
 771  * and perform the above parameter compression on A C instead of on A.
 772  * The resulting compression is then of the form
 773  *
 774  *      x'' = T(x') = x_0 + G x'
 775  *
 776  * and in constructing the new divs and the corresponding equalities,
 777  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 778  * by the corresponding row from C_2.
 779  */
 780 static struct isl_basic_map *normalize_divs(
 781         struct isl_basic_map *bmap, int *progress)
 782 {
 783         int i, j, k;
 784         int total;
 785         int div_eq;
 786         struct isl_mat *B;
 787         struct isl_vec *d;
 788         struct isl_mat *T = NULL;
 789         struct isl_mat *C = NULL;
 790         struct isl_mat *C2 = NULL;
 791         isl_int v;
 792         int *pos;
 793         int dropped, needed;
 794
 795         if (!bmap)
 796                 return NULL;
 797
 798         if (bmap->n_div == 0)
 799                 return bmap;
 800
 801         if (bmap->n_eq == 0)
 802                 return bmap;
 803
 804         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 805                 return bmap;
 806
 807         total = isl_space_dim(bmap->dim, isl_dim_all);
 808         div_eq = n_pure_div_eq(bmap);
 809         if (div_eq == 0)
 810                 return bmap;
 811
 812         if (div_eq < bmap->n_eq) {
 813                 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
 814                                         bmap->n_eq - div_eq, 0, 1 + total);
 815                 C = isl_mat_variable_compression(B, &C2);
 816                 if (!C || !C2)
 817                         goto error;
 818                 if (C->n_col == 0) {
 819                         bmap = isl_basic_map_set_to_empty(bmap);
 820                         isl_mat_free(C);
 821                         isl_mat_free(C2);
 822                         goto done;
 823                 }
 824         }
 825
 826         d = isl_vec_alloc(bmap->ctx, div_eq);
 827         if (!d)
 828                 goto error;
 829         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 830                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 831                         --j;
 832                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 833         }
 834         B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 835
 836         if (C) {
 837                 B = isl_mat_product(B, C);
 838                 C = NULL;
 839         }
 840
 841         T = isl_mat_parameter_compression(B, d);
 842         if (!T)
 843                 goto error;
 844         if (T->n_col == 0) {
 845                 bmap = isl_basic_map_set_to_empty(bmap);
 846                 isl_mat_free(C2);
 847                 isl_mat_free(T);
 848                 goto done;
 849         }
 850         isl_int_init(v);
 851         for (i = 0; i < T->n_row - 1; ++i) {
 852                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 853                 if (isl_int_is_zero(v))
 854                         continue;
 855                 isl_mat_col_submul(T, 0, v, 1 + i);
 856         }
 857         isl_int_clear(v);
 858         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 859         if (!pos)
 860                 goto error;
 861         /* We have to be careful because dropping equalities may reorder them */
 862         dropped = 0;
 863         for (j = bmap->n_div - 1; j >= 0; --j) {
 864                 for (i = 0; i < bmap->n_eq; ++i)
 865                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 866                                 break;
 867                 if (i < bmap->n_eq) {
 868                         bmap = isl_basic_map_drop_div(bmap, j);
 869                         isl_basic_map_drop_equality(bmap, i);
 870                         ++dropped;
 871                 }
 872         }
 873         pos[0] = 0;
 874         needed = 0;
 875         for (i = 1; i < T->n_row; ++i) {
 876                 if (isl_int_is_one(T->row[i][i]))
 877                         pos[i] = i;
 878                 else
 879                         needed++;
 880         }
 881         if (needed > dropped) {
 882                 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
 883                                 needed, needed, 0);
 884                 if (!bmap)
 885                         goto error;
 886         }
 887         for (i = 1; i < T->n_row; ++i) {
 888                 if (isl_int_is_one(T->row[i][i]))
 889                         continue;
 890                 k = isl_basic_map_alloc_div(bmap);
 891                 pos[i] = 1 + total + k;
 892                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 893                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 894                 if (C2)
 895                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 896                 else
 897                         isl_int_set_si(bmap->div[k][1 + i], 1);
 898                 for (j = 0; j < i; ++j) {
 899                         if (isl_int_is_zero(T->row[i][j]))
 900                                 continue;
 901                         if (pos[j] < T->n_row && C2)
 902                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 903                                                 C2->row[pos[j]], 1 + total);
 904                         else
 905                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 906                                                                 T->row[i][j]);
 907                 }
 908                 j = isl_basic_map_alloc_equality(bmap);
 909                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 910                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 911         }
 912         free(pos);
 913         isl_mat_free(C2);
 914         isl_mat_free(T);
 915
 916         if (progress)
 917                 *progress = 1;
 918 done:
 919         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 920
 921         return bmap;
 922 error:
 923         isl_mat_free(C);
 924         isl_mat_free(C2);
 925         isl_mat_free(T);
 926         return bmap;
 927 }
 928
 929 static struct isl_basic_map *set_div_from_lower_bound(
 930         struct isl_basic_map *bmap, int div, int ineq)
 931 {
 932         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 933
 934         isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
 935         isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
 936         isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
 937         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
 938         isl_int_set_si(bmap->div[div][1 + total + div], 0);
 939
 940         return bmap;
 941 }
 942
 943 /* Check whether it is ok to define a div based on an inequality.
 944  * To avoid the introduction of circular definitions of divs, we
 945  * do not allow such a definition if the resulting expression would refer to
 946  * any other undefined divs or if any known div is defined in
 947  * terms of the unknown div.
 948  */
 949 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
 950         int div, int ineq)
 951 {
 952         int j;
 953         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 954
 955         /* Not defined in terms of unknown divs */
 956         for (j = 0; j < bmap->n_div; ++j) {
 957                 if (div == j)
 958                         continue;
 959                 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
 960                         continue;
 961                 if (isl_int_is_zero(bmap->div[j][0]))
 962                         return 0;
 963         }
 964
 965         /* No other div defined in terms of this one => avoid loops */
 966         for (j = 0; j < bmap->n_div; ++j) {
 967                 if (div == j)
 968                         continue;
 969                 if (isl_int_is_zero(bmap->div[j][0]))
 970                         continue;
 971                 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
 972                         return 0;
 973         }
 974
 975         return 1;
 976 }
 977
 978 /* Given two constraints "k" and "l" that are opposite to each other,
 979  * except for the constant term, check if we can use them
 980  * to obtain an expression for one of the hitherto unknown divs.
 981  * "sum" is the sum of the constant terms of the constraints.
 982  * If this sum is strictly smaller than the coefficient of one
 983  * of the divs, then this pair can be used define the div.
 984  * To avoid the introduction of circular definitions of divs, we
 985  * do not use the pair if the resulting expression would refer to
 986  * any other undefined divs or if any known div is defined in
 987  * terms of the unknown div.
 988  */
 989 static struct isl_basic_map *check_for_div_constraints(
 990         struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
 991 {
 992         int i;
 993         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 994
 995         for (i = 0; i < bmap->n_div; ++i) {
 996                 if (!isl_int_is_zero(bmap->div[i][0]))
 997                         continue;
 998                 if (isl_int_is_zero(bmap->ineq[k][total + i]))
 999                         continue;
1000                 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1001                         continue;
1002                 if (!ok_to_set_div_from_bound(bmap, i, k))
1003                         break;
1004                 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1005                         bmap = set_div_from_lower_bound(bmap, i, k);
1006                 else
1007                         bmap = set_div_from_lower_bound(bmap, i, l);
1008                 if (progress)
1009                         *progress = 1;
1010                 break;
1011         }
1012         return bmap;
1013 }
1014
1015 static struct isl_basic_map *remove_duplicate_constraints(
1016         struct isl_basic_map *bmap, int *progress, int detect_divs)
1017 {
1018         unsigned int size;
1019         isl_int ***index;
1020         int k, l, h;
1021         int bits;
1022         unsigned total = isl_basic_map_total_dim(bmap);
1023         isl_int sum;
1024         isl_ctx *ctx;
1025
1026         if (!bmap || bmap->n_ineq <= 1)
1027                 return bmap;
1028
1029         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1030         bits = ffs(size) - 1;
1031         ctx = isl_basic_map_get_ctx(bmap);
1032         index = isl_calloc_array(ctx, isl_int **, size);
1033         if (!index)
1034                 return bmap;
1035
1036         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1037         for (k = 1; k < bmap->n_ineq; ++k) {
1038                 h = hash_index(index, size, bits, bmap, k);
1039                 if (!index[h]) {
1040                         index[h] = &bmap->ineq[k];
1041                         continue;
1042                 }
1043                 if (progress)
1044                         *progress = 1;
1045                 l = index[h] - &bmap->ineq[0];
1046                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1047                         swap_inequality(bmap, k, l);
1048                 isl_basic_map_drop_inequality(bmap, k);
1049                 --k;
1050         }
1051         isl_int_init(sum);
1052         for (k = 0; k < bmap->n_ineq-1; ++k) {
1053                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1054                 h = hash_index(index, size, bits, bmap, k);
1055                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1056                 if (!index[h])
1057                         continue;
1058                 l = index[h] - &bmap->ineq[0];
1059                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1060                 if (isl_int_is_pos(sum)) {
1061                         if (detect_divs)
1062                                 bmap = check_for_div_constraints(bmap, k, l,
1063                                                                  sum, progress);
1064                         continue;
1065                 }
1066                 if (isl_int_is_zero(sum)) {
1067                         /* We need to break out of the loop after these
1068                          * changes since the contents of the hash
1069                          * will no longer be valid.
1070                          * Plus, we probably we want to regauss first.
1071                          */
1072                         if (progress)
1073                                 *progress = 1;
1074                         isl_basic_map_drop_inequality(bmap, l);
1075                         isl_basic_map_inequality_to_equality(bmap, k);
1076                 } else
1077                         bmap = isl_basic_map_set_to_empty(bmap);
1078                 break;
1079         }
1080         isl_int_clear(sum);
1081
1082         free(index);
1083         return bmap;
1084 }
1085
1086
1087 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1088 {
1089         int progress = 1;
1090         if (!bmap)
1091                 return NULL;
1092         while (progress) {
1093                 progress = 0;
1094                 bmap = isl_basic_map_normalize_constraints(bmap);
1095                 bmap = remove_duplicate_divs(bmap, &progress);
1096                 bmap = eliminate_divs_eq(bmap, &progress);
1097                 bmap = eliminate_divs_ineq(bmap, &progress);
1098                 bmap = isl_basic_map_gauss(bmap, &progress);
1099                 /* requires equalities in normal form */
1100                 bmap = normalize_divs(bmap, &progress);
1101                 bmap = remove_duplicate_constraints(bmap, &progress, 1);
1102         }
1103         return bmap;
1104 }
1105
1106 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1107 {
1108         return (struct isl_basic_set *)
1109                 isl_basic_map_simplify((struct isl_basic_map *)bset);
1110 }
1111
1112
1113 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1114         isl_int *constraint, unsigned div)
1115 {
1116         unsigned pos;
1117
1118         if (!bmap)
1119                 return -1;
1120
1121         pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1122
1123         if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1124                 int neg;
1125                 isl_int_sub(bmap->div[div][1],
1126                                 bmap->div[div][1], bmap->div[div][0]);
1127                 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1128                 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1129                 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1130                 isl_int_add(bmap->div[div][1],
1131                                 bmap->div[div][1], bmap->div[div][0]);
1132                 if (!neg)
1133                         return 0;
1134                 if (isl_seq_first_non_zero(constraint+pos+1,
1135                                             bmap->n_div-div-1) != -1)
1136                         return 0;
1137         } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1138                 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1139                         return 0;
1140                 if (isl_seq_first_non_zero(constraint+pos+1,
1141                                             bmap->n_div-div-1) != -1)
1142                         return 0;
1143         } else
1144                 return 0;
1145
1146         return 1;
1147 }
1148
1149 int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set *bset,
1150         isl_int *constraint, unsigned div)
1151 {
1152         return isl_basic_map_is_div_constraint(bset, constraint, div);
1153 }
1154
1155
1156 /* If the only constraints a div d=floor(f/m)
1157  * appears in are its two defining constraints
1158  *
1159  *      f - m d >=0
1160  *      -(f - (m - 1)) + m d >= 0
1161  *
1162  * then it can safely be removed.
1163  */
1164 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1165 {
1166         int i;
1167         unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1168
1169         for (i = 0; i < bmap->n_eq; ++i)
1170                 if (!isl_int_is_zero(bmap->eq[i][pos]))
1171                         return 0;
1172
1173         for (i = 0; i < bmap->n_ineq; ++i) {
1174                 if (isl_int_is_zero(bmap->ineq[i][pos]))
1175                         continue;
1176                 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1177                         return 0;
1178         }
1179
1180         for (i = 0; i < bmap->n_div; ++i)
1181                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1182                         return 0;
1183
1184         return 1;
1185 }
1186
1187 /*
1188  * Remove divs that don't occur in any of the constraints or other divs.
1189  * These can arise when dropping some of the variables in a quast
1190  * returned by piplib.
1191  */
1192 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1193 {
1194         int i;
1195
1196         if (!bmap)
1197                 return NULL;
1198
1199         for (i = bmap->n_div-1; i >= 0; --i) {
1200                 if (!div_is_redundant(bmap, i))
1201                         continue;
1202                 bmap = isl_basic_map_drop_div(bmap, i);
1203         }
1204         return bmap;
1205 }
1206
1207 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1208 {
1209         bmap = remove_redundant_divs(bmap);
1210         if (!bmap)
1211                 return NULL;
1212         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1213         return bmap;
1214 }
1215
1216 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1217 {
1218         return (struct isl_basic_set *)
1219                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1220 }
1221
1222 struct isl_set *isl_set_finalize(struct isl_set *set)
1223 {
1224         int i;
1225
1226         if (!set)
1227                 return NULL;
1228         for (i = 0; i < set->n; ++i) {
1229                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1230                 if (!set->p[i])
1231                         goto error;
1232         }
1233         return set;
1234 error:
1235         isl_set_free(set);
1236         return NULL;
1237 }
1238
1239 struct isl_map *isl_map_finalize(struct isl_map *map)
1240 {
1241         int i;
1242
1243         if (!map)
1244                 return NULL;
1245         for (i = 0; i < map->n; ++i) {
1246                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1247                 if (!map->p[i])
1248                         goto error;
1249         }
1250         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1251         return map;
1252 error:
1253         isl_map_free(map);
1254         return NULL;
1255 }
1256
1257
1258 /* Remove definition of any div that is defined in terms of the given variable.
1259  * The div itself is not removed.  Functions such as
1260  * eliminate_divs_ineq depend on the other divs remaining in place.
1261  */
1262 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1263                                                                         int pos)
1264 {
1265         int i;
1266
1267         for (i = 0; i < bmap->n_div; ++i) {
1268                 if (isl_int_is_zero(bmap->div[i][0]))
1269                         continue;
1270                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1271                         continue;
1272                 isl_int_set_si(bmap->div[i][0], 0);
1273         }
1274         return bmap;
1275 }
1276
1277 /* Eliminate the specified variables from the constraints using
1278  * Fourier-Motzkin.  The variables themselves are not removed.
1279  */
1280 struct isl_basic_map *isl_basic_map_eliminate_vars(
1281         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1282 {
1283         int d;
1284         int i, j, k;
1285         unsigned total;
1286         int need_gauss = 0;
1287
1288         if (n == 0)
1289                 return bmap;
1290         if (!bmap)
1291                 return NULL;
1292         total = isl_basic_map_total_dim(bmap);
1293
1294         bmap = isl_basic_map_cow(bmap);
1295         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1296                 bmap = remove_dependent_vars(bmap, d);
1297
1298         for (d = pos + n - 1;
1299              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1300                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1301         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1302                 int n_lower, n_upper;
1303                 if (!bmap)
1304                         return NULL;
1305                 for (i = 0; i < bmap->n_eq; ++i) {
1306                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1307                                 continue;
1308                         eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1309                         isl_basic_map_drop_equality(bmap, i);
1310                         need_gauss = 1;
1311                         break;
1312                 }
1313                 if (i < bmap->n_eq)
1314                         continue;
1315                 n_lower = 0;
1316                 n_upper = 0;
1317                 for (i = 0; i < bmap->n_ineq; ++i) {
1318                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1319                                 n_lower++;
1320                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1321                                 n_upper++;
1322                 }
1323                 bmap = isl_basic_map_extend_constraints(bmap,
1324                                 0, n_lower * n_upper);
1325                 if (!bmap)
1326                         goto error;
1327                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1328                         int last;
1329                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1330                                 continue;
1331                         last = -1;
1332                         for (j = 0; j < i; ++j) {
1333                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1334                                         continue;
1335                                 last = j;
1336                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1337                                     isl_int_sgn(bmap->ineq[j][1+d]))
1338                                         continue;
1339                                 k = isl_basic_map_alloc_inequality(bmap);
1340                                 if (k < 0)
1341                                         goto error;
1342                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1343                                                 1+total);
1344                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1345                                                 1+d, 1+total, NULL);
1346                         }
1347                         isl_basic_map_drop_inequality(bmap, i);
1348                         i = last + 1;
1349                 }
1350                 if (n_lower > 0 && n_upper > 0) {
1351                         bmap = isl_basic_map_normalize_constraints(bmap);
1352                         bmap = remove_duplicate_constraints(bmap, NULL, 0);
1353                         bmap = isl_basic_map_gauss(bmap, NULL);
1354                         bmap = isl_basic_map_remove_redundancies(bmap);
1355                         need_gauss = 0;
1356                         if (!bmap)
1357                                 goto error;
1358                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1359                                 break;
1360                 }
1361         }
1362         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1363         if (need_gauss)
1364                 bmap = isl_basic_map_gauss(bmap, NULL);
1365         return bmap;
1366 error:
1367         isl_basic_map_free(bmap);
1368         return NULL;
1369 }
1370
1371 struct isl_basic_set *isl_basic_set_eliminate_vars(
1372         struct isl_basic_set *bset, unsigned pos, unsigned n)
1373 {
1374         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1375                         (struct isl_basic_map *)bset, pos, n);
1376 }
1377
1378 /* Eliminate the specified n dimensions starting at first from the
1379  * constraints using Fourier-Motzkin.  The dimensions themselves
1380  * are not removed.
1381  */
1382 __isl_give isl_basic_map *isl_basic_map_eliminate(
1383         __isl_take isl_basic_map *bmap,
1384         enum isl_dim_type type, unsigned first, unsigned n)
1385 {
1386         if (!bmap)
1387                 return NULL;
1388         if (n == 0)
1389                 return bmap;
1390
1391         if (first + n > isl_basic_map_dim(bmap, type))
1392                 isl_die(bmap->ctx, isl_error_invalid,
1393                         "index out of bounds", goto error);
1394
1395         first += isl_basic_map_offset(bmap, type) - 1;
1396         bmap = isl_basic_map_eliminate_vars(bmap, first, n);
1397         return isl_basic_map_finalize(bmap);
1398 error:
1399         isl_basic_map_free(bmap);
1400         return NULL;
1401 }
1402
1403 /* Don't assume equalities are in order, because align_divs
1404  * may have changed the order of the divs.
1405  */
1406 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1407 {
1408         int d, i;
1409         unsigned total;
1410
1411         total = isl_space_dim(bmap->dim, isl_dim_all);
1412         for (d = 0; d < total; ++d)
1413                 elim[d] = -1;
1414         for (i = 0; i < bmap->n_eq; ++i) {
1415                 for (d = total - 1; d >= 0; --d) {
1416                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1417                                 continue;
1418                         elim[d] = i;
1419                         break;
1420                 }
1421         }
1422 }
1423
1424 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1425 {
1426         compute_elimination_index((struct isl_basic_map *)bset, elim);
1427 }
1428
1429 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1430         struct isl_basic_map *bmap, int *elim)
1431 {
1432         int d;
1433         int copied = 0;
1434         unsigned total;
1435
1436         total = isl_space_dim(bmap->dim, isl_dim_all);
1437         for (d = total - 1; d >= 0; --d) {
1438                 if (isl_int_is_zero(src[1+d]))
1439                         continue;
1440                 if (elim[d] == -1)
1441                         continue;
1442                 if (!copied) {
1443                         isl_seq_cpy(dst, src, 1 + total);
1444                         copied = 1;
1445                 }
1446                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1447         }
1448         return copied;
1449 }
1450
1451 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1452         struct isl_basic_set *bset, int *elim)
1453 {
1454         return reduced_using_equalities(dst, src,
1455                                         (struct isl_basic_map *)bset, elim);
1456 }
1457
1458 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1459         struct isl_basic_set *bset, struct isl_basic_set *context)
1460 {
1461         int i;
1462         int *elim;
1463
1464         if (!bset || !context)
1465                 goto error;
1466
1467         if (context->n_eq == 0) {
1468                 isl_basic_set_free(context);
1469                 return bset;
1470         }
1471
1472         bset = isl_basic_set_cow(bset);
1473         if (!bset)
1474                 goto error;
1475
1476         elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1477         if (!elim)
1478                 goto error;
1479         set_compute_elimination_index(context, elim);
1480         for (i = 0; i < bset->n_eq; ++i)
1481                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1482                                                         context, elim);
1483         for (i = 0; i < bset->n_ineq; ++i)
1484                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1485                                                         context, elim);
1486         isl_basic_set_free(context);
1487         free(elim);
1488         bset = isl_basic_set_simplify(bset);
1489         bset = isl_basic_set_finalize(bset);
1490         return bset;
1491 error:
1492         isl_basic_set_free(bset);
1493         isl_basic_set_free(context);
1494         return NULL;
1495 }
1496
1497 static struct isl_basic_set *remove_shifted_constraints(
1498         struct isl_basic_set *bset, struct isl_basic_set *context)
1499 {
1500         unsigned int size;
1501         isl_int ***index;
1502         int bits;
1503         int k, h, l;
1504         isl_ctx *ctx;
1505
1506         if (!bset)
1507                 return NULL;
1508
1509         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1510         bits = ffs(size) - 1;
1511         ctx = isl_basic_set_get_ctx(bset);
1512         index = isl_calloc_array(ctx, isl_int **, size);
1513         if (!index)
1514                 return bset;
1515
1516         for (k = 0; k < context->n_ineq; ++k) {
1517                 h = set_hash_index(index, size, bits, context, k);
1518                 index[h] = &context->ineq[k];
1519         }
1520         for (k = 0; k < bset->n_ineq; ++k) {
1521                 h = set_hash_index(index, size, bits, bset, k);
1522                 if (!index[h])
1523                         continue;
1524                 l = index[h] - &context->ineq[0];
1525                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1526                         continue;
1527                 bset = isl_basic_set_cow(bset);
1528                 if (!bset)
1529                         goto error;
1530                 isl_basic_set_drop_inequality(bset, k);
1531                 --k;
1532         }
1533         free(index);
1534         return bset;
1535 error:
1536         free(index);
1537         return bset;
1538 }
1539
1540 /* Remove all information from bset that is redundant in the context
1541  * of context.  Both bset and context are assumed to be full-dimensional.
1542  *
1543  * We first * remove the inequalities from "bset"
1544  * that are obviously redundant with respect to some inequality in "context".
1545  *
1546  * If there are any inequalities left, we construct a tableau for
1547  * the context and then add the inequalities of "bset".
1548  * Before adding these inequalities, we freeze all constraints such that
1549  * they won't be considered redundant in terms of the constraints of "bset".
1550  * Then we detect all redundant constraints (among the
1551  * constraints that weren't frozen), first by checking for redundancy in the
1552  * the tableau and then by checking if replacing a constraint by its negation
1553  * would lead to an empty set.  This last step is fairly expensive
1554  * and could be optimized by more reuse of the tableau.
1555  * Finally, we update bset according to the results.
1556  */
1557 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1558         __isl_take isl_basic_set *context)
1559 {
1560         int i, k;
1561         isl_basic_set *combined = NULL;
1562         struct isl_tab *tab = NULL;
1563         unsigned context_ineq;
1564         unsigned total;
1565
1566         if (!bset || !context)
1567                 goto error;
1568
1569         if (isl_basic_set_is_universe(bset)) {
1570                 isl_basic_set_free(context);
1571                 return bset;
1572         }
1573
1574         if (isl_basic_set_is_universe(context)) {
1575                 isl_basic_set_free(context);
1576                 return bset;
1577         }
1578
1579         bset = remove_shifted_constraints(bset, context);
1580         if (!bset)
1581                 goto error;
1582         if (bset->n_ineq == 0)
1583                 goto done;
1584
1585         context_ineq = context->n_ineq;
1586         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1587         combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1588         tab = isl_tab_from_basic_set(combined, 0);
1589         for (i = 0; i < context_ineq; ++i)
1590                 if (isl_tab_freeze_constraint(tab, i) < 0)
1591                         goto error;
1592         tab = isl_tab_extend(tab, bset->n_ineq);
1593         for (i = 0; i < bset->n_ineq; ++i)
1594                 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1595                         goto error;
1596         bset = isl_basic_set_add_constraints(combined, bset, 0);
1597         combined = NULL;
1598         if (!bset)
1599                 goto error;
1600         if (isl_tab_detect_redundant(tab) < 0)
1601                 goto error;
1602         total = isl_basic_set_total_dim(bset);
1603         for (i = context_ineq; i < bset->n_ineq; ++i) {
1604                 int is_empty;
1605                 if (tab->con[i].is_redundant)
1606                         continue;
1607                 tab->con[i].is_redundant = 1;
1608                 combined = isl_basic_set_dup(bset);
1609                 combined = isl_basic_set_update_from_tab(combined, tab);
1610                 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1611                 k = isl_basic_set_alloc_inequality(combined);
1612                 if (k < 0)
1613                         goto error;
1614                 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1615                 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1616                 is_empty = isl_basic_set_is_empty(combined);
1617                 if (is_empty < 0)
1618                         goto error;
1619                 isl_basic_set_free(combined);
1620                 combined = NULL;
1621                 if (!is_empty)
1622                         tab->con[i].is_redundant = 0;
1623         }
1624         for (i = 0; i < context_ineq; ++i)
1625                 tab->con[i].is_redundant = 1;
1626         bset = isl_basic_set_update_from_tab(bset, tab);
1627         if (bset) {
1628                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1629                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1630         }
1631
1632         isl_tab_free(tab);
1633 done:
1634         bset = isl_basic_set_simplify(bset);
1635         bset = isl_basic_set_finalize(bset);
1636         isl_basic_set_free(context);
1637         return bset;
1638 error:
1639         isl_tab_free(tab);
1640         isl_basic_set_free(combined);
1641         isl_basic_set_free(context);
1642         isl_basic_set_free(bset);
1643         return NULL;
1644 }
1645
1646 /* Remove all information from bset that is redundant in the context
1647  * of context.  In particular, equalities that are linear combinations
1648  * of those in context are removed.  Then the inequalities that are
1649  * redundant in the context of the equalities and inequalities of
1650  * context are removed.
1651  *
1652  * We first compute the integer affine hull of the intersection,
1653  * compute the gist inside this affine hull and then add back
1654  * those equalities that are not implied by the context.
1655  *
1656  * If two constraints are mutually redundant, then uset_gist_full
1657  * will remove the second of those constraints.  We therefore first
1658  * sort the constraints so that constraints not involving existentially
1659  * quantified variables are given precedence over those that do.
1660  * We have to perform this sorting before the variable compression,
1661  * because that may effect the order of the variables.
1662  */
1663 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1664         __isl_take isl_basic_set *context)
1665 {
1666         isl_mat *eq;
1667         isl_mat *T, *T2;
1668         isl_basic_set *aff;
1669         isl_basic_set *aff_context;
1670         unsigned total;
1671
1672         if (!bset || !context)
1673                 goto error;
1674
1675         bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1676         if (isl_basic_set_plain_is_empty(bset)) {
1677                 isl_basic_set_free(context);
1678                 return bset;
1679         }
1680         bset = isl_basic_set_sort_constraints(bset);
1681         aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1682         if (!aff)
1683                 goto error;
1684         if (isl_basic_set_plain_is_empty(aff)) {
1685                 isl_basic_set_free(aff);
1686                 isl_basic_set_free(context);
1687                 return bset;
1688         }
1689         if (aff->n_eq == 0) {
1690                 isl_basic_set_free(aff);
1691                 return uset_gist_full(bset, context);
1692         }
1693         total = isl_basic_set_total_dim(bset);
1694         eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1695         eq = isl_mat_cow(eq);
1696         T = isl_mat_variable_compression(eq, &T2);
1697         if (T && T->n_col == 0) {
1698                 isl_mat_free(T);
1699                 isl_mat_free(T2);
1700                 isl_basic_set_free(context);
1701                 isl_basic_set_free(aff);
1702                 return isl_basic_set_set_to_empty(bset);
1703         }
1704
1705         aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1706
1707         bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1708         context = isl_basic_set_preimage(context, T);
1709
1710         bset = uset_gist_full(bset, context);
1711         bset = isl_basic_set_preimage(bset, T2);
1712         bset = isl_basic_set_intersect(bset, aff);
1713         bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1714
1715         if (bset) {
1716                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1717                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1718         }
1719
1720         return bset;
1721 error:
1722         isl_basic_set_free(bset);
1723         isl_basic_set_free(context);
1724         return NULL;
1725 }
1726
1727 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1728  * We simply add the equalities in context to bmap and then do a regular
1729  * div normalizations.  Better results can be obtained by normalizing
1730  * only the divs in bmap than do not also appear in context.
1731  * We need to be careful to reduce the divs using the equalities
1732  * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1733  * spurious constraints.
1734  */
1735 static struct isl_basic_map *normalize_divs_in_context(
1736         struct isl_basic_map *bmap, struct isl_basic_map *context)
1737 {
1738         int i;
1739         unsigned total_context;
1740         int div_eq;
1741
1742         div_eq = n_pure_div_eq(bmap);
1743         if (div_eq == 0)
1744                 return bmap;
1745
1746         if (context->n_div > 0)
1747                 bmap = isl_basic_map_align_divs(bmap, context);
1748
1749         total_context = isl_basic_map_total_dim(context);
1750         bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1751         for (i = 0; i < context->n_eq; ++i) {
1752                 int k;
1753                 k = isl_basic_map_alloc_equality(bmap);
1754                 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1755                 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1756                                 isl_basic_map_total_dim(bmap) - total_context);
1757         }
1758         bmap = isl_basic_map_gauss(bmap, NULL);
1759         bmap = normalize_divs(bmap, NULL);
1760         bmap = isl_basic_map_gauss(bmap, NULL);
1761         return bmap;
1762 }
1763
1764 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1765         struct isl_basic_map *context)
1766 {
1767         struct isl_basic_set *bset;
1768
1769         if (!bmap || !context)
1770                 goto error;
1771
1772         if (isl_basic_map_is_universe(bmap)) {
1773                 isl_basic_map_free(context);
1774                 return bmap;
1775         }
1776         if (isl_basic_map_plain_is_empty(context)) {
1777                 isl_basic_map_free(bmap);
1778                 return context;
1779         }
1780         if (isl_basic_map_plain_is_empty(bmap)) {
1781                 isl_basic_map_free(context);
1782                 return bmap;
1783         }
1784
1785         bmap = isl_basic_map_remove_redundancies(bmap);
1786         context = isl_basic_map_remove_redundancies(context);
1787
1788         if (context->n_eq)
1789                 bmap = normalize_divs_in_context(bmap, context);
1790
1791         context = isl_basic_map_align_divs(context, bmap);
1792         bmap = isl_basic_map_align_divs(bmap, context);
1793
1794         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1795                          isl_basic_map_underlying_set(context));
1796
1797         return isl_basic_map_overlying_set(bset, bmap);
1798 error:
1799         isl_basic_map_free(bmap);
1800         isl_basic_map_free(context);
1801         return NULL;
1802 }
1803
1804 /*
1805  * Assumes context has no implicit divs.
1806  */
1807 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1808         __isl_take isl_basic_map *context)
1809 {
1810         int i;
1811
1812         if (!map || !context)
1813                 goto error;;
1814
1815         if (isl_basic_map_plain_is_empty(context)) {
1816                 isl_map_free(map);
1817                 return isl_map_from_basic_map(context);
1818         }
1819
1820         context = isl_basic_map_remove_redundancies(context);
1821         map = isl_map_cow(map);
1822         if (!map || !context)
1823                 goto error;;
1824         isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error);
1825         map = isl_map_compute_divs(map);
1826         for (i = 0; i < map->n; ++i)
1827                 context = isl_basic_map_align_divs(context, map->p[i]);
1828         for (i = map->n - 1; i >= 0; --i) {
1829                 map->p[i] = isl_basic_map_gist(map->p[i],
1830                                                 isl_basic_map_copy(context));
1831                 if (!map->p[i])
1832                         goto error;
1833                 if (isl_basic_map_plain_is_empty(map->p[i])) {
1834                         isl_basic_map_free(map->p[i]);
1835                         if (i != map->n - 1)
1836                                 map->p[i] = map->p[map->n - 1];
1837                         map->n--;
1838                 }
1839         }
1840         isl_basic_map_free(context);
1841         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1842         return map;
1843 error:
1844         isl_map_free(map);
1845         isl_basic_map_free(context);
1846         return NULL;
1847 }
1848
1849 static __isl_give isl_map *map_gist(__isl_take isl_map *map,
1850         __isl_take isl_map *context)
1851 {
1852         context = isl_map_compute_divs(context);
1853         return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1854 }
1855
1856 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1857         __isl_take isl_map *context)
1858 {
1859         return isl_map_align_params_map_map_and(map, context, &map_gist);
1860 }
1861
1862 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1863                                                 struct isl_basic_set *context)
1864 {
1865         return (struct isl_basic_set *)isl_basic_map_gist(
1866                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1867 }
1868
1869 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1870         __isl_take isl_basic_set *context)
1871 {
1872         return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1873                                         (struct isl_basic_map *)context);
1874 }
1875
1876 __isl_give isl_set *isl_set_gist_params_basic_set(__isl_take isl_set *set,
1877         __isl_take isl_basic_set *context)
1878 {
1879         isl_space *space = isl_set_get_space(set);
1880         isl_basic_set *dom_context = isl_basic_set_universe(space);
1881         dom_context = isl_basic_set_intersect_params(dom_context, context);
1882         return isl_set_gist_basic_set(set, dom_context);
1883 }
1884
1885 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1886         __isl_take isl_set *context)
1887 {
1888         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1889                                         (struct isl_map *)context);
1890 }
1891
1892 __isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map,
1893         __isl_take isl_set *context)
1894 {
1895         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
1896         map_context = isl_map_intersect_domain(map_context, context);
1897         return isl_map_gist(map, map_context);
1898 }
1899
1900 __isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map,
1901         __isl_take isl_set *context)
1902 {
1903         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
1904         map_context = isl_map_intersect_range(map_context, context);
1905         return isl_map_gist(map, map_context);
1906 }
1907
1908 __isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
1909         __isl_take isl_set *context)
1910 {
1911         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
1912         map_context = isl_map_intersect_params(map_context, context);
1913         return isl_map_gist(map, map_context);
1914 }
1915
1916 __isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set,
1917         __isl_take isl_set *context)
1918 {
1919         return isl_map_gist_params(set, context);
1920 }
1921
1922 /* Quick check to see if two basic maps are disjoint.
1923  * In particular, we reduce the equalities and inequalities of
1924  * one basic map in the context of the equalities of the other
1925  * basic map and check if we get a contradiction.
1926  */
1927 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
1928         __isl_keep isl_basic_map *bmap2)
1929 {
1930         struct isl_vec *v = NULL;
1931         int *elim = NULL;
1932         unsigned total;
1933         int i;
1934
1935         if (!bmap1 || !bmap2)
1936                 return -1;
1937         isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
1938                         return -1);
1939         if (bmap1->n_div || bmap2->n_div)
1940                 return 0;
1941         if (!bmap1->n_eq && !bmap2->n_eq)
1942                 return 0;
1943
1944         total = isl_space_dim(bmap1->dim, isl_dim_all);
1945         if (total == 0)
1946                 return 0;
1947         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1948         if (!v)
1949                 goto error;
1950         elim = isl_alloc_array(bmap1->ctx, int, total);
1951         if (!elim)
1952                 goto error;
1953         compute_elimination_index(bmap1, elim);
1954         for (i = 0; i < bmap2->n_eq; ++i) {
1955                 int reduced;
1956                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1957                                                         bmap1, elim);
1958                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1959                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1960                         goto disjoint;
1961         }
1962         for (i = 0; i < bmap2->n_ineq; ++i) {
1963                 int reduced;
1964                 reduced = reduced_using_equalities(v->block.data,
1965                                                 bmap2->ineq[i], bmap1, elim);
1966                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1967                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1968                         goto disjoint;
1969         }
1970         compute_elimination_index(bmap2, elim);
1971         for (i = 0; i < bmap1->n_ineq; ++i) {
1972                 int reduced;
1973                 reduced = reduced_using_equalities(v->block.data,
1974                                                 bmap1->ineq[i], bmap2, elim);
1975                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1976                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1977                         goto disjoint;
1978         }
1979         isl_vec_free(v);
1980         free(elim);
1981         return 0;
1982 disjoint:
1983         isl_vec_free(v);
1984         free(elim);
1985         return 1;
1986 error:
1987         isl_vec_free(v);
1988         free(elim);
1989         return -1;
1990 }
1991
1992 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
1993         __isl_keep isl_basic_set *bset2)
1994 {
1995         return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
1996                                               (struct isl_basic_map *)bset2);
1997 }
1998
1999 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
2000         __isl_keep isl_map *map2)
2001 {
2002         int i, j;
2003
2004         if (!map1 || !map2)
2005                 return -1;
2006
2007         if (isl_map_plain_is_equal(map1, map2))
2008                 return 0;
2009
2010         for (i = 0; i < map1->n; ++i) {
2011                 for (j = 0; j < map2->n; ++j) {
2012                         int d = isl_basic_map_plain_is_disjoint(map1->p[i],
2013                                                                map2->p[j]);
2014                         if (d != 1)
2015                                 return d;
2016                 }
2017         }
2018         return 1;
2019 }
2020
2021 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2022         __isl_keep isl_set *set2)
2023 {
2024         return isl_map_plain_is_disjoint((struct isl_map *)set1,
2025                                         (struct isl_map *)set2);
2026 }
2027
2028 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
2029 {
2030         return isl_set_plain_is_disjoint(set1, set2);
2031 }
2032
2033 /* Check if we can combine a given div with lower bound l and upper
2034  * bound u with some other div and if so return that other div.
2035  * Otherwise return -1.
2036  *
2037  * We first check that
2038  *      - the bounds are opposites of each other (except for the constant
2039  *        term)
2040  *      - the bounds do not reference any other div
2041  *      - no div is defined in terms of this div
2042  *
2043  * Let m be the size of the range allowed on the div by the bounds.
2044  * That is, the bounds are of the form
2045  *
2046  *      e <= a <= e + m - 1
2047  *
2048  * with e some expression in the other variables.
2049  * We look for another div b such that no third div is defined in terms
2050  * of this second div b and such that in any constraint that contains
2051  * a (except for the given lower and upper bound), also contains b
2052  * with a coefficient that is m times that of b.
2053  * That is, all constraints (execpt for the lower and upper bound)
2054  * are of the form
2055  *
2056  *      e + f (a + m b) >= 0
2057  *
2058  * If so, we return b so that "a + m b" can be replaced by
2059  * a single div "c = a + m b".
2060  */
2061 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2062         unsigned div, unsigned l, unsigned u)
2063 {
2064         int i, j;
2065         unsigned dim;
2066         int coalesce = -1;
2067
2068         if (bmap->n_div <= 1)
2069                 return -1;
2070         dim = isl_space_dim(bmap->dim, isl_dim_all);
2071         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2072                 return -1;
2073         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2074                                    bmap->n_div - div - 1) != -1)
2075                 return -1;
2076         if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2077                             dim + bmap->n_div))
2078                 return -1;
2079
2080         for (i = 0; i < bmap->n_div; ++i) {
2081                 if (isl_int_is_zero(bmap->div[i][0]))
2082                         continue;
2083                 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2084                         return -1;
2085         }
2086
2087         isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2088         if (isl_int_is_neg(bmap->ineq[l][0])) {
2089                 isl_int_sub(bmap->ineq[l][0],
2090                             bmap->ineq[l][0], bmap->ineq[u][0]);
2091                 bmap = isl_basic_map_copy(bmap);
2092                 bmap = isl_basic_map_set_to_empty(bmap);
2093                 isl_basic_map_free(bmap);
2094                 return -1;
2095         }
2096         isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2097         for (i = 0; i < bmap->n_div; ++i) {
2098                 if (i == div)
2099                         continue;
2100                 if (!pairs[i])
2101                         continue;
2102                 for (j = 0; j < bmap->n_div; ++j) {
2103                         if (isl_int_is_zero(bmap->div[j][0]))
2104                                 continue;
2105                         if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2106                                 break;
2107                 }
2108                 if (j < bmap->n_div)
2109                         continue;
2110                 for (j = 0; j < bmap->n_ineq; ++j) {
2111                         int valid;
2112                         if (j == l || j == u)
2113                                 continue;
2114                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2115                                 continue;
2116                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2117                                 break;
2118                         isl_int_mul(bmap->ineq[j][1 + dim + div],
2119                                     bmap->ineq[j][1 + dim + div],
2120                                     bmap->ineq[l][0]);
2121                         valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2122                                            bmap->ineq[j][1 + dim + i]);
2123                         isl_int_divexact(bmap->ineq[j][1 + dim + div],
2124                                          bmap->ineq[j][1 + dim + div],
2125                                          bmap->ineq[l][0]);
2126                         if (!valid)
2127                                 break;
2128                 }
2129                 if (j < bmap->n_ineq)
2130                         continue;
2131                 coalesce = i;
2132                 break;
2133         }
2134         isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2135         isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2136         return coalesce;
2137 }
2138
2139 /* Given a lower and an upper bound on div i, construct an inequality
2140  * that when nonnegative ensures that this pair of bounds always allows
2141  * for an integer value of the given div.
2142  * The lower bound is inequality l, while the upper bound is inequality u.
2143  * The constructed inequality is stored in ineq.
2144  * g, fl, fu are temporary scalars.
2145  *
2146  * Let the upper bound be
2147  *
2148  *      -n_u a + e_u >= 0
2149  *
2150  * and the lower bound
2151  *
2152  *      n_l a + e_l >= 0
2153  *
2154  * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2155  * We have
2156  *
2157  *      - f_u e_l <= f_u f_l g a <= f_l e_u
2158  *
2159  * Since all variables are integer valued, this is equivalent to
2160  *
2161  *      - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2162  *
2163  * If this interval is at least f_u f_l g, then it contains at least
2164  * one integer value for a.
2165  * That is, the test constraint is
2166  *
2167  *      f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2168  */
2169 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2170         int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2171 {
2172         unsigned dim;
2173         dim = isl_space_dim(bmap->dim, isl_dim_all);
2174
2175         isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2176         isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2177         isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2178         isl_int_neg(fu, fu);
2179         isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2180                         1 + dim + bmap->n_div);
2181         isl_int_add(ineq[0], ineq[0], fl);
2182         isl_int_add(ineq[0], ineq[0], fu);
2183         isl_int_sub_ui(ineq[0], ineq[0], 1);
2184         isl_int_mul(g, g, fl);
2185         isl_int_mul(g, g, fu);
2186         isl_int_sub(ineq[0], ineq[0], g);
2187 }
2188
2189 /* Remove more kinds of divs that are not strictly needed.
2190  * In particular, if all pairs of lower and upper bounds on a div
2191  * are such that they allow at least one integer value of the div,
2192  * the we can eliminate the div using Fourier-Motzkin without
2193  * introducing any spurious solutions.
2194  */
2195 static struct isl_basic_map *drop_more_redundant_divs(
2196         struct isl_basic_map *bmap, int *pairs, int n)
2197 {
2198         struct isl_tab *tab = NULL;
2199         struct isl_vec *vec = NULL;
2200         unsigned dim;
2201         int remove = -1;
2202         isl_int g, fl, fu;
2203
2204         isl_int_init(g);
2205         isl_int_init(fl);
2206         isl_int_init(fu);
2207
2208         if (!bmap)
2209                 goto error;
2210
2211         dim = isl_space_dim(bmap->dim, isl_dim_all);
2212         vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2213         if (!vec)
2214                 goto error;
2215
2216         tab = isl_tab_from_basic_map(bmap, 0);
2217
2218         while (n > 0) {
2219                 int i, l, u;
2220                 int best = -1;
2221                 enum isl_lp_result res;
2222
2223                 for (i = 0; i < bmap->n_div; ++i) {
2224                         if (!pairs[i])
2225                                 continue;
2226                         if (best >= 0 && pairs[best] <= pairs[i])
2227                                 continue;
2228                         best = i;
2229                 }
2230
2231                 i = best;
2232                 for (l = 0; l < bmap->n_ineq; ++l) {
2233                         if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2234                                 continue;
2235                         for (u = 0; u < bmap->n_ineq; ++u) {
2236                                 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2237                                         continue;
2238                                 construct_test_ineq(bmap, i, l, u,
2239                                                     vec->el, g, fl, fu);
2240                                 res = isl_tab_min(tab, vec->el,
2241                                                   bmap->ctx->one, &g, NULL, 0);
2242                                 if (res == isl_lp_error)
2243                                         goto error;
2244                                 if (res == isl_lp_empty) {
2245                                         bmap = isl_basic_map_set_to_empty(bmap);
2246                                         break;
2247                                 }
2248                                 if (res != isl_lp_ok || isl_int_is_neg(g))
2249                                         break;
2250                         }
2251                         if (u < bmap->n_ineq)
2252                                 break;
2253                 }
2254                 if (l == bmap->n_ineq) {
2255                         remove = i;
2256                         break;
2257                 }
2258                 pairs[i] = 0;
2259                 --n;
2260         }
2261
2262         isl_tab_free(tab);
2263         isl_vec_free(vec);
2264
2265         isl_int_clear(g);
2266         isl_int_clear(fl);
2267         isl_int_clear(fu);
2268
2269         free(pairs);
2270
2271         if (remove < 0)
2272                 return bmap;
2273
2274         bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2275         return isl_basic_map_drop_redundant_divs(bmap);
2276 error:
2277         free(pairs);
2278         isl_basic_map_free(bmap);
2279         isl_tab_free(tab);
2280         isl_vec_free(vec);
2281         isl_int_clear(g);
2282         isl_int_clear(fl);
2283         isl_int_clear(fu);
2284         return NULL;
2285 }
2286
2287 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2288  * and the upper bound u, div1 always occurs together with div2 in the form
2289  * (div1 + m div2), where m is the constant range on the variable div1
2290  * allowed by l and u, replace the pair div1 and div2 by a single
2291  * div that is equal to div1 + m div2.
2292  *
2293  * The new div will appear in the location that contains div2.
2294  * We need to modify all constraints that contain
2295  * div2 = (div - div1) / m
2296  * (If a constraint does not contain div2, it will also not contain div1.)
2297  * If the constraint also contains div1, then we know they appear
2298  * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2299  * i.e., the coefficient of div is f.
2300  *
2301  * Otherwise, we first need to introduce div1 into the constraint.
2302  * Let the l be
2303  *
2304  *      div1 + f >=0
2305  *
2306  * and u
2307  *
2308  *      -div1 + f' >= 0
2309  *
2310  * A lower bound on div2
2311  *
2312  *      n div2 + t >= 0
2313  *
2314  * can be replaced by
2315  *
2316  *      (n * (m div 2 + div1) + m t + n f)/g >= 0
2317  *
2318  * with g = gcd(m,n).
2319  * An upper bound
2320  *
2321  *      -n div2 + t >= 0
2322  *
2323  * can be replaced by
2324  *
2325  *      (-n * (m div2 + div1) + m t + n f')/g >= 0
2326  *
2327  * These constraint are those that we would obtain from eliminating
2328  * div1 using Fourier-Motzkin.
2329  *
2330  * After all constraints have been modified, we drop the lower and upper
2331  * bound and then drop div1.
2332  */
2333 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2334         unsigned div1, unsigned div2, unsigned l, unsigned u)
2335 {
2336         isl_int a;
2337         isl_int b;
2338         isl_int m;
2339         unsigned dim, total;
2340         int i;
2341
2342         dim = isl_space_dim(bmap->dim, isl_dim_all);
2343         total = 1 + dim + bmap->n_div;
2344
2345         isl_int_init(a);
2346         isl_int_init(b);
2347         isl_int_init(m);
2348         isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2349         isl_int_add_ui(m, m, 1);
2350
2351         for (i = 0; i < bmap->n_ineq; ++i) {
2352                 if (i == l || i == u)
2353                         continue;
2354                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2355                         continue;
2356                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2357                         isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2358                         isl_int_divexact(a, m, b);
2359                         isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2360                         if (isl_int_is_pos(b)) {
2361                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2362                                                 b, bmap->ineq[l], total);
2363                         } else {
2364                                 isl_int_neg(b, b);
2365                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2366                                                 b, bmap->ineq[u], total);
2367                         }
2368                 }
2369                 isl_int_set(bmap->ineq[i][1 + dim + div2],
2370                             bmap->ineq[i][1 + dim + div1]);
2371                 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2372         }
2373
2374         isl_int_clear(a);
2375         isl_int_clear(b);
2376         isl_int_clear(m);
2377         if (l > u) {
2378                 isl_basic_map_drop_inequality(bmap, l);
2379                 isl_basic_map_drop_inequality(bmap, u);
2380         } else {
2381                 isl_basic_map_drop_inequality(bmap, u);
2382                 isl_basic_map_drop_inequality(bmap, l);
2383         }
2384         bmap = isl_basic_map_drop_div(bmap, div1);
2385         return bmap;
2386 }
2387
2388 /* First check if we can coalesce any pair of divs and
2389  * then continue with dropping more redundant divs.
2390  *
2391  * We loop over all pairs of lower and upper bounds on a div
2392  * with coefficient 1 and -1, respectively, check if there
2393  * is any other div "c" with which we can coalesce the div
2394  * and if so, perform the coalescing.
2395  */
2396 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2397         struct isl_basic_map *bmap, int *pairs, int n)
2398 {
2399         int i, l, u;
2400         unsigned dim;
2401
2402         dim = isl_space_dim(bmap->dim, isl_dim_all);
2403
2404         for (i = 0; i < bmap->n_div; ++i) {
2405                 if (!pairs[i])
2406                         continue;
2407                 for (l = 0; l < bmap->n_ineq; ++l) {
2408                         if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2409                                 continue;
2410                         for (u = 0; u < bmap->n_ineq; ++u) {
2411                                 int c;
2412
2413                                 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2414                                         continue;
2415                                 c = div_find_coalesce(bmap, pairs, i, l, u);
2416                                 if (c < 0)
2417                                         continue;
2418                                 free(pairs);
2419                                 bmap = coalesce_divs(bmap, i, c, l, u);
2420                                 return isl_basic_map_drop_redundant_divs(bmap);
2421                         }
2422                 }
2423         }
2424
2425         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2426                 return bmap;
2427
2428         return drop_more_redundant_divs(bmap, pairs, n);
2429 }
2430
2431 /* Remove divs that are not strictly needed.
2432  * In particular, if a div only occurs positively (or negatively)
2433  * in constraints, then it can simply be dropped.
2434  * Also, if a div occurs only occurs in two constraints and if moreover
2435  * those two constraints are opposite to each other, except for the constant
2436  * term and if the sum of the constant terms is such that for any value
2437  * of the other values, there is always at least one integer value of the
2438  * div, i.e., if one plus this sum is greater than or equal to
2439  * the (absolute value) of the coefficent of the div in the constraints,
2440  * then we can also simply drop the div.
2441  *
2442  * If any divs are left after these simple checks then we move on
2443  * to more complicated cases in drop_more_redundant_divs.
2444  */
2445 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2446         struct isl_basic_map *bmap)
2447 {
2448         int i, j;
2449         unsigned off;
2450         int *pairs = NULL;
2451         int n = 0;
2452
2453         if (!bmap)
2454                 goto error;
2455
2456         off = isl_space_dim(bmap->dim, isl_dim_all);
2457         pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2458         if (!pairs)
2459                 goto error;
2460
2461         for (i = 0; i < bmap->n_div; ++i) {
2462                 int pos, neg;
2463                 int last_pos, last_neg;
2464                 int redundant;
2465                 int defined;
2466
2467                 defined = !isl_int_is_zero(bmap->div[i][0]);
2468                 for (j = 0; j < bmap->n_eq; ++j)
2469                         if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2470                                 break;
2471                 if (j < bmap->n_eq)
2472                         continue;
2473                 ++n;
2474                 pos = neg = 0;
2475                 for (j = 0; j < bmap->n_ineq; ++j) {
2476                         if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2477                                 last_pos = j;
2478                                 ++pos;
2479                         }
2480                         if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2481                                 last_neg = j;
2482                                 ++neg;
2483                         }
2484                 }
2485                 pairs[i] = pos * neg;
2486                 if (pairs[i] == 0) {
2487                         for (j = bmap->n_ineq - 1; j >= 0; --j)
2488                                 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2489                                         isl_basic_map_drop_inequality(bmap, j);
2490                         bmap = isl_basic_map_drop_div(bmap, i);
2491                         free(pairs);
2492                         return isl_basic_map_drop_redundant_divs(bmap);
2493                 }
2494                 if (pairs[i] != 1)
2495                         continue;
2496                 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2497                                     bmap->ineq[last_neg] + 1,
2498                                     off + bmap->n_div))
2499                         continue;
2500
2501                 isl_int_add(bmap->ineq[last_pos][0],
2502                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2503                 isl_int_add_ui(bmap->ineq[last_pos][0],
2504                                bmap->ineq[last_pos][0], 1);
2505                 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2506                                 bmap->ineq[last_pos][1+off+i]);
2507                 isl_int_sub_ui(bmap->ineq[last_pos][0],
2508                                bmap->ineq[last_pos][0], 1);
2509                 isl_int_sub(bmap->ineq[last_pos][0],
2510                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2511                 if (!redundant) {
2512                         if (defined ||
2513                             !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2514                                 pairs[i] = 0;
2515                                 --n;
2516                                 continue;
2517                         }
2518                         bmap = set_div_from_lower_bound(bmap, i, last_pos);
2519                         bmap = isl_basic_map_simplify(bmap);
2520                         free(pairs);
2521                         return isl_basic_map_drop_redundant_divs(bmap);
2522                 }
2523                 if (last_pos > last_neg) {
2524                         isl_basic_map_drop_inequality(bmap, last_pos);
2525                         isl_basic_map_drop_inequality(bmap, last_neg);
2526                 } else {
2527                         isl_basic_map_drop_inequality(bmap, last_neg);
2528                         isl_basic_map_drop_inequality(bmap, last_pos);
2529                 }
2530                 bmap = isl_basic_map_drop_div(bmap, i);
2531                 free(pairs);
2532                 return isl_basic_map_drop_redundant_divs(bmap);
2533         }
2534
2535         if (n > 0)
2536                 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2537
2538         free(pairs);
2539         return bmap;
2540 error:
2541         free(pairs);
2542         isl_basic_map_free(bmap);
2543         return NULL;
2544 }
2545
2546 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2547         struct isl_basic_set *bset)
2548 {
2549         return (struct isl_basic_set *)
2550             isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2551 }
2552
2553 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2554 {
2555         int i;
2556
2557         if (!map)
2558                 return NULL;
2559         for (i = 0; i < map->n; ++i) {
2560                 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2561                 if (!map->p[i])
2562                         goto error;
2563         }
2564         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2565         return map;
2566 error:
2567         isl_map_free(map);
2568         return NULL;
2569 }
2570
2571 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2572 {
2573         return (struct isl_set *)
2574             isl_map_drop_redundant_divs((struct isl_map *)set);
2575 }