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