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_get_tuple_name(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
1280         if (n == 0)
1281                 return bmap;
1282         if (!bmap)
1283                 return NULL;
1284         total = isl_basic_map_total_dim(bmap);
1285
1286         bmap = isl_basic_map_cow(bmap);
1287         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1288                 bmap = remove_dependent_vars(bmap, d);
1289
1290         for (d = pos + n - 1;
1291              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1292                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1293         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1294                 int n_lower, n_upper;
1295                 if (!bmap)
1296                         return NULL;
1297                 for (i = 0; i < bmap->n_eq; ++i) {
1298                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1299                                 continue;
1300                         eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1301                         isl_basic_map_drop_equality(bmap, i);
1302                         break;
1303                 }
1304                 if (i < bmap->n_eq)
1305                         continue;
1306                 n_lower = 0;
1307                 n_upper = 0;
1308                 for (i = 0; i < bmap->n_ineq; ++i) {
1309                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1310                                 n_lower++;
1311                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1312                                 n_upper++;
1313                 }
1314                 bmap = isl_basic_map_extend_constraints(bmap,
1315                                 0, n_lower * n_upper);
1316                 if (!bmap)
1317                         goto error;
1318                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1319                         int last;
1320                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1321                                 continue;
1322                         last = -1;
1323                         for (j = 0; j < i; ++j) {
1324                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1325                                         continue;
1326                                 last = j;
1327                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1328                                     isl_int_sgn(bmap->ineq[j][1+d]))
1329                                         continue;
1330                                 k = isl_basic_map_alloc_inequality(bmap);
1331                                 if (k < 0)
1332                                         goto error;
1333                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1334                                                 1+total);
1335                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1336                                                 1+d, 1+total, NULL);
1337                         }
1338                         isl_basic_map_drop_inequality(bmap, i);
1339                         i = last + 1;
1340                 }
1341                 if (n_lower > 0 && n_upper > 0) {
1342                         bmap = isl_basic_map_normalize_constraints(bmap);
1343                         bmap = remove_duplicate_constraints(bmap, NULL, 0);
1344                         bmap = isl_basic_map_gauss(bmap, NULL);
1345                         bmap = isl_basic_map_remove_redundancies(bmap);
1346                         if (!bmap)
1347                                 goto error;
1348                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1349                                 break;
1350                 }
1351         }
1352         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1353         return bmap;
1354 error:
1355         isl_basic_map_free(bmap);
1356         return NULL;
1357 }
1358
1359 struct isl_basic_set *isl_basic_set_eliminate_vars(
1360         struct isl_basic_set *bset, unsigned pos, unsigned n)
1361 {
1362         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1363                         (struct isl_basic_map *)bset, pos, n);
1364 }
1365
1366 /* Don't assume equalities are in order, because align_divs
1367  * may have changed the order of the divs.
1368  */
1369 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1370 {
1371         int d, i;
1372         unsigned total;
1373
1374         total = isl_dim_total(bmap->dim);
1375         for (d = 0; d < total; ++d)
1376                 elim[d] = -1;
1377         for (i = 0; i < bmap->n_eq; ++i) {
1378                 for (d = total - 1; d >= 0; --d) {
1379                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1380                                 continue;
1381                         elim[d] = i;
1382                         break;
1383                 }
1384         }
1385 }
1386
1387 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1388 {
1389         compute_elimination_index((struct isl_basic_map *)bset, elim);
1390 }
1391
1392 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1393         struct isl_basic_map *bmap, int *elim)
1394 {
1395         int d;
1396         int copied = 0;
1397         unsigned total;
1398
1399         total = isl_dim_total(bmap->dim);
1400         for (d = total - 1; d >= 0; --d) {
1401                 if (isl_int_is_zero(src[1+d]))
1402                         continue;
1403                 if (elim[d] == -1)
1404                         continue;
1405                 if (!copied) {
1406                         isl_seq_cpy(dst, src, 1 + total);
1407                         copied = 1;
1408                 }
1409                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1410         }
1411         return copied;
1412 }
1413
1414 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1415         struct isl_basic_set *bset, int *elim)
1416 {
1417         return reduced_using_equalities(dst, src,
1418                                         (struct isl_basic_map *)bset, elim);
1419 }
1420
1421 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1422         struct isl_basic_set *bset, struct isl_basic_set *context)
1423 {
1424         int i;
1425         int *elim;
1426
1427         if (!bset || !context)
1428                 goto error;
1429
1430         if (context->n_eq == 0) {
1431                 isl_basic_set_free(context);
1432                 return bset;
1433         }
1434
1435         bset = isl_basic_set_cow(bset);
1436         if (!bset)
1437                 goto error;
1438
1439         elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1440         if (!elim)
1441                 goto error;
1442         set_compute_elimination_index(context, elim);
1443         for (i = 0; i < bset->n_eq; ++i)
1444                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1445                                                         context, elim);
1446         for (i = 0; i < bset->n_ineq; ++i)
1447                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1448                                                         context, elim);
1449         isl_basic_set_free(context);
1450         free(elim);
1451         bset = isl_basic_set_simplify(bset);
1452         bset = isl_basic_set_finalize(bset);
1453         return bset;
1454 error:
1455         isl_basic_set_free(bset);
1456         isl_basic_set_free(context);
1457         return NULL;
1458 }
1459
1460 static struct isl_basic_set *remove_shifted_constraints(
1461         struct isl_basic_set *bset, struct isl_basic_set *context)
1462 {
1463         unsigned int size;
1464         isl_int ***index;
1465         int bits;
1466         int k, h, l;
1467         isl_ctx *ctx;
1468
1469         if (!bset)
1470                 return NULL;
1471
1472         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1473         bits = ffs(size) - 1;
1474         ctx = isl_basic_set_get_ctx(bset);
1475         index = isl_calloc_array(ctx, isl_int **, size);
1476         if (!index)
1477                 return bset;
1478
1479         for (k = 0; k < context->n_ineq; ++k) {
1480                 h = set_hash_index(index, size, bits, context, k);
1481                 index[h] = &context->ineq[k];
1482         }
1483         for (k = 0; k < bset->n_ineq; ++k) {
1484                 h = set_hash_index(index, size, bits, bset, k);
1485                 if (!index[h])
1486                         continue;
1487                 l = index[h] - &context->ineq[0];
1488                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1489                         continue;
1490                 bset = isl_basic_set_cow(bset);
1491                 if (!bset)
1492                         goto error;
1493                 isl_basic_set_drop_inequality(bset, k);
1494                 --k;
1495         }
1496         free(index);
1497         return bset;
1498 error:
1499         free(index);
1500         return bset;
1501 }
1502
1503 /* Remove all information from bset that is redundant in the context
1504  * of context.  Both bset and context are assumed to be full-dimensional.
1505  *
1506  * We first * remove the inequalities from "bset"
1507  * that are obviously redundant with respect to some inequality in "context".
1508  *
1509  * If there are any inequalities left, we construct a tableau for
1510  * the context and then add the inequalities of "bset".
1511  * Before adding these inequalities, we freeze all constraints such that
1512  * they won't be considered redundant in terms of the constraints of "bset".
1513  * Then we detect all redundant constraints (among the
1514  * constraints that weren't frozen), first by checking for redundancy in the
1515  * the tableau and then by checking if replacing a constraint by its negation
1516  * would lead to an empty set.  This last step is fairly expensive
1517  * and could be optimized by more reuse of the tableau.
1518  * Finally, we update bset according to the results.
1519  */
1520 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1521         __isl_take isl_basic_set *context)
1522 {
1523         int i, k;
1524         isl_basic_set *combined = NULL;
1525         struct isl_tab *tab = NULL;
1526         unsigned context_ineq;
1527         unsigned total;
1528
1529         if (!bset || !context)
1530                 goto error;
1531
1532         if (isl_basic_set_is_universe(bset)) {
1533                 isl_basic_set_free(context);
1534                 return bset;
1535         }
1536
1537         if (isl_basic_set_is_universe(context)) {
1538                 isl_basic_set_free(context);
1539                 return bset;
1540         }
1541
1542         bset = remove_shifted_constraints(bset, context);
1543         if (!bset)
1544                 goto error;
1545         if (bset->n_ineq == 0)
1546                 goto done;
1547
1548         context_ineq = context->n_ineq;
1549         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1550         combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1551         tab = isl_tab_from_basic_set(combined);
1552         for (i = 0; i < context_ineq; ++i)
1553                 if (isl_tab_freeze_constraint(tab, i) < 0)
1554                         goto error;
1555         tab = isl_tab_extend(tab, bset->n_ineq);
1556         for (i = 0; i < bset->n_ineq; ++i)
1557                 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1558                         goto error;
1559         bset = isl_basic_set_add_constraints(combined, bset, 0);
1560         combined = NULL;
1561         if (!bset)
1562                 goto error;
1563         if (isl_tab_detect_redundant(tab) < 0)
1564                 goto error;
1565         total = isl_basic_set_total_dim(bset);
1566         for (i = context_ineq; i < bset->n_ineq; ++i) {
1567                 int is_empty;
1568                 if (tab->con[i].is_redundant)
1569                         continue;
1570                 tab->con[i].is_redundant = 1;
1571                 combined = isl_basic_set_dup(bset);
1572                 combined = isl_basic_set_update_from_tab(combined, tab);
1573                 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1574                 k = isl_basic_set_alloc_inequality(combined);
1575                 if (k < 0)
1576                         goto error;
1577                 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1578                 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1579                 is_empty = isl_basic_set_is_empty(combined);
1580                 if (is_empty < 0)
1581                         goto error;
1582                 isl_basic_set_free(combined);
1583                 combined = NULL;
1584                 if (!is_empty)
1585                         tab->con[i].is_redundant = 0;
1586         }
1587         for (i = 0; i < context_ineq; ++i)
1588                 tab->con[i].is_redundant = 1;
1589         bset = isl_basic_set_update_from_tab(bset, tab);
1590         if (bset) {
1591                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1592                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1593         }
1594
1595         isl_tab_free(tab);
1596 done:
1597         bset = isl_basic_set_simplify(bset);
1598         bset = isl_basic_set_finalize(bset);
1599         isl_basic_set_free(context);
1600         return bset;
1601 error:
1602         isl_tab_free(tab);
1603         isl_basic_set_free(combined);
1604         isl_basic_set_free(context);
1605         isl_basic_set_free(bset);
1606         return NULL;
1607 }
1608
1609 /* Remove all information from bset that is redundant in the context
1610  * of context.  In particular, equalities that are linear combinations
1611  * of those in context are removed.  Then the inequalities that are
1612  * redundant in the context of the equalities and inequalities of
1613  * context are removed.
1614  *
1615  * We first compute the integer affine hull of the intersection,
1616  * compute the gist inside this affine hull and then add back
1617  * those equalities that are not implied by the context.
1618  *
1619  * If two constraints are mutually redundant, then uset_gist_full
1620  * will remove the second of those constraints.  We therefore first
1621  * sort the constraints so that constraints not involving existentially
1622  * quantified variables are given precedence over those that do.
1623  * We have to perform this sorting before the variable compression,
1624  * because that may effect the order of the variables.
1625  */
1626 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1627         __isl_take isl_basic_set *context)
1628 {
1629         isl_mat *eq;
1630         isl_mat *T, *T2;
1631         isl_basic_set *aff;
1632         isl_basic_set *aff_context;
1633         unsigned total;
1634
1635         if (!bset || !context)
1636                 goto error;
1637
1638         bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1639         if (isl_basic_set_plain_is_empty(bset)) {
1640                 isl_basic_set_free(context);
1641                 return bset;
1642         }
1643         bset = isl_basic_set_sort_constraints(bset);
1644         aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1645         if (!aff)
1646                 goto error;
1647         if (isl_basic_set_plain_is_empty(aff)) {
1648                 isl_basic_set_free(aff);
1649                 isl_basic_set_free(context);
1650                 return bset;
1651         }
1652         if (aff->n_eq == 0) {
1653                 isl_basic_set_free(aff);
1654                 return uset_gist_full(bset, context);
1655         }
1656         total = isl_basic_set_total_dim(bset);
1657         eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1658         eq = isl_mat_cow(eq);
1659         T = isl_mat_variable_compression(eq, &T2);
1660         if (T && T->n_col == 0) {
1661                 isl_mat_free(T);
1662                 isl_mat_free(T2);
1663                 isl_basic_set_free(context);
1664                 isl_basic_set_free(aff);
1665                 return isl_basic_set_set_to_empty(bset);
1666         }
1667
1668         aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1669
1670         bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1671         context = isl_basic_set_preimage(context, T);
1672
1673         bset = uset_gist_full(bset, context);
1674         bset = isl_basic_set_preimage(bset, T2);
1675         bset = isl_basic_set_intersect(bset, aff);
1676         bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1677
1678         if (bset) {
1679                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1680                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1681         }
1682
1683         return bset;
1684 error:
1685         isl_basic_set_free(bset);
1686         isl_basic_set_free(context);
1687         return NULL;
1688 }
1689
1690 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1691  * We simply add the equalities in context to bmap and then do a regular
1692  * div normalizations.  Better results can be obtained by normalizing
1693  * only the divs in bmap than do not also appear in context.
1694  * We need to be careful to reduce the divs using the equalities
1695  * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1696  * spurious constraints.
1697  */
1698 static struct isl_basic_map *normalize_divs_in_context(
1699         struct isl_basic_map *bmap, struct isl_basic_map *context)
1700 {
1701         int i;
1702         unsigned total_context;
1703         int div_eq;
1704
1705         div_eq = n_pure_div_eq(bmap);
1706         if (div_eq == 0)
1707                 return bmap;
1708
1709         if (context->n_div > 0)
1710                 bmap = isl_basic_map_align_divs(bmap, context);
1711
1712         total_context = isl_basic_map_total_dim(context);
1713         bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1714         for (i = 0; i < context->n_eq; ++i) {
1715                 int k;
1716                 k = isl_basic_map_alloc_equality(bmap);
1717                 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1718                 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1719                                 isl_basic_map_total_dim(bmap) - total_context);
1720         }
1721         bmap = isl_basic_map_gauss(bmap, NULL);
1722         bmap = normalize_divs(bmap, NULL);
1723         bmap = isl_basic_map_gauss(bmap, NULL);
1724         return bmap;
1725 }
1726
1727 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1728         struct isl_basic_map *context)
1729 {
1730         struct isl_basic_set *bset;
1731
1732         if (!bmap || !context)
1733                 goto error;
1734
1735         if (isl_basic_map_is_universe(bmap)) {
1736                 isl_basic_map_free(context);
1737                 return bmap;
1738         }
1739         if (isl_basic_map_plain_is_empty(context)) {
1740                 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1741                 isl_basic_map_free(context);
1742                 isl_basic_map_free(bmap);
1743                 return isl_basic_map_universe(dim);
1744         }
1745         if (isl_basic_map_plain_is_empty(bmap)) {
1746                 isl_basic_map_free(context);
1747                 return bmap;
1748         }
1749
1750         bmap = isl_basic_map_remove_redundancies(bmap);
1751         context = isl_basic_map_remove_redundancies(context);
1752
1753         if (context->n_eq)
1754                 bmap = normalize_divs_in_context(bmap, context);
1755
1756         context = isl_basic_map_align_divs(context, bmap);
1757         bmap = isl_basic_map_align_divs(bmap, context);
1758
1759         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1760                          isl_basic_map_underlying_set(context));
1761
1762         return isl_basic_map_overlying_set(bset, bmap);
1763 error:
1764         isl_basic_map_free(bmap);
1765         isl_basic_map_free(context);
1766         return NULL;
1767 }
1768
1769 /*
1770  * Assumes context has no implicit divs.
1771  */
1772 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1773         __isl_take isl_basic_map *context)
1774 {
1775         int i;
1776
1777         if (!map || !context)
1778                 goto error;;
1779
1780         if (isl_basic_map_plain_is_empty(context)) {
1781                 struct isl_dim *dim = isl_dim_copy(map->dim);
1782                 isl_basic_map_free(context);
1783                 isl_map_free(map);
1784                 return isl_map_universe(dim);
1785         }
1786
1787         context = isl_basic_map_remove_redundancies(context);
1788         map = isl_map_cow(map);
1789         if (!map || !context)
1790                 goto error;;
1791         isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1792         map = isl_map_compute_divs(map);
1793         for (i = 0; i < map->n; ++i)
1794                 context = isl_basic_map_align_divs(context, map->p[i]);
1795         for (i = map->n - 1; i >= 0; --i) {
1796                 map->p[i] = isl_basic_map_gist(map->p[i],
1797                                                 isl_basic_map_copy(context));
1798                 if (!map->p[i])
1799                         goto error;
1800                 if (isl_basic_map_plain_is_empty(map->p[i])) {
1801                         isl_basic_map_free(map->p[i]);
1802                         if (i != map->n - 1)
1803                                 map->p[i] = map->p[map->n - 1];
1804                         map->n--;
1805                 }
1806         }
1807         isl_basic_map_free(context);
1808         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1809         return map;
1810 error:
1811         isl_map_free(map);
1812         isl_basic_map_free(context);
1813         return NULL;
1814 }
1815
1816 static __isl_give isl_map *map_gist(__isl_take isl_map *map,
1817         __isl_take isl_map *context)
1818 {
1819         context = isl_map_compute_divs(context);
1820         return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1821 }
1822
1823 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1824         __isl_take isl_map *context)
1825 {
1826         return isl_map_align_params_map_map_and(map, context, &map_gist);
1827 }
1828
1829 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1830                                                 struct isl_basic_set *context)
1831 {
1832         return (struct isl_basic_set *)isl_basic_map_gist(
1833                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1834 }
1835
1836 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1837         __isl_take isl_basic_set *context)
1838 {
1839         return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1840                                         (struct isl_basic_map *)context);
1841 }
1842
1843 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1844         __isl_take isl_set *context)
1845 {
1846         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1847                                         (struct isl_map *)context);
1848 }
1849
1850 /* Quick check to see if two basic maps are disjoint.
1851  * In particular, we reduce the equalities and inequalities of
1852  * one basic map in the context of the equalities of the other
1853  * basic map and check if we get a contradiction.
1854  */
1855 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
1856         __isl_keep isl_basic_map *bmap2)
1857 {
1858         struct isl_vec *v = NULL;
1859         int *elim = NULL;
1860         unsigned total;
1861         int i;
1862
1863         if (!bmap1 || !bmap2)
1864                 return -1;
1865         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1866                         return -1);
1867         if (bmap1->n_div || bmap2->n_div)
1868                 return 0;
1869         if (!bmap1->n_eq && !bmap2->n_eq)
1870                 return 0;
1871
1872         total = isl_dim_total(bmap1->dim);
1873         if (total == 0)
1874                 return 0;
1875         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1876         if (!v)
1877                 goto error;
1878         elim = isl_alloc_array(bmap1->ctx, int, total);
1879         if (!elim)
1880                 goto error;
1881         compute_elimination_index(bmap1, elim);
1882         for (i = 0; i < bmap2->n_eq; ++i) {
1883                 int reduced;
1884                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1885                                                         bmap1, elim);
1886                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1887                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1888                         goto disjoint;
1889         }
1890         for (i = 0; i < bmap2->n_ineq; ++i) {
1891                 int reduced;
1892                 reduced = reduced_using_equalities(v->block.data,
1893                                                 bmap2->ineq[i], bmap1, elim);
1894                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1895                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1896                         goto disjoint;
1897         }
1898         compute_elimination_index(bmap2, elim);
1899         for (i = 0; i < bmap1->n_ineq; ++i) {
1900                 int reduced;
1901                 reduced = reduced_using_equalities(v->block.data,
1902                                                 bmap1->ineq[i], bmap2, elim);
1903                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1904                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1905                         goto disjoint;
1906         }
1907         isl_vec_free(v);
1908         free(elim);
1909         return 0;
1910 disjoint:
1911         isl_vec_free(v);
1912         free(elim);
1913         return 1;
1914 error:
1915         isl_vec_free(v);
1916         free(elim);
1917         return -1;
1918 }
1919
1920 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
1921         __isl_keep isl_basic_set *bset2)
1922 {
1923         return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
1924                                               (struct isl_basic_map *)bset2);
1925 }
1926
1927 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
1928         __isl_keep isl_map *map2)
1929 {
1930         int i, j;
1931
1932         if (!map1 || !map2)
1933                 return -1;
1934
1935         if (isl_map_plain_is_equal(map1, map2))
1936                 return 0;
1937
1938         for (i = 0; i < map1->n; ++i) {
1939                 for (j = 0; j < map2->n; ++j) {
1940                         int d = isl_basic_map_plain_is_disjoint(map1->p[i],
1941                                                                map2->p[j]);
1942                         if (d != 1)
1943                                 return d;
1944                 }
1945         }
1946         return 1;
1947 }
1948
1949 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1950         __isl_keep isl_set *set2)
1951 {
1952         return isl_map_plain_is_disjoint((struct isl_map *)set1,
1953                                         (struct isl_map *)set2);
1954 }
1955
1956 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
1957 {
1958         return isl_set_plain_is_disjoint(set1, set2);
1959 }
1960
1961 /* Check if we can combine a given div with lower bound l and upper
1962  * bound u with some other div and if so return that other div.
1963  * Otherwise return -1.
1964  *
1965  * We first check that
1966  *      - the bounds are opposites of each other (except for the constant
1967  *        term)
1968  *      - the bounds do not reference any other div
1969  *      - no div is defined in terms of this div
1970  *
1971  * Let m be the size of the range allowed on the div by the bounds.
1972  * That is, the bounds are of the form
1973  *
1974  *      e <= a <= e + m - 1
1975  *
1976  * with e some expression in the other variables.
1977  * We look for another div b such that no third div is defined in terms
1978  * of this second div b and such that in any constraint that contains
1979  * a (except for the given lower and upper bound), also contains b
1980  * with a coefficient that is m times that of b.
1981  * That is, all constraints (execpt for the lower and upper bound)
1982  * are of the form
1983  *
1984  *      e + f (a + m b) >= 0
1985  *
1986  * If so, we return b so that "a + m b" can be replaced by
1987  * a single div "c = a + m b".
1988  */
1989 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
1990         unsigned div, unsigned l, unsigned u)
1991 {
1992         int i, j;
1993         unsigned dim;
1994         int coalesce = -1;
1995
1996         if (bmap->n_div <= 1)
1997                 return -1;
1998         dim = isl_dim_total(bmap->dim);
1999         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2000                 return -1;
2001         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2002                                    bmap->n_div - div - 1) != -1)
2003                 return -1;
2004         if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2005                             dim + bmap->n_div))
2006                 return -1;
2007
2008         for (i = 0; i < bmap->n_div; ++i) {
2009                 if (isl_int_is_zero(bmap->div[i][0]))
2010                         continue;
2011                 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2012                         return -1;
2013         }
2014
2015         isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2016         if (isl_int_is_neg(bmap->ineq[l][0])) {
2017                 isl_int_sub(bmap->ineq[l][0],
2018                             bmap->ineq[l][0], bmap->ineq[u][0]);
2019                 bmap = isl_basic_map_copy(bmap);
2020                 bmap = isl_basic_map_set_to_empty(bmap);
2021                 isl_basic_map_free(bmap);
2022                 return -1;
2023         }
2024         isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2025         for (i = 0; i < bmap->n_div; ++i) {
2026                 if (i == div)
2027                         continue;
2028                 if (!pairs[i])
2029                         continue;
2030                 for (j = 0; j < bmap->n_div; ++j) {
2031                         if (isl_int_is_zero(bmap->div[j][0]))
2032                                 continue;
2033                         if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2034                                 break;
2035                 }
2036                 if (j < bmap->n_div)
2037                         continue;
2038                 for (j = 0; j < bmap->n_ineq; ++j) {
2039                         int valid;
2040                         if (j == l || j == u)
2041                                 continue;
2042                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2043                                 continue;
2044                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2045                                 break;
2046                         isl_int_mul(bmap->ineq[j][1 + dim + div],
2047                                     bmap->ineq[j][1 + dim + div],
2048                                     bmap->ineq[l][0]);
2049                         valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2050                                            bmap->ineq[j][1 + dim + i]);
2051                         isl_int_divexact(bmap->ineq[j][1 + dim + div],
2052                                          bmap->ineq[j][1 + dim + div],
2053                                          bmap->ineq[l][0]);
2054                         if (!valid)
2055                                 break;
2056                 }
2057                 if (j < bmap->n_ineq)
2058                         continue;
2059                 coalesce = i;
2060                 break;
2061         }
2062         isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2063         isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2064         return coalesce;
2065 }
2066
2067 /* Given a lower and an upper bound on div i, construct an inequality
2068  * that when nonnegative ensures that this pair of bounds always allows
2069  * for an integer value of the given div.
2070  * The lower bound is inequality l, while the upper bound is inequality u.
2071  * The constructed inequality is stored in ineq.
2072  * g, fl, fu are temporary scalars.
2073  *
2074  * Let the upper bound be
2075  *
2076  *      -n_u a + e_u >= 0
2077  *
2078  * and the lower bound
2079  *
2080  *      n_l a + e_l >= 0
2081  *
2082  * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2083  * We have
2084  *
2085  *      - f_u e_l <= f_u f_l g a <= f_l e_u
2086  *
2087  * Since all variables are integer valued, this is equivalent to
2088  *
2089  *      - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2090  *
2091  * If this interval is at least f_u f_l g, then it contains at least
2092  * one integer value for a.
2093  * That is, the test constraint is
2094  *
2095  *      f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2096  */
2097 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2098         int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2099 {
2100         unsigned dim;
2101         dim = isl_dim_total(bmap->dim);
2102
2103         isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2104         isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2105         isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2106         isl_int_neg(fu, fu);
2107         isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2108                         1 + dim + bmap->n_div);
2109         isl_int_add(ineq[0], ineq[0], fl);
2110         isl_int_add(ineq[0], ineq[0], fu);
2111         isl_int_sub_ui(ineq[0], ineq[0], 1);
2112         isl_int_mul(g, g, fl);
2113         isl_int_mul(g, g, fu);
2114         isl_int_sub(ineq[0], ineq[0], g);
2115 }
2116
2117 /* Remove more kinds of divs that are not strictly needed.
2118  * In particular, if all pairs of lower and upper bounds on a div
2119  * are such that they allow at least one integer value of the div,
2120  * the we can eliminate the div using Fourier-Motzkin without
2121  * introducing any spurious solutions.
2122  */
2123 static struct isl_basic_map *drop_more_redundant_divs(
2124         struct isl_basic_map *bmap, int *pairs, int n)
2125 {
2126         struct isl_tab *tab = NULL;
2127         struct isl_vec *vec = NULL;
2128         unsigned dim;
2129         int remove = -1;
2130         isl_int g, fl, fu;
2131
2132         isl_int_init(g);
2133         isl_int_init(fl);
2134         isl_int_init(fu);
2135
2136         if (!bmap)
2137                 goto error;
2138
2139         dim = isl_dim_total(bmap->dim);
2140         vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2141         if (!vec)
2142                 goto error;
2143
2144         tab = isl_tab_from_basic_map(bmap);
2145
2146         while (n > 0) {
2147                 int i, l, u;
2148                 int best = -1;
2149                 enum isl_lp_result res;
2150
2151                 for (i = 0; i < bmap->n_div; ++i) {
2152                         if (!pairs[i])
2153                                 continue;
2154                         if (best >= 0 && pairs[best] <= pairs[i])
2155                                 continue;
2156                         best = i;
2157                 }
2158
2159                 i = best;
2160                 for (l = 0; l < bmap->n_ineq; ++l) {
2161                         if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2162                                 continue;
2163                         for (u = 0; u < bmap->n_ineq; ++u) {
2164                                 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2165                                         continue;
2166                                 construct_test_ineq(bmap, i, l, u,
2167                                                     vec->el, g, fl, fu);
2168                                 res = isl_tab_min(tab, vec->el,
2169                                                   bmap->ctx->one, &g, NULL, 0);
2170                                 if (res == isl_lp_error)
2171                                         goto error;
2172                                 if (res == isl_lp_empty) {
2173                                         bmap = isl_basic_map_set_to_empty(bmap);
2174                                         break;
2175                                 }
2176                                 if (res != isl_lp_ok || isl_int_is_neg(g))
2177                                         break;
2178                         }
2179                         if (u < bmap->n_ineq)
2180                                 break;
2181                 }
2182                 if (l == bmap->n_ineq) {
2183                         remove = i;
2184                         break;
2185                 }
2186                 pairs[i] = 0;
2187                 --n;
2188         }
2189
2190         isl_tab_free(tab);
2191         isl_vec_free(vec);
2192
2193         isl_int_clear(g);
2194         isl_int_clear(fl);
2195         isl_int_clear(fu);
2196
2197         free(pairs);
2198
2199         if (remove < 0)
2200                 return bmap;
2201
2202         bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2203         return isl_basic_map_drop_redundant_divs(bmap);
2204 error:
2205         free(pairs);
2206         isl_basic_map_free(bmap);
2207         isl_tab_free(tab);
2208         isl_vec_free(vec);
2209         isl_int_clear(g);
2210         isl_int_clear(fl);
2211         isl_int_clear(fu);
2212         return NULL;
2213 }
2214
2215 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2216  * and the upper bound u, div1 always occurs together with div2 in the form
2217  * (div1 + m div2), where m is the constant range on the variable div1
2218  * allowed by l and u, replace the pair div1 and div2 by a single
2219  * div that is equal to div1 + m div2.
2220  *
2221  * The new div will appear in the location that contains div2.
2222  * We need to modify all constraints that contain
2223  * div2 = (div - div1) / m
2224  * (If a constraint does not contain div2, it will also not contain div1.)
2225  * If the constraint also contains div1, then we know they appear
2226  * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2227  * i.e., the coefficient of div is f.
2228  *
2229  * Otherwise, we first need to introduce div1 into the constraint.
2230  * Let the l be
2231  *
2232  *      div1 + f >=0
2233  *
2234  * and u
2235  *
2236  *      -div1 + f' >= 0
2237  *
2238  * A lower bound on div2
2239  *
2240  *      n div2 + t >= 0
2241  *
2242  * can be replaced by
2243  *
2244  *      (n * (m div 2 + div1) + m t + n f)/g >= 0
2245  *
2246  * with g = gcd(m,n).
2247  * An upper bound
2248  *
2249  *      -n div2 + t >= 0
2250  *
2251  * can be replaced by
2252  *
2253  *      (-n * (m div2 + div1) + m t + n f')/g >= 0
2254  *
2255  * These constraint are those that we would obtain from eliminating
2256  * div1 using Fourier-Motzkin.
2257  *
2258  * After all constraints have been modified, we drop the lower and upper
2259  * bound and then drop div1.
2260  */
2261 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2262         unsigned div1, unsigned div2, unsigned l, unsigned u)
2263 {
2264         isl_int a;
2265         isl_int b;
2266         isl_int m;
2267         unsigned dim, total;
2268         int i;
2269
2270         dim = isl_dim_total(bmap->dim);
2271         total = 1 + dim + bmap->n_div;
2272
2273         isl_int_init(a);
2274         isl_int_init(b);
2275         isl_int_init(m);
2276         isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2277         isl_int_add_ui(m, m, 1);
2278
2279         for (i = 0; i < bmap->n_ineq; ++i) {
2280                 if (i == l || i == u)
2281                         continue;
2282                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2283                         continue;
2284                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2285                         isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2286                         isl_int_divexact(a, m, b);
2287                         isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2288                         if (isl_int_is_pos(b)) {
2289                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2290                                                 b, bmap->ineq[l], total);
2291                         } else {
2292                                 isl_int_neg(b, b);
2293                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2294                                                 b, bmap->ineq[u], total);
2295                         }
2296                 }
2297                 isl_int_set(bmap->ineq[i][1 + dim + div2],
2298                             bmap->ineq[i][1 + dim + div1]);
2299                 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2300         }
2301
2302         isl_int_clear(a);
2303         isl_int_clear(b);
2304         isl_int_clear(m);
2305         if (l > u) {
2306                 isl_basic_map_drop_inequality(bmap, l);
2307                 isl_basic_map_drop_inequality(bmap, u);
2308         } else {
2309                 isl_basic_map_drop_inequality(bmap, u);
2310                 isl_basic_map_drop_inequality(bmap, l);
2311         }
2312         bmap = isl_basic_map_drop_div(bmap, div1);
2313         return bmap;
2314 }
2315
2316 /* First check if we can coalesce any pair of divs and
2317  * then continue with dropping more redundant divs.
2318  *
2319  * We loop over all pairs of lower and upper bounds on a div
2320  * with coefficient 1 and -1, respectively, check if there
2321  * is any other div "c" with which we can coalesce the div
2322  * and if so, perform the coalescing.
2323  */
2324 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2325         struct isl_basic_map *bmap, int *pairs, int n)
2326 {
2327         int i, l, u;
2328         unsigned dim;
2329
2330         dim = isl_dim_total(bmap->dim);
2331
2332         for (i = 0; i < bmap->n_div; ++i) {
2333                 if (!pairs[i])
2334                         continue;
2335                 for (l = 0; l < bmap->n_ineq; ++l) {
2336                         if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2337                                 continue;
2338                         for (u = 0; u < bmap->n_ineq; ++u) {
2339                                 int c;
2340
2341                                 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2342                                         continue;
2343                                 c = div_find_coalesce(bmap, pairs, i, l, u);
2344                                 if (c < 0)
2345                                         continue;
2346                                 free(pairs);
2347                                 bmap = coalesce_divs(bmap, i, c, l, u);
2348                                 return isl_basic_map_drop_redundant_divs(bmap);
2349                         }
2350                 }
2351         }
2352
2353         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2354                 return bmap;
2355
2356         return drop_more_redundant_divs(bmap, pairs, n);
2357 }
2358
2359 /* Remove divs that are not strictly needed.
2360  * In particular, if a div only occurs positively (or negatively)
2361  * in constraints, then it can simply be dropped.
2362  * Also, if a div occurs only occurs in two constraints and if moreover
2363  * those two constraints are opposite to each other, except for the constant
2364  * term and if the sum of the constant terms is such that for any value
2365  * of the other values, there is always at least one integer value of the
2366  * div, i.e., if one plus this sum is greater than or equal to
2367  * the (absolute value) of the coefficent of the div in the constraints,
2368  * then we can also simply drop the div.
2369  *
2370  * If any divs are left after these simple checks then we move on
2371  * to more complicated cases in drop_more_redundant_divs.
2372  */
2373 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2374         struct isl_basic_map *bmap)
2375 {
2376         int i, j;
2377         unsigned off;
2378         int *pairs = NULL;
2379         int n = 0;
2380
2381         if (!bmap)
2382                 goto error;
2383
2384         off = isl_dim_total(bmap->dim);
2385         pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2386         if (!pairs)
2387                 goto error;
2388
2389         for (i = 0; i < bmap->n_div; ++i) {
2390                 int pos, neg;
2391                 int last_pos, last_neg;
2392                 int redundant;
2393                 int defined;
2394
2395                 defined = !isl_int_is_zero(bmap->div[i][0]);
2396                 for (j = 0; j < bmap->n_eq; ++j)
2397                         if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2398                                 break;
2399                 if (j < bmap->n_eq)
2400                         continue;
2401                 ++n;
2402                 pos = neg = 0;
2403                 for (j = 0; j < bmap->n_ineq; ++j) {
2404                         if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2405                                 last_pos = j;
2406                                 ++pos;
2407                         }
2408                         if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2409                                 last_neg = j;
2410                                 ++neg;
2411                         }
2412                 }
2413                 pairs[i] = pos * neg;
2414                 if (pairs[i] == 0) {
2415                         for (j = bmap->n_ineq - 1; j >= 0; --j)
2416                                 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2417                                         isl_basic_map_drop_inequality(bmap, j);
2418                         bmap = isl_basic_map_drop_div(bmap, i);
2419                         free(pairs);
2420                         return isl_basic_map_drop_redundant_divs(bmap);
2421                 }
2422                 if (pairs[i] != 1)
2423                         continue;
2424                 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2425                                     bmap->ineq[last_neg] + 1,
2426                                     off + bmap->n_div))
2427                         continue;
2428
2429                 isl_int_add(bmap->ineq[last_pos][0],
2430                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2431                 isl_int_add_ui(bmap->ineq[last_pos][0],
2432                                bmap->ineq[last_pos][0], 1);
2433                 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2434                                 bmap->ineq[last_pos][1+off+i]);
2435                 isl_int_sub_ui(bmap->ineq[last_pos][0],
2436                                bmap->ineq[last_pos][0], 1);
2437                 isl_int_sub(bmap->ineq[last_pos][0],
2438                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2439                 if (!redundant) {
2440                         if (defined ||
2441                             !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2442                                 pairs[i] = 0;
2443                                 --n;
2444                                 continue;
2445                         }
2446                         bmap = set_div_from_lower_bound(bmap, i, last_pos);
2447                         bmap = isl_basic_map_simplify(bmap);
2448                         free(pairs);
2449                         return isl_basic_map_drop_redundant_divs(bmap);
2450                 }
2451                 if (last_pos > last_neg) {
2452                         isl_basic_map_drop_inequality(bmap, last_pos);
2453                         isl_basic_map_drop_inequality(bmap, last_neg);
2454                 } else {
2455                         isl_basic_map_drop_inequality(bmap, last_neg);
2456                         isl_basic_map_drop_inequality(bmap, last_pos);
2457                 }
2458                 bmap = isl_basic_map_drop_div(bmap, i);
2459                 free(pairs);
2460                 return isl_basic_map_drop_redundant_divs(bmap);
2461         }
2462
2463         if (n > 0)
2464                 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2465
2466         free(pairs);
2467         return bmap;
2468 error:
2469         free(pairs);
2470         isl_basic_map_free(bmap);
2471         return NULL;
2472 }
2473
2474 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2475         struct isl_basic_set *bset)
2476 {
2477         return (struct isl_basic_set *)
2478             isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2479 }
2480
2481 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2482 {
2483         int i;
2484
2485         if (!map)
2486                 return NULL;
2487         for (i = 0; i < map->n; ++i) {
2488                 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2489                 if (!map->p[i])
2490                         goto error;
2491         }
2492         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2493         return map;
2494 error:
2495         isl_map_free(map);
2496         return NULL;
2497 }
2498
2499 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2500 {
2501         return (struct isl_set *)
2502             isl_map_drop_redundant_divs((struct isl_map *)set);
2503 }