isl_map_simplify.c

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