isl_map_simplify.c

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