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_ctx_private.h>
  11 #include <isl_map_private.h>
  12 #include "isl_equalities.h"
  13 #include <isl/map.h>
  14 #include <isl/seq.h>
  15 #include "isl_tab.h"
  16 #include <isl_dim_private.h>
  17 #include <isl_mat_private.h>
  18
  19 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
  20 {
  21         isl_int *t = bmap->eq[a];
  22         bmap->eq[a] = bmap->eq[b];
  23         bmap->eq[b] = t;
  24 }
  25
  26 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
  27 {
  28         if (a != b) {
  29                 isl_int *t = bmap->ineq[a];
  30                 bmap->ineq[a] = bmap->ineq[b];
  31                 bmap->ineq[b] = t;
  32         }
  33 }
  34
  35 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
  36 {
  37         isl_seq_cpy(c, c + n, rem);
  38         isl_seq_clr(c + rem, n);
  39 }
  40
  41 /* Drop n dimensions starting at first.
  42  *
  43  * In principle, this frees up some extra variables as the number
  44  * of columns remains constant, but we would have to extend
  45  * the div array too as the number of rows in this array is assumed
  46  * to be equal to extra.
  47  */
  48 struct isl_basic_set *isl_basic_set_drop_dims(
  49                 struct isl_basic_set *bset, unsigned first, unsigned n)
  50 {
  51         int i;
  52
  53         if (!bset)
  54                 goto error;
  55
  56         isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
  57
  58         if (n == 0 && !isl_dim_get_tuple_name(bset->dim, isl_dim_set))
  59                 return bset;
  60
  61         bset = isl_basic_set_cow(bset);
  62         if (!bset)
  63                 return NULL;
  64
  65         for (i = 0; i < bset->n_eq; ++i)
  66                 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
  67                                      (bset->dim->n_out-first-n)+bset->extra);
  68
  69         for (i = 0; i < bset->n_ineq; ++i)
  70                 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
  71                                      (bset->dim->n_out-first-n)+bset->extra);
  72
  73         for (i = 0; i < bset->n_div; ++i)
  74                 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
  75                                      (bset->dim->n_out-first-n)+bset->extra);
  76
  77         bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
  78         if (!bset->dim)
  79                 goto error;
  80
  81         ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
  82         bset = isl_basic_set_simplify(bset);
  83         return isl_basic_set_finalize(bset);
  84 error:
  85         isl_basic_set_free(bset);
  86         return NULL;
  87 }
  88
  89 struct isl_set *isl_set_drop_dims(
  90                 struct isl_set *set, unsigned first, unsigned n)
  91 {
  92         int i;
  93
  94         if (!set)
  95                 goto error;
  96
  97         isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
  98
  99         if (n == 0 && !isl_dim_get_tuple_name(set->dim, isl_dim_set))
 100                 return set;
 101         set = isl_set_cow(set);
 102         if (!set)
 103                 goto error;
 104         set->dim = isl_dim_drop_outputs(set->dim, first, n);
 105         if (!set->dim)
 106                 goto error;
 107
 108         for (i = 0; i < set->n; ++i) {
 109                 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
 110                 if (!set->p[i])
 111                         goto error;
 112         }
 113
 114         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 115         return set;
 116 error:
 117         isl_set_free(set);
 118         return NULL;
 119 }
 120
 121 /* Move "n" divs starting at "first" to the end of the list of divs.
 122  */
 123 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
 124         unsigned first, unsigned n)
 125 {
 126         isl_int **div;
 127         int i;
 128
 129         if (first + n == bmap->n_div)
 130                 return bmap;
 131
 132         div = isl_alloc_array(bmap->ctx, isl_int *, n);
 133         if (!div)
 134                 goto error;
 135         for (i = 0; i < n; ++i)
 136                 div[i] = bmap->div[first + i];
 137         for (i = 0; i < bmap->n_div - first - n; ++i)
 138                 bmap->div[first + i] = bmap->div[first + n + i];
 139         for (i = 0; i < n; ++i)
 140                 bmap->div[bmap->n_div - n + i] = div[i];
 141         free(div);
 142         return bmap;
 143 error:
 144         isl_basic_map_free(bmap);
 145         return NULL;
 146 }
 147
 148 /* Drop "n" dimensions of type "type" starting at "first".
 149  *
 150  * In principle, this frees up some extra variables as the number
 151  * of columns remains constant, but we would have to extend
 152  * the div array too as the number of rows in this array is assumed
 153  * to be equal to extra.
 154  */
 155 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
 156         enum isl_dim_type type, unsigned first, unsigned n)
 157 {
 158         int i;
 159         unsigned dim;
 160         unsigned offset;
 161         unsigned left;
 162
 163         if (!bmap)
 164                 goto error;
 165
 166         dim = isl_basic_map_dim(bmap, type);
 167         isl_assert(bmap->ctx, first + n <= dim, goto error);
 168
 169         if (n == 0 && !isl_dim_get_tuple_name(bmap->dim, type))
 170                 return bmap;
 171
 172         bmap = isl_basic_map_cow(bmap);
 173         if (!bmap)
 174                 return NULL;
 175
 176         offset = isl_basic_map_offset(bmap, type) + first;
 177         left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
 178         for (i = 0; i < bmap->n_eq; ++i)
 179                 constraint_drop_vars(bmap->eq[i]+offset, n, left);
 180
 181         for (i = 0; i < bmap->n_ineq; ++i)
 182                 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
 183
 184         for (i = 0; i < bmap->n_div; ++i)
 185                 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
 186
 187         if (type == isl_dim_div) {
 188                 bmap = move_divs_last(bmap, first, n);
 189                 if (!bmap)
 190                         goto error;
 191                 isl_basic_map_free_div(bmap, n);
 192         } else
 193                 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
 194         if (!bmap->dim)
 195                 goto error;
 196
 197         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 198         bmap = isl_basic_map_simplify(bmap);
 199         return isl_basic_map_finalize(bmap);
 200 error:
 201         isl_basic_map_free(bmap);
 202         return NULL;
 203 }
 204
 205 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
 206         enum isl_dim_type type, unsigned first, unsigned n)
 207 {
 208         return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
 209                                                         type, first, n);
 210 }
 211
 212 struct isl_basic_map *isl_basic_map_drop_inputs(
 213                 struct isl_basic_map *bmap, unsigned first, unsigned n)
 214 {
 215         return isl_basic_map_drop(bmap, isl_dim_in, first, n);
 216 }
 217
 218 struct isl_map *isl_map_drop(struct isl_map *map,
 219         enum isl_dim_type type, unsigned first, unsigned n)
 220 {
 221         int i;
 222
 223         if (!map)
 224                 goto error;
 225
 226         isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
 227
 228         if (n == 0 && !isl_dim_get_tuple_name(map->dim, type))
 229                 return map;
 230         map = isl_map_cow(map);
 231         if (!map)
 232                 goto error;
 233         map->dim = isl_dim_drop(map->dim, type, first, n);
 234         if (!map->dim)
 235                 goto error;
 236
 237         for (i = 0; i < map->n; ++i) {
 238                 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
 239                 if (!map->p[i])
 240                         goto error;
 241         }
 242         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
 243
 244         return map;
 245 error:
 246         isl_map_free(map);
 247         return NULL;
 248 }
 249
 250 struct isl_set *isl_set_drop(struct isl_set *set,
 251         enum isl_dim_type type, unsigned first, unsigned n)
 252 {
 253         return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
 254 }
 255
 256 struct isl_map *isl_map_drop_inputs(
 257                 struct isl_map *map, unsigned first, unsigned n)
 258 {
 259         return isl_map_drop(map, isl_dim_in, first, n);
 260 }
 261
 262 /*
 263  * We don't cow, as the div is assumed to be redundant.
 264  */
 265 static struct isl_basic_map *isl_basic_map_drop_div(
 266                 struct isl_basic_map *bmap, unsigned div)
 267 {
 268         int i;
 269         unsigned pos;
 270
 271         if (!bmap)
 272                 goto error;
 273
 274         pos = 1 + isl_dim_total(bmap->dim) + div;
 275
 276         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
 277
 278         for (i = 0; i < bmap->n_eq; ++i)
 279                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
 280
 281         for (i = 0; i < bmap->n_ineq; ++i) {
 282                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
 283                         isl_basic_map_drop_inequality(bmap, i);
 284                         --i;
 285                         continue;
 286                 }
 287                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
 288         }
 289
 290         for (i = 0; i < bmap->n_div; ++i)
 291                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
 292
 293         if (div != bmap->n_div - 1) {
 294                 int j;
 295                 isl_int *t = bmap->div[div];
 296
 297                 for (j = div; j < bmap->n_div - 1; ++j)
 298                         bmap->div[j] = bmap->div[j+1];
 299
 300                 bmap->div[bmap->n_div - 1] = t;
 301         }
 302         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 303         isl_basic_map_free_div(bmap, 1);
 304
 305         return bmap;
 306 error:
 307         isl_basic_map_free(bmap);
 308         return NULL;
 309 }
 310
 311 struct isl_basic_map *isl_basic_map_normalize_constraints(
 312         struct isl_basic_map *bmap)
 313 {
 314         int i;
 315         isl_int gcd;
 316         unsigned total = isl_basic_map_total_dim(bmap);
 317
 318         if (!bmap)
 319                 return NULL;
 320
 321         isl_int_init(gcd);
 322         for (i = bmap->n_eq - 1; i >= 0; --i) {
 323                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
 324                 if (isl_int_is_zero(gcd)) {
 325                         if (!isl_int_is_zero(bmap->eq[i][0])) {
 326                                 bmap = isl_basic_map_set_to_empty(bmap);
 327                                 break;
 328                         }
 329                         isl_basic_map_drop_equality(bmap, i);
 330                         continue;
 331                 }
 332                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 333                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
 334                 if (isl_int_is_one(gcd))
 335                         continue;
 336                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
 337                         bmap = isl_basic_map_set_to_empty(bmap);
 338                         break;
 339                 }
 340                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
 341         }
 342
 343         for (i = bmap->n_ineq - 1; i >= 0; --i) {
 344                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
 345                 if (isl_int_is_zero(gcd)) {
 346                         if (isl_int_is_neg(bmap->ineq[i][0])) {
 347                                 bmap = isl_basic_map_set_to_empty(bmap);
 348                                 break;
 349                         }
 350                         isl_basic_map_drop_inequality(bmap, i);
 351                         continue;
 352                 }
 353                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 354                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
 355                 if (isl_int_is_one(gcd))
 356                         continue;
 357                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
 358                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
 359         }
 360         isl_int_clear(gcd);
 361
 362         return bmap;
 363 }
 364
 365 struct isl_basic_set *isl_basic_set_normalize_constraints(
 366         struct isl_basic_set *bset)
 367 {
 368         return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
 369                 (struct isl_basic_map *)bset);
 370 }
 371
 372 /* Assumes divs have been ordered if keep_divs is set.
 373  */
 374 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
 375         unsigned pos, isl_int *eq, int keep_divs, int *progress)
 376 {
 377         unsigned total;
 378         int k;
 379         int last_div;
 380
 381         total = isl_basic_map_total_dim(bmap);
 382         last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
 383                                                 bmap->n_div);
 384         for (k = 0; k < bmap->n_eq; ++k) {
 385                 if (bmap->eq[k] == eq)
 386                         continue;
 387                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
 388                         continue;
 389                 if (progress)
 390                         *progress = 1;
 391                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
 392                 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
 393         }
 394
 395         for (k = 0; k < bmap->n_ineq; ++k) {
 396                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
 397                         continue;
 398                 if (progress)
 399                         *progress = 1;
 400                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
 401                 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
 402                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 403         }
 404
 405         for (k = 0; k < bmap->n_div; ++k) {
 406                 if (isl_int_is_zero(bmap->div[k][0]))
 407                         continue;
 408                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
 409                         continue;
 410                 if (progress)
 411                         *progress = 1;
 412                 /* We need to be careful about circular definitions,
 413                  * so for now we just remove the definition of div k
 414                  * if the equality contains any divs.
 415                  * If keep_divs is set, then the divs have been ordered
 416                  * and we can keep the definition as long as the result
 417                  * is still ordered.
 418                  */
 419                 if (last_div == -1 || (keep_divs && last_div < k))
 420                         isl_seq_elim(bmap->div[k]+1, eq,
 421                                         1+pos, 1+total, &bmap->div[k][0]);
 422                 else
 423                         isl_seq_clr(bmap->div[k], 1 + total);
 424                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 425         }
 426 }
 427
 428 /* Assumes divs have been ordered if keep_divs is set.
 429  */
 430 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
 431         unsigned div, int keep_divs)
 432 {
 433         unsigned pos = isl_dim_total(bmap->dim) + div;
 434
 435         eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
 436
 437         isl_basic_map_drop_div(bmap, div);
 438 }
 439
 440 /* Check if elimination of div "div" using equality "eq" would not
 441  * result in a div depending on a later div.
 442  */
 443 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
 444         unsigned div)
 445 {
 446         int k;
 447         int last_div;
 448         unsigned pos = isl_dim_total(bmap->dim) + div;
 449
 450         last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
 451                                                 bmap->n_div);
 452         if (last_div < 0 || last_div <= div)
 453                 return 1;
 454
 455         for (k = 0; k <= last_div; ++k) {
 456                 if (isl_int_is_zero(bmap->div[k][0]))
 457                         return 1;
 458                 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
 459                         return 0;
 460         }
 461
 462         return 1;
 463 }
 464
 465 /* Elimininate divs based on equalities
 466  */
 467 static struct isl_basic_map *eliminate_divs_eq(
 468                 struct isl_basic_map *bmap, int *progress)
 469 {
 470         int d;
 471         int i;
 472         int modified = 0;
 473         unsigned off;
 474
 475         bmap = isl_basic_map_order_divs(bmap);
 476
 477         if (!bmap)
 478                 return NULL;
 479
 480         off = 1 + isl_dim_total(bmap->dim);
 481
 482         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 483                 for (i = 0; i < bmap->n_eq; ++i) {
 484                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
 485                             !isl_int_is_negone(bmap->eq[i][off + d]))
 486                                 continue;
 487                         if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
 488                                 continue;
 489                         modified = 1;
 490                         *progress = 1;
 491                         eliminate_div(bmap, bmap->eq[i], d, 1);
 492                         isl_basic_map_drop_equality(bmap, i);
 493                         break;
 494                 }
 495         }
 496         if (modified)
 497                 return eliminate_divs_eq(bmap, progress);
 498         return bmap;
 499 }
 500
 501 /* Elimininate divs based on inequalities
 502  */
 503 static struct isl_basic_map *eliminate_divs_ineq(
 504                 struct isl_basic_map *bmap, int *progress)
 505 {
 506         int d;
 507         int i;
 508         unsigned off;
 509         struct isl_ctx *ctx;
 510
 511         if (!bmap)
 512                 return NULL;
 513
 514         ctx = bmap->ctx;
 515         off = 1 + isl_dim_total(bmap->dim);
 516
 517         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 518                 for (i = 0; i < bmap->n_eq; ++i)
 519                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
 520                                 break;
 521                 if (i < bmap->n_eq)
 522                         continue;
 523                 for (i = 0; i < bmap->n_ineq; ++i)
 524                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
 525                                 break;
 526                 if (i < bmap->n_ineq)
 527                         continue;
 528                 *progress = 1;
 529                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
 530                 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 531                         break;
 532                 bmap = isl_basic_map_drop_div(bmap, d);
 533                 if (!bmap)
 534                         break;
 535         }
 536         return bmap;
 537 }
 538
 539 struct isl_basic_map *isl_basic_map_gauss(
 540         struct isl_basic_map *bmap, int *progress)
 541 {
 542         int k;
 543         int done;
 544         int last_var;
 545         unsigned total_var;
 546         unsigned total;
 547
 548         bmap = isl_basic_map_order_divs(bmap);
 549
 550         if (!bmap)
 551                 return NULL;
 552
 553         total = isl_basic_map_total_dim(bmap);
 554         total_var = total - bmap->n_div;
 555
 556         last_var = total - 1;
 557         for (done = 0; done < bmap->n_eq; ++done) {
 558                 for (; last_var >= 0; --last_var) {
 559                         for (k = done; k < bmap->n_eq; ++k)
 560                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
 561                                         break;
 562                         if (k < bmap->n_eq)
 563                                 break;
 564                 }
 565                 if (last_var < 0)
 566                         break;
 567                 if (k != done)
 568                         swap_equality(bmap, k, done);
 569                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 570                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 571
 572                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
 573                                                 progress);
 574
 575                 if (last_var >= total_var &&
 576                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
 577                         unsigned div = last_var - total_var;
 578                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
 579                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 580                         isl_int_set(bmap->div[div][0],
 581                                     bmap->eq[done][1+last_var]);
 582                         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 583                 }
 584         }
 585         if (done == bmap->n_eq)
 586                 return bmap;
 587         for (k = done; k < bmap->n_eq; ++k) {
 588                 if (isl_int_is_zero(bmap->eq[k][0]))
 589                         continue;
 590                 return isl_basic_map_set_to_empty(bmap);
 591         }
 592         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
 593         return bmap;
 594 }
 595
 596 struct isl_basic_set *isl_basic_set_gauss(
 597         struct isl_basic_set *bset, int *progress)
 598 {
 599         return (struct isl_basic_set*)isl_basic_map_gauss(
 600                         (struct isl_basic_map *)bset, progress);
 601 }
 602
 603
 604 static unsigned int round_up(unsigned int v)
 605 {
 606         int old_v = v;
 607
 608         while (v) {
 609                 old_v = v;
 610                 v ^= v & -v;
 611         }
 612         return old_v << 1;
 613 }
 614
 615 static int hash_index(isl_int ***index, unsigned int size, int bits,
 616                         struct isl_basic_map *bmap, int k)
 617 {
 618         int h;
 619         unsigned total = isl_basic_map_total_dim(bmap);
 620         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
 621         for (h = hash; index[h]; h = (h+1) % size)
 622                 if (&bmap->ineq[k] != index[h] &&
 623                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
 624                         break;
 625         return h;
 626 }
 627
 628 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
 629                           struct isl_basic_set *bset, int k)
 630 {
 631         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
 632 }
 633
 634 /* If we can eliminate more than one div, then we need to make
 635  * sure we do it from last div to first div, in order not to
 636  * change the position of the other divs that still need to
 637  * be removed.
 638  */
 639 static struct isl_basic_map *remove_duplicate_divs(
 640         struct isl_basic_map *bmap, int *progress)
 641 {
 642         unsigned int size;
 643         int *index;
 644         int *elim_for;
 645         int k, l, h;
 646         int bits;
 647         struct isl_blk eq;
 648         unsigned total_var;
 649         unsigned total;
 650         struct isl_ctx *ctx;
 651
 652         if (!bmap || bmap->n_div <= 1)
 653                 return bmap;
 654
 655         total_var = isl_dim_total(bmap->dim);
 656         total = total_var + bmap->n_div;
 657
 658         ctx = bmap->ctx;
 659         for (k = bmap->n_div - 1; k >= 0; --k)
 660                 if (!isl_int_is_zero(bmap->div[k][0]))
 661                         break;
 662         if (k <= 0)
 663                 return bmap;
 664
 665         elim_for = isl_calloc_array(ctx, int, bmap->n_div);
 666         size = round_up(4 * bmap->n_div / 3 - 1);
 667         bits = ffs(size) - 1;
 668         index = isl_calloc_array(ctx, int, size);
 669         if (!index)
 670                 return bmap;
 671         eq = isl_blk_alloc(ctx, 1+total);
 672         if (isl_blk_is_error(eq))
 673                 goto out;
 674
 675         isl_seq_clr(eq.data, 1+total);
 676         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
 677         for (--k; k >= 0; --k) {
 678                 uint32_t hash;
 679
 680                 if (isl_int_is_zero(bmap->div[k][0]))
 681                         continue;
 682
 683                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
 684                 for (h = hash; index[h]; h = (h+1) % size)
 685                         if (isl_seq_eq(bmap->div[k],
 686                                        bmap->div[index[h]-1], 2+total))
 687                                 break;
 688                 if (index[h]) {
 689                         *progress = 1;
 690                         l = index[h] - 1;
 691                         elim_for[l] = k + 1;
 692                 }
 693                 index[h] = k+1;
 694         }
 695         for (l = bmap->n_div - 1; l >= 0; --l) {
 696                 if (!elim_for[l])
 697                         continue;
 698                 k = elim_for[l] - 1;
 699                 isl_int_set_si(eq.data[1+total_var+k], -1);
 700                 isl_int_set_si(eq.data[1+total_var+l], 1);
 701                 eliminate_div(bmap, eq.data, l, 0);
 702                 isl_int_set_si(eq.data[1+total_var+k], 0);
 703                 isl_int_set_si(eq.data[1+total_var+l], 0);
 704         }
 705
 706         isl_blk_free(ctx, eq);
 707 out:
 708         free(index);
 709         free(elim_for);
 710         return bmap;
 711 }
 712
 713 static int n_pure_div_eq(struct isl_basic_map *bmap)
 714 {
 715         int i, j;
 716         unsigned total;
 717
 718         total = isl_dim_total(bmap->dim);
 719         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 720                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 721                         --j;
 722                 if (j < 0)
 723                         break;
 724                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 725                         return 0;
 726         }
 727         return i;
 728 }
 729
 730 /* Normalize divs that appear in equalities.
 731  *
 732  * In particular, we assume that bmap contains some equalities
 733  * of the form
 734  *
 735  *      a x = m * e_i
 736  *
 737  * and we want to replace the set of e_i by a minimal set and
 738  * such that the new e_i have a canonical representation in terms
 739  * of the vector x.
 740  * If any of the equalities involves more than one divs, then
 741  * we currently simply bail out.
 742  *
 743  * Let us first additionally assume that all equalities involve
 744  * a div.  The equalities then express modulo constraints on the
 745  * remaining variables and we can use "parameter compression"
 746  * to find a minimal set of constraints.  The result is a transformation
 747  *
 748  *      x = T(x') = x_0 + G x'
 749  *
 750  * with G a lower-triangular matrix with all elements below the diagonal
 751  * non-negative and smaller than the diagonal element on the same row.
 752  * We first normalize x_0 by making the same property hold in the affine
 753  * T matrix.
 754  * The rows i of G with a 1 on the diagonal do not impose any modulo
 755  * constraint and simply express x_i = x'_i.
 756  * For each of the remaining rows i, we introduce a div and a corresponding
 757  * equality.  In particular
 758  *
 759  *      g_ii e_j = x_i - g_i(x')
 760  *
 761  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 762  * corresponding div (if g_kk != 1).
 763  *
 764  * If there are any equalities not involving any div, then we
 765  * first apply a variable compression on the variables x:
 766  *
 767  *      x = C x''       x'' = C_2 x
 768  *
 769  * and perform the above parameter compression on A C instead of on A.
 770  * The resulting compression is then of the form
 771  *
 772  *      x'' = T(x') = x_0 + G x'
 773  *
 774  * and in constructing the new divs and the corresponding equalities,
 775  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 776  * by the corresponding row from C_2.
 777  */
 778 static struct isl_basic_map *normalize_divs(
 779         struct isl_basic_map *bmap, int *progress)
 780 {
 781         int i, j, k;
 782         int total;
 783         int div_eq;
 784         struct isl_mat *B;
 785         struct isl_vec *d;
 786         struct isl_mat *T = NULL;
 787         struct isl_mat *C = NULL;
 788         struct isl_mat *C2 = NULL;
 789         isl_int v;
 790         int *pos;
 791         int dropped, needed;
 792
 793         if (!bmap)
 794                 return NULL;
 795
 796         if (bmap->n_div == 0)
 797                 return bmap;
 798
 799         if (bmap->n_eq == 0)
 800                 return bmap;
 801
 802         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 803                 return bmap;
 804
 805         total = isl_dim_total(bmap->dim);
 806         div_eq = n_pure_div_eq(bmap);
 807         if (div_eq == 0)
 808                 return bmap;
 809
 810         if (div_eq < bmap->n_eq) {
 811                 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
 812                                         bmap->n_eq - div_eq, 0, 1 + total);
 813                 C = isl_mat_variable_compression(B, &C2);
 814                 if (!C || !C2)
 815                         goto error;
 816                 if (C->n_col == 0) {
 817                         bmap = isl_basic_map_set_to_empty(bmap);
 818                         isl_mat_free(C);
 819                         isl_mat_free(C2);
 820                         goto done;
 821                 }
 822         }
 823
 824         d = isl_vec_alloc(bmap->ctx, div_eq);
 825         if (!d)
 826                 goto error;
 827         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 828                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 829                         --j;
 830                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 831         }
 832         B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 833
 834         if (C) {
 835                 B = isl_mat_product(B, C);
 836                 C = NULL;
 837         }
 838
 839         T = isl_mat_parameter_compression(B, d);
 840         if (!T)
 841                 goto error;
 842         if (T->n_col == 0) {
 843                 bmap = isl_basic_map_set_to_empty(bmap);
 844                 isl_mat_free(C2);
 845                 isl_mat_free(T);
 846                 goto done;
 847         }
 848         isl_int_init(v);
 849         for (i = 0; i < T->n_row - 1; ++i) {
 850                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 851                 if (isl_int_is_zero(v))
 852                         continue;
 853                 isl_mat_col_submul(T, 0, v, 1 + i);
 854         }
 855         isl_int_clear(v);
 856         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 857         if (!pos)
 858                 goto error;
 859         /* We have to be careful because dropping equalities may reorder them */
 860         dropped = 0;
 861         for (j = bmap->n_div - 1; j >= 0; --j) {
 862                 for (i = 0; i < bmap->n_eq; ++i)
 863                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 864                                 break;
 865                 if (i < bmap->n_eq) {
 866                         bmap = isl_basic_map_drop_div(bmap, j);
 867                         isl_basic_map_drop_equality(bmap, i);
 868                         ++dropped;
 869                 }
 870         }
 871         pos[0] = 0;
 872         needed = 0;
 873         for (i = 1; i < T->n_row; ++i) {
 874                 if (isl_int_is_one(T->row[i][i]))
 875                         pos[i] = i;
 876                 else
 877                         needed++;
 878         }
 879         if (needed > dropped) {
 880                 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
 881                                 needed, needed, 0);
 882                 if (!bmap)
 883                         goto error;
 884         }
 885         for (i = 1; i < T->n_row; ++i) {
 886                 if (isl_int_is_one(T->row[i][i]))
 887                         continue;
 888                 k = isl_basic_map_alloc_div(bmap);
 889                 pos[i] = 1 + total + k;
 890                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 891                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 892                 if (C2)
 893                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 894                 else
 895                         isl_int_set_si(bmap->div[k][1 + i], 1);
 896                 for (j = 0; j < i; ++j) {
 897                         if (isl_int_is_zero(T->row[i][j]))
 898                                 continue;
 899                         if (pos[j] < T->n_row && C2)
 900                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 901                                                 C2->row[pos[j]], 1 + total);
 902                         else
 903                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 904                                                                 T->row[i][j]);
 905                 }
 906                 j = isl_basic_map_alloc_equality(bmap);
 907                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 908                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 909         }
 910         free(pos);
 911         isl_mat_free(C2);
 912         isl_mat_free(T);
 913
 914         if (progress)
 915                 *progress = 1;
 916 done:
 917         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 918
 919         return bmap;
 920 error:
 921         isl_mat_free(C);
 922         isl_mat_free(C2);
 923         isl_mat_free(T);
 924         return bmap;
 925 }
 926
 927 static struct isl_basic_map *set_div_from_lower_bound(
 928         struct isl_basic_map *bmap, int div, int ineq)
 929 {
 930         unsigned total = 1 + isl_dim_total(bmap->dim);
 931
 932         isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
 933         isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
 934         isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
 935         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
 936         isl_int_set_si(bmap->div[div][1 + total + div], 0);
 937
 938         return bmap;
 939 }
 940
 941 /* Check whether it is ok to define a div based on an inequality.
 942  * To avoid the introduction of circular definitions of divs, we
 943  * do not allow such a definition if the resulting expression would refer to
 944  * any other undefined divs or if any known div is defined in
 945  * terms of the unknown div.
 946  */
 947 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
 948         int div, int ineq)
 949 {
 950         int j;
 951         unsigned total = 1 + isl_dim_total(bmap->dim);
 952
 953         /* Not defined in terms of unknown divs */
 954         for (j = 0; j < bmap->n_div; ++j) {
 955                 if (div == j)
 956                         continue;
 957                 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
 958                         continue;
 959                 if (isl_int_is_zero(bmap->div[j][0]))
 960                         return 0;
 961         }
 962
 963         /* No other div defined in terms of this one => avoid loops */
 964         for (j = 0; j < bmap->n_div; ++j) {
 965                 if (div == j)
 966                         continue;
 967                 if (isl_int_is_zero(bmap->div[j][0]))
 968                         continue;
 969                 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
 970                         return 0;
 971         }
 972
 973         return 1;
 974 }
 975
 976 /* Given two constraints "k" and "l" that are opposite to each other,
 977  * except for the constant term, check if we can use them
 978  * to obtain an expression for one of the hitherto unknown divs.
 979  * "sum" is the sum of the constant terms of the constraints.
 980  * If this sum is strictly smaller than the coefficient of one
 981  * of the divs, then this pair can be used define the div.
 982  * To avoid the introduction of circular definitions of divs, we
 983  * do not use the pair if the resulting expression would refer to
 984  * any other undefined divs or if any known div is defined in
 985  * terms of the unknown div.
 986  */
 987 static struct isl_basic_map *check_for_div_constraints(
 988         struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
 989 {
 990         int i;
 991         unsigned total = 1 + isl_dim_total(bmap->dim);
 992
 993         for (i = 0; i < bmap->n_div; ++i) {
 994                 if (!isl_int_is_zero(bmap->div[i][0]))
 995                         continue;
 996                 if (isl_int_is_zero(bmap->ineq[k][total + i]))
 997                         continue;
 998                 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
 999                         continue;
1000                 if (!ok_to_set_div_from_bound(bmap, i, k))
1001                         break;
1002                 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1003                         bmap = set_div_from_lower_bound(bmap, i, k);
1004                 else
1005                         bmap = set_div_from_lower_bound(bmap, i, l);
1006                 if (progress)
1007                         *progress = 1;
1008                 break;
1009         }
1010         return bmap;
1011 }
1012
1013 static struct isl_basic_map *remove_duplicate_constraints(
1014         struct isl_basic_map *bmap, int *progress, int detect_divs)
1015 {
1016         unsigned int size;
1017         isl_int ***index;
1018         int k, l, h;
1019         int bits;
1020         unsigned total = isl_basic_map_total_dim(bmap);
1021         isl_int sum;
1022
1023         if (!bmap || bmap->n_ineq <= 1)
1024                 return bmap;
1025
1026         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1027         bits = ffs(size) - 1;
1028         index = isl_calloc_array(ctx, isl_int **, size);
1029         if (!index)
1030                 return bmap;
1031
1032         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1033         for (k = 1; k < bmap->n_ineq; ++k) {
1034                 h = hash_index(index, size, bits, bmap, k);
1035                 if (!index[h]) {
1036                         index[h] = &bmap->ineq[k];
1037                         continue;
1038                 }
1039                 if (progress)
1040                         *progress = 1;
1041                 l = index[h] - &bmap->ineq[0];
1042                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1043                         swap_inequality(bmap, k, l);
1044                 isl_basic_map_drop_inequality(bmap, k);
1045                 --k;
1046         }
1047         isl_int_init(sum);
1048         for (k = 0; k < bmap->n_ineq-1; ++k) {
1049                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1050                 h = hash_index(index, size, bits, bmap, k);
1051                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1052                 if (!index[h])
1053                         continue;
1054                 l = index[h] - &bmap->ineq[0];
1055                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1056                 if (isl_int_is_pos(sum)) {
1057                         if (detect_divs)
1058                                 bmap = check_for_div_constraints(bmap, k, l,
1059                                                                  sum, progress);
1060                         continue;
1061                 }
1062                 if (isl_int_is_zero(sum)) {
1063                         /* We need to break out of the loop after these
1064                          * changes since the contents of the hash
1065                          * will no longer be valid.
1066                          * Plus, we probably we want to regauss first.
1067                          */
1068                         if (progress)
1069                                 *progress = 1;
1070                         isl_basic_map_drop_inequality(bmap, l);
1071                         isl_basic_map_inequality_to_equality(bmap, k);
1072                 } else
1073                         bmap = isl_basic_map_set_to_empty(bmap);
1074                 break;
1075         }
1076         isl_int_clear(sum);
1077
1078         free(index);
1079         return bmap;
1080 }
1081
1082
1083 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1084 {
1085         int progress = 1;
1086         if (!bmap)
1087                 return NULL;
1088         while (progress) {
1089                 progress = 0;
1090                 bmap = isl_basic_map_normalize_constraints(bmap);
1091                 bmap = remove_duplicate_divs(bmap, &progress);
1092                 bmap = eliminate_divs_eq(bmap, &progress);
1093                 bmap = eliminate_divs_ineq(bmap, &progress);
1094                 bmap = isl_basic_map_gauss(bmap, &progress);
1095                 /* requires equalities in normal form */
1096                 bmap = normalize_divs(bmap, &progress);
1097                 bmap = remove_duplicate_constraints(bmap, &progress, 1);
1098         }
1099         return bmap;
1100 }
1101
1102 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1103 {
1104         return (struct isl_basic_set *)
1105                 isl_basic_map_simplify((struct isl_basic_map *)bset);
1106 }
1107
1108
1109 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1110         isl_int *constraint, unsigned div)
1111 {
1112         unsigned pos;
1113
1114         if (!bmap)
1115                 return -1;
1116
1117         pos = 1 + isl_dim_total(bmap->dim) + div;
1118
1119         if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1120                 int neg;
1121                 isl_int_sub(bmap->div[div][1],
1122                                 bmap->div[div][1], bmap->div[div][0]);
1123                 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1124                 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1125                 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1126                 isl_int_add(bmap->div[div][1],
1127                                 bmap->div[div][1], bmap->div[div][0]);
1128                 if (!neg)
1129                         return 0;
1130                 if (isl_seq_first_non_zero(constraint+pos+1,
1131                                             bmap->n_div-div-1) != -1)
1132                         return 0;
1133         } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1134                 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1135                         return 0;
1136                 if (isl_seq_first_non_zero(constraint+pos+1,
1137                                             bmap->n_div-div-1) != -1)
1138                         return 0;
1139         } else
1140                 return 0;
1141
1142         return 1;
1143 }
1144
1145
1146 /* If the only constraints a div d=floor(f/m)
1147  * appears in are its two defining constraints
1148  *
1149  *      f - m d >=0
1150  *      -(f - (m - 1)) + m d >= 0
1151  *
1152  * then it can safely be removed.
1153  */
1154 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1155 {
1156         int i;
1157         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1158
1159         for (i = 0; i < bmap->n_eq; ++i)
1160                 if (!isl_int_is_zero(bmap->eq[i][pos]))
1161                         return 0;
1162
1163         for (i = 0; i < bmap->n_ineq; ++i) {
1164                 if (isl_int_is_zero(bmap->ineq[i][pos]))
1165                         continue;
1166                 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1167                         return 0;
1168         }
1169
1170         for (i = 0; i < bmap->n_div; ++i)
1171                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1172                         return 0;
1173
1174         return 1;
1175 }
1176
1177 /*
1178  * Remove divs that don't occur in any of the constraints or other divs.
1179  * These can arise when dropping some of the variables in a quast
1180  * returned by piplib.
1181  */
1182 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1183 {
1184         int i;
1185
1186         if (!bmap)
1187                 return NULL;
1188
1189         for (i = bmap->n_div-1; i >= 0; --i) {
1190                 if (!div_is_redundant(bmap, i))
1191                         continue;
1192                 bmap = isl_basic_map_drop_div(bmap, i);
1193         }
1194         return bmap;
1195 }
1196
1197 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1198 {
1199         bmap = remove_redundant_divs(bmap);
1200         if (!bmap)
1201                 return NULL;
1202         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1203         return bmap;
1204 }
1205
1206 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1207 {
1208         return (struct isl_basic_set *)
1209                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1210 }
1211
1212 struct isl_set *isl_set_finalize(struct isl_set *set)
1213 {
1214         int i;
1215
1216         if (!set)
1217                 return NULL;
1218         for (i = 0; i < set->n; ++i) {
1219                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1220                 if (!set->p[i])
1221                         goto error;
1222         }
1223         return set;
1224 error:
1225         isl_set_free(set);
1226         return NULL;
1227 }
1228
1229 struct isl_map *isl_map_finalize(struct isl_map *map)
1230 {
1231         int i;
1232
1233         if (!map)
1234                 return NULL;
1235         for (i = 0; i < map->n; ++i) {
1236                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1237                 if (!map->p[i])
1238                         goto error;
1239         }
1240         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1241         return map;
1242 error:
1243         isl_map_free(map);
1244         return NULL;
1245 }
1246
1247
1248 /* Remove definition of any div that is defined in terms of the given variable.
1249  * The div itself is not removed.  Functions such as
1250  * eliminate_divs_ineq depend on the other divs remaining in place.
1251  */
1252 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1253                                                                         int pos)
1254 {
1255         int i;
1256
1257         for (i = 0; i < bmap->n_div; ++i) {
1258                 if (isl_int_is_zero(bmap->div[i][0]))
1259                         continue;
1260                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1261                         continue;
1262                 isl_int_set_si(bmap->div[i][0], 0);
1263         }
1264         return bmap;
1265 }
1266
1267 /* Eliminate the specified variables from the constraints using
1268  * Fourier-Motzkin.  The variables themselves are not removed.
1269  */
1270 struct isl_basic_map *isl_basic_map_eliminate_vars(
1271         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1272 {
1273         int d;
1274         int i, j, k;
1275         unsigned total;
1276
1277         if (n == 0)
1278                 return bmap;
1279         if (!bmap)
1280                 return NULL;
1281         total = isl_basic_map_total_dim(bmap);
1282
1283         bmap = isl_basic_map_cow(bmap);
1284         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1285                 bmap = remove_dependent_vars(bmap, d);
1286
1287         for (d = pos + n - 1;
1288              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1289                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1290         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1291                 int n_lower, n_upper;
1292                 if (!bmap)
1293                         return NULL;
1294                 for (i = 0; i < bmap->n_eq; ++i) {
1295                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1296                                 continue;
1297                         eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1298                         isl_basic_map_drop_equality(bmap, i);
1299                         break;
1300                 }
1301                 if (i < bmap->n_eq)
1302                         continue;
1303                 n_lower = 0;
1304                 n_upper = 0;
1305                 for (i = 0; i < bmap->n_ineq; ++i) {
1306                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1307                                 n_lower++;
1308                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1309                                 n_upper++;
1310                 }
1311                 bmap = isl_basic_map_extend_constraints(bmap,
1312                                 0, n_lower * n_upper);
1313                 if (!bmap)
1314                         goto error;
1315                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1316                         int last;
1317                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1318                                 continue;
1319                         last = -1;
1320                         for (j = 0; j < i; ++j) {
1321                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1322                                         continue;
1323                                 last = j;
1324                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1325                                     isl_int_sgn(bmap->ineq[j][1+d]))
1326                                         continue;
1327                                 k = isl_basic_map_alloc_inequality(bmap);
1328                                 if (k < 0)
1329                                         goto error;
1330                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1331                                                 1+total);
1332                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1333                                                 1+d, 1+total, NULL);
1334                         }
1335                         isl_basic_map_drop_inequality(bmap, i);
1336                         i = last + 1;
1337                 }
1338                 if (n_lower > 0 && n_upper > 0) {
1339                         bmap = isl_basic_map_normalize_constraints(bmap);
1340                         bmap = remove_duplicate_constraints(bmap, NULL, 0);
1341                         bmap = isl_basic_map_gauss(bmap, NULL);
1342                         bmap = isl_basic_map_remove_redundancies(bmap);
1343                         if (!bmap)
1344                                 goto error;
1345                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1346                                 break;
1347                 }
1348         }
1349         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1350         return bmap;
1351 error:
1352         isl_basic_map_free(bmap);
1353         return NULL;
1354 }
1355
1356 struct isl_basic_set *isl_basic_set_eliminate_vars(
1357         struct isl_basic_set *bset, unsigned pos, unsigned n)
1358 {
1359         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1360                         (struct isl_basic_map *)bset, pos, n);
1361 }
1362
1363 /* Don't assume equalities are in order, because align_divs
1364  * may have changed the order of the divs.
1365  */
1366 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1367 {
1368         int d, i;
1369         unsigned total;
1370
1371         total = isl_dim_total(bmap->dim);
1372         for (d = 0; d < total; ++d)
1373                 elim[d] = -1;
1374         for (i = 0; i < bmap->n_eq; ++i) {
1375                 for (d = total - 1; d >= 0; --d) {
1376                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1377                                 continue;
1378                         elim[d] = i;
1379                         break;
1380                 }
1381         }
1382 }
1383
1384 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1385 {
1386         compute_elimination_index((struct isl_basic_map *)bset, elim);
1387 }
1388
1389 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1390         struct isl_basic_map *bmap, int *elim)
1391 {
1392         int d;
1393         int copied = 0;
1394         unsigned total;
1395
1396         total = isl_dim_total(bmap->dim);
1397         for (d = total - 1; d >= 0; --d) {
1398                 if (isl_int_is_zero(src[1+d]))
1399                         continue;
1400                 if (elim[d] == -1)
1401                         continue;
1402                 if (!copied) {
1403                         isl_seq_cpy(dst, src, 1 + total);
1404                         copied = 1;
1405                 }
1406                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1407         }
1408         return copied;
1409 }
1410
1411 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1412         struct isl_basic_set *bset, int *elim)
1413 {
1414         return reduced_using_equalities(dst, src,
1415                                         (struct isl_basic_map *)bset, elim);
1416 }
1417
1418 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1419         struct isl_basic_set *bset, struct isl_basic_set *context)
1420 {
1421         int i;
1422         int *elim;
1423
1424         if (!bset || !context)
1425                 goto error;
1426
1427         if (context->n_eq == 0) {
1428                 isl_basic_set_free(context);
1429                 return bset;
1430         }
1431
1432         bset = isl_basic_set_cow(bset);
1433         if (!bset)
1434                 goto error;
1435
1436         elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1437         if (!elim)
1438                 goto error;
1439         set_compute_elimination_index(context, elim);
1440         for (i = 0; i < bset->n_eq; ++i)
1441                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1442                                                         context, elim);
1443         for (i = 0; i < bset->n_ineq; ++i)
1444                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1445                                                         context, elim);
1446         isl_basic_set_free(context);
1447         free(elim);
1448         bset = isl_basic_set_simplify(bset);
1449         bset = isl_basic_set_finalize(bset);
1450         return bset;
1451 error:
1452         isl_basic_set_free(bset);
1453         isl_basic_set_free(context);
1454         return NULL;
1455 }
1456
1457 static struct isl_basic_set *remove_shifted_constraints(
1458         struct isl_basic_set *bset, struct isl_basic_set *context)
1459 {
1460         unsigned int size;
1461         isl_int ***index;
1462         int bits;
1463         int k, h, l;
1464
1465         if (!bset)
1466                 return NULL;
1467
1468         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1469         bits = ffs(size) - 1;
1470         index = isl_calloc_array(ctx, isl_int **, size);
1471         if (!index)
1472                 return bset;
1473
1474         for (k = 0; k < context->n_ineq; ++k) {
1475                 h = set_hash_index(index, size, bits, context, k);
1476                 index[h] = &context->ineq[k];
1477         }
1478         for (k = 0; k < bset->n_ineq; ++k) {
1479                 h = set_hash_index(index, size, bits, bset, k);
1480                 if (!index[h])
1481                         continue;
1482                 l = index[h] - &context->ineq[0];
1483                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1484                         continue;
1485                 bset = isl_basic_set_cow(bset);
1486                 if (!bset)
1487                         goto error;
1488                 isl_basic_set_drop_inequality(bset, k);
1489                 --k;
1490         }
1491         free(index);
1492         return bset;
1493 error:
1494         free(index);
1495         return bset;
1496 }
1497
1498 /* Tighten (decrease) the constant terms of the inequalities based
1499  * on the equalities, without removing any integer points.
1500  * For example, if there is an equality
1501  *
1502  *              i = 3 * j
1503  *
1504  * and an inequality
1505  *
1506  *              i >= 1
1507  *
1508  * then we want to replace the inequality by
1509  *
1510  *              i >= 3
1511  *
1512  * We do this by computing a variable compression and translating
1513  * the constraints to the compressed space.
1514  * If any constraint has coefficients (except the contant term)
1515  * with a common factor "f", then we can replace the constant term "c"
1516  * by
1517  *
1518  *              f * floor(c/f)
1519  *
1520  * That is, we add
1521  *
1522  *              f * floor(c/f) - c = -fract(c/f)
1523  *
1524  * and we can add the same value to the original constraint.
1525  *
1526  * In the example, the compressed space only contains "j",
1527  * and the inequality translates to
1528  *
1529  *              3 * j - 1 >= 0
1530  *
1531  * We add -fract(-1/3) = -2 to the original constraint to obtain
1532  *
1533  *              i - 3 >= 0
1534  */
1535 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1536         struct isl_basic_set *bset)
1537 {
1538         int i;
1539         unsigned total;
1540         struct isl_mat *B, *C;
1541         isl_int gcd;
1542
1543         if (!bset)
1544                 return NULL;
1545
1546         if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1547                 return bset;
1548
1549         if (!bset->n_ineq)
1550                 return bset;
1551
1552         bset = isl_basic_set_cow(bset);
1553         if (!bset)
1554                 return NULL;
1555
1556         total = isl_basic_set_total_dim(bset);
1557         B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1558         C = isl_mat_variable_compression(B, NULL);
1559         if (!C)
1560                 return bset;
1561         if (C->n_col == 0) {
1562                 isl_mat_free(C);
1563                 return isl_basic_set_set_to_empty(bset);
1564         }
1565         B = isl_mat_sub_alloc6(bset->ctx, bset->ineq,
1566                                                 0, bset->n_ineq, 0, 1 + total);
1567         C = isl_mat_product(B, C);
1568         if (!C)
1569                 return bset;
1570
1571         isl_int_init(gcd);
1572         for (i = 0; i < bset->n_ineq; ++i) {
1573                 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1574                 if (isl_int_is_one(gcd))
1575                         continue;
1576                 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1577                 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1578         }
1579         isl_int_clear(gcd);
1580
1581         isl_mat_free(C);
1582
1583         return bset;
1584 }
1585
1586 /* Remove all information from bset that is redundant in the context
1587  * of context.  Both bset and context are assumed to be full-dimensional.
1588  *
1589  * We first * remove the inequalities from "bset"
1590  * that are obviously redundant with respect to some inequality in "context".
1591  *
1592  * If there are any inequalities left, we construct a tableau for
1593  * the context and then add the inequalities of "bset".
1594  * Before adding these inequalities, we freeze all constraints such that
1595  * they won't be considered redundant in terms of the constraints of "bset".
1596  * Then we detect all redundant constraints (among the
1597  * constraints that weren't frozen), first by checking for redundancy in the
1598  * the tableau and then by checking if replacing a constraint by its negation
1599  * would lead to an empty set.  This last step is fairly expensive
1600  * and could be optimized by more reuse of the tableau.
1601  * Finally, we update bset according to the results.
1602  */
1603 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1604         __isl_take isl_basic_set *context)
1605 {
1606         int i, k;
1607         isl_basic_set *combined = NULL;
1608         struct isl_tab *tab = NULL;
1609         unsigned context_ineq;
1610         unsigned total;
1611
1612         if (!bset || !context)
1613                 goto error;
1614
1615         if (isl_basic_set_is_universe(bset)) {
1616                 isl_basic_set_free(context);
1617                 return bset;
1618         }
1619
1620         if (isl_basic_set_is_universe(context)) {
1621                 isl_basic_set_free(context);
1622                 return bset;
1623         }
1624
1625         bset = remove_shifted_constraints(bset, context);
1626         if (!bset)
1627                 goto error;
1628         if (bset->n_ineq == 0)
1629                 goto done;
1630
1631         context_ineq = context->n_ineq;
1632         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1633         combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1634         tab = isl_tab_from_basic_set(combined);
1635         for (i = 0; i < context_ineq; ++i)
1636                 if (isl_tab_freeze_constraint(tab, i) < 0)
1637                         goto error;
1638         tab = isl_tab_extend(tab, bset->n_ineq);
1639         for (i = 0; i < bset->n_ineq; ++i)
1640                 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1641                         goto error;
1642         bset = isl_basic_set_add_constraints(combined, bset, 0);
1643         combined = NULL;
1644         if (!bset)
1645                 goto error;
1646         if (isl_tab_detect_redundant(tab) < 0)
1647                 goto error;
1648         total = isl_basic_set_total_dim(bset);
1649         for (i = context_ineq; i < bset->n_ineq; ++i) {
1650                 int is_empty;
1651                 if (tab->con[i].is_redundant)
1652                         continue;
1653                 tab->con[i].is_redundant = 1;
1654                 combined = isl_basic_set_dup(bset);
1655                 combined = isl_basic_set_update_from_tab(combined, tab);
1656                 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1657                 k = isl_basic_set_alloc_inequality(combined);
1658                 if (k < 0)
1659                         goto error;
1660                 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1661                 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1662                 is_empty = isl_basic_set_is_empty(combined);
1663                 if (is_empty < 0)
1664                         goto error;
1665                 isl_basic_set_free(combined);
1666                 combined = NULL;
1667                 if (!is_empty)
1668                         tab->con[i].is_redundant = 0;
1669         }
1670         for (i = 0; i < context_ineq; ++i)
1671                 tab->con[i].is_redundant = 1;
1672         bset = isl_basic_set_update_from_tab(bset, tab);
1673         if (bset) {
1674                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1675                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1676         }
1677
1678         isl_tab_free(tab);
1679 done:
1680         bset = isl_basic_set_simplify(bset);
1681         bset = isl_basic_set_finalize(bset);
1682         isl_basic_set_free(context);
1683         return bset;
1684 error:
1685         isl_tab_free(tab);
1686         isl_basic_set_free(combined);
1687         isl_basic_set_free(context);
1688         isl_basic_set_free(bset);
1689         return NULL;
1690 }
1691
1692 /* Remove all information from bset that is redundant in the context
1693  * of context.  In particular, equalities that are linear combinations
1694  * of those in context are removed.  Then the inequalities that are
1695  * redundant in the context of the equalities and inequalities of
1696  * context are removed.
1697  *
1698  * We first compute the integer affine hull of the intersection,
1699  * compute the gist inside this affine hull and then add back
1700  * those equalities that are not implied by the context.
1701  *
1702  * If two constraints are mutually redundant, then uset_gist_full
1703  * will remove the second of those constraints.  We therefore first
1704  * sort the constraints so that constraints not involving existentially
1705  * quantified variables are given precedence over those that do.
1706  * We have to perform this sorting before the variable compression,
1707  * because that may effect the order of the variables.
1708  */
1709 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1710         __isl_take isl_basic_set *context)
1711 {
1712         isl_mat *eq;
1713         isl_mat *T, *T2;
1714         isl_basic_set *aff;
1715         isl_basic_set *aff_context;
1716         unsigned total;
1717
1718         if (!bset || !context)
1719                 goto error;
1720
1721         bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1722         if (isl_basic_set_plain_is_empty(bset)) {
1723                 isl_basic_set_free(context);
1724                 return bset;
1725         }
1726         bset = isl_basic_set_sort_constraints(bset);
1727         aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1728         if (!aff)
1729                 goto error;
1730         if (isl_basic_set_plain_is_empty(aff)) {
1731                 isl_basic_set_free(aff);
1732                 isl_basic_set_free(context);
1733                 return bset;
1734         }
1735         if (aff->n_eq == 0) {
1736                 isl_basic_set_free(aff);
1737                 return uset_gist_full(bset, context);
1738         }
1739         total = isl_basic_set_total_dim(bset);
1740         eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1741         eq = isl_mat_cow(eq);
1742         T = isl_mat_variable_compression(eq, &T2);
1743         if (T && T->n_col == 0) {
1744                 isl_mat_free(T);
1745                 isl_mat_free(T2);
1746                 isl_basic_set_free(context);
1747                 isl_basic_set_free(aff);
1748                 return isl_basic_set_set_to_empty(bset);
1749         }
1750
1751         aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1752
1753         bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1754         context = isl_basic_set_preimage(context, T);
1755
1756         bset = uset_gist_full(bset, context);
1757         bset = isl_basic_set_preimage(bset, T2);
1758         bset = isl_basic_set_intersect(bset, aff);
1759         bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1760
1761         if (bset) {
1762                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1763                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1764         }
1765
1766         return bset;
1767 error:
1768         isl_basic_set_free(bset);
1769         isl_basic_set_free(context);
1770         return NULL;
1771 }
1772
1773 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1774  * We simply add the equalities in context to bmap and then do a regular
1775  * div normalizations.  Better results can be obtained by normalizing
1776  * only the divs in bmap than do not also appear in context.
1777  * We need to be careful to reduce the divs using the equalities
1778  * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1779  * spurious constraints.
1780  */
1781 static struct isl_basic_map *normalize_divs_in_context(
1782         struct isl_basic_map *bmap, struct isl_basic_map *context)
1783 {
1784         int i;
1785         unsigned total_context;
1786         int div_eq;
1787
1788         div_eq = n_pure_div_eq(bmap);
1789         if (div_eq == 0)
1790                 return bmap;
1791
1792         if (context->n_div > 0)
1793                 bmap = isl_basic_map_align_divs(bmap, context);
1794
1795         total_context = isl_basic_map_total_dim(context);
1796         bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1797         for (i = 0; i < context->n_eq; ++i) {
1798                 int k;
1799                 k = isl_basic_map_alloc_equality(bmap);
1800                 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1801                 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1802                                 isl_basic_map_total_dim(bmap) - total_context);
1803         }
1804         bmap = isl_basic_map_gauss(bmap, NULL);
1805         bmap = normalize_divs(bmap, NULL);
1806         bmap = isl_basic_map_gauss(bmap, NULL);
1807         return bmap;
1808 }
1809
1810 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1811         struct isl_basic_map *context)
1812 {
1813         struct isl_basic_set *bset;
1814
1815         if (!bmap || !context)
1816                 goto error;
1817
1818         if (isl_basic_map_is_universe(bmap)) {
1819                 isl_basic_map_free(context);
1820                 return bmap;
1821         }
1822         if (isl_basic_map_plain_is_empty(context)) {
1823                 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1824                 isl_basic_map_free(context);
1825                 isl_basic_map_free(bmap);
1826                 return isl_basic_map_universe(dim);
1827         }
1828         if (isl_basic_map_plain_is_empty(bmap)) {
1829                 isl_basic_map_free(context);
1830                 return bmap;
1831         }
1832
1833         bmap = isl_basic_map_remove_redundancies(bmap);
1834         context = isl_basic_map_remove_redundancies(context);
1835
1836         if (context->n_eq)
1837                 bmap = normalize_divs_in_context(bmap, context);
1838
1839         context = isl_basic_map_align_divs(context, bmap);
1840         bmap = isl_basic_map_align_divs(bmap, context);
1841
1842         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1843                          isl_basic_map_underlying_set(context));
1844
1845         return isl_basic_map_overlying_set(bset, bmap);
1846 error:
1847         isl_basic_map_free(bmap);
1848         isl_basic_map_free(context);
1849         return NULL;
1850 }
1851
1852 /*
1853  * Assumes context has no implicit divs.
1854  */
1855 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1856         __isl_take isl_basic_map *context)
1857 {
1858         int i;
1859
1860         if (!map || !context)
1861                 goto error;;
1862
1863         if (isl_basic_map_plain_is_empty(context)) {
1864                 struct isl_dim *dim = isl_dim_copy(map->dim);
1865                 isl_basic_map_free(context);
1866                 isl_map_free(map);
1867                 return isl_map_universe(dim);
1868         }
1869
1870         context = isl_basic_map_remove_redundancies(context);
1871         map = isl_map_cow(map);
1872         if (!map || !context)
1873                 goto error;;
1874         isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1875         map = isl_map_compute_divs(map);
1876         for (i = 0; i < map->n; ++i)
1877                 context = isl_basic_map_align_divs(context, map->p[i]);
1878         for (i = map->n - 1; i >= 0; --i) {
1879                 map->p[i] = isl_basic_map_gist(map->p[i],
1880                                                 isl_basic_map_copy(context));
1881                 if (!map->p[i])
1882                         goto error;
1883                 if (isl_basic_map_plain_is_empty(map->p[i])) {
1884                         isl_basic_map_free(map->p[i]);
1885                         if (i != map->n - 1)
1886                                 map->p[i] = map->p[map->n - 1];
1887                         map->n--;
1888                 }
1889         }
1890         isl_basic_map_free(context);
1891         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1892         return map;
1893 error:
1894         isl_map_free(map);
1895         isl_basic_map_free(context);
1896         return NULL;
1897 }
1898
1899 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1900         __isl_take isl_map *context)
1901 {
1902         context = isl_map_compute_divs(context);
1903         return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1904 }
1905
1906 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1907                                                 struct isl_basic_set *context)
1908 {
1909         return (struct isl_basic_set *)isl_basic_map_gist(
1910                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1911 }
1912
1913 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1914         __isl_take isl_basic_set *context)
1915 {
1916         return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1917                                         (struct isl_basic_map *)context);
1918 }
1919
1920 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1921         __isl_take isl_set *context)
1922 {
1923         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1924                                         (struct isl_map *)context);
1925 }
1926
1927 /* Quick check to see if two basic maps are disjoint.
1928  * In particular, we reduce the equalities and inequalities of
1929  * one basic map in the context of the equalities of the other
1930  * basic map and check if we get a contradiction.
1931  */
1932 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
1933         __isl_keep isl_basic_map *bmap2)
1934 {
1935         struct isl_vec *v = NULL;
1936         int *elim = NULL;
1937         unsigned total;
1938         int i;
1939
1940         if (!bmap1 || !bmap2)
1941                 return -1;
1942         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1943                         return -1);
1944         if (bmap1->n_div || bmap2->n_div)
1945                 return 0;
1946         if (!bmap1->n_eq && !bmap2->n_eq)
1947                 return 0;
1948
1949         total = isl_dim_total(bmap1->dim);
1950         if (total == 0)
1951                 return 0;
1952         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1953         if (!v)
1954                 goto error;
1955         elim = isl_alloc_array(bmap1->ctx, int, total);
1956         if (!elim)
1957                 goto error;
1958         compute_elimination_index(bmap1, elim);
1959         for (i = 0; i < bmap2->n_eq; ++i) {
1960                 int reduced;
1961                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1962                                                         bmap1, elim);
1963                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1964                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1965                         goto disjoint;
1966         }
1967         for (i = 0; i < bmap2->n_ineq; ++i) {
1968                 int reduced;
1969                 reduced = reduced_using_equalities(v->block.data,
1970                                                 bmap2->ineq[i], bmap1, elim);
1971                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1972                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1973                         goto disjoint;
1974         }
1975         compute_elimination_index(bmap2, elim);
1976         for (i = 0; i < bmap1->n_ineq; ++i) {
1977                 int reduced;
1978                 reduced = reduced_using_equalities(v->block.data,
1979                                                 bmap1->ineq[i], bmap2, elim);
1980                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1981                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1982                         goto disjoint;
1983         }
1984         isl_vec_free(v);
1985         free(elim);
1986         return 0;
1987 disjoint:
1988         isl_vec_free(v);
1989         free(elim);
1990         return 1;
1991 error:
1992         isl_vec_free(v);
1993         free(elim);
1994         return -1;
1995 }
1996
1997 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
1998         __isl_keep isl_basic_set *bset2)
1999 {
2000         return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
2001                                               (struct isl_basic_map *)bset2);
2002 }
2003
2004 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
2005         __isl_keep isl_map *map2)
2006 {
2007         int i, j;
2008
2009         if (!map1 || !map2)
2010                 return -1;
2011
2012         if (isl_map_plain_is_equal(map1, map2))
2013                 return 0;
2014
2015         for (i = 0; i < map1->n; ++i) {
2016                 for (j = 0; j < map2->n; ++j) {
2017                         int d = isl_basic_map_plain_is_disjoint(map1->p[i],
2018                                                                map2->p[j]);
2019                         if (d != 1)
2020                                 return d;
2021                 }
2022         }
2023         return 1;
2024 }
2025
2026 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2027         __isl_keep isl_set *set2)
2028 {
2029         return isl_map_plain_is_disjoint((struct isl_map *)set1,
2030                                         (struct isl_map *)set2);
2031 }
2032
2033 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
2034 {
2035         return isl_set_plain_is_disjoint(set1, set2);
2036 }
2037
2038 /* Check if we can combine a given div with lower bound l and upper
2039  * bound u with some other div and if so return that other div.
2040  * Otherwise return -1.
2041  *
2042  * We first check that
2043  *      - the bounds are opposites of each other (except for the constant
2044  *        term)
2045  *      - the bounds do not reference any other div
2046  *      - no div is defined in terms of this div
2047  *
2048  * Let m be the size of the range allowed on the div by the bounds.
2049  * That is, the bounds are of the form
2050  *
2051  *      e <= a <= e + m - 1
2052  *
2053  * with e some expression in the other variables.
2054  * We look for another div b such that no third div is defined in terms
2055  * of this second div b and such that in any constraint that contains
2056  * a (except for the given lower and upper bound), also contains b
2057  * with a coefficient that is m times that of b.
2058  * That is, all constraints (execpt for the lower and upper bound)
2059  * are of the form
2060  *
2061  *      e + f (a + m b) >= 0
2062  *
2063  * If so, we return b so that "a + m b" can be replaced by
2064  * a single div "c = a + m b".
2065  */
2066 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2067         unsigned div, unsigned l, unsigned u)
2068 {
2069         int i, j;
2070         unsigned dim;
2071         int coalesce = -1;
2072
2073         if (bmap->n_div <= 1)
2074                 return -1;
2075         dim = isl_dim_total(bmap->dim);
2076         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2077                 return -1;
2078         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2079                                    bmap->n_div - div - 1) != -1)
2080                 return -1;
2081         if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2082                             dim + bmap->n_div))
2083                 return -1;
2084
2085         for (i = 0; i < bmap->n_div; ++i) {
2086                 if (isl_int_is_zero(bmap->div[i][0]))
2087                         continue;
2088                 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2089                         return -1;
2090         }
2091
2092         isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2093         if (isl_int_is_neg(bmap->ineq[l][0])) {
2094                 isl_int_sub(bmap->ineq[l][0],
2095                             bmap->ineq[l][0], bmap->ineq[u][0]);
2096                 bmap = isl_basic_map_copy(bmap);
2097                 bmap = isl_basic_map_set_to_empty(bmap);
2098                 isl_basic_map_free(bmap);
2099                 return -1;
2100         }
2101         isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2102         for (i = 0; i < bmap->n_div; ++i) {
2103                 if (i == div)
2104                         continue;
2105                 if (!pairs[i])
2106                         continue;
2107                 for (j = 0; j < bmap->n_div; ++j) {
2108                         if (isl_int_is_zero(bmap->div[j][0]))
2109                                 continue;
2110                         if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2111                                 break;
2112                 }
2113                 if (j < bmap->n_div)
2114                         continue;
2115                 for (j = 0; j < bmap->n_ineq; ++j) {
2116                         int valid;
2117                         if (j == l || j == u)
2118                                 continue;
2119                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2120                                 continue;
2121                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2122                                 break;
2123                         isl_int_mul(bmap->ineq[j][1 + dim + div],
2124                                     bmap->ineq[j][1 + dim + div],
2125                                     bmap->ineq[l][0]);
2126                         valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2127                                            bmap->ineq[j][1 + dim + i]);
2128                         isl_int_divexact(bmap->ineq[j][1 + dim + div],
2129                                          bmap->ineq[j][1 + dim + div],
2130                                          bmap->ineq[l][0]);
2131                         if (!valid)
2132                                 break;
2133                 }
2134                 if (j < bmap->n_ineq)
2135                         continue;
2136                 coalesce = i;
2137                 break;
2138         }
2139         isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2140         isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2141         return coalesce;
2142 }
2143
2144 /* Given a lower and an upper bound on div i, construct an inequality
2145  * that when nonnegative ensures that this pair of bounds always allows
2146  * for an integer value of the given div.
2147  * The lower bound is inequality l, while the upper bound is inequality u.
2148  * The constructed inequality is stored in ineq.
2149  * g, fl, fu are temporary scalars.
2150  *
2151  * Let the upper bound be
2152  *
2153  *      -n_u a + e_u >= 0
2154  *
2155  * and the lower bound
2156  *
2157  *      n_l a + e_l >= 0
2158  *
2159  * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2160  * We have
2161  *
2162  *      - f_u e_l <= f_u f_l g a <= f_l e_u
2163  *
2164  * Since all variables are integer valued, this is equivalent to
2165  *
2166  *      - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2167  *
2168  * If this interval is at least f_u f_l g, then it contains at least
2169  * one integer value for a.
2170  * That is, the test constraint is
2171  *
2172  *      f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2173  */
2174 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2175         int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2176 {
2177         unsigned dim;
2178         dim = isl_dim_total(bmap->dim);
2179
2180         isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2181         isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2182         isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2183         isl_int_neg(fu, fu);
2184         isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2185                         1 + dim + bmap->n_div);
2186         isl_int_add(ineq[0], ineq[0], fl);
2187         isl_int_add(ineq[0], ineq[0], fu);
2188         isl_int_sub_ui(ineq[0], ineq[0], 1);
2189         isl_int_mul(g, g, fl);
2190         isl_int_mul(g, g, fu);
2191         isl_int_sub(ineq[0], ineq[0], g);
2192 }
2193
2194 /* Remove more kinds of divs that are not strictly needed.
2195  * In particular, if all pairs of lower and upper bounds on a div
2196  * are such that they allow at least one integer value of the div,
2197  * the we can eliminate the div using Fourier-Motzkin without
2198  * introducing any spurious solutions.
2199  */
2200 static struct isl_basic_map *drop_more_redundant_divs(
2201         struct isl_basic_map *bmap, int *pairs, int n)
2202 {
2203         struct isl_tab *tab = NULL;
2204         struct isl_vec *vec = NULL;
2205         unsigned dim;
2206         int remove = -1;
2207         isl_int g, fl, fu;
2208
2209         isl_int_init(g);
2210         isl_int_init(fl);
2211         isl_int_init(fu);
2212
2213         if (!bmap)
2214                 goto error;
2215
2216         dim = isl_dim_total(bmap->dim);
2217         vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2218         if (!vec)
2219                 goto error;
2220
2221         tab = isl_tab_from_basic_map(bmap);
2222
2223         while (n > 0) {
2224                 int i, l, u;
2225                 int best = -1;
2226                 enum isl_lp_result res;
2227
2228                 for (i = 0; i < bmap->n_div; ++i) {
2229                         if (!pairs[i])
2230                                 continue;
2231                         if (best >= 0 && pairs[best] <= pairs[i])
2232                                 continue;
2233                         best = i;
2234                 }
2235
2236                 i = best;
2237                 for (l = 0; l < bmap->n_ineq; ++l) {
2238                         if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2239                                 continue;
2240                         for (u = 0; u < bmap->n_ineq; ++u) {
2241                                 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2242                                         continue;
2243                                 construct_test_ineq(bmap, i, l, u,
2244                                                     vec->el, g, fl, fu);
2245                                 res = isl_tab_min(tab, vec->el,
2246                                                   bmap->ctx->one, &g, NULL, 0);
2247                                 if (res == isl_lp_error)
2248                                         goto error;
2249                                 if (res == isl_lp_empty) {
2250                                         bmap = isl_basic_map_set_to_empty(bmap);
2251                                         break;
2252                                 }
2253                                 if (res != isl_lp_ok || isl_int_is_neg(g))
2254                                         break;
2255                         }
2256                         if (u < bmap->n_ineq)
2257                                 break;
2258                 }
2259                 if (l == bmap->n_ineq) {
2260                         remove = i;
2261                         break;
2262                 }
2263                 pairs[i] = 0;
2264                 --n;
2265         }
2266
2267         isl_tab_free(tab);
2268         isl_vec_free(vec);
2269
2270         isl_int_clear(g);
2271         isl_int_clear(fl);
2272         isl_int_clear(fu);
2273
2274         free(pairs);
2275
2276         if (remove < 0)
2277                 return bmap;
2278
2279         bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2280         return isl_basic_map_drop_redundant_divs(bmap);
2281 error:
2282         free(pairs);
2283         isl_basic_map_free(bmap);
2284         isl_tab_free(tab);
2285         isl_vec_free(vec);
2286         isl_int_clear(g);
2287         isl_int_clear(fl);
2288         isl_int_clear(fu);
2289         return NULL;
2290 }
2291
2292 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2293  * and the upper bound u, div1 always occurs together with div2 in the form
2294  * (div1 + m div2), where m is the constant range on the variable div1
2295  * allowed by l and u, replace the pair div1 and div2 by a single
2296  * div that is equal to div1 + m div2.
2297  *
2298  * The new div will appear in the location that contains div2.
2299  * We need to modify all constraints that contain
2300  * div2 = (div - div1) / m
2301  * (If a constraint does not contain div2, it will also not contain div1.)
2302  * If the constraint also contains div1, then we know they appear
2303  * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2304  * i.e., the coefficient of div is f.
2305  *
2306  * Otherwise, we first need to introduce div1 into the constraint.
2307  * Let the l be
2308  *
2309  *      div1 + f >=0
2310  *
2311  * and u
2312  *
2313  *      -div1 + f' >= 0
2314  *
2315  * A lower bound on div2
2316  *
2317  *      n div2 + t >= 0
2318  *
2319  * can be replaced by
2320  *
2321  *      (n * (m div 2 + div1) + m t + n f)/g >= 0
2322  *
2323  * with g = gcd(m,n).
2324  * An upper bound
2325  *
2326  *      -n div2 + t >= 0
2327  *
2328  * can be replaced by
2329  *
2330  *      (-n * (m div2 + div1) + m t + n f')/g >= 0
2331  *
2332  * These constraint are those that we would obtain from eliminating
2333  * div1 using Fourier-Motzkin.
2334  *
2335  * After all constraints have been modified, we drop the lower and upper
2336  * bound and then drop div1.
2337  */
2338 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2339         unsigned div1, unsigned div2, unsigned l, unsigned u)
2340 {
2341         isl_int a;
2342         isl_int b;
2343         isl_int m;
2344         unsigned dim, total;
2345         int i;
2346
2347         dim = isl_dim_total(bmap->dim);
2348         total = 1 + dim + bmap->n_div;
2349
2350         isl_int_init(a);
2351         isl_int_init(b);
2352         isl_int_init(m);
2353         isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2354         isl_int_add_ui(m, m, 1);
2355
2356         for (i = 0; i < bmap->n_ineq; ++i) {
2357                 if (i == l || i == u)
2358                         continue;
2359                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2360                         continue;
2361                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2362                         isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2363                         isl_int_divexact(a, m, b);
2364                         isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2365                         if (isl_int_is_pos(b)) {
2366                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2367                                                 b, bmap->ineq[l], total);
2368                         } else {
2369                                 isl_int_neg(b, b);
2370                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2371                                                 b, bmap->ineq[u], total);
2372                         }
2373                 }
2374                 isl_int_set(bmap->ineq[i][1 + dim + div2],
2375                             bmap->ineq[i][1 + dim + div1]);
2376                 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2377         }
2378
2379         isl_int_clear(a);
2380         isl_int_clear(b);
2381         isl_int_clear(m);
2382         if (l > u) {
2383                 isl_basic_map_drop_inequality(bmap, l);
2384                 isl_basic_map_drop_inequality(bmap, u);
2385         } else {
2386                 isl_basic_map_drop_inequality(bmap, u);
2387                 isl_basic_map_drop_inequality(bmap, l);
2388         }
2389         bmap = isl_basic_map_drop_div(bmap, div1);
2390         return bmap;
2391 }
2392
2393 /* First check if we can coalesce any pair of divs and
2394  * then continue with dropping more redundant divs.
2395  *
2396  * We loop over all pairs of lower and upper bounds on a div
2397  * with coefficient 1 and -1, respectively, check if there
2398  * is any other div "c" with which we can coalesce the div
2399  * and if so, perform the coalescing.
2400  */
2401 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2402         struct isl_basic_map *bmap, int *pairs, int n)
2403 {
2404         int i, l, u;
2405         unsigned dim;
2406
2407         dim = isl_dim_total(bmap->dim);
2408
2409         for (i = 0; i < bmap->n_div; ++i) {
2410                 if (!pairs[i])
2411                         continue;
2412                 for (l = 0; l < bmap->n_ineq; ++l) {
2413                         if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2414                                 continue;
2415                         for (u = 0; u < bmap->n_ineq; ++u) {
2416                                 int c;
2417
2418                                 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2419                                         continue;
2420                                 c = div_find_coalesce(bmap, pairs, i, l, u);
2421                                 if (c < 0)
2422                                         continue;
2423                                 free(pairs);
2424                                 bmap = coalesce_divs(bmap, i, c, l, u);
2425                                 return isl_basic_map_drop_redundant_divs(bmap);
2426                         }
2427                 }
2428         }
2429
2430         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2431                 return bmap;
2432
2433         return drop_more_redundant_divs(bmap, pairs, n);
2434 }
2435
2436 /* Remove divs that are not strictly needed.
2437  * In particular, if a div only occurs positively (or negatively)
2438  * in constraints, then it can simply be dropped.
2439  * Also, if a div occurs only occurs in two constraints and if moreover
2440  * those two constraints are opposite to each other, except for the constant
2441  * term and if the sum of the constant terms is such that for any value
2442  * of the other values, there is always at least one integer value of the
2443  * div, i.e., if one plus this sum is greater than or equal to
2444  * the (absolute value) of the coefficent of the div in the constraints,
2445  * then we can also simply drop the div.
2446  *
2447  * If any divs are left after these simple checks then we move on
2448  * to more complicated cases in drop_more_redundant_divs.
2449  */
2450 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2451         struct isl_basic_map *bmap)
2452 {
2453         int i, j;
2454         unsigned off;
2455         int *pairs = NULL;
2456         int n = 0;
2457
2458         if (!bmap)
2459                 goto error;
2460
2461         off = isl_dim_total(bmap->dim);
2462         pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2463         if (!pairs)
2464                 goto error;
2465
2466         for (i = 0; i < bmap->n_div; ++i) {
2467                 int pos, neg;
2468                 int last_pos, last_neg;
2469                 int redundant;
2470                 int defined;
2471
2472                 defined = !isl_int_is_zero(bmap->div[i][0]);
2473                 for (j = 0; j < bmap->n_eq; ++j)
2474                         if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2475                                 break;
2476                 if (j < bmap->n_eq)
2477                         continue;
2478                 ++n;
2479                 pos = neg = 0;
2480                 for (j = 0; j < bmap->n_ineq; ++j) {
2481                         if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2482                                 last_pos = j;
2483                                 ++pos;
2484                         }
2485                         if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2486                                 last_neg = j;
2487                                 ++neg;
2488                         }
2489                 }
2490                 pairs[i] = pos * neg;
2491                 if (pairs[i] == 0) {
2492                         for (j = bmap->n_ineq - 1; j >= 0; --j)
2493                                 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2494                                         isl_basic_map_drop_inequality(bmap, j);
2495                         bmap = isl_basic_map_drop_div(bmap, i);
2496                         free(pairs);
2497                         return isl_basic_map_drop_redundant_divs(bmap);
2498                 }
2499                 if (pairs[i] != 1)
2500                         continue;
2501                 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2502                                     bmap->ineq[last_neg] + 1,
2503                                     off + bmap->n_div))
2504                         continue;
2505
2506                 isl_int_add(bmap->ineq[last_pos][0],
2507                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2508                 isl_int_add_ui(bmap->ineq[last_pos][0],
2509                                bmap->ineq[last_pos][0], 1);
2510                 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2511                                 bmap->ineq[last_pos][1+off+i]);
2512                 isl_int_sub_ui(bmap->ineq[last_pos][0],
2513                                bmap->ineq[last_pos][0], 1);
2514                 isl_int_sub(bmap->ineq[last_pos][0],
2515                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2516                 if (!redundant) {
2517                         if (defined ||
2518                             !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2519                                 pairs[i] = 0;
2520                                 --n;
2521                                 continue;
2522                         }
2523                         bmap = set_div_from_lower_bound(bmap, i, last_pos);
2524                         bmap = isl_basic_map_simplify(bmap);
2525                         free(pairs);
2526                         return isl_basic_map_drop_redundant_divs(bmap);
2527                 }
2528                 if (last_pos > last_neg) {
2529                         isl_basic_map_drop_inequality(bmap, last_pos);
2530                         isl_basic_map_drop_inequality(bmap, last_neg);
2531                 } else {
2532                         isl_basic_map_drop_inequality(bmap, last_neg);
2533                         isl_basic_map_drop_inequality(bmap, last_pos);
2534                 }
2535                 bmap = isl_basic_map_drop_div(bmap, i);
2536                 free(pairs);
2537                 return isl_basic_map_drop_redundant_divs(bmap);
2538         }
2539
2540         if (n > 0)
2541                 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2542
2543         free(pairs);
2544         return bmap;
2545 error:
2546         free(pairs);
2547         isl_basic_map_free(bmap);
2548         return NULL;
2549 }
2550
2551 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2552         struct isl_basic_set *bset)
2553 {
2554         return (struct isl_basic_set *)
2555             isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2556 }
2557
2558 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2559 {
2560         int i;
2561
2562         if (!map)
2563                 return NULL;
2564         for (i = 0; i < map->n; ++i) {
2565                 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2566                 if (!map->p[i])
2567                         goto error;
2568         }
2569         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2570         return map;
2571 error:
2572         isl_map_free(map);
2573         return NULL;
2574 }
2575
2576 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2577 {
2578         return (struct isl_set *)
2579             isl_map_drop_redundant_divs((struct isl_map *)set);
2580 }